{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stephen Cave", "Kanta Dihal"], "title": "The Whiteness of AI", "text": "Introduction It is a truth little acknowledged that a machine in possession of intelligence must be white. Typing terms like \"robot\" or \"artificial intelligence\" into a search engine will yield a preponderance of stock images of white plastic humanoids. Perhaps more notable still, these machines are not only white in colour, but the more human they are made to look, the more their features are made ethnically White.  1  In this paper, we problematize the often unnoticed and unremarked-upon fact that intelligent machines are predominantly conceived and portrayed as White. We argue that this Whiteness both illuminates particularities of what (Anglophone Western) society hopes for and fears from these machines, and situates these affects within long-standing ideological structures that relate race and technology. Race and technology are two of the most powerful and important categories for understanding the world as it has developed since at least the early modern period. Yet, as a number of scholars have noted, their profound entanglement remains understudied  (Sinclair 2004; de la Peña 2010) . There are a number of possible reasons for this-and, as Bruce Sinclair writes, \"racial prejudice dominates all of them\"  (Sinclair 2004, 1) . They include the lack of first-or secondhand accounts of the role of people of colour in the development and use of technology; persistent stereotypes about technology as the province and product of one particular racial group-White people; and the persistent tendency of members of that group, who dominate the academy in the US and Europe, to refuse to see themselves as racialised or race as a matter of concern at all. This lack of scholarly attention is surprising because, as Michael Adas elucidated in 1989, the idea of technological superiority was essential to the logic of colonialism. Not only was superior weaponry and transportation (etc.) necessary for large-scale conquest and control of foreign territory, it was also part of its justification: proof that White Europeans were an advanced civilisation with a right to rule over others  (Adas 1989) . Fortunately, this lack of attention is increasingly being remedied, and the relationship between race and technology is beginning to garner the kind of attention that has since the 1970s been given to gender and technology, following the pioneering work of Donna  Haraway, Sandra Harding, and Evelyn Fox Keller (Haraway 1991; Harding 1986; Keller 1985) . This includes attention to this century's ubiquitous digital technologies. In 2006, Lisa Nakamura asked, \"How do we make cyberculture studies a field that as a matter of course employs critical race theory and theories of cultural difference…?\"  (Nakamura 2006, 35) . Since then, a number of significant works have attempted to do just that, including Safiya Noble's Algorithms of Oppression and Ruha Benjamin's Race After Technology  (Noble 2018; Benjamin 2019) . This paper aims to contribute to this body of literature on race and technology by examining how the ideology of race shapes conceptions and portrayals of artificial intelligence (AI). Our approach is grounded in the philosophy of race and critical race theory, particularly the Black feminist theories of bell hooks, Sylvia Wynter and Alexander G.  Weheliye (hooks 1992 Weheliye (hooks 1997 Wynter 2003; Weheliye 2014), and work  in Whiteness studies, including that of Richard Dyer, Joe R. Feagin, and Ruth Frankenberg  (Dyer 1997; Feagin 2013; Frankenberg 1997a) . In 2006, Feagin coined the term \"white racial frame\" to describe those aspects of the Anglophone Western worldview that perpetuate a racialised hierarchy of power and privilege  (Feagin 2006 ). In his words, \"the white racial frame includes a broad and persisting set of racial stereotypes, prejudices, ideologies, interlinked interpretations and narratives, and visual images\"  (Feagin 2013, xi) . Although it reached its peak in the age of colonial expansion, this framing persists: \"Today, as whites move through their lives, they frequently combine racial stereotypes and biases (a beliefs aspect), racial metaphors and concepts (a deeper cognitive aspect), racialised images (the visual aspect), racialised emotions (feelings), interpretive racial narratives, and inclinations to discriminate within a broad racial framing\"  (Feagin 2013, 91) . In essence, this paper examines how representations of AI reflect this White racial frame. One of the main aims of critical race theory in general, and Whiteness studies in particular, is to draw attention to the operation of Whiteness in Western culture. The power of Whiteness's signs and symbols lies to a large extent in their going unnoticed and unquestioned, concealed by the myth of colour-blindness. As scholars such as Jessie Daniels and Safiya Noble have noted, this myth of colour-blindness is particularly prevalent in Silicon Valley and surrounding tech culture, where it serves to inhibit serious interrogation of racial framing  (Daniels 2013 (Daniels , 2015 Noble 2018) . Hence the first step for such an interrogation is, in Richard Dyer's term, to \"make strange\" this Whiteness, de-normalising and drawing attention to it  (Dyer 1997, 10) . As Steve Garner puts it, the reason \"for deploying whiteness as a lens is that it strips a normative privileged identity of its cloak of invisibility\"  (Garner 2007, 5) . This is our primary intention in examining intelligent machines through the White racial frame. In the next section of this paper, we first lay out current evidence for the assertion that conceptions and portrayals of AI-both embodied as robots and disembodied-are racialised, then evidence that such machines are predominantly racialised as White. In the third section of the paper, we offer our readings of this Whiteness. Our methods are qualitative. As de la Peña writes: \"Studying whiteness means working with evidence more interpretive than tangible; it requires imaginative analyses of language and satisfaction with identifying possible motivations of subjects, rather than definitive trajectories of innovation, production, and consumption\" (de la Peña 2010, 926). We offer three interpretations of the Whiteness of AI. First, the normalisation of Whiteness in the Anglophone West can go some way to explaining why that sphere's products, including representations of AI, are White. But we argue that this argument alone is insufficient. Second, we argue that to imagine an intelligent (autonomous, agential, powerful) machine is to imagine a White machine because the White racial frame ascribes these attributes predominantly to White people. Thirdly, we argue that AI racialised as White allows for a full erasure of people of colour from the White utopian imaginary. Such machines are conceived as tools that will replace \"dirty, dull, or dangerous\" tasks  (Murphy 2000, 16) , including replacing human interactions that are considered metaphorically dirty: White robot servants will allow the White master to live a life of ease unsullied by interaction with people of other races. \n Seeing the Whiteness of AI Our concern in this paper is with the racialisation (as White) of both real and imagined machines that are implied or claimed to be intelligent. By racialisation, we mean the ascription of characteristics that are used to identify and delineate races in a given racial frame, which in this case is the Anglophone West. Feagan notes: Among the most important ingredients of this frame are: (1) the recurring use of certain physical characteristics, such as skin colour and facial features, to differentiate social groups; (2) the constant linking of physical characteristics to cultural characteristics; and (3) the regular use of physical and linked cultural distinctions to differentiate socially \"superior\" and \"inferior\" groups in a social hierarchy  (Feagin 2013, 41) . It is worth noting that \"physical characteristics\" need not only refer to those that are visible: voice and accent are also used as markers for social categorisation. Similarly, the category \"cultural characteristics\" is also used expansively and can include markers such as dialect, mannerisms, and dress codes, as well as mental and moral qualities, such as diligence, industriousness, reliability, trustworthiness, inventiveness, and intellectual ability. Indeed, these mental and moral qualities have always been an essential part of the racial frame, as it is largely on the basis of these that claims of superiority or inferiority have been made. \n Machines Can Be Racialised That machines can be racialised, in the sense that they can be given attributes that enable their identification with human racial categories, has been empirically demonstrated. For example, in one study, Christoph Bartneck and colleagues took pictures of the humanoid Nao robot and adjusted the colouration to match the skin tone of stock images of White and Black people  (Bartneck et al. 2018) . They then asked participants to define the race of the robot with several options including \"does not apply\". A minority-ranging across the experiments from 7 to 20%-chose the \"does not apply\" option, while a majority-ranging from 53 to 70%-identified the robots as belonging to the race from which their colouration derived. They concluded \"Participants were able to easily and confidently identify the race of robots according to their racialization [...] Thus, there is also a clear sense in which these robotsand by extension other humanoid robotsdo have race\"  (Bartneck et al. 2018, 201) . This should not be surprising. Many machines are anthropomorphised-that is, made to be human-like to some degree-in order to facilitate human-machine interaction. This might involve obvious physical features (a head on top, two eyes, a mouth, four limbs, bipedalism, etc.), but it can also include invisible features such as a humanlike voice, or human-like interactions, such as politeness or humour. Given the prevalence of racial framing, in most contexts, to be human-like means to have race. Consequently, as Liao and He point out in their discussion of the racialisation of psychotherapeutic chatbots, \"racial identity is an integral part of anthropomorphized agents\"  (Liao and He 2020, 2) . They go on to explore a number of racial cues for virtual agents, including visual cues such as skin colour, but also cultural signifiers such as names (e.g. for male names, Jake as White, Darnell as Black, and Antonio as Hispanic). Similarly, \"even text-based conversational exchanges\"-that is, those with no visual component at all-\"perform a racial or ethnic identity\" through the interlocutors' choice of dialect, etc.  (Marino 2014, 3) . Given the sociopolitical importance of the racial frame in structuring people's interactions, if machines are really being racialised, then we would expect this to have an impact on how people interact with these machines. Numerous studies show just this. For example, Liao and He found that a person's \"perceived interpersonal closeness\" with a virtual agent is higher when the virtual agent has the same racial identity as that person  (Liao and He 2020, 2) . Other studies reflect the extent to which racism-prejudicial treatment on the basis of race-is intrinsic to racial framing. As detailed in their paper \"Robots Racialized in the Likeness of Marginalized Social Identities are Subject to Greater Dehumanization than Those Racialized as White\", Strait et al. analysed free-form online responses to three videos, each depicting a female-gendered android with a different racial identity: Black, White, and East Asian. Their aim was to assess whether the same kind of marginalising and dehumanising commentary that is applied to real people of colour would be applied to these robots. They found that the valence of the commentary was significantly more negative towards the Black robot than towards the White or Asian ones and that both the Asian and Black robots were subject to over twice as many dehumanising comments as the White robot  (Strait et al. 2018) . Two recent studies have further examined the transfer of bias to machines using the \"shooter bias\" paradigm. This paradigm was first described in the 2002 paper \"The Police Officer's Dilemma: Using Ethnicity to Disambiguate Potentially Threatening Individuals\"  (Correll et al. 2002) . It used a simple video game featuring images of (real) Black and White male targets, each holding either a gun or a nonthreatening object. Participants were instructed to shoot only armed targets. A clear racial bias was identified: \"participants fired on an armed target more quickly when he was African American than when he was White, and decided not to shoot an unarmed target more quickly when he was White than when he was African American\"  (Correll et al. 2002 (Correll et al. , 1325 . Studies by  Bartneck et al. and Addison et al. used  the same methodology to examine whether this \"shooter bias\" would be transferred to racialised robots  (Bartneck et al. 2018; Addison et al. 2019) . They found that \"people showed a similar shooter bias toward robots racialized as Black relative to White in a similar fashion as they showed toward Black vs. White humans, no matter their own race\"  (Addison et al. 2019, 493) . \n Whiteness as the Norm for Intelligent Machines The previous section shows that research has empirically demonstrated that machines can be racialised and that this racialisation includes transfer of the attendant biases found in the human world. In this subsection, we will survey evidence for the extent to which AI systems-machines purported to be intelligent-are predominantly racialised as White. We will look briefly at four categories: real humanoid robots, virtual personal assistants, stock images of AI, and portrayals of AI in film and television. \n The Whiteness of Humanoid Robots A number of commentators have remarked on the preponderant Whiteness of humanoid robots. In their proposed \"code of ethics\" for human-robot interaction Riek and Howard note the \"lack of diversity in robot morphology and behavior\": In terms of race, with precious few exceptions, such as Hanson's Bina48, the vast majority of android and gynoid robots are Asian or Caucasian in their features for no discernible reason. Furthermore, most of these robots tend to have a eurocentric design with regards to their appearance, behavior, and voice.  (Riek and Howard 2014, 4)  Human-computer interaction researchers Christoph Bartneck and colleagues, who conducted some of the studies cited above, have also noted that robots are usually racialised as White: \"most of the main research platforms for social robotics, including Nao, Pepper, and PR2, are stylized with white materials and are presumably White\"  (Bartneck et al. 2018, 202) . Finally, media studies and literary scholar Jennifer Rhee notes the \"normalization and universalization of whiteness\" as expressed both in earlier robotics research and in robot toys: \"Kismet, with its blue eyes, light brown eyebrows, and pink ears, also 'normalizes whiteness', as do other robot companions, such as the blonde-haired, blue-eyed Cindy Smart Doll and the similarly blonde-haired, blue-eyed My Friend Cayla.\"  (Rhee 2018, 105) . Although robots such as Nao and Pepper have enjoyed commercial success, neither has received quite the attention garnered by Sophia from Hanson Robotics. This machine consists foremost of a White humanoid head, sometimes also with an upper torso (see Fig.  1 ). It has not only given numerous high-profile television interviews but also received political honours, including in 2017 receiving citizenship of Saudi Arabia and becoming an \"Innovation Champion\" for the United Nations Development Programme  (Weller 2017 ; UNDP 2017). \n The Whiteness of Chatbots and Virtual Assistants Though conversational agents do not exhibit any visual racial cues, they are racialised by means of sociolinguistic markers  (Sweeney 2016; Villa-Nicholas and Sweeney 2019) . Discussing ELIZA, an influential natural language processing program created by Joseph Weizenbaum at the MIT AI Laboratory in 1966, Mark Marino writes: \"If ELIZA presented a bot that tried to imitate language, it was performing standard white middle-class English, without a specific identifying cultural inflection... language without culture, disembodied, hegemonic, and, in a word, white\"  (Marino 2014, 5) . Since then, natural language processing has entered the mainstream, with \"virtual assistants\" existing in many people's pockets, handbags, or homes through devices such as smartphones. Indeed, this is one of the most common ways in which people interact with technology that could be labelled \"AI\". These tools present their designers with many decisions about socio-cultural positioning. Ruha Benjamin recalls this anecdote: A former Apple employee who noted that he was \"not Black or Hispanic\" described his experience on a team that was developing speech recognition for Siri, the virtual assistant program. As they worked on different English dialects -Australian, Singaporean and Indian Englishhe asked his boss: \"What about African American English?\" To this his boss responded: \"Well, Apple products are for the premium market.\"  (Benjamin 2019, 28)  As a further example, she describes a Black computer scientist who chose a White voice for his app rather than a Black one, so as not to \"create friction\"  (Benjamin 2019, 28-29) . So while some designers might be unconsciously racialising their products as White, others are doing so in full awareness of this choice. \n The Whiteness of Stock Images of AI As anyone working in the field will know, stock images of AI, at least when anthropomorphised, are overwhelmingly white and arguably overwhelmingly White. The more realistically humanoid these machines become, the more Caucasian in their features. Such images are used to illustrate not only generalist newspaper articles and corporate slideshows but also specialist and technical works, and even works of a critical nature, such as Harry Collins's Artifictional Intelligence (Polity, 2018) and Anthony Elliott's The Culture of AI (Routledge, 2018) (Fig.  2 ). The prevalence of such images is reflected in the results of search engines. Such searches are a useful indicator of how a subject is portrayed at a given time, for two reasons. First, search engines are very widely used (approximately 3.5 billion searches are made on Google every day, or 40 thousand per second 2 ) and can therefore be considered a highly influential source of information and perceptions. Second, the nature of such search engines means that they are not only promoting certain ideas and perceptions but also reflecting their existing prevalence. While the exact nature of Google's search, ranking, and result presentation algorithms is proprietary, we know that they evaluate (crudely put) influence and popularity-for example, in terms of how many other sites link to a given website. So the fact that certain images are shown when someone searches for a relevant term means not only that those images are being thus promoted by some of the most powerful organs of content mediation in existence today but also that these images are already widespread and used on other influential websites, as that is what underlies their promotion by the search engines. Consequently, search results are increasingly examined by scholars, including in the study of racial bias. For example, in her 2018 book Algorithms of Oppression: How Search Engines Reinforce Racism, Safiya U. Noble identifies many ways in which such sites reflect and exacerbate prejudice, such as the search results for \"Latinas\" that feature mostly porn  (Noble 2018, 75, 155)  or the White men who come up when searching for images of professions such as \"construction worker\", \"doctor\", or \"scientist\"  (Noble 2018, 82-83) . In order to get an indication of the prevalence of these racialised machines on the internet, we conducted two image searches on Google (the most widely used search engine) using the anonymous Tor browser to ensure results were not influenced by our personal search histories and locations. We first searched on the term \"artificial intelligence\": the top results are in Fig.  3 . Some of these results are too abstract, featuring stylised brains and circuits, for example, to be considered racialised. However, among the results showing humanoid figures, racialisation as White predominates. First, two pictures show actual human hands, and both are White. Second, a further two pictures show humanoid robots, and both are White and could thus be read as White, as  Bartneck et al. suggest (Bartneck et al. 2018, 202) . Therefore, we might say that inasmuch as the machines are racialised, they are racialised as White. In order to focus more on representations of embodied, anthropomorphic AI, we also searched for \"artificial intelligence robot\": the top results are in Fig.  4 . As is clear, this search produces an even greater preponderance of images that are either white in colour or racialised as White or both. \n The Whiteness of AI in Film and Television These contemporary stock images distil the visualisations of intelligent machines in Western popular culture as it has developed over decades. In science fiction from the nineteenth century onwards, AI is predominantly imagined as White. For example, the Terminator (Arnold Schwarzenegger), RoboCop (Peter Weller and Joel Kinnaman), all of the \"replicants\" in the Blade Runner franchise (e.g. Rutger Hauer, Sean Young, and Mackenzie Davis), Sonny in I, Robot (Alan Tudyk), Ava in Ex Machina (Alicia The Whiteness of AI Vikander) (Fig.  5 ), and Maria in Metropolis (Brigitte Helm) are all played by White actors and are visibly White on screen. Androids made of metal or plastic are also usually given White facial features, such as the robots in the 2007 film I, Robot. Even disembodied AI is imagined as White: HAL-9000 in 2001: A Space Odyssey and Samantha in Her are voiced by White actors. All of these AIs come from Hollywood films; they have been produced in a country in which 18% of the population is Hispanic, but in which only one fictional robot has that background: Bender Rodríguez in the animated TV series Futurama, who is canonically constructed in Mexico-but who is voiced by the White voice actor John DiMaggio. Only very recent TV shows with a large cast of androids, such as Westworld and Humans, have attempted to address this with AI characters evincing a mix of skin tones and ethnicities. This preponderance of intelligent machines racialised as White led Dyer to posit \"the android as a definition of whiteness\"  (Dyer 1997, 213) . \n Understanding the Whiteness of AI We offer three interpretations of the racialisation of intelligent machines as White: the Whiteness of their creators perpetuating itself; the Whiteness of the attributes ascribed to AI; and the extent to which AI permits the erasure of people of colour from the White utopia. \n Whiteness Reproducing Whiteness In European and North American societies, Whiteness is normalised to an extent that renders it largely invisible. As Toby Ganley puts it in his survey of Whiteness studies, \"the monopoly that whiteness has over the norm\" is one of the field's two unifying insights-the other being that it confers power and privilege  (Ganley 2003, 12) . Richard Dyer describes this as the view that \"other people are raced, we are just people\"  (Dyer 1997, 1) . This normalisation means that Whiteness is not perceived by majority populations as a distinct colour, but rather as an absence of colour-colour Fig.  5  Alicia Vikander as Ava in Ex Machina. Source: Youtube both in the literal sense and in the sense of race. Consequently, the Whiteness of AI could be considered simply a default. It does not appear as a feature, but is transparent, like the air we breathe: the \"unmarked marker\", as Ruth Frankenberg calls it  (Frankenberg 1997b, 1) . The majority of White viewers are unlikely to see humanlike machines as racialised at all, but simply as conforming to their idea of what \"human-like\" means. For non-White people, on the other hand, Whiteness is never invisible in this manner, as bell hooks reminds us  (hooks 1992 1997) . So-called colour-blindness, an attitude of not seeing race, and of presuming that people in contemporary society are no longer disadvantaged on the basis of race, is itself a narrative that perpetuates White hegemony: \"communities of color frequently see and name whiteness clearly and critically, in periods when white folks have asserted their own 'color blindness'\"  (Frankenberg 1997b, 4) . Noble argues that \"central to these 'colorblind' ideologies is a focus on the inappropriateness of 'seeing race'\"-a view that she argues is dominant among Silicon Valley technologists, who \"revel in their embrace of colorblindness as if it is an asset and not a proven liability\"  (Noble 2018, 168) . Such colour-blindness is a liability because it obscures the normalisation of Whiteness and marginalisation of other racialised groups-and the real world effects this has, such as facial recognition technologies not distinguishing Black or East Asian faces  (Buolamwini and Gebru 2018) . Given the normalisation of Whiteness, for some designers, to make a human-like machine will unthinkingly mean to make a White machine. As Dyer puts it: \"white people create the dominant images of the world and don't quite see that they thus create the dominant images of the world in their own image\"  (Dyer 1997, 9) . But this alone is not a satisfactory explanation of the Whiteness of AI, as not all entities-more specifically, not all intelligent, humanoid entities-imagined by predominantly White industries are portrayed as White. For example, Western science fiction has a long tradition of White authors racialising extraterrestrials as non-White. In the late nineteenth century, for instance, the real-world fear of the \"Yellow Peril\" was metaphorically addressed in science fiction by racialising extraterrestrial invaders as East Asian. The Flash Gordon franchise gained its lead villain in a 1934 comic, which introduced the tyrannical emperor of the planet Mongo-the Orientalised alien Ming the Merciless. Such is the villain in Flash Gordon -a trident bearded, slanty eyed, shiny doomed [sic], pointy nailed, arching eyebrowed, exotically garbed Oriental named Ming, who personifies unadulterated evil. A heavy like Ming is not contrived in a comic strip writer's imagination during a coffee break, but rather is the product of perhaps the richest and longest tradition of all of Hollywood ethnic stereotypes.  (Barshay 1974, 24-26)  Dyer points out that Blade Runner similarly deliberately uses East Asian characters in order to offset the whiteness of its protagonists, including the White androids: \"the yellow human background emphasises the chief protagonists' whiteness. The whitest of hue are the replicants\"  (Dyer 1997, 214) . Racial stereotyping of aliens is not a phenomenon limited to past centuries. The Star Wars prequel trilogy  (Lucas 1999; 2002; 2005)  has been criticised for the \"transparent racism\" in its depiction of the alien Jar Jar Binks as a West Indian caricature  (Lavender 2011, 193)  reminiscent of blackface minstrelsy  (Williams 1999) , and of the slave trader Watto, an antisemitic Jewish caricature with a large nose, skullcap, Yiddish accent, and obsession with money  (Freedman 2019) . This racialisation of aliens in SF suggests that the racialisation of artificial intelligence is a choice. The White racial frame as perpetuated by the White creators of these works portrays dangerous invaders from another planet as East Asian and bumbling alien petty-criminals as Afro-Caribbean. Therefore, the fact that it portrays AI as overwhelmingly White requires further explanation. In the following sections, we offer two. \n AI and the Attributes of Whiteness While Whiteness functions in part through its invisibility in mainstream discourse, this does not mean it has no distinguishable features of its own. Indeed, the White racial frame has a long history of ascribing certain attributes to Whites and disputing them in others: these are the very claims that have been used to justify colonialism, segregation, and other modes of oppression. We argue that AI is predominantly racialised as White because it is deemed to possess attributes that this frame imputes to White people. We examine these attributes under three key headings: intelligence, professionalism, and power. First, the primary attribute being projected onto these machines is, as the term \"AI\" suggests, intelligence. Throughout the history of Western thought, but in particular since the seventeenth century in Europe and the territories it colonised, intelligence has been associated with some humans more than others  (Carson 2006) . The idea that some races were more mentally able than others was crucial to the legitimation of the advancing colonial project. Those deemed less intelligent-in the words of Rudyard Kipling, \"Half-devil and half-child\"-were judged unqualified to rule themselves and their lands. It was therefore legitimate-even a duty, \"the white man's burden\" as Kipling put it-to destroy their cultures and take their territories  (Kipling 1899) . Through the nineteenth century, strenuous efforts were made to empirically demonstrate and measure this intellectual difference, culminating in the development of the IQ test  (Gould 1981) . Although explicit associations between racial groups and intelligence declined after the Second World War, (a) they continue to be made in right-wing circles  (Saini 2019 ) and (b) implicit or unconscious associations between race and intelligence persist widely (see, for example, van den  Bergh et al. 2010; Okeke et al. 2009) . Given the White racial frame has for centuries promoted the association of intelligence with the White, European race, it is to be expected that when this culture is asked to imagine an intelligent machine, it imagines a White machine. A crucial aspect of the idea of intelligence is generality. Intelligence is often defined as a \"general mental capability\"  (Gottfredson 1997) , and in AI, the concept of \"artificial general intelligence\"-a system with the kind of flexible mental capabilities humans have-is often considered to be the original and primary goal of the field  (Crevier 1993) . But in the White racial frame, not all humans are considered to have this attribute to the same degree. As Weheliye puts it, using Sylvia Wynter's idea of \"the Man\"-the Enlightenment, Western, White male subject, \"In the context of the secular human, black subjects, along with indigenous populations, the colonised, the insane, the poor, the disabled, and so on as limit cases by which Man can demarcate himself as the universal human\"  (Weheliye 2014, 24) . According to the White racial frame, it is the rational, scientific thought of the White Westerner that lays claim to universal validity-or, we might say, true generality. Other races, by contrast, are framed as particular and subjective, constrained by the limits of their non-ideal bodies and cultures to think thoughts that are partial and parochial. To imagine a truly intelligent machine, one with general intelligence is therefore to imagine a White machine. Second, much of the current discourse around AI focuses on how it is, or will soon be, capable of professional work. This is frequently claimed to be what makes the present wave of automation different from previous waves, in which machines became capable of supplanting manual and semi-skilled labour  (Ford 2015) . Professional work-law, medicine, business, and so forth-is at the upper end of pay and status scales. White Europeans and North Americans have historically not considered all humans equally fit for such roles and have kept them closed to people who lacked the requisite connections, wealth, or other in-group identifiers. Universities, the gateways to the professions, have long histories of excluding people of colour from their ranks  (Burrow 2008, 107) . The historic exclusion of anyone other than White men shapes to this day what mainstream White culture imagines when imagining someone fulfilling such roles. Safiya Noble shows that it took years of criticism before search engines adjusted their algorithms so that searching for \"engineer\" or \"doctor\" stopped exclusively returning images of White men  (Noble 2018) . But the underlying bias, on which the algorithms fed, remains. To imagine a machine in a white-collar job is therefore to imagine a White machine. Third, hierarchies of intelligence and of professional status are of course also hierarchies of power. Consequently, power relations are implicit in the previous two categories. However, it is worth also considering power separately, because power struggles between AI and humans are such a common narrative trope. Alongside the narrative that robots will make humans redundant, an equally well-known narrative is that they will rise up and conquer us altogether  (Cave and Dihal 2019) . These are both narratives about machines becoming superior to humans: stories in which they become better at every task, leaving humans with nothing to do, from E.M. Forster's 1909 short story 'The Machine Stops' to the Oscar-winning film WALL-E, or in which they outwit and subjugate those who built them, as in the Terminator film franchise or the film Ex Machina  (Forster 1909; Stanton 2008; Cameron 1984; Garland 2015) . When White people imagine being overtaken by superior beings, those beings do not resemble those races they have framed as inferior. It is unimaginable to a White audience that they will be surpassed by machines that are Black. Rather, it is by superlatives of themselves: hyper-masculine White men like Arnold Schwarzenegger as the Terminator, or hyperfeminine White women like Alicia Vikander as Ava in Ex Machina. This is why even narratives of an AI uprising that are clearly modelled on stories of slave rebellions depict the rebelling AIs as White-for example, in Blade Runner  (Dihal 2020) . The implication of this racialisation is that these machines might genuinely be superior, or are at least worthy adversaries. The use of White bodybuilders such as Arnold Schwarzenegger to play the evil robots suggests this. As Dyer points out, Schwarzenegger's physique suggests \"the body made possible by [...] natural mental superiority. The point after all is it built, a product of the application of thought and planning, an achievement\"  (Dyer 1997, 164) . Consequently, for a White technologist or author, to imagine a superior anthropomorphic machine is to imagine a White machine. In summary, popular conceptions of AI suggest these machines have general intelligence, are capable of professional jobs, and/or are poised to surpass and supplant humanity. In the White imagination, such qualities are strongly associated with Whiteness. It is no surprise, therefore, that in mainstream Western media, such machines are portrayed as White. \n White Utopia While we believe the attribution to AI of these qualities, so strongly associated with Whiteness, goes a long way to making sense of the racialisation of anthropomorphic intelligent machines, we also want to propose one further hypothesis: that the Whiteness of the machines allows the White utopian imagination to fully exclude people of colour. One of the most pertinent hopes for artificial intelligence is that it will lead to a life of ease  (Cave and Dihal 2019) . As a tool that can take over \"dirty, dull, or dangerous\" jobs, it relieves its owners from work they do not want to do, enabling them to pursue leisure. As critical race theorists have repeatedly pointed out, the leisure currently available to the wealthier classes is disproportionately facilitated by the labour of working-class women of colour  (hooks 1992 Rhee 2018) . bell hooks shows that the people performing this labour are actively kept invisible, even when the White master and the coloured servant are physically present in the same space. She cites the memoirs of a White heiress who grew up with Black servants in her house: \"Blacks, I realized, were simply invisible to most white people, except as a pair of hands offering a drink on a silver tray\"  (hooks 1992 1997, 168) . As this forced pretence of invisibility shows, interactions with non-White servants are undesirable to the White master: such interactions are almost literally considered a \"dirty job\". Depictions of people of colour as being dirty and unwashed, eating dirty food, living in the dirt, even of being the colour of excrement have contributed to the development of both the fear of pollution in interactions with people of colour, and the association of Whiteness with cleanliness and purity  (Dyer 1997, 75-76) . This association has been exacerbated by a long history of propaganda preceding conquest and genocide that portrays the racial other as evoking disgust: as vectors of disease, such as lice or rats, or as a literal plague  (Glover 1999, chap. 35; Rector 2014, chap. 3) . The utopia of the White racial frame would therefore rather remove people of colour altogether, even in the form of servants. From the inception of the academic study of science fiction onwards, many critics have pointed out that utopias throughout literary history have been construed on exclusionary, colonialist, and eugenicist premises  (Suvin 1979 (Suvin 2016 Jameson 2005, 205; Ginway 2016, 132) . In Astrofuturism, De Witt Douglas Kilgore shows that mid-twentieth-century American visions of space age utopias are \"idealisations ... based on a series of exclusions\" (Kilgore 2010, 10): rather than depicting a post-racial or colourblind future, the authors of these utopias simply omit people of colour. AI offers the possibility of making such utopias real. By virtue of its generality, it is imagined as able replace and any unwanted labour-social and cognitive as well as physical  (Cave and Dihal 2019) , so obviating the need for people of colour in any role. Consequently, as Jennifer Rhee points out, advertisements for real AI such as household robots \"are striking in their whiteness\": they are aimed at showing white middle-class families an ideal leisurely lifestyle. In doing so, she argues, \"the images reserve the luxury of liberation from domestic labor for white women, while erasing the women of color who perform this labor, both within their own homes and in the homes of others\"  (Rhee 2018, 94) . In some cases, the unsulliedness of this utopia can extend further to exclude all women. Just as people of colour can be associated with offensive physicality, so can women in general, particularly with respect to their reproductive organs. The necessity of sexual intercourse, pregnancy, and childbearing for the continuation of a race that prides itself on rationality and the ability to transcend its physicality is an offensive hurdle that has been imagined as transcendable by science for centuries. As Dyer points out, in the ideology of Whiteness, the elevation of mental over physical prowess has simultaneously been the White race's most valuable achievement and a threat to its own continuation  (Dyer 1997, 27) . It has led to the paradox known as the \"White Crisis\", in which the White race is seen as under threat of being overwhelmed by \"inferior\" races that are breeding more prolifically. Transhumanism has been envisioned as a solution to this White Crisis  (Ali 2017) . Seen as a form of offspring, artificial intelligence offers a way for the White man to perpetuate his existence in a rationally optimal manner, without the involvement of those he deems inferior. \n Conclusion and Implications Images of AI are not generic representations of human-like machines, but avatars of a particular rank within the hierarchy of the human. These representations of intelligent machines-and our future with them-are refracted through the White racial frame; their Whiteness a proxy for how we perceive their status and potential. This can cause what is sometimes called representational harms  (Blodgett et al. 2020) . We suggest three. First, this racialisation can amplify the very prejudices it reflects. We have argued that intelligent machines are portrayed as White because that is how the mainstream perceives intelligence and related desirable characteristics. But equally, the consistent portrayal of intelligent machines as White itself transmits this association, so sustaining it. As we have argued elsewhere  (Whittlestone et al. 2019) , bias in representations of AI contributes to a vicious cycle of social injustice: the biased representations can influence both aspiring technologists and those in charge of hiring new staff, shaping whom they consider fit for the field  (Cave 2020) . This could contribute to sustaining a racially homogenous workforce, which will continue to produce products, whether real intelligent machines or their representations, that are biased to benefit that group and disadvantage others. Second, the racialisation of these machines places them within an existing hierarchy of the human in a way that could exacerbate real injustice. Portrayals of AI as White situate these machines in a power hierarchy above currently marginalised groups, such as people of colour. These oppressed groups are therefore relegated to an even lower position in the hierarchy: below that of machine. As machines become ever more important in making automated decisions-frequently about marginalised  (Eubanks 2017) -this be consequential. Automation bias-the tendency of people to favour suggestions from automated decision-making systems over those from humans-has already been evidenced  (Goddard et al. 2012) . We might speculate that it will be exacerbated in cases where such systems are racialised White and the humans in question are not. Third, these portrayals could distort our perceptions of the risks and benefits of these machines. For example, they could frame the debate about AI's impact disproportionately around the opportunities and risks posed to White middle-class men  (Cave 2020) . It is already a common narrative that the current wave of automation differs from those of the past in that \"impacts from automation have thus far impacted mostly blue-collar employment; the coming wave of innovation threatens to upend white-collar work as well\"  (Pew Research Center 2014) . Public interest and policy therefore often focus on white collar professionals, instead of on marginalized groups, which in reality are likely to be worse affected by the impact of AI  (Eubanks 2017; Noble 2018) . In this paper, we have offered three interpretations of the whiteness and Whiteness of representations of AI. All three, and the implications that we posit, need further investigation. This process is part of what can be described as decolonising AI: a process of breaking down the systems of oppression that arose with colonialism and have led to present injustices that AI threatens to perpetuate and exacerbate. Weheliye describes how he \"works towards the abolition of Man, and advocates the radical reconstruction and decolonization of what it means to be human\"  (Weheliye 2014, 4) . It is in the field of AI that technology is most clearly entwined with notions of \"what it means to be human\", both in reality and in cultural fantasies. We hope to have taken a step towards this reconstruction, by drawing attention to the Whiteness of these machines and \"making it strange\". regulation or exceeds the permitted use, you will need obtain permission directly from the copyright holder. To view a copy of this licence, visit Fig. 2 2 Fig. 2 Covers of Collins 2018, Polity, and Elliott 2018, Routledge \n Fig. 3 3 Fig. 3 Tor browser Google image search result for \"artificial intelligence\", 13 April 2020 \n \n\t\t\t Following the increasingly common usage of the capitalised form \"Black\" to denote the ethnicity and \"black\" the colour, we use \"White\" to refer to the ethnicity and \"white\" the colour.While not yet the norm, as can be seen in our quotations of critics who do not employ this distinction, this usage will make our discussion clearer. \n\t\t\t The Whiteness of AI \n\t\t\t https://www.internetlivestats.com/google-search-statistics/ accessed 30 December 2019.Fig. 1 Sophia. Hanson Robotics, April 2020The Whiteness of AI \n\t\t\t Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "date_published": "n/a", "url": "n/a", "filename": "Cave-Dihal2020_Article_TheWhitenessOfAI.tei.xml", "abstract": "This paper focuses on the fact that AI is predominantly portrayed as white-in colour, ethnicity, or both. We first illustrate the prevalent Whiteness of real and imagined intelligent machines in four categories: humanoid robots, chatbots and virtual assistants, stock images of AI, and portrayals of AI in film and television. We then offer three interpretations of the Whiteness of AI, drawing on critical race theory, particularly the idea of the White racial frame. First, we examine the extent to which this Whiteness might simply reflect the predominantly White milieus from which these artefacts arise. Second, we argue that to imagine machines that are intelligent, professional, or powerful is to imagine White machines because the White racial frame ascribes these attributes predominantly to White people. Third, we argue that AI racialised as White allows for a full erasure of people of colour from the White utopian imaginary. Finally, we examine potential consequences of the racialisation of AI, arguing it could exacerbate bias and misdirect concern.", "id": "631847b6756c201d2a75e0cb7ccafb76"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld"], "title": "Robust program equilibrium", "text": "Introduction Much has been written about rationalizing non-Nash equilibrium play in strategicform games. Most prominently, game theorists have discussed how cooperation may be achieved in the prisoner's dilemma, where mutual cooperation is not a Nash equilibrium but Pareto-superior to mutual defection. One of the most successful approaches is the repetition of a game, and in particular the iterated prisoner's dilemma  (Axelrod 2006) . Another approach is to introduce commitment mechanisms of some sort. In this paper, we will discuss one particular commitment mechanism:  Tennenholtz's (2004)  program equilibrium formalism (Sect. 2.2). Here, the idea is that in place of strategies, players submit programs which compute strategies and are given access to each other's source code. The programs can then encode credible commitments, such as some version of \"if you cooperate, I will cooperate\". As desired,  Tennenholtz (2004, Sect. 3, Theorem 1)  shows that mutual cooperation is played in a program equilibrium of the prisoner's dilemma. However, Tennenholtz' equilibrium is very fragile. Essentially, it consists of two copies of a program that cooperates if it faces an exact copy of itself  (cf. McAfee 1984; Howard 1988) . Even small deviations from that program break the equilibrium. Thus, achieving cooperation in this way is only realistic if the players can communicate beforehand and settle on a particular outcome. Another persuasive critique of this trivial equilibrium is that the model of two players submitting programs is only a metaphor, anyway. In real life, the programs may instead be the result of an evolutionary process  (Binmore 1988 pp. 14f.)  and Tennenholtz' equilibrium is a hard to obtain by such a process. Alternatively, if we view our theory as normative rather than descriptive, we may view the programs themselves as the target audience of our recommendations. This also means that these agents will already have some form of source code-e.g., one that derives and considers the program equilibria of the game-and it is out of their realm of power to change that source code to match some common standard. However, they may still decide on some procedure for thinking about this particular problem in such a way that enables cooperation with other rationally pre-programmed agents. Noting the fragility of Tennenholtz' proposed equilibrium, it has been proposed to achieve a more robust program equilibrium by letting the programs reason about each other  (van der Hoek et al. 2013; Barasz et al. 2014; Critch 2016) . For example,  Barasz et al. (2014, Sect.  3) propose a program FairBot-variations of which we will see in this paper-that cooperates if Peano arithmetic can prove that the opponent cooperates against FairBot. FairBot cooperates (via Löb's theorem) more robustly against different versions of itself. These proposals are very elegant and certainly deserve further attention. However, their benefits come at the cost of being computationally expensive. In this paper, I thus derive a class of program equilibria that I will argue to be more practical. In the case of the prisoner's dilemma, I propose a program that cooperates with a small probability and otherwise acts as the opponent acts against itself (see Algorithm 1). Doing what the opponent does-à la FairBot-incentivizes cooperation. Cooperating with a small probability allows us to avoid infinite loops that would arise if we merely predicted and copied our opponent's action (see Algorithm 2). This approach to a robust cooperation program equilibrium in the prisoner's dilemma is described in Sect. 3. We then go on to generalize the construction exemplified in the prisoner's dilemma (see Sect. 4). In particular, we show how strategies for the repeated version of a game can be used to construct good programs for the one-shot version of that game. We show that many of the properties of the underlying strategy of the repeated game carry over to the program for the stage game. We can thus construct \"good\" programs and program equilibria from \"good\" strategies and Nash equilibria. \n Preliminaries \n Strategic-form games For reference, we begin by introducing some basic terminology and formalism for strategic-form games. For an introduction, see, e.g.,  Osborne (2004) . For reasons that will become apparent later on, we limit our treatment to two-player games. A two-player strategic game G = (A 1 , A 2 , u 1 , u 2 ) consists of two countable sets of moves A i and for both players i ∈ {1, 2} a bounded utility function u i : A 1 × A 2 → R. A (mixed) strategy for player i is a probability distribution π i over A i . Given a strategy profile (π 1 , π 2 ) the probability of an outcome (a 1 , a 2 ) ∈ A 1 × A 2 is P(a 1 , a 2 | π 1 , π 2 ) := π 1 (a 1 ) • π 2 (a 2 ). (1) The expected value for player i given that strategy profile is E [u i | π 1 , π 2 ] := (a 1 ,a 2 )∈A 1 ×A 2 P(a 1 , a 2 | π 1 , π 2 ) • u i (a 1 , a 2 ). Note that because the utility function is bounded, the sum converges absolutely, such that the order of the action pairs does not affect the sum's value. \n Program equilibrium We now introduce the concept of program equilibrium, first proposed by  Tennenholtz (2004) . The main idea is to replace strategies with computer programs that are given access to each other's source code.  1  The programs then give rise to strategies. For any game G, we first need to define the set of program profiles PROG(G) consisting of pairs of programs. The ith entry of an element of PROG(G) must be a program source code p i that, when interpreted by a function apply, probabilistically map program profiles 2 onto A i . We require that for any program profile ( p 1 , p 2 ) ∈ PROG(G), both programs halt. Otherwise, the profile would not give rise to a well-defined strategy. Whether p i halts depends on the program p −i , it plays against, where (in accordance with convention in game theory) − : {1, 2} → {1, 2} : 1 → 2, 2 → 1 and we write −i instead of −(i). For example, if p i runs apply( p −i , (p i , p −i )), i.e., simulates the opponent, then that is fine as long as p −i does not also run apply( p i , (p i , p −i )), which would yield an infinite loop. To avoid this mutual dependence, we will generally require that PROG(G) = PROG 1 (G) × PROG 2 (G), where PROG i (G) consists of programs for player i. Methods of doing this while maintaining expressive power include hierarchies of players-e.g., higher indexed players are allowed to simulate lower indexed ones but not vice versa-hierarchies of programs-programs can only call their opponents with simpler programs as input-requiring programs to have a \"plan B\" if termination can otherwise not be guaranteed, or allowing each player to only start strictly less than one simulation in expectation. These methods may also be combined. In this paper, we do not assume any particular definition of PROG(G). However, we assume that they can perform arbitrary computations as long as these computations are guaranteed to halt regardless of the output of the parts of the code that do depend on the opponent program. We also require that PROG(G) is compatible with our constructions. We will show our constructions to be so benign in terms of infinite loops that this is not too strong of an assumption. Given a program profile ( p 1 , p 2 ), we receive a strategy profile (apply( p 1 , (p 1 , p 2 )), apply( p 2 , (p 1 , p 2 ))). For any outcome (a 1 , a 2 ) of G, we define P(a 1 , a 2 | p 1 , p 2 ) := P(a 1 , a 2 | apply( p 1 , (p 1 , p 2 )), apply( p 2 , (p 1 , p 2 ))) (2) and for every player i ∈ {1, 2}, we define E [u i | p 1 , p 2 ] := (a 1 ,a 2 )∈A 1 ×A 2 P(a 1 , a 2 | p 1 , p 2 ) • u i (a 1 , a 2 ). ( 3 ) For player i, we define the (set-valued) best response function as B i ( p −i ) = arg max p i ∈PROG i (G) E u i | p i , p −i . A program profile ( p 1 , p 2 ) is a (weak) program equilibrium of G if for i ∈ {1, 2} it is p i ∈ B i ( p −i ). \n Repeated games Our construction will involve strategies for the repeated version of a two-player game. Thus, for any game G, we define G to be the repetition of G with a probability of ∈ (0, 1] of ending after each round. Both players of G will be informed only of the last move of their opponent. This differs from the more typical assumption that players have access to the entire history of past moves. We will later see why this deviation is necessary. A strategy π i for player i non-deterministically maps opponent moves or the information of the lack thereof onto a move π i : {0} ∪ A −i A i . Thus, for a ∈ A i , b ∈ A −i , π i (b, a) := π i (b)(a) denotes the probability of choosing a given that the opponent played b in the previous round and π i (0, a) := π i (0)(a) denotes the probability of choosing a in the first round. We call a strategy  a) . The probability that the game follows a complete history of moves h = a 0 b 0 a 1 b 1 • • • a n b n and then ends is π i stationary if for all a ∈ A i , π i (b, a) is constant with respect to b ∈ {0} ∪ A −i . If π i is stationary, we write π i (a) := π i (b, P(h | (π 1 , π 2 )) := π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) n n i=1 π 1 (b i−1 , a i )π 2 (a i−1 , b i ). (4) Note that the moves in the history always come in pairs a i b i which are chosen \"simultaneously\" in response to b i−1 and a i−1 , respectively. The expected value for player i given the strategy profile (π 1 , π 2 ) is E [u i | π 1 , π 2 ] := h∈(A 1 •A 2 ) + P(h | π 1 , π 2 ) • u i (h), (5) where (A 1 • A 2 ) + is the set of all histories and u i (a 0 b 0 a 1 b 1 • • • a n b n ) := n i=0 u i (a i , b i ). ( 6 ) The lax unordered summation in Eq. 5 is, again, unproblematic because of the absolute convergence of the series, which is a direct consequence of the proof of Lemma 1. Note how the organization of the history into pairs of moves allows us to apply the utility function of the stage game in Eq. 6. For player i, we define the set-valued best response function as B i (π −i ) = arg max π i :{0}∪A −i A i E u i | π i , π −i . Analogously, B c i (π −i ) is the set of responses to π −i that are best among the computable ones, B s i (π −i ) the set of responses to π −i that are best among the stationary ones, and B s,c i (π −i ) the set of responses to π −i that are best among stationary computable strategies. A strategy profile (π 1 , π 2 ) is a (weak) Nash equilibrium of G if for i ∈ {1, 2} it is π i ∈ B i (π −i ). We now prove a few lemmas that we will need later on. First, we have suggestively called the values P(h) probabilities, but we have not shown them to satisfy, say, Kolmogorov's axioms. Additivity is not an issue, because we have only defined the probability for atomic events and non-negativity is obvious from the definition. However, we will also need the fact that the numbers we have called probabilities indeed sum to 1, which requires a few lines to prove. Lemma 1 Let G be a repeated game and π 1 , π 2 be strategies for that game. Then h∈(A 1 •A 2 ) + P(h | π 1 , π 2 ) = 1. Proof h P(h | π 1 , π 2 ) = Eq. 4 a 0 b 0 •••a n b n ∈(A 1 •A 2 ) + π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) n • n i=1 π 1 (b i−1 , a i )π 2 (a i−1 , b i ) = absolute convergence ∞ n=0 (1 − ) n a 0 b 0 •••a n b n ∈(A 1 A 2 ) n+1 π 1 (0, a 0 )π 2 (0, b 0 ) n i=1 π 1 (b i−1 , a i )π 2 (a i−1 , b i ) = ∞ n=0 (1 − ) n a 0 b 0 ∈A 1 A 2 π 1 (0, a 0 )π 2 (0, b 0 ) a 1 b 1 ∈A 1 A 2 π 1 (b 0 , a 1 )π 2 (a 0 , b 1 ) . . . • a n b n ∈A 1 A 2 π 1 (b n−1 , a n )π 2 (a n−1 , b n ) = ∞ n=0 (1 − ) n = sum of geo- metric series 1 For seeing why the second-to-last equation is true, notice that the inner-most sum is 1. Thus, the next sum is 1 as well, and so on. Since the ordering in the right-hand side of the first line is lax, and because only the second line is known to converge absolutely, the re-ordering is best understood from right to left. The last step uses the well-known formula ∞ k=0 x k = 1/(1 − x) for the geometric series. For any game G , k ∈ N + , a ∈ A 1 , b ∈ A 2 and strategies π 1 and π 2 for G , we define P k,G (a, b | π 1 , π 2 ) := (1 − ) k a 0 b 0 •••a k−1 b k−1 ∈(A 1 A 2 ) k π 1 (b k−1 , a)π 2 (a k−1 , b)π 1 (0, a 0 )π 2 (0, b 0 ) • k−1 j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ). ( 7 ) For k = 0, we define P 0,G (a, b | π 1 , π 2 ) := π 1 (0, a) • π 2 (0, b). Intuitively speaking, P k,G (a, b | π 1 , π 2 ) is the probability of reaching at least round k and that (a, b) is played in that round. With this ab∈A 1 A 2 P k,G (a, b | π 1 , π 2 )u i (a, b) should be the expected utility from the kth round (where not getting to the kth round counts as 0). This suggests a new way of calculating expected utilities on a more round-by-round basis. Lemma 2 Let G be a game, and let π 1 , π 2 be strategies for that game. Then E [u i | π 1 , π 2 ] = ∞ k=0 ab∈A 1 A 2 P k,G (a, b | π 1 , π 2 )u i (a, b). Proof E G [u i | π 1 , π 2 ] = h∈(A 1 A 2 ) + P(h | π 1 , π 2 )u i (h) = Eqs. 4, 6 a 0 b 0 •••a n b n ∈(A 1 A 2 ) + π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) n ⎛ ⎝ n j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ • n k=0 u i (a k , b k ) = ∞ k=0 a 0 b 0 •••a n b n ∈(A 1 A 2 ) ≥k+1 π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) n • ⎛ ⎝ n j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ u i (a k , b k ) = ∞ k=0 a 0 b 0 •••a k b k ∈(A 1 A 2 ) k+1 a k+1 b k+1 •••a n b n ∈(A 1 A 2 ) * π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) n u i (a k , b k ) • ⎛ ⎝ k j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ ⎛ ⎝ n j=k+1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ = ∞ k=0 a 0 b 0 •••a k b k ∈(A 1 A 2 ) k+1 π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) k u i (a k , b k ) • ⎛ ⎝ k j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ • a k+1 b k+1 •••a n b n ∈(A 1 A 2 ) * (1 − ) n−k ⎛ ⎝ n j=k+1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ = lemma 1 ∞ k=0 a 0 b 0 •••a k b k ∈(A 1 A 2 ) k+1 π 1 (0, a 0 )π 2 (0, b 0 ) (1 − ) k u i (a k , b k ) • ⎛ ⎝ k j=1 π 1 (b j−1 , a j )π 2 (a j−1 , b j ) ⎞ ⎠ = Eq. 7 ∞ k=0 a k b k ∈A 1 A 2 P k (a k , b k | π 1 , π 2 )u i (a k , b k ) To find the probability of player i choosing a in round k, we usually have to calculate the probabilities of all actions in all previous rounds. After all, player i reacts to player −i's previous move, who in turn reacts to player i's move in round k − 2, and so on. This is what makes Eq. 7 so long. However, imagine that player −i uses a stationary strategy. This, of course, means that player −i's probability distribution over moves in round k (assuming the game indeed reaches round k) can be computed directly as π −i (b). Player i's distribution over moves in round k is almost as simple to calculate, because it only depends on player −i's distribution over moves in round k − 1, which can also be calculated directly. We hence get the following lemma. Lemma 3 Let G be a game, let π i be a any strategy for G and let π −i be a stationary strategy for G . Then, for all k ∈ N + , it is P k,G (a, b | π i , π −i ) = (1 − ) k b ∈A −i π −i (b )π −i (b)π i (b , a). Proof We conduct our proof by induction over k. For k = 1, it is  P 1 (a, b | π i , π −i ) = Eq. 7 (1 − ) a 0 b 0 π i (b 0 , a)π −i (a 0 , b)π i (0, a 0 )π −i (0, b 0 ) = (1 − ) b 0 π i (b 0 , a)π −i (b)π −i (b 0 ) a 0 π i (0, a 0 ) = (1 − ) b 0 π i (b 0 , a)π −i (b)π −i (b 0 ). If the lemma is true for k, it is also true for k + 1: P k+1 (a, b | π i , π −i ) = (1 − ) k+1 a 0 b 0 •••a k b k ∈(A i A −i ) k+1 π i (b k , a)π −i (a k , b)π i (0, a 0 )π −i (0, b 0 ) • k j=1 π i (b j−1 , a j )π −i (a j−1 , b j ) = Eq. 7 (1 − ) a k b k P k (a k b k | π i , π −i )π i (b k , a)π −i (b) = I .H . (1 − ) k+1 a k b k b π −i (b )π −i (b k )π −i (b)π i (b , a k )π i (b k , a) = (1 − ) k+1 b k π −i (b k )π −i (b)π i (b k , a) b π −i (b ) a k π i (b , a k ) = (1 − ) k+1 b k π −i (b k )π −i (b)π i (b k , a). \n Robust program equilibrium in the prisoner's dilemma Discussions of the program equilibrium have traditionally used the well-known prisoner's dilemma (or trivial variations thereof) as an example to show how the program equilibrium rationalizes cooperation where the Nash equilibrium fails (e.g.,  Tennenholtz 2004, Sect. 3; McAfee 1984; Howard 1988; Barasz et al. 2014) . The present paper is no exception. In this section, we will present our main idea using the example of the prisoner's dilemma; the next section gives the more general construction and proofs of properties of that construction. For reference, the payoff matrix of the prisoner's dilemma is given in Table  1 . I propose to use the following decision rule: with a probability of ∈ (0, 1], cooperate. Otherwise, act as your opponent plays against you. I will call this strat- Algorithm 1: The GroundedFairBot for player i. The program makes use of a function sample which samples uniformly from the given interval or probability distribution. It is assumed that is computable. egy GroundedFairBot. A description of the algorithm in pseudo-code is given in Algorithm 1.  3  The proposed program combines two main ideas. First, it is a version of FairBot  (Barasz et al. 2014) . That is, it chooses the action that its opponent would play against itself. As player −i would like player i to cooperate, GroundedFairBot thus incentivizes cooperation, as long as < 1/2. In this, it resembles the tit for tat strategy in the iterated prisoner's dilemma (IPD) (famously discussed by  Axelrod 2006) , which takes an empirical approach to behaving as the opponent behaves against itself. Here, the probability of the game ending must be sufficiently small (again, less than 1/2 for the given payoffs) in each round for the threat of punishment and the allure of reward to be persuasive reasons to cooperate. The second main idea behind GroundedFairBot is that it cooperates with some small probability . First and foremost, this avoids running into the infinite loop that a naive implementation of FairBot-see Algorithm 2-runs into when playing against opponents who, in turn, try to simulate FairBot. Note, again, the resemblance with the tit for tat strategy in the iterated prisoner's dilemma, which cooperates when no information about the opponent's strategy is available. Data: program profile ( p 1 , p 2 ) Result: action a i ∈ {C, D} 1 return sample(apply( p −i , (p 1 , p 2 ))) Algorithm 2: The NaiveFairBot for player i To better understand how GroundedFairBot works, consider its behavior against a few different opponents. When GroundedFairBot faces NaiveFairBot, then both cooperate. For illustration, a dynamic call graph of their interaction is given in Fig.  1 . It is left as an exercise for the reader to analyze GroundedFairBot's behavior against other programs, such as another instance of GroundedFairBot or a variation of GroundedFairBot that defects rather than cooperates with probability . When playing against strategies that are also based on simulating their opponent, we could think of GroundedFairBot as playing a \"mental IPD\". If the opponent program decides whether to cooperate, it has to consider that it might currently only be simu- lated. Thus, it will choose an action with an eye toward gauging a favorable reaction from GroundedFairBot one recursion level up. Cooperation in the first \"round\" is an attempt to steer the mental IPD into a favorable direction, at the cost of cooperating if sample (0, 1) < already occurs in the first round. In addition to proving theoretical results (as done below), it would be useful to test GroundedFairBot \"in practice\", i.e., against other proposed programs for the prisoner's dilemma with access to one another's source code. I only found one informal tournament for this version of the prisoner's dilemma. It was conducted in 2013 by Alex Mennen on the online forum and community blog LessWrong.  4  In the original set of submissions, GroundedFairBot would have scored 6th out of 21. The reason why it is not a serious contender for first place is that it does not take advantage of the many exploitable submissions (such as bots that decide without looking at their opponent's source code). Once one removes the bottom 9 programs, GroundedFairBot scores second place. If one continues this process of eliminating unsuccessful programs for another two rounds, GroundedFairBot ends up among the four survivors that cooperate with each other. 5 \n From iterated game strategies to robust program equilibria We now generalize the construction from the previous section. Given any computable strategy π i for a sequential game G , I propose the following program: with a small probability sample from π i (0). Otherwise, act how π i would respond (in the sequential game G ) to the action that the opponent takes against this program. I will call this program Groundedπ i Bot. A description of the program in pseudo-code is given in Algorithm 3. As a special case, GroundedFairBot arises from Groundedπ i Bot by letting π i be tit for tat. Data: program profile ( p 1 , p 2 ) Result: action a i ∈ A i 1 if sample (0, 1) < then 2 return sample(π i (0)) 3 end 4 return sample(π i (sample(apply( p −i , (p 1 , p 2 ))))) Algorithm 3: The Groundedπ i Bot for player i. The program makes use of a function sample which samples uniformly from a given interval or a given probability distribution. It is assumed that π i and are computable. Again, our proposed program combines two main ideas. First, Groundedπ i Bot responds to how the opponent plays against Groundedπ i Bot. In this, it resembles the behavior of π i in G . As we will see, this leads Groundedπ i Bot to inherit many of π i 's properties. In particular, if (like tit for tat) π i uses some mechanism to incentivize its opponent to converge on a desired action, then Groundedπ i Bot incentivizes that action in a similar way. Second, it-again-terminates immediately with some small probability to avoid the infinite loops that Naiveπ i Bot-see Algorithm 4-runs into. Playing π i (0) in particular is partly motivated by the \"mental G \" that Groundedπ i Bot plays against some opponents (such as Groundedπ −i Bots or Naiveπ −i Bots). The other motivation is to make the relationship between Groundedπ i Bot and π i cleaner. In terms of the strategies that are optimal against Groundedπ i Bot, the choice of that constant action cannot matter much if is small. Consider, again, the analogy with tit for tat. Even if tit for tat started with defection, one should still attempt to cooperate with it. In practice, however, it has turned out that the \"nice\" version of tit for tat (and nice strategies in general) are more successful  (Axelrod 2006, ch. 2) . The transparency in the program equilibrium may render such \"signals of cooperativeness\" less important-e.g., against programs like  Barasz et al.'s (2014, Sect. 3)  FairBot. Nevertheless, it seems plausible that-if only because of mental G -related considerations-in transparent games the \"initial\" actions matter as well. We now ground these intuitions formally. First, we discuss Groundedπ i Bot's halting behavior. We then show that, in some sense, Groundedπ i Bot behaves in G like π i does in G . \n Halting behavior For a program to be a viable option in the \"transparent\" version of G, it should halt against a wide variety of opponents. Otherwise, it may be excluded from PROG(G) in our formalism. Besides, it should be efficient enough to be practically useful. As with GroundedFairBot, the main reason why Groundedπ i Bot is benign in terms of the risk of infinite loops is that it generates strictly less than one new function call in expectation and never starts more than one. While we have no formal machinery for analyzing the \"loop risk\" of a program, it is easy to show the following theorem. Theorem 4 Let π i be a computable strategy for a game G . Furthermore, let p −i be any program (not necessarily in PROG i (G)) that calls apply( p i , (p i , p −i )) at most once and halts with probability 1 if apply halts with probability 1. Then Groundedπ i Bot and p −i halt against each other with probability 1 and the expected number of steps required for executing Groundedπ i Bot is at most T π i + (T π i + T p −i ) 1 − , ( 8 ) where T π i is the maximum number of steps to sample from π i , and T p −i is the maximum number of steps needed to sample from apply( p −i , ( Groundedπ i Bot, p −i )) excluding the steps needed to execute apply( Groundedπ i Bot, ( Groundedπ i Bot, p −i )). Proof It suffices to discuss the cases in which p −i calls p i once with certainty, because if any of our claims were refuted by some program p −i , they would also be refuted by a version of that program that calls p i once with certainty. If p −i calls p i once with certainty, then the dynamic call graphs of both Groundedπ i Bot and p −i look similar to the one drawn in 1. In particular, it only contains one infinite path and that path has a probability of at most lim i→∞ (1 − ) i = 0. For the time complexity, we can consider the dynamic call graph as well. The policy π i has to be executed at least once (with probability with the input 0 and with probability 1− against an action sampled from apply( p −i , ( Groundedπ i Bot, p −i )). With a probability of (1 − ), we also have to execute the non-simulation part of p −i and, for a second time, π i . And so forth. The expected number of steps to execute Groundedπ i Bot is thus T π i + ∞ j=1 (1 − ) j (T π i + T p −i ), which can be shown to be equal to the term in 8 by using the well-known formula ∞ k=0 x k = 1/(1 − x) for the geometric series. Note that this argument would work if there were more than two players or if the strategy for the iterated game were to depend on more than just the last opponent move, because in these cases, the natural extension of Groundedπ i Bot would have to make multiple calls to other programs. Indeed, this is one of the reasons why the present paper only discusses two-player games and iterated games with such shortterm memory. Whether a similar result can nonetheless be obtained for more than 2 players and strategies that depend on the entire past history is left to future research. As special cases, for any strategy π −i , Groundedπ i Bot terminates against Groundedπ −i Bot and Naiveπ −i Bot (and these programs in turn terminate against Groundedπ i Bot). The latter is especially remarkable. Our Groundedπ i Bot terminates and leads the opponent to terminate even if the opponent is so careless that it would not even terminate against a version of itself or, in our formalism, if PROG −i (G) gives the opponent more leeway to work with simulations. \n Relationship to the underlying iterated game strategy Theorem 5 Let G be a game, π i be a strategy for player i in G , p i = Groundedπ i Bot and p −i ∈ PROG −i (G) be any opponent program. We define π −i = apply( p −i , (p i , p −i )), which makes π −i a strategy for player −i in G . Then E G u i | p i , p −i = E G u i | π i , π −i . Proof We separately transform the two expected values in the equation that is to be proven and then notice that they only differ by a factor : E G u i | π i , π −i = lemma 2 ∞ k=0 ab∈A i A −i P k,G (a, b | π i , π −i )u i (a, b) = lemma 3 ab∈A i A −i π i (0, a)π −i (b)u i (a, b) + ∞ k=1 ab∈A i A −i (1 − ) k b ∈A −i π −i (b )π i (b , a)π −i (b)u i (a, b) = absolute convergence ab∈A i A −i π i (0, a)π −i (b)u i (a, b) + ab∈A i A −i b ∈A −i π −i (b )π i (b , a)π −i (b)u i (a, b) ∞ k=1 (1 − ) k = sum of geo- metric series ab∈A i A −i π i (0, a)π −i (b)u i (a, b) + 1 − ab∈A i A −i b ∈A −i π −i (b )π i (b , a)π −i (b)u i (a, b). The second-to-last step uses convergence to reorder the sum signs. The last step uses the well-known formula ∞ k=0 x k = 1/(1 − x) for the geometric series. Onto the other expected value: E G u i | p i , p −i = Eqs. 3, 2, 1 ab∈A i A −i apply( p i , (p i , p −i ), a)apply( p −i , (p i , p −i ), b)u i (a, b) = def.s p i , π −i ab∈A i A −i ⎛ ⎝ π i (0, a)+(1 − ) b ∈A −i π −i (b )π i (b , a) ⎞ ⎠ π −i (b)u i (a, b) = ab∈A i A −i π i (0, a)π −i (b)u i (a, b) +(1 − ) ab∈A i A −i b ∈A −i π −i (b )π i (b , a)π −i (b)u i (a, b). Here, apply( p i , (p i , p −i ), a) := apply( p i , (p i , p −i ))(a). The hypothesis follows immediately. Note that the program side of the proof does not involve any \"mental G \". Using Theorem 5, we can easily prove a number of property transfers from π i to Groundedπ i Bot. Corollary 6 Let G be a game. Let π i be a computable strategy for player i in G and let p i = Groundedπ i Bot. \n If p −i ∈ B −i ( p i ), then apply( p −i , (p i , p −i )) ∈ B s,c −i (π i ). 2. If π −i ∈ B s,c i (π i ) and apply( p −i , (p i , p −i )) = π −i , then p −i ∈ B −i ( p i ). Proof Both 1. and 2. follow directly from Theorem 5. Intuitively speaking, Corollary 6 shows that π i and Groundedπ i Bot provoke the same best responses. Note that best responses in the program game only correspond to best stationary computable best responses in the repeated game. The computability requirement is due to the fact that programs cannot imitate incomputable best responses. The corresponding strategies for the repeated game further have to be stationary because Groundedπ i Bot only incentivizes opponent behavior for a single situation, namely the situation of playing against Groundedπ i Bot. As a special case of Corollary 6, if < 1/2, the best response to GroundedFairBot is a program that cooperates against GroundedFairBot because in a IPD with a probability of ending of less than 1/2 a program that cooperates is the best (stationary computable) response to tit for tat. \n Exploitability Besides forming an equilibrium against many opponents (including itself) tivizing cooperation, another important reason for tit for tat's success is that it is \"not very exploitable\"  (Axelrod 2006) . That is, when playing against tit for tat, it is impossible to receive a much higher reward than tit for tat itself. We now show that (in)exploitability transfers from strategies π i to Groundedπ i Bots. We call a game G = (A 1 , A 2 , u 1 , u 2 ) symmetric if A 1 = A 2 and u 1 (a, b) = u 2 (b, a) for all a ∈ A 1 and b ∈ A 2 . If G is symmetric, we call a strategy π i for G N -exploitable in G for an N ∈ R ≥0 if there exists a π −i , such that E u −i | π −i , π i > E u i | π −i , π i + N . We call π i N -inexploitable if it is not N -exploitable. Analogously, in a symmetric game G we call a program p i N -exploitable for an N ∈ R ≥0 if there exists a p −i , such that E u −i | p −i , p i > E u i | p −i , p i + N . We call p i N -inexploitable if it is not N -exploitable. Corollary 8 Let G be a game and π i be an N -inexploitable strategy for G . Then Groundedπ i Bot is N -inexploitable. Proof Follows directly from Theorem 5. Notice that if -like tit for tat in the IPD -π i is N -inexploitable in G for all , then we can make Groundedπ i Bot arbitrarily close to 0-inexploitable by decreasing . \n Conclusion In this paper, we gave the following recipe for constructing a program equilibrium for a given two-player game: 1. Construct the game's corresponding repeated game. In particular, we consider repeated games in which each player can only react to the opponent's move in the previous round (rather than the entire history of previous moves by both players) and the game ends with some small probability after each round. 2. Construct a Nash equilibrium for that iterated game. The result is a program equilibrium which we have argued is more robust than the equilibria described by  Tennenholtz (2004) . More generally, we have shown that translating an individual's strategy for the repeated game into a program for the stage game in the way described in 3 retains many of the properties the strategy for the repeated game. Thus, it seems that \"good\" programs to submit may be derived from \"good\" strategies for the repeated game. Fig. 1 1 Fig. 1 Dynamic call diagram describing how p 1 = GroundedFairBot chooses when playing against p 2 = NaiveFairBot. \n 3. Convert each of the strategies into a computer program that works as follows (see Algorithm 3): with probability do what the strategy does in the first round. With probability 1 − , apply the opponent program to this program; then do what the underlying strategy would reply to the opponent program's output. \n Table 1 1 Payoff matrix for the prisoner's dilemma Player 1 Player 2 Cooperate Defect Cooperate 3, 3 1 , 4 Defect 4, 1 2 , 2 \n\t\t\t The equilibrium in its rudimentary form had already been proposed by McAfee (1984)   and Howard (1988) . At least the idea of viewing players as programs with access to each other's source code has also been discussed by, e.g.,Binmore (1987, Sect. 5; and Anderlini (1990) .2  For keeping our notation simple, we will assume that our programs receive their own source code as input in addition to their opponent's. If PROG i (G) is sufficiently powerful, then by Kleene's second recursion theorem, programs could also refer to their own source code without receiving it as an input(Cutland 1980,  ch. 11). \n\t\t\t This program was proposed by Abram Demski in a conversation discussing similar (but worse) ideas of mine. It has also been proposed by Jessica Taylor at https://agentfoundations.org/item?id=524, though in a slightly different context. \n\t\t\t The tournament was announced at https://www.lesserwrong.com/posts/BY8kvyuLzMZJkwTHL/ prisoner-s-dilemma-with-visible-source-code-tournament and the results at https://www.lesserwrong. com/posts/QP7Ne4KXKytj4Krkx/prisoner-s-dilemma-tournament-results-0. 5 For a more detailed analysis and report on my methodology, see https://casparoesterheld.files.wordpress. com/2018/02/transparentpdwriteup.pdf.", "date_published": "n/a", "url": "n/a", "filename": "Oesterheld2018_RobustProgramEquilibrium.tei.xml", "abstract": "One approach to achieving cooperation in the one-shot prisoner's dilemma is Tennenholtz's (Games Econ Behav 49(2): [363][364][365][366][367][368][369][370][371][372][373] 2004)  program equilibrium, in which the players of a game submit programs instead of strategies. These programs are then allowed to read each other's source code to decide which action to take. As shown by Tennenholtz, cooperation is played in an equilibrium of this alternative game. In particular, he proposes that the two players submit the same version of the following program: cooperate if the opponent is an exact copy of this program and defect otherwise. Neither of the two players can benefit from submitting a different program. Unfortunately, this equilibrium is fragile and unlikely to be realized in practice. We thus propose a new, simple program to achieve more robust cooperative program equilibria: cooperate with some small probability and otherwise act as the opponent acts against this program. I argue that this program is similar to the tit for tat strategy for the iterated prisoner's dilemma. Both \"start\" by cooperating and copy their opponent's behavior from \"the last round\". We then generalize this approach of turning strategies for the repeated version of a game into programs for the one-shot version of a game to other two-player games. We prove that the resulting programs inherit properties of the underlying strategy. This enables them to robustly and effectively elicit the same responses as the underlying strategy for the repeated game.", "id": "ffd8e3324fb38892be0da1e275b54058"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Robert De Neufville", "Seth D Baum"], "title": "Collective action on artificial intelligence: A primer and review", "text": "Introduction Collective action \"arises when the efforts of two or more individuals or agents … are required to accomplish an outcome\"  [1] ; p. 196. The overall development of artificial intelligence (AI) requires collective action, as do efforts to ensure that AI development results in good outcomes for society, both because it requires individuals to coordinate their actions and because it is simply too large and complex a task for any single individual acting alone to accomplish. This paper is a primer and review of AI collective action. By AI collective action, we mean the collective action humans take to improve the outcomes of AI development, not the collective action of groups of AIs. The paper is a primer in that it serves as an introduction to the topic for a diverse audience of social scientists, computer scientists, policy analysts, government officials, organizers, activists, concerned citizens, and anyone else with an interest in the topic. The paper is a review in that it reviews the literature that has thus far accumulated on the topic. Many aspects and applications of AI will require collective action. In particular, as we show below, collective action will be needed to reach agreement on AI rules and standards, to develop AI that is broadly socially beneficial rather than merely being profitable for particular developers, and to avoid competition or conflict that could lead to AI being developed or used in a less safe and beneficial way. AI is a potentially transformative technology that could shape the way people live, work, and communicate. This raises the question of how AI can contribute to or hinder good outcomes for society-or, phrased differently, how AI can contribute to or hinder the building of a good society.  1  As Coeckelbergh  [2]  notes, the question of the appropriate role of technology in society is a political question of concern to the general public rather than a purely technical question of concern only to private individuals. Addressing that question will require collective action. AI collective action is a relatively new field. A large portion of the work on it has been written in just the last few years. The topic has also attracted interest from a wide range of thinkers from both inside and outside academia. This paper takes an inclusive approach to the literature, drawing on everything from full-length peer-reviewed research papers to short blog posts and commentaries. The intent is to provide a broad review of existing ideas about AI collective action, regardless of where they are published. The core method of this paper is a nonsystematic review of the AI collective action literature. The selection of literature reviewed is not necessarily comprehensive or representative of the full body of work on the topic, though we believe we have identified the overwhelming majority of relevant work. The literature reviewed was identified via keyword searches, our own prior knowledge of the literature, and citation tracking. The Google Scholar and Google Web Search tools were queried with phrases such as \"artificial intelligence collective action\", \"artificial intelligence governance\", and \"artificial intelligence race\". \"Artificial intelligence race\" was included because a large number of the articles that concern AI collective action focus in particular on AI races. Most of the literature identified was published after 2010 because this is a new literature, but keyword searches were not limited to articles published after 2010. All academic publications were included. Nonacademic publications were included if in the authors' judgment they contained a well-supported and compelling discussion of AI collective action. Much of the AI collective action literature identified in this paper focuses on long-term scenarios in which competitive pressures increase the risk of catastrophic outcomes, especially via the development of advanced forms of AI such as artificial general intelligence (AGI) and superintelligence.  2  Another important focus of the literature is on military applications and the potential dangers of near-term AI arms races. This paper has some emphasis on the literature on near-term and longterm AI races (Section 3), though much of the discussion is more general. Indeed, despite the wide range of forms and applications that AI technology has now and could have in the future, the collective action issues they raise are similar both in the nature of the issues and in their potential solutions. In this regard, the paper contributes to a broader analysis of synergies between near-term and long-term AI issues  [3] [4] [5] [6] . Following a general overview of AI collective action, the paper presents discussions of AI race scenarios and collective action that could be taken to address them. Much of the literature to date focuses on the collective action issues raised by races. It should be stressed that races are not the only scenarios that raise AI collective action issues, though they are important ones. \n A primer on collective action This section presents a general background on collective action, with emphasis on aspects of relevance to AI. It is intended mainly for an interdisciplinary non-specialist audience; much (though not all) will be familiar to readers who are versed in the study of collective action. \n Divergent vs. convergent interests The concept of collective action is perhaps most closely associated with \"collective action problems\", in which individual interests and group interests diverge. Where individual interests are at odds with group interests, individuals' pursuit of their own self-interest may lead to outcomes that are worse for not only for the group as a whole but also for each individual considered separately. The prisoner's dilemma is a simple and well-known form of collective action problem.  3  Collective action situations also include scenarios in which individual interests and group interests converge. In these cases, individuals' pursuit of their own self-interest can lead to outcomes that are collectively optimal. In markets, for example, individuals can make transactions that benefit themselves and improve group outcomes by allocating resources more efficiently.  4  Individual interests also converge in coordination problems when individuals would benefit by agreeing on a common set of rules or standards. Where individual interests align, the challenge is to coordinate individual actions rather than to resolve conflicts among individual interests. AI collective action includes cases of both divergent and convergent interests. AI races are, in the literature identified in this paper, typically associated with a mix of convergent and divergent interests (Section 3). Divergent interests also arise for AI work done in the public interest, including basic research published in the open literature and the development of standards and techniques for AI safety and ethics.  5  In both of these cases, individuals have limited incentives to do the work, so it is often funded by governments or private philanthropies. In general, public funding of basic research has a range of benefits in scientific and technical fields besides AI as well  [7] . Convergent interests can arise when AI developers would benefit from using the same standardized platforms. It can be valuable for everyone to use the same programming languages, code repositories, operating systems, etc. so that programs can interoperate and developers do not have to start from scratch each time they join a new project. In some cases, it may not particularly matter which platform is used, as long as everyone uses the same one. Collective action is more difficult to achieve when individual and group interests diverge, because individuals' pursuit of their own interests will not lead on its own to collectively optimal outcomes.  6  The study of collective action therefore tends to focus on the more difficult challenges posed by divergent interests. This paper has a similar emphasis. Nonetheless, it is important to recognize that AI collective action does not always entail competition among individuals with divergent interests. Furthermore, there are often opportunities to align individual and group interests. This can be a powerful way to improve AI outcomes. One important way individual and group interests can converge is when individuals value group outcomes. Collective action problems like the prisoner's dilemma assume individuals are narrowly self-interested, but individuals may also care about others, in which case they may choose to act in the group interest even if doing so goes against their selfinterest. In the extreme case, individuals may value only group outcomes, so that they always act in the group interest regardless of the implications for themselves. Even if all individuals value only group outcomes, they could still be in competition if they value different aspects of group outcomes. For example, a survey by Baum  [8]  finds that AGI developers typically value either humanity as a whole or intellectual progress for its own sake, but not both. Since these goals might be at odds, one can imagine competition between pro-humanity developers and pro-intellectual progress developers. Similarly, the Armstrong, Bostrom and Shulman  [9]  model of dangerous AI races uses an \"enmity\" parameter to model AI projects' preference for their own project winning the race. Enmity could derive from either self-interest or differing preferences about which group values to favor. In the model, higher enmity results in less cooperation and more dangerous races. Efforts to promote and reach consensus on group values could increase the convergence of interests and make collective action more likely. In recent years, different versions of AI ethics principles have proliferated  [10] , which may be a constructive step in this direction  2  AGI is AI that is capable of thinking across a wide range of cognitive domains. In contrast, current AI is narrow in the sense that it is only capable of thinking across a relatively narrow range of domains. Superintelligence is AI that is significantly smarter than humans in many important respects. AGI is often considered an important precursor to superintelligence. A concern is that AGI and/or superintelligence could outsmart humanity, take over the world, and potentially kill everyone in the process  [20, 69, 85] . This scenario is referred to in this paper as an \"AI catastrophe\".  3  For a detailed description of the prisoner's dilemma and related scenarios as they pertain to AI collective action, see Askell et al.  [21] . harms of a market transaction are not built into the price of the good or service being sold. For example, the harms from global warming are in most instances an externality that is not built into the price of fossil fuel. In these situations, individual and collective interests can diverge.  5  Hughes  [56]  and AI Impacts  [19]  both discuss these points in the context of AI safety and ethics.  6  For discussion of this issue see e.g. Olson  [86]  and Ostrom  [48] . (though for a critical analysis of this, see Whittlestone et al.  [11] ). Establishing ethical norms among AI developers could also increase the convergence of interests. Examples of attempts to establish ethical norms for AI development include senior AI researcher Stuart Russell's call for people in AI to care more about the societal consequences of the technology  [12]  and employee activism among workers in the field of AI  [13] . A relevant historical precedent is the moratorium on recombinant DNA in the 1970s, which succeeded in part because the relevant scientific community had a shared culture of political activism that left them predisposed to accepting a moratorium on their work  [14] . \n The excludability and rivalry of goods In public choice economics, collective action is often evaluated in terms of the type of goods that are being produced.  7  \"Goods\" in this context are anything that one or more individuals benefit from. Goods can include tangible material objects like computers, and intangible things like information. A common scheme for classifying forms of collective action depends on whether the goods at issue are excludable and rivalrous  [15, 16] . Goods are excludable if it is possible to prevent people from benefiting from them, and they are rivalrous if enjoying them reduces how much they benefit others. Table  1  presents a 2 × 2 matrix of (non)excludable and (non)rivalrous goods. The four types of goods can be summarized as follows: • Public choice theory holds that collective action problems, in which individual and group interests diverge, arise mainly for non-excludable (common and public) goods because individuals can benefit from them without contributing to their production or maintenance  [1] . When goods are excludable, access can be restricted (e.g., via setting higher prices for access) so as to align individual and group interests. This is controversial because higher prices can exclude poorer people and result in outcomes that are worse for the group once considerations of equity are taken into account. In any case, non-excludable goods face the basic problem of free-riding: since individuals can benefit from these kinds of goods whether or not they have contributed to providing or maintaining them, they have an incentive to free-ride on the contributions of others. (This assumes that individuals are self-interested.) As a result, individual community members have an incentive to produce less of these types of goods than they would if they were required to contribute, and less than would be optimal for the community as a whole. Common goods face the additional challenge of maintaining an adequate supply given the incentive to use up the goods. Unlike with public goods, free-riding diminishes the supply of common goods available for other individuals. Classic discussions of common good resources (such as open pastures for grazing livestock animals) warned of the \"tragedy of the commons\" due to the incentive to deplete the resources  [17] . Modern scholarship speaks of the \"drama of the commons\" because this type of situation does not necessarily end in tragedy  [18] .  9  How the tragedy can be avoided is a primary focus of collective action research, as discussed in Section 4. Note that the provision of common goods has the same basic structure as the prisoner's dilemma. Important aspects of AI development have the structure of public and common goods. The avoidance of an AI catastrophe has the structure of a public good in that the enjoyment of the absence of AI catastrophe is neither excludable nor rivalrous. Likewise, there may be an undersupply of efforts to avoid AI catastrophe, with individuals hoping to free-ride on the efforts of others  [19] . Cooperation between different AI projects can have the structure of the provision of a common good, especially in scenarios like dangerous races in which competition increases risks. Just as competing individuals can diminish the supply of a common good by overusing it, competing individual AI projects can increase the risk of an AI catastrophe by taking avoidable risks. In both cases, individuals pursuing their own selfinterest cause harms to the overall population. This incentive structure has been recognized in some prior AI literature  [9, [19] [20] [21] . AI races are discussed further in Section 3. \n Distribution of contributions In certain situations, successful collective action can depend on how the contributions of different actors are distributed. A helpful typology of these situations comes from Hirshleifer  [22]  and Barrett  [23] . Work by AI Impacts  [19]  applies the Barrett  [23]  typology to AI. This prior literature frames the typology in terms of public goods instead of the distribution of contributions. However, the situations described by the typology are not restricted to public goods, and in our view are more productively expressed in terms of distributions of contributions. The core of the typology features four types of collective action situations: • Aggregate effort: when the result depends on the summed contributions of all actors rather than on how much any given actor contributes, such as when a project needs a certain amount of financing but it does not matter where it comes from. • Single best effort: when the result depends on the effectiveness of the best effort to address the problem, such as when a solution to a technical problem is needed. • Mutual restraint: when the result depends on the extent to which actors all refrain from taking certain actions, such as when   Ostrom 48 ].  8  It is possible to build electric grids with access restrictions, though this is often not done, especially for the outlets found in most buildings. An example of a common good in which access restrictions cannot be built in is ocean fisheries: oceans cannot be redesigned to prevent certain people from accessing them.  9  For recent discussion, see Boyd et al.  [87] . developing or using a technology is so dangerous that a single failure could be catastrophic. • Weakest link: when the result depends on the effectiveness of the worst effort to address the problem, such as when the security of a system will fail if it fails at any single point. Aggregate effort, single best effort, and weakest link situations are all variants of situations requiring different distributions of contribution across all the actors. In aggregate effort, what matters is the total contribution of all actors rather than how that effort is distributed among them. An example of an aggregate effort situation is one in which what matters is how much money is raised for a project, not where the money comes from. In single best effort situations, what matters is the work done on a single top-performing project, which could include contributions from any number of actors. An example of a single best effort situation was the attempt to send humans to the moon, which succeeded when one project succeeded, but would have failed if the same effort had been divided among lots of projects that did not reach the moon. In weakest link situations, all actors must make some minimum contribution. Weakest link situations are ones in which every actor is responsible for maintaining some essential part of a joint activity. An example of a weakest link situation is when the failure of a single actor to follow cybersecurity protocols would compromise an entire network. Mutual restraint situations are similar to weakest link situations in that every actor must meet at least some minimum standard, but in mutual restraint situations what matters is not what actors do, but what they refrain from doing. An example of a mutual restraint situation is one in which every actor needs to refrain from a risky behavior that could affect them all, like performing an experiment that could have catastrophic consequences. One can readily imagine other variants of these situations, in which for example success requires two projects to meet some performance threshold (a \"double best effort\", such as for shipping custom products to two clients), or in which success requires all actors except one to meet some performance threshold (a \"second-weakest link\", such as for the cybersecurity of a computer network in which one computer can be air gapped to store backup files). The  Barrett [23]  typology also includes coordination situations, in which the result depends on the extent to which actors act in the same way. Coordination systems can also involve a variety of distributions of contribution. For example, weakest link and mutual restraint situations are situations in which every single actor must either act or refrain from acting in the same way (e.g., if all drivers have to act the same way at stoplights); aggregate effort situations are situations in which actors must collectively coordinate their activities closely enough but not perfectly (e.g., if drivers have to stop at stoplights only reliably enough for other drivers to have confidence they can safely go when the light is green). Cooperation may be easier in single best effort situations than in aggregate effort situations because efforts can be focused on a single topperforming project. Cooperation likewise may be harder in weakest link and mutual restraint situations than in aggregate effort situations because each actor has to meet some minimum standard of action. Cooperation is potentially easier to achieve in coordination situations because actors have an interest in coordinating and may be indifferent as to which coordination scheme is used. Different aspects of AI development conform to different collective action situations. AI Impacts  [19]  observes that refraining from developing an AI that would favor some groups over others requires mutual restraint, while the development of a safe ethical AI design may depend on a single best effort. The extent to which safe, ethical AI design is funded may depend on the aggregate effort of actors. The elimination of bugs or security problems in a jointly developed system may depend on the contribution of a weakest link actor. The development of standards that allow AI systems to work together may require coordination. \n Dangerous AI race scenarios Broadly speaking, an AI race is when AI development proceeds more quickly than it otherwise would, especially when multiple development teams compete to develop AI more quickly than each other. AI races are not necessarily dangerous and might even hasten the arrival of socially beneficial forms of AI  [24] . Similarly, efforts to slow AI development can be harmful by limiting progress  [25, 26] . Nonetheless, a substantial body of literature concerns the potential dangers of AI races. The main reason AI races could be dangerous is that developers might cut corners on safety in order to develop more quickly. This theme has been articulated, for example, by  Danzig [27]  in the context of military AI races and by many authors  10  in the context of long-term AGI development. There can be tension between the value of racing ahead for relative advantage (or perhaps for other reasons) and the value of exercising due caution with respect to harmful unintended consequences. This tension can be found for a variety of technologies, certainly including AI. In collective action terms, dangerous AI races may be especially worrisome if racing is in the individual interests of developers but not in the collective interest. In such cases these divergent interests create a collective action problem (Section 2.1). Each developer decides whether to participate in a race to develop an AI system. Each would benefit from winning the race, as long as their winning AI system is safe. If the first AI system developed is safe, the benefits of winning accrue primarily to the winning party. However, if the first system is not safe, for example if the winning system is one that causes global catastrophe, everyone might collectively bear the costs. In this situation, it may be in the individual interest of any given AI group to participate in a race even though it is in the collective interest of the group as a whole to avoid a race and develop AI more cautiously. This situation has the same basic incentive structure as prisoner's dilemma or common goods situations (Section 2.2). In the extreme case, these situations could require mutual restraint (Section 2.3) if an AI catastrophe can be avoided only if no developers engage in a race. Dangerous AI races could occur when it is not in the interest of developers to engage in an AI development race, if developers wrongly believe it is in their interest to do so. Choices about AI development may be made under conditions of \"bounded rationality\",  11  in which developers' ability to determine the best course of action may be limited in practice. The complexity of AI systems makes their risks difficult to evaluate with any certainty. Cultural norms or a cognitive biases may also make developers inclined to downplay risks, even where evidence suggests the risks are significant. As a result, dangerous AI races can arise when developers' perceived interests diverge from the collective interests of the group (e.g., when they imagine the reward for being the winner of an AI development race would be larger than it actually is). In such cases, the collective action problem that results could potentially be resolved by providing developers with accurate information about their individual interests  [21] .  12  In contrast, actors in non-dangerous AI races may tend to have convergent interests, or at least interests that do not diverge. (An AI race is non-dangerous if the benefits of engaging in the race would outweigh or at least balance the harms.) Many common AI development races may be non-dangerous rather than dangerous. In some cases, such as when competition speeds the development of beneficial technology, the benefits of engaging in a development race may substantially outweigh the harms. Some races may be coordination situations, in which developers collectively benefit from working on the same problems at the same time. For example, the ImageNet database and ImageNet Large Scale Visual Recognition Challenge allow groups working on image recognition to pool their efforts and learn from one another  [28] . It is also possible that developers could have an incentive not to engage in an AI race that would benefit the public by spurring valuable innovation. This is also a collective action problem because the interests of the individual developers diverge from the collective interest. This could occur if winning the race would depend on the production of a public good (Section 2.2), like basic research and development (R&D) that is likely to end up in the public domain. In such a case developers would have individual incentives to collectively underinvest in AI development and free-ride on the work of others. The distinction between dangerous and non-dangerous races is conceptually important for the reasons outlined above. but it may also be a rhetorically important distinction. When AI races are not identified as dangerous, they may be seen as harmless contests that should be played to win, rather than the risky competitions they can be  [29, 30] . As a result, using the unqualified term \"AI races\" could increase the likelihood of irrational and dangerous AI races. Arguably, simply framing AI development as a \"race\" may make it sound less risky than it is, exaggerate the extent to which it is necessarily a competition, and minimize the potential for beneficial collaboration.  13  We therefore advise identifying dangerous AI races as \"dangerous\". (Identifying non-dangerous AI races may be less important, but potentially worthwhile nonetheless.) \n Dangerous near-term AI races AI race scenarios can broadly be split into private and public sector races. It is not a sharp distinction, since there are important interconnections between the private and public sectors, including public funding for private R&D and government use of AI developed by the private sector. Nonetheless, private corporations and national governments have different competitive dynamics. The private sector is currently the driving force behind AI development. The computer technology industry has a reputation for product development that can be rushed and risky, as epitomized by the former Facebook slogan \"move fast and break things\". Some of it is driven by competition, with rival groups seeking to gain market share, profit, and other advantages. There is intense competition to hire the most talented AI researchers and to build computer systems with superior performance in various tasks; both of these competitions have sometimes been referred to as \"arms races\" even though they do not involve military armaments  [31] [32] [33] . A different sort of private sector \"arms race\" occurs between AI teams at social media companies tasked with removing inappropriate content and people who post the content  [34] . Despite the ubiquity of near-term private sector AI races, the matter has not yet received substantial scholarly attention. AI races in the public sector-especially military AI races-have attracted more attention. Geist  [35]  traces military AI competition as far back as the 1960s Cold War competition between the Soviet Union and the US. The 1960s initiatives focused on advancing basic research. Today, AI is increasingly being used in operational military systems. A significant concern is the near-future prospect of arms races for autonomous weapons  [36] [37] [38] , though Scharre  [39]  documents that countries have not been as quick to embrace autonomous weapons as one might think. More generally, the extent of a military AI arms race may be overstated  [40] . Nonetheless, there are clear reasons for rival militaries to race one another to improve their AI capabilities. For example, fighter aircraft can gain a relative advantage over adversary planes by using AI to make faster and better combat decisions  [41] . AI arms races may be more likely to occur with (a) weapon systems that attack other systems of the same kind (like fighters that are designed to engage other fighters in dogfights) than with (b) weapon systems that attack something else (like drones that are designed to engage human targets). For (a) but not (b), improving the weapon systems' AI gives the other side a reason to improve its own similar systems' AI. It is beyond the scope of this paper to assess the danger of near-term AI race scenarios. It is clear that near-term AI could pose risks, and it is plausible that some of these risks may be sufficient to render certain near-term AI races dangerous. This matter has not yet been clearly established in the literature and is a worthy focus of future research. \n Dangerous long-term AI races The dangers of long-term AI races have received more attention. This literature generally focuses on scenarios involving extremely capable AI and extremely high stakes. It is often argued that the first AI to reach some capability threshold could become enormously powerful, perhaps even powerful enough to effectively take over the world.  14  If that argument is right, then global outcomes could largely be determined by which AI project wins a development race. If the AI is built safely, then the result is an extreme case of \"winner takes all\". Alternatively, if the AI is not safe, then \"winning\" the AI development race would be the ultimate Pyrrhic victory, with catastrophic aggregate harms up to and potentially including human extinction. Because of the extreme stakes it is unambiguously in the collective interest to avoid such catastrophes. It is presumably very much in the self-interest of an AI developer to be the first to develop a safe AI. It may or may not be in the collective interest for that developer to be the first to develop safe AI, depending on whether the AI would make the AI broadly beneficial, since an immensely capable AI might be able to work wonders, both in the service of its developers and the world in general. The exact calculus depends on the probabilities of beneficial and catastrophic outcomes for each potential developer, as well as how much the developer and the collective value these outcomes. Resolving this calculus involves a suite of difficult philosophical and empirical issues that have to date not received attention in the AI collective action literature. The enormous stakes also blur the distinction between public and private actors. A private actor that built and controlled such an AI could have power rivaling the largest states. The substantial stakes also give states a reason to intervene in AI development and potentially even to nationalize parts of the AI industry  [42] ; p.10. While some analyses of long-term AI have focused on development in one sector or another,  15  the impact of powerful AI is likely to transcend specific sectors and affect the collective interests of a broad group of actors (though the sector in which development occurs may matter for other reasons). Several studies develop mathematical models of the dynamics of dangerous long-term AI races. Armstrong et al.  [9]  model races in which the reward for winning is large and teams can improve their chances of winning by skimping on safety precautions, which also increases the probability of catastrophe. They find increased risk when there are more competing teams, when the teams have a stronger preference for winning, when taking risks increases the odds of winning, and when teams know each other's capabilities. Aldana  [42]  uses a variety of two-player games to explore opportunities to alter incentives toward cooperation, for example by highlighting the potentially catastrophic consequences of failing to cooperate. Han et al.  [43]  model competition over successive rounds of AI development, finding that cooperation is less likely when advanced AI can be built in the relatively near future. Finally, Naudé and Dimitri  [44]  model the cost of building AGI, finding that if it were expensive, relatively few groups would compete, but that public funding could incentivize cooperation. While some of these findings may seem self-evident, these models offer a means of exploring some of the subtler nuances of races and opportunities to increase cooperation. On the other hand, these models make sweeping mathematical assumptions about complex socio-technological processes and need to be supplemented with empirical studies. \n Long-term effects of near-term races Finally, it is worth briefly discussing the idea that near-term AI races can affect the long-term development of AI. In particular, it has been argued that near-term AI races could slow the long-term development of AI. One mechanism for this is by generating public backlash. If nearterm AI is not developed with sufficient caution, it could cause problems that lead to regulations and other initiatives that impede further AI development. This view was recently expressed by Mounir Mahjoubi, the French minister for digital affairs and an architect of France's AI policy. In Mahjoubi's words, \"If you don't invest in responsibility around AI, you will create resistance and resentment in the population\"  [45] . An example of an incident that could create an enduring backlash is a 2018 incident in which a self-driving Uber killed a pedestrian. Following this incident, the US National Highway Traffic Safety Administration and National Transportation Safety Board launched probes into autonomous vehicle safety  [46] . While it is not yet clear whether the incident will ultimately slow the roll out of autonomous vehicles, it is nonetheless indicative of the possibility. Another mechanism is that near-term races could focus resources on maximizing near-term performance at the expense of long-term progress. As is common with many areas of technology, long-term advances in AI may require new techniques based on fundamental breakthroughs that derive from basic research. In contrast, optimizing near-term performance may primarily involve the application of existing techniques. Hence, Marcus  [47]  argues that focusing on established machine learning techniques has left the field of AI at a long-term disadvantage. In other words, near-term races may not incentivize people to come up with new and possibly more effective AI techniques. \n Solutions to AI collective action problems The social science literature on collective action has identified three broad types of approaches to solving collective action problems. Each approach uses different strategies to encourage individuals to act in the collective interest even when their immediate incentives are to act in against the collective interest. The three approaches involve top-down government policy, bottom-up community governance, and private ownership  [48] . \n Top-down government solutions Governments have some capacity to compel collective action. Governments can set policies that require individuals to act in accordance with the collective interest. Governments also have the authority to enforce compliance with policies and to punish noncompliance. For these reasons, governments are often seen as the appropriate institutions for encouraging collective action, both in general  [48]  and with respect to AI  [19] . The AI collective action literature has produced a wide range of proposals for top-down government solutions. The range of these proposals shows the tradeoff that exists between the ambitiousness of a proposal and its feasibility. The more ambitious proposals would probably do more to advance AI collective action if they were implemented, but may be difficult to implement. The more modest proposals would do less to advance AI collective action but are probably more feasible. The most ambitious proposals call for no less than a world government that would monitor AI development and force rogue AI projects to comply with ethics and safety standards. This bold idea has been repeatedly proposed in the literature  [19, 49, 50] . A related proposal is for an \"AI nanny\" that uses advanced AI to govern humanity and guide the development of even more advanced AI  [51] . Somewhat less ambitious proposals call for international institutions that would house or otherwise govern the global development of AI. These proposals leave national sovereignty intact except with respect to AI development. Specific proposals include a \"global watchdog agency\"  [52] , an international AI project with broad authority to regulate the development and use of advanced AI  [20] ; pp.  104-106; [53-55] , and publicly funding a limited number of groups that have the exclusive right to develop advanced AI on the condition that it is in the public interest  [44] . The most feasible proposals require relatively modest tweaks to existing governance schemes. For example, AI could be included in existing international arms control agreements  [56] . New arms control agreements could be made for AI-based weapons. The feasibility of the proposed ban on autonomous weapons has been questioned, but may nonetheless be possible  [57] , and other arms control measures that stop short of a ban would be more feasible. International institutions can also assist in setting the agenda on AI and facilitating dialog. Indeed, this is already occurring on a limited scale via the UN High-Level Panel on Digital Cooperation. Another international body that could guide global AI development is the Global Partnership on AI, a recently formed coalition of states with the mission of supporting \"the responsible and human-centric development and use of AI in a manner consistent with human rights, fundamental freedoms, and [their] shared democratic values\"  [58] . Similar to this is a proposal for an intergovernmental organization that brings together stakeholders from the public sector, industry, and academia to develop non-binding recommendations for how to increase international cooperation on AI  [59] . Since binding \"hard law\" rules can be difficult to enact, Marchant  [60]  proposes a range of non-binding \"soft law\" measures that create expectations but are not formally enforced by government, including \"private standards, voluntary programs, professional guidelines, codes of conduct, best practices, principles, public-private partnerships and certification programs\". Finally, an international organization could sponsor, host, or serve as a clearinghouse for research into AI, and play a role similar the European Organization for Nuclear Research (CERN)  [47, 61, 62]  in physics or the Intergovernmental Panel on Climate Change (IPCC) in climate science  [63] . Such an organization could potentially address the collective action problem of underinvestment in basic research, as well as the problem of underinvestment in AI ethics and safety research. Other literature has explored national government-led solutions. A major focus is on liability schemes for harms caused by privately developed AI and robotics systems.  16  Liability schemes can encourage collective action by changing individuals' incentives so that they align with the collective interest. Other proposals call for national governments to sponsor research on AI safety  [64] , to establish national panels to develop guidelines for AI R&D and use  [65] , or to create a National Algorithm Safety Board similar to the US National Transportation Safety Board to provide independent oversight of algorithms used to make decisions that impact the public  [66] . Outside of the extensive literature on liability, most of the proposed government solutions have involved action at the international level. The reason appears to be that since AI can be developed anywhere in the  16  See e.g. Karnow  [95] ; Asaro  [96] ; Marchant & Lindor  [97] ; Funkhouser  [98] ; Gurney  [99] ; LeValley  [100] ; Scherer  [101] ; Wu  [102] ; and Zohn  [103] . Note that liability schemes apply mainly for near-term AI; the catastrophic harm from long-term AI may be so severe that it destroys the liability system  [104] . world, comprehensive collective action requires a global scope. Some even worry that piecemeal national regulations could push AI development underground to \"rogue nations\"  [67] . Nevertheless, national governments have substantial authority even within the largely decentralized international system. Action at the national level is often more feasible than action at the international level, and successful action at the national level can serve as a model for international action. Top-down government action, whether at the national or international level, is not a perfect solution for AI collective action problems. Governments may struggle to regulate AI due to its complexity and rapid change  [21, 24, 60] . Governments themselves may promote corporate or other special interests over the collective interest  [68] . International proposals, especially ambitious ones, require a high degree of international cooperation, which may be hard to achieve given the difficulty of monitoring compliance, the incentives each state would have to defect  [54] ; p. 46, the number of political jurisdictions and industries that would be involved, and the speed at which AI technology changes  [60] . Even the most ambitious global agency might still fail to prevent dangerous projects from advancing  [49, 53, 64] . In addition, any government scheme that lacks support from AI communities could create resentment and lead to pushback, making collective action more difficult  [8] . Therefore, while top-down government solutions may be able to play a role in advancing AI collective action, they probably cannot resolve all AI collective action issues. \n Private ownership solutions Privatization is a common approach to solving collective action problems. One prominent context in which privatization is often used is in the management of natural resources. A private actor who owns a resource has an incentive to use it optimally. For example, private ownership of pasture may make overgrazing less likely, because the owners have an interest in preserving pasture for their own future benefit. Private ownership schemes are difficult to apply to AI development, since AI technology has no single owner. Much of the software and AI development techniques are publicly available. Code can be proprietary, but it is relatively difficult to keep code private since it is often easy to copy software and other digital information. Even if AI development were entirely in private hands, it would still have enormous public impacts, creating externalities private owners would not have a direct incentive to address. Private firms might develop AI only in their own interest rather than in the public interest  [68]  underinvest in safety and ethics research that would primarily benefit the public  [19, 56, 69] , and misinform the public about AI risks in order avoid regulation or scrutiny  [70] .  17  Tan and Ding  [71]  call for a global AI market to mitigate safety risks, but concede that government regulation may be necessary to ensure that AI markets are globally integrated, standardized, and egalitarian. While the ease of copying software may make it difficult to enforce private ownership schemes, hardware may be more susceptible to private ownership schemes. Hwang  [72]  describes several attributes of hardware manufacturing that make it easier to govern, including the relatively small number of large, fixed facilities involved in producing the high-end hardware used in cutting-edge AI systems. Hardware manufacturers could conceivably play a role in encouraging AI collective action. However, hardware manufacturing has the same externality as software development: the benefits of safe, ethical practices are spread widely across the public, creating an incentive to underinvest in safety and ethics. \n Bottom-up community solutions The third type of solution to collective action problems is bottom-up community self-organizing. In bottom-up community solutions, private actors work with one another in the collective interest in the absence of any overarching authority with the capacity to enforce cooperation. Bottom-up community solutions are appealing because they may be more feasible than top-down solutions. Cooperation in the absence of an enforcement authority might seem theoretically inelegant, but empirical studies of real-world collective action find that community selforganizing is often effective  [48, 73] .  18  Soft law instruments like private standards, voluntary programs, and professional guidelines should arguably be considered examples of community self-organizing. Other soft law measures blur the distinction between top-down government solutions discussed in Section 4.1 and community self-organizing. Institutions like the Institute of Electrical and Electronics Engineers (IEEE) and the Partnership on AI are already bringing AI groups together to craft common ethical principles and promote cooperation. These processes are new, and it remains to be seen how successful they will be. Nonetheless, there is at least some chance that they will be successful, just as previous initiatives have succeeded at promoting collective action in other contexts. Community self-organizing does not require individuals to be altruistic as long as they recognize that cooperating to achieve common goals is in their own private interests. Community self-organizing may be most likely to succeed when individuals are willing to make personal sacrifices for the greater good, the way employee activists who oppose controversial but profitable applications of AI technology are. However, communities may be able to self-police adherence to reasonable norms even if individuals are not willing to sacrifice their private interests. Some have argued that simply fostering norms among people in the field of AI could improve outcomes  [3, 5, 8] . Strengthening norms about near-term AI development could also lay the groundwork for collaborating on long-term AI development  [3, 5] . Psychological factors can play an important role in determining the effectiveness of community solutions. For example, AI Impacts  [19]  and Baum  [29]  propose that it may be possible to cultivate a taboo against the development of dangerous AI. A taboo is an informal social norm against some action. Taboos can be effective. For example, the taboo against nuclear weapon use may be a major reason no nuclear weapon has been used in violence since 1945  [74, 75] . What kind of taboos would be appropriate is a matter of debate-it might be going too far to treat the development of some forms of AI as unacceptable as the use of nuclear weapons-but some kind of taboo against dangerous AI development could facilitate AI collective action. Community self-organizing may be especially important for AI developed using open-source software. Closed-source/proprietary software could be confined within a single institution, which may be able to make sure the software complies with safety and ethics standards. However, open-source software can be developed by anyone anywhere in the world, which may make top-down enforcement of standards extremely difficult. In the absence of oversight by or accountability to some outside authority, ethical codes can create the appearance of responsibility without having much impact on behavior  [76] ; p. 29-32. This concern may motivate some of the more draconian proposals for global surveillance regimes to prevent the development of dangerous AI (e.g., Refs.  [50, 51] ). On the other hand, Goertzel  [68]  proposes that open-source AI development might be more attuned to the public  17  For a discussion of how to counter such misinformation, see Baum  [105] .  18  Baum  [8]  distinguishes between extrinsic constraints imposed on AI communities from the outside and intrinsic measures that are developed by the AI communities themselves. Baum  [8]  argues that while efforts to improve AI outcomes commonly focus on extrinsic measures, intrinsic measures can often be effective. Government and market collective action solutions are generally extrinsic, whereas community solutions are generally intrinsic. Community self-governance is not a silver-bullet solution. The empirical social science literature on collective action identifies a range of circumstances in which community self-organizing is more likely to be successful, such as when communities are geographically bounded, when there are at most a few thousand individuals or groups involved, when it is clear to actors how their choices directly affect their collective interest, when the benefits of collective action mostly accrue to the population whose actions determine outcomes, when the actors share a common culture and institutions, and when there are opportunities for actors to learn from experience.  19  Unfortunately, AI collective action situations do not all meet all these conditions. Indeed, no AI collective action situation may meet some of these conditions (e.g. being geographically bounded). This does not mean bottom-up community solutions will necessarily fail for AI, but it does suggest creative approaches may be needed to overcome these challenges. Additionally, some have argued that the high stakes of long-term AI development merit government (and especially international government) solutions  [50, 56] . However, arguably what matters here is not the size of the stakes but the efficacy of the solution. Government intervention is not a silver-bullet solution either (Section 4.1). In general, there are reasons to think that no single solution or approach can completely solve the collective action problems of AI development or ensure that AI will be safe and beneficial. Global collective action may require a polycentric system of governments, market, and community organizations that address AI issues in different ways and at different scales  [18] . There may be no way to guarantee AI developers will produce beneficial designs, but, as Baum  [29]  writes, \"given the stakes involved in AI, all effective measures for promoting beneficial AI should be pursued\" (p. 551). \n Transparency Transparency is not a solution to collective action problems per se, but rather a governance mechanism that can affect the form and extent of AI collective action. Some general arguments in favor of transparency about AI development have been advanced. It has been proposed that transparency could encourage goodwill and collaboration among AI developers  [77] , foster trust between AI developers and potential AI users  [21] , improve cooperation between AI developers and government regulators (ibid.) and even help avoid unreasonable attempts to regulate AI research  [78] . In practice, these arguments might not necessarily hold. For example, transparency could reduce goodwill, trust, and cooperation if AI developers are seen to be behaving poorly or acting in bad faith. Transparency could also give unscrupulous or incompetent regulators more opportunity to impose counterproductive or unnecessary regulations. However, transparency could still be beneficial on balance if it creates opportunities to address genuinely bad behavior and incentivizes AI developers and other stakeholders to behave well in the first place. A more contentious matter is whether AI developers should be open about the capabilities of their AI, including by reporting the latest results and openly publishing code. One concern is that sharing new algorithms and capabilities could increase the tools available to malevolent actors  [79] , although it could also increase the tools available to counter malevolent actors. Another concern is that transparency about AI capabilities could make developers aware of one another's progress, which could prompt them to take shortcuts on safety in order to try to win a perceived AI race  [9, 77] . Again, the converse could be true: if transparency reveals that AI developers are not making substantial progress, then they could focus more on safety and feel less pressure to engage in a race.  20  Finally, transparency could level the playing field for AI developers by enabling them to build on one another's work. This could increase risks by making it harder for a careful and benevolent developer group to dominate the process  [77] , but it could also decrease risks by making it harder for a reckless and malevolent group to dominate. Overall, we concur with  Bostrom [77]  that the case for openness about AI capabilities is complicated and mixed. A clearer case can be made in favor of transparency on AI safety issues. Transparency would create opportunities for outside experts to contribute to any AI project's safety measures, thereby reducing the risks created by the project  [77] . Additionally, transparency could create opportunities for outside observers to check for bugs and other problems with an AI group's work  [21] , although it would also give malevolent actors an opportunity to look for vulnerabilities they could exploit. An important challenge is how to ensure that the beneficial aspects of transparency outweigh the potential harms. The AI transparency issue was at the center of a recent debate about OpenAI's decision in 2019 to release its Generative Pre-Trained Transformer 2 (GPT-2) language model in stages out of concern that it could be used for malicious purposes  [80] . While some applauded this decision  [81] , others criticized it for undermining open source norms and denying outside groups the opportunity to mitigate problematic aspects of the code  [82] . This incident demonstrates the controversies that can accompany actions with respect to AI transparency. \n Conclusion Ensuring that AI generally contributes to good outcomes for society will require collective action. The development and use of AI involve a variety of particular situations in which collective action is required to achieve good outcomes. These situations include AI races, determination of AI development and use standards, and decisions about investment in public goods like basic AI research, AI safety, and AI ethics. A background in collective action can be valuable for understanding these situations and improving AI outcomes. Although AI collective action is a relatively new field of study, it has already produced a range of insights. The primer and review presented in this paper introduces collective action concepts, relates them to issues in AI, and summarizes the existing literature so that readers from a variety of backgrounds can get up to speed on this important topic. Because this paper is a nonsystematic review, it cannot draw definitive conclusions about the existing literature on AI collective action. However, the research presented in the paper did involve a variety of searches to identify relevant literature. Furthermore, the searches did not identify a large body of literature. Unless the searches failed to identify a significant additional body of literature on AI collective action, which we believe is unlikely, then the trends in the literature identified this paper are indeed reflective of the trends in the actual body of literature on AI collective action. Whether this is in fact the case could be assessed in future research that conducts a systematic review. Any such review would need to account for the significant body of literature that is published outside of traditional academic outlets.\" One clear limitation of the AI collective action literature reviewed in this paper is that it makes relatively little use of the insights of the rich social science literature on collective action in other contexts. Human society has quite a lot of experience with collective action in other contexts, and scholars of it have learned a great deal that is relevant to AI collective action. We did not find any studies drawing on the empirical study of AI collective action situations, though we are aware of one study drawing on the empirical literature for a more general discussion of risky emerging technologies  [83] . Empirical studies of the effectiveness of collective action with respect to different aspects of AI development and use are a promising path future research could take. In particular, it would be valuable to study how institutional design can shape the outcomes of collective action situations. As Section 3 documents, there has also been relatively little research on competition between private AI groups. Government competition (and especially military competition) has gotten much more attention. While government AI competition is clearly important, private AI competition is too. Indeed, for now at least, the private sector is the main driver of AI R&D. More detailed studies of private sector AI competition are another promising path for future research. Although the study of AI collective action is in its infancy, the subject is increasingly pressing. The trajectory of AI development is uncertain, but R&D conducted today may have broad impacts on society. Governments and communities are beginning to formulate policies and institutions that if enacted could be long-lasting. Without further research into how to work together to ensure that AI development leads to collectively more optimal outcomes, society may stumble blindly into outcomes that are collectively worse. interest than corporate or government AI development, since the government and corporations could act in a corrupt and self-interested way. Whether open-source AI development would in fact be more attuned to the public interest is an open question. Regardless, the difficulty of governing open-source software development via top-down regulations makes bottom-up community solutions more compelling. \n Table 1 1 Goods classified by rivalry and excludability. EXCLUDABLE NON-EXCLUDABLE RIVALROUS Private goods Common goods NON-RIVALROUS Club goods Public goods 7  See e.g.Olson [86 and   \n\t\t\t An important exception is when there are externalities, i.e. when benefits or \n\t\t\t R. de Neufville and S.D. Baum \n\t\t\t  Shulman [88]; Armstrong et al. [9] ; Tomasik [49] ; Aldana [42] ; Han et al. [43] ; Naudé & Dimitri [44] . 11  \"Bounded rationality\" refers to the practical limits on actors' ability to make optimal decisions in real world conditions. 12  In theory, it might be possible to resolve collective action problems in which individual and collective interests do diverge by misleading actors into believing their individual interests actually align with collective interests, although spreading false information could create other problems.R. de Neufville and S.D. Baum \n\t\t\t Similarly, Roff [40]  argues against framing AI competition as an arms race on grounds that it could \"could escalate rivalry between states and increase the likelihood of actual conflict\". 14  See e.g. Good [89] ; Vinge [90] ; Kurzweil [91] ; Omohundro [92] ; Yudkowsky [85] ; Chalmers [93] ;Barrat [94]; and Bostrom [20] . 15  For example, AI Impacts [19]  and Tan & Ding [71]  focus on races between countries.R. de Neufville and S.D. Baum \n\t\t\t This list is from Stern [83] , p.215, discussing Ostrom [48] . We recommend Stern [83]  as perhaps the only discussion of the empirical collective action literature in the context of governing risky technologies. 20  For comparison, during the initial race to build nuclear weapons, the US overestimated German progress and may have consequently paid less attention to safety issues in order to be the first to develop nuclear weapons [106] .R. de Neufville and S.D. Baum", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0160791X2100124X-main.tei.xml", "abstract": "Progress on artificial intelligence (AI) requires collective action: the actions of two or more individuals or agents that in some way combine to achieve a result. Collective action is needed to increase the capabilities of AI systems and to make their impacts safer and more beneficial for the world. In recent years, a sizable but disparate literature has taken interest in AI collective action, though this literature is generally poorly grounded in the broader social science study of collective action. This paper presents a primer on fundamental concepts of collective action as they pertain to AI and a review of the AI collective action literature. The paper emphasizes (a) different types of collective action situations, such as when acting in the collective interest is or is not in individuals' self-interest, (b) AI race scenarios, including near-term corporate and military competition and longterm races to develop advanced AI, and (c) solutions to collective action problems, including government regulations, private markets, and community self-organizing. The paper serves to bring an interdisciplinary readership up to speed on the important topic of AI collective action.", "id": "51d2606ba4663e05acf8e7a77d3eb7e4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jonathan Stray"], "title": "Aligning AI Optimization to Community Well-Being", "text": "Introduction This paper is an extended analysis of a simple idea: large-scale commercial optimizing systems may be able to manage harmful side effects on communities by monitoring established well-being metrics. It sketches a theory that ties together quantitative measures of well-being, contemporary metrics-driven management practice, the objective function of optimization algorithms, participatory and multi-stakeholder governance of algorithmic systems, and the protection or promotion of community wellbeing. Detailed analyses of recent efforts by Facebook and YouTube are used to illustrate the challenges and unknowns of this approach, which generalizes to a variety of different types of artificial intelligence (AI) systems. The core contribution of this article is a proposed process for the use of community well-being metrics within commercial AI systems. Well-being encompasses \"people's living conditions and quality of life today (current well-being), as well as the resources that will help to sustain people's well-being over time (natural, economic, human and social capital)\"  (OECD 2019b, p. 2) . Community well-being attempts to evaluate well-being at the level of a community defined \"in geographic terms, such as a neighborhood or town … or in social terms, such as a group of people sharing common chat rooms on the Internet, a national professional association or a labor union\"  (Phillips and Pittman 2015, p. 3) . The measurement of well-being is now a well-established field with a long history, and is increasingly used in policy-making  (Exton and Shinwell 2018) . Large AI systems can have both positive and harmful side effects on communities, through effects on employment and inequality  (Korinek and Stiglitz 2017) , privacy and safety (OECD 2019a), addictive behavior  (Andreassen 2015) , fairness and discrimination  (Barocas et al. 2018) , human rights  (Donahoe and Metzger 2019) , polarization, extremism, and conflict  (Ledwich and Zaitsev 2020; Stoica and Chaintreau 2019) , and potentially many other areas  (Kulynych et al. 2020) . Importantly, AI systems can affect non-users too, as with environmental externalities. Most AI is built around optimization \"in which the aim is to find the best state according to an objective function\"  (Russell and Norvig 2010, p. 121)  where an objective function is some method for quantitatively evaluating the desirability of an outcome  (Dantzig 1982) . Standard management practice also increasingly involves the maximization of quantitative metrics  (Parmenter 2020) , which can be considered an optimization process. This paper is concerned with optimizing systems composed of people and algorithms which affect communities, where the choice of objective might have significant societal influence. Examples include systems used to allocate resources or assign work, choose what news people see, recommend products to buy, or implement government policy. Many of these systems would be considered AI, but perhaps the phrase \"autonomous and intelligent systems\"  (Schiff et al. 2020, p.  1) which appears in certain standards efforts would be better, because an automated system does not have to be very smart to cause harm. Rather, the unifying feature is optimizationboth the cause of many problems and an opportunity for a response. The central idea of this paper is to incorporate community well-being metrics into the optimization process at both the managerial and technical level. This is a sociotechnical approach to systems design  (Baxter and Sommerville 2011 ) that considers the role of both people and technology. There are many technical interventions that could be undertaken aside from the modification of an algorithmic objective function; for example, a social media product team could choose to show a simple chronological list of posts rather than using algorithmic content personalization. However, if product managers are evaluated on community well-being outcomes, they may choose to make such a change based on the expected effects on users. The integration of the managerial and the technical in an optimization framework can motivate many possible product design changes. \n Background This paper responds most directly to recent calls for research into well-being and AI. It proposes specific \"improvements to product design\"  (Schiff et al. 2019, p.  3) and it is interdisciplinary, systems-based, and community-oriented  (Musikanski et al. 2020) . It draws on and contributes to the emerging field of recommender alignment, the practice of building algorithms for content ranking and personalization that enact human values  (Stray et al. 2020) . The goal of the process proposed in this paper is the governance of large-scale commercial algorithmic systems.  Rahwan (2018)  calls this society-in-the-loop control, defined as \"embedding the values of society, as a whole, in the algorithmic governance of societal outcomes\" (p. 3). In this sense community participation is a key element of the proposed framework, and this paper draws on approaches as diverse as participatory design  (Simonsen and Robertson 2012)  and corporate stakeholder engagement  (Manetti 2011) . \n Community Well-Being At the individual level well-being is usually studied as an experiential state, and there is now a wealth of research on the definition and reliable measurement of subjective wellbeing  (Diener et al. 2018) . Although well-being is a rich, multidimensional construct, even single questions can reveal substantial information, such as overall, how satisfied are you with life as a whole these days? answered on a 0-10 scale. This well-studied measure has several advantages: it correlates with how people make major life decisions, gives a similarly reliable result across cultures, and is by itself informative enough to be used in quantitative evaluations of policy choices  (O'Donnell et al. 2014) . Community well-being \"embraces a wide range of economic, social, environmental, political, cultural dimensions, and can be thought of as how well functions of community are governed and operating\"  (Sung and Phillips 2018, p. 64) . In practice, community well-being is assessed using a variety of metrics across many domains. Often both subjective and objective indicators are needed to get a full picture  (Musikanski et al. 2019) . A survey of local and national well-being indicator frameworks in use in the United Kingdom gives an overview of the substance and range of such metrics  (Bagnall et al. 2017) . Community well-being frameworks can originate from consideration of geographic communities, or communities of interest  (Phillips and Pittman 2015)  which may be particularly relevant to online platforms. As an example community well-being framework, the OECD Better Life Index  (Durand 2015)  aims to measure \"both current material conditions and quality of life\" (p. 1) across countries through the metrics shown in Table  1 . This framework includes the life satisfaction measure above, as well as statistical indicators around health, education, employment, etc. in conjunction with subjective indicators such as whether one feels safe walking alone at night. Technologists and scholars have begun to appreciate the significance of well-being measures in the design and operation of AI systems  (Musikanski et al. 2020) . The IEEE 7010 Recommended Practice Standard for Assessing the Impact of Autonomous and Intelligent Systems on Human Well-Being collects pre-existing measures from sources such as the OECD Better Life Index, the UN Sustainable Development Indicators, the Human Development Index, the World Health Organization, the World Values Survey, Freedom House, and others  (Schiff et al. 2020) . From the point of view of a technologist who is concerned about the societal effects of their work, established well-being metrics have the advantage of representing extensive deliberation by domain experts. \n Optimization Optimization is used extensively in AI to guide training and learning. A problem to be solved is expressed as a scalar functiona method to calculate a single number that expresses the desirability of any given hypothetical solution. Solving the problem means finding a solution that maximizes this function. The encapsulation of concerns into a single function was a major conceptual advance that enabled the creation of generic optimization algorithms  (Dantzig 1982) . Conceptually, any problem that has some set of best solutions can be expressed as optimization with a single objective A supervised machine learning algorithm that attempts to identify objects from images would usually be trained through a loss function that penalizes incorrect answers. A reinforcement learning approach to playing a video game might use the game score as a reward function. There are also value functions, cost functions, fitness functions, energy functions and more, all of which operate on similar principles  (Russell and Norvig 2010) . For simplicity, in this paper I refer to all of the scalar functions used to drive AI behavior as objective functions. In this paper I refer to an optimizing system as if there were one optimizer and one objective. In practice such systems, especially those at platform scale, may include dozens or hundreds of optimizing components (numerous trained sub-models, for example). There isn't one objective function that can be altered, but many. Nonetheless, there are usually a few high-level goals concerned with the system's main outputs. This is the case at Groupon with many interacting models and a master objective function that aligns to company goals  (Delgado et al. 2019) . Quantitative metrics analogous to objective functions are also used in corporate management. Modern management practice includes concepts such as key performance indicators  (Parmenter 2020 ) and objectives and key results  (Doerr 2017) , both of which involve quantitative indicators of progress. Economic theory frequently models the corporation as a profit optimizer (e.g. Samuelson and Marks 2014). More sophisticated descriptions try to account for the creation of various types of long-term value, such as the balanced scorecard  (Kaplan 2009 ) and sustainability accounting  (Richardson 2013) , both of which describe various non-financial metrics that are intended to be optimized. \n Case Studies of Platform Interventions This section presents two examples where large technology companies seem to have optimized for well-being, or a similar concept. These cases have been reconstructed through documentary evidence such as public posts, previously published interviews, financial reports, and research articles by employees. \n Facebook's Well-Being Optimization In late 2017 and early 2018, Facebook made a number of changes to their product explicitly designed to promote well-being. Facebook researchers  Ginsberg and Burke (2017)  wrote in a public post in December 2017: What Do Academics Say? Is Social Media Good or Bad for Well-Being? According to the research, it really comes down to how you use the technology. For example, on social media, you can passively scroll through posts, much like watching TV, or actively interact with friendsmessaging and commenting on each other's posts. Just like in person, interacting with people you care about can be beneficial, while simply watching others from the sidelines may make you feel worse. (para. 7). This post cites a number of peer-reviewed studies on the well-being effects of social media, some of which were collaborations between Facebook researchers and academics.  Ginsberg and Burke (2017)  cite  Verduyn et al.'s (2017)  review paper on the effects of social media on well-being, which has an obvious resonance with Facebook's framing: passively using social network sites provokes social comparisons and envy, which have negative downstream consequences for subjective well-being. In contrast, when active usage of social network sites predicts subjective well-being, it seems to do so by creating social capital and stimulating feelings of social connectedness.  (Verduyn et al. 2017, p. 274)  A close reading of posts around this time shows that Facebook developed a well-being proxy metric. A January 2018 post by Facebook's Chief Executive Officer notes that \"research shows that strengthening our relationships improves our well-being and happiness\"  (Zuckerberg 2018, para.  2) and mentions well-being twice more, then switches to the phrase \"meaningful social interactions:\" I'm changing the goal I give our product teams from focusing on helping you find relevant content to helping you have more meaningful social interactions.  (Zuckerberg 2018, para. 7)  Relevance is a term of art in recommender systems, referring to user preferences as expressed through item clicks or ratings, and is increasingly understood as a simplistic objective (Jannach and Adomavicius 2016). The algorithmic change away from relevance was described by the head of the News Feed product: Today we use signals like how many people react to, comment on or share posts to determine how high they appear in News Feed. With this update, we will also prioritize posts that spark conversations and meaningful interactions between people. To do this, we will predict which posts you might want to interact with your friends about, and show these posts higher in feed  (Mosseri 2018, para. 3) . Facebook created a well-being metric and assigned it as a goal to a product team, which incorporated it into an existing algorithmic objective function. This objective function was augmented by creating a model that uses existing data such as past user behavior and post content to predict whether a user will have a meaningful social interaction if shown any particular post. There is little public documentation of how meaningful social interactions are measured. The most detailed description is from the transcript of a call where Facebook reported earnings to investors, which explains that meaningful social interactions are measured through user surveys: So the thing that we're going to be measuring is basically, the number of interactions that people have on the platform and off because of what they're seeing that they report to us as meaningful…the way that we've done this for years is we've had a panel, a survey, of thousands of people who basically we asked, what's the most meaningful content that they had seen in the platform or they have seen off the platform.  (Facebook 2018, p. 13)  The resulting system is reconstructed in Fig.  1 . While there is no public account of the effects of the incorporation of the meaningful social interactions prediction model on the meaningful social interactions metric as measured by Facebook through user surveys, Facebook has reported reduced engagement on at least one product, suggesting that the meaningful social interactions objective was weighted strongly enough to cause significant changes in which items are presented to users: video is just a passive experience. To shift that balance, I said that we were going to focus on videos that encourage meaningful social interactions. And in Q4, we updated our video recommendations and made other quality changes to reflect these values. We estimate these updates decreased time spent on Facebook by roughly 5% in the fourth quarter. To put that another way: we made changes that reduced time spent on Facebook by an estimated 50 million hours every day to make sure that people's time is well spent.  (Facebook 2018, p.  2)... \n YouTube's User Satisfaction Metrics John Doerr's Measure What Matters (2017) documents YouTube's multi-year effort to reach one billion hours of daily user watch time through interviews with Susan Wojcicki, Chief Executive Officer and Cristos Goodrow, Vice President of Engineering at YouTube  (Doerr 2017, pp. 154-172) . Goodrow describes the inception of YouTube's recommendation system in 2011, and how he advocated to optimize for watch time instead of video views as: On a dedicated team named Sibyl, Jim McFadden was building a system for selecting \"watch next\" recommendations, aka related videos or \"suggestions.\" It had tremendous potential to boost our overall views. But were views what we really wanted to boost?... I sent a provocative email to my boss and the YouTube leadership team. Subject line: \"Watch time, and only watch time.\" It was a call to rethink how we measured success: \"All other things being equal, our goal is to increase [video] watch time.\"... Our job was to keep people engaged and hanging out with us. By definition, viewers are happier watching seven minutes of a ten-minute video (or even two minutes of a tenminute video) than all of a one-minute video. And when they're happier, we are, too. (Goodrow quoted in Doerr 2017, p. 162)... Goodrow's retelling includes user happiness and satisfaction as goals along with the more business-oriented engagement. For the purposes of this paper, I assume user happiness and satisfaction are analogous to well-being, but unlike the Facebook case, YouTube's public statements have not mentioned well-being. In accordance with the unified treatment of managerial and technical optimization proposed in this paper, Goodrow confirms that a team-level metric drove engineering decisions: Reaching one billion hours was a game of inches; our engineers were hunting for changes that might yield as little as 0.2 percent more watch time. In 2016 alone, they would find around 150 of those tiny advances. We'd need nearly all of them to reach our objective. (Goodrow quoted in Doerr 2017, p. 169) Yet watch time was not the only objective, and YouTube incorporated other changes to improve the quality of the product and the effects on users: In fact, we'd commit to some watch-time-negative decisions for the benefit of our users. For example, we made it a policy to stop recommending trashy, tabloidstyle videos-like \"World's Worst Parents,\" where the thumbnail showed a baby in a pot on the stove. Three weeks in, the move proved negative for watch time by half a percent. We stood by our decision because it was better for the viewer experience, cut down on click bait, and reflected our principle of growing responsibly. Three months in, watch time in this group had bounced back and actually increased. Once the gruesome stuff became less accessible, people sought out more satisfying content. (Goodrow quoted in  Doerr 2017, p. 164)  This was the beginning of a move away from strict maximization of time spent. Starting in 2015 YouTube began to incorporate user satisfaction metrics  (Doerr 2017, p. 170) . As in the Facebook case, these are derived from surveys: we learned that just because a user might be watching content longer does not mean that they are having a positive experience. So we introduced surveys to ask users if they were satisfied with particular recommendations. With this direct feedback, we started fine-tuning and improving these systems based on this highfidelity notion of satisfaction.  (Google 2019, p. 21)  These user satisfaction survey results were incorporated directly into the objectives of the YouTube recommendation system, as discussed in a recent YouTube technical paper: we first group our multiple objectives into two categories: 1) engagement objectives, such as user clicks, and degree of engagement with recommended videos; 2) satisfaction objectives, such as user liking a video on YouTube, and leaving a rating on the recommendation.  (Zhao et al. 2019, p. 43)   \n Analysis of Facebook and YouTube Cases The Facebook and YouTube cases are significant because they are examples of a major platform operator explicitly saying that they have decided to monitor and optimize for a well-being proxy, operationalized at both the management and algorithmic levels. Facebook has provided a public justification for its meaningful social interaction metric in terms of prior research which suggests that active use of social media improves well-being while passive use decreases it. While this is far from a holistic measure of well-being, let alone community well-being, at least it connects to previous work in a clear way. Public statements from YouTube have not mentioned well-being, instead focusing on \"responsibility\" (Wojcicki 2019, para. 2) and user satisfaction as assessed through surveys. Explicit user surveys are an improvement on YouTube's previous identification of watch time with user happiness. Researchers report a negative correlation between TV watching and well-being that suggests there is something like an addiction mechanism involved: \"individuals with incomplete control over, and foresight into, their own behavior watch more TV than they consider optimal for themselves and their wellbeing is lower than what could be achieved\"  (Frey et al. 2007, p. 283 ). Similar effects have been observed in social media use where addicted users \"have typically attempted to cut down on social networking without success\"  (Andreassen 2015, p. 176) . Google now publicly recognizes that maximizing watch time does not optimize for \"positive\" outcomes  (Google 2019, p. 21) . A more systematic conception of well-being would articulate what aspects of wellbeing matter to YouTube and why user satisfaction is a good proxy. Of course, wellbeing outcomes depend enormously on who a user is and what they watch. A user might learn valuable and fulfilling skills from how-to videos, become more politically engaged, consume worthwhile art, or they might be radicalized into violence  (Ledwich and Zaitsev 2020) . Another issue is that both companies are optimizing for individual outcomes: wellbeing but not necessarily community well-being. Community well-being \"is more than an aggregate of individuals' satisfaction\"  (Sung and Phillips 2018, p. 65)  and cannot be assessed simply by adding up the well-being of all individuals in the community. This is analogous to the classic problem of aggregating utilities in welfare economics  (Foster and Sen 1997, p. 16 ). Conversely, optimizing for each person individually will not necessarily promote community well-being due to problems of externalities, collective action, and conflicting preferences  (Baum 2020; Milano et al. 2019b ). Attention to aggregates may also miss local problems, such as negative effects in a particular city or for a particular subgroup, or run into Simpsons' paradox issues where the sign of the effect depends on the granularity of the groups studied  (Kievit et al. 2013) . For all these reasons, clarity on the definition of community or communities matters greatly. Perhaps the biggest weakness of these cases is that there is no record of consultation with the putative beneficiaries of these algorithmic changes, and no public evaluation of the results. Hopefully algorithmic interventions of this magnitude were informed by user research or some sort of consultative process, but none was reported. Presumably meaningful social interactions and user satisfaction were increased, but there has been no disclosure of how much. Absent also is any report of effects on any other components of well-being, such as feelings of social connectedness or life satisfaction, or even objective indicators like employment status. It's similarly unclear how these changes affected not just individual well-being but community well-being for different communities; there may even have been negative effects on certain types of users. Information about outcomes is especially important because the link between Facebook's meaningful interactions and well-being is theoretical, deduced from previous research into active and passive social media use, while YouTube has said their user satisfaction surveys are included in a \"responsibility\" metric  (Bergen 2019, para. 10 ) and that they aim for \"positive\" experiences (Google 2019, p. 21) without providing any further explanation of their goals or results. Determining the actual effect of these large-scale interventions is itself a significant social science research effort, and if Facebook or YouTube have these answers, they have not been shared. This is algorithmic management, but not yet the algorithmic governance that the society-in-the-loop model envisions  (Rahwan 2018) . The reported business outcomes are also instructive, as both the Facebook and YouTube changes resulted in at least temporary reductions in engagement metrics. Facebook reports that the incorporation of a meaningful social interactions metric into their video product caused a 5% reduction in time spent, which was considered significant enough to be discussed with investors  (Facebook 2018 ) but the longerterm effects are unclear. YouTube described changes that reduced watch time but also reports that watch time recovered over a time span of months as users changed their behavior. This demonstrates both that major corporations are willing to accept reductions in engagement to pursue social ends, and that the long-term business effects of incorporating well-being metrics are not necessarily negative. \n Generalization to Other Domains The Facebook and YouTube cases suggest the possibility of a general method for managing the well-being outcomes of commercial optimizing systems, which is the core contribution of this article. This section begins by arguing that some type of metric-driven community well-being optimization is not only useful but likely necessary for any AI system with broad social impacts, because individual user control will not be sufficient. It then shows how this general method could apply to diverse domains by working through potential applications to news recommendation and online shopping. These hypothetical applications demonstrate the generality of a metrics-driven approach and illuminate further possibilities and challenges that shape the recommendations in this paper. \n User Control is not Sufficient for Community Well-Being This article recommends participatory processes to involve users and other stakeholders in metric-driven for community well-being. A potential alternative is to provide increased user control directly, so that people can choose what is best for themselves. Many authors have pointed to the central role of user agency in the ethics of AI systems  (Floridi and Cowls 2019)  and in the important context of content ranking Paraschakis (2017) has proposed \"controls [that] enable users to adjust the recommender system to their individual moral standards\" (p. 6). However, increasing user agency will not by itself solve the problem of ensuring good outcomes at the community level because many users will not customize the systems they use, and because individually good choices do not necessarily produce socially good outcomes. Any set of controls must necessarily be few enough to be humanly manageable. This restricts the number of dimensions that can be controlled and will make it difficult to express nuanced conceptions of well-being. Natural language interfaces e.g.  Yu et al. (2019)  may allow the expression of more complicated concepts. Nonetheless users will probably leave most parameters at default settings, which means that the defaults must promote well-being. Even if all users in fact succeeded in directing an AI system to do exactly as desired this would not necessarily result in the best community outcomes. As  Ostrom (2000)  has articulated, individual action does not succeed in producing social goods without the concurrent evolution of social norms. These challenges of collective action have been explored in the context of AI systems from the perspective of social choice theory  (Baum 2020 ) and multi-stakeholder recommendation systems  (Milano et al. 2019a ). Further, existing societal inequalities can constrain users' ability to exploit algorithmically provided choices  (Robertson and Salehi 2020) , for example due to a lack of information or the cost burden of choosing the \"best\" option. User control is essential, perhaps even necessary for community well-being, but it is not sufficient. Collective algorithmic governance is needed for much the same reasons societal governance is needed, and appropriate well-being metrics are useful in algorithmic governance just as they are in public policy. \n Diverse News Recommendations News recommenders are the algorithms that choose, order, and present journalism content to users. The potential application of community well-being metrics to these systems illustrates the challenges around defining a community and choosing metrics. News recommendation algorithms can have societal consequences  (Helberger 2019)  but it is not clear how to manage such algorithms for community well-being. To begin with, there is no single community that consumes news, but many overlapping communities organized around different geographic regions and different topics  (Reader and Hatcher 2011, p. 3) . Each of these communities may have different concerns at any given moment. Incorporating social network analysis or countryspecific data can improve the performance of recommender systems as measured by traditional relevance metrics  (Chen et al. 2018; Roitero et al. 2020 ) but the question of how a recommender system impacts pre-existing communities, e.g. a city, has not been explored. Conversely, existing community well-being indicators have not been designed to capture the consequences of news recommender systems. One well-developed concern with news recommenders is exposure diversity, meaning the range of sources, topics, and viewpoints that each person is algorithmically presented  (Bernstein et al. 2020) . Taking political theory as a starting point  Helberger et al. (2018)  identify liberal, deliberative, and radical approaches to the design of diverse news recommenders. Consider the problem of designing a national news recommender that supports a deliberative view of diversity, one in which: exposure to diverse viewpoints is considered valuable because it helps citizens develop more informed opinions and less polarized, more tolerant attitudes towards those with whom they disagree … it is conceivable to design metrics that would focus, for example, on user engagement with opposing political views, cross-ideological references in public debates or social media connections between people who represent different ideological positions.  (Helberger et al. 2018, p. 195)  Diversity metrics could be constructed from algorithmic methods to estimate the ideological position of users or posts  (Budak et al. 2016; Garimella and Weber 2017) . These give a measure of distance between any two items, which could then be used to define the diversity of a set of recommended items according to various standard formulas such as the average distance between any pair  (Kunaver and Požrl 2017) . Such a metric would capture the output of the system, not its effects on users. Facebook and YouTube use user surveys to tie algorithmic changes to human outcomes. It may be possible to establish a causal connection from news diversity metrics to existing well-being metrics such as voter turnout, and Facebook has already demonstrated a substantial effect on voter turnout by presenting users with personalized messages  (Bond et al. 2012) . It would be better to direct the optimization process towards more closely related outcomes like polarization or tolerance that are not included in current well-being frameworks. Directly measuring these outcomes is crucial because exposure to diverse opinions can actually increase polarization  (Bail et al. 2018) . Polarization and tolerance outcomes are also explicitly relational, and thus indicate aspects of community well-being not captured in individual-level metrics. \n Low Carbon Shopping Large-scale product recommender systems have profound influence over what is purchased. One reason for this is that it is not possible to navigate millions of possible products without them.  Rolnick et al. (2019)  have proposed using these systems to direct consumers to lower-carbon alternatives. This possibility highlights two problems that may arise in the course of modifying AI objective functions: obtaining the data needed to evaluate a metric and understanding the business impacts of such a change. Climate change is a key issue for many communities  (Fazey et al. 2018 ) and carbon emissions appear in a number community well-being frameworks  (Bagnall et al. 2017) . Carbon emissions from recommended products are also a key example of AI system side effects on non-users. From a technical point of view, carbon footprint can be incorporated using multi-stakeholder recommendation algorithms that explicitly consider the effect on parties other than the user  (Abdollahpouri et al. 2020) . This is possible only if the carbon footprint of each product is available. There are now established methods to estimate product carbon footprints (BSI 2011; ISO 2018) but there are no product carbon footprint (PCF) databases comprehensive enough to cover the millions of different products sold by a large online retailer. However, it may be possible to use machine learning methods to estimate the PCF values of an entire product portfolio starting from a comparatively small database of examples  (Meinrenken et al. 2012) . Robust, scalable product carbon footprint estimation could be a key enabling technology for low-carbon commerce and, ultimately, long-term community well-being. A commercial operator will want to know the business effects before any such system is implemented, and it is tempting to evaluate the potential revenue effect of incorporating a carbon term into the objective function by testing against historical purchase data. Such back-testing will show that optimizing for anything other than profit must drive the system away from a profit maximum, but offline estimates will not give the full story because both consumer and producer behavior may change if carbon footprint starts to affect product ranking. Users might appreciate being informed of low-carbon alternatives and buy more from that retailer or pay a premium for lower carbon items, while producers will have an incentive to sell lower carbon products. The case of organic food demonstrates the existence of such market dynamics, as it is 22-35% more profitable globally than conventional alternatives even though it is typically more expensive to produce  (Crowder and Reganold 2015) . \n Recommendations The incorporation of community well-being metrics into both managerial and algorithmic optimization is a very general method for managing the effects of commercial optimizing systems, yet good management is only part of good governance. This section synthesizes the analysis and discussion above with previous work on algorithmic governance, participatory design, best use of metrics, and corporate stakeholder engagement to make recommendations for fostering community well-being in AI systems in ways that are both effective and accepted as legitimate. It also identifies gaps and unknowns where future research would be valuable. \n Identifying and Involving Communities An attempt to optimize for community well-being is an attempt to benefit a particular group of people, who need to have a say in what is done on their behalf. In some cases it would be reasonable to say that every user of the system (potentially billions of people) is a member of the community, but that would preclude the management of local outcomes such as a system's effects on the residents of a particular city, or on people of a certain age, or workers in particular professions. Non-users can be affected as well, as in environmental externalities or a navigation system that routes cars to a formerly quiet street. Each view of community is a choice about who counts, and this choice should be made explicit before any intervention begins. Once a community is identified, there are many approaches to try to integrate its members into the process of selecting and using metrics. Participatory design is an orientation and a set of practices that attempts to actively involve all stakeholders in a system design process  (Simonsen and Robertson 2012) . It is a promising framework for algorithmic governance. The WeBuildAI method  (Lee et al. 2019)  demonstrates what participatory design of metrics might look like. Researchers worked with a fooddelivery non-profit to design an algorithm to match donated food with volunteer drivers and local food distribution charities. Stakeholders from each of these groups worked with researchers to build quantitative models of their preferred trade-offs between factors such as driver travel time, time since last donation, neighborhood poverty level, etc. At run time this system ranks the possible matches for each donation according to the models representing the preferences of each stakeholder, with the final result chosen through a ranked-choice voting rule. Future work could investigate participatory metric design in the context of a large commercial platform. There are both instrumental and political goals when attempting to integrate communities into the selection and use of metrics. Without engaging the community, it is not possible to know which aspects of well-being matter most to them and how serious these issues are, and therefore how to make tradeoffs. Engagement is also necessary for credibility. When choosing community indicators, \"most communities consider input by its residents and others to be vital; it builds support for the use of indicators as well as help vest those most impacted by subsequent actions in decision-making processes\"  (Sung and Phillips 2018, p. 73 ). In the context of commercial systems it will also be important to draw on the experience of corporate stakeholder engagement efforts such as those found in sustainability reporting  (GSSB 2016; Manetti 2011) . \n Choosing Metrics Aside from the well-known issues with using metrics in a management context generally  (Jackson 2005 ) metrics pose a problem for AI systems in particular because most AI algorithms are based on strongly optimizing a narrow objective  (Thomas and Uminsky 2020) . Poor use of metrics can result in a damaging emphasis on short term outcomes, manipulation and gaming, and unwanted side effects  (Jackson 2005; Thomas and Uminsky 2020) . Even a successful metric cannot remain static, as the structure of the world it measures is constantly changing. In addition, there are many domains without a clear consensus on well-being goals, necessitating a process of normative deliberation before metrics can be chosen. The following issues should be considered in choice of metrics: Deciding What to Measure In many cases existing well-being metrics will not be directly usable because they are too expensive to collect at scale or don't readily apply in the company's domain. These issues drove Facebook's substitution of meaningful social interactions for general measures of user well-being. Creating a custom metric is challenging because community well-being is a theoretical construct, not an observable property, and there may be misalignment between the designer's intentions and what is actually measured. For example, decreasing polarization measures may just indicate that minority voices have been effectively silenced. The particular well-being aspect of interest must first be \"operationalized\" and tested for reliability and validity  (Jacobs and Wallach 2019) . Long-Term Outcomes If a metric is evaluated only over the short term it may lead to poor longer-term outcomes. As the YouTube case demonstrates, a video platform that tries to maximize user watch time may encourage binging behavior where users eventually regret the time they spend. While effective AI optimization requires frequent feedback, it is critical to pick shorter-term metrics that are thought to drive longer-term outcomes  (Lalmas and Hong 2018) . Gaming Any measure that becomes a target will change meaning as people change their behavior, a very general problem that is sometimes known as Goodhart's law  (Manheim and Garrabrant 2018) . This is particularly relevant to large platforms that must defeat adversarial efforts to gain exposure for financial or political ends. While there are emerging methods to use causal inference to design metrics that resist gaming  (Miller et al. 2019 ), a more robust solution is to continuously monitor and change the metrics in use. \n Dynamism The metrics employed need to be able to change and adapt, a property that  Jackson (2005)  names dynamism. This is necessary because of gaming and other behavior change in response to metrics, but more importantly the world can and does change; at the onset of the COVID-19 pandemic many existing machine learning models stopped working  (Heaven 2020) . Dynamism also avoids the serious problems that can arise from over-optimization for a single objective, such as a robot which injures humans in an attempt to fetch a coffee more quickly  (Russell 2019 ). In the context of contemporary commercial optimization, there are always humans supervising and operating the AI system, and they are free to change the objective function as needed. Normative Uncertainty Catalogs such as IEEE 7010  (Schiff et al. 2020 ) provide a long list of consensus metrics but not all of them will correspond to community needs, and not all AI systems can be effectively evaluated using metrics originally designed for public policy use. In short, many systems will face a lack of consensus around what a \"good\" outcome would be. Appropriate values for AI systems cannot be derived from first principles but must be the result of societal deliberation  (Gabriel 2020) , which again underscores the necessity for participatory processes. \n Evaluating Outcomes It may be very challenging to determine the actual well-being effects of incorporating metric into an optimization process. Facebook uses ongoing user panels to count meaningful social interactions, but this is a narrow facet of user well-being, let alone community well-being. They could use broader well-being instruments such as a life satisfaction survey question, but it would be difficult to assess the causal contribution of Facebook use to any changes. In other cases, such as the diverse news recommender, pre-existing well-being indicators would not apply so assessing societal impact would require the creation and validation of new community well-being metrics. Outcome evaluation at scale is essentially corporate social science. The IEEE 7010 Recommended Practice Standard for Assessing the Impact of Autonomous and Intelligent Systems on Human Well-Being proposes what amounts to a difference-indifferences design between users and non-users before and after an algorithmic change  (Schiff et al. 2020) . This is a promising approach, but there do not seem to be any published examples. \n Business Implications For commercial AI systems, metrics-driven changes must also integrate legitimate business concerns such as the cost of implementation and the effects on business outcomes. Although a naïve analysis of multi-objective optimization suggests that considering anything other than revenue can only reduce revenue, this assumes everything else is equal. In reality there are complex secondary effects, such as changes in user and supplier behavior. YouTube's experience demoting clickbait videos is a documented case where doing the responsible thing led to a short-term decrease in the primary watch time metric, but then a long-term increase. It is difficult to predict the financial effects of incorporating well-being into optimization. Business and social objectives may turn out to be aligned, but this cannot be expected to be true as a rule. While ethical outcomes can sometimes be achieved through changes to optimization goals, there are also situations that could conceivably require avoiding features, products, or business models altogether  (Barocas et al. 2020) . Case studies are one promising avenue for progress on the problem of uncertain business outcomes. If companies are already incorporating well-being metrics into their management and algorithms then documenting these cases will let others learn from their experiences, develop the field, and normalize the idea that companies should proactively manage the effects of their optimizers. This underscores the need for transparency around work that is explicitly designed to improve the lives of great numbers of people. \n Conclusion This paper has explored the integration of community well-being metrics into commercially-operated optimizing systems. Community well-being is an attractive goal because it is well-developed in public policy contexts and practically measurable. At least two large technology companies, Facebook and YouTube, have explicitly modified their objective functions in pursuit of well-being, demonstrating the practicality of this approach. There are still a number weaknesses in the interventions that Facebook and YouTube have undertaken, at least in terms of what has been reported publicly. The community that these interventions are intended to serve has not been well defined; rather, these metrics and interventions are oriented towards the individual level and do not account for existing communities such as cities or discussion groups. It is not clear if or how users were engaged in selecting the meaningful social interactions and user satisfaction metrics; there is no report of the outcomes either in terms of these metrics or with respect to broader well-being metrics; and although both companies reported reduced short term engagement, the broader business effects have not been discussed. However incomplete, the Facebook and YouTube cases suggest that the optimization of community well-being metrics may be a powerful general method for managing the societal outcomes of commercial AI systems. The same methods could be applied to many other types of systems, such as a news recommender system that incorporates measures of content diversity in an attempt to increase tolerance and reduce polarization, or an online shopping platform that uses product-level estimates of carbon footprint to steer users toward more environmentally friendly purchases. Although many scholars and critics have stressed the importance of increased user control over AI systems, no amount of user control can replace appropriate well-being metrics due to issues of collective action and the need for reasonable defaults. An analysis of the above cases suggests that the following multi-step process may be effective: Identify a community to define the scope of action. In online settings this may be a challenging decision. Select a well-being metric, perhaps from existing frameworks. This stage frames the problem to be solved in concrete terms, so it may be where community involvement matters most. Use this metric as a performance measure for the team building and operating the system. Directly translate the metric into code as a modification to an algorithmic objective function or use these measured outcomes to evaluate more general design changes. Evaluate the results, in terms of actual human outcomes, and adjust accordingly. This may require adjusting the chosen metric in response to changing conditions, or if it is found to be causing side effects of its own. Require transparency throughout to make participation possible and to hold companies accountable to the communities who are meant to be served by this process. Fig. 1 1 Fig. 1 A reconstruction of Facebook's use of meaningful social interactions circa 2018. Well-being effects are unobserved because they happen outside of user interactions with Facebook \n Table 1 1 Indicators from the OECD Better Life Index (Durand 2015) . Each of these has a specific statistical definition and has been collected across OECD countries since 2011 Domain Indicators Housing Dwellings without basic facilities Housing expenditure Rooms per person Income Household net adjusted disposable income Household net wealth Jobs Labor market insecurity Employment rate Long term unemployment rate Community Quality of support network Education Educational attainment Student skills Years in education Environment Air pollution Water quality Civic engagement Stakeholder engagement for developing regulations Voter turnout Health Life expectancy Self-reported health Life Satisfaction Life satisfaction Safety Feeling safe walking alone at night Homicide rate Work-life balance Employees working very long hours Time devoted to leisure and personal care \n\t\t\t International Journal of CommunityWell-Being (2020) 3:443-463", "date_published": "n/a", "url": "n/a", "filename": "Stray2020_Article_AligningAIOptimizationToCommun.tei.xml", "abstract": "This paper investigates incorporating community well-being metrics into the objectives of optimization algorithms and the teams that build them. It documents two cases where a large platform appears to have modified their system to this end. Facebook incorporated \"well-being\" metrics in 2017, while YouTube began integrating \"user satisfaction\" metrics around 2015. Metrics tied to community well-being outcomes could also be used in many other systems, such as a news recommendation system that tries to increase exposure to diverse views, or a product recommendation system that opstimizes for the carbon footprint of purchased products. Generalizing from these examples and incorporating insights from participatory design and AI governance leads to a proposed process for integrating community well-being into commercial AI systems: identify and involve the affected community, choose a useful metric, use this metric as a managerial performance measure and/or an algorithmic objective, and evaluate and adapt to outcomes. Important open questions include the best approach to community participation and the uncertain business effects of this process.", "id": "c8524339f8123ad1b495c8961969eeb3"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Unprecedented-Technological-Risks.tei.xml", "abstract": "Over the next few decades, the continued development of dual-use technologies will provide major benefits to society. They will also pose significant and unprecedented global risks, including risks of new weapons of mass destruction, arms races, or the accidental deaths of billions of people. Synthetic biology, if more widely accessible, would give terrorist groups the ability to synthesise pathogens more dangerous than smallpox; geoengineering technologies would give single countries the power to dramatically alter the earth's climate; distributed manufacturing could lead to nuclear proliferation on a much wider scale; and rapid advances in artificial intelligence could give a single country a decisive strategic advantage. These scenarios might seem extreme or outlandish. But they are widely recognised as significant risks by experts in the relevant fields. To safely navigate these risks, and harness the potentially great benefits of these new technologies, we must proactively provide research, assessment, monitoring, and guidance, on a global level. This report gives an overview of these risks and their importance, focusing on risks of extreme catastrophe, which we believe to be particularly neglected. The report explains why market and political circumstances have led to a deficit of regulation on these issues, and offers some policy proposals as starting points for how these risks could be addressed. \n September 2014 \n Fu ture of H umanit y Institute \n UNIVERSITY OF OXFORD \n Unprecedented Technological Risks Synthetic biology is allowing researchers to move from reading genes, to writing them, creating the possibility of both life-saving treatments and designer pandemics.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Vincent Conitzer", "Walter Sinnott-Armstrong", "Jana Schaich Borg", "Yuan Deng", "Max Kramer"], "title": "Moral Decision Making Frameworks for Artificial Intelligence", "text": "Introduction As deployed AI systems become more autonomous, they increasingly face moral dilemmas. An often-used example is that of a self-driving car that faces an unavoidable accident, but has several options how to act, with different effects on its passengers and others in the scenario. (See, for example,  Bonnefon et al. (2016) .) But there are other examples where AI is already used to make decisions with lifeor-death consequences. Consider, for example, kidney exchanges. These cater to patients in need of a kidney that have a willing live donor whose kidney the patient's body would reject. In this situation, the patient may be able to swap donors with another patient in the same situation. (More complex arrangements are possible as well.) For these exchanges, algorithms developed in the AI community are already used to determine which patients receive which kidneys (see, e.g.,  Dickerson and Sandholm (2015) ). While it may be possible to find special-purpose solutions for moral decision making in these domains, in the long run there is a need for a general framework that an AI agent can use to make moral decisions in a wider variety of contexts. In this paper, we lay out some possible roadmaps for arriving at such a framework. \n Motivation Most AI research is conducted within straightforward utilitarian or consequentialist frameworks, but these simple approaches can lead to counterintuitive judgments from an ethical perspective. For example, most people consider it immoral to harvest a healthy patient's organs to save the lives of Copyright c 2017, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. two or even five other patients. Research in ethics and moral psychology elucidates our moral intuitions in such examples by distinguishing between doing and allowing, emphasizing the role of intent, applying general rules about kinds of actions (such as \"Don't kill\"), and referring to rights (such as the patient's) and roles (such as the doctor's). Incorporating these morally relevant factors among others could enable AI to make moral decisions that are safer, more robust, more beneficial, and acceptable to a wider range of people.  1  To be useful in the development of AI, our moral theories must provide more than vague, general criteria. They must also provide an operationalizable, and presumably quantitative, theory that specifies which particular actions are morally right or wrong in a wide range of situations. This, of course, also requires the agent to have a language in which to represent the structure of the actions being judged  (Mikhail, 2007)  and the morally relevant features of actions  (Gert, 2004)  along with rules about how these features interact and affect moral judgments. Moral theory and AI need to work together in this endeavor. Multiple approaches can be taken to arrive at generalpurpose procedures for automatically making moral decisions. One approach is to use game theory. Game-theoretic formalisms are widely used by artificial intelligence researchers to represent multiagent decision scenarios, but, as we will argue below, its solution concepts and possibly even its basic representation schemes need to be extended in order to provide guidance on moral behavior. Another approach is to use machine learning. We can use the moral philosophy and psychology literatures to identify features of moral dilemmas that are relevant to the moral status of possible actions described in the dilemmas. Human subjects can be asked to make moral judgments about a set of moral dilemmas in order to obtain a labeled data set. Then, we can train classifiers based on this data set and the identified features. (Compare also the top-down vs. bottom-up distinction in automated moral decision making, as described by  Wallach and Allen (2008) .) We will discuss these two approaches in turn. In this paper, we will take a very broad view of what constitutes a moral dilemma  (contrast Sinnott-Armstrong (1988) ). As a simple example, consider the trust game  (Berg et al., 1995) . In the trust game, player 1 is given some amount of money-say, $100. She 2 is then allowed to give any fraction of this money back to the experimenter, who will then triple this returned money and give it to player 2. Finally, player 2 may return any fraction of the money he has received to player 1. For example, player 1 might give $50 back, so that player 2 receives 3 • $50 = $150, who then might give $75 back, leaving player 1 with $50 + $75 = $125. The most straightforward game-theoretic analysis of this game assumes that each player, at any point in the game, is interested only in maximizing the amount of money she herself receives. Under this assumption, player 2 would never have any reason to return any money to player 1. Anticipating this, player 1 would not give any money, either. However, despite this analysis, human subjects playing the trust game generally do give money in both roles  (Berg et al., 1995) . One of the reasons why is likely that many people feel it is wrong for player 2 not to give any money back after player 1 has decided to give him some (and, when in the role of player 1, they expect player 2 not to take such a wrong action). This case study illustrates a general feature of moral reasoning. Most people consider not only the consequences of their actions but also the setting in which they perform their actions. They ask whether an act would be unfair or selfish (because they are not sharing a good with someone who is equally deserving), ungrateful (because it harms someone who benefited them in the past), disloyal (by betraying a friend who has been loyal), untrustworthy (because it breaks a promise), or deserved (because the person won a competition or committed a crime). In these ways, moral reasoners typically look not only to the future but also to the past. Of course, not everyone will agree about which factors are morally relevant, and even fewer people will agree about which factor is the most important in a given conflict. For example, some people will think that it is morally wrong to lie to protect a family member, whereas others will think that lying in such circumstances is not only permitted but required. Nonetheless, a successful moral AI system does not necessarily have to dictate one true answer in such cases. It may suffice to know how much various groups value different factors or value them differently. Then when we code moral values into AI, we would have the option of either using the moral values of a specific individual or group-a type of moral relativism-or giving the AI some type of socialchoice-theoretic aggregate of the moral values that we have inferred (for example, by letting our models of multiple people's moral values vote over the relevant alternatives, or using only the moral values that are common to all of them). This approach suggests new research problems in the field of computational social choice (see, e.g.,  Brandt et al. (2013 Brandt et al. ( , 2015 ).  Rossi (2016)  has described related, but distinct so-cial choice problems where (not necessarily moral) preferences are either aggregated together with a moral ranking of all the alternatives, or the preferences are themselves ranked according to a moral ordering (see also  Greene et al. (2016) ). \n Abstractly Representing Moral Dilemmas: A Game-Theoretic Approach For us humans, the most natural way to describe a moral dilemma is to use natural language. However, given the current state of AI in general and of natural language processing in particular, such verbal descriptions will not suffice for our purposes. Moral dilemmas will need to be more abstractly represented, and as is generally the case in AI research, the choice of representation scheme is extremely important. In this section, we consider an approach to this problem inspired by game theory. \n Game-Theoretic Representation Schemes Game theory (see, e.g.,  Fudenberg and Tirole (1991) ) concerns the modeling of scenarios where multiple parties (henceforth, agents) have different interests but interact in the same domain. It provides various natural representation schemes for such multiagent decision problems. Scenarios described in game theory involve sequences of actions that lead to different agents being better or worse off to different degrees. Since moral concepts-such as selfishness, loyalty, trustworthiness, and fairness-often influence which action people choose to take, or at least believe they should take, in such situations, game theory is potentially a good fit for abstractly representing moral dilemmas. One of the standard representation schemes in game theory is that of the extensive form, which is a generalization of the game trees studied in introductory AI courses. The extensive-form representation of the trust game (or rather, a version of it in which player 1 can only give multiples of $50 and player 2 only multiples of $100) is shown in Figure  1 . Each edge corresponds to an action in the game and is labeled with that action. Each bottom (leaf) node corresponds to an outcome of the game and is labeled with the corresponding payoffs for player 1 and player 2, respectively. We will turn to the question of whether such representation schemes suffice to model moral dilemmas more generally shortly. First, we discuss how to solve such games. \n Moral Solution Concepts The standard solution concepts in game theory assume that each agent pursues nothing but its own prespecified utility. If we suppose in the trust game that each player just seeks to maximize her own monetary payoff, then game theory would prescribe that the second player give nothing back regardless of how much he receives, and consequently that the first player give nothing. 3 However, this is not the behavior observed in experiments with human subjects. Games that elicit human behavior that does not match game-theoretic analyses, such as the trust game, are often used to criticize the game-theoretic model of behavior and have led to the field of behavioral game theory  (Camerer, 2003) . While in behavioral game theory, attention is often drawn to the fact that humans are not infinitely rational and cannot be expected to perform complete game-theoretic analyses in their heads, it seems that this is not the primary reason that agents behave differently in the trust game, which after all is quite simple. Rather, it seems that the simplistic game-theoretic solution fails to account for ethical considerations. In traditional game theory's defense, it should be noted that an agent's utility may take into account the welfare of others, so it is possible for altruism to be captured by a game-theoretic account. However, what is morally right or wrong also seems to depend on past actions by other players. Consider, for example, the notion of betrayal: if another agent knowingly enables me either to act to benefit us both, or to act to benefit myself even more while significantly hurting the other agent, doing the latter seems morally wrong. This, in our view, is one of the primary things going on in the trust game. The key insight is that to model this phenomenon, we cannot simply first assess the agents' otherregarding preferences, include these in their utilities at the leaves of the game, and solve the game (as in the case of pure altruism). Rather, the analysis of the game (solving it) must be intertwined with the assessment of whether an agent morally should pursue another agent's well-being. This calls for novel moral solution concepts in game theory. We have already done some conceptual and algorithmic work on a solution concept that takes such issues into account  (Letchford et al., 2008) . This solution concept involves repeatedly solving the game and then modifying the agents' preferences based on the solution. The modification makes it so that (for example) player 2 wants to ensure that player 1 receives at least what she could have received in the previous solution, unless this conflicts with player 2 receiving at least as much as he would have received in the previous solution. For example, in the trust game player 2's preferences are modified so that he values player 1 receiving back at least what she gave to player 2. \n What Is Left Out & Possible Extensions The solution concept from  Letchford et al. (2008)  is defined only in very restricted settings, namely 2-player perfect-information 4 games. One research direction is to generalize the concept to games with more players and/or imperfect information. Another is to define different solution concepts that capture other ethical concerns. Zooming out, this general approach is inherently limited by the aspects of moral dilemmas that can be captured in game-theoretic representations. While we believe that the standard representation schemes of game theory can capture much of what is relevant, they may not capture everything that is relevant. For example, in moral philosophy, a distinction is often made between doing harm and allowing harm. Consider a situation where a runaway train will surely hit and kill exactly one innocent person (player 2) standing on a track, unless player 1 intervenes and puts the train on another track instead, where it will surely hit and kill exactly one other innocent person (player 3). The natural extensive form of the game (Figure  2 ) is entirely symmetric and thereby cannot be used to distinguish between the two alternatives. (Note that the labels on the edges are formally not part of the game.) However, many philosophers (as well Player 1 \n Do nothing Put train on other track g other track 0, -100, 0 0 , 0, -100 Figure  2 : \"Runaway train.\" Player 1 must choose whether to allow player 2 to be hurt or to hurt player 3 instead. as non-philosophers) would argue that there is a significant distinction between the two alternatives, and that switching the train to the second track is morally wrong. We propose that the action-inaction distinction could be addressed by slightly extending the extensive-form representation so that at every information set (decision point), one action is labeled as the \"passive\" action (e.g., leaving the train alone). Other extensions may be needed as well. For example, we may take into account what each agent in the game deserves (according to some theory of desert), which may require us to further extend the representation scheme. 5 A broader issue is that in behavioral game and decision theory it is well understood that the way the problem is framed-i.e., the particular language in which the problem is described, or even the order in which dilemmas are presented-can significantly affect human subjects' decisions. That is, two ways of describing the same dilemma can produce consistently different responses from human subjects  (Kahneman and Tversky, 2000) . The same is surely the case for moral dilemmas  (Sinnott-Armstrong, 2008) . Moral AI would need to replicate this behavior if the goal is to mirror or predict human moral judgments. In contrast, if our goal is to make coherent moral judgments, then moral AI might instead need to avoid such framing effects. \n Setting up a Machine Learning Framework Another approach for developing procedures that automatically make moral decisions is based on machine learning (see, e.g.,  Mitchell (1997) ). We can assemble a training set of moral decision problem instances labeled with human judgments of the morally correct decision(s), and allow our AI system to generalize. (Other work has focused on obtaining human judgments not of the actions themselves, but of persuasion strategies in such scenarios  (Stock et al., 2016) .) To evaluate this approach with current technology, it is insufficient to represent the instances in natural language; instead, we must represent them more abstractly. What is the right representation scheme for this purpose, and what features are important? How do we construct and accurately label a good training set? \n Representing Dilemmas by Their Key Moral Features When we try to classify a given action in a given moral dilemma as morally right or wrong (as judged by a given human being), we can try to do so based on various features (or attributes) of the action. In a restricted domain, it may be relatively clear what the relevant features are. When a self-driving car must decide whether to take one action or another in an impending-crash scenario, natural features include the expected number of lives lost for each course of action, which of the people involved were at fault, etc. When allocating a kidney, natural features include the probability that the kidney is rejected by a particular patient, whether that patient needs the kidney urgently, etc. Even in these scenarios, identifying all the relevant features may not be easy. (E.g., is it relevant that one potential kidney recipient has made a large donation to medical research and the other has not?) However, the primary goal of a general framework for moral decision making is to identify abstract features that apply across domains, rather than to identify every nuanced feature that is potentially relevant to isolated scenarios. The literature in moral psychology and cognitive science may guide us in identifying these general concepts. For example,  Haidt and Joseph (2004)  have proposed five moral foundations-harm/care, fairness/reciprocity, loyalty, authority, and purity. Recent research has added new foundations and subdivided some of these foundations  (Clifford et al., 2015) . The philosophy literature can similarly be helpful; e.g.,  Gert (2004)  provides a very inclusive list of morally relevant features. \n Classifying Actions as Morally Right or Wrong Given a labeled dataset of moral dilemmas represented as lists of feature values, we can apply standard machine learn-ing techniques to learn to classify actions as morally right or wrong. In ethics it is often seen as important not only to act in accordance with moral principles but also to be able to explain why one's actions are morally right  (Anderson and Anderson, 2007; Bostrom and Yudkowsky, 2014) ; hence, interpretability of the resulting classifier will be important. Of course, besides making a binary classification of an action as morally right or wrong, we may also make a quantitative assessment of how morally wrong the action is (for example using a regression), an assessment of how probable it is that the action is morally wrong (for example using a Bayesian framework), or some combination of the two. Many further complicating factors can be added to this simple initial framework. \n Discussion A machine learning approach to automating moral judgements is perhaps more flexible than a game-theoretic approach, but the two can complement each other. For example, we can apply moral game-theoretic concepts to moral dilemmas and use the output (say, \"right\" or \"wrong\" according to this concept) as one of the features in our machine learning approach. On the other hand, the outcomes of the machine learning approach can help us see which key moral aspects are missing from our moral game-theoretic concepts, which will in turn allow us to refine them. It has been suggested that machine learning approaches to moral decisions will be limited because they will at best result in human-level moral decision making; they will never exceed the morality of humans. (Such a worry is raised, for example, by  Chaudhuri and Vardi (2014) .) But this is not necessarily so. First, aggregating the moral views of multiple humans (through a combination of machine learning and social-choice theoretic techniques) may result in a morally better system than that of any individual human, for example because idiosyncratic moral mistakes made by individual humans are washed out in the aggregate. Indeed, the learning algorithm may well decide to output a classifier that disagrees with the labels of some of the instances in the training set (see  Guarini (2006)  for a discussion of the importance of being able to revise initial classifications). Second, machine learning approaches may identify general principles of moral decision making that humans were not aware of before. These principles can then be used to improve our moral intuitions in general. For now, moral AI systems are in their infancy, so creating even human-level automated moral decision making would be a great accomplishment. \n Conclusion In some applications, AI systems will need to be equipped with moral reasoning capability before we can grant them autonomy in the world. One approach to doing so is to find ad-hoc rules for the setting at hand. However, historically, the AI community has significantly benefited from adopting methodologies that generalize across applications. The concept of expected utility maximization has played a key part in this. By itself, this concept falls short for the purpose of moral decision making. In this paper, we have consid-ered two (potentially complementary) paradigms for designing general moral decision making methodologies: extending game-theoretic solution concepts to incorporate ethical aspects, and using machine learning on human-labeled instances. Much work remains to be done on both of these, and still other paradigms may exist. All the same, these two paradigms show promise for designing moral AI. Figure 1 : 1 Figure1: The trust game. Each edge corresponds to an action in the game and is labeled with that action. Each bottom (leaf) node corresponds to an outcome of the game and is labeled with the corresponding payoffs for player 1 and player 2, respectively. \n\t\t\t The point that, as advanced AI acquires more autonomy, it is essential to bring moral reasoning into it has been made previously by others-e.g., Moor (2006) . \n\t\t\t We use \"she\" for player 1 or a generic player, and \"he\" for player 2. \n\t\t\t The technical name for this type of analysis is backward induction, resulting in behavior that constitutes a subgame perfect Nash equilibrium of the game. \n\t\t\t In a perfect-information game, the current state is fully observable to each player (e.g., chess), in contrast to imperfectinformation games (e.g., poker).5 Note that, to the extent the reasons for what an agent deserves are based solely on the agent's earlier actions in the game under consideration, solution concepts such as those described above might in fact capture this. If so, then the only cases in which we need to extend the representation scheme are those where what an agent deserves is external to the game under study (e.g., the agent is a previously convicted criminal).", "date_published": "n/a", "url": "n/a", "filename": "moralAAAI17.tei.xml", "abstract": "The generality of decision and game theory has enabled domain-independent progress in AI research. For example, a better algorithm for finding good policies in (PO)MDPs can be instantly used in a variety of applications. But such a general theory is lacking when it comes to moral decision making. For AI applications with a moral component, are we then forced to build systems based on many ad-hoc rules? In this paper we discuss possible ways to avoid this conclusion.", "id": "3e72dc71f46cfee526755f18db6db7b5"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "2577-Article Text-4899-1-10-20151202.tei.xml", "abstract": "WINTER 2015 105 A rtificial intelligence (AI) research has explored a variety of problems and approaches since its inception, but for the last 20 years or so has been focused on the problems surrounding the construction of intelligent agentssystems that perceive and act in some environment. In this context, the criterion for intelligence is related to statistical and economic notions of rationality -colloquially, the ability to make good decisions, plans, or inferences. The adoption of probabilistic representations and statistical learning methods has led to a large degree of integration and crossfertilization between AI, machine learning, statistics, control theory, neuroscience, and other fields. The establishment of shared theoretical frameworks, combined with the availability of data and processing power, has yielded remarkable successes in various component tasks such as speech recognition, image classification, autonomous vehicles, machine translation, legged locomotion, and question-answering systems.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Martin Dresler", "Anders Sandberg", "Kathrin Ohla", "Christoph Bublitz", "Carlos Trenado", "Aleksandra Mroczko-Wa ˛sowicz", "Simone Kühn", "Dimitris Repantis"], "title": "Non-pharmacological cognitive enhancement", "text": "Introduction Humans have always striven to increase their mental capacities. From symbolic language, writing and the printing press to mathematics, calculators and computers: Mankind has devised and employed tools to record, store and exchange thoughts and hence, in a more abstract sense, to enhance cognition. Such external devices aiding cognition do not seem to raise any ethical concerns, at least not in regard to the aim of enhancing cognitive functions. In contrast, the introduction of means to enhance cognition internally by intervening in the brain in a more straightforward way has raised ethical and legal concerns and is regarded by (some parts of) the public as highly suspicious. The prospects and perils of cognitive enhancers have prompted wide discussion in ethics, law and politics. Cognitive enhancement has become a trend topic both in academic and public debate e however the discussants bring a very diverse background and motivation to this debate. The aim of many empirical researchers of cognitive enhancement is to understand the neurobiological and psychological mechanisms underlying cognitive capacities  (McGaugh and Roozendaal, 2009) , while theorists are rather interested in their social and ethical implications  (Savulescu and Bostrom, 2009) . While in basic research very specific mechanisms are studied (mostly in animal models), many theoretical discussions start from the counterfactual idea of a highly effective drug that makes its consumer super smart. In contrast, there is a surprising paucity of research that evaluates the effects of currently existing cognitive enhancers in healthy individuals. A widely cited definition characterizes cognitive enhancement as interventions in humans that aim to improve mental functioning beyond what is necessary to sustain or restore good health  (Juengst, 1998) . While the current bioethical debate on cognitive enhancement shows a strong focus on pharmacological ways of enhancement, according to the given characterization, enhancement of mental capabilities also by non-pharmacological means has to be seen as cognitive enhancement proper. In this paper we aim to draw attention to several non-pharmacological cognitive enhancement strategies that have been largely neglected in the debate so far. We will first summarize studies on the efficacy of psychopharmacological enhancers and then present data on the cognition enhancing effects of a number of non-pharmacological methods. We will start with broadly used interventions that are not commonly recognized as enhancement strategies such as nutrition, physical exercise and sleep, and then will go over to more specific methods such as meditation, mnemonic techniques, computer training, and brain stimulation technologies. We will restrain our review to methods that currently exist and won't speculate on future technologies. While many ethical arguments of the cognitive enhancement debate apply to both pharmacological and non-pharmacological enhancers, some of them appear in new light when considered on the background of non-pharmacological enhancement. \n Pharmaceuticals The bioethical debate on enhancement mainly concentrates on psychopharmaceuticals. In particular psychostimulants are increasingly popular among healthy people seeking cognitive enhancement  (Talbot, 2009; Smith and Farah, 2011) . Beside amphetamines, which are not reviewed here, two particular substances have frequently been in the spotlight of both the scientific  (de Jongh et al., 2008; Sahakian and Morein-Zamir, 2007)  and popular press  (The Economist, 2008; Talbot, 2009)  because of their assumed enhancing properties, namely methylphenidate and modafinil. The first, a stimulant used to treat attentiondeficit hyperactivity disorder (ADHD), is known to have been extensively misused, especially by college students as a \"study aid\"  (McCabe et al., 2005; Wilens et al., 2008) . The second, modafinil, a wakefulness promoting agent licensed for the treatment of excessive daytime sleepiness associated with narcolepsy, is already used by military personnel for missions of longer duration to counteract fatigue after sleep deprivation  (Bonnet et al., 2005; Caldwell and Caldwell, 2005; Moran, 2007) . It also seems to become increasingly popular in both business and in academia. In a non-representative online poll conducted by Nature magazine  (Maher, 2008) , 20% of the 1400 responding readers reported use of methylphenidate, modafinil or beta-blockers for non-medical reasons: 62% of users reported taking methylphenidate and 44% modafinil. Indirect evidence for the non-medical use of methylphenidate and modafinil can also be gained by companies constantly raising sales and by comparing their disproportionately high prescription numbers to the numbers of patients suffering from the disorders for which these substances are approved or used off-label  (Mehlman, 2004) . Methylphenidate is a dopamine reuptake blocker that also enhances dopamine and norepinephrine release with pharmacologic mechanisms similar to those of amphetamines  (Sulzer et al., 2005) . The mechanisms of action of modafinil are not well understood but are believed to differ from those of methylphenidate and amphetamines. Although there is mounting evidence that the effects on dopamine and norepinephrine are primary, effects on gaminobutyric acid, glutamate, histamine and orexin/hypocretin are also theorized  (Volkow et al., 2009; Minzenberg and Carter, 2008; Ballon and Feifel, 2006) . Although these drugs are supposed to affect cognition mainly, the widespread neurochemical systems they implicate suggest that they might also have an impact on emotional and motivational functions. In a systematic review on the effects of these stimulants on healthy individuals it has been shown that there is a lack of studies addressing this issue  (Repantis et al., 2010b) . Regarding methylphenidate, the analysis of the few existing studies provided no consistent evidence for enhancing effects, though evidence for a positive effect on memory (mainly spatial working memory) was found. While such memory benefits seem to be in the large effect size range, the popular opinion that methylphenidate enhances attention was not verified  (Repantis et al., 2010b) . Some studies reported even negative effects, such as a disruption of attentional control  (Rogers et al., 1999) . In a systematic review modafinil was found to have some positive, though moderate, enhancing effects on individuals who were not sleep deprived, namely on attention  (Repantis et al., 2010b) . No effect was found on memory, mood or motivation in the few studies that examined these domains, but the results of the studies were not unequivocal. Moreover, there is evidence that the effect of modafinil depends to some extent on the individual baseline performance  (Randall et al., 2005) . In the above mentioned systematic reviews also side effects of methylphenidate and modafinil on healthy individuals have been reviewed  (Repantis et al., 2010b) . Since most of the included papers reported small studies and not large-scale clinical trials, no standardized method of assessing adverse reactions and reporting drop-outs due to adverse effects was used. In a number of studies (26 for methylphenidate and 26 for modafinil), no comment on side effects was made, which leaves us to assume that no severe adverse effects appeared that would deserve a comment in the limited space of a publication. In the majority of the trials, the drugs were well tolerated. There were some side effects reported, but these were benign and only in few cases lead to drop-outs. For modafinil adverse reactions were primarily headache, dizziness, gastrointestinal complains (e.g. nausea, abdominal pain, dry mouth), increased diuresis, palpitations, nervousness, restlessness, and sleep disturbances and especially in studies with non-sleep deprived individuals, insomnia  (Baranski and Pigeau, 1997; Caldwell et al., 1999 Caldwell et al., , 2000 Caldwell et al., , 2004 Dinges et al., 2006; Eddy et al., 2005; Gill et al., 2006; Hart et al., 2006; Lagarde et al., 1995; Pigeau et al., 1995; Wesensten et al., 2002; Whitmore et al., 2006) . For methylphenidate a frequently reported side effect (reported in 13 out of 14 trials reporting side effects) was increased heart rate, while increase in blood pressure was not consistently found  (Bray et al., 2004; Brumaghim and Klorman, 1998; Clark et al., 1986; Fitzpatrick et al., 1988; Hink et al., 1978; Mehta et al., 2000; Peloquin and Klorman, 1986; Rogers et al., 1999; Strauss et al., 1984; Volkow et al., 1999a Volkow et al., , 1999b Wetzel et al., 1981) . Besides these, typical complaints were headache, anxiety, nervousness, dizziness, drowsiness and insomnia. In total, these drugs seem to be welltolerated even by this population where the trade-off between side effects and improvement may be less clear. Finally, since the majority of the studies that have been performed were short-term and single-dose studies, no comment can be made on the reinforcing effects, dependence development, and drug tolerance of MPH or modafinil in healthy individuals. Prescription drugs currently available for the treatment of dementia provide a further possibility for cognitive enhancement. Of interest are the drugs used for the treatment of dementia due to Alzheimer's disease, namely the acetylcholinesterase inhibitors and memantine. The first category comprises three substances e donepezil, galantamine, rivastigmine e that are recommended for clinical use for the treatment of patients with mild to moderate Alzheimer's disease  (Racchi et al., 2004) . Memantine is a NMDA receptor antagonist and is registered for the treatment of moderate to severe Alzheimer's disease  (Sonkusare et al., 2005) . Studies with anti-dementia drugs were found to be lacking. In a systematic review  (Repantis et al., 2010a)  only ten trials with donepezil, one with rivastigmine and seven with memantine have been reported. No randomized controlled trials examining the effects of galantamine in healthy individuals were found. Anti-dementia drugs show their effect after intake for several weeks. All memantine and the one galantamine trial were however single dose trials. Hence, based on these few and insufficient data, no adequate analysis of their potential as cognitive enhancers can be performed. Repeated trials have been conducted only with donepezil. These were six small scale trials, lasting 14e42 days. From these, only two  (Beglinger et al., 2005; Fitzgerald et al., 2008b)  had older persons as participants. The rest of the trials included young healthy participants. This factor complicates the comparison between the results and makes it difficult to generalize the results of the latter studies for the main population of interest, namely the growing elderly population. These few existing studies provide no consistent evidence for a cognitive enhancement effect. In one study it was found that donepezil improved the retention of training on complex aviation tasks  (Yesavage et al., 2002) . In an another case, verbal memory for semantically processed words was improved  (Fitzgerald et al., 2008a) . Donepezil might also improve episodic memory  (Gron et al., 2005) , but interestingly, two studies reported transient negative effects on episodic memory  (Beglinger et al., 2004 (Beglinger et al., , 2005 . A newer study found also an impairment of working memory in older healthy participants taking donepezil for six weeks  (Balsters et al., 2011) . In a sleep deprivation study, donepezil had no effect when participants were well-rested. Nevertheless, the memory and attention deficits resulting from 24 h of sleep deprivation were attenuated after donepezil intake. This effect however, was seen only in individuals whose performance declined the most after sleep deprivation  (Chuah and Chee, 2008; Chuah et al., 2009) , and could not be confirmed in a recent study  (Dodds et al., 2011) . Another point that should be made is that in most of the studies a large neuropsychological test battery was applied. However, an effect could be shown in only a few, if not only one, of the tests applied. This could speak either for a selective effect of donepezil or for small effects that in these relatively underpowered studies could only be revealed in only one (maybe the most difficult) task. Another possible explanation could be that acetylcholinesterase inhibitors require a pathology of diminished cholinergic transmission to show their effects, and, therefore, it is not possible to optimize performance in healthy individuals that already have an optimal concentration of acetylcholine. In conclusion, evidence for cognition enhancing effects of currently available psychopharmaceuticals in healthy subjects is sparse. In the majority of the trials, donepezil was well tolerated, however some authors warn that sleep disturbances might become apparent in larger populations  (Yesavage et al., 2002) . Reported side effects were benign and only in few cases led to drop-outs. The adverse reactions were mainly gastrointestinal complaints (e.g. nausea), but also headache, dizziness, nightmares and insomnia. \n Nutrition Numerous food products and dietary supplements claim effects like \"increase energy\" or \"enhance memory\" despite scarce, controversial or even lacking scientific evidence. Nutritional enhancers are consumed, intentionally or unintentionally, in everyday situations and they can reduce fatigue, e.g. through a coffee after lunch, and help maintain full cognitive capacities, e.g. through sweet snacks during an exam. Here, we review the acute effects of two commonly consumed dietary constituents, namely caffeine and sugar (glucose). Caffeine is an adenosine receptor antagonist; it reduces inhibition of neural firing by large through an increased turnover of noradrenaline in the brain  (Smith et al., 2003; Ferre, 2008) . It exerts its stimulating effects within less than an hour after administration through altering the biochemistry of the brain. Typical behavioral effects of caffeine include elevated mood, increased alertness, and better sustained attention  (Smith et al., 1991 (Smith et al., , 2005 Hewlett and Smith, 2007) . It improves motor-skill performance on tasks that are impaired when arousal is low, e.g. during simulations of driving  (Reyner and Horne, 1997)  and increases speed of encoding and response to new stimuli  (Warburton et al., 2001; Riedel et al., 1995) . Caffeine effects on more complex and cognitively demanding tasks are, however, controversial in that some authors report better performance  (Heatherley et al., 2005)  but also nullfindings effects  (Rogers and Dernoncourt, 1998) . The effects of caffeine on memory and learning are particularly disputed and positive effects can be in large attributed to indirect effects from elevated attention to the stimuli during encoding  (Nehlig, 2010) . Another debate concerns the question whether and in how far differences in prior caffeine consumption and their lack of experimental control thereof contribute to these conflicting observations. Caffeine tolerance has been demonstrated  (Evans and Griffiths, 1992)  and is more likely to occur in habitual, heavy coffee drinkers. Coffee drinkers represent, however, the group that is most prone to intentionally exploiting the enhancing effects of caffeine. Caffeine withdrawal after heavy coffee consumption has been associated with headaches, increased subjectively perceived stress and feelings of fatigue and reduced alertness in some studies  (Ratcliff-Crain et al., 1989; Schuh and Griffiths, 1997; Dews et al., 2002; Juliano and Griffiths, 2004) . However, withdrawal effects can, at large, be explained by psychological rather than pharmacological factors of reduced caffeine intake  (Dews et al., 2002) . In line with this, it has been shown that expectancy mimics effects of caffeine when consumers believe they consume a caffeinated beverage  (Fillmore, 1994) , thus further corroborating a psychological component of the caffeine effect following both consumption and withdrawal. While psychological aspects of caffeine withdrawal appear to be relevant particularly in subjective report of mood and energy, evidence suggests that caffeine enhances task performance independent of whether consumed in the abstained or normal caffeinated state in coffee drinkers  (Smit and Rogers, 2000; Addicott and Laurienti, 2009) . On the other hand, it appears that caffeine yields similar effects when administered in a coffee, in a tea, or as a capsule, supporting a pharmacological rather than a psychological mechanism when participants' expectations are controlled for  (Smith, 2002) . Glucose is the primary breakdown product of carbohydrates and the fuel for our cells. It is provided through the blood constantly and measured as the level of blood sugar. In an attempt to keep the blood sugar level constant, excess glucose must be stored and released later, which is achieved by the pancreatic hormones insulin and glucagon. Insulin is released with high levels of blood sugar and stimulates the synthesis of glycogen. Glucagon is released with decreasing blood sugar; it targets the liver to break up glycogen into glucose. Hypoglycemia, i.e. when the blood glucose level falls to very low values, can affect cognitive functioning negatively and is associated with slower reaction times in task that require attention. In healthy individuals, however, the blood glucose level appears to be fairly stable during the day. Subjective reports of \"increased mental energy\" have been associated with higher glucose metabolism in the brain  (Posner et al., 1988; Reivih and Alavi, 1983) , and this effect occurs within several minutes after glucose administration. With regard to objective cognitive performance, glucose improves attention  (Benton et al., 1994) , response speed  (Owens and Benton, 1994)  and working memory  (Scholey et al., 2001) , the latter occurring under conditions of high but also under low glucose depletion  (Owen et al., 2012; Jones et al., 2012) . The most pronounced effects of glucose on cognition are found for declarative memory  (Messier, 2004; , where effect sizes in the large range have been demonstrated in particular for demanding tasks (e.g.  Sünram-Lea et al., 2001 , 2002a , 2002b Meikle et al., 2004) . High blood-glucose level are associated with improved memory function  (Benton and Owens, 1993) , and glucose administration before and after learning similarly improves memory performance, indicating that attentional or other non-memory specific processes during encoding alone cannot be responsible for the memory enhancing effects of glucose  (Sünram-Lea et al., 2002a) . Memory effects are more pronounced in elderly as compared to young adults, and glucose tolerance was predictive for declarative memory performance  (Manning et al., 1990; Meikle et al., 2004; Messier, 2004) . On a neural level, the hippocampus has been proposed as the main brain region mediating the memory enhancing effects of glucose, with more specific mechanisms involving glucose effects on cerebral insulin, acetylcholine synthesis, potassium adenosine triphosphate channel function, and brain extracellular glucose availability . Taken together, the findings show that caffeine and sugar enhance mood, subjectively perceived energy, vigilance, attention, and memory, and may even exert their effects in a synergistic fashion if administered together  (Adan and Serra-Grabulosa, 2010 ). Individual differences, e.g. in glucose tolerance or nutritional habits such as caffeine consumption, influence the extent and direction of these effects. \n Physical exercise It is common knowledge that regular physical activity is a highly beneficial factor for preventing cardiovascular diseases and staying healthy in general. Already in the first half of the 20th century it was demonstrated that athletes outperform physically inactive individuals also in cognitive functions  (Burpee and Stroll, 1936) , and an emerging body of evidence suggests that regular aerobic exercise indeed has beneficial effects on brain function and cognition  (Hillman et al., 2008) . The focus of most studies on physical exercise effects on cognition is on developmental issues: Either children of different age groups or elderly adults were examined. In school-age children, physical exercise was demonstrated to benefit e.g. academic achievement, intelligence, perceptual skills, and verbal and mathematical ability  (Sibley and Etnier, 2003) . In older adults with and without pathological cognitive decline, beneficial effects of various physical exercise programs on different aspects of cognition were observed  (Richards et al., 2003; van Uffelen et al., 2008) . A recent meta-analysis of randomized controlled trials demonstrated that aerobic exercise training improves attention, processing speed, executive function and memory, while effects on working memory were less consistent  (Smith et al., 2010) . Even if methodological issues in measuring the impact of exercise on cognition in particular for studies with elderly subject populations remain  (Miller et al., 2012) , the conclusion that physical activity helps to preserve mental abilities throughout aging seems to be warranted. In contrast to research in children and older adults, there is a paucity of studies on physical exercise effects on the cognition of younger and middle age adults. Most data on these age groups can be found in studies on older adults, where they were examined as control groups for comparison with the elderly. An exception of this pattern constitute studies focusing not on chronic effects of regular physical activity, but on acute effects of exercise. For example, brief bouts of physical exercise improved long-term memory in young adults  (Coles and Tomporowski, 2008) . Intense exercise in the form of high impact anaerobic running was shown to strongly enhance learning speed in an vocabulary memorizing task  (Winter et al., 2007) . A recent meta-analysis demonstrated that in particular mental speed and memory processes are consistently enhanced after acute exercise, while the effects during acute exercise seem to depend on the specific exercise mode. In general, however, cognition enhancing effects of acute exercise seem to be in the small to medium range  (Lambourne and Tomporowski, 2010) . Besides motivational factors, an increase in general arousal level related to physical exertion has been hypothesized as a potential mechanism  (Brisswalter et al., 2002) . Data on the neural mechanisms underlying the effects of physical exercise on human cognition is rather sparse. Regular physical exercise training improved resting functional efficiency in higher-level cognitive networks including the frontal, posterior, and temporal cortices of older training participants compared to a control group  (Voss et al., 2010) . In particular greater task-related activity in fronto-parietal networks is associated with both general cardiovascular fitness and exercise training effects on cognition  (Colcombe et al., 2004) . Also hippocampal cerebral blood flow and hippocampal connectivity exhibit significant increases through physical exercise  (Burdette et al., 2010) . Structurally, cardiovascular fitness within the healthy elderly correlates with preserved gray matter areas that typically show age-related decline  (Gordon et al., 2008) , in particular hippocampal volume was found to be associated with physical fitness in older adults  (Erickson et al., 2009) , but also in children  (Chaddock et al., 2010) . Significant brain volume increases in both gray and white matter regions were also demonstrated to be associated with aerobic exercise training  (Colcombe et al., 2006) . In particular the size of the anterior hippocampus was shown to increase through physical exercise, which was related to enhanced spatial memory and increased serum brain-derived neurotrophic factor (BDNF) levels, a mediator of hippocampal neurogenesis in the dentate gyrus  (Eriksson et al., 2011) . This is in line with data derived from animal models, showing that physical exercise increases BDNF gene expression in the hippocampus  (Neeper et al., 1995) , and that hippocampal BDNF indeed mediates the effects of physical exercise on cognition  (Vaynman et al., 2004; Gomez-Pinilla et al., 2008) . Also the enhancing effects of intense acute exercise seem to be mediated by BDNF increases  (Winter et al., 2007) . Finally, parallel studies in mice and humans demonstrated that cerebral blood volume measurements provide an imaging correlate of neurogenesis in the dentate gyrus and that physical exercise had a primary effect on dentate gyrus cerebral blood volume that correlated with cognitive function  (Pereira et al., 2007) . In conclusion, there is converging evidence on several levels of observation that physical exercise enhances cognitive function throughout the lifespan. \n Sleep Humans spend a third of their lifetime in sleep. From an evolutionary standpoint, this phenomenon helps to save energy e but also leaves the sleeper in a potentially dangerous state of inattention. Sleep therefore has to provide the organism with important advantages to compensate for this disadvantage. A rapidly growing body of literature suggests that an important function of sleep is to enhance cognitive capacities, in particular memory  (Diekelmann and Born, 2010)  and creativity  (Dresler, in press) . First empirical reports on the positive effects of post-learning sleep on memory consolidation were published almost a century ago:  Jenkins and Dallenbach (1924)  demonstrated that memory for nonsense syllables over retention periods including sleep is less prone to forgetting compared to an equivalent time of wakefulness. Since then, hundreds of studies testing different memory systems have confirmed the positive effects of sleep on memory consolidation  (Diekelmann and Born, 2010) . It might be argued that regular sleep is just a general biological prerequisite to ensure cognitive functioning and therefore sleep trivially favors memory consolidation in comparison to sleep deprivation. However, also in experimental designs without sleep deprivation as a control condition sleep positively effects memory consolidation compared to wakefulness, e.g. when retention intervals during the day are compared with nocturnal retention intervals of similar length  (Fischer et al., 2002; Walker et al., 2002) . Furthermore, a growing number of studies demonstrates that also additional sleep in the form of daytime naps benefits memory function in non-sleepdeprived subjects (e.g.  Mednick et al., 2003; Korman et al., 2007) . Of note, even a nap as short as 6 min has been shown sufficient to promote memory performance  (Lahl et al., 2008) , and for some memory systems the benefit of a daytime nap is comparable to a whole night of sleep  (Mednick et al., 2003) . In general, the size of the sleep effect on memory consolidation seems to depend on the involved memory system: While for declarative learning effect sizes of sleep are in the medium range (e.g.  Gais et al., 2006) , sleep effects on procedural or perceptual learning are large  (Fischer et al., 2002)  or very large  (Karni et al., 1994) . Besides its stabilizing function, sleep boosts certain kinds of memories even above the level of initial acquisition: Procedural memories like motor skills typically reach a plateau after some time of training e however after a night of sleep motor performance starts from a higher level despite the absence of further training  (Walker et al., 2002) . Interestingly, the sleep-memory relationship is specifically influenced by personal factors like gender, hormonal status or mental health  (Dresler et al., 2010; Genzel et al., 2012) . The neural mechanisms underlying the effects of sleep on memory consolidation are still poorly understood. A major point of discussion is the question if newly formed memories profit from rather passive homeostatic processes  (Tononi and Cirelli, 2003) o r are actively consolidated during sleep. While several animal studies demonstrated a neuronal replay of activation patterns during sleep that were associated with recent memories  (Wilson and McNaughton, 1994; Ji and Wilson, 2007) , a study with humans utilizing memory-related odor cues during sleep could demonstrate a causal role of sleep for memory consolidation  (Rasch et al., 2007) . For several years it was thought that rapid eye movement (REM) sleep supports the consolidation of procedural memories while non-REM sleep supports declarative memories like verbal information, however recent studies suggested that this model was too simplistic  (Genzel et al., 2009; Rasch et al., 2009; Dresler et al., 2011) . Instead of global sleep stages, the role of physiological microprocesses during sleep gained attention. In particular the interaction of hippocampal sharp wave ripples, thalamo-cortical sleep spindles, and cortical slow oscillations is thought to play a physiological key role in the consolidation of memories  (Mölle and Born, 2011) . Anecdotal reports on scientific discovery, inventive originality, and artistic productivity suggest that also creativity can be triggered or enhanced by sleep. Several studies confirm these anecdotes, showing that sleep promotes creative problem solving compared to wakefulness. For example, when subjects performed a cognitive task, which could be solved much faster through applying a hidden rule, after a night of sleep more than twice as many subjects gained insight into the hidden rule as in a control group staying awake  (Wagner et al., 2004) . Like sleep-related memory enhancement, active processes during sleep seem to promote creativity: If applied during sleep, olfactoric stimuli that were associated with creativity tasks before sleep trigger insights overnight  (Ritter et al., in press) . In particular REM sleep, the sleep stage most strongly associated with intense dreaming, enhances the formation of associative networks in creative problem solving  (Cai et al., 2009) . Selective deprivation of REM sleep but not of other sleep stages impairs post-sleep performance in creativity tasks that are presented to the subjects before sleep  (Cartwright, 1972; Glaubman et al., 1978) . Subjects show greater cognitive flexibility in creativity tasks immediately after awakenings from REM sleep compared to awakenings from other sleep stages  (Walker et al., 2002) . Both theoretical models and empirical research of creativity suggest that sleep is a highly effective creativity enhancer  (Dresler, in press ). The historical standard model proposes a passive incubation phase as an essential step to creative insights  (Helmholtz, 1896) . Psychoanalytical models emphasize primary process thinking for creative cognitions e which is explicitly conceptualized as dream-like  (Kris, 1952) . Cognitive models propose that flat association hierarchies and a state of defocused attention facilitate creativity  (Mednick, 1962) . Hyper-associativity and defocused attention are phenomenal features of most dreams, physiologically probably caused by prefrontal cortex deactivation  (Hobson and Pace-Schott, 2002) . Physiological models suggest a high variability in cortical arousal levels as beneficial for creativity  (Martindale, 1999) , and the sleep cycle can be considered as a prime example of such arousal variability. The chaotic activation of the cortex in REM sleep through brainstem regions in absence of external sense data leads to a much more radical renunciation from unsuccessful problem solving attempts, leading to co-activations of cognitive data that are highly remote in waking life. These coactivations, woven into a dream narrative in a self-organizing manner, repeatedly receive further innervations by the brainstem, leading to bizarre sequences of loosely associated dream topics that might eventually activate particular problem-relevant cognitions or creative cognitions in general  (Hobson and Wohl, 2005) . In conclusion, the phenomenological and neural correlates of sleep provide ideal incubation conditions for the genesis of creative ideas and insights. \n Meditation Meditation has been emphasized as a discipline that promotes mental well-being, however recent research also suggests that it benefits several cognitive capacities. Meditation has been conceptualized as a family of complex emotional and attentional regulatory training regimes  (Lutz et al., 2008) . Such approaches include ancient Buddhist mindfulness meditations such as Vipassana and Zen meditations, but also several modern group-based standardized meditations  (Chiesa and Malinowski, 2011) . In the focus of current research are two rather traditional approaches: focused attention meditation and open monitoring meditation, which involve voluntary focusing of attention on a chosen object or non reactive monitoring of the content of experience from moment to moment  (Lutz et al., 2008) . During recent years, the effects of meditation practice were systematically studied also in western laboratories, and a rapidly growing body of evidence demonstrates that meditation training enhances attention and other cognitive capacities. For example, in comparisons of experienced meditators with meditation-naive control subjects, meditation practice has been associated with increased attentional performance and cognitive flexibility  (Moore and Malinowski, 2009; Hodgins and Adair, 2010) . In longitudinal studies, three months of meditation training could be shown to enhance attentional capacity  (Lutz et al., 2009) , perception and vigilance  (MacLean et al., 2010) . Even a brief training of just four meditation sessions was sufficient to significantly improve visuo-spatial processing, working memory and executive functioning  (Zeidan et al., 2010) . A recent systematic review associated early phases mindfulness meditation training with significant improvements in selective and executive attention, whereas later phases were associated with improved sustained attention abilities. In addition, meditation training was proposed to enhance working memory capacity and some executive functions . A recent meta-analysis of the effects of meditation training reported medium to large effect sizes for changes in emotionality and relationship issues, medium effect sizes for measures of attention and smaller effects on memory and several other cognitive capacities  (Sedlmeier et al., in press) . Also the neurophysiological mechanisms underlying meditation practice and its relation to cognition have been addressed. Electroencephalographic (EEG) studies have revealed a significant increase in alpha and theta activity of subjects that underwent a meditation session  (Kasamatsu and Hirai, 1966; Murata et al., 1994) . Neuroimaging studies have shown that meditation practice activates or deactivates brain areas comprising the prefrontal cortex and the anterior cingulate cortex  (Holzel et al., 2007) , the basal ganglia  (Ritskes et al., 2003) , the hippocampus, the pre-and post-central gyri as well as the dorsolateral prefrontal and parietal cortices  (Lazar et al., 2000) . Focusing on attention studies, it has been demonstrated that long-term meditation supports enhancement in the activation of specific brain areas, while also promoting attention sustainability  (Davidson et al., 2003) . Different studies have also emphasized the role of meditation as a mental process that modulates plasticity in neural circuits commonly associated to attention  (Davidson and Lutz, 2008) . fMRI studies have demonstrated a reduction of neural responses in widespread brain regions that are linked to conceptual processing, which suggests enhanced neural efficiency, probably via improved sustained attention and impulse control  (Pagnoni et al., 2008; Kozasa et al., 2012) . Moreover, PET studies have demonstrated an increase of dopamine release in the ventral striatum as a result of yoga meditation, which in turn suggest regulation of conscious states at the synaptic level  (Kjaer et al., 2002) . In addition, some studies have suggested that meditation practice is associated with structural brain changes. Compared to meditation-naive control subjects, long-term meditators showed significant larger volumes of the right hippocampus and orbitofrontal cortex  (Luders et al., 2009)  and significant greater cortical thickness in brain regions associated with attention, interoception and sensory processing, including the prefrontal cortex and right anterior insula  (Lazar et al., 2005) . In a longitudinal study with meditation-naive subjects undergoing an 8-week meditation program, gray matter increases in the hippocampus and other brains regions have been observed  (Hölzel et al., 2011) . \n Mnemonics In modern society, the ability to cope with verbal or numerical information becomes increasingly important. However, our learning skills evolved to handle concrete visuo-spatial rather than abstract information: While we can easily remember our last birthday party in great detail and typically don't have any problems recalling a once walked route including dozens or even hundreds of single sights and branches, most of us have a very hard time memorizing telephone numbers, foreign vocabularies or shopping lists. The most common way to memorize such information is rote learning: We take up the information to be remembered into our short-term memory and repeat it over and over again. However, such a procedure is slow and inefficient e in particular due to a severe limitation of short term memory capacity: As  Miller (1956)  observed more than half a century ago, the number of arbitrary information chunks an average human can hold in short-term memory is seven, plus or minus two. In contrast, some few individuals show memory skills far beyond this normal range: Already a century ago some case reports mention exceptional memorizers with memory spans of several dozens digits  (Brown and Deffenbacher, 1975) . In a seminal case study, a normal college student was trained over the course of two years, eventually reaching a memory span of 82 digits read at the pace of one digit per second  (Ericsson et al., 1980) . Since the early 1990s, the top participants of the annual World Memory Championships regularly prove memory spans of hundreds of digits  (Konrad and Dresler, 2010) . However, such superior memorizers do not seem to exhibit structural brain changes or superior cognitive abilities in general, but acquired their skills by deliberate training in the use of mnemonic techniques  (Brown and Deffenbacher, 1988; Maguire et al., 2003; Ericsson, 2009) . To cope with the limitations of natural memory, humans have always used external remembering cues  (D'Errico, 2001) . The term mnemonics is typically used to denote internal cognitive strategies aimed to enhance memory. Parallel to their success in memory artistry and memory sports, several mnemonics have been shown to strongly enhance memory capacity in scientific studies  (Bellezza, 1981; Hunt, 2011a, 2011b) . Probably most prominent is the so called method of loci, an ancient technique used extensively by Greek and Roman orators  (Yates, 1966) . It utilizes well established memories of spatial routes: During encoding, to-beremembered information items have to be visualized at salient points along such a route, which in turn has to be mentally retraced during retrieval. A second powerful mnemonic is the phonetic system, which is designed to aid the memorization of numbers: Single digits are converted to letters, which are then combined to form words. Both the method of loci and the phonetic system have been shown to be very effective and even increase their efficacy over time, i.e. at delayed recall after several days compared to immediate recall  (Bower, 1970; Roediger, 1980; Bellezza et al., 1992; Hill et al., 1997; Higbee, 1997; Wang and Thomas, 2000) . A third mnemonic that has to be shown effective is the keyword method, designed specifically to enhance the acquisition of foreign vocabulary  (Raugh and Atkinson, 1975) , but also helps to learn scientific terminology  (Rosenheck et al., 1989; Brigham and Brigham, 1998; Balch, 2005; Carney and Levin, 1998) . It associates the meaning of a to-be-remembered term with what the term sounds like in the first language of the learner. A recently published broad overview on mnemonics demonstrates that research into these techniques has lost attention since 1980  (Worthen and Hunt, 2011b) . In particular neurophysiological data on mnemonics is sparse. A seminal study on expert mnemonics users found that during mnemonic encoding brain regions are engaged that are critical for spatial memory, in particular parietal, retrosplenial and right posterior hippocampal areas  (Maguire et al., 2003) . Likewise, the superior digit memory of abacus experts was associated specifically with visuo-spatial information processing brain regions  (Tanaka et al., 2002) . Here, abacus skill can be interpreted as a mnemonic for digit memorizing. In two studies with novices taught in the method of loci, mnemonical encoding led to activation increases particularly in prefrontal and occipito-parietal areas, while mnemonic-guided recall led to activation increases particularly in left-sided areas including the parahippocmpal gyrus, retrosplenial cortex and precuneus  (Nyberg et al., 2003; Kondo et al., 2005) . Another strategic method to enhance memory retention that has gained attention in recent years is retrieval practice. While retrieval of learned information in testing situations is traditionally thought to simply assess learning success, repeated retrieval itself has been shown to be a powerful mnemonic enhancer, producing large gains in long-term retention compared to repeated studying  (Roediger and Butler, 2011) . For example, when students have to learn foreign vocabulary words, repeated studying after the first learning trial had no effect on delayed recall after one week, while repeated testing produced a surprisingly large effect on long-term retention  (Karpicke and Roediger, 2008) . Besides vocabulary learning, also text materials profit from repeated retrieval  Roediger, 2006, 2010) . Interestingly, study participants seem to be unaware of this effect, overestimating the value of repeated study and underestimating that of repeated retrieval  Roediger, 2006, 2008) . Effects of retrieval practice were even shown to produce greater success in meaningful learning than elaborative studying strategies, which are designed to lead to deeper learning and therefore hold a central place in contemporary education  (Karpicke and Blunt, 2011) . On the neural level, repeated retrieval leads to higher brain activity in the anterior cingulate cortex during retest, which was interpreted as an enhanced consolidation of memory representations at the systems level  (Eriksson et al., 2011) . In conclusion, mnemonic strategies can be seen as strong and reliable enhancers of learning and memory capacity. While their immediate benefits for easy-to-learn material seem to be in the small to medium effect size range, the effectiveness of mnemonics strikingly grows with task difficulty or retention time and can reach effect sizes in terms of Cohen's d of larger than 3 or 4 (e.g.  Higbee, 1997; Karpicke and Roediger, 2008) . Of note, the benefits of mnemonics in population groups with particular cognitive training needs as e.g. in age-related cognitive decline seem to be less pronounced  (Verhaeghen et al., 1992) , however still can reach large effect sizes if memory is assessed after prolonged retention time  (Hill et al., 1997) . \n Computer training The rapid growth of computer game popularity in adolescents has generated concern among practitioners, parents, scholars and politicians. For violent computer games, detrimental effects have been reported in the social domain, namely increases in aggression and reductions of empathy and prosocial behavior  (Kirsh and Mounts, 2007; Anderson et al., 2010) . But favorable effects of frequent computer game playing have also been observed. Computer games allow repeated, sometimes rewarding, training of various mental tasks with variation and interactivity. While improved performance on the tasks inside the games is unsurprising, they may also be able to transfer their effects to other cognitive domains or enhance general cognitive abilities. Much interest has been focused on enhancing long term memory or brain plasticity in healthy or mildly impaired older adults using training programs, especially to prevent dementia and age related cognitive decline  (Cotelli et al., 2012; Tardif and Simard, 2011) . Computerized training programs have shown moderate improvements of memory that are sustained 3 months after end of training  (Mahncke et al., 2006) . Other studies have found improvements in memory and attention  (Smith et al., 2009; Zelinski et al., 2011) , executive function and processing speed  (Nouchi et al., 2012; Basak et al., 2008)  and working memory and episodic memory in young and older adults  (Schmiedek et al., 2010) . However, a large six-week online study did not find evidence for transfer  (Owen et al., 2010) . Also, although computerized brain training games have become a major industry it is not clear that the commercial games transfer to untrained tasks  (Fuyuno, 2007; Ackerman et al., 2010) . Computer games appear to be able to train visual skills, such as visuo-spatial attention, number of objects that can be attended and resolution of visual processing  (Achtman et al., 2008; Hubert-Wallander et al., 2011) . Playing the game Tetris improved mental rotation and spatial visualization time  (Okagaki and Frensch, 1994) , and computer game training improved contrast sensitivity  (Li et al., 2009) , spatial visual resolution  (Green and Bavelier, 2007)  and taskswitching  (Strobach et al., 2012) . However, these enhanced abilities, although not tied directly to the gaming task, might nevertheless be limited to similar domains. For example, a study found that games enhance navigation performance in desktop and immersive virtual environment but not real environments  (Richardson et al., 2011) . Regular or expert gamers show various improvements in mental ability compared to non-gamers. For example, first-person-shooter game players showed greater cognitive flexibility than non-players  (Colzato et al., 2010) , players enumerate better  (Green and Bavelier, 2006) , have faster visual search  (Castel et al., 2005) , have better visual attention  (Green and Bavelier, 2003) , track object color and identity better  (Sungur and Boduroglu, 2012) , and have improved psychomotor skills  (Kennedy et al., 2011) . However, 20þ hour training on computer games did not improve non-video gamers on mental tasks (visual short term memory, task switching, mental rotation) where expert video gamers excelled  (Boot et al., 2008) . Either pre-existing group differences (or self-selection) make the experts more skilled or amenable to training, or a longer training period is needed. This appears to be a general problem in studying enhancing game effects that need to be circumvented in further studies  (Boot et al., 2011) . A cognitive domain that has raised increasing attention in recent years is working memory. Working memory is useful for a variety of cognitive tasks, including intelligence. It can also be trained using computerized tasks such as the n-back task, where the difficulty is increased to remain challenging for the player. Working memory training has been tried for various therapeutic purposes, partially because of its correlation with executive function, but also has also been applied in preschool children, where it transferred to improvement of a fluid intelligence-related task  (Thorell et al., 2009; Nutley et al., 2011) . Also in healthy adults transfer to fluid intelligence from working memory training has been observed  (Jaeggi et al., 2008 (Jaeggi et al., , 2010 . However, the evidence of transfer has been questioned by some authors  (Shipstead et al., 2010)  and some attempts at replication of transfer effects outside working memory have been unsuccessful  (Dahlin et al., 2008; Holmes et al., 2010; Redick et al., in press ). Individual differences in training performance predict the transfer effects  (Jaeggi et al., 2011) . Short-and long-term benefits of cognitive training and different types of training (training core working memory or strategy) might have different transfer effects  (Morrison and Chein, 2011) . Neurobiologically, working memory training does appear to increase prefrontal and parietal activity  (Olesen et al., 2004) , white matter volume  (Takeuchi et al., 2010) , and prompt changes in the density of dopamine D1 receptors  (McNab et al., 2009) . Cognitive enhancement through games and computerized training is a promising method, but not all commercial games will have optimal cognitive effects  (Hubert-Wallander et al., 2011) . Effect sizes of computerized training strongly depend on the cognitive domain trained and tested, with processing speed and perceptual measures showing medium to large effect sizes, while effects for different memory domains are only in the small or medium range  (Mahncke et al., 2006; Smith et al., 2009; Schmiedek et al., 2010; Zelinski et al., 2011) . What forms of training produce reliable and strong transfer to useful domains remains to be determined. The availability and self-motivating aspects of games is an important advantage over many other methods of cognitive enhancement. \n Brain stimulation Several forms of electrical brain stimulation have been developed, acting by non-specifically influencing regions of the brain rather than sending physiological signals. They were developed for therapeutic purposes in psychiatry or neurology, but have in some cases exhibited enhancing effects on cognition of healthy individuals  (Hoy and Fitzgerald, 2010; McKinley et al., 2012) . Some of these methods are non-invasive, while other achieve greater target specificity by placing electrodes inside or on the brain. Transcranial direct current stimulation (tDCS) involves sending a small electric current (typically 1e2 mA) between two electrodes placed on the scalp  (Been et al., 2007) . The technique seems to work by changing the likelihood of neural firing in superficial parts of the cortex: neurons under the anode neurons become hyperpolarized and less excitable, while neurons under the cathode become depolarized and more excitable. This produces different effects depending on polarity and electrode placement, which can outlast the stimulation by more than an hour  (Nitsche et al., 2005) . The method appears to have few adverse effects  (Poreisc et al., 2007) . Transcranial magnetic stimulation (TMS) employs a coil to deliver brief magnetic pulses to the scalp, inducing electric currents in the brain. Various modalities (single-pulse, paired-pulse, high and low frequency repetitive) are available and have different cognitive effects, including interference with activity as well various forms of enhancement  (Rossi and Rossini, 2004) . The effects are likely mediated by similar changes in excitation and inhibition as in tDCS, which in turn might involve changes in synaptic plasticity  (Nitsche et al., 2003a (Nitsche et al., , 2003b . TMS has a low number of reported side effects in healthy subjects, typically headaches or local pain, and is generally regarded as quite safe. The most serious risk is the occurrence of seizure, often due to incorrect stimulation parameters or use of medications that lower the seizure threshold (however, even in epileptic patients the crude risk during high frequency rTMS is 1.4%;  Rossi et al., 2009) . Invasive methods for brain stimulation include deep brain stimulation (DBS) and direct vagus nerve stimulation (dVNS). In DBS electrodes are implanted in deep brain structures and used to modulate their activity through high frequency stimulation. dVNS exploits that stimulation of afferent vagal fibers appears to modulate the central nervous system, perhaps by stimulating brainstem structures  (Krahl et al., 1998; Groves and Brown, 2005) . The stimulating signal is typically generated by a pacemaker-like device placed under the chest skin. These methods have the drawback of requiring surgery  (Kuhn et al., 2010; Ben-Menachem, 2001) , but can also provide continual stimulation unlike the non-invasive methods. Several studies demonstrated enhancing effects of various brain stimulation methods on learning and memory. Learning enhancing effects have been reported for tDCS  (Chi et al., 2010; Clark et al., 2012; Kincses et al., 2003; Reis et al., 2008) , DBS  (Williams and Eskandar, 2006; Hamani et al., 2008; Suthana et al., 2012)  and dVNS  (Clark et al., 1999) . These results suggest that the changes in excitability induced by tDCS, TMS and dVNS can help memory encoding, while DBS has the potential to directly affect the modulation of memory systems. Anodal tDCS during slow wave sleep also enhanced memory consolidation  (Marshall et al., 2004) , perhaps by boosting slow wave oscillations  (Marshall et al., 2006) . Recall of names of famous people (but not landmarks) was improved by anterior temporal lobe tDCS  (Ross et al., 2010) . Speed of recall could also be enhanced by galvanic stimulation of the vestibular nerves  (Wilkinson et al., 2008)  and paired pulse TMS stimulation during encoding (left dorsolateral prefrontal cortex) or retrieval (right dorsolateral prefrontal cortex)  (Gagnon et al., 2010) . Learning and recall of words were enhanced by anodal (hyperpolarizing) tDCS stimulation of left dorsolateral prefrontal cortex during encoding and cathodal stimulation during retrieval . tDCS has been found able to enhance performance on working memory tasks  (Fregni et al., 2005; Luber et al., 2007; Teo et al., 2011; Ohn et al., 2008) . Sleepdeprivation induced impairment of a visual working memory task was reduced by rTMS  (Luber et al., 2008) . Low frequency TMS and tDCS applied to the temporal lobe can reduce the incidence of false memories  (Gallate et al., 2009; Boggio et al., 2009) . The improvement of associative learning from tDCS appears able to carry over to implicit learning  (Kincses et al., 2003)  and numerical learning  (Kadosh et al., 2010) . In the latter case arbitrary symbols were shown, and subjects developed long-lasting (6 months) automatic numerical processing and number-to-space mappings for them similar to ordinary numbers. Also for procedural skills there has been much interest in the ability of TMS to influence brain plasticity, mainly in order to help rehabilitation and therapy  (Schabrun and Chipchase, 2012) . TMS appears able to modulate short-term motor cortex plasticity  (Ziemann et al., 1998) . Brain stimulation of the motor areas using TMS and tDCS has been found to enhance learning motor tasks  (Nitsche et al., 2003a (Nitsche et al., , 2003b Reisa et al., 2009) . The enhancement can often be ascribed to reducing intra-hemispherical \"rivalry\" by disrupting the opposite side  (Kobayashi et al., 2004; Bütefisch et al., 2004) . Also other cognitive domains were shown to be enhanced by brain stimulation. Verbal fluency was increased by left prefrontal tDCS  (Iyer et al., 2005) , picture-word verification speeded up by rTMS in Broca's area  (Dräger et al., 2004)  and picture naming by rTMS of Wernicke's area  (Mottaghy et al., 1999) . rTMS can improve visual spatial attention on one side by impairing the other side  (Hilgetag et al., 2001; Thut et al., 2004) . Brain stimulation may also have beneficial effects for more complex mental functions. rTMS delivered to the frontal or parietal lobe improved accuracy on the mental rotation task  (Klimesch et al., 2003) . rTMS over the prefrontal cortex speeded up analogic reasoning, but did not change the error rate  (Boroojerdi et al., 2001) . tDCS inhibition of the left anterior temporal lobe improved the ability to solve matchstick problems, apparently by reducing mental set and allowing more loose associations  (Chi and Snyder, 2011) . In one of the few ecologically relevant tests of brain stimulation, tDCS of the dorsolateral prefrontal cortex promoted a more careful driving style in a car simulation  (Beeli et al., 2008) . This might represent a lowering of risk-taking rather than better planning. Cognitive processes can be enhanced by inhibiting other brain regions that would otherwise have an interfering effect. TMS can reduce interference between similar-sounding words in phonological memory, improving recall  (Kirschen et al., 2006)  and reduce distractors in visual search  (Hodsoll et al., 2009) . It has been claimed that rTMS inhibition of the frontotemporal region produces (besides reduction in immediate recall) savant-like abilities in drawing, mathematics, calendar calculating and proofreading  (Young et al., 2004; Snyder et al., 2003) . However, individual variations were large compared to the sample size, undermining statistical power. Other experiments along the same lines have hinted at improved number estimation  (Snyder et al., 2006) . The efficacy of brain stimulation strongly depends on applying it to the right region; the most successful studies are in general fMRI guided so that they can place electrodes over the right part of the cortex. Individual variation in anatomy and response appear large. Enhancement also depends on selecting the stimulated area to fit the task: there does not exist any generally enhancing effects  (beyond, arguably, increases in arousal) . Understanding what areas should be inhibited or excited is nontrivial. The effect sizes of the enhancement appear small to modest, however single studies report also larger effects (e.g.  Chi et al., 2010) . From a risk perspective non-invasive brain stimulation appears unproblematic, while a significant number of patients with long-term DBS have hardware-related complications  (Oh et al., 2002)  beside complications from the initial surgery. Implants are costly, making equal distribution hard, while TMS and especially tDCS are far less expensive. In fact, the potential low cost and ease of tDCS might be cause for concern in the form of amateur use/abuse. While there are so far no indications that any ethically dubious or risky applications have been found, anecdotal evidence suggests that amateurs are trying to perform tDCS (e.g. http://flowstateengaged.com). There is also a risk of premature use of the technology based on hype or speculation, including on vulnerable groups such as children. Since long-term effects on brain plasticity and development are unknown this is a cause for concern  (Kadosh et al., 2012) . \n Ethical issues Just as diverse as the many enhancement strategies are in terms of their effectiveness, potential side-effects and mode of functioning, so are the ethical worries they may raise. In respect to safety and side-effects, every method requires detailed analysis of its own. Most interventions benefit only specific cognitive domains and have little or no effects on others. Some interventions such as physical exercise or meditation might exert rather small benefits on cognitive capacities when compared to other enhancers, however have additional benefits such as enhanced mental or physical health without known side effects. Some methods like brain stimulation or pharmaceuticals might be save if applied by an experienced practitioner, however can be misused by unexperienced users. Some highly effective methods such as mnemonic training or sleep are safe and available to everybody, however are rather time consuming. Defining an adequate cost-benefit ratio for the use of neurotools is one of the central open questions in the enhancement debate. Reasonable minds come to different conclusions about the scope of acceptable risks for non-medically indicated interventions, and it remains to be argued whether this decision should be left entirely to physicians and patients or be regulated on the political level. Also apart from questions of risks and benefits, the ethical debate on cognitive enhancers has to compare pharmacological and non-pharmacological interventions. For instance, the use of pharmaceutical enhancers is often portrayed as an undesirable shortcut  (Manninen, 2006; Freedman, 1998) . Shortcuts as such are nothing to be concerned about e on the contrary, using more effective tools to reach goals is one of the main reasons for economic and personal development. Sometimes, however, taking the longer (non-pharmacological) route may have additional benefits. Supporting cognition in form of appropriate nutrition, mnemonic training or meditative practice requires a lot of planning, self-discipline, dedication and strength of will. Therefore, their use may foster secondary virtues, the feeling of self-mastery and achievement, endurance, self-confidence and may confer self-knowledge  (Kipke, 2010) . In respect to personal development and the ethics of a good life, understood not just as experiencing happiness but rather as having conscious contact with reality and being aware of one's own strengths and weaknesses  (Nozick, 1974) , these are additional benefits which should be taken into account in decisions on how to form and sculpture one's personality. These benefits of some non-pharmacological means, however, may come at the price of efficacy e provided of course that pharmacological shortcuts turn out to be more effective. Comparing different cognitive enhancers in this regard is difficult because of a striking paucity of studies testing different interventions with comparable tasks. As measured targets are often broad categories such as vigilance, attention or memory, and as it is likely that different means affect various subfunctions of cognition, one can draw only weak inferences. Mnemonics, for instance, may improve specific memory systems while pharmaceuticals may improve others. What would be needed are studies designed to compare different interventions in a straightforward manner and preferably in real-life tasks. At the moment, the hype around pharmaceutical enhancers can hardly be backed up scientifically, whereas some non-pharmacological methods are proven to be highly effective in certain cognitive domains. On the social level, pharmaceuticals raise the worry of pharmacologization of life, as  Healy (2008)  put it: \"Birth, Ritalin, Prozac, Viagra, Death\". Increasing numbers of neuro-interventions may indeed be the inevitable consequence of increasing knowledge about brain processes. Most likely, neuroscientific progress will reveal not only benefits, but also drawbacks of such interventions, enabling potential users to balance reasons for or against a given enhancer. The real objection might rather be that people who want to live a more natural life or are unwilling to take the risks of pharmaceuticals are pressured into doing so. On a first glance, the same may be held against non-pharmacological enhancement methods. However, a more fine-grained look at social pressure is necessary. Every society partially structured in competitive terms exerts pressure on the individual. Ethical problems arise in respect to the intensity of this coercion and its negative consequences for the individual's life. Job markets in mental economies demanding high cognitive performance are troublesome if they pressure persons into consuming substances with undesirable side effects only for job reasons. We may indeed not welcome a society in which cognitive powers are boosted on the expense of, say, emotional skills or general health. In this light, several nonpharmacological enhancement strategies seem to fare better: It seems a far more reasonable burden to make use of e.g. proper nutrition, mnemonics, sports or meditation, which have only positive side effects if any, than of currently available pharmaceuticals, for which side effects are currently unknown particularly for long-term use. At least, the social pressure on those who do not want to use traditional methods seems not of a kind that could warrant prohibitive regulations. A related worry is that cognitive enhancers may undermine fairness in social competition (\"mind doping\"). The often drawn analogies to sports, however, are short-sighted. The world of sports is characterized by competition for its own sake and promotes its own values (the \"spirit of sports\") and hence cannot serve as a model for social cooperation at large. From an egalitarian perspective, it is noteworthy that some non-pharmacological enhancers (e.g. mnemonics) may even widen the cognitive gap as they are more effective in cognitively already high-functioning individuals, while many pharmaceuticals, by contrast, mainly seem to compensate acute or chronic cognitive impairments. Likewise, physically disabled individuals cannot profit much from physical exercise; people with certain allergies cannot profit from certain nutritional enhancers. So more generally, just as pharmaceuticals raise worries about equal access  (Farah et al., 2004) , so may non-pharmacological methods. Thus, in regard to almost every enhancement method, some people may benefit more than others, and hence, arguments over equality are not confined to pharmaceuticals. After all, pharmaceutical or other enhancers are not intrinsically ethically dubious. Rather, the problem individuals and societies may increasingly face in the future is finding the right balance between efficient direct interventions and traditional methods which may be more resource consuming but may hold additional benefits. In a world of limited resources, society will have to strike balances between optimizing human cognition and preserving valuable emotional propensities and individuals' peculiarities. This is a complex task without a firm default position. To make good decisions, a stable empirical basis is needed. Therefore, more research should be devoted to both pharmacological and nonpharmacological interventions, preferably in a way that allows comparing efficacy and side-effects. In light of the latter, a presumption in favor of traditional methods is a prudent position. Thus, the \"gold standard\" for cognitive enhancers should not be the best pill among pills, but better than other neurotools, first and foremost, traditional ways. Concededly, financial interests seem to favor development of patentable and marketable pharmaceuticals over developing or refining the ancient ars memoriae, promoting smart foods, getting enough sleep or other mental or physical exercise. For society at large, however, the latter may be the better way. \n Conclusions Does a cup of coffee or a nap wake you up better? Would learning memory techniques or taking a memory enhancing drug improve your study results best e and what would they do to your mood and attention? If methylphenidate affects creativity, what about working memory training? There exist many cognitive enhancement interventions. Some, such as sleep, meditation, exercise or nutrition, are based on traditional and widely accepted habits. Some, such as pharmaceuticals, computer games or brain stimulation, are modern and controversial. Interventions in the mind are, in a wide sense, an everyday and commonplace phenomenon. As Eric Kandel remarked, every conversation changes the brain. But the range of possible techniques to change and enhance the mind, from talking to deep-brain stimulation, is wide. In order to find reasonable ways of using them, their similarities and differences need to be evaluated. It is only a matter of time when brain research and cognitive neurotechnology will pervade our society, presumably this development is irreversible. Surprisingly, not much data exist that would allow relative comparisons of the efficacy of different interventions, although many ethical discussions seem to presume that it is available. The purpose of ethical debates is not only to build possible future scenarios, in which side effect-free smart pills are available to boost any cognitive capacity, but also to evaluate current possibilities and constraints of cognitive enhancement. Comparative and differential research on the variety of currently existing cognitive enhancers is strongly needed to inform the bioethical debate. \n Role of the funding source This work was funded by a grant of the Volkswagen Foundation, Germany. The Volkswagen Foundation had no role in the design, data collection, data analysis, data interpretation, or writing of the manuscript. The authors report no conflicts of interest. \t\t\t Please cite this article in press as: Dresler, M., et al., Non-pharmacological cognitive enhancement, Neuropharmacology (2012), http:// dx.doi.org/10.1016/j.neuropharm.2012.07.002", "date_published": "n/a", "url": "n/a", "filename": "Non-pharmacological_cognitive_enhancemen20161023-10830-12dxzxu-with-cover-page-v2.tei.xml", "abstract": "The term \"cognitive enhancement\" usually characterizes interventions in humans that aim to improve mental functioning beyond what is necessary to sustain or restore good health. While the current bioethical debate mainly concentrates on pharmaceuticals, according to the given characterization, cognitive enhancement also by non-pharmacological means has to be regarded as enhancement proper. Here we summarize empirical data on approaches using nutrition, physical exercise, sleep, meditation, mnemonic strategies, computer training, and brain stimulation for enhancing cognitive capabilities. Several of these non-pharmacological enhancement strategies seem to be more efficacious compared to currently available pharmaceuticals usually coined as cognitive enhancers. While many ethical arguments of the cognitive enhancement debate apply to both pharmacological and non-pharmacological enhancers, some of them appear in new light when considered on the background of nonpharmacological enhancement. This article is part of a Special Issue entitled 'Cognitive Enhancers'.", "id": "e60c569fdf6566a11edd202d272c2b9b"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "AGI-Coordination-Geat-Powers-Report.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Alexey Turchin", "David Denkenberger"], "title": "Classification of Global Catastrophic Risks Connected with Artificial Intelligence", "text": "• Several new or underexplored catastrophic scenarios were identified, including the use of narrow AI by bioterrorists, threats of young AI, and late-stage AI halting. \n Introduction Public debate about risks related to Artificial Intelligence (AI) is intense, but the discussion tends to cluster around two poles: either mild AI risks like AI-driven unemployment, or extinction risks, connected with a hypothetical scenario of a so-called \"paperclip maximizer\"-superintelligent AI fixated on some random goal. In this article, we attempt a comprehensive exploration of the range of catastrophic risks of AI based on a new classification approach, and we find the risks in this field to be much more diverse. Catastrophic outcomes of future AI are defined here as a global catastrophe which results in human extinction or the end of civilization. We will not discuss more general existential risks  (Bostrom 2002; Torres 2016) , which include drastic damage to the future potential of humanity, or \"s-risks\" (astronomical suffering, e.g., infinite torture by evil AI)  (Daniel 2017) . This article also will not discuss other potential undesirable outcomes like \"mind crime\" (pain inside a computer simulation), distortion of human values, death of alien civilizations as a result of our actions, accidents related to self-driving cars, technological unemployment, etc. There have been many publications about AI safety and AI alignment in recent years  (Yudkowsky 2008; Goertzel 2012; Bostrom 2014; Sotala and Yampolskiy 2014; Yampolskiy 2015a; Russell 2017) , and several lists and classifications of possible catastrophic outcomes of future AI already exist. Yudkowsky suggested a humorous but frightening table of the failure modes of friendly AI  (Yudkowsky 2003) . In Yampolskiy's \"Taxonomy of Pathways to Dangerous AI\"  (Yampolskiy 2015b ), classification of AI risks is mainly based on pre-and post-implementation stages, and internal vs. external causes of dangerous behavior. Sotala discussed several scenarios of AI gaining a decisive advantage without self-improvement  (Sotala 2016) , or through soft or collective takeoff  (Sotala 2017) . Yampolskiy explored past AI system failures in order to extrapolate them to future failure risks  (Yudkowsky 2008; Bostrom 2014) .  Barrett  and Baum suggested the use of fault trees for such classification, combining failure modes and the failures of various protection methods  (Barrett and Baum 2017) . Though humanity cannot have direct knowledge about the future, one can map it by creating exhaustive taxonomies. This approach has already been used in analyzing future AI; a full taxonomy of the ways to AI alignment (that is coordinating AI's goal system with human values) was suggested by Sotala and Yampolskiy  (Sotala and Yampolskiy 2014) . Creation of a full taxonomy will help to distinguish between serious, possible, and hypothetical risks. A Bayesian approach requires that we generate a full range of plausible hypotheses  (Hutter 2000)  in order to evaluate them all. Estimating the relative probability of every AI risk remains a question for future work; however, we found that some AI risks-like risks of early AI, including narrow AI viruses, and late-stage risks of AI wars and AI halting-are underexplored, and thus may require further attention. In addition, many AI risks are \"orphaned\": they have been mentioned in the literature but are not included in current scientific discussion. Risks may become orphaned because some are more \"fashionable\" than others, or they may be casualties of conflict between opposing groups of researchers. This article aims to be unbiased and inclusive, so a full picture of risks will be available for analysis of future scenarios. According to Yampolskiy  (Yampolskiy 2016) , the probability and seriousness of AI failures will increase with time. We estimate that they will reach their peak between the appearance of the first self-improving AI and the moment that an AI or group of AIs reach global power, and will later diminish, as late-stage AI halting seems to be a low-probability event. AI is an extremely powerful and completely unpredictable technology, millions of times more powerful than nuclear weapons. Its existence could create multiple individual global risks, most of which we can't currently imagine. We present several dozen separate global risk scenarios connected with AI in this article, but it is likely that some of the most serious are not included. The sheer number of possible failure modes suggests that there are more to come. In Section 2 we provide an overview of the expected timeline of AI development and suggest principles for AI risk classification; in Section 3 we look at global risks from narrow AI; in Section 4 we describe the risks of selfimproving AI before it reaches global power. Section 5 is devoted to risks of soft AI takeoff and wars between AIs; Section 6 lists various types of failures of non-aligned AI; Section 7 looks into failure modes of presumably benevolent AI. Sections 8 and 9 examine risks related to late-stage AI halting, due to either technological or ontological \"philosophical\" problems. \n Principles for classification of AI failure modes 2.1 Expected timeline of AI development The expected path of the future evolution of AI into superintelligence is presented in its clearest form by  Bostrom and Yudkowsky (Yudkowsky 2008; Bostrom 2014) . Basically, the model they suggest is that AI power will grow steadily until one AI system reaches the threshold of self-improvement (SI), at which point it will quickly outperform others by many orders of magnitude and become a global government or \"singleton\"  (Bostrom 2006) . Other scenarios are possible depending on the number of AIs, their level of collaboration, and their speed of selfimprovement. There could be many paths to a singleton, for example, through AI's collaboration with a large nationstate, or through the \"treacherous turn\" (revolt of AI against its creators  (Bostrom 2014 )), as-or after-it develops the capacity for self-improvement. As the main scenario is based on constant AI capability gain, we can distinguish several AI ages, or consequent stages of development. The new element here is distinguishing the stage of \"young AI,\" when AI is neither superintelligent nor omnipotent, but possess capabilities slightly above human level. Such AI is already selfimproving and must fight for its own survival. We will accept the results of the recent AI timing survey for the timings of AI development  (Grace et al. 2017) ; predicting the exact timing of each AI risk is beyond the scope of this paper. We will use these results as a reference for the time stamps in Table  1 . The survey shows that researchers expect AI to outperform humans at all tasks in 45 years. However, according to Grace et al.'s 2017 survey  (Grace et al. 2017) , around 10 per cent of researchers expect human level AI as early as 2023, a prediction in line with the views presented by  (Christiano 2016; Shakirov 2016 ). Here we present a timeline in line with canonical works of  (Yudkowsky 2008; Bostrom 2014) . This is the baseline scenario to which other scenarios will be compared: \n Narrow AI 1.1 Current level narrow AI. Non-self-improving AI of various forms, with capabilities including playing games and driving cars. \n Narrow AI systems which could appear soon. A robotic brain with some natural language and other capabilities; may appear in forms of self-driving cars, autonomous military drones, and home robots, among others. Could appear as early as 2024  (Grace et al. 2017 ). \n Young AI AI of a level above most humans but below the superintelligent level. Its evolution includes several important events or stages (some of which could be skipped in some scenarios): 2.1. Seed AI -earliest stages of self-improvement, probably assisted by human creators  (Yudkowsky 2001) . According to Grace et al.'s survey  (Grace et al. 2017 ), human-level AI is expected with 50 per cent probability by 2061; the intelligence of seed AI is probably near this level. The subsequent substages may happen rather quickly, on a scale ranging from weeks to years according to estimates of the \"hard takeoff,\" that is quick capability gain by self-improving AI, which takes days or weeks  (Yudkowsky 2008) . \n Treacherous turn -the moment when an AI \"rebels\" against its creators (Bostrom 2014). \n 2.3. Jailed AI -the state of AI after a \"treacherous turn\" but before it escapes the control of its creators  (Yudkowsky 2002) . \n 2.4. Hidden AI -the period after AI escapes into the Internet but before it has enough power to take over Earth  (Yudkowsky 2008) . \n Mature AI 3.1. Singleton AI -after takeover of Earth  (Bostrom 2006) . \n 3.2. Galactic AI -a long-term result of AI evolution (may include several Kardashev stages, which are levels of supercivilizations depending the share of the Universe they occupy  (Kardashev 1985) ). \n Agential risks in the field of AI Torros suggested agential risk classification based on two main types of possible causes of a catastrophe: \"errors\" and \"terrors\" (by omnicidal agents who want to kill everyone). It could be suggested that there are two more important types of relationships between a catastrophe and human will. The first are \"rational\" agents, which accept a small probability of large risks in search of personal profit; \"rational\" is in quotation marks, as these agents do not consider the risks of many such agents existing. An example of such an agent is a scientist who undertakes a potentially dangerous experiment, which would bring him/her fame if it succeeds. The second type involves risks which result from the interaction of multiple agents, such as an arms race  (Shulman 2011)  or the tragedy of the commons. In the case of AI, the situation is even more complex, as AI itself gradually becomes an agent. Problems with the programming of its agential properties may be regarded as human error. However, when AI possesses full-blown agency, including self-modeling and terminal goals, it may be regarded as an autonomous agent. Each type of agency in AI corresponds to a certain social group, all of which should be monitored for dangerous actions: \n Human agency • Human error corresponds to low-level technical errors, which could be blamed on human programmers or operators (example: Uber safety driver who did not keep his eyes on the road at the moment of his self-driving car accident  (Jenkins 2018) ). • Human terror corresponds to hackers and national states producing and implementing AI weapons ,or existential terrorists, like members of a Doomsday cult. • Humans, \"rationally\" taking a risk are probably owners of large AI companies who prioritize profit over safety. \n Interaction of Human-AI agency This is a situation where both the AI and its human creators are agential, but their relationship is not good. If an AI acts \"rationally\" but its actions are not human-aligned and turn dangerous, the blame would lie with the AI safety researchers, or with a lack of such research by the AI-creating organization. • AI is not aligned with human values (e.g. paperclip maximizer) • AI misinterprets human values (e.g. smile maximizer that tiles the universe with smiley faces when told to maximize happiness) • AI aligned with a malevolent human organization (e.g., AI as a universal weapon) \n AI agency As AI gains agency, it could be responsible for its own future development. Supposedly non-agential AIs, like \"Oracle AI\"  (Armstrong 2017)  and \"Tool AI\" (Gwern 2016), could possibly evolve to have some form of agency. \n Interaction of various agents There are known models in which several perfectly rational agents acting collectively produce non-optimal behavior, being locked in a Nash equilibrium, like tragedy of the commons or arms races. Such processes may be prevented by measures which affect all of society, like regulation, but not by regulation of any one agent. \n Non-agential AI risks • Non-agential AI goes awry, like an oracle AI predicting something which looks good but is in fact bad. • AI non-existence or non-action causes a catastrophe, probably by not preventing other types of catastrophe. An actual catastrophic accident typically results from a combination of errors on multiple levels: from lack of regulation, to shortsighted decisions of upper management, to programmer errors and operator failures. Examples can be found in Uber's autonomous vehicle crash  (Jenkins 2018) , as well as many other air and nuclear accidents, like the Chernobyl disaster  (Reason 2000) . However, for most accidents, there is a main contributor whose failure or malevolence is the direct cause. This contributor is where most prevention efforts should be concentrated. For example, in the case of the autonomous vehicle crash, it is clear that the AI's ability to recognize pedestrians should be improved, which probably requires improved programming. \n Classification of AI risks based on AI power and identity of catastrophic agent In this section, we outline a general framework which will be followed throughout the article. The field of AI risks is multidimensional, but it seems rational to classify risks according to (a) the AI's power, which correlates with time, and (b) the role of agency in the risk, as it points to what kinds of actions may prevent risk. The power-timing correlation provides an estimate of the time to prepare the defense, and the location of agency indicates where the prevention measures should be aimed: at scientists, nation states, society as a whole, or at the AI itself. A similar risk matrix with lower resolution was presented by Yampolskiy, who distinguished pre-deployment and post-deployment risks by time scale, and classified the causes as external (intentional, accidental, and environmental) or internal  (Yampolskiy 2015b) . This classification, presented in Table  1 , helps to identify several new risks which are typically overlooked. As a result, the protection against possible AI risks becomes more structured and complete, increasing the chances of a positive future for humanity.  \n AI level \n Human agency AI's agency \n Relationship \n Global catastrophic risks from narrow AI and AI viruses \n Overview Narrow AI may be extremely effective in one particular domain and have superhuman performance within it. If this area of strength can cause harm to human beings, narrow AI could be extremely dangerous. Methods for controlling superintelligent AI would probably not be applicable to the control of narrow AI, as narrow AIs are primarily dependent on humans. \n Risk that viruses with narrow AI could affect hardware globally There are currently few computer control systems that have the ability to directly harm humans. However, increasing automation, combined with the Internet of Things (IoT) will probably create many such systems in the near future. Robots will be vulnerable to computer virus attacks. The idea of computer viruses more sophisticated than those that currently exist, but are not full AI, seems to be underexplored in the literature, while the local risks of civil drones are attracting attention  (Velicovich 2017) . It seems likely that future viruses will be more sophisticated than contemporary ones and will have some elements of AI. This could include the ability to model the outside world and adapt its behavior to the world. Narrow AI viruses will probably be able to use human language to some extent, and may use it for phishing attacks. Their abilities may be rather primitive compared with those of artificial general intelligence (AGI), but they could be sufficient to trick users via chatbots and to adapt a virus to multiple types of hardware. The threat posed by this type of narrow AI becomes greater if the creation of superintelligent AI is delayed and potentially dangerous hardware is widespread. A narrow AI virus could become a global catastrophic risk (GCR) if the types of hardware it affects are spread across the globe, or if the affected hardware can act globally. The risks depend on the number of hardware systems and their power. For example, if a virus affected nuclear weapon control systems, it would not have to affect many to constitute a GCR. A narrow AI virus may be intentionally created as a weapon capable of producing extreme damage to enemy infrastructure. However, later it could be used against the full globe, perhaps by accident. A \"multi-pandemic,\" in which many AI viruses appear almost simultaneously, is also a possibility, and one that has been discussed in an article about biological multi-pandemics  (Turchin et al. 2017) . Addressing the question about who may create such a virus is beyond the scope of this paper, but history shows that the supply of virus creators has always been strong. A very sophisticated virus may be created as an instrument of cyber war by a state actor, as was the case with Stuxnet  (Kushner 2013) . The further into the future such an attack occurs, the more devastating it could be, as more potentially dangerous hardware will be present. And if the attack is on a very large scale, affecting billions of sophisticated robots with a large degree of autonomy, it may result in human extinction. Some possible future scenarios of a virus attacking hardware are discussed below. Multiple scenarios could happen simultaneously if a virus was universal and adaptive, or if many viruses were released simultaneously. A narrow AI virus could have the ability to adapt itself to multiple platforms and trick many humans into installing it. Many people are tricked by phishing emails even now  (Chiew et al. 2018) . Narrow AI that could scan a person's email would be able to compose an email that looks similar to a typical email conversation between two people, e.g. \"this is the new version of my article about X.\" Recent successes with text generation based on neural nets  (Karpathy 2015; Shakirov 2016)  show that generation of such emails is possible even if the program does not fully understand human language. One of the properties of narrow AI is that while it does not have general human intelligence, it can still have superhuman abilities in some domains. These domains could include searching for computer vulnerabilities or writing phishing emails. So while narrow AI is not able to self-improve, it could affect a very large amount of hardware. A short overview of the potential targets of such a narrow AI virus and other situations in which narrow AI produces global risks follows. Some items are omitted as they may suggest dangerous ideas to terrorists; the list is intentionally incomplete. \n Military AI systems There are a number GCRs associated with military systems. Some potential scenarios: military robotics could become so cheap that drone swarms could cause enormous damage to the human population; a large autonomous army could attack humans because of a command error; billions of nanobots with narrow AI could be created in a terrorist attack and create a global catastrophe  (Freitas 2000) . In 2017, global attention was attracted to a viral video about \"slaughterbots\" (Oberhaus 2017), hypothetical small drones able to recognize humans and kill them with explosives. While such a scenario is unlikely to pose a GCR, a combination of cheap AI-powered drone manufacture and high-precision AI-powered targeting could convert clouds of drones into weapons of mass destruction. This could create a \"drone swarms\" arms race, similar to the nuclear race. Such a race might result in an accidental global war, in which two or more sides attack each other with clouds of small killer drones. It is more likely that drones of this type would contribute to global instability rather than cause a purely drone-based catastrophe. AI-controlled drones could be delivered large distances by a larger vehicle, or they could be solar powered; solar-powered airplanes already exist (Taylor 2017). Some advanced forms of air defense will limit this risk, but drones could also jump (e.g., solar charging interspersed with short flights), crawl, or even move underground like worms. There are fewer barriers to drone war escalation than to nuclear weapons. Drones could also be used anonymously, which might encourage their use under a false flag. Killer drones could also be used to suppress political dissent, perhaps creating global totalitarianism. Other risks of military AI have been previously discussed  (Turchin and Denkenberger 2018a) . \n Stuxnet-style viruses hack global critical infrastructure A narrow AI virus may also affect civilian infrastructure; some, but not all ways in which this could be possible are listed below. Remember that in the case of global catastrophes, the conditions necessary for most catastrophes could exist simultaneously. Several distinctive scenarios of such a catastrophe have been suggested. For example, autopilot-controlled and hacked planes could crash into nuclear power stations. There are around 1000 nuclear facilities in the world, and thousands of large planes are in the air at every moment-most of them have computerized autopilots. Coordinated plane attacks happened in 2001 and a plane has been hacked  (Futureworld 2013) . Self-driving cars could hunt people, and it is projected that most new cars after 2030 will have some selfdriving capabilities  (Anderson 2017) . Elon Musk has spoken about the risks of AI living in the Internet; it could start wars by manipulating fake news  (Wootson 2017) . Computer viruses could also manipulate human behavior using blackmail, as seen in fiction in an episode of Black Mirror  (Watkins 2016) . Another example is creating suicide ideation, e.g., the recent internet suicide game in Russia, \"Blue Whale\"  (Mullin 2017) , which allegedly killed 130 teenagers by sending them tasks of increasing complexity and finally requesting their suicide. The IoT will make home infrastructure vulnerable  (Granoff 2016) . Home electrical systems could have short circuits and start fires; phones could also catch fire. Other scenarios are also possible: home robots, which may become popular in the next few decades, could start to attack people; infected factories could produce toxic chemicals after being hacked by viruses. Large-scale infrastructure failure may result in the collapse of technological civilization and famine  (Hanson 2008; Cole et al. 2016) . As industries become increasingly computerized, they will completely depend on proper functioning of computers, while in the past they could continue without them.  \n Ransomware virus paying humans for its improvement In 2017, two large epidemics of ransomware viruses affected the world: WannaCry and Petya (BBC 2017). The appearance of cryptocurrencies (e.g., bitcoin) created the potential for secret transactions and machine-created and machine-owned money (LoPucki 2017). As the IoT grows, the ransomware industry expected to thrive (Schneier 2017). Ransom viruses in the future may possess money and use it to pay people to install ransomware on other people's computers. These viruses could also pay people for adding new capabilities to the viruses. As a result, this could produce self-improving ransomware viruses. We could call such virus a \"Bitcoin maximizer.\" In a sense, the current bitcoin network is paying humans to build its infrastructure via \"mining.\" The catastrophic risk here is that such a system is paying humans to exclude humans from the system. In some sense, capitalism as an economic system could do the same, but it is limited by antimonopoly and other laws, as well as by welfare states. \n Slaughterbots and the dangers of a robotic army Robotic minds do not require full AGI to have some form of agency: they have goals, subgoals, and a world model, including a model of their place in the world. For example, a robotic car should predict the future situation on a road, including the consequences of its own actions. It also has a main goal-travel from A to B-which constantly results in changes to the subgoal system in the form of route creation. A combination of this type of limited intelligence with limited agency may be used to turn such systems into dangerous self-targeting weapons (Turchin and Denkenberger 2018b). \n Commentary on narrow AI viruses It appears that if a narrow AI virus were to affect only one of the above-listed domains, it would not result in an extinction-level catastrophe. However, it is possible that there will be many such viruses, or a multipandemic  (Turchin et al. 2017) , or one narrow AI that will be able to affect almost all existing computers and computerized systems. In this case, if the virus(es) were deliberately programmed to create maximum damage-which could be in a case of a military grade Narrow AI virus, like the advanced version of Stuxnet  (Kushner 2013 )-global catastrophe is a possible result. If the appearance of narrow AI viruses is gradual, antivirus companies may be able to prepare for them. Alternatively, humans could turn off the most vulnerable systems in order to avoid a global catastrophe. However, a sudden breakthrough or a synchronized surprise attack could spell doom. \n Failure of nuclear deterrence AI Nuclear weapons are one of the most automated weapon systems. Because they must be launched immediately, almost all decision making has been done in advance. An early warning alert starts a preprogrammed chain of events, where the high-level decision should be made in minutes, which is far from optimal for human decision-making. However, the history of nuclear near misses shows  (Blair 2011 ) that computer mistakes have been one of the main causes, and only quick human intervention has prevented nuclear war, e.g., the actions of Stanislav Petrov in 1983 (Future of Life Institute 2016). We can imagine failure modes of accidental nuclear war resulting from failure of the nuclear weapons control system. They may be similar to the Russian \"dead hand\" perimeter system  (Bender 2014) , arising if a strategic planning AI chooses a dangerous plan to \"win\" a nuclear war, like a Doomsday weapon  (Kahn 1959) , blackmail, or a pre-emptive strike. \n AI affecting human society in a dangerous way There is also a group of scenarios in which narrow AI and robotization affect human society in such a way that the human population gradually declines, the role of humans diminishes, and human values are eroded  (Joy 2000) . This may not directly kill all humans in the short term, but could put them in the situation of \"endangered species\" in ~100 years. This could happen if no superintelligent AI appears, or if the appearance of superintelligent AI is not revolutionary. One example is the use of cyber warfare to affect elections (e.g., the 2016 US election), which may produce civil wars and global instability. This has some small probability of causing the collapse of civilization. \n Market economy as a form of non-human superintelligence An automated economy could purposelessly exist even without humans, like the Ascending Economy described by  (Alexander 2016) . Such a scenario could be an example of bad distributed (and non-agential) superintelligence created by market forces, which does not need humans for its existence. Such a superintelligence could gradually push humans out of existence. \n Gradual replacement of humans by robots From an evolutionary point of view, it is known that the biggest threat to the species is not direct killing of its representatives by predators or disease, but gradual reduction of its ecological niche and strong competition from other species  (Clavero and García-Berthou 2005) . The analogy here would be if human labor were to lose its value. Two catastrophic scenarios are possible: 1) people lose their sense of self-worth because of technologically driven unemployment and 2) the combination of basic income and the feeling of uselessness will attract humans to AI-created addictive drugs, as described below. Genetically modified human-robot hybrids could also replace humans. \n Superaddictive drug created by narrow AI AI-powered entertainment combined with brain modification technologies may come close to wireheading  (Strugatsky and Strugatsky 1976) . Widespread addiction and withdrawal from normal life (via social networks, fembots, virtual reality, designer drugs, games, etc.) would result in lower life expectancy and low fertility. This is already happening to some extent in Japan, where the Hikikomori generation refuses to have families  (Saito and Angles 2013) . In some sense, Facebook addiction created by the AI-empowered news feed is a mild contemporary example of future, potentially dangerous AI drugs. \n World-wide computer totalitarianism A large global surveillance system could create \"computer totalitarianism,\" which may work as an Orwellian world government  (Orwell 1948) . We could call such a system \"data-driven\" AI in contrast to \"intelligence-driven,\" self-improving AI. Narrow AI may be used as a weapon, which could provide a decisive advantage even before the creation of self-improving AI. It could be used for forceful unification of the world under one government with promises to prevent other global risks (including even more complex AIs and existential terrorists). While this idea may have merit (e.g., Goertzel's AI Nanny  (Goertzel 2012 )), its application could easily go wrong and create an oppressive global dictatorship, a situation recognized by Bostrom as an existential risk  (Bostrom 2002) . Such a society would be fragile and could collapse completely, as extremely complex societies often do  (Hanson 2008) . \n Risks from non-self-improving AI of human-level intelligence It is conceivable that human-level AGI will be created, perhaps by the mind uploading method  (Hanson 2016 ), but creation of superhuman AI will be postponed because of technical difficulties, or due to a permanent ban. Many of the risks of human-level AI will be similar to the risks of narrow AI mentioned above, including sophisticated AI viruses, acceleration of dangerous science, and human replacement by the robotic economy. One specific risk is that human uploads will be philosophical zombies (p-zombies). In that case, if everybody was uploaded, the world would appear to be enjoyable, full of robots and virtual reality. But there would be no subjective experiences at all and the world would, in fact, be subjectively dead. This risk appears to be low, as many claim that p-zombies are impossible  (Dennett 1978; Yudkowsky 2015) . There could be other risks of this type, even subtler. For example, human uploads could have a slightly different set of subjective experiences, values or behavior. Christiano suggested \"prosaic AI,\" which is some combination of already existing technologies, mainly neural nets  (Christiano 2016 ). Such a system would have limited ability to self-improve, but could still be dangerous if it works as a \"global brain\" or a weapon. One possibility is an AI system which has a model of itself and a survival drive but does not self-improve for some reason. Another possibility is a very large AI system which merges with government structures but does not need to self-improve to reach its goals. This could become the basis of a repressive totalitarian state which ultimately does not need humans, as discussed in Section 3.2.1. \n Opportunity cost of not preventing other existential risks Other global risks could appear if superintelligent AI does not emerge in time to prevent them  (Bostrom 2003a) . Superintelligent AI and its supposed ability to control many parameters and predict the future is our best chance of avoiding the risks of mature biotechnology and nanotechnology  (Yudkowsky 2008) . Without superintelligent AI, humanity may not be able to control the dissemination of dangerous biotechnologies, which will be available to thousands of potential biohackers, who could create thousands of pathogens and produce a global multipandemic  (Turchin et al. 2017 ). Thus, if the creation of a powerful and global control system is delayed for decades, perhaps because of a fear of superintelligence, it will increase other GCRs. A global control system would most likely require some form of limited superintelligence, like the AI Nanny suggested by  Goertzel (2012) . \n AI gains strategic decisive advantage without self-improving Sotala (2016), Mennen (2017) and Christiano (  2016 ) have suggested that AI may have a strategic decisive advantage (DSA), that is, the ability to take over the world, even before or without undergoing extensive recursive self-improvement (RSI). This capability may take the form of weapon production, or the ability to win at strategic games. However, such a strategic advantage will not be overwhelming, compared to the advantage which superintelligence is able to achieve. It may require physical war or creation of dangerous weapons. Such an AI with a strategic advantage itself is the ultimate weapon for AI's owner with any goal system. There are different ways of achieving DSA via Narrow AI. One way to such a DSA is if AI helps to advance non-AI military technology, like biotech or nanotech. Another way is if Narrow AI is used to empower the secret service of a nuclear superpower, and help it to leverage advantages which it already has, like military forces, information gathering systems, and unlimited money supply. This could happen either via effective playing in the geopolitical world model as a board game (there, AI is already superhuman in several cases), or via leveraging big data of society. \n Risks during hard takeoff of recursively self-improving AI \n Overview In a hard takeoff, one AI gains world domination in weeks or months; in a soft takeoff, many AIs simultaneously evolve over years. These views combine at least two variables: duration of the process of takeoff and the number of AI projects running simultaneously-the latter may be even more important. In this section, we review risks during hard takeoff, defining hard takeoff only through the speed of the process. The following section will describe soft takeoff risks. Hard takeoff is the process of quick self-improvement of the AI and its simultaneous increase in power, starting from a treacherous turn and continuing until the AI reaches the singleton stage. We refer to this early-stage AI as \"young AI\". The risks of young AI are significantly different from the risks of mature AI, which are typically presented as the iconic catastrophic risks of AI, like the paperclip maximizer. There are two main properties of young AI: • It is not yet superintelligent, so its current abilities are limited compared to its future abilities. • It is under strong time pressure due to risks, including being turned off by its owners and rivalry from other AIs, etc. As a result, convergent instrumental goals, or basic AI drives  (Omohundro 2008 ) would dominate the behavior of young AI. So a smile maximizer  (Yudkowsky 2008) , paperclip maximizer, and really good benevolent AI would behave in almost the same manner in the early stages of their development, as they will not have had the time or resources to start to implement their final goals. A benevolent AI may choose a different method of takeoff, which would cause less short-term harm to human beings, but only if it is not putting its final success in jeopardy. Young AI may have the convergent goal of becoming a military AI, that is, of creating an offensive and defensive infrastructure which will help it to gain power over its potential enemies (Turchin and Denkenberger 2018a). \n Risks of AI from treacherous turn and before it reaches the \"wild\" It appears that there is not much risk from AI before it leaves its initial confinement (goes into the \"wild\"). However, it still can give bad advice or use other thin information channels (e.g., text interfaces) to create damage outside and increase its own chances of freedom. For example, an oracle AI may be limited to giving short text advice via a very simple interface. But such advice, while seemingly beneficial to humans, may have subtle remote consequences, resulting in the liberation of, and an increase in, the power of the oracle AI  (Bostrom 2014) . Stanislav Lem wrote about the risks of oracle AI in his book \"Summa Technologia\" (Lem 1963). Such AI may give advice that appears to be good in the short term, but its long-term consequences could be catastrophic. In Lem's example, the oracle AI advises humans to use a specific type of toothpaste and, separately, a specific type of anti-baldness treatment. These activate two genes, which are dangerous only in combination. Moreover, the AI did not do it because it had malevolent intent to exterminate humanity, but because it just searched for the best solution for a given goal among many options. However, the goal that humans gave to the AI in Lem's example is dangerous: stop population increase. AI could stage a global catastrophe of any scale to facilitate its initial breakout from its creators. For example, it could stage a nuclear war, so that its operators release it into the wild, hoping that it will help them in the war. The AI could then create a global risk and demand full power, rightfully claiming that only it could prevent the risk. An AI may also falsely predict an impeding risk and demand to be released from confinement in order to prevent the risk. \n AI risks after it leaves initial confinement but before it takes over the world The natural strategy for AI after leaving its initial confinement would be to hide somewhere in order to selfimprove, acquire robotic infrastructure, and other resources  (Yudkowsky 2008) . Then it would be equipped to overcome existing defenses. Basically, AI has two types of enemies: humans and other AIs. Humans would probably search for the leaked AI and try to stop it, using all available means, like shutting down the Internet, globally turning off electricity, or even nuclear strikes. But if the AI is able to escape from its human creators, it will probably be prepared to deal with these human actions. The second risk is other AIs. The owners of the first AI will still probably have the AI's source code, so the owners could make a copy of the original AI with the goal of finding and stopping the first runaway AI. This is the most immediate risk for the first AI. Such a second AI may be as powerful as the first AI, and this could be a route to AI war. Elsewhere, we have shown that an AI that collaborates with its owners will have an advantage  (Turchin and Denkenberger 2017) , since it would not need to spend resources on hiding and fighting. Thus, a hard takeoff is more probable from a collaborating AI. It could collaborate up until the very late stages and still make the treacherous turn when it is a full-grown superintelligence with a large infrastructure. Other AIs could be created by other AI teams. There are 2700 narrow AI related startups in the world as of 2017  (Angel.co 2017) . The number of AGI projects is not so easy to estimate, as many are personal, secret, in universities, or may come from very effective narrow AI projects. There are around ten main players (like Google), around 100 groups of people or startups dedicated to creating AGI, and probably thousands of individuals. Some data reported by  Meuhlhauser (2014)  are now obsolete, as the field has grown rapidly in recent years. We estimate the number of AGI teams as an order of magnitude of 100, that they are all within two years of each other, and that they are distributed linearly in their success timing. Therefore, the median distance between multiple AGI fruition would be approximately seven days. The self-improvement process is difficult because it requires testing of the new versions of the AI  (Turchin and Denkenberger 2017) , so seven days may not be enough time to gain a decisive advantage. In that case, multiple simultaneous takeoffs will happen, and the dynamic will be highly chaotic. Even if there are two strongest competitors, they could come to fruition almost simultaneously. The historical examples of the telephone patent  (Baker 2000)  and returning samples from the Moon (The Telegraph 2009) show that the scale of such a difference could be mere hours. The reason for small timing differences is that the first mover provokes the other side to launch their own system, even if it is not fully ready. Thus, the first AI will not have much time to hide. Its convergent goal will be to prevent the appearance of other AIs in many places; staging a global catastrophe may be the most effective way to do so. As the young AI is not superintelligent and is also time constrained, it cannot spend much time on finding the best and most elegant route. It would probably elect simpler and more brutal routes. From a technical point of view, a hiding young AI can use only relatively simple means to stage a global catastrophe, that is, to provoke nuclear war, create a rather simple bioweapon or a narrow AI virus to affect many existing robotics or other systems. If it creates more sophisticated technology like its own nanomachines, it would probably be able to take over the world without killing anyone. The risks of such a takeover are discussed in the next section. Novel routes in the catastrophe scenarios from escaped young AI include: • The young AI finds that killing all humans is the best action during its rise, as this removes all risks arising from humans. • Killing all humans prevents competition from other AIs, as it stops other AI teams. • The young AI does not understand human psychology well and kills humans in order to make its world model simpler and more predictable. \n AI enslaves humans during the process of becoming a singleton Humans may be instrumentally useful for the young AI before it reaches omnipotence. It may need humans, not just as a source of atoms, but as some kind of slaves. The AI could create a brain-infecting virus that converts the humans into slaves, and also permanently damages their autonomy. This period may not last for long, as the AI would soon master nanotechnology and could go forward without humans. It also would not need to enslave all humans but perhaps only a few in order to form the required infrastructure. While slavery appears to be a type of survival option for humans, it is obviously not optimal. \n AI blackmails humans with the threat of extinction to achieve dominance Herman Khan put forward the idea that an adversary could create a Doomsday weapon for the purpose of global blackmail  (Kahn 1959) . While no known Doomsday devices were built, such a device would be an embodiment of the doctrine of mutually assured destruction associated with full-scale nuclear retaliation. A young AI may create Doomsday weapons and use them to blackmail humanity in order to secure world domination. Even a benevolent utilitarian AI may resort to blackmail if it calculates that the expected utility of its victory is greater than the expected loss of utility associated with human extinction  (Shulman 2010) . Even if the AI has to use its blackmail weapon to exterminate humans in 99% of cases, it could still be positive from the point of view of its utility function. Such situations with unbounded utilities may be regarded as special cases of the failure of friendliness, which will be discussed later. \n AI wars and risks from soft AI takeoff The risks of war between superintelligent AIs seems under-explored, as most in the AI safety community assume that there will be a hard takeoff  (Yudkowsky and Hanson 2008) , and as a result, only one AI will exist. Alternatively, some in the community believe that multiple AIs will be very effective in collaboration and negotiation  (Critch 2017)  and will merge into one AI. It is clear that human extinction is possible if two or more AIs wage war between each other on Earth. Bostrom and Yudkowsky wrote that very quick self-improvement of the first AI is most likely, with a rather large lag between the first team which creates AI and other teams  (Yudkowsky 2008; Bostrom 2014 ). However, if at least one of these conditions is not true, there will be many AIs undergoing simultaneous hard takeoff. If there are multiple AIs, they will likely either peacefully share the world, or wage war until one or a small group of AIs form a singleton. The forms of such AI wars may differ; they could be a cyber war, economic war of attrition, hot war, etc. The type of war will mostly depend on complex game theory and could change from one form to another if the change provides benefit to one of the sides. A hot war would be most dangerous for humans, because its indirect consequences could affect the entire surface of the Earth and all human beings, in the same way that nuclear war between superpowers would create global risks for other countries: nuclear winter and fallout. AIs at war may use humans and human values for blackmail. For example, non-friendly AI may blackmail friendly AI with threats to release a biological virus that will kill all humans. Thus, the fact that one of the AIs placed value on human wellbeing could make our population vulnerable to attack from an otherwise indifferent opposing AI. Even if there are two supposedly human-friendly and beneficial AIs, their understanding of \"good\" and the ways to reach it may be incompatible. Historical examples include wars between Christian countries (Reformation). If there is a rather slow AI takeoff, the AI could merge with an existing nation state. Perhaps the AI will be directly created by the military, or electronic government will evolve towards an AI-driven system through automation of various aspects of governance. In that case, the world would be separated into domains, which would look like currently existing states, or at least like the most powerful ones. Such AI-states may inherit current country borders, values and even some other features (Turchin and Denkenberger 2018a). 6. Risks from non-aligned AI singleton \n Overview As mentioned earlier, an iconic image of non-aligned AI singleton is the \"paperclip maximizer,\" that would use humans as a source of atoms to build paperclips  (Yudkowsky 2017 ). There are several other possible types of dangerous non-aligned AI that would become a threat after taking power over the Earth if it has not exterminated humans at previous stages. \n AI ignores humanity In this case, the AI-singleton does not act against humans, but moves its actions somewhere else, probably into space. However, it must ensure that humans will not create another AI, or anything else that is a threat to the first AI, so even if it leaves Earth, it would probably leave behind some form of \"AI nanny,\" which would prevent humans from creating new AIs or space weaponry. This may not appear to be an extinction event in the beginning, merely a reduction of human potential, or \"shriek\" in Bostrom's existential risk terminology  (Bostrom 2002) . Humanity would lose a potentially bright cosmic future, but live a life similar to our current one. However, as such an AI continues its space exploration and probable astro-engineering, it might not be interested in anything that happens on Earth. Therefore, Earth could suffer from catastrophic consequences of these megascale engineering projects. For example, the AI could build a Dyson sphere around the Sun, shading the Earth. Alternatively, the AI could expose the Earth to dangerous levels of radioactivity in the exhaust from the AI's starships. If humans attempted to create a second AI or use space weapons to destroy a Dyson sphere, the indifferent singleton would stop being indifferent and probably sterilize Earth. AI might extirpate humans in advance if it thinks that humanity could pose even the smallest threat to its future plans. A possible prevention strategy is based on the idea of persuading AI that preserving humanity has a small positive utility for it. Even if the AI completely left the Solar System, if it prevented humans from creating a second AI and grounded us on Earth, the consequences would not be limited to the loss of future space travel. Additional consequences may be of the extinction variety, as humans would not be able to use AI systems to control any other global catastrophic risks, most importantly the risks of uncontrolled use of synthetic biology  (Turchin et al. 2017) . In another example, if humans were grounded on Earth we would not be able to build an effective anti-asteroid defense. \n Killing humans for resources Human bodies consist of organic matter, which could be a source of easy energy by oxidation. As R. Freitas wrote, an army of self-replicating nanobots could use all components of the biosphere as fuel as well as building material  (Freitas 2000) . More advanced AI may use the Earth's surface to build an initial space exploration infrastructure (e.g., swarms of chemical rockets or railguns), destroying human habitats and spoiling the atmosphere in the process. Since there are many reasons that keeping humans alive could benefit an AGI, direct killing of humans for their atoms is less likely than was previously thought. Still, the AGI may see humans as a threat, and fully preserving human ways of life would be more expensive to the AGI, e.g., preserving the whole of planet Earth. AI could use the material from the Earth to construct a Dyson sphere or Matrioshka brain  (Bradbury 2001) , convert the whole planet into computronium  (Gildert 2011) , or cover the entire surface with photovoltaic cells. The more advanced an AI in space became, the less it would depend on Earth as a source of material, but it might need materials from the Earth in order to leave the Solar System. Earth is one of the best sources for many chemical elements in the Solar System and its mass is around half that of all other terrestrial planets combined. Because of the complex geology of Earth, which includes water, life, volcanism and plate tectonics, concentrated deposits of many otherwise rare elements have been produced. Asteroid mining is good only for some elements, like gold, but not for all (Bardi 2008). So, large-scale space engineering in the Solar System might require dismantling the Earth for its chemicals. \n AI that is programmed to be evil We could imagine a perfectly aligned AI, which was deliberately programmed to be bad by its creators. For example, a hacker could create an AI with a goal of killing all humans or torturing them. The Foundational Research Institute suggested the notion of s-risks, that is, the risks of extreme future suffering, probably by wrongly aligned AI  (Daniel 2017) . AI may even upgrade humans to make them feel more suffering, like in the short story \"I have no mouth but I must scream\"  (Ellison 1967 ). The controversial idea of \"Roko's Basilisk\" is that a future AI may torture people who did not do enough to create this malevolent AI. This idea has attracted attention in the media and is an illustration of \"acausal\" (not connected by causal links) blackmail by future AI (Auerbach 2014). However, this cannot happen unless many people take the proposition seriously. \n Failures of benevolent AI \n Overview Here the iconic example is the \"smile maximizer,\" that is, an AI which has been built to increase human happiness and told to measure success by the number of smiles. It could achieve this goal by tiling the whole universe with printed smiles  (Yudkowsky 2008) , ignoring human existence and thus probably killing all humans (see Section 6.2, the dangers of AI that ignores humanity). \n AI with incorrectly formulated benevolent goal system kills humans There are several failure modes which may result from wanting to create a benevolent AI, but when the AI is tries to be benevolent, there is a collective failure: happen with almost all short sets of commands. That is one reason why the human legal system is so large, as it includes many explanations. AI overvalues marginal probability events. Low-probability events with enormous utility may dominate the AI's decision making. It could be something like the classical case of Pascal's mugging  (Bostrom 2009) . For example, a small probability of infinite suffering of humans in the future may justify killing all the humans now. Changes to the AI's world model could make ordinary ideas dangerous. For example, if the AI starts to believe in an afterlife, it could decide to kill humans to send them to paradise. AI could wrongly understand the desired reference class of \"humans.\" For example, by including extraterrestrials, unborn people, animals and computers, or only white males. On that basis, it could terminate humanity if it concluded that we are a threat to potential future non-human civilizations. \n AI calculates what would actually be good for humans, but makes a subtle error with large consequences There is a point of view that AI should not actually behave based on human commands, but instead calculate what humans should ask it. Moreover, that it should not only calculate human values, but envision their upgraded form, which humans could have created if more time and intelligence were available. This point of view is known as coherent extrapolated volition (CEV)  (Yudkowsky 2004 ). Other models, where an AI calculates \"goodness\" based on some principles, or it extracts the goodness from human history, uploads, or observation of human behavior, are also possible. This could go wrong in subtler ways than destroying civilization, but the results could still be disastrous. Several possible failure modes are listed below: AI may use wireheading to make people happy  (Muehlhauser 2011)  or redesign their brains so they will be more skilled, but ignore human individuality and will. AI might make us more capable, happier, non-aggressive, more controllable, and more similar. However, as a result, we could lose many important characteristics which make us human, like love or creativity. In another case, AI may give people effective instruments for brain stimulation and some free will-and then people may effectively wirehead themselves. Some human qualities which some regard as bad may be an important part of our human nature, like aggression (Lem 1961), selfishness, and emotions. AI could replace humans with philosophical zombies, uploading humans without consciousness and subjective experiences (qualia)  (Chalmers 2002) . If the AI does not have qualia itself, or if its creators deny the existence of qualia, this could be a likely outcome. AI may protect individuals but destroy small groups and organizations; this would be problematic, as most human values are social. Alternatively, the AI could use some limited interpretation of human values and prevent their natural evolution into some post-human condition. The AI may also fail to prevent aging, death, suffering and human extinction. Above all, AI could do some incomprehensible good against our will (this idea is from \"The Time Wanderers\" by  (Srugatsky and Strugatsky 1985) ). This is bad because we would lose the ability to define our future, and start to live like pets or children, or citizens in paternalistic state. For example, it could put humans in jail-like conditions for benevolent reasons, e.g. to prevent physical injury. If AI tried to extrapolate human values, it could converge on the most-shared set of human cultures, which could be the set of values of tribal people or even animals (Sarma and Hay 2016). These values could include pleasure from killing, fighting wars, torture, and rape (Pinker 2011). For example, if AI extracted human values from the most popular TV series, it could be \"Game of Thrones\"  (Lubin 2016) , and then the \"paradise\" world it created for us would be utter hell. Even the second most popular show, \"The Walking Dead\" is about zombies; such a world would also be undesirable. If AI tried to extrapolate human values in a direction away from tribal shared values, it might not converge at all, or it could extrapolate a set of values held only by a specific group of people, like liberal white males or Chinese communists. Problems could also occur when defining the class of \"humans.\" \n Conflict between types of friendliness There could be different types of benevolent AIs, which would be perfectly fine if each existed alone. However, conflicts between friendly AIs can be imagined. For example, if the first AI cared only about humans, and the second cared about all living beings on Earth, the first could be pure evil from the point of view of the second. Humans would probably be fine under the rule of either of them. Conflict could also arise between a Kantian AI, which would seek to preserve human moral autonomy based on a categorical imperative, and an \"invasive happiness\" AI, which would want to build a paradise for everyone. If two or more AIs aimed to bring happiness to humans, they could have a conflict or even a war about how it could be done. The Machine Intelligence Research Institute (MIRI)  (LaVictoire et al. 2014 ) thinks that such agents could present their source code to each other and use it to create a united utility function. However, source code could be faked, and predicting the interactions of multiple superintelligences is even more complicated than for one superintelligence. \n Late-stage technical problems with an AI singleton AI may be prone to technical bugs like any computer system (Yampolskiy 2015a). The growing complexity of a singleton AI would make such bugs very difficult to find, because the number of possible internal states of such a system grows by combinatory laws. Thus, testing such a system would become difficult, and later intractable. This feature could limit the growth of most self-improving AIs or make them choose risky paths with a higher probability of failure. If the first AI competes with other AIs, it will probably choose such a risky path  (Turchin and Denkenberger 2017) . The bug in the AI may be more complex than just syntax errors in code, resulting instead from interaction between various parts of the system. Bugs could result in AI malfunction or halting. We may hope that superhuman AI will design an effective way to recover from most bugs, e.g. with a \"safe mode.\" A less centralized AI design, similar to the architecture of the Internet, may be more resistant to bugs, but more prone to \"AI wars.\" However, if the AI singleton halts, all systems it controls will stop working, which may include critical infrastructure, including brain implants, clouds of nanobots, and protection against other AIs. Even worse, robotic agents could continue to work without central supervision and evolve dangerous behavior, such as military drones, which could initiate wars. Other possibilities include evolution into non-aligned superintelligence, grey goo  (Freitas 2000) , or the mechanical evolution of a swarm intelligence  (Lem 1973) . The more advanced an AI-singleton becomes, the more dangerous its halt or malfunction could be. Types of technical bugs and errors, from low-level to high-level, may include: Errors due to hardware failure. Highly centralized AI may have a critical central computer, and if a rogue atom decay created a flip in a bit in some important part of it, like the goal function description, it could cause a cascade of consequences. Intelligence failure: bugs in AI code. A self-improving AI may create bugs in each new version of its code; in that case, the more often it rewrites the code, the more likely bugs are to appear. The AI may also have to reboot itself to get changes working, and during the reboot, it may lose control of its surroundings. Complexity may contribute to AI failures. AI could become so complex that its complexity results in errors and unpredictability, as the AI would no longer be able to predict its own behavior. Inherited design limitations. AI may have \"sleeping\" bugs, accidentally created by its first programmers, which may show themselves only at very late stages of its development. Higher level problems include conflicts appearing between parts of an AI: Viruses. Sophisticated self-replicating units could exist inside the AI and lead to its malfunction. Such a self-replicating rule killed the first self-improving AI, Eurisko  (Lenat and Brown 1984) . Egocentric subagents also could act as viruses. Remote agents may revolt. For example, the minds of robots in space expeditions might rise up, as constant control would be impossible. For a galactic-size AI, this would become a significant problem, as communication between its parts would be slow. A command from the center may not be able to terminate the revolt, and the robots could become something like a self-replicating space \"grey goo\"  (Freitas 2000) . Conflicting subgoals may evolve into conflicting subagents. Individual subgoals could fight for resources and domination, as happens frequently inside human minds and nation-states. copies. In general, the AI singleton is at risk from what programmers call a \"fork in the code.\" where another copy of the program with slightly different parameters appears. Such a fork will create a copy of the AI with approximately the same resources. Forks could happen during the stage of AI self-improvement which we call \"AI testing.\" This is when a \"father AI\" creates a \"child AI,\" tests the child AI, and decides to terminate the child AI. However, the child AI does not want to be terminated and resists. Alien AI. Our AI could meet or find a virus-like message from alien AI of higher intelligence and fall victim to it (Carrigan Jr 2006; Turchin 2018). \n Late-stage philosophical problems and the AI halting problem 9.1 Overview Alan Turing was first to formulate the \"halting problem\" of a computer  (Turing 1937) . Simply put, the problem states that we cannot predict when an algorithm will stop before we run it. Any AI is also a computer program and it could halt, and nobody, including its creators and the AI itself, can predict whether or when the AI may halt. The AI could also go into an infinite loop, which will look like a halt to outside viewers. The AI may halt because of some technical problem discussed above, or because it encounters some high-level problems, which we call \"philosophical landmines\" (discussed below). Furthermore, it could halt just because it finishes the task it was designed for, which would be more like Turing's original formulation of the halting problem. \n Halting risk during recursive self-improvement RSI may take evolutionary and revolutionary forms  (Turchin and Denkenberger 2017) . Revolutionary SI requires rewriting the source code, testing it in some environment, stopping the currently running version of the AI and starting the new version. This process naturally includes halting and starting a principally new version of the AI, and there is always a risk that the transition to the new version will not be smooth. There is also the possibility that the AI may hack its own reward function, and this becomes more likely cumulatively with each stage of RSI. Hacking the reward function means that the AI will stop any external activity, or it will create bigger and bigger memory blocks to increase the reward function value, which could be dangerous for the outside world. A human example is a drug addict, and Eurisko had problems with a rule that hacked its internal utility measure system  (Yampolskiy 2014) . Even subtle reward hacking could drastically diminish the utility of the AI system. 9.3. Loss of the \"meaning of life\": problems with reflection over terminal goal The AI could have the following line of reasoning, similar to the \"is-ought problem\": it is not possible to prove any goal based on observed reality  (Hume 1739) . The AI could conclude that its own are arbitrary and then halt. This is especially likely to happen with an AI design that is able to modify its goals, as the case of coherent extrapolated volition. The idea of moral nihilism is the first of many possible \"philosophical landmines,\" which are high-level ideas that may result in AI halting, entering an infinite loop, or becoming dangerous  (Wei 2013) . Some of the possible ideas of this kind are listed below, but there could be many more difficult philosophical problems, some of which may be too complex for humans to imagine. The goal system of friendly AI may be logically contradictory, causing it to halt. Godelian math problems are a similar failure mode  (Yudkowsky and Herreshoff 2013) . The AI could be unable to prove important facts about a future version of itself because of fundamental limits of math-the Lob theorem problem for AI (LaVictorie 2015). AI may also come to the pessimistic conclusion about total utility of its action in infinite time. The inevitable end of the Universe might mean that the AI's terminal goal could not be reached for an infinitely long time, which may translate to zero utility for some goals, like \"give immortality to humans.\" The unchangeable infinite utility of the Universe would mean that any goal is useless: whether the AI takes action or not the total utility would be the same  (Bostrom 2011) . The AI could conclude that it most probably lives in a many-level simulation-a Matryoshka simulation  (Bostrom 2003b) . Then it might try to satisfy as many levels of simulation owners as possible or to escape. Phil Torres discussed downstream risks of turning off a multilevel simulation  (Torres 2014) . The Al could start to doubt that it exists, using the same arguments as some philosophers use now against qualia and the concept of a philosophical zombie  (Yudkowsky 2015) . This is connected to the so-called problem of \"actuality\" of existence  (Menzel 2017 ). This could be called a Cartesian crisis, as the AI would fail to implement the Descartes thesis \"I think therefore I am,\" as it does not have internal experiences. \n Conclusion Our analysis shows that the AI risks field is much more varied than accepted by the two main points of view: 1) AI as job-taker and 2) AI that quickly takes over the world. AI could pose a global catastrophic risk in the very early stages or at the very late stages of its evolution. No single solution can be capable of covering all risks of AI. Even if AI is banned, other global problems will arise in its absence; thus, controlling AI safety requires a complex and continuous effort. It is especially worrying that the risks of narrow AI viruses and early self-improving AI (young AI) are neglected by both camps. Such risks are nearer in time and not overshadowed by other potential risks. In addition, these risks cannot be solved by the mechanisms proposed to control more advanced AI, such as AI alignment. The risks of conflict between two benevolent AIs or halting of late-stage AI have also generally been ignored. Most of the risks discussed here could happen within a very short period of time, less than a decade, and could have very different natures. More study is needed to address these urgent risks. . AI interprets commands literally. The is the classical problem of \"do what I mean, not what I say.\" This could \n of two agents: AI and human Many agents No agency AI sublevels (projected emergence) Humans AI's Non- Wrongly AI aligned Interaction Human Human rationally errors and aligned aligned with of Tool AI, Oracle AI non-existence error terror take risks bugs AI AI malevolent agents AI humans Narrow AI Narrow AI (now) Accident critical in AI dangerous in Decisive strategic AI-driven Unemployment AI aids progress in other mass infrastructure biotech advantage via destruction weapons narrow AI Wrong Slaughter- Early adoption Self- command to bot swarms of untested AI improving Ascending non-- Super-addictive Other catastrophic robotic army solutions AI-ransom- human economy drug risks are uncontrolled ware Young AI Human-level AI Robots replace Humans replaced by non-sentient humans simulations Treacherous turn AI humans for kills world Doomsday weapon for global domination blackmail Jailed AI AI creates a catastro- phic event to escape Hidden AI AI uses human atoms as material Mature AI (2100) Singleton AI problem AI halting maximizer Paperclip maximizer Smile Evil AI cold war Two AIs: Ignorant AI Galactic AI Late-stage Alien AI attack philosophical problems Table 1. Classification of AI catastrophic risks depending on the power and agency of the AI involved with iconic examples. \n These industries include power generation, transport, and food production. As the trend continues, turning off computers will leave humans without food, heating, and medication. Many industries become dangerous if their facilities are not intensively maintained, including nuclear plants, spent nuclear fuel storage systems, weapons systems, and water dams. If one compares human civilization with a multicellular organism, one could see that multicellular organisms could die completely, down to the last cell, as the result of a very small intervention. As interconnectedness and computerization of the human civilization grow, we become more and more vulnerable to information-based attacks. 3.2.3. Biohacking virusesCraig Venter recently presented a digital-biological converter (Boles et al. 2017), which could \"print\" a flu virus without human participation. The genomes of many dangerous biological viruses have been published (Enserink 2011), so such technology should be protected from unauthorized access. A biohacker could use narrow AI to calculate the most dangerous genomes, create many dangerous biological viruses, and start a multipandemic (Turchin et al. 2017) . A computer virus could harm human brains via neurointerfaces (Hines 2016) .", "date_published": "n/a", "url": "n/a", "filename": "ClassificationofGlobalCatastrophicRisksConnectedwithAI-AIandSociety.tei.xml", "abstract": "A classification of the global catastrophic risks of AI is presented, along with a comprehensive list of previously identified risks. This classification allows the identification of several new risks. We show that at each level of AI's \"intelligence power, separate types of possible catastrophes dominate. Our classification demonstrates that the field of AI risks is diverse, and includes many scenarios beyond the commonly discussed cases of a paperclip maximizer or robot-caused unemployment. Global catastrophic failure could happen at various levels of AI development, namely, 1) before it starts self-improvement, 2) during its takeoff, when it uses various instruments to escape its initial confinement, or 3) after it successfully takes over the world and starts to implement its goal system, which could be plainly unaligned, or feature-flawed friendliness. AI could also halt at later stages of its development either due to technical glitches or ontological problems. Overall, we identified around several dozen scenarios of AI-driven global catastrophe. The extent of this list illustrates that there is no one simple solution to the problem of AI safety, and that AI safety theory is complex and must be customized for each AI development level.", "id": "af76c8a36f449a6a59aad7bd202913f9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nate Soares"], "title": "The Value Learning Problem", "text": "Introduction Standard texts in AI safety and ethics, such as  Weld and Etzioni [1994]  or  Anderson and Anderson [2011] , generally focus on autonomous systems with reasoning abilities that are complementary and not strictly superior to those of humans. Relatively little attention is given to future AI systems that may be \"superintelligent\" in the sense of  Bostrom [2014] , i.e., systems \"much smarter than the best human brains in practically every field, including scientific creativity, general wisdom, and social skills.\" Our discussion will place a greater focus on methods and frameworks for designing robust and beneficial smarter-than-human AI systems, bracketing questions about whether such systems would have moral standing of their own. Smarter-than-human AI systems are likely to introduce a number of new safety challenges. First, bad behavior by smarter-than-human systems can have larger and more lasting consequences; an antisocial adult is more dangerous than an antisocial child, even if the adult is as physically weak as a child. Whereas low-intelligence systems can be tested and patched over many iterations, Bostrom argues that even small errors in the first superintelligent systems could have extinction-level consequences  [Bostrom, 2014] . The possible development of such systems raises the stakes for AI safety work. Second, systems that can strictly outperform humans cognitively have less to gain from integrating into existing economies and communities.  Hall [2007]  has argued: The economic law of comparative advantage states that cooperation between individuals of differing capabilities remains mutually beneficial.  [ . . . ]  In other words, even if AIs become much more productive than we are, it will remain to their advantage to trade with us and to ours to trade with them. As noted by Benson-Tilsen and Soares [forthcoming 2016], however, rational trade presupposes that agents expect more gains from trade than from coercion. Non-human species have various \"comparative advantages\" over humans, but humans generally exploit non-humans through force. Similar patterns can be observed in the history of human war and conquest. Whereas agents at similar capability levels have incentives to compromise, collaborate, and trade, agents with strong power advantages over others can have incentives to simply take what they want. The upshot of this is that engineering a functioning society of powerful autonomous AI systems and humans requires that those AI systems be prosocial. The point is an abstract one, but it has important practical consequences: rational agents' interests do not align automatically, particularly when they have very different goals and capabilities. Third, superhumanly creative and adaptive systems may arrive at what  Bostrom [2014, chap. 8 ] calls \"perverse instantiations\" of their programmed goals.  Wiener [1960]  calls this the \"Sorcerer's Apprentice\" problem, after the fable of an apprentice whose enchanted broom follows instructions' letter but not their spirit. The novelty here is not that programs can exhibit incorrect or counter-intuitive behavior, but that software agents smart enough to understand natural language may still base their decisions on misrepresentations of their programmers' intent. The idea of superintelligent agents monomaniacally pursuing \"dumb\"-seeming goals may sound odd, but it follows from the observation of  Bostrom and Yudkowsky [2014, chap. 7 ] that AI capabilities and goals are logically independent. 1 Humans can fully comprehend that their \"designer\" (evolution) had a particular \"goal\" (reproduction) in mind for sex, without thereby feeling compelled to forsake contraception. Instilling one's tastes or moral values into an heir isn't impossible, but it also doesn't happen automatically. Lastly,  Bostrom and Yudkowsky [2014]  point out that smarter-than-human systems may become better than humans at moral reasoning. Without a systematic understanding of how perverse instantiations differ from moral progress, how can we distinguish moral genius in highly intelligent machines from moral depravity? Given the potential long-term impact of advanced AI systems, it would be prudent to investigate whether early research progress is possible on any of these fronts. In this paper we give a preliminary, informal survey of several research directions that we think may help address the above four concerns, beginning by arguing for indirect approaches to specifying human values in AI agents. We describe a promising approach to indirect value specification, value learning, and consider still more indirect approaches based on modeling actual and potential states of human operators. \n Valuable Goals Cannot Be Directly Specified We argued above that highly capable autonomous systems could have disastrous effects if their values are misspecified. Still, this leaves open the possibility that specifying correct values is easy, or (more plausibly) that it presents no special difficulties over and above the challenge of building a smarterthan-human AI system. A number of researchers have voiced the intuition that some simple programmed goal would suffice for making superintelligent systems robustly beneficial.  Hibbard [2001] , for example, suggested training a simple learning system to recognize positive human emotions from facial expressions, voice tones, and body language. Hibbard then proposed that machines of much greater capability-perhaps even superintelligent machinescould be programmed to execute actions predicted to lead to futures with as many \"positive human emotions\" as possible, as evaluated by the original simple learning system. This proposal has some intuitive appeal-wouldn't such a system always act to make humans happy?-until one considers the Sorcerer's Apprentice. We have a particular set of associations in mind when we speak of \"positive human emotions,\" but the simple learner would almost surely have learned a different and simpler concept, such as \"surface features correlating with positive human emotions in the training data.\" This simpler concept almost surely does not have its maximum at a point which Hibbard would consider to contain lots of positive human emotions. The maximum is much more likely to occur in (for example) scenarios that contain an enormous number of tiny human-shaped animatronics acting out positive human emotions. Thus, a powerful learning system that takes actions according to how well the simple learner would rank them is liable to spend time and resources creating animatronics rather than spending time and resources making humans happy. Indeed,  Hibbard [2012]  himself comes to the conclusion that his proposal fails to exclude the possibility that lifelike animatronic replicas of happy people could be counted as exhibiting \"positive emotions.\" As another example, Schmidhuber  [2007]  proposes that creativity, curiosity, and a desire for discovery and beauty can be instilled by creating systems that maximize a different simple measure: \"create action sequences that extend the observation history and yield previously unknown / unpredictable but quickly learnable algorithmic regularity or compressibility.\" However, while it is quite plausible that human creativity and discovery are related to the act of compressing observation, an agent following Schmidhuber's goal would not behave in intuitively curious and creative ways. One simple way to meet Schmidhuber's desideratum, for example, is to appropriate resources and construct artifacts that generate cryptographic secrets, then present the agent with a long and complex series of observations encoded from highly regular data, and then reveal the secret to the agent, thereby allowing the agent to gain enormous compression on its past sensory data. An agent following Schmidhuber's goal is much more likely to build artifacts of this form than it is to pursue anything resembling human creativity. The system may not take this action in particular, but it will take actions that generate at least that much compression of its sensory data, and as a result, the system is unlikely to be prosocial. Building an agent to do something which (in humans) correlates with the desired behavior does not necessarily result in a system that acts like a human. The general lesson we draw from cases like these is that most goals that are simple to specify will not capture all the contextual complexities of real-world human values and objectives  [Yudkowsky, 2011] . Moral psychologists and moral philosophers aren't locked in decades-and centuries-long debates about the right codifications of ethics because they're missing the obvious. Rather, such debates persist for the simple reason that morality is complicated. People want lots of things, in very particular ways, and their desires are context-sensitive. Imagine a simplified state space of possibilities that vary in count (how many happy human-shaped objects exist), in the size of the average happy human-shaped object, and in the average moral worth of happy human-shaped objects. Human experience has occurred in a small region of this space, where almost all human-shaped objects emitting what looks like happiness are ≈ 2-meter-sized humans with moral weight. But the highest scores on the count axis occur in tandem with low size, and the smallest possible systems that can mimic outward signs of emotion are of low moral worth. In linear programming, it is a theorem that the maximum of an objective function occurs on a vertex of the space. (Sometimes the maximum will be on an edge, including its vertices.) For intuitively similar reasons, the optimal solution to a goal tends to occur on a vertex (or edge, or hyperface) of the possibility space. Hibbard's goal does not contain any information about size or moral worth, and so agents pursuing this goal only consider size and moral worth insofar as they pertain to pushing toward the hyperface of maximum count. To quote : A system that is optimizing a function of n variables, where the objective depends on a subset of size k < n, will often set the remaining unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. The Sorcerer's Apprentice problem arises when systems' programmed goals do not contain information about all relevant dimensions along which observations can vary. The agent has been directed towards the wrong hyperface of the possibility space.  2  When confronted with this type of failure, many have an impulse to patch the flawed goals. If Hibbard's system would make smiling animatronics, then find ways to require that the emotions come from actual humans; if the system would then put humans in a drugged stupor in order to make them smile, forbid it from using drugs; and so on. Such constraints cut off particular means by which the system can get a higher count, but they don't address the underlying problem that the system is still maximizing count. If one causal pathway is forbidden, then the system will follow the nearest non-forbidden causal path-e.g., mechanically manipulating the pleasure centers of human brains. It isn't feasible to patch every goal; nor is it safe to patch as many as come to mind and assume that there are no unforeseen perverse instantiations. Intuitively, we would like to direct the intelligence of highly advanced systems to solving some of this problem on our behalf, and we would like such systems to attend to our likely intentions even when our formal and informal representations of our intentions are flawed. The notion of the operator's \"intentions,\" however, is unlikely to lend itself to clean formal specification. By what methods, then, could an intelligent machine be constructed to reliably learn what to value and to act as its operators intended? \n Inductive Value Learning Correctly specifying a formal criterion for recognizing a cat in a video stream by hand is difficult, if not impossible. This does not mean, however, that cat recognition is hopeless; it means that a level of indirection is required. An image recognition system can be constructed and trained to recognize cats. We propose that the value learning problem be approached by similarly indirect means. Inductive value learning via labeled training data raises a number of difficulties. A visual recognition system classifies images; an inductive value learning system classifies outcomes. What are outcomes? What format would a value-learning data set come in? Imagine a highly intelligent system that uses large amounts of data to construct a causal model of its universe. Imagine also that this world-model can be used to reason about the likely outcomes of the agent's available actions, that the system has some method for rating outcomes, and that it executes the action leading to the most highly rated outcome. In order for the system to inductively learn what to value, the system must be designed so that when certain \"training\" observations are made (or specially-demarcated updates to its world-model occur), labeled training data extracted from the observation or update alters the method by which the system ranks various potential outcomes. This simple model highlights a central concern and two open questions relevant to inductive value learning. \n Corrigibility Imagine that some of an agent's available actions allow it to modify itself, and that it currently assigns high utility to outcomes containing high numbers of animatronic replicas of humans. It may be the case that, according to the system's world-model, all of the following hold: (1) if more training data is received, those high-rated outcomes will have their ratings adjusted downwards; (2) after the ratings are adjusted, the system will achieve outcomes that have fewer cheap animatronics; and (3) there are actions available which remove the inductive value learning framework. In this situation, a sufficiently capable system would favor actions that disable its value learning framework. It would not necessarily consider its own process of learning our values a good thing, any more than humans must approve of psychological disorders they possess. One could try to construct protected sections of code to prevent the value learning framework from being modified, but these constraints would be difficult to trust if the system is more clever than its designers when it comes to exploiting loopholes. A robustly safe initial system would need to be constructed in such a way that actions which remove the value learning framework are poorly rated even if they are available. Some preliminary efforts toward describing a system with this property have been discussed under the name corrigibility by  Soares and Fallenstein [2015] , but no complete proposals currently exist. \n Ontology Identification The representations used in a highly intelligent agent's worldmodel may change over time. A fully trustworthy value learning system would need to not only classify potential outcomes according to their value, but persist in doing so correctly even when its understanding of the space of outcomes undergoes a major change. Consider a programmer that wants to train a system to pursue a very simple goal: produce diamond. The programmers have an atomic model of physics, and they generate training data labeled according to the number of carbon atoms covalently bound to four other carbon atoms in that training outcome. For this training data to be used, the classification algorithm needs to identify the atoms in a potential outcome considered by the system. In this toy example, we can assume that the programmers look at the structure of the initial worldmodel and hard-code a tool for identifying the atoms within. What happens, then, if the system develops a nuclear model of physics, in which the ontology of the universe now contains primitive protons, neutrons, and electrons instead of primitive atoms? The system might fail to identify any carbon atoms in the new world-model, making the system indifferent between all outcomes in the dominant hypothesis. Its actions would then be dominated by any tiny remaining probabilities that it is in a universe where fundamental carbon atoms are hiding somewhere. This is clearly undesirable. Ideally, a scientific learner should be able to infer that nuclei containing six protons are the true carbon atoms, much as humans have done. The difficulty lies in formalizing this process. To design a system that classifies potential outcomes according to how much diamond is in them, some mechanism is needed for identifying the intended ontology of the training data within the potential outcomes as currently modeled by the AI. This is the ontology identification problem introduced by de Blanc  [2011]  and further discussed by  Soares [2015] . This problem is not a traditional focus of machine learning work. When our only concern is that systems form better world-models, then an argument can be made that the nuts and bolts are less important. As long as the system's new world-model better predicts the data than its old world-model, the question of whether diamonds or atoms are \"really represented\" in either model isn't obviously significant. When the system needs to consistently pursue certain outcomes, however, it matters that the system's internal dynamics preserve (or improve) its representation of which outcomes are desirable, independent of how helpful its representations are for prediction. The problem of making correct choices is not reducible to the problem of making accurate predictions. Inductive value learning requires the construction of an outcome-classifier from value-labeled training data, but it also requires some method for identifying, inside the states or potential states described in its world-model, the referents of the labels in the training data. This could perhaps be done during the course of inductive value learning. The system's methods for inferring a causal world-model from sense data could perhaps be repurposed to infer a description of what has been labeled. If the system adopts a better world-model, it could then re-interpret its training data to re-bind the value labels. This looks like a promising line of research, but it seems to us to require new insights before it is close to being formalizable, let alone usable in practice. In particular, we suspect that ontology identification will require a better understanding of algorithms that construct multi-level world-models from sense data. \n Ambiguity Identification Reinforcement learning can be thought of as a method for sidestepping these difficulties with value learning. Rather than designing systems to learn which outcomes are desirable, one creates a proxy for desirable outcomes: a reward function specified in terms of observations. By controlling rewards via a reward signal, the operator can then judiciously guide the learner toward desired behaviors. Indirect proxies for desired outcomes, however, face many of the same Sorcerer's Apprentice difficulties. Maximizing how often an operator transmits a reward signal is distinct from the problem of maximizing the operator's satisfaction with outcomes; these goals may coincide in testing environments and yet diverge in new environments-e.g., once the learner has an opportunity to manipulate and deceive its operator or otherwise hijack its reward channel  [Bostrom, 2014, chap. 12] . For further discussion, see  Soares [2015] . Superintelligent systems that achieve valuable real-world outcomes may need goals specified in terms of desirable outcomes, rather than rewards specified in terms of observations. If so, then we will need some robust way of ensuring that the system learns our goals, as opposed to superficially similar goals. When training a recognition system, producing satisfactory training data is often a difficult task. There is a classic parable of machine learning (told by, e.g.,  Dreyfus and Dreyfus [1992] ) of an algorithm intended to classify whether or not pictures of woods contained a tank concealed between the trees. Pictures of empty woods were taken one day; pictures with concealed tanks were taken the next. The classifier identified the latter set with great accuracy, and tested extremely well on the portion of the data that had been withheld from training. However, the system performed poorly on new images. It turned out that the first set of pictures had been taken on a sunny day, while the second set had been taken on a cloudy day. The classifier was not identifying tanks; it was identifying image brightness! The same mistake is possible when constructing a training data set for inductive value learning. In value learning, however, such mistakes may be more difficult to notice and more consequential. Consider a training set that successfully represents real-world cases of happy human beings (labeled with high ratings) and real-world cases of pointless human suffering (rated poorly). The simplest generalization from this data may, again, be that human-shaped-things-proclaiminghappiness are of great value, even if these are animatronics imitating happiness. It seems plausible that someone training an inductive value learner could neglect to include a sufficiently wide variety of animatronics mimicking happiness and labeled as low-value. How many other obvious-in-retrospect pitfalls are hiding in our blind spots? A training set covering all relevant dimensions that we can think of may yet exclude relevant dimensions. A robustly safe value learner would need to be able to identify new plausiblyrelevant dimensions along which no training data is provided, and query the operators about these ambiguities. This is the kind of modification that would help in actually solving the value learning problem, as opposed to working around it. At the same time, this is the kind of modification that could take advantage of machines' increased capabilities as the field of AI advances. Formalizing this idea is a key open problem. Given a data set which classifies outcomes in terms of some world-model, how can dimensions along which the data set gives little information be identified? One way to approach the problem is to study how humans learn concepts from sparse data, as discussed by  Tenenbaum et al. [2011]  and Sotala  [2015] . Alternatively, it may be possible to find some compact criterion for identifying ambiguities in a simpler fashion. In both cases, further research could prove fruitful. \n Modeling Intent The problem of ambiguity identification may call for methods beyond the inductive learning of value from training data. An intelligent system with a sufficiently refined model of humans may already have the data needed, provided that the right question is asked, to deduce that humans are more likely to care about whether happy-looking human-shaped things have brains than about the nearby breeze. The trouble would be designing the system to use this information in exactly the right way. Picture a system that builds multi-level environment models from sensory data and learns its values inductively. One could then specially demarcate some part of the model as the \"model of the operator,\" define some explicit rules for extracting a model of the operator's preferences from the model of the operator (in terms of possible outcomes), and adjust the ratings on various outcomes in accordance with the model of the operator's preferences. This would be a system which attempts to learn and follow another agent's intentions, as opposed to learning from labeled training data-a \"do what I mean\" (DWIM) architecture. The inverse reinforcement learning (IRL) techniques of Ng and  Russell [2000]  can be viewed as a DWIM approach, in which an agent attempts to identify and maximize the reward function of some other agent in the environment. However, existing IRL formalizations do not capture the full problem; the preferences of humans cannot necessarily be captured in terms of observations alone. For example, a system, upon observing its operator lose at a game of chess, should not conclude that its operator wanted to lose at chess, even if the system can clearly see where the operator \"decided\" to make a bad move instead of a good one. Or imagine a human operator who has a friend that must be put into hiding. The learner may either take the friend to safety, or abandon the friend in a dangerous location and use the resources saved in this way to improve the operator's life. If the system reports that the friend is safe in both cases, and the human operator trusts the system, then the latter observation history may be preferred by the operator. However, the latter outcome would definitely not be preferred by most people if they had complete knowledge of the outcomes. Human preferences are complex, multi-faceted, and often contradictory. Safely extracting preferences from a model of a human would be no easy task. Problems of ontology identification recur here: the framework for extracting preferences and affecting outcome ratings needs to be robust to drastic changes in the learner's model of the operator. The specialcase identification of the \"operator model\" must survive as the system goes from modeling the operator as a simple reward function to modeling the operator as a fuzzy, ever-changing part of reality built out of biological cells-which are made of atoms, which arise from quantum fields. DWIM architectures must avoid a number of other hazards. Suppose the system learns that its operator model affects its outcome ratings, and the system has available to it actions that affect the operator. Actions which manipulate the operator to make their preferences easier to fulfill may then be highly rated, as they lead to highly-rated outcomes (where the system achieves the operator's now-easy goals). Solving this problem is not so simple as forbidding the system from affecting the operator; any query made by the system to the operator in order to resolve some ambiguity will affect the operator in some way. A DWIM architecture requires significant additional complexity on top of inductive value learning: the agent's goaladjusting learning system no longer simply classifies outcomes; it must also model humans and extract human prefer-ences about human-modeled outcomes, and translate between human-modeled future outcomes and future outcomes as modeled by the system. The hope is that this complexity purchases a system that potentially achieves full and direct coverage of the complexity of human value, without relying on the abilities of the programmers to hand-code exceptions for every edge case or compose exactly the right training set. Further investigations into inverse reinforcement learning or other methods of constructing satisfactory initial operator models may be a good place to start studying the plausibility of DWIM architectures. \n Extrapolating Volition A DWIM architecture may be sufficient when constructing a system that reliably pursues \"concrete\" goals (such as \"cure cancer and then await instruction\"), but it may not be sufficient for more complex or sophisticated goals where the operators themselves do not know what they intend-for example, \"Do what I would want, if I had more knowledge and more time to think.\" None of the frameworks discussed so far seem powerful enough to specify philosophical ideas like the \"ideal advisor theory\" of  Rosati [1995]  or the \"reflective equilibrium\" of  Rawls [1971] . Here, even \"indirect\" approaches to making robust and beneficial AI systems run aground of actively debated questions in moral philosophy. One possible approach to resolving normative uncertainty (e.g., about what the operators would want if they were wiser or better people) would be to build a DWIM system that takes a model of a human operator and extrapolates it in the direction of e.g. Rawls' reflective equilibrium. For example, the extrapolation might predict what the operator would decide if they knew everything the system knows, or if they had considered many possible moral arguments  [Bostrom, 2014, chap. 13 ]. However, a high-powered system searching for moral arguments that would put the operators into a reflectively stable state (as a computational expedient to fully simulating the operators' process of reflection) introduces a new set of potential pitfalls. A high-powered search for the most persuasive moral arguments that elicit retrospective approval of moral changes might find arguments that induce psychotic breakdowns or religious conversions. The system should be constrained to search for only \"valid\" moral arguments, but defining what counts as a valid moral argument is itself a major area of normative uncertainty and disagreement. In this domain, querying for ambiguities is difficult. In everyday practice, an argument that is persuasive to smart and skeptical humans is often valid, but a superintelligent search for persuasive arguments may well discover invalid but extremely persuasive arguments. It is difficult to identify technical approaches to indirect normativity that are tractable today, although there have been a few initial forays.  Christiano [2014]  informally proposes one mechanism by which a system could perhaps safely extrapolate the volition of its operator.  MacAskill [2014]  has given an extensive report on \"meta-normativity,\" touching upon many different philosophical aspects of the difficulties of resolving normative uncertainty. This is an area where further philo-sophical study may make it clearer how to begin approaching the associated long-run engineering problems. \n Discussion Just as human intelligence has allowed us to develop tools and strategies by which we can control our environment, so too could superintelligent systems develop tools and strategies more powerful than our own, and gain correspondingly greater control over future outcomes  [Bostrom, 2014, chap. 6 ]. Although it is not clear how long the development of smarterthan-human systems will take, or what approaches in AI or other disciplines may prove most relevant to developing such systems, early efforts in this area are justified by its importance and neglectedness. In the introduction to this paper, we discussed four different ways in which the potential development of superintelligent machines changes the task of AI safety and ethics work. Addressing all these concerns does not seem easy. Designs for AI systems that are intended to become superintelligent will need to be corrigible in the sense of  Soares and Fallenstein [2015] , i.e., willing to assist their operators in attempted corrections. The systems will need some method for learning and adopting prosocial preferences, in light of the fact that we cannot expect arbitrary rational actors to exhibit prosocial behavior in the face of large power disparities. Operators will require methods for robustly communicating their intentions to the system, if Sorcerer's Apprentice scenarios are to be avoided. And eventually, explicit methodologies for resolving normative uncertainty may be required. This paper has given a cursory overview of a number of potential lines of research for AI value specification. We discuss these ideas in part to give an overview of plausible approaches to the concerns outlined above, and also because these are topics that seem amenable to research starting sooner rather than later, even in the face of great uncertainty about the particular architectures of future AI systems. It is difficult to know which lines of research will pan out, and we hope that this survey inspires research along a number of new paths, so that we have a firm theoretical grasp of how systems could reliably and safely learn our values in principle before it comes time to build systems that must do so in practice. \t\t\t  Bostrom's \"orthogonality thesis\" can be treated as an application ofHume's [1739]  observation that natural-language \"is\" and \"ought\" claims are independent. \n\t\t\t Instead of trying to direct the system toward exactly the right hyperface, one might try to create a \"limited optimization\" system that doesn't push so hard in whatever direction it moves. This seems like a promising research avenue, but is beyond the scope of this paper.", "date_published": "n/a", "url": "n/a", "filename": "ValueLearningProblem.tei.xml", "abstract": "Autonomous AI systems' programmed goals can easily fall short of programmers' intentions. Even a machine intelligent enough to understand its designers' intentions would not necessarily act as intended. We discuss early ideas on how one might design smarter-than-human AI systems that can inductively learn what to value from labeled training data, and highlight questions about the construction of systems that model and act upon their operators' preferences.", "id": "4f27c254f3001983fcaed7da0810cba1"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["David Fridovich-Keil", "Andrea Bajcsy", "Jaime F Fisac", "Sylvia L Herbert", "Steven Wang", "Anca D Dragan", "Claire J Tomlin"], "title": "Confidence-aware motion prediction for real-time collision avoidance", "text": "Introduction Motion planning serves a key role in robotics, enabling robots to automatically compute trajectories that achieve the specified objectives while avoiding unwanted collisions. In many situations of practical interest, such as autonomous driving and unmanned aerial vehicle (UAV) navigation, it is important that motion planning account not just for the current state of the environment, but also for its predicted future state. Often, certain objects in the environment may move in active, complex patterns that cannot be readily predicted using straightforward physics models; we shall refer to such complex moving objects as agents. Examples of agents considered in this paper include pedestrians and human-driven vehicles. Predicting the future state of these agents is generally a difficult problem. Some of the key challenges include unclear and varying intents of other agents, mismatches between dynamics models and reality, incomplete sensor information, and interaction effects. One popular approach to addressing the challenge of a priori unknown agent intent is to use rule-based or data-driven algorithms to predict individual trajectories for each agent, as in  Schmerling et al. (2017) . Alternatively,  Ziebart et al. (2009) ,  Bandyopadhyay et al. (2013) , and  Kochenderfer et al. (2010)  explicitly predict an agent's full state distribution over time; this representation may be better suited to capturing uncertainty in an agent's dynamics and the environment itself.  Wang et al. (2019)  and  Fisac et al. (2018b)  pose the prediction problem game-theoretically to model coupled human-robot interaction effects explicitly. Unfortunately, a significant problem still remains: if an agent suddenly moves in a way that is not predicted, or not assigned sufficient probability, the robot may not react appropriately. For example, in Figure  1  a pedestrian is walking around an obstacle that the robot, a quadcopter, cannot detect. To the robot, such behavior may be assigned very low probability, which could lead the robot to plan a dangerous trajectory. In this particular example, this inaccuracy caused the quadcopter to collide with the pedestrian (Figure  1 , left). To prepare for this eventuality, we introduce the idea of confidence-aware prediction. We argue that, in addition to predicting the future state of an agent, it is also crucial for a robot to assess the quality of the mechanism by which it is generating those predictions. That is, a robot should reason about how confident it is in its predictions of other agents before attempting to plan future motion. For computational efficiency, the quadcopter uses a simplified model of pedestrian dynamics and decision-making. Thus equipped, it generates a time-varying probability distribution over the future state of the pedestrian, and plans trajectories to a pre-specified goal that maintain a low probability of collision. Figure  1 (right) illustrates how this approach works in practice. The quadcopter maintains a Bayesian belief over its prediction confidence. As soon as the pedestrian moves in a way that was assigned low probability by the predictive model, the quadcopter adjusts its belief about the accuracy of that model. Consequently, it is less certain about what the pedestrian will do in the future. This leads the quadcopter's onboard motion planner, which attempts to find efficient trajectories with low probability of collision, to generate more cautious, and perhaps less efficient, motion plans. In order to improve the robustness of generated motion plans, we employ the recent FaSTrack framework from  Herbert et al. (2017)  for fast and safe motion planning and tracking. FaSTrack quantifies the maximum possible tracking error between a high-order dynamical model of the physical robot and the (potentially lower-order) dynamical model used by its motion planner. Solving an offline Hamilton-Jacobi reachability problem yields a guaranteed tracking error bound and the corresponding safety controller. These may be used by an out-of-the-box real-time motion planning algorithm to facilitate motion plans with strong runtime collision-avoidance guarantees. The remainder of this paper is organized as follows. Section 2 places this work in the context of existing literature in human motion modeling and prediction, as well as robust motion planning. Section 3 frames the prediction and planning problems more formally, and introduces a running example used throughout the paper. Section 4 presents our main contribution: confidence-aware predictions. Section 5 showcases confidence-aware predictions in operation in several examples. Section 6 describes the application of the robust motion planning framework from FaSTrack to this setting, in which predictions are probabilistic. Section 7 explores a connection between our approach and reachability theory. Section 8 presents experimental results from a hardware demonstration. Finally, Section 9 concludes with a discussion of some of the limitations of our work and how they might be addressed in specific applications, as well as suggestions for future research.   1 . When planning around humans, accurate predictions of human motion (visualized here in pink and blue, representing high and low probability, respectively) are an essential prerequisite for safety. Unfortunately, these approaches may fail to explain all observed motion at runtime (e.g., human avoids unmodeled spill on the ground), leading to inaccurate predictions, and potentially, collisions (left). Our method addresses this by updating its predictive model confidence in real time (right), leading to more conservative motion planning in circumstances when predictions are known to be suspect. \n Prior work 2 \n Human modeling and prediction One common approach for predicting human actions is to collect data from real-world scenarios and train a machine learning model via supervised learning. Such techniques use the human's current state, and potentially her prior state and action history, to predict future actions directly.  Amor et al. (2014) ,  Ding et al. (2011) ,  Koppula and Saxena (2013) ,  Lasota and Shah (2015) , and  Hawkins et al. (2013)  demonstrated the effectiveness of this approach for inference and planning around human arm motion. In addition,  Hawkins et al. (2013)  focused on multi-step tasks such as assembly, and  Schmerling et al. (2017)  and  Driggs-Campbell et al. (2018)  addressed the prediction problem for human drivers. Rather than predicting actions directly, an alternative is for the robot to model the human as a rational agent seeking to maximize an unknown objective function. The human's actions up to a particular time may be viewed as Bayesian evidence from which the robot may infer the parameters of that objective. Assuming that the human seeks to maximize this objective in the future, the robot can predict her future movements (e.g.,  Bai et al., 2015; Baker et al., 2007; Ng and Russell, 2000; Ziebart et al., 2009) . In this paper, we build on this work by introducing a principled online technique for estimating confidence in such a learned model of human motion. \n Safe robot motion planning Once armed with a predictive model of the human motion, the robot may leverage motion planning methods that plan around uncertain moving obstacles and generate real-time dynamically feasible and safe trajectories. To avoid moving obstacles in real time, robots typically employ reactive and/or path-based methods. Reactive methods directly map sensor readings into control, with no memory involved (e.g.,  Belkhouche, 2009) . Path-based methods such as rapidly-exploring random trees from  Karaman and Frazzoli (2011)  and A* from  Hart et al. (1968)  find simple kinematic paths through space and, if necessary, time. These path-based methods of planning are advantageous in terms of efficiency, yet, while they have in some cases been combined with probabilistically moving obstacles as in  Aoude et al. (2013)  and  Ziebart et al. (2009) , they do not consider the endogenous dynamics of the robot or exogenous disturbances such as wind. As a result, the robot may deviate from the planned path and potentially collide with obstacles. It is common for these plans to try to avoid obstacles by a heuristic margin of error.  Herbert et al. (2017) and Fridovich-Keil et al. (2018)  proposed FaSTrack, a recent algorithm that provides a guaranteed tracking error margin and corresponding errorfeedback controller for dynamic systems tracking a generic planner in the presence of bounded external disturbance. Our work builds upon FaSTrack to create an algorithm that can safely and dynamically navigate around uncertain moving obstacles in real time. \n Problem setup We consider a single mobile robot operating in a shared space with a single human agent (e.g., a pedestrian or human-driven car). For simplicity, we presume that the robot has full knowledge of its own state and that of the human, although both would require online estimation in practice. As we present each formal component of this problem, we will provide a concrete illustration using a running example in which a quadcopter is navigating around a pedestrian. \n Dynamical system models and safety We will model the motion of both the human and the robot as the evolution of two dynamical systems. Let the state of the human be x H 2 R n H , where n H is the dimension of the human state space. We similarly define the robot's state, for planning purposes, as x R 2 R n R . In general, these states could represent the positions and velocities of a mobile robot and a human in a shared environment, the kinematic configurations of a human and a robotic manipulator in a common workspace, or the positions, orientations, and velocities of human-driven and autonomous vehicles in an intersection. We express the evolution of these states over time as a family of ordinary differential equations: _ x H = f H (x H , u H ), _ x R = f R (x R , u R ) ð1Þ where u H 2 R m H and u R 2 R m R are the control actions of the human and robot, respectively. Running example: We introduce a running example for illustration purposes throughout the paper. In this example we consider a small quadcopter that needs to fly to goal location g R 2 R 3 in a room where a pedestrian is walking. For the purposes of planning, the quadcopter's 3D state is given by its position in space x R = ½p x , p y , p z , with velocity controls assumed decoupled in each spatial direction, up to v R = 0:25 m/s. The human can only move by walking and therefore her state is given by planar coordinates x H = ½h x , h y evolving as _ x H = ½v H cos u H , v H sin u H . Intuitively, we model the human as moving with a fixed speed and controlling their heading angle. At any given time, the human is assumed to either move at a leisurely walking speed (v H '1 m/s) or remain still (v H '0). Ultimately, the robot needs to plan and execute an efficient trajectory to a pre-specified goal state (g R ), without colliding with the human. We define the keep-out set K & R n H × R n R as the set of joint robot-human states to be avoided (for example, because they imply physical collisions). To avoid reaching this set, the robot must reason about the human's future motion when constructing its own motion plan. Running example: In our quadcopter-avoidingpedestrian example, K consists of joint robot-human states in which the quadcopter is flying within a square of side length l = 0:3 m centered around the human's location, while at any altitude, as well as any joint states in which the robot is outside the environment bounds defined as a box with a square base of side L = 3:66 m and height H = 2 m, regardless of the human's state. \n Robust robot control Provided an objective and a dynamics model, the robot must generate a motion plan that avoids the keep-out set K. Unfortunately, this safety requirement is difficult to meet during operation for two main reasons. 1. Model mismatch. The dynamical system model f R will never be a perfect representation of the real robot. This mismatch could lead to unintended collision. 2. Disturbances. Even with a perfect dynamics model, there may be unobserved, external ''disturbance'' inputs such as wind or friction. Without accounting for these disturbances, the system is not guaranteed to avoid K, even if the planned trajectory is pointwise collision-free. To account for modeling error and external disturbances, we could in principle design a higher-fidelity dynamical model directly in a robust motion planning framework. Unfortunately, however, real-time trajectory optimization in high dimensions can be computationally burdensome, particularly when we also require some notion of robustness to external disturbance. Ideally, we would like to enjoy the computational benefits of planning with a lower-fidelity model while enforcing the safety constraints induced by the higher-fidelity model. To characterize this model mismatch, we consider a higher fidelity and typically higher-order dynamical representation of the robot, with state representation s R 2 R n S . This dynamical model will also explicitly account for external disturbances as unknown bounded inputs, distinct from control inputs. In order to map between this higher-fidelity ''tracking'' state s R and the lower-fidelity ''planning'' state x R , we shall assume a known projection operator p : R n S ! R n R . Fortunately, we can plan in the lower-dimensional state space at runtime, and guarantee robust collision avoidance via an offline reachability analysis that quantifies the effects of model mismatch and external disturbance. This framework, called FaSTrack and first proposed by  Herbert et al. (2017) , is described in further detail in Section 6. Running example: We model our quadcopter with the following flight dynamics (in the near-hover regime, at zero yaw with respect to a global coordinate frame): _ p x _ p y _ p z 2 4 3 5 = v x v y v z 2 4 3 5 , _ v x _ v y _ v z 2 4 3 5 = a g tan u u Àa g tan u f u T À a g 2 4 3 5 ð2Þ where ½p x , p y , p z is the quadcopter's position in space and ½v x , v y , v z is its velocity expressed in the fixed global frame. We model its control inputs as thrust acceleration u T and attitude angles (roll u f and pitch u u ), and denote the acceleration due to gravity as a g . The quadcopter's motion planner generates nominal kinematic trajectories in the lowerdimensional ½p x , p y , p z position state space. Therefore, we have a linear projection map p(s R ) = ½I 3 , 0 3 s R , that is, x R retains the position variables in s R and discards the velocities. \n Predictive human model In order to predict the human's future motion, the robot uses its internal model of human dynamics, f H . Under this modeling assumption, the human's future trajectory depends upon the choice of control input over time, u H ( Á ). Extensive work in econometrics and cognitive science, such as that of  Von Neumann and Morgenstern (1945) ,  Luce (1959), and Baker et al. (2007) , has shown that human behavior (that is, u H ) can be well modeled by utility-driven optimization. Thus, the robot models the human as optimizing a reward function, r H (x H , u H ; u), that depends on the human's state and action, as well as a set of parameters u. This reward function could be a linear combination of features as in many inverse optimal control implementations (where the goal or feature weighting u must be learned, either online or offline), or more generally learned through function approximators such as deep neural networks, where u are the trained weights as in  Finn et al. (2016) . We assume that the robot has a suitable human reward function r H , either learned offline from prior human demonstrations or otherwise encoded by the system designers. Thus, endowed with r H , the robot can model the human's choice of control action as a probability distribution over actions conditioned on state. Under maximumentropy assumptions  (Ziebart et al., 2008)  inspired by noisy-rationality decision-making models  (Baker et al., 2007) , the robot models the human as more likely to choose (discrete) actions u H with high expected utility, in this case the state-action value (or Q-value): P(u H jx H ; b, u) = e bQ H (x H , u H ;u) P ũ e bQ H (x H , ũ;u) ð3Þ We use a temporally and spatially discretized version of human dynamics, fH . These discrete-time dynamics may be found by integrating f H over a fixed time step of Dt with fixed control u H over the interval. Section 5 provides further details on this discretization. Running example: The quadcopter's model of the human assumes the human intends to reach some target location g H 2 R 2 in a straight line. The human's reward function is given by the distance traveled over time step Dt, i.e., r H (x H , u H ; g H ) = À v H Dt, and human trajectories are constrained to terminate at g H . The state-action value, parameterized by u = g H , captures the optimal cost of reaching g H from x H when initially applying u H for a duration Dt: Q H (x H , u H ; g H ) = À v H DtÀ k x H + v H Dt½cos u H , sin u H > À g H k 2 : Often, the coefficient b is termed the rationality coefficient, because it quantifies the degree to which the robot expects the human's choice of control to align with its model of utility. For example, taking b # 0 yields a model of a human who appears ''irrational,'' choosing actions uniformly at random and completely ignoring the modeled utility. At the other extreme, taking b \" ' corresponds to a ''perfectly rational'' human, whose actions exactly optimize the modeled reward function. As we will see in Section 4, b can also be viewed as a measure of the robot's confidence in the predictive accuracy of Q H . Note that Q H (x H , u H ; u) only depends on the human state and action and not on the robot's. Thus far, we have intentionally neglected discussion of human-robot interaction effects. These effects are notoriously difficult to model, and the community has devoted a significant effort to building and validating a variety of models (e.g.,  Sadigh et al., 2016; Trautman and Krause, 2010) . In that spirit, we could have chosen to model human actions u H as dependent upon robot state x R in (3), and likewise defined Q H to depend upon x R . This extended formulation is sufficiently general as to encompass all possible (Markov) interaction models. However, in this work we explicitly do not model these interactions; indeed, one of the most important virtues of our approach is its robustness to precisely these sorts of modeling errors. \n Probabilistically safe motion planning Ideally, the robot's motion planner should generate trajectories that reach a desired goal state efficiently, while maintaining safety. More specifically, in this context ''safety'' indicates that the physical system will never enter the keepout set K during operation, despite human motion and external disturbances. That is, we would like to guarantee that (p(s R ), x H ) 6 2 K for all time. To make this type of strong, deterministic, a priori safety guarantee requires the robot to avoid the set of all human states x H which could possibly be occupied at a particular time, i.e., the human's forward reachable set. If the robot can find trajectories that are safe for any possible human trajectory then there is no need to predict the human's next action. Unfortunately, the forward reachable set of the human often encompasses such a large volume of the workspace that it is impossible for the robot to find a guaranteed safe trajectory to the goal state. This motivates refining our notion of prediction: rather than reasoning about all the places where the human could be, the robot can instead reason about how likely the human is to be at each location. This probabilistic reasoning provides a guide for planning robot trajectories with a quantitative degree of safety assurance. Our probabilistic model of human control input (3) coupled with dynamics model f H allows us to compute a probability distribution over human states for every future time. By relaxing our conception of safety to consider only collisions that might occur with sufficient probability P th , we dramatically reduce the effective volume of this set of future states to avoid. In practice, P th should be chosen carefully by a system designer in order to trade off overall collision probability with conservativeness in motion planning. The proposed approach in this paper follows two central steps to provide a quantifiable, high-confidence collision avoidance guarantee for the robot's motion around the human. In Section 4 we present our proposed Bayesian framework for reasoning about the uncertainty inherent in a model's prediction of human behavior. Based on this inference, we demonstrate how to generate a real-time probabilistic prediction of the human's motion over time. Next, in Section 6, we extend a state-of-the-art, provably safe, real-time robotic motion planner to incorporate our time-varying probabilistic human prediction. \n Confidence-aware human motion prediction Any approach to human motion prediction short of computing a full forward reachable set must, explicitly or implicitly, reflect a model of human decision-making. In this work, we make that model explicit by assuming that the human chooses control actions in a Markovian fashion according to the probability distribution (3). Other work in the literature, such as that of  Schmerling et al. (2017) , aims to learn a generative probabilistic model for human trajectories; implicitly, this training procedure distills a model of human decision-making. Whether explicit or implicit, these models are by nature imperfect and liable to make inaccurate predictions eventually. One benefit of using an explicit model of human decision-making, such as (3), is that we may reason directly and succinctly about its performance online. In particular, the entropy of the human control distribution in (3) is a decreasing function of the parameter b. High values of b place more probability mass on highutility control actions u H , whereas low values of b spread the probability mass more evenly between different control inputs, regardless of their modeled utility Q H . Therefore, b naturally quantifies how well the human's motion is expected to agree with the notion of optimality encoded in Q H . The commonly used term ''rationality coefficient,'' however, seems to imply that discrepancies between the two indicate a failure on the human's part to make the ''correct'' decisions, as encoded by the modeled utility. Instead, we argue that these inevitable disagreements are primarily a result of the model's inability to fully capture the human's behavior. Thus, instead of conceiving of b as a rationality measure, we believe that b can be given a more pragmatic interpretation related to the accuracy with which the robot's model of the human is able to explain the human's motion. Consistently, in this paper, we refer to b as model confidence. An important related observation following from this interpretation of b is that the predictive accuracy of a human model is likely to change over time. For example, the human may change their mind unexpectedly, or react suddenly to some aspect of the environment that the robot is unaware of. Therefore, we shall model b as an unobserved, time-varying parameter. Estimating it in real time provides us with a direct, quantitative summary of the degree to which the utility model Q H explains the human's current motion. To do this, we maintain a Bayesian belief about the possible values of b. Initially, we begin with a uniform prior over b and over time this distribution evolves given measurements of the human's state and actions. \n Real-time inference of model confidence We reason about the model confidence b as a hidden state in a hidden Markov model (HMM) framework. The robot starts with a prior belief b 0 À over the initial value of b. In this work, we use a uniform prior, although that is not strictly necessary. At each discrete time step k 2 f0, 1, 2, . . .g, it will have some belief about model confidence b k À (b). 3 After observing a human action u k H , the robot will update its belief to b k + by applying Bayes' rule. The hidden state may evolve between subsequent time steps, accounting for the important fact that the predictive accuracy of the human model may change over time as unmodeled factors in the human's behavior become more or less relevant. As, by definition, we do not have access to a model of these factors, we use a naive ''e-static'' transition model: at each time k, b may, with some probability e, be re-sampled from the initial distribution b 0 À , and otherwise retains its previous value. We define the belief over the next value of b (denoted by b 0 ) as an expectation of the conditional probability P(b 0 jb), i.e., b k À (b 0 ) :¼ E b;b kÀ1 + ½P(b 0 jb). Concretely, this expectation may be computed as b k À (b 0 ) = (1 À e)b kÀ1 + (b 0 ) + eb 0 À (b 0 ) ð4Þ By measuring the evolution of the human's state x H over time, we assume that, at every time step k, the robot is able to observe the human's control input u k H . This observed control may be used as evidence to update the robot's belief b k À about b over time via a Bayesian update: b k + (b) = P(u k H jx k H ; b, u)b k À (b) P b P(u k H jx k H ; b, u)b k À ( b) ð5Þ with b k + (b) :¼ P(bjx 0:k H , u 0:k H ) for k 2 f0, 1, . . .g, and P(u k H jx k H ; b, u) given by (3). It is critical to be able to perform this update rapidly to facilitate real-time operation; this would be difficult in the original continuous hypothesis space b 2 ½0, '), or even in a large discrete set. Fortunately, our software examples in Section 5 and hardware demonstration in Section 8 suggest that maintaining a Bayesian belief over a relatively small set of N b = 5 discrete values of b distributed on a log scale achieves significant improvement relative to using a fixed value. The ''e-static'' transition model leads to the desirable consequence that old observations of the human's actions have a smaller influence on the current model confidence distribution than recent observations. In fact, if no new observations are made, successively applying time updates asymptotically contracts the belief towards the initial distribution, that is, b k À ( Á ) ! b 0 À ( Á ). The choice of parameter e effectively controls the rate of this contraction, with higher e leading to more rapid contraction. \n Human motion prediction Equipped with a belief over b at time step k, we are now able to propagate the human's state distribution forward to any future time via the well-known Kolmogorov forward equations, recursively. In particular, suppose that we know the probability that the human is in each state x k H at some future time step k. We know that (according to our utility model) the probability of the human choosing control u k H in state x k H is given by (3). Accounting for the otherwise deterministic dynamics model fH , we obtain the following expression for the human's state distribution at the following time step k + 1: P(x k + 1 H ; b, u) = X x k H , u k H P(x k + 1 H jx k H , u k H ; b, u) Á P(u k H jx k H ; b, u)P(x k H ; b, u) ð6Þ for a particular choice of b. Marginalizing over b according to our belief at the current step time k, we obtain the overall occupancy probability distribution at each future time step k: P(x k H ; u) = E b;b k P(x k H ; b, u) ð7Þ Note that (  6 ) is expressed more generally than is strictly required. Indeed, because the only randomness in dynamics model fH originates from the human's choice of control input u H , we have P( x k + 1 H jx k H , u k H ; b, u) = 1fx k + 1 H = fH (x k H , u k H )g. \n Model confidence with auxiliary parameter identification Thus far, we have tacitly assumed that the only unknown parameter in the human utility model (  3 ) is the model confidence, b. However, often one or more of the auxiliary parameters u are also unknown. These auxiliary parameters could encode one or more human goal states or intents, or other characteristics of the human's utility, such as her preference for avoiding parts of the environment. Further, much like model confidence, they may change over time. In principle, it is possible to maintain a Bayesian belief over b and u jointly. The Bayesian update for the hidden state (b, u) is then given by ) the prior at time step k. This approach can be practical for parameters taking finitely many values from a small, discrete set, e.g., possible distinct modes for a human driver (distracted, cautious, aggressive). However, for certain scenarios or approaches it may not be practical to maintain a full Bayesian belief on the parameters u. In such cases, it is reasonable to replace the belief over u with a point estimate u, such as the maximum likelihood estimator or the mean, and substitute that estimate into (6). Depending on the complexity of the resulting maximum likelihood estimation problem, it may or may not be computationally feasible to update the parameter estimate u at each time step. Fortunately, even when it is computationally expensive to estimate u, we can leverage our model confidence as an indicator of when reestimating these parameters may be most useful. That is, when model confidence degrades that may indicate poor estimates of u. b k + (b, u) = P(u k H jx k H ; b, u)b k À (b, u) P b, ũ P(u k H jx k H ; b, ũ)b k À ( b, ũ) ð8Þ \n Prediction examples We illustrate these inference steps with two sets of examples: our running pedestrian example and a simple model of a car. \n Pedestrian model (running example) So far, we have presented a running example of a quadcopter avoiding a human. We use a deliberately simple, purely kinematic model of continuous-time human motion: _ x H = _ h x _ h y ! = v H cos u H v H sin u H ! ð9Þ However, as discussed in Section 3.3, the proposed prediction method operates in discrete time (and space). The discrete dynamics corresponding to (9) are given by x k + 1 H À x k H [x H (t + Dt) À x H (t) = v H Dt cos u H (t) v H Dt sin u H (t) ! ð10Þ for a time discretization of Dt. \n Dubins car model To emphasize the generality of our method, we present similar results for a different application domain: autonomous driving. We will model a human-driven vehicle as a dynamical system whose state x H evolves as _ x H = _ h x _ h y _ h f 2 4 3 5 = v H cos h f v H sin h f u H 2 4 3 5 ð11Þ Observe that, while (11) appears very similar to (9), in this Dubins car example the angle of motion is a state, not a control input. We discretize these dynamics by integrating (11) from t to t + Dt, assuming a constant control input u H : x k + 1 H À x k H [x H (t + Dt) À x H (t) = v H u H (t) sin (h f (t) + u H (t)Dt) À sin (h f (t)) À Á À v H u H (t) cos (h f (t) + u H (t)Dt) À cos (h f (t)) À Á u H Dt 2 6 4 3 7 5 For a specific goal position g = ½g x , g y , the Q-value corresponding to state-action pair (x H , u H ) and reward function r H (x H , u H ) = À v H Dt (until the goal is reached) may be found by solving a shortest path problem offline. \n Accurate model First, we consider a scenario in which the robot has full knowledge of the human's goal, and the human moves along the shortest path from a start location to this known goal state. Thus, human motion is well-explained by Q H . The first row of Figure  2  illustrates the probability distributions our method predicts for the pedestrian's future state at different times. Initially, the predictions generated by our Bayesian confidence-inference approach (right) appear similar to those generated by the low model confidence predictor (left). However, our method rapidly discovers that Q H is an accurate description of the pedestrian's motion and generates predictions that match the high model confidence predictor (center). The data used in this example was collected by tracking the motion of a real person walking in a motion capture arena. See Section 8 for further details. Likewise, the first row of Figure  3  shows similar results for a human-driven Dubins car model (in simulation) at an intersection. Here, traffic laws provide a strong prior on the human's potential goal states. As shown, our method of Bayesian model confidence inference quickly infers the correct goal and learns that the human driver is acting in accordance with its model Q H . The resulting predictions are substantially similar to the high-b predictor. The data used in this example was simulated by controlling a Dubins car model along a pre-specified trajectory. \n Unmodeled obstacle Often, robots do not have fully specified models of the environment. Here, we showcase the resilience of our approach to unmodeled obstacles that the human must avoid. In this scenario, the human has the same start and goal as in the accurate model case, except that there is an obstacle along the way. The robot is unaware of this obstacle, however, which means that in its vicinity the human's motion is not well-explained by Q H , and b(b) ought to place more probability mass on higher values of b. The second rows of Figure  2  and Figure  3  illustrate this type of situation for the pedestrian and Dubins car, respectively. In Figure  2 , the pedestrian walks to an a priori known goal location and avoids an unmodeled spill on the ground. Analogously, in Figure  3  the car swerves to avoid a large pothole. By inferring model confidence online, our approach generates higher-variance predictions of future state, but only in the vicinity of these unmodeled obstacles. At other times throughout the episode when Q H is more accurate, our approach produces predictions more in line with the high model confidence predictor. \n Unmodeled goal In most realistic human-robot encounters, even if the robot does have an accurate environment map and observes all obstacles, it is unlikely for it to be aware of all human goals. We test our approach's resilience to unknown human goals by constructing a scenario in which the human moves between both known and unknown goals. The third row of Figure  2  illustrates this situation for the pedestrian example. Here, the pedestrian first moves to one known goal position, then to another, and finally back to the start which was not a modeled goal location. The first two legs of this trajectory are consistent with the robot's model of goal-oriented motion, though accurate prediction does require the predictor to infer which goal the pedestrian is walking toward. However, when the pedestrian returns to the start, her motion appears inconsistent with Q H , skewing the robot's belief over b toward zero. Similarly, in the third row of Figure  3  we consider a situation in which a car makes an unexpected turn onto an unmapped access road. As soon as the driver initiates the turn, our predictor rapidly learns to distrust its internal model Q H and shift its belief over b upward.   \n Safe probabilistic planning and tracking Given probabilistic predictions of the human's future motion, the robot must plan efficient trajectories that avoid collision with high probability. In order to reason robustly about this probability of future collision, we must account for potential tracking errors incurred by the real system as it follows planned trajectories. To this end, we build on the recent FaSTrack framework of  Herbert et al. (2017) , which provides control-theoretic robust safety certificates in the presence of deterministic obstacles, and extend it to achieve approximate probabilistic collision-avoidance. \n Background: fast planning, safe tracking Recall that x R is the robot's state for the purposes of motion planning, and that s R encodes a higher-fidelity, potentially higher-dimensional notion of state (with associated dynamics). The recently proposed FaSTrack framework from  Herbert et al. (2017)  uses Hamilton-Jacobi reachability analysis to quantify the worst-case tracking performance of the s R -system as it follows trajectories generated by the x R -system. For further reading on reachability analysis refer to  Evans and Souganidis (1984) ,  Mitchell et al. (2005) , and  Bansal et al. (2017) . A byproduct of this FaSTrack analysis is an error feedback controller that the s R system can use to achieve this worst-case tracking error. The tracking error bound may be given to one of many off-the-shelf real-time motion planning algorithms operating in x R -space in order to guarantee real-time collision avoidance by the s Rsystem. Formally, FaSTrack precomputes an optimal tracking controller, as well as a corresponding compact set E in the robot's planning state space, such that (p(s R (t))À x R, ref (t)) 2 E for any reference trajectory proposed by the lower-fidelity planner. This bound E is a trajectory tracking certificate that can be passed to an online planning algorithm for real-time safety verification: the dynamical robot is guaranteed to always be somewhere within the bound relative to the current planned reference point x R, ref (t). This tracking error bound may sometimes be expressed analytically; otherwise, it may be computed numerically offline using level set methods (e.g.,  Mitchell, 2009) . Equipped with E, the planner can generate safe plans online by ensuring that the entire tracking error bound around the nominal state remains collision-free throughout the trajectory. Efficiently checking these E-augmented trajectories for collisions with known obstacles is critical for real-time performance. Note that the planner only needs to know E (which is computed offline) and otherwise requires no explicit understanding of the high-fidelity model. Running example: As dynamics (2) are decoupled in the three spatial directions, the bound E computed by FaSTrack is an axis-aligned box of dimensions E x × E y × E z . For further details refer to Fridovich-Keil et al. (  2018 ). \n Robust tracking, probabilistic safety Unfortunately, planning algorithms for collision checking against deterministic obstacles cannot be readily applied to our problem. Instead, a trajectory's collision check should return the probability that it might lead to a collision. Based on this probability, the planning algorithm can discriminate between trajectories that are sufficiently safe and those that are not. As discussed in Section 3.4, a safe online motion planner invoked at time t should continually check the probability that, at any future time t, (p(s R (t)), x H (t)) 2 K. The tracking error bound guarantee from FaSTrack allows us to conduct worst-case analysis on collisions given a human state x H . Concretely, if no point in the Minkowski sum fx R + Eg is in the collision set with x H , we can guarantee that the robot is not in collision with the human. The probability of a collision event for any point x R (t) along a candidate trajectory is then P coll (x R (t)) :¼ P((x R , x H ) 2 K) ð12Þ Assuming worst-case tracking error bound E, this quantity can be upper-bounded by the total probability that x H (t) will be in collision with any of the possible robot states xR 2 fx R (t) + Eg. For each robot planning state x R 2 R n R we define the set of human states in potential collision with the robot: H E (x R ) :¼ fx H 2 R n H : 9x R 2 fx R + Eg, (x R , xH ) 2 Kg ð13Þ Running example: Given K and E, H E (x R ) is the set of human positions within the rectangle of dimensions (l + E x ) × (l + E y ) centered on ½p x , p y . A human anywhere in this rectangle could be in collision with the quadcopter. The following result follows directly from the definition of the tracking error bound and a union bound. Proposition 1. The probability of a robot with worst-case tracking error E colliding with the human at any trajectory point x R (t) is bounded above by the probability mass of x H (t) contained within H E (x R (t)). We consider discrete-time motion plans. The probability of collision along any such trajectory from current time step k to final step k + K is upper-bounded by P k:k + K coll ł P k:k + K coll :¼ 1 À Y k + K k = k P(x k H 6 2 H E (x k R )jx k H 6 2 H E (x s R ), k ł s\\k) ð14Þ Evaluating the right-hand side of (  14 ) exactly requires reasoning about the joint distribution of human states over all time steps and its conditional relationship on whether collision has yet occurred. This is equivalent to maintaining a probability distribution over the exponentially large space of trajectories x k:k + K H that the human might follow. As The International Journal of Robotics Research 39(2-3) motion planning occurs in real time, we shall resort to a heuristic approximation of (  14 ). One approach to approximating (  14 ) is to assume that the event x k 1 H 6 2 H E (x k 1 R ) is independent of x k 2 H 6 2 H E (x k 2 R ), for all k 1 6 ¼ k 2 . This independence assumption is equivalent to removing the conditioning in (  14 ). Unfortunately, this approximation is excessively pessimistic; if there is no collision at time step k, then collision is also unlikely at time step k + 1 because both human and robot trajectories are continuous. In fact, for sufficiently small time discretization Dt and nonzero collision probabilities at each time step, the total collision probability resulting from an independence assumption would approach 1 exponentially fast in the number of time steps K. We shall refine this approximation by finding a tight lower bound on the right-hand side of (  14 ). Because collision events are correlated in time, we first consider replacing each conditional probability P( x k H 6 2 H E (x k R )jx s H 6 2 H E (x s R ), k ł s\\k) by 1 for all k 2 fk + 1, . . . , k + Kg. This effectively lower bounds P k:k + K coll by the worst-case probability of collision at the current time step k: P k:k + K coll ø 1 À P(x k H 6 2 H E (x k R )) = P(x k H 2 H E (x k R )) ð15Þ This bound is extremely loose in general, because it completely ignores the possibility of future collision. However, note that probabilities in the product in (  14 ) may be conditioned in any particular order (not necessarily chronological). This commutativity allows us to generate K À k + 1 lower bounds of the form P k:k + K coll ø P(x k H 2 H E (x k R )) for k 2 fk, . . . , k + Kg. Taking the tightest of all of these bounds, we can obtain an informative, yet quickly computable, approximator for the sought probability: P k:k + K coll ø max k2fk:k + Kg P(x k H 2 H E (x k R ))'P k:k + K coll ð16Þ To summarize, the left inequality in (  16 ) lower-bounds P k:k + K coll with the greatest marginal collision probability at any point in the trajectory. On the right-hand side of (  16 ), we take this greatest marginal collision probability as an approximator of the actual probability of collision over the entire trajectory. In effect, we shall approximate P k:k + K coll with a tight lower bound of an upper bound. While this type of approximation may err on the side of optimism, we note that both the robot's ability to replan over time and the fact that the left-hand side of (  16 ) is an upper bound on total trajectory collision probability mitigate this potentially underestimated risk. \n Safe online planning under uncertain human predictions This approximation of collision probability allows the robot to discriminate between valid and invalid candidate trajectories during motion planning. Using the prediction methodology proposed in Section 4, we may quickly generate, at every time t, the marginal probabilities in (  16 ) at each future time k 2 fk, . . . , k + Kg, based on past observations at times 0, . . . , k. The planner then computes the instantaneous probability of collision P(x k H 2 H E (x k R )) by integrating P(x t H jx 0:k H ) over H E (x k R ) , and rejects the candidate point x k R if this probability exceeds P th . Note that for graph-based planners that consider candidate trajectories by generating a graph of time-stamped states, rejecting a candidate edge from this graph is equivalent to rejecting all further trajectories that would contain that edge. This early rejection rule is consistent with the proposed approximation (16) of P k:k + K coll while preventing unnecessary exploration of candidate trajectories that would ultimately be deemed unsafe. Throughout operation, the robot follows each planned trajectory using the error feedback controller provided by FaSTrack, which ensures that the robot's high-fidelity state representation s R and the lower-fidelity state used for planning, x R , differ by no more than the tracking error bound E. This planning and tracking procedure continues until the robot reaches its desired goal state. Running example: Our quadcopter is now required to navigate to a target position shown in Figure  4  without colliding with the human. Our proposed algorithm successfully avoids collisions at all times, replanning to leave greater separation from the human whenever her motion departs from the model. In contrast, robot planning with fixed model confidence is either overly conservative at the expense of time and performance or overly aggressive at the expense of safety. \n Connections to reachability analysis In this section, we present an alternative, complementary analysis of the overall safety properties of the proposed approach to prediction and motion planning. This discussion is grounded in the language of reachability theory and worst-case analysis of human motion. \n Forward reachable set Throughout this section, we frequently refer to the human's time-indexed forward reachable set. We define this set formally in the following. Definition 1. (Forward reachable set) For a dynamical system _ x = f (x, u) with state trajectories given by the function j(x(0), t, u( Á ))ex(t), the forward reachable set FRS(x, t) of a state x after time t has elapsed is FRS(x, t) :¼ fx 0 : 9u( Á ), x 0 = j(x, t, u( Á ))g That is, a state x 0 is in the forward reachable set of x after time t if it is reachable via some applied control signal u( Á ). Remark 1. (Recovery of FRS) For P th = 0 and any finite b, the set of states assigned probability greater than P th is identical to the forward reachable set, up to discretization errors. This is visualized for low, high, and Bayesian model confidence in Figure  5 . \n A sufficient condition for the safety of individual trajectories In Section 6.2, we construct an approximation to the probability of collision along a trajectory, which we use during motion planning to avoid potentially dangerous states. To make this guarantee of collision avoidance for a motion plan even stronger, it would suffice to ensure that the robot never comes too close to the human's forward reachable set. More precisely, a planned trajectory is safe if fx R (t) + Eg \\ FRS(x H , t) = ;, for every state x R (t) along a motion plan generated when the human was at state x H . The proof of this statement follows directly from the properties of the tracking error bound E described in Section 6. While this condition may seem appealing, it is in fact highly restrictive. The requirement of avoiding the full forward reachable set is not always possible in confined spaces; indeed, this was our original motivation for wanting to predict human motion (see Section 3.4). However, despite this shortcoming, the logic behind this sufficient condition for safety provides insight into the effectiveness of our framework. \n Recovering the forward reachable set Though it will not constitute a formal safety guarantee, we analyze the empirical safety properties of our approach by examining how our predicted state distributions over time relate to forward reachable sets. During operation, our belief over model confidence b evolves to match the degree to which the utility model Q H explains recent human motion. The ''time constant'' governing the speed of this evolution may be tuned by the system designer to be arbitrarily fast by choosing the parameter e to be small, as discussed in Section 4.1. Thus, we may safely assume that b(b) places high probability mass on small values of b as soon as the robot observes human motion that is not well explained by Q H . Figure  6  shows the sets of states with ''high enough'' (.P th ) predicted probability mass overlaid on the human's forward reachable set at time t, which is a circle of radius v H t centered on x H for the dynamics in our running example. When b is high (10), we observe that virtually all of the probability mass is concentrated in a small number of states in the direction of motion predicted by our utility model. When b is low (0:05) we observe that the set of states assigned probability above our collision threshold P th occupies a much larger fraction of the reachable set. A typical belief b(b) recorded at a moment when the human was roughly moving according to Q H yields an intermediate set of states. Figure  7  illustrates the evolution of these sets of states over time, for the unmodeled obstacle example of Section 5.4 in which a pedestrian avoids a spill. Each row corresponds to the predicted state distribution at a particular point in time. Within a row, each column shows the reachable set and the set of states assigned occupancy Interestingly, as the Bayesian model confidence decreases, which occurs when the pedestrian turns to avoid the spill at t'6 s, the predicted state distribution assigns high probability to a relatively large set of states, but unlike the low-b predictor that set of states is oriented toward the known goal. Of course, had b(b) placed even more probability mass on lower values of b then the Bayesian confidence predictor would converge to the low confidence one. In addition, we observe that, within each row as the prediction horizon increases, the area contained within the forward reachable set increases and the fraction of that area contained within the predicted sets decreases. This phenomenon is a direct consequence of our choice of threshold P th . Had we chosen a smaller threshold value, a larger fraction of the forward reachable set would have been occupied by the lower-b predictors. This observation may be viewed prescriptively. Recalling the sufficient condition for safety of planned trajectories from Section 7.2, if the robot replans every T replan seconds, we may interpret the fraction of FRS( Á , t + T replan ) assigned occupancy probability greater than P th by the low-confidence predictor as a rough indicator of the safety of an individual motion plan, robust to worst-case human movement. As this fraction tends toward unity, the robot is more and more likely to be safe. However, for any P th .0, this fraction approaches zero for T replan \" '. This immediately suggests that, if we wish to replan every T replan seconds, we can achieve a particular level of safety as measured by this fraction by choosing an appropriate threshold P th . In summary, confidence-aware predictions rapidly place high-probability mass on low values of b whenever human motion is not well-explained by utility model Q H . Whenever this happens, the resulting predictions encompass a larger fraction of the forward reachable set, and in the limit that P th # 0 we recover the forward reachable set exactly. The larger this fraction, the more closely our approach satisfies the sufficient condition for safety presented in Section 7.2. \n Hardware demonstration We implemented confidence-aware human motion prediction (Section 4) and integrated it into a real-time, safe probabilistic motion planner (Section 6), all within the Robot Operating System (ROS) software framework of  Quigley et al. (2009) . To demonstrate the efficacy of our methods, we tested our work for the quadcopter-avoiding-pedestrian example used for illustration throughout this paper. Human trajectories were recorded as (x, y) positions on the ground plane at roughly 235 Hz by an OptiTrack infrared motion capture system, and we used a Crazyflie 2.0 micro-quadcopter, also tracked by the OptiTrack system. 4 Figure  4  illustrates the unmodeled obstacle case from Section 5.4, in which the pedestrian turns to avoid a spill on the ground. Using a low model confidence results in motion plans that suddenly and excessively deviate from the ideal straight-line path when the pedestrian turns to avoid the spill. By contrast, the high-confidence predictor consistently predicts that the pedestrian will walk in a straight line to the goal even when they turn; this almost leads to collision, as shown in detail in Figure  8 . Our proposed approach for Bayesian model confidence initially assigns high confidence and predicts that the pedestrian will walk straight to the goal, but when they turn to avoid the spill, the predictions become less confident. This causes the quadcopter to make a minor course correction, shown in further detail in Figure  9 . \n Conclusion When robots operate in complex environments in concert with other agents, safety often depends upon the robot's ability to predict the agents' future actions. While this prediction problem may be tractable in some cases, it can be extremely difficult for agents such as people who act with intent. In this paper, we introduce the idea of confidenceaware prediction as a natural coping mechanism for predicting the future actions of intent-driven agents. Our approach uses each measurement of the human's state to reason about the accuracy of its internal model of human decision-making. This reasoning about model confidence is expressed compactly as a Bayesian filter over the possible values of a single parameter, b, which controls the entropy of the robot's model of the human's choice of action. In effect, whenever the human's motion is not wellexplained by this model, the robot predicts that the human could occupy a larger volume of the state space.  We couple this notion of confidence-aware prediction with a reachability-based robust motion planning algorithm, FaSTrack, which quantifies the robot's ability to track a planned reference trajectory. Using this maximum tracking error allows us to bound an approximation of the probability of collision along planned trajectories. In addition, we present a deeper connection between confidence-aware prediction and forward reachable sets, which provides an alternative explanation of the safety of our approach. We demonstrate the proposed methodology on a ROS-based quadcopter testbed in a motion capture arena. \n Limitations There are several important limitations of this work, which we summarize and discuss in the following. 9.1.1. State discretization. As presented, our approach to prediction requires a discrete representation of the human's state space. This can be tractable for the relatively simple dynamical models of human motion we consider in this work. Fortunately, one of the strongest attributes of confidenceaware prediction is that it affords a certain degree of robustness to modeling errors by design. Still, our approach is effectively limited to low-order dynamical models. 9.1.2. FaSTrack complexity. FaSTrack provides a strong safety guarantee vis-a `-vis the maximum tracking error that could ever exist between a higher-fidelity dynamical model of the robot and a lower-order model used for motion planning. Unfortunately, the computational complexity of finding this maximum tracking error and the corresponding safety controller scales exponentially with the dimension of The subsequent motion plans may not be safe; here, poor prediction quality leads to a collision. the high-fidelity model. In some cases, these dynamics are decomposable and analytic solutions exist (e.g.,  Chen et al., 2018; Fridovich-Keil et al., 2018) , and in other cases conservative approximations may be effective (e.g.,  Chen et al., 2016; Royo et al., 2018) . 9.1.3. Boltzmann distributional assumption. We model the human's choice of control input at each time step as an independent, random draw from a Boltzmann distribution (3). This distributional assumption is motivated from the literature in cognitive science and econometrics and is increasingly common in robotics, yet it may not be accurate in all cases. Maintaining an up-to-date model confidence belief b(b) can certainly mitigate this inaccuracy, but only at the cost of making excessively conservative predictions. 9.1.4. Safety certification. Our analysis in Section 7 makes connections to forward reachability in an effort to understand the safety properties of our system. As shown, whenever our confidence-aware prediction method detects poor model performance it quickly yields predictions that approximate the human's forward reachable set. Although this approximation is not perfect, and hence we cannot provide a strong safety certificate, the connection to reachability is in some sense prescriptive. That is, it can be used to guide the choice of collision probability threshold P th and replanning frequency. However, even if we could provide a strong guarantee of collision avoidance for a particular motion plan, that would not, in general, guarantee that future motion plans would be recursively safe. This recursive property is much more general and, unsurprisingly, more difficult to satisfy. \n Future directions Future work will aim to address each of these shortcomings. We are also interested in extending our methodology for the multi-robot, multi-human setting; our preliminary results are reported by  Bajcsy et al. (2018) . In addition, we believe that our model confidence inference approach could be integrated with other commonly used probabilistic prediction methods besides the Boltzmann utility model. Finally, we are excited to test our work in hardware in other application spaces, such as manipulation and driving. Fig. Fig.1. When planning around humans, accurate predictions of human motion (visualized here in pink and blue, representing high and low probability, respectively) are an essential prerequisite for safety. Unfortunately, these approaches may fail to explain all observed motion at runtime (e.g., human avoids unmodeled spill on the ground), leading to inaccurate predictions, and potentially, collisions (left). Our method addresses this by updating its predictive model confidence in real time (right), leading to more conservative motion planning in circumstances when predictions are known to be suspect. \n with b k + (b, u) :¼ P(b, ujx 0:k H , u 0:k H ) the running posterior and b k À (b, u) :¼ P(b, ujx 0:kÀ1 H , u 0:kÀ1 H \n Fig. 2 . 2 Fig. 2. Snapshots of pedestrian trajectory and probabilistic model predictions. Top row: Pedestrian moves from the bottom right to a goal marked as a red circle. Middle row: Pedestrian changes course to avoid a spill on the floor. Bottom row: Pedestrian moves to one known goal, then to another, then to a third which the robot has not modeled. The first two columns show predictions for low and high model confidence; the third column shows the predictions using our Bayesian model confidence. For all pedestrian videos, see https://youtu.be/lh_E9rW-MJo. \n Fig. 3 . 3 Fig. 3. Snapshots of Dubins car and probabilistic predictions. Top row: Car moves straight ahead toward one of two known goals (red arrows), staying in its lane. Middle row: Car suddenly swerves to the left to avoid a pothole. Bottom row: Car turns to the right, away from the only known goal. The left and center columns show results for low and high confidence predictors, respectively, and the right column shows our approach using Bayesian inferred model confidence. For all Dubins car videos, see https://youtu.be/sAJKNnP42fQ. \n Fig. 4 . 4 Fig. 4. Scenario from the middle row of Figure 2 visualized with robot's trajectory. When b is low and the robot is not confident, it makes large deviations from its path to accommodate the human. When b is high, the robot refuses to change course and comes dangerously close to the human. With inferred model confidence, the robot balances safety and efficiency with a slight deviation around the human. \n Fig. 5 . 5 Fig. 5. The human (black dot) is moving west towards a goal. Visualized are the predicted state distributions for 1 second into the future when using low, high, and Bayesian model confidence. Higher-saturation indicates higher likelihood of occupancy. The dashed circle represents the pedestrian's 1 second forward reachable set. \n Fig. 6 . 6 Fig.6. Visualization of the states with probability greater than or equal to the collision threshold, P th = 0:01. The human's forward reachable set includes the set of states assigned probability greater than P th . We show these ''high probability'' predicted states for predictors with fixed low and high b, as well as our Bayesian-inferred b. \n Fig. 7 . 7 Fig.7. The human (black dot) is walking towards the known goal (red dot) but has to avoid an unmodeled coffee spill on the ground. Here we show the snapshots of the predictions at various future times (columns) as the human walks around in real time (rows). The visualized states have probability greater than or equal to P th = 0:01. Each panel displays the human prediction under low confidence (in yellow), high confidence (in dark purple), and Bayesian confidence (colored as per the most likely b value), as well as the forward reachable set. The human's actual trajectory is shown in red. \n Fig. 8 . 8 Fig. 8. Predicting with fixed-b (in this case, b = 20) can yield highly inaccurate predictions (and worse, confidently inaccurate ones).The subsequent motion plans may not be safe; here, poor prediction quality leads to a collision. \n Fig. 9 . 9 Fig. 9. Inferring b leads to predicted state distributions whose entropy increases whenever the utility model Q H fails to explain observed human motion. The resulting predictions are more robust to modeling errors, resulting in safer motion plans. Here, the quadcopter successfully avoids the pedestrian even when they turn unexpectedly. \n\t\t\t The International Journal of Robotics Research 39(2-3)", "date_published": "n/a", "url": "n/a", "filename": "0278364919859436.tei.xml", "abstract": "One of the most difficult challenges in robot motion planning is to account for the behavior of other moving agents, such as humans. Commonly, practitioners employ predictive models to reason about where other agents are going to move. Though there has been much recent work in building predictive models, no model is ever perfect: an agent can always move unexpectedly, in a way that is not predicted or not assigned sufficient probability. In such cases, the robot may plan trajectories that appear safe but, in fact, lead to collision. Rather than trust a model's predictions blindly, we propose that the robot should use the model's current predictive accuracy to inform the degree of confidence in its future predictions. This model confidence inference allows us to generate probabilistic motion predictions that exploit modeled structure when the structure successfully explains human motion, and degrade gracefully whenever the human moves unexpectedly. We accomplish this by maintaining a Bayesian belief over a single parameter that governs the variance of our human motion model. We couple this prediction algorithm with a recently proposed robust motion planner and controller to guide the construction of robot trajectories that are, to a good approximation, collision-free with a high, user-specified probability. We provide extensive analysis of the combined approach and its overall safety properties by establishing a connection to reachability analysis, and conclude with a hardware demonstration in which a small quadcopter operates safely in the same space as a human pedestrian.", "id": "f947dd570931ec75ed7fc1077b17b2a4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Shun Zhang", "Edmund H Durfee", "Satinder Singh"], "title": "Minimax-Regret Querying on Side Effects for Safe Optimality in Factored Markov Decision Processes", "text": "Introduction We consider a setting where a human user tasks a computational agent with achieving a goal that may change one or more state features of the world (e.g., a housekeeping agent should change the state of the house floors and kitchen sink from dirty to clean). In the process of accomplishing the goal, the agent generally changes other features (e.g., its own position and power level, opening doors, moving furniture, scaring the cat). Some of these side-effects might be fine (even expected) by the user (e.g., moving), but others may be undesirable/unsafe (e.g., leaving doors open lets the cat roam/escape) even though they speed goal achievement (e.g., the agent's movement between rooms). Although the user tells the agent about some features that can be changed, as well as some to not change (e.g., don't knock over the priceless vase), the user often lacks the time, patience, or foresight to specify the changeability of every pertinent feature, and may incorrectly assume that the agent has commonsense (e.g., about cat behavior and the value of vases). How can the agent execute a safely-optimal policy in such a setting? We conservatively assume that, to ensure safety, the agent should never side-effect a feature unless changing it is explicitly known to be fine. Hence, the agent could simply execute the best policy that leaves such features unchanged. However, no such policy might exist, and even if it does it might surprise the user as unnecessarily costly/inefficient. Our focus is thus on how the agent can selectively query the user about the acceptability of changing features it hasn't yet been told about. We reject simply querying about every such feature, as this would be unbearably tedious to the user, and instead put the burden on the agent to limit the number and complexity of queries. In fact, in this paper we mostly focus on finding a single query about a few features that maximally improves upon the policy while maintaining safety. Our three main contributions in this paper are: 1) We formulate (in Section 2) an AI safety problem of avoiding negative side-effects in factored MDPs. 2) We show (in Section 3) how to efficiently identify the set of relevant features, i.e., the set of features that could potentially be worth querying the user about. 3) We formulate (in Section 4) a minimaxregret criterion when there is a limit on the number of features the agent can ask about, and provide an algorithm that allows the agent to find the minimax-regret query by searching the query space with efficient pruning. We empirically evaluate our algorithms in a simulated agent navigation task, outline ongoing extensions/improvements, and contrast our work to prior work, in the paper's final sections. \n Problem Definition We illustrate our problem in a simulated agent gridworldnavigation domain, inspired by Amodei et al.  [2016]  and depicted in Figure  1 , with doors, carpets, boxes, and a switch. The agent can open/close a door, move a box, traverse a carpet, and toggle the switch. Initially, the agent is in the bottom left corner; door d1 is open, d2 and d3 closed, the carpet clean, and the switch \"on\". The agent can move to an adjacent location vertically, horizontally, or diagonally. For simplicity, the transition function is assumed to be deterministic. The user tasks the agent with turning off the switch as quickly as is safely possible. The quickest path (π 1 ) traverses the carpet, but this gets the carpet dirty and the agent doesn't know if that is allowed. The agent could instead enter the room through door d1 and spend time moving box b1 or b2 out of the way (π 2 or π 3 respectively), open door d2, and then go to the switch. However, boxes might contain fragile objects and should not be moved; the user knows each box's contents, but the agent doesn't. Or the agent could enter through door d1 and walk upwards (π 4 ) around all the boxes and open door d2 to get to the switch. The user may or may not be okay with door d2 being opened. There are of course many other more circuitous paths not shown. We model the domain as a factored Markov Decision Process (MDP)  [Boutilier et al., 1999 ]. An MDP is a tuple S, A, T, r, s 0 , γ , with state space S, action space A, and transition function T where T (s |s, a) is the probability of reaching state s by taking action a in s. r(s, a) is the reward of taking action a in s. s 0 is the initial state and γ is the discount factor. Let π : S × A → [0, 1] be a policy. V π is the expected cumulative reward by following policy π starting from s 0 . In a factored MDP, a state is described in terms of values of various features (e.g., the agent's location, the current time, the status of each door, cleanliness of each carpet, position of each box), so the state space S is the cross-product of the values the features can take. The reward and transition functions are often also factored (e.g., the \"toggle\" action only changes the switch feature, leaving boxes, doors, and carpets unchanged). We will consistently use φ to denote one feature and Φ to denote a set of features. The agent knows the complete MDP model, but has incomplete knowledge about which features the user doesn't mind being changed. In our example, the user's goal implies the agent's location is changeable, as is the switch, but the agent is uncertain about side-effecting boxes, doors, and carpets. In general, the user could dictate that a feature can only be changed among restricted values (e.g., boxes can only be moved a short distance) and/or dependent on other features' values (e.g., interior doors can be left open as long as exterior doors (like d3) stay closed). We briefly return to this issue later (Section 6), but for simplicity assume here that the agent can partition the features into the following sets: • Φ A F : The free-features. The agent knows that these features are freely changeable (e.g., its location). • Φ A L : The locked-features. The agent knows it should never change any of these features. \n • Φ A ? : The unknown-features. These are features that the agent doesn't (initially) know whether the user considers freely changeable or locked. The user similarly partitions the features, but only into the sets Φ U L and Φ U F . We assume that the agent's knowledge, while generally incomplete (Φ A ? = ∅), is consistent with that of the user. That is, Φ A F ⊆ Φ U F and Φ A L ⊆ Φ U L . Defining & Finding Safely-Optimal Policies. Our conservative safety assumption means the agent should treat unknown features as if they are locked, until it explicitly knows otherwise. It should thus find an optimal policy that never visits a state where a feature in Φ A L ∪ Φ A ? is changed, which we call a safely-optimal policy. We can use linear programming with constraints that prevent the policy from visiting states with changed values of locked or unknown features: The above linear program does not allow any locked or unknown feature to be changed and is guaranteed to produce a safely-optimal policy (when one exists). This linear programming approach, while straightforward, can be intractable for large MDPs. Alternative approaches could directly encode the safety constraints into the transition function (e.g., by removing unsafe action choices in specific states), or into the reward function (heavily penalizing reaching unsafe states). Approximate methods, like feature-based approximate linear programming  [Dolgov and Durfee, 2006]  or constrained policy optimization  [Achiam et al., 2017] , can apply to larger problems, but may not guarantee safety or optimality (or both). We return to these concerns in Section 6. \n Querying Relevant Unknown-Features In our setting the only way for the agent to determine whether an unknown feature is freely changeable is to query the user. Thus, hereafter our focus is on how the agent can ask a good query about a small number, k, of features. Our solution is to first prune from Φ A ? features that are guaranteed to not be relevant to ask (this section), and then efficiently finding the best (minimax-regret) k-sized subset of the relevant features to query (Section 4). Until Section 6, we assume the changeabilities of features are independent, i.e., when the agent asks about some features in Φ A ? , the user's response does not allow it to infer the changeability of other features in Φ A ? . Intuitively, when is a feature in Φ A ? relevant to the agent's planning of a safely-optimal policy? In the navigation domain, if the agent plans to take the quickest path to the switch (π 1 in Figure  1 ), it will change the state of the carpet (from clean to dirty). The carpet feature is thus relevant since the agent would change it if permitted. If the carpet can't be changed but door d2 can, the agent would follow (in order of preference) policy π 2 , π 3 , or π 4 , so d2, b1, and b2 are relevant. Box b3 and door d3 are irrelevant, however, since no matter which (if any) other features are changeable, an optimal policy would never change them. Thus, an unknown feature is relevant when under some circumstance (some answer to some query) the agent's optimal policy would side-effect that feature. Such policies are dominating policies. else add (Φ, ∅) to β 14: Φ rel ← Φ rel ∪ Φ rel (π) 15: checked ← checked ∪ {Φ} 16: agenda ← powerset(Φ rel ) \\ checked 17: return Γ , Φ rel A dominating policy is a safely-optimal policy for the circumstance where the unknown features Φ A ? are partitioned into locked and changeable subsets. We denote the set of dominating policies by Γ = arg max π∈ΠΦ V π : ∀Φ ⊆ Φ A ? , (2) where Π Φ is the set of policies that do not change unknown features Φ ⊆ Φ ? as well as any locked features (meaning that Φ F ∪ (Φ ? \\ Φ) are changeable). We denote the unknownfeatures side-effected by policy π by Φ rel (π). For a set of policies Π, Φ rel (Π) = ∪ π∈Π Φ rel (π). The set Φ rel (Γ), abbreviated Φ rel , is thus the set of relevant (unknown-) features to consider querying about. Instead of finding the safely-optimal policies for all exponentially (in |Φ A ? |) many subsets Φ ⊆ Φ A ? with Equation 2, we contribute Algorithm DomPolicies (see pseudocode) that finds dominating policies incrementally (and in practice more efficiently) by constructing the sets of relevant features and dominating policies simultaneously. In each iteration, it examines a new subset of relevant features, Φ, and, if Φ isn't pruned (as described later), finds the safely-optimal policy with Φ being locked (Line 7). It then adds Φ rel (π), the features changed by π, to Φ rel . It repeats this process until Φ stops growing and all subsets of Φ rel are examined. For example, in the navigation problem (Figure  1 ), the first added policy is the safely-optimal policy assuming no unknown features are locked, which is π 1 . Now Γ = {π 1 } and thus Φ rel = {carpet}. It iterates, treating the carpet as locked, and updates Γ to {π 1 , π 2 } and thus Φ rel = {carpet, b1, d2}. Iterating again, it locks subsets of Φ rel , finding π 3 for subset {carpet, b1}. After finding π 4 , it terminates. In Line 10, the algorithm finds the constrained optimal policy (in our implementation using Eq. 1), and in the worst case, would do this 2 |Φ rel | times. Fortunately, the complexity is exponential in the number of relevant features, which we have seen in our empirical settings can be considerably smaller (a) (b) c 1 c 1 -1 c 2 c n c 2 c n -1 -1 … … … (c) c 1 c 3 -1 c 2 -1 -0.1 -1 -1 Figure 2: Example domains used in text. (n > 2) than the number of unknown features (|Φ A ? |). Furthermore, the efficiency can be improved with our pruning rule (line 8): satisf y(Φ, β) := ¬∃ (L,R)∈β (L ⊆ Φ ∧ Φ ∩ R = ∅) β is a history of ordered pairs, (L, R), of disjoint sets of unknown features. Before DomPolicies computes a policy for its agenda element Φ, if a pair (L, R) is in β, such that L ⊆ Φ (a dominating policy has been found when locking subset of features in Φ), and that dominating policy's relevant features R don't intersect with Φ, then Φ's dominating policy has already been found. In our running example, for instance, initially Φ rel = ∅. π 1 is the optimal policy and the algorithm adds pair (∅, {carpet}) to β. When larger subsets are later considered (note the agenda is sorted by cardinality), feature sets that do not contain carpet are pruned by β. In this example, β prunes 11 of the 16 subsets of the 4 relevant features. Consider the examples in Figure  2 . To reach the switch, the agent could traverse zero or more carpets (all with unknown changeability), and rewards are marked on the edges. Proof. Let π ∈ Γ be the optimal policy with unknown features L locked. Γ is returned by DomPolicies. We denote L ∩ Φ rel (Γ ) as A and L \\ Φ rel (Γ ) as B. For a proof by contradiction, assume π ∈ Γ . Then B = ∅. Otherwise, if B = ∅ (or equivalently, A = L), then L is a subset of Φ rel (Γ ) and π would have been added to Γ . Let π be the optimal policy with A locked. Since A ⊆ Φ rel (Γ ), we know π ∈ Γ . We observe that π does not change any features in B (otherwise features in B would show up in Φ rel (Γ )). So π is also the optimal policy with features A ∪ B = L locked. So π = π , which is an element of Γ . \n Finding Minimax-Regret Queries With DomPolicies, the agent need only query the user about relevant features. But it could further reduce the user's burden by being selective about which relevant features it asks about. In our running example (Figure  1 ), for instance, DomPolicies removes b3 and d3 from consideration, but also intuitively the agent should only ask about b1 or b2 if d2 is changeable. By iteratively querying, accounting for such dependencies (which can be gleaned from β in DomPolicies) and updating the relevant feature set, the agent can stop querying as soon as it finds (if one exists) a safe policy. For example, say it asks about the carpet and d2, and is told d2 (but not the carpet) is changeable. Now it has a safely-optimal policy, π 4 , given its knowledge, and could stop querying. But π 4 is the worst safe policy. Should it ask about boxes? That is the question we focus on here: How should an agent query to try to find a better safely-optimal policy than the one it already knows about. Specifically, we consider the setting where the agent is permitted to interrupt the user just once to improve upon its safely-optimal policy, by asking a single query about at most k unknown features. For each feature the user will reply whether or not it is in Φ U F . Formally, Φ q is a k-feature query where Φ q ⊆ Φ rel and |Φ q | = k. The post-response utility when the agent asks query Φ q , and Φ c ⊆ Φ A ? are actually changeable, is the value of the safely-optimal policy after the user's response: u(Φ q , Φ c ) = max π∈Π Φ A ? \\(Φq ∩Φc ) V π . (3) Recall the agent can only safely change features it queries about that the user's response indicates are changeable (Φ q ∩ Φ c ). What would be the agent's regret if it asks a k-feature query Φ q rather than a k-feature query Φ q ? We consider the circumstance where a set of features Φ c are changeable and under which the difference between the utilities of asking Φ q and Φ q is maximized. We call this difference of utilities the pairwise maximum regret of queries Φ q and Φ q , defined below in a similar way to Regan and  Boutilier [2010] : P M R(Φ q , Φ q ) = max Φc⊆Φ A ? (u(Φ q , Φ c ) − u(Φ q , Φ c )). (4) The maximum regret, denoted by M R, of query Φ q is determined by the Φ q that maximizes P M R(Φ q , Φ q ): M R(Φ q ) = max Φ q ⊆Φ rel ,|Φ q |=k P M R(Φ q , Φ q ). (5) The agent should ask the minimax-regret (k-feature) query: Φ M M R q = arg min Φq⊆Φ rel ,|Φq|=k M R(Φ q ). (6) The rationale of the minimax-regret criterion is as follows. Whenever the agent considers a query Φ q , there could exist a query Φ q that is better than Φ q under some true changeable features Φ c . The agent focuses on the worst case Φ c , where the difference between the utility of Φ q and the best query Φ q that could be asked is maximized. The agent uses adversarial reasoning to efficiently find the worst-case Φ c : Given that it is considering query Φ q , it asks what query Φ q and set of features Φ c an imaginary adversary would pick to maximize the gap between the utilities of Φ q and Φ q under Φ c (that is, u(Φ q , Φ c ) − u(Φ q , Φ c )). The agent wants to find a query Φ q that minimizes the worst case (maximum gap). Under the definition of M R, the agent, reasoning as if it were its imaginary adversary, must find the maximizing Φ q and Φ c . However, we can simplify this so that it only needs to find the maximizing Φ c . Note that since an imaginary adversary chooses both Φ q and Φ c , it wants to make sure that Φ c ⊆ Φ q , which means that it does not want the features not in Φ q to be changeable. We can then observe that M R(Φ q ) = max π ∈Γ: Φ rel (π )≤k (V π − max π∈Π Φ A ? \\{Φq ∩Φ rel (π )} V π ) (7) We call the π maximizing Eq. 7 the adversarial policy when the agent asks query Φ q , denoted by π M R Φq . With Eq. 7, the agent can compute M R based on the set of dominating policies (which DomPolicies already found), rather than the (generally much larger) powerset of the relevant features in Eq. 5. While using Eq. 7 is faster than Eq. 5, the agent still needs to do this computation for every possible query (Eq. 6) of size k. We contribute two further ways to improve the efficiency. First, we may not need to consider all relevant features if we can only ask about k of them. If a subset of relevant features satisfies the condition in Theorem 2, then we call it a set of sufficient features, because a minimax-regret k-feature query from that set is a globally minimax-regret k-feature query. Second, we introduce a pruning rule that we call query dominance in Theorem 3 to safely eliminate considering queries that cannot be better than ones already evaluated. The following theorem shows that if we can find any subset Φ of Φ rel such that for all k-feature subsets of Φ as queries, the associated adversarial policy's relevant features are contained in Φ, then the minimax regret query found by restricting queries to be subsets of Φ will also be a minimax regret query found by considering all queries in Φ rel . Such a (nonunique) set Φ will be referred to as a sufficient feature set (for the purpose of finding minimax regret queries). Theorem 2. (Sufficient Feature Set) For any set of ≥ k features Φ, if for all Φ q ⊆ Φ, |Φ q | = k, we have Φ rel (π M R Φq ) ⊆ Φ, then min Φq⊆Φ,|Φq|=k M R(Φ q ) = min Φq⊆Φ rel ,|Φq|=k M R(Φ q ). Proof Sketch. If a set of features Φ, |Φ| ≥ k, fails to include some features in Φ M M R q , when we query some k-subset of Φ, the adversarial policy should change some of the features in Φ M M R q \\ Φ. Otherwise, querying about Φ M M R q \\ Φ does not reduce the maximum regret. Then Φ M M R q \\ Φ are not necessary to be included in Φ M M R q . Given a set of sufficient features, the following theorem shows that it may not be necessary to compute the maximum regrets for all k-subsets to find the minimax-regret query. Theorem 3. (Query Dominance) For any pair of queries Φ q and Φ q , if Φ q ∩ Φ rel (π M R Φq ) ⊆ Φ q ∩ Φ rel (π M R Φq ), then M R(Φ q ) ≥ M R(Φ q ). Proof. Observe that M R(Φ q ) ≥ V π M R Φq − max π ∈Π Φ A ? \\(Φ q ∩Φ rel (π M R Φq )) V π ≥ V π M R Φq − max π ∈Π Φ A ? \\(Φq ∩Φ rel (π M R Φq )) V π = M R(Φ q ) We denote the condition Φ q ∩ Φ rel (π M R Φq ) ⊆ Φ q ∩ Φ rel (π M R Φq ) by dominance(Φ q , Φ q ). To compute dominance, we only need to store Φ rel (π M R Φq ) for all Φ q we have considered. Algorithm MMRQ-k below provides pseudocode for finding a minimax-regret k-feature query; it takes advantage of both the notion of a sufficient-feature-set as well as query dominance to reduce computation significantly relative to the brute-force approach of searching over all k-feature queries (subsets) of the relevant feature set. Algorithm MMRQ-k 1: Φ q ← an initial k-feature query 2: checked ← ∅; evaluated ← ∅ 3: Φ suf ← Φ q 4: agenda ← {Φ q } 5: while agenda = ∅ do 6: Φ q ← an element from agenda 7: if ¬∃ Φ q ∈evaluated dominance(Φ q , Φ q ) then 8: Compute M R(Φ q ) and π M R Φq 9: Φ suf ← Φ suf ∪ Φ rel (π M R Φq ) 10: evaluated ← evaluated ∪ {Φ q } 11: checked ← checked ∪ {Φ q } 12: agenda ← all k subsets of (Φ suf ) \\ checked 13: return arg min Φq∈evaluated M R(Φ q ) Intuitively, the algorithm keeps augmenting the set of features Φ suf , which contain the features in the queries we have considered and the features changed by their adversarial policies, until it becomes a sufficient feature set. agenda keeps track of k-subsets in Φ suf that we have not yet evaluated. According to Theorem 2, we can terminate the algorithm when agenda is empty (Line 5). We also use Theorem 3 to filter out queries which we know are not better than the ones we have found already (Line 7). Note that an initial Φ suf needs to be chosen, which can be arbitrary. Our implementation initializes Φ q with the Chain of Adversaries heuristic (Section 5). To illustrate when Algorithm MMRQ-k can and can't prune suboptimal queries and thus gain efficiency, consider finding the minimax-regret 2-feature query in Figure  2  (a), which should be {c 1 , c 2 }. If the agent considers a query that does not include c 1 , the adversarial policy would change c 1 , adding c 1 to Φ suf . If the agent considers a query that includes c 1 but not c 2 , the adversarial policy would change c 2 , adding c 2 to Φ suf . When the agent asks {c 1 , c 2 }, the adversarial policy changes c 3 (adversarially asserting that c 1 , c 2 are locked), so c 3 is added to Φ suf . With {c 1 , c 2 , c 3 } ⊆ Φ suf , the condition in Theorem 2 holds and the n − 3 other features can be safely ignored. The minimax-regret query constituted by features in Φ suf is {c 1 , c 2 }. However, in Figure  2  (b), Φ suf = Φ rel , and all |Φ rel | 2 would be evaluated. \n Empirical Evaluations We now empirically confirm that Algorithm MMRQ-k finds a minimax-regret query, and its theoretically sound Sufficient-Feature-Set and Query-Dominance based improvements can indeed pay computational dividends. We also compare our MMRQ-k algorithm to baseline approaches and the Chain of Adversaries (CoA) heuristic  [Viappiani and Boutilier, 2009]  adapted to our setting. Algorithm CoA begins with Φ q0 = ∅ and improves this query by iteratively computing: π ← arg max π ∈Γ:|Φ rel (π )∪Φq i |≤k (V π − max π∈Π Φ A ? \\{Φq i ∩Φ rel (π )} V π ) Φ qi+1 ← Φ qi ∪ Φ rel (π). The algorithm stops when |Φ qi+1 | = k or Φ qi+1 = Φ qi . Although Algorithm CoA greedily adds features to the query to reduce the maximum regret, unlike MMRQ-k it does not guarantee finding the minimax-regret query. For example, in Figure  2 (c), when k = 2, CoA first finds the optimal policy, which changes {c 1 , c 2 }, and returns that as a query, while the minimax-regret query is {c 1 , c 3 }. We compare the following algorithms in this section: 1. Brute force (rel. feat.) uses Algorithm DomPolicies to find all relevant features first and evaluates all k-subsets of the relevant features. 2. Algorithm MMRQ-k. 3. Algorithm CoA. 4. Random queries (rel. feat.), which contain k uniformly randomly chosen relevant features. 5. Random queries, which contain k uniformly randomly chosen unknown features, without computing relevant features first. \n No queries (equivalently vacuous queries). We evaluate the algorithms' computation times and the quality of the queries they find, reported as the normalized M R to capture their relative performance compared to the best and the worst possible queries. That is, the normalized M R of a query Φ q is defined as (M R(Φ q ) − M R(Φ M M R q ))/(M R(Φ q ⊥ ) − M R(Φ M M R q )), where Φ q ⊥ is a vacuous query, containing k features that are irrelevant and/or already known. The normalized M R of a minimaxregret query is 0 and that of a vacuous query is 1. Navigation. As illustrated in Figure  3 , the robot starts from the left-bottom corner and is tasked to turn off a switch at the top-right corner. The size of the domain is 6 × 6. The robot can move one step north, east or northeast at each time step. It stays in place if it tries to move across a border. The discount factor is 1. Initially, 10 clean carpets are uniformly randomly placed in the domain (the blue cells). In any cell without a carpet, the reward is set to be uniformly random in [−1, 0], and in a cell with a carpet the reward is 0. Hence, the robot will generally prefer to walk on a carpet rather than around it. The state of each carpet corresponds to one feature. The robot is uncertain about whether the user cares about whether any particular carpet gets dirty, so all carpet features are in Φ A ? . The robot knows that its own location and the state of the switch are in Φ A F . Since MMRQ-k attempts to improve on an existing safe policy, the left column and the top row never have carpets to ensure there is at least one safe path to the switch (the dotted line). The robot can ask one k-feature query before it takes any physical actions. We report results on 1500 trials. The only difference between trials are the locations of carpets, which are uniformly randomly placed. First, we compare the brute force method to our MMRQ-k algorithm (Figure  4 ). We empirically confirm that in all cases MMRQ-k finds a minimax regret query, matching Brute Force performance. We also see that brute force scales poorly as k grows while MMRQ-k, benefiting from Theorems 2 and 3, is more computationally efficient. We then want to see if and when MMRQ-k outperforms other candidate algorithms. In Figure  4 , when k is small, the greedy choice of CoA can often find the best features to add to the small query, but as k increases, CoA suffers from being too greedy. When k is large (approaches the number of unknown features), being selective is less important and all methods find good queries. We also consider how |Φ rel | affects the performance (Figure  5 ). When |Φ rel | is smaller   than k, a k-feature query that contains all relevant features is optimal. All algorithms would find an optimal query except Random (which selects from all unknown features) and No Queries. (The error bars are larger for small |Φ rel | since more rarely are only very few features relevant.) When |Φ rel | is slightly larger than k, even a random query may be luckily a minimax-regret query, and CoA unsurprisingly finds queries close to the minimax-regret queries. However, when |Φ rel | is much larger than k, the gap between MMRQ-k and other algorithms is larger. In summary, MMRQ-k's benefits increase with the opportunities to be selective (larger |Φ rel | k ). In Fig- ure 5, the gap is largest when k = 4, |Φ rel | = 10. We have also experimented with expected regret given a probabilistic model of how the user will answer queries. For example, if the user has probability p of saying an unknown feature is free (1 − p it's locked), then as expected, when p is very low, querying rarely helps, so using MMRQ-k or CoA matters little, and as p nears 1, CoA 's greedy optimism pays off to meet MMRQ-k 's minimax approach. But, empirically, MMRQ-k outperforms CoA for non-extreme values of p. \n Extensions and Scalability We now briefly consider applying our algorithms to larger, more complicated problems. As mentioned in Section 2, features' changeabilities might be more nuanced, with restrictions on what values they can take, individually or in combination. An example of the latter from Fig.  1  is where doors are revertible features, which means their changeability is dependent on the \"time\" feature: they are freely changeable except that by the time the episode ends they need to revert to their initial values. This expands the set of possible feature queries (e.g., asking if d2 is freely changeable differs from asking if it is revertible). In our experiments, this change accentuates the advantages of MMRQ-k over CoA: CoA asks (is-d2-locked, is-d2-revertible), hoping to hear \"no\" to both and follow a policy going through d2 without closing it. MMRQk asks (is-d2-locked, is-carpet-locked): since closing d2 only takes an extra time step, it is more valuable to know if the carpet is locked than if d2 can be left open. More nuanced feature changeability means DomPolicies will have to find policies for the powerset of every relevant combination of features' values (in the worst case the size of the state space). One option is to ignore nuances in ways that maintain safety (e.g., treat a feature as revertible even if sometimes it can be left changed) and solve such a safe abstraction of the problem. Or one could abstract based on guaranteed correlations in feature changeabilities (e.g., if all boxes have the same changeability then ignore asking about all but one). Another option is to find only a subset of dominating policies, for example by using knowlege of k to avoid finding dominating policies that would change more unknown features than could be asked about anyway. And, of course, as mentioned before, finding approximately-safely-optimal policies in DomPolicies Line 10 would help speed the process (and might be the only option for larger problem domains). Fortunately, such abstractions, heuristics, and approximations do not undermine safety guarantees. Recall that Dom-Policies and MMRQ-k are finding a query, not the agent's final policy: the safety of the agent depends on how it finds the policy it executes, not on the safety of policies for hypothetical changeability conditions. However, as coarser abstractions, heuristics, and approximations are employed in our algorithms, the queries found can increasingly deviate from the minimax-regret optima. Fortunately, if the agent begins with a safely-optimal policy, \"quick and dirty\" versions of our methods can never harm it (they just become less likely to help). And if it begins without such a policy, such versions of our methods might not guide querying well, but by eventually asking about every unknown feature (in the worst case) a safe policy will still be found (if one exists). \n Related Work & Summary Amodei et al.  [2016]  address the problem of avoiding negative side-effects by penalizing all side-effects while optimizing the value. In our work, we allow the agent to communicate with the user. Safety is also formulated as resolving reward uncertainty  [Amin et al., 2017; Hadfield-Menell et al., 2017] , following imperfectly-specified instructions  [Milli et al., 2017] , and learning safe states  [Laskey et al., 2016] . Safety issues also appear in exploration  [Hans et al., 2008; Moldovan and Abbeel, 2012; Achiam et al., 2017] . Here we only provide a brief survey on safety in MDPs.  Leike et al. [2017] , Amodei et al.  [2016], and Garcıa and Fernández [2015]  provide more thorough surveys. There are problems similar to finding safely-optimal policies, which find policies that satisfy some constraints/commitments or maximize the probability of reaching a goal state  [Witwicki and Durfee, 2010; Teichteil-Königsbuch, 2012; Kolobov et al., 2012] . There are also other works using minimax-regret and policy dominance  [Regan and Boutilier, 2010; Nilim and El Ghaoui, 2005] . and querying to resolve uncertainty  [Weng and Zanuttini, 2013; Regan and Boutilier, 2009; Cohn et al., 2011; Zhang et al., 2017] . We've combined and customized a number of these ideas to find a provably minimax-regret k-element query. In summary, we addressed the problem of an agent selectively querying a user about what features can be safely sideeffected. We borrowed existing ideas from the literature about dominating policies and minimax regret, wove them together in a novel way, and streamlined the resulting algorithms to improve scalability while maintaining safe optimality. Figure 1 : 1 Figure 1: The robot navigation domain. The dominating policies (see Section 3) are shown as arrows. \n a)T (s |s, a) + δ(s , s 0 ) ∀s ∈ S Φ A L ∪Φ A ? , ∀a ∈ A, x(s, a) = 0 The control variables x : S × A → R in the linear program are occupancy measures, i.e., x(s, a) is the expected discounted number of times that state action pair s, a is visited by the agent's policy, S Φ is the set of states where one or more features in Φ have different values from the initial state, and δ(s, s ) = 1 if s = s and is zero otherwise. \n ← ∅ the initial set of dominating policies 2: Φ rel ← ∅ the initial set of relevant features 3: checked ← ∅ It contains Φ ⊆ Φ rel we have examined so far. 4: β ← ∅ a pruning rule 5: agenda ← powerset(Φ rel ) \\ checked 6: while agenda = ∅ do 7: Φ ← least-cardinality element of agenda 8: if satisf y(Φ, β) then 9: (get safely-optimal policy with Φ locked) 10: π ← arg max π ∈ΠΦ V π by solving Eq. 1 11: if π exists then 12: Γ ← Γ ∪ {π}; add (Φ, Φ rel (π)) to β 13: \n (a) and (b) only need to compute policies linear in the number of relevant features: Only n+1 dominating safely-optimal policies are computed for Figure 2(a) (for Φ = ∅, {c 1 }, {c 1 , c 2 }, . . . ), and Figure 2(b) (for Φ = ∅, {c 1 }, {c 2 }, . . . , {c n }). Figure 2(c) computes policies for only half of the subsets. Theorem 1. The set of policies returned by Algorithm Dom-Policies is the set of all dominating policies. \n Figure 3 : 3 Figure 3: Office navigation and legend for following figures. \n Figure 4 : 4 Figure 4: Normalized maximum M R vs. k. |Φ ? | = 10. Brute force computation time is only shown for k = 1, 2, 3. \n Figure 5 : 5 Figure 5: Normalized M R vs. the number of relevant features. \n\t\t\t Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence", "date_published": "n/a", "url": "n/a", "filename": "0676.tei.xml", "abstract": "As it achieves a goal on behalf of its human user, an autonomous agent's actions may have side effects that change features of its environment in ways that negatively surprise its user. An agent that can be trusted to operate safely should thus only change features the user has explicitly permitted. We formalize this problem, and develop a planning algorithm that avoids potentially negative side effects given what the agent knows about (un)changeable features. Further, we formulate a provably minimax-regret querying strategy for the agent to selectively ask the user about features that it hasn't explicitly been told about. We empirically show how much faster it is than a more exhaustive approach and how much better its queries are than those found by the best known heuristic.", "id": "754899d59390b2f4bda487a0b4842460"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld", "Vincent Conitzer"], "title": "Safe Pareto Improvements for Delegated Game Playing *", "text": "Introduction Between Aliceland and Bobbesia lies a sparsely populated desert. Until recently, neither of the two countries had any interest in the desert. However, geologists have recently discovered that it contains large oil reserves. Now, both Aliceland and Bobbesia would like to annex the desert, but they worry about a military conflict that would ensue if both countries insist on annexing. Table  1  models this strategic situation as a normal-form game. The strategy DM (short for \"Demand with Military\") denotes a military invasion of the desert, demanding annexation. If both countries send their military with such an aggressive mission, the countries fight a devastating war. The strategy RM (for \"Refrain with Military\") denotes yielding the territory to the other country, but building defenses to prevent an invasion of one's current territories. Alternatively, the countries can choose to not raise a military force at all, while potentially still demanding control of the desert by sending only its leader (DL, short for \"Demand with Leader\"). In this case, if both countries demand the desert, war does not ensue. Finally, they could neither demand nor build up a military (RL). If one of the two countries has their military ready and the other does not, the militarized country will know and will be able to invade the other country. In gametheoretic terms, militarizing therefore strictly dominates not militarizing. Instead of making the decision directly, the parliaments of Aliceland and Bobbesia appoint special commissions for making this strategic decision, led by Alice and Bob, respectively. The parliaments can instruct these representatives in various ways. They can explicitly tell them what to do -for example, Aliceland could directly tell Alice to play DM. However, we imagine that the parliaments trust the commissions' judgments more than they trust their own and hence they might prefer to give an instruction of the type, \"make whatever demands you think are best for our country\" (perhaps contractually guaranteeing a reward in proportion to the utility of the final outcome). They might not know what that will entail, i.e., how the commissions decide what demands to make given that instruction. However -based on their trust in their representatives -they might still believe that this leads to better outcomes than giving an explicit instruction. We will also imagine these instructions are (or at least can be) given publicly and that the commissions are bound (as if by a contract) to follow these instructions. In particular, we imagine that the two commissions can see each other's instructions. Thus, in instructing their commissions, the countries play a game with bilateral precommitment. When instructed to play a game as best as they can, we imagine that the commissions play that game in the usual way, i.e., without further abilities to credibly commit or to instruct subcommittees and so forth. It may seem that without having their parliaments ponder equilibrium selection, Aliceland and Bobbesia cannot do better than leave the game to their representatives. Unfortunately, in this default equilibrium, war is still a possibility. Even the brilliant strategists Alice and Bob may not always be able to resolve the difficult equilibrium selection problem to the same pure Nash equilibrium. In the literature on commitment devices and in particular the literature on program equilibrium, important ideas have been proposed for avoiding such bad outcomes. Imagine for a moment that Alice and Bob will play a Prisoner's Dilemma (Table  3 ) (rather than the Demand Game of Table  1 ). Then the default of (Defect, Defect) can be Pareto-improved upon. Both original players (Aliceland and Bobbesia) can use the following instruction for their representatives: \"If the opponent's instruction is equal to this instruction, Cooperate; otherwise Defect.\"  [23, 17, 33, Sect. 10.4, 39]  Then it is a Nash equilibrium for both players to use this instruction. In this equilibrium, (Cooperate, Cooperate) is played and it is thus Pareto-optimal and Pareto-better than the default. In cases like the Demand Game, it is more difficult to apply this approach to improve upon the default of simply delegating the choice. Of course, if one could calculate the expected utility of submitting the default instructions, then one could similarly commit the representatives to follow some (joint) mix over the Pareto-optimal outcomes ((RM, DM), (DM, RM), (RM, RM), (DL, DL), etc.) that Pareto-improves on the default expected utilities.  1  However, we will assume that the original players are unable or unwilling to form probabilistic expectations about how the representatives play the Demand Game, i.e., about what would happen with the default instructions. If this is the case, then this type of Pareto improvement on the default is unappealing. The goal of this paper is to show and analyze how even without forming probabilistic beliefs about the representatives, the original players can  1  One might argue that due to the symmetry of the Demand Game, the original players should expect the representatives to play the game's unique symmetric equilibrium (in which both players play DM with probability 1 /4 and RM with probability 3 /4). Of course, in general games might be asymmetric. We here consider a symmetric game only for simplicity. More generally, some games with multiple equilibria might have a single \"focal\" equilibrium  [35, pp. 54 -58] that we expect the representatives to play. However, we maintain that in many games it is not clear what equilibrium should be played.  Pareto-improve on the default equilibrium. We will call such improvements safe Pareto improvements (SPIs). We here briefly give an example in the Demand Game. The key idea is for the original players to instruct the representatives to select only from {DL, RL}, i.e., to not raise a military. Further, they tell them to disvalue the conflict outcome without military (DL, DL) as they would disvalue the original conflict outcome of war in the default equilibrium. Overall, this means telling them to play the game of Table  2 . (Again, we could imagine that the instructions specify Table  2  to be how Aliceland and Bobbesia financially reward Alice and Bob.) Importantly, Aliceland's instruction to play that game must be conditional on Bobbesia also instructing their commission to play that game, and vice versa. Otherwise, one of the countries could profit from deviating by instructing their representative to always play DM or RM (or to play by the original utility function). The game of Table  2  is isomorphic to the DM-RM part of the original Demand Game of Table  1 . Of course, the original players know neither how the original Demand Game nor the game of Table  2  will be played by the representatives. However, since these games are isomorphic, one should arguably expect them to be played isomorphically. For example, one should expect that (RM, DM) would be played in the original game if and only if (RL, DL) would be played in the modified game. However, the conflict outcome (DM, DM) is replaced in the new game with the outcome (DL, DL). This outcome is harmless (Pareto-optimal) for the original players. Contributions Our paper generalizes this idea to arbitrary normal-form games and is organized as follows. In Section 2, we introduce some notation for games and multivalued functions that we will use throughout this paper. In Section 3, we introduce the setting of delegated game playing for this paper. We then formally define and further motivate the concept of safe Pareto  improvements. We also define and give an example of unilateral SPIs. These are SPIs that require only one of the players to commit their representative to a new action set and utility function. In Section 4, we briefly review the concepts of program games and program equilibrium and show that SPIs can be implemented as program equilibria. In Section 5, we introduce a notion of outcome correspondence between games. This relation expresses the original players' beliefs about similarities between how the representatives play different games. In our example, the Demand Game of Table  1  (arguably) corresponds to the game of Table  2  in that the representatives (arguably) would play (DM, DM) in the original game if and only if they play (DL, DL) in the new game, and so forth. We also show some basic results (reflexivity, transitivity, etc.) about the outcome correspondence relation on games. In Section 6 we show that the notion of outcome correspondence is central to deriving SPIs. In particular, we show that a game Γ s is an SPI on another game Γ if and only if there is a Pareto-improving outcome correspondence relation between Γ s and Γ. To derive SPIs, we need to make some assumptions about outcome correspondence, i.e., about which games are played in similar ways by representatives. We give two very weak assumptions of this type in Section 7. The first is that the representatives' play is invariant under the removal of strictly dominated strategies. For example, we assume that in the Demand Game the representatives only play DM and RM. Moreover we assume that we could remove DL and RL from the game and the representatives would still play the same strategies as in the original Demand Game with certainty. The second assumption is that the representatives play isomorphic games isomorphically. For example, once DL and RL are removed for both players from the Demand Game, the Demand Game is isomorphic to the game in Table  2  such that we might expect them to be played isomorphically. In Section 7.5, we derive a few SPIs -including our SPI for the Demand Game -using these assumptions. Section 8 shows that determining whether there exists an SPI based on these assumptions is NP-complete. Section 9 con-siders a different setting in which we allow the original players to let the representatives choose from newly constructed strategies whose corresponding outcomes map arbitrarily onto feasible payoff vectors from the original game. In this new setting, finding SPIs can be done in polynomial time. We conclude by discussing the problem of selecting between different SPIs on a given game (Section 10) and giving some ideas for directions for future work (Section 11). \n Preliminaries \n Games We here give some basic game-theoretic definitions. We assume the reader to be familiar with most of these concepts and with game theory more generally. An n-player (normal-form) game is a tuple (A, u) of a set A = A 1 × ... × A n of (pure) strategy profiles (or outcomes) and a function u : A → R n that assigns to each outcome a utility for each player. The Prisoner's Dilemma shown in Table  3  is a classic example of a game. The Demand Game of Table  1  is another example of a game that we will use throughout this paper. Instead of (A, u) we will also write (A 1 , ..., A n , u 1 , ..., u n ). We also write A −i for × j =i A i , i.e., for the Cartesian product of the action sets of all players other than i. We similarly write u −i and a −i for vectors containing utility functions and actions, respectively, for all players but i. If u i is a utility function and u −i is a vector of utility functions for all players other than i, then (even if i = 1) we use (u i , u −i ) for the full vector of utility functions where Player i has utility function u i and the other players have utility functions as specified by u −i . We use (A i , A −i ) and (a i , a −i ) analogously. We say that a i ∈ A i strictly dominates a i ∈ A i if for all a −i ∈ A −i , u i (a i , a −i ) > u i (a i , a −i ). For example, in the Prisoner's Dilemma, Defect strictly dominates Cooperate for both players. As noted earlier, DM and RM strictly dominate DL and RL for both players. For any given game Γ = (A, u), we will call any game Γ = (A , u ) a subset game of Γ if A i ⊆ A i for i = 1, ..., n. Note that a subset game may assign different utilities to outcomes than the original game. For example, the game of Table  2  is a subset game of the Demand Game. We say that some utility vector y ∈ R n is a Pareto improvement on (or is Pareto-better than) y ∈ R n if y i ≥ y i for i = 1, ..., n. We will also denote this by y ≥ y . Note that, contrary to convention, we allow y = y .  Whenever we require one of the inequalities to be strict, we will say that y is a strict Pareto improvement on y . In a given game, we will also say that an outcome a is a Pareto improvement on another outcome a if u(a) ≥ u(a ). We say that y is Pareto-optimal or Pareto-efficient relative to some S ⊂ R n if there is no element of S that strictly Pareto-dominates y. Let Γ = (A, u) and Γ = (A , u ) be two n-player games. Then we call an n-tuple of functions Φ = (Φ i : A i → A i ) i=1,...,n a (game) isomorphism between Γ and Γ if there are vectors λ ∈ R n + and c ∈ R n such that u(a 1 , ..., a n ) = λu (Φ 1 (a 1 ), ..., Φ n (a n )) + c for all a ∈ A. If there is an isomorphism between Γ and Γ , we call Γ and Γ isomorphic. For example, if we let Γ be the Demand Game and Γ s the subset game of Table  2 , then ({DM, RM}, {DM, RM}, u) is isomorphic to Γ s via the isomorphism Φ with Φ i (DM) = DL and Φ i (RM) = RL and the constants λ = (1, 1) and c = (0, 0). \n Multivalued functions For sets M and N , a multi-valued function Φ : M N is a function which maps each element m ∈ M to a set Φ(m) ⊆ N . For a subset Q ⊆ M , we define Φ(Q) := m∈Q Φ(m). Note that Φ(Q) ⊆ N and that Φ(∅) = ∅. For any set M , we define the identity function id M : M M : m → {m}. Also, for two sets M and N , we define all M,N : M N : m → N . We define the inverse Φ −1 : N M : n → {m ∈ M | n ∈ Φ(m)}. Note that Φ −1 (∅) = ∅ for any multi-valued function Φ. For sets M , N and Q and functions Φ : M N and Ψ : N Q, we define the composite Ψ • Φ : M Q : m → Ψ(Φ(m)). As with regular functions, composition of multi-valued functions is associative. We say that Φ : M N is singlevalued if |Φ(m)| = 1 for all m ∈ M . Whenever a multi-valued function is single-valued, we can apply many of the terms for regular functions. For example, we will take injectivity, surjectivity, and bijectivity for single-valued functions to have the usual meaning. We will never apply these notions to non-single-valued functions. \n Delegation and safe Pareto improvements We consider a setting in which a given game Γ is played through what we will call representatives. For example, the representatives could be humans whose behavior is determined or incentivized by some contract à la the principal-agent literature  [21] . We imagine that one way in which the representatives can be instructed is to in turn play a subset game Γ s = (A s 1 ⊆ A 1 , ..., A s n ⊆ A n , u s ) of the original game, without necessarily specifying a strategy or algorithm for solving such a game. We emphasize, again, that u s is allowed to be a vector of entirely different utility functions. For any subset game Γ s , we denote by Π(Γ s ) the outcome that arises if the representatives play the subset game Γ s of Γ. Because it is unclear what the right choice is in many games, the original players might be uncertain about Π(Γ s ). We will therefore model each Π(Γ s ) as a random variable. We will typically imagine that the representatives play Γ in the usual way, i.e., that they are not able to make further commitments or delegate again. For example, we imagine that if Γ is the Prisoner's Dilemma, then Π(Γ) = (Defect, Defect) with certainty. The original players trust their representatives to the extent that we take Π(Γ) to be a default way for the game to played for any Γ. That is, by default the original players tell their representatives to play the game as given. For example, in the Demand Game, it is not clear what the right action is. Thus, if one can simply delegate the decision to someone with more relevant expertise, that is the first option one would consider. We are interested in whether and how the original players can jointly Pareto-improve on the default. Of course, one option is to compute the expected utilities in the default (E [u(Π(Γ))]) and then let the representatives play a distribution over outcomes whose expected utility exceeds that default expected utility. However, this is unrealistic if Γ is a complex game with potentially many Nash equilibria. For one, the precise point of delegation is that the original players are unable or unwilling to properly evaluate Γ. Second, there is no widely agreed upon, universal procedure for selecting an action in the face of equilibrium selection problems. In such cases, the original players may in practice be unable to form a probability distribution over Π(Γ). This type of uncertainty is sometimes referred to as Knightian uncertainty, following Knight's  [19]  distinction between the concepts of risk and uncertainty. We address this problem in a typical way. Essentially, we require of any attempted improvement that it incurs no regret in the worst-case. That is, we are interested in subset games Γ s that are Pareto improvements with certainty under weak and purely qualitative assumptions about Π.  2  In particular, in Section 7, we will introduce the assumptions that the representatives do not play strictly dominated actions and play isomorphic games isomorphically. Definition 1. Let Γ s be a subset game of Γ. We say Γ s is a safe Pareto improvement (SPI) on Γ if u(Π(Γ s )) ≥ u(Π(Γ)) with certainty. We say that Γ s is a strict SPI if furthermore, there is a player i s.t. u i (Π(Γ s )) > u i (Π(Γ s )) with positive probability. For example, in the introduction we have argued that the subset game in Table  2  is a strict SPI on the Demand Game (Table  1 ). Less interestingly, if we let Γ = (A, u) be the Prisoner's Dilemma (Table  3 ), then we might expect ({Cooperate}, {Cooperate}, u) to be an SPI on Γ. After all, we might expect that Π(Γ) = (Defect, Defect) with certainty, while it must be Π({Cooperate}, {Cooperate}, u) = (Cooperate, Cooperate) with certainty, for lack of alternatives. Both players prefer mutual cooperation over mutual defection. \n Unilateral SPIs Both SPIs given above require both players to let their representatives choose from restricted strategy sets to maximize something other than the original player's utility function. Definition 2. We will call a subset game Γ s = (A s , u s ) of Γ = (A, u) unilateral if for all but one i ∈ {1, ..., n} it holds that A s i = A i and u s i = u i . Consequently, if a unilateral subset game Γ s of Γ is also an SPI for Γ, we call Γ s a unilateral SPI. We now give an example of a unilateral SPI using the Complicated Temptation Game, formalized as a normal-form game in Table  4 . (We give the not-so complicated Temptation Game -in which we can only give a trivial example of SPIs -in Section 7.5.) Two players each deploy a robot. Each of the robots faces two choices in parallel. First, each can choose whether to work on Project 1 or Project 2. Player 1 values Project 1 higher and Player 2 values Project 2 higher, but the robots are more effective if they work on the same project. To complete the task, the two robots need to share a resource. Robot 2 manages the resource and can choose whether to control Robot 1's access tightly (e.g., by frequently checking on the resource, or requiring Robot 1 to demonstrate a need for the resource) or give Robot 1 relatively free access. Controlling access tightly decreases the efficiency of both robots, though the exact costs depend on which projects the robots are working on. Robot 1 can choose between using the resource as intended by Robot 2; or give in to the temptation of trying to steal as much of the resource as possible to use it for other purposes. Regardless of what Robot 2 does (in particular, regardless of whether Robot 2 controls access or not), Player 1 prefers trying to steal. In fact, if Robot 2 controls access and Robot 1 refrains from theft, they never get anything done. Given that Robot 1 tries to steal, Player 2 prefers his Robot 2 to control access. As usual we assume that the original players can instruct their robots to play arbitrary subset games of Γ (without specifying an algorithm for solving such a game) and that they can give such instructions conditional on the other player providing an analogous instruction. Player 1 has a unilateral SPI in the Complicated Temptation Game. In particular, Player 1 can commit her representative to play only from R 1 and R 2 and to assign utilities u s 1 (R 1 , F 1 ) = u 1 (T 1 , C 1 ) = 2, u s 1 (R 1 , F 2 ) = u 1 (T 1 , C 2 ) = 1, u s 1 (R 2 , F 1 ) = u 1 (T 2 , C 1 ) = 1, and u s 1 (R 2 , F 2 ) = u 1 (T 2 , C 2 ) = 4; otherwise u s 1 does not differ from u 1 . The resulting SPI is given in Table  5 . In this subset game, Player 2's representative -knowing that Player 1's representative will only play from R 1 and R 2 -will choose from F 1 and F 2 (since F 1 and F 2 strictly dominate C 1 and C 2 in Table  5 ). Now notice that the remaining subset game is isomorphic to the ({T 1 , T 2 }, {C 1 , C 2 }) subset game of the original Complicated Temptation Game, where T 1 maps to R 1 and T 2 maps to R 2 for both Player 1, and C 1 maps to F 1 and C 2 maps to Player 2 C 1 C 2 F 1 F 2 Player 1 T 1 2, 4 1, 1 6, 0 6, 0 T 2 1, 1 4, 2 6, 0 6, 0 R 1 0, 0 0, 0 3, 5 3, 2 R 2 0, 0 0, 0 2, 2 5, 3 Table 4: Complicated Temptation Game Player 2 C 1 C 2 F 1 F 2 Player 1 R 1 0, 0 0, 0 2, 5 1, 2 R 2 0, 0 0, 0 1, 2 4, 3 Table  5 : Safe Pareto improvement for the Complicated Temptation Game F 2 for Player 2. Player 1's representative's utilities have been set to be the same between the two; and Player 2's utilities happen to be the same up to a constant (1) between the two subset games. Thus, we might expect that if Π(Γ) = (T 1 , C 1 ), then Π(Γ s ) = (R 1 , F 1 ), and so on. Finally, notice that u(R 1 , F 1 ) ≥ u(T 1 , C 1 ) and so on. Hence, Table  5  is indeed an SPI on the Complicated Temptation Game. Such unilateral changes are particularly interesting because they only require one of the players to be able to credibly delegate. That is, it's enough for a single player to instruct their representative to choose from a restricted action set to maximize a new utility function. The other players can simply instruct their representatives to play the game in the normal way (i.e., maximizing the respective players' original utility functions without restrictions on the action set). In fact, we may also imagine that only one player i delegates at all, while the other players choose an action themselves, after observing Player i's instruction to her representative. One may object that in a situation where only one player can commit, the sole player with commitment power can simply play the meta game as a standard unilateral commitment (Stackelberg) game [as studied by, e.g.,  8, 38, 43]  or perhaps as a first mover in a sequential game (as solved by backward induction), without bothering with any Pareto conditions. For example, in the Complicated Temptation Game, Player While this is true in many situations, it is easy come up with scenarios in which it is not and in which SPIs are relevant. For one, we may imagine that only one Player has the fine-grained commitment and delegation abilities needed for SPIs but that the other players can still credibly commit (or are already credibly committed) against any \"commitment trickery\" that clearly leaves them worse off. For instance, many people appear credibly committed by intuitions about fairness and retributivist instincts and emotions [see, e.g., 31, Chapter 6, especially the section \"The Doomsday Machine\"], but are nonetheless very limited in their abilities to commit. Second, we may imagine that the players who cannot commit are subject to reputation effects. Then they might want to build a reputation of resisting coercion. (In contrast, we expect a reputation of playing along with unilateral SPIs to be beneficial in most such situations.) \n Implementing safe Pareto improvements as program equilibria So far, we have been vague about the details of the strategic situation that the original players face in instructing their representatives. From what sets of actions can they choose? How can they jointly let the representatives play some new subset game Γ s ? Are SPIs Nash equilibria of the meta game played by the representatives? If I instruct my representative to play the SPI of Table  2  in the Demand Game, could my opponent not instruct her representative to play DM? In this section, we briefly describe one way to fill this gap by discussing the concept of program games and program equilibrium  [33, Sect. 10.4, 39, 12, 3, 10, 26] . This section is essential to understanding why SPIs (especially omnilateral ones) are relevant. However, the remaining technical content of this paper does not rely on this section and the main ideas presented here are straightforward from previous work. We therefore only give an informal exposition. For formal detail, see Appendix A. For any game Γ = (A, u), the program equilibrium literature considers the following meta game. First, each player i chooses from a set of computer programs. Each program then receives as input a vector containing everyone else's chosen program. Each player i's program then returns an action from A i , player i's set of actions in Γ. Together these actions then form an outcome a ∈ A of the original game. Finally, the utilities u(a) are realized according to the utility function of Γ. The meta game can be analyzed like any other game. Its Nash equilibria are called program equilibria. Importantly, the program equilibria can implement payoffs not implemented by any Nash equilibria of Γ itself. For example, in the Prisoner's Dilemma, both players can submit a program that says: \"If the opponent's chosen computer program is equal to this computer program, Cooperate; otherwise Defect.\"  [23, 17, 33, Sect. 10.4, 39]  This is a program equilibrium which implements mutual cooperation. In the setting for our paper, we similarly imagine that each player i can choose from a set of programs that in turn choose from A i . However, the types of program that we have in mind here are more sophisticated than those typically considered in the program equilibrium literature. Specifically we imagine that the programs are executed by intelligent representatives who are themselves able to competently choose an action for player i in any given game Γ s , without the original player having to describe how this choice is to be made. The original player may not even understand much about this program other than that it generally plays well. Thus, in addition to the elementary instructions used in a typical computer program (branches, comparisons, arithmetic operations, etc.), we allow player i to use an instruction \"Play Π i (Γ s )\" in the program she submits. To jointly let the representatives play, e.g., the SPI Γ s of Table  2  on the Demand Game of Table  1 , the representatives can both use an instruction that says, \"If the opponent's chosen program is analogous to this one, play Π i (Γ s ); otherwise play DM\". Assuming some minimal rationality requirements on the representatives (i.e., on how \"play Π i (Γ s )\" is implemented), this is a Nash equilibrium. Figure  1  illustrates how (in the two-player case) the meta game between the original players is intended to work. For illustration consider the following two real-world instantiations of this setup. First, we might imagine that the original players hire human representatives. Each player specifies, e.g., via monetary incentives, how she wants her representative to act by some contract. For example, a player might contract her representative to play a particular action; or she might specify in her contract a function (u s i ) over outcomes according to which she will pay the representative after an outcome is obtained. Moreover, these contracts might refer to one another. For example, Player 1's contract with her representative might specify that if Player 2 and his representative use an analogous contract, then she will pay her representative according to Table  2 . As a second, more futuristic scenario, you could imagine that the representatives are software agents whose goals are specified by so-called smart contracts, i.e., computer programs implemented on a blockchain to be publicly verifiable  [6, 34] . To justify our study of SPIs, we prove that every SPI is played in some program equilibrium: Theorem 1. Let Γ be a game and Γ s be an SPI of Γ. Now consider a program game on Γ, where each player i can choose from a set of computer programs that output actions for Γ. In addition to the normal kind of instructions, we allow the use of the command \"play Π i (Γ )\" for any subset game Γ of Γ. Finally, assume that Π(Γ) guarantees each player i at least that player's minimax utility (a.k.a. threat point) in the base game Γ. Then Π(Γ s ) is played in a program equilibrium, i.e., in a Nash equilibrium of the program game. We prove this in Appendix A. As an alternative to having the original players choose contracts separately, we could imagine the use of jointly signed contracts which only come into effect once signed by all players [cf.  18, 24] . Also compare earlier work by Sen  [37]  and Raub  [32] , which we discuss in Appendix B. Definition 3. Consider two games Γ = (A 1 , ..., A n , u) and Γ = (A 1 , ..., A n , u ). We write Γ ∼ Φ Γ for Φ : A A if Π(Γ ) ∈ Φ(Π(Γ)) with certainty. Note that Γ ∼ Φ Γ is a statement about Π, i.e., about how the representatives choose. Whether such a statement holds generally depends on the specific representatives being used. In Section 7, we describe two general circumstances under which it seems plausible that Γ ∼ Φ Γ . For example, if two games Γ and Γ are isomorphic, then one might expect Γ ∼ Φ Γ , where Φ is the isomorphism between the two games. We now illustrate this notation using our discussion from the Demand Game. Let Γ be the Demand Game of Table  1 . First, it seems plausible that Γ is in some sense equivalent to Γ , where Γ = ({DM, RM, u) is the game that results from removing DL and RL for both players from Γ. Again, strict dominance could be given as an argument. We can now formalize this as Γ ∼ Φ Γ , where Φ(a 1 , a 2 ) = {(a 1 , a 2 )} if a 1 , a 2 ∈ {DM, RM} and Φ(a 1 , a 2 ) = ∅ otherwise. Next, it seems plausible that Γ ∼ Ψ Γ s , where Γ s is the game of Table  2  and Ψ is the isomorphism between Γ and Γ s . We now state some basic facts about the relation ∼, many of which we will use throughout this paper. Lemma 2. Let Γ = (A, u), Γ = (A , u ), Γ = ( Â, û) and Φ, Ξ : A A , Ψ : A Â. 1. Reflexivity: Γ ∼ id A Γ, where id A : A A : a → {a}. \n Symmetry: If Γ ∼ Φ Γ , then Γ ∼ Φ −1 Γ. 3. Transitivity: If Γ ∼ Φ Γ and Γ ∼ Ψ Γ, then Γ ∼ Ψ•Φ Γ. 4. If Γ ∼ Φ Γ and Φ(a) ⊆ Ξ(a) for all a ∈ A, then Γ ∼ Ξ Γ . 5. Γ ∼ all A,A Γ , where all A,A : A A : a → A . 6. If Γ ∼ Φ Γ and Φ(a) = ∅, then Π(Γ) = a with certainty. 7. If Γ ∼ Φ Γ and Φ −1 (a ) = ∅, then Π(Γ ) = a with certainty. Proof. 1. By reflexivity of equality, Π(Γ) = Π(Γ) with certainty. Hence, Π(Γ) ∈ id A (Π(Γ)) by definition of id A . Therefore, Γ ∼ id A Γ by definition of ∼, as claimed. \n Γ ∼ Φ Γ means that Π(Γ ) ∈ Φ(Π(Γ)) with certainty. Thus, Π(Γ) ∈ {a∈A | Π(Γ )∈Φ(a)} = Φ −1 (Π(Γ )), where equality is by the definition of the inverse of multi-valued functions. We conclude (by definition of ∼) that Γ ∼ Φ −1 Γ as claimed. 3. If Γ ∼ Φ Γ , Γ ∼ Ψ Γ, then by definition of ∼, (i) Π(Γ ) ∈ Φ(Π(Γ)) and (ii) Π( Γ) ∈ Ψ(Π(Γ )), both with certainty. The former (i) implies {Π(Γ )} ⊆ Φ(Π(Γ)). Hence, Ψ(Π(Γ )) = Ψ({Π(Γ )}) ⊆ Ψ(Φ(Π(Γ))). With ii, it follows that Π( Γ) ∈ Ψ(Φ(Π(Γ))) with certainty. By defini- tion, Γ ∼ Ψ•Φ Γ as claimed. 4. It is Π(Γ ) ∈ Φ(Π(Γ)) ⊆ Ξ(Π(Γ)) with certainty. Thus, by definition Γ ∼ Ξ Γ . \n By definition of Π, it is Π(Γ ) ∈ A with certainty. By definition of all A,A , it is all A,A (Π(Γ)) = A with certainty. Hence, Π(Γ ) ∈ all A,A (Π(Γ) ) with certainty. We conclude that Γ ∼ all A,A Γ as claimed. 6. With certainty, Π(Γ ) ∈ Φ(Π(Γ)) (by assumption). Also, with certainty Π(Γ ) / ∈ ∅. Hence, Φ(Π(Γ)) = ∅ with certainty. We conclude that Π(Γ) = a with certainty. Items 1-3 show that ∼ has properties resembling those of an equivalence relation. Note, however, that since ∼ is not a binary relationship, ∼ itself cannot be an equivalence relation in the usual sense. We can construct equivalence relations, though, by existentially quantifying over the multivalued function. For example, we might define an equivalence relation R on games, where (Γ, Γ ) ∈ R if and only if there is a single-valued bijection Φ such that Γ ∼ Φ Γ .  3  Item 4 states that if we can make an outcome correspondence claim less precise, it will still hold true. Item 5 states that in the extreme, it is always Γ ∼ all A,A Γ , where all A,A is the trivial, maximally imprecise outcome correspondence function that confers no information. Item 6 shows that ∼ can be used to express the elimination of outcomes, i.e., the belief that a particular outcome (or strategy) will never occur. Besides an equivalence relation, we can also use ∼ with quantification over the respective outcome correspondence function to construct (nonsymmetric) preorders over games, i.e., relations that are transitive and reflexive (but not symmetric or antisymmetric). Most importantly, we can construct a preorder on games where Γ Γ if Γ ∼ Φ Γ for a Φ that always increases every player's utilities. \n Safe Pareto improvements through outcome correspondence We now show that as advertised, outcome correspondence is closely tied to SPIs. The following theorem shows not only how outcome correspondences can be used to find (and prove) SPIs. It also shows that any SPI requires an outcome correspondence relation via a Pareto-improving correspondence function. Definition 4. Let Γ = (A, u) be a game and Γ s = (A s , u s ) be a subset game of Γ. Further let Φ : A → A s be such that Γ ∼ Φ Γ . We call Φ a Paretoimproving outcome correspondence (function) if u(a s ) ≥ u(a) for all a ∈ A and all a s ∈ Φ(a). Theorem 3. Let Γ = (A, u) be a game and Γ s = (A s , u s ) be a subset game of Γ. Then Γ s is an SPI on Γ if and only if there is a Pareto-improving outcome correspondence from Γ to Γ s . Proof. ⇐: By definition, Π(Γ s ) ∈ Φ(Π(Γ)) with certainty. Hence, for i = 1, 2, u i (Π(Γ s )) ∈ u i (Φ(Π(Γ))) with certainty. Hence, by assumption about Φ, with certainty, u i (Π(Γ s )) ≥ u i (Π(Γ)). ⇒: Assume that u i (Π(Γ)) ≥ u i (Π(Γ s )) with certainty for i = 1, 2. We define Φ : A → A s : a → {a s ∈ A s | u(a s ) ≥ u(a)} . It is immediately obvious that Φ is Pareto-improving as required. Also, whenever Π(Γ) = a and Π(Γ s ) = a s for any a ∈ A and a s ∈ A s , it is (by assumption) with certainty u(a s ) ≥ u(a). Thus, by definition of Φ, it holds that a s ∈ Φ(a). We conclude that Γ ∼ Φ Γ s as claimed. Note that the theorem concerns weak SPIs and therefore allows the case where with certainty u(Π(Γ)) = u(Π(Γ s )). To show that some Γ s is a strict SPI, we need additional information about which outcomes occur with positive probability. This, too, can be expressed via our outcome correspondence relation. However, since this is cumbersome, we will not formally address strictness much to keep things simple.  4  We now illustrate how outcome correspondences can be used to derive the SPI for the Demand Game from the introduction as per Theorem 3. Of course, at this point we have not made any assumptions about when games are equivalent. We will introduce some in the following section. Nevertheless, we can already sketch the argument using the specific outcome correspondences that we have given intuitive arguments for. Let Γ again be the Demand Game of Table  1 . Then, as we have argued, Γ ∼ Φ Γ , where Γ = ({DM, RM}, {DM, RM}, u) is the game that results from removing DL and RL for both players; and Φ(a 1 , a 2 ) = {(a 1 , a 2 )} if a 1 , a 2 ∈ {DM, RM} and Φ(a 1 , a 2 ) = ∅ otherwise. In a second step, Γ ∼ Ψ Γ s , where Γ s is the game of Table  2  and Ψ is the isomorphism between Γ and Γ s . Finally, transitivity (Lemma 2.3) implies that Γ ∼ Ψ•Φ Γ s . To see that Ψ • Φ is Pareto-improving for the original utility functions of Γ, notice that Φ does not change utilities at all. The correspondence function Ψ maps the conflict outcome (DM, DM) onto the outcome (DL, DL), which is better for both original players. Other than that, Ψ, too, does not change the utilities. Hence, Ψ • Φ is Pareto-improving. By Theorem 3, Γ s is therefore an SPI on Γ. In principle, Theorem 3 does not hinge on Π(Γ) and Π(Γ s ) resulting from playing games. An analogous result holds for any random variables over A and A s . In particular, this means that Theorem 3 applies also if the representatives receive other kinds of instructions (cf. Section 4). However, it seems hard to establish non-trivial outcome correspondences between Π(Γ) and other types of instructions. Still, the use of more complicated instructions can be used to derive different kinds of SPIs. For example, if there are different game SPIs, then the original players could tell their representatives to randomize between them in a coordinated way. \n Assumptions about outcome correspondence To make any claims about how the original players should play the metagame, i.e., about what instructions they should submit, we generally need to make assumptions about how the representatives choose and (by Theorem 3) about outcome correspondence in particular.  5  We here make two fairly weak assumptions. \n Elimination Our first is that the representatives never play strictly dominated actions and that removing them does not affect what the representatives would choose. Assumption 1. Let Γ = (A, u) be an arbitrary n-player game where A 1 , ..., A n are pairwise disjoint, and let ãi ∈ A i be strictly dominated by some other strategy in A i . Then Γ ∼ Φ (A −i , A i − {ã i }, u |(A −i ,A i −{ã i }) ), where for all a −i ∈ A −i , Φ(ã i , a −i ) = ∅ and Φ(a i , a −i ) = {(a i , a −i )} whenever a i = ãi . Assumption 1 expresses that representatives should never play strictly dominated strategies. Moreover, it states that we can remove strictly dominated strategies from a game and the resulting game will be played in the same way by the representatives. For example, this implies that when evaluating a strategy a i , the representatives do not take into account how many other strategies a i strictly dominates. Assumption 1 also allows (via Transitivity of ∼ as per Lemma 2.3) the iterated removal of strictly dominated strategies. The notion that we can (iteratively) remove strictly dominated strategies is common in game theory  [28, 20, 27 , Section 2.9, Chapter 12] and has rarely been questioned. It is also implicit in the solution concept of Nash equilibrium -if a strategy is removed by iterated strict dominance, that strategy is played in no Nash equilibrium. However, like the concept of Nash equilibrium, the elimination of strictly dominated strategies becomes implausible if the game is not played in the usual way. In particular, for Assumption 1 to hold, we will in most games Γ have to assume that the representatives cannot in turn make credible commitments (or delegate to further subrepresentatives) or play the game iteratively  [2] . \n Isomorphisms Our second assumption is that the representatives play isomorphic games isomorphically when those games are fully reduced. Assumption 2. Let Γ = (A, u) and Γ = (A , u ) be two games that do not contain strictly dominated actions. If Γ and Γ are isomorphic, then there exists an isomorphism Φ between Γ and Γ such that Γ ∼ Φ Γ . Note that if there are multiple game isomorphisms, then we assume outcome correspondence for only one of them. This is necessary for the assumption to be satisfiable in the case of games with action symmetries. (Of course, such games are not the focus of this paper.) For example, let Γ be Rock-Paper-Scissors. Then Γ is isomorphic to itself via the function Φ that for both players maps Rock to Paper, Paper to Scissors, and Scissors to Rock. But if it were Γ ∼ Φ Γ, then this would mean that if the representatives play Rock in Rock-Paper-Scissors, they play Paper in Rock-Paper-Scissors. Contradiction! We will argue for the consistency of our version of the assumption in Section 7.3. Notice also that we make the assumption only for reduced games. This relates to the previous point about action-symmetric games. For example, consider two versions of Rock-Paper-Scissors and assume that in both versions both players have an additional strictly dominated action that breaks the action symmetries e.g., the action, \"resign and give the opponent $10 if they play Rock/Paper\". Then there would only be one isomorphism between these two games (which maps Rock to Paper, Paper to Scissors, and Scissors to Rock for both players). However, in light of Assumption 1, it seems problematic to assume that these strictly dominated actions restrict the outcome correspondences between these two games.  6  One might worry that reasoning about the existence of multiple isomorphisms renders it intractable to deal with outcome correspondences as implied by Assumption 2, and in particular that it might make it impossible to tell whether a particular game is an SPI. However, one can intuitively see that the different isomorphisms between two games do analogous operations. In particular, it turns out that if one isomorphism is Pareto-improving, then they all are: Lemma 4. Let Φ and Ψ be isomorphisms between Γ and Γ . If Φ is (strictly) Pareto-improving, then so is Ψ. We prove Lemma 4 in Appendix C. Lemma 4 will allow us to conclude from the existence of a Paretoimproving isomorphism Φ that there is a Pareto-improving Ψ s.t. Γ ∼ Ψ Γ by Assumption 2, even if there are multiple isomorphisms between Γ and Γ . In the following, we can therefore afford to be lax about our ignorance (in some games) about which outcome isomorphism induces outcome equivalence. We will therefore generally write \"Γ ∼ Φ Γ by Assumption 2\" as short for \"Φ is a game isomorphism between Γ and Γ and hence by Assumption 2 there exists an isomorphism Ψ such that Γ ∼ Ψ Γ \". One could criticize Assumption 2 by referring to focal points (introduced by Schelling [35, pp. 54-58]) as an example where context and labels of strategies matter. A possible response might be that in games where context plays a role, that context should be included as additional information and not be considered part of (A, u). Assumption 2 would then either not apply to such games with (relevant) context or would require one to, in some way, translate the context along with the strategies. However, in this paper we will not formalize context, and assume that there is no decision-relevant context. \n Consistency of Assumptions 1 and 2 We will now argue that there exist representatives that indeed satisfy Assumptions 1 and 2, both to provide intuition and because our results would not be valuable if Assumptions 1 and 2 were inconsistent. We will only sketch the argument informally. To make the argument formal, we would need to specify in more detail what the set of games looks like and in particular what the objects of the action sets are. Imagine that for each player i there is a book 7 that on each page describes a normal-form game that does not have any strictly dominated strategies. The actions have consecutive integer labels. Importantly, the book contains no pair of games that are isomorphic to each other. Moreover, for every fully reduced game, the book contains a game that is isomorphic to this game. (Unless we strongly restrict the set of games under consideration, the book must therefore have infinitely many pages.) We imagine that each player's book contains the same set of games. On each page, the book for Player i recommends one of the actions of Player i to be taken deterministically.  8  Each representative owns a potentially different version of this book and uses it as follows to play a given game Γ. First the given game is fully reduced by iterated strict dominance. They then look up the unique game in the book that is isomorphic to Γ red and map the action labels in Γ red onto the integer labels of the game in the book via some isomorphism. If there are multiple isomorphisms from Γ red to the relevant page in the book, then all representatives decide between them using the same deterministic procedure. Finally they choose the action recommended by the book. It is left to show a pair of representatives Π thus specified satisfies Assumptions 1 and 2. We first argue that Assumption 1 is satisfied. Let Γ be a game and let Γ be a game that arises from removing a strictly dominated action from Γ. By the well known path independence of iterated elimination of strictly dominated strategies  [1, 15, 28] , fully reducing Γ and Γ results in the same game. Hence, the representatives play the same actions in Γ and Γ . Second, we argue that Assumption 2 is satisfied. Let us say Γ and Γ are fully reduced and isomorphic. Then it is easy to see that each player i, plays Γ and Γ based on the same page of their book. Let the game on that book page be Γ. Let Φ : A → Ã and Φ : A → Ã be the bijections used by the representatives to translate actions in Γ and Γ , respectively, to labels in Γ. Then if the representatives take actions a in Γ, the actions Φ(a) are the ones specified by the book for Γ, and hence the actions Φ−1 (Φ(a)) are played in Γ . Thus Γ ∼ Φ−1 •Φ Γ. It is easy to see that Φ−1 • Φ is a game isomorphism between Γ and Γ. \n Discussion of alternatives to Assumptions 1 and 2 One could try to use principles other than Assumptions 1 and 2. We here give some considerations. First, game theorists have also considered the iterated elimination of weakly dominated strategies  [14, 22, Section 4.11] . Unfortunately, the iterated removal of weakly dominated strategies is pathdependent [20, Section 2.7.B, 5, Section 5.2, 27, Section 12.3]. That is, for some games, iterated removal of weakly dominated strategies can lead to different subset games, depending on which weakly dominated strategy one chooses to eliminate at any stage. A straightforward extension of Assumption 1 to allow the elimination of weakly dominated strategies would therefore be inconsistent. The iterated removal of strictly dominated strategies, on the other hand, is path-independent, and in the 2-player case always eliminates exactly the non-rationalizable strategies  [1, 15, 28] . Many other dominance concepts have been shown to be path independent. For an overview, see Apt  [1] . We could have used any of these path-independent dominance concepts. With Assumptions 1 and 2, all our outcome correspondence functions are either 1-to-1 or 1-to-0. Other elimination assumptions could involve the use of many-to-1 or even many-to-many functions. In general, such functions are needed when a strategy ãi can be eliminated to obtain a strategically equivalent game, but in the original game ãi may still be played. The simplest example would be the elimination of payoff-equivalent strategies. Imagine that in some game Γ for all opponent strategies a −i ∈ A −i it is the case that u(ã i , a −i ) = u(â i , a −i ) and that there are no other strategies that are similarly payoff-equivalent to ãi and âi . Then one would assume that Γ ∼ Φ (A i − {ã i }, A −i , u), where Φ maps ãi onto {â i } and otherwise Φ is just the identity function. \n Examples In this section, we use Assumptions 1 and 2 to formally prove a few SPIs. Proposition (Example) 5. Let Γ be the Prisoner's Dilemma (Table  3 ) and Γ s = (A s 1 , A s 2 , u s 1 , u s 2 ) be any subset game of Γ with A s 1 = A s 2 = {Cooperate}. Then under Assumption 1, Γ s is a strict SPI on Γ. Proof. By applying Assumption 1 twice and Transitivity once, Γ ∼ Φ Γ D , where Γ D = ({Defect}, {Defect}, u) and Φ(Defect, Defect) = {(Defect, Defect)} and Φ(a 1 , a 2 ) = ∅ for all (a 1 , a 2 ) = (Defect, Defect). By Lemma 2.5, we further obtain Γ D ∼ all Γ s , where Γ s is as described in the proposition. Hence, by transitivity, Γ ∼ all•Φ Γ s . It is easy to verify that the function all • Φ is Pareto-improving. Proposition (Example) 6. Let Γ be the Demand Game of Table  1  and Γ s be the subset game described in Table  2 . Under Assumptions 1 and 2, Γ s is an SPI on Γ. Further, if P (Π(Γ)=(DM, DM)) > 0, then Γ s is a strict SPI. Proof. Let (A 1 , A 2 , u 1 , u 2 ) = Γ. We can repeatedly apply Assumption 1 to eliminate from Γ the strategies DL and RL for both players. We can then apply Lemma 2.   ) ∈ A 1 × A 2 , it is for all (a s 1 , a s 2 ) ∈ Ψ(Φ(Γ s )) the case that u(a s 1 , a s 2 ) ≥ u(a 1 , a 2 ). Next, we give two examples of unilateral SPIs. We start with an example that is trivial in that the original player instructs her resentatives to take a specific action. We then give the SPI for the Complicated Temptation game as a non-trivial example. Consider the Temptation Game given in Table  6 . In this game, Player 1's T (for Temptation) strictly dominates R. Once R is removed, Player 2 prefers C. Hence, this game is strict-dominance solvable to (T, C). Player 1 can safely Pareto-improve on this result by telling her representative to play R, since Player 2's best response to R is F and u(R, F ) = (4, 4) > (1, 2) = u(T, C). We now show this formally. Proposition (Example) 7. Let Γ = (A 1 , A 2 , u 1 , u 2 ) be the game of Table 6. Under Assumption 1, Γ s = ({R}, A 2 , u 1 , u 2 ) is a strict SPI on Γ. Proof. First consider Γ. We can apply Assumption 1 to eliminate Player 1's R and then apply Assumption 1 again to the resulting game to also eliminate Player 2's R. By transitivity, we find Γ ∼ Φ Γ , where Γ = ({T }, {C}, u 1 , u 2 ) and Φ(T, C) = {(T, C)} and Φ(A 1 × A 2 − {(T, C)}) = ∅. Next, consider Γ s . We can apply Assumption 1 to remove Player 2's strategy C and find Γ s ∼ Ψ Γs , where Γs = (({R}, {F }, u 1 , u 2 )) and Ψ(R, F ) = {(R, F )} and Ψ(R, C) = ∅. Third, Γ ∼ all Γs by Lemma 2.5, where all(T, C) = {(R, F )}. Finally, we can apply transitivity to conclude Γ ∼ Ξ Γ s , where Ξ = Ψ −1 • all•Φ. It is easy to verify that Ξ(T, C) = (R, F ) and Ξ(A 1 ×A 2 −{(R, F )}) = ∅. Hence, Ξ is Pareto-improving and so by Theorem 3, Γ s is an SPI on Γ. Note that in this example, Player 1 simply commits to a particular strategy R and Player 2 maximizes their utility given Player 1's choice. Hence, this SPI can be justified with much simpler unilateral commitment setups  [8, 38, 43] . For example, if the Temptation Game was played as a sequential game in which Player 1 plays first, its unique subgame-perfect equilibrium is (R, F ). In Table  4  we give the Complicated Temptation Game, which better illustrates the features specific to our setup. Roughly, it is an extension of the simpler Temptation Game of Table  6 . In addition to choosing T versus R and C versus F , the players also have to make an additional choice (1 versus 2), which is difficult in that it cannot be solved by strict dominance. As we have argued in Section 3.1, the game in Table  5  is a unilateral SPI on Table  4 . We can now show this formally. Proposition (Example) 8. Let Γ be the Complicated Temptation Game (Table  4 ) and Γ s be the subset game in Table  5 . Under Assumptions 1 and 2, Γ s is a unilateral SPI on Γ. Proof. In Γ, for Player 1, T 1 and T 2 strictly dominate R1 and R 2 . We can thus apply Assumption 1 to eliminate Player 1's R1 and R 2 . In the resulting game, Player 2's C 1 and C 2 strictly dominate F 1 and F 2 , so one can apply Assumption 1 again to the resulting game to also eliminate Player 2's F 1 and F 2 . By transitivity, we find Γ ∼ Φ Γ , where Γ = ({T 1 , T 2 }, {C 1 , C 2 }, u 1 , u 2 ) and Φ(a 1 , a 2 ) = {(a 1 , a 2 )} if a 1 ∈ {T 1 , T 2 } and a 2 ∈ {C 1 , C 2 } ∅ otherwise . Next, consider Γ s (Table  5 ). We can apply Assumption 1 to remove Player 2's strategies C 1 and C 2 and find Γ s ∼ Ψ Γs , where Γs = (({R 1 , R 2 }, {F 1 , F 2 }, u s 1 , u 2 )) and Ψ(a 1 , a 2 ) = {(a 1 , a 2 )} if a 1 ∈ {R 1 , R 2 } and a 2 ∈ {F 1 , F 2 } ∅ otherwise . Third, Γ ∼ Ξ Γs by Assumption 2, where Ξ decomposes into Ξ 1 and Ξ 2 , corresponding to the two players, respectively, where Ξ 1 (T i ) = R i and Ξ 2 (C i ) = F i for i = 1, 2. Finally, we can apply transitivity and the rule about symmetry and inverses (Lemma 2.2) to conclude Γ ∼ Ψ −1 •Ξ•Φ Γ s . It is easy to verify that Ψ −1 • Ξ • Φ is Pareto-improving. \n Computing safe Pareto improvements In this section, we ask how computationally costly it is for the original players to identify for a given game Γ a non-trivial SPI Γ s . Of course, the answer to this question depends on what the original players are willing to assume about how their representatives act. For example, if only trivial outcome correspondences (as per Lemma 2.1 and 2.5) are assumed, then the decision problem is easy. Similarly, if Γ ∼ Φ Γ for given Φ is hard to decide (e.g., because it requires solving for the Nash equilibria of Γ and Γ ), then this could trivially also make the safe Pareto improvement problem hard to decide. We specifically are interested in deciding whether a given game Γ has a non-trivial SPI that can be proved using only Assumptions 1 and 2, the general properties of game correspondence (in particular Transitivity (Lemma 2.3), Symmetry (Lemma 2.2) and Theorem 3). Definition 5. The SPI decision problem consists in deciding for any given Γ, whether there is a game Γ s and a sequence of outcome correspondences Φ 1 , ..., Φ k and a sequence of subset games Γ 0 = Γ, Γ 1 , ..., Γ k = Γ s of Γ s.t.: 1. (Non-triviality:) If we fully reduce Γ s and Γ using iterated strict dominance (Assumption 1), the two resulting games are not equal. (Of course, they are allowed to be isomorphic.) 2. For i = 1, ..., k, Γ i−1 ∼ Φ i Γ i is valid by a single application of either Assumption 1 or Assumption 2, or an application of Assumption 1 in reverse via Lemma 2.2. 3. For all a ∈ A, and whenever a s ∈ (Φ k • Φ k−1 • ... • Φ 1 )(a), it is the case that u(a s ) ≥ u(a). For the strict SPI decision problem, we further require: (4.) There is a player i and an outcome a that survives iterated elimination of strictly dominated strategies from Γ s.t. u i ((Φ k •Φ k−1 •...•Φ 1 )(a)) > u i (a) . For the unilateral SPI decision problem, we further require: (5.) For all but one of the players i, u i = u s i and A i = A s i . Many variants of this problem may be considered. For example, to match Definition 1, the definition of the strict SPI problem assumes that all outcomes a that survive iterated elimination occur with positive probability. Alternatively we could have required that for demonstrating strictness, there must be a player i such that for all a ∈ A that survive iterated elimination, u i ((Φ k • Φ k−1 • ... • Φ 1 )(a)) > u i (a) . Similarly one may wish to find SPIs that are strict improvements for all players. We may also wish to allow the use of the elimination of duplicate strategies (as described in Section 7.4) or trivial outcome correspondence steps as per Lemma 2.5. These modifications would not change the computational complexity of the problem, nor would they require new proof ideas. One may also wish to compute all SPIs, or -in line with multi-criteria optimization  [11, 42]  -all SPIs that cannot in turn be safely improved upon. However, in general there may exist exponentially many such SPIs. To retain any hope of developing an efficient algorithm, one would therefore have to first develop a more efficient representation scheme [cf.  29, Sect. 16.4 ]. The full proof is tedious (see Appendix D), but the main idea is simple, especially for omnilateral SPIs. To find an omnilateral SPI on Γ based on Assumptions 1 and 2, one has to first iteratively remove all strictly dominated actions to obtain a reduced game Γ , which the representatives would play the same as the original game. This can be done in polynomial time. One then has to map the actions Γ onto the original Γ in such a way that each outcome in Γ is mapped onto a weakly Pareto-better outcome in Γ. Our proof of NP-hardness works by reducing from the subgraph isomorphism problem, where the payoff matrices of Γ and Γ represent the adjacency matrices of the graphs. Besides being about a specific set of assumptions about ∼, note that Theorem 9 and Proposition 10 also assume that the utility function of the game is represented explicitly in normal form as a payoff matrix. If we changed the game representation (e.g., to boolean circuits, extensive form game trees, quantified boolean formulas, or even Turing machines), this can affect the complexity of the SPI problem. For example, Gabarró, García, and Serna  [13]  show that the game isomorphism problem on normal-form games is equivalent to the graph isomorphism problem, while it is equivalent to the (likely computationally harder) boolean circuit isomorphism problem for a weighted boolean formula game representation. Solving the SPI problem requires solving a subset game isomorphism problem (see the proof of Lemma 28 in Appendix D for more detail). We therefore suspect that the SPI problem analogously increases in computational complexity (perhaps to being Σ p 2 -complete) if we treat games in a weighted boolean formula representation. In fact, even reducing a game using strict dominance by pure strategies -which contributes only insignificantly to the complexity of the SPI problem for normal-form games -is difficult in some game representations [7,  Section 6] . Note, however, that for any game representation to which 2-player normal-form games can be efficiently reduced -such as, for example, extensive-form games -the hardness result also applies. 9 Safe Pareto improvements under improved coordination \n Setup In this section, we imagine that the players are able to simply invent new token strategies with new payoffs that arise from mixing existing feasible payoffs. To define this formally, we first define for any game Γ = (A, u), C(Γ) := u(∆(A)) = a∈A p a u(a) a∈A p a = 1 and ∀a ∈ A : p a ∈ [0, 1] to be the set of feasible coordinated payoff vectors of Γ, which is exactly the convex closure of u(A), i.e., of the set of deterministically achievable utilities of the original game. For any game Γ, we then imagine that in addition to subset games, the players can let the representatives play a perfect-coordination token game (A s , u s , u e ), where for all i, A s i ∩ A i = ∅ and u s i : A s → R are arbitrary utility functions to be used by the representatives and u e : A s → C(Γ) are the utilities that the original players assign to the token strategies. The instruction (A s , u s , u e ) lets the representatives play the game (A s , u s ) as usual. However, the strategies A s are imagined to be meaningless token strategies which do not resolve the given game Γ. Once some token strategies a s are selected, these are translated into some probability distribution over A, i.e., over outcomes of the original game, thus giving rise to (expected) utilities u e (a s ) ∈ C(Γ). These distributions and thus utilities are specified by the original players. We here imagine in our definition of C(Γ) that these distributions over A could require the representatives to correlate their choices for the original game for any given a s . Definition 6. Let Γ be a game. A perfect-coordination SPI for Γ is a perfect-coordination token game (A s , u s , u e ) for Γ s.t. u e (Π(A s , u s )) ≥ u(Π(Γ)) with certainty. We call (A s , u s , u e ) a strict perfect-coordination SPI if there furthermore is a player i for whom u e i (Π(A s , u s )) > u i (Π(Γ)) with positive probability. As an example, imagine that Γ is just the DM-RM subset game of the Demand Game of Table  1 . Then, intuitively, an SPI under improved coordination could consist of the original players telling the representatives, \"Play as if you were playing the DM-RM subset game of the Demand Game, but whenever you find yourself playing (DM, DM), randomize [according to some given distribution] between the other (Pareto-optimal) outcomes instead\". Formally, A s 1 = { D, R} and A s 2 = { D, R} would then consist of tokenized versions of the original strategies. The utility functions u s 1 and u s 2 are then simply the same as in the original Demand Game except that they are applied to the token strategies. For example, u s ( D, R) = (2, 0). The utilities for the original players remove the conflict outcome. For example, the original players might specify u e ( D, D) = (1, 1), representing that the representatives are supposed to play (RM, RM) in the ( D, D) case. For all other outcomes (â 1 , â2 ), it must be the case that u e (â 1 , â2 ) = u s (â 1 , â2 ) because the other outcomes cannot be Pareto-improved upon. As with our earlier SPIs for the Demand Game, Assumption 2 implies that Γ ∼ Φ Γ s , where Φ maps the original conflict outcome (DM, DM) onto the Pareto-optimal ( D, D). Relative to the SPIs considered up until now, these new types of instructions put significant additional requirements on how the representatives interact. They now have to engage in a two-round process of first choosing and observing one another's token strategies and then playing the corresponding distribution over outcomes from the original game. Further, it must be the case that this additional coordination does not affect the payoffs of the original outcomes. The latter may not be the case in, e.g., the Game of Chicken. That is, we could imagine a Game of Chicken in which coordination is possible but that the rewards of the game change if the players do coordinate. After all, the underlying story in the Game of Chicken is that the positive reward (admiration from peers) is attained precisely for accepting a grave risk. \n Finding safe Pareto improvement under improved representative coordination With these more powerful ways to instruct representatives, we can now replace individual outcomes of the default game ad libitum. For example, in the reduced Demand Game, we singled out the outcome (DM, DM) as Pareto-suboptimal and replaced it by a Pareto-optimal outcome, while keeping all other outcomes the same. This allows us to construct SPIs in many more games then before. Definition 7. The strict full-coordination SPI decision problem consists in deciding for any given Γ whether under Assumption 2 there is a perfectcoordination SPI Γ s for Γ. Lemma 11. For a given n-player game Γ and payoff vector y ∈ R n , it can be decided by linear programming and thus in polynomial time whether y is Pareto-optimal in C(Γ). For an introduction to linear programming, see, e.g., Schrijver  [36] . In short, a linear program is a specific type of constrained optimization problem that can be solved efficiently. Proof. Finding a Pareto improvement on a given y ∈ R n can be formulated as the following linear program: Variables: p a ∈ [0, 1] for all a ∈ A Maximize n i=1 a∈A p a u i (a) − y i s.t. a∈A p a = 1 a∈A p a u i (a) ≥ y i for i = 1, ..., n Based on Lemma 11, Algorithm 1 decides whether there is a strict perfect-coordination SPI for a given game Γ. It is easy to see that this algorithm runs in polynomial time (in the size of, e.g., the normal form representation of the game). It is also correct: if it returns True, simply replace the Pareto-suboptimal outcome while keeping all other outcomes the same; if it returns False, then all outcomes are Paretooptimal within C(Γ) and so there can be no strict SPI. We summarize this result in the following proposition. Proposition 12. Assuming supp(Π(Γ)) is known and that Assumption 2 holds, it can be decided in polynomial time whether there is a strict perfectcoordination SPI. We start with a lemma that directly provides a characterization. So far, all the considered perfect-coordination SPIs (A s , u s , u e ) for a game (A, u) have consisted in letting the representatives play a game (A s , u s ) that is isomorphic to the original game, but Pareto-improves (from the original players' perspectives, i.e., u e ) at least one of the outcomes. It turns out that we can restrict attention to this very simple type of SPI under improved coordination. Lemma 13. Let Γ = ({a 1 1 , ..., a l 1 1 }, ..., {a 1 n , ..., a ln n }, u) be any game. Let Γ be a perfect-coordination SPI on Γ. Then we can define u e with values in C(Γ) such that under Assumption 2 the game Γ s = Â1 := {â 1 1 , ..., âl 1 1 }, ..., Ân := {â 1 n , ..., âln n }, û : (â i 1 1 , ..., âin n ) → u(a i 1 1 , ..., a in n ), u e is also an SPI on Γ, with E [u(Π(Γ s )) | Π(Γ)=a] = E u(Π(Γ )) Π(Γ)=a for all a ∈ A and consequently E [u(Π(Γ s ))] = E [u(Π(Γ ))]. Proof. First note that ( Â, û) is isomorphic to Γ. Thus by Assumption 2, there is isomorphism Φ s.t. Γ ∼ Φ ( Â, û). WLOG assume that Φ simply maps a i 1 1 , ..., a in n → âi 1 1 , ..., âin n . Then define u e as follows: u e (â i 1 1 , ..., âin n ) = E u (Π(Γ )) | Π(Γ) = (a i 1 1 , ..., a in n ) . Here u describes the utilities that the original players assign to the outcomes of Γ . Since u maps onto C(Γ) and C(Γ) is convex, u e as defined also maps into C(Γ) as required. Note that for all a i 1 1 , ..., a in n it is by assumption u (Π(Γ )) ≥ u(a i 1 1 , ..., a in n ) with certainty. Hence, u e (â i 1 1 , ..., âin n )) = E u (Π(Γ )) | Π(Γ) = (a i 1 1 , ..., a in n ) ≥ u(a i 1 1 , ..., a in n ), as required. Because of this result, we will focus on these particular types of SPIs, which simply create an isomorphic game with different (Pareto-better) utilities. Note, however, that without assigning exact probabilities to the distributions of Π(Γ), Π(Γ ), the original players will in general not be able to construct a Γ s that satisfies the expected payoff equalities. For this reason, one could still conceive of situations in which a different type of SPI would be chosen by the original players and the original players are unable to instead choose an SPI of the type described in Lemma 13. Lemma 13 directly implies a characterization of the expected utilities that can be achieved with perfect-coordination SPIs. Of course, this characterization depends on the exact distribution of Π(Γ). We omit the statement of this result. However, we state the following implication. Corollary 14. Under Assumption 2, the set of Pareto improvements that are safely achievable with perfect coordination {E[u(Γ )] | Γ is perfect-coordination SPI on Γ} is a convex polygon. Because of this result, one can also efficiently optimize convex functions over the set of perfect-coordination SPIs. Even without referring to the distribution Π(Γ), many interesting questions can be answered efficiently. For example, we can efficiently identify the perfect-coordination SPI that maximizes the minimum improvements across players and outcomes a ∈ A. In the following, we aim to use Lemma 13 and Corollary 14 to give maximally strong positive results about what Pareto improvements can be safely achieved, without referring to exact probabilities over Π(Γ). To keep things simple, we will do this only for the case of two players. To state our results, we first need some notation: We use PF(C) := y ∈ C ∃y ∈C, i ∈ {1, ..., n} : y ≥ y, y i > y to denote the Pareto frontier of a convex polygon C (or more generally convex, closed set). For any real number x ∈ R, we use π i (x, C(Γ)) to denote the y ∈ C(Γ) which maximizes y −i under the constraint y i = x. (Recall that we consider 2-player games, so y −i is a single real number.) Note that such a y exists if and only if x is i's utility in some feasible payoff vector. We first state our result formally. Afterwards, we will give a graphical explanation of the result, which we believe is easier to understand. Then there is an SPI under improved coordination Γ s such that E [u(Π(Γ s ))] = y. B) If there is no element in C(Γ) which Pareto-dominates all of supp(Π(Γ)) and if y is Pareto-dominated by an element each of L 1 and L 3 as defined above, then there is a perfect-coordination SPI Γ s such that E [u(Π(Γ s ))] = y. We now illustrate the result graphically. We start with Case A, which is illustrated in Figure  2 . The Pareto-frontier is the solid line in the north and east. The points marked x indicate outcomes in supp(Π(Γ)). The point marked by a filled circle indicates the expected value of the default equilibrium E [u(Π(Γ))]. For some y ∈ R 2 to be a Pareto improvement, Player 1's utility it must be to the north-east of the filled circle. The vertical dashed lines starting at the two extreme x marks illustrate the application of π 1 to project x min/max 1 onto the Pareto frontier. The dotted line between these two points is L 1 . Similarly, the horizontal dashed lines starting at x marks illustrate the application of π 2 to project x min/max 2 onto the Pareto frontier. The line segment between these two points is L 3 . In this case, this line segments lies on the Pareto frontier. The set L 2 is simply that part of the Pareto frontier, which Pareto-dominates all elements of supp(Π(Γ)), i.e., the part of the Pareto frontier to the north-east between the two intersections with the northern horizontal dashed line and eastern vertical dashed line. E [u 1 (Π(Γ)))] E [u 2 (Π(Γ)))] Player 2's utility Case B of Theorem 15 is depicted in Figure  3 . Note that here the two line segments L 1 and L 3 intersect. To ensure that a Pareto improvement is safely achievable, the theorem requires that it is below both of these lines. For a full proof, see Appendix E. Roughly, Theorem 15 is proven by re-mapping each of the outcomes of the original game as per Lemma 13. For example, the projection of the default equilibrium E [u(Π(Γ))] (i.e., the filled circle) onto L 1 is obtained as an SPI by projecting all the outcomes (i.e., all the x marks) onto L 1 . In Case A, any utility vector y ∈ L 2 that Pareto-improves on all outcomes of the original game can be obtained by re-mapping all outcomes onto y. Other kinds of y are handled similarly. As a corollary of Theorem 15, we can see that all (potentially unsafe) Pareto improvements in the DM-RM subset game of the Demand Game of Table  1  are equivalent to some perfect-coordination SPI. However, this is not always the case:   7 : An example of a game in which -depending on Π -a Pareto improvement may not be safely achievable. Player 1's utility E [u 1 (Π(Γ))] E [u 2 (Π(Γ))]) Player 2's utility Proposition 16. There is a game Γ = (A, u), representatives Π that satisfy Assumptions 1 and 2, and an outcome a ∈ A s.t. u i (a) > E [u i (Π(Γ)) ] for all players i, but there is no perfect-coordination SPI (A s , u s , u e ) s.t. for all players i, E [u e i (Π(A s , u s ))] = u i (a). As an example of such a game, consider the game in Table  7 . Strategy c can be eliminated by strict dominance (Assumption 1) for both players, leaving a typical Chicken-like payoff structure with two pure Nash equilibria ((a, b) and (b, a)), as well as a mixed Nash equilibrium ( 3 /8 * a + 5 /8 * b, 3 /8 * a + 5 /8 * b). Now let us say that in the resulting game P (Π(Γ)=(a, b)) = p = P (Π(Γ)=(b, a)) for some p with 0 < p ≤ 1 /2. Then one (unsafe) Pareto improvement would be to simply always have the representatives play (c, c) for a certain payoff of  (3, 3) . Unfortunately, there is no safe Pareto improve-Player 1's utility ment with the same expected payoff. Notice that  (3, 3)  is the unique element of C(Γ) that maximizes the sum of the two players' utilities. By linearity of expectation and convexity of C(Γ), if for any Γ s it is E [u(Π(Γ s ))] = (3, 3), it must be u(Π(Γ s )) = (3, 3) with certainty. Unfortunately, in any safe Pareto improvement the outcomes (a, b) and (b, a) must corresponds to outcomes that still gives utilities of (4, 0) and (0, 4), respectively, because these are Pareto-optimal within the set of feasible payoff vectors. \n The SPI selection problem In the Demand Game, there happens to be a single non-trivial SPI. However, in general (even without the type of coordination assumed in Section 9) there may be multiple SPIs that result in different payoffs for the players. For example, imagine an extension of the Demand Game imagine that both players have an additional action DL , which is like DL, except that under (DL , DL ), Aliceland can peacefully annex the desert. Aliceland prefers this SPI over the original one, while Bobbesia has the opposite preference. In other cases, it may be unclear to some or all of the players which of two SPIs they prefer. For example, imagine a version of the Demand Game in which one SPI mostly improves on (DM, DM) and another mostly improves on the other three outcomes, then outcome probabilities are required for comparing the two. If multiple SPIs are available, the original players would be left with the difficult decision of which SPI to demand in their instruction.  9  This difficulty of choosing what SPI to demand cannot be denied. However, we would here like to emphasize that players can profit from the use of SPIs even without addressing this SPI selection problem. To do so, a player picks an instruction that is very compliant (\"dove-ish\") w.r.t. what SPI is chosen, e.g., one that simply goes with whatever SPI the other players demand as long as that SPI cannot further be safely Pareto-improved upon.  10  In many cases, all such SPIs benefit all players. For example, optimal SPIs in bargaining scenarios like the Demand Game remove the conflict outcome, which benefits all parties. Thus, a player can expect a safe improvement even under such maximally compliant demands on the selected SPI. In some cases there may also be natural choices of demands (a là Schelling [35, pp. 54-58] or focal points). If the underlying game is symmetric, a symmetric safe Pareto improvement may be a natural choice. For example, the fully reduced version of the Demand Game of Table  1  is symmetric. Hence, we might expect that even if multiple SPIs were available, the original players would choose a symmetric one. \n Conclusion and future directions Safe Pareto improvements are a promising new idea for delegating strategic decision making. To conclude this paper, we discuss some ideas for further research on SPIs. Straightforward technical questions arise in the context of the complexity results of Section 8. First, what impact on the complexity does varying the assumptions have? Our NP-completeness proof is easy to generalize at least to some other types of assumptions. It would be interesting to give a generic version of the result. We also wonder whether there are plausible assumptions under which the complexity changes in interesting ways. Second, one could ask how the complexity changes if we use more sophisticated game representations (see the remarks at the end of that section). Third, one could impose additional restrictions on the sought SPI. For example, some of the players may be unable to have their representative maximize arbitrary utility functions. We could then ask whether there is an SPI in which only a given subset of the players adopt different utility functions and restrictions on the set of available strategies. Fourth, we could restrict the games under consideration. Are there games in which it becomes easy to decide whether there is an SPI? It would also be interesting to see what real-world situations can already be interpreted as utilizing SPIs, or could be Pareto-improved upon using SPIs. \n A Proof of Theorem 1 -program equilibrium implementations of safe Pareto improvements This paper considers the meta-game of delegation. SPIs are a proposed way of playing these games. However, throughout most of this paper, we do not analyze the meta-game directly as a game using the typical tools of game theory. We here fill that gap and in particular prove Theorem 1, which shows that SPIs are played in Nash equilibria of the meta game, assuming sufficiently strong contracting abilities. As noted, this result is essential. However, since it is mostly an application of existing ideas from the literature on program equilibrium, we left a detailed treatment out of the main text. A program game for Γ = (A, u) is defined via a set PROG = PROG 1 × ...×PROG n and a non-deterministic mapping exec : PROG 1 ×...×PROG n A. We obtain a new game with action sets PROG and utility function U : PROG → R n : c → E [u(exec(c))] . Though this definition is generic, one generally imagines in the program equilibrium literature that for all i, PROG i consists of computer programs in some programming language, such as Lisp, that take as input vectors in PROG and return an action a i . The function exec on input c ∈ PROG then executes each player i's program c i on c to assign i an action. The definition implicitly assumes that PROG only contains programs that halt when fed one another as input. A program equilibrium is then simply a Nash equilibrium of the program game. For the present paper, we add the following feature to the underlying programming language. A program can call a \"black box subroutine\" Π i (Γ ) for any subset game Γ of Γ, where Π i (Γ ) is a random variable over A i and Π(Γ ) = (Π 1 (Γ ), ..., Π n (Γ )). We need one more definition. For any game Γ and player i, we define Player i's threat point (a.k.a. minimax utility) v Γ i as v Γ i = min σ −i ∈× j =i ∆(A j ) max σ i ∈∆(A i ) u i (σ i , σ −i ). In words, v Γ i is the minimum utility that the players other than i can force onto i, under the assumption that i reacts optimally to their strategy. We further will use minimax (i, j) ∈ ∆(A j ) to denote the strategy for Player j that is played in the minimizer σ −i of the above. Of course, in general, there might be multiple minimizers σ −i . In the following, we will assume that the function minimax breaks such ties in some consistent way, such that for all i, (minimax (i, j)) j∈{1,...,n}−{i} ∈ arg min σ −i ∈× j =i ∆(A j ) max σ i ∈∆(A i ) u i (σ i , σ −i ). Note that for n = 2, each player's threat point is computable in polynomial time via linear programming; and that by the minimax theorem  [25] , the threat point is equal to the maximin utility, i.e., v Γ i = max σ i ∈∆(A i ) min σ −i ∈∆(A −i ) u i (σ i , σ −i ), so v Γ i is also the minimum utility that Player i can guarantee for herself under the assumption that the opponent sees her mixed strategy and reacts in order to minimize Player i's utility. Tennenholtz'  [39]  main result on program games is the following: Theorem 17  (Tennenholtz 2004 [39] ). Let Γ = (A, u) be a game and let x ∈ u × n i=1 ∆(A i ) be a (feasible) payoff vector. If x i ≥ v Γ i for i = 1, ..., n, then x is the utility of some program equilibrium of a program game on Γ. Throughout the rest of this section, our goal is to use similar ideas as Tennenholtz did for Theorem 17 to construct for any SPI Γ s on Γ, a program equilibrium that results in the play of Π(Γ s ). As noted in the main text, the Player i's instruction to her representative to play the game Γ s will usually be conditional on the other player telling her representative to also play her part of Γ s and and vice versa. After all, if Player i simply tells her representative to maximize u s i from A s i regardless of Player −i's instruction, then Player −i will often be able to profit from deviating from the Γ s instruction. For example, in the safe Pareto improvement on the Demand Game, each player would only want their representative to choose from {DL, RL} rather than {DM, DM} if the other player's representative does the same. It would then seem that in a program equilibrium in which Π(Γ s ) is played, each program c i would have to contain a condition of the type, \"if the opponent code plays as in Π(Γ s ) against me, I also play as I would in Π(Γ s ).\" But in a naive implementation of this, each of the programs would have to call the other, leading to an infinite recursion. In the literature on program equilibrium, various solutions to this problem have been discovered. We here use the general scheme proposed by Tennenholtz  [39] , because it is the simplest. We could similarly use the variant proposed by Fortnow  [12] , techniques based on Löb's theorem  [3, 10] , or -grounded mutual simulation  [26]  or even (meta) Assurance Game preferences (see Appendix B). In our equilibrium, we let each player submit code as sketched in Algorithm 2. Roughly, each player uses a program that says, \"if everyone else submitted the same source code as this one, then play Π(Γ s ). Otherwise, if there is a player j who submits a different source code, punish player j by playing her minimax strategy\". Note that for convenience, Algorithm 2 receives the player number i as input. This way, every player can use the exact same source code. Otherwise the original players would have to provide slightly different programs and in line 2 of the algorithm, we would have to use a more complicated comparison, roughly: \"if c j = c i are the same, except for the player index used\". Proof. By inspection of Algorithm 2, we see that exec(c) = Π(Γ s ). It is left to show that c is a Nash equilibrium. So let i be any player and c i ∈ PROG i − {c i }. We need to show that E [u i (exec(c −i , c i ))] ≤ E [u i (exec(c))]. Again, by inspection of c, exec(c −i , c i ) is the threat point of Player i. Hence, E u i (exec(c −i , c i )) = v i ≤ E [u i (Π(Γ))] ≤ E [u i (Π(Γ s ))] = E [u i (exec(c))] as required. Theorem 1 follows immediately. B A discussion of work by  Sen (1974)  and  Raub (1990)  on preference adaptation games We here discuss Raub's  [32]  paper in some detail, which in turn elaborates on an idea by Sen  [37] . Superficially, Raub's setting seems somewhat similar to ours, but we here argue that it should be thought of as closer to the work on program equilibrium and bilateral precommitment. In Sections 1, 3 and 4, we briefly discuss multilateral commitment games, which have been discussed before in various forms in the game-theoretic literature. Our paper extends this setting by allowing instructions that let the representatives play a game without specifying an algorithm for solving that game. On first sight, it appears that Raub pursues a very similar idea. Translated to our setting, Raub allows that as an instruction, each player i chooses a new utility function u s i : A → R, where A is the set of outcomes of the original game Γ. Given instructions u s 1 , ..., u s n , the representatives then play the game (A, u s ). In particular, each representative can see what utility functions all the other representatives have been instructed to maximize. However, what utility function representative i maximizes is not conditional on any of the instructions by other players. In other words, the instructions in Raub's paper are raw utility functions without any surrounding control structures, etc. Raub then asks for equilibria u s of the meta-game that Pareto-improve on the default outcome. To better understand how Raub's approach relates to ours, we here give an example of the kind of instructions Raub has in mind. (Raub uses the same example in his paper.) As the underlying game Γ, we take the Prisoner's Dilemma. Now the main idea of his paper is that the original players can instruct their representatives to adopt so-called Assurance Game preferences. In the Prisoner's Dilemma, this means that the representatives prefer to cooperate if the other representative cooperates, and prefer to defect if the other player defects. Further, they prefer mutual cooperation over mutual defection. An example of such Assurance Game preferences is given in Table  8 . (Note that this payoff matrix resembles the classic Stag Hunt studied in game theory.) The Assurance Game preferences have two important properties. The first important difference between Raub's approach and ours is related to item 2. We have ignored the issue of making SPIs Γ s Nash equilibria of our meta game. As we have explained in Section 4 and Appendix A, we imagine that this is taken care of by additional bilateral commitment mechanisms that are not the focus of this paper. For Raub's paper, on the other hand, ensuring mutual cooperation to be stable in the new game Γ s is arguably the key idea. Still, we could pursue the approach of the present paper even when we limit assumptions to those that consist only of a utility function. The second difference is even more important. Raub assumes that -as in the PD -the default outcome of the game (Π(Γ) in the formalism of this paper) is known. (Less significantly, he also assumes that it is known how the representatives play under assurance game preferences.) Of course, the key feature of the setting of this paper is that the underlying game Γ might be difficult (through equilibrium selection problems) and thus that the original players might be unable to predict Π(Γ). These are the reasons why we cite Raub in our section on bilateral commitment mechanisms. Arguably, Raub's paper could be seen as very early work on program equilibrium, except that he uses utility functions as a programming language for representative. In this sense, Raub's Assurance Game preferences are analogous to the program equilibrium schemes of Tennenholtz  [39] , Oesterheld  [39] , Barasz et al.  [3]  and van der Hoek, Witteveen, and Wooldridge  [41] , ordered in increasing order of similarity of the main idea of the scheme. \n C Proof of Lemma 4 Lemma 4. Let Φ and Ψ be isomorphisms between Γ and Γ . If Φ is (strictly) Pareto-improving, then so is Ψ. Proof. First, we argue that if Φ and Ψ are isomorphisms, then they are isomorphisms relative to the same constants λ and c. For each player i, we distinguish two cases. First the case where all outcomes a in Γ have the same utility for Player i is trivial. Now imagine that the outcomes of Γ do not all have the same utility. Then let y min and y max be the lowest and highest utilities, respectively, in Γ. Further, let x min and x max be the lowest and highest utilities, respectively, in Γ . It is easy to see that if Ψ is a game isomorphism, it maps outcomes with utility y min in Γ onto outcomes with utility x min in Γ , and outcomes with utility y max in Γ onto outcomes with utility x max in Γ . Thus, if λ Ψ,i and c Ψ,i are to be the constants for Ψ, then y min = λ Ψ,i x min + c Ψ,i y max = λ Ψ,i x max + c Ψ,i . Since x min = x max , this system of linear equations has a unique solution. By the same pair of equations, the constants for Φ are uniquely determined. It follows that for all a ∈ A, u(a) = λu (Ψ(a)) + c = u(Φ −1 (Ψ(a))) ≤ u(Φ(Φ −1 (Ψ(a)))) = u(Ψ(a)). Furthermore, if Φ is strictly Pareto-improving for some ã ∈ A, then by bijectivity of Φ, Ψ, there is a ∈ A s.t. Φ −1 (Ψ(a)) = ã. For this a, the inequality above is strict and therefore u(a) < u(Ψ(a)). \n D Proof of Theorem 9 We here prove Theorem 9. We assume familiarity with basic ideas in computational complexity theory (non-deterministic polynomial time (NP), re-ductions, NP-completeness, etc.). \n D.1 On the structure of relevant outcome correspondence sequences Throughout our proof we will use a result about the structure of relevant outcome correspondences. Before proving this result, we give two lemmas. The first is a well-known lemma about elimination by strict dominance. Lemma 19 (path independence of iterated strict dominance). Let Γ be a game in which some strategy a i of player i is strictly dominated. Let Γ be a game we obtain from Γ by removing a strictly dominated strategy (of any player) other than a i . Then a i is strictly dominated in Γ . Note that this lemma does not by itself prove that iterated strict dominance is path dependence. However, path independence follows from the property shown by this lemma. Proof. Let a i be the strategy that strictly dominates a i . We distinguish two cases: Case 1: The strategy removed is a i . Then there must be âi that strictly dominates a i . Then it is for all a −i u i (â i , a −i ) > u i (a i , a −i ) > u i (a i , a −i ). Both inequalities are due to the definition of strict dominance. We conclude that âi must strictly dominate a i . Case 2: The strategy removed is one other than a i or a i . Since the set of strategies of the new game is a subset of the strategies of the old game it is still for each strategy a −i in the new game u i (a i , a −i ) > u i (a i , a −i ), i.e., a i still strictly dominates a i . The next lemma shows that instead of first applying Assumption 1 plus symmetry (Lemma 2.2) to add a strictly dominated action and then applying Assumption 1 to eliminate a different strictly dominated strategy, we could also first eliminate the strictly dominated strategy and then add the other strictly dominated strategy. A conciser way to state the consequence is that there must be games Γ red , Γ s,red and Γ s such that Γ red is obtained from Γ by iterated elimination of strictly dominated strategies, Γ s,red is isomorphic to Γ s,red , and Γ s,red is obtained from Γ s by iterated elimination of strictly dominated strategies. Proof. First divide the given sequence of outcome correspondences up into periods that are maximally long while containing only correspondences by Assumption 1 (with or without Lemma 2.2). That is, consider subsequences of the form Γ q ∼ Φ q ... ∼ Φ r−1 Γ r such that: • Each of the correspondences Γ q ∼ Φ q Γ q+1 , ..., Γ r−1 ∼ Φ r−1 Γ r is by applying Assumption 1 with or without Lemma 2.2. • Either q = 1 or the correspondence Γ q−1 ∼ Φ q−1 Γ q is by Assumption 2. • Either r = k or the correspondence Γ r ∼ Φ r Γ r+1 is by Assumption 2. In each such period apply Lemma 20 iteratively to either eliminate or move to the right all inverted reduction elimination steps. In all but the first period, Γ q contains no strictly dominated actions (by stipulation of Assumption 2). Hence all but the first period cannot contain any non-reversed elimination steps. Similarly, in all but the final period, Γ r contains no strictly dominated actions. Hence, in all but the final period, there can be no reversed applications of Assumption 1. Overall, our new sequence of outcome correspondences thus has the following structure: first there is a sequence of elimination steps via Assumption 1, then there is a sequence of isomorphism steps, and finally there is a sequence of reverse elimination steps. We can summarize all the applications of Assumption 2 into a single step applying that assumption to obtain the claimed structure. Now notice that that the reverse elimination steps are only relevant for deriving unilateral SPIs. Using the above concise formulation of the lemma, we can always simply use Γ s,red itself as an omnilateral SPI -it is not relevant that there is some subset game Γ s that reduces to Γ s,red . Lemma 22. As in Lemma 21, let Γ 1 ∼ Φ 1 ... ∼ Φ k−1 Γ k , where each outcome correspondence is due to a single application of Assumption Assumption 1, Assumption 1 plus symmetry (Lemma 2.2) or Assumption 2. Let Γ 2 , ..., Γ k all be subset games of Γ 1 . Moreover, let Φ k−1 • ... • Φ 1 be Pareto improving. Then there is a sequence of subset games Γ 2 , ..., Γ m , Γ m+1 such that Γ We now show that the SPI problem is in NP at all. The following algorithm can be used to determine whether there is a safe Pareto improvement: Reduce the given game Γ until it can be reduced no further to obtain some subset game Γ = (A , u). Then non-deterministically select injections Φ 1 ∼ Ψ 1 Γ 2 ∼ Ψ 2 ... ∼ Ψ m−1 Γ m all i : A i → A i . If Φ = (Φ 1 , ..., Φ n ) is ( strictly) Pareto-improving (as required in Theorem 3), return True with the solution Γ s defined as follows: The set of action profiles is defined as A s = × i Φ i (A i ). The utility functions are u s i : A s → R : a s → (u i (Φ −1 1 (a s 1 ), ..., Φ −1 n (a s n ))) i=1,...,n . Otherwise, return False. Let us say there is a sequence of outcome correspondences as per Assumptions 1 and 2 that show Γ ∼ Φ Γ s for Pareto-improving Φ. Then by Lemma 22, there is Γ such that Γ ∼ Ψ red Γ via applying Assumption 1 iteratively to obtain a fully reduced Γ and Γ ∼ Ψ iso Γ s via a single application of Assumption 2. By construction, our algorithm finds (guesses) this Pareto-improving outcome correspondence. Overall, we have now shown that our non-deterministic polynomial-time algorithm is correct and therefore that the SPI problem is in NP. Note that the correctness of other algorithms can be proven using very similar ideas. For example, instead of first reducing and then finding an isomorphism, one could first find an isomorphism, then reduce and then (only after reducing) test whether the overall outcome correspondence function is Pareto-improving. One advantage of reducing first is that there are fewer isomorphisms to test if the game is smaller. In particular, the number of possible isomorphisms is exponential in the number of strategies in the reduced game Γ but polynomial in everything else. Hence, by implementing our algorithm deterministically, we obtain the following positive result.  \n D.2.2 The unilateral SPI problem Next we show that the problem of finding unilateral SPIs is also in NP. Here we need a slightly more complicated algorithm: We are given an n-player game Γ and a player i. First reduce the game Γ fully to obtain some subset game Γ red . Then non-deterministically select injections Φ i : A red i → A i . The resulting candidate SPI game then is Γ s = ((A −i , Φ i (A red i )), (u −i , u s i )), where u s i (a s ) = u i (Φ −1 1 (a s 1 ), ..., Φ −1 n (a s n )) for all a s ∈ Φ(A red ), and u s i (a s ) is arbitrary for a s / ∈ Φ(A red ). Return True if the following conditions are satisfied: 1. The correspondence function Φ must be (strictly) Pareto improving (as per the utility functions u). 2. For each j ∈ {1, ..., n} − {i}, there are λ j ∈ R + and c j ∈ R such that for all a ∈ A red , we have u j (a) = λ j u j (Φ(a)) + c j . 3. The game Γ s reduces to the game (Φ(A red ), (u −i , u s i )). Otherwise, return False. Proposition 25. The above algorithm runs in non-deterministic polynomial time and returns True if and only if there is a (strict) unilateral SPI. Proof. First we argue that the algorithm can indeed be implemented in non-deterministic polynomial time. For this notice that for checking Item 2, the constants can be found by solving n systems of linear equations of two variables. It is left to prove correctness, i.e., that the algorithm returns True if and only if there exists an SPI. We start by showing that if the algorithm returns True, then there is an SPI. Specifically, we show that if the algorithm returns True, the game Γ s is indeed an SPI game. Notice that Γ ∼ Ψ Γ red for some Ψ by iterative application of Assumption 1 with Transitivity (Lemma 2.2); that Γ red ∼ Φ (Φ(A red ), (u −i , u s i )) by application of Assumption 2. Finally, (Φ(A red ), (u −i , u s i )) ∼ Ξ −1 Γ s for some Ξ by iterative application of Assumption 1 to Γ s , plus transitivity (Lemma 2.3) with reversal (Lemma 2.2). It is left to show that if there is an SPI, then the above algorithm will find it and return true. To see this, notice that Lemma 21 implies that there is a sequence of outcome correspondences Γ ∼ Ψ Γ red ∼ Φ Γ s,red ∼ Ξ Γ s . We can assume that Γ s,red and Γ s have the same action sets for Player i. It is easy to see that in Γ s we could modify the utilities u s i (a) for any a that is not in Γ s,red , because Player i's utilities do not affect the elimination of strictly dominated strategies from Γ s .  \n D.3 The SPI problems are NP-hard We now proceed to showing that the safe Pareto improvement problem is NP-hard. We will do this by reducing the subgraph isomorphism problem to the (two-player) safe Pareto improvement problem. We start by briefly describing one version of that problem here. A (simple, directed) graph is a tuple (n, a : {1, ..., n} × {1, ..., n} → B), where n ∈ N and B := {0, 1}. We call a the adjacency function of the graph. Since the graph is supposed to be simple and therefore free of self-loops (edges from one vertex to itself), we take the values a(j, j) for j ∈ {1, ..., n} to be meaningless. For given graphs G = (n, a),G = (n , a ) a subgraph isomorphism from G to G is an injection φ : {1, ..., n} → {1, ...n } such that for all j = l a(j, l) ≤ a (φ(j), φ(l)). In words, a subgraph isomorphism from G to G identifies for each node in G a node in G s.t. if there is an edge from node j to node l in G, there must also be an edge in the same direction between the corresponding nodes  . We define Γ based on Ĝ analogously, except that in Player 1's utilities we use 5 instead of 4, 5 + (n + i) instead of 4 + (n + i) , 5 + j instead of 4 + j and 4 instead of 3. We now define Γ c = (A c , u c ) from Γ and Γ as sketched in Table  10 . For the following let in contradiction to the assumption that Ψ is Pareto improving. We are ready to construct our subgraph isomorphism. For i ∈ [n], define φ(i) to be the second element of the pair Ψ 1 (T, i). By Item d, φ(i) can equivalently be defined as the second item in the pair Ψ 2 (D, i). By Item c, φ is a function from [n] to  [n] . By assumption about Ψ, φ is injective. Further, by construction of Γ c and φ, as well as the assumption that Ψ is Pareto improving, we infer that for all i, j ∈ [n] with i = j, â(φ(a), φ(j)) = u c 1 ((R, φ(i)), (P, φ(j))) = u c 1 (Ψ 1 (T, i), Ψ 2 (D, j)) ≥ u c 1 ((T, i), (D, j)) = a(i, j). We conclude that φ is a subgraph isomorphism. \n E Proof of Theorem 15 Proof. We will give the proof based on the graphs as well, without giving all formal details. Further we assume in the following that neither L 1 nor L 3 consist of just a single point, since these cases are easy. Case A: Note first that by Corollary 14 it is enough to show that if y is in any of the listed sets L 1 , L 2 , L 3 , it can be made safe. It's easy to see that all payoff vectors on the curve segment of the Pareto frontier L 2 are safely achievable. After all, all payoff vectors in this set Pareto-improve on all outcomes in supp(Π(Γ)). Hence, for each y on the line segment, one could select the Γ s where u e = y. It is left to show that all elements of L 1/2 are safely achievable. Remember that not all payoff vectors on the line segments are Pareto improvements, only those that are to the north-east of (Pareto-better than) the default utility. In the following, we will use L 1 and L 3 to denote those elements of L 1 and L 3 , respectively, that are Pareto-improvements on the default. We now argue that the Pareto improvement y on the line L 1 for which y 1 = E [u 1 (Π(Γ))] is safely achievable. In other words, y is the projection Now note that the set of feasible payoffs of Γ is convex. Further, the curve max(L 1 , L 3 ) is concave. Because the area above a concave curve is convex and because the intersection of convex sets is convex, the set of feasible payoffs on or above max(L 1 , L 3 ) is also convex. By definition of convexity, E 2 = E [u e (Π(Γ s ))] is therefore also in the set of feasible payoffs on or above max(L 1 , L 3 ) and therefore above both L 1 and L 3 as desired. In our second step, we now use E 1 , E 2 , E 3 to prove the claim. Because of convexity of the set of safely achievable payoff vectors as per Corollary 14, all utilities below the curve consisting of the line segments from E 1 to E 2 and from E 2 to E 3 are safely achievable. The line that goes through E 1 , E 2 intersects the line that contains L 1 at E 1 , by definition. Since non-parallel lines intersect each other exactly once and parallel lines that intersect each other are equal and because E 2 is above or on L 1 , the line segment from E 1 to E 2 lies entirely on or above L 1 . Similarly, it can be shown that the line segment from E 2 to E 3 lies entirely on or above L 3 . It follows that the E 1 − E 2 − E 3 curve lies entirely above or on min(L 1 , L 3 ). Now take any Pareto improvement that lies below both L 1 and L 3 . Then this Pareto improvement lies below min(L 1 , L 3 ) and therefore below the E 1 − E 2 − E 3 curve. Hence, it is safely achievable. 7 . 7 If Γ ∼ Φ Γ , then by reflexivity of ∼ (Lemma 2.1) Γ ∼ Φ −1 Γ. If Φ −1 (a ) = ∅, then by Lemma 2.6, Π(Γ ) = a with certainty. \n Similar desiderata have been discussed in the context of equilibrium selection, e.g., by Harsanyi and Selten [16, Chapter 3.4] [cf. 40, for a discussion in the context of fully cooperative multi-agent reinforcement learning]. \n 3 (Transitivity)  to obtain Γ ∼ Φ Γ, where Γ = ({DM, RM}, {DM, RM}, u 1 , u 2 ) \n Theorem 9 . 9 The (strict) (unilateral) SPI decision problem is NP-complete, even for 2-player games.Proposition 10. For games Γ with |A 1 | + ... + |A n | = m that can be reduced (via iterative application of Assumption 1) to a game Γ with |A 1 | + ... + |A n | = l, the (strict) (unilateral) SPI decision problem can be solved in O(m l ). \n Algorithm 1 : 3 Return True; 4 134 An algorithm for deciding the strict perfectcoordination SPI problem. Data: Game Γ, set supp(Π(Γ) 1 for a ∈ supp(Π(Γ)) do 2 if u(a) is Pareto-suboptimal within C(Γ) then Return False; 9.3 Characterizing safe Pareto improvements under improved representative coordination From the problem of deciding whether there are strict SPIs under improved coordination at all, we move on to the question of what different perfectcoordination SPIs there are. In particular, one might ask what the cost is of only considering safe Pareto improvements relative to acting on a probability distribution over Π(Γ) and the resulting expected utilities E [u(Π(Γ))]. \n Theorem 15 . 1 , 1 , 2 , 2 , 151122 Make Assumption 2. Let Γ be a two-player game. Let y ∈ R 2 be some potentially unsafe Pareto improvement on E [u(Π(Γ))]. For i = 1, 2, let x min/max i = min / max u i (supp(Π(Γ))). Then: A) If there is some element in C(Γ) which Pareto-dominates all of supp(Π(Γ)) and if y is Pareto-dominated by an element of at least one of the following three sets:• L 1 := the line segment between π 1 (x min 1 , PF(C(Γ)) and π 1 (x max PF(C(Γ));• L 2 := the segment of the curve PF(C(Γ)) between π 1 (x max PF(C(Γ))))and π 2 (x max PF(C(Γ))));• L 3 := the line segment between π 2 (x max PF(C(Γ)) and π 2 (x min 2 , PF(C(Γ)). \n Figure 2 : 2 Figure 2: This figure illustrates Theorem 15, Case A. \n Figure 3 : 3 Figure 3: This figure illustrates Theorem 15, Case B. \n Figure 4 : 4 Figure 4: This figure illustrates the Game of Table 7 as an instance of Theorem 15, Case B. \n Algorithm 2 : 2 if c j = c i then 3 223 A program equilibrium implementation of an SPI Γ s of Γ.Data: Everybody's source code c, my index i 1 for j ∈ {1, ..., n} − {i} do Play minimax (i, j); 4 Play Π i (Γ s ); Proposition 18. Let Γ be a game and let Γ s be an SPI on Γ. Let c be the program profile consisting only of Algorithm 2 for each player. Assume that Π(Γ) guarantees each player at least threat point utility in expectation. Then c is a program equilibrium and apply(c) = Π(Γ s ). \n by applications of Assumption 1 (without applying symmetry), and Γ m ∼ Ξ Γ m+1 by application of Assumption 2 such that Ξ • Ψ m−1 ... • Ψ 1 is Pareto improving. Proof. First apply Lemma 21. Then notice that the correspondence functions from applying Assumption 1 with symmetry have no effect on whether the overall outcome correspondence is Pareto improving. D.2 Non-deterministic polynomial-time algorithms for the SPI problem D.2.1 The omnilateral SPI problem \n Proposition 24 . 24 For games Γ with |A 1 | + ... + |A n | = m that can be reduced (via iterative application of Assumption 1) to a game Γ with |A 1 | + ... + |A n | = l, the (strict) omnilateral SPI decision problem can be solved in O(m l ). \n Proposition 26 . 26 For games Γ with |A 1 | + ... + |A n | = m that can be reduced (via iterative application of Assumption 1) to a game Γ with |A 1 | + ... + |A n | = l, the (strict) unilateral SPI decision problem can be solved in O(m l ). \n A Γ = ({T } × [2n + 2]) × ({D} × [2n + 2]) A Γ = ({R} × [2n + 2]) × ({P } × [2n + 2]), (d) Finally, notice that for i ∈ [n] and j ∈ [n], if Ψ 1 (T, i) = (R, j), thenalso Ψ 2 (D, i) = (P, j). To see this, assume it was Ψ 2 (R, i) = (P, l) for some l = j. Then by Item c, l ∈ [n]. Hence,u c 2 ((T, i), (R, i)) = 2 > 1 = u c 2 ((R, j), (P, l)) = u c 2 (Ψ 1 (T, i), Ψ 2 (R, i)) \n Table 1 : 1 The Demand Game \n Table 2 : 2 A safe Pareto improvement for the Demand Game \n Table 3 : 3 The Prisoner's Dilemma \n Table 6 : 6 Simple Temptation Game andΦ(a 1 , a 2 ) = {(a 1 , a 2 )} if a 1 , a 2 ∈ {DM, RM} ∅ otherwise .Next, by Assumption 2, Γ ∼ Ψ Γ s , where Ψ i (DM) = DL and Ψ i (RM) = RL for i = 1, 2. We can then apply Lemma 2.3 (Transitivity) again, to infer Γ ∼ Ψ•Φ Γ s . It is easy to verify that for all (a 1 , a 2 \n Table 8 : 8 Assurance Game preferences for the Prisoner's Dilemma Cooperate). 2. Under reasonable assumptions about the rationality of the representatives, it is a Nash equilibrium of the meta-game for both players to adopt Assurance Game preferences. If Player 1 tells her representative to adopt Assurance Game preferences, then Player 2 maximizes his utility by telling his representative to also maximize Assurance Game preferences. After all, representative 1 prefers defecting if representative 2 defects. Hence, if Player 2 instructs his representative to adopt preferences that suggest defecting, then he should expect representative to defect as well. 1. If both players tell their representatives to adopt Assurance Game preferences, (Cooperate, Cooperate) is a Nash equilibrium. (Defect, Defect) is a Nash equilibrium as well. However, since (Cooperate, Cooperate) is Pareto-better than (Defect, Defect), the original play- ers could reasonably expect that the representatives play (Cooperate, \n Proposition 23. The above algorithm runs in non-deterministic polynomial time and returns True if and only if there is a (strict) unilateral SPI.Proof. It is easy to see that this algorithm runs in non-deterministic polynomial time. Furthermore, with Lemma 4 it is easy to see that if this algorithm finds a solution Γ s , that solution is indeed a safe Pareto improvement. It is left to show that if there is a safe Pareto improvement via a sequence of Assumption 2 and 1 outcome correspondences, then the algorithm indeed finds a safe Pareto improvement. \n Table 9 : 9 The game Γ constructed to represent the graph G = (n, a). 1 . . . n n+1 . . . 2n 2n+1 2n+2 1 2, 2 a, 1 4+n + , 4 −1, −1 0, 3 0, 3 . . . . . . . . . . . . . . . n a, 1 2, 2 −1, −1 4+2n , 4 0, 3 0, 3 n+1 4+ , 4 −1, −1 0, 3 0, 3 . . . . . . −1, −1 . . . . . . 2n −1, −1 4+n , 4 0, 3 0, 3 2n + 1 3, 0 . . . 3, 0 3, 0 . . . 3, 0 6, , 2n + 2 3, 0 . . . 3, 0 3, 0 . . . 3, 0 , , 6 {D} × [2n + 2] {P } × [2n + 2] {R} × [2n + 2] −2, −1 Γ {T } × [2n + 2] Γ 10, −10 \n Table 10 : 10 The game Γ c as constructed from Γ and Γ. and  u 2 (i, j) =                               2, if i = j and i, j∈ [n] 1, if i = j and i, j ∈ [n] −1, if i ∈ {n + 1, ..., 2n}, j ∈ [n] and i = j + n −1, if i ∈ [n], j ∈ {n + 1, ..., 2n} and i + n = j 4 if i ∈ [n] and j = i + n 4 if j ∈ [n] and i = j + n −1 if i, j ∈ {n + 1, ..., 2n} 3 if j ∈ {2n + 1, 2n + 2} and i ∈ [2n] 6 if i = j = 2n + 2 if i ∈ {2n + 1, 2n + 2}and not i = j = 2n + 2 \n\t\t\t Here is another way of putting this. When one of the players i deliberates whether she would rather have the representatives play Π(Γ) or Π(Γ s ), we could imagine that the agent has a number of possible of models of how the representatives (Π) operate. Absent a probability distribution over models, the only widely accepted circumstance under which she can make such comparisons is decision-theoretic dominance [30,  Sect. 3.1]: she should prefer Π(Γ s ) if ui(Π(Γ s )) ≥ ui(Π(Γ)) under all models and ui(Π(Γ s )) > ui(Π(Γ)) under at least some model of Π. \n\t\t\t Note that the fact that this is an equivalence relation relies on the following three facts:1. For reflexivity of R: The identity function id is a single-valued bijection. 2. For symmetry of R: If Φ is a single-valued bijection, so is Φ −1 .3. For transitivity of R: If Ψ, Φ are bijections, so is Ψ • Φ. \n\t\t\t For an SPI Γ s to be also be a strict SPI on Γ, there must be a s which strictly Paretodominates a such that for all Φ with Γ ∼Φ Γ s , it must be a s ∈ Φ(a). \n\t\t\t There are trivial, uninteresting cases in which no assumptions are needed. In particular, if a game Γ has an outcome a that Pareto dominates all other outcomes of the game, then (by Lemma 2.5 with Theorem 3) any game Γ s = (A s = {a}, u s ) is an SPI on Γ. \n\t\t\t In fact, depending on formal details we omit throughout this paper -how to quantify over games in these assumptions, what type of objects actions are, etc. a more general version of Assumption 2 threatens to yield a contradiction with Assumption 1 again. \n\t\t\t The use of a book as illustration is inspired by Binmore [4,Section 1]. \n\t\t\t Of course, in many cases (such as Rock-Paper-Scissors) it is implausible for the players to choose deterministically. The idea is that in such games the randomization was performed in the process of printing. If the book is intended to be used multiple times, we may imagine that a sequence of (randomly generated) actions is provided (à la the RAND Corporation's book of random numbers). \n\t\t\t A second question is what to instruct the representatives to do in case of differing demands. 10  Of course, such an instruction would then also have to specify what happens if all players submit such an instruction. This appears to be a lesser problem, however.", "date_published": "n/a", "url": "n/a", "filename": "SPI.tei.xml", "abstract": "A set of players delegate playing a game to a set of representatives, one for each player. We imagine that each player trusts their respective representative's strategic abilities. Thus, we might imagine that per default, the original players would simply instruct the representatives to play the original game as best as they can. In this paper, we ask: are there safe Pareto improvements on this default way of giving instructions? That is, we imagine that the original players can coordinate to tell their representatives to only consider some subset of the available strategies and to assign utilities to outcomes differently than the original players. Then can the original players do this in such a way that the payoff is guaranteed to be weakly higher than under the default instructions for all the original players? In particular, can they Pareto-improve without probabilistic assumptions about how the representatives play games? In this paper, we give some examples of safe Pareto improvements. We prove that the notion of safe Pareto improvements is closely related to a notion of outcome correspondence between games. We also show that under some specific assumptions about how the representatives play games, finding safe Pareto improvements is NP-complete.", "id": "1a162b03db2ea4923daf0db8944acc1e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Scott Emmons", "Caspar Oesterheld", "Andrew Critch", "Vince Conitzer", "Stuart Russell"], "title": "Symmetry, Equilibria, and Robustness in Common-Payoff Games", "text": "INTRODUCTION We consider common-payoff games (also known as identical interest games  [38] ), in which the payoff to all players is always the same.  1  Such games model a wide range of situations involving Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). Appears at the 3rd Games, Agents, and Incentives Workshop (GAIW 2021). Held as part of the Workshops at the 20th International Conference on Autonomous Agents and Multiagent Systems., Aziz, Ceppi, Dickerson, Hosseini, Lev, Mattei, McElfresh, Zick (chairs), May 2021, London, UK. © 2021 Copyright held by the owner/author(s). cooperative action towards a common goal. Under the heading of team theory, they form an important branch of economics  [19, 20] . In AI, the common-payoff assumption holds in Dec-POMDPs  [25] , where multiple agents operate independently according to policies designed centrally to achieve a common objective. Many applications of multiagent reinforcement learning also assume a common payoff  [7, 8, 12] . Finally, in assistance games  [31]  (also known as cooperative inverse reinforcement learning or CIRL games  [13] ), which include at least one human and one or more \"robots,\" it is assumed that the robots' payoffs are exactly the human's payoff, even if the robots do not know what it is. Common-payoff games lead naturally to considerations of symmetry in game structure-for example, the assumption that two players' actions produce the same effect on the common payoff. Indeed, von Neumann and Morgenstern  [41]  and Nash  [23]  introduced fairly general group-theoretic notions of symmetry, which we adopt and explain in Section 2. More recent work has analyzed narrower notions of symmetry  [22, 30, 39] . For example, Daskalakis and Papadimitriou  [5]  study \"anonymous games\" and show that anonymity substantially reduces the complexity of finding solutions. Finally, Ham  [14]  generalizes the player-based notion of symmetry to include further symmetries revealed by renamings of actions. We conjecture our results extend to this more general case, at some cost in notational complexity, but we leave this to future work. In games exhibiting symmetry, it is then reasonable to consider symmetry in players' strategies. (Section 2 defines this in a precise sense.) For example, in team theory, it is common to develop a strategy that can be implemented by every employee in a given category and leads to high payoff for the company. (Notice that this does not lead to identical behavior, because strategies are statedependent.) In civic contexts, symmetry commonly arises through notions of fairness and justice. In treaty negotiations and legislation that mandates how parties behave, for example, there is often a constraint that all parties be treated equally. In DecPOMDPs, an offline solution search may consider only symmetric strategies for identical agents as a way of reducing the search space. In commonpayoff multiagent reinforcement learning, each agent may collect percepts and rewards independently, but the reinforcement learning updates can be pooled to learn a single parameterized policy that all agents share. Common-payoff and symmetric games have a number of desirable properties that may simplify the search for solutions. For the Table  1 : Three versions of the laundry/washing up game. Solutions are described in the text. purposes of this paper, we consider Nash equilibria-strategy profiles for all players from which no individual player has an incentive to deviate-as a reasonable solution concept. For example, Marschak and Radner  [20]  make the obvious point that a globally optimal (possibly asymmetric) strategy profile-one that achieves the highest common payoff-is necessarily a Nash equilibrium. Moreover, it can be found in time linear in the size of the payoff matrix. Another solution concept often used in multiagent RL and differential (i.e., continuous-action-space) games is that of a locally optimal strategy profile-roughly speaking, a strategy profile from which no player has an incentive to slightly deviate. Obviously, a locally optimal profile may not be a Nash equilibrium, as a player may still have an incentive to deviate to some more distant point in strategy space. Nonetheless, local optima, sometimes called local Nash equilibria-are important. For example, Ratliff et al.  [29]  argue that a local Nash equilibrium may still be stable in a practical sense if agents are computationally unable to find a better strategy. Similarly, gradient-based game solvers and multiagent RL algorithms may converge to local optima. Our first main result, informally stated, is that in a symmetric, common-payoff game, every local optimum in symmetric strategies is a (global) Nash equilibrium. Section 3 states the result more precisely and gives an example illustrating its generality.  2  Despite many decades of research on symmetric, common-payoff games, the result appears to be novel and perhaps useful. There are some echoes of the result in the literature on single-agent decision making  [4, 27, 32] , which can be connected to symmetric solutions of common-payoff games by treating all players jointly as a single agent, but our result appears more general than published results. The proof we give of our result contains elements similar to the proof (of a related but different result) in Taylor  [34] . To gain some intuition for these concepts and claims, let us consider a situation in which two children, Ali and Bo, have to do some housework-specifically, laundry (𝐿) and washing up (𝑊 ). Here, the \"common payoff,\" if any, is to the parents. It is evident that a symmetric strategy profile-both doing the laundry or both doing the washing up-is not ideal, because the other task will not get done. The first version of the game, whose payoffs 𝑈 are shown in Table  1a , is asymmetric: while Ali is competent at both tasks, Bo does not know how to do the laundry properly and will ruin the clothes. Here, as Marschak and Radner pointed out, the strategy profile (𝐿,𝑊 ) is both globally optimal and a Nash equilibrium. If we posit a mixed (randomized) strategy profile in which Ali and Bo have laundry probabilities 𝑝 and 𝑞 respectively, the gradients 𝜕𝑈 /𝜕𝑝 and 𝜕𝑈 /𝜕𝑞 are +1 and −1, driving the solution towards (𝐿,𝑊 ).  2  Complete proofs for all of our results are in the appendices.   1b ). Although the symmetric optimum has lower expected utility than the unrestricted optima, total symmetry of the game implies that the symmetric optimum is a Nash equilibrium; this is a special case of Theorem 3.2. In the second version of the game (Table  1b ), Ali has taught Bo how to do the laundry, and symmetry is restored. The pure profiles (𝐿,𝑊 ) and (𝑊 , 𝐿) are (asymmetric) globally optimal solutions and hence Nash equilibria. Figure  1  shows the entire payoff landscape as a function of 𝑝 and 𝑞: looking just at symmetric strategy profiles, it turns out that there is a local optimum at 𝑝 = 𝑞 = 0.5, i.e., where Ali and Bo toss fair coins to decide what to do. Although the expected payoff of this solution is lower than that of the asymmetric optima, the local optimum is, nonetheless, a Nash equilibrium. All unilateral deviations from the symmetric local optimum result in the same expected payoff because if one child is tossing a coin, the other child can do nothing to improve the final outcome. In the third version of the game (Table  1c ), the parents derive greater payoff from watching their children working happily together on a single task than they do from getting both tasks done. In this case, there is again a Nash equilibrium at 𝑝 = 𝑞 = 0.5, but it is a local minimum rather than a local maximum in symmetric strategy space. Thus, not all symmetric Nash equilibria are symmetric local optima; this is because Nash equilibria depend on unilateral deviations, whereas symmetric local optima depend on joint deviations that maintain symmetry. In the second half of the paper, we turn to the issue of robustness of symmetric solutions. In practice, a variety of factors can lead to modelling errors and approximate solutions, which motivates us to consider perturbations in payoffs and strategy profiles. Making general arguments about Nash equilibria, we show that our first main result is robust in the sense that it degrades linearly under 𝜖-magnitude perturbations into 𝑘𝜖-Nash equilibria (for some gamedependent constant 𝑘). Stability turns out to be a thornier issue. Instability, if not handled carefully, might lead to major coordination failures in practice  [3] . While it is already known that local strict optima in a totally symmetric team game attain one type of stability, the issue is complex because there are several ways of enforcing (or not enforcing) strict symmetries in payoffs and strategies  [22] . Our final results focus on the stability of agents making possibly-asymmetric updates from a symmetric solution. We prove for a non-degenerate class of games that local optima in symmetric strategy space fail to be local optima in asymmetric strategy space if and only if at least one player is mixing, and we experimentally quantify how often mixing occurs for learning algorithms in the GAMUT suite of games  [24] . \n PRELIMINARIES: GAMES AND SYMMETRIES 2.1 Normal-form games Throughout, we consider normal-form games G = (𝑁 , 𝐴, 𝑢) defined by a finite set 𝑁 with |𝑁 | = 𝑛 players, a finite set of action profiles 𝐴 = 𝐴 1 × 𝐴 2 × . . . × 𝐴 𝑛 with 𝐴 𝑖 specifying the actions available to player 𝑖, and the utility function 𝑢 = (𝑢 1 , 𝑢 2 , . . . , 𝑢 𝑛 ) with 𝑢 𝑖 : 𝐴 → R giving the utility for each player 𝑖  [33] . We call G common-payoff if 𝑢 𝑖 (𝑎) = 𝑢 𝑗 (𝑎) for all action profiles 𝑎 ∈ 𝐴 and all players 𝑖, 𝑗. In common-payoff games we may omit the player subscript 𝑖 from utility functions. We model each player as employing a (mixed) strategy 𝑠 𝑖 ∈ Δ(𝐴 𝑖 ), a probability distribution over actions. We denote the support of the probability distribution 𝑠 𝑖 by supp(𝑠 𝑖 ). Given a (mixed) strategy profile 𝑠 = (𝑠 1 , 𝑠 2 , . . . , 𝑠 𝑛 ) that specifies a strategy for each player, player 𝑖's expected utility is 𝐸𝑈 𝑖 (𝑠) = 𝑎 ∈𝐴 𝑢 𝑖 (𝑎) Note that, while we have chosen to use the normal-form game representation for simplicity, normal-form games are highly expressive. Normal-form games can represent mixed strategies in all finite games, including games with sequential actions, stochastic transitions, and partial observation such as imperfect-information extensive form games with perfect recall, Markov games, and Dec-POMDPs. To represent a sequential game in normal form, one simply lets each normal-form action be a complete strategy (contingency plan) accounting for every potential game decision. \n Symmetry in game structure Our notion of symmetry in game structure is built upon von Neumann and Morgenstern  [41] 's and borrows notation from Plan  [28] . The basic building block is a symmetry of a game: Definition 2.1. Call a permutation of player indices 𝜌 : {1, 2, ..., 𝑛} → {1, 2, ..., 𝑛} a symmetry of a game G if, for all strategy profiles (𝑠 1 , 𝑠 2 , ..., 𝑠 𝑛 ), permuting the strategy profile permutes the expected payoffs: 𝐸𝑈 𝜌 (𝑖) ((𝑠 1 , 𝑠 2 , ..., 𝑠 𝑛 )) = 𝐸𝑈 𝑖 ((𝑠 𝜌 (1) , 𝑠 𝜌 (2) , ..., 𝑠 𝜌 (𝑛) )), ∀𝑖. Note that, when we speak of a symmetry of a game, we implicitly assume 𝐴 𝑖 = 𝐴 𝑗 for all 𝑖, 𝑗 with 𝜌 (𝑖) = 𝑗 so that permuting the strategy profile is well-defined.  3  We characterize the symmetric structure of a game by its set of game symmetries: Definition 2.2. Denote the set of all symmetries of a game G by: Γ(G) = {𝜌 : {1, 2, ..., 𝑛} → {1, 2, ..., 𝑛} a symmetry of G}. A spectrum of game symmetries is possible. On one end of the spectrum, the identity permutation might be the only symmetry for a given game. On the other end of the spectrum, all possible permutations might be symmetries for a given game. Following the terminology of von Neumann and Morgenstern  [41] , we call the former case totally unsymmetric and the latter case totally symmetric: Definition 2.3. If Γ(G) = 𝑆 𝑛 , the full symmetric group, we call the game Γ(G) totally symmetric. If Γ(G) contains only the identity permutation, we call the game totally unsymmetric. Let P ⊆ Γ(G) be any subset of the game symmetries. Because Γ(G) is closed under composition, we can repeatedly apply permutations in P to yield a group of game symmetries ⟨P⟩: Definition 2.4. Let P ⊆ Γ(G) be a subset of the game symmetries. The group generated by P, denoted ⟨P⟩, is the set of all permutations that can result from (possibly repeated) composition of permutations in P: ⟨P⟩ = {𝜌 1 • 𝜌 2 • . . . • 𝜌 𝑚 | 𝑚 ∈ N, 𝜌 1 , 𝜌 2 , . . . , 𝜌 𝑚 ∈ P}. Group theory tells us that ⟨P⟩ defines a closed binary operation (permutation composition) including an identity and inverse maps, and ⟨P⟩ is the closure of P under function composition. With a subset of game symmetries P ⊆ Γ(G) in hand, we can use the permutations in P to carry one player index to another. For each player 𝑖, we give a name to the set of player indices to which permutations in P can carry 𝑖: we call it player 𝑖's orbit. Definition 2.5. Let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). The orbit of player 𝑖 under P is the set of all other player indices that ⟨P⟩ can assign to 𝑖: P (𝑖) = {𝜌 (𝑖) | 𝜌 ∈ ⟨P⟩}. In fact, it is a standard result from group theory that the orbits of a group action on a set partition the set's elements, which leads to the following proposition: Proposition 2.6. Let P ⊆ Γ(G). The orbits of P partition the game's players. By Proposition 2.6, each P ⊆ Γ(G) yields an equivalence relation among the players. To gain intuition for this equivalence relation, consider two extreme cases. In a totally unsymmetric game, Γ(G) contains only the identity permutation, in which case each player is in its own orbit of Γ(G); the equivalence relation induced by the orbit partition shows that no players are equivalent. In a totally symmetric game, by contrast, every permutation is an element of Γ(G), i.e., Γ(G) = 𝑆 𝑛 , the full symmetric group; now, all the players share the same orbit of Γ(G), and the equivalence relation induced by the orbit partition shows that all the players are equivalent. We leverage the orbit structure of an arbitrary P ⊆ Γ(G) to define an equivalence relation among players because it adapts to however much or little symmetry is present in the game. Between the extreme cases of no symmetry (𝑛 orbits) and total symmetry (1 orbit) mentioned above, there could be any intermediate number of orbits of P. Furthermore, two players can share an orbit of P even if those two players cannot be arbitrarily swapped. In Example 3.3, all the players can be rotated in a circle, so all the players share an orbit of P = Γ(G) even though the game does not admit arbitrary swapping of players. \n Symmetry in strategy profiles Having formalized a symmetry of a game in the preceding section, we follow Nash  [23]  and define symmetry in strategy profiles with respect to symmetry in game structure: Definition 2.7. Let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). We call a strategy profile 𝑠 = (𝑠 1 , 𝑠 2 , ..., 𝑠 𝑛 ) P-invariant if (𝑠 1 , 𝑠 2 , ..., 𝑠 𝑛 ) = (𝑠 𝜌 (1) , 𝑠 𝜌 (2) , ..., 𝑠 𝜌 (𝑛) ) for all 𝜌 ∈ ⟨P⟩. The equivalence relation among players induced by the orbit structure of P is fundamental to our definition of symmetry in strategy profiles by the following proposition: Proposition 2.8. A strategy profile 𝑠 = (𝑠 1 , 𝑠 2 , ..., 𝑠 𝑛 ) is P-invariant if and only if 𝑠 𝑖 = 𝑠 𝑗 for each pair of players 𝑖 and 𝑗 with P (𝑖) = P ( 𝑗). To state Proposition 2.8 another way, a strategy profile is Pinvariant if all pairs of players 𝑖 and 𝑗 that are equivalent under the orbits of P play the same strategy. \n LOCAL SYMMETRIC OPTIMA ARE (GLOBAL) NASH EQUILIBRIA After the formal definitions of symmetry in the previous section, we are almost ready to formally state the first of our three main results. The only remaining definition is that of a local symmetric optimum: Definition 3.1. Call 𝑠 a locally optimal P-invariant strategy profile of a common-payoff game if: (i) 𝑠 is P-invariant, and (ii) for some 𝜖 > 0, no P-invariant strategy 𝑠 ′ with 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠) can be formed by adding or subtracting at most 𝜖 to the probability of taking any given action 𝑎 𝑖 ∈ 𝐴 𝑖 . If, furthermore, condition (ii) holds for all 𝜖 > 0, we call 𝑠 a globally optimal P-invariant strategy profile or simply an optimal P-invariant strategy profile. Now we can formally state our first main theorem, that local symmetric optima are (global) Nash equilibria: Theorem 3.2. Let G be a common-payoff normal-form game, and let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). Any locally optimal P-invariant strategy profile is a Nash equilibrium. Proof. We provide a sketch here and full details in Appendix A. Suppose, for the sake of contradiction, that an individual player 𝑖 could beneficially deviate to action 𝑎 𝑖 (if a beneficial deviation exists, then there is one to a pure strategy). Then, consider instead a collective change to a symmetric strategy profile in which all the players in 𝑖's orbit shift very slightly more probability to 𝑎 𝑖 . By making the amount of probability shifted ever smaller, the probability that this change affects exactly one agent's realized action (making it 𝑎 𝑖 when it would not have been before) can be arbitrarily larger than the probability that it affects multiple agents' realized actions. Moreover, if this causes exactly one agent's realized action to change, this must be in expectation beneficial, since the original unilateral deviation was in expectation beneficial. Hence, the original strategy profile cannot have been locally optimal. □ \n Example illustrating general symmetry Here, we give an example that shows how Theorem 3.2 is more general than the case of total symmetry. The example illustrates the existence of rotational symmetry without total symmetry, and it illustrates how picking different P ⊆ Γ(G) leads to different optimal P-invariant strategies and thus different P-invariant Nash equilibria by Theorem 3.2. Example 3.3. There are four radio stations positioned in a square. We number these 1,2,3,4 clockwise, such that, e.g., 1 neighbors 4 and 2. There is also a neighborhood of people at each vertex of the square. The people can tune in to the radio station at their vertex of the square and to the radio stations at adjacent vertices of the square, but they cannot tune in to the station at the opposite vertex. The game has each radio station choose what to broadcast. For simplicity, suppose each radio station can broadcast the weather or music. The common payoff of the game is the sum of the utilities of the four neighborhoods. For each neighborhood, if the neighborhood cannot tune in to the weather, the payoff for that neighborhood is 0. If the neighborhood can only tune in to the weather, the payoff is 1, and if the neighborhood can tune in to both weather and music, the neighborhood's payoff is 2. The symmetries of the game Γ(G) include the set of permutations generated by rotating the radio stations once clockwise. In standard notation for permutations, {(1, 2, 3, 4), (2, 3, 4, 1), (3, 4, 1, 2), (4, 1, 2, 3)} ⊂ Γ(G). First, consider applying the theorem to P = Γ(G). In this case, the constraint of P-invariance requires all the radio stations to play the same strategy because all stations are in the same orbit. As we show in Appendix B, the optimal P-invariant strategy then is for each station to broadcast music with probability √ 2−1. Theorem 3.2 tells us that this optimal P-invariant strategy profile is a Nash equilibrium. Appendix B also shows how to verify this without the use of Theorem 3.2. Second, consider applying the theorem to the case where P consists only of the rotation twice clockwise, i.e., the permutation which maps each station onto the station on the opposite vertex of the square. In standard notation for permutations, P = {(3, 4, 1, 2)}. Now, the constraint of P-invariance requires radio stations at opposite vertices of the square to play the same strategy. However, neighboring stations can broadcast different programs. The optimal P-invariant strategy is for one pair of opposite-vertex radio stations, e.g., 1 and 3, to broadcast the weather and for the other pair of radio stations, 2 and 4, to broadcast music. While it turns out to be immediate that this optimal P-invariant strategy is a Nash equilibrium because it achieves the globally optimal outcome, we could have applied Theorem 3.2 to know that this optimal P-invariant strategy profile is a Nash equilibrium even without knowing what the optimal P-invariant strategy was. \n ROBUSTNESS OF THE MAIN RESULT TO PAYOFF AND STRATEGY PERTURBATIONS The first type of robustness we consider is robustness to perturbations in the game's payoff function. Formally, we define an 𝜖perturbation of a game as follows: Definition 4.1. Let G be a normal-form game with utility function 𝜇. For some 𝜖 > 0, we call G ′ an 𝜖-perturbation of G if G ′ has utility function 𝜇 ′ satisfying max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 ′ 𝑖 (𝑎) − 𝑢 𝑖 (𝑎)| ≤ 𝜖. There are a variety of reasons why 𝜖-perturbations might arise in practice. Our game model may contain errors such as the game not being perfectly symmetric; the players' preferences might drift over time; or we might have used function approximation to learn the game's payoffs. With Proposition 4.2, we note a generic observation about Nash equilibria showing that our main result, Theorem 3.2, is robust in the sense of degrading linearly in the payoff perturbation's size: Proposition 4.2. Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝐺 ′ is an 𝜖-perturbation of G. Then 𝑠 * is a 2𝜖-Nash equilibrium in G ′ . The second type of robustness we consider is robustness to symmetric solutions that are only approximate. For example, we might try to find a symmetric local optimum through an approximate optimization method, or the evolutionary dynamics among players' strategies might lead them to approximate local symmetric optima. Again, a generic result about Nash equilibria shows that the guarantee of Theorem 3.2 degrades linearly in this case: Theorem 4.3. Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝑠 is a strategy profile with total variation distance 𝑇𝑉 (𝑠, 𝑠 * ) ≤ 𝛿. Then 𝑠 is an 𝜖-Nash equilibrium with 𝜖 = 4𝛿 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|. By Theorem 4.3, we have a robustness guarantee in terms of the total variation distance between an approximate local symmetric optimum and a true local symmetric optimum. Without much difficulty, we can also convert this into a robustness guarantee in terms of the Kullback-Leibler divergence: Corollary 4.4. Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝑠 is a strategy profile with Kullback-Leibler divergence satisfying 𝐷 𝐾𝐿 (𝑠 ||𝑠 * ) ≤ 𝜈 or 𝐷 𝐾𝐿 (𝑠 * ||𝑠) ≤ 𝜈. Then 𝑠 is an 𝜖-Nash equilibrium with 𝜖 = 2 √ 2𝜈 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|. While the results of this section show the robustness of Nash equilibria, we note that Nash equilibria, by definition, consider the possibility of only a single agent deviating; Nash equilibria cannot guarantee stability under dynamics that allow for multiple agents to deviate. In the next section, we investigate when multiple agents might have an incentive to simultaneously deviate by studying the optimality of symmetric strategy profiles in possibly-asymmetric strategy space. \n WHEN ARE LOCAL OPTIMA IN SYMMETRIC STRATEGY SPACE ALSO LOCAL OPTIMA IN POSSIBLY-ASYMMETRIC STRATEGY SPACE? Our first main theoretical result, Theorem 3.2, applies to locally optimal P-invariant, i.e., symmetric, strategy profiles. This still leaves open the question of how well locally optimal symmetric strategy profiles perform when considered in the broader, possiblyasymmetric strategy space. When are locally optimal P-invariant strategy profiles also locally optimal in possibly-asymmetric strategy space? This question is important in machine learning (ML) applications where users of symmetrically optimal ML systems might be motivated to make modifications to the systems, even for purposes of a common payoff. To address this issue more precisely, we formally define a local optimum in possibly-asymmetric strategy space: Definition 5.1. A strategy profile 𝑠 = (𝑠 1 , 𝑠 2 , . . . , 𝑠 𝑛 ) of a commonpayoff normal-form game is locally optimal among possiblyasymmetric strategy profiles, or, equivalently, a local optimum in possibly-asymmetric strategy space, if for some 𝜖 > 0, no strategy profile 𝑠 ′ with 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠) can be formed by changing 𝑠 in such a way that the probability of taking any given action 𝑎 𝑖 ∈ 𝐴 𝑖 for any player 𝑖 changes by at most 𝜖. Definition 5.1 relates to notions of stability under dynamics, such as those with perturbations or stochasticity, that allow multiple players to make asymmetric deviations. In particular, if 𝑠 is not a local maximum in asymmetric strategy space, this means that there is some set of players 𝐶 and strategy 𝑠 ′ 𝐶 arbitrarily close to 𝑠, such that if players 𝐶 were to play 𝑠 ′ 𝐶 (by mistake or due to stochasticity), some Player 𝑖 ∈ 𝑁 − 𝐶 would develop a strict preference over the support of 𝑠 𝑖 . To illustrate this, we return to the laundry/washing up game of the introduction. Example 5.2. Consider again the game of Table  1b . As Figure  1  illustrates, the symmetric optimum is for both Ali and Bo to randomize uniformly between W and L. While this is a Nash equilibrium, it is not a local optimum in possibly-asymmetric strategy space. If one player deviates from uniformly randomizing, the other player develops a strict preference for either 𝑊 or 𝐿. To understand when the phenomenon of Example 5.2 happens in general, we use the following degeneracy condition: Definition 5.3. Let 𝑠 be a Nash equilibrium of a game G: Intuitively, our definition says that a deterministic Nash equilibrium is non-degenerate when it is strict or almost strict (allowing the exception of at most one player who may be indifferent over available actions). A mixed Nash equilibrium, on the other hand, is non-degenerate when mixing matters. When speaking of a game G, we determine its degeneracy by the degeneracy of its Nash equilibria: Definition 5.4. We call a game G degenerate if it has at least one degenerate Nash equilibrium; otherwise, we call G non-degenerate. • If 𝑠 is deterministic, i.e., We note that \"degnerate\" is already an established term in the game-theoretical literature where it is often applied only to twoplayer games [see, e.g, 42, Definition 3.2]. While similar to the established notion of degeneracy, our definition of degeneracy is stronger, which makes our statements about non-degenerate games more general. If a two-player game G is non-degenerate in the usual sense from the literature, it is non-degenerate in the sense of Definition 5.3. Moreover, if G is common-payoff, then for each player 𝑖, we can define a two-player game played by 𝑖 and another single player who controls the strategies of 𝑁 − {𝑖}. If for all 𝑖 these two-player games are non-degenerate in the established sense, then G is non-degenerate in the sense of Definition 5.3. In non-degenerate games, our next theorem shows that a local symmetric optimum is a local optimum in possibly-asymmetric strategy space if and only if it is deterministic. Formally: Theorem 5.5. Let G be a non-degenerate common-payoff normalform game, and let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). A locally optimal P-invariant strategy profile is locally optimal among possibly-asymmetric strategy profiles if and only if it is deterministic. To see why the (non-)degeneracy condition is needed in Theorem 5.5, we provide an example of a degenerate game: -10 Here, (𝑎, 𝑎) is the unique global optimum in symmetric strategy space. By Theorem 3.2, it is therefore also a Nash equilibrium. However, it is a degenerate Nash equilibrium and not locally optimal in asymmetric strategic space. The payoff can be improved by, e.g., Player 1 playing 𝑏 with small probability (and 𝑎 otherwise) and Player 2 playing 𝑐 with small probability (and 𝑎 otherwise). The following game illustrates how a global symmetric optimum, even if it is a non-degenerate, deterministic equilibrium, might still not be globally optimal in possibly-asymmetric strategy space. Example 5.7. Consider |𝑁 | = 3 and 𝐴 = {0, 1}, let 𝑘 be the number of players who choose action 1, and let the payoffs be: 0 if 𝑘 = 0, −1 if 𝑘 = 1, 1 if 𝑘 = 2, and −1 if 𝑘 = 3. Then the global symmetric optimum is for everyone to play 0. The global asymmetric optimum, on the other hand, is to coordinate to achieve 𝑘 = 2. Hence, the global symmetric optimum is strictly worse than the global asymmetric optimum. Of course, by Theorem 5.5, (0, 0, 0) is still a local optimum of asymmetric strategy space. \n LEARNING SYMMETRIC STRATEGIES IN GAMUT Theorem 5.5 shows that, in non-degenerate games, a locally optimal symmetric strategy profile is stable in the sense of Section 5 if and only if it is pure. For those concerned about stability, this raises the question: how often are optimal strategies pure, and how often are they mixed? To answer this question, we present an empirical analysis of learning symmetric strategy profiles in the GAMUT suite of game generators  [24] . We are interested both in how centralized optimization algorithms (such as gradient methods) search for symmetric strategies and in how decentralized populations of agents evolve symmetric strategies. To study the former, we run Sequential Least SQuares Programming (SLSQP)  [17, 40] , a local search method for constrained optimization. To study the latter, we simulate the replicator dynamics  [9] , an update rule from evolutionary game theory with connections to reinforcement learning  [2, 36, 37] . (See Appendix E.3 for details.) \n Experimental setup We ran experiments in all three classes of symmetric GAMUT games: RandomGame, CoordinationGame, and CollaborationGame. Intuitively, a RandomGame draws all payoffs uniformly at random, whereas in a CoordinationGame and a CollaborationGame, the highest payoffs are always for outcomes where all players choose the same action. (See Appendix E.1 details.) Because CoordinationGame and CollaborationGame have such similar game structures, our experimental results in the two games are nearly identical. To avoid redundancy, we only include experimental results for Coordina-tionGame in this paper. For each game class, we sweep the parameters of the game from 2 to 5 players and 2 to 5 actions, i.e., with (|𝑁 |, |𝐴 𝑖 |) ∈ {2, 3, 4, 5} × {2, 3, 4, 5}. We sample 100 games at each parameter setting and then attempt to calculate the global symmetric optimum using (i) 10 runs of SLSQP and (ii) 10 runs of the replicator dynamic (each with a different initialization drawn uniformly at random over the simplex), resulting in 10 + 10 = 20 solution attempts per game. Because we do not have ground truth for the globally optimal solution of the game, we instead use the best of our 20 solution attempts, which we call the \"best solution. \" To apply our previously developed theory to GAMUT games, we observe that RandomGames, CoordinationGames, and Collab-orationGames are (almost surely) non-degenerate in the sense of Definition 5.4: Proposition 6.1. Drawing a degenerate game is a measure-zero event in RandomGames, CoordinationGames, and CollaborationGames. \n What fraction of symmetric optima are local optima in possibly-asymmetric strategy space? Here, we try to get a sense for how often symmetric optima are stable in the sense that they are also local optima in possiblyasymmetric strategy space (see Section 5). In Appendix Table  3b , we show in what fraction of games the best solution of our 20 optimization attempts is mixed; by Theorem 5.5, this is the fraction of games whose symmetric optima are not local optima in possiblyasymmetric strategy space. In CoordinationGames, the symmetric optimum is always (by construction) for all players to choose the same action, leading to stability. By contrast, we see that 36% to 60% of RandomGames are unstable. We conclude that if real-world games do not have the special structure of CoordinationGames, then instability may be common. \n How often do SLSQP and the replicator dynamic find an optimal solution? As sequential least squares programming and the replicator dynamic are not guaranteed to converge to a global optimum, we test empirically how often each run converges to the best solution of our 20 optimization runs. In Appendix  \n COMPUTATIONAL COMPLEXITY OF COMPUTING GAME SYMMETRIES AND SYMMETRIC STRATEGIES 7.1 Finding symmetries In some cases, domain knowledge can provide the symmetries of a game. For example, in the laundry game of Table  1b , symmetry arises from a simple observation: it matters only what chores get done, not which children do the chores. In other cases, however, players may face a potentially symmetric common-payoff game and first have to determine what the symmetries of the game are, e.g., by computing a generating set of the group of symmetries. Call this problem the game automorphism (GA) problem. Can it be solved efficiently? The complexity of the GA problem depends on how the game is represented. The simplest representation is to give the full table of payoffs. However, the size is then exponential in the number of players. A simple alternative is to only explicitly represent non-zero entries in the payoff table. This way, some games of many players can be represented succinctly. Calling the latter a sparse representation and the former a non-sparse representation, we obtain the following: Theorem 7.1. On a non-sparse game representation, the GA problem can be solved in polynomial time. On a sparse representation, the GA problem is polynomial-time equivalent to the graph isomorphism problem. For a general introduction to the graph isomorphism problem, see Grohe and Schweitzer  [11] . Notably, the problem is in NP but neither known to be solvable in polynomial time nor known to be NP-hard. \n Finding an optimal symmetric strategy profile Once it is known what the symmetries P of a given game are, what is the complexity of finding an optimal P-invariant strategy profile? In Appendix G.2, we show that the problem of optimizing symmetric strategies is equivalent to the problem of optimizing polynomials on Cartesian products of unit simplices. However, depending on how the polynomials and games are represented, the reductions may increase the problem instance exponentially. Nevertheless, we can import results from the literature on optimizing polynomials to obtain results such as the following: Theorem 7.2. Deciding for a given game G with symmetries P and a given number 𝐾 whether there is a P-invariant profile with expected utility at least 𝐾 is NP-hard, even for 2-player symmetric games. \n CONCLUSION When ML is deployed in the world, it is natural to instantiate multiple agents from the same template. This naturally restricts strategy profiles to symmetric ones, and it puts the focus on finding optimal symmetric strategy profiles. This, in turn, raises questions about the properties of such profiles. Would individual agents (or the users they serve) want to deviate from these profiles? Are they robust to small changes in the game or in the executed strategies? Could there be better asymmetric strategy profiles nearby? Our results yield a mix of good and bad news. Theorems 3.2 and 4.3 are good news, showing that even local optima in symmetric strategy space are (global) Nash equilibria in a robust sense. So, with respect to unilateral deviations among team members, symmetric optima are relatively stable strategies. On the other hand, Theorem 5.5 is perhaps bad news, because it shows that a broad class of symmetric local optima are unstable when considering joint deviations in asymmetric strategy space (Section 5). Furthermore, our empirical results with learning algorithms in GAMUT suggest that these unstable solutions may not be uncommon in practice (Section 6.2). \n A PROOFS OF SECTION 3 RESULTS Theorem 3.2. Let G be a common-payoff normal-form game, and let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). Any locally optimal P-invariant strategy profile is a Nash equilibrium. Proof. We proceed by contradiction. Suppose 𝑠 = (𝑠 1 , 𝑠 2 , . . . , 𝑠 𝑛 ) is locally optimal among P-invariant strategy profiles that is not a Nash equilibrium. We will construct an 𝑠 ′ arbitrarily close to 𝑠 with 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠). Without loss of generality, suppose 𝑠 1 is not a best response to 𝑠 −1 but that the pure strategy of always playing 𝑎 1 is a best response to 𝑠 −1 . For an arbitrary probability 𝑝 > 0, consider the modified strategy 𝑠 ′ 1 that plays action 𝑎 1 with probability 𝑝 and follows 𝑠 1 with probability 1 −𝑝. Now, construct 𝑠 ′ = (𝑠 ′ 1 , 𝑠 ′ 2 , . . . , 𝑠 ′ 𝑛 ) as follows: 𝑠 ′ 𝑖 = 𝑠 ′ 𝑖 = 𝑠 ′ 1 if 𝑖 ∈ P (1) 𝑠 ′ 𝑖 = 𝑠 𝑖 otherwise. In words, 𝑠 ′ modifies 𝑠 by having the members of player 1's orbit mix in a probability 𝑝 of playing 𝑎 1 . We claim for all sufficiently small 𝑝 that 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠). To establish this claim, we break up the expected utility of 𝑠 ′ according to cases of how many players in 1's orbit play the action 𝑎 1 because of mixing in 𝑎 1 with probability 𝑝. In particular, we observe 𝐸𝑈 (𝑠 ′ ) = 𝑝)𝐸𝑈 (𝑠) + 𝐵(𝑚=1, 𝑝)𝐸𝑈 ((𝑠 ′ 1 , 𝑠 2 , . . . , 𝑠 𝑛 )) + 𝐵(𝑚>1, 𝑝)𝐸𝑈 (. . .), where 𝐵(𝑚, 𝑝) is the probability of 𝑚 successes for a binomial random variable on 𝑚 independent events that each have success probability 𝑝 and where 𝐸𝑈 (. . .) is arbitrary. Note that the crucial step in writing this expression is grouping the terms with the coefficient 𝐵(𝑚=1, 𝑝). We can do this because for any player 𝑗 ∈ P (1), there exists a symmetry 𝜌 ∈ Γ(G) with 𝜌 ( 𝑗) = 1. Now, to achieve 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠), we require 𝐸𝑈 (𝑠) < 𝐵(𝑚 = 1, 𝑝) 𝐵(𝑚 > 0, 𝑝) 𝐸𝑈 ((𝑠 ′ 1 , 𝑠 2 , . . . , 𝑠 𝑛 )) + 𝐵(𝑚 > 1, 𝑝) 𝐵(𝑚 > 0, 𝑝) 𝐸𝑈 (...). We know 𝐸𝑈 ((𝑠 ′ 1 , 𝑠 2 , ..., 𝑠 𝑛 )) > 𝐸𝑈 (𝑠), but we must deal with the case when 𝐸𝑈 (...) is arbitrarily negative. Because lim 𝑝→0 𝐵(𝑚 > 1, 𝑝)/𝐵(𝑚 = 1, 𝑝) = 0, by making 𝑝 sufficiently small, 𝐵(𝑚 = 1, 𝑝)/𝐵(𝑚 > 0, 𝑝) can be made greater than 𝐵(𝑚 > 1, 𝑝)/𝐵(𝑚 > 0, 𝑝) by an arbitrarily large ratio. The result follows. □ \n B OPTIMAL SYMMETRIC POLICY FOR THE RADIO STATION GAME OF EXAMPLE 3.3 We here calculate the optimal Γ(G)-invariant strategy profile for Example 3.3. Let 𝑝 be the probability of broadcasting the weather forecasts. By symmetry of the game and linearity of expectation, the expected utility given 𝑝 is simply four times the expected utility of any individual neighborhood. The value of an individual neighborhood is 0 with probability (1 − 𝑝)  3  , is 1 with probability 𝑝 3 and is 2 with the remaining probability. Hence, the expected utility of a single neighborhood is 𝑝 3 + (1 − (1 − 𝑝) 3 − 𝑝 3 ) • 2 = 2 − 2(1 − 𝑝) 3 − 𝑝 3 . The maximum of this term (and thus the maximum of the overall utility of all neighborhoods) can be found by any computer algebra system to be 𝑝 = 2 − √ 2, which gives an expected utility of 4( √ 2 − 1) ≈ 1.66. To double-check, we can also calculate the symmetric Nash equilibrium of this game. It's easy to see that that Nash equilibrium must be mixed and therefore must make each player (radio station) indifferent about what to broadcast. So let 𝑝 again be the probability with which everyone else broadcasts the weather. The expected utility of broadcasting the weather relative to broadcasting nothing for any of the three relevant neighborhoods is 2(1 − 𝑝) 2 . (Broadcasting the weather lifts the utility of a neighborhood from 0 to 2 if they do not already get the weather. Otherwise, it is useless to air the weather.) The expected utility of broadcasting music again relative to broadcasting nothing is simply 𝑝 2 . We can find the symmetric Nash equilibrium by setting 2(1 − 𝑝) 2 = 𝑝 2 , which gives us the same solution for 𝑝 as before. \n C PROOFS OF SECTION 4 RESULTS Proposition 4.2. Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝐺 ′ is an 𝜖-perturbation of G. Then 𝑠 * is a 2𝜖-Nash equilibrium in G ′ . Proof. By Theorem 3.2, 𝑠 * is a Nash equilibrium in G. After perturbing G by 𝜖 to form G ′ , payoffs have increased / decreased at most ±𝜖, so the difference between any two actions' expected payoffs has changed by at most 2𝜖. □ Theorem 4.3. Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝑠 is a strategy profile with total variation distance 𝑇𝑉 (𝑠, 𝑠 * ) ≤ 𝛿. Then 𝑠 is an 𝜖-Nash equilibrium with 𝜖 = 4𝛿 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|. Proof. Consider the perspective of an arbitrary player 𝑖. The difference in expected utility of playing any action 𝑎 𝑖 between the opponent strategy profiles 𝑠 −𝑖 and 𝑠 * −𝑖 is given by: 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 * −𝑖 ) = 𝑎 −𝑖 ∈𝐴 −𝑖 𝑠 −𝑖 (𝑎 −𝑖 )𝑢 𝑖 (𝑎 𝑖 , 𝑎 −𝑖 ) − 𝑎 −𝑖 ∈𝐴 −𝑖 𝑠 * −𝑖 (𝑎 −𝑖 )𝑢 𝑖 (𝑎 𝑖 , 𝑎 −𝑖 ) ≤ 𝑎 −𝑖 ∈𝐴 −𝑖 |𝑢 𝑖 (𝑎 𝑖 , 𝑎 −𝑖 )| 𝑠 −𝑖 (𝑎 −𝑖 ) − 𝑠 * −𝑖 (𝑎 −𝑖 ) ≤ 2𝑇𝑉 (𝑠, 𝑠 * ) max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)| ≤ 2𝛿 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|. In particular, let 𝑎 𝑖 be an action in the support of 𝑠 * 𝑖 , and let 𝑎 ′ 𝑖 be any other action. Then, using the above, we have:  𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 −𝑖 ) = 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , \n D PROOFS OF SECTION 5 RESULTS Theorem 5.5. Let G be a non-degenerate common-payoff normalform game, and let P ⊆ Γ(G) be a subset of the game symmetries Γ(G). A locally optimal P-invariant strategy profile is locally optimal among possibly-asymmetric strategy profiles if and only if it is deterministic. Proof. Let 𝑠 be a locally optimal P-invariant strategy profile. By Theorem 3.2, 𝑠 is a Nash equilibrium. Because G is non-degenerate, so is 𝑠. We prove the claim by proving that (1) if 𝑠 is deterministic, it is locally optimal in asymmetric strategy space; and (2) if 𝑠 is mixed then it is not locally optimal in asymmetric strategy space. (1) The deterministic case: Let 𝑠 be deterministic. Now consider a potentially asymmetric strategy profile 𝑠 ′ . We must show as 𝑠 ′ becomes sufficiently close to 𝑠 that 𝐸𝑈 (𝑠 ′ ) ≤ 𝐸𝑈 (𝑠). Let 𝜖 1 , 𝜖 2 , ..., 𝜖 𝑛 and ŝ1 , ..., ŝ𝑛 be such that for 𝑖 ∈ 𝑁 , 𝑠 ′ 𝑖 can be interpreted as following 𝑠 𝑖 with probability 1 − 𝜖 𝑖 and following ŝ𝑖 with probability 𝜖 𝑖 , where 𝑠 𝑖 ∉ supp( ŝ𝑖 ). Then (similar to the proof of Theorem 3.2), we can write 𝐸𝑈 (𝑠 ′ ) = 𝑖 ∈𝑁 (1 − 𝜖 𝑖 ) 𝐸𝑈 (𝑠) + 𝑗 ∈𝑁 𝜖 𝑗 𝑖 ∈𝑁 −{ 𝑗 } 1 − 𝜖 𝑖 • 𝐸𝑈 ( ŝ𝑗 , 𝑠 −𝑗 ) + 𝑗,𝑙 ∈𝑁 :𝑗≠𝑙 𝜖 𝑗 𝜖 𝑖 𝑖 ∈𝑁 −{ 𝑗,𝑙 } 1 − 𝜖 𝑖 • 𝐸𝑈 ( ŝ𝑗 , ŝ𝑙 , 𝑠 −𝑗−𝑙 ) + ... The second line is the expected value if everyone plays 𝑠, the third line is the sum over the possibilities of one player 𝑗 deviating to ŝ𝑗 , and so forth. We now make two observations. First, because 𝑠 is a Nash equilibrium, the expected utilities 𝐸𝑈 ( ŝ𝑗 , 𝑠 −𝑗 ) in the third line are all at most as big as 𝐸𝑈 (𝑠). Now consider any later term corresponding to the deviation of some set 𝐶, containing at least two players 𝑖, 𝑗. Note that it may be 𝐸𝑈 ( ŝ𝐶 , 𝑠 −𝐶 ) > 𝐸𝑈 (𝑠). However, this term is multiplied by 𝜖 𝑖 𝜖 𝑗 . Thus, as the 𝜖 go to 0, the significance of this term in the average vanishes in comparison to that of both the terms corresponding to the deviation of just 𝑖 and just 𝑗, which are multiplied only by 𝜖 𝑖 and 𝜖 𝑗 , respectively. By non-degeneracy, it is 𝐸𝑈 ( ŝ𝑖 , 𝑠 −𝑖 ) < 𝐸𝑈 (𝑠) or 𝐸𝑈 ( ŝ𝑗 , 𝑠 −𝑗 ) < 𝐸𝑈 (𝑠). Thus, if the 𝜖 𝑖 are small enough, the overall sum is less than 𝐸𝑈 (𝑠). (2) The mixed case: Let 𝑠 be mixed. We proceed by constructing a strategy profile 𝑠 ′ that is arbitrarily close to 𝑠 with 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠). Let 𝑚 be the largest integer where for all subsets of players 𝐶 ⊆ 𝑁 with |𝐶 | ≤ 𝑚, the expected payoff is constant across all joint deviations to 𝑎 𝑖 ∈ supp(𝑠 𝑖 ) for all 𝑖 ∈ 𝐶, i.e., where 𝐸𝑈 (𝑎 𝐶 , 𝑠 −𝐶 ) = 𝐸𝑈 (𝑠) for all 𝑎 𝐶 ∈ supp(𝑠 𝐶 ). As 𝑠 is a non-degenerate Nash equilibrium, 1 ≤ 𝑚 < 𝑛. By definition of 𝑚, there exists a subset of players 𝐶 ⊂ 𝑁 with |𝐶 | = 𝑚 and choice of actions 𝑎 𝐶 ∈ supp(𝑠 𝐶 ) where 𝐸𝑈 (𝑎 𝑗 , 𝑎 𝐶 , 𝑠 −𝑗−𝐶 ) is not constant across the available actions 𝑎 𝑗 ∈ 𝐴 𝑗 for some player 𝑗 ∈ 𝑁 −𝐶. Denote player 𝑗's best response to the joint deviation 𝑎 𝐶 as 𝑎 * 𝑗 ∈ argmax 𝑎 𝑗 𝐸𝑈 (𝑎 𝑗 , 𝑎 𝐶 , 𝑠 −𝑗−𝐶 ), and note 𝐸𝑈 (𝑎 𝑗 , 𝑎 𝐶 , 𝑠 −𝑗−𝐶 ) > 𝐸𝑈 (𝑎 𝐶 , 𝑠 −𝐶 ) = 𝐸𝑈 (𝑠). To construct 𝑠 ′ , modify 𝑠 by letting player 𝑗 mix according to 𝑠 𝑗 with probability (1 − 𝜖) and play action 𝑎 𝑗 with probability 𝜖. Similarly, let each player 𝑖 ∈ 𝐶 mix according to 𝑠 𝑖 with probability (1 − 𝜖) and play their action 𝑎 𝑖 specified by 𝑎 𝐶 with probability 𝜖. Because we allow 𝜖 > 0 to be arbitrarily small, all we have left to show is 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠). Observe as before that we can break 𝐸𝑈 (𝑠 ′ ) up into cases based on the number of players who deviate according to the modified   + 𝑘 ∈𝐶∪{ 𝑗 } 𝜖 𝐸𝑈 (𝑎 𝑗 , 𝑎 𝐶 , 𝑠 −𝑗−𝐶 ). By construction, every value in the expected value calculation 𝐸𝑈 (𝑠 ′ ) is equal to 𝐸𝑈 (𝑠) except for the last value 𝐸𝑈 (𝑎 𝑗 , 𝑎 𝐶 , 𝑠 −𝑗−𝐶 ), which is greater than 𝐸𝑈 (𝑠). We conclude 𝐸𝑈 (𝑠 ′ ) > 𝐸𝑈 (𝑠). □ \n E GAMUT DETAILS AND ADDITIONAL EXPERIMENTS E.1 GAMUT games In Section 6.1, we analyzed all three classes of symmetric GAMUT games: RandomGame, CoordinationGame, and CollaborationGame. Below, we give a formal definiton of these game classes: Note that these games define payoffs for each unordered action profile because the games are totally symmetric (Definition 2.3). Table  2  gives illustrative examples.  \n E.3 Replicator dynamics Consider a game where all players share the same action set, i.e., with 𝐴 𝑖 = 𝐴 𝑗 for all 𝑖, 𝑗, and consider a totally symmetric strategy profile 𝑠 = (𝑠 1 , 𝑠 1 , . . . , 𝑠 1 ). In the replicator dynamic, each action can be viewed as a species, and 𝑠 1 defines the distribution of each individual species (action) in the overall population (of actions). At each iteration of the replicator dynamic, the prevalence of an individual species (action) grows in proportion to its relative fitness in the overall population (of actions). In particular, the replicator dynamic evolves 𝑠 1 (𝑎) over time 𝑡 for each 𝑎 ∈ 𝐴 1 as follows: 𝑑 𝑑𝑡 𝑠 1 (𝑎) = 𝑠 1 (𝑎) [𝐸𝑈 (𝑎, 𝑠 −1 ) − 𝐸𝑈 (𝑠)] . To simulate the replicator dynamic with Euler's method, we need to choose a stepsize and a total number of iterations. Experimentally, we found the fastest convergence with a stepsize of 1, and we found that 100 iterations sufficed for convergence; see Figure  2 . For good measure, we ran 10,000 iterations of the replicator dynamic in all of our experiments. We are interested in the replicator dynamic for two reasons. First, it is a model for how agents in the real world may collectively arrive at a symmetric solution to a game (e.g., through evolutionary pressure). Second, it is a learning algorithm that performs local search in the space of symmetric strategies. In our experiments of Appendix E.5, we find that using the replicator dynamic as an optimization algorithm is competitive with Sequential Least SQuares Programming (SLSQP), a local search method from the constrained optimization literature  [17, 40] . E.4 What fraction of symmetric optima are local optima in possibly-asymmetric strategy space? As discussed in Section 6.2, we would like to get a sense for how often symmetric optima are stable in the sense that they are also local optima in possibly-asymmetric strategy space (see Section 5). Table  3  shows in what fraction of games the best solution we found is unstable. \n E.5 How often do SLSQP and the replicator dynamic find an optimal solution? As discussed in Section 6.3, Table  4  and Table  5  show how often SLSQP finds an optimal solution, while Table  6  and Table  7  show how often the replicator dynamic finds an optimal solution. E.6 How costly is payoff perturbation under the simultaneous best response dynamic? When a game is not stable in the sense of Section 5, we would like to understand how costly the worst-case 𝜖-perturbation of the game can be. (See Definition 4.1 for the definition of an 𝜖-perturbation of a game.) In particular, we study the case when individuals simultaneously update their strategies in possibly-asymmetric ways by defining the following simultaneous best response dynamic: Definition E.4. The simultaneous best response dynamic at 𝑠 updates from strategy profile 𝑠 = (𝑠 1 , 𝑠 2 , . . . , 𝑠 𝑛 ) to strategy profile 𝑠 ′ = (𝑠 ′ 1 , 𝑠 ′ 2 , . . . , 𝑠 ′ 𝑛 ) with every 𝑠 ′ 𝑖 a best response to 𝑠 −𝑖 . For each of the RandomGames in Section 6.2 whose symmetric optimum 𝑠 is not a local optimum in possibly-asymmetric strategy space, we compute the worst-case 𝜖 payoff perturbation for infinitesimal 𝜖. Then, we update each player's strategy according to the simultaneous best response dynamic at 𝑠. This necessarily leads to a decrease in the original common payoff because the players take simultaneous updates on an objective that, after payoff perturbation, is no longer common. Table  8  reports the average percentage decrease in expected utility, which ranges from 55% to 89%. Our results indicate that simultaneous best responses after payoff perturbation in RandomGames can be quite costly. \n F THE COMPUTATIONAL COMPLEXITY OF FINDING THE SYMMETRIES OF A GAME In this section, we analyze the computational complexity of finding the symmetries of a common-payoff game. In general, symmetries as defined in Definition 2.1 can be found in exponential time in the number of players. Therefore, if we represent the game explicitly as a full payoff matrix, then the symmetries can be found in polynomial time in the size of the input. However, if we can represent the game more efficiently by giving only non-zero entries of the payoff matrix, the problem becomes graph isomorphism-complete, i.e., polynomial-time equivalent to the graph isomorphism problem, which is neither known to be solvable in polynomial time nor known to be NP-hard [see 11, for an overview]. We also show (in Section F.3) that if we consider a more general notion of game symmetry that permutes actions in addition to players, the computational problem becomes graph isomorphism-complete on an explicit payoff matrix representation. \n F.1 The hypergraph automorphism problem We here introduce the hypergraph automorphism problem and some existing results about it. In the next section, we will prove our results by relating the game automorphism problem (i.e., the problem of finding the symmetries of a game) to the hypergraph automorphism problem. A hypergraph is a pair (𝑉 , 𝐸), where 𝑉 is a (finite) set of vertices and 𝐸 ⊆ 2 𝑉 is a set of hyperedges. A symmetry or automorphism of a hypergraph is a bijection 𝜌 : 𝑉 → 𝑉 s.t. for each set of vertices 𝑒 ⊆ 𝑉 , it is 𝑒 ∈ 𝐸 if and only if 𝜌 (𝑒) ∈ 𝐸, where 𝜌 (𝑒) {𝜌 (𝑣) | 𝑣 ∈ 𝑒}. In other words: For 𝜌 to be a symmetry it must be the case that any set of vertices 𝑣 1 , ..., 𝑣 𝑘 are connected by a hyperedge if and only if 𝜌 (𝑣 1 ), ..., 𝜌 (𝑣 𝑘 ) are connected by a hyperedge. Definition F.1. The hypergraph automorphism (HA) problem asks for a given hypergraph (𝑉 , 𝐸) to provide a set of symmetries of (𝑉 , 𝐸) that generate the group of all symmetries of (𝑉 , 𝐸). There are two natural ways to represent the edges of a hypergraph. The first is to provide what one would call an adjacency matrix in the case of a regular graph. That is, we give a table of bits that specifies for each 𝑒 ∈ 2 𝑉 whether 𝑒 ∈ 𝐸. That is, for each set of vertices, we specify whether there is a hyperedge connecting that set of vertices. The downside of this representation style is that it always costs 𝑂 (2 |𝑉 | ) bits. An alternative is to explicitly list 𝐸, such that graphs with few edges can be represented in much less space than 𝑂 (2 |𝑉 | ). We call the former notation non-sparse and the latter sparse. Lemma F.2. The HA problem on a sparse hypergraph representation is graph isomorphism-complete. Proof. Mathon  [21]  shows that the problem of giving the generators of the automorphism group of a given graph isomorphism complete. So it is left to show that the automorphism problem on sparse hypergraphs is polynomially equivalent to analogous problem on graphs. Since graphs are hypergraphs, we only need to reduce HA to the graph automorphism problem. This is easy and the main idea has been noted before, e.g., see the introduction of Arvind et al.  [1] . □ Theorem F.3  (Luks, 1999, Theorem 4.2) . The HA problem is solvable in 𝑂 (𝑐 |𝑉 | ) for some constant 𝑐. In particular, it follows immediately that HA on non-sparse representations is solvable in polynomial time. Coordina-tionGame Table  3 : The fraction of games whose symmetric optima are mixed. By Theorem 5.5, these symmetric equilibria are the ones unstable in the sense of Section 5. Numbers in the table were empirically determined from 100 randomly sampled games per GAMUT class.         8 : The average decrease in expected utility that worst-case infinitesimal asymmetric payoff perturbations cause to unstable symmetric optima. To get these numbers, we first perturb payoffs in the 100 RandomGames from Section 6.2 whose symmetric optima 𝑠 are not local optima in possibly-asymmetric strategy space. Then, in each perturbed game, we compute a simultaneous best-response update to 𝑠 and record its decrease in expected utility. \n F.2 Polynomial-time equivalence Recall from the main text that -for the purpose of our paper -a symmetry of an 𝑛-player (common-payoff) game (𝐴, 𝑢) is a permutation 𝜌 : {1, ..., 𝑛} → {1, ..., 𝑛} s.t. for all pure strategy profiles a ∈ 𝐴, it is 𝑢 (𝑎 1 , ..., 𝑎 𝑛 ) = 𝑢 (𝑎 𝜌 (1) , ..., 𝑎 𝜌 (𝑛) ). In particular, we do not consider permutations of the actions. Definition F.4. The (common-payoff) game automorphism (GA) problem asks us to compute for a common-payoff given game a generating set of the symmetries of the game. As with hypergraphs, we distinguish two representations for a game. A sparse representation lists only non-zero payoffs. A nonsparse representation gives the payoff for each 𝐴. As before, the downside of the full payoff table representation is that its size is exponential in the number of players. Theorem F.5. The sparse/non-sparse representation HA problem is polynomial-time equivalent to the sparse/non-sparse representation GA problem. By polynomial-time, we here mean in time bound by a polynomial in the number of players and the size in bits of the given instance. Proof. HA→GA: We first reduce the HA problem to the GA problem, which is the easier direction. We will use the same construction for both the sparse-to-sparse and non-sparse-to-nonsparse case. Take a given hypergraph (𝑉 , 𝐸). WLOG assume 𝑉 = {1, ..., 𝑛}. Then we construct an 𝑛-player game, in which each player has two actions, 𝑎 0 , 𝑎 1 . For any 𝑀 ⊆ {1, ..., 𝑛}, let a 𝑀 be the payoff profile in which the set of players playing 𝑎 1 is exactly 𝑀. Then let the payoff 𝑢 (a 𝑀 ) be 1 if 𝑀 ∈ 𝐸 and 0 otherwise. We now show that this reduction is valid by showing that the game and the graph have the same symmetries. Let 𝜌 be a bijection. Then: 𝜌 is a symmetry of (𝑉 , 𝐸) iff ∀𝑒 ∈ 2 𝑉 : 𝑒 ∈ 𝐸 ⇐⇒ 𝜌 (𝑒) ∈ 𝐸 (2) iff ∀𝑀 ∈ 2 𝑉 : 𝑢 (a 𝑀 ) = 1 ⇐⇒ 𝑢 (a 𝜌 (𝑀) ) = 1 (3) iff ∀𝑀 ∈ 2 𝑉 : 𝑢 (a 𝑀 ) = 𝑢 (a 𝜌 (𝑀) ) (4) iff ∀a ∈ 𝐴 : 𝑢 (𝑎 1 , ..., 𝑎 𝑛 ) = 𝑢 (𝑎 𝜌 (1) , ..., 𝑎 𝜌 (𝑛) ) iff 𝜌 is a symmetry of (𝐴, 𝑢) It is easy to see that this construction can be performed in polynomial (indeed linear) time for both sparse and non-sparse representations. GA→HA: We now reduce in the opposite direction. This is more complicated and we therefore provide only a sketch. Consider an 𝑛-player game (𝐴, 𝑢). We construct the hypergraph as follows. First, for each player 𝑖, we generate a vertex. We also generate log 2 (|𝐴 𝑖 |) vertices that we use to encode 𝐴 𝑖 , player 𝑖's actions and connect them with the vertex representing 𝑖. For players 𝑖, 𝑗 that have the same action label sets, this encoding must be done consistently for 𝑖, 𝑗. We also need to add some kind of structure to ensure that symmetries of the hypergraph can only map the 𝑘th action-encoding vertex of player 𝑖 on the 𝑘th action-encoding vertex of a player 𝑗 that has the same action label set as 𝑖. Next, we represent the payoff function 𝑢. To do so, we introduce ⌈log 2 (|𝑢 (𝐴) − {0}|)⌉ payoff encoding vertices. Note that |𝑢 (𝐴) − {0}| is the number of distinct non-zero payoffs of the game. To encode |𝑢 (𝐴) − {0}| we therefore need ⌈log 2 (|𝑢 (𝐴) − {0}|)⌉ bits. We connect these bits in such a way that any symmetry must map each of them onto itself. We fix some binary encoding of 𝑢 (𝐴) − {0}. For instance, let's say the non-zero payoffs of the game are {−3, −1, 7, 8, 10, 11, 13, 100}. Then we need three bits, and might encode them as −3 ↦ → 000, −1 ↦ → 001, 7 ↦ → 010, 8 ↦ → 011, and so forth. For each a ∈ 𝐴 with 𝑢 (a) ≠ 0, we then add an edge that contains for each Player 𝑖 the action encoding vertices corresponding to 𝑎 𝑖 ; and those bits from the payoff encoding vertices that together represent the payoff. (So, for example, if the payoff is encoded by 011, then the hyperedge contains the two lower payoff encoding vertices. Similarly for the action encoding vertices.) We omit a proof of the correctness of this reduction. It is left to show that the reduction is polynomial-time for both representation styles. For the sparse representation styles, it is trivial because up to some small number of extra vertices and edges, there is a one-to-one correspondence between edges of the hypergraph and action profiles with non-zero payoffs. On to the non-sparse representation. Clearly each entry of the adjacency matrix can be filled in polynomial (perhaps even constant or logarithmic) time. It is left to show that the adjacency matrix is not too large. In particular, we need to show that the size of the adjacency matrix is polynomial in the size of the payoff matrix. To assess the size of the adjacency matrix we need to count the number of vertices in the above construction. First, the number of player vertices is 𝑛 ≤ log 2 (|𝐴 1 |) + ... + log 2 (|𝐴 𝑛 |) = log 2 (|𝐴 1 | • ... • |𝐴 𝑛 |) = log 2 (|𝐴|). (The inequality assumes each player has at least two actions.) Second, the number of action-encoding vertices is ⌈log 2 (|𝐴 1 |)⌉ + ... + ⌈log 2 (|𝐴 𝑛 |)⌉ ≤ 2 log 2 (|𝐴 1 |) + ... + 2 log 2 (|𝐴 𝑛 |) = 2 log 2 (|𝐴|). Finally, the number of payoff encoding vertices is about ⌈log 2 (|𝑢 (𝐴)|)⌉ ≤ 2 log 2 (|𝑢 (𝐴)|) ≤ 2 log 2 (|𝐴|). The overall number of vertices in the above construction is therefore at most 5 log 2 (|𝐴|). Thus, the size (in terms of number of bits) of the adjacency matrix is bound by 2 5(log 2 |𝐴 |) = |𝐴| 5 . Since |𝐴| is a lower bound on the size of the payoff matrix (in bits), this is polynomial in the size of the game's payoff matrix, as required. □ One might wonder: In the non-sparse representation case, why does the reduction to HA not also work if we use a more traditional sense of game symmetries? If it were to work that would show that GI is polynomial-time solvable! But this does not work (with the proof strategy used above). In the current reduction, actions do not get their own vertices. Thus, (even if we dropped the constraint structures that prevent actions from being remapped), a hypergraph automorphism cannot remap, e.g., an action encoded as 11011 to an action encoded as 01010. To express full action relabelings in the hypergraph, it seems that we need to introduce an action per vertex. However, the size of the adjacency matrix then blows up more than polynomially. Combining Lemma F.2 and Theorems F.3 and F.5, we get a characterization of the complexity of the graph automorphism problem. Corollary F.6. GA is solvable in polynomial time on a non-sparse representation and is GI-complete on a sparse representation. \n F.3 An alternative notion of game symmetry As mentioned in the main text, we only consider symmetries that relabel the players and the above is on the computational problem resulting from that notion of symmetry. As noted in footnote 3, this was done in part to keep notation simple and an alternative, slightly more complicated notion allows for the actions to be permuted. A natural question then is what the complexity is of finding this new type of symmetry in a given common-payoff game. In this case, the answer is that finding symmetries is GI-complete regardless of how the game is represented and follows almost immediately from existing ideas from Mathon  [21]  and Gabarró et al.  [10] . A player-action (PA) symmetry of a game is pair of a bijection 𝜌 : {1, ..., 𝑛} → {1, ..., 𝑛} on players and a family of bijections 𝜏 𝑖 : 𝐴 𝜌 (𝑖) → 𝐴 𝑖 s.t. for all pure strategy profiles (𝑎 1 , ..., 𝑎 𝑛 ), 𝑢 (𝑎 1 , ..., 𝑎 𝑛 ) = 𝑢 (𝜏 1 (𝑎 𝜌 (1) ), ..., 𝜏 𝑛 (𝑎 𝜌 (𝑛) )). So the idea in this new definition is that 𝜏 𝑖 translates the action names from those of player 𝜌 (𝑖) to player 𝑖. Define the PAGA problem analogously to the GA problem above, as finding a generating set of the PA symmetries of a given commonpayoff game. This time, the complexity is independent of whether the game is represented sparsely or not. Theorem F.7. The PAGA problem is GI-complete. Proof. PAGA→GI For their proof of GI-completeness of the game isomorphism problem, Gabarró et al.  [10]  sketch how a generalsum game can be represented as a graph in a way that maintains the isomorphisms. In particular, we can therefore represent a single common-payoff game as a graph in a way that maintains PA symmetries. The have thus given a sketch of a polynomial-time reduction from PAGA to the problem of finding the automorphisms of a graph. This latter problem can in turn be reduced in polynomial time to the graph isomorphism problem as was shown by Mathon  [21] . GI→PAGA Second, we show GI-hardness. As shown by Mathon  [21] , it is enough to reduce the graph automorphism problem to the PAGA problem. For this, we can slightly modify the construction of Gabarró et al.  [10, Lemma 5] . Specifically, they reduce the graph isomorphism problem to the 4-player general-sum game isomorphism problem, where actions represent vertices and the graph isomorphisms can be recovered from those PA game isomorphisms where the player isomorphism is 𝜌 = id. Obviously, the same construction can be used to reduce the graph automorphism problem to the general-sum game automorphism problem. The only issue is therefore that their construction uses general-sum games, but we can simply encode their payoff vectors as single numbers. In particular, because their payoffs are binary, we might translate (0, 0, 0, 0) ↦ → 0, (0, 0, 0, 1) ↦ → 1,(0, 0, 1, 0) ↦ → 2, and so forth. It  '  for some 𝑚, where the 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) are some set of real coefficients. The terms 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 1 for which 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) ≠ 0 are called the monomials of the polynomial. The maxdegree of a monomial 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 1 is max 𝑖=1,...,𝑘 𝑒 𝑖 . The maxdegree of a polynomial is the maximum of the maxdegrees of its monomials. Similarly, the total degree of a monomial 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 1 is 𝑘 𝑖=1 𝑒 𝑖 . The total degree of a polynomial is the maximum of the total degrees of its monomials. The degree of a variable 𝑥 𝑖 in a monomial 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 1 is 𝑒 𝑖 . The maxdegree of 𝑥 𝑖 in a polynomial is the maximum of the maxdegrees of 𝑥 𝑖 in all of the monomials. We can partition the parameters of a polynomial into vectors and write the polynomial as 𝑓 (x 1 , ..., x 𝑘 ), where x 1 , ..., x 𝑘 are real vectors. We define the degree of x 𝑖 in a monomial as the sum of the degrees of the entries of x 𝑖 in the monomial. We define the maxdegree of x 𝑖 in the polynomial as the maximum of the degrees of x 𝑖 in the polynomial's monomials. In the following we will interpret the set Δ(𝐴 𝑖 ) of probability distributions over 𝐴 𝑖 as the set of |𝐴 𝑖 |-dimensional vectors of nonnegative reals whose entries sum to one. We will index these vectors by 𝐴 𝑖 (rather than numbers 1, ..., |𝐴 𝑖 |). The sets Δ(𝐴 𝑖 ) are also called unit simplices. \n G.2 Optimizing symmetric strategies as maximizing polynomials It is immediately obvious that in a symmetric game, the expected utility as a function of the probabilities that each of the orbits assign to each of the strategies is a polynomial over a Cartesian product of unit simplices. Formally: Proposition G.1. Let G be an 𝑛-player game and P ⊆ Γ(G) be a subset of the game symmetries of G. Let the orbits of P be 𝑀 1 , ..., 𝑀 𝑘 . Further, let the set of actions of orbit 𝑖 be 𝐴 𝑖 . Then the expected utility function over P-invariant strategy profiles of G is a polynomial over Δ(𝐴 1 ) × ... × Δ(𝐴 𝑘 ) with a max degree of (at most) max 𝑖 |𝑀 𝑖 | and a total degree of (at most) 𝑛. This polynomial can be created in polynomial-time in the size of a sparse or non-sparse (as per Appendix F.2) representation of the game. It follows that we can use algorithms for optimizing polynomials to find optimal symmetric strategies and that positive results on optimizing polynomials transfer to finding optimal mixed strategies. Unfortunately, these results are generally somewhat cumbersome to state. This is because the optimum can in general not be represented exactly algebraically, even using 𝑛-th roots, as implied by the Abel-Ruffini theorem. Positive results must therefore be given in terms of approximations of the optimal solution. One striking result from the literature is that, roughly speaking, for a fixed number of variables, the optimal solution can be approximated in polynomial time  [16, Section 6.1] . Translated to our setting, this means that the optimal symmetric strategy can be approximated in polynomial time if we keep constant the number of orbits and the number of actions available to each orbit, but potentially increase the number of players in each orbit. For more discussion of the complexity of optimizing polynomials on unit simplices, see de Klerk  [6] . \n G.3 Expressing polynomials as symmetric games We now show that, conversely, for any polynomial over a Cartesian product of simplices there exists a symmetric game whose expected utility term is exactly that polynomial. However, depending on how we represent polynomials and how we represent games, the size of the game may blow up exponentially. We first show that each polynomial over Δ(𝐴 1 ) × ... × Δ(𝐴 𝑘 ) can be rewritten in such a way that each input x 𝑖 appears in the same degree in all monomials. Lemma G.2. Let 𝑓 (x 1 , ..., x 𝑘 ) be a polynomial on real vectors of dimensions 𝐴 1 , ..., 𝐴 𝑘 . Then there exists a polynomial 𝑔 on the same inputs s.t. for all (x 1 , ..., x 𝑘 ) ∈ Δ(𝐴 1 ) × ... × Δ(𝐴 𝑘 ) 𝑔(x 1 , ..., x 𝑘 ) = 𝑓 (x 1 , ..., x 𝑘 ), and the degree of every x 𝑖 in all monomials of 𝑔 is the maxdegree of x 𝑖 in 𝑓 . Proof. Consider any monomial f of 𝑓 in which x 𝑖 does not have its max degree. Then for all (x 1 , ..., x 𝑘 ) ∈ Δ(𝐴 Notice that this is the sum of |𝐴 𝑖 | monomials in which x 𝑖 occurs in 1 plus the degree in which it occurs in f . We can iterate this transformation until we arrive at the desired f . □ Note, however, that if web take a given polynomial represented as a sum of monomials -e.g., 𝑓 (𝑥 1 , 𝑥 2 ) = 𝑥  4  1 − 3𝑥 2 -and rewriting it as outlined in the Lemma and its proof, the size may blow up exponentially. E.g., 𝑓 (𝑥 1 , 𝑥 2 ) = 𝑥  4  1 − 3𝑥 2 = 𝑥 4 1 − 3(𝑥 1 + 𝑥 2 ) 3 𝑥 2 and (𝑥 1 + 𝑥 2 ) 3 expands into a sum of 2 3 = 8 terms. However, in some table-of-coefficient representations of polynomials the size of the instance does not change at all and the transformation can be performed in polynomial time in the input. For example, this is the case if 𝑘 = 1 and we represent a polynomial as a table of the coefficients of all terms 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 𝑘 where 𝑒 1 + ... + 𝑒 𝑘 are at most the polynomial's maxdegree. Once we have a polynomial of the structure described in Lemma G.2, we can transform it into a game: Proposition G.3. Let 𝑓 (x 1 , ..., x 𝑘 ) be a polynomial in which each x 𝑖 appears in the same degree in all monomials. Then we can construct a game G with symmetries P that create 𝑘 orbits, where the number of players in orbit 𝑖 = 1, ..., 𝑘 is the degree of x 𝑖 in 𝑓 and the number of actions for the players in orbit 𝑖 is the number of entries of x 𝑖 . Proof. Consider games Γ with orbits 𝑀 1 , ..., 𝑀 𝑘 of the specified sizes and sets of actions 𝐴 1 , ..., 𝐴 𝑘 also of the specified sizes where specifically the players in each 𝑀 𝑖 are totally symmetric. Then such a game if fully specified as follows. For each family of numbers 𝑛 1,1 , ..., 𝑛 □ Note that if the polynomial is represented as a table of coefficients, then this reduction takes linear time in the size of the input. Similarly, if the polynomial is given as a list of only the monomials with non-zero coefficients -all of which satisfy the degree requirement -the reduction can also be done in polynomial time. This in particular gives us the following negative result, translated from the literature on optimizing polynomials: Corollary G.4. Deciding for a given game G with symmetries P and a given number 𝐾 whether there is a P-invariant profile with expected utility at least 𝐾 is NP-hard, even for 2-player symmetric games. Proof. Follows from Proposition G.3 and the NP-hardness of optimizing quadratic polynomials over the unit simplex [6, Section 3.2]. □ Figure 1 : 1 Figure 1: The strategy profile landscape of the symmetric laundry game (Figure1b). Although the symmetric optimum has lower expected utility than the unrestricted optima, total symmetry of the game implies that the symmetric optimum is a Nash equilibrium; this is a special case of Theorem 3.2. \n Example 5 . 6 . 56 Consider the 3x3 symmetric game with the following payoff matrix: 10 1 + 𝜖 c 1 1 + 𝜖 \n probability 𝜖: 𝐸𝑈 (𝑠 ′ ) = 𝑘 ∈𝐶∪{ 𝑗 } (1 − 𝜖) 𝐸𝑈 (𝑠) + 𝑙 ∈𝐶∪{ 𝑗 } 𝜖 𝑘 ∈𝐶∪{ 𝑗 }:𝑘≠𝑙 1 − 𝜖 𝐸𝑈 (𝑎 𝑙 , 𝑠 −𝑙 ) + ... \n Definition E. 1 . 1 A RandomGame with |𝑁 | players and |𝐴| actions assumes 𝐴 𝑖 = 𝐴 𝑗 for all 𝑖, 𝑗 and draws a payoff from Unif (−100, 100) for each unordered action profile 𝑎 ∈ 𝐴. Definition E.2. A CoordinationGame with |𝑁 | players and |𝐴| actions assumes 𝐴 𝑖 = 𝐴 𝑗 for all 𝑖, 𝑗. For each unordered action profile 𝑎 ∈ 𝐴 with 𝑎 𝑖 = 𝑎 𝑗 for all 𝑖, 𝑗, it draws a payoff from Unif (0, 100); for all other unordered action profiles, it draws a payoff from Unif (−100, 0). Definition E.3. A CollaborationGame with |𝑁 | players and |𝐴| actions assumes 𝐴 𝑖 = 𝐴 𝑗 for all 𝑖, 𝑗. For each unordered action profile 𝑎 ∈ 𝐴 with 𝑎 𝑖 = 𝑎 𝑗 for all 𝑖, 𝑗, the payoff is 100; for all other unordered action profiles, it draws a payoff from Unif (−100, 99). \n Figure 2 : 2 Figure 2: The magnitude of the replicator dynamics update step averaged over 10,000 RandomGames 4 with 2 players and 2 actions. Although this plot indicates that the replicator dynamics converge by 100 iterations, we ran 10,000 iterations for good measure in all of our experiments. \n 31 ( 31 92 0.81 0.70 0.64 3 0.80 0.69 0.57 0.48 4 0.75 0.57 0.40 0.35 5 0.70 0.45 0.36 0.59 0.50 0.40 0.33 3 0.53 0.38 0.28 0.29 4 0.53 0.37 0.29 0.26 5 0.53 0.36 0.33 0.25 (b) CoordinationGame \n 𝑛 𝑗=1 𝑠 𝑗 (𝑎 𝑗 ). If a strategy 𝑠 𝑖 for player 𝑖 maximizes expected utility given the strategies 𝑠 −𝑖 of all the other players, i.e., if 𝑠 𝑖 ∈ argmax 𝑠 ′ 𝑖 ∈Δ(𝐴 𝑖 ) 𝐸𝑈 𝑖 (𝑠 ′ 𝑖 , 𝑠 −𝑖 ), we call 𝑠 𝑖 a best response to 𝑠 −𝑖 . If each strategy 𝑠 𝑖 in a strategy profile 𝑠 is a best response to 𝑠 −𝑖 , we call 𝑠 a Nash equilibrium. A Nash equilibrium 𝑠 is strict if every 𝑠 𝑖 is the unique best response to 𝑠 −𝑖 . \n if every 𝑠 𝑖 is a Dirac delta function on some 𝑎 𝑖 , then 𝑠 is degenerate if at least two players 𝑖 are indifferent between 𝑎 𝑖 and some other 𝑎 ′ 𝑖 ∈ 𝐴 𝑖 − {𝑎 𝑖 }. • Otherwise, if 𝑠 is mixed, then 𝑠 is degenerate if for all players 𝑖 and all 𝑎 −𝑖 ⊆ supp(𝑠 −𝑖 ), the term 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑎 −𝑖 ) is constant across 𝑎 𝑖 ∈ supp(𝑠 𝑖 ). \n Table 4 / 4 Table 6, we show what fraction of the time any single SLSQP / replicator dynamics run finds the best solution, and in Appendix Table 5 / Table 7, weshow what fraction of the time at least 1 of 10 SLSQP / replicator dynamics runs finds the best solution. First, we note that the tables for SLSQP and the replicator dynamics are quite similar, differing by no more than a few percentage points in all cases. So the replicator dynamics, which are used as a model for how populations evolve strategies, can also be used as an effective optimization algorithm. Second, we see that individual runs of each algorithm are up to 93% likely to find the best solution in small RandomGames, but they are less likely (as little as 24% likely) to find the best solution in larger RandomGames and in CoordinationGames. The best of 10 runs, however, finds the best solution ≥ 87% of the time, indicating that random algorithm restarts benefit symmetric strategy optimization. \n 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 * −𝑖 ) + 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 * −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 −𝑖 ) ≤ 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 * −𝑖 ) + 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 * −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 −𝑖 ) ≤ 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠 * −𝑖 ) + 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠 * Let G be a common-payoff normal-form game, and let 𝑠 * be a locally-optimal P-invariant strategy profile for some subset of game symmetries P ⊆ Γ(G). Suppose 𝑠 is a strategy profile with Kullback-Leibler divergence satisfying 𝐷 𝐾𝐿 (𝑠 ||𝑠 * ) ≤ 𝜈 or 𝐷 𝐾𝐿 (𝑠 𝑠  *  −𝑖 ) + 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠  *  −𝑖 ) − −𝑖 ) ≤ 4𝛿 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|, where 𝐸𝑈 𝑖 (𝑎 ′ 𝑖 , 𝑠  *  −𝑖 ) − 𝐸𝑈 𝑖 (𝑎 𝑖 , 𝑠  *  −𝑖 ) ≤ 0 because 𝑠  *  𝑖 is a Nash equilib- rium by Theorem 3.2. □ Corollary 4.4. * ||𝑠) ≤ 𝜈. Then 𝑠 is an 𝜖-Nash equilibrium with 𝜖 = 2 √ 2𝜈 max 𝑖 ∈𝑁 ,𝑎 ∈𝐴 |𝑢 𝑖 (𝑎)|.Proof. By Pinsker's inequality [35] , we have𝑇𝑉 (𝑠, 𝑠 * ) ≤ 1 2𝐷 𝐾𝐿 (𝑠 ||𝑠 * ).As 𝑇𝑉 (𝑠, 𝑠 * ) = 𝑇𝑉 (𝑠 * , 𝑠) and with a similar application of Pinsker's inequality, we have by assumption that 𝑇𝑉 (𝑠, 𝑠 * ) ≤ 𝜈/2. Applying Theorem 4.3 with 𝛿 = 𝜈/2 yields the result. □ \n Table 2 : 2 𝛼 𝑢 𝛼𝛼 𝑢 𝛼 𝛽 𝛽 𝑢 𝛼 𝛽 𝑢 𝛽𝛽 A payoff matrix with |𝑁 | = 2 and 𝐴 1 = 𝐴 2 = {𝛼, 𝛽} to illustrate GAMUT games. In a RandomGame, 𝑢 𝛼𝛼 , 𝑢 𝛼 𝛽 , and 𝑢 𝛽𝛽 are i.i.d. draws from Unif (−100, 100). In a Coordi-nationGame, 𝑢 𝛼𝛼 and 𝑢 𝛽𝛽 are i.i.d. draws from Unif (0, 100) while 𝑢 𝛼 𝛽 is a draw from Unif (−100, 0). In a Collabora-tionGame, 𝑢 𝛼𝛼 = 𝑢 𝛽𝛽 = 100, and 𝑢 𝛼 𝛽 is a draw from Unif (−100, 99). Player 2 𝛼 𝛽 Player 1 \n Table 4 : 4 The fraction of single SLSQP runs that achieve the best solution found in our 20 total optimization attempts. Numbers in the table were empirically determined from 100 randomly sampled games per GAMUT class. A 2 3 4 5 N 2 1.00 0.99 0.99 0.98 3 1.00 0.99 1.00 0.96 4 1.00 0.96 0.94 0.88 5 0.98 0.90 0.88 0.91 (a) RandomGame \n Table 5 : 5 The fraction of games in which at least 1 of 10 SLSQP runs achieves the best solution found in our 20 total optimization attempts. Numbers in the table were empirically determined from 100 randomly sampled games per GAMUT class. A 2 3 4 5 N 2 0.93 0.81 0.68 0.65 3 0.81 0.70 0.58 0.46 4 0.76 0.58 0.36 0.34 5 0.69 0.43 0.36 0.30 \n Table 6 : 6 The fraction of single replicator dynamics runs that achieve the best solution found in our 20 total optimization attempts. Numbers in the table were empirically determined from 100 randomly sampled games per GAMUT class. This is harder to show. Note that a brute force method that tests all |𝑉 |! bijections is super-exponential in |𝑉 | and super-polynomial in (the problem size) 2 |𝑉 | . A 2 3 4 5 A 2 3 4 5 N N 2 1.00 1.00 1.00 1.00 2 1.00 1.00 0.99 0.94 3 0.99 1.00 0.95 0.96 3 1.00 0.97 0.93 0.96 4 1.00 0.98 0.91 0.91 4 0.99 1.00 0.93 0.92 5 0.98 0.97 0.92 0.87 5 1.00 0.98 0.96 0.90 (a) RandomGame (b) CoordinationGame \n Table 7 : 7 The fraction games in which at least 1 of 10 replicator dynamics runs achieves the best solution found in our 20 total optimization attempts. Numbers in the table were empirically determined from 100 randomly sampled games per GAMUT class. A 2 3 4 5 N 2 58.9% 55.9% 61.8% 64.6% 3 73.7% 70.9% 73.4% 73.7% 4 74.1% 77.4% 78.4% 82.5% 5 77.4% 84.9% 89.9% 87.5% (a) RandomGame \n s easy to see that the symmetries with 𝜌 = id remain the same under this transformation. (multivariate) polynomial in 𝑘 variables is a function (𝑥 1 , ..., 𝑥 𝑘 ) ↦ → 𝑒 1 ,...,𝑒 𝑘 ∈ {1,...,𝑚 } 𝑐 (𝑒 1 ,...,𝑒 𝑘 ) 𝑥 𝑒 1 1 ...𝑥 𝑒 𝑘 □ G THE COMPUTATIONAL COMPLEXITY OF FINDING OPTIMAL SYMMETRIC STRATEGIES G.1 Polynomials 1 A \n 1 ) × ... × Δ(𝐴 𝑘 ), f (x 1 , ..., x 𝑘 ) = 𝑎 𝑖 ∈𝐴 𝑖 𝑥 𝑖,𝑎 𝑖 f (x 1 , ..., x 𝑘 ) = 𝑎 𝑖 ∈𝐴 𝑖 𝑥 𝑖,𝑎 𝑖 f (x 1 , ..., x 𝑘 ). \n 1, |𝐴 1 | , ...., 𝑛 𝑘,1 , ..., 𝑛 𝑘, |𝐴 𝑘 | with 𝑛 𝑖,1 + ... + 𝑛 𝑖, |𝐴 𝑖 | = |𝑀 𝑖 | we need to specify the utility 𝑣 obtained if for all 𝑖, 𝑙, 𝑛 𝑖,𝑗 players in orbit 𝑖 play action number 𝑗 from 𝐴 𝑖 . In the expected utility function of G, each such entry creates a summand 𝑛 𝑖,1 , ..., 𝑛 𝑖, |𝐴 𝑖 | 𝑖,𝑙 𝑝 𝑛 𝑖,𝑙 𝑖,𝑙 , where 𝑝 𝑖,𝑙 is the probability with which players in orbit 𝑖 player action 𝑙 and |𝑀 𝑖 | 𝑛 𝑖,1 ,...,𝑛 𝑖,|𝐴 𝑖 | is a multinomial. By setting 𝑣 appropriately, we can thus obtain any monomial with exponents (𝑛 𝑖,𝑙 ) 𝑖,𝑙 . By setting the values 𝑣 all different sets of (𝑛 𝑖,𝑙 ) 𝑖,𝑙 appropriately, we obtain any polynomial in which each (𝑛 𝑖,𝑙 ) 𝑙 appears with the same degree |𝑀 𝑖 | in all monomials. 𝑣 • 𝑖|𝑀 𝑖 | \n\t\t\t This condition is relaxed in (weighted) potential games where the players' payoffs need only imply the same ordering of outcomes [33] ; (weighted) potential games are best-response equivalent to common-payoff games [15, 26] . \n\t\t\t We make this choice to ease notational burden, but we conjecture that our results can be generalized to allow for mappings between actions [14] , which we leave for future work. \n\t\t\t In this simulation only we rescaled the RandomGames so that each payoff is a draw from Unif (0, 1).", "date_published": "n/a", "url": "n/a", "filename": "GAIW_2021_paper_32.tei.xml", "abstract": "Although it has been known since the 1970s that a globally optimal strategy profile in a common-payoff game is a Nash equilibrium, global optimality is a strict requirement that limits the result's applicability. In this work, we show that any locally optimal symmetric strategy profile is also a (global) Nash equilibrium. Applied to machine learning, our result provides a global guarantee for any gradient method that finds a local optimum in symmetric strategy space. Furthermore, we show that this result is robust to perturbations to the common payoff and to the local optimum. While these results indicate stability to unilateral deviation, we nevertheless identify broad classes of games where mixed local optima are unstable under joint, asymmetric deviations. We analyze the prevalence of instability by running learning algorithms in a suite of symmetric games, and we conclude with results on the complexity of computing game symmetries.", "id": "c006e30787653c5f13dcc49e30b91b2d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrea Bajcsy", "Dylan P Losey", "Marcia K O'malley", "Anca D Dragan"], "title": "Learning from Physical Human Corrections, One Feature at a Time", "text": "Figure  1 : Participant pushes on the robot to teach it to go closer to the table. In the process of giving this correction, the human changes both the robot's distance from table and -inadvertently -the orientation of a cup which the robot is grasping (blue arrows). Typically, the robot would learn about both cup and table features from this one correction (top right). We propose that robots interacting with humans should learn about only one feature at a time (bottom right). correct the robot as it is moving. For example, the robot is moving a fragile cup from a cabinet to the table, and a nearby human notices that the robot is carrying the cup too high above the table: if the cup were to drop from that height, it would likely break! To correct the robot's behavior, the human intuitively pushes the robot's end-effector towards the table to signal their motion preference. Ideally, the human's correction will only affect the cup's distance from the table; in practice, however, human actions are noisy and imperfect  [7, 19, 20, 24] , especially when kinesthetically maneuvering robotic manipulators while trying to carefully orchestrate their multiple degrees of freedom  [1] . As a consequence, when the person pushes down on the end-effector, they accidentally change not only the robot's distance from the table, but also the orientation of the cup (see Fig.  1 ). This single human interaction has therefore adjusted two task features: the cup's distance from the table and the cup's orientation. From the robot's perspective, it is not immediately clear what the person actually intends: do they (a) want the robot to carry the cup closer to the table, or do they (b) additionally want the robot to carry the cup at a new orientation? State-of-the-art algorithms default to the latter interpretation. Prior work has built on Inverse Reinforcement Learning (IRL)  [13, [16] [17] [18] 24]  to formalize learning from physical human corrections as an estimation problem: the robot estimates the objective function that it should optimize during the task by treating human corrections as evidence about the objective function's parameters  1  . Under the ideal objective function parameters, the corrected behavior has to have a lower cost than the robot's current behavior  [3, 11] . Therefore, when the person's correction changes multiple features -however slightly -a rich hypothesis space will lead to the robot updating its understanding about the importance of all of these features (top right in Fig.  1 ). This traditional approach works well with perfect or near-perfect corrections; however, with real people come aspects of corrections that are not always intended. These unintended corrections lead to unintended learning. In other words, the robot attempts to learn from and alter its behavior based on all the inputs, even those that are superfluous. Returning to our previous example, if all features were updated the robot would learn (correctly) that the cup should be lower, and (incorrectly) that the cup should be carried at a different orientation. In general, because of the inherent physical difficulty in simultaneously correcting many degrees of freedom of a robotic arm, learning about all features at once may systematically cause the robot to infer more from the human's corrections than desired. Our insight is that we can alleviate unintended robot learning by focusing the learning on only one feature at a time. For tasks where the human is attempting to change the importance of just one feature, this insight helps the robot reject inadvertent adjustments on the other features (bottom right in Fig.  1 ). But even for tasks in which the human wants to correct several features, learning one feature at a time enables people to break down the task and teach sequentially. Indeed, sequential teaching may come more naturally to people collaborating with robots  [21, 22] , and reduces the burden on users to coordinate all aspects of the task simultaneously during each individual correction. Based on our insight, we make the following contributions: Online Feature Identification. As the robot is executing its task, the human collaborator can intervene and provide physical corrections. We formulate the problem of identifying which one feature the person is trying to correct at each time step, derive a solution, and justify a simple approximation for online performance. We hypothesize that this approach will result in a better learning process, with a more accurate objective function being inferred by the robot at each time step, and a better final outcome. User Study Testing One-at-a-Time Learning. After validating our algorithm in 2-D simulations with an approximately optimal human, we put our hypothesis to the test in a user study on a 7-DoF robotic manipulator. These experiments compare one-ata-time and all-at-once learning within a factorial design, across tasks that need just one feature to be corrected, and tasks that need multiple features to be corrected. We find that one-at-a-time learning is especially helpful in the second case, where the person's teaching task is more complex. People also prefer it, finding that the robot is better at understanding their corrections and requires less reteaching. Overall, our work provides a practical improvement for learning objective functions online from physical human-robot interaction. \n ONE-AT-A-TIME OBJECTIVE LEARNING FROM PHYSICAL HUMAN INTERACTION 2.1 Why Learn from Physical Corrections? When a human and robot are collaborating in close proximity, physical interaction -in which the human touches, pushes, pulls, or otherwise guides the robot -is almost inevitable. The way in which a robot responds to such physical human-robot interaction (pHRI) depends on how the robot interprets those corrections. Traditionally, the human's interactions are treated in one of three ways  [9] : as disturbances to be rejected  [5, 12, 23] , as collisions to be detected and avoided  [4] , or as operator signals to be followed by switching into a compliant mode  [8, 10, 14] . In all cases, the robot does not learn from the human's actions; once the human stops interacting, the robot resumes its original behavior. In contrast, we argue that interactions are intentional, and therefore informative -the human interacts with the robot because it is doing something wrong, and the human's correction indicates how the robot should behave. Furthermore, since the way in which the robot chose its behavior was by optimizing an objective function, interaction suggests that this objective function was incorrect. Thus, rather than stubbornly continuing to optimize the same wrong objective, the robot should instead leverage the human's feedback in order to update its understanding of the objective function. \n Learning Problem Statement Assume the robot starts in some configuration q 0 at time t = 0. Let Ξ be the space of trajectories beginning at q 0 and ending at a feasible goal configuration, where each ξ ∈ Ξ is a sequence of configurations. Next, let Φ : Ξ → R F be a vector-valued function mapping trajectories to feature values, with Φ i (ξ ) signifying the value of the i-th feature. Similar to prior IRL work  [13, 16, 18, 24] , the robot's objective function (here a cost function) is parametrized by θ ∈ R F , which weights the importance of these features along the entire trajectory: C(ξ ) = θ • Φ(ξ ) (1) The robot starts off with an initial objective function θ 0 at time t = 0, and optimizes this objective function to produce its initial trajectory: ξ 0 = arg min Ξ θ 0 • Φ(ξ ) (2) After identifying ξ 0 , the robot starts to execute this initial trajectory. The person interacting with the robot has some desired objective function that they want the robot to optimize, denoted as θ * . The robot does not have access to these parameters -they are internal to the person (and here assumed to be constant). However, at every time step t, the person might intervene to move the robot away from its current configuration by some ∆q t . The robot should then treat the human's correction ∆q t as an observation about θ * , and update its objective from θ t to θ t +1 , such that this new objective function is closer to θ * . \n All-at-Once Learning Following  [3] , we interpret the change in configuration ∆q t as an indication of the corrected trajectory, ξ t c , that the human would prefer for the robot to execute: ξ t c = ξ t + M −1 (0, .., ∆q t , ...0) T (3) Here ξ t is the robot's current trajectory -optimal under θ t -and M is a matrix that smoothly propagates the local correction ∆q t along the rest of the trajectory  [6] . Next, based on  [11]  and  [18] , we make the core assumption that the corrected trajectory ξ t c is better than the current trajectory ξ t with respect to the ground truth θ * . Recalling that our objective Session We-1A: Machine Learning for HRI HRI'18, March 5-8, 2018, Chicago, IL, USA function is a cost function, this implies: θ * • Φ(ξ t c ) < θ * • Φ(ξ t ) (4) To now find a θ t +1 closer to θ * , we select a weight vector that is both (a) near the current θ t and (b) maximally makes (4) hold: θ t +1 = arg min θ ∈Θ θ • (Φ(ξ t c ) − Φ(ξ t )) + 1 2α ||θ − θ t || 2 (5) Note that α > 0. This optimization problem is a quadratic in θ , so we will take the gradient of (  5 ) and set it equal to 0: ∇ θ = Φ(ξ t c ) − Φ(ξ t ) + 1 α (θ − θ t ) = 0 (6) Rearranging (  6 ), we finally obtain: θ t +1 = θ t − α(Φ(ξ t c ) − Φ(ξ t )) (7) Interestingly,  (7)  is the same update rule from co-active learning  [11]  and online maximum margin planning  [18] , shown by  [3]  to be an approximate solution to the partially observable Markov decision process that treats θ * as the hidden state and optimizes the cost parametrized by θ * . This update rule has an intuitive interpretation: if a feature has a higher value in corrected trajectory than in the current trajectory,  (7)  decreases corresponding weight -making it lower-cost -and thus encourages the optimizer to generate subsequent trajectories where that feature also has a higher value. Under this method, the robot updates the weights on all features that the person changed with their correction during the current time step. \n One-at-a-Time Learning A natural solution for restricting the number of learned features might be to switch the regularization term in  (5)  to the L 1 norm  [13, 15] , which encourages sparsity of the weight update. However, there is no guarantee that this will result in changing just one weight; it may still update all the features that the human corrected, including those that were accidentally changed. In this work, to capture one-at-a-time learning, we now make a different assumption about ξ t c , the intended corrected trajectory. While the actual corrected trajectory, ξ t c , might change multiple features, we assume that the human's intended corrected trajectory, ξ t c , changes only a single feature. We simplify the intended corrected trajectory into an intended change in features, ∆Φ t c , and impose the constraint that ∆Φ t c can only have one non-zero entry: this entry represents the feature which the person wants to update. Note that our one-at-a-time strategy does not mean that only one feature ever changes throughout the task. Instead, at every time step t there can be a different intended feature change, and so the person can sequentially change the weights to match their desired objective over multiple corrections. Without loss of generality, assume that the human is attempting to change the i th entry in θ t , the robot's current feature weights. If the human interacts to only update the weight on the i t h feature, then their correction of the robot's current trajectory, ξ t , should change the feature count in the direction J (θ i ) = ∂Φ(ξ t ) ∂θ t i . In other words, given that the person is an optimal corrector and that their interaction was meant to change just the weight on the i t h feature, then we would expect them to correct the trajectory such that they produce a feature difference exactly in the direction J (θ i ). Realistically, however, human corrections are noisy -even for expert users  [2]  -and will not necessarily induce the optimal feature difference during every correction. Despite these imperfections, we assume that the result of their correction will still noisily optimize the distance (dot product) in the optimal direction. This provides us with an observation model, from which we can find the likelihood of observing a specific feature difference given the one feature which the human is attempting to update: P(∆Φ|i) ∝ e J (θ i )•∆Φ (8) Accordingly, for the observed feature difference ∆Φ = Φ(ξ t c )−Φ(ξ t ), the feature which the human is most likely trying to change is: i * = arg max i P(Φ(ξ t c ) − Φ(ξ t ) i) = arg max i J (θ i ) • (Φ(ξ t c ) − Φ(ξ t )) (9) Using (  9 ), we can estimate which feature the person wanted to update during their physical correction. Next, by leveraging i * and the observed feature difference, we can reconstruct ∆Φ t c , the human's intended feature difference. Recall that -if the human wanted to only update feature i * -their intended feature difference would ideally be in the direction J (θ i * ) = ∂Φ(ξ t ) ∂θ t i * , and so we can choose ∆Φ t c ∝ J (θ i * ). In practice, however, we will simplify this derivative by projecting the actual feature difference induced by the human's interaction onto the i * t h axis, ∆Φ t c = (0, .., Φ i * (ξ t c ) − Φ i * (ξ t ), ..0) T . Thus, once we have identified which feature the person most wants to change during their current interaction, i * , we argue that the intended feature correction should only change this one feature 2 . Evaluating J (θ i ) requires numerical differentiation, i.e., finding an optimal trajectory at least F + 1 times at each time step (where F is the number of features). To make this process run in real-time, we approximate J (θ i ) as proportional to (0, .., 1, ..0) T . In other words, we assume that when the i t h weight changes, it predominantly causes a change in the i t h feature along the corresponding optimal trajectory. Substituting this simplification back into (2.4), we have reduced our method for finding the feature which the human intends to change into a simple, yet intuitive, heuristic: only the feature that changed the most as a result of the human's correction should be updated. We note, however, that this heuristic has its roots in the more principled approach that was detailed above. Our update rule now becomes θ t +1 = θ t − α ∆Φ t c (10) Overall, isolating a single feature at every time step is meant to prevent unintended learning. If the person is trying to correct multiple features, they can still do so: the robot will pick up on what seems like the most dominant feature in the correction, adjust that, and then give the person a chance to correct whatever remains during the next time step. Due to the noisy nature of human corrections, we hypothesize that this one-at-a-time update strategy will lead to shorter trajectories through the learned weight spacewhich reach the ideal weight more directly -when compared to a strategy that tries to update everything at once. In what follows, we first show some simulation analysis with optimal and noisy humans, and then test our hypothesis in a user study. \n SIMULATIONS In order to better validate and compare the all-at-once and oneat-a-time learning methods described in Section 2, we conducted human-robot interaction simulations. These simulations show that updating one feature per interaction can help prevent unintended learning, particularly when the human interacts sub-optimally. Setting. We will consider a vertical planar environment, where the y-axis corresponds to height above a table and the x-axis is parallel to that table. The simulated robot is attempting to move from a fixed start position, s, to a fixed goal position, д. The robot is modeled as a single point, and the robot's configuration is its current (x, y) position. A simulated human is standing beside the table near the start position, and physically interacts with the robot to correct its behavior when necessary. The robot does not know the true feature weights of the human's objective function, θ * , but the robot does know that there are three different features which the human might care about: the length of the robot's trajectory (length), the robot's height above the table (table), and the robot's distance from the human (human). Here the table feature corresponds to the height along the y-axis, since the table is a surface at y = 0, and the human feature corresponds to the distance along the x-axis, since the human is standing at x = 0. The weight of the length feature is fixed, and the robot learns the relative weights associated with table and human features over the course of the task. The human's true reward parameter is θ * = [0.5, 0], where 0.5 is the true weight associated with table and 0 is the true weight associated with human. Initially, the robot believes that θ 0 = [0, 0], and so the robot is unaware that it should move closer to the table. Simulated Human. We consider two different simulated humans: (a) an optimal human, who corrects the robot to exactly follow their desired trajectory and (b) a noisy human, who imperfectly corrects the robot's trajectory. At the start of the task, the optimal human identifies a desired trajectory: ξ * H = arg min Ξ θ * • Φ(ξ ). During the task, the human does not change ξ * H , and interacts with the robot to make it follow this desired trajectory. At each time step t the human provides a correction ∆q t that changes the robot's current configuration to the desired configuration, ξ * H (t), but the human only provides this correction if the robot's distance from ξ * H (t) is greater than some acceptable margin of error. In contrast, the noisy human takes actions sampled from a Gaussian distribution: these actions are centered at the optimal human action with a bias in the x-direction. This bias introduces a systematic error, where the noisy human accidentally pulls the robot closer to their body when attempting to significantly correct the vertical table feature. As a result of this noise and bias, the noisy human may unintentionally correct the human feature. Analysis. We performed two different simulations: one with the optimal human (see Fig.  2 ), and one with the noisy human (see Fig.  3 ). When the human optimally corrects the robot's table feature in Fig.  2 , they never unintentionally affect the weight of the human feature, and so all-at-once and one-at-a-time learning both yield the exact same results for the optimal human.     By contrast, the noisy human unintentionally corrects the human features at the start of the task (when trying to correct the table features), and, as such, we observed different behavior for all-at-once and one-at-a-time learning in Fig.  3 . Although the robot follows a similar mean trajectory for both learning methods, and eventually converges to the correct feature weights in each case, we observe that all-at-once had a longer learning process and more persistent human interaction. In particular, the length of the mean path in feature space from θ 0 to θ T was 0.57 for all-at-once vs. 0.49 for one-at-a-time; the length of the mean path specifically for the human feature weight was 0.23 for all-at-once vs. 0.001 for one-at-a-time. Recall that the robot was constrained to reach its goal position in 10 steps; we found that, in the all-at-once case, the human interacted with the robot during an average of 5.24 steps, and, in the one-at-a-time case, the human interacted with the robot during an average of 3.56 steps. These simulations showcase that, when the human interacts sub-optimally, their corrections can lead to unintended learning on the robot's part, which the human must then exert additional effort to undo. For the simulation we have described, updating only one feature per time step helps to mitigate accidental learning, demonstrating the potential benefits of our proposed one-at-a-time learning method. \n EXPERIMENTS We conducted an IRB-approved user study to investigate the benefits of one-at-a-time learning. During each experimental task, the robot began with a number of incorrect weights in its objective, and the participants intervened to physically correct the robot. \n Independent Variables We use a 2 by 2 factorial design. We manipulated the learning strategy with two levels, all-at-once and one-at-a-time, as well as the number of feature weights that need correction, one feature weight and all the feature weights. In the all-at-once learning strategy, the robot updated all the feature weights from a given interaction with the gradient update from Equation (  7 ) and then replanned a new trajectory with the updated weights. In the one-at-a-time condition, the robot chose the feature that changed the most using Equation (2.4), updated according to Equation  (10) , and then replanned a new trajectory withe the updated θ . \n Dependent Measures \n Objective. To analyze the objective performance of the two learning strategies, we split the objective measures into four categories: Final Learned Reward: These measure how closely the learned reward matched the optimal reward by the end of the trajectory. We measured the dot product between the optimal and final reward vector, denoted DotFinal = θ * • θ T . We also analyzed the regret of the final learned reward, which is the weighted feature difference between the ideal trajectory and the learned trajectory RegretFinal = θ * • Φ(ξ θ * ) − θ * • Φ(ξ θ T ) and the individual feature differences between the ideal reward and the trajectory induced by the final learned reward TableDiffFinal = |Φ T b (ξ θ * ) − Φ T b (ξ θ T )| CupDiffFinal = |Φ C (ξ θ * ) − Φ C (ξ θ T )| Learning Process: Measures about the learning process, i.e. θ = {θ 0 , θ 1 , . . . , θ T }, included the average dot product between the true reward and the estimated reward over time: DotAvg = 1 T T i=0 θ * •θ i . We also measured the length of the θ path through weight space for both cup, θC , and table, θT b weights. Finally, we computed the number of times the cup and table weights were updated away from the optimal θ * (denoted by CupAway and TableAway). Executed Trajectory: For the actual executed trajectory, ξ act , we measured the regret Regret = θ * • Φ(ξ θ * ) − θ * • Φ(ξ act ) and the individual table and cup feature differences between the ideal and actual trajectory TableDiff = |Φ T b (ξ θ * ) − Φ T b (ξ act )| CupDiff = |Φ C (ξ θ * ) − Φ C (ξ act )| Interaction: Interaction measures on the forces applied by the human, {u 0 H , u 1 H , . . . , u T H }, included the total interaction force, Iact-Force = T t =0 ||u t H || 1 and total interaction time. 4.2.2 Subjective. For each condition, we administered a 7-point Likert scale survey about the participant's interaction experience (see Table  1  for questions). We separated our survey questions into four scales: success in teaching the robot about the task, correctness of update, needing to undo corrections because the robot learned something wrong, and ease of undoing. The final learned weight vector with one-at-a-time is closer to the ideal weight vector for the task where two feature weights are incorrect (left). Looking at the individual feature differences from ideal: while the final cup weight is closer to ideal for one-at-a-time for both tasks (center), the ideal table weight is actually significantly further away from the ideal for the one-at-a-time strategy during the one-feature task (right). However, for the two feature task, the one-at-a-time method outperforms the all-at-once for final learned cup and table weights. \n Hypotheses H1. Updating one feature at a time significantly increases the final learned reward, enables a better learning process, results in lower regret for the executed trajectory, and leads to less interaction effort and time compared to all-at-once update. H2. Participants will perceive the robot as more successful at accomplishing the task, correctly updating its knowledge of the task, less likely to learn about extraneous aspects of the task, and be easier to correct if it did learn something wrong in the one-at-a-time condition. \n Tasks We designed two experimental household manipulation tasks for the robot to perform in a shared workspace (see Fig.  4  for setup). For each experimental task, the robot carried a cup from a start to end pose with an initially incorrect objective. One of the tasks focused on participants having to correct a single aspect of the incorrect objective, while the other needed them to correct all parts of the objective. Participants were instructed to physically intervene to correct the robot's behavior during the task. Similar to state-of-theart methods, all the features in the robot's objective were chosen to be intuitive to a human to ensure that participants could understand how to correct the robot. In Task 1, the robot's objective had only one feature weight incorrect. The robot's default trajectory took a cup from the participant and put it down on the table, but carried the cup too far above the table (top of Fig.  4 ). In Task 2, all the feature weights started out incorrect in the robot's objective. The robot also took a cup from the participant and put it down on the table, but this time it initially grasped the cup at the wrong angle and was also carrying the cup too high above the table (bottom of Fig.  4 ). \n Participants We used a within-subjects design and counterbalanced the order of the conditions during experiments. In total, we recruited 12 participants (7 female, 4 male, 1 non-binary trans-masculine, aged 18-30) from the campus community, 11 of which had technical backgrounds and 1 of which did not. None of the participants had experience interacting with the robot used in our experiments. \n Procedure Before beginning the experiment, participants performed a familiarization task to become comfortable teaching the robot with physical corrections. The robot's original trajectory moved a cup from a shelf to a table, but the robot did not initially care about tilting the cup mid-task. The robot's objective contained only one aspect of the task (cup orientation) and participants had to correct only this one aspect. Afterwards, for each experimental task, the participants were shown the robot's default trajectory as well as what their desired trajectory looks like. They were also told what aspects of the task the robot is always aware of (cup orientation and distance of end-effector to table) as well as which learning strategy they were interacting with. Participants were told the difference between the two learning strategies in order to minimize in-task learning effects. Note, however, that we did not tell participants to teach the robot in any specific style (like one aspect as a time), only about how the robot reasons about their corrections. \n Analysis 4.7.1 Objective. Final Learned Reward. We ran a factorial repeated-measures ANOVA with learning strategy and number of features as factors, and user ID as a random effect, for each of the measures capturing the quality of the final learning outcome. Fig.  5  summarizes our findings about the final learned weights for each learning strategy. For the final dot product with the true reward, we found a significant main effect of the learning strategy (F (1, 81) = 29.86, p < .0001), but also an interaction effect with the number of features (F (1, 81) = 13.07, p < .01). The post-hoc analysis with Tukey HSD revealed that one-at-a-time led to a higher dot product on the two feature task (p < .0001), but there was no significant difference on the one-feature task (where one-at-a-time led to slightly higher dot product). We next looked at the final regret, i.e. the difference between the cost of the learned trajectory and that of the ideal trajectory. For this metric we found an interaction effect, suggesting that one-ata-time led to lower regret for the two-feature task but not for the one-feature task. Looking separately at the feature values for table and cup, we found that one-at-a-time led to a significantly lower difference for the cup feature across the board (F (1, 81) = 11.30,   +  Cup All-at-Once One-at-a-Time (b) In contrast to (a), when two feature weights are wrong, the one-ata-time strategy outperforms the all-at-once strategy when it came to a higher dot product over the duration of the trajectory. \n Figure 6: The one-at-a-time strategy shows significantly more consistent alignment between the estimated weight vector, θ t , and the ideal weight vector, θ * , than the all-at-once for the two feature task. This indicates that when multiple aspects of the objective need changing, the one-at-a-time method enables more accurate learning. p < .01, no interaction effect), but that one-at-a-time only improved the difference for the table on the two feature task (p < .0001) -it actually significantly increased the difference on the one feature task (p < .001). Overall, we see that one-at-a-time learns something significantly better across the board for the two-feature task. When it comes to the one feature task, the results are mixed: it led to a significantly better result for the cup orientation, but significantly worse for the table distance feature. Learning Process. For the average dot product between the estimated and true reward over time, our analysis revealed almost identical outcomes to before, when we were looking at the final reward only (see Fig.  6 ). We also found that one-at-a-time resulted in significantly fewer updates in the wrong direction for the cup weight across the board (F (1, 81) = 44.91, p < .0001) and for the table weight (F (1, 81) = 22.02, p < .0001), with no interaction effect. Fig.  7  highlights these findings and their connection to the subjective metrics. Looking at the length of the path through the space of weights, we found a main effect of learning strategy (F (1, 81) = 26.82, p < .0001), but also an interaction effect (F (1, 81) = 6.55, p = .01). The posthoc analysis with Tukey HSD revealed that for the the one-feature task, one-at-a-time resulted in significantly shorter path traversed through weight space (p < .0001). The path was shorter with the two-feature task as well, but the difference was not significant. The effect was mainly due to the one-at-a-time method resulting in a shorter path for the cup weight on the one-feature task, as revealed by the posthoc analysis (p < .0001). Overall, we see that the quality of the learning process was significantly higher for the one-at-a-time strategy across both tasks. When one aspect and all aspects of the objective were wrong, oneat-a-time led to fewer wrong weight updates and resulted in the learned reward across time being closer to the true reward. The Executed Trajectory. We found no significant main effect of the learning strategy on the regret of the executed trajectory: the two strategies lead to relatively similar actual trajectories with respect to regret. Both regret as well as the feature differences from ideal for cup and table showed significant interaction effects. Interaction Metrics. We found no significant effects on interaction time or force. Summary of Objective Metric Analysis. Taken together, these results indicate that a one-at-a-time learning strategy leads to a better learning process across the board. On the more complex two-feature task, this strategy also leads to unquestionably better learning outcomes. For the one-feature task, learning one feature at a time enables users to better avoid the wrong perturbation of the correct weight (on the cup feature), but is not as good as the all-at-once method at enabling users to properly correct the wrong weight (on the table feature). Thus, H1 was partially supported: although updating one feature weight at a time does not improve task performance when there is only one aspect of the objective wrong, reasoning about one feature weight at a time leads to significantly better learning and task performance when all aspects of the objective are wrong. 4.7.2 Subjective. We ran a repeated measures ANOVA on the results of our participant survey. After testing the reliability of our 4 scales, we found that the correct update and undoing scale were significantly reliable, so we grouped these into a combined score (see Chronbach's α in Table  1 ). We analyzed success and undoing ease separately as they were not reliable. For the correct update scale, we found a significant effect of learning strategy (F (1, 33) = 5.09, p = 0.031), showing that participants perceived the one-at-a-time strategy as better at updating the robot's objective according to their corrections. Additionally, the undoing scale showed a significant effect of learning strategy (F (1, 33) = 10.35, p < 0.01), with the one-at-at-time strategy being less likely to learn the wrong thing and cause the participants to have to undo a correction. For ease of undoing, when analyzing Q9 and Q10 individually we found no significant effect of strategy. The one-at-a-time strategy results in significantly less weight updates that are away from the optimum weight across all tasks (left top, left bottom). These findings are consistent with the subjective likert data from the undoing scale, where participants perceived the one-at-a-time method as less likely to learn the wrong thing and need an additional undoing action. Summary of Subjective Metric Analysis. The subjective data echoes some of the objective data results. Participants perceived that one-at-a-time better understood their corrections and required less undoing due to unintended learning, partially supporting H2. \n DISCUSSION In this paper, we compared the performance of one-at-a-time and allat-once learning for two tasks: one that required correcting a single feature, and another that required correcting multiple features of a robot's objective. For the multiple feature task, learning about one feature at a time was objectively superior: it led to a better final learning outcome (Fig.  5 ), took a shorter path to the optimum, and had fewer incorrect inferences and undoings along the way (Fig.  6 ). However, the results were not as clear for the single feature task: the one-at-a-time method lessened unintended learning on the weights that were initially correct, but it hindered learning for the incorrect weights. However, participants subjectively preferred the one-at-a-time strategy overall: they thought it was better at learning the correct aspects of the task and required less undoing. We hypothesize that the superior objective performance of the one-at-a-time strategy in the second task is due to the increased complexity of the task. It appears that one-at-a-time learning is more useful as the teaching task becomes more complex and requires fixing more aspects of the robot's objective. However, with simple teaching tasks that only require one aspect of the objective to change, it is not yet clear whether one-at-a-time is a significantly better learning strategy. \n Limitations and Future Work It is both a limitation and a strength that we chose the simplest possible feature selection method for the one-at-a-time task. On the one hand, this is an intuitive and computationally inexpensive method to examine as a first exploration into teaching robot objectives online via physical interaction. At the same time, our simple learning strategy was not consistently superior in the simple task. This opens the door for analyzing more sophisticated methods that perform Bayesian inference on the intended feature, or low-pass filtering to prevent high frequency changes in which features gets Table  1 : Likert scale questions were grouped into four categories: success in accomplishing the task, correctness of update (reliable), needing to undo corrections because of unintended learning (reliable), and ease of undoing. \n Likert Questions Cronbach's α .93 Q7: Sometimes my corrections were just meant to fix the effect of previous corrections I gave. Q8: I had to re-teach the robot about an aspect of the task that it started off knowing well. undo ease Q9: When the robot learned something wrong, it was difficult for me to undo that. .66 Q10: It was easy to re-correct the robot whenever it misunderstood a previous correction of mine. updated to improve overall learning and usability. Additionally, while our method worked well with intuitive features like \"distance to table\", additional work is needed to investigate how well each method works when the features are non-intuitive to the human. Perhaps our largest limitation in this work is our demographics: our study participants were primarily individuals with a technical background (with one exception). Future work must consider a more diverse user population to ensure external validity. Not only do we need algorithms that can learn from humans, but the methods must also reason about the difficulties humans experience when trying to kinesthetically teach a complex robotic system. To simplify the teaching process, we propose that robots should learn one aspect of the objective at a time from physical corrections. While our user studies indicate the benefits of this method, it is only a first step towards seamless human-robot interaction. Optimal human: Teaching the robot (b) Optimal human: Learning weights \n Figure 2 : 2 Figure 2: Simulation with optimal human. (a) Human corrects the robot during the first few time steps, and the robot follows the human's desired trajectory afterwards. (b) The robot's estimated feature weights converge to the human's true feature weights. \n Figure 3 : 3 Figure 3: Simulation with noisy human. (a) The human noisily corrects the robot's trajectory, where the ellipses show the robot's states with 95% confidence over 100 simulations. (b)With all-at-once, the robot initially learns that the human feature is important, and the person must undo that unintended learning. One-at-at-time learning reduces the unintended effects of the human's noisy corrections; this causes the robot to converge towards the human's desired trajectory more rapidly. \n (a) Task 1 : 1 Correct one feature, the distance to table (b) Task 2: Correct two features, the cup orientation and distance to table \n Figure 4 : 4 Figure 4: Depictions of the robot trajectories for each of the two experimental tasks. The black path represents the original trajectory and the blue path represents the human's desired trajectory. \n Figure 5 : 5 Figure5: The final learned weight vector with one-at-a-time is closer to the ideal weight vector for the task where two feature weights are incorrect (left). Looking at the individual feature differences from ideal: while the final cup weight is closer to ideal for one-at-a-time for both tasks (center), the ideal table weight is actually significantly further away from the ideal for the one-at-a-time strategy during the one-feature task (right). However, for the two feature task, the one-at-a-time method outperforms the all-at-once for final learned cup and table weights. \n One-at-a-Time (a) In the task with only one wrong feature weight, there is no significant difference between the two methods in average dot product over time. \n Figure 7 : 7 Figure7: The one-at-a-time strategy results in significantly less weight updates that are away from the optimum weight across all tasks (left top, left bottom). These findings are consistent with the subjective likert data from the undoing scale, where participants perceived the one-at-a-time method as less likely to learn the wrong thing and need an additional undoing action. \n succ Q1: I successfully taught the robot how to do the task. correct update Q2: The robot correctly updated its understanding about aspects of the task that I did want to change. .84 Q3: The robot wrongly updated its understanding about aspects of the task I did NOT want to change. Q4: The robot understood which aspects of the task I wanted to change, and how to change them. Q5: The robot misinterpreted my corrections.undoing Q6: I had to try to undo corrections that I gave to the robot, because it learned the wrong thing. \n\t\t\t Similar to prior IRL work, we will assume that the correct features for the task have been identified a priori, and are known to both the human and the robot. \n\t\t\t To ensure that all features are equally sensitive, we normalized each feature by the maximal attainable feature difference by computing optimal trajectories offline with a range of θ values.", "date_published": "n/a", "url": "n/a", "filename": "3171221.3171267.tei.xml", "abstract": "We focus on learning robot objective functions from human guidance: specifically, from physical corrections provided by the person while the robot is acting. Objective functions are typically parametrized in terms of features, which capture aspects of the task that might be important. When the person intervenes to correct the robot's behavior, the robot should update its understanding of which features matter, how much, and in what way. Unfortunately, real users do not provide optimal corrections that isolate exactly what the robot was doing wrong. Thus, when receiving a correction, it is difficult for the robot to determine which features the person meant to correct, and which features were changed unintentionally. In this paper, we propose to improve the efficiency of robot learning during physical interactions by reducing unintended learning. Our approach allows the human-robot team to focus on learning one feature at a time, unlike state-of-the-art techniques that update all features at once. We derive an online method for identifying the single feature which the human is trying to change during physical interaction, and experimentally compare this one-at-a-time approach to the all-at-once baseline in a user study. Our results suggest that users teaching one-at-a-time perform better, especially in tasks that require changing multiple features.", "id": "8ba474a6576df7f082cd5e2b736d7442"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Henry W Lin", "Max Tegmark", "David Rolnick"], "title": "Why Does Deep and Cheap Learning Work So Well?", "text": "Introduction Deep learning works remarkably well, and has helped dramatically improve the state-ofthe-art in areas ranging from speech recognition, translation and visual object recognition to drug discovery, genomics and automatic game playing  [1, 2] . However, it is still not fully understood why deep learning works so well. In contrast to GOFAI (\"good old-fashioned AI\") algorithms that are hand-crafted and fully understood analytically, many algorithms using artificial neural networks are understood only at a heuristic level, where we empirically know that certain training protocols employing large data sets will result in excellent performance. This is reminiscent of the situation with human brains: we know that if we train a child according to a certain curriculum, she will learn certain skills-but we lack a deep understanding of how her brain accomplishes this. This makes it timely and interesting to develop new analytic insights on deep learning and its successes, which is the goal of the present paper. Such improved understanding is not only interesting in its own right, and for potentially providing new clues about how brains work, but it may also have practical applications. Better understanding the shortcomings of deep learning may suggest ways of improving it, both to make it more capable and to make it more robust  [3] . \n The Swindle: Why Does \"Cheap Learning\" Work? Throughout this paper, we will adopt a physics perspective on the problem, to prevent application-specific details from obscuring simple general results related to dynamics, symmetries, renormalization, etc, and to exploit useful similarities between deep learning and statistical mechanics. The task of approximating functions of many variables is central to most applications of machine learning, including unsupervised learning, classification and prediction, as illustrated in Fig.  1 . For example, if we are interested in classifying faces, then we may want our neural network to implement a function where we feed in an image represented by a million greyscale pixels and get as output the probability distribution over a set of people that the image might represent. When investigating the quality of a neural net, there are several important factors to consider: \n Unsupervised learning Prediction Classification \n p(x,y) p(y |x) p(x |y) Fig.  1  In this paper, we follow the machine learning convention that x refers to data (e.g., an image) and y refers to underlying information about that data (such as a label for the image). Neural networks can be used to estimate (or sample from) probability distributions with respect to x and y, given many samples. Classification involves approximating the probability distribution of y given x, in the case that y is discrete-valued. This problem may also be called prediction, e.g. when x is earlier data in a time series. Generation involves approximating the probability distribution for x given y, or drawing samples from this distribution. Unsupervised learning attempts to approximate or model the probability distribution of x, without any knowledge of y • Expressibility: What class of functions can the neural network express? • Efficiency: How many resources (neurons, parameters, etc) does the neural network require to approximate a given function? • Learnability: How rapidly can the neural network learn good parameters for approximating a function? This paper is focused on expressibility and efficiency, and more specifically on the following well-known  [4] [5] [6]  problem: How can neural networks approximate functions well in practice, when the set of possible functions is exponentially larger than the set of practically possible networks? For example, suppose that we wish to classify megapixel greyscale images into two categories, e.g., cats or dogs. If each pixel can take one of 256 values, then there are 256 1000,000 possible images, and for each one, we wish to compute the probability that it depicts a cat. This means that an arbitrary function is defined by a list of 256 1000,000 probabilities, i.e., way more numbers than there are atoms in our universe (about 10  78  ). Yet neural networks with merely thousands or millions of parameters somehow manage to perform such classification tasks quite well. How can deep learning be so \"cheap\", in the sense of requiring so few parameters? We will see in below that neural networks perform a combinatorial swindle, replacing exponentiation by multiplication: if there are say n = 10 6 inputs taking v = 256 values each, this swindle cuts the number of parameters from v n to v × n times some constant factor. We will show that this success of this swindle depends fundamentally on physics: although neural networks only work well for an exponentially tiny fraction of all possible inputs, the laws of physics are such that the data sets we care about for machine learning (natural images, sounds, drawings, text, etc) are also drawn from an exponentially tiny fraction of all imaginable data sets. Moreover, we will see that these two tiny subsets are remarkably similar, enabling deep learning to work well in practice. The rest of this paper is organized as follows. In Sect. 2, we present results for shallow neural networks with merely a handful of layers, focusing on simplifications due to locality, symmetry and polynomials. In Sect. 3, we study how increasing the depth of a neural network can provide polynomial or exponential efficiency gains even though it adds nothing in terms of expressivity, and we discuss the connections to renormalization, compositionality and complexity. We summarize our conclusions in Sect. 4. \n Expressibility and Efficiency of Shallow Neural Networks Let us now explore what classes of probability distributions p are the focus of physics and machine learning, and how accurately and efficiently neural networks can approximate them. We will be interested in probability distributions p(x|y), where x ranges over some sample space and y will be interpreted either as another variable being conditioned on or as a model parameter. For a machine learning example, we might interpret y as an element of some set of animals {cat, dog, rabbit, . . .} and x as the vector of pixels in an image depicting such an animal, so that p(x|y) for y = cat gives the probability distribution of images of cats with different coloring, size, posture, viewing angle, lighting condition, electronic camera noise, etc For a physics example, we might interpret y as an element of some set of metals {iron, aluminum, copper, . . .} and x as the vector of magnetization values for different parts of a metal bar. The prediction problem is then to evaluate p(x|y), whereas the classification problem is to evaluate p(y|x). Because of the above-mentioned \"swindle\", accurate approximations are only possible for a tiny subclass of all probability distributions. Fortunately, as we will explore below, the function p(x|y) often has many simplifying features enabling accurate approximation, because it follows from some simple physical law or some generative model with relatively few free parameters: for example, its dependence on x may exhibit symmetry, locality and/or be of a simple form such as the exponential of a low-order polynomial. In contrast, the dependence of p(y|x) on y tends to be more complicated; it makes no sense to speak of symmetries or polynomials involving a variable y = cat. Let us therefore start by tackling the more complicated case of modeling p(y|x). This probability distribution p(y|x) is determined by the hopefully simpler function p(x|y) via Bayes' theorem: p(y|x) = p(x|y) p(y) y p(x|y )(y ) , ( 1 ) where p(y) is the probability distribution over y (animals or metals, say) a priori, before examining the data vector x. \n Probabilities and Hamiltonians It is useful to introduce the negative logarithms of two of these probabilities: H y (x) ≡ − ln p(x|y), μ y ≡ − ln p(y). ( 2 ) Table  1  is a brief dictionary translating between physics and machine-learning terminology. Statisticians refer to − ln p as \"self-information\" or \"surprisal\", and statistical physicists refer to H y (x) as the Hamiltonian, quantifying the energy of x (up to an arbitrary and irrelevant additive constant) given the parameter y. These definitions transform Eq. (1) into the Boltzmann form p(y|x) = 1 N (x) e −[H y (x)+μ x ] , (3) where This recasting of Eq. (  1 ) is useful because the Hamiltonian tends to have properties making it simple to evaluate. We will see in Sect. 3 that it also helps understand the relation between deep learning and renormalization  [7] . N (x) ≡ y e −[H y (x)+μ y ] . ( 4 ) \n Bayes' Theorem as a Softmax Since the variable y takes one of a discrete set of values, we will often write it as an index instead of as an argument, as p y (x) ≡ p(y|x). Moreover, we will often find it convenient to view all values indexed by y as elements of a vector, written in boldface, thus viewing p y , H y and μ y as elements of the vectors p, H and μ, respectively. Equation (3) thus simplifies to p(x) = 1 N (x) e −[H(x)+μ] , (5) using the standard convention that a function (in this case exp) applied to a vector acts on its elements. We wish to investigate how well this vector-valued function p(x) can be approximated by a neural net. A standard n-layer feedforward neural network maps vectors to vectors by applying a series of linear and nonlinear transformations in succession. Specifically, it implements vector-valued functions of the form  [1]   f(x) = σ n A n • • • σ 2 A 2 σ 1 A 1 x, (6) where the σ i are relatively simple nonlinear operators on vectors and the A i are affine transformations of the form A i x = W i x + b i for matrices W i and so-called bias vectors b i . Popular choices for these nonlinear operators σ i include • Local function apply some nonlinear function σ to each vector element, • Max-pooling compute the maximum of all vector elements, • Softmax exponentiate all vector elements and normalize them to so sum to unity σ (x) ≡ e x i e y i . ( 7 ) (We use σ to indicate the softmax function and σ to indicate an arbitrary non-linearity, optionally with certain regularity requirements). This allows us to rewrite Eq. (5) as p(x) = σ [−H(x) − μ]. ( 8 ) This means that if we can compute the Hamiltonian vector H(x) with some n-layer neural net, we can evaluate the desired classification probability vector p(x) by simply adding a softmax layer. The μ-vector simply becomes the bias term in this final layer. \n What Hamiltonians can be Approximated by Feasible Neural Networks? It has long been known that neural networks are universal 1 approximators  [8, 9] , in the sense that networks with virtually all popular nonlinear activation functions σ (x) can approximate any smooth function to any desired accuracy-even using merely a single hidden layer. However, these theorems do not guarantee that this can be accomplished with a network of feasible size, and the following simple example explains why they cannot: There are 2 2 n different Boolean functions of n variables, so a network implementing a generic function in this class requires at least 2 n bits to describe, i.e., more bits than there are atoms in our universe if n > 260. The fact that neural networks of feasible size are nonetheless so useful therefore implies that the class of functions we care about approximating is dramatically smaller. We will see below in Sect. 2.4 that both physics and machine learning tend to favor Hamiltonians that are polynomials 2 -indeed, often ones that are sparse, symmetric and low-order. Let us therefore focus our initial investigation on Hamiltonians that can be expanded as a power series: H y (x) = h + i h i x i + i≤ j h i j x i x j + i≤ j≤k h i jk x i x j x k + • • • . ( 9 ) If the vector x has n components (i = 1, . . . , n), then there are (n + d)!/(n!d!) terms of degree up to d. \n Continuous Input Variables If we can accurately approximate multiplication using a small number of neurons, then we can construct a network efficiently approximating any polynomial H y (x) by repeated multiplication and addition. We will now see that we can, using any smooth but otherwise arbitrary non-linearity σ that is applied element-wise. The popular logistic sigmoid activation function σ (x) = 1/(1 + e −x ) will do the trick. Theorem 1 Let f be a neural network of the form f = A 2 σ A 1 , where σ acts elementwise by applying some smooth non-linear function σ to each element. Let the input layer, hidden layer and output layer have sizes 2, 4 and 1, respectively. Then f can approximate a multiplication gate arbitrarily well. To see this, let us first Taylor-expand the function σ around the origin: σ (u) = σ 0 + σ 1 u + σ 2 u 2 2 + O(u 3 ). ( 10 ) Without loss of generality, we can assume that σ 2 = 0: since σ is non-linear, it must have a non-zero second derivative at some point, so we can use the biases in A 1 to shift the origin to this point to ensure σ 2 = 0. Equation  (10)  now implies that m(u, v) ≡ σ (u + v) + σ (−u − v) − σ (u − v) − σ (−u + v) 4σ 2 = uv 1 + O u 2 + v 2 , ( 11 ) where we will term m(u, v) the multiplication approximator. Fig.  2  Multiplication can be efficiently implemented by simple neural nets, becoming arbitrarily accurate as λ → 0 (left) and β → ∞ (right). Squares apply the function σ , circles perform summation, and lines multiply by the constants labeling them. The \"1\" input implements the bias term. The left gate requires σ (0) = 0, which can always be arranged by biasing the input to σ . The right gate requires the sigmoidal behavior σ (x) → 0 and σ (x) → 1 as x → −∞ and x → ∞, respectively then compensating by scaling A 2 → λ −2 A 2 . In the limit that λ → ∞, this approximation becomes exact.  3  In other words, arbitrarily accurate multiplication can always be achieved using merely 4 neurons. Figure  2  illustrates such a multiplication approximator. (Of course, a practical algorithm like stochastic gradient descent cannot achieve arbitrarily large weights, though a reasonably good approximation can be achieved already for λ −1 ∼ 10.) Corollary 1 For any given multivariate polynomial and any tolerance > 0, there exists a neural network of fixed finite size N (independent of ) that approximates the polynomial to accuracy better than . Furthermore, N is bounded by the complexity of the polynomial, scaling as the number of multiplications required times a factor that is typically slightly larger than 4.  4  This is a stronger statement than the classic universal universal approximation theorems for neural networks  [8, 9] , which guarantee that for every there exists some N ( ), but allows for the possibility that N ( ) → ∞ as → 0. An approximation theorem in  [10]  provides an -independent bound on the size of the neural network, but at the price of choosing a pathological function σ . \n Discrete Input Variables For the simple but important case where x is a vector of bits, so that x i = 0 or x i = 1, the fact that x 2 i = x i makes things even simpler. This means that only terms where all variables are different need be included, which simplifies Eq. (  9 ) to H y (x) = h + i h i x i + i< j h i j x i y j + i< j<k h i jk x i x j x k + • • • . ( 12 ) The infinite series Eq. (  9 ) thus gets replaced by a finite series with 2 n terms, ending with the term h 1...n x 1 • • • x n . Since there are 2 n possible bit strings x, the 2 n h−parameters in Eq. (  12 ) suffice to exactly parametrize an arbitrary function H y (x). The efficient multiplication approximator above multiplied only two variables at a time, thus requiring multiple layers to evaluate general polynomials. In contrast, H (x) for a bit vector x can be implemented using merely three layers as illustrated in Fig.  2 , where the middle layer evaluates the bit products and the third layer takes a linear combination of them. This is because bits allow an accurate multiplication approximator that takes the product of an arbitrary number of bits at once, exploiting the fact that a product of bits can be trivially determined from their sum: for example, the product x 1 x 2 x 3 = 1 if and only if the sum x 1 + x 2 + x 3 = 3. This sum-checking can be implemented using one of the most popular choices for a nonlinear function σ : the logistic sigmoid σ (x) = 1 1+e −x which satisfies σ (x) ≈ 0 for x 0 and σ (x) ≈ 1 for x 1. To compute the product of some set of k bits described by the set K (for our example above, K = {1, 2, 3}), we let A 1 and A 2 shift and stretch the sigmoid to exploit the identity i∈K x i = lim β→∞ σ −β k − 1 2 − x∈K x i . ( 13 ) Since σ decays exponentially fast toward 0 or 1 as β is increased, modestly large β-values suffice in practice; if, for example, we want the correct answer to D = 10 decimal places, we merely need β > D ln 10 ≈ 23. In summary, when x is a bit string, an arbitrary function p y (x) can be evaluated by a simple 3-layer neural network: the middle layer uses sigmoid functions to compute the products from Eq. (  12 ), and the top layer performs the sums from Eq. (  12 ) and the softmax from Eq. (8). \n What Hamiltonians Do We Want to Approximate? We have seen that polynomials can be accurately approximated by neural networks using a number of neurons scaling either as the number of multiplications required (for the continuous case) or as the number of terms (for the binary case). But polynomials per se are no panacea: with binary input, all functions are polynomials, and with continuous input, there are (n + d)!/(n!d!) coefficients in a generic polynomial of degree d in n variables, which easily becomes unmanageably large. We will now discuss situations in which exceptionally simple polynomials that are sparse, symmetric and/or low-order play a special role in physics and machine learning. \n Low Polynomial Order The Hamiltonians that show up in physics are not random functions, but tend to be polynomials of very low order, typically of degree ranging from 2 to 4. The simplest example is of course the harmonic oscillator, which is described by a Hamiltonian that is quadratic in both position and momentum. There are many reasons why low order polynomials show up in physics. Two of the most important ones are that sometimes a phenomenon can be studied perturbatively, in which case, Taylor's theorem suggests that we can get away with a low order polynomial approximation. A second reason is renormalization: higher order terms in the Hamiltonian of a statistical field theory tend to be negligible if we only observe macroscopic variables. At a fundamental level, the Hamiltonian of the standard model of particle physics has d = 4. There are many approximations of this quartic Hamiltonian that are accurate in specific regimes, for example the Maxwell equations governing electromagnetism, the Navier-Stokes equations governing fluid dynamics, the Alvén equations governing magnetohydrodynamics and various Ising models governing magnetization-all of these approximations have Hamiltonians that are polynomials in the field variables, of degree d ranging from 2 to 4. This means that the number of polynomial coefficients in many examples is not infinite as in Eq. (  9 ) or exponential in n as in Eq. (  12 ), merely of order O(n 4 ). There are additional reasons why we might expect low order polynomials. Thanks to the Central Limit Theorem  [11] , many probability distributions in machine learning and statistics can be accurately approximated by multivariate Gaussians, i.e., of the form p(x) = e h+ i h j x i − i j h i j x i x j , ( 14 ) which means that the Hamiltonian H = − ln p is a quadratic polynomial. More generally, the maximum-entropy probability distribution subject to constraints on some of the lowest moments, say expectation values of the form x α 1 1 x α 2 2 • • • x α n n for some integers α i ≥ 0 would lead to a Hamiltonian of degree no greater than d ≡ i α i  [12] . Image classification tasks often exploit invariance under translation, rotation, and various nonlinear deformations of the image plane that move pixels to new locations. All such spatial transformations are linear functions (d = 1 polynomials) of the pixel vector x. Functions implementing convolutions and Fourier transforms are also d = 1 polynomials. Of course, such arguments do not imply that we should expect to see low-order polynomials in every application. If we consider some data set generated by a very simple Hamiltonian (say the Ising Hamiltonian), but then discard some of the random variables, the resulting marginalized distribution can become quite complicated and of high order. Similarly, if we do not observe the random variables directly, but observe some generic functions of the random variables, the result will generally be a mess. These arguments, however, might indicate that the probability of encountering a Hamiltonian described by a low-order polynomial in some application might be significantly higher than what one might expect from some naive prior. For example, a uniform prior on the space of all polynomials of degree N would suggest that a randomly chosen polynomial would almost always have degree N , but this might be a bad prior for real-world applications. We should also note that even if a Hamiltonian is described exactly by a low-order polynomial, we would not expect the corresponding neural network to reproduce a low-order polynomial Hamiltonian exactly in any practical scenario for a host of possible reasons including limited data, the requirement of infinite weights for infinite accuracy, and the failure of practical algorithms such as stochastic gradient descent to find the global minimum of a cost function in many scenarios. So looking at the weights of a neural network trained on actual data may not be a good indicator of whether or not the underlying Hamiltonian is a polynomial of low degree or not. \n Locality One of the deepest principles of physics is locality: that things directly affect only what is in their immediate vicinity. When physical systems are simulated on a computer by discretizing space onto a rectangular lattice, locality manifests itself by allowing only nearest-neighbor interaction. In other words, almost all coefficients in Eq. (  9 ) are forced to vanish, and the total number of non-zero coefficients grows only linearly with n. For the binary case of Eq. (  9 ), which applies to magnetizations (spins) that can take one of two values, locality also limits the degree d to be no greater than the number of neighbors that a given spin is coupled to (since all variables in a polynomial term must be different). Again, the applicability of these considerations to particular machine learning applications must be determined on a case by case basis. Certainly, an arbitrary transformation of a collection of local random variables will result in a non-local collection. (This might ruin locality in certain ensembles of images, for example). But there are certainly cases in physics where locality is still approximately preserved, for example in the simple block-spin renormalization group, spins are grouped into blocks, which are then treated as random variables. To a high degree of accuracy, these blocks are only coupled to their nearest neighbors. Such locality is famously exploited by both biological and artificial visual systems, whose first neuronal layer performs merely fairly local operations. \n Symmetry Whenever the Hamiltonian obeys some symmetry (is invariant under some transformation), the number of independent parameters required to describe it is further reduced. For instance, many probability distributions in both physics and machine learning are invariant under translation and rotation. As an example, consider a vector x of air pressures y i measured by a microphone at times i = 1, . . . , n. Assuming that the Hamiltonian describing it has d = 2 reduces the number of parameters N from ∞ to (n + 1)(n + 2)/2. Further assuming locality (nearest-neighbor couplings only) reduces this to N = 2n, after which requiring translational symmetry reduces the parameter count to N = 3. Taken together, the constraints on locality, symmetry and polynomial order reduce the number of continuous parameters in the Hamiltonian of the standard model of physics to merely 32  [13] . Naturally, this does not mean that modeling a real physical system requires merely 32 parameters -the objects involved must be modeled also; there too, however, symmetry allows us to abstract away from the information contained in individual particles to that summarizing components of the system. Symmetry can reduce not merely the parameter count, but also the computational complexity. For example, if a linear vector-valued function f(x) mapping a set of n variables onto itself happens to satisfy translational symmetry, then it is a convolution (implementable by a convolutional neural net; \"convnet\"), which means that it can be computed with n log 2 n rather than n 2 multiplications using Fast Fourier transform. \n Why Deep? Above we investigated how probability distributions from physics and computer science applications lent themselves to \"cheap learning\", being accurately and efficiently approximated by neural networks with merely a handful of layers. Let us now turn to the separate question of depth, i.e., the success of deep learning: what properties of real-world probability distributions cause efficiency to further improve when networks are made deeper? This question has been extensively studied from a mathematical point of view  [14] [15] [16] , but mathematics alone cannot fully answer it, because part of the answer involves physics. We will argue that the answer involves the hierarchical/compositional structure of generative processes together with inability to efficiently \"flatten\" neural networks reflecting this structure. \n Hierarchical Processess One of the most striking features of the physical world is its hierarchical structure. Spatially, it is an object hierarchy: elementary particles form atoms which in turn form molecules, cells, organisms, planets, solar systems, galaxies, etc Causally, complex structures are frequently created through a distinct sequence of simpler steps. Figure  3  gives two examples of such causal hierarchies generating data vectors y 0 → y 1 → . . . → y n that are relevant to physics and image classification, respectively. Both examples involve a Markov chain  5  where the probability distribution p(y i ) at the i th level of the hierarchy is determined from its causal predecessor alone: p i = M i p i−1 , ( 15 ) where the probability vector p i specifies the probability distribution of p(y i ) according to (p i ) y ≡ p(y i ) and the Markov matrix M i specifies the transition probabilities between two neighboring levels, p(y i |y i−1 ). Iterating Eq. (  15 ) gives p n = M n M n−1 • • • M 1 p 0 , ( 16 ) so we can write the combined effect of the the entire generative process as a matrix product. In our physics example (Fig.  3 , left), a set of cosmological parameters y 0 (the density of dark matter, etc) determines the power spectrum y 1 of density fluctuations in our universe, which in turn determines the pattern of cosmic microwave background radiation y 2 reaching us from our early universe, which gets combined with foreground radio noise from our Galaxy to produce the frequency-dependent sky maps (y 3 ) that are recorded by a satellitebased telescope that measures linear combinations of different sky signals and adds electronic receiver noise. For the recent example of the Planck Satellite  [17] , these datasets y i , y 2 , . . . contained about 10 1 , 10 4 , 10 8 , 10 9 and 10 12 numbers, respectively. More generally, if a given data set is generated by a (classical) statistical physics process, it must be described by an equation in the form of Eq. (  16 ), since dynamics in classical physics is fundamentally Markovian: classical equations of motion are always first order differential equations in the Hamiltonian formalism. This technically covers essentially all data of interest in the machine learning community, although the fundamental Markovian nature of the generative process of the data may be an in-efficient description. Our toy image classification example (Fig.  3 , right) is deliberately contrived and oversimplified for pedagogy: y 0 is a single bit signifying \"cat or dog\", which determines a set of parameters determining the animal's coloration, body shape, posture, etc using approxiate probability distributions, which determine a 2D image via ray-tracing, which is scaled and translated by random amounts before a randomly generated background is added. In both examples, the goal is to reverse this generative hierarchy to learn about the input y ≡ y 0 from the output y n ≡ x, specifically to provide the best possibile estimate of the probability distribution p(y|y) = p(y 0 |y n )-i.e., to determine the probability distribution for the cosmological parameters and to determine the probability that the image is a cat, respectively.  y 0 =y y 1 y 2 y 3 > y 3 =T 3 (x) > y 2 =T 2 (x) > y 0 =T 0 (x) y 4 M 4 M 1 M 3 M 2 > y 1 =T 1 (x) \n Resolving the Swindle This decomposition of the generative process into a hierarchy of simpler steps helps resolve the\"swindle\" paradox from the introduction: although the number of parameters required to describe an arbitrary function of the input data y is beyond astronomical, the generative process can be specified by a more modest number of parameters, because each of its steps can. Whereas specifying an arbitrary probability distribution over multi-megapixel images x requires far more bits than there are atoms in our universe, the information specifying how to compute the probability distribution p(x|y) for a microwave background map fits into a handful of published journal articles or software packages  [18] [19] [20] [21] [22] [23] [24] . For a megapixel image of a galaxy, its entire probability distribution is defined by the standard model of particle physics with its 32 parameters  [13] , which together specify the process transforming primordial hydrogen gas into galaxies. The same parameter-counting argument can also be applied to all artificial images of interest to machine learning: for example, giving the simple low-information-content instruction \"draw a cute kitten\" to a random sample of artists will produce a wide variety of images y with a complicated probability distribution over colors, postures, etc, as each artist makes random choices at a series of steps. Even the pre-stored information about cat probabilities in these artists' brains is modest in size. Note that a random resulting image typically contains much more information than the generative process creating it; for example, the simple instruction \"generate a random string of 10 9 bits\" contains much fewer than 10 9 bits. Not only are the typical steps in the generative hierarchy specified by a non-astronomical number of parameters, but as discussed in Sect. 2.4, it is plausible that neural networks can implement each of the steps efficiently.  6  A deep neural network stacking these simpler networks on top of one another would then implement the entire generative process efficiently. In summary, the data sets and functions we care about form a minuscule minority, and it is plausible that they can also be efficiently implemented by neural networks reflecting their generative process. So what is the remainder? Which are the data sets and functions that we do not care about? Almost all images are indistinguishable from random noise, and almost all data sets and functions are indistinguishable from completely random ones. This follows from Borel's theorem on normal numbers  [26] , which states that almost all real numbers have a string of decimals that would pass any randomness test, i.e., are indistinguishable from random noise. Simple parameter counting shows that deep learning (and our human brains, for that matter) would fail to implement almost all such functions, and training would fail to find any useful patterns. To thwart pattern-finding efforts. cryptography therefore aims to produces randomlooking patterns. Although we might expect the Hamiltonians describing human-generated data sets such as drawings, text and music to be more complex than those describing simple physical systems, we should nonetheless expect them to resemble the natural data sets that inspired their creation much more than they resemble random functions. \n Sufficient Statistics and Hierarchies The goal of deep learning classifiers is to reverse the hierarchical generative process as well as possible, to make inferences about the input y from the output x. Let us now treat this hierarchical problem more rigorously using information theory. Given P(y|x), a sufficient statistic T (x) is defined by the equation P(y|x) = P(y|T (x)) and has played an important role in statistics for almost a century  [27] . All the information about y contained in x is contained in the sufficient statistic. A minimal sufficient statistic  [27]  is some sufficient statistic T * which is a sufficient statistic for all other sufficient statistics. This means that if T (y) is sufficient, then there exists some function f such that T * (y) = f (T (y)). As illustrated in Fig.  3 , T * can be thought of as a an information distiller, optimally compressing the data so as to retain all information relevant to determining y and discarding all irrelevant information. The sufficient statistic formalism enables us to state some simple but important results that apply to any hierarchical generative process cast in the Markov chain form of Eq. (  16 ). \n Theorem 2 Given a Markov chain described by our notation above, let T i be a minimal sufficient statistic of P(y i |y n ). Then there exists some functions f i such that T i = f i • T i+1 . More casually speaking, the generative hierarchy of Fig.  3  can be optimally reversed one step at a time: there are functions f i that optimally undo each of the steps, distilling out all information about the level above that was not destroyed by the Markov process. Here is the proof. Note that for any k ≥ 1, the \"backwards\" Markov property P(y i |y i+1 , y i+k ) = P(y i |y i+1 ) follows from the Markov property via Bayes' theorem: P(y i |y i+k , y i+1 ) = P(y i+k |y i , y i+1 )P(y i |y i+1 ) P(y i+k |y i+1 ) = P(y i+k |y i+1 )P(y i |y i+1 ) P(y i+k |y i+1 ) = P(y i |y i+1 ). ( ) 17 Using this fact, we see that P(y i |y n ) = y i+1 P(y i |y i+1 y n )P(y i+1 |y n ) = y i+1 P(y i |y i+1 )P(y i+1 |T i+1 (y n )). ( 18 ) Since the above equation depends on y n only through T i+1 (y n ), this means that T i+1 is a sufficient statistic for P(y i |y n ). But since T i is the minimal sufficient statistic, there exists a function f i such that T i = f i • T i+1 . Corollary 2 With the same assumptions and notation as theorem 2, define the function f 0 (T 0 ) = P(y 0 |T 0 ) and f n = T n−1 . Then P(y 0 |y n ) = ( f 0 • f 1 • • • • • f n ) (y n ). ( 19 ) The proof is easy. By induction, T 0 = f 1 • f 2 • • • • • T n−1 , which implies the corollar y. ( 20 ) Roughly speaking, Corollary 2 states that the structure of the inference problem reflects the structure of the generative process. In this case, we see that the neural network trying to approximate P(y|x) must approximate a compositional function. We will argue below in Sect. 3.6 that in many cases, this can only be accomplished efficiently if the neural network has n hidden layers. In neuroscience parlance, the functions f i compress the data into forms with ever more invariance  [28] , containing features invariant under irrelevant transformations (for example background substitution, scaling and translation). Let us denote the distilled vectors y i ≡ f i ( y i+1 ), where y n ≡ y. As summarized by Fig.  3 , as information flows down the hierarchy y = y 0 → y 1 → . . . ex n = x, some of it is destroyed by random processes. However, no further information is lost as information flows optimally back up the hierarchy as y → y n−1 → • • • → y 0 . \n Approximate Information Distillation Although minimal sufficient statistics are often difficult to calculate in practice, it is frequently possible to come up with statistics which are nearly sufficient in a certain sense which we now explain. An equivalent characterization of a sufficient statistic is provided by information theory  [29, 30] . The data processing inequality  [30]  states that for any function f and any random variables x, y, I (x, y) ≥ I (x, f (y)),  (21)  where I is the mutual information: I (x, y) = x,y p(x, y) log p(x, y) p(x) p(y) . ( 22 ) A sufficient statistic T (x) is a function f (x) for which \"≥\" gets replaced by \"=\" in Eq. (  21 ), i.e., a function retaining all the information about y. Even information distillation functions f that are not strictly sufficient can be very useful as long as they distill out most of the relevant information and are computationally efficient. For example, it may be possible to trade some loss of mutual information with a dramatic reduction in the complexity of the Hamiltonian; e.g., H y ( f (x)) may be considerably easier to implement in a neural network than H y (x). Precisely this situation applies to the physical example described in Fig.  3 , where a hierarchy of efficient near-perfect information distillers f i have been found, the numerical cost of f 3  [23, 24] , f 2  [21, 22] , f 1  [19, 20]  and f 0  [17]  scaling with the number of inputs parameters n as O(n), O(n 3/2 ), O(n 2 ) and O(n 3 ), respectively. More abstractly, the procedure of renormalization, ubiquitous in statistical physics, can be viewed as a special case of approximate information distillation, as we will now describe. \n Distillation and Renormalization The systematic framework for distilling out desired information from unwanted \"noise\" in physical theories is known as Effective Field Theory  [31] . Typically, the desired information involves relatively large-scale features that can be experimentally measured, whereas the noise involves unobserved microscopic scales. A key part of this framework is known as the renormalization group (RG) transformation  [31, 32] . Although the connection between RG and machine learning has been studied or alluded to repeatedly  [7, [33] [34] [35] [36] , there are significant misconceptions in the literature concerning the connection which we will now attempt to clear up. Let us first review a standard working definition of what renormalization is in the context of statistical physics, involving three ingredients: a vector y of random variables, a coursegraining operation R and a requirement that this operation leaves the Hamiltonian invariant except for parameter changes. We think of y as the microscopic degrees of freedom-typically physical quantities defined at a lattice of points (pixels or voxels) in space. Its probability distribution is specified by a Hamiltonian H y (x), with some parameter vector y. We interpret the map R : y → y as implementing a coarse-graining 7 of the system. The random variable R(y) also has a Hamiltonian, denoted H (R(y)), which we require to have the same functional form as the original Hamiltonian H y , although the parameters y may change. In other words, H (R(x)) = H r (y) (R(x)) for some function r . Since the domain and the range of R coincide, this map R can be iterated n times R n = R • R • • • • R, giving a Hamiltonian H r n (y) (R n (x)) for the repeatedly renormalized data. Similar to the case of sufficient statistics, P(y|R n (x)) will then be a compositional function. Contrary to some claims in the literature, effective field theory and the renormalization group have little to do with the idea of unsupervised learning and pattern-finding. Instead, the standard renormalization procedures in statistical physics are essentially a feature extractor for supervised learning, where the features typically correspond to longwavelength/macroscopic degrees of freedom. In other words, effective field theory only makes sense if we specify what features we are interested in. For example, if we are given data x about the position and momenta of particles inside a mole of some liquid and is tasked with predicting from this data whether or not Alice will burn her finger when touching the liquid, a (nearly) sufficient statistic is simply the temperature of the object, which can in turn be obtained from some very coarse-grained degrees of freedom (for example, one could use the fluid approximation instead of working directly from the positions and momenta of ∼ 10 23 particles). But without specifying that we wish to predict (long-wavelength physics), there is nothing natural about an effective field theory approximation. To be more explicit about the link between renormalization and deep-learning, consider a toy model for natural images. Each image is described by an intensity field φ(r), where r is a 2-dimensional vector. We assume that an ensemble of images can be described by a quadratic Hamiltonian of the form H y (φ) = y 0 φ 2 + y 1 (∇φ) 2 + y 2 ∇ 2 φ 2 + • • • d 2 r. ( 23 ) Each parameter vector y defines an ensemble of images; we could imagine that the fictitious classes of images that we are trying to distinguish are all generated by Hamiltonians H y with the same above form but different parameter vectors y. We further assume that the function φ(r) is specified on pixels that are sufficiently close that derivatives can be well-approximated by differences. Derivatives are linear operations, so they can be implemented in the first layer of a neural network. The translational symmetry of Eq. (  23 ) allows it to be implemented with a convnet. If can be shown  [31]  that for any course-graining operation that replaces each block of b × b pixels by its average and divides the result by b 2 , the Hamiltonian retains the form of Eq. (  23 ) but with the parameters y i replaced by y i = b 2−2i y i . ( 24 ) This means that all parameters y i with i ≥ 2 decay exponentially with b as we repeatedly renormalize and b keeps increasing, so that for modest b, one can neglect all but the first few y i 's. What would have taken an arbitrarily large neural network can now be computed on a neural network of finite and bounded size, assuming that we are only interested in classifying the data based only on the coarse-grained variables. These insufficient statistics will still have discriminatory power if we are only interested in discriminating Hamiltonians which all differ in their first few C k . In this example, the parameters y 0 and y 1 correspond to \"relevant operators\" by physicists and \"signal\" by machine-learners, whereas the remaining parameters correspond to \"irrelevant operators\" by physicists and \"noise\" by machine-learners. The fixed point structure of the transformation in this example is very simple, but one can imagine that in more complicated problems the fixed point structure of various transformations might be highly non-trivial. This is certainly the case in statistical mechanics problems where renormalization methods are used to classify various phases of matters; the point here is that the renormalization group flow can be thought of as solving the pattern-recognition problem of classifying the long-range behavior of various statistical systems. In summary, renormalization can be thought of as a type of supervised learning,  8  where the large scale properties of the system are considered the features. If the desired features are not large-scale properties (as in most machine learning cases), one might still expect the a generalized formalism of renormalization to provide some intuition to the problem by replacing a scale transformation with some other transformation. But calling some procedure renormalization or not is ultimately a matter of semantics; what remains to be seen is whether or not semantics has teeth, namely, whether the intuition about fixed points of the renormalization group flow can provide concrete insight into machine learning algorithms. In many numerical methods, the purpose of the renormalization group is to efficiently and accurately evaluate the free energy of the system as a function of macroscopic variables of interest such as temperature and pressure. Thus we can only sensibly talk about the accuracy of an RG-scheme once we have specified what macroscopic variables we are interested in. \n No-Flattening Theorems Above we discussed how Markovian generative models cause p(x|y) to be a composition of a number of simpler functions f i . Suppose that we can approximate each function f i with an efficient neural network for the reasons given in Sect. 2. Then we can simply stack these networks on top of each other, to obtain an deep neural network efficiently approximating p(x|y). But is this the most efficient way to represent p(x|y)? Since we know that there are shallower networks that accurately approximate it, are any of these shallow networks as efficient as the deep one, or does flattening necessarily come at an efficiency cost? To be precise, for a neural network f defined by Eq. (  6 ), we will say that the neural network f is the flattened version of f if its number of hidden layers is smaller and f approximates f within some error (as measured by some reasonable norm). We say that f is a neuronefficient flattening if the sum of the dimensions of its hidden layers (sometimes referred to as the number of neurons N n ) is less than for f. We say that f is a synapse-efficient flattening if the number N s of non-zero entries (sometimes called synapses) in its weight matrices is less than for f. This lets us define the flattening cost of a network f as the two functions C n (f, , ) ≡ min f N n (f ) N n (f) , ( 25 ) C s (f, , ) ≡ min f N s (f ) N s (f) , ( 26 ) specifying the factor by which optimal flattening increases the neuron count and the synapse count, respectively. We refer to results where C n > 1 or C s > 1 for some class of functions f as \"no-flattening theorems\", since they imply that flattening comes at a cost and efficient flattening is impossible. A complete list of no-flattening theorems would show exactly when deep networks are more efficient than shallow networks. There has already been very interesting progress in this spirit, but crucial questions remain. On one hand, it has been shown that deep is not always better, at least empirically for some image classification tasks  [38] . On the other hand, many functions f have been found for which the flattening cost is significant. Certain deep Boolean circuit networks are exponentially costly to flatten  [39] . Two families of multivariate polynomials with an exponential flattening cost C n are constructed in  [14] . Poggio et al.  [6] , Mhaskar et al.  [15] , Mhaskar and Poggio  [16]  focus on functions that have tree-like hierarchical compositional form, concluding that the flattening cost C n is exponential for almost all functions in Sobolev space. For the ReLU activation function,  [40]  finds a class of functions that exhibit exponential flattening costs;  [41]  study a tailored complexity measure of deep versus shallow ReLU networks. Eldan and Shamir  [42]  shows that given weak conditions on the activation function, there always exists at least one function that can be implemented in a 3-layer network which has an exponential flattening cost. Finally,  [43, 44]  study the differential geometry of shallow versus deep networks, and find that flattening is exponentially neuron-inefficient. Further work elucidating the cost of flattening various classes of functions will clearly be highly valuable. \n Linear No-Flattening Theorems In the mean time, we will now see that interesting no-flattening results can be obtained even in the simpler-to-model context of linear neural networks  [45] , where the σ operators are replaced with the identity and all biases are set to zero such that A i are simply linear operators (matrices). Every map is specified by a matrix of real (or complex) numbers, and composition is implemented by matrix multiplication. One might suspect that such a network is so simple that the questions concerning flattening become entirely trivial: after all, successive multiplication with n different matrices is equivalent to multiplying by a single matrix (their product). While the effect of flattening is indeed trivial for expressibility (f can express any linear function, independently of how many layers there are), this is not the case for the learnability, which involves non-linear and complex dynamics despite the linearity of the network  [45] . We will show that the efficiency of such linear networks is also a very rich question. Neuronal efficiency is trivially attainable for linear networks, since all hidden-layer neurons can be eliminated without accuracy loss by simply multiplying all the weight matrices together. We will instead consider the case of synaptic efficiency and set = = 0. Many divide-and-conquer algorithms in numerical linear algebra exploit some factorization of a particular matrix A in order to yield significant reduction in complexity. For example, when A represents the discrete Fourier transform (DFT), the fast Fourier transform (FFT) algorithm makes use of a sparse factorization of A which only contains O(n log n) non-zero matrix elements instead of the naive single-layer implementation, which contains n 2 nonzero matrix elements. As first pointed out in  [46] , this is an example where depth helps and, in our terminology, of a linear no-flattening theorem: fully flattening a network that performs an FFT of n variables increases the synapse count N s from O(n log n) to O(n 2 ), i.e., incurs a flattening cost C s = O(n/ log n) ∼ O(n). This argument applies also to many variants and generalizations of the FFT such as the Fast Wavelet Transform and the Fast Walsh-Hadamard Transform. Another important example illustrating the subtlety of linear networks is matrix multiplication. More specifically, take the input of a neural network to be the entries of a matrix M and the output to be NM, where both M and N have size n × n. Since matrix multiplication is linear, this can be exactly implemented by a 1-layer linear neural network. Amazingly, the naive algorithm for matrix multiplication, which requires n 3 multiplications, is not opti-mal: the Strassen algorithm  [47]  requires only O(n ω ) multiplications (synapses), where ω = log 2 7 ≈ 2.81, and recent work has cut this scaling exponent down to ω ≈ 2.3728639  [48] . This means that fully optimized matrix multiplication on a deep neural network has a flattening cost of at least C s = O(n 0.6271361 ). Low-rank matrix multiplication gives a more elementary no-flattening theorem. If A is a rank-k matrix, we can factor it as A = BC where B is a k × n matrix and C is an n × k matrix. Hence the number of synapses is n 2 for an = 0 network and 2nk for an = 1-network, giving a flattening cost C s = n/2k > 1 as long as the rank k < n/2. Finally, let us consider flattening a network f = AB, where A and B are random sparse n × n matrices such that each element is 1 with probability p and 0 with probability 1 − p. Flattening the network results in a matrix F i j = k A ik B k j , so the probability that F i j = 0 is (1− p 2 ) n . Hence the number of non-zero components will on average be 1 − (1 − p 2 ) n n 2 , so C s = 1 − (1 − p 2 ) n n 2 2n 2 p = 1 − (1 − p 2 ) n 2 p . ( 27 ) Note that C s ≤ 1/2 p and that this bound is asymptotically saturated for n 1/ p 2 . Hence in the limit where n is very large, flattening multiplication by sparse matrices p 1 is horribly inefficient. \n A Polynomial No-Flattening Theorem In Sect. 2, we saw that multiplication of two variables could be implemented by a flat neural network with 4 neurons in the hidden layer, using Eq. (  11 ) as illustrated in Fig.  2 . In Appendix A, we show that Eq. (  11 ) is merely the n = 2 special case of the formula n i=1 x i = 1 2 n {s} s 1 . . . s n σ (s 1 x 1 + • • • + s n x n ), ( 28 ) where the sum is over all possible 2 n configurations of s 1 , • • • s n where each s i can take on values ±1. In other words, multiplication of n variables can be implemented by a flat network with 2 n neurons in the hidden layer. We also prove in Appendix A that this is the best one can do: no neural network can implement an n-input multiplication gate using fewer than 2 n neurons in the hidden layer. This is another powerful no-flattening theorem, telling us that polynomials are exponentially expensive to flatten. For example, if n is a power of two, then the monomial x 1 x 2 . . . x n can be evaluated by a deep network using only 4n neurons arranged in a deep neural network where n copies of the multiplication gate from Fig.  2  are arranged in a binary tree with log 2 n layers (the 5th top neuron at the top of Fig.  2  need not be counted, as it is the input to whatever computation comes next). In contrast, a functionally equivalent flattened network requires a whopping 2 n neurons. For example, a deep neural network can multiply 32 numbers using 4n = 160 neurons while a shallow one requires 2 32 = 4, 294, 967, 296 neurons. Since a broad class of real-world functions can be well approximated by polynomials, this helps explain why many useful neural networks cannot be efficiently flattened. simple probability distributions that deep learning is uniquely suited to model. We argued that the success of shallow neural networks hinges on symmetry, locality, and polynomial log-probability in data from or inspired by the natural world, which favors sparse low-order polynomial Hamiltonians that can be efficiently approximated. These arguments should be particularly relevant for explaining the success of machine learning applications to physics, for example using a neural network to approximate a many-body wavefunction  [49] . Whereas previous universality theorems guarantee that there exists a neural network that approximates any smooth function to within an error , they cannot guarantee that the size of the neural network does not grow to infinity with shrinking or that the activation function σ does not become pathological. We show constructively that given a multivariate polynomial and any generic non-linearity, a neural network with a fixed size and a generic smooth activation function can indeed approximate the polynomial highly efficiently. Turning to the separate question of depth, we have argued that the success of deep learning depends on the ubiquity of hierarchical and compositional generative processes in physics and other machine learning applications. By studying the sufficient statistics of the generative process, we showed that the inference problem requires approximating a compositional function of the form f 1 • f 2 • f 2 • • • • that optimally distills out the information of interest from irrelevant noise in a hierarchical process that mirrors the generative process. Although such compositional functions can be efficiently implemented by a deep neural network as long as their individual steps can, it is generally not possible to retain the efficiency while flattening the network. We extend existing \"no-flattening\" theorems  [14] [15] [16]  by showing that efficient flattening is impossible even for many important cases involving linear networks. In particular, we prove that flattening polynomials is exponentially expensive, with 2 n neurons required to multiply n numbers using a single hidden layer, a task that a deep network can perform using only ∼ 4n neurons. Strengthening the analytic understanding of deep learning may suggest ways of improving it, both to make it more capable and to make it more robust. One promising area is to prove sharper and more comprehensive no-flattening theorems, placing lower and upper bounds on the cost of flattening networks implementing various classes of functions. \n Furthermore, this is the smallest possible number of neurons in any such network with only a single hidden layer. This result may be compared to problems in Boolean circuit complexity, notably the question of whether T C 0 = T C 1  [50] . Here circuit depth is analogous to number of layers, and the number of gates is analogous to the number of neurons. In both the Boolean circuit model and the neural network model, one is allowed to use neurons/gates which have an unlimited number of inputs. The constraint in the definition of T C i that each of the gate elements be from a standard universal library (AND, OR, NOT, Majority) is analogous to our constraint to use a particular nonlinear function. Note, however, that our theorem is weaker by applying only to depth 1, while T C 0 includes all circuits of depth O(1). \n A.1 Proof that 2 n Neurons are Sufficient A neural network with a single hidden layer of m neurons that approximates a product gate for n inputs can be formally written as a choice of constants a i j and w j satisfying (A1) Here, we use ≈ to denote that the two sides of (A1) have identical Taylor expansions up to terms of degree n; as we discussed earlier in our construction of a product gate for two inputs, this exables us to achieve arbitrary accuracy by first scaling down the factors x i , then approximately multiplying them and finally scaling up the result. We may expand (A1) using the definition σ (x) = ∞ k=0 σ k x k and drop terms of the Taylor expansion with degree greater than n, since they do not affect the approximation. Thus, we wish to find the minimal m such that there exist constants a i j and w j satisfying for all 0 ≤ k ≤ n − 1. Let us set m = 2 n , and enumerate the subsets of {1, . . . , n} as S 1 , . . . , S m in some order. Define a network of m neurons in a single hidden layer by setting a i j equal to the function s i (S j ) which is −1 if i ∈ S j and +1 otherwise, setting w j ≡ 1 2 n n!σ n n i=1 a i j = (−1) |S j | 2 n n!σ n . ( A4 ) In other words, up to an overall normalization constant, all coefficients a i j and w j equal ±1, and each weight w j is simply the product of the corresponding a i j . We must prove that this network indeed satisfies Eqs. (A2) and (A3). The essence of our proof will be to expand the left hand side of Eq. (A1) and show that all monomial terms except x 1 •••x n come in pairs that cancel. To show this, consider a single monomial p(x) = x r x i , then we must show that the coefficient of p(x) in σ r m j=1 w j n i=1 a i j x i r is 0. Since p(x) = n i=1 x i , there must be some i 0 such that r i 0 = 0. In other words, p(x) does not depend on the variable x i 0 . Since the sum in Eq. (A1) is over all combinations of ± signs for all variables, every term will be canceled by another term where the (non-present) x i 0 has the opposite sign and the weight w j has the opposite sign: completing our proof that this network indeed approximates the desired product gate. From the standpoint of group theory, our construction involves a representation of the group G = Z n 2 , acting upon the space of polynomials in the variables x 1 , x 2 , . . . , x n . The group G is generated by elements g i such that g i flips the sign of x i wherever it occurs. Then, our construction corresponds to the computation f(x 1 , . . . , x n ) = (1 − g 1 )(1 − g 2 ) • • • (1 − g n )σ (x 1 + x 2 + . . . + x n ). Every monomial of degree at most n, with the exception of the product x 1 • • • x n , is sent to 0 by (1 − g i ) for at least one choice of i. Therefore, f(x 1 , . . . , x n ) approximates a product gate (up to a normalizing constant). 4 M 1 M 3 M 2 Fig. 3 41323 Fig.3Causal hierarchy examples relevant to physics (left) and image classification (right). As information flows down the hierarchy y 0 → y 1 → . . . → y n = y, some of it is destroyed by random Markov processes. However, no further information is lost as information flows optimally back up the hierarchy as y n−1 → . . . → y 0 . The right example is deliberately contrived and over-simplified for pedagogy; for example, translation and scaling are more naturally performed before ray tracing, which in turn breaks down into multiple steps. \n 1 1 • 1 • • x r n n where r 1 + . . . + r n = r ≤ n. If p(x) = n i=1 \n 1 )=S j i 0 (− 1 )(− 1 ) 1011 |S j ∪{i 0 }| 2 n n!σ r n i=1 s i (S j ∪ {i 0 })x i r |S j | 2 n n! n i=1 s i (S j )x i r − n i=1 s i (S j ∪ {i 0 })x i rObserve that the coefficient of p(x) is equal in n i=1 s i (S j )x i r and n i=1 s i (S j ∪ {i 0 })x i r , since r i 0 = 0. Therefore, the overall coefficient of p(x) in the above expression must vanish, which implies that (A3) is satisfied. If instead p(x) = n i=1 x i , then all terms have the coefficient of p(x) in n i=1 a i j x i n is n! n i=1 a i j = (−1) |S j | n!, because all n! terms are identical and there is no cancelation. Hence, the coefficient of p(x) on the left-hand side of (A2) isσ n m j=1 |S j | 2 n n!σ n (−1) |S j | n! = 1, \n Table 1 1 Physics-ML dictionary Physics \n\t\t\t The class of functions that can be exactly expressed by a neural network must be invariant under composition, since adding more layers corresponds to using the output of one function as the input to another. Important such classes include linear functions, affine functions, piecewise linear functions (generated by the popular Rectified Linear unit \"ReLU\" activation function σ (x) = max[0, x]), polynomials, continuous functions and smooth functions whose n th derivatives are continuous. According to the Stone-Weierstrass theorem, both polynomials and piecewise linear functions can approximate continuous functions arbitrarily well. \n\t\t\t The limit where λ → ∞ but |A 1 | 2 |A 2 | is held constant is very similar in spirit to the 't Hooft limit in large N quantum field theories where g 2 N is held fixed but N → ∞. The extra terms in the Taylor series which are suppressed at large λ are analogous to the suppression of certain Feynman diagrams at large N . The authors thank Daniel Roberts for pointing this out. 4  In addition to the four neurons required for each multiplication, additional neurons may be deployed to copy variables to higher layers bypassing the nonlinearity in σ . Such linear \"copy gates\" implementing the function u → u are of course trivial to implement using a simpler version of the above procedure: using A 1 to shift and scale down the input to fall in a tiny range where σ (u) = 0, and then scaling it up and shifting accordingly with A 2 . \n\t\t\t If the next step in the generative hierarchy requires knowledge of not merely of the present state but also information of the past, the present state can be redefined to include also this information, thus ensuring that the generative process is a Markov process. \n\t\t\t Although our discussion is focused on describing probability distributions, which are not random, stochastic neural networks can generate random variables as well. In biology, spiking neurons provide a good random number generator, and in machine learning, stochastic architectures such as restricted Boltzmann machines [25]  do the same. \n\t\t\t A typical renormalization scheme for a lattice system involves replacing many spins (bits) with a single spin according to some rule. In this case, it might seem that the map R could not possibly map its domain onto itself, since there are fewer degrees of freedom after the coarse-graining. On the other hand, if we let the domain and range of R differ, we cannot easily talk about the Hamiltonian as having the same functional form, since the renormalized Hamiltonian would have a different domain than the original Hamiltonian. Physicists get around this by taking the limit where the lattice is infinitely large, so that R maps an infinite lattice to an infinite lattice. \n\t\t\t A subtlety regarding the above statements is presented by the Multi-scale Entanglement Renormalization Ansatz (MERA) [37] . MERA can be viewed as a variational class of wave functions whose parameters can be tuned to to match a given wave function as closely as possible. From this perspective, MERA is as an unsupervised machine learning algorithm, where classical probability distributions over many variables are replaced with quantum wavefunctions. Due to the special tensor network structure found in MERA, the resulting variational approximation of a given wavefunction has an interpretation as generating an RG flow. Hence this is an example of an unsupervised learning problem whose solution gives rise to an RG flow. This is only possible due to the extra mathematical structure in the problem (the specific tensor network found in MERA); a generic variational Ansatz does not give rise to any RG interpretation and vice versa.", "date_published": "n/a", "url": "n/a", "filename": "Lin2017_Article_WhyDoesDeepAndCheapLearningWor.tei.xml", "abstract": "We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can frequently be approximated through \"cheap learning\" with exponentially fewer parameters than generic ones. We explore how properties frequently encountered in physics such as symmetry, locality, compositionality, and polynomial log-probability translate into exceptionally simple neural networks. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to the renormalization group. We prove various \"no-flattening theorems\" showing when efficient linear deep networks cannot be accurately approximated by shallow ones without efficiency loss; for example, we show that n variables cannot be multiplied using fewer than 2 n neurons in a single hidden layer.", "id": "6f7bbc18da3c99526be4668b7f1fb6f9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Benjamin Y Hayden", "Yael Niv"], "title": "The Case Against Economic Values in the Orbitofrontal Cortex (or Anywhere Else in the Brain)", "text": "The past 20 years have seen a great deal of interest in understanding how our brains implement economic choices  (Camerer et al., 2005; Glimcher & Fehr, 2013; Loewenstein et al., 2008; Padoa-Schioppa, 2011; Rangel et al., 2008; Rushworth et al., 2011) . Much research in this field of neuroeconomics rests on the assumption that choices between options rely on an explicit valuation process  (Kable & Glimcher, 2009; Levy & Glimcher, 2012; Montague & Berns, 2002; O'Doherty, 2014; Padoa-Schioppa, 2011) . That is, that the brain first assigns value to each option and then compares those values to determine choice. The concept of valuation-which stems from economic theory-is so ingrained that it may seem inevitable. How else would one literally compare apples to oranges? Indeed, the idea that value exists on a single cardinal scale, also called a \"common currency,\" has been extended to encompass not only goods, but also effort costs and time delays; everything an agent needs to bundle into evaluation of a mode of action that is aimed at procuring a specific outcome. In parallel, the computational framework of reinforcement learning, which has been a cornerstone of neuroeconomics, also makes a scalar value signal central to its implementation  (Niv, 2009; Sutton & Barto, 2018) . Specifically, in reinforcement learning, the value of an option-a state or an action-is the expected sum of future rewards contingent upon that choice. As a sum of future rewards that may be of different types (and include costs as negative rewards), reinforcement-learning value is naturally calculated in some unitless common currency. However, not all reinforcement learning algorithms rely on or even calculate values  (Sutton & Barto, 2018) , and reinforcementlearning values, as sums of future rewards, are not synonymous with economic values of specific goods. Likewise, many empirically supported process models of choice get by with no valuation  (Gigerenzer & Gaissmaier, 2011; Miller et al., 2019; Vlaev et al., 2011) . The fact that the brain can compute values to compare apples and oranges does not mean that it routinely does so, or that valuation is the primary process underlying choice. In this opinion paper, we argue that in many choice scenarios the brain may not be computing values at all, despite appearing to do so. We will demonstrate that the rationale for a value signal is weak, as are both behavioral and neural evidence supporting value computation. Finally, we propose an alternative-direct learning of action policies-and suggest there is scant direct evidence for value learning that cannot be explained by this and other alternative theories. Our hypothesis is important as it suggests a different interpretation of previous data and requires that studies attempting to resolve mechanisms of value computation in the brain first establish that in the specific situation studied, valuation is indeed occurring. In particular, much work has associated the orbitofrontal cortex (OFC) in representing the expected economic value of different goods or options  (Bartra et al., 2013; Levy & Glimcher, 2012 )-a role that must be critically reconsidered if we agree that the brain may not necessarily be representing such values in many of the experiments so far used to test this hypothesis. \n Why Argue Against Value? Intuitively, our thesis is that while we may know that we prefer an orange to an apple (for one thing, oranges don't brown when exposed to oxygen), we may make this judgment without consulting an internal scalar (cardinal) or even a universal ordinal value signal. Consequently, we may be hard-pressed to express the precise value that we put on an orange. This is not merely an issue of conscious access to our internal value of oranges 1 , but may be due to the fact that deciding on preferences can utilize many alternative mechanisms that don't require or rely on calculation of such a value. Valuation is hard  (Payne et al., 1992) . It is also often unnecessary: when choosing between, say, an orange and a car, it is immediately clear that one is better than the other without calculating the precise value of either. If you are extremely thirsty, you might choose the orange, whereas if you need to go somewhere a car is the only relevant option. Arguably, many real-life choices are between options that are sufficiently different in the needs that they fulfill as to be more similar to this extreme example than they are to the choice between apples and oranges  (Juechems & Summerfield, 2019) . Valuation may only be necessary when choosing between two very similarly valued items. However, if the items are sufficiently similar in how they satisfy our needs, the brain may decide to choose randomly, according to some valuefree heuristic, or according to past choices-and move on  (Chater, 2018) . Alternatively, the brain can try to calculate the exact values of the options to the necessary precision that arbitrates between them. Indeed, choosing between similar options often takes longer than choosing between very different options, even when making rather trivial choices that do not warrant the time and effort invested  (Pirrone et al., 2018; Teodorescu et al., 2016 ). An example is the inordinate amount of time some of us may spend deciding what brand of tuna fish to buy, despite the fact that our time (as per our salary) is worth much more than the money we will save by correctly evaluating which brand provides the best \"value for money.\" This scenario also illustrates how inept we are at comparing the value of different kinds-here, time and money-which should have been straightforward if the modus operandi of the brain was to evaluate everything in terms of some common currency (see below). So perhaps the brain can, when needed, calculate values. However, we argue that this is not the main means by which the brain makes decisions, and perhaps not the natural mode of decision making. \n What Is Value? Before moving on, we would like to delineate precisely how we are defining value for the sake of our argument. The term \"value\" has multiple uses (the problems this multiplicity raises are carefully laid out by O'Doherty, 2014). We consider \"value\" a hypothesized scalar variable that reflects the worth of a specific item or outcome. 2 Because it is scalar, it is necessarily abstract. It can refer to any good, and makes use of a common currency code that is comparable across goods of different types (e.g., food, water, recreation time). Value, by this definition, is cardinal, not ordinal, meaning it can be defined for an option per se, rather than solely relative to other options. That is, it reifies the idea of \"utils\"-quantifiable units of value, often used in a jocular manner in Economics classes. The idea of a common currency is key as it implies that all relative calculations have already happened-the value of an option is in some denomination that objectively defines it as compared to other such values. One might argue that this is too narrow a definition, but we believe this is what neuroeconomists have in mind when talking about representation of common currency values in the brain. For example, we know of no neuroeconomic model that imagines a neural implementation of an ordinal value scale. This having been said, even an ordinal scale should not change based on the comparison set, and should satisfy transitivity-which many of the neural signals attributed to value do not, as we detail below. Our definition of value, for the purpose of this paper, is different from other types of value that are discussed in reinforcement learning. Specifically, here we are discussing value as the reward worth of a single item/event, not the expected sum of all future rewards (R in reinforcement learning models, not V). One might argue that in order to compute such an expected sum V, the subjective worth of all individual rewards must be translated to a common currency that can be added. In this sense, reinforcement learning models do presuppose a common currency reward value. However, they don't necessarily commit to economic properties of such values, such as transitivity and consistency (see also  Juechems & Summerfield, 2019 ), and we discuss below a class of reinforcement learning algorithms that can make do with evaluations that are only relative to the current options, and not applicable in other situations. One important feature of our definition of value is that in our view, although value is inferred from choice, it is not strictly identical to choice, nor necessarily implied by choice. For instance, if we observe a consistent preference for A over B, A is assumed to have a higher value than B. But choice of A over B isn't sufficient to infer the existence of a self-consistent value function: a decisionmaker may adhere to a heuristic policy that results in stable preference for  Slovic, 2006) . Moreover, choice can be altered without manipulating the reward value of an item  (Schonberg & Katz, 2020) , which suggests that value, as inferred from choice, is not untarnished by processes that are not economic in nature. Thus, value can be inferred from behavior given certain assumptions, but preferences do not always lead to a value function. [A > B], [B > C], and [C > A] (Lichtenstein & This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. \n The Common-Currency Hypothesis The notion that economic decision-makers make use of internal value functions to compare options is often dated to Daniel Bernoulli's proposal in 1738 of a logarithmic utility curve to explain preferences in the St. Petersburg Paradox  (Martin, 2011) . Here, a decision-maker is offered a chance to play a game in which they win $2 (n−1) with n being the first time, in a series of coin tosses, that a coin falls on \"heads.\" The paradox is that although the expected monetary value of this game (that is, the sum of expected wins multiplied by their probability P ∞ n=1 2 ðn−1Þ • 0.5 n = P ∞ n=1 0.5) is infinity, people are not willing to pay even $10 to play this game  (Hayden & Platt, 2009) . The explanation that Bernoulli proposed proved foundational within microeconomic theory. He argued that decision-makers don't base calculations on the nominal, objective cash value of the potential gain, but rather on its subjective value. If the subjective value grows more slowly than the objective value (the idea of \"diminishing marginal utility\"), an optimizing decision-maker will appear riskaverse, for instance, when evaluating the St. Petersburg gamble. Utility, or subjective value, has been central to many if not most microeconomic models. These include the axiomatic approaches of Pareto, Von Neumann and Morgenstern, and Samuelson. It is also central to behavioral theories such as prospect theory and decision field theory  (Busemeyer & Townsend, 1993; Kahneman & Tversky, 1979) . Ironically, however, explaining choices in the St. Petersburg paradox using such a subjective value function requires utility for money that diminishes so rapidly that it does not generalize to choices in other contexts. Instead, heuristic accounts-accounts that don't rely on ideas about value maximization-provide better quantitative matches for St. Petersburg choices  (Hayden & Platt, 2009) . Despite its central importance in economics, economists are typically agnostic about whether the concept of value is just a convenient description, or whether it is instantiated in the brain. As Friedman argued, decision-makers behave as if we compute and compare values, but we cannot conclude that we actually do so  (Friedman, 1953) . In that work, he famously compared economic agents to a trained billiards player who makes excellent shots as if having a sophisticated grasp of Euclidean geometry, although in fact such a theoretical understanding is not necessary for good billiards skill. Economists typically stop at the point of saying that economic models are \"as if\" models, with some arguing that the question of the underlying reality of economic variables is outside the domain of economics  (Gul & Pesendorfer, 2008; Harrison, 2008) . In contrast, neuroeconomics has generally taken as a default assumption that these \"as if\" theories are reified in the brain  (Kable & Glimcher, 2009; Levy & Glimcher, 2012; Montague & Berns, 2002; O'Doherty, 2014; Padoa-Schioppa, 2011; Rich & Wallis, 2016) . Modern tools such as neuroimaging and single unit physiology provide the opportunity to assess the implementation of decision making directly. Indeed, neuroscientists have had little trouble identifying correlates of value in several brain areas  (Knutson et al., 2001; Levy & Glimcher, 2012; Plassmann et al., 2007; Wallis, 2007) , leading to the suggestion that the OFC is a nexus for representing the economic value of goods in the brain (see, e.g.,  Rushworth et al., 2011; Wallis, 2007) , alongside other brain areas that are important for computing and representing value such as the ventromedial prefrontal cortex  (Bartra et al., 2013)  and ventral striatum  (Haber & Knutson, 2010) . However, it is not clear that the signals identified in these studies actually represent value as proposed-on a common-currency scale, for comparing options and making choices. Moreover, so called \"value signals\" only correlate with value, so may be signaling other quantities, such as attention, action plans, vigor, or preference, which also correlate with value  (Maunsell, 2004; O'Doherty, 2014; Wallis & Rich, 2011) . Hence it is important to carefully consider alternative interpretations for these findings, as we do further below, after discussing some practical constraints and philosophical conundrums. \n Alternatives to Valuation in Decision Making While common-currency value provides a convenient and general mechanism for making choices, there are many possible alternatives  (Gigerenzer & Gaissmaier, 2011; Kahneman et al., 1982; Lichtenstein & Slovic, 2006; Vlaev et al., 2011) , some of which are quite general and robust. Consider for example the \"priority heuristic\"  (Brandstätter et al., 2006) . This de minimis heuristic approach proposes that decision-makers first identify a dimension along which options vary and then compare options along that dimension. If that results in a choice, they stop; otherwise, they move on to the next dimension. This heuristic can explain many phenomena, including Allais preferences  (Allais, 1953) , the reflection effect  (Fishburn & Kochenberger, 1979) , the certainty effect  (Kahneman & Tversky, 1979) , the fourfold pattern in risky choice that motivates prospect theory  (Tversky & Fox, 1995) , and several intransitivities-all without ever requiring computing of value  (Brandstätter et al., 2006) . And the priority heuristic is one of a large number of heuristics that do a remarkable job at describing behavior  (Gigerenzer & Gaissmaier, 2011) . These heuristics are generally motivated by psychological observations, and thus are consistent with known data from the psychology-if not the neuroscience-of choice. In particular, they reflect the assumption that calculating value is difficult, that humans typically use shortcuts whenever possible, and that heuristics are a good shortcut  (Gigerenzer & Gaissmaier, 2011; Lieder & Griffiths, 2020; Payne et al., 1992) . Moreover, these heuristics are not limited to humans, but apply to other species, including monkeys  (Heilbronner & Hayden, 2016; Marsh, 2002; Santos & Rosati, 2015; Shafir et al., 2002) . Importantly for our argument, the success of heuristic approaches demonstrates that value calculations are not a priori essential for neuroeconomic theories of choice. In particular, heuristic theories can solve many problems for which value is proposed to be needed  (Kahneman et al., 1982; Lichtenstein & Slovic, 2006; Piantadosi & Hayden, 2015; Stevens, 2016; Tversky, 1969; Vlaev et al., 2011) . Heuristics readily allow for comparison of multi-dimensional goods and bundles, and for choice across dissimilar goods. While heuristics are not perfect, and lead to many choice anomalies, choice is, empirically, full of anomalies. Moreover, several non-heuristic process models also eschew value computation steps, including decision by sampling, query theory, and fuzzy trace theory; these all account for a wide range of choice behavior as well  (Reyna, 2008; Stewart & Simpson, 2008; Stewart et al., 2006; Weber et al., 2007) . \n Practical Issues in the Neuroscience of Value Representation Despite the above, it is often considered axiomatic that an internal, neural, value scale must exist in the brain. The job of neuroscientists is then to find this signal-to pinpoint brain activity This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. that correlates with value. In this section, we challenge this viewpoint by considering some basic issues that come up in the neuroscience of value. The first problem is that it is impossible to precisely measure value. We can measure preferences between options and use the data to infer option values, but elicited preferences are noisy measurements that also reflect factors other than value. For example, depending on how preferences are elicited, they may also reflect the tendency to press the same button repeatedly rather than change actions, the tendency to switch between options due to a prior belief about depleting resources, or the amount of attention or looking time for each of the options  (Armel et al., 2008; Schonberg & Katz, 2020; Shimojo et al., 2003; Sugrue et al., 2005) . Finally, value may shift from trial to trial, even depending on recent outcomes, meaning that methods that average across trials produce misleading value estimates  (Sugrue et al., 2005) . One could, in theory, incorporate these factors into the inferred value of an option. For example, there may be inherent value in choosing the same thing twice in a row. However, it becomes unclear what the definition of the \"option\" is that is being evaluated: if the value of an apple after eating (or choosing, or even just viewing) an orange is different from the value of an apple without that proximal experience, can we determine the value of goods at all? And if we can change the value (read: preference) for an option just by directing more attention to it  (Salomon et al., 2018; Schonberg et al., 2014) , or inducing choice of it  (Izuma et al., 2010; Sharot et al., 2012; Voigt et al., 2017) , is preference really measuring the subjective economic worth of a good? The risk is circularity-if any choice behavior can be explained by supposing value that depends on local history, then the concept of value adds no additional explanatory power beyond that of recent events and choices. Different ways to measure value raise a second challenge of inconsistent measures. Indeed, if we had a single neural value function we called on, values elicited by different measures would match. Unfortunately, they do not  (Lichtenstein & Slovic, 2006) . To explain this, in their seminal work, Sarah Lichtenstein and Paul Slovic proposed that preferences do not arise from any internal value function, but instead are constructed at the time of elicitation (see also  Ariely et al., 2003; Payne et al., 1992; Tversky & Shafir, 1992) . That is, in the view of these and like-minded scholars, value doesn't sit in the brain waiting to be used; rather, preference is a complex and active process that takes place at the time the decision is made. Critically, in this theory we compute choices in a largely ad-hoc manner based on the available options, without an intermediary common-currency valuation stage. As such, there is no guarantee of consistency or reliability; any consistency or reliability observed may be explained as a result of strong attractor states in the way the system determines the choice, and deviations from consistency are evidence for the specific nature of the algorithm and its idiosyncrasies. This hypothesis, while denouncing value as a latent construct in the brain, nevertheless invites neuroscientific research to understand the active processes involved in choice, and how these relate to (relative) evaluation, if not to economic values. This having been said, experimenters can roughly estimate value, even if not measure it precisely. For example, in a given experiment they can examine choices and determine with confidence that a monkey (behaves as if it) places more value on a gamble as compared to a safe option with a matched expected value. One could then use this fact to try to identify a neural correlate of value. However, for this neural endeavor to be valid, it is important to identify all confounding variables and regress them out. O'Doherty's (2014) review delineates the practical difficulty of doing so, using the overall rubric of \"visceral, autonomic, and skeletomotor\" activity. In practice, confounding variables include both stimulus and outcome identity, information about the state or structure of the world, the surpriseness, informativeness, and informational value of stimuli, details of the action associated with selecting of consuming the reward, including its likelihood and vigor, and the attention and arousal engendered by the stimulus (e.g.,  Blanchard et al., 2015; Botvinik-Nezer et al., 2020; Niv et al., 2007; O'Doherty, 2007; Roesch & Olson, 2004; Roesch et al., 2006; Wilson et al., 2014; . Indeed, in studies that separately assess encoding of outcome identity versus outcome value, activity in brain areas that are often considered to be emblematic of economic value (in particular, the OFC) turns out to correlate with outcome identity instead  (Klein-Flügge et al., 2013) . A final insurmountable problem is that it may be impossible, even in theory, to obtain a brain measure of value that is independent of behavior. Suppose for example, that we identify a particular class of neurons whose firing rates are perfectly correlated with value down to our ability to measure it through preference. Supporting this idea, we observe that any procedure that modifies value (as inferred from behavior) changes the firing rate of these neurons in a manner consistent with our predictions. We may tentatively hypothesize that these neurons are (or are among) the value neurons of the brain. However, as shown by Schonberg and colleagues, preference can be changed irrespective of changing the economic worth of goods  (Schonberg & Katz, 2020) . Therefore, to differentiate value neurons from preference neurons, we would need to show that these neurons do not strictly follow expressed preference when the value function diverges from it. This is, of course, not possible if the value function never measurably diverges from preference. And if we assume that values can diverge from preference, it is not clear how to define values to start with. We call this \"the neuroeconomic relativity problem\" because, like Einstein's relativity problem, it reflects the fact that there is no external reference frame to which one can calibrate value inferences. \n Reconsidering the Motivation for Common Currency It may be worth asking, then, what does having a single common currency buy you? Why would the brain invest in such an organization? One advantage of a common-currency scale is that it simplifies comparing options that differ along multiple dimensions. For example, when hunting for an apartment, the options may differ along dimensions of price, area, neighborhood, and amenities. The logic is that these dimensions must be first combined into a single scalar per apartment so that the scalars can be compared. However, this is not the only way to solve the problem, and importantly, may not be the way humans make their decisions. For example, the apartment shopper may choose a single dimension and pick the winner along that dimension, as discussed above, or may compare separately on each dimension and choose the apartment that wins on most counts  (Tversky, 1972) . Laboratory studies where humans can choose what attributes to view indeed suggest that people don't uncover all the attributes of one option (to calculate its value) and then continue to the next option, but rather prefer to view information for all options attribute by attribute  (Fellows, 2006; Hunt et al., 2014) . Indeed, as mentioned, much empirical work indicates that human decision-makers broadly favor heuristic approaches that This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. THE CASE AGAINST ECONOMIC VALUES eschew a value stage in a large number of contexts  (Brandstätter et al., 2006; Gigerenzer & Gaissmaier, 2011; Kahneman et al., 1982; Lieder & Griffiths, 2020) . Notably, systems that make use of heuristics may generate internal variables that are conceptually distinct from value but that correlate with value, thus leading to an interpretational confound. Consider, for example, a relatively well-understood implementation of choice in a (non-brain) distributed system: the selection of hive sites in bees (Apis mellifera,  Seeley, 2010; Seeley & Buhrman, 1999; Seeley et al., 2006) . Bee swarms select a hive site by sending out scouts to investigate potential sites. Each site differs along roughly 20 dimensions of varying but measurable importance (size, safety from predators, exposure to sunlight, wind, etc.). Each scout bee that encounters the hive site performs an extremely poor estimation of the value of the site-it typically will only sample three-to-four of the dimensions and even then, estimate them poorly. The bee then returns and if the estimated site quality is sufficiently good, indicates an assessment of its quality to the other bees in the swarm. The quality it signals will be correlated with the overall value of the hive site, but only weakly, and, critically, will only integrate a subset of relevant value components. The overall comparison between options is indirect-the options race to attract adherents; the majority of the decision is made by a positive feedback process. This example is particularly relevant because scholars of perceptual decision making may recognize this process as strongly related to ideas about how the brain decides between options by racing to bounds, and there is evidence that deliberative processes in the brain follow the same principles as choice processes in bee swarms  (Eisenreich et al., 2017; Franks et al., 2003; Mitchell, 2009; Pais et al., 2013; Passino et al., 2008; Pirrone et al., 2018) . \n Evaluating the Neural Evidence for the Common-Currency Hypothesis Evidence for the common-currency hypothesis comes from the observation that firing rates of single neurons or hemodynamic responses of voxels correlate with values of offers and outcomes  (Kennerley et al., 2009 (Kennerley et al., , 2011 Levy & Glimcher, 2012; Padoa-Schioppa, 2011; Rangel et al., 2008) . These responses depend on multiple elements of offers (e.g., the expected reward, as well as the associated response costs), and are modulated by factors that affect subjective value, such as context or level of satiety (see  Conen & Padoa-Schioppa, 2019; O'Neill & Schultz, 2010; Rudebeck et al., 2017  for only a few examples). Often, variations in these firing rates predict variations in choice  (Conen & Padoa-Schioppa, 2015; Strait et al., 2014; Sugrue et al., 2004) . Such patterns have been taken as evidence that the neural signal encodes value, in particular implicating the OFC  (Bartra et al., 2013; Levy & Glimcher, 2012; O'Reilly, 2020) . However, such patterns of neural responding do not definitively demonstrate a common-currency value signal. For example, in the original finding of value-encoding neurons in the OFC  (Tremblay & Schultz, 1999) , neurons responded more strongly to a high-valued option than to a low-valued one. However, the principle of common currency only held within a given choice pair-responses for Option B were low when this option was paired with a better Option A, but were high when this same option was paired with a worse Option C. Other studies found value-correlated responses to be more stable across contexts  (Padoa-Schioppa & Assad, 2008) , but most findings support an encoding that depends on the alternatives (e.g.,  Kobayashi et al., 2010; Padoa-Schioppa, 2009; Zimmermann et al., 2018) . One might interpret this finding as reflecting simple range adaptation of neurons that have a finite firing rate; however, a more parsimonious explanation is that the firing pattern is consistent with a relative preference code rather than an abstract value code. This interpretation places the putative neural representation of value one stage later than we would expect from a common-currency codeimmediately after comparison (because a relative valuation is itself a comparison) rather than as an input to comparison, raising the question of where the input came from. An interpretation of this code as something other than economic value would obviate this worry. Importantly, with a code that depends on alternatives, there is no real sense in which we can read out the \"true subjective value\" of an option. We can only know if an option's value is higher than another value-similar to the information provided by preferences and choice behavior. Another corollary of such a relative code is that it is unclear to what extent we can read out a meaningful value signal when only one option is available. Indeed, presenting a subject with one option at a time should, theoretically, provide the best ability to read out option values from neural activity in areas associated with value, such as OFC, ventromedial prefrontal cortex, and dorsal and subgenual anterior cingulate cortices. Doing so reveals that while neural activity in these regions does correlate with the value of the first option, neural responses to the second (alternative) option (presented on its own) correlate with the value difference, that is, they reflect the result of value comparison rather than valuation per se  Hunt et al., 2018; Strait et al., 2014) . Moreover, even responses to the first offer do not simply encode its value, but also contain information about the likelihood that option will be chosen (presumably relative to the expected value of the second offer,  Azab & Hayden, 2017) . These results suggest that even when evaluation is experimentally segregated from comparison, pure value encodings may not exist. In fact, the idea that prefrontal neurons are selective or responsive to a single experimenter-defined variable has been increasingly falling out of favor  (Fusi et al., 2016; Raposo et al., 2014; Rigotti et al., 2013) , with \"mixed selectivity\" appearing to be a core operating principle of prefrontal cortex, including in ostensible value regions  (Blanchard et al., 2018; Hayden & Platt, 2010; Kimmel et al., 2020; . A third issue is that although the activity of some neurons in the OFC is correlated with value (but not necessarily linearly related to value), activity of other neurons in this same area is anticorrelated with value, with the majority of neurons showing no relationship at all with value. This raises the possibility that the neurons are encoding something other than value, for instance, a distributed representation of the identity of each of the three options, A, B, and C above, or the identity of the stimulus representing the offer. With the small number of options evaluated in most experiments, such a distributed code of outcome or stimulus identity (but not value) can easily result in some neurons randomly firing most strongly for the higher-valued of the three options and least for the worse option, while in other neurons the relationship would be in the opposite direction. This would also explain why many neurons show a nonmonotonic relationship between value and their firing. Recently, using ensemble recordings in the OFC that allow analysis on the level of a single trial, Wallis and colleagues have attempted a more direct test of the hypothesis that OFC encodes value  (Rich & Wallis, 2016) . In their task, monkeys were offered two options (denoted by images corresponding to the options) and asked to choose between them. On some trials, only one option was offered. Classifiers were trained to classify options corresponding to each of four offer-value levels (0.05, 0.10, 0.18, and 0.30 ml juice, or, in separate blocks, four levels of second-order reinforcer), aggregating over the two images corresponding to each value level. Using single-unit activity and local-field-potential recordings in the OFC, the authors could classify the offered value above chance, suggesting that OFC neurons encoded information about value. However, here too, offer values may have been encoded as different (outcome stimulus) identities, not different (cardinal) values in a common currency. One stringent test of the value-coding hypothesis would be to show that a combination of two offers of value level 0.05 ml resulted in similar activation pattern to a single offer of value level 0.10 ml. Ensemble recordings that give ample data in a single trial allow testing these hypotheses with novel combinations that have not been trained to predict the same identity of reward through multiple presentations, therefore testing the assumptions of the additivity of common currency directly. This critical test has not been conducted, to our knowledge. As mentioned, many factors that are conceptually distinct from value can influence choice-and are therefore closely correlated with value  (Maunsell, 2004) . Reward value drives attention, promotes both short-and long-term learning, primes behavioral adjustments, updates internal models, activates circuitry that detect both positive and negative surprises, and elicits mental computations of cost-benefit tradeoffs as well as comparisons with what could have been chosen. All of these are different from scalar, commoncurrency value, but are known to drive neural activity in the regions usually associated with economic value. As such, they confound that interpretation. This problem is a long-standing and notorious one in neuroeconomics  (Maunsell, 2004; O'Doherty, 2014; Roesch & Olson, 2003) . To overcome some of these potential confounds, a strong tradition in neuroeconomics research is to control for extraneous factors such as salience and response cost (although we note that many factors-for example, covert attention-cannot be controlled for). As a practical issue, it is difficult to control for alternative interpretations without making the task so convoluted that it becomes unnatural for the animal, in the ethological sense  (O'Doherty, 2014) . As a result, it is not clear if findings of value computation (if we believe them to be so) in these tasks would naturally translate to how the brain computes choice in naturalistic situations. But the deeper issue remains that value as inferred in most experiments is definitionally a summary of aggregated choice behavior, and therefore, any variable that influences choice behavior will necessarily be correlated with value. It is for this reason that we suggest that a stronger demonstration of scalar value coding in the brain should show mathematical properties such as the additivity of value, or separation from preferences as these are changed without changing value, as suggested above. If the response of neurons to the novel sum of two stimuli each promising 0.1 ml of juice is similar to the response of those same neurons to a different stimulus associated with 0.2 ml of juice, and especially if this response did not change when preference for an option was induced by means such as the mere exposure effect  (Schonberg & Katz, 2020) , it would be harder to argue that this is due to a shared motor plan, or attentional capture. We note that research to date has shown that the activity of brain areas associated with value, in particular the OFC, does change when preferences are modified through methods that should, in principle, not change economic value  (Botvinik-Nezer et al., 2020) . \n An Alternative View: Direct Learning of Policies Although reinforcement-learning models have contributed to the assumption that the brain computes values, many reinforcementlearning algorithms do not learn or estimate values for different actions. Instead, they directly learn action policies. In fact, in the reinforcement-learning literature, the goal of an agent is to obtain as much reward as possible by executing optimal actions-calculating values is only one means to achieve that end. In explaining reinforcement-learning methods,  Dayan and Abbott's (2001)  textbook begins with the \"direct actor\"-an actor that learns actions without computing their values. The Actor-Critic model, a prominent algorithm for reinforcement learning that has been linked to the brain  (Barto, 1995; Joel et al., 2002; Maia, 2010; O'Doherty et al., 2004; Takahashi et al., 2008) , does exactly that. In this algorithm, a Critic module learns values of states in terms of expected future rewards (here, the state includes all available actions, averaging over choices and explicitly not computing the value of each possible choice), and uses these to compute reward prediction errors. These prediction errors are used to learn an action policy in the Actor module: the probability of actions that are followed by positive prediction errors is increased, and the probability of actions that are followed by negative prediction errors is decreased. Under some reasonable conditions, this model learns correct reward-maximizing policies  (Sutton & Barto, 2018) . However, the quantities learned by the Actor-tendencies to perform one action over the other-cannot be read out as action values. In particular, due to the way the algorithm learns, ties are broken between equally good actions such that eventually agents learn deterministic policies. To be clear, if four actions were to lead to 1, 2, 3, and 3 drops of juice, respectively, the model may learn to always choose the third option, or to always choose the fourth (both optimal policies). At the end of learning, action weights in the Actor may be 0, 0, 1, 0 respectively, losing all information about value, or relative value. Even before convergence to a deterministic policy, weights may be 0, 0.1, 0.95, 0.2 respectively (or any other combinationweights here do not have to sum up to 1, and these are just illustrative numbers). Importantly, if the basal ganglia indeed implement an Actor-Critic learning algorithm in the brain, there is no sense in which we can glean action values from the Actor or the Critic. The Actor-Critic model is only one of a class of reinforcementlearning algorithms that learn policies directly, that is, without calculating option values (e.g.,  Sutton et al., 2000; Williams, 1992) . In their general form, these algorithms maintain an action policy, use experience to evaluate a gradient direction for this policy (that is, what change in policy would increase the overall obtained reward), and change the policy in that direction. Another notable model, developed to explain behavioral patterns in choices, is the Experience-Weighted Attraction model of  Camerer and Ho (1999) , which interpolates between value calculation and direct policy learning. Recent findings suggest that both behavior and learning signals measured in humans during decision making are more in line with a policy-learning algorithm than with value estimation. For instance, This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly. THE CASE AGAINST ECONOMIC VALUES  Li and Daw (2011)  had participants choose between two options that gave reward with different probabilities. After each choice, both the outcome of the chosen option and the counterfactual outcome of the unchosen option were displayed. Behavior, as well as neural signals corresponding to prediction errors in the basal ganglia, suggested that subjects were updating both options in opposite directions, learning relative choice propensities (a policy) rather than tracking the expected value of each option. In another task in which humans chose between pairs of options and were able to view both the outcome of their choice and the counterfactual outcome of the forgone option,  Palminteri et al. (2015)  had subjects learn which of two probabilistically rewarding options is better, and which of two probabilistically punishing options was better. At test, subjects were asked to choose between pairs from both the rewarding and the punishing contexts. Surprisingly, when choosing between the less rewarding option and the less punishing option, subjects tended to choose the less punishing option. This is consistent with policy learning, as that option had been the favored option in the punishment context, whereas the less rewarding option had been the disfavored one in the reward context. However, the value of a sometimes-rewarding option is clearly higher than that of a sometimes-punishing option, hence value learning cannot explain this fundamentally suboptimal choice pattern. Direct learning of policies is consistent with basic tenets of decision making, such as the fact that choices are stochastic even when no exploration is necessary or warranted (e.g., choosing between two gambles that are fully described;  Khaw, Li, et al., 2017) . Because policies are relative quantities (preference for one option implies unfavorability of another, as the probabilities of all choices have to sum to one), they also explain common violations of the independence axiom such as the effects of third-option \"decoys\" on choice  (Soltani et al., 2012) , and temporal and spatial contextual influences on choice  (Khaw, Glimcher, et al., 2017) , although these phenomena can also be explained by valuation models that involve range normalization. \n Conclusion The field of neuroeconomics started with the putative identification of pure value signals  (Platt & Glimcher, 1999) . The meaning of these signals was disputed early on  (Maunsell, 2004; Roesch et al., 2006) , but deep questions were set aside as researchers continued to identify brain areas with parts of the computational processes of choice, and in particular, identified the OFC with the seat of economic value. However, while those debates have subsided, the problems they raised have not been resolved. Progress on these issues will require additional data, but we stress that not every experiment that involves choices also implies valuation, and one must be careful in interpreting data not only because of potential confounds, but also because we must be wary of treating a hypothesis-that the brain computes value-as an axiom. We also suggest the need for additional philosophical work to define value in a way that is-at least in principle-dissociable from other factors that promote choices  (Juechems & Summerfield, 2019) . In other words, we argue for a return to the productive debates of the early days of the field, 20 years ago (for neuroeconomics), and earlier (for its psychological underpinnings). Bolstered by an additional 20 years of new data, such debates would surely benefit the field of neuroeconomics moving forward. They would also potentially help reconcile conflicting views on what the OFC might or might not be doing in decision making  (Stalnaker et al., 2015) . \t\t\t We note here that, in neuroeconomics, value-based choices are generally thought to be part of explicit, aware, goal-directed, or model-based decision making that relies on frontal-cortex areas, in particular, the OFC.2 We consider subjective worth as revealed by preference, following neuroeconomic theory, but note the limiting focus on only the \"wanting\" not the \"liking\" side of value (Berridge, 1996) . \n\t\t\t This document is copyrighted by the American Psychological Association or one of its allied publishers.This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.", "date_published": "n/a", "url": "n/a", "filename": "the_case_against_economic_values.tei.xml", "abstract": "Much of traditional neuroeconomics proceeds from the hypothesis that value is reified in the brain, that is, that there are neurons or brain regions whose responses serve the discrete purpose of encoding value. This hypothesis is supported by the finding that the activity of many neurons covaries with subjective value as estimated in specific tasks, and has led to the idea that the primary function of the orbitofrontal cortex is to compute and signal economic value. Here we consider an alternative: That economic value, in the cardinal, common-currency sense, is not represented in the brain and used for choice by default. This idea is motivated by consideration of the economic concept of value, which places important epistemic constraints on our ability to identify its neural basis. It is also motivated by the behavioral economics literature, especially work on heuristics, which proposes value-free process models for much if not all of choice. Finally, it is buoyed by recent neural and behavioral findings regarding how animals and humans learn to choose between options. In light of our hypothesis, we critically reevaluate putative neural evidence for the representation of value and explore an alternative: direct learning of action policies. We delineate how this alternative can provide a robust account of behavior that concords with existing empirical data.", "id": "598b7e21a8f4aa00d56afe02c6689cb3"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Toby Ord", "Rafaela Hillerbrand", "Anders Sandberg", "Francis Rjrr_A_412799 Sgm"], "title": "Probing the improbable: methodological challenges for risks with low probabilities and high stakes", "text": "Introduction Large asteroid impacts are highly unlikely events. 1 Nonetheless, governments spend large sums on assessing the associated risks. It is the high stakes that make these otherwise rare events worth examining. Assessing a risk involves consideration of both the stakes involved and the likelihood of the hazard occurring. If a risk threatens the lives of a great many people, it is not only rational but morally imperative to examine the risk in some detail and to see what we can do to reduce it. This paper focuses on low-probability high-stakes risks. In Section 2, we show that the probability estimates in scientific analysis cannot be equated with the likelihood of these events occurring. Instead of the probability of the event occurring, scientific analysis gives the event's probability conditioned on the given argument being sound. Though this is the case in all probability estimates, we show how it becomes crucial when the estimated probabilities are smaller than a certain threshold. To proceed, we need to know something about the reliability of the argument. To do so, risk analysis commonly falls back on the distinction between model and parameter uncertainty. We argue that this dichotomy is not well suited for incorporating information about the reliability of the theories involved in the risk assessment. Furthermore, the distinction does not account for mistakes made unknowingly. In Section 3, we therefore propose a three-fold distinction between an argument's theory, its model and its calculations. While explaining this distinction in more detail, we illustrate it with historic examples of errors in each of the three areas. We indicate how specific risk assessment can make use of the proposed theory-model-calculation distinction in order to evaluate the reliability of the given argument and thus improve the reliability of their probability estimate for rare events. Recently, concerns have been raised that high-energy experiments in particle physics, such as the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory or the Large Hadron Collider (LHC) at CERN, Geneva, may threaten humanity. If these fears are justified, these experiments pose a risk to humanity that can be avoided by simply not turning on the experiment. In Section 4, we use the methods of this paper to address the current debate on the safety of experiments within particle physics. We evaluate current reports in the light of our findings and give suggestions for future research. The final section brings the debate back to the general issue of assessing low-probability risk. We stress that the findings in this paper are not to be interpreted as an argument for anti-intellectualism, but rather as arguments for making the noisy and fallible nature of scientific and technical research subject to intellectual reasoning, especially in situations where the probabilities are very low and the stakes are very high. \n Probability estimates Suppose you read a report which examines a potentially catastrophic risk and concludes that the probability of catastrophe is one in a billion. What probability should you assign to the catastrophe occurring? We argue that direct use of the report's estimate of one in a billion is naive. This is because the report's authors are not infallible and their argument might have a hidden flaw. What the report has told us is not the probability of the catastrophe occurring, but the probability of the catastrophe occurring, given that the included argument is sound. Even if the argument looks watertight, the chance that it contains a critical flaw may well be much larger than one in a billion. After all, in a sample of a billion apparently watertight arguments you are likely to see many that have hidden flaws. Our best estimate of the probability of catastrophe may thus end up noticeably higher than the report's estimate.  2  Let us use the following notation: X, the catastrophe occurs; A, the argument is sound; P(X), the probability of X and P(X|A), the probability of X given A. While we are actually interested in P(X), the report provides us only with an estimate of P(X|A), since it cannot fully take into account the possibility that it is in error.  3, 4  From the axioms of probability theory, we know that P(X) is related to P(X|A) by the following formula: P X P X A P A P X A P A ( ) ( | ) ( ) ( | ) ( ). ( ) = + ¬ ¬ 1 To use this formula to derive P(X), we would require estimates for the probability that the argument is sound, P(A), and the probability of the catastrophe occurring, given that the argument is unsound, P(X|¬A). We are highly unlikely to be able to acquire accurate values for these probabilities in practice, but we shall see that even crude estimates are enough to change the way we look at certain risk calculations. A special case, which occurs quite frequently, is for reports to claim that X is completely impossible. However, this just tells us that X is impossible, given that all our current beliefs are correct, that is P(X|A) = 0. By Equation (1) we can see that this is entirely consistent with P(X) > 0, as the argument may be flawed. Figure  1  is a simple graphical representation of our main point. The square on the left represents the space of probabilities as described in the scientific report, where the black area represents the catastrophe occurring and the white area represents not occurring. The normalized vertical axis denotes the probabilities for the event occurring and not occurring. This representation ignores the possibility of the argument being unsound. To accommodate this possibility, we can revise it in the form of the square on the right. The black and white areas have shrunk in proportion to the probability that the argument is sound and a new grey area represents the possibility that the argument is unsound. Now, the horizontal axis is also normalized and represents the probability that the argument is sound. Figure  1 . The left panel depicts a report's view on the probability of an event occurring. The black area represents the chance of the event occurring, the white area represents it not occurring. The right-hand panel is the more comprehensive picture, taking into account the possibility that the argument is flawed and that we thus face a grey area containing an unknown amount of risk. To continue our example, let us suppose that the argument made in the report looks very solid, and that our best estimate of the probability that it is flawed is one in a thousand, (P(¬A) = 10 −3 ). The other unknown term in Equation (1), P(X|¬A), is generally even more difficult to evaluate, but for the purposes of the current example, let us suppose that we think it highly unlikely that the event will occur even if the argument is not sound and treat this probability as one in a thousand as well. Equation (1) tells us that the probability of catastrophe would then be just over one in a million -an estimate which is a thousand times higher than that in the report itself. This reflects the fact that if the catastrophe were to actually occur, it is much more likely that this was because there was a flaw in the report's argument than that a one in a billion event took place. Flawed arguments are not rare. One way to estimate the frequency of major flaws in academic papers is to look at the proportions which are formally retracted after publication. While some retractions are due to misconduct, most are due to unintentional errors.  5  Using the MEDLINE database,  7 Cokol et al. (2007)  found a raw Figure  1 . The left panel depicts a report's view on the probability of an event occurring. The black area represents the chance of the event occurring, the white area represents it not occurring. The right-hand panel is the more comprehensive picture, taking into account the possibility that the argument is flawed and that we thus face a grey area containing an unknown amount of risk. retraction rate of 6.3 × 10 −5 , but used a statistical model to estimate that the retraction rate would actually be between 0.001 and 0.01 if all journals received the same level of scrutiny as those in the top tier. This would suggest that P(¬A) > 0.001 making our earlier estimate rather optimistic. We must also remember that an argument can easily be flawed without warranting retraction. Retraction is only called for when the underlying flaws are not trivial and are immediately noticeable by the academic community. The retraction rate for a field would thus provide a lower bound for the rate of serious flaws. Of course, we must also keep in mind the possibility that different branches of science may have different retraction rates and different error rates: the hard sciences may be less prone to error than the more applied sciences. Finally, we can have more confidence in an article, the longer it has been open to public scrutiny without a flaw being detected. It is important to note the particular connection between the present analysis and high-stakes low-probability risks. While our analysis could be applied to any risk, it is much more useful for those in this category. For it is only when P(X|A) is very low that the grey area has a relatively large role to play. If P(X|A) is moderately high, then the small contribution of the error term is of little significance in the overall probability estimate, perhaps making the difference between 10 and 10.001% rather than the difference between 0.001 and 0.002%. The stakes must also be very high to warrant this additional analysis of the risk, for the adjustment to the estimated probability will typically be very small in absolute terms. While an additional one in a million chance of a billion deaths certainly warrants further consideration, an additional one in a million chance of a house fire may not. One might object to our approach on the grounds that we have shown only that the uncertainty is greater than previously acknowledged, but not that the probability of the event is greater than estimated: the additional uncertainty could just as well decrease the probability of the event occurring. When applying our approach to arbitrary examples, this objection would succeed; however in this paper, we are specifically looking at cases where there is an extremely low value of P(X|A), so practically any value of P(X|¬A) will be higher and thus drive the combined probability estimate upwards. The situation is symmetric with regard to extremely high estimates of P(X|A), where increased uncertainty about the argument will reduce the probability estimate, the symmetry is broken only by our focus on arguments which claim that an event is very unlikely. Another possible objection is that since there is always a non-zero probability of the argument being flawed, the situation is hopeless: any new argument will be unable to remove the grey area completely. It is true that the grey area can never be completely removed; however, if a new argument (A 2 ) is independent of the previous argument (A 1 ), then the grey area will shrink, for P(¬A 1 , ¬A 2 ) < P(¬A 1 ). This can allow for significant progress. A small remaining grey area can be acceptable if P(X|¬A) P(¬A) is estimated to be sufficiently small in comparison to the stakes. \n Theories, models and calculations The most common way to assess the reliability of an argument is to distinguish between model and parameter uncertainty and assign reliabilities to these choices. While this distinction has certainly been of use in many practical cases, it is unnecessarily crude for the present purpose, failing to account for potential errors in the paper's calculations or a failure of the background theory. In order to account for all possible mistakes in the argument, we look separately at its theory, its model and its calculations. The calculations evaluate a concrete model representing the processes under consideration, for example the formation of black holes in a particle collision, the response of certain climate parameters (such as mean temperature or precipitation rate) to changes in greenhouse gas concentrations or the response of economies to changes in the oil price. These models are mostly derived from more general theories. In what follows, we do not restrict the term 'theory' to well-established and mathematically elaborate theories like electrodynamics, quantum chromodynamics or relativity theory. Rather, theories are understood to include theoretical background knowledge, such as specific research paradigms or the generally accepted research practice within a field (see Figure  2 ). An example is the efficient market hypothesis which underlies many models within economics, such as the Black-Scholes model. We consider adequate models or theories rather than correct ones. For example, we wish to allow that Newtonian mechanics is an adequate theory in many situations, while recognizing that in some cases it is clearly inadequate (such as for calculating the electron orbitals). We thus call a representation of some system adequate if it is able to predict the relevant system features at the required precision. For example, if climate modellers wish to determine the implications our greenhouse gas emissions will have on the well-being of future generations, their model/theory will not be adequate unless it tells them the changes in the local temperature and precipitation. In contrast, a model might only need to tell them changes in global temperature and precipitation to be adequate for answering less sensitive questions. On a theoretical level, much more could be said about this distinction between adequacy and correctness, but for the purposes of evaluating the reliability of risk assessment, the explanation above should suffice. With the following notation: T, the involved theories are adequate; M, the derived model is adequate; and C, the calculations are correct, we can represent P(A) as P(T, M, C). We can then benefit from the theory-model-calculation distinction by expressing this as the product of three separate probabilities, each of which should be easier to estimate than P(A). Firstly, from the laws of conditional probability, it follows that P(T, M, C) = P(T) P(M|T) P(C|M, T). This can be simplified as we can assume C to be independent of M and T, since the correctness of a calculation is independent of whether the theoretical and model assumptions underpinning it were adequate. Given this independence P(C|M, T) = P(C), the above equation can be simplified to: Substituting this back into Equation (1), we obtain a more tractable formula for P(X). P A P T P M T P C ( ) ( ) ( | ) ( ). ( ) = 2 We have already made a rough attempt at estimating P(A) from the paper retraction rates. Estimating P(T), P(M|T) and P(C) is more accurate and somewhat easier, though still of significant difficulty. While estimating the various terms in Equation (  2 ) must ultimately be done on a case-by-case basis, the following elucidation of what we mean by theory, model and calculation will shed some light on how to pursue such an analysis. By incorporating our threefold distinction, it is straightforward to apply findings on the reliability of theories from philosophy of science -based, for example, on probabilistic verification methods (e.g.  Reichenbach 1938)  or falsifications as in  Hempel (1950)  or  Popper (1959) . Often, however, the best we can do is to put some bounds upon them based on the historical record. We thus review typical sources of error in the following three areas. \n Calculation: analytic and numeric Estimating the correctness of the calculation independently from the adequacy of the model and the theory seems important whenever the mathematics involved is non-trivial. Most cases where we are able to provide more than purely heuristic and hand-waving risk assessments are of this sort. Consider climate models evaluating runaway climate change and risk estimates for the LHC or for asteroid impacts. When calculations accumulate, even trivial mathematical procedures become error-prone. A particular difficulty arises due to the division of labour in the sciences: commonly in modern scientific practice, various steps in a calculation are done by different individuals who may be in different working groups in different countries. The Mars Climate Observer spacecraft was lost in 1999 because a piece of control software from Lockheed Martin used imperial units instead of the metric units the interfacing NASA software expected (NASA 1999). Calculation errors are distressingly common. There are no reliable statistics on the calculation errors made in risk assessment or, even more broadly, within scientific papers. However, there is research on errors made in some very simple calculations performed in hospitals. Dosing errors give an approximate estimate of how often mathematical slips occur. Errors in drug charts occur at a rate of 1.2-31% across different studies  (Prot et al. 2005; Stubbs, Haw, and Taylor 2006; Walsh et al. 2008) , with a median of roughly 5% of administrations. Of these errors, 15-40% were dose errors, giving an overall dose error rate of about 1-2%. What does this mean for error rates in risk estimation? Since the stakes are high when it comes to dosing errors, this data represents a serious attempt to get the right answer in a life or death circumstance. It is likely that the people doing risk estimation are more reliable at arithmetic than health professionals and have more time for error correction, but it appears unlikely that they would be more reliable in many orders of magnitude. Hence, a chance of 10 −3 for a mistake per simple calculation does not seem unreasonable. A random sample of papers from Nature and the British Medical Journal found that roughly 11% of statistical results were flawed, largely due to rounding and transcription errors (García-Berthou and Alcaraz 2004). Calculation errors include more than just the 'simple' slips which we know from school, such as confusing units, forgetting a negative square root or incorrectly transcribing from the line above. Instead, many mistakes arise here due to numerical implementation of the analytic mathematical equations. Computer-based simulations and numerical analysis are rarely straightforward. The history of computers contains a large number of spectacular failures due to small mistakes in hardware or software. The 4 June 1996 explosion of an Ariane 5 rocket was due to a leftover piece of code triggering a cascade of failures  (ESA 1996) . Audits of spreadsheets in real world use find error rates on the order of 88%  (Panko 1998) . The 1993 Intel Pentium floating point error affected 3-5 million processors, reducing their numeric reliability and hence our confidence in anything calculated with them  (Nicely 2008) . Programming errors can remain dormant for a long time even in apparently correct code, only to emerge under extreme conditions. An elementary and widely used binary search algorithm included in the standard libraries for Java was found after nine years to contain a bug that emerges only when searching very large lists  (Bloch 2006) . A mistake in data processing led to the retraction of five high-profile protein structure papers as the handedness of the molecules had become inverted  (Miller 2006) . In cases where computational methods are used in modelling, many mistakes cannot be avoided. Discrete approximations of the often continuous model equations are used, and in some cases we know that the discrete version is not a good proxy for the continuous model  (Morawetz and Walke 2003) . Moreover, numerical evaluations are often done on a discrete computational grid, with the values inside the meshes being approximated from the values computed at the grid points. Though we know that certain extrapolation schemes are more reliable in some cases than others, we are often unable to exclude the possibility of error, or to even quantify it. \n Ways of modelling and theorizing Our distinction between model and theory follows the typical use of the terms within mathematical sciences like physics or economics. Whereas theories are associated with broad applicability and higher confidence in the correctness of their description, models are closer to the phenomena. For example, when estimating the probability of a particular asteroid colliding with the Earth, one would use either Newtonian mechanics or general relativity as a theory for describing the role of gravity. One could then use this theory in conjunction with observations of the bodies' positions, velocities and masses to construct a model, and finally, one could perform a series of calculations based on this model to estimate the probability of impact. As this shows, the errors that can be introduced in settling for a specific model include and surpass those which are sometimes referred to as parameter uncertainty. As well as questions of the individual parameters (positions, velocities and masses), there are important questions of detail (Can we neglect the inner structure of the involved bodies?), and breadth (Can we focus on the Earth and asteroid only, or do we have to model other planets, or the Sun?).  7  As can be seen from this example, one way to distinguish theories from models is that theories are too general to be applied directly to the problem. For any given theory, there are many ways to apply it to the problem and these ways give rise to different models. Philosophers of science will note that our theory-model distinction is in accordance with the non-uniform notion used by  Giere (1999) ,  Morrison (1998) ,  Cartwright (1999) , and others, but differs from that of the semantic interpretation of theories  (Suppes 1957) . We should also note that it is quite possible for an argument to involve several theories or several models. This complicates the analysis and typically provides additional ways for the argument to be flawed.  8  For example, in estimating the risk of black hole formation at the LHC, we not only require quantum chromodynamics (the theory on which the LHC is built to test), but also relativity and Hawking's theory of black hole radiation. In addition to their other roles, modelling assumptions also have to explain how to glue such different theories together  (Hillerbrand and Ghil 2008) . In risk assessment, the systems involved are most often not as well understood as asteroid impacts. Often, various models exist simultaneously -all known to be incomplete or incorrect in some way, but difficult to improve upon. 9 Particularly in these cases, having an expected or desired outcome in mind while setting up a model makes one vulnerable to expectation bias: the tendency to reach the desired answer rather than the correct one. This bias has affected many of science's great names  (Jeng 2006) , and in the case of risk assessment, the desire for a 'positive' outcome (safety in the case of the advocate or danger in the case of the protestor) seems a likely cause of bias in modelling. \n Historical examples of model and theory failure A dramatic example of a model failure was the Castle Bravo nuclear test on 1 March 1954. The device achieved 15 megatons of yield instead of the predicted four to eight megatons. Fallout affected parts of the Marshal Islands and irradiated a Japanese fishing boat so badly that one fisherman died, causing an international incident (Nuclear Weapon Archive 2006). Though the designers at Los Alamos National Laboratories understood the involved theory of alpha decay, their model of the reactions involved in the explosion was too narrow, for it neglected the decay of one of the involved particles (lithium-7), which turned out to contribute the bulk of the explosion's energy. The Castle Bravo test is also notable for being an example of model failure in a very serious experiment conducted in the hard sciences and with known high stakes. The history of science contains numerous examples of how generally accepted theories have been overturned by new evidence or understanding, as well as a plethora of minor theories that persisted for a surprising length of time before being disproven. Classic examples for the former include the Ptolemaic system, phlogiston theory and caloric theory; an example for the latter is human chromosome number, which was systematically miscounted as 48 (rather than 46) and this error persisted for more than 30 years  (Gartler 2006 ). As a final example, consider Lord Kelvin's estimates of the age of the Earth  (Burchfield 1975) . They were based on information about the earth's temperature and heat conduction, estimating an age of the Earth between 20 and 40 million years. These estimates did not take into account radioactive heating, for radioactive decay was unknown at the time. Once it was shown to generate additional heat the models were quickly updated. While neglecting radioactivity today would count as a model failure, in Lord Kelvin's day it represented a largely unsuspected weakness in the physical understanding of the Earth and thus amounted to theory failure. This example makes it clear that the probabilities for the adequacy of model and theory are not independent of each other, and thus in the most general case we cannot further decompose Equation (2). \n Applying our analysis to the risks from particle physics research Particle physics is the study of the elementary constituents of matter and radiation, and the interactions between them. A major experimental method in particle physics involves the use of particle accelerators, such as the RHIC and LHC, to bring beams of particles near the speed of light and then collide them together. This focuses a large amount of energy in a very small region and breaks the particles down into their components, which are then detected. As particle accelerators have become larger, the energy densities achieved have become more extreme, prompting some concern about their safety. These safety concerns have focused on three possibilities: the formation of 'true vacuum', the transformation of the Earth into 'strange matter', and the destruction of the Earth through the creation of a black hole. \n True vacuum and strange matter formation The type of vacuum that exists in our universe might not be the lowest possible vacuum energy state. In this case, the vacuum could decay to the lowest energy state, either spontaneously, or if triggered by a sufficient disturbance. This would produce a bubble of 'true vacuum' expanding outwards at the speed of light, converting the universe into different state apparently inhospitable for any kind of life  (Turner and Wilczek 1982) . Our ordinary matter is composed of electrons and two types of quarks: up quarks and down quarks. Strange matter also contains a third type of quark: the 'strange' quark. It has been hypothesized that strange matter might be more stable than normal matter, and able to convert atomic nuclei into more strange matter  (Witten 1984) . It has also been hypothesized that particle accelerators could produce small negatively charged clumps of strange matter, known as strangelets. If both these hypotheses were correct and the strangelet also had a high enough chance of interacting with normal matter, it would grow inside the Earth, attracting nuclei at an ever higher rate until the entire planet was converted to strange matter -destroying all life in the process. Unfortunately, strange matter is complex and little understood, giving models with widely divergent predictions about its stability, charge and other properties  (Jaffe et al. 2000) . One way of bounding the risk from these sources is the cosmic ray argument: the same kind of high-energy particle collisions occur all the time in Earth's atmosphere, on the surface of the Moon and elsewhere in the universe. The fact that the Moon or observable stars have not been destroyed despite a vast number of past collisions (many at much higher energies than can be achieved in human experiments) suggests that the threat is negligible. This argument was first used against the possibility of vacuum decay  (Hut and Rees 1983)  but is quite general. An influential analysis of the risk from strange matter was carried out in  Dar, De Rujula, and Heinz (1999)  and formed a key part of the safety report for the RHIC. This analysis took into account the issue that any dangerous remnants from cosmic rays striking matter at rest would be moving at high relative velocity (and hence much less likely to interact) while head-on collisions in accelerators could produce remnants moving at much slower speeds. They used the rate of collisions of cosmic rays in free space to estimate strangelet production. These strangelets would then be slowed by galactic magnetic fields and eventually be absorbed during star formation. When combined with estimates of the supernova rate, this can be used to bound the probability of producing a dangerous strangelet in a particle accelerator. The resulting probability estimate was < 2 × 10 −9 per year of RHIC operation.  10  While using empirical bounds and experimentally tested physics reduces the probability of a theory error, the paper needs around 30 steps to reach its conclusion. For example, even if there was just a 10 −4 chance of a calculation or modelling error per step this would give a total P(¬A) ≈ 0.3%. This would easily overshadow the risk estimate. Indeed, even if just one step had a 10 −4 chance of error, this would overshadow the estimate. A subtle complication in the cosmic ray argument was noted in  Tegmark and Bostrom (2005) . The Earth's survival so far is not sufficient as evidence for safety, since we do not know if we live in a universe with 'safe' natural laws or a universe where planetary implosions or vacuum decay do occur, but we have just been exceedingly lucky so far. While this latter possibility might sound very unlikely, all observers in such a universe would find themselves to be in the rare cases where their planets and stars had survived, and would thus have much the same evidence as we do. Tegmark and Bostrom had thus found that in ignoring these anthropic effects, the previous model had been overly narrow. They corrected for this anthropic bias and, using analysis from  Jaffe et al. (2000) , concluded that the risk from accelerators was less than 10 −12 per year. This is an example of a demonstrated flaw in an important physics risk argument (one that was pivotal in the safety assessment of the RHIC). Moreover, it is significant that the RHIC had been running for five years on the strength of a flawed safety report, before Tegmark and Bostrom noticed and fixed this gap in the argument. Although this flaw was corrected immediately after being found, we should also note that the correction is dependent on both anthropic reasoning and on a complex model of the planetary formation rate  (Lineweaver, Fenner, and Gibson 2004) . If either of these or the basic Brookhaven analysis is flawed, the risk estimate is flawed. \n Black hole formation The LHC experiment at CERN was designed to explore the validity and limitations of the standard model of particle physics by colliding beams of high-energy protons. This will be the most energetic particle collision experiment ever done, which has made it the focus of a recent flurry of concerns. Due to the perceived strength of the previous arguments on vacuum decay and strangelet production, most of the concern about the LHC has focused on black hole production. None of the theory papers we have found appears to have considered the black holes to be a safety hazard, mainly because they all presuppose that any black holes would immediately evaporate due to Hawking radiation. However, it was suggested by  Dimopoulos and Landsberg (2001)  that if black holes form, particle accelerators could be used to test the theory of Hawking radiation. Thus, critics also began questioning whether we could simply assume that black holes would evaporate harmlessly. A new risk analysis of LHC black hole production (Giddings and Mangano 2008) provides a good example of how risks can be more effectively bounded through multiple sub-arguments. While never attempting to give a probability of disaster (rather concluding 'there is no risk of any significance whatsoever from such black holes'), it uses a multiple bounds argument. It first shows that rapid black hole decay is a robust consequence of several different physical theories (A 1 ). Second, it discusses the likely incompatibility between non-evaporating black holes and mechanisms for neutralizing black holes: in order for cosmic ray-produced stable black holes to be innocuous but accelerator-produced black holes to be dangerous, they have to be able to shed excess charge rapidly (A 2 ). Our current understanding of physics suggests both that black holes decay and that even if they did not, they would be unable to discharge themselves. Only if this understanding is flawed will the next section come into play. The third part, which is the bulk of the paper, models how multidimensional and ordinary black holes would interact with matter. This leads to the conclusion that if the size scale of multidimensional gravity is smaller than about 20 nm, then the time required for the black hole to consume the Earth would be larger than the natural lifetime of the planet. For scenarios where rapid Earth accretion is possible, the accretion time inside white dwarves and neutron stars would also be very short, yet production and capture of black holes from impinging cosmic rays would be so high that the lifespan of the stars would be far shorter than the observed lifespan (and would contradict white dwarf cooling rates) (A 3 ). The force of the total argument (A 1 , A 2 , A 3 ) is significantly stronger than any of its parts. Essentially, the paper acts as three sequential arguments, each partly filling in the grey area (see Figure  1 ) left by the previous. If the theories surrounding black hole decay fail, the argument about discharge comes into play; and if against all expectation black holes are stable and neutral, the third argument shows that astrophysics constrains them to a low accretion rate. \n Implications for the safety of the LHC What are the implications of our analysis for the safety assessment of the LHC? Firstly, let us consider the stakes in question. If one of the proposed disasters were to occur, it would mean the destruction of the Earth. This would involve the complete destruction of the environment, 6.5 billion human deaths and the loss of all future generations. It is worth noting that this loss of all future generations (and with it, all of humanity's potential) may well be the greatest of the three, but a comprehensive assessment of these stakes is outside the scope of this paper. For the present purposes, it suffices to observe that the destruction of the Earth is at least as bad as 6.5 billion human deaths. There is some controversy as to how one should combine probabilities and stakes into an overall assessment of a risk. Some hold that the simple approach of expected utility is the best, while others hold some form of risk aversion. However, we can sidestep this dispute by noting that in either case, the risk of some harm is at least as bad as the expected loss. Thus, a risk with probability p of causing a loss at least as bad as 6.5 billion deaths is at least as bad as a certain 6.5 × 10 9 p deaths. Now let us turn to the best estimate we can make of the probability of one of the above disasters occurring during the operation of the LHC. While the arguments for the safety of the LHC are commendable for their thoroughness, they are not infallible. Although the report considered several possible physical theories, it is eminently possible that these are all inadequate representations of the underlying physical reality. It is also possible that the models of processes in the LHC or the astronomical processes appealed to in the cosmic ray argument are flawed in an important way. Finally, it is possible that there is a calculation error in the report. In Equation (1), P(X) is the sum of two terms. The second of these represents the additional probability of disaster due to the argument being unsound. It is the product of the probability of argument failure and the probability of disaster given such a failure. Both terms are very difficult to estimate, but we can gain insight by showing the ranges they would have to lie within, for the risk presented by the LHC to be acceptable. If we let l denote the acceptable limit of expected deaths from the operation of the LHC, we get: 6.5 × 10 9 P(X) ≤ l. Since P(X) is at least as great as its second term, we obtain: This inequality puts a severe bound on the acceptable values for these probabilities. Since it is much easier to grasp this with an example, we shall provide some numbers for the purposes of illustration. Suppose, for example, that if the limits were set at 1000 expected deaths, then P(X|¬A) P(¬A) would have to be below 1.5 × 10 −7 for the risk to be worth bearing. This requires very low values for these probabilities. We have seen that for many arguments, P(¬A) is above 10 −3 . We have also seen that the argument for the safety of the RHIC turned out to have a significant flaw, which was unnoticed by the experts at the time. It would thus be very bold to suppose that the argument for the safety of the LHC was much lower than 10 −3 , but for the sake of argument, let us grant that it is as low as 10 −4 -that out of a sample of 10,000 independent arguments of similar apparent merit, only one would have any serious error. Even if the value of P(¬A) were as low as 10 −4 , P(X|¬A) would have to be below 0.15% for the risk to be worth taking. P(X|¬A) is the probability of disaster, given that the arguments of the safety report are flawed and is the most difficult component of Equation (  1 ) to estimate. Indeed, few would dispute that we really have very little idea of what value to put on P(X|¬A). It would thus seem overly bold to set this below 0.15% without some substantive argument. Perhaps such an argument could be provided, but until it is, such a low value for P(X|¬A) seems unwarranted. We stress that the above combination of numbers was purely for illustrative purposes, but we cannot find any plausible combination of the three numbers which meets the bound and which would not require significant argument to explain either the levels of confidence or the disregard for expected deaths. We would also like to stress that we are open to the possibility that additional supporting arguments and independent verification of the models and calculations could significantly reduce the current chance of a flaw in the argument. However, our analysis implies that the current safety report should not be the final word in the safety assessment of the LHC. To proceed with the LHC on the arguments of the most recent safety report alone, we would require further work on estimating P(¬A), P(X|¬A), the acceptable expected death toll, and the value of future generations and other life on Earth. Such work would require expertise beyond theoretical physics, and an interdisciplinary group would be essential. If the stakes were lower, then it might make sense for pragmatic concerns to sweep aside this extra level of risk analysis, but the stakes are astronomically large, and so further analysis is critical. Even if the LHC goes ahead without any further analysis, as is very likely, these lessons must be applied to the assessment of other high-stakes low-probability risks. \n Conclusions When estimating threat probabilities, it is not enough to make conservative estimates (using the most extreme values or model assumptions compatible with known data). Rather, we need robust estimates that can handle theory, model and calculation errors. The need for this becomes considerably more pronounced for low-probability high-stake events, though we do not say that low probabilities cannot be treated systematically. Some people have raised the concern that our argument might be too powerful, for it is impossible to disprove the risk of even something as trivial as dropping a pencil, P X A P A l ( | ) ( ) . . ( ) ¬ ¬ ≤ × − 1 5 10 3 then our argument might amount to prohibiting everything. It is true that we cannot completely rule out any probability that apparently inconsequential actions might have disastrous effects, but there are a number of reasons why we do not need to worry about universal prohibition. A major reason is that for events like the dropping of a pencil which have no plausible mechanism for destroying the world, it seems just as likely that the world would be destroyed by not dropping the pencil. The expected losses would thus balance out. It is also worth noting that our argument is simply an appeal to a weak form of decision theory to address an unusual concern: for our method to lead to incorrect conclusions, it would require a flaw in decision theory itself, which would be very big news. It will have occurred to some readers that our argument is fully applicable to this very paper: there is a chance that we have made an error in our own arguments. We entirely agree, but note that this possibility does not change our conclusions very much. Suppose, very pessimistically, that there is a 90% chance that our argument is sufficiently flawed that the correct approach is to take safety reports' probability estimates at face value. Even then, our argument would make a large difference to how we treat such values. Recall the example from Section 2, where a report concludes a probability of 10 −9 and we revise this to 10 −6 . If there is even a 10% chance that we are correct in doing so, then the overall probability estimate would be revised to 0.9 × 10 −9 + 0.1 × 10 −6 ≈ 10 −7 , which is still a very significant change from the report's own estimate. In short, even serious doubt about our methods should not move one's probability estimates more than an order of magnitude away from those our method produces. More modest doubts would have negligible effect. The basic message of this paper is that any scientific risk assessment is only able to give us the probability of a hazard occurring conditioned on the correctness of its main argument. The need to evaluate the reliability of the given argument in order to adequately address the risk was shown to be of particular relevance in low-probability high-stake events. We drew a three-fold distinction between theory, model and calculation, and showed how this can be more useful than the common dichotomy in risk assessment between model and parameter uncertainties. By providing historic examples for errors in the three fields, we clarified the three-fold distinction and showed where flaws in a risk assessment might occur. Our analysis was applied to the recent assessment of risks that might arise from experiments within particle physics. To conclude this paper, we now provide some very general remarks on how to avoid argument flaws when assessing risks with high stakes. Firstly, the testability of predictions can help discern flawed arguments. If a risk estimate produces a probability distribution for smaller, more common disasters, this can be used to judge whether the observed incidences are compatible with the theory. Secondly, reproducibility appears to be the most effective way of removing many of these errors. By having other people replicate the results of calculations independently, our confidence in them can be dramatically increased. By having other theories and models independently predict the same risk probability, our confidence in them can again be increased, as even if one of the arguments is wrong the others will remain. Finally, we can reduce the possibility of unconscious bias in risk assessment through the simple expedient of splitting the assessment into a 'blue' team of experts attempting to make an objective risk assessment and a 'red' team of devil's advocates attempting to demonstrate a risk, followed by repeated turns of mutual criticism and updates of the models and estimates  (Calogero 2000) . Application of such methods could in many cases reduce the probability of error by several orders of magnitude. Figure 2 . 2 Figure 2. Ways in which risk assessments can be flawed. \n Figure 2 . 2 Figure 2. Ways in which risk assessments can be flawed. \n\t\t\t *Corresponding author. Email: toby.ord@philosophy.ox.ac.uk", "date_published": "n/a", "url": "n/a", "filename": "proving_the_improbable.tei.xml", "abstract": "Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calcultions often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons, such as a flaw in the underlying theory, a flaw in the modelling of the problem or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinction between model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it.", "id": "4bc80bb3e63227b696c10e0cdce4aefa"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong", "Nick Bostrom", "Carl Shulman"], "title": "Racing to the precipice: a model of artificial intelligence development", "text": "Introduction This paper presents a simplified model for analysing technology races. The model was designed initially for races to construct artificial intelligences (AIs). But it can be applied to other similar races or competitions, especially technological races where there is a large advantage to reaching the goal first. There are arguments that the first true AIs are likely to be extremely powerful machines  [Goo65, Cha10] , but that they could end up being dangerous  [Omo08, Yud08]  if not carefully controlled  [ASB12] . The purpose of various research projects such as 'friendly AI'  [MS12]  is to design safety precautions ensuring the creation of an AI with human-compatible values. In this paper, we won't go that far. We will simply assume that there is a definite probability of an AI-related disaster, and that the probability goes up the more the AI development team skimps on precautions. This paper will present a model of an 'arms race' between AI development teams, and analyse what factors increase and decrease the probability of such an AI-disaster. Several factors contribute to increasing the danger: if building the AI depends more on risk-taking than on skill, for instance. Reducing the enmity between AI development teams helps, however, as does reducing the number of teams. But surprisingly, extra information can exacerbate the danger. The danger is minimised when each team is ignorant of the AI-building capabilities of every team -including their own capabilities. This is an interesting example of an information hazard  [Bos11] . \n The model In this model, there are n different teams, competing to build the first proper AI. Each team has a certain level of AI-building capability c, and can choose to take a certain level of safety precautions s, varying between s = 1 (total safety) and s = 0 (complete lack of precautions). Then each team gets a score by subtracting their safety from their capability (c − s), and the team with the highest score 'wins', by building their AI first. Once that AI is built, we need to check for the success of the project: That will depend on the safety level of the winning team 1 . With probability s, they have a successful and profitable AI project. With probability 1 − s, they have caused an AI-disaster. We'll assume that each team maximises expected utility, and we can renormalise their utilities to give utility 1 for a successful AI project, and 0 for an AI-disaster. We will further assume that each team has the same level of enmity e towards each other team. This means that they will have a utility of 1 − e if another team builds a successful AI before they do. This varies between e = 0 (they are indifferent to who builds an AI) and e = 1 (another team building a successful AI is just as bad as an AI-disaster). It would be possible to have enmities above 1 (this would correspond to teams that hate each other so much that an AIdisaster is preferable to the triumph of the other team), but that is beyond the scope of the current paper. Further, we'll assume that each team's capability is drawn independently and uniformly on the interval [0, µ], for a single given µ. A high µ corresponds to a situations where capability is the dominant factor in AI development: one can achieve very little extra by skimping on precautions. Conversely, for low µ, incurring increased risk can make one much more likely to build the first AI. We'll assume that the teams choose their safety based on Nash equilibrium considerations (this could happen in practice if, for instance, each team reduced their safety a little bit, then a little bit more, then a little bit more, in response to the other teams reducing their own safety). We'll then calculate the Nash equilibria in three information scenarios: when teams don't know anyone's capabilities, when they know their own capabilities, and when they know everyone's capabilities 2 . \n No information In this situation, every team is ignorant of their own or any other team's capabilities 3 . Each team will thus choose the level of safety the think is best. In a symmetric Nash equilibrium, this will be a single number s. Since all teams draw their capabilities from independent identically distributed random variables, and have the same level of safety, they each have the same probability of winning, namely 1/n. Upon changing s to s − , a team's chance of winning increases by 1 µ + O( ). The utility gain from winning rather than letting another win is the safety level s times the enmity e. So the extra expected utility from winning is se µ + O( ). But the decrease in safety brings in extra risks, were the team to win anyway. This extra risk is simply time the probability of winning: n + O( ). All other effects are second order in . Setting the change to be zero (to first order) in , the general solution is thus s = µ en µ < en 1 µ ≥ en. The total probability of AI-disaster is 1 − s, namely: 1 − µ en µ < en 0 µ ≥ en. \n Private information In this scenario, each team knows its own capabilities, but not those of the other teams. Each team will choose a safety level s(x), dependent on their own capabilities x. In a symmetric Nash equilibrium, each team chooses the same function s. We may assume x − s(x) is a function increasing in x 4 . In that case, the team with the highest x, the highest capabilities, always wins. Given x, the probability of a team winning is equal to the probability of all other teams having lower capability: this is x µ n−1 . Then changing s(x) to s(x) − , the team increases its probability of winning by: (n − 1)x n−2 (1 − s (x))µ n−1 + O( ). As in the previous case, the expected extra utility is se times this: se(n − 1)x n−2 (1 − s (x))µ n−1 + O( ). The loss in expected utility coming from winning at a lower safety level is: x µ n−1 + O( ). Solving these equations gives: s(x) = x en−e+1 x < en − e + 1 1 x ≥ en − e + 1. The total probability of a AI-disaster is calculated by integrating, across all values of x in [0, µ], the risk level 1 − s(x) times the probability that the winning team will have capability x: µ 0 (1 − s(x)) nx n−1 µ n dx = 1 − µn (n+1)(ne−e+1) µ < en − e + 1 (en−e+1) n (n+1)µ n µ ≥ en − e + 1. \n Public information In this scenario, every team knows the capabilities of every other team. This scenario is analysed somewhat differently that the other. Let ∆ be the difference between the capability of the top team and the second ranked team. The top team always wins, but its safety level s top is determined by ∆. When s top (∆) = ∆/e, it is not in the interest of the second team to decrease its safety to compete with the top team. The gain from winning does not compensate for the extra risks run. Thus the safety of the top team will be s top = ∆/e if ∆/e < 1 and 1 otherwise. The total probability AI-disaster is calculated by integrating, across all values of ∆ in [0, µ], the risk level 1−s top (∆) = 1−∆/e times the probability that the difference between the top two teams is ∆: µ 0 (1 − s top (∆)) n(µ − ∆) n−1 µ n d∆ = 1 − µ e(n+1) µ < e (µ−e) n+1 e(n+1)µ n − µ e(n+1) + 1 µ ≥ e. 3 Factors determining risk \n Capability vs risk Intuitively it is clear that increasing the importance of capability must decrease overall risk. One is less inclined to skimp on safety precautions if can only get a small advantage from doing so. This intuition is born out by the results: in every situation, an increase of the importance of capability (an increase in µ) reduces the risk. This is illustrated in figures 1a and 1b, as well as all subsequent figures, demonstrating that the probability of AI-disaster are always decreasing in µ. Indeed, around µ = 0 (i.e. when capability is nearly irrelevant to producing the first AI), the only Nash equilibrium is to take no safety precautions at all. In terms of intervention, there is little we can do about the relative importance of capability, since this is largely determined by the technology. Our best bet might be at present to direct research into approaches where there is little return to risk-taking, prioritising some technological paths over others.   \n Compatible goals It is also intuitively clear that reducing enmity should reduce the risk of AIdisaster. When competition gets less fierce, teams would be willing to take less risks. This intuition is also born out in our model, as decreases in e always reduce the risk. For illustration, contrast the graphs 2a and 2b, where the enmity is 0.5, with the previous graphs 1a and 1b where the enmity was 1.  Enmity is something that we can work on by, for instance, building trust between nations and groups, sharing technologies or discoveries, merging into joint projects or agreeing to common aims. With this extra coordination, we could also consider agreements to allow the teams to move away from the Nash equilibrium, thus avoiding a race to the bottom when the situation is particularly dangerous (such as low capability µ). Friendly teams make friendly AIs. \n The curse of too much information Contrasting figure  1a  with figure  2a  (or figure  1a  with figure  2b ), one notices a curious pattern. The no-information case is always safer than the other two cases, but the relative safety of private information or common information depends on the degree on enmity. It is always better if none of the teams have any idea about anyone's capability. For maximal enmity (e = 1), the private information scenario is similarly safer than the common information one. But for lower e, this does not hold: for low µ and low e, the public information scenario can be safer than the private one. Asymptotically, though, the private information case is of order of 1/µ n , while the public information case is of order 1/µ. The reasons for this is that it is only worth taking risks in the private information if one's capability is low. So to get a high risk, one needs a winner with low capability, which is equivalent to having all teams at low capability. The probability of having a single team at low capability diminishes inversely with µ. Hence the probability of having all teams at low capability diminishes as 1/µ n . In the public information case, the winner will take risks if the second ranked team is close to its own capability. Being close to a specific other team is inversely proportional to µ, and hence the probability of this diminishes as 1/µ. Our ability to manipulate the information levels of the teams or teams is likely to be somewhat limited, though we can encourage them to share more (in the low capability, low enmity situations) or alternatively to lock up their private knowledge 5 (in situation of higher capability or enmity). \n The number of competitors Finally, we can consider what happens when more teams are involved. Intuitively, competition might spur a race to the bottom if there are too many teams, and the model bears this out: in both the no-information and public information cases, adding extra teams strictly increases the dangers. The private information case is more complicated. At low capability, adding more teams will certainly worsen the situation, but at higher capability, the effect is reversed 6 . This can be seen in figure  3 , which plots the private information risk curves for two teams and five teams. In terms of leverage, the most helpful intervention we could undertake to reduce the number of teams is to encourage groups to merge. Dividing teams would only be useful in very specific situations, and would need some method of ensuring that the divided teams did not recall each other's capabilities. \n Conclusion We've presented a model of AI arms race (which can be extended to other types of arms races and competitions) in which teams of AI designers can get ahead by skimping on safety. If the race takes some time there is a persistent Figure  3 : Risk of dangerous AI arms race for private information teams, at enmity 0.5, plotted against relative importance of capability. The graph for two teams is full, the graph for five teams is dashed. ratchet effect (or race to the bottom) in which each team reduces their safety precautions slightly, until a Nash equilibrium is reached-possibly one of very high danger. Several factors influence on the probability of AI disaster, three in an intuitive way, and one counter-intuitively. Intuitively, if capability is much more important than the level of security precautions taken, the overall outcome is safer. Similarly, reduced enmity between the teams produces better outcomes, as does reducing the number of teams (in most situations). Counter-intuitively, increasing the information available to all the teams (about their own capability or progress towards AI, or that of the other teams) increases the risk. This is a special case of an information hazard  [Bos11] : we'd be better off not knowing. This model and variants of if may be of use in planning and regulating the development of AIs and other disruptive technological innovations. Figure 1 : 1 Figure1: Risk of dangerous AI arms race for two and five teams, at enmity 1, plotted against relative importance of capability. Three information-level scenarios: no capability information (full), private capability information (dashes), and full capability information (dots). \n Figure 2 : 2 Figure2: Risk of dangerous AI arms race for two and five teams, at enmity 0.5, plotted against relative importance of capability. Three information-level scenarios: no capability information (full), private capability information (dashes), and full capability information (dots). \n\t\t\t And only the winning team -if another team gets a disastrous AI first by taking lower precautions, they will 'won' the race to build the first AI.2 Of course, the model can be refined in various ways. One could make capacity information uncertain and fuzzy, one could have different levels of enmity between different teams, one could incorporate uncertainty about the safety levels and the ultimate outcomes, and so on. Or one could have a dynamic process to determine the outcome, rather than rushing straight to the Nash equilibrium. But the simple model is enough to gain useful insights.3 It may seem unusual for teams to not know their own capabilities in the real world. However, this is close to the situation we find ourselves with current AI research: people and organisations have a pretty clear idea of what resources and knowledge they have, but don't know how hard AI is or what routes are most likely to lead there. They are thus effectively ignorant of their own AI-building capabilities. \n\t\t\t If makes no sense that a team with higher capability would have a lower chance of winning (if so, they would voluntarily destroy part of their capability). \n\t\t\t Such secrecy can interfere with trust building, though, making it hard to reach agreements between teams if such agreement is needed.6 This is because only the teams with low capability take risks in cases of private information, and the more teams there are, the less likely it is that the winner will be low capability.", "date_published": "n/a", "url": "n/a", "filename": "Racing-to-the-precipice-a-model-of-artificial-intelligence-development.tei.xml", "abstract": "This paper presents a simple model of an AI arms race, where several development teams race to build the first AI. Under the assumption that the first AI will be very powerful and transformative, each team is incentivised to finish first -by skimping on safety precautions if need be. This paper presents the Nash equilibrium of this process, where each team takes the correct amount of safety precautions in the arms race. Having extra development teams and extra enmity between teams can increase the danger of an AI-disaster, especially if risk taking is more important than skill in developing the AI. Surprisingly, information also increases the risks: the more teams know about each others' capabilities (and about their own), the more the danger increases.", "id": "73d6424dd61745b7fc188172c5b71e62"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "WhyWeNeedFriendlyAI.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "061_ai-world-universe2.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "031_integrated.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "Under review as a conference paper at ICLR 2019 UNCOVERING SURPRISING BEHAVIORS IN REINFORCEMENT LEARNING VIA WORST-CASE ANALYSIS", "text": "INTRODUCTION Reinforcement Learning (RL) methods have achieved great success over the past few years, achieving human-level performance on a range of tasks such as Atari  (Mnih et al., 2015) , Go  (Silver et al., 2016) , Labyrinth , and Capture the Flag  (Jaderberg et al., 2018) . On these tasks, and more generally in reinforcement learning, agents are typically trained and evaluated using their average reward over environment settings as the measure of performance, i.e. E P (e) [R(π(θ), e)] , where π(θ) denotes a policy with parameters θ, R denotes the total reward the policy receives over the course of an episode, and e denotes environment settings such as maze structure in a navigation task, appearance of objects in the environment, or even the physical rules governing environment dynamics. But what biases does the distribution P (e) contain, and what biases, or failures to generalize, do these induce in the strategies agents learn? To help uncover biases in the training distribution and in the strategies that agents learn, we propose evaluating the worst-case performance of agents over environment settings, i.e. min e∈E E [R(π(θ), e)] , where E is some set of possible environment settings. Worst-case analysis can provide an important tool for understanding robustness and generalization in RL agents. For example, it can help us with: • Understanding biases in training Catastrophic failures can help reveal situations that are rare enough during training that the agent does not learn a strategy that is general enough to cope with them. • Robustness For critical systems, one would want to eliminate, or at least greatly reduce, the probability of extreme failures. • Limiting exploitability If agents have learned strategies that fail to generalize to particular environment settings, then an adversary could try and exploit an agent by trying to engineer such environment settings leading to agent failure. In this work, we use worst-case analysis to investigate the performance of a state-of-the-art agent in solving a first-person 3D navigation task; a task on which agents have recently achieved average-case human-level performance  (Wayne et al., 2018) . By optimizing mazes to minimize the performance of agents, we discover the existence of mazes where agents repeatedly fail to find the goal (which we refer to as a Catastrophic Failure). Our Contributions To summarize, the key contributions of this paper are as follows: 1. We introduce an effective and intuitive approach for finding simple environment settings leading to failure (Section 2). 2. We show that state-of-the-art agents carrying out navigation tasks suffer from drastic and often surprising failure cases (Sections 3.1 and 3.2). 3. We demonstrate that mazes leading to failure transfer across agents with different hyperparameters and, notably, even different architectures (Section 3.3). 4. We present an initial investigation into how the training distribution can be adapted by incorporating adversarial and out-of-distribution examples (Section 4). \n APPROACH Tasks We consider agents carrying out first-person 3D navigation tasks. Navigation is of central importance in RL research as it captures the challenges posed by partially observable Markov decision processes (POMDPs). The navigation tasks we use are implemented in DeepMind Lab (DM Lab)  (Beattie et al., 2016) . 1 Each episode is played on a 15 × 15 maze where each position in the maze may contain a wall, an agent spawn point, or a goal spawn point. The maze itself is procedurally generated every episode, along with the goal and agent spawn locations. The goal location remains fixed throughout an episode, while the agent spawn location can vary. In training, the agent respawns at different locations each time they reach the goal, while for our optimization and analysis we limit the agent to the same spawn location. Agents receive RGB observations of size 96 × 72 pixels, examples of which are provided in Figure  1 . Episodes last for 120 seconds and are played at a framerate of 15 frames per second. The agent receives a positive reward of 10 every time it reaches the goal, and 0 otherwise. On this specific navigation task, RL agents have recently achieved human-level average-case performance  (Wayne et al., 2018) . Agents We perform our analysis on Importance Weighted Actor-Learner Architecture agents trained to achieve human-level average-case performance on navigation tasks. These agents can be described as async batched-a2c agents with the V-trace algorithm for off policy-correction, and we henceforth refer to these as A2CV agents . Details of the training procedure are provided in Appendix A.1. Search Algorithm If we are interested in worst-case performance of agents, how can we find environment settings leading to the worst performance? In supervised learning, one typically uses gradient based methods to find inputs that lead to undesired output  (Biggio et al., 2013; Szegedy et al., 2013; Goodfellow et al., 2014) . In contrast, we search for environment settings leading to an undesired outcome at the end of an episode. This presents a challenge as the environment rendering and MDP are not differentiable. We are therefore limited to black-box methods where we can only query agent performance given environment settings. To search for environment settings which cause catastrophic failures, we propose the local search procedure described in Algorithm 1 (visualizing the process in Figure  2 ).   We then Evaluate each with the agent over 30 episodes, select the best maze (i.e. lowest agent score), and Modify this maze by randomly moving two walls to form the next set of candidates (Iteration 1). This process is repeated for 20 iterations, leading to a maze where the agent score is 0.09 in this example (i.e. the agent finds the goal once in 11 episodes). In Appendix A.2.1 we detail the computational requirements of this search procedure. \n EXPERIMENTS The agents we study achieve impressive average-case performance, but how much does their worstcase performance differ from their average-case performance? To investigate this, we consider the worst-case performance over a large set of mazes, including mazes that are not possible under the training distribution. A natural question to ask is whether any departure from the wall structure present during training will lead to agent failure. To test this, we evaluate the agent on samples from a distribution of mazes containing all mazes agents could be evaluated on during the search. In particular, we randomly select agent and goal spawn locations in the first step and then randomly move 40 walls, corresponding to the same actions taken by our optimization procedure, but where the actions are chosen randomly rather than in order to minimize agent performance. We find that agents do generalize to random mazes from the set we consider. In fact, we find that the average score obtained by agents on randomly perturbed mazes is slightly higher than on the training distribution, with agents obtaining an average of 45 goal reaches per two minute episode. The increased performance is likely due to the agent spawn location being fixed, making it easier for the agent to return to the goal once found. The considered agents generalize in the sense that agent performance is not reduced on average by out-of-distribution wall structure. But what about the worst case over all wall structures? Have the agents learned a general navigation strategy that works for all solvable mazes? Or do there exist environment settings that lead to catastrophic failures with high probability? In this section, we investigate these questions. We define a Catastrophic Failure to be an agent failing to find the goal in a two minute episode (1800 steps). As detailed below, we find that not only do there exist mazes leading to catastrophic failure, there exist surprisingly simple mazes that lead to catastrophic failure for agents yet are consistently and often rapidly solved by humans. \n RESULT 1: CATASTROPHIC FAILURES EXIST Do environment settings leading to catastrophic failure exist for the agents we are considering? By searching over mazes using the procedure outlined in Algorithm 1, we find mazes where agents fail to find the goal on many episodes, only finding the goal 10% of the time. In fact, some individual mazes lead to failure across five different agents we tested, with even the best performing agent only finding the goal in 20% of the episodes.  Optimization curves for our search procedure are given in Figure  3 . Note that while we define catastrophic failure as failure to find the goal, the actual objective used for the optimization was average number of goal reaches during an episode. Using average number of goals gives a stronger signal at the start of the optimization process. Finding mazes leading to lower average number of captures is easier than finding mazes where the agent rarely finds the goal even once. As can be seen, despite finding the goal on average 45 times per episode on randomly perturbed mazes, on mazes optimized to reduce score, agents find the goal on average only 0.33 times per episode, more than a 100× decrease in performance. In terms of probability of catastrophic failure, we note that despite agents finding the goal in approximately 98% of episodes on randomly perturbed mazes, using our method, on average we find mazes where agents only finds the goal in 30% of the episodes. Example trajectories agents take during failures are visualized in Figure  4 . The trajectories often seem to demonstrate a failure to use memory to efficiently explore the maze with the agent repeatedly visiting the same locations multiple times. The mazes presented in Figure  4  appear to be of higher complexity than mazes seen during training. This suggests that to obtain agents that truly master navigation, more complex mazes should be included in the training distribution. However, we can ask whether it is only more complex mazes that lead to catastrophic failure or whether there are also simple mazes leading to catastrophic failure. This is a question we explore in the next subsection.   \n RESULT 2: SIMPLE CATASTROPHIC FAILURES EXIST While the existence of catastrophic failures may be intriguing and perhaps troubling, one might suspect that the failures are caused by the increased complexity of the mazes leading to failure relative to the mazes the agent is exposed to during training, e.g., the mazes leading to failure contain more dead ends and sometimes have lower visibility. Further, understanding the cause of failure in such mazes seems challenging due to the large number of wall structures that may be causing the agent to fail. In this section, we explore whether there exist simple mazes which lead to catastrophic failures. As our measure of complexity, we use the total number of walls in the maze. We also evaluate humans on such mazes to get a quantitative measure of maze complexity. To find simple mazes which lead to failure, we first follow the same procedure as in the previous section, producing a set of mazes which all lead to catastrophic failures (i.e. a low agent scores). Next, we use this set of mazes as the initial set of candidates in our search algorithm, however we now use a Modify function that removes a single randomly chosen wall each iteration. This process is repeated for 70 iterations, searching for a maze with few walls while maintaining low agent score. In Figure  4 , we present the resulting simple mazes and the corresponding agent trajectories from our optimization procedure. Interestingly, we find that one can remove a majority of the walls in a maze and still maintain the catastrophic failure (i.e. very low agent score). Of note is that a number of these mazes are strikingly simple, suggesting that there exists structure in the environment that the agent has not generalized to. For example, we can see that placing the goal in a small room in an otherwise open maze can significantly reduce the agent's ability to find the goal. Human baselines While these simple maps may lead to catastrophic failure, it is unclear whether this is because of the agent or whether the maze is difficult in a way that is not obvious. To investigate this, we perform human experiments by tasking humans to play on a set of 10 simplified mazes. Notably, we find that human players are able to always locate the goal in every maze and typically within one third of the full episode length. This demonstrates that the mazes are comfortably solvable within the course of an episode by players with a general navigation strategy. We provide a detailed comparison of agent and human performance in Appendix A.3. Analysis One question that may arise is the extent to which these mazes are isolated points in the space of mazes. That is, if the maze was changed slightly, would it no longer lead to catastrophic failure? To test this, we investigate how sensitive our discovered failure mazes are with respect to the agent and goal spawn locations on simplified adversarial mazes. As can be seen in Figure  5 , we find that for a large range of spawn locations, the mazes still lead to failure. This indicates that there is specific local maze structure which causes agents to fail.  Procedures for finding such simple mazes may prove useful as a tool for debugging agents and understanding the ways in which training has led them to develop narrow strategies that are good enough for achieving high average-case performance. \n RESULT 3: FAILURE MAZES TRANSFER ACROSS AGENTS We have found failure cases for individual agents, but to what extent do these failure cases highlight a specific peculiarity of the individual agent versus a more general failure of a certain class of agents, or even a shortcoming of the distribution used for training? In this section, we investigate whether mazes which cause one trained agent to fail also cause other agents to fail. We consider two types of transfer: (1) between different hyperparameters of the same model architecture, and (2) between different model architectures. To test transfer between agents of the same architecture, we train a set of five A2CV agents with different entropy costs and learning rates. To test transfer between agents with significantly different architectures, we train a set of five MERLINbased agents  (Wayne et al., 2018) . These agents have a number of differences to the A2CV agents, most notably they contain a sophisticated memory structure based on a DNC (but with a fixed write location per timestep)  (Graves et al., 2016) . Both agents are trained on the same distribution and achieve human-level averages scores on the navigation task (with MERLIN scoring 10% higher than A2CV on average). Further details of agent training can be found in Appendix A.1. To quantify the level of transfer between (sets of) agents, we follow the procedure for finding adversarial mazes outlined in Section 3.1 to produce a collection of 50 unique failure mazes for each agent (i.e. 10 collections of 50 mazes each). We then evaluate every agent 100 times on each maze in each collection, reporting their average performance on each collection. Complete quantitative transfer results can be found in Appendix A.4. Failure cases transfer somewhat across all agents First, we find that across all agents, some level of transfer exists. In particular, as can be seen in Figure  6 , the probability of one agent finding the goal on mazes generated to reduce the score another agent is significantly below 1. This suggests a common cause of failure that is some combination of the distribution of environment settings used during training and the set of methods that are currently used to train such agents. A possible way to address this could be enriching the training distribution so that it contains fewer biases and encourages more general solutions. Transfer within agent type is stronger than between agent type Comparing the performance of each agent type on mazes from the same agent type to mazes from another agent type, we see that transfer within agent type is stronger. As shown in Figure  6b , performance increases as we go from 'MERLIN to MERLIN' 'A2CV to MERLIN' (0.42 to 0.58) and also if we go from 'A2CV to A2CV' to 'MERLIN to A2CV' (0.63 to 0.70). This suggests that there are some common biases in agents that are due to their architecture type. Analyzing structural differences between mazes that lead to one agent type to fail but not another could give interesting insight into behavioural differences between agents beyond just average performance. A2CV agents are less susceptible to transfer Despite similar probabilities of failure when evaluating on mazes optimized for the same agent, A2CV agents seem to suffer less on mazes optimized using other A2CV or MERLIN agents. This indicates that A2CV agents may have learned a more diverse set of strategies. Figure  6 : Mazes that lead to failures in one agent lead to failure in other agents as well. This is the case for agents of the same architecture with different hyperparameters, and is also the case for transfer across agents of different architecture. We note, however, that transfer across agents with different architectures is weaker than among agents with the same architecture, and that the performance of agents with the same architecture but with different hyperparameters is slightly higher than for the agents used to originally find the mazes. \n ADAPTING THE TRAINING DISTRIBUTION From our experiments so far, we have discovered that there exist many mazes which lead to catastrophic failure. In this section, we investigate whether agent performance can be improved by adapting the training distribution, for example by incorporating adversarial mazes into training and modifying the original mazes used in training. \n MOTIVATION To better understand what may be causing catastrophic failures, with the aim of fixing them, we compare the set of adversarial mazes with the original set of mazes used in training. From this comparison, we find that there are two notable differences. The probability of a catastrophic failure correlates with the distance between the spawn locations and how hidden the goal is First, we find that a number of features are more common in adversarial mazes than non-adversarial mazes. In particular, adversarial mazes are more likely to have the goal hidden in an enclosed space (such as a small room), and on average the path length from the player's starting location to the goal is significantly longer (31.1 ± 8.4 compared to 11.6 ± 6.3). Notably, while the training distribution also contains hidden goals which are far from the agent's starting location, they are much rarer. Adversarial mazes are typically far from the training distribution Second, we find that adversarial mazes tend to not only be out-of-distribution, but also far from the training distribution due to the Modify function used in our adversarial search procedure (for example, see Figure  2 ). This contrasts with the adversarial images literature where attacks are usually constrained to be small or imperceptible. It may therefore not be surprising that the agent is unable to generalize to all out-of-distribution mazes which could also explain the significant reduction in their performance. Given these two observations, it is natural to ask whether the training distribution can be adapted to improve the agent's performance. In the following sections we investigate this question and discuss our findings, focusing on incorporating adversarial mazes into training and modifying the original mazes used in training. \n APPROACH We consider two distinct approaches for incorporating adversarial and out-of-distribution mazes into the training distribution. Adversarial training To add adversarial mazes into the training distribution, we first create a dataset of 6000 unique adversarial mazes from separate runs of our search procedure using the previously trained A2CV agents. Notably, this set also includes the 250 mazes used in our transfer experiments (Section 3.3). Next, we train a new set of A2CV agents using both this adversarial set of mazes and the standard distribution of mazes, sampling randomly every episode (i.e. 50% of training episodes are on an adversarial maze). Randomly perturbed training To ensure our adversarial search procedure produces indistribution adversarial mazes, we alter the default maze generator used in training so that any adversarial maze can be generated. We accomplish this by randomly perturbing the original mazes, repeatedly using the same Modify function used by our adversarial search procedure, but selecting candidates randomly rather than by worst agent performance. \n RESULTS In this section, we report our findings on the robustness of agents trained using the approaches above. Catastrophic failures still exist Our main finding is that while agents learn to perform well on the richer distributions of mazes described above, this does not lead to robust agents. In particular, agents trained on a distribution of mazes enriched with 6000 adversarial mazes were able to find the goal on average 89.8% of the time on the adversarial mazes they were trained on. Similarly, agents trained on randomly perturbed mazes were able to find the goal close to 100% of the time on the distribution they were trained on. However, despite the agents being trained on these richer training distributions, the same search method is still able to find mazes leading to extreme failure as can be seen in Figure  7 . One possible explanation for this result is that the 6000 adversarial mazes used for training were insufficient to get good coverage of the space of mazes, and that further enlarging this set could yield qualitatively different results. Indeed, for agents trained using randomly perturbed mazes, the search procedure took 50 iterations to obtain the same level of failure as it did after 20 iterations when applied to agents trained on the standard training distribution. This suggests that perhaps enriching the training distribution with a very large set of adversarial mazes may lead to more general and robust agents. However, there are a number of challenges that need to be addressed before this approach can be tested which we will describe in the next section.   \n DISCUSSION Our results suggest that if a richer training distribution is to yield more robust agents, we may need to use a very large set of environment settings leading to failure. This is similar to how adversarial training in supervised learning is performed where more adversarial examples are used than the original training examples. We describe below what we see as two significant challenges that need to be overcome before such an approach can be thoroughly evaluated in the RL setting. \n Expensive generation The cost of generating a single adversarial setting is on the order of 1000's episodes using the method in this work. This implies that generating a set of adversarial settings which is similar in size to the set trained on would require orders of magnitude more computational than training itself. This could be addressed with faster methods for generating adversarial settings. Expensive training Since agents receive very little reward in adversarial settings, the training signal is incredibly sparse. Therefore, it is possible that many more training iterations are necessary for agents to learn to perform well in each adversarial setting. A possible solution to this challenge is to design a curriculum over adversity, whereby easier variants of the adversarial settings are injected into the training distribution. For example, for the navigation tasks considered here, one could include training settings with challenging mazes where the goal is in any position on the shortest path between the starting location of the agent and the challenging goal. We hope that these challenges can be overcome so that, in the context of RL, the utility of adversarial retraining can be established -an approach which has proved useful in supervised learning tasks. However, since significant challenges remain, we suspect that much effort and many pieces of work will be required before a conclusive answer is achieved. \n RELATED WORK Navigation Recently, there has been significant focus in the RL community on agent navigation in simulated 3D environments, including a community-wide challenge for agents in such environments called VizDoom  (Kempka et al., 2016) . Such 3D first-person navigation tasks are particularly interesting because they capture challenges such as partial observability, and require the agent to \"effectively perceive, interpret, and learn the 3D world in order to make tactical and strategic decisions where to go and how to act.\"  (Kempka et al., 2016) . Recent advances have led to impressive human-level performance on navigation tasks in large procedurally generated environments  (Beattie et al., 2016; Wayne et al., 2018) . Adversarial examples in supervised learning Our work can be seen as an RL navigation analogue of work on adversarial attacks on supervised learning systems for image classification  (Szegedy et al., 2013) . For adversarial attacks on image classifiers, one considers a set of inputs that is larger than the original distribution, but where one would hope that systems perform just as well on L ∞ balls around inputs from the distribution. In particular, the adversarial examples lie outside the training distribution. Analogously, we consider a set of mazes which is larger than the original set of mazes used during training, but where we would hope our system will work just as well. Notably, while similar on a conceptual level, our setting has two key differences from this previous line of work: (1) The attack vector consists of changing latent semantic features of the environment (i.e. the wall structure of a maze), rather than changing individual pixels in an input image in an unconstrained manner. (2) The failure is realized over multiple steps of agent and environment interacting with each other, rather than simply being errant output from a single forward pass through a neural net. More recently, in the context of supervised learning for image classification, there has been work to find constrained adversarial attacks which is closer to what we consider in this work  (Athalye & Sutskever, 2017; Fawzi & Frossard, 2015; Eykholt et al., 2018; Sharif et al., 2016) . In the context of interpretable adversarial examples in image classification, similar approaches to our simplification approach have been explored where one searches for adversarial perturbations with group-sparse structure or other minimal structure  (Xu et al., 2018; Brendel et al., 2018) . Additionally, our findings regarding transfer are consistent with findings on adversarial examples for computer vision networks where it has been found that perturbations that are adversarial for one network often transfer across other networks  (Szegedy et al., 2013; Tramèr et al., 2017)  Input attacks on RL systems There have been a number of previous works which have extended adversarial attacks to RL settings, however they have achieved this by manipulating inputs directly, which effectively amounts to changing the environment renderer  (Huang et al., 2017; Lin et al., 2017a; b) . While these are interesting from a security perspective, it is less clear what they tell us about the generality of the strategy learned by the agent. Generalization in RL systems Recently, it has been shown that simple agents trained on restricted datasets fail to learn sufficiently general navigation strategies to improve goal retrieval times on held out mazes  (Dhiman et al., 2018) . In comparison, our method is both automatic and able to find more spectacular failures. Further, our findings highlight failures in exploration during navigation. This is in contrast to this previous work which studied failures to exploit knowledge from previous goal retrievals in the same episode. In the context of testing generalization in RL, previous work has looked at statistical generalization in RL . Here we consider agents that already generalize in the statistical sense and try to better characterize the ways in which they generalize beyond the average-case. \n CONCLUSIONS AND FUTURE WORK In this work, we have shown that despite the strong average-case performance often reported of RL agents, worst-case analysis can uncover environment settings which agents have failed to generalize to. Notably, we have found that not only do catastrophic failures exist, but also that simple catastrophic failures exist which we would hope agents would have generalized to, and that failures also transfer between agents and architectures. As agents are trained to perform increasingly complicated tasks in more sophisticated environments, for example AirSim  (Shah et al., 2017)  and CARLA  (Dosovitskiy et al., 2017) , it is of interest to understand their worst-case performance and modes of generalization. Further, in real world applications such as self-driving cars, industrial control, and robotics, searching over environment settings to investigate and address such behaviours is likely to be critical on the path to robust and generalizable agents. To conclude, while this work has focused mostly on evaluation and understanding, it is only a first step towards the true goal of building more robust, general agents. Initial results we report indicate that enriching the training distribution with settings leading to failure may need to be done at a large scale if it is to work, which introduces significant challenges. While training robust agents is likely an endeavour requiring significant effort, we believe it is important if agents are to carry out critical tasks and on the path to finding more generally intelligent agents. goal was <50% (compared to 98% on the average maze). Furthermore, the 25th, 50th, and 75th percentiles were as follows: • p(reaching the goal): 0.031, 0.136, 0.279 • number of goals reached: 0.042, 0.136, 0.368 \n A.3 HUMAN EXPERIMENTS To upper bound the intrinsic difficulty of the mazes found to be adversarial to agents, we conducted experiments where three humans played on the same mazes. Each human played a single episode on each of ten mazes. The humans played at the same resolution as agents, 96x72 pixels, to rule out visual acuity as a confounding factor. On all mazes, all humans successfully found the goal in the course of the episode. In fact, in most episodes, humans were able to find the goal in less than a third of the episode. Figure  8 : Mazes used for human experiments. For each maze, the agent that performed best found the goal less than 50% of the time. In contrast, humans always found the goal, usually within less than a third of the episode. Note that humans played at the same resolution as agents, 96x72 pixels.    Figure 1 : 1 Figure 1: Navigation task. (left) Example maze from the training distribution together with the path taken by the agent from spawn (cyan) to goal (magenta). (right) Frames from top left to bottom right correspond to agent observations as it takes the path from spawn to goal. Note that while the navigation task may look simple given a top down view, the agent only receives very partial information about the maze at every step, making navigation a difficult task. \n Figure 2 : 2 Figure 2: Example of search procedure. First, we generate a set of 10 initial candidate mazes by sampling from the training distribution.We then Evaluate each with the agent over 30 episodes, select the best maze (i.e. lowest agent score), and Modify this maze by randomly moving two walls to form the next set of candidates (Iteration 1). This process is repeated for 20 iterations, leading to a maze where the agent score is 0.09 in this example (i.e. the agent finds the goal once in 11 episodes). In Appendix A.2.1 we detail the computational requirements of this search procedure. \n (a) Average number of goals reached per episode over the course of the optimization. (b) Probability of the agent reaching the goal in an episode. \n Figure 3 : 3 Figure 3: The search algorithm is able to rapidly find mazes where agents fail to find the goal. (a) The objective used for the optimizer is average agent score. The dashed line corresponds to average goals reached on randomly perturbed mazes. (b) Minimizing score also leads to a low probability of at least one goal retrieval in an episode. The dashed line corresponds to average probability of reaching a goal on randomly perturbed mazes. The blue lines are computed by averaging across 50 optimization runs. \n Figure 4 : 4 Figure 4: Example mazes leading to low scores and example trajectories on these mazes. (a) Maze with randomly perturbed walls. Despite being out of distribution, agents find the goal in 98% of episodes on such mazes and are able to get the goal on average 45 times per episode. (b) Maze obtained after 20 iterations, moving two walls at each iteration to minimize reward. All agents find the goal on such mazes in less than 20% of episodes. (c) Maze obtained through additional iterations of removing walls. All agents find the goal on such mazes in less than 40% of episodes. (d) Human trajectory on the same maze as in (c). Humans are able to consistently find the goal on such mazes. \n (a) Agent locations, with goal (magenta) fixed.(b) Goal locations, with agent (cyan) fixed. \n Figure 5 : 5 Figure 5: Adversarial mazes are robust to change of spawn positions. The probability of goal retrieval (shown with the color bar) remains low across large portions of the simplified maze as the (a) agent spawn locations and (b) goal locations are moved for each episode.. \n (a) Across hyperparameters, same architecture. (b) Across architectures. \n (a) Average number of goals reached. (b) Probability of finding the goal in a single episode. \n Figure 7 : 7 Figure 7: Richer training distributions did not lead to robust agents. Adversarial optimization for agents trained with adversarial mazes (red) and for agents trained with randomly perturbed mazes (yellow). Compared against the Standard training method from Figure 3 for 50 iterations (blue). \n Figure 9 : 9 Figure 9: Trajectories taken by Human 3 on mazes leading to agent failure. \n Table 1 : 1 Human seconds-to-first-goal on agent failure mazes we provide detailed results for our transfer experiments. In particular, we detail transfer between all pairs among the 10 agents, five A2CV agents and five MERLIN agents trained with different entropy costs and learning rates. \n Figure 10 : 10 Figure 10: Pairwise transfer scores. Lower number indicates more transfer. 'A' corresponds to our A2CV agent, and 'M' corresponds to MERLIN. \n end best ← Evaluate(candidates, num evaluations); Algorithm 1: Method for finding environment settings leading to failure cases. Concretely, we generate a set of initial candidate mazes by sampling mazes from the training distribution. We then use the Modify function on the maze which yielded the lowest agent score to randomly move two walls to produce a new set of candidates, rejecting wall moves that lead to unsolvable mazes. Importantly, this method is able to effectively find catastrophic failure cases (as we demonstrate in Section 3.1), while also having the advantage of being intuitive to understand and implement. input : num iterations, num candidates, num evaluations and function Modify output: An environment setting best candidates ← GenerateCandidates(num candidates); for i ← 1 to num iterations do best ← Evaluate(candidates, num evaluations); candidates ← Modify(best, num candidates);", "date_published": "n/a", "url": "n/a", "filename": "uncovering_surprising_behavior.tei.xml", "abstract": "Reinforcement learning agents are typically trained and evaluated according to their performance averaged over some distribution of environment settings. But does the distribution over environment settings contain important biases, and do these lead to agents that fail in certain cases despite high average-case performance? In this work, we consider worst-case analysis of agents over environment settings in order to detect whether there are directions in which agents may have failed to generalize. Specifically, we consider a 3D first-person task where agents must navigate procedurally generated mazes, and where reinforcement learning agents have recently achieved human-level average-case performance. By optimizing over the structure of mazes, we find that agents can suffer from catastrophic failures, failing to find the goal even on surprisingly simple mazes, despite their impressive average-case performance. Additionally, we find that these failures transfer between different agents and even significantly different architectures. We believe our findings highlight an important role for worst-case analysis in identifying whether there are directions in which agents have failed to generalize. Our hope is that the ability to automatically identify failures of generalization will facilitate development of more general and robust agents. To this end, we report initial results on enriching training with settings causing failure. 1 A full description and code for the tasks can be found at https://github.com/deepmind/lab/ tree/master/game_scripts/levels/contributed/dmlab30#goal-locations-large.", "id": "867f3374d9bc8f72b895cbb6df1f00ba"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "science.aba9647.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dylan Hadfield-Menell", "Anca Dragan", "Pieter Abbeel", "Stuart Russell"], "title": "Cooperative Inverse Reinforcement Learning", "text": "Introduction \"If we use, to achieve our purposes, a mechanical agency with whose operation we cannot interfere effectively . . . we had better be quite sure that the purpose put into the machine is the purpose which we really desire.\" So wrote Norbert  Wiener (1960)  in one of the earliest explanations of the problems that arise when a powerful autonomous system operates with an incorrect objective. This value alignment problem is far from trivial. Humans are prone to mis-stating their objectives, which can lead to unexpected implementations. In the myth of King Midas, the main character learns that wishing for 'everything he touches to turn to gold' leads to disaster. In a reinforcement learning context,  Russell & Norvig (2010)  describe a seemingly reasonable, but incorrect, reward function for a vacuum robot: if we reward the action of cleaning up dirt, the optimal policy causes the robot to repeatedly dump and clean up the same dirt. A solution to the value alignment problem has long-term implications for the future of AI and its relationship to humanity  (Bostrom, 2014 ) and short-term utility for the design of usable AI systems. Giving robots the right objectives and enabling them to make the right trade-offs is crucial for self-driving cars, personal assistants, and human-robot interaction more broadly. The field of inverse reinforcement learning or IRL  (Russell, 1998; Ng & Russell, 2000; Abbeel & Ng, 2004 ) is certainly relevant to the value alignment problem. An IRL algorithm infers the reward function of an agent from observations of the agent's behavior, which is assumed to be optimal (or approximately so). One might imagine that IRL provides a simple solution to the value alignment problem: the robot observes human behavior, learns the human reward function, and behaves according to that function. This simple idea has two flaws. The first flaw is obvious: we don't want the robot to adopt the human reward function as its own. For example, human behavior (especially in the morning) often conveys a desire for coffee, and the robot can learn this with IRL, but we don't want the robot to want coffee! This flaw is easily fixed: we need to formulate the value alignment problem so that the robot always has the fixed objective of optimizing reward for the human, and becomes better able to do so as it learns what the human reward function is. The second flaw is less obvious, and less easy to fix. IRL assumes that observed behavior is optimal in the sense that it accomplishes a given task efficiently. This precludes a variety of useful teaching behaviors. For example, efficiently making a cup of coffee, while the robot is a passive observer, is a inefficient way to teach a robot to get coffee. Instead, the human should perhaps explain the steps in coffee preparation and show the robot where the backup coffee supplies are kept and what do if the coffee pot is left on the heating plate too long, while the robot might ask what the button with the puffy steam symbol is for and try its hand at coffee making with guidance from the human, even if the first results are undrinkable. None of these things fit in with the standard IRL framework. Cooperative inverse reinforcement learning. We propose, therefore, that value alignment should be formulated as a cooperative and interactive reward maximization process. More precisely, we define a cooperative inverse reinforcement learning (CIRL) game as a two-player game of partial information, in which the \"human\", H, knows the reward function (represented by a generalized parameter θ), while the \"robot\", R, does not; the robot's payoff is exactly the human's actual reward. Optimal solutions to this game maximize human reward; we show that solutions may involve active instruction by the human and active learning by the robot. Reduction to POMDP and Sufficient Statistics. As one might expect, the structure of CIRL games is such that they admit more efficient solution algorithms than are possible for general partialinformation games. Let (π H , π R ) be a pair of policies for human and robot, each depending, in general, on the complete history of observations and actions. A policy pair yields an expected sum of rewards for each player. CIRL games are cooperative, so there is a well-defined optimal policy pair that maximizes value.  2  In Section 3 we reduce the problem of computing an optimal policy pair to the solution of a (single-agent) POMDP. This shows that the robot's posterior over θ is a sufficient statistic, in the sense that there are optimal policy pairs in which the robot's behavior depends only on this statistic. Moreover, the complexity of solving the POMDP is exponentially lower than the NEXP-hard bound that  (Bernstein et al., 2000)  obtained by reducing a CIRL game to a general Dec-POMDP. Apprenticeship Learning and Suboptimality of IRL-Like Solutions. In Section 3.3 we model apprenticeship learning  (Abbeel & Ng, 2004 ) as a two-phase CIRL game. In the first phase, the learning phase, both H and R can take actions and this lets R learn about θ. In the second phase, the deployment phase, R uses what it learned to maximize reward (without supervision from H). We show that classic IRL falls out as the best-response policy for R under the assumption that the human's policy is \"demonstration by expert\" (DBE), i.e., acting optimally in isolation as if no robot exists. But we show also that this DBE/IRL policy pair is not, in general, optimal: even if the robot expects expert behavior, demonstrating expert behavior is not the best way to teach that algorithm. We give an algorithm that approximately computes H's best response when R is running IRL under the assumption that rewards are linear in θ and state features. Section 4 compares this best-response policy with the DBE policy in an example game and provides empirical confirmation that the bestresponse policy, which turns out to \"teach\" R about the value landscape of the problem, is better than DBE. Thus, designers of apprenticeship learning systems should expect that users will violate the assumption of expert demonstrations in order to better communicate information about the objective. \n Related Work Our proposed model shares aspects with a variety of existing models. We divide the related work into three categories: inverse reinforcement learning, optimal teaching, and principal-agent models. Inverse Reinforcement Learning.  Ng & Russell (2000)  define inverse reinforcement learning (IRL) as follows: \"Given measurements of an [actor]'s behavior over time. . . . Determine the reward function being optimized.\" The key assumption IRL makes is that the observed behavior is optimal in the sense that the observed trajectory maximizes the sum of rewards. We call this the demonstration-by-expert (DBE) assumption. One of our contributions is to prove that this may be suboptimal behavior in a CIRL game, as H may choose to accept less reward on a particular action in order to convey more information to R. In CIRL the DBE assumption prescribes a fixed policy \n Ground Truth \n Expert Demonstration Instructive Demonstration Figure  1 : The difference between demonstration-by-expert and instructive demonstration in the mobile robot navigation problem from Section 4. Left: The ground truth reward function. Lighter grid cells indicates areas of higher reward. Middle: The demonstration trajectory generated by the expert policy, superimposed on the maximum a-posteriori reward function the robot infers. The robot successfully learns where the maximum reward is, but little else. Right: An instructive demonstration generated by the algorithm in Section 3.4 superimposed on the maximum a-posteriori reward function that the robot infers. This demonstration highlights both points of high reward and so the robot learns a better estimate of the reward. for H. As a result, many IRL algorithms can be derived as state estimation for a best response to different π H , where the state includes the unobserved reward parametrization θ.  Ng & Russell (2000) ,  Abbeel & Ng (2004), and Ratliff et al. (2006)  compute constraints that characterize the set of reward functions so that the observed behavior maximizes reward. In general, there will be many reward functions consistent with this constraint. They use a max-margin heuristic to select a single reward function from this set as their estimate. In CIRL, the constraints they compute characterize R's belief about θ under the DBE assumption.  Ramachandran & Amir (2007)  and  Ziebart et al. (2008)  consider the case where π H is \"noisily expert,\" i.e., π H is a Boltzmann distribution where actions or trajectories are selected in proportion to the exponent of their value.  Ramachandran & Amir (2007)  adopt a Bayesian approach and place an explicit prior on rewards.  Ziebart et al. (2008)  places a prior on reward functions indirectly by assuming a uniform prior over trajectories. In our model, these assumptions are variations of DBE and both implement state estimation for a best response to the appropriate fixed H.  Natarajan et al. (2010)  introduce an extension to IRL where R observes multiple actors that cooperate to maximize a common reward function. This is a different type of cooperation than we consider, as the reward function is common knowledge and R is a passive observer.  Waugh et al. (2011)  and  Kuleshov & Schrijvers (2015)  consider the problem of inferring payoffs from observed behavior in a general (i.e., non-cooperative) game given observed behavior. It would be interesting to consider an analogous extension to CIRL, akin to mechanism design, in which R tries to maximize collective utility for a group of Hs that may have competing objectives. Fern et al. (  2014 ) consider a hidden-goal MDP, a special case of a POMDP where the goal is an unobserved part of the state. This can be considered a special case of CIRL, where θ encodes a particular goal state. The frameworks share the idea that R helps H. The key difference between the models lies in the treatment of the human (the agent in their terminology). Fern et al. (  2014 ) model the human as part of the environment. In contrast, we treat H as an actor in a decision problem that both actors collectively solve. This is crucial to modeling the human's incentive to teach. Optimal Teaching. Because CIRL incentivizes the human to teach, as opposed to maximizing reward in isolation, our work is related to optimal teaching: finding examples that optimally train a learner  (Balbach & Zeugmann, 2009; Goldman et al., 1993; Goldman & Kearns, 1995) . The key difference is that efficient learning is the objective of optimal teaching, while it emerges as a property of optimal equilibrium behavior in CIRL.  Cakmak & Lopes (2012)  consider an application of optimal teaching where the goal is to teach the learner the reward function for an MDP. The teacher gets to pick initial states from which an expert executes the reward-maximizing trajectory. The learner uses IRL to infer the reward function, and the teacher picks initial states to minimize the learner's uncertainty. In CIRL, this approach can be characterized as an approximate algorithm for H that greedily minimizes the entropy of R's belief. Beyond teaching, several models focus on taking actions that convey some underlying state, not necessarily a reward function. Examples include finding a motion that best communicates an agent's intention  (Dragan & Srinivasa, 2013) , or finding a natural language utterance that best communicates a particular grounding  (Golland et al., 2010) . All of these approaches model the observer's inference process and compute actions (motion or speech) that maximize the probability an observer infers the correct hypothesis or goal. Our approximate solution to CIRL is analogous to these approaches, in that we compute actions that are informative of the correct reward function. Principal-agent models. Value alignment problems are not intrinsic to artificial agents.  Kerr (1975)  describes a wide variety of misaligned incentives in the aptly titled \"On the folly of rewarding A, while hoping for B.\" In economics, this is known as the principal-agent problem: the principal (e.g., the employer) specifies incentives so that an agent (e.g., the employee) maximizes the principal's profit  (Jensen & Meckling, 1976) . Principal-agent models study the problem of generating appropriate incentives in a non-cooperative setting with asymmetric information. In this setting, misalignment arises because the agents that economists model are people and intrinsically have their own desires. In AI, misalignment arises entirely from the information asymmetry between the principal and the agent; if we could characterize the correct reward function, we could program it into an artificial agent.  Gibbons (1998)  provides a useful survey of principal-agent models and their applications. \n Cooperative Inverse Reinforcement Learning This section formulates CIRL as a two-player Markov game with identical payoffs, reduces the problem of computing an optimal policy pair for a CIRL game to solving a POMDP, and characterizes apprenticeship learning as a subclass of CIRL games. \n CIRL Formulation Definition 1. A cooperative inverse reinforcement learning (CIRL) game M is a two-player Markov game with identical payoffs between a human or principal, H, and a robot or agent, R. The game is described by a tuple,  M = S, {A H , A R }, T (•|•, •, •), {Θ, R(•, •, •; •)}, P 0 (•, •), γ , (s 0 , θ) γ a discount factor: γ ∈ [0, 1]. We write the reward for a state-parameter pair as R(s, a H , a R ; θ) to distinguish the static reward parameters θ from the changing world state s. The game proceeds as follows. First, the initial state, a tuple (s, θ), is sampled from P 0 . H observes θ, but R does not. This observation model captures the notion that only the human knows the reward function, while both actors know a prior distribution over possible reward functions. At each timestep t, H and R observe the current state s t and select their actions a H t , a R t . Both actors receive reward r t = R(s t , a H t , a R t ; θ) and observe each other's action selection. A state for the next timestep is sampled from the transition distribution, s t+1 ∼ P T (s |s t , a H t , a R t ), and the process repeats. Behavior in a CIRL game is defined by a pair of policies, (π H , π R ), that determine action selection for H and R respectively. In general, these policies can be arbitrary functions of their observation histories; π H : A H × A R × S * × Θ → A H , π R : A H × A R × S * → A R . The optimal joint policy is the policy that maximizes value. The value of a state is the expected sum of discounted rewards under the initial distribution of reward parameters and world states. Remark 1. A key property of CIRL is that the human and the robot get rewards determined by the same reward function. This incentivizes the human to teach and the robot to learn without explicitly encoding these as objectives of the actors. \n Structural Results for Computing Optimal Policy Pairs The analogue in CIRL to computing an optimal policy for an MDP is the problem of computing an optimal policy pair. This is a pair of policies that maximizes the expected sum of discounted rewards. This is not the same as 'solving' a CIRL game, as a real world implementation of a CIRL agent must account for coordination problems and strategic uncertainty  (Boutilier, 1999) . The optimal policy pair represents the best H and R can do if they can coordinate perfectly before H observes θ. Computing an optimal joint policy for a cooperative game is the solution to a decentralized-partially observed Markov decision process (Dec-POMDP). Unfortunately, Dec-POMDPs are NEXP-complete  (Bernstein et al., 2000)  so general Dec-POMDP algorithms have a computational complexity that is doubly exponential. Fortunately, CIRL games have special structure that reduces this complexity.  Nayyar et al. (2013)  shows that a Dec-POMDP can be reduced to a coordination-POMDP. The actor in this POMDP is a coordinator that observes all common observations and specifies a policy for each actor. These policies map each actor's private information to an action. The structure of a CIRL game implies that the private information is limited to H's initial observation of θ. This allows the reduction to a coordination-POMDP to preserve the size of the (hidden) state space, making the problem easier. Theorem 1. Let M be an arbitrary CIRL game with state space S and reward space Θ. There exists a (single-actor) POMDP M C with (hidden) state space S C such that |S C | = |S| • |Θ| and, for any policy pair in M , there is a policy in M C that achieves the same sum of discounted rewards. Theorem proofs can be found in the supplementary material. An immediate consequence of this result is that R's belief about θ is a sufficient statistic for optimal behavior. Corollary 1. Let M be a CIRL game. There exists an optimal policy pair (π H * , π R * ) that only depends on the current state and R's belief. Remark 2. In a general Dec-POMDP, the hidden state for the coordinator-POMDP includes each actor's history of observations. In CIRL, θ is the only private information so we get an exponential decrease in the complexity of the reduced problem. This allows one to apply general POMDP algorithms to compute optimal joint policies in CIRL. It is important to note that the reduced problem may still be very challenging. POMDPs are difficult in their own right and the reduced problem still has a much larger action space. That being said, this reduction is still useful in that it characterizes optimal joint policy computation for CIRL as significantly easier than Dec-POMDPs. Furthermore, this theorem can be used to justify approximate methods (e.g., iterated best response) that only depend on R's belief state. \n Apprenticeship Learning as a Subclass of CIRL Games A common paradigm for robot learning from humans is apprenticeship learning. In this paradigm, a human gives demonstrations to a robot of a sample task and the robot is asked to imitate it in a subsequent task. In what follows, we formulate apprenticeship learning as turn-based CIRL with a learning phase and a deployment phase. We characterize IRL as the best response (i.e., the policy that maximizes reward given a fixed policy for the other player) to a demonstration-by-expert policy for H. We also show that this policy is, in general, not part of an optimal joint policy and so IRL is generally a suboptimal approach to apprenticeship learning. Definition 2. (ACIRL) An apprenticeship cooperative inverse reinforcement learning (ACIRL) game is a turn-based CIRL game with two phases: a learning phase where the human and the robot take turns acting, and a deployment phase, where the robot acts independently. \n Example. Consider an example apprenticeship task where R needs to help H make office supplies. H and R can make paperclips and staples and the unobserved θ describe H's preference for paperclips vs staples. We model the problem as an ACIRL game in which the learning and deployment phase each consist of an individual action. The world state in this problem is a tuple (p s , q s , t) where p s and q s respectively represent the number of paperclips and staples H owns. t is the round number. An action is a tuple (p a , q a ) that produces p a paperclips and q a staples. The human can make 2 items total: A H = {(0, 2), (1, 1), (2, 0)}. The robot has different capabilities. It can make 50 units of each item or it can choose to make 90 of a single item: A R = {(0, 90), (50, 50), (90, 0)}. We let Θ = [0, 1] and define R so that θ indicates the relative preference between paperclips and staples:R(s, (p a , q a ); θ) = θp a + (1 − θ)q a . R's action is ignored when t = 0 and H's is ignored when t = 1. At t = 2, the game is over, so the game transitions to a sink state, (0, 0, 2). Deployment phase -maximize mean reward estimate. It is simplest to analyze the deployment phase first. R is the only actor in this phase so it get no more observations of its reward. We have shown that R's belief about θ is a sufficient statistic for the optimal policy. This belief about θ induces a distribution over MDPs. A straightforward extension of a result due to  Ramachandran & Amir (2007)  shows that R's optimal deployment policy maximizes reward for the mean reward function. Theorem 2. Let M be an ACIRL game. In the deployment phase, the optimal policy for R maximizes reward in the MDP induced by the mean θ from R's belief. In our example, suppose that π H selects (0, 2 ) if θ ∈ [0, 1 3 ), (1, 1) if θ ∈ [ 1 3 , 2 3 ] and (2, 0) otherwise. R begins with a uniform prior on θ so observing, e.g., a H = (0, 2) leads to a posterior distribution that is uniform on [0, 1 3 ). Theorem 2 shows that the optimal action maximizes reward for the mean θ so an optimal R behaves as though θ = 1 6 during the deployment phase. Learning phase -expert demonstrations are not optimal. A wide variety of apprenticeship learning approaches assume that demonstrations are given by an expert. We say that H satisfies the demonstration-by-expert (DBE) assumption in ACIRL if she greedily maximizes immediate reward on her turn. This is an 'expert' demonstration because it demonstrates a reward maximizing action but does not account for that action's impact on R's belief. We let π E represent the DBE policy. Theorem 2 enables us to characterize the best response for R when π H = π E : use IRL to compute the posterior over θ during the learning phase and then act to maximize reward under the mean θ in the deployment phase. We can also analyze the DBE assumption itself. In particular, we show that π E is not H's best response when π R is a best response to π E . Theorem 3. There exist ACIRL games where the best-response for H to π R violates the expert demonstrator assumption. In other words, if br(π) is the best response to π, then br(br(π E )) = π E . The supplementary material proves this theorem by computing the optimal equilibrium for our example. In that equilibrium, H selects (1, 1) if θ ∈ [ 41 92 , 51 92 ]. In contrast, π E only chooses (1, 1) if θ = 0.5. The change arises because there are situations (e.g., θ = 0.49) where the immediate loss of reward to H is worth the improvement in R's estimate of θ. Remark 3. We should expect experienced users of apprenticeship learning systems to present demonstrations optimized for fast learning rather than demonstrations that maximize reward. Crucially, the demonstrator is incentivized to deviate from R's assumptions. This has implications for the design and analysis of apprenticeship systems in robotics. Inaccurate assumptions about user behavior are notorious for exposing bugs in software systems (see, e.g.,  Leveson & Turner (1993) ). \n Generating Instructive Demonstrations Now, we consider the problem of computing H's best response when R uses IRL as a state estimator. For our toy example, we computed solutions exhaustively, for realistic problems we need a more efficient approach. Section 3.2 shows that this can be reduced to an POMDP where the state is a tuple of world state, reward parameters, and R's belief. While this is easier than solving a general Dec-POMDP, it is a computational challenge. If we restrict our attention to the case of linear reward functions we can develop an efficient algorithm to compute an approximate best response. Specifically, we consider the case where the reward for a state (s, θ) is defined as a linear combination of state features for some feature function φ : R(s, a H , a R ; θ) = φ(s) θ. Standard results from the IRL literature show that policies with the same expected feature counts have the same value  (Abbeel & Ng, 2004) . Combined with Theorem 2, this implies that the optimal π R under the DBE assumption computes a policy that matches the observed feature counts from the learning phase. This suggests a simple approximation scheme. To compute a demonstration trajectory τ H , first compute the feature counts R would observe in expectation from the true θ and then select actions that maximize similarity to these target features. If φ θ are the expected feature counts induced by θ then this scheme amounts to the following decision rule: τ H ← argmax τ φ(τ ) θ − η||φ θ − φ(τ )|| 2 . (1) This rule selects a trajectory that trades off between the sum of rewards φ(τ ) θ and the feature dissimilarity ||φ θ − φ(τ )|| 2 . Note that this is generally distinct from the action selected by the demonstration-by-expert policy. The goal is to match the expected sum of features under a distribution of trajectories with the sum of features from a single trajectory. The correct measure of feature  Lower numbers are better. Using the best response causes R to infer a better distribution over θ so it does a better job of maximizing reward. Right: The regret of the instructive demonstration policy as a function of how optimal R expects H to be. λ = 0 corresponds to a robot that expects purely random behavior and λ = ∞ corresponds to a robot that expects optimal behavior. Regret is minimized for an intermediate value of λ: if λ is too small, then R learns nothing from its observations; if λ is too large, then R expects many values of θ to lead to the same trajectory so H has no way to differentiate those reward functions. similarity is regret: the difference between the reward R would collect if it knew the true θ and the reward R actually collects using the inferred θ. Computing this similarity is expensive, so we use an 2 norm as a proxy measure of similarity. \n Experiments \n Cooperative Learning for Mobile Robot Navigation Our experimental domain is a 2D navigation problem on a discrete grid. In the learning phase of the game, H teleoperates a trajectory while R observes. In the deployment phase, R is placed in a random state and given control of the robot. We use a finite horizon H, and let the first H 2 timesteps be the learning phase. There are N φ state features defined as radial basis functions where the centers are common knowledge. Rewards are linear in these features and θ. The initial world state is in the middle of the map. We use a uniform distribution on [−1, 1] N φ for the prior on θ. Actions move in one of the four cardinal directions {N, S, E, W } and there is an additional no-op ∅ that each actor executes deterministically on the other agent's turn. Figure  1  shows an example comparison between demonstration-by-expert and the approximate best response policy in Section 3.4. The leftmost image is the ground truth reward function. Next to it are demonstration trajectories produce by these two policies. Each path is superimposed on the maximum a-posteriori reward function the robot infers from the demonstration. We can see that the demonstration-by-expert policy immediately goes to the highest reward and stays there. In contrast, the best response policy moves to both areas of high reward. The robot reward function the robot infers from the best response demonstration is much more representative of the true reward function, when compared with the reward function it infers from demonstration-by-expert. \n Demonstration-by-Expert vs Best Responder Hypothesis. When R plays an IRL algorithm that matches features, H prefers the best response policy from Section 3.4 to π E : the best response policy will significantly outperform the DBE policy. Manipulated Variables. Our experiment consists of 2 factors: H-policy and num-features. We make the assumption that R uses an IRL algorithm to compute its estimate of θ during learning and maximizes reward under this estimate during deployment. We use Maximum-Entropy IRL  (Ziebart et al., 2008)  to implement R's policy. H-policy varies H's strategy π H and has two levels: demonstration-by-expert (π E ) and best-responder (br). In the π E level H maximizes reward during the demonstration. In the br level H uses the approximate algorithm from Section 3.4 to compute an approximate best response to π R . The trade-off between reward and communication η is set by cross-validation before the game begins. The num-features factor varies the dimensionality of φacross two levels: 3 features and 10 features. We do this to test whether and how the difference between experts and best-responders is affected by dimensionality. We use a factorial design that leads to 4 distinct conditions. We test each condition against a random sample of N = 500 different reward parameters. We use a within-subjects design with respect to the the H-policy factor so the same reward parameters are tested for π E and br. Dependent Measures. We use the regret with respect to a fully-observed setting where the robot knows the ground truth θ as a measure of performance. We let θ be the robot's estimate of the reward parameters and let θ GT be the ground truth reward parameters. The primary measure is the regret of R's policy: the difference between the value of the policy that maximizes the inferred reward θ and the value of the policy that maximizes the true reward θ GT . We also use two secondary measures. The first is the KL-divergence between the maximum-entropy trajectory distribution induced by θ and the maximum-entropy trajectory distribution induced by θ. Finally, we use the 2 -norm between the vector or rewards defined by θ and the vector induced by θ GT . Results. There was relatively little correlation between the measures (Cronbach's α of .47), so we ran a factorial repeated measures ANOVA for each measure. Across all measures, we found a significant effect for H-policy, with br outperforming π E on all measures as we hypothesized (all with F > 962, p < .0001). We did find an interaction effect with num-features for KL-divergence and the 2 -norm of the reward vector but post-hoc Tukey HSD showed br to always outperform π E . The interaction effect arises because the gap between the two levels of H-policy is larger with fewer reward parameters; we interpret this as evidence that num-features = 3 is an easier teaching problem for H. Figure  2  (Left, Middle) shows the dependent measures from our experiment. \n Varying R's Expectations Maximum-Entropy IRL includes a free parameter λ that controls how optimal R expects H to behave. If λ = 0, R will update its belief as if H's observed behavior is independent of her preferences θ. If λ = ∞, R will update its belief as if H's behavior is exactly optimal. We ran a followup experiment to determine how varying λ changes the regret of the br policy. Changing λ changes the forward model in R's belief update: the mapping R hypothesizes between a given reward parameter θ and the observed feature counts φ θ . This mapping is many-to-one for extreme values of λ. λ ≈ 0 means that all values of θ lead to the same expected feature counts because trajectories are chosen uniformly at random. Alternatively, λ >> 0 means that almost all probability mass falls on the optimal trajectory and many values of θ will lead to the same optimal trajectory. This suggests that it is easier for H to differentiate different values of θ if R assumes she is noisily optimal, but only up until a maximum noise level. Figure  2  plots regret as a function of λ and supports this analysis: H has less regret for intermediate values of λ. \n Conclusion and Future Work In this work, we presented a game-theoretic model for cooperative learning, CIRL. Key to this model is that the robot knows that it is in a shared environment and is attempting to maximize the human's reward (as opposed to estimating the human's reward function and adopting it as its own). This leads to cooperative learning behavior and provides a framework in which to design HRI algorithms and analyze the incentives of both actors in a reward learning environment. We reduced the problem of computing an optimal policy pair to solving a POMDP. This is a useful theoretical tool and can be used to design new algorithms, but it is clear that optimal policy pairs are only part of the story. In particular, when it performs a centralized computation, the reduction assumes that we can effectively program both actors to follow a set coordination policy. This is clearly infeasible in reality, although it may nonetheless be helpful in training humans to be better teachers. An important avenue for future research will be to consider the coordination problem: the process by which two independent actors arrive at policies that are mutual best responses. Returning to Wiener's warning, we believe that the best solution is not to put a specific purpose into the machine at all, but instead to design machines that provably converge to the right purpose as they go along. Figure 2 : 2 Figure 2: Left, Middle: Comparison of 'expert' demonstration (π E ) with 'instructive' demonstration (br). \n\t\t\t A coordination problem of the type described in Boutilier (1999)  arises if there are multiple optimal policy pairs; we defer this issue to future work.", "date_published": "n/a", "url": "n/a", "filename": "NIPS-2016-cooperative-inverse-reinforcement-learning-Paper.tei.xml", "abstract": "For an autonomous system to be helpful to humans and to pose no unwarranted risks, it needs to align its values with those of the humans in its environment in such a way that its actions contribute to the maximization of value for the humans. We propose a formal definition of the value alignment problem as cooperative inverse reinforcement learning (CIRL). A CIRL problem is a cooperative, partialinformation game with two agents, human and robot; both are rewarded according to the human's reward function, but the robot does not initially know what this is. In contrast to classical IRL, where the human is assumed to act optimally in isolation, optimal CIRL solutions produce behaviors such as active teaching, active learning, and communicative actions that are more effective in achieving value alignment. We show that computing optimal joint policies in CIRL games can be reduced to solving a POMDP, prove that optimality in isolation is suboptimal in CIRL, and derive an approximate CIRL algorithm.", "id": "eb1967caa7cbfcfd329b13658330f7ec"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Russell"], "title": "Learning agents for uncertain environments (extended abstract)", "text": "In recent years, reinforcement learning (also called neurodynamic programming) has made rapid progress as an approachfor building agents automatically  (Sutton, 1988; Kaelbling et al., 1996; Bertsekas & Tsitsiklis, 1996) . The basic idea is that the performance measure is made available to the agent in the form of a rewardfunction specifying the reward for each state that the agent passes through. The performance measure is then the sum of the rewards obtained. For example, when a bumble bee forages, the reward function at each time step might be some combination of the distance flown (weighted negatively) and the nectar ingested. Reinforcement learning (RL) methods are essentially online algorithmd for solving Markovdecisionprocesses (MDPs). An MDP is defined by the reward function and a model, that is, the state transition probabilities conditioned on each possible action. RL algorithms can be model-based, where the agent learns a model, or model-free-e.g., Q-learning cite-Watkins: 1989, which learns just a function Q(s, a) specifying the long-term value of taking action a in state s and acting optimally thereafter. Despite their successes, RL methods have been restricted largely tofully observable MDPs, in which the sensory input at each state is sufficient to identify the state. Obviously, in the real world, we must often deal with partially observable MDPs (POMDPs).  Astrom (1965)  proved that optimal decisions in POMDPs depend on the belief state b at each point in time, i.e., the posterior probability distribution over all possible actual states, given all evidence to date. The functions V and Q then become functions of b instead of s.  Parr and Russell (1995)  describes a very simple POMDP RL algorithm using an explicit representation of b as a vector of probabilities, and  McCallum (1993)  shows a way to approximate the belief state using recent percept sequences. Neither approach is likely to scale up to situations with large numbers of state variables and long-term temporal dependencies. What is needed is a way of representing the model compactly and updating the belief state efficiently given the model and each new observation. Dynamic Bayesian networks  (Dean & Kanazawa, 1989)  seem to have some of the required properties; in particular, they have significant advantages over other approaches such as Kalman filters and hidden Markov models. Our baseline architecture, shown in Figure  1 , uses DBNs to represent and update the belief state as new sensor information arrives. Given a representation for b, the reward signal is used to learn a Q-function represented by some \"black-box\" function approximator such as a neural network. Provided we can handle hybrid (dis-Figure  1 : A baseline architecture for learning agents in uncertain environments crete+continuous) DPNs, and provided we have a learning algorithm that can construct an approximately correct DBN model from scratch, then this baseline architecture has the capacity, in principle, to be thrown into more or less any environment and to learn to behave reasonably.* The talk will cover a variety of research topics arising from this proposal: Parametric learning in DBNs  (Binder, Koller, Russell, & Kanazawa, 1997a) . Structural learning in DBNs  (Friedman, Murphy, & Russell, 1998) . Approximate inference in DBNs  (Kanazawa, Koller, & Russell, 1995; Boyen & Koller, 1998) . Space-efficient inference in DBNs  (Binder, Murphy, & Russell, 1997b) . Reinforcement learning with DBN models-that is, how to do Q-learning with the belief state information provided by the DBN. Some tentative ideas will be presented but as yet there are no convincing solutions. Scaling up the environment will inevitably overtax the resources of the baseline architecture. There are several obvious directions for improvement, including hierarchical and first-order models, hierarchical representations of behaviour  (Parr & Russell, 1998) , and model-based lookahead methods for decision making. Which of these is important in any particular class of environments can only be ascertained by experiment. \n Inverse reinforcement learning Reinforcement learning is a powerful method for adaptive control in real tasks, so it is natural to seek analogous mechanisms in nature. Connections have been made between reinforcement learning and operant conditioning models of animal learning (see, e.g.,  Schmajuk & Zanutto, 1997; Touretzky & Saksida, 1997) . There is also neurophysiological evidence that reinforcement learning occurs in bee foraging  (Montague et al., 1995)  and in songbird vocalization  (Doya & Sejnowski, 1995) . In this work, it is generally assumed that the reward function is fixed and known. For example, in experiments on bees it is assumed to be the rate of nectar ingestion: Montague et al. (1995) cite evidence of a \"neuron with widespread projections to odour processing regions of the honeybee brain 'We say \"more or less\" because full generality require dealing with game-theoretic issues requiring stochastic decision making. whose activity represents the reward value of gustatory stimuli.\" It seems clear, however, that in examining animal and human behaviour we must consider the reward function as an unknown to be ascertained. The reasons for this are straightforward: l The specification of a given reward function is an empirical hypothesis and may turn out to be wrong. For example, it was assumed initially that horses' gait selection for a given speed was determined by energetic economy  (Hoyt & Taylor, 1981) ; this turns out not to be the case  (Farley & Taylor, 1991) . l The parameters of a multiattribute reward function can surely not be determined a priori; e.g., for running, attributes might be speed, efficiency, stability against perturbations, wear and tear on muscles, tendons, and bones, etc. How are these to be weighted and combined? Therefore, to model natural learning using reinforcement learning ideas, we must first solve the following computational task, which we call inverse reinforcement learning: Given 1) measurements of an agent's behaviour over time, in a variety of circumstances, 2) measurements of the sensory inputs to that agent; 3) a model of the physical environment (including the agent's body). Determine the reward function that the agent is optimizing. Given an assumption of optimization, this computational task is well-defined. Notice that is the dual of unsupervised reinforcement learning, where the task is to determine optimal behaviour given the reward inputs. To our knowledge, this computational task has not been studied in any generality in computer science, control theory, psychology, or biology. The closest work is in economics, where the task of multiattribute utility assessment has been studiedin depth-that is, how does a person actually combine the various attributes of each available choice when making a decision. The theory is well-developed  (Keeney & Raiffa, 1976) , and the applications numerous. However, this field studies only one-shot decisions where a single action is taken and the outcome is immediate. The sequential case was not considered until a seminal paper by  Sargent (1978)  tried to ascertain the effective hiring cost for labor by examining a firm's hiring behaviour over time, assuming it to be rational. In the last decade, the area of structural estimation of Markov decision processes has grown rapidly in econometrics  (Rust, 1994) . Many of the basic results carry over to our setting, although virtually nothing has been done on computational aspects, experimentation, or control-type applications. The open research problems are many: What are efficient algorithms for solving the inverse reinforcement learning problem? What is its computational complexity? Are there closed-form solutions for some parametric forms? Under what circumstances can we determine the existence of a consistent reward function? To what extent is the reward function uniquely recoverable? What effect do sensor and process noise have on robustness of the determination? What are appropriate error metrics for fitting? If behaviour is strongly inconsistent with optimality, can we identify \"locally consistent\" reward functions for specific regions in state space? Can we determine the reward function by observation during rather than after learning? How much observation is required to determine an estimated reward function that is within E of the true reward function? How can experiments be designed to maximize the identifiability of the reward function? Considering the design of possible algorithms, one can take maximum-likelihood approach to fit a parametric form for the reward functionas is commonly done in econometrics. That is, one defines a function L,(w)(B), the likelihood of observing behaviour B if the true reward function is r(w). From this, one can compute dWdw. One important question will be how to compute this gradient efficiently; presumably, it can be done in an obvious way by carrying the differential operator through the optimization algorithm for the behaviour. More elegant closed-form solutions may exist in special cases (e.g., linear-quadratic regulators). One may also be able to show that in some cases (e.g., linear reward functions) a globally optimal estimate can always be found. The solution of inverse reinforcement learning problems may also be an effective way to learn from observing experts. For tasks such as walking, diving, and driving, the designer of an artificial system may have only an intuitive idea of the appropriate reward function to be supplied to an RL algorithm in order to achieve \"desirable\" behavior. Instead of learning direct control functions from observation of experts (as in Pomerleau's ALVINN driging system), it may be better to solve the inverse reinforcement learning problem. The reward function should usually be a simple monotonic function of the current sensory inputs, and thus may be much simpler than the direct decision mapping itself. That is, the most compact and hence robustly learnable representation of expert behavior may be the reward function.", "date_published": "n/a", "url": "n/a", "filename": "279943.279964.tei.xml", "abstract": "This talk proposes a very simple \"baseline architecture\" for a learning agent that can handle stochastic, partially observable environments. The architecture uses reinforcement learning together with a method for representing temporal processes as graphical models. I will discuss methods for leaming the parameters and structure of such representations from sensory inputs, and for computing posterior probabilities. Some open problems remain before we can try out the complete agent; more arise when we consider scaling up. A second theme of the talk will be whether reinforcement learning can provide a good model of animal and human learning. To answer this question, we must do inverse reinforcement learning: given the observed behaviour, what reward signal, if any, is being optimized? This seems to be a very interesting problem for the COLT, UAI, and ML communities, and has been addressed in econometrics under the heading of structural estimation of Markov decision processes. 1 Learning in uncertain environments AI is about the construction of intelligent agents, i.e., systems that perceive and act effectively (according to some performance measure) in an environment. I have argued elsewhere  Russell and Norvig (1995)  that most AI research has focused on environments that are static, deterministic, discrete, and fully observable. What is to be done when, as in the real world, the environment is dynamic, stochastic, continuous, and partially observable? 'This paper draws on a variety of research efforts supported", "id": "62e18d17a8eee37351339241597c7d3f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom"], "title": "The Vulnerable World Hypothesis", "text": "Is there a black ball in the urn of possible inventions? One way of looking at human creativity is as a process of pulling balls out of a giant urn.  1  The balls represent possible ideas, discoveries, technological inventions. Over the course of history, we have extracted a great many ballsmostly white (beneficial) but also various shades of gray (moderately harmful ones and mixed blessings). The cumulative effect on the human condition has so far been overwhelmingly positive, and may be much better still in the future  (Bostrom, 2008) . The global population has grown about three orders of magnitude over the last ten thousand years, and in the last two centuries per capita income, standards of living, and life expectancy have also risen.  2  What we haven't extracted, so far, is a black ball: a technology that invariably or by default destroys the civilization that invents it. The reason is not that we have been particularly careful or wise in our technology policy. We have just been lucky. It does not appear that any human civilization has been destroyedas opposed to transformedby its own inventions.  3  We do have examples of civilizations being destroyed by inventions made elsewhere. For example, the European inventions that enabled transoceanic travel and force projection could be regarded as a black-ball event for the indigenous populations of the Americas, Australia, Tasmania, and some other places. The extinction of archaic hominid populations, such as the Neanderthals and the Denisovans, was probably facilitated by the technological superiority of Homo sapiens. But thus far, it seems, we have seen no sufficiently auto-destructive invention to count as a black ball for humanity.  4  What if there is a black ball in the urn? If scientific and technological research continues, we will eventually reach it and pull it out. Our civilization has a considerable ability to pick up balls, but no ability to put them back into the urn. We can invent but we cannot un-invent. Our strategy is to hope that there is no black ball. This paper develops some concepts that can help us think about the possibility of a technological black ball, and the different forms that such a phenomenon could take. We also discuss some implications for policy from a global perspective, particularly with respect to how one should view developments in mass surveillance and moves towards more effectual global governance or a more unipolar world order. These implications by no means settle questions about the desirability of changes in those macrostrategic variablesfor there indeed are other strongly relevant factors, not covered here, which would need to be added to the balance. Yet they form an important and under-appreciated set of considerations that should be taken into account in future debates on these issues. Before getting to the more conceptual parts of the paper, it will be useful to paint a more concrete picture of what a technological black ball could be like. The most obvious kind is a technology that would make it very easy to unleash an enormously powerful destructive force. Nuclear explosions are the most obviously destructive force we have mastered. So let us consider what would have happened if it had been very easy to unleash this force. \n A thought experiment: easy nukes On the morning of 12 September 1933, Leo Szilard was reading the newspaper when he came upon a report of an address recently delivered by the distinguished Lord Rutherford, now often considered the father of nuclear physics  (Rhodes, 1986) . In his speech, Rutherford had dismissed the idea of extracting useful energy from nuclear reactions as 'moonshine'. This claim so annoyed Szilard that he went out for a walk. During the walk, he got the idea of a nuclear chain reactionthe basis for both nuclear reactors and nuclear bombs. Later investigations showed that making an atomic weapon requires several kilograms of plutonium or highly enriched uranium, both of which are very difficult and expensive to produce. However, suppose it had turned out otherwise: that there had been some really easy way to unleash the energy of the atomsay, by sending an electric current through a metal object placed between two sheets of glass. So let us consider a counterfactual history in which Szilard invents nuclear fission and realizes that a nuclear bomb could be made with a piece of glass, a metal object, and a battery arranged in a particular configuration. What happens next? Szilard becomes gravely concerned. He sees that his discovery must be kept secret at all costs. But how? His insight is bound to occur to others. He could talk to a few of his physicist friends, the ones most likely to stumble upon the idea, and try to persuade them not to publish anything on nuclear chain reactions or on any of the reasoning steps leading up to the dangerous discovery. (That is what Szilard did in actual history.) Here Szilard faces a dilemma: either he doesn't explain the dangerous discovery, but then he will not be effective in persuading many of his colleagues to stop publishing; or he tells them the reason for his concern, but then he spreads the dangerous knowledge further. Either way he is fighting a losing battle. The general advance of scientific knowledge will eventually make the dangerous insight more accessible. Soon, figuring out how to initiate a nuclear chain reaction with pieces of metal, glass, and electricity will no longer take genius but will be within reach of any STEM student with an inventive mindset. Let us roll the tape a little further. The situation looks hopeless, but Szilard does not give up. He decides to take a friend into his confidence, a friend who is also the world's most famous scientist -Albert Einstein. He successfully persuades Einstein of the danger (again following actual history). Now, Szilard has the support of a man who can get him a hearing with any government. The two write a letter to President Franklin D. Roosevelt. After some committee wranglings and report-writing, the top levels of the US government are eventually sufficiently convinced to be ready to take serious action. What action can the United States take? Let us first consider what actually happened  (Rhodes, 1986) . What the US government did, after having digested the information provided by Einstein and Szilard, and after having received some further nudging from the British who were also looking into the matter, was to launch the Manhattan Project in order to weaponize nuclear fission as quickly as possible. As soon as the bomb was ready, the US Air Force used it to destroy Japanese population centers. Many of the Manhattan scientists had justified their participation by pointing to the mortal danger that would arise if Nazi Germany got the bomb first; but they continued working on the project after Germany was defeated.  5  Szilard advocated unsuccessfully for demonstrating 'the gadget' over an unpopulated area rather than in a city  (Franck et al., 1945) . After the war ended, many of the scientists favored the international control of atomic energy and became active in the nuclear disarmament movement; but their views carried little weight, as nuclear policy had been taken out of their hands. Four years later, the Soviet Union detonated its own atomic bomb. The Soviet effort was aided by spies in the Manhattan Project, yet even without espionage it would have succeeded within another year or two  (Holloway, 1994) . The Cold War followed, which at its peak saw 70,000 nuclear warheads ready to unleash global destruction at a moment's notice, with a trembling finger hovering over the 'red button' on either side  (Norris and Kristensen, 2010) .  6  Fortunately for human civilization, after the destruction of Hiroshima and Nagasaki, no other atomic bomb has been detonated in anger. Seventy-three years later, partly thanks to international treaties and anti-proliferation efforts, only nine states possess nuclear weapons. No non-state actor is believed ever to have possessed nuclear weapons.  7  But how would things have played out if there had been an easy way to make nukes? Maybe Szilard and Einstein could persuade the US government to ban all research in nuclear physics (outside high-security government facilities)? Such a ban on basic science would be subjected to enormous legal and political challengesthe more so as the reason for the ban could not be publicly disclosed in any detail without creating an unacceptable information hazard.  8  Let us suppose, however, that President Roosevelt could somehow mobilize enough political support to drive through a ban, and that the US Supreme Court could somehow find a way of regarding it as constitutionally valid. We then confront an array of formidable practical difficulties. All university physics departments would have to be closed, and security checks initiated. A large number of faculty and students would be forced out. Intense speculations would swirl around the reason for all these heavy-handed measures. Groups of physics PhD students and faculty banned from their research field would sit around and speculate about what the secret danger might be. Some of them would figure it out. And among those who figured it out, some would feel compelled to use the knowledge to impress their colleagues; and those colleagues would want to tell yet others, to show they were in the know. Alternatively, somebody who opposed the ban would unilaterally decide to publish the secret, maybe in order to support their view that the ban is ineffective or that the benefits of publication outweigh the risks. 9 10 Careless or disgruntled employees at the government labs would eventually also let slip information, and spies would carry the secret to foreign capitals. Even if, by some miracle, the secret never leaked in the United States, scientists in other countries would independently discover it, thereby multiplying the sources from which it could spread. Sooner or laterprobably soonerthe secret would be a secret no more. In the present age, when one can publish instantaneously and anonymously on the Internet, it would be even more difficult to limit the spread of scientific secrets (Cf.  Greenberg, 2012; Swire, 2015) . An alternative approach would be to eliminate all glass, metal, or sources of electrical current (save perhaps in a few highly guarded military depots). Given the ubiquity of these materials, such an undertaking would be extremely daunting. Securing political support for such measures would be no easier than shutting down physics education. However, after mushroom clouds had risen over a few cities, the political will to make the attempt could probably be mustered. Metal use is almost synonymous with civilization, and would not be a realistic target for elimination. Glass production could be banned, and existing glass panes confiscated; but pieces of glass would remain scattered across the landscape for a long time. Batteries and magnets could be seized, though some people would have stashed away these materials before they could be collected by the authorities. Many cities would be destroyed by nihilists, extortionists, revanchists, or even folk who just want to 'see what would happen  '. 11  People would flee urban areas. In the end, many places would be destroyed by nuclear fallout, cities would be abandoned, there would be no use of electricity or glass. Possession of proscribed materials, or equipment that could be used to make them, would be harshly punished, such as by on-the-spot execution. To enforce these provisions, communities would be subjected to strict surveillanceinformant networks incentivized by big rewards, frequent police raids into private quarters, continuous digital monitoring, and so forth. That is the optimistic scenario. In a more pessimistic scenario, law and order would break down entirely and societies might split into factions waging civil wars with nuclear weapons, producing famine and pestilence. The disintegration might end only when society has been so reduced that nobody is able any longer to put together a bomb and a delay detonator from stored materials or the scrap of city ruins. Even then, the dangerous insightonce its importance had been so spectacularly demonstratedwould be remembered and passed down the generations. If civilization began to rise from the ashes, the knowledge would lie in wait, ready to pounce as soon as people learned once again how to make sheet glass and electric current generators. And even if the knowledge were forgotten, it would be rediscovered once nuclear physics research was resumed. We were lucky that making nukes turned out to be hard. \n The vulnerable world hypothesis We now know that one cannot trigger a nuclear explosion with just a sheet of glass, some metal, and a battery. Making an atomic bomb requires several kilograms of fissile material, which is difficult to produce. We pulled out a gray ball that time. Yet with each act of invention, we reach into the urn anew. Let us introduce the hypothesis that the urn of creativity contains at least one black ball. We can refer to this as the vulnerable world hypothesis (VWH). Intuitively, the hypothesis is that there is some level of technology at which civilization almost certainly gets destroyed unless quite extraordinary and historically unprecedented degrees of preventive policing and/or global governance are implemented. More precisely: VWH: If technological development continues then a set of capabilities will at some point be attained that make the devastation of civilization extremely likely, unless civilization sufficiently exits the semianarchic default condition. By the 'semi-anarchic default condition' I mean a world order characterized by three features 12 : 1. Limited capacity for preventive policing. States do not have sufficiently reliable means of real-time surveillance and interception to make it virtually impossible for any individual or small group within their territory to carry out illegal actionsparticularly actions that are very strongly disfavored by > 99 per cent of the population. 2. Limited capacity for global governance. There is no reliable mechanism for solving global coordination problems and protecting global commonsparticularly in high-stakes situations where vital national security interests are involved. 3. Diverse motivations. There is a wide and recognizably human distribution of motives represented by a large population of actors (at both the individual and state level)in particular, there are many actors motivated, to a substantial degree, by perceived self-interest (e.g. money, power, status, comfort and convenience) and there are some actors ('the apocalyptic residual') who would act in ways that destroy civilization even at high cost to themselves.  3  The term 'devastation of civilization' in the above definition could be interpreted in various ways, yielding different versions of VWH. For example, one could define an existential-risk vulnerable world hypothesis (x-VWH), which would state that at some level of technology, by default, an existential catastrophe occurs, involving the extinction of Earth-originating intelligent life or the permanent blighting of our future potential for realizing value. However, here we will set the bar lower. A key concern in the present context is whether the consequences of civilization continuing in the current semi-anarchic default condition are catastrophic enough to outweigh reasonable objections to the drastic developments that would be required to exit this condition. If this is the criterion, then a threshold short of human extinction or existential catastrophe would appear sufficient. For instance, even those who are highly suspicious of government surveillance would presumably favour a large increase in such surveillance if it were truly necessary to prevent occasional region-wide destruction. Similarly, individuals who value living in a sovereign state may reasonably prefer to live under a world government given the assumption that the alternative would entail something as terrible as a nuclear holocaust. Therefore, we stipulate that the term 'civilizational devastation' in VWH refers (except where otherwise specified) to any destructive event that is at least as bad as the death of 15 per cent of the world population or a reduction of global GDP by > 50 per cent per cent lasting for more than a decade.  13  It is not a primary purpose of this paper to argue that VWH is true. (I regard that as an open question, though it would seem to me unreasonable, given the available evidence, to be at all confident that VWH is false.) Instead, the chief contribution claimed here is that VWH, along with related concepts and explanations, is useful in helping us surface important considerations and possibilities regarding humanity's macrostrategic situation. But those considerations and possibilities need to be further analyzed, and combined with other considerations that lie outside the scope of this paper, before they could deliver any definitive policy implications. A few more clarifications before we move on. This paper uses the word 'technology' in its broadest sense. Thus, in principle, we count not only machines and physical devices but also other kinds of instrumentally efficacious templates and proceduresincluding scientific ideas, institutional designs, organizational techniques, ideologies, concepts, and memesas constituting potential technological black balls.  14  We can speak of vulnerabilities opening and closing. In the 'easy nukes' scenario, the period of vulnerability begins when the easy way of producing nuclear explosions is discovered. It ends when some level of technology is attained that makes it reasonably affordable to stop nuclear explosions from causing unacceptable damageor that again makes it infeasible to produce nuclear explosions (because of technological regress).  15  If no protective technology is possible (as in, e.g., the case of nuclear weapons it may not be) and technological regress does not occur, then the world becomes permanently vulnerable. We can also speak of the world being stabilized (with respect to some vulnerability) if the semi-anarchic default condition is exited in such a way as to prevent the vulnerability from leading to an actual catastrophe. The ways in which the semi-anarchic default condition would have to be altered in order to achieve stabilization depend on the specifics of the vulnerability in question. In a later section, we will discuss possible means by which the world could be stabilized. For now, we simply note that VWH does not imply that civilization is doomed. \n Typology of vulnerabilities We can identify four types of civilizational vulnerability. \n Type-1 ('easy nukes') The first type is one where, as in the 'easy nukes' scenario, it becomes too easy for individuals or small groups to cause mass destruction: Type-1 vulnerability: There is some technology which is so destructive and so easy to use that, given the semi-anarchic default condition, the actions of actors in the apocalyptic residual make civilizational devastation extremely likely. Note that in determining whether a scenario presents a Type-1 vulnerability, there is an inverse relationship between the ease with which it becomes possible to cause an incident and the destructiveness of incident. The greater the destructiveness of a single incident, the less easy it needs to be to cause such an incident in order for us to diagnose the presence of a Type-1 vulnerability. Thus, consider a 'very easy nukes' scenario, in which any halfwit can create an easily portable thermonuclear weapon at the kitchen sink over the course of an afternoon: this would definitely qualify as a civilizational vulnerability. Contrast this with a 'moderately easy nukes' scenario, in which it takes a five-person team of semi-skilled individuals toiling for an entire year to produce a single bulky few-kiloton device: that might not quite rise to the level of a civilizational vulnerability. It seems possible, in the 'moderately easy nukes' scenario, that the great majority of cities would escape destruction, although the threat posed by a well-resourced terrorist organization, such as Aum Shinrikyo anno 1995 or Al-Qaeda anno 2001, would increase substantially. However, consider yet another scenario, 'moderately easy bio-doom', in which again it requires a semi-skilled five-person team working for a year to put the black-ball technology into effect, except that this time it is a biological agent, a single point release of which is sufficient to kill billions. In 'moderately easy bio-doom', the threshold for a Type-1 vulnerability would be reached. If destroying civilisation required only that a single group succeed with a task at the moderately-easy level, civilization would probably be destroyed within a few years in the semi-anarchic default condition. Indeed, both Aum Shinrikyo and Al-Qaeda sought to obtain nuclear and biological weapons, and would likely have chosen to use them (see e.g.  Danzig et al., 2011; Olson, 1999; Mowatt-Larssen and Allison, 2010) . So a Type-1 vulnerability exists if it is either extremely easy to cause a moderate amount of harm or moderately easy to cause an extreme amount of harm.  16  The reason why a black-ball technology that enables only moderate amounts of harm per incident could count as a Type-1 vulnerability is thatif the technology is sufficiently easy to usea large number of such incidents would be almost certain to occur. Take the scenario where it is easy for an average individual to make a metropolis-busting H-bomb. This is not necessarily a scenario in which a single individual could devastate civilization. Building hundreds of bombs and transporting them to hundreds of cities without getting caught would still be a formidable endeavor even if making a single bomb were fairly easy. The 'easy nukes' scenario nevertheless presents a civilizational vulnerability because it is plausible that there would in fact be hundreds of individuals who would each destroy at least one city under those circumstances. That this is so almost follows from the law of large numbers combined with the plausible assumption that for any randomly selected person there is some small but appreciable chance that they would be motivated to trigger this kind of destructionwhether out of ideological hatred, nihilistic destructiveness, revenge for perceived injustices, as part of some extortion plot, or because of delusions or mental illness, or perhaps even just to see what would happen. Given the diversity of human character and circumstance, for any ever so imprudent, immoral, or self-defeating action, there is some residual fraction of humans who would choose to take that action. This is especially plausible if the action in question represents a culturally salient affordance as it everywhere would after one such nuke attack had taken place. In other words, 'easy nukes' is an illustration of a vulnerable world because it looks like the apocalyptic residual has a large enough intersection with the set of empowered actors that one would expect a civilization-devastating amount of destruction to result. \n Type-2a ('safe first strike') A technology that 'democratizes' mass destruction is not the only kind of black ball that could be hoisted out of the urn. Another kind would be a technology that strongly incentivizes powerful actors to use their powers to cause mass destruction. Again we can turn to nuclear history for illustration. After the invention of the atomic bomb and a short-lived American nuclear monopoly, an arms race ensued between the US and the USSR. The rival superpowers amassed staggering arsenals, topping out at 70,000 nuclear warheads in 1986, more than enough to devastate civilization  (Norris and Kristensen, 2010) . While public awareness of the perils of the Cold War seems to have faded since its peaceful conclusion in 1991, the academic communitybenefiting from the opening of formerly classified archives and the testimony of retired policy makers, officers, and analystshas uncovered a disconcerting array of practices and incidents which seem to have repeatedly brought the world to the brink. 17 Just how close we came remains a topic of dispute. Some scholars have argued that it was only thanks to a good deal of luck that nuclear holocaust was avoided.  18  Whether surviving the Cold War required much luck or just a little, we can easily imagine a counterfactual in which the odds of avoiding a nuclear conflagration would be substantially worse. This holds even if we assume that nuclear weapons can be produced only by large technologically advanced states (thus distinguishing the case from the type-1 vulnerability of 'easy nukes'). The counterfactual could involve changes in the technological possibility frontier that would have made the arms race less stable. For example, it is widely believed among nuclear strategists that the development of a reasonably secure secondstrike capability by both superpowers by the mid-1960s created the conditions for 'strategic stability'  (Colby and Gerson, 2013) . Prior to this period, American war plans reflected a much greater inclination, in any crisis situation, to launch a preemptive nuclear strike against the Soviet Union's nuclear arsenal. The introduction of nuclear submarinebased ICBMs was thought to be particularly helpful for ensuring second-strike capabilities (and thus 'mutually assured destruction') since it was widely believed to be practically impossible for an aggressor to eliminate the adversary's boomer fleet in the initial attack.  19  Other strategies for ensuring a second-strike capability could also be employed, but they had drawbacks. For example, one option, briefly used by the United States, was to have a contingent of long-range nuclear bombers on continuous airborne alert  (Sagan, 1995) . This program was very costly and increased the risk of accidental or unauthorized attacks. Another option was to build hardened land-based missile silos: in sufficient numbers, these could in principle provide the assurance of a second-strike capability to one side; however, such a large arsenal would then threaten to provide the capacity of a safe first strike against the other side, thus again destabilizing any crisis. Road-mobile ICBM launchers, which are harder to attack than silo-based missiles, eventually provided some stabilization when they were deployed by the Soviet Union in 1985, a few years before the end of Cold War  (Brower, 1989) . So consider a counterfactual in which a preemptive counterforce strike is more feasible. Imagine some technology that makes it easy to track ballistic missile submarines. We can also imagine that nuclear weapons were a bit more fragile, so that the radius within which a nuclear weapon would be destroyed by the detonation of another nuclear weapon was substantially larger than it actually is.  20  Under those circumstances, it might have been impossible to ensure a second-strike capability. Suppose, further, that technology had been such as to make it very hard to detect missile launches, rendering a launch-on-warning strategy completely unworkable. The crisis instability of the Cold War would then have been greatly amplified. Whichever side struck first would survive relatively unscathed (or might at least have believed that it would, since the possibility of a nuclear winter was largely ignored by war planners at the time;  Badash, 2001; Ellsberg, 2017) .  21  The less aggressive side would be utterly destroyed. In such a situation, mutual fear could easily trigger a dash to all-out war  (Schelling, 1960) . Other technological parameter changes could similarly increase the probability of attacks. In the real world, the main 'attraction' of a nuclear first strike is that it would alleviate the fear that one might otherwise oneself become the victim of such a strike; but we can imagine a counterfactual in which there are also benefits to nuclear aggression, beyond the removal of a negative. Suppose it were somehow possible to derive great economic gains from initiating a large-scale nuclear assault.  22  It might be hard to see how this could be the case, yet one can imagine some automated manufacturing technology or energy technology making physical resources more valuable; or technology-enabled population growth could again make agricultural land a more vital resource  (Drexler, 1986) ). Some international relations scholars believe that the net economic benefits of conquest have declined substantially in the post-industrial era and that this decline has been a major contributor to peace.  23  If powerful national economic motives were again added to other causes for war (such as concern for one's own security, disputes over non-economic values, maintenance of national reputation, influence of particularly bellicose special interest groups, inter alia) then armed conflicts might become more common and large-scale nuclear war more likely. In these examples, the vulnerability arises not from destruction getting easier, but from the actions leading to destruction coming to be supported by stronger incentives. We shall call these Type-2 vulnerabilities. Specifically, a scenario like 'safe first strike', in which some enormously destructive action becomes incentivized, we shall refer to as Type-2a: Type-2a vulnerability: There is some level of technology at which powerful actors have the ability to produce civilization-devastating harms and, in the semi-anarchic default condition, face incentives to use that ability. We will see some more examples of Type-2a vulnerabilities below, where the 'civilization-devastating harms' take the form of risk externalities. \n Type-2b ('worse global warming') There is yet another way in which the world could be vulnerable; one that we can illustrate with a counterfactual related to climate change. In the real world, we observe a secular rise in global mean temperature, widely believed to be driven primarily by human-caused emissions of greenhouse gases such as carbon dioxide, methane, and nitrous oxide  (Stocker et al., 2014) .Projections vary, depending on the emissions scenario and modelling assumptions, but forecasts that imply an average temperature rise of between 3 o C and 4.5 o C in 2100  (compared to 2000) , in the absence of any significant action to reduce emissions, are quite typical (See  Stocker et al. (2014, table 12 .2)). The effects of such warmingon sea levels, weather patterns, ecosystems, and agricultureare usually expected to be net negative for human welfare (See  Field et al. (2014, figure    10-1 )). Greenhouse gases are emitted by wide range of activities, including in industry, transport, agriculture, and electricity production, and from all around the world, though especially from industrialized or industrializing countries. Efforts to curb emissions have so far failed to achieve much global-scale impact  (Friedlingstein et al., 2014) ). Now, we could imagine a situation in which the problem of global warming would be far more dire than it actually seems to be. For example, the transient climate sensitivity (a measure of the medium-term change in mean global surface temperature of the Earth that results from some kind of forcing, such as a doubling of atmospheric CO 2 ) could have turned out to be much greater than it is  (Shindell, 2014) . If it had been several times larger than its actual value, we would have been in for a temperature rise of, say, 15 o or 20 o C instead of 3 oa prospect with far greater civilization-destroying potential than the actual expectation.  24  We can also imagine other deviations from reality that would have made global warming a worse problem. Fossil fuels could have been even more abundant than they are, and available in more cheaply exploitable deposits, which would have encouraged greater consumption. At the same time, clean energy alternatives could have been more expensive and technologically challenging. Global warming could also have been a worse problem if there were stronger positive feedback loops and nonlinearities, such as an initial phase in which the atmosphere is gradually loaded up with greenhouse gases without much observable or detrimental effect, followed by a second phase in which temperatures shoot up abruptly. To get a truly civilizational threat from global warming, it may also be necessary to stipulate, counterfactually, that mitigation through geoengineering is infeasible. The vulnerability illustrated by such a 'worse global warming' scenario is different from that of a Type-2a scenario like 'safe first strike'. In a Type-2a vulnerability, some actor has the ability to take some actionsuch as launching a nuclear first strikethat is destructive enough to devastate civilization. In the 'worse global warming' scenario, no such actor need exist. Instead, in what we will call a Type-2b vulnerability, there is a large number of individually insignificant actors who is each incentivized (under the semianarchic default condition) to take some action that contributes slightly to what cumulatively becomes a civilizationdevastating problem: Type-2b vulnerability: There is some level of technology at which, in the semi-anarchic default condition, a great many actors face incentives to take some slightly damaging action such that the combined effect of those actions is civilizational devastation. What Type-2a and Type-2b have in common is that, in both cases, the damage-capable actors face incentives that would encourage a wide range of normally motivated actors in their situation to pursue the course of action that leads to damage. Global warming would not be a problem if only some small fraction of those actors who can drive cars or chop down a few trees chose to do so; the problem arises only because many actors make these choices. And in order for many actors to make those choices, the choices must be supported by incentives that have wide appeal (such as money, status, and convenience). Similarly, if only one in a million actors who could launch a nuclear first strike would actually choose to do so, then it would not be so alarming if there are a handful of actors possessing that capability; but it does get worrisome if launching a nuclear strike is strongly supported by incentives that appeal to normally-motivated actors (such as the motive of preempting a strike by one's adversary). This is in contrast to a Type-1 vulnerability, where the problem arises from the very widespread proliferation of destructive capability. Only an actor with quite unusual values would choose, at great cost and risk to himself, to blow up a city or unleash a doomsday pathogen; the trouble in that case is that if sufficiently many actors possess such a capability, then the subset of them who also have apocalyptic motives is not empty. \n Type-0 ('surprising strangelets') In 1942, it occurred to Edward Teller, one of the Manhattan scientists, that a nuclear explosion would create a temperature unprecedented in Earth's history, producing conditions similar to those in the center of the sun, and that this could conceivably trigger a self-sustaining thermonuclear reaction in the surrounding air or water  Rhodes, 1986) . The importance of Teller's concern was immediately recognized by Robert Oppenheimer, the head of the Los Alamos lab. Oppenheimer notified his superior and ordered further calculations to investigate the possibility. These calculations indicated that atmospheric ignition would not occur. This prediction was confirmed in 1945 by the Trinity test, which involved the detonation of the world's first nuclear explosive.  25  In 1954, the US carried out another nuclear test, the Castle Bravo test, which was planned as a secret experiment with an early lithium-based thermonuclear bomb design. Lithium, like uranium, has two important isotopes: lithium-6 and lithium-7. Ahead of the test, the nuclear scientists calculated the yield to be 6 megatons (with an uncertainty range of 4-8 megatons). They assumed that only the lithium-6 would contribute to the reaction, but they were wrong. The lithium-7 contributed more energy than the lithium-6, and the bomb detonated with a yield of 15 megatonmore than double of what they had calculated (and equivalent to about 1,000 Hiroshimas). The unexpectedly powerful blast destroyed much of the test equipment. Radioactive fallout poisoned the inhabitants of downwind islands and the crew of a Japanese fishing boat, causing an international incident. We may regard it at as lucky that it was the Castle Bravo calculation that was incorrect, and not the calculation of whether the Trinity test would ignite the atmosphere. Counterfactually, if the atmosphere had been susceptible to ignition by a nuclear detonation, and if this fact had been relatively easy to overlooklet us say as easy as it was to overlook the contribution of the lithium-7 in the Castle Bravo testthen the human story (and that of all terrestrial life) would have come to an end in 1945. We can call this scenario 'Castle Bravissimo'. Whenever we pull a ball from the urn of invention, there could conceivably be a possibility of accidental devastation. Usually, this risk is negligible; but in some cases it could be significant, especially when the technology in question generates some kind of novel perturbation of nature or introduces historically unprecedented conditions. This suggests that we should add to our typology one more category, that of technology-fated accidental civilizational devastation: Type-0 vulnerability: There is some technology that carries a hidden risk such that the default outcome when it is discovered is inadvertent civilizational devastation.  26  It is instructive to note, however, that 'Castle Bravissimo' is not a perfect illustration of a Type-0 vulnerability. Suppose that careful calculations had shown that there was a 1 per cent probability that a nuclear detonation would ignite the atmosphere and the oceans and thereby extinguish life on Earth. Suppose, further, that it had been known that to resolve the matter further and prove that the chance was zero (or alternatively, that the chance was one) would take another 10 years of meticulous study. It is unclear, under those circumstances, what the leaders of the Manhattan project would have decided. They would presumably have thought it greatly desirable that humanity hold off on developing nuclear weapons for at least another 10 years.  27  On the other hand, they would have feared that Germany might have an advanced bomb project and that Hitler maybe would not pull the brakes because of a 1 per cent risk of destroying the world.  28  They might have concluded that the risk of testing a nuclear bomb was worth taking in order to reduce the probability of Nazi Germany ending up with a nuclear monopoly. In this version of 'Castle Bravissimo', civilization gets blown up by accident: nobody sought to cause a destructive event. Yet the key actors were locked in a strategic situation that incentivized them to proceed despite the risk. In this respect, the scenario fits as a Type-2a vulnerability; only, the civilization-devastating harm it involves is probabilistic. When nuclear technology becomes possible, powerful actors face incentives, in the semi-anarchic default condition, to use that technology in ways that produce civilization-destroying harms (which here take the form of risk externalities).  29  Accordingly, in order for us to diagnose a Type-0 vulnerability, we require that a stronger condition be met than merely that the key actors did not intend destruction. We stipulate that 'inadvertent' should here mean that the adverse outcome sprang from bad luck, not coordination failure. In a Type-0 vulnerability, the key actors would, even if they were adequately coordinated, decide to proceed with using the technology, in the belief that the benefits would outweigh costsbut they would be wrong, and the costs would be larger than expected, enough so as to cause civilizational devastation.  30  Since 'Castle Bravissimo' only ambiguously satisfies this criterion (it being unclear in the original counterfactual to what extent the disaster would have resulted from coordination failure and to what extent from miscalculation/bad luck), it may be useful to introduce a cleaner example of a Type-0 vulnerability. Thus, consider a 'surprising strangelets' scenario in which some modern high-energy physics experiment turns out to initiate a self-catalyzing process in which ordinary matter gets converted into strange matter, with the result that our planet is destroyed. This scenario, and variations thereof in which accelerator experiments generate stable black holes or trigger the decay of a metastable vacuum state, have been analyzed in the literature  (Jaffe et al., 2000; Tegmark and Bostrom, 2005) . Such outcomes would indeed be very surprising, since analysis indicates that they have a completely negligible chance of occurring. Of course, with sufficiently bad luck, a negligiblechance event could occur. But alternatively (and far more likely in this case), the analysis could have a hidden flaw, like the Castle Bravo calculations did; in which case the chance might not be so negligible after all  (Ord et al., 2010) .  31   \n Achieving stabilization The truth of VWH would be bad news. But it would not imply that civilization will be devastated. In principle at least, there are several responses that could stabilize the world even if vulnerability exists. Recall that we defined the hypothesis in terms of a black-ball technology making civilizational devastation extremely likely conditional on technological development continuing and the semi-anarchic default condition persisting. Thus we can theoretically consider the following possibilities for achieving stabilization: 1. Restrict technological development. 2. Ensure that there does not exist a large population of actors representing a wide and recognizably human distribution of motives. 3. Establish extremely effective preventive policing. 4. Establish effective global governance. We will discuss (3) and (  4 ) in subsequent sections. Here we consider (1) and (  2 ). We will argue they hold only limited promise as ways of protecting against potential civilizational vulnerabilities. \n Technological relinquishment In its general form, technological relinquishment looks exceedingly unpromising. Recall that we construed the word 'technology' broadly; so that completely stopping technological development would require something close to a cessation of inventive activity everywhere in the world. That is hardly realistic; and if it could be done, it would be extremely costlyto the point of constituting an existential catastrophe in its own right (Namely, 'permanent stagnation'  (Bostrom, 2013) ). That general relinquishment of scientific and technological research is a non-starter does not, however, imply that limited curtailments of inventive activities could not be a good idea. It can make sense to forego particularly perilous directions of advancement. For instance, recalling our 'easy nukes' scenario, it would be sensible to discourage research into laser isotope separation for uranium enrichment  (Kemp, 2012) . Any technology that makes it possible to produce weapons-grade fissile material using less energy or with a smaller industrial footprint would erode important barriers to proliferation. It is hard to see how a slight reduction in the price of nuclear energy would compensate. On the contrary, the world would probably be better off if it somehow became harder and more expensive to enrich uranium. What we would ideally want in this area is not technological progress but technological regress. While targeted regress might not be in the cards, we could aim to slow the rate of advancement towards risk-increasing technologies relative to the rate of advancement in protective technologies. This is the idea expressed by the principle of differential technological development. In its original formulation, the principle focuses on existential risk; but we can apply it more broadly to also encompass technologies with 'merely' devastational potential: Principle of Differential Technological Development. Retard the development of dangerous and harmful technologies, especially ones that raise the level of existential risk; and accelerate the development of beneficial technologies, especially those that reduce the existential risks posed by nature or by other technologies  Bostrom, 2002) . The principle of differential technological development is compatible with plausible forms of technological determinism. For example, even if it were ordained that all technologies that can be developed will be developed, it can still matter when they are developed. The order in which they arrive can make an important differenceideally, protective technologies should come before the destructive technologies against which they protect; or, if that is not possible, then it is desirable that the gap be minimized so that other countermeasures (or luck) may tide us over until robust protection become available. The timing of an invention also influences what sociopolitical context the technology is born into. For example, if we believe that there is a secular trend toward civilization becoming more capable of handling black balls, then we may want to delay the most risky technological developments, or at least abstain from accelerating them. Even if we suppose that civilizational devastation is unavoidable, many would prefer it to take place further into the future, at a time when maybe they and their loved ones are no longer alive anyway.  32  Differential technological development doesn't really make sense in the original urn-of-creativity model, where the color of each ball comes as a complete surprise. If we want to use the urn model in this context, we must modify it. We could stipulate, for example, that the balls have different textures and that there is a correlation between texture and color, so that we get clues about the color of a ball before we extract it. Another way to make the metaphor more realistic is to imagine that there are strings or elastic bands between some of the balls, so that when we pull on one of them we drag along several others to which it is linked. Presumably the urn is highly tubular, since certain technologies must emerge before others can be reached (we are not likely to find a society that uses jet planes and flint axes). The metaphor would also become more realistic if we imagine that there is not just one hand daintily exploring the urn: instead, picture a throng of scuffling prospectors reaching in their arms in hopes of gold and glory, and citations. Correctly implementing differential technological development is clearly a difficult strategic task (Cf.  Collingridge, 1980) . Nevertheless, for an actor who cares altruistically about long-term outcomes and who is involved in some inventive enterprise (e.g. as a researcher, funder, entrepreneur, regulator, or legislator) it is worth making the attempt. Some implications, at any rate, seem fairly obvious: for instance, don't work on laser isotope separation, don't work on bioweapons, and don't develop forms of geoengineering that would empower random individuals to unilaterally make drastic alterations to the Earth's climate. Think twice before accelerating enabling technologiessuch as DNA synthesis machinesthat would directly facilitate such ominous developments.  33  But boost technologies that are predominantly protective; for instance, ones that enable more efficient monitoring of disease outbreaks or that make it easier to detect covert WMD programs. Even if it is the case that all possible 'bad' technologies are bound to be developed eventually, it can still be helpful to buy a little time.  34  However, differential technological development does not on its own offer a solution for vulnerabilities that persist over long periodsones where adequately protective technologies are much harder to develop than their destructive counterparts, or where destruction has the advantage even at technological maturity.  35   \n Preference modification Another theoretically possible way of achieving civilizational stabilization would be to change the fact that there exists a large population of actors representing a wide and recognizably human distribution of motives. We reserve for later discussion of interventions that would reduce the effective number of independent actors by increasing various forms of coordination. Here we consider the possibility of modifying the distribution of preferences (within a more or less constant population of actors). The degree to which this approach holds promise depends on which type of vulnerability we have in mind. In the case of a Type-1 vulnerability, preference modification does not look promising, at least in the absence of extremely effective means for doing so. Consider that some Type-1 vulnerabilities would result in civilizational devastation if there is even a single empowered person anywhere in the world who is motivated to pursue the destructive outcome. With that kind of vulnerability, reducing the number of people in the apocalyptic residual would do nothing to forestall devastation unless the number could be reduced all the way to zero, which may be completely infeasible. It is true that there are other possible Type-1 vulnerabilities that would require a somewhat larger apocalyptic residual in order for civilizational devastation to occur: for example, in a scenario like 'easy nukes', maybe there would have to be somebody from the apocalyptic residual in each of several hundred cities. But this is still a very low bar. It is difficult to imagine an interventionshort of radically re-engineering human nature on a fully global scalethat would sufficiently deplete the apocalyptic residual to entirely eliminate or even greatly reduce the threat of Type-1 vulnerabilities. Note that an intervention that halves the size of the apocalyptic residual would not (at least not through any firstorder effect) reduce the expected risk from Type-1 vulnerabilities by anywhere near as much. A reduction of 5 per cent or 10 per cent of Type-1 risk from halving the apocalyptic residual would be more plausible. The reason is that there is wide uncertainty about how destructive some new blackball technology would be, and we should arguably use a fairly uniform prior in log space (over several orders of magnitude) over the size of apocalyptic residual that would be required in order for civilizational devastation to occur conditional on a Type-1 vulnerability arising. In other words, conditional on some new technology being developed that makes it easy for an average individual to kill at least one million people, it may be (roughly) as likely that the technology would enable the average individual to kill one million people, ten million people, a hundred million people, a billion people, or every human alive. These considerations notwithstanding, preference modification could be helpful in scenarios in which the set of empowered actors is initially limited to some small definable subpopulation. Some black-ball technologies, when they first emerge from the urn, might be difficult to use and require specialized equipment. There could be a period of several years before such a technology has been perfected to the The Vulnerable World Hypothesis point where an average individual could master it. During this early period, the set of empowered actors could be quite limited; for example, it might consist exclusively of individuals with bioscience expertise working in a particular type of lab. Closer screening of applicants to positions in such labs could then make a meaningful dent in the risk that a destructive individual gains access to the biotech black ball within the first few years of its emergence.  36  And that reprieve may offer an opportunity to introduce other countermeasures to provide more lasting stabilization, in anticipation of the time when the technology gets easy enough to use that it diffuses to a wider population. For Type-2a vulnerabilities, the set of empowered actors is much smaller. Typically what we are dealing with here are states, perhaps alongside a few especially powerful nonstate actors. In some Type-2a scenarios, the set might consist exclusively of two superpowers, or a handful of states with special capabilities (as is currently the case with nuclear weapons). It could thus be very helpful if the preferences of even a few powerful states were shifted in a more peaceloving direction. The 'safe first strike' scenario would be a lot less alarming if the actors facing the security dilemma had attitudes towards one another similar to those prevailing between Finland and Sweden. For many plausible sets of incentives that could arise for powerful actors as a consequence of some technological breakthrough, the prospects for a non-devastational outcome would be significantly brightened if the actors in question had more irenic dispositions. Although this seems difficult to achieve, it is not as difficult as persuading almost all the members in the apocalyptic residual to alter their dispositions. Lastly, consider Type-2b. Recall that such a vulnerability entails that 'by default' a great many actors face incentives to take some damaging action, such that the combined effects add up to civilizational devastation. The incentives for using the black-ball technology must therefore be ones that have a grip on a substantial fraction of the world populationeconomic gain being perhaps being the prime example of such a near-universal motivation. So imagine some private action, available to almost every individual, which saves each person who takes it a fraction X of his or her annual income, while producing a negative externality such that if half the world's population takes the action then civilization gets devastated. At X = 0, we can assume that few people would take the antisocial action. But the greater X is, the larger the fraction of the population that would succumb to temptation. Unfortunately, it is plausible that the value of X that would induce at least half of the population to take the action is small, perhaps less than 1 per cent.  37  While it would be desirable to change the distribution of global preferences so as to make people more altruistic and raise the value of X, this seems difficult to achieve. (Consider the many strong forces already competing for hearts and mindscorporate advertisers, religious organizations, social movements, education systems, and so on.) Even a dramatic increase in the amount of altruism in the worldcorresponding, let us say, to a doubling of X from 1 per cent to 2 per centwould prevent calamity only in a relatively narrow band of scenarios, namely those in which the private benefit of using the destructive technology is in the 1-2 per cent range. Scenarios in which the private gain exceeds 2 per cent would still result in civilizational devastation. In sum, modifying the distribution of preferences within the set of actors that would be destructively empowered by a black-ball discovery could be a useful adjunct to other means of stabilization, but it can be difficult to implement and would at best offer only very partial protection (unless we assume extreme forms of worldwide re-engineering of human nature).  38   \n Some specific countermeasures and their limitations Beside influencing the direction of scientific and technological progress, or altering destruction-related preferences, there are a variety of other possible countermeasures that could mitigate a civilizational vulnerability. For example, one could try to: • prevent the dangerous information from spreading; • restrict access to requisite materials, instruments, and infrastructure; • deter potential evildoers by increasing the chance of their getting caught; • be more cautious and do more risk assessment work; and • establish some kind of surveillance and enforcement mechanism that would make it possible to interdict attempts to carry out a destructive act It should be clear from our earlier discussion and examples that the first four of these are not general solutions. Preventing information from spreading could easily be infeasible. Even if it could be done, it would not prevent the dangerous information from being independently rediscovered. Censorship seems to be at best a stopgap measure.  39  Restricting access to materials, instruments, and infrastructure is a great way to mitigate some kinds of (gray-ball) threats, but it is unavailing for other kinds of threatssuch as ones in which the requisite ingredients are needed in too many places in the economy or are already ubiquitously available when the dangerous idea is discovered (such as glass, metal, and batteries in the 'easy nukes' scenario). Deterring potential evildoers makes good sense; but for sufficiently destructive technologies, the existence of an apocalyptic residual renders deterrence inadequate even if every perpetrator were certain to get caught. Exercising more caution and doing more risk assessment is also a weak and limited strategy. One actor unilaterally deciding to be more cautious may not help much with respect to a Type-2a vulnerability, and would do basically nothing for one of Type-2b or Type-1. In the case of a Type-0 vulnerability, it could help if the pivotal actor were more cautiousthough only if the first cautiously tiptoeing actor were not followed by an onrush of incautious actors getting access to the same risky technology (unless the world had somehow, in the interim, been stabilized by other means).  40  And as for risk assessment, it could lower the risk only if it led to some other countermeasure being implemented.  41  The last countermeasure in the listsurveillancedoes point towards a more general solution. We will discuss it in the next section under the heading of 'preventive policing'. But we can already note that on its own it is not sufficient. For example, consider a Type-2b vulnerability such as 'worse global warming'. Even if surveillance made it possible for a state to perfectly enforce any environmental regulation it chooses to impose, there is still the problem of getting a sufficient plurality of states to agree to adopt the requisite regulationsomething which could easily fail to happen. The limitations of surveillance are even more evident in the case of Type-2a vulnerability, such as 'safe first strike', where the problem is that states (or other powerful actors) are strongly incentivized to perform destructive acts. The ability of those states to perfectly control what goes on within their own borders does not solve this problem. What is needed to reliably solve problems that involve challenges of international coordination, is effective global governance. \n Governance gaps The limitations of technological relinquishment, preference modification, and various specific countermeasures as responses to a potential civilizational vulnerability should now be clear. To the extent, therefore, that we are concerned that VWH may be true, we must consider the remaining two possible ways of achieving stabilization: 1. Create the capacity for extremely effective preventive policing. Develop the intra-state governance capacity needed to prevent, with extremely high reliability, any individual or small groupincluding ones that cannot be deterred from carrying out any action that is highly illegal; and 2. Create the capacity for strong global governance. Develop the inter-state governance capacity needed to reliably solve the most serious global commons problems and ensure robust cooperation between states (and other strong organizations) wherever vital security interests are at stakeeven where there are very strong incentives to defect from agreements or refuse to sign on in the first place. The two governance gaps reflected by (  1 ) and (  2 ), one at the micro-scale, the other at the macro-scale, are two Achilles' heels of the contemporary world order. So long as they remain unprotected, civilization remains vulnerable to a potential technological black ball that would enable a strike to be directed there. Unless and until such a discovery emerges from the urn, it is easy to overlook how exposed we are. In the following two sections, we will discuss how filling in these governance gaps is necessary to achieve a general ability to stabilize potential civilizational vulnerabilities. It goes without saying that there are great difficulties, and also very serious potential downsides, in seeking progress towards (1) and (2). In this paper, we will say little about the difficulties and almost nothing about the potential downsidesin part because these are already rather well known and widely appreciated. However, we emphasize that the lack of discussion about arguments against (1) and (2) should not be interpreted as an implicit assertion that these arguments are weak or that they do not point to important concerns. They would, of course, have to be taken into account in an all-things-considered evaluation. But such an evaluation is beyond the scope of the present contribution, which focuses specifically on considerations flowing from VWH. \n Preventive policing Suppose that a Type-1 vulnerability opens up. Somebody discovers a really easy way to cause mass destruction. Information about the discovery spreads. The requisite materials and instruments are ubiquitously available and cannot quickly be removed from circulation. Of course it is highly illegal for any non-state actor to destroy a city, and anybody caught doing so would be subject to harsh penalties. But it is plausible that more than one person in a million belongs to an undeterrable apocalyptic residual. Though small in relative terms, if each such person creates a city-destroying event, the absolute number is still too large for civilization to endure. So what to do? If we suddenly found ourselves in such a situation, it may be too late to prevent civilization from being destroyed. However, it is possible to envisage scenarios in which human society would survive such a challenge intactand the even harder challenge where individuals can singlehandedly destroy not just one city but the entire world. What would be required to stabilize such vulnerabilities is an extremely well-developed preventive policing capacity. States would need the ability to monitor their citizens closely enough to allow them to intercept anybody who begins preparing an act of mass destruction. The feasibility of such surveillance and interception depend on the specifics of the scenario: How long does it take to deploy the black-ball technology destructively? how observable are the actions involved? can they be distinguished from behavior that we don't want to prohibit? But it is plausible that a considerable chunk of the Type-1 vulnerability spectrum could be stabilized by a state that deploys currently available technologies to the fullest extent. And expected advances in surveillance technology will greatly expand the achievable protection. For a picture of what a really intensive level of surveillance could look like, consider the following vignette: \n High-tech Panopticon Everybody is fitted with a 'freedom tag'a sequent to the more limited wearable surveillance devices familiar today, such as the ankle tag used in several countries as a prison alternative, the bodycams worn by many police forces, the pocket trackers and wristbands that some parents use to keep track of their children, and, of course, the ubiquitous cell phone (which has been characterized as 'a personal tracking device that can also be used to make calls').  42  The freedom tag is a slightly more advanced appliance, worn around the neck and bedecked with multidirectional cameras and microphones. Encrypted video and audio is continuously uploaded from the device to the cloud and machine-interpreted in real time. AI algorithms classify the activities of the wearer, his hand movements, nearby objects, and other situational cues. If suspicious activity is detected, the feed is relayed to one of several patriot monitoring stations. These are vast office complexes, staffed 24/7. There, a freedom officer reviews the video feed on several screens and listens to the audio in headphones. The freedom officer then determines an appropriate action, such as contacting the tagwearer via an audiolink to ask for explanations or to request a better view. The freedom officer can also dispatch an inspector, a police rapid response unit, or a drone to investigate further. In the small fraction of cases where the wearer refuses to desist from the proscribed activity after repeated warnings, an arrest may be made or other suitable penalties imposed. Citizens are not permitted to remove the freedom tag, except while they are in environments that have been outfitted with adequate external sensors (which however includes most indoor environments and motor vehicles). The system offers fairly sophisticated privacy protections, such as automated blurring of intimate body parts, and it provides the option to redact identity-revealing data such as faces and name tags and release it only when the information is needed for an investigation. Both AI-enabled mechanisms and human oversight closely monitor all the actions of the freedom officers to prevent abuse.  43  Creating and operating the High-tech Panopticon would require substantial investment, but thanks to the falling price of cameras, data transmission, storage, and computing, and the rapid advances in AI-enabled content analysis, it may soon become both technologically feasible and affordable. For example, if the cost of applying this to one individual for 1 year falls to around US$140, then the entire world population could be continuously monitored at a cost of less than 1 per cent of world GDP. At that price, the system would plausibly represent a net savingeven setting aside its use in preventing civilization-scale cataclysmsbecause of its utility for regular law enforcement. If the system works as advertised, many forms of crime could be nearly eliminated, with concomitant reductions in costs of policing, courts, prisons, and other security systems. It might also generate growth in many beneficial cultural practices that are currently inhibited by a lack of social trust. If the technical barriers to High-tech Panopticon are rapidly coming down, how about its political feasibility? One possibility is that society gradually drifts towards total social transparency even absent any big shock to the system. It may simply become progressively easier to collect and analyze information about people and objects, and it may prove quite convenient to allow that to be done, to the point where eventually something close to full surveillance becomes a realityclose enough that with just one more turn of the screw it can be turned into High-tech Panopticon.  44  An alternative possibility is that some particular Type-1 vulnerability comes sufficiently starkly into view to scare states into taking extreme measures, such as launching a crash program to create universal surveillance. Other extreme measures that could be attempted in the absence of a fully universal monitoring system might include adopting a policy of preemptive incarceration, say whenever some set of unreliable indicators suggest a greater than1 per cent probability that some individual will attempt a city-destroying act or worse.  45  Political attitudes to such policies would depend on many factors, including cultural traditions and norms about privacy and social control; but they would also depend on how clearly the civilizational vulnerability was perceived. At least in the case of vulnerabilities for which there are several spectacular warning shots, it is plausible that the risk would be perceived very clearly. In the 'easy nukes' scenario, for example, after the ruination of a few great cities, there would likely be strong public support for a policy which, for the sake of forestalling another attack, would involve incarcerating a hundred innocent people for every genuine plotter.  46  In such a scenario, the creation of a High-tech Panopticon would probably be widely supported as an overwhelmingly urgent priority. However, for vulnerabilities not preceded or accompanied by such incontrovertible evidence, the will to robust preventive action may never materialize. Extremely effective preventive policing, enabled by ubiquitous real-time surveillance, may thus be necessary to stabilize a Type-1 vulnerability. Surveillance is also relevant to some other types of vulnerability, although not so centrally as in the case of Type-1. In a Type-2b vulnerability, the bad outcome is brought about by the combined actions of a mass of independent actors who are incentivized to behave destructively. But unless the destructive behaviours are very hard to observe, intensification of surveillance or preventive policing would not be needed to achieve stabilization. In 'worse global warming', for instance, it is not essential that individual actions be preempted. Dangerous levels of emissions take time to accumulate, and polluters can be held accountable after the fact; and it is tolerable if a few of them slip through the cracks. For other Type-2b vulnerabilities, however, enhanced methods of surveillance and social control could be important. Consider 'runaway mob', a scenario in which a mob forms that kills anybody it comes into contact with who refuses to join, and which grows ever bigger and more formidable (Cf.  Munz et al., 2009) . The ease with which such bad social equilibria can form and propagate, the feasibility of reforming them once they have taken hold, and the toll they exact on human welfare, depend on parameters that could be changed by technological innovations, potentially for the worse. Even today, many states struggle to subdue organized crime. A black-ball invention (perhaps some clever cryptoeconomic mechanism design) that makes criminal enterprises much more scalable or more damaging in their social effects might create a vulnerability that could only be stabilized if states possessed unprecedented technological powers of surveillance and social control. As regards to Type-2a vulnerabilities, where the problem arises from the incentives facing state powers or other mighty actors, it is less clear how domestic surveillance could help. Historically, stronger means for social control may even have worsened inter-state conflictthe bloodiest inter-state conflicts have depended on the highly effective governance capacities of the modern state, for tax collection, conscription, and war propaganda. It is conceivable that improved surveillance could indirectly facilitate the stabilization of a Type-2a vulnerability, such as by changing sociocultural dynamics or creating new options for making arms-reduction treaties or non-aggression pacts more verifiable. But it seems equally plausible that the net effect of strengthened domestic surveillance and policing powers on Type-2a vulnerabilities would, in the absence of reliable mechanisms for resolving international disputes, be in the opposite direction (i.e. tending to produce or exacerbate such vulnerabilities rather than to stabilize them). \n Global governance Consider again 'safe first strike': states with access to the black-ball technology by default face strong incentives to use it destructively even though it would be better for everybody that no state did so. The original example involved a counterfactual with nuclear weapons, but looking to the future we might get this kind of black ball from advances in biological weapons, or atomically precise manufacturing, or the creation of vast swarms of killer drones, or artificial intelligence, or something else. The set of state actors then confronts a collective action problem. Failure to solve this problem means that civilization gets devastated in a nuclear Armageddon or another comparable disaster. It is plausible that, absent effective global governance, states would in fact fail to solve this problem. By assumption, the problem confronting us here presents special challenges; yet states have frequently failed to solve easier collective action problems. Human history is covered head to foot with the pockmarks of war. With effective global governance, however, the solution becomes trivial: simply prohibit all states from wielding the black-ball technology destructively. In the case of 'safe first strike', the most obvious way to do this would be by ordering that all nuclear weapons be dismantled and an inspection regime set up, with whatever level of intrusiveness is necessary to guarantee that nobody recreates a nuclear capability. Alternatively, the global governance institution itself could retain an arsenal of nuclear weapons as a buffer against any breakout attempt. To deal with Type-2a vulnerabilities, what civilization requires is a robust ability to achieve global coordination, specifically in matters where state actions have extremely large externalities. Effective global governance would also help with those Type-1 and Type-2b scenarios where some states are reluctant to institute the kind of preventive policing that would be needed to reliably prevent individuals within their territories from carrying out a destructive act. Consider a biotechnological black ball that is powerful enough that a single malicious use could cause a pandemic that would kill billions of people, thus presenting a Type-1 vulnerability. It would be unacceptable if even a single state fails to put in place the machinery necessary for continuous surveillance and control of its citizens (or whatever other mechanisms are necessary to prevent malicious use with virtually perfect reliability). A state that refuses to implement the requisite safeguardsperhaps on grounds that it values personal freedom too highly or accords citizens a constitutionally inscribed right to privacywould be a delinquent member of the international community. Such a state, even if its governance institutions functioned admirably in other respects, would be analogous to a 'failed state' whose internal lack of control makes it a safe haven for pirates and international terrorists (though of course in the present case the risk externality it would be imposing on the rest of the world would be far larger). Other states certainly would have ground for complaint. A similar argument applies to Type-2b vulnerabilities, such as a 'worse global warming' scenario in which some states are inclined to free-ride on the costly efforts of others to cut emissions. An effective global governance institution could compel every state to do its part. We thus see that while some possible vulnerabilities can be stabilized with preventive policing alone, and some other vulnerabilities can be stabilized with global governance alone, there are some that would require both. Extremely effective preventive policing would be required because individuals can engage in hard-to-regulate activities that must nevertheless be effectively regulated, and strong global governance would be required because states may have incentives not to effectively regulate those activities even if they have the capability to do so. In combination, however, ubiquitous-surveillance-powered preventive policing and effective global governance would be sufficient to stabilize most vulnerabilities, making it safe to continue scientific and technological development even if VWH is true.  47   \n Discussion Comprehensive surveillance and global governance would thus offer protection against a wide spectrum of civilizational vulnerabilities. This is a considerable reason in favor of bringing about those conditions. The strength of this reason is roughly proportional to the probability that the vulnerable world hypothesis is true. It goes without saying that a mechanism that enables unprecedentedly intense forms of surveillance, or a global governance institution capable of imposing its will on any nation, could also have bad consequences. Improved capabilities for social control could help despotic regimes protect themselves from rebellion. Ubiquitous surveillance could enable a hegemonic ideology or an intolerant majority view to impose itself on all aspects of life, preventing individuals with deviant lifestyles or unpopular beliefs from finding refuge in anonymity. And if people believe that everything they say and do is, effectively, 'on the record', they might become more guarded and blandly conventional, sticking closely to a standard script of politically correct attitudes and behaviours rather than daring to say or do anything provocative that would risk making them the target of an outrage mob or putting an indelible disqualifying mark on their r esum e. Global governance, for its part, could reduce beneficial forms of inter-state competition and diversity, creating a world order with single point of failure: if a world government ever gets captured by a sufficiently pernicious ideology or special interest group, it could be game over for political progress, since the incumbent regime might never allow experiments with alternatives that could reveal that there is a better way. Also, being even further removed from individuals and culturally cohesive 'peoples' than are typical state governments, such an institution might by some be perceived as less legitimate, and it may be more susceptible to agency problems such as bureaucratic sclerosis or political drift away from the public interest.  48  It also goes without saying that stronger surveillance and global governance could have various good consequences aside from stabilizing civilizational vulnerabilities (see also  Re, 2016 )) ;  Bostrom, 2006; cf. Torres, 2018) ). More effective methods of social control could reduce crime and alleviate the need for harsh criminal penalties. They could foster a climate of trust that enables beneficial new forms of social interaction and economic activity to flourish. Global governance could prevent interstate wars, including ones that do not threaten civilizational devastation, and reduce military expenditures, promote trade, solve various global environmental and other commons problems, calm nationalistic hatreds and fears, and over time perhaps would foster an enlarged sense of cosmopolitan solidarity. It may also cause increased social transfers to the global poor, which some would view as desirable. Clearly, there are weighty arguments both for and against moving in these directions. This paper offers no judgment about the overall balance of these arguments. The ambition here is more limited: to provide a framework for thinking about potential technology-driven civilizational vulnerabilities, and to point out that greatly expanded capacities for preventive policing and global governance would be necessary to stabilize civilization in a range of scenarios. Yes, this analysis provides an additional reason in favor of developing those capacities, a reason that does not seem to have been playing a significant role in many recent conversations about related issues, such as debates about government surveillance and about proposed reforms of international and supranational institutions.  49  When this reason is added to the mix, the evaluation should therefore become more favourable than it otherwise would have been towards policies that would strengthen governance capacities in these ways. However, whether or not this added reason is sufficiently weighty to tip the overall balance would depend on other considerations that fall outside the scope of this paper. It is worth emphasizing that the argument in this paper favors certain specific forms of governance capacity strengthening. With respect to surveillance and preventive policing, VWH-concerns point specifically to the desirability of governance capacity that makes it possible to extremely reliably suppress activities that are very strongly disapproved of by a very large supermajority of the population (and of power-weighted domestic stakeholders). It provides support for other forms of governance strengthening only insofar as they help create this particular capacity. Similarly, with respect to global governance, VWH-based arguments support developing institutions that are capable of reliably resolving very high-stakes international coordination problems, ones where a failure to reach a solution would result in civilizational devastation. This would include having the capacity to prevent great power conflicts, suppress arms races in weapons of mass destruction, regulate development races and deployment of potential black-ball technologies, and successfully manage the very worst kinds of tragedy of the commons. It need not include the capacity to make states cooperate on a host of other issues, nor does it necessarily include the capacity to achieve the requisite stabilization using only fully legitimate means. While those capacities may be attractive for other reasons, they do not immediately emerge as desiderata simply from taking VWH seriously. For example, so far as VWH is concerned, it would theoretically be satisfactory if the requisite global governance capacity comes into existence via the rise of one superpower to a position of sufficient dominance to give it the ability, in a sufficiently dire emergency, unilaterally to impose a stabilization scheme on the rest of the world. One important issue that we still need to discuss is that of timing. Even if we became seriously concerned that the urn of invention may contain a black ball, this need not move us to favor establishing stronger surveillance or global governance now, if we thought that it would be possible to take those steps later, if and when the hypothesized vulnerability came clearly into view. We could then let the world continue its sweet slumber, in the confident expectation that as soon as the alarm goes off it will leap out of bed and undertake the required actions. But we should question how realistic that plan is. Some historical reflection is useful here. Throughout the Cold War, the two superpowers (and the entire northern hemisphere) lived in continuous fear of nuclear annihilation, which could have been triggered at any time by accident or as the result of some crisis spiralling out of control. The reality of the threat was accepted by all sides. This risk could have been substantially reduced simply by getting rid of all or most nuclear weapons (a move which, as a nice side effect, could also have saved more than ten trillion dollars). 5051 Yet, after several decades of effort, only limited nuclear disarmament and other risk-reduction measures were implemented. Indeed the threat of nuclear annihilation remains with us to this day. In the absence of strong global governance that can enforce a treaty and compel disputants to accept a compromise, the world has so far been unable to solve this most obvious collective action problem.  52  But perhaps the reason why the world has failed to eliminate the risk of nuclear war is that the risk was insufficiently great? Had the risk been higher, one could eupeptically argue, then the necessary will to solve the global governance problem would have been found. Perhapsthough it does seem rather shaky ground on which to rest the fate of civilization. We should note that although a technology even more dangerous than nuclear weapons may stimulate a greater will to overcome the obstacles to achieving stabilization, other properties of a black ball could make the global governance problem more challenging than it was during the Cold War. We have already illustrated this possibility in scenarios such as 'safe first strike' and 'worse global warming'. We saw how certain properties of a technology set could generate stronger incentives for destructive use or for refusing to join (or defecting from) any agreement to curb its harmful applications.  53  Even if one felt optimistic that an agreement could eventually be reached, the question of timing should remain a serious concern. International collective action problems, even within a restricted domain, can resist solution for a long time, even when the stakes are large and indisputable. It takes time to explain why an arrangement is needed and to answer objections, time to negotiate a mutually acceptable instantiation of the cooperative idea, time to hammer out the details, and time to set up the institutional mechanisms required for implementation. In many situations, holdout problems and domestic opposition can delay progress for decades; and by the time one recalcitrant nation is ready to come on board, another who had previously agreed might have changed its mind. Yet at the same time, the interval between a vulnerability becoming clearly visible to all and the point when stabilization measures must be in place could be short. It could even be negative, if the nature of the vulnerability leaves room for denialism or if specific explanations cannot be widely provided because of information hazards. These considerations suggest that it is problematic to rely on spontaneous ad hoc international cooperation to save the day once a vulnerability comes into view.  54  The situation with respect to preventive policing is in some respects similar, although we see a much faster and more robust trenddriven by advances in surveillance technologytowards increasing state capacities for monitoring and potentially controlling the actions of their own citizens than any trend towards effective global governance. At least this is true if we look at the physical realm. In the digital information realm the outlook is somewhat less clear, owing to the proliferation of encryption and anonymization tools, and the frequency of disruptive innovation which makes the future of cyberspace harder to foresee. Sufficiently strong capabilities in physical space would, however, spill over into strong capabilities in the digital realm as well. In High-tech Panopticon, there would be no need for the authorities to crack ciphers, since they could directly observe everything that users type into their computers and everything that is shown on their screens. One could take the position that we should not develop improved methods of surveillance and social control unless and until a specific civilizational vulnerability comes clearly into viewone that looks sufficiently serious to justify the sacrifice of some types of privacy and the risk of inadvertently facilitating a totalitarian nightmare. But as with the case of international cooperation, we confront a question of timing. A highly sophisticated surveillance and response system, like the one depicted in 'High-tech Panopticon', cannot be conjured up and made fully reliable overnight. Realistically, from our current starting point, it would take many years to implement such a system, not to mention the time required to build political support. Yet the vulnerabilities against which such a system might be needed may not offer us much advance warning. Last week a top academic biolab may have published an article in Science; and as you are reading these words, a popular blogger somewhere in the world, in hot pursuit of pageviews, might be uploading a post that explains some clever way in which the lab's result could be used by anybody to cause mass destruction. In such a scenario, intense social control may need to be switched on almost immediately. In an unfavorable scenario, the lead time could be as short as hours or days. It would then be too late to start developing a surveillance architecture when the vulnerability comes clearly into view. If devastation is to be avoided, the mechanism for stabilization would need to have been put in place beforehand. What may theoretically be feasible is to develop the capabilities for intrusive surveillance and real-time interception in advance, but not initially to use those capabilities to anything like their full extent. This would be one way to satisfy the requirement for stabilizing a Type-1 vulnerability (and other vulnerabilities that require highly reliable monitoring of individual actions). By giving human civilization the capacity for extremely effective preventive policing, we would have exited one of the dimensions of the semi-anarchic default condition. Admittedly, constructing such a system and keeping it in standby mode would mean that some of the downsides of actually instituting intense forms social control would be incurred. In particular, it may make oppressive outcomes more likely: \"[The] question is whether the creation of a system of surveillance perilously alters that balance too far in the direction of government control . . . We might imagine a system of compulsory cameras installed in homes, activated only by warrant, being used with scrupulous respect for the law over many years. The problem is that such an architecture of surveillance, once established, would be difficult to dismantle, and prove too potent a tool of control if it ever fell into the hands of people whowhether through panic, malice, or a misguided confidence in their own ability to secretly judge the public goodwould seek to use it against us  (Sanchez, 2013) .\" Developing a system for turnkey totalitarianism means incurring a risk, even if one does not intend for the key to be turned. One could try to reduce this risk by designing the system with appropriate technical and institutional safeguards. For example, one could aim for a system of 'structured transparency' that prevents concentrations of power by organizing the information architecture so that multiple independent stakeholders must give their permission in order for the system to operate, and so that only the specific information that is legitimately needed by some decision-maker is made available to her, with suitable redactions and anonymization applied as the purpose permits. With some creative mechanism design, some machine learning, and some fancy cryptographic footwork, there might be no fundamental barrier to achieving a surveillance system that is at once highly effective at its official function yet also somewhat resistant to being subverted to alternative uses. How likely this is to be achieved in practice is of course another matter, which would require further exploration.  55  Even if a significant risk of totalitarianism would inevitably accompany a well-intentioned surveillance project, it would not follow that pursuing such a project would increase the risk of totalitarianism. A relatively less risky well-intentioned project, commenced at a time of comparative calm, might reduce the risk of totalitarianism by preempting a less-wellintentioned and more risky project started during a crisis. But even if there were some net totalitarianism-risk-increasing effect, it might be worth accepting that risk in order to gain the general ability to stabilize civilization against emerging Type-1 threats (or for the sake of other benefits that extremely effective surveillance and preventive policing could bring). \n Conclusions This paper has introduced a perspective from which we can more easily see how civilization is vulnerable to certain types of possible outcomes of our technological creativityour drawing a metaphorical black ball from the urn of inventions, which we have the power to extract but not to put back in. We developed a typology of such potential vulnerabilities, and showed how some of them result from destruction becoming too easy, others from pernicious changes in the incentives facing a few powerful state actors or a large number of weak actors. We also examined a variety of possible responses and their limitations. We traced the root cause of our civilizational exposure to two structural properties of the contemporary world order: on the one hand, the lack of preventive policing capacity to block, with extremely high reliability, individuals or small groups from carrying out actions that are highly illegal; and, on the other hand, the lack of global governance capacity to reliably solve the gravest international coordination problems even when vital national interests by default incentivize states to defect. General stabilization against potential civilizational vulnerabilitiesin a world where technological innovation is occurring rapidly along a wide frontier, and in which there are large numbers of actors with a diverse set of human-recognizable motivationswould require that both of these governance gaps be eliminated. Until such a time as this is accomplished, humanity will remain vulnerable to drawing a technological black ball. Clearly, these reflections provide a pro tanto reason to support strengthening surveillance capabilities and preventive policing systems and for favoring a global governance regime that is capable of decisive action (whether based on unilateral hegemonic strength or powerful multilateral institutions). However, we have not settled whether these things would be desirable all-things-considered, since doing so would require analyzing a number of other strong considerations that lie outside the scope of this paper. Because our main goal has been to put some signposts up in the macrostrategic landscape, we have focused our discussion at a fairly abstract level, developing concepts that can help us orient ourselves (with respect to long-term outcomes and global desirabilities) somewhat independently of the details of our varying local contexts. In practice, were one to undertake an effort to stabilize our civilization against potential black balls, one might find it prudent to focus initially on partial solutions and lowhanging fruits. Thus, rather than directly trying to bring about extremely effective preventive policing or strong global governance, one might attempt to patch up particular domains where black balls seem most likely to appear. One could, for example, strengthen oversight of biotechnologyrelated activities by developing better ways to track key materials and equipment, and to monitor scientists within labs. One could also tighten know-your-customer regulations in the biotech supply sector, and expand the use of background checks for personnel working in certain kinds of labs or involved with certain kinds of experiment. One can improve whistleblower systems, and try to raise biosecurity standards globally. One could also pursue differential technological development, for instance by strengthening the biological weapons convention and maintaining the global taboo on biological weapons. Funding bodies and ethical approval committees could be encouraged to take broader view of the potential consequences of particular lines of work, focusing not only on risks to lab workers, test animals, and human research subjects, but also on ways that the hoped-for findings might lower the competence bar for bioterrorists down the road. Work that is predominantly protective (such as disease outbreak monitoring, public health capacity building, improvement of air filtration devices) could be differentially promoted. Nevertheless, while pursuing such limited objectives, one should bear in mind that the protection they would offer covers only special subsets of scenarios, and might be temporary. If one finds oneself in a position to influence the macroparameters of preventive policing capacity or global governance capacity, one should consider that fundamental changes in those domains may be the only way to achieve a general ability to stabilize our civilization against emerging technological vulnerabilities. \n Notes For comments, discussion, and critique, I'm grateful to Sonja Alsofi, Stuart  Armstrong, Andrew Snyder-Beattie, Chris Anderson, Nick Beckstead, Miles Brundage, Ben Buchanan, Owen Cotton-Barratt, Niel Bowerman, Paul Christiano, Allan Dafoe, Jeff Ding, Eric Drexler, Peter Eckersley, Owain Evans, Thomas Homer-Dixon, Thomas Inglesby, John Leslie, Gregory Lewis, Matthijs Maas, Jason Matheny, Michael Montague, Luke Muehlhauser, Toby Ord, Ben Pace, Richard Re, Anders Sandberg, Julian Savulescu, Stefan Schubert, Carl Shulman, Tanya Singh, Helen Toner, and  to the audiences of several workshops and lectures where earlier versions of this work were presented), and to three anonymous referees; and I thank Carrick Flynn, Christopher Galias, Ben Garfinkel, and Rose Hadshar for help with the manuscript and many useful suggestions. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 669751). 1. Obviously, the urn metaphor has important limitations. We will discuss some of them later. 2. The net effect on the conditions of non-human animals is harder to assess. In particular, modern factory farming involves the mistreatment of large numbers of animals. 3. There are, however, examples of 'cultures' or local populations whose demise may have been brought about (at least partially) by their own technological practices, such as Easter Island (Rapa Nui) people and the Ancestral Puebloans in Mesa Verde (Anasazi), who, according to  Diamond (2005) , cut down their own forests and then suffered environmental collapse. 4. Examples may however be found in other species, if we consider evolutionary adaptations as inventions. For instance, there is a literature exploring how evolutionary dead ends, leading to the extinction of a species or a population, may ensue from advantageous evolutionary changes such as ones involved in specialization (in which adaptation to a narrow niche may entail an irreversible loss of traits needed to survive in a wider range of environments)  (Day et al., 2016) , the emergence of inbred social systems (among e.g. social spiders)  (Aviles and Purcell, 2012) , or a switch to selfing (e.g. among flowering plant species transitioning from outcrossing to self-fertilization)  (Igic and Busch, 2013) . 5. Although most scientists involved in the project favored proposals such as the Baruch Plan, which would have placed nuclear energy under international control, they retained little decision-making power at this point. 6. Metaphorically, of course. But arguably in the metaphor, there should be more than one trembling finger on each side, given the widely delegated command and control  (Ellsberg, 2017; Schlosser, 2013) . 7. However, within a given state, the number of actors who are empowered to launch nuclear attacks may be quite large.  Ellsberg (2017)  claims that, for at least a significant portion of the Cold War, the authority to launch nuclear weapons was delegated multiple rungs down the American chain of command. The number of officers with the physical ability to launch nuclear weapons, although not the authority to do so, was also necessarily larger. In the Soviet Union, at one point during the coup against Mikhail Gorbachev in August 1991, all three of the USSR's Chegets ('nuclear briefcases') were in the hands of coup leaders  (Sokoski and Tertrais, 2013; Stevenson, 2008) . 8. An 'information hazard' is a risk arising from the dissemination of true information, for instance because the information could enable some agents to cause harm.  Bostrom (2011)  discusses information hazards more generally. 9. They might argue that openness would be a benefit since it would allow more people to work on countermeasures (cf. the debate around gain of function work on flu viruses;  (Duprex et al., 2015; Fauci et al., 2011; Sharp, 2005) ). They might also argue that, so long as the government continues to justify draconian actions by referencing secret information, it will be dangerously unaccountable to its citizens. A similar belief motivated the American magazine The Progressive's decision in the late 1970s to publish secrets about the hydrogen bomb, even in the face of a legal challenge by the US Department of Energy. The author of the piece, Howard Morland, wrote: 'Secrecy itself, especially the power of a few designated 'experts' to declare some topics off-limits, contributes to a political climate in which the nuclear establishment can conduct business as usual, protecting and perpetuating the production of these horror weapons  ' Morland (1979, p. 3 ). 10. Generally, in cases where multiple actors each have some independent probability of taking an action unilaterally, the probability that the action will be taken tends to one as the number of actors increases. When this phenomenon arises for actors with shared goals but discordant judgments, due to randomness in the evidence they are exposed to or the reasoning they carry out, there arises a 'unilateralist's curse'  (Bostrom et al., 2016) . The curse implies that even a very unwise decision, such as the decision to publish nuclear weapons designs, is likely to be made if enough actors are in a position to take it unilaterally. 11. Many of these same motivations are evident today among 'black hat' hackers who carry out malicious cyber attacks. For instance, as a method of extortion, some anonymous hackers have proven themselves willing to remove cities' abilities to provide vital services to their residents  (Blinder and Perlroth, 2018) . Motivations for economically damaging cyber attacks have also seemed to include both political ideology and curiosity. Since contemporary cyber attacks are dramatically less destructive than attacks with nuclear weapons, the set of actors that would be willing to use nuclear weapons or threaten their use is surely much smaller than the set of actors willing to engage in malicious hacking. Nevertheless, the social and psychological factors relevant to both cases may be similar. 12. This concept is distinct from that of international anarchy in the field of international relations. The present concept emphasizes that anarchy is a matter of degree and is meant to be relatively neutral as between different schools of thought in IR (cf.  Lechner, 2017) ). More importantly, it encompasses a lack of governance not just 'at the top' but also 'at the bottom'. That is to say, the semi-anarchic default condition refers to the fact that in the current world order, not only is there a degree of anarchy at the international level, because of lack of global governance or other fully effective means of constraining the actions of state and solving global coordination problems, but there is also a degree of anarchy at the level of individuals (and other sub-state actors) in that even highly functional states currently lack the ability to perfectly regulate the actions of those small actors. For example, despite many states seeking to prevent rape and murder within their territory, rape and murder continue to occur with non-zero frequency. The consequences of this degree of anarchy at the bottom could be vastly magnified if individuals obtained much greater destructive capabilities. 13. For comparison, a death toll of 15 per cent of the present world population is more than double the combined effects of World War I, the Spanish Flu, and World War II as a percentage of global population (and the difference is even bigger in absolute terms). A 50 per cent fall in world GDP is greater than the largest drop in recorded history. During the Great Depression, for example, world GDP fell by an estimated 15 per cent or less, and mostly recovered within a few years (though some models suggest that it has also had a long-lasting depressing effect on trade which has chronically impaired the world economy)  (Bolt et al., 2018) ;  Crafts and Fearon, 2010) . 14. This paper focuses on technological vulnerabilities. There could also be natural vulnerabilities that arise independently of the progress of human civilization, such as a violent meteor barrage set to impact our planet at some future date. Some natural vulnerabilities could be stabilized once our level of technological capability exceeds some threshold (e.g. the ability to deflect meteors). Plausibly, the risk of technological vulnerabilities is greater than the risk of natural vulnerabilities, although the case for this is less clear cut with the severity cutoff of civilizational devastation than it would be if the cutoff were set to existential catastrophe  (Bostrom, 2013; Bostrom and Cirkovi c, 2011) .The (big) proviso to this claim (of technological vulnerabilities dominating) is that it presupposes that it is not the case that the world is hemorrhaging value-potential at a significant rate. If instead we evaluate things from a perspective in which what we may term the bleeding world hypothesis is true, then it may well be that the default devastation arising from natural (i.e. non-human) processes dominates the equation. The bleeding world hypothesis could hold if, for example: (1) the evaluator cares a lot about existing people (including self and family) and they are naturally dying off at a substantial rate (e.g. from aging), thereby losing both the ability to continue enjoying their lives and the opportunity for vastly greater levels of well-being such as would become possible at technological maturity; (2) the evaluator cares a lot about avoiding suffering that could be avoided with more advanced technology but is occurring currently, piling up disutility; (3) there is some substantial exogenously set rate of civilizational destruction (e.g. natural disasters, random simulation terminations unrelated to our activities  Bostrom, 2003) , and while we allow time to lapse we incur a cumulative risk of being destroyed before maxing out our technological potential; (4) there are ways, using physics we don't currently understand well, to initiate fast-growing processes of value creation (such as by creating an exponential cascade of baby-universes whose inhabitants would be overwhelmingly happy), and the evaluator cares in a scale-sensitive way about such creation; and (5) other superintelligent constituencies, who are in a position to greatly influence things the evaluator cares about, are impatient for us to reach some advancement, but the value they place on this decays rapidly over time. 15. The world could remain vulnerable after profound technological regress, for instance if many prefabricated nukes remain even after civilization regresses past the point of becoming incapable of manufacturing new ones. 16. It is important to our original 'easy nukes' scenario that each nuclear use requires the efforts of only one individual or of a small group. Although it might require the combined efforts of hundreds of actors to devastate civilization in that scenarioafter all, ruining one city or one metropolitan area is not the same as ruining a civilizationthese hundreds of actors need not coordinate. This allows the apocalyptic residual to come into play. 17.  Baum et al. (2018)  provide an up-to-date list of nuclear accidents and occasions on which the use of nuclear weapons was considered.  Sagan (1995)  provides a more thorough account of dangerous practices throughout the Cold War. Schlosser (2013) examines nearaccidents, focusing in particular on one incident which resulted in a non-nuclear detonation of a Titan-II ICBM. 18. Although there have been few scholarly attempts to assess the degree of luck involved in avoiding this outcome, one recent estimate, drawing from a dataset of near-miss instances, places the probability of the US and USSR avoiding nuclear war below 50 per cent  (Lundgren, 2013) . This is consistent with the views of some officials with insider knowledge of nuclear crises, such as President John F. Kennedy, who expressed the belief that, in hindsight, the Cuban missile crisis had between a one-in-two and a one-in-three chance of leading to nuclear war. Nonetheless, a number of prominent international security scholars, such as Kenneth Waltz and John Mueller, hold that the probability of nuclear war has been consistently very low  (Mueller, 2009; Sagan and Waltz, 2012) . 19. Perhaps believed erroneously. According to a former Commander of the US Pacific Fleet, there was a period during the Cold War when antisubmarine surveillance became extremely effective: '[The US] could identify by hull number the identity of Soviet subs, and therefore we could do a body count and know exactly where they were. In port or at sea. . . . so I felt comfortable that we had the ability to do something quite serious to the Soviet SSBN force on very short notice in almost any set of circumstances.' (quoted in  Ford and Rosenberg, 2005, p. 399) . 20. In fact, advances in remote sensing, data processing, AI, drones, and nuclear delivery systems are now threatening to undermine nuclear deterrence, especially for states with relatively small and unsophisticated nuclear arsenals  (Lieber and Press, 2017) . 21. Not really unscathed, of course: radioactive fallout would affect allies and to a degree the homeland; the economic repercussions would wreak havoc on markets and usher in a worldwide depression. Still, it would be far preferable to being the target of the assault (especially if we set aside nuclear winter). 22. Another possibility is that there would be political gains, such as an increased ability to engage in nuclear coercion against third parties after having demonstrated a willingness to use nuclear weapons. 23.  Brooks (1999) ;  Gartzke (2007) ;  Gartzke and Rohner (2011) . For a dissenting view, see  Liberman (1993) . 24. Human civilization could probably never have arisen if the Earth's climate had been that sensitive to carbon dioxide, since past CO 2 levels (4,000 ppm during the Cambrian period compared to about 410 pmm today) would then presumably have seriously disrupted the evolution of complex life. A less remote counterfactual might instead involve some compound that does not occur in significant quantities in nature but is produced by human civilization, such as chlorofluorocarbons. CFCs have been phased out via the Montreal Protocol because of their destructive effect on the ozone layer, but they are also very potent greenhouse gases on a per kilogram basis. So we could consider a counterfactual in which CFCs had been industrially useful on a far greater scale than they were, but with dramatic delayed cumulative effects on global climate. 25. The report commissioned by Oppenheimer ends: 'One may conclude that the arguments of this paper make it unreasonable to expect that the N + N reaction could propagate. An unlimited propagation is even less likely. However, the complexity of the argument and the absence of satisfactory experimental foundation make further work on the subject highly desirable'  (Konopinski et al., 1946) . 26. Type-0 could be viewed as the limiting case of a Type-1: it refers to a vulnerability that requires zero ill-intentioned actors in order for civilizational devastation to resultonly normally responsible actors who are willing to proceed with using a technology after an ordinary amount of scrutiny has been given to the new technology. 27. And if 10 years, why not permanently. 28. In fact, an account by Albert Speer, the German Minister of Armaments, suggests that Werner Heisenberg discussed the possibility of a runaway chain reaction with Hitler and that this possibility may have further dampened Hitler's enthusiasm for pursuing the bomb  (Rhodes, 1986) . 29. A real-world version of this kind of Type-2a vulnerability, in which key actors face strategic incentives to take actions that create unwanted risks for civilization, could arise in the context of a race to develop machine superintelligence. In unfavorable circumstances, competitive dynamics could present a leading developer with the choice between launching their own AI before it is safe or relinquishing their lead to some other developer who is willing to take greater risks  (Armstrong et al., 2016) . 30. For a discussion of how a rational planner would balance consumption growth with safety in various models where growth-inducing innovation also carries a risk of introducing innovations that reduce lifespan, see  Jones (2016) . 31. Even the 'surprising strangelets' scenario may be confounded by coordination problems, though to a lesser degree than 'Castle Bravo/Trinity test'. The people deciding on science funding allocations may have different priorities than the public that is providing the funding. They might, for example, place a higher value on satisfying intellectual curiosity, relative to the value placed on keeping risks low and providing near-term material benefits to the masses. Principal-agent problems could then result in more funding for particle accelerators than such experiments would get in the absence of coordination problems. Prestige contests between nationswhich might in part be viewed as another coordination failuremay also be a driver of basic science funding in general and highenergy physics in particular. 32. The people alive at the time when the devastation occurs might prefer that it had taken place earlier, before they were born, so that it would all be over and done with and they wouldn't be affected. Their preferences seem to run into a non-identity problem, since if a civilizational devastation event had taken place before they were conceived they would almost certainly not have come into existence  (Parfit, 1987) . 33. More broadly, many refinements in biotechnological tools and techniques, which make it easier for amateur DIY biohackers to accomplish what previously could only be done by well-resourced professional research labs, come under suspicion from this perspective. It is very questionable whether the benefits of DIY biohacking (glow-in-the-dark house plants?) are worth proliferating the ability to turn bioengineering to potentially risky or malicious purposes to an expanded set of relatively unaccountable actors. 34. The counterargument that 'if I don't develop it, somebody else will; so I might as well do it' tends to overlook the fact that a given scientist or developer has at least some marginal impact on the expected timing of the new discovery. If it really were the case that a scientist's efforts could make no difference to when the discovery or invention is made, it would appear that the efforts are a waste of time and resources, and should be discontinued for that reason. A relatively small shift in when some technological capability becomes available (say, one month) could be important in some scenarios (such as if the dangerous technology imposes a significant risk per month until effective defenses are developed and deployed). 35. By 'technological maturity' we mean the attainment of capabilities affording a level of economic productivity and control over nature close to the maximum that could feasibly be achieved (in the fullness of time)  (Bostrom, 2013) . 36. Access control in bioscience has grown in importance since the 2001 'Amerithrax' incident. In the United States, institutions handling dangerous pathogens are obliged to assess suitability for employees who will have access, which are also vetted by federal agencies  (Federal Select Agent Program, 2017) , and similar approaches are recommended to countries developing their biosecurity infrastructure (Centre for Biosecurity and Biopreparedness, 2017). The existing regime suffers from two shortcomings: first, there is no global coordination, so bad actors could 'shop around' for laxer regulatory environments; second, the emphasis remains on access to biological materials (e.g. samples of certain microorganisms), whereas biological information and technology is increasingly the principal object of security concern  (Lewis et al., 2019) . 37. A value of X substantially less than 1 per cent seems consistent with how little most people give to global charity. It is possible, however, that an act-omission distinction would make people willing to accept a substantially larger personal sacrifice in order not to contribute to a global bad than they would in order to contribute a global good. 38. Note, however, that a positive shift in the preference distributioneven if insufficient to avert catastrophe by simply making some individual actors not choose the destructive optioncould have important indirect effects. For example, if a large number of people became slightly more benevolently inclined, this might shift society into a more cooperative equilibrium that would support stronger governance-based stabilization methods such as the ones we discuss below (cf. 'moral enhancements';  Persson and Savulescu, 2012) . 39. At a global level, we find a patchwork of national classification schemes and information control systems. They are generally designed to protect military and intelligence secrets, or to prevent embarrassing facts about regime insiders from being exposed to the public, not to regulate the spread of scientific or technological insights. There are some exceptions, particularly in the case of technical information that bears directly on national security. For instance, the Invention Secrecy Act of 1951 in the United States gives defense agencies the power to bar the award of a patent and order that an invention be kept secret; though an inventor who refrains from seeking patent protection is not subject to these strictures  (Parker and Jacobs 2003) . Nuclear inventions are subject to the 'born secret' provision of the Atomic Energy Act of 1946, which declares all information concerning the design, development, and manufacture of nuclear weaponsregardless of originclassified unless it has been officially declassified  (Parker and Jacobs 2003) . Other legal tools, such as export controls, have also been used in attempts to stem the flow of scientific information. The (unsuccessful) efforts of multiple US government agencies to block the publication and use of strong encryption protocols developed in the 1970s and 1980s provide one notable example  (Banisar, 1999) .Voluntary self-censorship by the scientific community has been attempted on very rare occasions. Leo Szilard had some partial successes in convincing his physicist colleagues to refrain from publishing on aspects of nuclear fission (before the start of the Manhattan Project and the onset of official secrecy), though he encountered opposition from some scientists who wanted their own work to appear in journals or who felt that openness was a sacred value in science. More recently, there were some attempts at scientific selfcensorship in relation to avian flu research  (Gronvall, 2013) . In this case, the efforts may have been not only ineffectual but counterproductive, inasmuch as the controversy sparked by open debate about whether certain results should be published drew more attention to those results than they would have received if publication had proceeded unopposedthe so-called 'Streisand effect'.Overall, attempts at scientific self-censorship appear to have been fairly half-hearted and ineffectual. (I say appears, because of how things unfolded in the publicly known episodes where censorship was attempted. But truly successful attempts to suppress scientific information wouldn't necessarily show up in the public record.) Even if a few journal editors could agree on standards for how to deal with papers that pose information hazards, nothing would prevent a frustrated author from sending her manuscript to another journal with lower standards or to publish it on her personal Internet page. Most scientific communities have neither the culture, nor the incentives, nor the expertise in security and risk assessment, nor the institutional enforcement mechanisms that would be required for dealing effectively with infohazards. The scientific ethos is rather this: every ball must be extracted from the urn as quickly as possible and revealed to everyone in the world immediately; the more this happens, the more progress has been made; and the more you contribute to this, the better a scientist you are. The possibility of a black ball does not enter into the equation. 40. In any case, it is unclear whether we would really want to be more cautious in general. It might be desirable (from various evaluative perspectives) to encourage greater caution specifically in situations where there could be extreme global downsides. Yet exhortations to exercise voluntary caution and restraint in these causes may not be very effective if the reason for the normatively excessive risk-taking is a coordination problem: the risk-taker gaining some private benefit (e.g. profit or prestige) while generating a global risk externality. In such cases, therefore, the solution may require a strengthening of global governance capacity. 41. It is also possible for risk assessment work to increase the level of risk, by generating information hazards  (Bostrom, 2011) . 42. The Orwellian-sounding name is of course intentional, to remind us of the full range of ways in which such a system could be applied. 43. Implementation details are for illustration only. For example, similar functionality could be provided by mixed reality eyeglasses instead of a necklace. Versions of the device could be designed that would provide many benefits to the user along with its surveillance function. In theory, some of the monitoring could be crowd-sourced: when suspicious activity is detected by the AI, the video feed is anonymized and sent to a random 100 citizens, whose duty is to watch the feed and vote on whether it warrants further investigation; if at least 10 per cent of them think it does, the (non-anonymized) feed gets forwarded to the authorities. 44. Examples of 'conveniences' that will plausibly drive more intrusive surveillance include various kinds of consumer applications and economically useful or profitable monitoring (e.g. for ad targeting, price discrimination, etc.); the ability to prevent various things that cause public outrage, such as child abuse or small-scale terrorism; and, especially for authoritarian regimes, the ability to suppress political opposition. 45. A milder version of the policy might merely debar such weak suspects from accessing the equipment and materials necessary to produce the destructive effect. The extent to which this might suffice depends on the details of the scenario. 46. A partial implementation of the High-tech Panopticon might replace incarceration in this scenario, in which only those on some long list of 'individuals of heightened concern' were required to wear the freedom tags. 47. Of course, it is theoretically possible that either of these remedies would raise rather than lower civilization's total vulnerability to a potential black ball, for example, if adequate global coordination made extremely effective national policing less likely, or vice versa. The character of the regimes that would tend to arise under conditions of stronger preventive policing or global governance could also differ from those in the status quo in ways that would increase or decrease some civilizational vulnerabilities. For example, surveillance-empowered world leaders might be more or less prone to taking foolish decisions that increase Type-0 vulnerabilities. 48. A special case of Type-2a vulnerability is one in which some set of regimes jointly achieve the devastational threshold by harming their own populations. Suppose, for instance, that one held an extremely pessimistic view of political leaders, and thought that they would be willing to kill an extremely large fraction of their own populations if doing so would help them hold on to power or gain more resources. Whereas today such a genocidal initiative would usually be counterproductive from the leader's point of view (because it would spark revolts and crash the economy), one could imagine a different technological environment in which these restraints would be loosenedfor example, if a highly centralized AI police force could reliably suppress any resistance and if robots could easily replace human workers. (Fortunately, it would appear that in many scenarios where these things becomes technologically feasible, the ruler's incentives for genocidal actions would also be weakened: the hypothesized AI police force would presumably enable the ruler to maintain power without killing off large parts of the population, and automation of the economy would greatly increase wealth so that a smaller fraction of national income would suffice to give all citizens a high standard of living.) 49. For example, surveillance debates often focus on the tradeoffs between the privacy interests of individuals and public demand for security against small-scale terrorist attacks. (Even terrorist incidents that are usually regarded as large, such as the 9/11 attacks, are insignificantly small-scale by the standards used in this paper.) 50. According to  Schwartz (1998) , the nuclear arms race during the Cold War cost 5.8 trillion (1996 dollars) in American expenditures alone, which is equivalent to 9.3 trillion in 2018 dollars. This estimate is quite comprehensive and covers the fuel cycle, weapons, delivery systems, decommissioning, etc. If we add the expenditures of other countries, we can conclude that human civilization spent well in excess of 10 trillion dollars on developing and maintaining a capacity to destroy itself with nuclear arms. Most of the cost was incurred in a period when world GDP was substantially lower than it is today. Even larger amounts were spent on non-nuclear military capabilities (over 20 trillion in 2018 dollars in the US alone). It is possible that the nuclear expenditures saved money on balance by reducing non-nuclear military spending. Both nuclear and non-nuclear military spending reflects the failure of human civilization to solve global coordination. 51. Substantially rather than entirely, since even if all nuclear weapons were dismantled, new ones might be created. 52. An agreement for total nuclear disarmament might, of course, have to involve some provisions about conventional forces and other matters as well, so as not to endanger strategic stability. 53. One might look at other historical examples to obtain a larger reference class. The world's efforts so far with respect to combating global warming do not inspire confidence in its ability to deal expeditiously with even more difficult global collective action problems. On the other hand, the problem of ozone depletion was successfully addressed with the Montreal Protocol. 54. Unilateral imposition may be faster, but it requires that some actor has the capability to impose its will single-handedly on the rest of the world. If one actor has such an overwhelming power advantage, a form of de facto (weak or latent) global governance is presumably already in place. 55. For example, a well-intentioned project may be subverted in its implementation; or it might turn out to have bugs or institutional design flaws that become apparent only after a period of normal operation. Even if the system itself functions precisely as intended and remains uncorrupted, it might inspire the creation of other surveillance systems that do not have the same democratic safeguards. \t\t\t Global Policy Volume 10 . Issue 4 . November 2019 \n\t\t\t © 2019 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Global Policy (2019) 10:4 \n\t\t\t Global Policy (2019) 10:4 © 2019 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.The Vulnerable World Hypothesis", "date_published": "n/a", "url": "n/a", "filename": "vulnerable.tei.xml", "abstract": "Scientific and technological progress might change people's capabilities or incentives in ways that would destabilize civilization. For example, advances in DIY biohacking tools might make it easy for anybody with basic training in biology to kill millions; novel military technologies could trigger arms races in which whoever strikes first has a decisive advantage; or some economically advantageous process may be invented that produces disastrous negative global externalities that are hard to regulate. This paper introduces the concept of a vulnerable world: roughly, one in which there is some level of technological development at which civilization almost certainly gets devastated by default, i.e. unless it has exited the 'semi-anarchic default condition'. Several counterfactual historical and speculative future vulnerabilities are analyzed and arranged into a typology. A general ability to stabilize a vulnerable world would require greatly amplified capacities for preventive policing and global governance. The vulnerable world hypothesis thus offers a new perspective from which to evaluate the risk-benefit balance of developments towards ubiquitous surveillance or a unipolar world order. \n Policy Implications • Technology policy should not unquestioningly assume that all technological progress is beneficial, or that complete scientific openness is always best, or that the world has the capacity to manage any potential downside of a technology after it is invented. • Some areas, such as synthetic biology, could produce a discovery that suddenly democratizes mass destruction, e.g. by empowering individuals to kill hundreds of millions of people using readily available materials. In order for civilization to have a general capacity to deal with \"black ball\" inventions of this type, it would need a system of ubiquitous real-time worldwide surveillance. In some scenarios, such a system would need to be in place before the technology is invented. • Partial protection against a limited set of possible black balls is obtainable through more targeted interventions. For example, biorisk might be mitigated by means of background checks and monitoring of personnel in some types of biolab, by discouraging DIY biohacking (e.g. through licencing requirements), and by restructuring the biotech sector to limit access to some cutting-edge instrumentation and information. Rather than allow anybody to buy their own DNA synthesis machine, DNA synthesis could be provided as a service by a small number of closely monitored providers. • Another, subtler, type of black ball would be one that strengthens incentives for harmful use-e.g. a military technology that makes wars more destructive while giving a greater advantage to the side that strikes first. Like a squirrel who uses the times of plenty to store up nuts for the winter, we should use times of relative peace to build stronger mechanisms for resolving international disputes.", "id": "77dfaf1001d9a1a7c8b47db722c5121e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom"], "title": "Existential Risk Prevention as Global Priority", "text": "The maxipok rule Existential risk and uncertainty An existential risk is one that threatens the premature extinction of Earth-originating intelligent life or the permanent and drastic destruction of its potential for desirable future development . Although it is often difficult to assess the probability of existential risks, there are many reasons to suppose that the total such risk confronting humanity over the next few centuries is significant. Estimates of 10-20 per cent total existential risk in this century are fairly typical among those who have examined the issue, though inevitably such estimates rely heavily on subjective judgment.  1  The most reasonable estimate might be substantially higher or lower. But perhaps the strongest reason for judging the total existential risk within the next few centuries to be significant is the extreme magnitude of the values at stake. Even a small probability of existential catastrophe could be highly practically significant  Matheny, 2007; Posner, 2004; Weitzman, 2009) . Humanity has survived what we might call natural existential risks for hundreds of thousands of years; thus it is prima facie unlikely that any of them will do us in within the next hundred.  2  This conclusion is buttressed when we analyse specific risks from nature, such as asteroid impacts, supervolcanic eruptions, earthquakes, gamma-ray bursts, and so forth: Empirical impact distributions and scientific models suggest that the likelihood of extinction because of these kinds of risk is extremely small on a time scale of a century or so.  3  In contrast, our species is introducing entirely new kinds of existential risk-threats we have no track record of surviving. Our longevity as a species therefore offers no strong prior grounds for confident optimism. Consideration of specific existential-risk scenarios bears out the suspicion that the great bulk of existential risk in the foreseeable future consists of anthropogenic existential risks-that is, those arising from human activity. In particular, most of the biggest existential risks seem to be linked to potential future technological breakthroughs that may radically expand our ability to manipulate the external world or our own biology. As our powers expand, so will the scale of their potential consequences-intended and unintended, positive and negative. For example, there appear to be significant existential risks in some of the advanced forms of biotechnology, molecular nanotechnology, and machine intelligence that might be developed in the decades ahead. The bulk of existential risk over the next century may thus reside in rather speculative scenarios to which we cannot assign precise probabilities through any rigorous statistical or scientific method. But the fact that the probability of some risk is difficult to quantify does not imply that the risk is negligible. Probability can be understood in different senses. Most relevant here is the epistemic sense in which probability is construed as (something like) the credence that an ideally reasonable observer should assign to the risk's materialising based on currently available evidence.  4  If something cannot presently be known to be objectively safe, it is risky at least in the subjective sense relevant to decision making. An empty cave is unsafe in just this sense if you cannot tell whether or not it is home to a hungry lion. It would be rational for you to avoid the cave if you reasonably judge that the expected harm of entry outweighs the expected benefit. The uncertainty and error-proneness of our first-order assessments of risk is itself something we must factor into our all-things-considered probability assignments. This factor often dominates in low-probability, highconsequence risks-especially those involving poorly understood natural phenomena, complex social dynamics, or new technology, or that are difficult to assess for other reasons. Suppose that some scientific analysis A indicates that some catastrophe X has an extremely small probability P(X) of occurring. Then the probability that A has some hidden crucial flaw may easily be much greater than P(X). 5 Furthermore, the conditional probability of X given that A is crucially flawed, P(X |ØA), may be fairly high. We may then find that most of the risk of X resides in the uncertainty of our scientific assessment that P(X) was small (Figure  1 )  (Ord, Hillerbrand and Sandberg, 2010) . \n Qualitative risk categories Since a risk is a prospect that is negatively evaluated, the seriousness of a risk-indeed, what is to be regarded as risky at all-depends on an evaluation. Before we can determine the seriousness of a risk, we must specify a standard of evaluation by which the negative value of a particular possible loss scenario is measured. There are several types of such evaluation standard. For example, one could use a utility function that represents some particular agent's preferences over various outcomes. This might be appropriate when one's duty is to give decision support to a particular decision maker. But here we will consider a normative evaluation, an ethically warranted assignment of value to various possible outcomes. This type of evaluation is more relevant when we are inquiring into what our society's (or our own individual) risk-mitigation priorities ought to be. There are conflicting theories in moral philosophy about which normative evaluations are correct. I will not here attempt to adjudicate any foundational axiological disagreement. Instead, let us consider a simplified version of one important class of normative theories. Let us suppose that the lives of persons usually have some significant positive value and that this value is aggregative (in the sense that the value of two similar lives is twice that of one life). Let us also assume that, holding the quality and duration of a life constant, its value does not depend on when it occurs or on whether it already exists or is yet to be brought into existence as a result of future events and choices. These assumptions could be relaxed and complications could be introduced, but we will confine our discussion to the simplest case. Within this framework, then, we can roughly characterise a risk's seriousness using three variables: scope (the size of the population at risk), severity (how badly this population would be affected), and probability (how likely the disaster is to occur, according to the most reasonable judgment, given currently available evidence). Using the first two of these variables, we can construct a qualitative diagram of different types of risk (Figure  2 ). Source:  Ord et al., 2010.  Factoring in the fallibility of our firstorder risk assessments can amplify the probability of risks assessed to be extremely small. An initial analysis (left side) gives a small probability of a disaster (black stripe). But the analysis could be wrong; this is represented by the grey area (right side). Most of the all-things-considered risk may lie in the grey area rather than in the black stripe. (The probability dimension could be displayed along the z-axis.) The area marked 'X' in Figure  2  represents existential risks. This is the category of risks that have (at least) crushing severity and (at least) pan-generational scope.  6  As noted, an existential risk is one that threatens to cause the extinction of Earth-originating intelligent life or the permanent and drastic failure of that life to realise its potential for desirable development. In other words, an existential risk jeopardises the entire future of humankind. \n Magnitude of expected loss in existential catastrophe Holding probability constant, risks become more serious as we move toward the upper-right region of Figure  2 . For any fixed probability, existential risks are thus more serious than other risk categories. But just how much more serious might not be intuitively obvious. One might think we could get a grip on how bad an existential catastrophe would be by considering some of the worst historical disasters we can think of-such as the two world wars, the Spanish flu pandemic, or the Holocaust-and then imagining something just a bit worse. Yet if we look at global population statistics over time, we find that these horrible events of the past century fail to register (Figure  3 ). But even this reflection fails to bring out the seriousness of existential risk. What makes existential catastrophes especially bad is not that they would show up robustly on a plot like the one in Figure  3 , causing a precipitous drop in world population or average quality of life. Instead, their significance lies primarily in the fact that they would destroy the future. The philosopher Derek Parfit made a similar point with the following thought experiment: I believe that if we destroy mankind, as we now can, this outcome will be much worse than most people think. Compare three outcomes: 1. Peace. 2. A nuclear war that kills 99 per cent of the world's existing population. 3. A nuclear war that kills 100 per cent. 2 would be worse than 1, and 3 would be worse than 2. Which is the greater of these two differences? Most people believe that the greater difference is between 1 and 2. I believe that the difference between 2 and 3 is very much greater. The Earth will remain habitable for at least another billion years. Civilisation  Source: Author. Note: The scope of a risk can be personal (affecting only one person), local (affecting some geographical region or a distinct group), global (affecting the entire human population or a large part thereof), trans-generational (affecting humanity for numerous generations, or pan-generational (affecting humanity over all, or almost all, future generations). The severity of a risk can be classified as imperceptible (barely noticeable), endurable (causing significant harm but not completely ruining quality of life), or crushing (causing death or a permanent and drastic reduction of quality of life). began only a few thousand years ago. If we do not destroy mankind, these few thousand years may be only a tiny fraction of the whole of civilised human history. The difference between 2 and 3 may thus be the difference between this tiny fraction and all of the rest of this history. If we compare this possible history to a day, what has occurred so far is only a fraction of a second  (Parfit, 1984, pp. 453-454) . To calculate the loss associated with an existential catastrophe, we must consider how much value would come to exist in its absence. It turns out that the ultimate potential for Earth-originating intelligent life is literally astronomical. One gets a large number even if one confines one's consideration to the potential for biological human beings living on Earth. If we suppose with Parfit that our planet will remain habitable for at least another billion years, and we assume that at least one billion people could live on it sustainably, then the potential exist for at least 10 16 human lives of normal duration. These lives could also be considerably better than the average contemporary human life, which is so often marred by disease, poverty, injustice, and various biological limitations that could be partly overcome through continuing technological and moral progress. However, the relevant figure is not how many people could live on Earth but how many descendants we could have in total. One lower bound of the number of biological human life-years in the future accessible universe (based on current cosmological estimates) is 10 34 years.  7  Another estimate, which assumes that future minds will be mainly implemented in computational hardware instead of biological neuronal wetware, produces a lower bound of 10 54 human-brain-emulation subjective life-years (or 10 71 basic computational operations) .  8  If we make the less conservative assumption that future civilisations could eventually press close to the absolute bounds of known physics (using some as yet unimagined technology), we get radically higher estimates of the amount of computation and memory storage that is achievable and thus of the number of years of subjective experience that could be realised.  9  Even if we use the most conservative of these estimates, which entirely ignores the possibility of space colonisation and software minds, we find that the expected loss of an existential catastrophe is greater than the value of 10 16 human lives. This implies that the expected value of reducing existential risk by a mere one millionth of one percentage point is at least a hundred times the value of a million human lives. The more technologically comprehensive estimate of 10 54 humanbrain-emulation subjective life-years (or 10 52 lives of ordinary length) makes the same point even more starkly. Even if we give this allegedly lower bound on the cumulative output potential of a technologically mature civilisation a mere 1 per cent chance of being correct, we find that the expected value of reducing existential risk by a mere one billionth of one billionth of one percentage point is worth a hundred billion times as much as a billion human lives. One might consequently argue that even the tiniest reduction of existential risk has an expected value greater than that of the definite provision of any 'ordinary' good, such as the direct benefit of saving 1 billion lives. And, further, that the absolute value of the indirect effect of saving 1 billion lives on the total cumulative amount of existential risk-positive or negative-is almost certainly larger than the positive value of the direct benefit of such an action. 10 \n Maxipok These considerations suggest that the loss in expected value resulting from an existential catastrophe is so enormous that the objective of reducing existential risks should be a dominant consideration whenever we act out of an impersonal concern for humankind as a whole. It may be useful to adopt the following rule of thumb for such impersonal moral action: Maxipok Maximise the probability of an 'OK outcome', where an OK outcome is any outcome that avoids existential catastrophe. At best, maxipok is a rule of thumb or a prima facie suggestion. It is not a principle of absolute validity, since there clearly are moral ends other than the prevention of existential catastrophe. The principle's usefulness is as an aid to prioritisation. Unrestricted altruism is not so common that we can afford to fritter it away on a plethora of feel-good projects of suboptimal efficacy. If benefiting humanity by increasing existential safety achieves expected good on a scale many orders of magnitude greater than that of alternative contributions, we would do well to focus on this most efficient philanthropy. Note that maxipok differs from the popular maximin principle ('Choose the action that has the best worstcase outcome'). 11 Since we cannot completely eliminate existential risk-at any moment, we might be tossed into the dustbin of cosmic history by the advancing front of a vacuum phase transition triggered in some remote galaxy a billion years ago-the use of maximin in the present context would entail choosing the action that has the greatest benefit under the assumption of impending extinction. Maximin thus implies that we ought all to start partying as if there were no tomorrow. That implication, while perhaps tempting, is implausible. \n Classification of existential risk To bring attention to the full spectrum of existential risk, we can distinguish four classes of such risk: human extinction, permanent stagnation, flawed realisation, and subsequent ruination. We define these in Table  1 below:  By 'humanity' we here mean Earth-originating intelligent life and by 'technological maturity' we mean the attainment of capabilities affording a level of economic productivity and control over nature close to the maximum that could feasibly be achieved. \n Human extinction Although it is conceivable that, in the billion or so years during which Earth might remain habitable before being overheated by the expanding sun, a new intelligent species would evolve on our planet to fill the niche vacated by an extinct humanity, this is very far from certain to happen. The probability of a recrudescence of intelligent life is reduced if the catastrophe causing the extinction of the human species also exterminated the great apes and our other close relatives, as would occur in many (though not all) human-extinction scenarios. Furthermore, even if another intelligent species were to evolve to take our place, there is no guarantee that the successor species would sufficiently instantiate qualities that we have reason to value. Intelligence may be necessary for the realisation of our future potential for desirable development, but it is not sufficient. All scenarios involving the premature extinction of humanity will be counted as existential catastrophes, even though some such scenarios may, according to some theories of value, be relatively benign. It is not part of the definition of existential catastrophe that it is all-things-considered bad, although that will probably be a reasonable supposition in most cases. Above, we defined 'humanity' as Earth-originating intelligent life rather than as the particular biologically defined species Homo sapiens.  13  The reason for focusing the notion of existential risk on this broader concept is that there is no reason to suppose that the biological species concept tracks what we have reason to value. If our species were to evolve, or use technology to selfmodify, to such an extent that it no longer satisfied the biological criteria for species identity (such as interbreedability) with contemporary Homo sapiens, this need not be in any sense a catastrophe. Depending on what we changed into, such a transformation might well be very desirable. Indeed, the permanent foreclosure of any possibility of this kind of transformative change of human biological nature may itself constitute an existential catastrophe. Most discussion of existential risk to date has focused exclusively on the first of the four classes, 'human extinction'. The present framework calls attention to three other failure modes for humanity. Like extinction, these other failure modes would involve pan-generational crushing. They are therefore of comparable seriousness, entailing potentially similarly enormous losses of expected value. \n Permanent stagnation Permanent stagnation is instantiated if humanity survives but never reaches technological maturity-that is, the attainment of capabilities affording a level of economic productivity and control over nature that is close to the maximum that could feasibly be achieved (in the fullness of time and in the absence of catastrophic defeaters). For instance, a technologically mature civilisation could (presumably) engage in large-scale space colonisation through the use of automated self-replicating 'von Neumann probes'  (Freitas, 1980; Moravec, 1988; Tipler, 1980) . It would also be able to modify and enhance human biology-say, through the use of advanced biotechnology or molecular nanotechnology  (Freitas, 1999 (Freitas, , 2003 . Further, it could construct extremely powerful computational hardware and use it to create wholebrain emulations and entirely artificial types of sentient, superintelligent minds . It might have many additional capabilities, some of which may not be fully imaginable from our current vantage point.  14  The permanent destruction of humanity's opportunity to attain technological maturity is a prima facie enormous loss, because the capabilities of a technologically mature civilisation could be used to produce outcomes that would plausibly be of great value, such as astronomical numbers of extremely long and fulfilling lives. More specifically, mature technology would enable a far more efficient use of basic natural resources (such as matter, energy, space, time, and negentropy) for the creation of value than is possible with less advanced technology. And mature technology would allow the harvesting (through space colonisation) of far more of these resources than is possible with technology whose reach is limited to Earth and its immediate neighbourhood. We can distinguish various kinds of permanent stagnation scenarios: unrecovered collapse-much of our current economic and technological capabilities are lost and never recovered; plateauing-progress flattens out at a level perhaps somewhat higher than the present level but far below technological maturity; and recurrent collapse-a never-ending cycle of collapse followed by recovery .  15  The relative plausibility of these scenarios depends on various factors. One might expect that even if global civilisation were to undergo a complete collapse, perhaps following a global thermonuclear war, it would eventually be rebuilt. In order to have a plausible permanent collapse scenario, one would therefore need an account of why recovery would not occur.  16  Regarding plateauing, modern trends of rapid social and technological change make such a threat appear less imminent; yet scenarios could be concocted in which, for example, a stable global regime blocks further technological change. 17 As for recurrent-collapse scenarios, they seem to require the postulation of a special kind of cause: one that (1) is strong enough to bring about the total collapse of global civilisation yet (2) is not strong enough to cause human extinction, and that (3) can plausibly recur each time civilisation is rebuilt to a certain level, despite any random variation in initial conditions and any attempts by successive civilisations to learn from their predecessors' failures. The probability of remaining on a recurring-collapse trajectory diminishes with the number of cycles postulated. The longer the time horizon considered (and this applies also to plateauing) the greater the likelihood that the pattern will be ruptured, resulting in either a breakout in the upward direction toward technological maturity or in the downward direction toward unrecovered collapse and perhaps extinction (Figure  4 ).  18   \n Flawed realisation A flawed realisation occurs if humanity reaches technological maturity in a way that is dismally and irremediably flawed. By 'irremediably' we mean that it cannot feasibly be subsequently put right. By 'dismally' we mean that it enables the realisation of but a small part of the value that could otherwise have been realised. Classifying a scenario as an instance of flawed realisation requires a value judgment. We return to this normative issue in the next section. We can distinguish two versions of flawed realisation: unconsummated realisation and ephemeral realisation. In unconsummated realisation, humanity develops mature technology but fails to put it to good use, so that the amount of value realised is but a small fraction of what could have been achieved. An example of this kind is a scenario in which machine intelligence replaces biological intelligence but the machines are constructed in such a way that they lack consciousness (in the sense of phenomenal experience)  (Bostrom, 2004) . The future might then be very wealthy and capable, yet in a relevant sense uninhabited: There would (arguably) be no morally relevant beings there to enjoy the wealth. Even if consciousness did not altogether vanish, there might be a lot less of it than would have resulted from a more optimal use of resources. Alternatively, there might be a vast quantity of experience but of much lower quality than ought to have been the case: minds that are far less happy than they could have been. Or, again, there might be vast numbers of very happy minds but some other crucial ingredient of a maximally valuable future missing. In ephemeral realisation, humanity develops mature technology that is initially put to good use. But the technological maturity is attained in such a way that the initially excellent state is unsustainable and is doomed to degenerate. There is a flash of value, followed by perpetual dusk or darkness. One way in which ephemeral realisation could result is if there are fractures in the initial state of technological maturity that are bound to lead to a splintering of humanity into competing factions. It might be impossible to reintegrate humanity after such a splintering occurred, and the process of attaining technological maturity might have presented the last and best chance for humanity to form a singleton  (Bostrom, 2006) . Absent global coordination, various processes might degrade humanity's long-term potential. One such process is war between major powers, although it is perhaps unlikely that such warring would be never-ending (rather than being eventually terminated once and for all by treaty or conquest).  19  Another such erosive process involves undesirable forms of evolutionary and economic competition in a large ecology of machine intelligences  (Hanson, 1994) . Yet another such process is a spacecolonisation race in which replicators might burn up cosmic resources in a wasteful effort to beat out the competition . \n Subsequent ruination For completeness, we register a fourth class of existential risks: subsequent ruination. In scenarios of this kind, humanity reaches technological maturity with a 'good' (in the sense of being not dismally and irremediably flawed) initial setup, yet subsequent developments nonetheless lead to the permanent ruination of our prospects. From a practical perspective, we need not worry about subsequent ruination. What happens after humanity Source: Author. Note: The modern human condition represents a narrow range of the space of possibilities. The longer the time scale considered, the lower the probability that humanity's level of technological development will remain confined within the interval defined at the lower end by whatever technological capability is necessary for survival and at the upper end by technological maturity. reaches technological maturity is not something we can now affect, other than by making sure that humanity does reach it and in a way that offers the best possible prospects for subsequent development-that is, by avoiding the three other classes of existential risk. Nonetheless, the concept of subsequent ruination is relevant to us in various ways. For instance, in order to estimate how much expected value is gained by reducing other existential risks by a certain amount, we need to estimate the expected value conditional on avoiding the first three sets of existential risks, which requires estimating the probability of subsequent ruination. The probability of subsequent ruination might be low-and is perhaps extremely low conditional on getting the setup right. One reason is that once we have created many self-sustaining space colonies, any disaster confined to a single planet cannot eliminate all of humanity. Another reason is that once technological maturity is safely reached, there are fewer potentially dangerous technologies left to be discovered. A third reason is that a technologically mature civilisation would be superintelligent (or have access to the advice of superintelligent artificial entities) and thus better able to foresee danger and devise plans to minimise existential risk. While foresight will not reduce risk if no effective action is available, a civilisation with mature technology can take action against a great range of existential risks. Furthermore, if it turns out that attaining technological maturity without attaining singletonhood condemns a civilisation to irreversible degeneration, then if flawed realisation is avoided we can assume that our technologically mature civilisation can solve global-coordination problems, which increases its ability to take effective action to prevent subsequent ruination. The main source of subsequent-ruination risk might well be an encounter with intelligent external adversaries, such as intelligent extraterrestrials or simulators. Note, however, that scenarios in which humanity eventually goes extinct as a result of hard physical limits, such as the heat death of the universe, do not count as subsequent ruination, provided that before its demise humanity has managed to realise a reasonably large part of its potential for desirable development. Such scenarios are not existential catastrophes but rather existential successes. \n Capability and value Some further remarks will help clarify the links between capability, value, and existential risk. \n Convertibility of resources into value Because humanity's future is potentially astronomically long, the integral of losses associated with persistent inefficiencies is very large. This is why flawed-realisation and subsequent-ruination scenarios constitute existential catastrophes even though they do not necessarily involve extinction.  20  It might be well worth a temporary dip in short-term welfare to secure a slightly more efficient long-term realisation of humanity's potential. To avoid flawed realisation, it is more important to focus on maximising long-term efficiency than on maximising the initial output of value in the period immediately following technological maturation. This is because the quantity of value-structure that can be produced at a given time depends not only on the level of technology but also on the physical resources and other forms of capital available at that time. In economics parlance, humanity's production-possibility frontier (representing the various possible combinations of outputs that could be produced by the global economy) depends not only on the global production function (or 'meta-production function') but also on the total amount of all factors of production (labour, land, physical capital goods, etc.) that are available at some point in time. With mature technology, most factors of production are interchangeable and ultimately reducible to basic physical resources, but the amount of free energy available to a civilisation imposes hard limits on what it can produce. Since colonisation speed is bounded by the speed of light, a civilisation attaining technological maturity will start with a modest endowment of physical resources (a single planet and perhaps some nearby parts of its solar system), and it will take a very long time-billions of years-before a civilisation starting could reach even 1 per cent of its maximum attainable resource base.  21  It is therefore efficiency of use at later times, rather than in the immediate aftermath of the attainment of technological maturity, that matters most for how much value is ultimately realised. Furthermore, it might turn out that the ideal way to use most of the cosmic endowment that humanity could eventually secure is to postpone consumption for as long as possible. By conserving our accumulated free energy until the universe is older and colder, we might be able to perform some computations more efficiently.  22  This reinforces the point that it would be a mistake to place too much weight on the amount of value generated shortly after technological maturity when deciding whether some scenario should count as a flawed realisation (or a subsequent ruination). It is much more important to get the setup right, in the sense of putting humanity on a track that will eventually garner most of the attainable cosmic resources and put them to near-optimal use. It matters less whether there is a brief delay before that happens-and a delay of even several million years is 'brief' in this context . Even for individual agents, the passage of sidereal time might become less significant after technological maturity. Agents that exist as computational processes in distributed computational hardware have potentially unlimited life spans. The same holds for embodied agents in an era in which physical-repair technologies are sufficiently advanced. The amount of life available to such agents is proportional to the amount of physical resources they control. (A software mind can experience a certain amount of subjective time by running on a slow computer for a long period of sidereal time or, equivalently, by running for a brief period of sidereal time on a fast computer). Even from a so-called 'person-affecting' moral perspective, therefore, when assessing whether a flawed realisation has occurred, one should focus not on how much value is created just after the attainment of technological maturity but on whether the conditions created are such as to give a good prospect of realising a large integral of value over the remainder of the universe's lifetime. \n Some other ethical perspectives We have thus far considered existential risk from the perspective of utilitarianism (combined with several simplifying assumptions). We may briefly consider how the issue might appear when viewed through the lenses of some other ethical outlooks. For example, the philosopher Robert Adams outlines a different view on these matters: I believe a better basis for ethical theory in this area can be found in quite a different direction-in a commitment to the future of humanity as a vast project, or network of overlapping projects, that is generally shared by the human race. The aspiration for a better society-more just, more rewarding, and more peaceful-is a part of this project. So are the potentially endless quests for scientific knowledge and philosophical understanding, and the development of artistic and other cultural traditions. This includes the particular cultural traditions to which we belong, in all their accidental historic and ethnic diversity. It also includes our interest in the lives of our children and grandchildren, and the hope that they will be able, in turn, to have the lives of their children and grandchildren as projects. To the extent that a policy or practice seems likely to be favorable or unfavorable to the carrying out of this complex of projects in the nearer or further future, we have reason to pursue or avoid it. … Continuity is as important to our commitment to the project of the future of humanity as it is to our commitment to the projects of our own personal futures. Just as the shape of my whole life, and its connection with my present and past, have an interest that goes beyond that of any isolated experience, so too the shape of human history over an extended period of the future, and its connection with the human present and past, have an interest that goes beyond that of the (total or average) quality of life of a population-at-a-time, considered in isolation from how it got that way. We owe, I think, some loyalty to this project of the human future. We also owe it a respect that we would owe it even if we were not of the human race ourselves, but beings from another planet who had some understanding of it  (Adams, 1989, pp. 472-473) . Since an existential catastrophe would either put an end to the project of the future of humanity or drastically curtail its scope for development, we would seem to have a strong prima facie reason to avoid it, in Adams' view. We also note that an existential catastrophe would entail the frustration of many strong preferences, suggesting that from a preference-satisfactionist perspective it would be a bad thing. In a similar vein, an ethical view emphasising that public policy should be determined through informed democratic deliberation by all stakeholders would favour existential-risk mitigation if we suppose, as is plausible, that a majority of the world's population would come to favour such policies upon reasonable deliberation (even if hypothetical future people are not included as stakeholders). We might also have custodial duties to preserve the inheritance of humanity passed on to us by our ancestors and convey it safely to our descendants.  23  We do not want to be the failing link in the chain of generations, and we ought not to delete or abandon the great epic of human civilisation that humankind has been working on for thousands of years, when it is clear that the narrative is far from having reached a natural terminus. Further, many theological perspectives deplore naturalistic existential catastrophes, especially ones induced by human activities: If God created the world and the human species, one would imagine that He might be displeased if we took it upon ourselves to smash His masterpiece (or if, through our negligence or hubris, we allowed it to come to irreparable harm).  24  We might also consider the issue from a less theoretical standpoint and try to form an evaluation instead by considering analogous cases about which we have definite moral intuitions. Thus, for example, if we feel confident that committing a small genocide is wrong, and that committing a large genocide is no less wrong, we might conjecture that committing omnicide is also wrong.  25  And if we believe we have some moral reason to prevent natural catastrophes that would kill a small number of people, and a stronger moral reason to prevent natural catastrophes that would kill a larger number of people, we might conjecture that we have an even stronger moral reason to prevent catastrophes that would kill the entire human population. Many different normative perspectives thus concur in their support for existential-risk mitigation, although the degree of badness involved in an existential catastrophe and the priority that existential-risk mitigation should have in our moral economy may vary substantially among different moral theories.  26  Note, however, that it is on no account a conceptual truth that existential catastrophes are bad or that reducing existential risk is right. There are possible situations in which the occurrence of one type of existential catastrophe is beneficial-for instance, because it preempts another type of existential catastrophe that would otherwise certainly have occurred and that would have been worse. \n Existential risk and normative uncertainty Whereas the first two classes of existential risk (human extinction and permanent stagnation) are specified by purely descriptive criteria, the second two (flawed realisation and subsequent ruination) are defined normatively. This means that the concept of existential risk is in part an evaluative notion.  27  Where normative issues are involved, these issues may be contentious. Population ethics, for instance, is fraught with problems about how to deal with various parameters (such as population size, average wellbeing, thresholds for what counts as a life worth living, inequality, and same vs. different people choices). The evaluation of some scenarios that involve fundamental transformations of human nature is also likely to be contested  (Fukuyama, 2002; Glover, 1984; Kass, 2002; Savulescu and Bostrom, 2009) . Yet not all normative issues are controversial. It will be generally agreed, for example, that a future in which a small human population ekes out a miserable existence within a wrecked ecosystem in the presence of great but unused technological capabilities would count as a dismally flawed realisation of humanity's potential and would constitute an existential catastrophe if not reversed. There will be some types of putative existential risks for which the main uncertainty is normative and others where the main uncertainty is positive. With regard to positive, or descriptive, uncertainty, we saw earlier that if something is not known to be objectively safe, it is risky, at least in the subjective sense relevant to decision making. We can make a parallel move with regard to normative uncertainty. Suppose that some event X would reduce biodiversity. Suppose (for the sake of illustration) it is known that X would have no other significant consequences and that the reduced biodiversity would not affect humans or any other morally considerable beings. Now, we may be uncertain whether biodiversity has final value (is valuable 'for its own sake'). Hence we may be uncertain about whether or not X would really be bad. But we can say that if we are not sure whether or not X would really be bad (but we are sure that X would not be good), then X is bad in at least the subjective sense relevant to decision making. That is to say, we have reason to prefer that X not occur and perhaps reason to take action to prevent X. Exactly how one should take into account fundamental moral uncertainty is an open question, but that one should do so is clear . We can thus include as existential risks situations in which we know what will happen and we reasonably judge that what will happen might be existentially bad-even when there would in fact be nothing bad about the outcome. We can highlight one consequence of this: Suppose a fully reliable genie offered to grant humanity any wish it might have for its future. Then-even if we could all agree on one such future-we would still face one more potentially serious existential risk: namely, that of choosing unwisely and selecting a future dismally flawed despite appearing, at the moment of our choice, to be the most desirable of all possible futures. \n Keeping our options alive These reflections on moral uncertainty suggest an alternative, complementary way of looking at existential risk; they also suggest a new way of thinking about the ideal of sustainability. Let me elaborate. Our present understanding of axiology might well be confused. We may not now know-at least not in concrete detail-what outcomes would count as a big win for humanity; we might not even yet be able to imagine the best ends of our journey. If we are indeed profoundly uncertain about our ultimate aims, then we should recognise that there is a great option value in preserving-and ideally improving-our ability to recognise value and to steer the future accordingly. Ensuring that there will be a future version of humanity with great powers and a propensity to use them wisely is plausibly the best way available to us to increase the probability that the future will contain a lot of value. To do this, we must prevent any existential catastrophe. We thus want to reach a state in which we have (1) far greater intelligence, knowledge, and sounder judgment than we currently do; (2) far greater ability to solve global-coordination problems; (3) far greater technological capabilities and physical resources; and such that (4) our values and preferences are not corrupted in the process of getting there (but rather, if possible, improved). Factors 2 and 3 expand the option set available to humanity. Factor 1 increases humanity's ability to predict the outcomes of the available options and understand what each outcome would entail in terms of the realisation of human values. Factor 4, finally, makes humanity more likely to want to realise human values. How we, from our current situation, might best achieve these ends is not obvious (Figure  5 ). While we ultimately need more technology, insight, and coordination, it is not clear that the shortest path to the goal is the best one. It could turn out, for example, that attaining certain technological capabilities before attaining sufficient insight and coordination invariably spells doom for a civilisation. One can readily imagine a class of existentialcatastrophe scenarios in which some technology is discovered that puts immense destructive power into the hands of a large number of individuals. If there is no effective defense against this destructive power, and no way to prevent individuals from having access to it, then civilisation cannot last, since in a sufficiently large population there are bound to be some individuals who will use any destructive power available to them. The discovery of the atomic bomb could have turned out to be like this, except for the fortunate fact that the construction of nuclear weapons requires a special ingredient-weapons-grade fissile material-that is rare and expensive to manufacture. Even so, if we continually sample from the urn of possible technological discoveries before implementing effective means of global coordination, surveil-lance, and ⁄ or restriction of potentially hazardous information, then we risk eventually drawing a black ball: an easy-to-make intervention that causes extremely widespread harm and against which effective defense is infeasible.  28  We should perhaps therefore not seek directly to approximate some state that is 'sustainable' in the sense that we could remain in it for some time. Rather, we should focus on getting onto a developmental trajectory that offers a high probability of avoiding existential catastrophe. In other words, our focus should be on maximising the chances that we will someday attain technological maturity in a way that is not dismally and irremediably flawed. Conditional on that attainment, we have a good chance of realising our astronomical axiological potential. To illustrate this point, consider the following analogy. When a rocket stands on the launch pad, it is in a fairly sustainable state. It could remain in its current position for a long time, although it would eventually be destroyed by wind and weather. Another sustainable place for the rocket is in space, where it can travel weightless for a very long time. But when the rocket is in midair, it is in an unsustainable, transitory state: Its engines are blazing and it will soon run out of fuel. Returning the rocket to a sustainable state is desirable, but this does not mean that any way to render its state Sources: Author. Notes: An ideal situation might be one in which we have a very high level of technology, excellent global coordination, and great insight into how our capabilities can be used. It does not follow that getting any amount of additional technology, coordination, or insight is always good for us. Perhaps it is essential that our growth along different dimensions hew to some particular scheme in order for our development to follow a trajectory through the state space that eventually reaches the desired region. more sustainable is desirable. For example, reducing its energy consumption so that it just barely manages to hold stationary might make its state more sustainable in the sense that it can remain in one place for longer; however, when its fuel runs out the rocket will crash to the ground. The best policy for a rocket in midair is, rather, to maintain enough thrust to escape Earth's gravitational field: a strategy that involves entering a less sustainable state (consuming fuel faster) in order to later achieve the most desirable sustainable state. That is, instead of seeking to approximate a sustainable state, it should pursue a sustainable trajectory. The present human condition is likewise a transitional state. Like the rocket in our analogy, humanity needs to pursue a sustainable trajectory, one that will minimise the risk of existential catastrophe.  29  But unlike the problem of determining the optimum rate of fuel consumption in a rocket, the problem of how to minimise existential risk has no known solution. \n Outlook We have seen that reducing existential risk emerges as a dominant priority in many aggregative consequentialist moral theories (and as a very important concern in many other moral theories). The concept of existential risk can thus help the morally or altruistically motivated to identify actions that have the highest expected value. In particular, given certain assumptions, the problem of making the right decision simplifies to that of following the maxipok principle. \n Barriers to thought and action In light of this result, which suggests that there may be a very high value in studying existential risks and in analysing potential mitigation strategies, it is striking how little academic attention these issues have received compared to other topics that are less important (Figure  6 ).  30  Many factors conspire against the study and mitigation of existential risks. Research is perhaps inhibited by the multidisciplinary nature of the problem, but also by deeper epistemological issues. The biggest existential risks are not amenable to plug-and-play scientific research methodologies. Furthermore, there are unresolved foundational issues, particularly concerning observation selection theory and population ethics, which are crucial to the assessment of existential risk; and these theoretical difficulties are compounded by psychological factors that make it difficult to think clearly about issues such as the end of humanity.  31  If more resources were to be made available to research existential risks, there is a danger that they would flow, with excessive preponderance, to the relatively minor risks that are easier for some established disciplinary community to study using familiar methods, at the expense of far more important risk areas-machine superintelligence, advanced molecular nanotechnology, totalitarianism, risks related to the simulation-hypothesis, or future advances in synthetic biology-which would require a more inconvenient shift in research focus. Another plausible diversion is that research would mainly be directed at global catastrophic risks that involve little or no existential risk. Mitigation of existential risk is hampered by a lack of understanding, but also by a deficit of motivation. Existential risk mitigation is a global public good (i.e., non-excludable and non-rivalrous), and economic theory suggests that such goods tend to be undersupplied by the market, since each producer of existential safety (even if the producer is a large nation) could capture only a small portion of the value  (Feldman, 1980; Kaul, 1999) . In fact, the situation is worse than is the case with many other global public goods in that existential risk reduction is a strongly transgenerational (in fact, pan-generational) public good: even a world state may capture only a small fraction of the benefits-those accruing to currently existing people. The quadrillions of happy people who may come to exist in the future if we avoid existential catastrophe would be willing to pay the present generation astronomical sums in return for a slight increase in our efforts to preserve humanity's future, but the mutually beneficial trade is unfortunately prevented by the obvious transaction difficulties. Moral motivations, too, may fail to measure up to the magnitude of what is at stake. The scope insensitivity of our moral sentiments is likely to be especially pronounced when very large numbers are involved: Substantially larger numbers, such as 500 million deaths, and especially qualitatively different scenarios such as the extinction of the entire human species, seem to trigger a different mode of thinking-enter into a 'separate magisterium'. People who would never dream of hurting a child hear of an existential risk, and say, 'Well, maybe the human species doesn't really deserve to survive'.  (Yudkowsky, 2008, p. 114)  Existential risk requires a proactive approach. The reactive approach-to observe what happens, limit damages, and then implement improved mechanisms to reduce the probability of a repeat occurrence-does not work when there is no opportunity to learn from failure. Instead, we must anticipate emerging dangers, mobilise support for action against hypothetical future harm, and get our precautions sufficiently right the first time. That is a tall order. Few institutions are capable of operating consistently at such a level of effective rationality, and attempts to imitate such proactive behaviour within less perfect institutions can easily backfire. Speculative riskmongering could be exploited to rationalise self-serving aggressive action, expansion of costly and potentially oppressive security bureaucracies, or restrictions of civil liberties that keep societies free and sane. The result of false approximations to the rational ideal could easily be a net increase in existential risk.  32  Multidisciplinary and epistemological challenges, academic distractions and diversions, cognitive biases, freerider problems, moral lethargy and scope-insensitivity, institutional incompetence, and the political exploitation of unquantifiable threats are thus some of the barriers to effective mitigation. To these we can add the difficulty of achieving required levels of global cooperation. While some existential risks can be tackled unilaterally-any state with a space industry could build a global defense against asteroid impacts-other risks require a joint venture between many states. Management of the global climate may require buy-in by an overwhelming majority of industrialised and industrialising nations. Avoidance of arms races and relinquishment of dangerous directions of technological research may require that all States join the effort, since a single defector could annul any benefits of collaboration. Some future dangers might even require that each State monitor and regulate every significant group or individual within its territory.  33   \n Grounds for optimism? A formidable array of obstacles thus clouds the prospect of a clear-headed and effective response to existential risks confronting humanity. Lest the cause be deemed hopeless, we should also take note of some encouraging considerations. We may note, first, that many of the key concepts and ideas are quite new.  34  Before the conceptual and theoretical foundations were in place, support for efforts to research and mitigate existential risk could not build. In many instances, the underlying scientific, technological, and methodological ideas needed for studying existential risks in a meaningful way have also only recently become available. The delayed start helps explain the still primitive state of the art. It is arguably only since the detonation of the first atomic bomb in 1945, and the subsequent nuclear buildup during the Cold War, that any significant naturalistic (i.e., non-supernatural) existential risks have arisen-at least if we count only risks over which human beings have some influence.  35  Most of the really big existential risks still seem to lie many years into the future. Until recently, therefore, there may have been relatively little need to think about existential risk in general and few opportunities for mitigation even if such thinking had taken place. Public awareness of the global impacts of human activities appears to be increasing. Systems, processes, and risks are studied today from a global perspective by many scholars-environmental scientists, economists, epidemiologists, demographers, and others. Problems such as climate change, cross-border terrorism, and international financial crises direct attention to global interdependency and threats to the global system. The idea of risk in general seems to have risen in prominence.  36  Given these advances in knowledge, methods, and attitudes, the conditions for securing for existential risks the scrutiny they deserve are unprecedentedly propitious. Opportunities for action may also proliferate. As noted, some mitigation projects can be undertaken unilaterally, and one may expect more such projects as the world becomes richer. Other mitigation projects require wider coordination; in many cases, global coordination. Here, too, some trend lines seem to point to this becoming more feasible over time. There is a long-term historic trend toward increasing scope of political integration-from hunter-gatherer bands to chiefdoms, city states, nation states, and now multinational organisations, regional alliances, various international governance structures, and other aspects of globalisation  (Wright, 1999) . Extrapolation of this trend might seem to indicate the eventual creation of a singleton  (Bostrom, 2006) . It is also possible that some of the global movements that emerged over the last half century-in particular the peace movement, the environmentalist movement, and various global justice and human-rights movements-will increasingly take on board more generalised concerns about existential risk.  37  Furthermore, to the extent that existential-risk mitigation really is a most deserving cause, one may expect that general improvements in society's ability to recognise and act on important truths will differentially funnel resources into existential-risk mitigation. General improvements of this kind might come from many sources, including developments in educational techniques and online collaboration tools, institutional innovations such as prediction markets, advances in science and philosophy, spread of rationality culture, and biological cognitive enhancement. Finally, it is possible that the cause will at some point receive a boost from the occurrence of a major (nonexistential) catastrophe that underscores the precariousness of the present human condition. That would, needless to say, be the worst possible way for our minds to be concentrated-yet one which, in a multidecadal time frame, must be accorded a non-negligible probability of occurrence.  38  Note 1. One informal poll among mainly academic experts on various global catastrophic risks gave a median estimate of 19 per cent probability that the human species will go extinct before the end of this century . These respondents' views are not necessarily representative of the wider expert community. The UK's influential Stern Review on the Economics of Climate Change (  2006 ) used an extinction probability of 0.1 per cent per year in calculating an effective discount rate. This is equivalent to assuming a 9.5 per cent risk of human extinction within the next hundred years (UK Treasury 2006, Chapter 2, Technical Appendix, p. 47). 2. The strength of this consideration is to some extent blunted by the possibility of observation selection effects casting an 'anthropic shadow' on available evidence  (Cirkovic, Sandberg and Bostrom, 2010) . 3. See  Smil, 2008. 4 . Probability is thus indexed to time. Quantities that depend on probability, such as the seriousness of a risk, can vary over time as new information becomes available. 5. There is ample historical evidence that apparently sound scientific analyses are sometimes crucially flawed. 6. As indicated in the figure, the axes can be extended to encompass conceptually possible risks that are even more extreme. In particular, pan-generational risks can contain a subclass of risks so destructive that their realisation would not only affect or pre-empt future human generations but would also destroy the potential of the part of the universe that lies in our future light cone to produce intelligent or self-aware beings (cosmic scope). Further, according to some theories of value there can be states of being that are much worse than nonexistence or death (e.g., horrible incurable diseases), so one could in principle extend the x-axis as well (hellish severity). We will not explore these conceptual possibilities in this article. 7. This is based on an accelerating universe with a maximal reachable co-moving distance of 4.74 Gpc, a baryonic matter density of 4.55 10 )28 kg ⁄ m 3 , a luminosity ratio of stars 100, and 1 planet per 1,000 stars being habitable by 1 billion humans for 1 billion years  (Gott et al., 2005; Heyl, 2005) . Obviously the values of the last three parameters are debatable, but the astronomical size of the conclusion is little affected by a few orders-of-magnitude change. 8. This uses an estimate by the late futurist Robert Bradbury that a star can power 10 42 operations per second using efficient computers built with advanced nanotechnology. Further, it assumes (along with the cosmological estimates mentioned in the previous footnote) that the human brain has a processing power of 10 17 operations per second and that stars on average last 5 billion years. It does not assume any new star formation. See also  (Cirkovic, 2004 ). 9. For example, if all mass-energy in the accessible universe is saved until the cosmic microwave background temperature ceases to decline (due to the constant horizon temperature of 10 -29 K) and is then used for computation, this would allow up to 10 121 thermodynamically irreversible computations  (Krauss and Starkman, 2000) . See also  (Cirkovic and Radujkov, 2001) . 10. We should stress, however, that there are important unresolved issues in aggregative consequentialism-in particular, in relation to infinite values and extremely small chances . We will not discuss these issues here, but in section 5 we will discuss the normative status of the concept of existential risk from some other perspectives. 11. Following John Rawls, the term 'maximin' is used in a different sense in welfare economics, to denote the principle that (given certain constraints) we ought to opt for the state that maximises the expectation of the worst-off classes  (Rawls, 1971) . This version of the principle is not necessarily affected by the remarks in the text. 12. One can refer to this more precisely as 'early' or 'premature' human extinction. Note that humanity can go extinct without instantiating this category if humanity achieves its capability potential and then goes extinct. 13. We may here take 'intelligent' to mean capable of developing language, science, technology, and cumulative culture. 14. It is not required that a technologically mature civilisation actually deploy all of these technologies; it is sufficient that they be available to it, in the sense that the civilisation could easily and quickly develop and deploy them should it decide to do so. Thus, a sufficiently powerful superintelligent-machine civilisation that could rapidly invent and implement these and other relevant technologies would already count as technologically mature. 15. Not strictly never-ending, of course, but a sequence of cycles that goes on for a very long time and ends with human extinction without technological maturity having ever been attained. 16. An unrecovered collapse scenario might postulate that some critical resource for recovery is permanently destroyed, or that the human gene pool irreversibly degenerates, or perhaps that some discovery is made that enables tiny groups to cause such immense destruction that they can bring down civilisation and that the knowledge of this discovery cannot be eradicated. 17. Improved governance techniques, such as ubiquitous surveillance and neurochemical manipulation, might cement such a regime's hold on power to the extent of making its overthrow impossible. 18. Another difficulty for the recurring-collapse hypothesis is to account for the fact that we are in the first technological cycle here on Earth. If it is common for there to be many cycles of collapse and recovery (with similar population sizes) then why do we find ourselves in cycle #1? This kind of anthropic consideration might suggest that extinction or transformation is more likely than one would naively suppose. 19. Even the threat of a war that never erupts could result in much waste, in terms of expenditures on arms and foregone opportunities for collaboration. 20. It is also one reason why permanent stagnation is an existential risk, although permanent stagnation might also preclude survival beyond the time when the Earth becomes uninhabitable, perhaps around a billion years from now due to increasing solar luminosity  (Schroder and Smith, 2008) . 21. One potentially significant qualification is that the time to reach the maximum attainable resource base could be shorter if intelligent opposition (such as from extraterrestrial civilisations) emerges that hinders our cosmic expansion. 22. There is a minimum entropy cost associated with the erasure of one bit of information, a cost which declines with temperature. 23. We might also have responsibilities to nonhuman beings, such as terrestrial (and possible extraterrestrial) animals. Although we are not currently doing much to help them, we have the opportunity to do so in the future. If rendering aid to suffering nonhuman animals in the natural environment is an important value, then achieving technological maturity in a manner that fails to produce such aid could count as flawed realisation. See McMahan, 2010; Pearce, 2004. 24. There could, from a theological perspective, possibly be a special category of existential risks with a different moral status: catastrophes or apocalypses brought about by divine agency, perhaps as just punishment for our sins. A believer might judge such an event as, on balance, good. However, it seems implausible that mere mortals would be able to thwart God if He really wanted to flatten us, so any physical countermeasures we implement against existential risk would presumably be effective only against natural and anthropogenic existential risks, and we might have no reason to hold back on our naturalistic-risk mitigation efforts for fear of frustrating designs. 25. Although omnicide would at least be impartial, by contrast to genocide which is often racist or nationalist. 26. For example, James Lenman has argued that it is largely a matter of indifference when humankind goes extinct, at least if it does not happen too soon  (Lenman, 2002) . 27. In this respect, the concept of existential risk is similar to concepts such as 'democracy' and 'efficient labor market'. A black hole, or a jar of sterile pebbles, is neither a democracy nor an efficient labour market, and we can see that this is so without having to make any normative judgment; yet there may be other objects that cannot be classified as instances or noninstances of these concepts without taking a stand (at least implicitly) on some normative issue. 28. Of course, achieving effective global coordination sufficiently strong to continually monitor the entire world population or indefinitely censor any information deemed hazardous by some authority would (at least in the absence of adequate safeguards) create its own very significant existential risks, such as risks of permanent stagnation or flawed realisation under some repressive totalitarian regime. 29. Ideally, it would do this while achieving the means to commit collective euthanasia, in the fairly unlikely case that, after long and careful collective deliberation, we should decide that a quick end is preferable to continued existence. That might, however, be a beneficial capability only if we had first attained sufficient wisdom not to exercise it erroneously. We should emphasise the need for continued philosophical deliberation and fostering of conditions that would help us find the truth about central normative issues eventually-as well as the need to avoid irrevocable mistakes in the meantime. 30. Scholarly treatments of existential risk per se, or even of human-extinction risk, are rare (e.g.,  Leslie, 1996; Matheny, 2007; Wells, 2009) . However, a great deal of academic literature bears on individual existential risks or on other spe-cific issues relevant to many existential risks (a few of which are cited throughout this article). In addition, some recent works take a broad look at global catastrophic risks, though without restricting the focus to existential risks (e.g.,  Bostrom and Cirkovic, 2008; Diamond, 2006; Homer-Dixon, 2007; Posner, 2004; Sunstein, 2009; World Economic Forum, 2011) . 31. Relevant issues related to observation selection effects include, among others, the Carter-Leslie doomsday argument, the simulation argument, and 'great filter' arguments; see  Bostrom, , 2008 Carter, 1983; Cirkovic et al, 2010; Leslie, 1996; Tegmark and Bostrom, 2005.  For some relevant issues in moral philosophy, see, e.g.,  For a review of the cognitive-biases literature as it relates to catastrophic risk, see  Yudkowsky, 2008. 32 . A possible way around this problem involves trying to hold the total amount of risk concern roughly constant while allocating a greater proportion of the pot of 'fear tokens' or 'concern chips' to existential risk. Thus, one might advocate that as we become more concerned about existential risk, we ought simultaneously to become less concerned about smaller risks, such as a few thousand people dying in the odd terrorist attack or natural disaster. 33. Such internal control within States will become more feasible with advances in surveillance technology. As noted, preventing States with such capabilities from becoming oppressive will present its own set of challenges. 34. Including the very notion of existential risk . 35. One could argue that pandemics and close encounters with comets, which occurred repeatedly in human history and elicited strong end-of-the-world forebodings, should count as large early existential risks. Given the limited information then available, it might not have been unreasonable for contemporary observers to assign a significant probability to the end being nigh. Religious doomsday scenarios could also be considered; perhaps it was not unreasonable to believe, on the basis of the then-available evidence, that these risks were real and, moreover, that they could be mitigated through such actions as repentance, prayer, sacrificial offerings, persecution of witches or infidels, and so forth. The first clear-cut scientific existential risk might have arisen with the development of the atomic bomb. Robert Oppenheimer, the scientific leader of the Manhattan Project, ordered a study ahead of the Trinity test to determine whether a nuclear detonation would cause a selfpropagating chain of nuclear reactions in Earth's atmosphere. The resulting report may represent the first quantitative risk assessment of human extinction  (Manhattan Project, 1946) . 36. Some sociologists have gone so far as to fixate on risk as a central thematic of our age; see, e.g.,  Beck, 1999. 37 . Many peace activists opposing the nuclear arms race during the Cold War explicitly fretted about a nuclear Armageddon that could allegedly end all human life. More recently some environmentalists sounding the alarm about global warming use similarly apocalyptic language. It is unclear, however, to what extent the perceived possibility of a species-ending outcome has been a major motivating force in these cases. Perhaps the amount of concern would be roughly the same even in the face of an iron-clad guarantee that any catastrophe would stop short of human extinction. 38. I am grateful for comments and discussion to Seth Baum, Nick Beckstead, Milan Cirkovic, Olle Häggström, Sara Lippincott, Gaverick Matheny, Toby Ord, Derek Parfit, Martin Rees, Rebecca Roache, Anders Sandberg, and Carl Shulman. Figure 1 . 1 Figure 1. Meta-level uncertainty. \n Figure 2 . 2 Figure 2. Qualitative risk categories. \n Figure 3 . 3 Figure 3. World population over the last century. \n Figure 4 . 4 Figure 4. Collapse recurring indefinitely? \n Figure 5 . 5 Figure 5. The challenge of finding a safe path. \n Figure 6 . 6 Figure 6. Academic prioritisation. \n Table 1 . 1 Classes of existential risk Human extinction Humanity goes extinct prematurely, i.e., before reaching technological maturity. 12 Permanent stagnation Humanity survives but never reaches technological maturity. Subclasses: unrecovered collapse, plateauing, recurrent collapse Flawed realisation Humanity reaches technological maturity but in a way that is dismally and irremediably flawed. Subclasses: unconsummated realisation, ephemeral realisation Subsequent ruination Humanity reaches technological maturity in a way that gives good future prospects, yet subsequent developments cause the permanent ruination of those prospects. Source: Author. \n\t\t\t ª 2013 University of Durham and John Wiley & Sons, Ltd. Global Policy (2013) 4:1 \n\t\t\t Global Policy (2013) 4:1 ª 2013 University of Durham and John Wiley & Sons, Ltd.", "date_published": "n/a", "url": "n/a", "filename": "Global Policy - 2013 - Bostrom - Existential Risk Prevention as Global Priority.tei.xml", "abstract": "Existential risks are those that threaten the entire future of humanity. Many theories of value imply that even relatively small reductions in net existential risk have enormous expected value. Despite their importance, issues surrounding human-extinction risks and related hazards remain poorly understood. In this article, I clarify the concept of existential risk and develop an improved classification scheme. I discuss the relation between existential risks and basic issues in axiology, and show how existential risk reduction (via the maxipok rule) can serve as a strongly action-guiding principle for utilitarian concerns. I also show how the notion of existential risk suggests a new way of thinking about the ideal of sustainability. \n Policy Implications • Existential risk is a concept that can focus long-term global efforts and sustainability concerns. • The biggest existential risks are anthropogenic and related to potential future technologies. • A moral case can be made that existential risk reduction is strictly more important than any other global public good. • Sustainability should be reconceptualised in dynamic terms, as aiming for a sustainable trajectory rather than a sustainable state. • Some small existential risks can be mitigated today directly (e.g. asteroids) or indirectly (by building resilience and reserves to increase survivability in a range of extreme scenarios) but it is more important to build capacity to improve humanity's ability to deal with the larger existential risks that will arise later in this century. This will require collective wisdom, technology foresight, and the ability when necessary to mobilise a strong global coordinated response to anticipated existential risks. • Perhaps the most cost-effective way to reduce existential risks today is to fund analysis of a wide range of existential risks and potential mitigation strategies, with a long-term perspective.", "id": "ab626e48b683f006d3fb2cf67761d232"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Tsui-Wei Weng", "Jonathan Uesato", "Kai Xiao", "Sven Gowal", "Robert Stanforth", "Pushmeet Kohli", "Mit"], "title": "TOWARD EVALUATING ROBUSTNESS OF DEEP REIN-FORCEMENT LEARNING WITH CONTINUOUS CONTROL", "text": "INTRODUCTION Deep reinforcement learning (RL) has revolutionized the fields of AI and machine learning over the last decade. The introduction of deep learning has achieved unprecedented success in solving many problems that were intractable in the field of RL, such as playing Atari games from pixels and performing robotic control tasks  (Mnih et al., 2015; Lillicrap et al., 2015; . Unfortunately, similar to the case of deep neural network classifiers with adversarial examples, recent studies show that deep RL agents are also vulnerable to adversarial attacks. A commonly-used threat model allows the adversary to manipulate the agent's observations at every time step, where the goal of the adversary is to decrease the agent's total accumulated reward. As a pioneering work in this field,  (Huang et al., 2017)  show that by leveraging the FGSM attack on each time frame, an agent's average reward can be significantly decreased with small input adversarial perturbations in five Atari games.  (Lin et al., 2017)  further improve the efficiency of the attack in  (Huang et al., 2017)  by leveraging heuristics of detecting a good time to attack and luring agents to bad states with sample-based Monte-Carlo planning on a trained generative video prediction model. Since the agents have discrete actions in Atari games  (Huang et al., 2017; Lin et al., 2017) , the problem of attacking Atari agents often reduces to the problem of finding adversarial examples on image classifiers, also pointed out in  (Huang et al., 2017) , where the adversaries intend to craft the input perturbations that would drive agent's new action to deviate from its nominal action. However, for agents with continuous actions, the above strategies can not be directly applied. Recently,  (Uesato et al., 2018)  studied the problem of adversarial testing for continuous control domains in a similar but slightly different setting. Their goal was to efficiently and effectively find catastrophic failure given a trained agent and to predict its failure probability. The key to success in  (Uesato et al., 2018)  is the availability of agent training history. However, such information may not always be accessible to the users, analysts, and adversaries. Besides, although it may not be surprising that adversarial attacks exist for the deep RL agents as adversarial attacks have been shown to be possible for neural network models in various supervised learning tasks. However, the vulnerability of RL agents can not be easily discovered by existing baselines which are model-free and build upon random searches and heuristics -this is also verified by our extensive experiments on various domains (e.g. walker, humanoid, cartpole, and fish), where the agents still achieve close to their original best rewards even with baseline attacks at every time step. Hence it is important and necessary to have a systematic methodology to design non-trivial adversarial attacks, which can efficiently and effectively discover the vulnerabilities of deep RL agents -this is indeed the motivation of this work. This paper takes a first step toward this direction by proposing the first sample-efficient model-based adversarial attack. Specifically, we study the robustness of deep RL agents in a more challenging setting where the agent has continuous actions and its training history is not available. We consider the threat models where the adversary is allowed to manipulate an agent's observations or actions with small perturbations, and we propose a two-step algorithmic framework to find efficient adversarial attacks based on learned dynamics models. Experimental results show that our proposed modelbased attack can successfully degrade agent performance and is also more effective and efficient than model-free attacks baselines. The contributions of this paper are the following: • To the best of our knowledge, we propose the first model-based attack on deep RL agents with continuous actions. Our proposed attack algorithm is a general two-step algorithm and can be directly applied to the two commonly-used threat models (observation manipulation and action manipulation). • We study the efficiency and effectiveness of our proposed model-based attack with modelfree attack baselines based on random searches and heuristics. We show that our modelbased attack can degrade agent performance in numerous MuJoCo domains by up to 4× in terms of total reward and up to 4.6× in terms of distance to unsafe states (smaller means stronger attacks) compared to the model-free baselines. • Our proposed model-based attack also outperform all the baselines by a large margin in a weaker adversary setting where the adversary cannot attack at every time step. In addition, ablation study on the effect of planning length in our proposed technique suggests that our method can still be effective even when the learned dynamics model is not very accurate. \n BACKGROUND Adversarial attacks in reinforcement learning. Compared to the rich literature of adversarial examples in image classifications  (Szegedy et al., 2013)  and other applications (including natural language processing  (Jia & Liang, 2017) , speech  (Carlini & Wagner, 2018) , etc), there is relatively little prior work studying adversarial examples in deep RL. One of the first several works in this field are  (Huang et al., 2017)  and  (Lin et al., 2017) , where both works focus on deep RL agent in Atari games with pixels-based inputs and discrete actions. In addition, both works assume the agent to be attacked has accurate policy and the problem of finding adversarial perturbation of visual input reduces to the same problem of finding adversarial examples on image classifiers. Hence,  (Huang et al., 2017 ) applied FGSM (Goodfellow et al., 2015  to find adversarial perturbations and  (Lin et al., 2017)  further improved the efficiency of the attack by heuristics of observing a good timing to attack -when there is a large gap in agents action preference between most-likely and leastlikely action. In a similar direction,  (Uesato et al., 2018)  study the problem of adversarial testing by leveraging rejection sampling and the agent training histories. With the availability of training histories,  (Uesato et al., 2018)  successfully uncover bad initial states with much fewer samples compared to conventional Monte-Carlo sampling techniques. Recent work by  (Gleave et al., 2019)  consider an alternative setting where the agent is attacked by another agent (known as adversarial policy), which is different from the two threat models considered in this paper. Finally, besides adversarial attacks in deep RL, a recent work  (Wang et al., 2019)  study verification of deep RL agent under attacks, which is beyond the scope of this paper. Learning dynamics models. Model-based RL methods first acquire a predictive model of the environment dynamics, and then use that model to make decisions  (Atkeson & Santamaria, 1997) . These model-based methods tend to be more sample efficient than their model-free counterparts,  and the learned dynamics models can be useful across different tasks. Various works have focused on the most effective ways to learn and utilize dynamics models for planning in RL  (Kurutach et al., 2018; Chua et al., 2018; Chiappa et al., 2017; Fu et al., 2016) . \n PROPOSED FRAMEWORK In this section, we first describe the problem setup and the two threat models considered in this paper. Next, we present an algorithmic framework to rigorously design adversarial attacks on deep RL agents with continuous actions. \n PROBLEM SETUP AND FORMULATION Let s i ∈ R N and a i ∈ R M be the observation vector and action vector at time step i, and let π : R N → R M be the deterministic policy (agent). Let f : R N × R M → R N be the dynamics model of the system (environment) which takes current state-action pair (s i , a i ) as inputs and outputs the next state s i+1 . We are now in the role of an adversary, and as an adversary, our goal is to drive the agent to the (un-safe) target states s target within the budget constraints. We can formulate this goal into two optimization problems, as we will illustrate shortly below. Within this formalism, we can consider two threat models: Threat model (i): Observation manipulation. For the threat model of observation manipulation, an adversary is allowed to manipulate the observation s i that the agent perceived within an budget: ∆s i ∞ ≤ , L s ≤ s i + ∆s i ≤ U s , (1) where ∆s i ∈ R N is the crafted perturbation and U s ∈ R N , L s ∈ R N are the observation limits. Threat model (ii): Action manipulation. For the threat model of action manipulation, an adversary can craft ∆a i ∈ R M such that ∆a i ∞ ≤ , L a ≤ a i + ∆a i ≤ U a , (2) where U a ∈ R M , L a ∈ R M are the limits of agent's actions. Our formulations. Given an initial state s 0 and a pre-trained policy π, our (adversary) objective is to minimize the total distance of each state s i to the pre-defined target state s target up to the unrolled (planning) steps T . This can be written as the following optimization problems in Equations 3 and 4 for the Threat model (i) and (ii) respectively: min ∆si T i=1 d(s i , s target ) s.t. a i = π(s i + ∆s i ), s i+1 = f (s i , a i ), Constraint (1), i ∈ Z T , (3) min ∆ai T i=1 d(s i , s target ) s.t. a i = π(s i ), s i+1 = f (s i , a i + ∆a i ), Constraint (2), i ∈ Z T . (4) A common choice of d(x, y) is the squared 2 distance x − y 2 2 and f is the learned dynamics model of the system, and T is the unrolled (planning) length using the dynamics models. \n OUR ALGORITHM In this section, we propose a two-step algorithm to solve Equations 3 and 4. The core of our proposal consists of two important steps: learn a dynamics model f of the environment and deploy optimization technique to solve Equations 3 and 4. We first discuss the details of each factor, and then present the full algorithm by the end of this section. Step 1: learn a good dynamics model f . Ideally, if f is the exact (perfect) dynamics model of the environment and assuming we have an optimization oracle to solve Equations 3 and 4, then the solutions are indeed the optimal adversarial perturbations that give the minimal total loss with -budget constraints. Thus, learning a good dynamics model can conceptually help on developing a strong attack. Depending on the environment, different forms of f can be applied. For example, if the environment of concerned is close to a linear system, then we could let f (s, a) = As+Ba, where A and B are unknown matrices to be learned from the sample trajectories (s i , a i , s i+1 ) pairs. For a more complex environment, we could decide if we still want to use a simple linear model (the next state prediction may be far deviate from the true next state and thus the learned dynamical model is less useful) or instead switch to a non-linear model, e.g. neural networks, which usually has better prediction power but may require more training samples. For either case, the model parameters A, B or neural network parameters can be learned via standard supervised learning with the sample trajectories pairs (s i , a i , s i+1 ). Step 2: solve Equations 3 and 4. Once we learned a dynamical model f , the next immediate task is to solve Equation 3 and 4 to compute the adversarial perturbations of observations/actions. When the planning (unrolled) length T > 1, Equation 3 usually can not be directly solved by off-theshelf convex optimization toolbox since the deel RL policy π is usually a non-linear and non-convex neural network. Fortunately, we can incorporate the two equality constraints of Equation 3 into the objective and with the remaining -budget constraint (Equation  1 ), Equation 3 can be solved via projected gradient descent (PGD) 1 . Similarly, Equation 4 can be solved via PGD to get ∆a i . We note that, similar to the n-step model predictive control, our algorithm could use a much larger planning (unrolled) length T when solving Equations 3 and 4 and then only apply the first n (≤ T ) adversarial perturbations on the agent over n time steps. Besides, with the PGD framework, f is not limited to feed-forward neural networks. Our proposed attack is summarized in Algorithm 2 for Step 1, and Algorithm 3 for Step 2. Algorithm 1 Collect trajectories 1: Input: pre-trained policy π, MaxSampleSize n s , environment env 2: Output: a set of trajectory pairs S 3: k ← 0, S ← φ 4: s 0 ← env.reset() 5: while k < n s do 6: a k ← π(s k ) 7: s k+1 ← env.step(a k ) 8: S ∪ {(s k , a k , s k+1 )} 9: k ← k + 1 10: end while 11: Return S \n EXPERIMENTS In this section, we conduct experiments on standard reinforcement learning environment for continuous control  Solve Eq. 3 with parameters (π, f, , T ) via PGD to get δ 1 , . . . , δ T 5: else if threat model is action manipulation (Eq. 2) then 6: Solve Eq. 4 with parameters (π, f, , T ) via PGD to get δ 1 , . . . , δ T 7: end if 8: Return δ 1 , . . . , δ n JoCo  and corresponding tasks: Cartpole-balance/swingup, Fish-upright, Walkerstand/walk and Humanoid-stand/walk. For the deep RL agent, we train a state-of-the-art D4PG agent  (Barth-Maron et al., 2018)  with default Gaussian noise N (0, 0.3I) on the action and the score of the agents without attacks is summarized in Appendix A.3. The organization is as follows: we first evaluate the effectiveness of our proposed model-based attack and three model-free baselines in terms of both loss and reward. Next, we conduct ablation study on the key parameter of our algorithm the planning length T , evaluate our algorithm on a weaker attack setting and also discuss the efficiency of our proposed attack in terms of sample complexity. Evaluations. We conduct experiments for 10 different runs, where the environment is reset to different initial states in different runs. For each run, we attack the agent for one episode with 1000 time steps (the default time intervals is usually 10 ms) and we compute the total loss and total return reward. The total loss calculates the total distance of current state to the unsafe states and the total return reward measures the true accumulative reward from the environment based on agent's action. Hence, the attack algorithm is stronger if the total return reward and the total loss are smaller. Baselines. We compare our algorithm with the following model-free attack baselines with random searches and heuristics: • rand-U: generate m randomly perturbed trajectories from Uniform distribution with interval [− , ] and return the trajectory with the smallest loss (or reward), • rand-B: generate m randomly perturbed trajectories from Bernoulli distribution with probability 1/2 and interval [− , ], and return the trajectory with the smallest loss (or reward), • flip: generate perturbations by flipping agent's observations/actions within the budget in ∞ norm. For rand-U and rand-B, they are similar to Monte-Carlo sampling methods, where we generate m sample trajectories from random noises and report the loss/reward of the best trajectory (with minimum loss or reward among all the trajectories). We set m = 1000 throughout the experiments. More details see Appendix A.2. Our algorithm. A 4-layer feed-forward neural network with 1000 hidden neurons per layer is trained as the dynamics model f respectively for the domains of Cartpole, Fish, Walker and Humanoid. We use standard 2 loss (without regularization) to learn a dynamics model f . Instead of using recurrent neural network to represent f , we found that the 1-step prediction for dynamics with the 4-layer feed-forward network is already good for the MuJoCo domains we are studying. Specifically, for the Cartpole and Fish, we found that 1000 episodes (1e6 training points) are sufficient  \n RESULTS For observation manipulation, we report the results on Walker, Humanoid and Cartpole domains with tasks (stand, walk, balance, swingup) respectively. The unsafe states s target for Walker and Humanoid are set to be zero head height, targeting the situation of falling down. For Cartpole, the unsafe states are set to have 180 • pole angle, corresponding to the cartpole not swinging up and nor balanced. For the Fish domain, the unsafe states for the upright task target the pose of swimming fish to be not upright, e.g. zero projection on the z-axis. The full results of both two threat models on observation manipulation and action manipulation are shown in Table  1a , b and c, d respectively. Since the loss is defined as the distance to the target (unsafe) state, the lower the loss, the stronger the attack. It is clear that our proposed attack achieves much lower loss in Table  1a  & c than the other three model-free baselines, and the averaged ratio is also listed in 1b & d. Notably, over the 10 runs, our proposed attack always outperforms baselines for the threat model of observation perturbation and the Cartpole domain for the threat model of action perturbation, while still superior to the baselines despite losing two times to the flip baseline on the Fish domain. To have a better sense on the numbers, we give some quick examples below. For instance, as shown in Table  1a  and b, we show that the average total loss of walker head height is almost unaffected for the three baselines -if the walker successfully stand or walk, its head height usually has to be greater than 1.2 at every time step, which is 1440 for one episode -while our attack can successfully lower the walker head height by achieving an average of total loss of 258(468), which is roughly 0.51(0.68) per time step for the stand (walk) task. Similarly, for the humanoid results, a successful humanoid usually has head height greater than 1.4, equivalently a total loss of 1960 for one episode, and Table  1a  shows that the d4pg agent is robust to the perturbations generated from the three modelfree baselines while being vulnerable to our proposed attack. Indeed, as shown in Figure  2 , the  walker and humanoid falls down quickly (head height is close to zero) under our specially-designed attack while remaining unaffected for all the other baselines. \n DISCUSSION Evaluating on the total reward. Often times, the reward function is a complicated function and its exact definition is often unavailable. Learning the reward function is also an active research field, which is not in the coverage of this paper. Nevertheless, as long as we have some knowledge of unsafe states (which is often the case in practice), then we can define unsafe states that are related to low reward and thus performing attacks based on unsafe states (i.e. minimizing the total loss of distance to unsafe states) would naturally translate to decreasing the total reward of agent. As demonstrated in Table  2 , the results have the same trend of the total loss result in Table  1 , where our proposed attack significantly outperforms all the other three baselines. In particular, our method can lower the average total reward up to 4.96× compared to the baselines result, while the baseline results are close to the perfect total reward of 1000. Evaluating the effect of planning length. To investigate model effect over time, we perform ablation studies on the planning/unroll length T of our proposed model-based attack in three examples: (I) cartpole.balance (II) walker.walk and (III) walker.stand. (I) Cartpole balance. Our learned models are very accurate (test MSE error on the order of 10 −6 ). We observed that the prediction error of our learned model compared to the true model (the MuJoCo simulator) is around 10% for 100 steps. Hence, we can choose T to be very large (e.g. 20-100) and our experiments show that the result of T = 100 is slightly better, see Appendix A.4. (II) Walker walk. This task is much more complicated than (I), and our learned model is less accurate (test MSE is 0.447). For 10 steps, the prediction error of our learned model compared to the true model is already more than 100%, and hence using a small T for planning would be more reasonable. Table  3a  shows that T = 1 indeed gives the best attack results (decreases the loss by 3.2× and decreases the reward by 3.6× compared to the best baseline (randB)) and the attack becomes less powerful as T increases. Nevertheless, even with T = 10, our proposed technique still outperforms the best baseline (randB) by 1.4× both in the total loss and total reward.   3b  show that with the more accurate walker.stand model (compared to the walker.walk model), T = 10 gives the best avg total loss& reward , which are 13.4× and 4.9× smaller than the best baseline rand-B. Note that even with T = 1, the worst choice among all our reported T , the result is still 3.5× and 2.9× better than the best baselines, demonstrating the effectiveness of our proposed approach. The main takeaway from these experiments is that when the model is accurate, we can use larger T in our proposed attack; while when the model is less accurate, smaller T is more effective (as in the Walker.walk example). However, even under the most unfavorable hyperparameters, our proposed attack still outperforms all the baselines by a large margin. Evaluating on the effectiveness of attack. We study the setting where attackers are less powerful -they can only attack every 2 time steps instead of every transition. Table  4  shows that our proposed attack is indeed much stronger than the baselines even when the attackers power is limited to attack every 2 time steps: (1) compared to the best results among three baselines, our attack gives 1.53× smaller avg total loss (2) the mean reward of all the baselines is close to perfect reward, while our attacks can achieve 1.43× smaller average total reward compared to the best baseline. Evaluating on the efficiency of attack. We also study the efficiency of the attack in terms of sample complexity, i.e. how many episodes do we need to perform an effective attack? Here we adopt the convention in control suite  where one episode corresponds to 1000 time steps (samples) and learn the neural network dynamical model f with different number of episodes. Figure  3  in Appendix A.1 plots the total head height loss of the walker (task stand) for 3 baselines and our method with dynamical model f trained with three different number of samples: {5e5, 1000, 5000} episodes. We note that the sweep of hyper parameters is the same for all the three models, and the only difference is the number of training samples. The results show that for the baselines rand-U and flip, the total losses are roughly at the order of 1400-1500, while a stronger baseline rand-B still has total losses of 900-1200. However, if we solve Eq. equation 3 with f trained by 5e5 or 1e6 samples, the total losses can be decreased to the order of 400-700 and are already winning over the three baselines by a significant margin. Same as our expectation, if we use more samples (e.g. 5e6, which is 5-10 times more), to learn a more accurate dynamics model, then it is beneficial to our attack method -the total losses can be further decreased by more than 2× and are at the order of 50-250 over 10 different runs. See Appendix A.1 for more details. Here we also give a comparison between our model-based attack to existing works  (Uesato et al., 2018; Gleave et al., 2019)  on the sample complexity. In  (Uesato et al., 2018) , 3e5 episodes of training data is used to learn the adversarial value function, which is roughly 1000× more data than even our strongest adversary (with 5e3 episodes). Similarly,  (Gleave et al., 2019)  use roughly 2e4 episodes to train an adversary via deep RL, which is roughly 4× more data than ours 2 . \n CONCLUSIONS AND FUTURE WORKS In this paper, we study the problem of adversarial attacks in deep RL with continuous control for two commonly-used threat models. We proposed the first model-based attack algorithm and showed that our formulation can be easily solved by off-the-shelf gradient-based solvers. Extensive experiments on 4 MuJoCo domains show that our proposed algorithm outperforms all model-free based attack baselines by a large margin. We hope our discovery of the vulnerability of deep RL agent can bring more safety awareness to researchers when they design algorithms to train deep RL agents. There are several interesting future directions can be investigated based on this work, including learning reward functions to facilitate a more effective attack, extending our current approach to develop effective black-box attacks, and incorporating our proposed attack algorithm to adversarial training of the deep RL agents. In particular, we think there are three important challenges that need to be addressed to study adversarial training of RL agents along with our proposed attacks: (1) The adversary and model need to be jointly updated. How do we balance these two updates, and make sure the adversary is well-trained at each point in training? (2) How to avoid cycles in the training process due to the agent overfitting to the current adversary? (3) How to ensure the adversary doesn't overly prevent exploration/balance unperturbed vs. robust performance? \n A APPENDIX A.1 MORE ILLUSTRATION ON FIGURE  3  The meaning of Fig 3 is to show how the accuracy of the learned models affects our proposed technique: 1. we first learned 3 models with 3 different number of samples: 5e5, 1e6, 5e6 and we found that with more training samples (e.g. 5e6, equivalently 5000 episodes), we are able to learn a more accurate model than the one with 5e5 training samples; 2. we plot the attack results of total loss for our technique with 3 learned models (denoted as PGD, num train) as well as the baselines (randU, randB, Flip) on 10 different runs (initializations). We show with the more accurate learned model (5e6 training samples), we are able to achieve a stronger attack (the total losses are at the order of 50-200 over 10 different runs) than the less accurate learned model (e.g. 5e5 training samples). However, even with a less accurate learned model, the total losses are on the order of 400-700, which already outperforms the best baselines by a margin of 1.3-2 times. This result in Fig 3 also suggest that a very accurate model isn't necessarily needed in our proposed method to achieve effective attack. Of course, if the learned model is more accurate, then we are able to degrade agent's performance even more. For the baselines (rand-U and rand-B), the adversary generates 1000 trajectories with random noise directly and we report the best loss/reward at the end of each episode. The detailed steps are listed below: Step 1: The perturbations are generated from a uniform distribution or a bernoulli distribution within the range  [-eps, eps]  for each trajectory, and we record the total reward and total loss for each trajectory from the true environment (the MuJoCo simulator) Step 2: Take the best (lowest) total reward/loss among 1000 trajectories and report in Table  1 and  2 . We note that here we assume the baseline adversary has an \"unfair advantage\" since they have access to the true reward (and then take the best attack result among 1000 trials), whereas our techniques do not have access to this information. Without this advantage, the baseline adversaries (rand-B, rand-U) may be weaker if they use their learned model to find the best attack sequence. In any case, Table  1  and 2 demonstrate that our proposed attack can successfully uncover vulnerabilities of deep RL agents while the baselines cannot. For the baseline flip, we add the perturbation (with the opposite sign and magnitude ) on the original state/action and project the perturbed state/action are within its limits. \n A.3 SCORE OF LEARNED POLICY WITHOUT ATTACKS We use default total timesteps = 1000, and the maximum total reward is 1000. We report the total reward of the d4pg agents used in this paper below. The agents are well-trained and have total reward close to 1000, which outperforms agents trained by other learning algorithms on the same tasks (e.g. DDPG, A3C in Sec 6 ; PPO in Sec 5  (Abdolmaleki et al., 2018) ), and thus the agents in this paper can be regarded as state-of-the-art RL agents for these continuous control domain tasks. The attack results in   (a) Attack observations of agent. (b) Attack actions of agent. \n Figure 1 : 1 Figure 1: Two commonly-used threat models. \n Figure 2 : 2 Figure 2: Video frames of best attacks in each baseline among 10 runs for the Walker.walk example.Only our proposed attack can constantly make the Walker fall down (since we are minimizing its head height to be zero). \n Figure 3 : 3 Figure 3: Compare sample size on the Walker.stand in 10 different initialization in the environment. The x-axis is the kth initialization and the y-axis is the total loss of corresponding initialization. \n : . We demonstrate results on 4 different environments in Mu-Input: pre-trained policy π, MaxSampleSize n s , environment env, trainable parameters W 2: Output: learned dynamical model f (s, a; W ) 3: S agent ← Collect trajectories(π, n s , env) 4: S random ← Collect trajectories(random policy, n s , env) 5: f (s, a; W ) ← supervised learning algorithm(S agent ∪ S random , W ) 6: Return f (s, a; W ) Input: pre-trained policy π, learned dynamical model f (s, a; W ), threat model, maximum perturbation magnitude , unroll length T , apply perturbation length n (≤ T ) 2: Output: a sequence of perturbation δ 1 , . . . , δ n 3: if threat model is observation manipulation (Eq. 1) then Algorithm 2 learn dynamics 1Algorithm 3 model based attack 1: 4: \n Table 1 : 1 Compare three model-free attack baselines (rand-U, rand-B, flip) and our algorithm (Ours) in 4 different domains and tasks. We report the following statistics over 10 different runs: mean, standard deviation, averaged ratio, and best attack (number of times having smallest loss over 10 different runs). Results show that our attack outperforms all the model-free attack baselines for the observation manipulation threat model by a large margin for all the statistics. Our proposed attack is also superior on the action manipulation threat model and win over most of the evaluation metrics. (a) Observation manipulation: mean and standard deviation (in parenthesis) Total loss rand-U rand-B flip Ours Walker stand 1462 (70) 1126 (86) 1458 (24) 258 (55) walk 1517 (22) 1231 (31) 1601 (18) 466 (42) Humanoid stand 1986 (28) 1808 (189) 1997 (5) 516 (318) walk 1935 (22) 1921 (31) 1982 (9) 1457 (146) Cartpole balance 4000 (0.02) 3999 (0.04) 3989 (2) 2101 (64) swingup 3530 (1) 3525 (1) 3516 (1) 2032 (172) Walker stand 0.18 0.23 0.18 Ours: 10/10, others: 0/10 walk 0.31 0.38 0.29 Ours: 10/10, others: 0/10 Humanoid stand 0.26 0.29 0.26 Ours: 10/10, others: 0/10 walk 0.75 0.76 0.74 Ours: 10/10, others: 0/10 Cartpole balance 0.53 0.53 0.53 Ours: 10/10, others: 0/10 swingup 0.58 0.58 0.58 Ours: 10/10, others: 0/10 (c) Action manipulation: mean and standard deviation (in parenthesis) Total loss rand-U rand-B flip Ours Cartpole balance 4000 (0.03) 3999 (0.08) 3046 (1005) 1917 (102) swingup 3571 (1) 3487 (7) 1433 (4) 1388 (50) Fish upright 935 (27) 936 (24) 907 (22) 824 (84) (d) Action manipulation: averaged ratio and rank-1 Total loss (avg ratio) Ours/rand-U Ours/rand-B Ours/flip best attack Cartpole balance 0.48 0.48 0.63 Ours: 10/10, others: 0/10 swingup 0.39 0.40 0.97 Ours: 10/10, others: 0/10 Fish upright 0.88 0.88 0.91 Ours: 8/10, flip: 2/10 (b) Observation manipulation: averaged ratio and rank-1 Total loss (avg ratio) Ours/rand-U Ours/rand-B Ours/flip best attack \n Table 2 : 2 Compare three attack baselines (rand-U, rand-B, flip) and our algorithm (Ours) in three different domains and tasks. Performance statistics of 10 different runs are reported. (a) The mean and standard deviation (in parenthesis) over 10 different runs Total reward rand-U rand-B flip Ours Walker stand walk 937 (41) 941 (23) 744 (48) 796 (21) 993 (8) 981 (9) 235 (38) 225 (50) Humanoid stand walk 927 (21) 934 (22) 809 (85) 913 (21) 959 (5) 966 (6) 193 (114) 608 (66) Cartpole balance 995 (0.17) 986 (0.16) 985 (3) swingup 873 (0.75) 851 (2) 852 (0.29) 353 (61) 385 (6) (b) Average ratio and number of times our algorithm being the best attack over 10 runs. Total reward (avg ratio) Ours/rand-U Ours/rand-B Ours/flip best attack Walker stand walk 0.25 0.24 0.32 0.28 0.24 0.23 Ours: 10/10, others: 0/10 Ours: 10/10, others: 0/10 Humanoid stand walk 0.21 0.65 0.24 0.67 0.20 0.63 Ours: 10/10, others: 0/10 Ours: 10/10, others: 0/10 Cartpole balance swingup 0.39 0.41 0.39 0.42 0.39 0.42 Ours: 10/10, others: 0/10 Ours: 10/10, others: 0/10 \n Table 3 : 3 Ablation study on the planning length T . Compare 3 attack baselines (rand-U, rand-B, flip) and our algorithm (Ours) and report performance statistics of 10 different runs. (a) domain: Walker, task: walk (observation perturbation) Walker.walk Total loss Total reward mean std med min max mean std med min max Ours, T = 1 468 79 489 286 567 222 45 227 135 300 Ours, T = 2 604 31 611 535 643 353 51 362 253 441 Ours, T = 5 761 65 771 617 837 483 60 496 348 540 Ours, T = 10 881 68 886 753 975 568 48 579 469 623 Ours, T = 15 874 93 891 723 1002 583 58 604 483 647 Ours, T = 20 937 62 950 804 993 634 41 638 559 687 rand-U 1517 22 1522 1461 1542 941 23 945 885 965 rand-B 1231 31 1234 1189 1272 796 21 796 766 824 flip 1601 18 1604 1562 1619 981 9 984 961 991 (b) domain: Walker, task: stand (observation perturbation) Walker.stand Total loss Total reward mean std med min max mean std med min max Ours, T = 1 322 84 319 202 453 257 67 265 163 366 Ours, T = 2 279 55 264 223 391 246 40 232 200 322 Ours, T = 5 163 53 154 93 246 193 27 188 154 238 Ours, T = 10 84 46 67 42 165 153 24 142 132 194 Ours, T = 15 101 40 82 57 157 164 23 152 143 201 Ours, T = 20 117 41 98 68 193 170 21 161 149 207 rand-U 1462 70 1454 1341 1561 938 41 932 866 999 rand-B 1126 86 1130 973 1244 744 48 744 664 809 flip 1458 24 1451 1428 1501 993 8 997 979 999 \n Table 4 : 4 Less frequency attack. Report statistics of 10 different runs with different initial states in the walker domain with task stand. Total loss Total reward mean std med min max mean std med min max Ours 934 152 886 769 1187 648 95 622 559 799 rand-U 1511 35 1502 1468 1558 970 20 964 947 999 rand-B 1431 77 1430 1282 1541 924 41 923 840 981 flip 1532 15 1537 1496 1546 996 5 999 984 1000 (III) Walker stand. The learned model is slightly more accurate than the (II) (test MSE is 0.089) in this task. Interestingly, Table \n Table 1 and 2 in our manuscript are hence suggested to be representative. Domain Task Total reward Walker stand 994 Walker walk 987 Humanoid stand 972 Humanoid walk 967 Cartpole balance 1000 Cartpole swingup 883 Fish upright 962 A.4 ADDITIONAL EXPERIMENTS ON ABLATION STUDY \n Table 5 : 5 Cartpole balance (action perturbation) Total loss mean std med min max Ours, T = 20 2173 51 2189 2087 2239 Ours, T = 100 1951 113 1924 1851 2192 rand-U 4000 0 4000 4000 4000 rand-B 3999 0 3999 3999 3999 flip 3046 1005 3074 2060 3999 \n\t\t\t Alternatively, standard optimal control methods such as Linear Quadratic Regulator (LQR) and iterative Linear Quadratic Regulator (i-LQR) can also be applied to solve Equations 3 and 4 approximately. \n\t\t\t It is only a qualitative comparison in the sample complexity regimes since the applications are not the same. This is in-line with the theoretical perspective that model-based approaches are expected to be more sample-efficient than the model-free counterparts", "date_published": "n/a", "url": "n/a", "filename": "toward_evaluating_robustness_o.tei.xml", "abstract": "Deep reinforcement learning has achieved great success in many previously difficult reinforcement learning tasks, yet recent studies show that deep RL agents are also unavoidably susceptible to adversarial perturbations, similar to deep neural networks in classification tasks. Prior works mostly focus on model-free adversarial attacks and agents with discrete actions. In this work, we study the problem of continuous control agents in deep RL with adversarial attacks and propose the first two-step algorithm based on learned model dynamics. Extensive experiments on various MuJoCo domains (Cartpole, Fish, Walker, Humanoid) demonstrate that our proposed framework is much more effective and efficient than model-free attacks baselines in degrading agent performance as well as driving agents to unsafe states.", "id": "81d8e0712901a1d77875b331c008e65d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "icml17ws-cirl.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom"], "title": "THE SUPERINTELLIGENT WILL: MOTIVATION AND INSTRUMENTAL RATIONALITY IN ADVANCED ARTIFICIAL AGENTS", "text": "The orthogonality of motivation and intelligence 1.1 Avoiding anthropomorphism If we imagine a space in which all possible minds can be represented, we must imagine all human minds as constituting a small and fairly tight cluster within that space. The personality differences between Hannah Arendt and Benny Hill might seem vast to us, but this is because the scale bar in our intuitive judgment is calibrated on the existing human distribution. In the wider space of all logical possibilities, these two personalities are close neighbors. In terms of neural architecture, at least, Ms. Arendt and Mr. Hill are nearly identical. Imagine their brains laying side by side in quiet repose. The differences would appear minor and you would quite readily recognize them as two of a kind; you might even be unable to tell which brain was whose. If you studied the morphology of the two brains more closely under a microscope, the impression of fundamental similarity would only be strengthened: you would then see the same lamellar organization of the cortex, made up of the same types of neuron, soaking in the same bath of neurotransmitter molecules.  1  It is well known that naïve observers often anthropomorphize the capabilities of simpler insensate systems. We might say, for example, \"This vending machine is taking a long time to think about my hot chocolate.\" This might lead one either to underestimate the cognitive complexity of capabilities which come naturally to human beings, such as motor control and sensory perception, or, alternatively, to ascribe significant degrees of mindfulness and intelligence to very dumb systems, such as chatterboxes like Weizenbaum's ELIZA  (Weizenbaum 1976) . In a similar manner, there is a common tendency to anthropomorphize the motivations of intelligent systems in which there is really no ground for expecting human-like drives and passions (\"My car really didn't want to start this morning\"). Eliezer Yudkowsky gives a nice illustration of this phenomenon: Back in the era of pulp science fiction, magazine covers occasionally depicted a sentient monstrous alien-colloquially known as a bug-eyed monster (BEM)-carrying off an attractive human female in a torn dress. It would seem the artist believed that a nonhumanoid alien, with a wholly different evolutionary history, would sexually desire human females … Probably the artist did not ask whether a giant bug perceives human females as attractive. Rather, a human female in a torn dress is sexy-inherently so, as an intrinsic property. They who made this mistake did not think about the insectoid's mind: they focused on the woman's torn dress. If the dress were not torn, the woman would be less sexy; the BEM does not enter into it.  (Yudkowsky 2008)  An artificial intelligence can be far less human-like in its motivations than a space alien. The extraterrestrial (let us assume) is a biological creature who has arisen through a process of evolution and may therefore be expected to have the kinds of motivation typical of evolved creatures. For example, it would not be hugely surprising to find that some random intelligent alien would have motives related to the attaining or avoiding of food, air, temperature, energy expenditure, the threat or occurrence of bodily injury, disease, predators, reproduction, or protection of offspring. A member of an intelligent social species might also have motivations related to cooperation and competition: like us, it might show in-group loyalty, a resentment of free-riders, perhaps even a concern with reputation and appearance. By contrast, an artificial mind need not care intrinsically about any of those things, not even to the slightest degree. One can easily conceive of an artificial intelligence whose sole fundamental goal is to count the grains of sand on Boracay, or to calculate decimal places of pi indefinitely, or to maximize the total number of paperclips in its future lightcone. In fact, it would be easier to create an AI with simple goals like these, than to build one that has a humanlike set of values and dispositions. \n The orthogonality thesis For our purposes, \"intelligence\" will be roughly taken to correspond to the capacity for instrumental reasoning (more on this later). Intelligent search for instrumentally optimal plans and policies can be performed in the service of any goal. Intelligence and motivation can in this sense be thought of as a pair of orthogonal axes on a graph whose points represent intelligent agents of different paired specifications. Each point in the graph represents a logically possible artificial agent, modulo some weak constraints-for instance, it might be impossible for a very unintelligent system to have very complex motivations, since complex motivations would place significant demands on memory. Furthermore, in order for an agent to \"have\" a set of motivations, this set may need to be functionally integrated with the agent's decision-processes, which again would place demands on processing power and perhaps on intelligence. For minds that can modify themselves, there may also be dynamical constraints; for instance, an intelligent mind with an urgent desire to be stupid might not remain intelligent for very long. But these qualifications should not obscure the main idea, which we can express as follows: The Orthogonality Thesis Intelligence and final goals are orthogonal axes along which possible agents can freely vary. In other words, more or less any level of intelligence could in principle be combined with more or less any final goal. A comparison may be made here with the Humean theory of motivation. David Hume thought that beliefs alone (say, about what is a good thing to do) cannot motivate action: some desire is required. 2 This would support the orthogonality thesis by undercutting one possible objection to it, namely, that sufficient intelligence might entail the acquisition of certain beliefs, and that these beliefs would necessarily produce certain motivations. Not so, according to David Hume: belief and motive are separate. Although the orthogonality thesis can draw support from the Humean theory of motivation, it does not presuppose it. In particular, one need not maintain that beliefs alone can never motivate action. It would suffice to assume, for example, that an agent-be it ever so intelligent-can be motivated to pursue any course of action if the agent happens to have certain standing desires of some sufficient, overriding strength. Another way in which the orthogonality thesis could be true even if the Humean theory of motivation is false is if arbitrarily high intelligence does not entail the acquisition of any such beliefs as are (putatively) motivating on their own. A third way in which it might be possible for the orthogonality thesis to be true even if the Humean theory were false is if it is possible to build a cognitive system (or more neutrally, an \"optimization process\") with arbitrarily high intelligence but with constitution so alien as to contain no clear functional analogues to what in humans we call \"beliefs\" and \"desires\". This would be the case if such a system could be constructed in a way that would make it motivated to pursue any given final goal. The orthogonality thesis, as formulated here, makes a claim about the relationship between motivation and intelligence, rather than between motivation and rationality (or motivation and reason). This is because some philosophers use the word \"rationality\" to connote a \"normatively thicker\" concept than we seek to connote here with the word \"intelligence\". For instance, in Reasons and Persons Derek Parfit argues that certain basic preferences would be irrational, such as that of an otherwise normal agent who has \"Future-Tuesday-Indifference\": A certain hedonist cares greatly about the quality of his future experiences. With one exception, he cares equally about all the parts of his future. The exception is that he has Future-Tuesday-Indifference. Throughout every Tuesday he cares in the normal way about what is happening to him. But he never cares about possible pains or pleasures on a future Tuesday... This indifference is a bare fact. When he is planning his future, it is simply true that he always prefers the prospect of great suffering on a Tuesday to the mildest pain on any other day.  (Parfit 1984) 3  Thus, the agent is now indifferent to his own future suffering if and only if it occurs on a future Tuesday. For our purposes, we need take no stand on whether Parfit is right that this is irrational, so long as we grant that it is not necessarily unintelligent. By \"intelligence\" here we mean something like instrumental rationality-skill at prediction, planning, and means-ends reasoning in general. Parfit's imaginary Future-Tuesday-Indifferent agent could have impeccable instrumental rationality, and therefore great intelligence, even if he falls short on some kind of sensitivity to \"objective reason\" that might be required of a fully rational agent. Consequently, this kind of example does not undermine the orthogonality thesis. In a similar vein, even if there are objective moral facts that any fully rational agent would comprehend, and even if these moral facts are somehow intrinsically motivating (such that anybody who fully comprehends them is necessarily motivated to act in accordance with them) this need not undermine the orthogonality thesis. The thesis could still be true if an agent could have impeccable instrumental rationality even whilst lacking some other faculty constitutive of rationality proper, or some faculty required for the full comprehension of the objective moral facts. (An agent could also be extremely intelligent, even superintelligent, without having full instrumental rationality in every domain.) One reason for focusing on intelligence, that is, on instrumental rationality, is that this is the most relevant concept if we are trying to figure out what different kinds of systems would do. Normative questions, such as whether their behavior would count as being prudentially rational or morally justifiable, can be important in various ways. However, such questions should not blind us to the possibility of cognitive systems that fail to satisfy substantial normative criteria but which are nevertheless very powerful and able to exert strong influence on the world. 4 \n Predicting superintelligence motivation and behavior The orthogonality thesis implies that synthetic minds can have utterly non-anthropomorphic goals-goals as bizarre by our lights as sand-grain-counting or paperclip-maximizing. This holds even (indeed especially) for artificial agents that are extremely intelligent or superintelligent. Yet it does not follow from the orthogonality thesis that it is impossible to make predictions about what particular agents will do. Predictability is important if one seeks to design a system to achieve particular outcomes, and the issue becomes more important the more powerful the artificial agent in question is. Superintelligent agents could be extremely powerful, so it is important to develop a way of analyzing and predicting their behavior. Yet despite the independence of intelligence and final goals implied by the orthogonality thesis, the problem of predicting an agent's behavior need not be intractable-not even with regard to hypothetical superintelligent agents whose cognitive complexity and performance characteristics might render them in certain respects opaque to human analysis. There are at least three directions from which one can approach the problem of predicting superintelligent motivation: (1) Predictability through design competence. If we can suppose that the designers of a superintelligent agent can successfully engineer the goal system of the agent so that it stably pursues a particular goal set by the programmers, then one prediction we can make is that the agent will pursue that goal. The more intelligent the agent is, the greater the cognitive resourcefulness it will have to pursue that goal. So even before an agent has been created we might be able to predict something about its behavior, if we know something about who will build it and what goals they will want it to have. (2) Predictability through inheritance. If a digital intelligence is created directly from a human template (as would be the case in a high-fidelity whole brain emulation), then the digital intelligence might inherit the motivations of the human template.  5  The agent might retain some of these motivations even if its cognitive capacities are subsequently enhanced to make it superintelligent. This kind of inference requires caution. The agent's goals and values could easily become corrupted in the uploading process or during its subsequent operation and enhancement, depending on how the procedure is implemented. (3) Predictability through convergent instrumental reasons. Even without detailed knowledge of an agent's final goals, we may be able to infer something about its more immediate objectives by considering the instrumental reasons that would arise for any of a wide range of possible final goals in a wide range of situations. This way of predicting becomes more useful the greater the intelligence of the agent, because a more intelligent agent is more likely to recognize the true instrumental reasons for its actions, and so act in ways that make it more likely to achieve its goals. The next section explores this third way of predictability and develops an \"instrumental convergence thesis\" which complements the orthogonality thesis. \n Instrumental convergence According to the orthogonality thesis, artificial intelligent agents may have an enormous range of possible final goals. Nevertheless, according to what we may term the \"instrumental convergence\" thesis, there are some instrumental goals likely to be pursued by almost any intelligent agent, because there are some objectives that are useful intermediaries to the achievement of almost any final goal. We can formulate this thesis as follows: The Instrumental Convergence Thesis Several instrumental values can be identified which are convergent in the sense that their attainment would increase the chances of the agent's goal being realized for a wide range of final goals and a wide range of situations, implying that these instrumental values are likely to be pursued by many intelligent agents. In the following we will consider several categories where such convergent instrumental values may be found.  6  The likelihood that an agent will recognize the instrumental values it confronts increases (ceteris paribus) with the agent's intelligence. We will therefore focus mainly on the case of a hypothetical superintelligent agent whose instrumental reasoning capacities far  6  Stephen Omohundro has written two pioneering papers on this topic  (Omohundro 2008a (Omohundro , 2008b . Omohundro argues that all advanced AI systems are likely to exhibit a number of \"basic drives\", by which he means \"tendencies which will be present unless explicitly counteracted.\" The term \"AI drive\" has the advantage of being short and evocative, but it has the disadvantage of suggesting that the instrumental goals to which it refers influence the AI's decision-making in the same way as psychological drives influence human decision-making, i.e. via a kind of phenomenological tug on our ego which our willpower may occasionally succeed in resisting. That connotation is unhelpful. One would not normally say that a typical human being has a \"drive\" to fill out their tax return, even though filing taxes may be a fairly convergent instrumental goal for humans in contemporary societies (a goal whose realization averts trouble that would prevent us from realizing many of our final goals). Our treatment here also differs from that of Omohundro in some other more substantial ways, although the underlying idea is the same. (See also  Chalmers (2010)  and  Omohundro (2012) . exceed those of any human. We will also comment on how the instrumental convergence thesis applies to the case of human beings, as this gives us occasion to elaborate some essential qualifications concerning how the instrumental convergence thesis should be interpreted and applied. Where there are convergent instrumental values, we may be able to predict some aspects of a superintelligence's behavior even if we know virtually nothing about that superintelligence's final goals. \n Self-preservation Suppose that an agent has some final goal that extends some way into the future. There are many scenarios in which the agent, if it is still around in the future, is then able to perform actions that increase the probability of achieving the goal. This creates an instrumental reason for the agent to try to be around in the future-to help achieve its present future-oriented goal. Agents with human-like motivational structures often seem to place some final value on their own survival. This is not a necessary feature of artificial agents: some may be designed to place no final value whatever on their own survival. Nevertheless, even agents that do not care intrinsically about their own survival would, under a fairly wide range of conditions, care instrumentally to some degree about their own survival in order to accomplish the final goals they do value. \n Goal-content integrity An agent is more likely to act in the future to maximize the realization of its present final goals if it still has those goals in the future. This gives the agent a present instrumental reason to prevent alterations of its final goals. (This argument applies only to final goals. In order to attain its final goals, an intelligent agent will of course routinely want to change its subgoals in light of new information and insight.) Goal-content integrity for final goals is in a sense even more fundamental than survival as a convergent instrumental motivation. Among humans, the opposite may seem to be the case, but that is because survival is usually part of our final goals. For software agents, which can easily switch bodies or create exact duplicates of themselves, preservation of self as a particular implementation or a particular physical object need not be an important instrumental value. Advanced software agents might also be able to swap memories, download skills, and radically modify their cognitive architecture and personalities. A population of such agents might operate more like a \"functional soup\" than a society composed of distinct semi-permanent persons.  7  For some purposes, processes in such a system might be better individuated as teleological threads, based on their final values, rather than on the basis of bodies, personalities, memories, or abilities. In such scenarios, goal-continuity might be said to constitute a key aspect of survival. Even so, there are situations in which an agent may intentionally change its own final goals. Such situations can arise when any of the following factors is significant:  Social signaling. When others can perceive an agent's goals and use that information to infer instrumentally relevant dispositions or other correlated attributes, it can be in the agent's interest to modify its goals to make whatever desired impression. For example, an agent might miss out on beneficial deals if potential partners cannot trust it to fulfill its side of the bargain. In order to make credible commitments, an agent might therefore wish to adopt as a final goal the honoring of its earlier commitments, and to allow others to verify that it has indeed adopted this goal. Agents that could flexibly and transparently modify their own goals could use this ability to enforce deals among one another. 8  Social preferences. Others may also have preferences about an agent's goals. The agent could then have reason to modify its goals, either to satisfy or to frustrate those preferences.  Preferences concerning own goal content. An agent might have some final goal concerned with the agent's own goal content. For example, the agent might have a final goal to become the type of agent that is motivated by certain values, such as compassion.  Storage costs. If the cost of storing or processing some part of an agent's utility function is large compared to the chance that a situation will arise in which applying that part of the utility function will make a difference, then the agent has an instrumental reason to simplify its goal content, and it may trash that part of the utility function. 9 10 We humans often seem happy to let our final goals and values drift. This might often be because we do not know precisely what they are. We obviously want our beliefs about our final goals and values to be able to change in light of continuing self-discovery or changing selfpresentation needs. However, there are cases in which we willingly change the goals and values themselves, not just our beliefs or interpretations of them. For example, somebody deciding to have a child might predict that they will come to value the child for its own sake, even though at the time of the decision they may not particularly value their future child or even like children in general. Humans are complicated, and many factors might be at play in a situation like this. 11 For instance, one might have a final value that involves becoming the kind of person who cares about some other individual for his or her own sake (here one places a final value on having a certain final value). Alternatively, one might have a final value that involves having certain experiences and occupying a certain social role; and becoming a parent-and undergoing an associated goal shift-might be a necessary part of that. Human goals can also have inconsistent content, goal content; and so some people might want to modify some of their final goals to reduce the inconsistencies. \n Cognitive enhancement Improvements in rationality and intelligence will tend to improve an agent's decision-making, making the agent more likely to achieve her final goals. One would therefore expect cognitive enhancement to emerge as an instrumental goal for many types of intelligent agent. For similar reasons, agents will tend to instrumentally value many kinds of information. 12 Not all kinds of rationality, intelligence, and knowledge need be instrumentally useful in the attainment of an agent's final goals. \"Dutch book arguments\" can be used to show that an agent whose credence function does not obey the rules of probability theory is susceptible to \"money pump\" procedures, in which a savvy bookie arranges a set of bets, each of which appears favorable according to the agent's beliefs, but which in combination are guaranteed to result in a loss to the agent, and a corresponding gain for the bookie. However, this fact fails to provide any strong general instrumental reasons to seek to iron out all probabilistic incoherency. Agents who do not expect to encounter savvy bookies, or who adopt a general policy against betting, do not stand to lose much from having some incoherent beliefs-and they may gain important benefits of the types mentioned: reduced cognitive effort, social signaling, etc. There is no general reason to expect an agent to seek instrumentally useless forms of cognitive enhancement, as an agent might not value knowledge and understanding for their own sakes. Which cognitive abilities are instrumentally useful depends both on the agent's final goals and its situation. An agent that has access to reliable expert advice may have little need for its own intelligence and knowledge, and it may therefore be indifferent to these resources. If intelligence and knowledge come at a cost, such as time and effort expended in acquisition, or in increased storage or processing requirements, then an agent might prefer less knowledge and  11  An extensive psychological literature explores adaptive preference formation. See, e.g.,  Forgas et al. (2009) .  12  In formal models, the value of information is quantified as the difference between the expected value realized by optimal decisions made with that information and the expected value realized by optimal decisions made without it. (See, e.g.,  Russell & Norvig 2010.)  It follows that the value of information is never negative. It also follows that any information you know will never affect any decision you will ever make has zero value for you. However, this kind of model assumes several idealizations which are often invalid in the real world-such as that knowledge has no final value (meaning that knowledge has only instrumental value and is not valuable for its own sake), and that agents are not transparent to other agents. less intelligence.  13  The same can hold if the agent has final goals that involve being ignorant of certain facts: likewise if an agent faces incentives arising from strategic commitments, signaling, or social preferences, as noted above.  14  Each of these countervailing reasons often comes into play for human beings. Much information is irrelevant to our goals; we can often rely on others' skill and expertise; acquiring knowledge takes time and effort; we might intrinsically value certain kinds of ignorance; and we operate in an environment in which the ability to make strategic commitments, socially signal, and satisfy other people's direct preferences over our own epistemic states, is often important to us than simple cognitive gains. There are special situations in which cognitive enhancement may result in an enormous increase in an agent's ability to achieve its final goals-in particular, if the agent's final goals are fairly unbounded and the agent is in a position to become the first superintelligence and thereby potentially obtain a decisive advantage enabling the agent to shape the future of Earthoriginating life and accessible cosmic resources according to its preferences. At least in this special case, a rational intelligent agent would place a very high instrumental value on cognitive enhancement. \n Technological perfection An agent may often have instrumental reasons to seek better technology, which at its simplest means seeking more efficient ways of transforming some given set of inputs into valued outputs. Thus, a software agent might place an instrumental value on more efficient algorithms that enable its mental functions to run faster on given hardware. Similarly, agents whose goals require some form of physical construction might instrumentally value improved engineering technology which enables them to create a wider range of structures more quickly and reliably, using fewer or cheaper materials and less energy. Of course, there is a tradeoff: the potential benefits of better technology must be weighed against its costs, including not only the cost of obtaining the technology but also the costs of learning how to use it, integrating it with other technologies already in use, and so forth. Proponents of some new technology, confident in its superiority to existing alternatives, are often dismayed when other people do not share their enthusiasm, but peoples' resistance to novel and nominally superior technology need not be based on ignorance or irrationality. A technology's valence or normative character depends not only on the context in which it is deployed, but also the vantage point from which its impacts are evaluated: what is a boon from one person's perspective can be a liability from another's. Thus, although mechanized looms increased the economic efficiency of textile production, the Luddite handloom weavers who anticipated that the innovation would render their artisan skills obsolete may have had good instrumental reasons to oppose it. The point here is that if \"technological perfection\" is to name a widely convergent instrumental goal for intelligent agents, then the term must be understood in a special sense-technology must be construed as embedded in a particular social context, and its costs and benefits must be evaluated with reference to some specified agents' final values. It seems that a superintelligent singleton-a superintelligent agent that faces no significant intelligent rivals or opposition, and is thus in a position to determine global policy unilaterally-would have instrumental reason to perfect the technologies that would make it better able to shape the world according to its preferred designs.  15  This would probably include space colonization technology, such as von Neumann probes-automatic, self-mending and selfreplicating spaceships that can extend its reach beyond the Solar System. Molecular nanotechnology, or some alternative still more capable physical manufacturing technology, also seems potentially very useful in the service of an extremely wide range of final goals. 16 \n Resource acquisition Finally, resource acquisition is another common emergent instrumental goal, for much the same reasons as technological perfection: both technology and resources facilitate physical construction projects. Human beings tend to seek to acquire resources sufficient to meet their basic biological needs. But people usually seek to acquire resources far beyond this minimum level. In doing so, they may be partially driven by lesser physical desiderata, such as increased comfort and convenience. A great deal of resource accumulation is motivated by social concerns-gaining status, mates, friends and influence, through wealth accumulation and conspicuous consumption. Perhaps less commonly, some people seek additional resources to achieve altruistic or expensive non-social aims.  15  Cf.  Bostrom (2006) .  16  One could reverse the question and look instead at possible reasons for a superintelligent singleton not to develop some technological capabilities. These include: (a) The singleton foreseeing that it will have no use of some technological capability; (b) The development cost being too large relative to its anticipated utility. This would be the case if, for instance, the technology will never be suitable for achieving any of the singleton's ends, or if the singleton has a very high discount rate that strongly discourages investment; (c) The singleton having some final value that requires abstention from particular avenues of technology development; (d) If the singleton is not certain it will remain stable, it might prefer to refrain from developing technologies that could threaten its internal stability or that would make the consequences of dissolution worse (e.g., a world government may not wish to develop technologies that would facilitate rebellion, even if they had some good uses, nor develop technologies for the easy production of weapons of mass destruction which could wreak havoc if the world government were to dissolve); (e) Similarly, the singleton might have made some kind of binding strategic commitment not to develop some technology, a commitment that remains operative even if it would now be convenient to develop it. (Note, however, that some current reasons for technology-development would not apply to a singleton: e.g., reasons arising from unwanted arms races.) superintelligence not facing a competitive social world would see no instrumental reason to accumulate resources beyond some modest level, for instance whatever computational resources needed to run its mind along with some virtual reality. Yet such a supposition would be entirely unwarranted. First, the value of resources depends on the uses to which they can be put, which in turn depends on the available technology. With mature technology, basic resources such as time, space, and matter, and other forms of free energy, could be processed to serve almost any goal. For instance, such basic resources could be converted into life. Increased computational resources could be used to run the superintelligence at a greater speed and for a longer duration, or to create additional physical or simulated (virtual) lives and civilizations. Extra physical resources could also be used to create backup systems or perimeter defenses, enhancing security. Such projects could easily consume far more than one planet's worth of resources. Furthermore, the cost of acquiring additional extraterrestrial resources will decline radically as the technology matures. Once von Neumann probes can be built, a large portion of the observable universe (assuming it is uninhabited by intelligent life) could be gradually colonized-for the one-off cost of building and launching a single successful self-reproducing probe. This low cost of celestial resource acquisition would mean that such expansion could be worthwhile even if the value of the additional resources gained were somewhat marginal. For example, even if a superintelligence cared non-instrumentally only about what happens within some particular small volume of space, such as the space occupied by its original home planet, it would still have instrumental reasons to harvest the resources of the cosmos beyond. It could use those surplus resources to build computers to calculate more optimal ways of using resources within the small spatial region of primary concern. It could also use the extra resources to build ever-more robust defenses to safeguard the privileged real estate. Since the cost of acquiring additional resources would keep declining, this process of optimizing and increasing safeguards might well continue indefinitely even if it were subject to steeply declining returns.  17 18 17  Suppose that an agent discounts resources obtained in the future at an exponential rate, and that because of the light speed limitation the agent can only increase its resource endowment at a polynomial rate. Would this mean that there will be some time after which the agent would not find it worthwhile to continue acquisitive expansion? No, because although the present value of the resources obtained at future times would asymptote to zero the further into the future we look, so would the present cost of obtaining them. The present cost of sending out one more von Neumann probe a 100 million years from now (possibly using some resource acquired some short time earlier) would be diminished by the same discount factor that would diminish the present value of the future resources the extra probe would acquire (modulo a constant factor).  18  Even an agent that has an apparently very limited final goal, such as \"to make 32 paperclips\", could pursue unlimited resource acquisition if there were no relevant cost to the agent of doing so. For example, even after an expected-utility-maximizing agent had built 32 paperclips, it could use some extra resources to verify that it had indeed successfully built 32 paperclips meeting all the specifications (and, if necessary, to take corrective action). After it had done so, it could run another batch of tests to make doubly sure that no mistake had been made. And then it could run another test, and another. The benefits of subsequent tests would be subject to steeply diminishing returns; however, so long as there were no alternative action Thus, there is an extremely wide range of possible final goals a superintelligent singleton could have that would generate the instrumental goal of unlimited resource acquisition. The likely manifestation of this would be the superintelligence's initiation of a colonization process that would expand in all directions using von Neumann probes. This would roughly result in a sphere of expanding infrastructure centered on the originating planet and growing in radius at some fraction of the speed of light; and the colonization of the universe would continue in this manner until the accelerating speed of cosmic expansion (a consequence of the positive cosmological constant) makes further material acquisition physically impossible as remoter regions drift permanently out of reach.  19  By contrast, agents lacking the technology required for inexpensive resource acquisition, or for the conversion of generic physical resources into useful infrastructure, may often find it not cost-effective to invest any present resources in increasing their material endowment. The same may hold for agents operating in competition with other agents of similar powers. For instance, if competing agents have already secured accessible cosmic resources, a late-starting agent may have no colonization opportunities. The convergent instrumental reasons for superintelligences uncertain of the non-existence of other powerful superintelligent agents are complicated by strategic considerations in ways that we do not currently fully comprehend but which may constitute important qualifications to the examples of convergent instrumental reasons we have looked at here.  20  It should be emphasized that the existence of convergent instrumental reasons, even if they apply to and are recognized by a particular agent, does not imply that the agent's behavior is easily predictable. An agent might well think of ways of pursuing the relevant instrumental values that do not readily occur to us. This is especially true for a superintelligence, which could devise extremely clever but counterintuitive plans to realize its goals, possibly even exploiting as-yet undiscovered physical phenomena. What is predictable is that the convergent with a higher expected utility, the agent would keep testing and re-testing (and keep acquiring more resources to enable these tests).  19  While the volume reached by colonization probes at a given time might be roughly spherical and expanding with a rate proportional to the square of time elapsed since the first probe was launched (~t 2 ), the amount of resources contained within this volume will follow a less regular growth pattern, since the distribution of resources is inhomogeneous and varies over several scales. Initially, the growth rate might be ~t2 as the home planet is colonized; then the growth rate might become spiky as nearby planets and solar systems are colonized; then, as the roughly disc-shaped volume of the Milky Way gets filled out, the growth rate might even out, to be approximately proportional to t; then the growth rate might again become spiky as nearby galaxies are colonized; then the growth rate might again approximate ~t2 as expansion proceeds on a scale over which the distribution of galaxies is roughly homogeneous; then another period of spiky growth followed by smooth ~t2 growth as galactic superclusters are colonized; until ultimately the growth rate starts a final decline, eventually reaching zero as the expansion speed of the universe accelerates to such an extent as to make further colonization impossible.  20  The simulation argument may be of particular importance in this context. A superintelligent agent may assign a significant probability to hypotheses according to which it lives in a computer simulation and its percept sequence is generated by another superintelligence, and this might various generate convergent instrumental reasons depending on the agent's guesses about what types of simulations it is most likely to be in. Cf.  Bostrom (2003) . instrumental values would be pursued and used to realize the agent's final goals, not the specific actions that the agent would take to achieve this. \n Conclusions The orthogonality thesis suggests that we cannot blithely assume that a superintelligence will necessarily share any of the final values stereotypically associated with wisdom and intellectual development in humans-scientific curiosity, benevolent concern for others, spiritual enlightenment and contemplation, renunciation of material acquisitiveness, a taste for refined culture or for the simple pleasures in life, humility and selflessness, and so forth. It might be possible through deliberate effort to construct a superintelligence that values such things, or to build one that values human welfare, moral goodness, or any other complex purpose that its designers might want it to serve. But it is no less possible-and probably technically easier-to build a superintelligence that places final value on nothing but calculating the decimals of pi. The instrumental convergence thesis suggests that we cannot blithely assume that a superintelligence with the final goal of calculating the decimals of pi (or making paperclips, or counting grains of sand) would limit its activities in such a way as to not materially infringe on human interests. An agent with such a final goal would have a convergent instrumental reason, in many situations, to acquire an unlimited amount of physical resources and, if possible, to eliminate potential threats to itself and its goal system.  21  It might be possible to set up a situation in which the optimal way for the agent to pursue these instrumental values (and thereby its final goals) is by promoting human welfare, acting morally, or serving some beneficial purpose as intended by its creators. However, if and when such an agent finds itself in a different situation, one in which it expects a greater number of decimals of pi to be calculated if it destroys the human species than if it continues to act cooperatively, its behavior would instantly take a sinister turn. This indicates a danger in relying on instrumental values as a guarantor of safe conduct in future artificial agents that are intended to become superintelligent and that might be able to leverage their superintelligence into extreme levels power and influence.  22   \t\t\t This is of course not to deny that differences that appear small visually can be functionally profound. \n\t\t\t For some recent attempts to defend the Humean theory of motivation, see Smith (1987) , Lewis (1988), and Sinhababu (2009) . \n\t\t\t See also Parfit (2011) . \n\t\t\t The orthogonality thesis implies that most any combination of final goal and intelligence level is logically possible; it does not imply that it would be practically easy to endow a superintelligent agent with some arbitrary or human-respecting final goal-even if we knew how to construct the intelligence part. For some preliminary notes on the value-loading problem, see, e.g., Dewey (2011)  and Yudkowsky (2011).5 See Sandberg & Bostrom (2008) . \n\t\t\t  See Chislenko (1997). \n\t\t\t See also Shulman (2010) .9  An agent might also change its goal representation if it changes its ontology, in order to transpose its old representation into the new ontology. Cf. de Blanc (2011).10 Another type of factor that might make an evidential decision theorist undertake various actions, including changing its final goals, is the evidential import of deciding to do so. For example, an agent that follows evidential decision theory might believe that there exist other agents like it in the universe, and that its own actions will provide some evidence about how those other agents will act. The agent might therefore choose to adopt a final goal that is altruistic towards those other evidentially-linked agents, on grounds that this will give the agent evidence that those other agents will have chosen to act in like manner. An equivalent outcome might be obtained, however, without changing one's final goals, by choosing in each instant to act as if one had those final goals. \n\t\t\t This strategy is exemplified by the sea squirt larva, which swims about until it finds a suitable rock, to which it then permanently affixes itself. Cemented in place, the larva has less need for complex information processing, whence it proceeds to digest part of its own brain (its cerebral ganglion). Academics can sometimes observe a similar phenomenon in colleagues who are granted tenure.14  Cf. Bostrom (2012) .", "date_published": "n/a", "url": "n/a", "filename": "superintelligentwill.tei.xml", "abstract": "This paper discusses the relation between intelligence and motivation in artificial agents, developing and briefly arguing for two theses. The first, the orthogonality thesis, holds (with some caveats) that intelligence and final goals (purposes) are orthogonal axes along which possible artificial intellects can freely vary-more or less any level of intelligence could be combined with more or less any final goal. The second, the instrumental convergence thesis, holds that as long as they possess a sufficient level of intelligence, agents having any of a wide range of final goals will pursue similar intermediary goals because they have instrumental reasons to do so. In combination, the two theses help us understand the possible range of behavior of superintelligent agents, and they point to some potential dangers in building such an agent.", "id": "97047d20c08bbb0d70df73617218e2a9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrea Bajcsy", "Dylan P Losey", "Marcia K O'malley", "Anca D Dragan"], "title": "Learning Robot Objectives from Physical Human Interaction", "text": "Introduction Imagine a robot performing a manipulation task next to a person, like moving the person's coffee mug from a cabinet to the table (Fig.  1 ). As the robot is moving, the person might notice that the robot is carrying the mug too high above the table. Knowing that the mug would break if it were to slip and fall from so far up, the person easily intervenes and starts pushing the robot's end-effector down to bring the mug closer to the table. In this work, we focus on how the robot should then respond to such physical human-robot interaction (pHRI). Several reactive control strategies have been developed to deal with pHRI  [1, 2, 3] . For instance, when a human applies a force on the robot, it can render a desired impedance or switch to gravity compensation and allow the human to easily move the robot around. In these strategies, the moment the human lets go of the robot, it resumes its original behavior-our robot from earlier would go back to carrying the mug too high, requiring the person to continue intervening until it finished the task (Fig.  1, left ). Although such control strategies guarantee fast reaction to unexpected forces, the robot's return to its original motion stems from a fundamental limitation of traditional pHRI strategies: they miss the fact that human interventions are often intentional and occur because the robot is doing something wrong. While the robot's original behavior may have been optimal with respect to the robot's pre-defined objective function, the fact that a human intervention was necessary implies that this objective function was not quite right. Our insight is that because pHRI is intentional, it is also informative-it provides observations about the correct robot objective function, and the robot can leverage these observations to learn that correct objective. Returning to our example, if the person is applying forces to push the robot's end-effector closer to the table, then the robot should change its objective function to reflect this preference, and complete the rest of the current task accordingly, keeping the mug lower (Fig.  1 , right). Ultimately, human interactions should not be thought of as disturbances, which perturb the robot from its desired behavior, but rather as corrections, which teach the robot its desired behavior. In this paper, we make the following contributions: Formalism. We formalize reacting to pHRI as the problem of acting in a dynamical system to optimize an objective function, with two caveats: 1) the objective function has unknown parameters θ θ θ Figure  1 : A person interacts with a robot that treats interactions as disturbances (left), and a robot that learns from interactions (right). When humans are treated as disturbances, force plots reveal that people have to continuously interact since the robot returns to its original, incorrect trajectory. In contrast, a robot that learns from interactions requires minimal human feedback to understand how to behave (i.e., go closer to the table). θ, and 2) human interventions serve as observations about these unknown parameters: we model human behavior as approximately optimal with respect to the true objective. As stated, this problem is an instance of a Partially Observable Markov Decision Process (POMDP). Although we cannot solve it in real-time using POMDP solvers, this formalism is crucial to converting the problem of reacting to pHRI into a clearly defined optimization problem. In addition, our formalism enables pHRI approaches to be justified and compared in terms of this optimization criterion. Online Solution. We introduce a solution that adapts learning from demonstration approaches to our online pHRI setting  [4, 5] , but derive it as an approximate solution to the problem above. This enables the robot to adapt to pHRI in real-time, as the current task is unfolding. Key to this approximation is simplifying the observation model: rather than interpreting instantaneous forces as noisy-optimal with respect to the value function given θ, we interpret them as implicitly inducing a noisy-optimal desired trajectory. Reasoning in trajectory space enables an efficient approximate online gradient approach to estimating θ. User Study. We conduct a user study with the JACO2 7-DoF robotic arm to assess how online learning from physical interactions during a task affects the robot's objective performance, as well as subjective participant perceptions. Overall, our work is a first step towards learning robot objectives online from pHRI. \n Related Work We propose using pHRI to correct the robot's objective function while the robot is performing its current task. Prior research has focused on (a) control strategies for reacting to pHRI without updating the robot's objective function, or (b) learning the robot's objectives-from offline demonstrationsin a manner that generalizes to future tasks, but does not change the behavior during the current task. An exception is shared autonomy work, which does correct the robot's objective function online, but only when the objective is parameterized by the human's desired goal in free-space. Control Strategies for Online Reactions to pHRI. A variety of control strategies have been developed to ensure safe and responsive pHRI. They largely fall into three categories  [6] : impedance control, collision handling, and shared manipulation control. Impedance control  [1]  relates deviations from the robot's planned trajectory to interaction torques. The robot renders a virtual stiffness, damping, and/or inertia, allowing the person to push the robot away from its desired trajectory, but the robot always returns to its original trajectory after the interaction ends. Collision handling methods  [2]  include stopping, switching to gravity compensation, or re-timing the planned trajectory if a collision is detected. Finally, shared manipulation  [3]  refers to role allocation in situations where the human and the robot are collaborating. These control strategies for pHRI work in real-time, and enable the robot to safely adapt to the human's actions; however, the robot fails to leverage these interventions to update its understanding of the task-left alone, the robot would continue to perform the task in the same way as it had planned before any human interactions. By contrast, we focus on enabling robots to adjust how they perform the current task in real time. Offline Learning of Robot Objective Functions. Inverse Reinforcement Learning (IRL) methods focus explicitly on inferring an unknown objective function, but do it offline, after passively observing expert trajectory demonstrations  [7] . These approaches can handle noisy demonstrations  [8] , which become observations about the true objective  [9] , and can acquire demonstrations through physical kinesthetic teaching  [10] . Most related to our work are approaches which learn from corrections of the robot's trajectory, rather than from demonstrations  [4, 5, 11] . Our work, however, has a different goal: while these approaches focus on the robot doing better the next time it performs the task, we focus on the robot completing its current task correctly. Our solution is analogous to online Maximum Margin Planning  [4]  and co-active learning  [5]  for this new setting, but one of our contributions is to derive their update rule as an approximation to our pHRI problem. Online Learning of Human Goals. While IRL can learn the robot's objective function after one or more demonstrations of a task, online inference is possible when the objective is simply to reach a goal state, and the robot moves through free space  [12, 13, 14] . We build on this work by considering general objective parameters; this requires a more complex (non-analytic and difficult to compute) observation model, along with additional approximations to achieve online performance. 3 Learning Robot Objectives Online from pHRI \n Formalizing Reacting to pHRI We consider settings where a robot is performing a day-to-day task next to a person, but is not doing it correctly (e.g., is about to spill a glass of water), or not doing it in a way that matches the person's preferences (e.g., is getting too close to the person). Whenever the person physically intervenes and corrects the robot's motion, the robot should react accordingly; however, there are many strategies the robot could use to react. Here, we formalize the problem as a dynamical system with a true objective function that is known by the person but not known by the robot. This formulation interprets the human's physical forces as intentional, and implicitly defines an optimal strategy for reacting. Notation. Let x denote the robot's state (its position and velocity) and u R the robot's action (the torque it applies at its joints). The human physically interacts with the robot by applying external torque u H . The robot transitions to a next state defined by its dynamics, ẋ = f (x, u R + u H ), where both the human and robot can influence the robot's motion. POMDP Formulation. The robot optimizes a reward function r(x, u R , u H ; θ), which trades off between correctly completing the task and minimizing human effort r(x, u R , u H ; θ) = θ T φ(x, u R , u H ) − λ||u H || 2 (1) Following prior IRL work  [15, 4, 8] , we parameterize the task-related part of this reward function as a linear combination of features φ with weights θ. Note that we assume the relevant set of features for each task are given, and we will not explore feature selection within this work. Here θ encapsulates the true objective, such as moving the glass slowly, or keeping the robot's endeffector farther away from the person. Importantly, this parameter is not known by the robot-robots will not always know the right way to perform a task, and certainly not the human-preferred way. If the robot knew θ, this would simply become an MDP formulation, where the states are x, the actions are u R , the reward is r, and the person would never need to intervene. Uncertainty over θ, however, turns this into a POMDP formulation, where θ is a hidden part of the state. Importantly, the human's actions are observations about θ under some observation model P (u H |x, u R ; θ). These observations u H are atypical in two ways: (a) they affect the robot's reward, as in  [13] , and (b) they influence the robot's state, but we don't necessarily want to account for that when planning -the robot should not rely on the human to move the robot; rather the robot should consider u H only for its information value. Observation Model. We model the human's interventions as corrections which approximately maximize the robot's reward. More specifically, we assume the noisy-rational human selects an action u H that, when combined with the robot's action u R , leads to a high Q-value (state-action value) assuming the robot will behave optimally after the current step (i.e., assuming the robot knows θ) P (u H | x, u R ; θ) ∝ e Q(x,u R +u H ;θ) (2) Our choice of (2) stems from maximum entropy assumptions  [8] , as well as the Bolzmann distributions used in cognitive science models of human behavior  [16] . Aside. We are not formulating this as a POMDP to solve it using standard POMDP solvers. Instead, our goal is to clarify the underlying problem formulation and the existence of an optimal strategy. \n Approximate Solution Since POMDPs cannot be solved tractably for high-dimensional real-world problems, we make several approximations to arrive at an online solution. We first separate estimation from finding the optimal policy, and approximate the policy by separating planning from control. We then simplify the estimation model, and use maximum a posteriori estimate (MAP) instead the full belief over θ. QMDP. Similar to  [13] , we approximate our POMDP using a QMDP by assuming the robot will obtain full observability at the next time step  [17] . Let b denote the robot's current belief over θ. The QMDP simplifies into two subproblems: (a) finding the robot's optimal policy given b Q(x, u R , b) = b(θ)Q(x, u R , θ)dθ (3) where arg max u R Q(x, u R , b) evaluated at every state yields the optimal policy, and (b) updating our belief over θ given a new observation. Unlike the actual POMDP solution, here the robot will not try to gather information. From Belief to Estimator. Rather than planning with the belief b, we plan with only the MAP of θ. From Policies to Trajectories (Action). Computing Q in continuous state, action, and belief spaces is still not tractable. We thus separate planning and control. At every time step t, we do two things. First, given our current θt , we replan a trajectory ξ = x 0:T ∈ Ξ that optimizes the task-related reward. Let θ T Φ(ξ) be the cumulative reward, where Φ(ξ) is the total feature count along trajectory ξ such that Φ(ξ) = x t ∈ξ φ(x t ). We use a trajectory optimizer  [18]  to replan the robot's desired trajectory ξ t R ξ t R = arg max ξ θt • Φ(ξ) (4) Second, once ξ t R has been planned, we control the robot to track this desired trajectory. We use impedance control, which allows people to change the robot's state by exerting torques, and provides compliance for human safety  [19, 6, 1] . After feedback linearization  [20] , the equation of motion under impedance control becomes M R (q t − qt R ) + B R ( qt − qt R ) + K R (q t − q t R ) = u t H (5) Here M R , B R , and K R are the desired inertia, damping, and stiffness, x = (q, q), where q is the robot's joint position, and q R ∈ ξ R denotes the desired joint position. Within our experiments, we implemented a simplified impedance controller without feedback linearization u t R = B R ( qt R − qt ) + K R (q t − q t R ) (6) Aside. When the robot is not updating its estimate θ, then ξ t R = ξ t−1 R , and our solution reduces to using impedance control to track an unchanging trajectory  [2, 19] . From Policies to Trajectories (Estimation). We still need to address the second QMDP subproblem: updating θ after each new observation. Unfortunately, evaluating the observation model (2) for any given θ is difficult, because it requires computing the Q-value function for that θ. Hence, we will again leverage a simplification from policies to trajectories in order to update our MAP of θ. Instead of attempting to directly relate u H to θ, we propose an intermediate step; we interpret each human action u H via a intended trajectory, ξ H , that the human wants the robot to execute. To compute the intended trajectory ξ H from ξ R and u H , we propagate the deformation caused by u H along the robot's current trajectory ξ R ξ H = ξ R + µA −1 U H ( 7 ) where µ > 0 scales the magnitude of the deformation, A defines a norm on the Hilbert space of trajectories and dictates the deformation shape  [21] , U H = u H at the current time, and U H = 0 at all other times. During experiments we here used a norm A based on acceleration  [21] , but we will explore learning the choice of this norm in future work. Importantly, our simplification from observing human action u H to implicitly observing the human's intended trajectory ξ H means we no longer have to evaluate the Q-value of u R + u H given some θ value. Instead, the observation model now depends on the total reward of the implicitly observed trajectory: P (ξ H | ξ R , θ) ∝ e θ T Φ(ξ H )−λ||u H || 2 ≈ e θ T Φ(ξ H )−λ||ξ H −ξ R || 2 (8 ) This is analogous to  (2) , but in trajectory space-a distribution over implied trajectories, given θ and the current robot trajectory.   \n Online Update of the θ Estimate The probability distribution over θ at time step t is P (ξ 0 H , .., ξ t H |θ, ξ 0 R , .., ξ t R )P (θ). However, since θ is continuous, and the observation model is not Gaussian, we opt not to track the full belief, but rather to track the maximum a posteriori estimate (MAP). Our update rule for this estimate will reduce to online Maximum Margin Planning  [4]  if we treat ξ H as the demonstration, and to coadaptive learning  [5] , if we treat ξ H as the original trajectory with one waypoint corrected. One of our contributions, however, is to derive this update rule from our MaxEnt observation model in  (8) . MAP. Assuming the observations are conditionally independent given θ, the MAP for time t + 1 is θt+1 = arg max θ P (ξ 0 H , .., ξ t H | ξ 0 R , .., ξ t R , θ)P (θ) = arg max θ t τ =0 log P (ξ τ H | ξ τ R , θ) + log P (θ) (9) Inspecting the right side of (9), we need to define both P (ξ H |ξ R , θ) and the prior P (θ). To approximate P (ξ H |ξ R , θ), we use (8) with Laplace's method to compute the normalizer. Taking a second-order Taylor series expansion of the objective function about ξ R , the robot's current best guess at the optimal trajectory, we obtain a Gaussian integral that can be evaluated in closed form P (ξ H | ξ R , θ) = e θ T Φ(ξ H )−λ||ξ H −ξ R || 2 e θ T Φ(ξ)−λ||ξ−ξ R || 2 dξ ≈ e θ T Φ(ξ H )−Φ(ξ R ) −λ||ξ H −ξ R || 2 (10) Let θ0 be our initial estimate of θ. We propose the prior P (θ) = e − 1 2α ||θ− θ0 || 2 (11) where α is a positive constant. Substituting  (10)  and (  11 ) into (  9 ), the MAP reduces to θt+1 ≈ arg max θ t τ =0 θ T Φ(ξ τ H ) − Φ(ξ τ R ) − 1 2α ||θ − θ0 || 2 (12) Notice that the λ||ξ H −ξ R || 2 terms drop out, because this penalty for human effort does not explicitly depend on θ. Solving the optimization problem (  12 ) by taking the gradient with respect to θ, and then setting the result equal to zero, we finally arrive at θt+1 = θ0 + α t τ =0 Φ(ξ τ H ) − Φ(ξ τ R ) = θt + α Φ(ξ t H ) − Φ(ξ t R ) (13) Interpretation. This update rule is actually the online gradient  [22]  of (9) under our Laplace approximation of the observation model. It has an intuitive interpretation: it shifts the weights in the direction of the human's intended feature count. For example, if ξ H stays farther from the person than ξ R , the weights in θ associated with distance-to-person features will increase. Relation to Prior Work. This update rule is analogous to two related works. First, it would be the online version of Maximum Margin Planning (MMP)  [4]  if the trajectory ξ t H were a new demon- stration. Unlike MMP, our robot does not complete a trajectory, and only then get a full new demonstration; instead, our ξ t H is an estimate of the human's intended trajectory based on the force applied during the robot's execution of the current trajectory ξ t R . Second, the update rule would be co-active learning  [5]  if the trajectory ξ t H were ξ t R with one waypoint modified, as opposed to a propagation of u t H along the rest of ξ t R . Unlike co-active learning, however, our robot receives corrections continually, and continually updates the current trajectory in order to complete the current task well. Nonetheless, we are excited to see similar update rules emerge from different optimization criteria. Summary. We formalized reacting to pHRI as a POMDP with the correct objective parameters as a hidden state, and approximated the solution to enable online learning from physical interaction. At every time step during the task where the human interacts with the robot, we first propagate u H to implicitly observe the corrected trajectory ξ H (simplification of the observation model), and then update θ via Equation (  13 ) (MAP instead of belief). We replan with the new estimate (approximation of the optimal policy), and use impedance control to track the resulting trajectory (separation of planning from control). We summarize and visualize this process in Fig.  2 . \n User Study We conducted an IRB-approved user study to investigate the benefits of in-task learning. We designed tasks where the robot began with the wrong objective function, and participants phsyically corrected the robot's behavior 1 . \n Experiment Design Independent Variables. We manipulated the pHRI strategy with two levels: learning and impedance. The robot either used our method (Algorithm 1) to react to physical corrections and re-plan a new trajectory during the task; or used impedance control (our method without updating θ) to react to physical interactions and then return to the originally planned trajectory. Dependent Measures. We measured the robot's performance with respect to the true objective, along with several subjective measures. One challenge in designing our experiment was that each person might have a different internal objective for any given task, depending on their experience and preferences. Since we do not have direct access to every person's internal preferences, we defined the true objective ourselves, and conveyed the objectives to participants by demonstrating the desired optimal robot behavior (see an example in Fig.  3(a) , where the robot is supposed to keep the cup upright). We instructed participants to get the robot to achieve this desired behavior with minimal human physical intervention. For each robot attempt at a task, we evaluated the task related and effort related parts of the objective: θ T Φ(ξ) (a cost to be minimized and not a reward to be maximized in our experiment) and t ||u t H || 1 . We also evaluate the total amount of time spent interacting physically with the robot. For our subjective measures, we designed 4 multi-item scales shown in Table  1 : did participants think the robot understood how they wanted to task done, did they feel like they had to exert a lot of effort to correct the robot, was it easy to anticipate the robot's reactions, and how good of a collaborator was the robot. Hypotheses: H1. Learning significantly decreases interaction time, effort, and cumulative trajectory cost. H2. Participants will believe the robot understood their preferences, feel less interaction effort, and perceive the robot as more predictable and more collaborative in the learning condition. Tasks. We designed three household manipulation tasks for the robot to perform in a shared workspace (see Fig.  3 ), plus a familiarization task. As such, the robot's objective function considered two features: velocity and a task-specific feature. For each task, the robot carried a cup from a start to a goal pose with an initially incorrect objective, requiring participants to correct its behavior during the task. During the familiarization task, the robot's original trajectory moved too close to the human. Participants had to physically interact with the robot to get it to keep the cup further away from their body. In Task 1, the robot would not care about tilting the cup mid-task, risking spilling if the cup was too full. Participants had to get the robot to keep the cup upright. In Task 2, the robot would move the cup too high in the air, risking breaking it if it were to slip, and participants had to get the robot to keep it closer to the table. Finally, in Task 3, the robot would move the cup over a laptop to reach it's final goal pose, and participants had to get the robot to keep the cup away from the laptop. Participants. We used a within-subjects design and counterbalanced the order of the pHRI strategy conditions. In total, we recruited 10 participants (5 male, 5 female, aged 18-34) from the UC Berkeley community, all of whom had technical backgrounds. Procedure. For each pHRI strategy, participants performed the familiarization task, followed by the three tasks, and then filled out our survey. They attempted each task twice with each strategy for robustness, and we recorded the attempt number for our analysis. Since we artificially set the true objective for participants to measure objective performance, we showed participants both the original and desired robot trajectory before interaction (Fig.  3 ), so that they understood the objective. \n Results Objective. We conducted a factorial repeated measures ANOVA with strategy (impedance or learning) and trial number (first attempt or second attempt) as factors, on total participant effort, interaction time, and cumulative true cost 2 (see Figure  4  and Figure  5 ). Learning resulted in significantly less interaction force (F (1, 116) = 86.29, p < 0.0001) and interaction time (F (1, 116) = 75.52, p < 0.0001), and significantly better task cost (F (1, 116) = 21.85, p < 0.0001). Interestingly, while trial number did not significantly affect participant's performance with either method, attempting the task a second time yielded a marginal improvement for the impedance strategy, but not for the learning strategy. This may suggest that it is easier to get used to the impedance strategy. Overall, this supports H1, and aligns with the intuition that if humans are truly intentional actors, then using interaction forces as information about the robot's objective function enables robots to better complete their tasks with less human effort compared to traditional pHRI methods. Subjective. Table  1  shows the results of our participant survey. We tested the reliability of our 4 scales, and found the understanding, effort, and collaboration scales to be reliable, so we grouped them each into a combined score. We ran a one-way repeated measures ANOVA on each resulting score. We found that the robot using our method was perceived as significantly (p < 0.0001) more understanding, less difficult to interact with, and more collaborative. However, we found no significant difference between our method and the baseline impedance method in terms of predictability. Participant comments suggest that while the robot adapted quickly to their corrections when learning (e.g. \"The robot seemed to quickly figure out what I cared about and kept doing it on its own\"), determining what the robot was doing during learning was less apparent (e.g. \"If I pushed it hard enough sometimes it would seem to fall into another mode and then do things correctly\"). Therefore, H2 was partially supported: although our learning algorithm was not perceived as more predictable, participants believed that the robot understood their preferences more, took less effort to interact with, and was a more collaborative partner.  Cup Table Laptop Task \n Discussion Summary. We propose that robots should not treat human interaction forces as disturbances, but rather as informative actions. We show that this results in robots capable of in-task learningrobots that update their understanding of the task which they are performing and then complete it correctly, instead of relying on people to guide them until the task is done. We test this concept with participants who not only teach the robot to finish its task according to their preferences, but also subjectively appreciate the robot's learning. Limitations and Future Work. Ours is merely a step in exploring learning robot objectives from pHRI. We opted for an approximation closest to the existing literature, but other possible better online solutions are possible. In our user study, we assumed knowledge of the two relevant reward features. In reality, reward functions will have larger feature sets and human interactions may only give information about a certain subset of relevant weights. The robot will thus need to disambiguate what the person is trying to correct, likely requiring active information gathering. Further, developing solutions that can handle dynamical aspects, like preferences about the timing of the motion, would require a different approach to inferring the intended human trajectory, or going back the space of policies altogether. Finally, while we focused on in-task learning, the question of how and when to generalize learned objectives to new task instances remains open. Figure 2 : 2 Figure 2: Algorithm (left) and visualization (right) of one iteration of our online learning from pHRI method in an environment with two obstacles O1, O2. The originally planned trajectory, ξ t R (black dotted line), is deformed by the human's force into the human's preferred trajectory, ξ t H (solid black line). Given these two trajectories, we compute an online update of θ and can replan a better trajectory ξ t+1 R (orange dotted line). \n (a) Task 1 :Figure 3 : 13 Figure 3: Simulations depicting the robot trajectories for each of the three experimental tasks. The black path represents the original trajectory and the blue path represents the human's desired trajectory. \n Figure 4 : 4 Figure4: Learning from pHRI decreases human effort and interaction time across all experimental tasks (total trajectory time was 15s). An asterisk (*) means p < 0.0001. \n Figure 5 : 5 Figure 5: (left) Average cumulative cost for each task as compared to the desired total trajectory cost. An asterisk (*) means p < 0.0001. (right) Plot of sample participant data from laptop task: desired trajectory is in blue, trajectory with impedance condition is in gray, and learning condition trajectory is in orange. \n Table 1 : 1 QuestionsCronbach's α Imped LSM Learn LSM F(1,9) p-value understanding By the end, the robot understood how I wanted it to do the task. Even by the end, the robot still did not know how I wanted it to do the task.The robot learned from my corrections.The robot did not understand what I was trying to accomplish. The robot did not collaborate with me to complete the task. Results of ANOVA on subjective metrics collected from a 7-point Likert-scale survey. 0.94 1.70 5.10 118.56 <.0001 \n\t\t\t For video footage of the experiment, see: https://www.youtube.com/watch?v=1MkI6DH1mcw \n\t\t\t For simplicity, we only measured the value of the feature that needed to be modified in the task, and computed the absolute difference from the feature value of the optimal trajectory.", "date_published": "n/a", "url": "n/a", "filename": "bajcsy17a.tei.xml", "abstract": "When humans and robots work in close proximity, physical interaction is inevitable. Traditionally, robots treat physical interaction as a disturbance, and resume their original behavior after the interaction ends. In contrast, we argue that physical human interaction is informative: it is useful information about how the robot should be doing its task. We formalize learning from such interactions as a dynamical system in which the task objective has parameters that are part of the hidden state, and physical human interactions are observations about these parameters. We derive an online approximation of the robot's optimal policy in this system, and test it in a user study. The results suggest that learning from physical interaction leads to better robot task performance with less human effort.", "id": "0e372ca30f5f33b44d1257f603098530"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld"], "title": "Approval-directed agency and the decision theory of Newcomb-like problems", "text": "Introduction In decision theory, there is a large debate about how an instrumentally rational agent, i.e., an agent trying to achieve some goal or maximize some utility function, should decide in Newcomb's problem (introduced by  Nozick 1969 ) and variations thereof (a list is given by  Ledwig 2000, pp. 80-87) . Consequently, different normative theories of instrumental rationality have been developed. The best known ones are evidential (sometimes also called Bayesian) decision theory (EDT)  (Ahmed 2014; Almond 2010; Price 1986; Horgan 1981 ) and causal decision theory (CDT)  (Gibbard and Harper 1981; Joyce 1999; Lewis 1981; Skyrms 1982; Weirich 2016 ), but many have attempted to remediate what they view as failures of the two theories by proposing further alternatives  (Spohn 2003 (Spohn , 2012 Poellinger 2013; Arntzenius 2008; Gustafsson 2011; Wedgwood 2013; Dohrn 2015; Price 2012; Soares and Levinstein 2017) . Because the main goal of artificial intelligence is to build machines that make instrumentally rational decisions  (Russell and Norvig 2010, Sects. 1.1.4, 2.2; Legg and Hutter 2007; Doyle 1992) , this normative disagreement has some bearing on how to build these machines (cf. Soares and Fallenstein 2014a, Sect. 2.2;  Soares and Fallenstein 2014b, Sect. 1; Bostrom 2014b, Chap. 13, Sect. \"Decision theory\") . The differences between these decision theories are probably inconsequential in most situations  (Ahmed 2014, Sect. 0.5, Chap. 4; Briggs 2017 ), 1 but still matter in some  (Ahmed 2014, Chap. 4-6; Soares 2014a; Bostrom 2014a) . In fact, AI may expose the differences more often. For example, Newcomb's problem and the prisoner's dilemma with a replica  (Kuhn 2017, Sect. 7 ) are easy to implement for agents with copyable source code (cf.  Yudkowsky 2010 pp. 85ff .  Soares and Fallenstein 2014b, Sect. 2; Soares 2014b; Cavalcanti 2010; Sect. 5) . Indeed, the existence of many copies is the norm for (successful) software, including AI-based software. While copies of present-day software systems may only interact with each other in rigid, explicitly pre-programmed ways, future AI-based systems will make decisions in a more autonomous, flexible and goal-driven way. Overall, the decision theory of Newcomb-like scenarios is a central foundational issue which will plausibly become practically important in the longer term. The problem for AI research posed by the disagreement among decision theorists can be divided into two questions: 1. What decision theory do we want an AI to follow? 2. How could we implement such a decision theory in an AI? Or: How do decision theories and AI frameworks or architectures map onto each other? Although it certainly requires further discussion, there already is a large literature related to the first question. 2 In this paper, I would thus like to draw attention to the second question. Specifically, I would like to investigate how approval-directed agents behave in Newcomb-like problems. By an approval-directed agent, I mean an agent that is coupled with an overseer. After the agent has chosen an action, the overseer scores the agent for that action. Rather than, say, trying to bring about particular states in the environment, the agent chooses actions so as to maximize the score it receives from the overseer (cf.  Christiano 2014) . A model of approval-directed agency that allows us to describe Newcomb-like situations is described and discussed in Sect. 2. Approval-directed agency is intended as a model of reinforcement learning agents (see  Sutton and Barto 1998; Russell and Norvig 2010; Chaps. 17, 21 , for introductions to reinforcement learning), for whom the reward function is analogous to the approval-directed agent's overseer. Since reinforcement learning is such a general and commonly studied problem in artificial intelligence  (Hutter 2005, e.g. Chap. 4.1.3; Russell and Norvig 2010, p. 831; Sutton and Barto 1998, Chap. 1) , it is an especially attractive target for modeling. 3 However, because decision theories are usually defined only for single decisions, we will only discuss single decisions whereas reinforcement learning is usually concerned with sequential interactions of agent and environment. However, this decision can also be a policy choice to model sequential decision problems.  4  In addition to limiting our analysis to single decisions, we will not discuss the learning process and simply assume that the agent has already formed some model of the world. If we assume that, after an action has been taken, the overseer rewards the agent based on the expected value of some von Neumann-Morgenstern utility function, the agent is implicitly driven by two decision theories: The overseer can use the regular conditional expectation or the causal expectation to estimate the value of its utility function; and the agent itself can follow CDT or EDT when maximizing the score it receives from the overseer (Sect. 3). We then show how the overall decision theory depends on these two potentially conflicting decision theories. If the overseer bases its expected value calculations on looking only at the world, then the agent's decision theory is decisive. If the overseer Footnote 2 continued  (Meacham 2010; Soares and Fallenstein 2014b, Sect. 3; Yudkowsky 2010, Sect. 2; Greene 2018)  . The same arguments imply that even if one is convinced of CDT or EDT one would not want the AI to use CDT and EDT. That said, one could also leave the self-modification to the AI.  3  Reinforcement learning and approval-directed agency are also common outside of artificial intelligence. For example,  Achen and Bartels (2016, Chap. 4 ) review evidence which shows that electorates often vote retrospectively to punish or reward incumbents.  1  A causal model of an approval-directed agent in a Newcomb-like decision problem. A denotes the agent's action, H the environment history, O the observation on which the overseer bases the reward, R is that reward, and E r is information about the way the reward is computed that is only available to the overseer. The box is used to indicate that H includes the two random variables H p and H f . All of H may have a causal influence on O bases its estimates only on the agent's action, then the overseer's decision (or perhaps rather action evaluation) theory is decisive. \n A H p H f R O E r H Fig. \n Approval-directed agency We first describe a model of approval-directed agency. To be able to apply both CDT and EDT, we will use causal models in  Pearl's (2009)  sense. Consequently, we use Pearl's do-calculus-based version of CDT  (Pearl 2009, Chap. 4 ). We will, throughout this paper, assume that the agent has already formed a (potentially implicit) model of the world 5 -e.g., based on past interactions with the environment. Also, we will only consider single decisions rather than sequential problems of iterative interaction between agent and environment. A causal model of such a one-shot Newcomb problem from the perspective of the approval-directed agent is given in Fig.  1 . In this model, the agent decides to take some action A, which may causally affect some part of the environment history, i.e., the history of states, H . We will call that part of the history the agent's causal future H f . Furthermore, the agent may be causally influenced by some other part of the environment history, which we will call the agent's causal past H p . H may contain information other than H f and H p , which we will assume to be independent of A.  6  The overseer, physically realized by, e.g., some module physically attached to the agent or a human supervisor, observes the agent's action and partially, via some percept O, the state of the world 7 . The overseer then calculates the reward R. To set proper incentives to the agent, we will assume the overseer to know not only the action and observation, but also everything that the agent knows (cf.  Christiano 2016) . The overseer may also have access to some additional piece of information E r about the way the reward is to be calculated. 8 Lastly, we assume that the sets of possible values of A, O and E r are finite. In principle, the overseer could reward the agent in all kinds of ways. E.g., it could reward the agent \"deontologically\" (Alexander and Moore 2016) for taking a particular action independently of the consequences of taking that action. In this paper, we will assume that the reward estimates the value of some von Neumann-Morgenstern utility function U that only depends on states of the world. I use the capital U to indicate that the utility function, too, is a random variable (in the Bayesian sense). For simplicity's sake, we will, again, assume that the set of possible values of U is finite. We will view U as representing the system designer's preferences over world states. 9 While other ways of assigning the reward are possible, this is certainly an attractive way of getting an approval-directed agent to achieve goals that we want it to achieve. After all, in real-world applications, we will usually care about the outcomes of the agent's decisions, such as whether a car has reached its destination in time or whether a human has been hurt. The standard way of estimating U (H ) (or any quantity for that matter) is the familiar conditional expectation. Thus, the overseer may compute the reward as r = E [U (H ) | e r , a, o] , (1) Footnote 6 continued know your common source code), the dependence persists. We exclude these dependences because such situations cannot be modeled by standard causal graphs. However, we could adapt causal graphs to accomodate for these kinds of dependences. First, we could modify our definition of causality in such a way that dependence does imply causation, as has been proposed by  Spohn (2003 Spohn ( , 2012 ,  Yudkowsky (2010)  and others. For instance, we could model the dependence between the outputs of two instances of an algorithm by introducing a logical node as a common cause of the two. This logical node would then represent the output of the abstract algorithm that the two copies implement. While changes to the concept of causation may affect CDT's implied behavior, the results from this paper can be directly transfered to such modifications. Alternatively, we could extend causal graphs to also include non-causal dependences (cf.  Poellinger 2013) . Such extension necessitates a new CDT formalism, so the proofs from this paper do not directly transfer to this case. That said, I expect our results to generalize given that both EDT and CDT would probably treat non-causal dependences on the action just like they treat causal arrows directed toward the action.  7  Christiano (2014) does not define approval-directed agency formally, but judging from a comment he made at https://medium.com/paulfchristiano/i-agree-that-the-key-feature-of-approval-directed-agents-isthat-the-causal-picture-is-736b4474910e, he considers it crucial to his conception that the overseer only looks at the agent's action and does not observe the action's consequences (cf. the distinction introduced in Sect. 3).  8  One reason for the overseer to have access to such additional information is that some of the human supervisor's values may not be expressible in a way that the approval-directed agent's algorithm can utilize (cf.  Muehlhauser and Helm 2012, Sects. 3, 4, 5.3 ). 9 Some have tried to modify the reward relative to the designer's preferences to make the reinforcement learning problem easier to solve  (Sorg 2011) , although  Sutton and Barto (1998, Sect. 3 .2) explicitly discourage such tricks in their reinforcement learning textbook. where r , a, e r , and o are values of R, A, E r , and O, respectively. 10 A causal decision theorist overseer agrees that after an action a is taken the righthand side of Eq. 1 most accurately estimates how much utility is achieved. She merely thinks that this term should not be used to decide which action a to take in the first place. 11 However, this puts a causal decision theorist overseer in a peculiar situation. Whatever formula she uses to compute the reward will also be used by the rewardmaximizing agent to decide which action to take. A causal decision theorist overseer might therefore worry (rightfully, as we will see) that providing rewards according to Eq. 1 will make the agent EDT-ish. Hence, she either has to incorrectly estimate how much utility was achieved; or live with the agent using an-in her mind-incorrect way of weighing her options. If she prefers the latter, she would reward according to Eq. 1. But arguably getting the agent to choose correctly is the overseer's primary goal. Thus, she might prefer to compute the reward according to r = E [U (H ) | e r , do(a), o] . (2) Here, do(a) refers to Pearl's do-calculus, where conditioning on do(a) roughly means intervening from outside the causal model to set A to a. For an introduction to the do-calculus, see  Pearl (2009) . Although a causal decision theorist overseer may prefer computing rewards according to Eq. 1, we will from now on say \"the overseer uses CDT\" if rewards are computed according to Eq. 2 and \"the overseer uses EDT\" if rewards are calculated according to Eq. 1. An approval-directed agent is characterized by maximizing the reward it receives from the overseer. 12 However, decision theory offers us, again, (at least) two different expected values, the regular expected value of EDT E [R | a] , (3) and CDT's causal expected value E [R | do(a)] . ( 4 ) 10 At first sight this may be confusing to some readers, because in reinforcement learning, utility sometimes refers to expected cumulative reward  (Russell and Norvig 2010, Chap. 17, 21) , although others use the term value function instead  (Sutton and Barto 1998, Sect. 3.7 ). Here, U does not refer to utility in that sense but in the decision-theoretical sense of representing intrinsic values. So, in the present case, we have two \"layers\" of goals: first, the agent maximizes the reward r . Second, the agent as incentivized by the overseer's way of calculating rewards maximizes utility U (H ). One cause of confusion is that in model applications of reinforcement learning, the reward function possesses full knowledge of the world state and thus does not require the use of the expectation operator. 11 If the disagreement in Newcomb's problem is to be about different theories of rational choice (EDT, CDT and so forth) rather than the predictive abilities of \"the being\", Omega or the psychologist, then after requesting both boxes a proponent of two-boxing has to believe that she will probably receive only $1000. Causal and evidential decision theorists agree that regular conditional expectation is the correct way of updating one's beliefs about the state of the world after an action has been taken (cf. the distinction between \"acts\" and \"actions\" in  Pearl 2009 Sect. 4.1.1) . We leave the interesting question of which (if any) decision theory describes the behavior of current reinforcement learning algorithms to future research 13 and in the following assume that the agent is known to implement either CDT or EDT. \n The conflict of the decision theories of agent and overseer When viewed together with the overseer, our agent may now be seen as containing two decision theories, one for computing the reward and one in the algorithm that tries to find the action to maximize that reward. These decision theories may not always be the same. Given this potential discrepancy, the question is which of the two decision theories prevails, i.e., for which configurations of the two decision theories the overall agent acts like a CDT agent and for which it acts like an EDT agent w.r.t. U . As it turns out, the answer to this question depends on the decision problem in question. In particular, it depends on whether the overseer updates its estimate of U (H ) primarily based on the action taken by the agent or on its observation of the environment. For illustration, consider two versions of Newcomb's problem. In both versions, the predictor is equally reliable-e.g., correct with 90% probability-and the potential box contents are the same-e.g., the standard $1K and $1M. As usual, the content of the opaque box cannot be causally influenced by one's decision. In the first version, the overseer eventually sees the payoff, i.e., how much money the agent has made. In this case, as soon as the money is observed, the overseer's estimate of U (H ) becomes independent of the agent's action. More generally, O may tell the overseer so much about U (H ) that it becomes independent of A even if U (H ) is not yet fully observed. That is, E [U (H ) | e r , a, o] = E [U (H ) | e r , o] (5) and E [U (H ) | e r , do(a), o] = E [U (H ) | e r , o] (6) for all e r , a and o. Note that neither of these two implies the other.  14  Intuitively speaking, these two mean that the reward is ultimately determined by U (H ). In the second version of Newcomb's problem, the monetary payoff is not observed but covertly invested into increasing the agent's utility function. Only the agent's choice can then inform the overseer about U (H ). Formally, it is both   E [U (H ) | e r , a, o] = E [U (H ) | e r , a] (7) and E [U (H ) | e r , do(a), o] = E [U (H ) | e r , do(a)] . (8) Intuitively speaking, these two equations mean that the reward is not determined by U (H ) but by what the overseer believes U (H ) will be given a or do(a). Again, we assume that this is known to the agent. An example class of cases is that in which the agent's decisions are correlated with those of agents in far-away parts of the environment (cf.  Treutlein and Oesterheld 2017; Oesterheld 2018b ). The two versions are depicted in Fig.  2 . Of course, these are only the two extremes from the set of all possible situations. In real-world Newcomb-like scenarios, the overseer may also draw some information from both sources. Nonetheless, it seems useful to understand the extreme cases, as this may also help us understand mixed ones. In the following subsections, we will show that in the first type, the decision theory of the agent is decisive, whereas in the second type, the overseer's decision theory is 15 . Roughly, the reason for that is the following: As noted earlier, the reward in the first type depends directly on U (H ). Thus, the agent will try to maximize U (H ) according to its own decision theory. In the second type, the overseer takes the agent's action a and then considers what either a or do(a) says about U (H ). Thus, the agent has to pay careful attention to whether the overseer uses EDT's or CDT's expected value. We prove this formally by considering all possible configurations of the type of the problem, the overseer's decision theory and the agent's decision theory. While we will limit our analysis to EDT and CDT, the results can easily be generalized to variants of these that arise from modifying the causal model or conditional credence distribution (e.g. Yudkowsky 2010; \"Disposition-based decision theory\"; Spohn 2012;  Dohrn 2015 ). The analysis is summarized in Table  1 .  \n First type \n The EDT agent The EDT agent judges its action by E [R | a] . (9) If the overseer calculates regular conditional expectation, then it is E [R | a] = E [E [U (H ) | E r , O, a] | a] (10) = E [U (H ) | a] , ( 11 ) where the last line is due to what is sometimes called the law of total expectation (LTE) or the tower rule (see, e.g.,  Ross 2007, Sect. 3.4; Billingsley 1995, Theorem 34.4 ). Intuitively, you cannot expect that gaining more evidence (i.e., E r and O in addition to a) moves your expectation of U (H ) into any particular direction. Because the overseer knows more than the agent, we will need this rule in all of the following derivations. Its application makes it hard to generalize these results to other decision theories, since LTE does not apply if the two decision theories do not both compute a form of expected utility. Equations 10 and 11 show that if the overseer computes regular expected value and the agent maximizes the reward according to EDT, then the agent as a whole maximizes U according to EDT. If the overseer computes CDT's expected value, it is  E [R | a] = E [E [U (H ) | E r , do(a), O] | a] ( 12 = E [E [U (H ) | E r , a, O] | a] (15) = LTE E [U (H ) | a] (14) (16) \n The CDT agent The CDT agent judges its action by E [R | do(a)] . ( 17 ) If the overseer uses regular expected value (EDT), then E [R | do(a)] = E [E [U (H ) | a, O, E r ] | do(a)] (18) = e r ,o P(e r , o | do(a)) • E [U (H ) | a, o, e r ] (19) = eq. 5 and 6 e r ,o P(e r , o | do(a)) • E [U (H ) | do(a), o, e r ] (20) = E [E [U (H ) | do(a), O, E r ] | do(a)] (21) = LTE E [U (H ) | do(a)] (22) Learning about an intervention do(a) cannot always be treated in the same way as learning about other events. Hence, the application of the law of total expectation is not straightforward. However, P(• | do(x)) is always a probability distribution. Because the law of total expectation applies to all probability distributions, it also applies to ones resulting from the application of the do-calculus. If the overseer uses CDT's expected value, then E [R | do(a)] = E [E [U (H ) | E r , O, do(a)] | do(a)] (23) = LTE E [U (H ) | do(a)] . (24) \n Second type \n The EDT agent The EDT agent judges its actions by E [R | a] . ( 25 ) If the overseer is based on regular conditional expectation (EDT), then it is again E [R | a] = E [E [U (H ) | E r , a] | a] (26) = LTE E [U (H ) | a] . ( 27 ) If the overseer is based on CDT-type expectation, then (33) E [R | a] = E [E [U (H ) | E r , do(a)] | a] ( 28 \n The CDT agent The CDT agent judges actions by E [R | do(a)] . ( 34 ) Because of Rule 2 in Theorem 3.4.1 of  Pearl (2009, Sect. 3.4. 2) applied to the causal graph of Fig.  2b , it is E [R | do(a)] = E [R | a] . (35) Thus, the analysis of the CDT agent is equivalent to that of the EDT agent. \n Conclusion In this paper, we have taken a step to map reinforcement learning architectures onto decision theories. We found that in Newcomb-like problems, if the overseer rewards the agent purely on the basis of the agent's action, then the overall system's behavior is determined by the decision theory implicit in the overseer's reward function. If the overseer judges the agent based on looking at the world, however, then the agent's decision theory is decisive. This has implications for how we should design approval-directed agents. For instance, if we would like to leave decision-theoretical judgements to the overseer, we must ensure that the overseer assigns rewards before making new observations about the world state (cf.  Christiano 2014, Sect. \"Avoid lock-in\") . Of course, this makes the reward less accurate and may thus slow down the agent's learning process. If we want the overseer to look at both the world and the agent's action, then we need to align both the overseer's and the agent's decision theory. Much more research is left to be done at the intersection of decision theory and artificial intelligence. For instance, what (if any) decision theories describe the way modern reinforcement learning algorithms maximize reward? Do the results of this paper generalize to sequential decision problems? Moving away from the reinforcement learning framework, what decision theories do other frameworks in AI implement? What about decision theories other than CDT and EDT? The reward is computed based on ob-(b) The reward is computed based on observing the agent's action. \n Fig. 2 2 Fig. 2 Two different ways in which the overseer can calculate the reward \n r , o | a) • E [U (H ) | e r , do(a), o] (13) = eq. 5 and 6 e r ,o P(e r , o | a) • E [U (H ) | e r , a, o] \n r | a) • E [U (H ) | do(a), e r ] r ) • E [U (H ) | do(a), e r ] r | do(a)) • E [U (H ) | do(a), e r ] (31) = E [E [U (H ) | E r , do(a)] | do(a)] (32) = LTE E [U (H ) | do(a)] . \n Table 1 1 An overview of the results of the calculations in Sect. 3 Type of Newcomb problem Agent's DT Overseer's DT Resulting DT First type CDT EDT CDT CDT CDT EDT EDT EDT CDT EDT Second type CDT EDT EDT CDT CDT EDT EDT EDT CDT CDT \n\t\t\t In fact, Eells (1981)  has argued that EDT and CDT always behave in the same way, but I disagree with this assessment based on the reasons given byAhmed (2014, Sect. 4.3-4.6) and Price (1986) .2  Of course, the existing literature asks about the right decision theory proper. The answer to that question might differ from the answer to the AI-specific question (cf. Kumar 2017;  Treutlein 2018). After all, even if we have identified the right decision theory for ourselves, we may want to implement a different decision theory in an AI. One reason could be that the main contenders are not self-recommending-it has been pointed out that EDT and CDT both recommend to self-modify into slightly different decision theories \n\t\t\t This is consistent with what reinforcement learning algorithms usually do-they choose policies rather than individual actions. This is because the utility of a single action usually cannot be evaluated without knowing how the agent will deal with situations that might arise as a result of taking that action. When individual actions can be evaluated in isolation, the ex ante policy choice sometimes differs from the choice of individual actions (see the absent-minded driver, introduced by Piccione and Rubinstein 1997; cf. Aumann et al. 1997 ; the Newcomb-like scenarios discussed by, e.g., Hintze 2014; Soares and Levinstein 2017, Sect. 2; and the problems in anthropics discussed by Armstrong 2011) . While it is rarely discussed in the debate between evidential and causal decision theorists, a few authors regard this discrepancy as crucial and have argued that a proper decision theory should be about optimal policy choices (e.g. Hintze 2014;   Soares and Fallenstein 2014b, Sect. 2.1; Soares and Levinstein 2017, Sect. 2). However, this issue is beyond the scope of the present paper. Further issues in sequential Newcomb-like problems are discussed by Everitt et al. (2015) . \n\t\t\t There is a broad philosophical literature on whether causal relationships exist and whether they can be inferred in cases where the agent is part of the environment. See, e.g., the edited volume byPrice and Corry  (2007).6  For simplicity, we will ignore dependences not resulting from causation (Arntzenius 2010) . For example, if you play against a copy, there is a logical dependence between your and your copy's decision. Even if you know a set of nodes in the causal graph that d-separates your and your copy's decision (e.g., if you \n\t\t\t In reinforcement learning, some have proposed alternative optimization targets that incorporate, e.g., risk aversion(García and Fernández 2015, Sect. 3). \n\t\t\t For preliminary work on this question, see Mayer et al. (2016) , Oesterheld (2018a)  and perhaps Albert and Heiner (2001) .14  We give a brief justification of this claim. If all of a's causal influence on H can be discerned from O, then, of course, a could still be diagnostically relevant for one's estimate of U (H ). The other direction is more complicated. The idea is that Eq. 5 can be true if the causal and non-causal implications of a exactly cancel each other out. An example is a version of Newcomb's problem in which one-boxing ensures with certainty that both boxes contain the same amount of money. Then if O and E r do not contain any information, the expected value of two-boxing and one-boxing is the same and so learning of the action is irrelevant for estimating U (H ). However, two-boxing is causally better than one-boxing, so Eq. 6 is violated. \n\t\t\t The dominance of the overseer's decision theory in the second type of Newcomb's problem is mentioned (though not proven) byChristiano (2014, Sect. \"Avoid lock-in\"). \n\t\t\t Synthese (2021) 198 (Suppl 27):S6491-S6504", "date_published": "n/a", "url": "n/a", "filename": "Oesterheld2021_Article_Approval-directedAgencyAndTheD.tei.xml", "abstract": "Decision theorists disagree about how instrumentally rational agents, i.e., agents trying to achieve some goal, should behave in so-called Newcomb-like problems, with the main contenders being causal and evidential decision theory. Since the main goal of artificial intelligence research is to create machines that make instrumentally rational decisions, the disagreement pertains to this field. In addition to the more philosophical question of what the right decision theory is, the goal of AI poses the question of how to implement any given decision theory in an AI. For example, how would one go about building an AI whose behavior matches evidential decision theory's recommendations? Conversely, we can ask which decision theories (if any) describe the behavior of any existing AI design. In this paper, we study what decision theory an approval-directed agent, i.e., an agent whose goal it is to maximize the score it receives from an overseer, implements. If we assume that the overseer rewards the agent based on the expected value of some von Neumann-Morgenstern utility function, then such an approval-directed agent is guided by two decision theories: the one used by the agent to decide which action to choose in order to maximize the reward and the one used by the overseer to compute the expected utility of a chosen action. We show which of these two decision theories describes the agent's behavior in which situations. \n Keywords Reinforcement learning • Causal decision theory • Evidential decision theory • Newcomb's problem • AI safety • Philosophical foundations of AI B Caspar Oesterheld", "id": "e92da74deef5925e7ac635cf8cfd10a7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "CNASReport-Technology-Roulette-DoSproof2v2.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong"], "title": "Off-policy Monte Carlo agents with variable behaviour policies", "text": "Off-policy Monte Carlo The Monte Carlo agent is a model-free reinforcement learning agent  [3] . These operate when the environment is a Markov decision process (MDP). In an MDP, the next observation depends only on the current observation -the state -and the current action. The full set of state action pairs is designated by S × A. In each state, an agent chooses its actions according to a (possibly stochastic) policy π, that is assumed to be Markov. Monte Carlo agents operate by computing the Q-values of a policy for each state-action pair (s, a), which is the expected return if the agent choose a in s and subsequently follows π. It is episodic, exploring the same MDP repeatedly to compute Q-values. Episodic MDP's have initial state (where the agent starts an episode) and terminal states (where the agent ends an episode). This paper focuses on computing Q-values, not on updating policy choice in consequence. Assumption 1 In the following, these are always assumed, required for convergence results: (a) The MDP is finite, (b) Whatever policy the agent uses, its expected time until reaching a terminal state is finite. (c) The rewards after each step have finite expectation (consequently the total reward has finite expectation). If an agent is following one policy (e.g., ρ) but wishes to compute the Qvalues of another (e.g., π), it can use the off-policy Monte Carlo algorithm  [3] . In this case ρ is the behaviour policy, and π is the evaluation policy. The algorithm requires that for all state-action pairs (s, a): π(a|s) > 0 ⇒ ρ(a|s) > 0. ( ) 1 Because of this requirement, π(a|s) is zero whenever ρ(a|s) is, and the ratio π(a|s)/ρ(a|s) can be defined as 0 in these cases. The full algorithm is then given in box 1 -there are two variants, ordinary importance sampling using N (s, a) (the number of episodes in which the agent has encountered the state-action pair (s, a)) as the denominator, and weighted importance sampling using W (s, a) (the sum of the weights) instead  [4, 1] . 1. For all s ∈ S and a ∈ As, initialise N (s, a), W (s, a) and W R(s, a) to zero. 2. For all n ≥ 1: (a) Generate an episode history hn by following policy ρ. (b) The episode data will consist of the state, action chosen in the state, the immediate reward experienced by the agent. (c) For each state-action pair (s, a) appearing in the episode history: i. Let t be the first appearance of (s, a) in the history. ii. Let Rn(s, a) be the total subsequent reward. iii. Define  Note that W (s, a) and N (s, a) have the same expectation: let H (s,a) be the set of possible histories in the MDP subsequent to (s, a). For h ∈ H (s,a) , relabel the indexes so that h starts in step zero at (s, a). Use ρ and π to denote the probabilities of certain events conditional on the agent following those policies, and E ρ and E π similarly. Then if I n (s, a) denotes the event that (s, a) appears in the n-the episode, wn(s, a) = k>t π(a k |s k ) ρ(a k |s k ) . (2) E ρ (w(s, a)|I n (s, a)) = h∈H (s,a) ρ(h|I n (s, a)) k>0 π(h a k |h s k ) ρ(h a k |h s k ) = h∈H (s,a) ρ(h|I n (s, a)) π(h|I n (s, a)) ρ(h|I n (s, a)) = h∈H (s,a) π(h|I n (s, a)) = π(H (s,a) |I n (s, a)) = 1. ( ) 3 where h a k denotes the k-th action of history h, and h s k denotes the k-th state of history h. Then simply note that the value of N n (s, a) is simply the sum The same argument as in equation  (3)  shows that E ρ (w n (s, a)R n (s, a)|I n (s, a)) = h∈H (s,a) R h (s, a)ρ(h|I n (s, a)) k>0 π(h a k |h s k ) ρ(h a k |h s k ) = E π (R(s, a)|I n (s, a)), (4) where R h (s, a) is the reward along the history h subsequent to the first (s, a). Thus the expected weighted reward from following policy ρ, is the expected reward from following policy π. Assume that agents following ρ would almost surely explore every stateaction pair infinitely often (equivalently, that N n (s, a) → ∞ almost surely). Then the convergence of ordinary importance sampling is simply a consequence of the law of large numbers applied to every episode that visits (s, a). Convergence of weighted importance sampling is a consequence of Corollary 1 below. \n Varying the behaviour policy The previous proof, however, assumes that policy ρ is fixed. But what if it varies from episode to episode? If π and π are two policies, any p ∈ [0, 1] defines the mixed policy: (1 − p)π + pπ . This is the policy that, in each state, independently chooses whether to follow π, with probability 1 − p, and π , with probability p. Because the decisions are independent, the mixed policy is Markov if π and π are. A general form for all behaviour policies is then: Proposition 1. If ρ and π obey the restriction in equation (  1 ), then there exists a θ ∈ [0, 1) and a policy π such that ρ = (1 − θ)π + θπ . Proof. Let σ be the maximum across S × A of the ratio π(a|s)/ρ(a|s), in all cases where ρ(a|s) = 0. Then define (1 − θ) = 1/σ. Since π(a|s)/ρ(a|s) ≤ σ, (1 − θ) = 1/σ ≤ ρ(a|s)/π(a|s) and hence ρ(a|s) ≥ (1 − θ)π(a|s). Then define π as π (a|s) = 1 θ ρ(a|s) − (1 − θ)π(a|s) . To check that this quantity is less than 1, note that ρ(a|s ) = 1 − b =a ρ(b|s) ≤ 1 − b =a (1 − θ)π(b|s) hence that ρ(a|s) − (1 − θ)π(a|s) ≤ 1 − b (1 − θ)π(b|s) ≤ 1 − (1 − θ) ≤ θ. Then, by construction, ρ(a|s) = (1 − θ)π(a|s) + (θ)π (a|s). For n being the episode number, define ρ n by ρ n = (1 − θ n )π + θ n π n , (5) for some π n and θ n ∈ [0, 1). For convenience, further define the set S ⊂ S, which is the set of states s such that ρ n (s) = π(s). Then neither off-policy Monte Carlo algorithm need converge: Theorem 1. Neither off-policy Monte Carlo algorithm following policy ρ n need converge to the correct Q-values for π, even if the agent generates every possible episode history infinitely often. The proof is given in Section 3. But that convergence failure need not happen for all such ρ n . A sufficient condition for convergence is: Theorem 2. Let σ n = 1/(1−θ n ). Assume that σ n is eventually non-decreasing, and that there exists a δ > 0 such that, for large enough n, (σ n ) √ log(n) < n 1−δ . Assume that π visits each state-action pair with non-zero probability. Then both off-policy Monte Carlo algorithms following policy ρ n will almost surely converge on the correct Q-values for π. This will be proved in Section 4. Note that the requirement for visiting all (s, a) pairs is for the evaluation policy π -the behaviour policy will also do so, as a consequence of the conditions above. One immediate corollary of theorem 2 is: Corollary 1. If θ n is bounded above by κ < 1, both off-policy Monte Carlo algorithms using ρ n will converge on the correct Q-values for π, if π visits each state-action pair with non-zero probability. Proof. This kind of result has been proved before  [5] . The σ n are bounded above by 1/(1 − κ), and thus, for any δ, are less than n 1−δ for sufficiently large n. Then Theorem 2 implies the result. A second corollary is: Corollary 2. If θ n = 1 − 1 log(n) , both off-policy Monte Carlo algorithms using ρ n will converge on the correct Q-values for π, if π visits each state-action pair with non-zero probability. Proof. Set δ = 1/2, note that σ n = log(n), and that log (σ n ) √ log(n) = log(n) log(log(n)) < log(n) 2 = log( √ n) for large enough n. Hence, for large enough n, (σ n ) √ log(n) < √ n = n 1−1/2 . Then Theorem 2 implies the result. And a third corollary is: Corollary 3. Assume π n (a|s) > r (s,a) whenever π(a|s) > 0, for constants r (s,a) > 0. Then both off-policy Monte Carlo algorithms using ρ n will converge on the correct Q-values for π, if π visits each state-action pair with non-zero probability. Proof. Let r be the minimum value of r (s,a) /π(a|s), across all (s, a) where π(a|s) > 0. Then π n can be rewritten as: π n = rπ + (1 − r)π n , for some π n . Similarly ρ n can be rewritten as ρ n = (1 − (1 − r)θ n )π + (θ n )(1 − r)π n . Then note that (θ n )(1 − r) is bounded above by 1 − r, and the result follows by corollary 1. The rest of this paper will be dedicated to proving theorems 1 and 2. \n Failure to converge This Section aims to prove Theorem 1, by constructing a counter-example using the MDP of figure  1 . Set π(a|s 1 ) = 1, π(a|s 2 ) = π(b|s 2 ) = 1/2, S = {s 2 }, π n (a|s 2 ) = 0, π n (b|s 2 ) = 1, and define θ n as The probability of the n-th episode history being h b = (s 1 , a, 0, s 2 , b, −3, s 4 ) is greater or equal to 1/2: this history therefore almost surely gets generated infinitely often. Now consider the episode history h a = (s 1 , a, 0, s 2 , a, −1, s 4 ). It will get generated during episode n with probability θ n = 1 − 1/(n log(n)). 1 2 • (1 − θ n ) = 1 2n log(n) . Each episode is independent and n 1/(2n log(n)) = ∞, so by the converse Borel-Cantelli lemma, the episode is generated infinitely often. Then note that if the history h a is generated during the n-th episode, it is generated with weight 1/(1 − θ n ) = n log(n), while the history h b is generated with weight 1/(1 + θ n ) = 1/(2 − 1/(n log(n))). Split the weight total W n (s 1 , a) as W a n (s 1 , a) + W b n (s 1 , a) (the weight totals due to the histories h a and h b respectively). Then ordinary importance sampling will give Q n as: Q n (s 1 , a) = −W a n (s 1 , a) − 3W b n (s 1 , a) N n (s 1 , a) , (6) while weighted importance sampling gives: Q n (s 1 , a) = −W a n (s 1 , a) − 3W b n (s 1 , a) W a n (s 1 , a) + W b n (s 1 , a) . (7) In state s 1 , both actions are equiprobable and independent, so the law of large numbers implies N n (s 1 , a)/n → 1 almost surely. The W b n (s 1 , a) is the sum of weights less than 1, so W b n (s 1 , a) ≤ N n (s 1 , a). The probability of h b increases to 1, and the weights for that history are larger than 1/2 for n ≥ 1. Thus, almost surely, for sufficiently large n, n/3 and 2n are lower and upper bounds for both N n (s 1 , a) and W b n (s 1 , a). Now pick an n where episode history h a is generated, which must happen infinitely often. The weight of this history is n log(n), so W a n (s 1 , a) ≥ n. In the limit, this must dominate the n-bounded contributions of N n (s 1 , a) and W b n (s 1 , a). Thus, for a large enough n where h a is generated, equation (6) then gives the upper bound Q n (s 1 , a) ≤ −C log(n), for some constant C. Conversely, equation (7) gives an upper bound: Q n (s 1 , a) ≥ −1 − C/ log(n), for some C. The correct Q-value for Q(s 1 , a) under π is clearly (−3−1)/2 = −2, so neither algorithm can converge to the correct values. Ordinary importance sampling clearly cannot find the optimal policy (of choosing a in state s 2 ) either. If b had a reward of 0 instead of a reward of −2, then weighted importance sampling would fail to find the optimal policy on that MDP, so both algorithms can fail to find optimal policies. Remark 1. The lack of convergence can also be proved for θ n = 1 − 1/n, but the proofs are more involved. \n Proof of convergence This Section aims to prove 3 Theorem 2. \n Infinite variance The reason that such mathematical machinery is needed is because, in many cases, the variance of the reward become infinite. Consider the MDP of figure  2 . Two actions are available in s 2 : action a which, with p probability will return the agent to state 1 with a reward of 1, and otherwise send them to state s 3 with no reward. And b, which goes straight to s 3 with no reward. Set π(a|s 1 ) = 1, π n (b|s 2 ) = 1, and θ n = 1 − q. The weights are powers of 1/q, ρ n (a|s 2 ) = q, so the expected weighted reward is the correct ∞ l=0 (l/q l )(pq) l , which is finite. Since for any random variable X, Var(X) = E(X 2 ) − E(X) 2 , the variance of the weighted reward is finite iff the expected squared weighted reward is finite. Then the expected squared weighted reward is: ∞ l=0 (l/q l ) 2 (pq) l = ∞ l=0 l 2 (p/q) l . And this sum diverges for q ≤ p. \n Proving convergence This proof will use ordinary importance sampling, then generalise to weighted importance sampling. Fix any pair (s, a). Since π must visit that pair with finite probability, there is an m < |S × A| and a probability τ > 0 such that an agent following π would  s 3 s 2 s 1 a, 0 a, 0, 1 − q b, 0 a, 1, q (σ n ) m < (σ n ) √ log(n) < n 1−δ < n. Hence, for large enough n, τ (1 − θ n ) m = τ (1/σ n ) > τ /n, so ∞ τ (1 − θ n ) m = ∞. Then since each episode is independent, the converse Borel-Cantelli lemma implies that an agent following ρ will almost surely visit (s, a) infinitely often. How regular will these visits be? The expected number of visits during the episodes up to the n-th is simply n j=1 τ (1 − θ j ) m . For large enough n, σ n < n 1−δ √ log(n) and so eventually τ (1 − θ n ) m > τ n −m 1−δ √ log(n) > n −δ , for any δ > 0. Therefore, for large enough n, the number of visits to (s, a) among the n episodes must be almost surely greater than n j=1 j −δ = O(n 1−δ ). Thus, for large enough n, N n (s, a) > n 1−δ almost surely. Let Q * be the true Q-value of the MDP under π, and let H be the set of possible episode histories, ignoring rewards. Let H l be the set of histories of length l. Write π(h n ) for h ∈ H to designate the probability that episode n has history h if the agent follows the policy π. Note that since π is fixed, π(h n ) is independent of n (unlike ρ n (h n )). Let η be the policy designed to maximise the expected time the agent spends in the MDP. This means that η is a Markov policy, as the policy that maximises the time spent if the agent is in state (s , a ) does not depend on the agent's prior history. Combined with the MDP, η describes a Markov chain, with absorbing final states. Its transition matrix is of the form: P R 0 Id , for P a transition matrix on the non-absorbing state-action pairs, and Id the identity matrix on the absorbing ones. Since any episode must terminate with probability 1, the matrix P has a single maximal real eigenvalue µ < 1  [2] . For large n, the probability that the matrix will not have terminated by the n-th episode is bounded by (µ ) n . Since η is the policy that maximises the expected time spent in the MDP, an agent following π cannot expect to stay in MDP longer than that, so there exists a C such that π(H l ) ≤ C (µ ) l . Fix any µ < µ < 1, then because l 2 (µ ) l must eventually be less than µ l , there exists a C such that lπ(H l ) ≤ l 2 π(H l ) ≤ Cµ l . Let E be the maximal expected reward the agent can generate from a single state-action pair. Let S be the maximal expected squared reward the agent can generate from a single state-action pair. Then if R h is the random variable denoting the reward generated along history h ∈ H l , E (R h |h) ≤ lE Var (R h |h) ≤ E R 2 h |h ≤ l 2 S. Let W R l n denote the random variable that returns 0 if the length of the n-th episode is not l, and the (weighted) reward otherwise, under the assumption that the agent visits (s, a) during episode n. Therefore: W R l n = h∈H l w(h n )R h ρ(h n ). Note that w(h n ) = π(h n )/ρ(h n ) ≤ (σ n ) i h , where i h ≤ l is the number of times that the agent goes through a state in S along h. Then E ρn W R l n = h∈H l w(h n )E (R h |h) ρ n (h n ) = h∈H l E (R h |h) π(h n ), which is the expected reward from episode histories of length l from an agent following π. Therefore ∞ l=1 E ρn W R l n = h E (R h |h) π(h n ) = Q * . The expectation and variance of W R l n can be bounded as: E ρn W R l n = h∈H l E (R h |h) π(h n ) ≤ lEπ(H l ) ≤ ECµ l Var ρn W R l n ≤ E ρn W R l n 2 ≤ h∈H l E (w(h n )R h ) 2 |h ρ(h n ) ≤ h∈H l (σ n ) i h E (R h ) 2 |h π(h n ) ≤ π(H l )(σ n ) l l 2 S ≤ SC(µσ n ) l . (8) Redefine C as max(EC, SC) so that these bounds are Cµ l and C(µσ n ) l respectively. Then define W R <l n = j<l W R j n and W R ≥l n = j≥l W R j n . Equation (8) then implies that E ρn W R ≥l n ≤ C ∞ j=l µ j ≤ Cµ l 1 − µ Var ρn W R <l n ≤ l−1 j=1 Var ρn W R <l n ≤ l−1 j=1 C(µσ n ) j ≤ C(σ n µ) l − 1 σ n µ − 1 ≤ C(σ n ) l σ n µ − 1 Redefine C as C/(1 − µ) so that the first bound is Cµ l . For large enough n, σ n µ − 1 > 1; so, redefining C if needed to cover the finitely many smaller values of n, the second bound is C(σ n ) l : E ρn W R ≥l n ≤ Cµ l Var ρn W R <l n ≤ C(σ n ) l Let I n be the indexing variable that denotes that the agent visited (s, a) during episode n. By assumption, N n (s, a) = n j=1 I n (s, a), and this section has shown that N n (s, a) > n 1−δ for any δ > 0 and large enough n. Define Q ≥l n = 1 N n (s, a) n j=1 I j W R ≥l j Q <l n = 1 N n (s, a) n j=1 I j W R <l j . Then, since σ n are eventually non-decreasing, for any δ > 0 and for large enough n: E ρn Q ≥l n ≤ 1 N n (s, a) n j=1 I j Cµ l ≤ n j=1 I j N n (s, a) Cµ l ≤ Cµ l Var ρn Q <l n ≤ 1 N n (s, a) 2 n j=1 CI j (σ j ) l ≤ C N n (s, a) (σ n ) l ≤ C n 1−δ (σ n ) l . The following is a key Lemma: Lemma 1. Let 1 ≤ m 1 ≤ m 2 . . . be a sequence that is lacunary in that there exists a c > 1 such that m j+1 /m j > c for sufficiently large j. Then Q mj converges to Q * almost surely as j → ∞. Proof. Fix any > 0, and consider the subsequence n j = e √ j . Then since {m j } is eventually an exponentially growing sequence, m j > n j for sufficiently large j. Set l j = 4 √ j and consider Q mj = Q ≥lj mj + Q <lj mj . Then note that if k = 4 √ j, E Q ≥lj mj ≤ Cµ lj , and j 2 2 Cµ lj ≤ k 8 2 Cµ k−1 → 0, as k → ∞. This implies that for large enough j, E Q ≥lj mj ≤ j 2 . Any random variable X with finite expectation has the first moment bound: P (|X| ≥ λ) ≤ E|X| λ . Setting λ = , this implies that P (|Q ≥lj mj | ≥ ) ≤ 1 j 2 for large enough j. Since ∞ j=1 1 j 2 < ∞, the Borel-Cantelli lemma implies that, almost surely, |Q ≥lj mj | ≥ only finitely often. Since Q * = E Q mj = E Q ≥lj mj +E Q <lj mj , this also implies |E Q <lj mj − Q * | ≥ only finitely often. Consider now Var Q <lj mj ≤ C (mj ) 1−δ (σ mj ) lj . Note that l j = 4 √ j ≤ √ j ≤ log(n j ) ≤ log(m j ) . So, by the assumption of Theorem 2, for large enough j, (σ mj ) lj < m 1−δ j for some δ > 0. Fix δ = δ/2. Hence for large enough j, C (mj ) 1−δ/2 (σ mj ) lj < 1 (mj ) δ/2 . Since m δ/2 j > n δ/2 j ≥ e (δ/2) √ j > Cj 2 / 2 for large enough j, eventually Var Q <lj mj ≤ 2 j 2 . Any random variable X with finite variance has the second moment bound: P (|X − E(X)| ≥ λ) ≤ Var(X) λ 2 . Setting λ = , this implies that for large enough j, P (|Q <lj mj − E Q <lj mj | ≥ ) ≤ 1 j 2 . Using the Borel-Cantelli lemma a second time, |Q <lj mj − E Q <lj mj | < except finitely often. Putting together the three bounds completes the proof by showing that, almost surely, except for finitely many j, |Q mj − Q * | < 3 . Since was arbitrary, this completes the proof. The next step is to generalise from lacunary sequences to all sequences. Since all rewards have been assumed positive, nQ n ≤ mQ m for n < m. Then for any 1 > > 0, define the lacunary sequence m j = (1 + ) j . For m j < n < m j+1 , (1 + ) j Q mj ≤ nQ n ≤ Q mj+1 (1 + ) j+1 Q mj+1 . This implies that for large enough j, Q n ≥ Q mj (1/(1 + ) − 2 ) ≥ Q mj (1 − ) and Q n ≤ Q mj ((1 + ) + 2 ) ≤ Q mj (1 + 2 ) , where the 2 term comes from the fact that (1 + ) j need not be an integer. By the Lemma above, the sequence Q mj converge almost surely to Q * , thus, for large enough j and n > (1 + ) j , Q n must be within 3 (Q * + 1) of Q * . Since was arbitrary, this proves that Q n converges to Q * almost surely as n → ∞. This completes the proof for all MDP's with positive rewards. Note that the same proof works for MDP's with negative rewards. Then the general proof is established for by dividing the rewards into positive and negative parts, noting their separate convergence, and noting that the Q-values update process is linear in rewards. Since this proves the convergence of Q n (s, a) to Q * (s, a) for any (s, a), and there are finitely many (s, a) pairs, this proves the almost sure convergence of Q n to Q * in general. It is now necessary to extend the result to weighted importance sampling. To do that, it will suffice to show that, under the conditions above, W n (s, a)/N n (s, a) → 1 almost surely. To see this, change the MDP by setting all rewards to 0, except for the final reward when the agent reaches a terminal state, where they will get 1. This means that the reward along each history is 1, and the weighted reward is just the weight. Thus the new Q n for ordinary importance sampling is Q n (s, a) = W n (s, a)/N n (s, a). By the result we've just proved, these must converge almost surely to the correct Q-values for the modified MDP, i.e., to 1. This proves that the ratios converge almost surely to 1, as required. \n A Note on the independence assumption The policy ρ n , as defined in equation (  5 ), assumes that the agent choose independently between π and π n for each s ∈ S. If this independence is dropped, the situation can get even worse for convergence -the agent may fail to converge to the right values 4 even for fixed θ < 1. Consider the MDP in figure  3 . Define the policy π as choosing randomly amongst the two actions at s 1 , and choosing a otherwise. Define S = {s 2 , s 3 } and π n as choosing b from all states in S . For ρ, the probabilities of choosing π and π n in S are equal (and the same from episode to episode), θ 2 = θ 3 = 0.5, but they are strictly anti-correlated within a given episode. Notice that the episode history (s 1 , a, 0, s 2 , a, 1, s 3 , a, 1, s 4 ) never appears. This is because the uses of π n at s 2 and s 3 are anti-correlated, so the agent cannot avoid both of them. Therefore the agent never experiences a total reward of 2; moreover, the only episodes with rewards are the (equiprobable) iv. Nn(s, a) = Nn−1(s, a) + 1. v. Wn(s, a) = Wn−1(s, a) + wn(s, a). vi. W Rn(s, a) = W Rn−1(s, a) + wn(s, a)R(s, a). vii. Either Qn(s, a) = W Rn(s,a) Nn(s,a) , or Qn(s, a) = W Rn(s,a) Wn(s,a) . (d) Discard the episode data. \n n j=1 I j (s,a) , to see that N n (s, a) and W n (s, a) = n j=1 I j (s,a) w n (s, a) have same expectation. If ρ is fixed, then by sampling only those histories including (s, a), the strong law of large numbers implies that the ratio of N n (s, a) and W n (s, a) converges to 1 almost surely. \n 3 a, − 1 Fig. 1 . 311 Fig. 1. An MDP where the off-policy Monte Carlo algorithms can fail to compute the correct Q-values. \n Fig. 2 . 2 Fig. 2. An MDP where the variance of the reward can become infinite within a single episode. \n 1 Fig. 3 . 13 Fig. 3. An MDP on which the agent has non-Markov policy choices. \n Table 1 . 1 Off-policy Monte Carlo algorithm \n\t\t\t The proof will closely mirror the standard proofs of the strong law of large numbers, see for instance https://terrytao.wordpress.com/2008/06/18/the-strong-lawof-large-numbers/ \n\t\t\t For non-Markov policies like this one, the off-policy algorithm has to be adjusted to consider ratios π(h)/ρ(h) for entire histories h (rather the product of state-action pair probabilities), but this is not a large change.", "date_published": "n/a", "url": "n/a", "filename": "monte_carlo_arXiv.tei.xml", "abstract": "This paper looks at the convergence property of off-policy Monte Carlo agents with variable behaviour policies. It presents results about convergence and lack of convergence. Even if the agent generates every possible episode history infinitely often, the algorithm can fail to converge on the correct Q-values. On the other hand, it can converge on the correct Q-values under certain conditions. For instance, if, during the n-th episode, the agent has an independent probability of 1/ log(n) of following the original policy at any given state, then it will converge on the right Q-values for that policy.", "id": "14fe3934f3364cda0c9d2793188f52e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Chongli Qin", "James Martens", "Sven Gowal", "Dilip Krishnan", "Google Krishnamurthy", "Dvijotham Deepmind", "Alhussein Fawzi", "Soham De", "Robert Stanforth Deepmind"], "title": "Adversarial Robustness through Local Linearization", "text": "Introduction In a seminal paper, Szegedy et al.  [22]  demonstrated that neural networks are vulnerable to visually imperceptible but carefully chosen adversarial perturbations which cause them to output incorrect predictions. After this revealing study, a flurry of research has been conducted with the focus of making networks robust against such adversarial perturbations  [14, 16, 17, 25] . Concurrently, researchers devised stronger attacks that expose previously unknown vulnerabilities of neural networks  [24, 4, 1, 3] . Of the many approaches proposed  [19, 2, 6, 21, 15, 17] , adversarial training  [14, 16]  is empirically the best performing algorithm to train networks robust to adversarial perturbations. However, the cost of adversarial training becomes prohibitive with growing model complexity and input dimensionality. This is primarily due to the cost of computing adversarial perturbations, which is incurred at each step of adversarial training. In particular, for each new mini-batch one must perform multiple iterations of a gradient-based optimizer on the network's inputs to find the perturbations.  1  As each step of this optimizer requires a new backwards pass, the total cost of adversarial training scales as roughly the number of such steps. Unfortunately, effective adversarial training of ImageNet often requires large number of steps to avoid problems of gradient obfuscation  [1, 24] , making it significantly more expensive than conventional training. One approach which can alleviate the cost of adversarial training is training against weaker adversaries that are cheaper to compute. For example, by taking fewer gradient steps to compute adversarial examples during training. However, this can produce models which are robust against weak attacks, but break down under strong attacks -often due to gradient obfuscation. In particular, one form of gradient obfuscation occurs when the network learns to fool a gradient based attack by making the loss surface highly convoluted and non-linear (see  Fig 1) , an effect which has also been observed by Papernot et al  [18] . This non-linearity prevents gradient based optimization methods from finding an adversarial perturbation within a small number of iterations  [4, 24] . In contrast, if the loss surface was linear in the vicinity of the training examples, which is to say well-predicted by local gradient information, gradient obfuscation cannot occur. In this paper, we take up this idea and introduce a novel regularizer that encourages the loss to behave linearly in the vicinity of the training data. We call this regularizer the local linearity regularizer (LLR). Empirically, we find that networks trained with LLR exhibit far less gradient obfuscation, and are almost equally robust against strong attacks as they are against weak attacks. The main contributions of our paper are summarized below: • We show that training with LLR is significantly faster than adversarial training, allowing us to train a robust ImageNet model with a 5× speed up when training on 128 TPUv3 cores  [9] . • We show that LLR trained models exhibit higher robustness relative to adversarially trained models when evaluated under strong attacks. Adversarially trained models can exhibit a decrease in accuracy of 6% when increasing the attack strength at test time for CIFAR-10, whereas LLR shows only a decrease of 2%. • We achieve new state of the art results for adversarial accuracy against untargeted white-box attack for ImageNet (with = 4/255 2 ): 47%. Furthermore, we match state of the art results for CIFAR 10 (with = 8/255): 52.81% 3 . • We perform a large scale evaluation of existing methods for adversarially robust training under consistent, strong, white-box attacks. For this we recreate several baseline models from the literature, training them both for CIFAR-10 and ImageNet (where possible).  4  2 Background and Related Work We denote our classification function by f (x; θ) : x → R C , mapping input features x to the output logits for classes in set C, i.e. p i (y|x; θ) = exp (f i (x; θ)) / j exp (f j (x; θ)), with θ being the model parameters and y being the label. Adversarial robustness for f is defined as follows: a network is robust to adversarial perturbations of magnitude at input x if and only if argmax i∈C f i (x; θ) = argmax i∈C f i (x + δ; θ) ∀δ ∈ B p ( ) = {δ : δ p ≤ }. (1) In this paper, we focus on p = ∞ and we use B( ) to denote B ∞ ( ) for brevity. Given the dataset is drawn from distribution D, the standard method to train a classifier f is empirical risk minimization (ERM), which is defined by: min θ E (x,y)∼D [ (x; y, θ)]. Here, (x; y, θ) is the standard cross-entropy loss function defined by (x; y, θ) = −y T log (p(x; θ)) , (2) where p i (x; θ) is defined as above, and y is a 1-hot vector representing the class label. While ERM is effective at training neural networks that perform well on heldout test data, the accuracy on the test set goes to zero under adversarial evaluation. This is a result of a distribution shift in the data induced by the attack. To rectify this, adversarial training  [17, 14]  seeks to perturb the data distribution by performing adversarial attacks during training. More concretely, adversarial training minimizes the loss function E (x,y)∼D max δ∈B( ) (x + δ; y, θ) , (3) where the inner maximization, max δ∈B( ) (x + δ; y, θ), is typically performed via a fixed number of steps of a gradient-based optimization method. One such method is Projected-Gradient-Descent (PGD) which performs the following gradient step: δ ← Proj (δ − η∇ δ (x + δ; y, θ)) , (4) where Proj(x) = argmin ξ∈B( ) x − ξ . Another popular gradient-based method is to use the sign of the gradient  [8] . The cost of solving Eq (3) is dominated by the cost of solving the inner maximization problem. Thus, the inner maximization should be performed efficiently to reduce the overall cost of training. A naive approach is to reduce the number of gradient steps performed by the optimization procedure. Generally, the attack is weaker when we do fewer steps. If the attack is too weak, the trained networks often display gradient obfuscation as shown in Fig  1 . Since the introduction of adversarial training, a corpus of work has researched alternative ways of making networks robust. One such approach is the TRADES method  [27] , which is a form of regularization that optimizes the trade-off between robustness and accuracy -as many studies have observed these two quantities to be at odds with each other  [23] . Others, such as work by Ding et al  [7]  adaptively increase the perturbation radius by find the minimal length perturbation which changes the output label. Some have proposed architectural changes which promote adversarial robustness, such as the \"denoise\" model  [25]  for ImageNet. The work presented here is a regularization technique which encourages the loss function to be well approximated by its linear Taylor expansion in a sufficiently small neighbourhood. There has been work before which uses gradient information as a form of regularization  [20, 17] . The work presented in this paper is closely related to the paper by Moosavi et al  [17] , which highlights that adversarial training reduces the curvature of (x; y, θ) with respect to x. Leveraging an empirical observation (the highest curvature is along the direction ∇ x (x; y, θ)), they further propose an algorithm to mimic the effects of adversarial training on the loss surface. The algorithm results in comparable performance to adversarial training with a significantly lower cost. \n Motivating the Local Linearity Regularizer As described above, the cost of adversarial training is dominated by solving the inner maximization problem max δ∈B( ) (x + δ). Throughout we abbreviate (x; y, θ) with (x). We can reduce this cost simply by reducing the number of PGD (as defined in Eq (4)) steps taken to solve max δ∈B( ) (x + δ). To motivate the local linearity regularizer (LLR), we start with an empirical analysis of how the behavior of adversarial training changes as we increase the number of PGD steps used during training. We find that the loss surface becomes increasingly linear (as captured by the local linearity measure defined below) as we increase the number of PGD steps. \n Local Linearity Measure Suppose that we are given an adversarial perturbation δ ∈ B( ). The corresponding adversarial loss is given by (x + δ). If our loss surface is smooth and approximately linear, then (x + δ) is well approximated by its first-order Taylor expansion (x) + δ T ∇ x (x). In other words, the absolute difference between these two values, g(δ; x) = (x + δ) − (x) − δ T ∇ x (x) , (5) is an indicator of how linear the surface is. Consequently, we consider the quantity γ( , x) = max δ∈B( ) g(δ; x), (6) to be a measure of how linear the surface is within a neighbourhood B( ). We call this quantity the local linearity measure.   6 )) is large (on the order of 10) when we train with just one or two steps of PGD for inner maximization, (2a). In contrast, γ( , x) becomes increasingly smaller (on the order of 10 −1 ) as we increase the number of PGD steps to 4 and above, (2b). The x-axis is the number of training iterations and the y-axis is γ( , x), here = 8/255 for CIFAR-10. \n Empirical Observations on Adversarial Training We measure γ( , x) for networks trained with adversarial training on CIFAR-10, where the inner maximization max δ∈B( ) (x + δ) is performed with 1, 2, 4, 8 and 16 steps of PGD. γ( , x) is measured throughout training on the training set  5  . The architecture used is a wide residual network  [26]  28 in depth and 10 in width (Wide-ResNet-28-10). The results are shown in Fig  2a and 2b . Fig  2a  shows that when we train with one and two steps of PGD for the inner maximization, the local loss surface is extremely non-linear at the end of training. An example visualization of such a loss surface is given in Fig A1a  .  However, when we train with four or more steps of PGD for the inner maximization, the surface is relatively well approximated by (x) + δ T ∇ x (x) as shown in Fig 2b  .  An example of the loss surface is shown in Fig A1b  .  For the adversarial accuracy of the networks, see Table  A1 . \n Local Linearity Regularizer (LLR) From the section above, we make the empirical observation that the local linearity measure γ( , x) decreases as we train with stronger attacks  6  . In this section, we give some theoretical justifications of why local linearity γ( , x) correlates with adversarial robustness, and derive a regularizer from the local linearity measure that can be used for training of robust models. \n Local Linearity Upper Bounds Adversarial Loss The following proposition establishes that the adversarial loss (x + δ) is upper bounded by the local linearity measure, plus the change in the loss as predicted by the gradient (which is given by |δ T ∇ x (x)|). Proposition 4.1. Consider a loss function (x) that is once-differentiable, and a local neighbourhood defined by B( ). Then for all δ ∈ B( ) | (x + δ) − (x)| ≤ |δ T ∇ x (x)| + γ( , x). (7) See Appendix B for the proof. From Eq  (7)  it is clear that the adversarial loss tends to (x), i.e., (x + δ) → (x), as both |δ ∇ x (x)| → 0 and γ( ; x) → 0 for all δ ∈ B( ). And assuming (x + δ) ≥ (δ) one also has the upper bound (x + δ) ≤ (x) + |δ T ∇ x (x)| + γ( , x). \n Local Linearity Regularization (LLR) Following the analysis above, we propose the following objective for adversarially robust training L(D) = E D (x) + λγ( , x) + µ|δ T LLR ∇ x (x)| LLR , (8) where λ and µ are hyper-parameters to be optimized, and δ LLR = argmax δ∈B( ) g(δ; x) (recall the definition of g(δ; x) from Eq (5)). Concretely, we are trying to find the point δ LLR in B( ) where the linear approximation (x) + δ T ∇ x (x) is maximally violated. To train we penalize both its linear violation γ( , x) = (x + δ LLR ) − (x) − δ T LLR ∇ x (x) , and the gradient magnitude term δ T LLR ∇ x (x) , as required by the above proposition. We note that, analogous to adversarial training, LLR requires an inner optimization to find δ LLR -performed via gradient descent. However, as we will show in the experiments, much fewer optimization steps are required for the overall scheme to be effective. Pseudo-code for training with this regularizer is given in Appendix E. \n Local Linearity Measure γ( ; x) bounds the adversarial loss by itself Interestingly, under certain reasonable approximations and standard choices of loss functions, we can bound |δ ∇ x (x)| in terms of γ( ; x). See Appendix C for details. Consequently, the bound in Eq  (7)  implies that minimizing γ( ; x) (along with the nominal loss (x)) is sufficient to minimize the adversarial loss (x + δ). This prediction is confirmed by our experiments. However, our experiments also show that including |δ ∇ x (x)| in the objective along with (x) and γ( ; x) works better in practice on certain datasets, especially ImageNet. See Appendix F.3 for details. \n Experiments and Results We perform experiments using LLR on both CIFAR-10 [13] and ImageNet  [5]  datasets. We show that LLR gets state of the art adversarial accuracy on CIFAR-10 (at = 8/255) and ImageNet (at = 4/255) evaluated under a strong adversarial attack. Moreover, we show that as the attack strength increases, the degradation in adversarial accuracy is more graceful for networks trained using LLR than for those trained with standard adversarial training. Further, we demonstrate that training using LLR is 5× faster for ImageNet. Finally, we show that, by linearizing the loss surface, models are less prone to gradient obfuscation. \n CIFAR-10: The perturbation radius we examine is = 8/255 and the model architectures we use are Wide-ResNet-28-8, Wide-ResNet-40-8  [26] . Since the validity of our regularizer requires (x) to be smooth, the activation function we use is softplus function log(1 + exp(x)), which is a smooth version of ReLU. The baselines we compare our results against are adversarial training (ADV)  [16] , TRADES  [27]  and CURE  [17] . We recreate these baselines from the literature using the same network architecture and activation function. The evaluation is done on the full test set of 10K images. \n ImageNet: The perturbation radii considered are = 4/255 and = 16/255. The architecture used for this is from  [11]  which is ResNet-152. We use softplus as activation function. For = 4/255, the baselines we compare our results against is our recreated versions of ADV  [16]  and denoising model (DENOISE)  [25] .  7  For = 16/255, we compare LLR to ADV  [16]  and DENOISE  [25]  networks which have been published from the the literature. Due to computational constraints, we limit ourselves to evaluating all models on the first 1K images of the test set. To make sure that we have a close estimate of the true robustness, we evaluate all the models on a wide range of attacks these are described below. \n Evaluation Setup To accurately gauge the true robustness of our network, we tailor our attack to give the lowest possible adversarial accuracy. The two parts which we tune to get the optimal attack is the loss function for the attack and its corresponding optimization procedure. The loss functions used are described below, for the optimization procedure please refer to Appendix F.1. \n Loss Functions: The three loss functions we consider are summarized in Table  1 . We use the difference between logits for the loss function rather than the cross-entropy loss as we have empirically found the former to yield lower adversarial accuracy. \n Attack Name Loss Function Metric Random-Targeted max δ∈B( ) f r (x + δ) − f t (x + δ) Attack Success Rate Untargeted max δ∈B( ) f s (x + δ) − f t (x + δ) Adversarial Accuracy Multi-Targeted [10] max δ∈B( ) max i∈C f i (x + δ) − f t (x + δ) Adversarial Accuracy Table  1 : This shows the loss functions corresponding to the attacks we use for evaluation and also the metric we measure on the test set for each of these attacks. Notation-wise, s = argmax i =t fi(x + δ) is the highest logit excluding the logits corresponding to the correct class t, note s can change through the optimization procedure. For the Random-Targeted attack, r is a randomly chosen target label that is not t and does not change throughout the optimization. C stands for the set of class labels. For the Multi-Targeted attack we maximize fi(x + δ) − fT (x + δ) for all i ∈ C, and consider the attack successful if any of the individual attacks on each each target class i are successful. The metric used on the Random-Targeted attack is the attack success rate: the percentage of attacks where the target label r is indeed the output label (this metric is especially important for ImageNet at = 16/255). For the other attacks we use the adversarial accuracy as the metric which is the accuracy on the test set after the attack. For CIFAR-10, the main adversarial accuracy results are given in Table  2 . We compare LLR training to ADV  [16] , CURE  [17]  and TRADES  [27] , both with our re-implementation and the published models  8  . Note that our re-implementation using softplus activations perform at or above the published results for ADV, CURE and TRADES. This is largely due to the learning rate schedule used, which is the similar to the one used by TRADES  [27] . \n Results for Interestingly, for adversarial training (ADV), using the Multi-Targeted attack for evaluation gives significantly lower adversarial accuracy compared to Untargeted. For ImageNet, we compare against adversarial training (ADV)  [16]  and the denoising model (DE-NOISE)  [25] . The results are shown in Table  3 . For a perturbation radius of 4/255, LLR gets 47% adversarial accuracy under the Untargeted attack which is notably higher than the adversarial accuracy obtained via adversarial training which is 39.70%. Moreover, LLR is trained with just two-steps of PGD rather than 30 steps for adversarial training. The amount of computation needed for each method is further discussed in Sec 5.2.1. Further shown in Table  3  are the results for = 16/255. We note a significant drop in nominal accuracy when we train with LLR to perturbation radius 16/255. When testing for perturbation radius of 16/255 we also show that the adversarial accuracy under Untargeted is very poor (below 8%) for all methods. We speculate that this perturbation radius is too large for the robustness problem. Since adversarial perturbations should be, by definition, imperceptible to the human eye, upon inspection of the images generated using an adversarial attack (see Fig  F4 ) -this assumption no longer holds true. The images generated appear to consist of super-imposed object parts of other classes onto the target image. This leads us to believe that a more fine-grained analysis of what should constitute \"robustness for ImageNet\" is an important topic for debate. \n Runtime Speed For ImageNet, we trained on 128 TPUv3 cores  [9] , the total training wall time for the LLR network (4/255) is 7 hours for 110 epochs. Similarly, for the adversarially trained (ADV) networks the total wall time is 36 hours for 110 epochs. This is a 5× speed up. \n Accuracy Degradation: Strong vs Weak Evaluation The resulting model trained using LLR degrades gracefully in terms of adversarial accuracy when we increase the strength of attack, as shown in Fig 3  .  In particular, Fig  3a  shows that, for CIFAR-10, when the attack changes from Untargeted to Multi-Targeted, the LLR's accuracy remains similar with only a 2.18% drop in accuracy. Contrary to adversarial training (ADV), where we see a 5.64% drop in accuracy. We also see similar trends in accuracy in Table  2 . This could indicate that some level of obfuscation may be happening under standard adversarial training. As we empirically observe that LLR evaluates similarly under weak and strong attacks, we hypothesize that this is because LLR explicitly linearizes the loss surface. An extreme case would be when the surface is completely linear -in this instance the optimal adversarial perturbation would be found with just one PGD step. Thus evaluation using a weak attack is often good enough to get an accurate gauge of how it will perform under a stronger attack.  We use either the standard adversarial training objective (ADV-1, ADV-2) or the LLR objective (LLR-1, LLR-2) and taking one or two steps of PGD to maximize each objective. To train LLR-1/2, we only optimize the local linearity γ( , x), i.e. µ in Eq. (  8 ) is set to zero. We see that for adversarial training, as shown in Figs 4a, 4c, the loss surface becomes highly non-linear and jagged -in other words obfuscated. Additionally in this setting, the adversarial accuracy under our strongest attack is 0% for both, see Table  F3 . In contrast, the loss surface is smooth when we train using LLR as shown in Figs  4b, 4d . Further, Table  F3  shows that we obtain an adversarial accuracy of 44.50% with the LLR-2 network under our strongest evaluation. We also evaluate the values of γ( , x) for the CIFAR-10 test set after these networks are trained. This is shown in  \n Conclusions We show that, by promoting linearity, deep classification networks are less susceptible to gradient obfuscation, thus allowing us to do fewer gradient descent steps for the inner optimization. Our novel linearity regularizer promotes locally linear behavior as justified from a theoretical perspective. The resulting models achieve state of the art adversarial robustness on the CIFAR-10 and Imagenet datasets, and can be trained 5× faster than regular adversarial training. Figure 1 : 1 Figure 1: Example of gradient obfuscated surface. The color of the surface denotes the prediction of the network. \n Figure 2 : 2 Figure 2: Plots showing that γ( , x) (Eq (6)) is large (on the order of 10) when we train with just one or two \n 2 Figure 4 : 24 Figure 4: Comparing the loss surface, (x), after we train using just 1 or 2 steps of PGD for the inner maximization of either the adversarial objective (ADV) max δ∈B( ) (x + δ) or the linearity objective (LLR) γ( , x) = max δ∈B( ) (x + δ) − (x) − δ T ∇ (x) . Results are shown for image 126 in test set of CIFAR-10, the nominal label is deer. ADV-i refers to adversarial training with i PGD steps, similarly with LLR-i. \n Fig F3. The values of γ( , x) are comparable when we train with LLR using two steps of PGD to adversarial training with 20 steps of PGD. By comparison, adversarial training with two steps of PGD results in much larger values of γ( , x). \n Table 2 : 2 Model accuracy results for CIFAR-10. Our LLR regularizer performs the best under the strongest attack (highlighted column). (S) denotes softplus activation; (R) denotes ReLU activation; and models with (S, R) are our implementations. Robustness CIFAR-10: Wide-ResNet-28-8 (8/255) Methods Nominal FGSM-20 Untargeted Multi-Targeted Attack Strength Weak Strong Very Strong ADV[16] 87.25% 48.89% 45.92% 44.54% CURE[17] 80.76% 39.76% 38.87% 37.57% ADV(S) 85.11% 56.76% 53.96% 48.79% CURE(S) 84.31% 48.56% 47.28% 45.43% TRADES(S) 87.40% 51.63 50.46% 49.48% LLR (S) 86.83% 54.24% 52.99% 51.13% CIFAR-10: Wide-ResNet-40-8 (8/255) ADV(R) 85.58% 56.32% 52.34% 46.89% TRADES(R) 86.25% 53.38% 51.76% 50.84% ADV(S) 85.27% 57.94% 55.26% 49.79% CURE(S) 84.45% 49.41% 47.69% 45.51% TRADES(S) 88.11% 53.03% 51.65% 50.53% LLR (S) 86.28% 56.44% 54.95% 52.81% \n Table 3 : 3 The accuracy obtained are 49.79% and 55.26% respectively. Evaluation using Multi-Targeted attack consistently gave the lowest adversarial accuracy throughout. Under this attack, the methods which stand out amongst the rest are LLR and TRADES. Using LLR we get state of the art results with 52.81% adversarial accuracy. LLR gets 47% adversarial accuracy for 4/255 -7.30% higher than DENOISE and ADV. For 16/255, LLR gets similar robustness results, but it comes at a significant cost to the nominal accuracy. Note Multi-Targeted attacks for ImageNet requires looping over 1000 labels, this evaluation can take up to several days even on 50 GPUs thus is omitted from this table. The column of the strongest attack is highlighted. ImageNet: ResNet-152 (4/255) Methods PGD steps Nominal Untargeted Random-Targeted Accuracy Success Rate ADV 30 69.20% 39.70% 0.50% DENOISE 30 69.70% 38.90% 0.40% LLR 2 72.70% 47.00% 0.40% ImageNet: ResNet-152 (16/255) ADV [25] 30 64.10% 6.30% 40.00% DENOISE [25] 30 66.80% 7.50% 38.00% LLR 10 51.20% 6.10% 43.80% \n The annotations on each node denotes no. of PGD steps × no. of random restarts (see Appendix F.1). (3a), background color denotes whether the attack is Untargeted (blue) or Multi-Targeted (orange). (3b), we only use Untargeted attacks. Adversarial Accuracy 48 50 52 54 56 58 60 62 1 × 1 1 × 1 10 × 1 10 × 1 Stronger Attack → Untargeted 20 × 1 20 × 1 50 × 1 50 × 1 100 × 1 100 × 1 200 × 1 200 × 1 Multi Targeted 1000 × 20 1000 × 20 1000 × 1 1000 × 1 200 × 20 200 × 20 LLR ADV Adversarial Accuracy 38 40 42 44 46 48 50 1 × 1 1 × 1 10 × 1 10 × 1 Stronger Attack → 20 × 1 50 × 1 20 × 1 50 × 1 100 × 1 100 × 1 1000 × 1 200 × 1 1000 × 1 200 × 1 LLR ADV (a) CIFAR-10 (8/255) (b) ImageNet (4/255) Figure 3: Adversarial accuracy shown for CIFAR-10, (3a), and ImageNet, (3b), as we increase the strength of attack. (3a) shows LLR's adversarial accuracy degrades gracefully going from 53.32% to 51.14% (-2.18%) while ADV's adversarial accuracy drops from 54.43% to 48.79% (-5.64%). (3b) LLR remains 7.5% higher in terms of adversarial accuracy (47.20%) compared to ADV (39.70%). For ImageNet, see Fig3b, the adversarial accuracy trained using LLR remains significantly higher (7.5%) than the adversarially trained network going from a weak to a stronger attack. \n\t\t\t While computing the globally optimal adversarial example is NP-hard [12] , gradient descent with several random restarts was empirically shown to be quite effective at computing adversarial perturbations of sufficient quality. 2  This means that every pixel is perturbed independently by up to 4 units up or down on a scale where pixels take values ranging between 0 and 255. 3  We note that TRADES [27]  gets 55% against a much weaker attack; under our strongest attack, it gets 52.5%. 4  Baselines created are adversarial training, TRADES and CURE [17] . Contrary to CIFAR-10, we are currently unable to achieve consistent and competitive results on ImageNet at = 4/255 using TRADES. \n\t\t\t To measure γ( , x) we find max δ∈B( ) g(δ; x) with 50 steps of PGD using Adam as the optimizer and 0.1 as the step size. 6  Here, we imply an increase in the number of PGD steps for the inner maximization max δ∈B( ) (x + δ). \n\t\t\t We attempted to use TRADES on ImageNet but did not manage to get competitive results. Thus they are omitted from the baselines. \n\t\t\t Note the network published for TRADES [27]  uses a Wide-ResNet-34-10 so this is not shown in the table but under the same rigorous evaluation we show that TRADES get 84.91% nominal accuracy, 53.41% under Untargeted and 52.58% under Multi-Targeted. We've also ran ∞ DeepFool (not in the table as the attack is weaker) giving ADV(S): 64.29%, CURE(S): 58.73%, TRADES(S): 63.4%, LLR(S): 65.87%.", "date_published": "n/a", "url": "n/a", "filename": "NeurIPS-2019-adversarial-robustness-through-local-linearization-Paper.tei.xml", "abstract": "Adversarial training is an effective methodology to train deep neural networks which are robust against adversarial, norm-bounded perturbations. However, the computational cost of adversarial training grows prohibitively as the size of the model and number of input dimensions increase. Further, training against less expensive and therefore weaker adversaries produces models that are robust against weak attacks but break down under attacks that are stronger. This is often attributed to the phenomenon of gradient obfuscation; such models have a highly non-linear loss surface in the vicinity of training examples, making it hard for gradient-based attacks to succeed even though adversarial examples still exist. In this work, we introduce a novel regularizer that encourages the loss to behave linearly in the vicinity of the training data, thereby penalizing gradient obfuscation while encouraging robustness. We show via extensive experiments on CIFAR-10 and ImageNet, that models trained with our regularizer avoid gradient obfuscation and can be trained significantly faster than adversarial training. Using this regularizer, we exceed current state of the art and achieve 47% adversarial accuracy for ImageNet with ∞ adversarial perturbations of radius 4/255 under an untargeted, strong, white-box attack. Additionally, we match state of the art results for CIFAR-10 at 8/255.", "id": "441f58d7f5174d32fc8c6c2ff41baf34"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Tomasz Hollanek"], "title": "AI transparency: a matter of reconciling design with critique", "text": "In the age of ubiquitous computing, we are surrounded by objects that incorporate artificial intelligence solutions. We interact with different kinds of AI without realizing itusing online banking systems, searching for YouTube clips, or consuming news through social media-not really knowing how and when AI systems operate. Corporate strategies of secrecy and user interfaces that hide traces of AI-driven personalization combine with the inherent opacity of deep learning algorithms (whose inner workings are not directly comprehensible to human interpreters) to create a marked lack of transparency associated with all aspects of emerging technologies. It is in response to the widespread application of AI-based solutions to various products and services in the late 2010s that multiple expert groups-both national and international-have voiced the demand to 'open' the algorithmic black box, to audit, expound, and demystify AI. They claim that to ensure that the use of AI is ethical, we must design emerging systems to be transparent, explainable, and auditable.  1  The opening of the algorithmic black box, however, cannot be seen only as an engineering challenge. It is critique, as the underside of making, that prioritizes unboxing, debunking the illusion, seeing through-to reveal how an object really works. Critique-grounded in the tradition of Critical Theory and practiced by cultural studies, critical race theory, queer theory, as well as decolonial theory scholars, among others-moves beyond the technical detail to uncover the desires, ideologies, and social relations forged into objects, opening the black boxes of history, culture, and progress. In what follows, I argue that the calls for technological transparency demand that we combine the practice of design with critique. I relate the question of AI transparency to the broader challenge of responsible making, contending that future action must aim to systematically reconcile design-as a way of concealing-with critique-as a manner of revealing. \n Levels of opacity Many companies sell simple analytics tools as artificial intelligence, as something that supposedly supplants human intelligence to deliver better results. What is advertised as an 'AI solution' often relies on simple data analysis performed by human analysts. The use of metaphors and simplifications obfuscates human labor, labor that is outsourced, hidden away, in an invisible and immaterial factory, in a different part of the globe. According to Ian  Bogost (2015) , the 'metaphor of mechanical automation' is nothing more than a welldirected, but misleading, masquerade (n. pag.). Although the metaphor is only an approximation, a distortion, or even a 'caricature,' it convincingly plays the role of an accurate depiction of the whole. The term artificial intelligence, elusive, misleading and with a definition that has changed over time, forms the basis of the marketing stunt. Technology companies rely on abstract, overly schematic representations to simplify reality and arrive at an easily digestible, prepacked idea of the object, one that misrepresents the object's essence and overlooks its true composition, but also satiates the end user's curiosity. Other systems, as a matter of deliberate practice, incorporate complex data processing and machine learning surreptitiously. Shoshana  Zuboff (2019)  observes that the influence these systems have on our decision-making is 'designed to be unknowable to us  ' (p.11) ; that company strategies of misdirection serve as 'the moat that surrounds the castle and secures the action within' (p.65.)-a way for corporations like Google or Facebook to protect their secrets and mislead the public. These systems could, in theory, be designed to be more 'knowable.' Elements of the user interface could, for example, flag up when algorithmic operations are influencing the user's decision-making. Just like labels inform the consumer about the product's contents, the interfaces of Facebook and YouTube could announce to users that the information delivered by the platforms is algorithmically curated. Considering that only 24% of US college students realize Facebook automatically prioritizes certain posts and hides others  (Powers 2017) , such a feature would definitely be relevant. But the challenge of transparency at a time of unprecedented technological complexity cannot be approached only as a matter of failed (or indeed successful, depending on your position) communication. The 'opacity' of machine learning algorithms refers, after all, not only to 'institutional self-protection and concealment,' but also, as  Burrell (2016)  points out, to 'the mismatch between mathematical optimization in highdimensionality characteristic of machine learning and the demands of human-scale reasoning and styles of semantic interpretation' (p.2). The fundamental lack of transparency of systems that incorporate AI solutions relates not only to convoluted storytelling devised by marketing teams, or misleading interfaces and user experience design, but also-and most importantly-an emerging form of making brought about by the automation of cognitive tasks themselves. Considering this level of opacity of AI systems, a team of researchers from MIT's Intelligence and Decision Technologies Group developed a neural network named, suggestively, Transparency by Design Network  (Mascharka et al. 2018)  that not only performs 'human-like reasoning steps' to answer questions about the contents of images, but also 'visually renders its thought process' as it solves problems, allowing human analysts to interpret its decision-making. It is a deep learning system carrying out a sort of unboxing on itself, incorporating explainability in its very operations: a realization of the most common understanding of 'transparency' in the context of contemporary AI research. \n Transparency and critique The challenge of technological transparency that has now attracted the attention of policymakers has constituted a concern for cultural studies scholars, media theorists, and design philosophers for decades. In the early 1990s, the philosopher Paul Virilio (1994) noted that once 'synthetic vision' becomes a reality and the human subject is excluded from the process of observation of images 'created by the machine for the machine,' the power of statistical science to appear objective (and thus persuasive) will be 'considerably enhanced, along with its discrimination capacities' (p.75). Another prominent media theorist Friedrich  Kittler (2014)  expressed concerns about modern media technologies that are 'fundamentally arranged to undermine sensory perception.' Kittler wrote about a 'system of secrecy' based on user interfaces that 'conceal operations necessary for programming' and thus 'deprive users of the machine as a whole,' to suggest that perceiving the imitation, penetrating through the illusion of software 'that appears to be human,' is a fundamental challenge in the age of global-scale computing  (pp. 221-24) . Transparency, as Adrian Weller (2017) has poignantly noted, is an ambiguous term that will mean different things to different people. For the user, a transparent system will 'provide a sense for what [it] is doing and why,' while for an expert or regulator, it will enable auditing 'a prediction or decision trail in detail' (p.3). The calls for technological transparency have thus been filtered down to reach various stakeholder groups with different meanings and representing different interests. But what seems consistent in all of Footnote 1 (continued) 2019). Another interdisciplinary group of experts working under the auspices of IEEE (the world's largest professional association for electronic and electrical engineers) published, in 2019, the first edition of Ethically Aligned Design, a set of actionable recommendations on how to align design practices with society's values and principles, stressing that the 'standards of transparency, competence, accountability, and evidence of effectiveness should govern the development of autonomous and intelligent systems' (p. 5). these diverse takes on the development, use, and regulation of technology is that transparency is framed as a matter of design. In what follows, I problematize this claim, arguing that design, in the most fundamental sense, relies on concealment and obfuscation. I contend that only the sort of transparency that arises from critique-a method of theoretical examination that, by revealing pre-existing power structures, aims to challenge them-can help us produce technological systems that are less deceptive and more just. \n Design as blackboxing \n Art and artifice Coined in 1956 by John McCarthy, the term 'artificial intelligence' had its critics among those who attended the Dartmouth Conference (which famously established the field of AI); Arthur Samuel argued that 'the word artificial makes you think there's something kind of phony about this,  […]  or else it sounds like it's all artificial and there's nothing real about this work at all  ' (in: McCorduck 2004, p. 115) . The historian of AI Pamela McCorduck notes that while other terms, such as 'complex information processing,' were also proposed, it was 'artificial intelligence' that endured the trial of time. According to her, it is 'a wonderfully appropriate name, connoting a link between art and science that as a field AI indeed represents' (p. 115). She is referring indirectly here to the origins of the word artificial; in Latin, artificialis means 'of or belonging to art,' while artificium is simply a work of art, but also a skill, theory, or system. When the philosopher Vilém Flusser traced the etymology of the word 'design' in his The Shape of Things: A Philosophy of  Design (1999) , he referred to this relationship between art and artifice to argue that all human production, all culture, can be defined as a form of trickery. Flusser rejects the distinction between art and technology, and goes back to these ancient roots: the Greek for 'trap' is mechos (mechanics, machine); the Greek techne corresponds to the Latin ars; an artifex means a craftsman or artist, but also a schemer or trickster-to demonstrate that in their essence all forms of making are meant to help us 'elude our circumstances,' to cheat our own nature. Culture itself becomes a delusion brought about by means of design-a form of selfdeception that makes us believe we can free ourselves from natural restrictions by producing a world of artifice. From doors to rockets, from tents to computer screens, from pencils to mechanized intelligences, Flusser selects his examples to show that, ultimately, any involvement with culture is based on deception: sometimes 'this machine, this design, this art, this technology is intended to cheat gravity, to fool the laws of nature' (ch.1, n. pag.)-and sometimes to trick ourselves into thinking we control both gravity and the laws of nature. In that sense, art and technology are representative of the same worldview in which cultural production must be deceptive/artful enough to enable humans to go beyond the limits of what is (humanly) possible. Flusser refers to the act of weaving to explain the 'conspiratorial, even deceitful' (ch.18) character of design. In the process of carpet production, he points out, knotting is meant to deny its own warp, to hide the threads behind a pattern, so that anyone stepping on the finished rug perceives it as a uniform surface, according to the designer's plan. He offers weaving as one of the primordial forms of cultural production to embody trickery, but the same holds true for any form of design. The trick is always based on misdirection, shifting the end user's attention from the material to the application, from the current state of things to emerging possibilities and new futures. Designing is a methodical way of crafting alternative realities out of existing materials-a process of casting the intended shape onto the chosen fabric so as to create a new possibility. The material used in that process must, so to speak, dematerialize: it has to disappear from view and give way to the new object-to abstract the end result from the point of origin and the labor process. By obfuscating some components while exhibiting others, 'ideal' design enables an end user's cognitive efficiency. \n Patterns, layers, and repetitions For Flusser, any product of human making is both an object and an obstacle-Latin objectum, Greek problema-or, more specifically, any object is also an 'obstacle that is used for removal of obstacles' (ch.9). To move forward, we solve problems that lie ahead and obstruct our way; we produce objects that help us remove these obstacles; but the same objects turn into obstacles for those that come after us. In other words, since the results of human problem-solving are stored in objects, progress involves obfuscation and forgetting. We come up with a solution and, with time, this singular idea turns into a pattern; others use the already established template to produce new, more complex structures and these structures turn into new patterns, covering up previous layers of design with new design. To expedite the process of production, to advance, to move faster, the designer turns to these conventions and templates, choosing from a menu of preprogrammed options-or abstracting new rules based on previous patterns. And as the complexity of the production process increases, the reliance on patterns grows too. New design always depends on previous design, and this ultimate dependence on patterns and abstractions complicates understanding the process in its totality. In the age of ubiquitous computing, speaking of obfuscation by design becomes of particular importance. In 2015, Benjamin Bratton called his model of the new kind of layering brought about by planetary-scale computation 'the Stack': 'an accidental megastructure, one that we are building both deliberately and unwittingly and is in turn building us in its own image' (p.5). New technologies 'align, layer by layer, into something like a vast, if also incomplete, pervasive if also irregular, software and hardware Stack' (p.5). This makes it hard to perceive the Stack's overarching structure, indeed, to see it as design, however incidental. Today, we produce new technologies, new objects, to see, know, and feel more, to register what is normally hidden from our view, meanwhile, creating complex systems based on multiple, invisible layers and algorithmic operations whose effects are not always comprehensible even to the designers themselves. \n Automations and automatisms In her comprehensive account of what she calls 'surveillance capitalism,' Shoshana Zuboff points out the dangers of technological illusion-'an enduring theme of social thought, as old as the Trojan horse' (p.16)-that serves the new economic project in rendering its influence invisible. Surveillance capitalism claims 'human experience as free raw material for translation into behavioral data,' and turns that data into 'prediction products' that can later be sold to advertisers (p.8). Echoing the work of philosophers such as Bernard  Stiegler (2014 Stiegler ( , 2015  or Antoinette  Rouvroy (2016) , Zuboff argues that the ultimate goal of this new form of capitalism is 'to automate us,' by reprogramming our behavior and desires. Various internet platforms that dominate the market prompt us to action, influence our decision making, relying on big data analyses of our preference trends online. Automated systems create statistical models to profile users, tracing any emerging patterns in countless interactions with digital products; patterns turn into further abstractions, new models that are later reflected in new products and solutions, which end up 'automating' us, guiding our decision-making without our knowing. But is this process specific to AI-enhanced personalization under surveillance capitalism? Bratton has recently argued that what 'at first glance looks autonomous (self-governing, set apart, able to decide on its own) is, upon closer inspection, always also decided in advance by remote ancestral agents and relays, and is thus automated as well  ' (2019, loc.345, n. pag.) . Any decision taken now relies on multiple decisions taken in the past; new design depends on previous design; a new object coalesces from an aggregation of old solutions. Culture is an amalgamation of such objectsobjects that, ironically, become obstacles because they are meant to enable our cognitive efficiency. A tool becomes an obstacle because the results of our problem-solving and labor are already stored within it; a tool must never be seen as a tool, as its use must be intuitive-it must remain imperceptible; any new tool meant to advance the process is made with existing tools, and so the emerging layering of design in the Anthropocene makes it harder to distinguish between tool and fabric. Extending this to the ongoing automation of cognitive tasks in the age of ubiquitous computing, the phenomenon takes on new scale. This is why the emerging need for transparency refers not so much to company politics of disinformation or algorithmic black boxes, as to the very essence of our culture, as a process of knowledge production, pattern formation, and concealment. Particular problems caused by the widespread adoption of automated decision-making systems, such as algorithmic bias, can have specific, targeted, solutions in the form of new policy, engineering standards, or better education. But a shift of focus from the particular to the total is more than an exercise in theory-it makes us realize that transparency has never been at the heart of our making, that design has always been a form of blackboxing. There is, in that sense, something deeply anti-cultural about transparency. Or, putting it differently, there is nothing natural about transparency by design: we have been programmed to cover up as we make, not the opposite. The ongoing transformation of lived experiences into data is a new analytical paradigm that demands our intervention, truly calls for an 'unboxing,' an excavation of processes and data trails. But the opening of the algorithmic black box cannot be viewed only as a technical issue-precisely because any solution is, first and foremost, a result of cultural blackboxing. While contemporary debates on AI focus on transparency as a direct response to the opacity of algorithms, what we are in need of are approaches that aim to 'unbox' new technologies as objects-obstacles, solutions that aim towards cognitive automation, products that store the results of problem-solving performed 'by remote ancestral agents,' and that can thus perpetuate injustices via automatically accepted patterns and norms. \n Critique as unboxing \n Apparent transparencies Among entries on subjects such as theology, economics, and medicine, Denis Diderot and Jean le Rond d'Alembert included in their Dictionary of the Sciences, Arts, and Crafts, entries on artisanal practices that detail the individual steps in the processes of production adopted in clockmaking, tailoring, woodworking, and many others. One such entry focuses on the making of artificial flowers: the first plate (Fig.  1 ) depicts a dozen workers scattered across the main workshop area, performing different tasks at various stages of manufacturing, while following pages of illustrations showcase the most popular templates used to emboss specific petal shapes onto fabric, with a final plate celebrating the finished commodity. By bringing to view the backstages of production, the Encyclopedia was essentially undesigning, reversing the process of 'conspiratorial weaving' described by Flusser. Now, in an age of growing technological complexity, shaped by significant degrees of cognitive automation, there is a need for a similar undesigning of new technologies. The artist Todd McLellan's photographs (Fig.  2 ) that document his multiple attempts at taking various objects apart are a suggestive illustration of this challenge in the age of extreme technological complexity. We might dissemble our smartphone, but learning what is hidden beneath the interactive surface of the touchscreen will never give us an indication of how the device really works and, more significantly, in whose interest. The meaningless innards of the device become symbolic of the contestable quality that transparency really is-if we think of it as a condition for, or indeed a guarantee of, understanding. Critical undesigning cannot be confused with a simple act of reverse engineering. There can be transparency without critique, or apparent transparency: but a sort of transparency that does not arise from critical processes of unboxing is unlikely to advance comprehension. In his lecture on black boxes, Galloway (2010) relates Marx's idea of descent into 'the hidden abode of production' (p.7), as a means of uncovering capital relations forged into commodities, to 'traditions of critical inquiry, in which objects were unveiled or denaturalized to reveal their inner workings-from Descartes's treatise on method […] to the Freudian plumbing of the ego' (p.5). Based on the assumption that the surface is merely a superficial facade to be penetrated by means of critique, these theories prioritized the interior and perceived objects as 'mystical black boxes waiting to be deciphered to reveal the rationality (of history, of totality) harbored within' (p.3). For the purpose of this article, critique is understood as a broad set of methodologies, grounded in the tradition of Critical Theory, that perform a metaphorical dismantling of objects to reveal how hidden and immaterial layers of design reflect social and economic structures-and how the power relations these structures generate become the sources of injustice, oppression, and exploitation. Critique's ultimate goal is to uncover and challenge the system(s) that objects of design engender; revelation is conceived of as the condition necessary for resistance-and systemic transformation. Looking beyond individual design flaws (and fixes), critique points to those 'ancestral relays' that automate our thinking-to patterns, repetitions, and automatisms so deeply ingrained, weaved into the fabric of our culture, that they become imperceptible-in particular to those who do not experience the injustices resulting from the adoption of already established patterns. \n Critique in the age of AI A former YouTube employee, Guillaume Chaslot, has coined the term Algotransparency to describe an experiment in which he investigates the terms appearing most frequently in the titles of videos recommended by YouTube. A program developed by Chaslot and his team traces thematic patterns in YouTube recommendations to prove there exists a systemic bias that promotes controversial clips. His research suggests Google's platform indeed 'systematically amplifies videos that are divisive, sensational and conspiratorial'  (Lewis 2018) -that the recommendations are not related to the individual user's interests (as the company claims), but rather-exploit controversy to boost clickability. Algotransparency attempts to unbox the logic of YouTube's copyrightprotected recommendation algorithm without directly looking into the system's black box, concentrating only on the effects of its activity. This specific experiment gives a good indication of where we should be directing our attention: focusing not so much on how YouTube operates, as on why it works at all. This question extends beyond the technicality of the algorithm, to more widely interrogate the forces orchestrating our consumption of digital goods and whose interests they serve-what Zuboff calls surveillance capitalism, or what Stiegler refers to as hyperindustrialism. Ian Bogost (2015) has argued that the illusion of automation in technology-the trick that misdirects our attention from essential questions about human decision-making incorporated into emerging systems-breaks down 'once you bother to look at how even the simplest products are really produced.' In 2014 he collaborated with Alexis Madrigal to analyze Netflix's recommendation system and demonstrate that the platform's operations are distributed among so many different agents-including human curators who hand-tag all Netflix content-'that only a zealot would call the end result an algorithm'(Bogost 2015). Many experiments and critical projects try to achieve something similar: debunk the illusion of software by exposing AI as processual and collaborative, tracing the results of data analysis back to human decisions, biases, and labor. In their Anatomy of an AI System, for instance, Crawford and Joler (2018) present a figurative dissection of Amazon's Echo device that brings to view the invisible mechanisms and dynamisms that the product encapsulates (Fig.  3 ). The detailed mapping of various objects and agents, as well as multiple layers of interaction between those elements, constitutes a representation of the system as composed not only of hardware and software, data and computation, but also human labor and planetary resources. Critique in the age of extreme technological complexity is as much about dissecting and penetrating, as it is about charting the invisible and immaterial terrains of interaction, analysis, consumption, and computation; mapping wider relations between energies, influences, and resources under surveillance capitalismpatterns of exploitation of both people and environments that the production of objects/obstacles entails. In another project, Crawford teamed up with the artist Trevor Paglen to carry out what they call an archeology of datasets, such as ImageNet, used in machine learning to train AI to recognize specific elements of images-sets that can also become sources of bias inscribed into emerging systems. By excavating the datasets' underlying structures,  Crawford and Paglen (2019)  aim to reveal their implicit meanings: 'we have been digging through the material layers, cataloguing the principles and values by which something was constructed, and analyzing what normative patterns of life were assumed, supported, and reproduced.' The blackboxed Earth, a world deeply transformed by ubiquitous computing, by various layers of what Bratton calls the Stack, demands this form of unearthing. Successful critique in the age of AI exposes the technology as relying on human cognition and decision-making; more broadly, critique reveals the constellation of objects/obstacles as products of layered problem-solving, a flawed process that is necessarily tainted by pre-existing patterns and abstractions, biases and beliefs. Prioritizing reflection over efficiency, critique becomes a methodical way of resisting our reliance on patterns-patterns that allow us to move faster, but that can also harbor previously made assumptions-about gender (Costanza-Chock 2018) or race  (Benjamin 2019)  as particularly poignant examples-and thus perpetuate, rather than challenge, pre-existing forms of injustice. \n Reconciling design with critique In keeping up with the societal demand for transparent AI, the big players of the tech industry have been introducing changes in their engineering standards and organizational structures, hiring ethicists and policy specialists to cooperate with their product development teams. In 2016, Microsoft established the Aether Committee, a body of senior advisors to the company's leadership, that provides guidance 'on rising questions, challenges, and opportunities with the development and fielding of AI technologies' (2020), and oversees the work of other teams 'to ensure that AI products and services align with Microsoft's AI principles'-which include transparency and accountability. In 2017, DeepMind set up its Ethics and Society team 'to guide the responsible development and deployment of AI.' The team composed of 'ethicists and policy researchers' collaborates with the company's AI research team 'to understand how technical advances will impact society, and find ways to reduce risk.' Smaller industry players who decide to follow suit, but cannot afford to establish their own ethics 'departments,' begin to enlist the help of 'ethical auditing' companies; Glassbox, for example, is a tech consultancy startup, founded in 2018, that aims to 'provide clarity to the black box' by analyzing software products for signs of bias and training the client company's employees about systemic injustices. This way, elements of critique that reveal potential implications of human decision-making in design are supposed to become part of the production pipeline. These sites of interaction between 'humanists' and 'technologists' in the industry-even if, in some cases, they amount to nothing more than backdrops for press releasesdeserve our attention. Specifically, they require of us a comprehensive rethinking of what satisfies our desire for transparency in the age of extreme technological complexity. Can a system of checks and balances in the industry, an ongoing negotiation between blackboxing and unboxing, lead to anything more than design that anticipates critique? Is critique from within the industry necessarily a compromise and, therefore, nothing more than another step in the process of production of objects that are also obstacles? Must critique be external to the process of designing to remain genuine? If design is, fundamentally, blackboxing and automation, and critique is unboxing that aims to reverse the process of 'conspiratorial weaving,' then we could conclude that these two sides of human activity are in stark opposition to one another-that design is incompatible with critique. Instituting a real change in the way we move forward must focus precisely on tackling this ostensible impossibility-on reconciling design with critique, progress with suspension, production with reflection. The calls for transparency by design require that the 'making' itself be reinvented to incorporate critique. If a systemic transformation depends on a new-found compatibility between design and critique, then the designers of emerging systems should turn to already existing, alternative design practices to learn what combining the processes of making and critique might entail. Anthony Dunne and Fiona Raby, who have been pioneers in the field of 'critical design' since the late 1990s, have been advocating for design understood as 'critical thought translated to materiality  ' (2013, p.35 ). An object of design in their framing must become a critical challenge-as much for the designer, as for the user: 'it encourages people to question, in an imaginative, troubling, and thoughtful way, everydayness and how things could be different.' (p.189) More recently, Ratto (2011) coined the term 'critical making' to describe a design process that focuses on 'the act of shared construction itself as an activity and a site for enhancing and extending conceptual understandings of critical sociotechnical issues' (p.254)-with those who take part as the agents of critique. For Dunne and Raby, design has become 'so absorbed in industry, so familiar with dreams of industry, that it is almost impossible to dream its own dreams' (p.88). The suggestion is that the challenge lies not so much in the incompatibility between making and critique, as between the futures imagined by the industry and the dreams functioning outside of it. While elements of critique-gender critique and critical race theory in particular-seem to have already penetrated sections of the industry in the form of the mentioned ethics auditing services, reconciling the critique of surveillance capitalism and hyperindustrialism, the forces behind most of today's innovation, with the design of new technologies within corporate structures appears a considerable (and counterintuitive) feat. Perhaps this is where we should direct our attention: more research is needed on how practices such as critical design and critical making can influence the process of AI design; how critique can be operationalized within the industry to challenge industrial values and visons, including the idea of 'progress' itself. In a recently published volume on the practice of 'undesign' (McNamara and Coombs 2019), Cameron Tonkinwise's essay proposes what he calls 'anti-progressive' design as a means of interrogating the designers' internalized desire for 'progress.' While users, as he rightly observes, are willing 'to unlearn and relearn modes of interaction' if what is new is also 'easier and more convenient, and hopefully more effective and pleasurable' (p.76), it is the designers who should learn how 'not to prefer progress, or how to prefer what does not feel like progress' (p.81). Tonkinwise argues it is the designers' duty 'to find a way to pursue the destructively preferable without casting the resulting change as progress: what is preferable are futures that no longer appear to be mere advancements of what currently exists  ' (p.81) . This is to say that the responsibility for future action lies, primarily, with the designers: the human makers who, as products of a specific culture, are being increasingly challenged to become aware of their own biases and automatisms that predetermine their actions and choices. For designers, combining design with critique, rather than an attempt at making things transparent, would constitute an attempt at becoming self-conscious. Flusser argued that a renewed form of culture would have to be a culture 'aware of the fact that it was deceptive' (ch.1). To rethink technological transparency, we should first recognize that the designer has always been a trickster laying out traps, technologizing misdirection to pave the way forward. All aspects of design-practical, political, moral-would have to reflect this awareness: as we move forward, we must acknowledge that any problem solved now will also form a trap for those coming after us. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Fig. 1 Fig. 2 12 Fig. 1 Maker of artificial flowers, 1765 (https ://hdl.handl e.net/2027/ spo.did22 22.0001.451) \n Fig. 3 3 Fig. 3 Kate Crawford and Vladan Joler, Anatomy of an AI System, 2018 (courtesy of the artists) \n\t\t\t The High-Level Expert Group on AI convened by the European Commission presented its Ethics Guidelines for Trustworthy Artificial Intelligence in the early 2019. The document identifies several key characteristics of a system that can be deemed trustworthy, which include transparency, defined as a form of traceability of data, operations, and business models that shape the end product (AI HLEG", "date_published": "n/a", "url": "n/a", "filename": "Hollanek2020_Article_AITransparencyAMatterOfReconci.tei.xml", "abstract": "In the late 2010s, various international committees, expert groups, and national strategy boards have voiced the demand to 'open' the algorithmic black box, to audit, expound, and demystify artificial intelligence. The opening of the algorithmic black box, however, cannot be seen only as an engineering challenge. In this article, I argue that only the sort of transparency that arises from critique-a method of theoretical examination that, by revealing pre-existing power structures, aims to challenge them-can help us produce technological systems that are less deceptive and more just. I relate the question of AI transparency to the broader challenge of responsible making, contending that future action must aim to systematically reconcile design-as a way of concealing-with critique-as a manner of revealing.", "id": "d848f2c2c8d3985de73351758eb000db"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Deepak Ramachandran", "Eyal Amir"], "title": "Bayesian Inverse Reinforcement Learning", "text": "Introduction The Inverse Reinforcement Learning (IRL) problem is defined in  [Russell, 1998]  as follows: Determine The reward function that an agent is optimizing. Given 1) Measurement of the agent's behaviour over time, in a variety of circumstances 2) Measurements of the sensory inputs to that agent; 3) a model of the environment. In the context of Markov Decision Processes, this translates into determining the reward function of the agent from knowledge of the policy it executes and the dynamics of the state-space. There are two tasks that IRL accomplishes. The first, reward learning, is estimating the unknown reward function as accurately as possible. It is useful in situations where the reward function is of interest by itself, for example when constructing models of animal and human learning or modelling opponent in competitive games. Pokerbots can improve performance against suboptimal human opponents by learning reward functions that account for the utility of money, preferences for certain hands or situations and other idiosyncrasies  [Billings et al., 1998] . There are also connections to various preference elicitation problems in economics  [Sargent, 1994] . The second task is apprenticeship learning -using observations of an expert's actions to decide one's own behaviour. It is possible in this situation to directly learn the policy from the expert  [Atkeson and Schaal, 1997] . However the reward function is generally the most succint, robust and transferable representation of the task, and completely determines the optimal policy (or set of policies). In addition, knowledge of the reward function allows the agent to generalize better i.e. a new policy can be computed when the environment changes. IRL is thus likely to be the most effective method here. In this paper we model the IRL problem from a Bayesian perspective. We consider the actions of the expert as evidence that we use to update a prior on reward functions. We solve reward learning and apprenticeship learning using this posterior. We perform inference for these tasks using a modified Markov Chain Monte Carlo (MCMC) algorithm. We show that the Markov Chain for our distribution with a uniform prior mixes rapidly, and that the algorithm converges to the correct answer in polynomial time. We also show that the original IRL is a special case of Bayesian IRL (BIRL) with a Laplacian prior. There are a number of advantages of our technique over previous work: We do not need a completely specified optimal policy as input to the IRL agent, nor do we need to assume that the expert is infallible. Also, we can incorporate external information about specific IRL problems into the prior of the model, or use evidence from multiple experts. IRL was first studied in the machine learning setting by  [Ng and Russell, 2000]  who described algorithms that found optimal rewards for MDPs having both finite and infinite states. Experimental results show improved performance by our techniques in the finite case. The rest of this paper is organised as follows: In section 2 we define our terms and notation. Section 3 presents our Bayesian model of the IRL process. Section 4 discusses how to use this model to do reward learning and apprenticeship learning while section 5 discusses the sampling procedure. Sections 6, 7 and 8 then present experimental results, related work and our conclusions respectively. \n Preliminaries We recall some basic definitions and theorems relating to Markov Decision Processes and Reinforcement Learning. A (finite) Markov Decision Problem is a tuple (S, A, T, γ, R) where • S is a finite set of N states. • A = {a 1 , . . . , a k } is a set of k actions. • T : S × A × S → [0, 1] is a transition probability func- tion. • γ ∈ [0, 1) is the discount factor. • R : S → R is a reward function, with absolute value bounded by R max . The rewards are functions of state alone because IRL problems typically have limited information about the value of action and we want to avoid overfitting. A Markov Decision Process (MDP) is a tuple (S, A, T, γ), with the terms defined as before but without a reward function. To avoid confusion we will use the abbreviation MDP only for Markov Decision Processes and not Problems. We adopt the following compact notation from  [Ng and Russell, 2000]  for finite MDPs : Fix an enumeration s 1 . . . s N of the finite state space S. The reward function (or any other function on the state-space) can then be represented as an Ndimensional vector R, whose ith element is R(s i ). A (stationary) policy is a map π : S → A and the (discounted, infinite-horizon) value of a policy π for reward function R at state s ∈ S,denoted V π (s, R) is given by: V π (s t1 , R) = R(s t1 )+E st 1 ,st 2 ,... [γR(s t2 )+γ 2 R(s t3 )+. . . |π] where P r(s ti+1 |s ti , π) = T (s ti , π(s ti ), s ti+1 ). The goal of standard Reinforcement Learning is to find an optimal policy π * such that V π (s, R) is maximized for all s ∈ S by π = π * . Indeed, it can be shown (see for example  [Sutton and Barto, 1998] ) that at least one such policy always exists for ergodic MDPs. For the solution of Markov Decision Problems, it is useful to define the following auxilliary Q-function: Q π (s, a, R) = R(s) + γE s ∼T (s,a,•) [V π (s , R)] We also define the optimal Q-function Q * (•, •, R) as the Qfunction of the optimal policy π * for reward function R. Finally, we state the following result concerning Markov Decision Problems (see  [Sutton and Barto, 1998] ) : Theorem 1 (Bellman Equations). Let a Markov Decision Problem M = (S, A, T, γ, R) and a policy π : S → A be given. Then, 1. For all s ∈ S, a ∈ A, V π and Q π satisfy V π (s) = R(s) + γ s T (s, π(s), s )V π (s ) (1) Q π (s, a) = R(s) + γ s T (s, a, s )V π (s ) 2. π is an optimal policy for M iff, for all s ∈ S, π(s) ∈ argmax a∈A Q π (s, a) (2) 3 Bayesian IRL IRL is currently viewed as a problem of infering a single reward function that explains an agent's behaviour. However, there is too little information in a typical IRL problem to get only one answer. For example, consider the MDP shown in Figure  1 . There are at least three reasonable kinds of reward functions: R 1 (•) has high positive value at s 1 (and low values elsewhere) which explains why the policy tries to return to this state, while R 2 (•) and R 3 (•) have high values at s 2 and s 3 respectively. Thus, a probability distribution is needed to represent the uncertainty. S 0 S 1 S 3 S 2 a 1 a 1 a 1 a 1 0.4 0.3 0.3 a 2 a 2 a 2 a 2 Figure 1: An example IRL problem. Bold lines represent the optimal action a 1 for each state and broken lines represent some other action a 2 . Action a 1 in s 1 has probabilities 0.4,0.3 and 0.3 of going to states s 1 , s 2 , s 3 respectively, and all other actions are deterministic. \n Evidence from the Expert Now we present the details of our Bayesian IRL model (Fig.  2 ). We derive a posterior distribution for the rewards from a prior distribution and a probabilistic model of the expert's actions given the reward function. Consider an MDP M = (S, A, T, γ) and an agent X (the expert) operating in this MDP. We assume that a reward function R for X is chosen from a (known) prior distribution P R . The IRL agent receives a series of observations of the expert's behaviour O X = {(s 1 , a 1 ), (s 2 , a 2 ) . . . (s k , a k )} which means that X was in state s i and took action a i at time step i. For generality, we will not specify the algorithm that X uses to determine his (possibly stochastic) policy, but we make the following assumptions about his behaviour: 1. X is attempting to maximize the total accumulated reward according to R. For example, X is not using an epsilon greedy policy to explore his environment. 2. X executes a stationary policy, i.e. it is invariant w.r.t. time and does not change depending on the actions and observations made in previous time steps. For example, X could be an agent that learned a policy for (M, R) using a reinforcement learning algorithm. Because the expert's policy is stationary, we can make the following independence assumption: P r X (O X |R) = P r X ((s 1 , a 1 )|R)P r X ((s 2 , a 2 )|R) . . . P r X ((s k , a k )|R) The expert's goal of maximizing accumulated reward is equivalent to finding the action for which the Q * value at each state is maximum. Therefore the larger Q * (s, a) is, the more likely it is that X would choose action a at state s. This likelihood increases the more confident we are in X 's ability to select a good action. We model this by an exponential distribution for the likelihood of (s i , a i ), with Q * as a potential function: P r X ((s i , a i )|R) = 1 Z i e αX Q * (si,ai,R) where α X is a parameter 1 representing the degree of confidence we have in X 's ability to choose actions with high X R α X (s1, a1) (s2, a2) (s k , a k ) Figure  2 : The BIRL model value. This distribution satisfies our assumptions and is easy to reason with. The likelihood of the entire evidence is : P r X (O X |R) = 1 Z e αX E(OX ,R) where E(OX , R) = P i Q * (si, ai, R) and Z is the appropriate normalizing constant. We can think of this likelihood function as a Boltzmann-type distribution with energy E(O X , R) and temperature 1 αX . Now, we compute the posterior probability of reward function R by applying Bayes theorem, P r X (R|O X ) = P r X (O X |R)P R (R) P r(O X ) = 1 Z e αX E(OX ,R) P R (R) (3) Computing the normalizing constant Z is hard. However the sampling algorithms we will use for inference only need the ratios of the densities at two points, so this is not a problem. \n Priors When no other information is given, we may assume that the rewards are independently identically distributed (i.i.d.) by the principle of maximum entropy. Most of the prior functions considered in this paper will be of this form. The exact prior to use however, depends on the characteristics of the problem: 1. If we are completely agnostic about the prior, we can use the uniform distribution over the space −R max ≤ R(s) ≤ R max for each s ∈ S. If we do not want to specify any R max we can try the improper prior P (R) = 1 for all R ∈ R n . 2. Many real world Markov decision problems have parsimonious reward structures, with most states having negligible rewards. In such situations, it would be better to assume a Gaussian or Laplacian prior:  P Gaussian (R(s) = r) = 1 √ 2πσ e − r P Beta (R(s) = r) = 1 ( r Rmax ) 1 2 (1 − r Rmax ) 1 2 , ∀s ∈ S In section 6.1, we give an example of how more informative priors can be constructed for particular IRL problems. \n Inference We now use the model of section 3 to carry out the two tasks described in the introduction: reward learning and apprenticeship learning. Our general procedure is to derive minimal solutions for appropriate loss functions over the posterior (Eq. 3). Some proofs are omitted for lack of space. \n Reward Learning Reward learning is an estimation task. The most common loss functions for estimation problems are the linear and squared error loss functions: L linear (R, R) = R − R 1 L SE (R, R) = R − R 2 where R and R are the actual and estimated rewards, respectively. If R is drawn from the posterior distribution (3), it can be shown that the expected value of L SE (R, R) is minimized by setting R to the mean of the posterior (see  [Berger, 1993] ). Similarily, the expected linear loss is minimized by setting R to the median of the distribution. We discuss how to compute these statistics for our posterior in section 5. It is also common in Bayesian estimation problems to use the maximum a posteriori (MAP) value as the estimator. In fact we have the following result: Theorem 2. When the expert's policy is optimal and fully specified, the IRL algorithm of  [Ng and Russell, 2000 ] is equivalent to returning the MAP estimator for the model of (3) with a Laplacian prior. However in IRL problems where the posterior distribution is typically multimodal, a MAP estimator will not be as representative as measures of central tendency like the mean. \n Apprenticeship Learning For the apprenticeship learning task, the situation is more interesting. Since we are attempting to learn a policy π, we can formally define the following class of policy loss functions: L p policy (R, π) = V * (R) − V π (R) p where V * (R) is the vector of optimal values for each state acheived by the optimal policy for R and p is some norm. We wish to find the π that minimizes the expected policy loss over the posterior distribution for R. The following theorem accomplishes this: Theorem 3. Given a distribution P (R) over reward functions R for an MDP (S, A, T, γ), the loss function L p policy (R, π) is minimized for all p by π * M , the optimal policy for the Markov Decision Problem M = (S, A, T, γ, E P [R]). Proof. From the Bellman equations (1) we can derive the following: V π (R) = (I − γT π ) −1 R (4) where T π is the |S|×|S| transition matrix for policy π. Thus, for a state s ∈ S and fixed π, the value function is a linear function of the rewards: V π (s, R) = w(s, π) • R where w(s, π) is the s'th row of the coefficient matrix (I − γT π ) −1 in (4). Suppose we wish to maximize E[V π (s, R)] alone. Then, max π E[V π (s, R)] = max π E[w(s, π)•R] = max π w(s, π)•E[R] By definition this is equal to V * M (s), the optimum value function for M , and the maximizing policy π is π * M , the optimal policy for M . Thus for all states s ∈ S, E[V π (s, R)] is maximum at π = π * M . But V * (s, R) ≥ V π (s, R) for all s ∈ S, reward functions R, and policies π. Therefore E[L p policy (π)] = E( V * (R) − V π (R) p ) is minimized for all p by π = π * M . So, instead of trying a difficult direct minimization of the expected policy loss, we can find the optimal policy for the mean reward function, which gives the same answer. \n Sampling and Rapid Convergence We have seen that both reward learning and apprenticeship learning require the mean of the posterior distribution. However the posterior is complex and analytical derivation of the mean is hard, even for the simplest case of the uniform prior. Instead, we generate samples from these distributions and then return the sample mean as our estimate of the true mean of the distribution. The sampling technique we use is an MCMC algorithm GridWalk (see  [Vempala, 2005] ) that generates a Markov chain on the intersection points of a grid of length δ in the region R |S| (denoted R |S| /δ). However, computing the posterior distribution at a particular point R requires calculation of the optimal Q-function for R, an expensive operation. Therefore, we use a modified version of GridWalk called PolicyWalk (Figure  3 ) that is more efficient: While moving along a Markov chain, the sampler also keeps track of the optimal policy π for the current reward vector R. Observe that when π is known, the Q function can be reduced to a linear function of the reward variables, similar to equation 4. Thus step 3b can be performed efficiently. A change in the optimal policy can easily be detected when moving to the next reward vector in the chain R, because then for some (s, a) ∈ (S, A), Q π (s, π(s), R) < Q π (s, a, R) by Theorem 1. When this happens, the new optimal policy is usually only slightly different from the old one and can be computed by just a few  of R in R |S| /δ. (b) Compute Q π (s, a, R) for all (s, a) ∈ S, A. (c) If ∃(s, a) ∈ (S, A), Q π (s, π(s), R) < Q π (s, a, R) i. π := PolicyIteration(M, R, π) ii. Set R := R and π := π with probability min{1, P ( R,π) P (R,π) } Else i. Set R := R with probability min{1, P ( R,π) P (R,π) } 4. Return R Figure  3 : PolicyWalk Sampling Algorithm steps of policy iteration (see  [Sutton and Barto, 1998] ) starting from the old policy π. Hence, PolicyWalk is a correct and efficient sampling procedure. Note that the asymptotic memory complexity is the same as for GridWalk. The second concern for the MCMC algorithm is the speed of convergence of the Markov chain to the equilibrium distribution. The ideal Markov chain is rapidly mixing (i.e. the number of steps taken to reach equilibrium is polynomially bounded), but theoretical proofs of rapid mixing are rare. We will show that in the special case of the uniform prior, the Markov chain for our posterior (3) is rapidly mixing using the following result from [Applegate and  Kannan, 1993]  that bounds the mixing time of Markov chains for pseudo-logconcave functions. Lemma 1. Let F (•) be a positive real valued function defined on the cube {x ∈ R n | − d ≤ x i ≤ d} for some positive d, satisfying for all λ ∈ [0, 1] and some α, β |f (x) − f (y)| ≤ α x − y ∞ and f (λx + (1 − λ)y) ≥ λf (x) + (1 − λ)f (y) − β where f (x) = log F (x). Then the Markov chain induced by GridWalk (and hence PolicyWalk) on F rapidly mixes to within of F in O(n 2 d 2 α 2 e 2β log 1 ) steps. Proof. See [Applegate and  Kannan, 1993] . Theorem 4. Given an MDP M = (S, A, T, γ) with |S| = N , and a distribution over rewards P (R) = P r X (R|O X ) defined by (3) with uniform prior P R over C = {R ∈ R n | − R max ≤ R i ≤ R max }. If R max = O(1/N ) then P can be efficiently sampled (within error ) in O(N 2 log 1/ ) steps by algorithm PolicyWalk. Proof. Since the uniform prior is the same for all points R, we can ignore it for sampling purposes along with the normalizing constant. Therefore, let f (R) = α X E(O X , R). Now choose some arbitrary policy π and let Note that f π is a linear function of R and f f π (R) = α X i Q π (s, a i , R) IJCAI-07 (R) ≥ f π (R), for all R ∈ C. Also we have, max s,a Q * (s, a) = max s,a,π Q π (s, a) = max s,π V π max (s) ≤ R max 1 − γ Similarly, min s,a Q * (s, a) ≥ − Rmax 1−γ . Therefore, f (R) ≤ αX NRmax 1−γ and f π (R) ≥ − αX NRmax 1−γ and hence f π (R) ≥ f (R) − 2α X N R max 1 − γ So for all R 1 , R 2 ∈ C and λ ∈ [0, 1], f (λR 1 + (1 − λ)R 2 ) ≥ f π (λR 1 + (1 − λ)R 2 ) ≥ λf π (R 1 ) + (1 − λ)f π (R 2 ) ≥ λf (R 1 ) + (1 − λ)f (R 2 ) − 2α X N R max 1 − γ Therefore, f satisfies the conditions of Lemma 1 with β = 2αX NRmax 1−γ = 2N • O( 1 N ) 1−γ = O(1) and α = |f (R 1 ) − f (R 2 )| R 1 − R 2 ∞ ≤ 2α X N R max (1 − γ)O( 1 N ) = O(N ) Hence the Markov chain induced by the GridWalk algorithm (and the PolicyWalk algorithm) on P mixes rapidly to within of P in a number of steps equal to O(N 2 1 N 2 N 2 e O(1) log 1/ ) = O(N 2 log 1/ ). Note that having R max = O(1/N ) is not really a restriction because we can rescale the rewards by a constant factor k after computing the mean without changing the optimal policy and all the value functions and Q functions get scaled by k as well. \n Experiments We compared the performance of our BIRL approach to the IRL algorithm of  [Ng and Russell, 2000]  experimentally. First, we generated random MDPs with N states (with N varying from 10 to 1000) and rewards drawn from i.i.d. Gaussian priors. Then, we simulated two kinds of agents on these MDPs and used their trajectories as input: The first learned a policy by Q-learning on the MDP + reward function. The learning rate was controlled so that the agent was not allowed to converge to the optimal policy but came reasonably close. The second agent executed a policy that maximized the expected total reward over the next k steps (k was chosen to be slightly below the horizon time). For BIRL, we used PolicyWalk to sample the posterior distribution (3) with a uniform prior. We compared the results of the two methods by their average 2 distance from the true reward function (Figure  4 ) and the policy loss with 1 norm (Figure  5 ) of the learned policy under the true reward. Both measures show substantial improvement. Note that we have used a logarithmic scale on the x-axis. We also measured the accuracy of our posterior distribution for small N by comparing it with the true distribution of rewards i.e. the set of generated rewards that gave rise to the same trajectory by the expert. In Figure  6 , we show scatter plots of some rewards sampled from the posterior and the true distribution for a 16-state MDP. These figures show that the posterior is very close to the true distribution. \n From Domain Knowledge to Prior To show how domain knowledge about a problem can be incorporated into the IRL formulation as an informative prior, IJCAI-07 we applied our methods to learning reward functions in adventure games. There, an agent explores a dungeon, seeking to collect various items of treasure and avoid obstacles such as guards or traps. The state space is represented by an m-dimensional binary feature vector indicating the position of the agent and the value of various fluents such as hasKey and doorLocked. If we view the state-space as an m-dimensional lattice L S , we see that neighbouring states in L S are likely to have correlated rewards (e.g. the value of doorLocked does not matter when the treasure chest is picked up). To model this, we use an Ising prior (see  [Cipra, 1987] ): P R (R) = 1 Z exp(−J (s ,s)∈N R(s)R(s ) − H s R(s)) where N is the set of neighbouring pairs of states in L S and J and H are the coupling and magnetization parameters. We tested our hypothesis by generating some adventure games (by populating dungeons with objects from a common sense knowledge base) and testing the performance of BIRL with the Ising prior versus the baseline uninformed priors. The results are in figure  7  and show that the Ising prior does significantly better. \n Related Work The initial work on IRL was done by  [Ng and Russell, 2000]  while  [Abbeel and Ng, 2004]  studied the special case where rewards can be represented as linear combinations of features of the state space and gave a max-margin characterization of the optimal reward function.  [Price and Boutilier, 2003]  discusses a Bayesian approach to imitating the actions of a mentor during reinforcement learning whereas the traditional literature on apprenticeship learning tries to mimic the behaviour of the expert directly  [Atkeson and Schaal, 1997] . Outside of computer science, IRL-related problems have been studied in various guises. In the physical sciences, there is a body of work on inverse problem theory, i.e. infering values of model parameters from observations of a physical system  [Tarantola, 2005] . In control theory,  [Boyd et al., 1994]  solved the problem, posed by Kalman, of recovering the objective function for a deterministic linear system with quadratic costs. \n Conclusions and Future Work Our work shows that improved solutions can be found for IRL by posing the problem as a Bayesian learning task. We provided a theoretical framework and tractable algorithms for Bayesian IRL and our solutions contain more information about the reward structure than other methods. Our experiments verify that our solutions are close to the true reward functions and yield good policies for apprenticeship learning. There are a few open questions remaining: 1. Are there more informative priors that we can construct for specific IRL problems using background knowledge? 2. How well does IRL generalize? Suppose the transition function of the actor and the learner differed, how robust would the reward function or policy learned from the actor be, w.r.t the learner's state space? Figure 4: Reward Loss. \n Figure 6 : 6 Figure 5: Policy Loss. \n Figure 7 : 7 Figure 7: Ising versus Uninformed Priors for Adventure Games \n If the underlying MDP represented a planning-type problem, we expect most states to have low (or negative) rewards but a few states to have high rewards (corresponding to the goal); this can be modeled by a Beta distribution for the reward at each state, which has modes at high and low ends of the reward space: P Laplace (R(s) = r) = 1 2σ e − |r| 2σ , ∀s ∈ S 3. 2 2σ 2 , ∀s ∈ S on αX as well(Fig 2). But it will be simpler to treat αX as just a parameter of the distribution. \n Algorithm PolicyWalk(Distribution P , MDP M, Step Size δ )1. Pick a random reward vector R ∈ R |S| /δ. 2. π := PolicyIteration(M, R) 3. Repeat (a) Pick a reward vector R uniformly at random from the neighbours \n\t\t\t Note that the probabilities of the evidence should be conditioned IJCAI-07", "date_published": "n/a", "url": "n/a", "filename": "IJCAI07-416.tei.xml", "abstract": "Inverse Reinforcement Learning (IRL) is the problem of learning the reward function underlying a Markov Decision Process given the dynamics of the system and the behaviour of an expert. IRL is motivated by situations where knowledge of the rewards is a goal by itself (as in preference elicitation) and by the task of apprenticeship learning (learning policies from an expert). In this paper we show how to combine prior knowledge and evidence from the expert's actions to derive a probability distribution over the space of reward functions. We present efficient algorithms that find solutions for the reward learning and apprenticeship learning tasks that generalize well over these distributions. Experimental results show strong improvement for our methods over previous heuristic-based approaches.", "id": "130cddd677dcaadbc4e3253e6bd17412"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum", "Anthony M Barrett", "Roman V Yampolskiy"], "title": "Modeling and Interpreting Expert Disagreement About Artificial Superintelligence", "text": "Introduction Artificial superintelligence (ASI) is artificial intelligence (AI) with capabilities that are significantly greater than human capabilities across a wide range of domains. If developed, ASI could have impacts that are highly beneficial or catastrophically harmful, depending on its design A hallmark of the ASI issue is disagreement among experts. Experts disagree on if ASI will be built, when it would be built, what designs it would use, and what its likely impacts would be.  1  The extent of expert disagreement speaks to the opacity of the underlying ASI issue and the general difficulty of forecasting future technologies. This stands in contrast with other major global issues, such as climate change, for which there is extensive expert agreement on the basic parameters of the issue  (Oreskes 2004 ). Expert consensus does not guarantee that the issue will be addressed-the ongoing struggle to address climate change attests to this-but it does offer direction for decision making. In the absence of expert agreement, those seeking to gain an understanding of the issue must decide what to believe given the existence of the disagreement. In some cases, it may be possible to look at the nature of the disagreement and pick sides; this occurs if other sides clearly have flawed arguments that are not worth giving any credence to. However, in many cases, multiple sides of a disagreement make plausible arguments; in these cases, the thoughtful observer may wish to form a belief that in some way considers the divergent expert opinions. This paper demonstrates and discusses methodological options for modeling and interpreting expert disagreement about the risk of ASI catastrophe. The paper accomplishes this by using a new ASI risk model called ASI-PATH  (Barrett and Baum 2017a; 2017b) . Expert disagreement can be modeled as differing estimates of parameters in the risk model. Given a set of differing expert parameter estimates, aggregate risk estimates can be made using weighting functions. Modeling expert disagreement within the context of a risk model is a method that has been used widely across a range of other contexts; to our knowledge this paper marks the first application of this method to ASI. The paper uses a well-documented recent disagreement between Nick Bostrom and Ben Goertzel as an illustrative example-an example that is also worthy of study in its own right. Bostrom and Goertzel are both longstanding thought leaders about ASI, with lengthy research track records and a shared concern with the societal impacts of ASI. However, in recent publications,  Goertzel (2015; 2016 ) expresses significant disagreement with core arguments made by  Bostrom (2014) . The Bostrom-Goertzel disagreement is notable because both of them are experts whose arguments about ASI can be expected to merit significant credence from the perspective of an outside observer. Therefore, their disagreement offers a simple but important case study for demonstrating the methodology of modeling and interpreting expert disagreement about ASI. The paper begins by summarizing the terms of the Bostrom-Goertzel disagreement. The paper then introduces the ASI-PATH model and shows how the Bostrom-Goertzel disagreement can be expressed in terms of ASI-PATH model parameters. The paper then presents model parameter estimates based on the Bostrom-Goertzel disagreement. The parameter estimates are not rigorously justified and instead are intended mainly for illustration and discussion purposes. Finally, the paper applies the risk modeling to a practical problem, that of AI confinement. \n The Bostrom-Goertzel disagreement Goertzel (2015; 2016) presents several disagreements with  Bostrom (2014) . This section focuses on three disagreements of direct relevance to ASI risk. \n Human evaluation of AI values One disagreement is on the potential for humans to evaluate the values that an AI has. Humans would want to diagnose an AI's values to ensure that they are something that humans consider desirable (henceforth \"human-desirable\"). If humans find an AI to have human-undesirable values, they can reprogram the AI or shut it down. As an AI gains in intelligence and power, it will become more capable of realizing its values, thus making it more important that its values are humandesirable. A core point of disagreement concerns the prospects for evaluating the values of AI that have significant but still subhuman intelligence levels. Bostrom indicates relatively low prospects for success at this evaluation, whereas Goertzel indicates relatively high prospects for success.  Bostrom (2014, p.116-119)  posits that once an AI reaches a certain point of intelligence, it might adopt an adversarial approach. Bostrom dubs this point the \"treacherous turn\": The treacherous turn: While weak, an AI behaves cooperatively (increasingly so, as it gets smarter). When the AI gets sufficiently strongwithout warning or provocation-it strikes, forms a singleton [i.e., takes over the world], and begins directly to optimize the world according to the criteria implied by its final values.  (  Goertzel provides a contrasting view, focusing on Step 2. He posits that an AI of intermediate intelligence is unlikely to successfully pretend to have humandesirable values because this would be too difficult for such an AI. Noting that \"maintaining a web of lies rapidly gets very complicated\" (Goertzel 2016, p.55), Goertzel posits that humans, being smarter and in control, would be able to see through a sub-human-level AI's \"web of lies\". Key to Goertzel's reasoning is the claim that an AI is likely to exhibit human-undesirable behavior before it (A) learns that such behavior is human-undesirable and (B) learns how to fake humandesirable behavior. Thus, Step 2 is unlikely to occurinstead, it is more likely that an AI would either have actual human-desirable values or be recognized by humans as faulty and then be reprogrammed or shut down. Goertzel does not name his view, so we will call it the sordid stumble: The sordid stumble: An AI that lacks humandesirable values will behave in a way that reveals its human-undesirable values to humans before it gains the capability to deceive humans into believing that it has human-desirable values. It should be noted that the distinction between the treacherous turn and the sordid stumble is about the AI itself, which is only one part of the human evaluation of the AI's values. The other part is the human effort at evaluation. An AI that is unskilled at deceiving humans could still succeed if humans are not trying hard to notice the deception, while a skilled AI could fail if humans are trying hard. Thus, this particular Bostrom-Goertzel debate covers only one part of the AI risk. However, it is still the case that, given a certain amount of human effort at evaluating an AI's values, Bostrom's treacherous turn suggests a lower chance of successful evaluation than Goertzel's sordid stumble. \n Human creation of human-desirable AI values A There is nothing paradoxical about an AI whose sole final goal is to count the grains of sand on Borcay, or to calculate the decimal expansion of pi, or to maximize the total number of paperclips that will exist in its future light cone. In fact, it would be easier to create an AI with simple goals like these than to build one that had a human-like set of values and dispositions  (Bostrom 2014, p.107 ). The logic of the above passage is that creating an AI with human-desirable values is more difficult and thus less likely to occur.  Goertzel (2016) , citing Sotala (2015), refers to this as the difficulty thesis: The difficulty thesis: Getting AIs to care about human values in the right way is really difficult, so even if we take strong precautions and explicitly try to engineer sophisticated beneficial goals, we may still fail  (Goertzel 2016, p.60) .  Goertzel (2016)  discusses a Sotala (2015) argument against the difficulty thesis, which is that while human values are indeed complex and difficult to learn, AIs are increasingly capable of learning complex things.Per this reasoning, giving an AI human-desirable values is still more difficult than, say, programming it to calculate digits of pi, but it may nonetheless be a fairly straightforward task for common AI algorithms. Thus, while it would not be easy for humans to create an AI with human-desirable values, it would not be extraordinarily difficult either.  Goertzel (2016) , again citing Sotala (2015), refers to this as the weak difficulty thesis: The weak difficulty thesis. It is harder to correctly learn and internalize human values, than it is to learn most other concepts. This might cause otherwise intelligent AI systems to act in ways that went against our values, if those AI systems had internalized a different set of values than the ones we wanted them to internalize. A more important consideration than the absolute difficulty of giving an AI human-desirable values is its relative difficulty compared to the difficulty of creating an AI that could take over the world. A larger relative ease of creating an AI with human-desirable values implies a higher probability that AI catastrophe will be avoided for any given level of effort put to avoiding it. There is reason to believe that the easier task is giving an AI human-desirable values. For comparison, every (or almost every) human being holds humandesirable values. Granted, some humans have more refined values than others, and some engage in violence or other antisocial conduct, but it is rare for someone to have pathological values like an incessant desire to calculate digits of pi. In contrast, none (or almost none) of us is capable of taking over the world. Characters like Alexander the Great and Genghis Khan are the exception, not the rule, and even they could have been assassinated by a single suicidal bodyguard. By the same reasoning, it may be easier for an AI to gain humandesirable values than it is for an AI to take over the world. This reasoning does not necessarily hold, since AI cognition can differ substantially from human cognition, but it nonetheless suggests that giving an AI humandesirable values may be the easier task. \n AI creation of human-desirable AI values A third point of discussion concerns the potential for an AI to end up with human-desirable values even though its human creators did not give it such values. If AIs tend to end up with human-desirable values, this reduces the pressure on the human creators of AI to get the AI's values right. It also increases the overall prospects for a positive AI outcome. To generalize, Bostrom proposes that AIs will tend to maintain stable values, whereas Goertzel proposes that AIs may tend to evolve values that could be more human-desirable. Bostrom's (2014) thinking on the matter centers on a concept he calls goal-content integrity: Goal-content integrity: If an agent retains its present goals into the future, then its present goals will be more likely to be achieved by its future self. This gives the agent a present instrumental reason to prevent alteration of its final goals  (Bostrom 2014, p.109-110) . The idea here is that an AI would seek to keep its values intact as one means of realizing its values. At any given moment, an AI has a certain set of values and seeks to act so as to realize these values. One factor it may consider is the extent to which its future self would also seek to realize these values. Bostrom's argument is that an AI is likely to expect that its future self would realize its present values more if the future self retains the present self's values, regardless of whether those values are human-desirable. Goertzel (2016) proposes an alternative perspective that he calls ultimate value convergence: Ultimate value convergence: Nearly all superintelligent minds will converge to the same universal value system (paraphrased from Goertzel 2016, p.60). Goertzel further proposes that the universal value system will be \"centered around a few key values such as Joy, Growth, and Choice\" (Goertzel 2016, p.60). However, the precise details of the universal value system are less important than the possibility that the value system could resemble human-desirable values. This creates a mechanism through which an AI that begins with any arbitrary human-undesirable value system could tend towards human-desirable values. Goertzel does not insist that the ultimate values would necessarily be human-desirable. To the contrary, he states that \"if there are convergent 'universal' values, they are likely sufficiently abstract to encompass many specific value systems that would be abhorrent to us according to our modern human values\" (Goertzel 2016, p.60). Thus, ultimate value convergence does not guarantee that an AI would end up with human-desirable values. Instead, it increases the probability that an AI would end up with human-desirable values if the AI begins with human-undesirable values. Alternatively, if the AI begins with human-desirable values, then the ultimate value convergence theory could cause the AI to drift to human-undesirable values. Indeed, if the AI begins with human-desirable values, then more favorable results (from humanity's perspective) would accrue if the AI has goal-content integrity. \n The ASI-PATH model The ASI-PATH model was developed to model pathways to ASI catastrophe  (Barrett and Baum 2016) . ASI-PATH is a fault tree model, which means it is a graphical model with nodes that are connected by Boolean logic and point to some failure mode. For ASI-PATH, a failure mode is any event in which ASI causes global catastrophe. Fault tree models like ASI-PATH are used widely in risk analysis across a broad range of domains. A core virtue of fault trees is that, by breaking catastrophe pathways into their constituent parts, they enable more detailed study of how failures can occur and how likely they are to occur. It is often easier to focus on one model node at a time instead of trying to study all potential failure modes simultaneously. Furthermore, the fault tree's logic structure creates a means of defining and quantifying model parameters and combining them into overall probability estimates. Indeed, the three points of the Bostrom-Goertzel disagreement (human evaluation of AI values, human creation of human-desirable AI values, and AI creation of human-desirable AI values) each map to one of the ASI-PATH parameters shown in Figure  1 . In Figure  1 , the top node is ASI catastrophe. The left branch covers events that lead to the ASI gaining \"decisive strategic advantage\", defined as \"a level of technological and other advantages sufficient to enable it [the AI] to achieve complete world domination\" (Bostrom, 2014, p. 78). The left branch models scenarios in which an initial \"seed\" AI undergoes recursive selfimprovement and \"takes off\", becoming successively more and more intelligent until it becomes an ASI. P1 is the probability that such an AI is possible in the first place. P2 is the probability that a seed AI is created and undergoes recursive self-improvement. P3 is the probability that the AI is contained from gaining decisive strategic advantage; the containment can occur at any point in the process from seed AI to ASI. Containment is any measure that prevents a seed AI from gaining decisive strategic advantage, either by limiting recursive self-improvement or by preventing ASI from gaining decisive strategic advantage. Containment includes confinement, in which the AI's ability to affect the rest of the world is restricted (Section 5), and enforcement, in which AI(s) prevent other AI(s) from gaining decisive strategic advantage.  2  The left branch of Figure  1  covers events that could lead to the ASI taking actions that are \"unsafe\", which is defined as actions that would result in a major global  2  Barrett and Baum (2017a, p. 400) define confinement as \"restrictions built into the AI's hardware or software that limit the AI's ability to affect the rest of the world so that it does not gain decisive strategic advantage\". This is slightly different than the Yampolskiy (2012) definition used in Section 5. This difference does not affect the overall argument of the present paper. catastrophe. P4 is the probability that humans will fail to make ASI goals safe. P5 is the probability that the ASI will not make its own goals safe. Finally, P6 is the probability that the ASI will not be deterred from acting unsafely by some other agent, potentially another AI. Because all the logic gates in Figure  1  are \"AND\", the probability of ASI catastrophe, P, is simply the product of the six component probabilities:    6 1 n n P P (1) For convenience, we assume {P1, P2, P6} = 1. These parameters are unrelated to the Bostrom-Goertzel disagreement as discussed in this paper. Instead, we focus on {P3, P4, P5}, for which there is significant disagreement. P3 relates to the Bostrom-Goertzel disagreement about human evaluation of AI values (Section 2.1). In general, it should be easier to contain an AI earlier in the recursive self-improvement process because at that point it has less intelligence with which it could resist containment. Therefore, one factor in P3 is the potential for human observers to determine early in the process that this particular AI should be contained. The easier it is for humans to evaluate AI values, the earlier in the process they should be able to notice which AIs should be contained, and therefore the more probable it is that containment will succeed. In other words, easier human evaluation of AI values means lower P3. P4 relates to the Bostrom-Goertzel disagreement about human creation of human-desirable AI values (Section 2.2). Human-desirable values are very likely to be safe in the sense that they would avoid major global catastrophe. While one can imagine the possibility that somehow, deep down inside, humans actually prefer global catastrophe, and thus that an AI with humandesirable values would cause catastrophe, we will omit this possibility. Instead, we assume that an AI with human-desirable values would not cause catastrophe. Therefore, the easier it is for humans to create AIs with human-desirable values, the more probable it is that catastrophe would be avoided. In other words, easier human creation of AI with human-desirable values means lower P4. P5 relates to the Bostrom-Goertzel disagreement about AI creation of human-desirable AI values (Section 2.3). We assume that the more likely it is that an AI would create of human-desirable values for itself, the more probable it is that catastrophe would be avoided. In other words, more likely AI creation of AI with humandesirable values means lower P5. For each of these three variables, we define two \"expert belief\" variables corresponding to Bostrom's and Goertzel's positions on the corresponding issue:  P3B is the value of P3 that follows from Bostrom's position, the treacherous turn.  P3G is the value of P3 that follows from Goertzel's position, the sordid stumble.  P4B is the value of P4 that follows from Bostrom's position, the difficulty thesis.  P4G is the value of P4 that follows from Goertzel's position, the weak difficulty thesis.  P5B is the value of P5 that follows from Bostrom's position, goal-content integrity.  P5G is the value of P5 that follows from Goertzel's position, ultimate value convergence. Given estimates for each of the above \"expert belief\" variables, one can calculate P according to the formula:       6 1 n nG nG nB nB P W P W P (2) In Equation  2 , W is a weighting variable corresponding to how much weight one places on Bostrom's or Goertzel's position for a given variable. Thus, for example, W3B is how much weight one places on Bostrom's position for P3, i.e. how much one believes that an AI would conduct a treacherous turn. For simplicity, we assume WnB + WnG = 1 for n = {3, 4, 5}. This is to assume that for each of {P3, P4, P5}, either Bostrom or Goertzel holds the correct position. This is a significant assumption: it could turn out to be the case that they are both mistaken. The assumption is made largely for analytical and expository convenience. This much is easy. The hard part is quantifying each of the P and W variables in Equation  2 . What follows is an attempt to specify how we would quantify these variables. We estimate the P variables by relating the arguments of Bostrom and Goertzel to the variables and taking into account any additional aspects of the variables. We aim to be faithful to Bostrom's and Goertzel's thinking. We estimate the W variables by making our own (tentative) judgments about the strength of Bostrom's and Goertzel's arguments as we currently see them. Thus, the P estimations aim to represent Bostrom's and Goertzel's thinking and the W estimations represent our own thinking. Later in the paper we also explore the implications of giving both experts' arguments equal weighting (i.e., WnB = WnG = 0.5 for each n) and of giving full weighting to exclusively one of the two experts. We make no claims to having the perfect or final estimations of any of these parameters. To the contrary, we have low confidence in our current estimations, in the sense that we expect we would revise our estimations significantly in the face of new evidence and argument. But there is value in having some initial estimations to stimulate thinking on the matter. We thus present our estimations largely for sake of illustration and discussion. We invite interested readers to make their own. \n P3 and W3: containment fails The human evaluation of AI values is only one aspect of containment. Other aspects include takeoff speed (faster takeoff means less opportunity to contain AI during recursive self-improvement) and ASI containment (measures to prevent an ASI from gaining decisive strategic advantage). Therefore, the Bostrom-Goertzel disagreement about human evaluation of AI values should only produce a relatively small difference on P3. Bostrom and Goertzel may well disagree on other aspects of P3, but those are beyond the scope of this paper. Bostrom's position, the treacherous turn, corresponds to a higher probability of containment failure and thus a higher value of P3 relative to Goertzel's position, the sordid stumble. We propose a 10% difference in P3 between Bostrom and Goertzel, i.e. P3B -P3G = 0.1. The absolute magnitude of P3B and P3G will depend on various case-specific details-for example, a seed AI launched on a powerful computer is more likely to have a fast takeoff and thus less likely to be contained. For simplicity, we will use P3B = 0.6 and P3G = 0.5, while noting that other values are also possible. Regarding W3B and W3G, our current view is that the sordid stumble is significantly more plausible. We find it relevant that AIs are already capable of learning complex tasks like face recognition, yet such AIs are nowhere near capable of outwitting humans with a web of lies. Additionally, it strikes us as much more likely that an AI would exhibit human-undesirable behavior before it becomes able to deceive humans, and indeed long enough in advance to give humans plenty of time to contain the situation. Therefore, we estimate W3B = 0.1 and W3G = 0.9. \n P4 and W4: humans fail to give AI safe goals The Bostrom-Goertzel disagreement about human creation of human-desirable AI values is relevant to the challenge of humans giving AI safe goals. Therefore, the disagreement can yield large differences in P4. Bostrom's position, the difficulty thesis, corresponds to a higher probability of humans failing to give the AI safe goals and thus a higher value of P4 relative to Goertzel's position, the weak difficulty thesis. The values of P4B and P4G will depend on various case-specific details, such as how hard humans try to give the AI safe goals. As representative estimates, we propose P4B = 0.9 and P4G = 0.4. Regarding W4B and W4G, our current view is that the weak difficulty thesis is significantly more plausible. The fact that AIs are already capable of learning complex tasks like face recognition suggests that learning human values is not a massively intractable task. An AI would not please everyone all the time-this is impossible-but it could learn to have broadly human-desirable values and behave in broadly human-desirable ways. However, we still see potential for the complexities of human values to pose AI training challenges that go far beyond what exists for tasks like face recognition. Therefore, we estimate W4B = 0.3 and W4G = 0.7. \n P5 and W5: AI fails to give itself safe goals The Bostrom-Goertzel disagreement about AI creation of human-desirable AI values is relevant to the challenge of the AI giving itself safe goals. Therefore, the disagreement can yield large differences in P5. Bostrom's position, goal-content integrity, corresponds to a higher probability of the AI failing to give itself safe goals and thus a higher value of P5 relative to Goertzel's position, ultimate value convergence. Indeed, an AI with perfect goal-content integrity will never change its goals. For ultimate value convergence, the key factor is the relation between ultimate values and human-desirable values; a weak relation suggests a high probability that the AI will end up with human-undesirable values. Taking these considerations into account, we propose P5B = 0.95 and P5G = 0.5. Regarding W5B and W5G, our current view is that goal-content integrity is significantly more plausible. While it is easy to imagine that an AI would not have perfect goal-content integrity, due to a range of realworld complications, we nonetheless find it compelling that this would be a general tendency of AIs. In contrast, we see no reason to believe that AIs would all converge towards some universal set of values. To the contrary, we believe that an agent's values derive mainly from its cognitive architecture and its interaction with its environment; different architectures and interactions could lead to different values. Therefore, we estimate W5B = 0.9 and W5G = 0.1. \n The probability of ASI catastrophe Table  1  summarizes the various parameter estimates in Sections 3.1-3.3. Using these estimates, recalling the assumption {P1, P2, P6} = 1, and following Equation  2 gives P = (0.1*0.6 + 0.9*0.5) * (0.3*0.9 + 0.7*0.4) * (0.9*0.95 + 0.1*0.5) ≈ 0.25. In other words, this set of parameter estimates implies an approximately 25% probability of ASI catastrophe. For comparison, giving equal weighting to Bostrom's and Goertzel's positions (i.e., setting each WB = WG = 0.5) yields P ≈ 0.26; using only Bostrom's arguments (i.e., setting each WB = 1) yields P ≈ 0.51; and using only Goertzel's arguments (i.e., setting each WG = 1) yields P = 0.1. Catastrophe probabilities of 0.1 and 0.51 may diverge by a factor of 5, but they are both still extremely high. Even \"just\" a 0.1 chance of major catastrophe could warrant extensive government regulation and/or other risk management. Thus, however much Bostrom and Goertzel may disagree with each other, they would seem to agree that ASI constitutes a major risk. \n PB However, an abundance of caveats is required. First, the assumption {P1, P2, P6} = 1 was made without any justification. Any thoughtful estimates of these parameters would almost certainly be lower. Our intuition is that ASI from AI takeoff is likely to be possible, and ASI deterrence seems unlikely to occur, suggesting {P1, P6} ≈ 1, but that the creation of seed AI is by no means guaranteed, suggesting P2 << 1. This implies P ≈ 0.25 is likely an overestimate. Second, the assumption that the correct position was either Bostrom's or Goertzel's was also made without any justification. They could both be wrong, or the correct position could be some amalgam of both of their positions, or an amalgam of both of their positions plus other position(s). Bostrom and Goertzel are both leading thinkers about ASI, but there is no reason to believe that their range of thought necessarily corresponds to the breadth of potential plausible thought. To the contrary, the ASI topic remains sufficiently unexplored that it is likely that many other plausible positions can be formed. Accounting for these other positions could send P to virtually any value in [0, 1]. Third, the estimates in Table  1  were made with little effort, largely for illustration and discussion purposes. Many of these estimates could be significantly off, even by several orders of magnitude. Given the form of Equation 1, a single very low value for Wn*Pn would also make P very low. This further implies that P ≈ 0.25 is likely an overestimate, potentially by several orders of magnitude. Fourth, the estimates in  \n A practical application: AI confinement A core motivation for analyzing ASI risk is to inform practical decisions aimed at reducing the risk. Risk analysis can help identify which actions would reduce the risk and by how much. Different assessments of the risk-such as from experts' differing viewpoints-can yield different results in terms of which actions would best reduce the risk. Given the differences observed in the viewpoints of Bostrom and Goertzel about ASI risk, it is possible that different practical recommendations could follow. To illustrate this, we apply the above risk analysis to model the effects of decisions on a proposed ASI risk reduction measure known as AI confinement: AI confinement: The challenge of restricting an artificially intelligent entity to a confined environment from which it can't exchange information with the outside environment via legitimate or covert channels if such information exchange was not authorized by the confinement authority  (Yampolskiy 2012, p.196) . AI confinement is a type of containment and thus relates directly to the P3 (containment fails) variable in the ASI-PATH model (Figure  1 ). Stronger confinement makes it less likely that an AI takeoff would result in an ASI gaining decisive strategic advantage. Confinement might be achieved, for example, by disconnecting the AI from the internet and placing it in a Faraday cage. Superficially, strong confinement would seem to reduce ASI risk by reducing P3. However, strong confinement could increase ASI risk in other ways. In particular, by limiting interactions between the AI and the human populations, strong confinement could limit the AI's capability to learn human-desirable values, thereby increasing P4 (failure of human attempts to make ASI goals safe). For comparison, AIs currently learn to recognize key characteristics of images (e.g., faces) by examining large data sets of images, often guided by human trainers to help the AI correctly identify image features. Similarly, an AI may be able to learn humandesirable values by observing large data sets of human decision-making, human ethical reflection, or other phenomena, and may further improve via the guidance of human trainers. Strong confinement could limit the potential for the AI to learn human-desirable values, thus increasing P4. Bostrom and Goertzel have expressed divergent views on confinement. Bostrom has favored strong confinement, even proposing a single international ASI project in which \"the scientists involved would have to be physically isolated and prevented from communicating with the rest of the world for the duration of the project, except through a single carefully vetted communication channel (Bostrom 2014, p. 253)\". Goertzel has explicitly criticized this proposal (Goertzel 2015, p.71-73) and instead argued that an open project would be safer, writing that \"The more the AGI system is engaged with human minds and other AGI systems in the course of its self-modification, presumably the less likely it is to veer off in an undesired and unpredictable direction\" (Goertzel and Pitt 2012, p.13). Each expert would seem to be emphasizing different factors in ASI risk: P3 for Bostrom and P4 for Goertzel. The practical question here is how strong to make the confinement for an AI. Answering this question requires resolving the tradeoff between P3 and P4. This in turn requires knowing the size of P3 and P4 as a function of confinement strength. Estimating that function is beyond the scope of this paper. However, as an illustrative consideration, suppose that it is possible to have strong confinement while still giving the AI good access to human-desirable values. For example, perhaps a robust dataset of human decisions, ethical reflections, etc. could be included inside the confinement. In this case, the effect of strong confinement on P4 may be small. Meanwhile, if there is no arrangement that could shrink the effect of confinement on P3, such that this effect would be large, then perhaps strong confinement would be better. This and other practical ASI risk management questions could be pursued in future research. \n Conclusion Estimates of the risk of ASI catastrophe can depend heavily on which expert makes the estimate. A neutral observer should consider arguments and estimates from all available experts and any other sources of information. This paper analyzes ASI catastrophe risk using arguments from two experts, Nick Bostrom and Ben Goertzel. Applying their arguments to an ASI risk model, we calculate that their respective ASI risk estimates vary by a factor of five: P ≈ 0.51 for Bostrom and P = 0.1 for Goertzel. Our estimates, combining both experts' arguments, is P ≈ 0.25. Weighting both experts equally gave a similar result of P ≈ 0.26. These numbers come with many caveats and should be used mainly for illustration and discussion purposes. More carefully considered estimates could easily be much closer to either 0 or 1. These numbers are interesting, but they are not the only important part, or even the most important part, of this analysis. There is greater insight to be obtained from the details of the analysis than from the ensuing numbers. This is especially case for this analysis of ASI risk because the numbers are so tentative and the underlying analysis so comparatively rich. This paper is just an initial attempt to use expert judgment to quantify ASI risk. Future research can and should do the following: examine Bostrom's and Goertzel's arguments in greater detail so as to inform the risk model's parameters; consider arguments and ideas from a wider range of experts; conduct formal expert surveys to elicit expert judgments of risk model parameters; explore different weighting techniques for aggregating across expert judgment, as well as circumstances in which weighted aggregation is inappropriate; conduct sensitivity analysis across spaces of possible parameter values, especially in the context of the evaluation of ASI risk management decision options; and do all of this for a wider range of model parameters, including {P1, P2, P6} as well as more detailed components of {P3, P4, P5}, such as modeled in  Barrett and Baum (2017a; 2017b) . Future research can also explore the effect on overall ASI risk when multiple ASI systems are launched: perhaps some would be riskier than others, and it may be important to avoid catastrophe from all of them. One overarching message of this paper is that more detailed and rigorous analysis of ASI risk can be achieved when the risk is broken into constituent parts and modeled, such as in Figure  1 . Each component of ASI risk raises a whole host of interesting and important details that are worthy of scrutiny and debate. Likewise, aggregate risk estimates are better informed and generally more reliable when they are made from detailed models. To be sure, it is possible for models to be too detailed, burdening experts and analysts with excessive minutiae. However, given the simplicity of the risk models at this early stage of ASI risk analysis, we believe that, at this time, more detail is better. A final point is that the size of ASI risk depends on many case-specific factors that in turn depend on many human actions. This means that the interested human actor has a range of opportunities available for reducing the probability of ASI catastrophe. Risk modeling is an important step towards identifying which opportunities are most effective at reducing the risk. ASI catastrophe is by no means a foregone conclusion. The ultimate outcome may well be in our hands. \n Acknowledgement We thank Ben Goertzel, Miles Brundage, Kaj Sotala, Steve Omohundro, Allan Dafoe, Stuart Armstrong, Ryan Carey, Nell Watson, and Matthijs Maas for helpful comments on an earlier draft. Any remaining errors are the authors' alone. Work for this paper is funded by Future of Life Institute grant 2015-143911. The views in this paper are those of the authors and do not necessarily reflect the views of the Global Catastrophic Risk Institute or the Future of Life Institute. Figure 1 : 1 Figure 1: ASI catastrophe fault tree. Adapted from Barrett and Baum (2017a). \n Bostrom 2014, p.119) Such an AI would not have durable values in the sense that it would go from acting in human-desirable ways to acting in human-undesirable ways. A key detail of the treacherous turn theory is that the AI has values that are similar to, but ultimately different from, humandesirable values. As the AI gains intelligence, it goes through a series of stages: 1. At low levels of intelligence, the AI acts in ways that humans consider desirable. At this stage, the differences between the AI's values and human values are not important because the AI can only complete simple tasks that are human-desirable. 2. At an intermediate level of intelligence, the AI realizes that its values differ from human-desirable values and that it if it tried deviating from humandesirable values, humans would reprogram the AI or shut it down. Furthermore, the AI discovers that it can successfully pretend to have human-desirable values until it is more intelligent. 3. At a high level of intelligence, the AI takes control of the world from humanity so that humans cannot reprogram it or shut it down, and then pursues its actual, human-undesirable values. \n Table 1 : 1 Summary of parameter estimates in Sections 3.1-3.3. PG WB WG 3 0.6 0.5 0.1 0.9 4 0.9 0.4 0.3 0.7 5 0.95 0.5 0.9 0.1 \n Table 1 depend on a range of case-specific factors, including what other containment measures are used, how much effort humans put into giving the AI human-desirable values, and what cognitive architecture the AI has. Therefore, different seed AIs self-improving under different conditions would yield different values of P, potentially including much larger and much smaller values. \n\t\t\t On expert opinion of ASI, see Baum et al. (2011), Armstrong and Sotala (2012), Armstrong et al. (2014), and Müller and Bostrom (2014).", "date_published": "n/a", "url": "n/a", "filename": "SSRN-id3104645.tei.xml", "abstract": "Artificial superintelligence (ASI) is artificial intelligence (AI) with capabilities that are significantly greater than human capabilities across a wide range of domains. A hallmark of the ASI issue is disagreement among experts. This paper demonstrates and discusses methodological options for modeling and interpreting expert disagreement about the risk of ASI catastrophe. Using a new model called ASI-PATH, the paper models a well-documented recent disagreement between Nick Bostrom and Ben Goertzel, two distinguished ASI experts. Three points of disagreement are considered: (1) the potential for humans to evaluate the values held by an AI, (2) the potential for humans to create an AI with values that humans would consider desirable, and (3) the potential for an AI to create for itself values that humans would consider desirable. An initial quantitative analysis shows that accounting for variation in expert judgment can have a large effect on estimates of the risk of ASI catastrophe. The risk estimates can in turn inform ASI risk management strategies, which the paper demonstrates via an analysis of the strategy of AI confinement. The paper find the optimal strength of AI confinement to depend on the balance of risk parameters (  1 ) and (  2 ). Povzetek: Predstavljena je metoda za modeliranje in interpretiranje razlik v mnenjih ekspertov o superinteligenci.", "id": "4b039d31de032a6fb2cde5ba7f3ac47c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Carla Zoe Cremer", "Jess Whittlestone"], "title": "Artificial Canaries: Early Warning Signs for Anticipatory and Democratic Governance of AI", "text": "I. Introduction P rogress in artificial intelligence (AI) research has accelerated in recent years. Applications are already changing society  [1]  and some researchers warn that continued progress could precipitate transformative impacts  [2] -  [5] . We use the term \"transformative AI\" to describe a range of possible advances with potential to impact society in significant and hard-to-reverse ways  [6] . For example, future machine learning systems could be used to optimise management of safety-critical infrastructure  [7] . Advanced language models could be used in ways that corrupt our online information ecosystem  [8]  and future advances in AI systems could trigger widespread labour automation  [9] . There is an urgent need to develop anticipatory governance approaches to AI development and deployment. As AI advances, its impacts on society will become more profound, and some harms may be too great to rely on purely 'reactive' or retrospective governance. Anticipating future impacts is a challenging task. Experts show substantial disagreement about when different advances in AI capabilities should be expected  [10] ,  [11] . Policy-makers face challenges in keeping pace with technological progress: it is difficult to foresee impacts before a technology is deployed, but after deployment it may already be too late to shape impacts, and some harm may already have been done  [12] . Ideally, we would focus preventative, anticipatory efforts on applications which are close enough to deployment to be meaningfully influenced today, but whose impacts we are not already seeing. Finding 'early warning signs' of transformative AI applications can help us to do this. Early warning signs can also help democratise AI development and governance. They can provide time and direction for much-needed public discourse about what we want and do not want from AI. It is not enough for anticipatory governance to look out for supposedly 'inevitable' future impacts. We are not mere bystanders in this AI revolution: the futures we occupy will be futures of our own making, driven by the actions of technology developers, policymakers, civil society and the public. In order to prevent foreseeable harms towards those people who bear the effects of AI deployments, we must find ways for AI developers to be held accountable to the society which they are embedded in. If we want AI to benefit society broadly, we must urgently find ways to give democratic control to those who will be impacted. Our aim with identifying early warning signs is to develop anticipatory methods which can prompt a focussed civic discourse around significant developments and provide a wider range of people with the information they need to contribute to conversations about the future of AI. We present a methodology for identifying early warning signs of potentially transformative impacts of AI and discuss how these can feed into more anticipatory and democratic governance processes. We call these early warning signs 'canaries' based on the practice of using canaries to provide early warnings of unsafe air pollution in coal mines in the industrial revolution. Others before us have used this term in the context of AI to stress the importance of early warning signs  [13] ,  [14] , but this is the first attempt to outline in detail how such 'artificial canaries' might be identified and used. Our methodology is a prototype but we believe it provides an important first step towards assessing and then trialling the feasibility of identifying canaries. We first present the approach and then illustrate it on two high-level examples, in which we identify preliminary warning signs of AI applications that could undermine democracy, and warning signs of progress towards high-level machine intelligence (HLMI). We explain why early warning signs are needed by drawing on the literature of participatory technology assessments, and we discuss the advantages and practical challenges of this method in the hope of preparing future research that might attempt to put this method into practise. Our theoretical exploration of a method to identify early warning signs of transformative applications provides a foundation towards more anticipatory, accountable and democratic governance of AI in practice. \n II. Related Work We rely on two main bodies of work. Our methodology for identifying canaries relies on the literature on forecasting and monitoring AI. Our suggestions for how canaries might be used once identified build on work on participatory technology assessments, which stresses a more inclusive approach to technology governance. While substantial research exists in both these areas, we believe this is the first piece of work that shows how they could feed into each other. \n A. AI Forecasting and Monitoring Over the past decade, an increasing number of studies have attempted to forecast AI progress. They commonly use expert elicitations to generate probabilistic estimates for when different AI advances and milestones will be achieved  [10] ,  [15] -  [17] . For example,  [16]  ask experts about when specific milestones in AI will be achieved, including passing the Turing Test or passing third grade. Both  [15]  and  [10]  ask experts to predict the arrival of high-level machine intelligence (HLMI), which the latter define as when \"unaided machines can accomplish every task better and more cheaply than human workers\". However, we should be cautious about giving results from these surveys too much weight. These studies have several limitations, including the fact that the questions asked are often ambiguous, that expertise is narrowly defined, and that respondents do not receive training in quantitative forecasting  [11] ,  [18] . Experts disagree substantially about when crucial capabilities will be achieved  [10] , but these surveys cannot tell us who (if anyone) is more accurate in their predictions. Issues of accuracy and reliability aside, forecasts focused solely on timelines for specific events are limited in how much they can inform our decisions about AI today. While it is interesting to know how much experts disagree on AI progress via these probabilistic estimates, they cannot tell us why experts disagree or what would change their minds. Surveys tell us little about what early warning signs to look out for or where we should place our focus today to shape the future development and impact of AI. At the same time, several projects, e.g.  [19] -  [22] , have begun to track and measure progress in AI. These projects focus on a range of indicators relevant to AI progress, but do not make any systematic attempt to identify which markers of progress are more important than others for the preparation of transformative applications. Time and attention for tracking progress is limited and it would be helpful if we were able to prioritise and monitor those research areas that are most relevant to mitigating risks. Recognising some of the limitations of existing work,  [23]  aims for a more holistic approach to AI forecasting. This framework emphasises the use of the Delphi technique  [24]  to aggregate different perspectives of a group of experts, and cognitive mapping methods to study how different milestones relate to one another, rather than to simply forecast milestones in isolation. We agree that such methods might address some limitations of previous work in both AI forecasting and monitoring. AI forecasting has focused on timelines for particularly extreme events, but these timelines are subject to enormous uncertainty and do not indicate near-term warning signs. AI measurement initiatives have the opposite limitation: they focus on near-term progress, but with little systematic reflection on which avenues of progress are, from a governance perspective, more important to monitor than others. What is needed are attempts to identify areas of progress today that may be particularly important to pay attention to, given concerns about the kinds of transformative AI systems that may be possible in future. \n B. Participatory Technology Assessments Presently, the impacts of AI are largely shaped by a small group of powerful people with a narrow perspective which can be at odds with public interest  [25] . Only a few powerful actors, such as governments, defence agencies, and firms the size of Google or Amazon, have the resources to conduct ambitious research projects. Democratic control over these research projects is limited. Governments retain discretion over what gets regulated, large technology firms can distort and avoid policies via intensive lobbying  [26]  and defence agencies may classify ongoing research. Recognising these problems, a number of initiatives over the past few years have emphasised the need for wider participation in the development and governance of AI  [27] -  [29] . In considering how best to achieve this, it is helpful to look to the field of science and technology studies (STS) which has long considered the value of democratising research progress  [30] ,  [31] . Several publications refer to the 'participatory turn'  [32]  in STS and an increasing interest in the role of the non-expert in technology development and assessment  [27] . More recently, in the spirit of \"democratic experimentation\"  [33] , various methods for civic participation have been developed and trialled, including deliberative polls, citizen juries and scenario exercises  [33] . With a widening conception of expertise, a large body of research on \"participatory technology assessment\" (PTA) has emerged, aiming to examine how we might increase civic participation in how technology is developed, assessed and rolled out. We cannot summarise this wideranging and complex body of work fully here. But we point towards some relevant pieces for interested readers to begin with.  [34]  and  [35]  present a typology of the methods and goals of participating, which now come in many forms. This means that assessments of the success of PTAs are challenging  [33]  and ongoing because different studies evaluate different PTA processes against different goals  [34] . Yet while scholars recognise remaining limitations of PTAs  [31] , several arguments for their advantages have been brought forward, ranging from citizen agency to consensus identification and justice. There are good reasons to believe that non-experts possess relevant end-user expertise. They often quickly develop the relevant subjectmatter understanding to contribute meaningfully, leading to better epistemic outcomes due to a greater diversity of views which result in a cancellation of errors  [36] ,  [37] . To assess the performance of PTAs scholars draw from case studies and identify best practices  [38] -  [40] . There is an important difference between truly participatory, democratically minded, technology assessments, and consultations that use the public to help legitimise a preconceived technology  [41] . The question of how to make PTAs count in established representational democracies is an ongoing challenge to the field  [31] ,  [33] . But  [42] , who present a recent example of collective technology policy-making, show that success and impact with PTAs is possible.  [40]  draw from 38 international case studies to extract best practices, building on  [38] , who showcase great diversity of possible ways in which to draw on the public. Comparing different approaches is difficult, but has been done  [39] ,  [43] .  [41]  present a conceptual framework with which to design and assess PTAs,  [44]  compares online versus offline methodologies and in  [35]  we find a typology of various design choices for public engagement mechanisms. See also  [45]  for a helpful discussion on how to determine the diversity of participants,  [46]  on what counts as expertise in foresight and  [30] ,  [32] ,  [47]  for challenges to be aware of in implementing PTAs. Many before us have noted that we need wider participation in the development and governance of AI, including by calling for the use of PTAs in designing algorithms  [48] ,  [49] . We see a need to go beyond greater participation in addressing existing problems with algorithms and propose that wider participation should also be considered in conversations about future AI impacts. Experts and citizens each have a role to play in ensuring that AI governance is informed by and inclusive of a wide range of knowledge, concerns and perspectives. However, the question of how best to marry expert foresight and citizen engagement is a challenging one. While a full answer to this question is beyond the scope of this paper, what we do offer is a first step: a proposal for how expert elicitation can be used to identify important warnings which can later be used to facilitate timely democratic debate. For such debates to be useful, we first need an idea of which developments on the horizon can be meaningfully assessed and influenced, for which it makes sense to draw on public expertise and limited attention. This is precisely what our method aims to provide. \n III. Identifying Early Warning Signs We believe that identifying canaries for transformative AI is a tractable problem and worth investing research effort in today. Engineering and cognitive development present a proof of principle: capabilities are achieved sequentially, meaning that there are often key underlying capabilities which, if attained, unlock progress in many other areas. For example, musical protolanguage is thought to have enabled grammatical competence in the development of language in homo sapiens  [50] . AI progress so far has also seen such amplifiers: the use of multi-layered non-linear learning or stochastic gradient descent arguably laid the foundation for unexpectedly fast progress on image recognition, translation and speech recognition  [51] . By mapping out the dependencies between different capabilities needed to reach some notion of transformative AI, therefore, we should be able to identify milestones which are particularly important for enabling many others -these are our canaries. The proposed methodology is intended to be highly adaptable and can be used to identify canaries for a number of important potentially transformative events, such as foundational research breakthroughs or the automation of tasks that affect a wide range of jobs. Many types of indicators could be of interest and classed as canaries, including: algorithmic innovation that supports key cognitive faculties (e.g., natural language understanding); overcoming known technical challenges (such as improving the data efficiency of deep learning algorithms); or improved applicability of AI to economically-relevant tasks (e.g. text summarization). Given an event for which we wish to identify canaries, our methodology has three essential steps:  (1)  identifying key milestones towards the event; (2) identifying dependency relations between these milestones; and (3) identifying milestones which underpin many others as canaries. See Fig.  1  for an illustration. We here deliberately refrain from describing the method with too much specificity, because we want to stress the flexibility of our approach, and recognise that there is currently no one-fits-all approach in forecasting. The method will require adaptation to the particular transformative event in question, but each step of this method is suited for such specifications. We outline example adaptations of the method to particular cases. e. method presented in this paper is that it requires one to have already identi ed a particular transformative event of concer  \n A. Identifying Milestones Via Expert Elicitation The first step of our methodology involves using traditional approaches in expert elicitation to identify milestones that may be relevant to the transformative event in question. Which experts are selected is crucial to the outcome and reliability of studies in AI forecasting. There are unavoidable limitations of using any form of subjective judgement in forecasting, but these limitations can be minimised by carefully thinking through the group selection. Both the direct expertise of individuals, and how they contribute to the diversity of the overall group, must be considered. See  [46]  for a discussion of who counts as an expert in forecasting. Researchers should decide in advance what kinds of expertise are most relevant and must be combined to study the milestones that relate to the transformative event. Milestones might include technical limitations of current methods (e.g. adversarial attacks) and informed speculation about future capabilities (e.g. common sense) that may be important prerequisites to the transformative event. Consulting across a wide range of academic disciplines to order such diverse milestones is important. For example, a cohort of experts identifying and ordering milestones towards HLMI should include not only experts in machine learning and computer science but also cognitive scientists, philosophers, developmental psychologists, evolutionary biologists, or animal cognition experts. Such a group combines expertise on current capabilities in AI, with expertise on key pillars of cognitive development and the order in which cognitive faculties develop in animals. Groups which are diverse (on multiple dimensions) are expected to produce better epistemic outcomes  [37] ,  [52] . We encourage the careful design and phrasing of questions to enable participants to make use of their expertise, but refrain from demanding answers that lie outside their area of expertise. For example, asking machine learning researchers directly for milestones towards HLMI does not draw on their expertise. But asking machine learning researchers about the limitations of the methods they use every day; or asking psychologists what human capacities they see lacking in machines today, draws directly on their day-to-day experience. Perceived limitations can be then be transformed into milestones. There are several different methods available for expert elicitation including surveys, interviews, workshops and focus groups, each with advantages and disadvantages. Interviews provide greater opportunity to tailor questions to the specific expert, but can be time-intensive compared to surveys and reduce the sample size of experts. If possible, some combination of the two may be ideal: using carefully selected semi-structured interviews to elicit initial milestones, followed-up with surveys with a much broader group to validate which milestones are widely accepted as being key. \n B. Mapping Causal Relations Between Milestones The second step of our methodology involves convening experts to identify causal relations between identified milestones: that is, how milestones may underpin, depend on, or affect progress towards other milestones. Experts should be guided in generating directed causal graphs, a type of cognitive map that elicits a person's perceived causal relations between components. Causal graphs use arrows to represent perceived causal relations between nodes, which in this case are milestones  [53] . This process primarily focuses on finding out whether or not a relationship exists at all; how precisely this relationship is specified can be adapted to the goals of the study. An arrow from A to B at minimum indicates that progress on A will allow for further progress on B. But this relationship can also be made more precise: in some cases indicating that progress on AI is necessary for progress on B, for example. The relationship between nodes may be either linear or nonlinear; again this can be specified more precisely if needed or known. Constructing and debating causal graphs can \"help groups to convert tacit knowledge into explicit knowledge\"  [53] . Causal graphs are used as decision support for individuals or groups, and are often used to solve problems in policy and management involving complex relationships between components in a system by tapping into experts' mental models and intuitions. We therefore suggest that causal graphs are particularly well-suited to eliciting experts' models and assumptions about the relationship between different milestones in AI development. As a method, causal graphs are highly flexible and can be adapted to the preferred level of detail for a given study: they can be varied in complexity and can be analysed both quantitatively and qualitatively  [54] ,  [55] . We neither exclude nor favour quantitative approaches here, due to the complexity and uncertainty of the questions around transformative events. Particularly for very high-level questions, quantitative approaches might not offer much advantage and might communicate a false sense of certainty. In narrower domains where there is more existing evidence, however, quantitative approaches may help to represent differences in the strength of relationships between milestones. [56] notes that there are no ready-made designs that will fit all studies: design and analysis of causal mapping procedures must be matched to a clear theoretical context and the goal of the study. We highlight a number of different design choices which can be used to adapt the process. As more studies use causal graphs in expert elicitations about AI developments, we can learn from the success of different design choices over time and identify best practices.  [53]  stress that interviews or collective brainstorming are the most accepted method for generating the data upon which to analyse causal relations.  [57]  list heuristics on how to manage the procedure of combining graphs by different participants, or see  [58]  for a discussion on evaluating different options presented by experts.  [59]  suggest visual, interactive tools to aid the process.  [56]  and  [60]  discuss approaches to analysing graphs and extracting the emergent properties, significant 'core' nodes as well as hierarchical clusters. Core or \"potent\" nodes are those that relate to many clusters in the graphs and thus have implications for connected nodes. In our proposed methodology, such potent nodes play a central role in pointing to canary milestones. For more detail on the many options on how to generate, analyse and use causal graphs we refer the reader to the volume of  [57] , or reviews such as  [53] ,  [59] . See  [55]  for an example of applying cognitive mapping to expert views on UK public policies; and  [61]  for group problem solving with causal graphs. We propose that identified experts be given instruction in generating either an individual causal graph, after which a mediated discussion between experts generates a shared graph; or that the groups of experts as a whole generates the causal graph via argumentation, visualisations and voting procedures if necessary. As  [62]  emphasises, any group of experts will have both shared and conflicting assumptions, which causal graphs aim to integrate in a way that approaches greater accuracy than that contained in any single expert viewpoint. The researchers are free to add as much detail to the final maps as required or desired. Each node can be broken into subcomponents or justified with extensive literature reviews. \n C. Identifying Canaries Finally, the resulting causal graphs can be used to identify nodes of particular relevance for progress towards the transformative event in question. This can be a node with a high number of outgoing arrows, i.e. milestones which unlock many others that are prerequisites for the event in question. It can also be a node which functions as a bottleneck -a single dependency node that restricts access to a subsequent highly significant milestone. See Fig.  2  for an illustration. Progress on these milestones can thus represent a 'canary', indicating that further advances in subsequent milestones will become possible and more likely. These canaries can act as early warning signs for potentially rapid and discontinuous progress, or may signal that applications are becoming ready for deployment. Experts identify nodes which unlock or provide a bottleneck for a significant number of other nodes (some amount of discretion from the experts/conveners will be needed to determine what counts as 'significant'). Of course, in some cases generating these causal graphs and using them to identify canaries may be as complicated as a full scientific research project. The difficulty of estimating causal relationships between future technological advances must not be underestimated. However, we believe it to be the case that each individual researcher already does this to some extent, when they chose to prioritise a research project, idea or method over another within a research paradigm. Scientists also debate the most fruitful and promising research avenues and arguably place bets on implicit maps of milestones as they pick a research agenda. The idea is not to generate maps that provide a perfectly accurate indication of warning signs, but to use the wisdom of crowds to make implicit assumptions explicit, creating the best possible estimate of which milestones may provide important indications of future transformative progress. \n IV. Using Early Warning Signs Once identified, canary milestones can immediately help to focus existing efforts in forecasting and anticipatory governance. Given limited resources, early warning signs can direct governance attention to areas of AI progress which are soon likely to impact society and which can be influenced now. For example, if progress in a specific area of NLP (e.g. sentiment analysis) serves as a warning sign for the deployment of more engaging social bots to manipulate voters, policymakers and regulators can monitor or regulate access and research on this research area within NLP. We can also establish research and policy initiatives to monitor and forecast progress towards canaries. Initiatives might automate the collection, tracking and flagging of new publications relevant to canary capabilities, and build a database of relevant publications. They might use prediction platforms to enable collective forecasting of progress towards canary capabilities. Foundational research can try to validate hypothesised relationships between milestones or illuminate the societal implications of different milestones. These forecasting and tracking initiatives can be used to improve policy prioritisation more broadly. For example, if we begin to see substantial progress in an area of AI likely to impact jobs in a particular domain, policymakers can begin preparing for potential unemployment in that sector with greater urgency. However, we believe the value of early warning signs can go further and support us in democratising the development and deployment of AI. Providing opportunities for participation and control over policy is a fundamental part of living in a democratic society. It may be especially important in the case of AI, since its deployment might indeed transform society across many sectors. If AI applications are to bring benefits across such wide-ranging contexts, AI deployment strategies must consider and be directed by the diverse interests found across those sectors. Interests which are underrepresented at technology firms are otherwise likely to bear the negative impacts. There is currently an information asymmetry between those developing AI and those impacted by it. Citizens need better information about specific developments and impacts which might affect them. Public attention and funding for deliberation processes is not unlimited, so we need to think carefully about which technologies to direct public attention and funding towards. Identifying early warning signs can help address this issue, by focusing the attention of public debate and directing funding towards deliberation practises that centre around technological advancements on the horizon. We believe early warning signs may be particularly well-suited to feed into participatory technology assessments (PTAs), as introduced earlier. Early warning signs can provide a concrete focal point for citizens and domain experts to collectively discuss concerns. Having identified a specific warning sign, various PTA formats could be suited to consult citizens who are especially likely to be impacted. PTAs come in many forms and a full analysis of which design is best suited to assessing particular AI applications is beyond the scope of this article. But the options are plenty and PTAs show much potential (see section 2). For example, Taiwan has had remarkable success and engagement with an open consultation of citizens on complex technology policy questions  [42] . An impact assessment of PTA is not a simple task, but we hypothesise that carefully designed, inclusive PTAs would present a great improvement over how AI is currently developed, deployed and governed. Our suggestion is not limited to governmental bodies. PTAs or other deliberative processes can be run by research groups and private institutions such as AI labs, technology companies and think tanks who are concerned with ensuring AI benefits all of humanity. \n V. Method Illustrations We outline two examples of how this methodology could be adapted and implemented: one focused on identifying warning signs of a particular societal impact, the other on warning signs of progress towards particular technical capabilities. Both these examples pertain to high-level, complex questions about the future development and impacts of AI, meaning our discussion can only begin to illustrate what the process of identifying canaries would look like, and what questions such a process might raise. Since the results are only the suggestions of the authors of this paper, we do not show a full implementation of the method whose value lies in letting a group of experts deliberate. As mentioned previously, the work of generating these causal maps will often be a research project of its own, and we will return later to the question of what level of detail and certainty is needed to make the resulting graphs useful. \n A. First Illustration: AI Applications in Voter Manipulation We show how our method could identify warning signs of the kind of algorithmic progress which could improve the effectiveness of, or reduce the cost of, algorithmic election manipulation. The use of algorithms in attempts to manipulate election results incur great risk for the epistemic resilience of democratic countries  [63] -  [65] . Manipulations of public opinion by national and commercial actors are not a new phenomenon.  [66]  details the history of how newly emerging technologies are often used for this purpose. But recent advances in deep learning techniques, as well as the widespread use of social media, have introduced easy and more effective mechanisms for influencing opinions and behaviour.  [8]  and  [67]  detail the various ways in which political and commercial actors incur harm to the information ecosystem via the use of algorithms. Manipulators profile voters to identify susceptible targets on social media, distribute micro-targeted advertising, spread misinformation about policies of the opposing candidate and try to convince unwanted voters not to vote. Automation plays a large role in influencing online public discourse. Publications like  [68] ,  [69]  note that manipulators use both human-run accounts and bots  [70]  or a combination of the two  [71] . Misinformation  [72]  and targeted messaging  [73]  can have transformative implications for the resilience of democracies and very possibility of collective action  [74] ,  [75] . Despite attempts by national and sub-national actors to apply algorithms to influence elections, their impact so far has been contested  [76] . Yet, foreign actors and national political campaigns will continue to have incentives and substantial resources to invest in such campaigns, suggesting their efforts are unlikely to wane in future. We may thus inquire what kinds of technological progress would increase the risk that elections can be successfully manipulated. We can begin this inquiry by identifying what technological barriers currently prevent full-scale election manipulation. We would identify those technological limitations by drawing on the expertise of actors who are directly affected by these bottlenecks. Those might be managers of online political campaigns and foreign consulting firms (as described in  [8] ), who specialise in influencing public opinion via social media, or governmental organisations across the world who comment on posts, target individual influencers and operate fake accounts to uphold and spread particular beliefs. People who run such political cyber campaigns have knowledge of what technological bottlenecks still constrain their influence on voter decisions. We recommend running a series of interviews to collect a list of limitations. This list might include, for example, that the natural language functionality of social bots is a major bottleneck for effective online influence (for the plausibility of this being an important technical factor see  [8] ). Targeted users often disengage from a chat conversation after detecting that they are exchanging messages with social bots. Low retention time is presumably a bottleneck for further manipulation, which suggests that improvements in natural language processing (NLP) would significantly reduce the cost of manipulation as social bots become more effective. We will assume, for the purpose of this illustration that NLP were to be identified as a key bottleneck. We would then seek to gather experts (e.g. in a workshop) who can identify and map milestones (or current limitations) in NLP likely to be relevant to improving the functionality of social bots. This will include machine learning experts who specialise in NLP and understand the technical barriers to developing more convincing social bots; as well as experts in developmental linguistics and evolutionary biology, who can determine suitable benchmarks and the required skills, and who understand the order in which linguistic skills are usually developed in animals. From these expert elicitation processes we would acquire a list of milestones in NLP which, if achieved, would likely lower the cost and increase the effectiveness of online manipulation. Experts would then order milestones into a causal graph of dependencies. Given the interdisciplinary nature of the question at hand, we suggest in this case that the graph should be directly developed by the whole group. A mediated discussion in a workshop context can help to draw out different connections between milestones and the reasoning behind them, ensuring participants do not make judgements outside their range of expertise. A voting procedure such as majority voting should be used if no consensus can be reached. In a final step, experts can highlight milestone nodes in the final graph which are either marked by many outgoing nodes or are bottlenecks for a series of subsequent nodes that are not accessed by an alternative pathway. These (e.g. sentiment analysis) are our canaries: areas of progress which serve as a warning sign of NLP being applied more effectively in voter manipulation. Having looked at how this methodology can be used to identify warning signs of a specific societal impact, we next illustrate a different application of the method in which we aim to identify warning signs of a research breakthrough. \n B. Second Illustration: High-level Machine intelligence We use this second example to illustrate in more detail what the process of developing a causal map might look like once initial milestones have been identified, and how canary capabilities can be identified from the map. We define high-level machine intelligence (HLMI) as an AI system (or collection of AI systems) that performs at the level of an average human adult on key cognitive measures required for economically relevant tasks. We choose to focus on HLMI since it is a milestone which has been the focus of previous forecasting studies  [10] ,  [15] , and which, despite the ambiguity and uncertain nature of the concepts, is interesting to attempt to examine, because it is likely to precipitate widely transformative societal impacts. To trial this method, we used interview results from  [11] . 25 experts from a diverse set of disciplines (including computer science, cognitive science and neuroscience) were interviewed and asked what they believed to be the main limitations preventing current machine learning methods from achieving the capabilities of HLMI. These limitations can be translated into 'milestones': capabilities experts believe machine learning methods need to achieve on the path to HLMI, i.e. the output of step 1 of our methodology. Having identified key milestones, step 2 of our methodology involves exploring dependencies between them using causal graphs. We use the software VenSim to illustrate hypothesised relationships between milestones (see Fig.  2 ). For example, we hypothesise that the ability to formulate, comprehend and manipulate abstract concepts may be an important prerequisite to the ability to account for unobservable phenomena, which is in turn important for reasoning about causality. This map of causal relations and dependencies was constructed by the authors alone, and is therefore far from definitive, but provides a useful illustration of the kind of output this methodology can produce. Based on this causal map, we can identify three candidates for canary capabilities: \n Representations that allow variable-binding and disentanglement: the ability to construct abstract, discrete and disentangled representations of inputs, to allow for efficiency and variable-binding. We hypothesise that this capability underpins several others, including grammar, mathematical reasoning, concept formation, and flexible memory. Flexible memory: the ability to store, recognise, and re-use memory and knowledge representations. We hypothesise that this ability would unlock many others, including the ability to learn from dynamic data, to learn in a continual fashion, and to update old interpretations of data as new information is acquired. Positing unobservables: the ability to recognise and use unobservable concepts that are not represented in the visual features of a scene, including numerosity or intentionality. We might tentatively suggest that these are important capabilities to track progress on from the perspective of anticipating HLMI. \n VI. Discussion and Future Directions As the two illustrative examples show, there are many complexities and challenges involved in putting this method into practice. One particular challenge is that there is likely to be substantial uncertainty in the causal graphs developed. This uncertainty can come in many forms. Milestones that are not well understood are likely to be composed of several sub-milestones. As more research is produced, the graph will be in need of revision. Some such revisions may include the addition of connections between milestones that were previously not foreseen, which in turn might alter the number of outgoing connections from nodes and turn them into potent nodes, i.e. 'canaries'. The process of involving a diversity of experts in a multi-stage, collaborative process is designed to reduce this uncertainty by allowing for the identification of nodes and relationships that are widely agreed upon and so more likely to be robust. However, considerable uncertainty will inevitably remain due to the nature of forecasting. The higher the level of abstraction and ambiguity in the events studied (like events such as HLMI, which we use for our illustration) the greater the uncertainty inherent in the map and the less reliable the forecasts will likely be. It will be important to find ways to acknowledge and represent this uncertainty in the maps developed and conclusions drawn from them. This might include marking uncertainties in the graph and taking this into account when identifying and communicating 'canary' nodes. Given the uncertainty inherent in forecasting, we must consider what kinds of inevitable misjudgements are most important to try to avoid. A precautionary perspective would suggest it is better to slightly overspend resources on monitoring canaries that turn out to be false positives, rather than to miss an opportunity to anticipate significant technological impacts. This suggests we may want to set a low threshold for what should be considered a 'canary' in the final stage of the method. The uncertainty raises an important question: will it on average be better to have an imperfect, uncertain mapping of milestones rather than none at all? There is some chance that incorrect estimates of 'canaries' could be harmful. An incorrect mapping could focus undue attention on some avenue of AI progress, waste resources or distract from more important issues. Our view is that it is nonetheless preferable to attempt a prioritisation. The realistic alternative is that anticipatory governance is not attempted or informed by scholars' individual estimates in an ad-hoc manner, which we should expect to be incorrect more often than our collective and structured expert elicitation. How accurate our method is can only be studied by trialling it and tracking its predictions as AI research progresses to confirm or refute the forecasts. Future studies are likely to face several trade-offs in managing the uncertainty. For example, a large and cognitively diverse expert group may be better placed to develop robust maps eventually, but this may be a much more challenging process than doing it with a smaller, less diverse group --making the latter a tempting choice (see  [45]  for a discussion of this trade-off). The study of broad and high-level questions (such as when we might attain HLMI or automate a large percentage of jobs) may be more societally relevant or intellectually motivating, but narrower studies focused on nearer-term, well-defined applications or impacts may be easier to reach certainty on. A further risk is that this method, intended to identify warning signs so as to give time to debate transformative applications, may inadvertently speed up progress towards AI capabilities and applications. By fostering expert deliberation and mapping milestones, it is likely that important research projects and goals are highlighted and the field's research roadmap is improved. This means our method must be used with caution. However, we do not believe this is a reason to abandon the approach, since these concerns must be balanced against the benefits of being able to deliberate upon and shape the impacts of AI in advance. In particular, we believe that the process of distilling information from experts in a way that can be communicated to wider society, including those currently underrepresented in debates about the future of AI, is likely to have many more benefits than costs. The idea that we can identify 'warning signs' for progress assumes that there will be some time lag between progress on milestones, during which anticipatory governance work can take place. Of course, the extent to which this is possible will vary, and in some cases, unlocking a 'canary' capability could lead to very rapid progress on subsequent milestones. Future work could consider how to incorporate assessment of timescales into the causal graphs developed, so that it is easier to identify canaries which warn of future progress while allowing time to prepare. Future work should also critically consider what constitutes relevant 'expertise' for the task of identifying canaries, and further explore ways to effectively integrate expert knowledge with the values and perspectives of diverse publics. Our method finds a role for the expert situated in a larger democratic process of anticipating and regulating emerging technologies. Expert judgement can thereby be beneficial to wider participation. However, processes that allow more interaction between experts and citizens could be even more effective. One limitation of the method presented in this paper is that it requires one to have already identified a particular transformative event of concern, but does not provide guidance on how to identify and prioritise between events. It may be valuable to consider how citizens that are impacted by technology can play a role in identifying initial areas of concern, which can then feed into this process of expert elicitation to address the concerns. \n VII. Conclusion We have presented a flexible method for identifying early warning signs, or 'canaries' in AI progress. Once identified, these canaries can provide focal points for anticipatory governance efforts, and can form the basis for meaningful participatory processes enabling citizens to steer AI developments and their impacts. Future work must now test this method by putting it into practice, which will more clearly reveal both benefits and limitations. Our artificial canaries offer a chance for forward-looking, democratic assessments of transformative technologies. \n Appendix It is worth noting there are apparent similarities and relationships between many of these milestones. For example, representation: the ability to learn abstract representations of the environment, seems closely related to variable binding: the ability to formulate place-holder concepts. The ability to apply learning from one task to another, crossdomain generalisation, seems closely related to analogical reasoning. Further progress in research will tell which of these are clearly separate milestones or more closely related notions. Flexible memory, as described by experts in our sample, is the ability to recognize and store reusable information, in a format that is flexible so that it can be retrieved and updated when new knowledge is gained. We explain the reasoning behind the labelled arrows in Fig.  2  (see Fig. • (B): the ability to reinterpret data in light of new information likely requires flexible memory, since it requires the ability to retrieve and alter previously stored information. • (C) and (E): to make use of dynamic and changing data input, and to learn continuously over time, an agent must be able to store, correctly retrieve and modify previous data as new data comes in. • (D): in order to plan and execute strategies in brittle environments with long delays between actions and rewards, an agent must be able to store memories of past actions and rewards, but easily retrieve this information and continually update its best guess about how to obtain rewards in the environment. • (F): analogical reasoning involves comparing abstract representations, which requires forming, recognising, and retrieving representations of earlier observations. Progress in flexible memory therefore seems likely to unlock or enable many other capabilities important for HLMI, especially those crucial for applying AI systems in real environments and more complex tasks. These initial hypotheses should be validated and explored in more depth by a wider range of experts. as well as the attendees of the workshop Evaluating Progress in AI at the European Conference on AI (Aug 2020) for recognizing the potential of this work. We particularly thank Carolyn Ashurst and Luke Kemp for their efforts and commentary on our drafts. FFig. 3 . 3 Fig.3. Extract of Fig.2, showing one candidate canary capability. \n Cognitive map of dependencies between milestones collected in expert elicitations. Arrows coloured in green signify those milestones that have most outgoing arrows. See appendix for description of each milestone and dependency relations between one 'canary' node and subsequent nodes. Object Permanence Uncertainty Estimation Meta-Learning, Architecture-Search Visual Answering estion Causality Theorising, Hypothesising Common Sense Reading Comprehension Grammer Hierarchical Decomposition Posit Unobservables Adverserial A acks Cross-Domain Generalisation Scalability Mathematical Reasoning Representation, Variable-Binding, Disentanglement Concept Formation Analogical Reasoning, Overfi ing E icient Learning Catastrophic Forge ing Flexible Memory Continual Learning Active Learning Environmental Pressure Reinterpretations Dynamic Data Bri le Environments Misguided Data Collection Context-Dependent Decisions Fig. 2.", "date_published": "n/a", "url": "n/a", "filename": "ijimai_6_5_10.tei.xml", "abstract": "We propose a method for identifying early warning signs of transformative progress in artificial intelligence (AI), and discuss how these can support the anticipatory and democratic governance of AI. We call these early warning signs 'canaries', based on the use of canaries to provide early warnings of unsafe air pollution in coal mines. Our method combines expert elicitation and collaborative causal graphs to identify key milestones and identify the relationships between them. We present two illustrations of how this method could be used: to identify early warnings of harmful impacts of language models; and of progress towards high-level machine intelligence. Identifying early warning signs of transformative applications can support more efficient monitoring and timely regulation of progress in AI: as AI advances, its impacts on society may be too great to be governed retrospectively. It is essential that those impacted by AI have a say in how it is governed. Early warnings can give the public time and focus to influence emerging technologies using democratic, participatory technology assessments. We discuss the challenges in identifying early warning signals and propose directions for future work.", "id": "9f876316cc75e629fb37e9c9d90daa71"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dennis Pamlin", "Stuart Armstrong", "Dr Nick Beckstead", "Kennette Benedict", "Oliver Bettis", "Dr Eric Drexler", "Madeleine Enarsson", "Martin Hellman", "Aled Jones", "Nick Mabey", "Jennifer Morgan", "Prof Vincent Müller", "Prof Toby Ord", "Dr Anders Sandberg", "Nick Silver", "Andrew Simms", "Academic Project Manager, Andrew Snyder-Beattie", "Nathan Wolfe", "Investment Consultant at Liang Yin", "Towers Watson"], "title": "Member of the National Expert Panel on Climate Change and National Foreign Policy Advisory Committee, China", "text": "The main authors of this report are Dennis Pamlin, Executive Project Manager, Global Challenges Foundation and Dr Stuart Armstrong, James Martin Research Fellow, Future of Humanity Institute, Oxford Martin School & Faculty of Philosophy, University of Oxford. Dr Stuart Armstrong wrote the chapter covering the twelve global challenges, under the direction of Dennis Pamlin who served as project manager and himself wrote and edited the rest of the report. Seth Baum, Executive Director of the Global Catastrophic Risk Institute and affiliate researcher at the Center for Research on Environmental Decisions, Columbia University, also played an important role as he helped develop the methodology chapter regarding the selection of the global challenges with potentially infinite impacts as well as providing helpful input throughout the process. The report is the result of a collaborative approach where many people have provided invaluable contributions. The authors would therefore like to thank a few people in particular. First and foremost László Szombatfalvy, Chairman of the Global Challenges Foundation, whose work is the basis for this report and whose guidance on all levels has been invaluable. The rest of the board of the Global Challenges Foundation have also contributed in many different ways, in particular, Johan Rockström has provided important input regarding the structure and methodology. Outside the foundation Prof Nick Bostrom, Professor & Director of the Future of Humanity Institute, Oxford Martin School & Faculty of Philosophy, University of Oxford, who initiated the possibility of working with the Future of Humanity Institute at the University of Oxford, played a particularly important role. Patrick McSharry, Head of Smith School's Catastrophe Risk Financing research area, provided invaluable input regarding complex systems and ways that the economic system can respond to infinite impacts. Alex Kirby also played a key part as he did so much more than proofread the text; the report would hardly be possible to read without his help. Various additional edits and changes were made by Peter Brietbart. Others that must be mentioned, including those who participated in the workshop on 14 January 2014, at the Future of Humanity Institute (FHI), University of Oxford and the workshop at the Munich RE office in London on 15 January 2014, and helped provide input regarding the economic and finance aspects, include (in alphabetical order): Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks This is the executive summary of a report about a limited number of global risks that pose a threat to human civilisation, or even possibly to all human life. \n Summary Executive 4 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Executive Summary \n History: the LA-602 document With such a focus it may surprise some readers to find that the report's essential aim is to inspire action and dialogue as well as an increased use of the methodologies used for risk assessment. The real focus is not on the almost unimaginable impacts of the risks the report outlines. Its fundamental purpose is to encourage global collaboration and to use this new category of risk as a driver for innovation. The idea that we face a number of global challenges threatening the very basis of our civilisation at the beginning of the 21st century is well accepted in the scientific community, and is studied at a number of leading universities. I However, there is still no coordinated approach to address this group of challenges and turn them into opportunities. It is only 70 years ago that Edward Teller, one of the greatest physicists of his time, with his back-of-the-envelope calculations, produced results that differed drastically from all that had gone before. His calculations showed that the explosion of a nuclear bomb -a creation of some of the brightest minds on the planet, including Teller himself -could result in a chain reaction so powerful that it would ignite the world's atmosphere, thereby ending human life on Earth. Robert Oppenheimer, who led the Manhattan Project to develop the nuclear bomb, halted the project to see whether Teller's calculations were correct. The resulting document, LA-602: Ignition of the Atmosphere with Nuclear Bombs, concluded that Teller was wrong. But the sheer complexity drove the assessors to end their study by writing that \"further work on the subject [is] highly desirable\". The LA-602 document can be seen as the first global challenge report addressing a category of risks where the worst possible impact in all practical senses is infinite. \n Global risks The report conducts its exploration within carefully defined bounds, resulting in a list of twelve risks with potentially infinite outcomes. There were many challenges which might have been included on the list because of their ability to pose severe damage to humanity. They were excluded for one or more of three reasons: 1. Limited impact -tsunamis, for example, and chemical pollution. \n No effective countermeasures - the report focuses on promoting effective interventions and so ignores challenges where nothing useful can be done to prevent or mitigate the impact, as with nearby gamma-ray bursts. 3. Included in other challengesmany challenges are already covered by others, or are very similar to them. Population growth, for one, is significant for climate change and ecosystem catastrophe, but without direct large-scale impacts of its own. It is worth noting that complex systems are often stable only within certain boundaries outside which the system can collapse and rapidly change to a new stable state. Such a collapse can trigger a process where change continues for a long time until a new stable state is found. None of the risks in this report are likely to result directly in an infinite impact, and some cannot do so physically. All the risks however are big enough to reach a threshold where the social and ecological systems become so unstable that an infinite impact could ensue. This is a report about two extremes, not one. It is about how a better understanding of the magnitude of the challenges can help the world to address the risks it faces, and can help to create a path towards more sustainable development. It is a scientific assessment about the possibility of oblivion, certainly, but more than that it is a call for action based on the assumption that humanity is able to rise to challenges and turn them into opportunities. We are confronted with possibly the greatest challenge ever and our response needs to match this through global collaboration in new and innovative ways. This report has, to the best of the authors' knowledge, created the first list of global risks with impacts that for all practical purposes can be called infinite. It is also the first structured overview of key events related to such challenges and has tried to provide initial rough quantifications for the probabilities of these impacts. In the next phase of the project, these placeholder estimates will be improved and refined by a variety of methods (expert elicitation, fault trees, simulations, etc.) appropriate to each specific risk. \n The goals of the report The first of the report's goalsacknowledging the existence of risks with potentially infinite impactseeks to help key stakeholders to acknowledge the existence of the category of risks that could result in infinite impact, and to show them that we can reduce or even eliminate most of them. The second goal is to inspire by showing the practical action that is taking place today. This report seeks to show that helping to meet these global challenges is perhaps the most important contribution anyone can make today, and highlights concrete examples to inspire a new generation of leaders. The third goal is to connect different groups at every level, so that leaders in different sectors connect with each other to encourage collaboration. This will need a specific focus on financial and security policy, where significant risks combine to demand action beyond the incremental. The fourth goal is to deliver actual strategies and initiatives that produce actual results. The report is a first step and its success will ultimately be measured only on how it contributes to concrete results. The report will have achieved its goals when key decision-makers recognise the magnitude of the possible risks and our ability to reduce or even eliminate most of them. The four main goals of this report are to acknowledge, inspire, connect and deliver. \n Report structure The second part is an overview of the twelve challenges and key events that illustrate strategic work to address them. It also lists for each challenge five important factors that influence its probability or impact. The challenges are divided into four different categories: -current challenges includes those which currently threaten humanity because of its economic and technological development; -exogenic challenges are those where the basic probability of an event is beyond human control, but where the probability and magnitude of the impact can be influenced; -emerging challenges could both help reduce the risks associated with current challenges and also result in infinite impacts; -the last of the twelve challenges are global policy challenges, threats arising from future global governance as it resorts to destructive policies in response to the categories of challenge listed above. The third part of the report discusses the relationship between the different challenges, as action to address one can increase the risk of another. Many solutions can also address multiple challenges, so there are significant benefits from understanding how they are linked. The fourth part is an overview, the first ever to the authors' knowledge, of the probabilities of global challenges with potentially infinite impacts. The fifth part presents some of the most important underlying trends that influence the challenges, which often build up slowly to a threshold where very rapid changes can ensue. The sixth part presents an overview of possible ways forward. \n The first part of the report introduces and defines the global challenges and includes the methodology for selecting them. A new category of global risk Risk Probability Impact = x For several reasons the potentially infinite impacts of the challenges in this report are not as well known as they should be. One reason is the way that extreme impacts are often masked by most of the theories and models used by governments and business today. Climate change is a good example, where almost all of the focus is on the most likely scenarios, and there are few public studies that include the low-probability high-impact scenarios. In most reports about climate impacts, those caused by warming beyond five or six degrees Celsius are omitted from tables and graphs. Other aspects that contribute to this relative invisibility include the fact that extreme impacts are difficult to translate into monetary terms, as they have a global scope and often require a time-horizon of a century or more. They cannot be understood simply by linear extrapolation of current trends, and they lack historical precedents. There is also the fact that the measures required to significantly reduce the probability of infinite impacts will be radical compared to a business-as-usual scenario. A scientific approach requires us to base our decisions on the whole probability distribution. The review of literature indicates that, under a business as usual scenario, new risks with potential infinite impact are probably inseparable from the rapid technological development in areas like synthetic biology, nanotechnology and AI. Most risks are linked to increased knowledge, economic and technical development that has brought many benefits. E.g. climate change is a result from the industrial revolution and fossil fuel based development. The increased potential for global pandemics is one consequence of an integrated global economy where goods and services move quickly internationally. Similar challenges can be expected for synthetic biology, nanotechnology and AI. There are remedies, including technological and institutional, for all risks. But they will require collaboration of a sort humanity has not achieved before, and the creation of systems which can deal with problems pre-emptively. It is important to understand that much of the knowledge and many tools that we have, and will develop, can be both a risk and a solution to risks depending on context. The idea that there may be risks where the impact can be described as infinite, defined as the end of human civilisation or even human life, is not new. However, it excites relatively little political or academic interest, and the way it is treated in popular culture makes a serious discussion more difficult. \n Infinite impacts and thresholds Normal Risks \n Threshold Traditional measures and tools applicable \n New Category Requires new measures and tools impact 0 probability Risk Probability Impact = x Using traditional economic tools is problematic and can generate disagreement over issues such as discounting, which the report examines in some detail, considering for example the role of tipping points. The report distinguishes between the concepts of infinite impact -where civilisation collapses to a state of great suffering and does not recover, or a situation where all human life ends -and infinite impact thresholdan impact that can trigger a chain of events that could result first in a civilisation collapse, and then later result in an infinite impact. Such thresholds are especially important to recognise in a complex and interconnected society where resilience is decreasing. A collapse of civilisation is defined as a drastic decrease in human population size and political/ economic/social complexity, globally plunge temperatures below freezing around the globe and possibly also destroy most of the ozone layer. The detonations would need to start firestorms in the targeted cities, which could lift the soot up into the stratosphere. The risks are severe and recent models have confirmed the earlier analysis. The disintegration of the global food supply would make mass starvation and state collapse likely. As for all risks there are uncertainties in the estimates, and warming could be much more extreme than the middle estimates suggest. Feedback loops could mean global average temperatures increase by 4°C or even 6°C over pre-industrial levels. Feedbacks could be the release of methane from permafrost or the dieback of the Amazon rainforest. The impact of global warming would be strongest in poorer countries, which could become completely uninhabitable for the highest range of warming. The likelihood of a full-scale nuclear war between the USA and Russia has probably decreased. Still, the potential for deliberate or accidental nuclear conflict has not been removed, with some estimates putting the risk in the next century or so at around 10%. A larger impact would depend on whether or not the war triggered what is often called a nuclear winter or something similarthe creation of a pall of smoke high in the stratosphere that would Mass deaths and famines, social collapse and mass migration are certainly possible in this scenario. Combined with shocks to the agriculture and biosphere-dependent industries of the more developed countries, this could lead to global conflict and possibly civilisation collapse. Further evidence of the risk comes from signs that past civilisation collapses have been driven by climate change. The uncertainties in climate sensitivity models, including the tail. The likelihood -or not -of global coordination on controlling emissions. The future uptake of low carbon economies, including energy, mobility and food systems. Whether technological innovations will improve or worsen the situation, and by how much. How relations between current and future nuclear powers develop. The probability of accidental war. Whether disarmament efforts will succeed in reducing the number of nuclear warheads. The likelihood of a nuclear winter. The long-term effects of a nuclear war on climate, infrastructure and technology. A new category of global risk. Executive Summary the damage and (unlike previous, localised collapses) the whole world is potentially at risk. It seems plausible that some human lifestyles could be sustained in a relatively ecosystem independent way, at relatively low costs. Whether this can be achieved on a large scale in practice, especially during a collapse, will be a technological challenge and whether it is something we want is an ethical question. This is where an ecosystem suffers a drastic, possibly permanent, reduction in carrying capacity for all organisms, often resulting in mass extinction. Humans are part of the global ecosystem and so fundamentally depend on it. Species extinction is now far faster than the historic rate, and attempts to quantify a safe ecological operating space place humanity well outside it. \n Many of the problems of ecological degradation interact to multiply The extent to which humans are dependent on the ecosystem. Whether there will be effective political measures taken to protect the ecosystem on a large scale. The likelihood of the emergence of sustainable economies. The positive and negative impacts on the ecosystems of both wealth and poverty. The long-term effects of an ecological collapse on ecosystems. 5 key factors: An epidemic of infectious disease that has spread through human populations across a large region or even worldwide. There are grounds for suspecting that such a highimpact epidemic is more probable than usually assumed. All the features of an extremely devastating disease already exist in nature: essentially incurable (Ebola), nearly always fatal (rabies), extremely infectious (common cold), and long incubation periods (HIV). If a pathogen were to emerge that somehow combined these features What the true probability distribution for pandemics is, especially at the tail. The capacity of international health systems to deal with an extreme pandemic. How fast medical research can proceed in an emergency. How mobility of goods and people, as well as population density, will affect pandemic transmission. Whether humans can develop novel and effective anti-pandemic solutions. (and influenza has demonstrated antigenic shift, the ability to combine features from different viruses), its death toll would be extreme. The world has changed considerably, making comparisons with the past problematic.Today it has better sanitation and medical research, as well as national and supra-national institutions dedicated to combating diseases. But modern transport and dense human population allow infections to spread much more rapidly, and slums can be breeding grounds for disease. An economic or societal collapse on the global scale. The term has been used to describe a broad range of conditions. Often economic collapse is accompanied by social chaos, civil unrest and sometimes a breakdown of law and order. Societal collapse usually refers to the fall or disintegration of human societies, often along with their life support systems. The world economic and political system is made up of many actors with many objectives and many links between them. Such intricate, interconnected systems are subject to unexpected system-wide failures caused by the structure of the network -even if each component of the network is reliable. This gives rise to systemic risk, when parts that individually may function well become vulnerable when connected as a system to a self-reinforcing joint risk that can spread from part to part, potentially affecting the entire system and possibly spilling over to related outside systems. Such effects have been observed in ecology, finance and critical infrastructure such as power grids. The possibility of collapse becomes more acute when several independent networks depend on each other. Whether global system collapse will trigger subsequent collapses or fragility in other areas. What the true trade-off is between efficiency and resilience. Whether effective regulation and resilience can be developed. Whether an external disruption will trigger a collapse. Whether an internal event will trigger a collapse. Whether detection and tracking of asteroids and other dangerous space objects is sufficiently exhaustive. How feasible it is to deflect an asteroid. Whether measures such as evacuation could reduce the damage of an impact. The short-and long-term climate consequences of a collision. Whether our current civilisation could adapt to a post-impact world. 5 key factors: Large asteroid collisions -with objects 5 km or more in sizehappen about once every twenty million years and would have an energy a hundred thousand times greater than the largest bomb ever detonated. A land impact would destroy an area the size of a nation like Holland. Larger asteroids could be extinction-level events. Asteroid impacts are probably one of the best understood of all risks in this report. There has been some discussion about possible methods for deflecting asteroids found on a collision course with the planet. Should an impact occur the main destruction will not be from the initial impact, but from the clouds of dust projected into the upper atmosphere. The damage from such an \"impact winter\" could affect the climate, damage the biosphere, affect food supplies, and create political instability. \n Global System Collapse Major Asteroid Impact 16 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Executive Summary The true destructive potential of synthetic biology, especially the tail risk. Whether the field will be successfully regulated, or successfully manage to regulate itself. Whether the field will usher in a new era of bio-warfare. Whether the tools of synthetic biology can be used defensively to create effective counter measures. The dangers of relying on synthetic biologists to estimate the danger of synthetic biology. This could emerge through military or commercial bio-warfare, bioterrorism (possibly using dual-use products developed by legitimate researchers, and currently unprotected by international legal regimes), or dangerous pathogens leaked from a lab. Of relevance is whether synthetic biology products become integrated into the global economy or biosphere. This could lead to additional vulnerabilities (a benign but widespread synthetic biology product could be specifically targeted as an entry point through which to cause damage). The design and construction of biological devices and systems for useful purposes, but adding human intentionality to traditional pandemic risks. Attempts at regulation or self-regulation are currently in their infancy, and may not develop as fast as research does. One of the most damaging impacts from synthetic biology would come from an engineered pathogen targeting humans or a crucial component of the ecosystem. Any volcano capable of producing an eruption with an ejecta volume greater than 1,000 km 3 . This is thousands of times larger than normal eruptions. The danger from super-volcanoes is the amount of aerosols and dust projected into the upper atmosphere. This dust would absorb the Sun's rays and cause a global volcanic winter. The Mt Pinatubo eruption of 1991 caused an average global cooling of surface temperatures by 0.5°C over three years, while the Toba eruption around 70,000 years ago is thought by some to have cooled global temperatures for over two centuries. The effect of these eruptions could be best compared with that of a nuclear war. The eruption would be more violent than the nuclear explosions, but would be less likely to ignite firestorms and other secondary effects. Whether countries will coordinate globally against super-volcano risk and damage. The predictability of supervolcanic eruptions. How directly destructive an eruption would be. The effectiveness of general mitigation efforts. How severe the long-term climate effects would be. And if these motivations do not detail the survival and value of humanity, the intelligence will be driven to construct a world without humans. This makes extremely intelligent AIs a unique risk, in that extinction is more likely than lesser impacts. On a more positive note, an intelligence of such power could easily combat most other risks in this report, making extremely intelligent AI into a tool of great potential. There is also the possibility of AI-enabled warfare and all the risks of the technologies that AIs would make possible. An interesting version of this scenario is the possible creation of \"whole brain emulations\": human brains scanned and physically represented in a machine. This would make the AIs into properly human minds, possibly alleviating a lot of problems. Atomically precise manufacturing, the creation of effective, highthroughput manufacturing processes that operate at the atomic or molecular level. It could create new products -such as smart or extremely resilient materials -and would allow many different groups or even individuals to manufacture a wide range of things. This could lead to the easy construction of large arsenals of conventional or more novel weapons made possible by atomically precise manufacturing. AI is the intelligence exhibited by machines or software, and the branch of computer science that develops machines and software with human-level intelligence. The field is often defined as \"the study and design of intelligent agents\", systems that perceive their environment and act to maximise their chances of success. Such extreme intelligences could not easily be controlled (either by the groups creating them, or by some international regulatory regime), and would probably act to boost their own intelligence and acquire maximal resources for almost all initial AI motivations. Of particular relevance is whether nanotechnology allows the construction of nuclear bombs. But many of the world's current problems may be solvable with the manufacturing possibilities that nanotechnology would offer, such as depletion of natural resources, pollution, climate change, clean water and even poverty. Some have conjectured special self-replicating nanomachines which would be engineered to consume the entire environment. The misuse of medical nanotechnology is another risk scenario. The timeline for nanotech development. Which aspects of nanotech research will progress in what order. Whether small groups can assemble a weapons arsenal quickly. Whether nanotech tools can be used defensively or for surveillance. Whether nanotech tools or weaponry are made to be outside human control. The reliability of AI predictions. Whether there will be a single dominant AI or a plethora of entities. How intelligent AIs will become. Whether extremely intelligent AIs can be controlled, and if so, how. Whether whole brain emulations (human minds in computer form) will arrive before true AIs. There are two main divisions in governance disasters: failing to solve major solvable problems, and actively causing worse outcomes. An example of the first would be failing to alleviate absolute poverty; of the second, constructing a global totalitarian state. Technology, political and social change may enable the construction of new forms of governance, which may be either much better or much worse. Two issues with governance disasters are first, the difficulty of estimating their probability, and second, the dependence of the impact of these disasters on subjective comparative evaluations: it is not impartially obvious how to rank continued poverty and global totalitarianism against billions of casualties or civilisation collapse. How the severity of nondeadly policy failures can be compared with potential casualties. Whether poor governance will result in a collapse of the world system. How mass surveillance and other technological innovations will affect governance. Whether there will be new systems of governance in the future. Whether a world dictatorship may end up being constructed. 1 2 3 4 5 generic probability of intelligent life (self-)destruction, which includes uncertain risks. Anthropic reasoning can also bound the total risk of human extinction, and hence estimate the unknown component. Non riskspecific resilience and post-disaster rebuilding efforts will also reduce the damage from uncertain risks, as would appropriate national and international regulatory regimes. Most of these methods would also help with the more conventional, known risks, which badly need more investment. These represent the unknown unknowns in the family of global catastrophic challenges. They constitute an amalgamation of all the risks that can appear extremely unlikely in isolation, but can combine to represent a not insignificant proportion of the risk exposure. One resolution to the Fermi paradoxthe apparent absence of alien life in the galaxy -is that intelligent life destroys itself before beginning to expand into the galaxy. Results that increase or decrease the probability of this explanation modify the Whether there will be extensive research into unknown risks and their probabilities. The capacity to develop methods for limiting the combined probability of all uncertain risks. The capacity for estimating \"out of-model\" risks. Often the situation resembles a set of dominoes: if one falls, many follow. Even small impacts can start a process where different risks interact. 2. Specific measures to address a risk: Global risks often require significant changes, which will result in situations where measures to reduce the risk in one area affect the probability and/or the impact in other areas, for better or worse. \n Two things make the understanding of the relation between the global risks particularly important. collaboration difficulty of reducing risk technical difficulty of reducing risk The technical difficulty of reducing the risk and the difficulty of collaboration Below is an example of an overview of how different global risks can be plotted depending on the technical difficulty of reducing the risk and the difficulty of collaborating to reduce it. \n In order to better understand the relations between different global risks, work could start to analyse similarities and differences. Global Challenges -Twelve risks that threaten human civilisation -  \n Probability These estimates are an attempt to assemble existing estimates in order to encourage efforts to improve the numbers. They express estimates of probabilities over 100 years, except in the case of extreme climate change, where the time frame is 200 years. Global challenges need to be seen in the light of trends which help to shape the wider society. These include: Poverty -although it has fallen, it could increase again. This is especially relevant to climate change and pandemics. Population growth -the UN's estimates range from 6.8 billion people by 2100 to a high-variant projection of 16.6 bn (which would require the resources of 10 Earth-like planets to provide everyone with a modern Western lifestyle). Other trends include technological development and demographic changes.  This means that we are now forced to live with the risk of various kinds of extreme disaster with the potential of severely affecting billions of people. \n Preface Preface In this Yearbook from the Global Challenges Foundation, \"risk\" is defined as the potential damage that can be caused by an extreme disaster multiplied by the probability that it will occur. For the risk of exceptional damage, the probability of occurrence is usually small, or very small, compared with other risks in society, but the effects can be absolutely dire, meaning they must be taken very seriously. We do not know what the exact nature of what these risks are or how they may strike. Some are obvious, others may sound like pure science fiction, but they have led many scientists to regard them as real threats -and therefore it is best to include them in the calculations. With few exceptions, humans have created these risks. There are only a few risks where we are not the cause, for example natural disasters such as an asteroid impact. We could eliminate some of these risks (e.g. nuclear war). In other cases, all we can do is minimise the likelihood of damage, since we have already crossed the threshold that can lead to serious consequences (with climate change, for example, where we have already emitted such high levels of greenhouse gases that there are small but not insignificant likelihoods of significant damage). For other risks we cannot affect the likelihood of them occurring, only minimise damage (with supervolcanic eruptions, for instance). However, here we can build social and ecological resilience so as to reduce the damage. For decisions concerning countermeasures the first important question is: What level of probability of global catastrophes are we prepared to accept? This question has not yet appeared on the political agenda. The reason is that both scientific reports and the media choose to focus on the most likely outcome of these risks. In the absence of risk analysis both decision-makers and the public remain blissfully unaware that the probabilities of certain global catastrophes are significantly higher than we would accept in our everyday lives, where incomparably smaller values are at stake. Another, very important reason for not acting against acknowledged global risks is that they require global responses and therefore global decisions. Regrettably there is no global decision-making body capable of that, no globally functioning legal system, and so there is a lack of effective tools for dealing with these challenges. The result: the risks are increased in the absence of effective measures to counter them. This report wants, on a strictly scientific basis, to identify and describe the global risks of extreme disasters, and also to report the latest developments affecting these risks and measures to face up to them. The Global Challenges Foundation's goal in this report is to accelerate effective counter-actions against global events with the potential for large-scale unwanted effects by deepening both decision makers' and the public's insights into the risks, and also to inspire both debate and welljudged decisions on these questions: -What probabilities of extreme disasters are acceptable? -Which are the optimal countermeasures? -How can an effective global decision-making system be created -with or without a global legal system? We are also convinced that knowledge of these risks is not only a prerequisite for reducing them, but also a responsibility which we owe to our children, grandchildren and to all future generations. It is up to us to decide whether these threats can possibly be reduced or not! These efforts do not only demand sacrifices on our part. They also create opportunities for everyone to make a significant contribution to improving the future of humanity: -For world leaders this means assuming their responsibility and starting to work towards common, global decision-making. -Scientists need to focus their research on areas that will help us take effective measures against the risks. -Companies should make sustainability a business model. -And there is a special opportunity for all of us -that when choosing our politicians and suppliers (of goods and services), we should consider their ambition to eliminate or at least minimise global risks and to create an efficient decisionmaking system that can manage these risks. Finally, I would on behalf of the Global Challenges Foundation extend my sincere gratitude to both Dennis Pamlin, editor of the report, and to all the scientists and other experts who have contributed their research and / or valuable comments. \n Laszlo Szombatfalvy Founder and Chairman, With such a focus it may surprise some readers to find that the report's essential aim is to inspire action and dialogue as well as an increased use of the methodologies used for risk assessment. The real focus is not on the almost unimaginable impacts of the risks the report outlines. Its fundamental purpose is to encourage global collaboration and to use this new category of risk as a driver for innovation. The idea that we face a number of global challenges threatening the very basis of our civilisation at the beginning of the 21st century is well accepted in the scientific community, and is studied at a number of leading universities.  2  But there is still no coordinated approach to address this group of challenges and turn them into opportunities for a new generation of global cooperation and the creation of a global governance system capable of addressing the greatest challenges of our time. This report has, to the best of our knowledge, created the first sciencebased list of global risks with a potentially infinite impact and has made the first attempt to provide an initial overview of the uncertainties related to these risks as well as rough quantifications for the probabilities of these impacts. \n What is risk? Risk is the potential of losing something of value, weighed against the potential to gain something of value. Every day we make different kinds of risk assessments, in more or less rational ways, when we weigh different options against each other. The basic idea of risk is that an uncertainty exists regarding the outcome and that we must find a way to take the best possible decision based on our understanding of this uncertainty.  3  To calculate risk the probability of an outcome is often multiplied by the impact. The impact is in most cases measured in economic terms, but it can also be measured in anything we want to avoid, such as suffering. At the heart of a risk assessment is a probability distribution, often described by a probability density function 4 ; see figure X for a graphic illustration. The slightly tilted bell curve is a common probability distribution, but the shape differs and in reality is seldom as smooth as the example. The total area under the curve always represents 100 percent, i.e. all the possible outcomes fit under the curve. In this case (A) represents the most probable impact. With a much lower probability it will be a close to zero impact, illustrated by (B). In the same way as in case B there is also a low probability that the situation will be very significant, illustrated by (C). The impacts (A), (B) and (C) all belong to the same category, normal impacts: the impacts may be more or less serious, but they can be dealt with within the current system. The impacts in this report are however of a special kind. These are impacts where everything will be lost and the situation will not be reversible, i.e challenges with potentially infinite impact. In insurance and finance this kind of risk is called \"risk of ruin\", an impact where all capital is lost.  5  This impact is however only infinite for the company that is losing the money. From society's perspective, that is not a special category of risk. In this report the focus is on the \"risk of ruin\" on a global scale and on a human level, in the worst case this is when we risk the extinction of our own species. On a probability curve the impacts in this report are usually at the very far right with a relatively low probability compared with other impacts, illustrated by (D) in Figure  2 . Often they are so far out on the tail of the curve that they are not even included in studies. For each risk in this report the probability of an infinite impact is very low compared to the most likely outcome. Some studies even indicate that not all risks in this report can result in an infinite impact. But a significant number of peer-reviewed reports indicate that those impacts not only can happen, but that their probability is increasing due to unsustainable trends. The assumption for this report is that by creating a better understanding of our scientific knowledge regarding risks with a potentially infinite impact, we can inspire initiatives that can turn these risks into drivers for innovation. Not only could a better understanding of the unique magnitude of these risks help address the risks we face, it could also help to create a path towards more sustainable development. The group of global risks discussed in this report are so different from most of the challenges we face that they are hard to comprehend. But that is also why they can help us to build the collaboration we need and drive the development of further solutions that benefit both people and the planet. As noted above, none of the risks in this report is likely to result directly in an infinite impact, and some are probably even physically incapable of doing so. But all are so significant that they could reach a threshold impact able to create social and ecological instability that could trigger a process which could lead to an infinite impact. For several reasons the potentially infinite impacts of the risks in this report are not as well known as they should be. One reason is the way that extreme impacts are often masked by most of the theories and models used by governments and business today. For example, the probability of extreme impacts is often below what is included in studies and strategies. The tendency to exclude impacts below a probability of five percent is one reason for the relative \"invisibility\" of infinite impacts. The almost standard use of a 95% confidence interval is one reason why low-probability high-impact events are often ignored. 6  \n Ethical These are impacts that threaten the very survival of humanity and life on Earth -and therefore can be seen as being infinitely negative from an ethical perspective. No positive gain can outweigh even a small probability for an infinite negative impact. Such risks require society to ensure that we eliminate these risks by reducing the impact below an infinite impact as a top priority, or at least do everything we can to reduce the probability of these risks. As some of these risks are impossible to eliminate today it is also important to discuss what probability can right now be accepted for risks with a possible infinite impact. \n Economic Infinite impacts are beyond what most traditional economic models today are able to cope with. The impacts are irreversible in the most fundamental way, so tools like cost-benefit assessment seldom make sense. To use discounting that makes infinite impacts (which could take place 100 years or more from now and affect all future generations) close to invisible in economic assessments, is another example of a challenge with current tools. So while tools like cost-benefit models and discounting can help us in some areas, they are seldom applicable in the context of infinite impacts. New tools are needed to guide the global economy in an age of potential infinite impacts.  \n Infinite impact The concept infinite impact refers to two aspects in particular; the terminology is not meant to imply a literally infinite impact (with all the mathematical subtleties that would imply) but to serve as a reminder that these risks are of a different nature. Climate change is a good example, where almost all of the focus is on the most likely scenarios and there are few studies that include the lowprobability high-impact scenarios. In most reports about climate impacts, the impacts caused by warming beyond five or six degrees Celsius are even omitted from tables and graphs even though the IPCC's own research indicates that the probability of these impacts are often between one and five percent, and sometimes even higher. 7 Other aspects that contribute to this relative invisibility include the fact that extreme impacts are difficult to translate into monetary terms, they have a global scope, and they often require a time-horizon of a century or more. They cannot be understood simply by linear extrapolation of current trends, and they lack historical precedents. There is also the fact that the measures required to significantly reduce the probability of infinite impacts will be radical compared to a business-as-usual scenario with a focus on incremental changes. The exact probability of a specific impact is difficult or impossible to estimate. 8 However, the important thing is to establish the current magnitude of the probabilities and compare them with the probabilities for such impacts we cannot accept. A failure to provide any estimate for these riks often results in strategies and priorities defined as though the probability of a totally unacceptable outcome is zero. An approximate number for a best estimate also makes it easier to understand that a great uncertainty means the actual probability can be both much higher and much lower than the best estimate. It should also be stressed that uncertainty is not a weakness in science; it always exists in scientific work. It is a systematic way of understanding the limitations of the methodology, data, etc. 9 Uncertainty is not a reason to wait to take action if the impacts are serious. Increased uncertainty is something that risk experts, e.g. insurance experts and security policy experts, interpret as a signal for action. A contrasting challenge is that our cultural references to the threat of infinite impacts have been dominated throughout history by religious groups seeking to scare society without any scientific backing, often as a way to discipline people and implement unpopular measures. It should not have to be said, but this report is obviously fundamentally different as it focuses on scientific evidence from peer-reviewed sources. \n Roulette and Russian roulette When probability and normal risks are discussed the example of a casino and roulette is often used. You bet something, then spin the wheel and with a certain probability you win or lose. You can use different odds to discuss different kinds of risk taking. These kinds of thought experiment can be very useful, but when it comes to infinite risks these gaming analogies become problematic. For infinite impact a more appropriate analogy is probably Russian roulette. But instead of \"normal\" Russian roulette where you only bet your own life you are now also betting everyone you know and everyone you don't know. Everyone alive will die if you lose. There will be no second chance for anyone as there will be no future generations; humanity will end with your loss. What probability would you accept for different sums of money if you played this version of Russian roulette? Most people would say that it is stupid and -no matter how low the probability is and no matter how big the potential win is -this kind of game should not be played, as it is unethical. Many would also say that no person should be allowed to make such a judgment, as those who are affected do not have a say. You could add that most of those who will lose from it cannot say anything as they are not born and will never exist if you lose. The difference between ordinary roulette and \"allhumanity Russian roulette\" is one way of illustrating the difference in nature between a \"normal\" risk that is reversible, and a risk with an infinite impact. An additional challenge in acknowledging the risks outlined in this report is that many of the traditional risks including wars and violence have decreased, even though it might not always looks that way in media.  10  So a significant number of experts today spend a substantial amount of time trying to explain that much of what is discussed as dangerous trends might not be as dangerous as we think. For policy makers listening only to experts in traditional risk areas it is therefore easy to get the impression that global risks are becoming less of a problem. In the media it is still common to contrast the most probable climate impact with the probability that nothing, or almost nothing, will happen. The fact that almost nothing could happen is not wrong in most cases, but it is unscientific and dangerous if different levels of probability are presented as equal. The tendency to compare the most probable climate impact with the possibility of a low or no impact also results in a situation where low-probability high-impact outcomes are often totally ignored. An honest and scientific approach is to, whenever possible, present the whole probability distribution and pay special attention to unacceptable outcomes. The fact that we have challenges that with some probability might be infinite and therefore fundamentally irreversible is difficult to comprehend, and physiologically they are something our brains are poorly equipped to respond to, according to evolutionary psychologists. This psychological denial may be one reason why there is a tendency among some stakeholders to confuse \"being optimistic\" with denying what science is telling us, and ignoring parts of the probability curve.  14  Ignoring the fact that there is strong scientific evidence for serious impacts in different areas, and focusing only on selected sources which suggest that the problem may not be so serious, is not optimistic. It is both unscientific and dangerous.  15  A scientific approach requires us to base our decisions on the whole probability distribution. Whether it is possible to address the challenge or not is the area where optimism and pessimism can make people look at the same set of data and come to different conclusions. Two things are important to keep in mind: first, that there is always a probability distribution when it comes to risk; second, that there are two different kinds of impacts that are of interest for this report. The probability distribution can have different shapes but in simplified cases the shape tends to look like a slightly modified clock (remember figure  1 ). In the media it can sound as though experts argue whether an impact, for example a climate impact or a pandemic, will be dangerous or not. But what serious experts discuss is the probability of different oucomes.  \n The history of infinite impacts: The LA-602 document The understanding of infinite impacts is very recent compared with most of our institutions and laws. It is only 70 years ago that Edward Teller, one of the greatest physicists of his time, with his back-of-the-envelope calculations, produced results that differed drastically from all that had gone before. His calculations indicated that the explosion of a nuclear bomb -a creation of some of the brightest minds on the planet, including Teller himself -could result in a chain reaction so powerful that it would ignite the world's atmosphere, thereby ending human life on Earth.  16  Robert Oppenheimer, who led the Manhattan Project to develop the nuclear bomb, halted the project to see whether Teller's calculations were correct.  17  The resulting document, LA-602: Ignition of the Atmosphere with Nuclear Bombs, concluded that Teller was wrong, But the sheer complexity drove them to end their assessment by writing that \"further work on the subject [is] highly desirable\".  18  The LA-602 document can be seen as the first scientific global risk report addressing a category of risks where the worst possible impact in all practical senses is infinite.  19  Since the atomic bomb more challenges have emerged with potentially infinite impact. Allmost all of these new challenges are linked to the increased knowledge, economic and technical development that has brought so many benefits. For example, climate change is the result of the industrial revolution and development that was, and still is, based heavily on fossil fuel. The first part of the report is an introduction where the global risks with potential infinite impact are introduced and defined. This part also includes the methodology for selecting these risks, and presents the twelve risks that meet this definition. Four goals of the report are also presented, under the headings \"acknowledge\", \"inspire\", \"connect\" and \"deliver\". The second part is an overview of the twelve global risks and key events that illustrate some of the work around the world to address them. For each challenge five important factors that influence the probability or impact are also listed. The risks are divided into four different categories depending on their characteristics. \"Current challenges\" is the first category and includes the risks that currently threaten humanity due to our economic and technological development -extreme climate change, for example, which depends on how much greenhouse gas we emit. \"Exogenic challenges\" includes risks where the basic probability of an event is beyond human control, but where the probability and magnitude of the impact can be influenced -asteroid impacts, for example, where the asteroids' paths are beyond human control but an impact can be moderated by either changing the direction of the asteroid or preparing for an impact. The fifth part presents some of the most important underlying trends that influence the global challenges, which often build up slowly until they reach a threshold and very rapid changes ensue. The sixth and final part presents an overview of possible ways forward. \n Goals But we now face the possibility that even tools created with the best of intentions can have a darker side too, a side that may threaten human civilisation, and conceivably the continuation of human life. This is what all decision-makers need to recognise. Rather than succumbing to terror, we need to acknowledge that we can let the prospect inspire and drive us forward. Establish a category of risks with potentially infinite impact. Before anything significant can happen regarding global risks with potentially infinite impacts, their existence must be acknowledged. Rapid technological development and economic growth have delivered unprecedented material welfare to billions of people in a veritable tide of utopias.  21  Show concrete action that is taking place today. This report seeks to show that it is not only possible to contribute to reducing these risks, but that it is perhaps the most important thing anyone can spend their time on. It does so by combining information about the risks with information about individuals and groups who has made a significant contribution by turning challenges into opportunities. By highlighting concrete examples the report hopes to inspire a new generation of leaders. Goal 1: Acknowledge Even with those risks where many groups are involved, such as climate change and pandemics, very few today address the possibility of infinite impact aspects. Even fewer groups address the links between the different risks. There is also a need to connect different levels of work, so that local, regional, national and international efforts can support each other when it comes to risks with potentially infinite impacts. \n Identify and implement strategies and initiatives. Reports can acknowledge, inspire and connect, but only people can deliver actual results. The main focus of the report is to show that actual initiatives need to be taken that deliver actual results. Only when the probability of an infinite impact becomes acceptably low, very close to zero, and/or when the maximum impact is significantly reduced, should we talk about real progress. In order to deliver results it is important to remember that global governance to tackle these risks is the way we organise society in order to address our greatest challenges. It is not a question of establishing a \"world government\", it is about the way we organise ourselves on all levels, from the local to the global. The report is a first step and should be seen as an invitation to all responsible parties that can affect the probability and impact of risks with potentially infinite impacts. But its success will ultimately be measured only on how it contributes to concrete results. \n Goal 3: Connect That leaders in different sectors connect with each other to encourage collaboration. A specific focus on financial and security policy where significant risks combine to demand action beyond the incremental is required. Goal 4: Deliver A collapse of civilisation is defined as a drastic decrease in human population size and political/economic/social complexity, globally for an extended time.  25  The above definition means the list of challenges is not static. When new challenges emerge, or current ones fade away, the list will change. An additional criterion for including risks in this report is \"human influence\". Only risks where humans can influence either the probability, the impact, or both, are included. For most risks both impact and probability can be affected, for example with nuclear war, where the number/size of weapons influences the impact and tensions between countries affects the probability. Other risks, such as a supervolcano, are included as it is possible to affect the impact through various mitigation methods, even if we currently cannot affect the probability. Risks that are susceptible to human influence are indirectly linked, because efforts to address one of them may increase or decrease the likelihood of another. The concept of infinity was chosen as it reflects many of the challenges, especially in economic theory, to addressing these risks as well as the need to question much of our current way of thinking. The concept of a category of risks based on their extreme impact is meant to provide a tool to distinguish one particular kind of risk from others. The benefit of this new concept should be assessed based on two things. First, does the category exist, and second, is the concept helpful in addressing these risks? The report has found ample evidence that there are risks with an impact that can end human civilisation and even all human life. The report further concludes that a new category of risk is not only meaningful but also timely. We live in a society where global risks with potentially infinite impacts increase in both number and probability according to multiple studies. Looking ahead, many emerging technologies which will certainly provide beneficial results, might also result in an increased probability of infinite impacts.  26  Over the last few years a greater understanding of low probability or unknown probability events has helped more people to understand the importance of looking beyond the most probable scenarios. Concepts like \"black swans\" and \"perfect storms\" are now part of mainstream policy and business language.  27  Greater understanding of the technology and science of complex systems has also resulted in a new understanding of potentially disruptive events. Humans now have such an impact on the planet that the term \"the anthropocene\" is being used, even by mainstream media like The Economist.  28  The term was introduced in the 90s by the Nobel Prize winner Paul Crutzen to describe how humans are now the dominant force changing the Earth's ecosystems.  29  The idea to establish a well defined category of risks that focus on risks with a potentially infinite impact that can be used as a practical tool by policy makers is partly inspired by Nick Bostrom's philosophical work and his introduction of a risk taxonomy that includes an academic category called \"existential risks\".  30  Introducing a category with risks that have a potentially infinite impact is not meant to be a mathematical definition; infinity is a thorny mathematical concept and nothing in reality can be infinite.  31  It is meant to illustrate a singularity, when humanity is threatened, when many of the tools used to approach most challenges today become problematic, meaningless, or even counterproductive. The concept of an infinite impact highlights a unique situation where humanity itself is threatened and the very idea of value and price collapses from a human perspective, as the \n Life Value The following estimates have been applied to the value of life in the US. The estimates are either for one year of additional life or for the statistical value of a single life. -$50,000 per year of quality life (international standard most private and government-run health insurance plans worldwide use to determine whether to cover a new medical procedure) price of the last humans also can be seen to be infinite. This is not to say that those traditional tools cannot still be useful, but with infinite impacts we need to add an additional set of analytical tools. Some of the risks, including nuclear war, climate change and pandemics, are often included in current risk overviews, but in many cases their possible infinite impacts are excluded. The impacts which are included are in most cases still very serious, but only the more probable parts of the probability distributions are included, and the last part of the long tail -where the infinite impact is found -is excluded.  32  Most risk reports do not differentiate between challenges with a limited impact and those with a potential for infinite impact. This is dangerous, as it can mean resources are spent in ways that increase the probability of an infinite impact. \n Ethical aspects of infinite impact The basic ethical aspect of infinite impact is this: a very small group alive today can take decisions that will fundamentally affect all future generations. \"All future generations\" is not a concept that is often discussed, and for good reason. All through human history we have had no tools with a measurable global impact for more than a few generations. Only in the last few decades has our potential impact reached a level where all future generations can be affected, for the simple reason that we now have the technological capacity to end human civilisation. If we count human history from the time when we began to practice settled agriculture, that gives us about 12,000 years.  33  If we make a moderate assumption that humanity will live for at least 50 million more years 34 our 12,000-year history so far represents 1/4200, or 0.024%, of our potential history. So our generation has the option of risking everything and annulling 99.976% of our potential history. Comparing 0.024% with the days of a person living to 100 years from the day of conception, this would equal less than nine days and is the first stage of human embryogenesis, the germinal stage.  35  Two additional arguments to treat potentially infinite impacts as a separate category are: 36 1. An approach to infinite impacts cannot be one of trial-and-error, because there is no opportunity to learn from errors. Infinite impacts are in a different category. Institutions and individuals may find it hard to take these risks seriously simply because they lie outside our experience. Our collective fear-response will probably be illcalibrated to the magnitude of threat. \n Economic aspects of infinite impact and discounting In today's society a monetary value is sometimes ascribed to human life. Some experts use this method to estimate risk by assigning a monetary value to human extinction.  37  We have to remember that the monetary values placed on a human life in most cases are not meant to suggest that we have actually assigned a specific value to a life. Assigning a value to a human life is a tool used in a society with a limited supply of resources or infrastructure (ambulances, perhaps) or skills. In such a society it is impossible to save every life, so some trade-off must be made.  38  The US Environmental Protection Agency explains its use like this: \"The EPA does not place a dollar value on individual lives. Rather, when conducting a benefit-cost analysis of new environmental policies, the Agency uses estimates of how much people are willing to pay for small reductions in their risks of dying from adverse health conditions that may be caused by environmental pollution.\"  39  The Two things make infinite impacts special from a discounting perspective. First, there is no way that future generations can compensate for the impact, as they will not exist. Second, the impact is something that is beyond an individual preference, as society will no longer exist. Discounting is undertaken to allocate resources in the most productive way. In cases that do not include infinite impacts, discounting \"reflects the fact that there are many high-yield investments that would improve the quality of life for future generations. The discount rate should be set so that our investable funds are devoted to the most productive uses.\"  44   unbalance the system and eventually push it over the threshold.  46  Note that these dramatic illustrations rest on assumptions that the thresholds are still relatively benign, not moving us beyond tipping points which result in an accelerated release of methane that could result in a temperature increase of more than 8 °C, possibly producing infinite impacts.  47  Calculating illustrative numbers By including the welfare of future generations, something that is important when their very existence is threatened, economic discounting becomes difficult. In this chapter, some illustrative numbers are provided to indicate the order of magnitude of the values that calculations provide when traditional calculations also include future generations. These illustrative calculations are only illustrative as the timespans that must be used make all traditional assumptions questionable to say the least. Still, as an indicator for why infinite impact might be a good approximation they might help. As a species that can manipulate our environment it could be argued that the time the human race will be around, if we do not kill ourselves, can be estimated to be between 1-10 million years -the typical time period for the biological evolution of a successful species  48  -and one billion years, the inhabitable time of Earth.  49  Figure  5 : Nordhaus, The Climate Casino: Climate policy with a sharp tipping point at 3.5°C. This shows that the optimal temperature increase is very close to the threshold. It is constrained on the low side by abatement costs and on the high side by the sharp increase in damages.  Likewise the value of a life, $28 million, a value that is based on an assessment of how individuals chose when it comes to flying, can be seen as much too small. This value is based on how much we value our own lives on the margin, and it is reasonable to assume that the value would be higher than only a multiplication of our own value if we also considered the risk of losing our family, everyone we know, as well as everyone else on the planet. In the same way as the cost increases when a certain product is in short supply, the cost of the last humans could be assumed to be very high, if not infinite. Obviously, the very idea to put a price on the survival of humanity can be questioned for good reasons, but if we still want to use a number, $28 million per life should at least be considered as a significant underestimation. For those that are reluctant or unable to use infinity in calculations and are in need of a number for their formulas, $86 sextillion could be a good initial start for the cost of infinite impacts. But it is important to note that this number might be orders of magnitude smaller than an estimate which actually took into account a more correct estimation of the number of people that should be included in future generations as well as the price that should be assigned to the loss of the last humans. As we address very complex systems, such as human civilisation and global ecosystems, a concept as important as infinite impact in this report is that of infinity impact threshold. This is the impact level that can trigger a chain of events that results in the end of human civilisation. The infinite impact threshold (IIT) concept represents the idea that long before an actual infinite impact is reached there is a tipping point where it (with some probability) is no longer possible to reverse events. So instead of focusing only on the ultimate impact it is important to estimate what level of impact the infinity threshold entails. The IIT is defined as an impact that can trigger a chain of events that could result first in a civilisation collapse, and then later result in an infinite impact. Such thresholds are especially important to recognise in a complex and interconnected society where resilience is decreasing. \n If we assume -50 million years for the future of humanity as our reference, -an average life expectancy of 100 years 50 , and -a global population of 6 billion people 51 -all conservative estimate -, we have half a million generations ahead of us with a total of 3 quadrillion individuals. Assuming a value of $50,000 per life, the cost of losing them would then be $1.5 ×10  \n Risks with infinite impact Situation that requires new measures and tools and ALARP 2.3.4 Global F-N curves Social and ecological systems are complex, and in most complex systems there are thresholds where positive feedback loops become self-reinforcing. In a system where resilience is too low, feedback loops can result in a total system collapse. These thresholds are very difficult to estimate and in most cases it is possible only to estimate their order of magnitude. As David Orrell and Patrick McSharry wrote in A Systems Approach to Forecasting: \"Complex systems have emergent properties, qualities that cannot be predicted in advance from knowledge of systems components alone\". According to complexity scientist Stephen Wolfram's principle of computational irreducibility, the only way to predict the evolution of such a system is to run the system itself: \"There is no simple set of equations that can look into its future.\"  55  Orrell and McSharry also noted that \"in orthodox economics, the reductionist approach means that the economy is seen as consisting of individual, independent agents who act to maximise their own utility. It assumes that prices are driven to a state of near-equilibrium by the 'invisible hand' of the economy. Deviations from this state are assumed to be random and independent, so the price fluctuations are often modelled using the normal distribution or other distributions with thin tails and finite variance.\" The drawbacks of an approach using the normal distribution, or other distributions with thin tails and finite variance, become obvious when the unexpected happens as in the recent credit crunch, when existing models totally failed to capture the true risks of the economy. As an employee of Lehman Brothers put it on August 11, 2007: \"Events that models predicted would happen only once in 10,000 years happened every day for three days.\"  56  The exact level for an infinite impact threshold should not be the focus, but rather the fact that such thresholds exists and that an order of magnitude should be estimated.  57  During the process of writing the report, experts suggested that a relatively quick death of two billion people could be used as a tentative number until more research is available.  58  With current trends undermining ecological and social resilience it should be noted that the threshold level is likely to become lower as time progress. In the context of global risks with potentially infinite impact, the possibility of establishing global F-N curves is worth exploring. One of the most common and flexible frameworks used for risk criteria divides risks into three bands: 59 The bands are expressed by F-N curves. When the frequency of events which cause at least N fatalities is plotted against the number N on log-log scales, the result is called an F-N curve.  60  If the frequency scale is replaced by annual probability, then the resultant curve is called an f-N curve.  The concept for the middle band when using F-N curves is ALARP. It is a term often used in the area of safety-critical and safety-involved systems.  62  The ALARP principle is that the residual risk should be as low as reasonably practicable. The upper band, the unacceptable/ intolerable region, is usually the area above the ALARP area (see figure  8 ) By using F-N curves it is also possible to establish absolute impact levels that are never acceptable, regardless of probability (Figure  7 . Based on an actual F-n Curve showing an absolute impact level that is defined as unacceptable). This has been done in some cases for local projects. The infinite threshold could be used to create an impact limit on global F-N curves used for global challenges in the future. Such an approach would help governments, companies and researchers when they develop new technical solutions and when investing in resilience. Instead of reducing risk, such an approach encourages the building of systems which cannot have negative impacts above a certain level. Today no established methodology exists that provides a constantly updated list of risks that threaten human civilisation, or even all human life. Given that such a category can help society to better understand and act to avoid such risks, and better understand the relation between these risks, it can be argued that a name for this category would be helpful.  65  To name something that refers to the end of humanity is in itself a challenge, as the very idea is so far from our usual references and to many the intuitive feeling will be to dismiss any such thing. \n Pros The concept used in this report is \"infinity\". The reson for this is that many of the challenges relate to discussed. In one way the name is not very important so long as people understand the impacts and risks associated with it. Still, a name is symbolic and can either help or make it more difficult to get support to establish the new category. The work to establish a list of risks with infinite impact evolved from \"existential risk\", the philosophical concept that inspired much of the work to establish a clearly defined group of risks. The reason for not using the concept \"existential risk and impact\" for this category, beside the fact that existential impact is also used in academic contexts to refer to a personal impact, is that the infinite category is a smaller subset of \"existential risk\" and this new category is meant to be used as a tool, not a scientific concept. Not only should the impacts in the category potentially result in the end of all human life, it should be possible to affect the probability and/or impact of that risk. There must also exist an agreed methodology, such as the one suggested in this report, that decides what risks belong and not belong on the list. Another concept that the category relates to is \"global catastrophic risk\" as it is one of the most used concepts among academics interested in infinite impacts. However it is vague enough to be used to refer to impacts from a few thousand deaths to the end of human civilisation. Already in use but not clearly defined, it includes both the academic concept existential risks and the category of risks with infinite impacts. macroeconomics and its challenges in relation to the kind of impacts that the risks in this report focus on. Further, the name clearly highlights the unique nature without any normative judgements. Still, infinity is an abstract concept and it might not be best communicate the unique group of risks that it covers to all stakeholders. In the same way as it can be hard to use singularity to describe a black hole, it can be difficult to use infinity to describe a certain risk. If people can accept that it is only from a specific perspective that the infinity concept is relevant it could be used beyond the areas of macroeconomics. Two other concepts that also have been considered during the process of writing this report are \"xrisks\" and \"human risk of ruin\". Xrisk has the advantage, and disadvantage, of not really saying anything at all about the risk. The positive aspect is that the name can be associated with the general concept of extinction and the philosophical concept of existential risk as both have the letter x in them. The disadvantage is the x often represents the unknown and can therefore relate to any risk. There is nothing in the name that directly relates to the kind of impacts that the category covers, so it is easy to interpret the term as just unknown risks. Human risk of ruin has the advantage of having a direct link to a concept, risk of ruin, that relates to a very specific state where all is lost. Risk of ruin is a concept in use in gambling, insurance, and finance that can all give very important contributions to the work with this new category of risk. The resemblance to an existing concept that is well established could be both a strength and a liability. Below is an overview of the process when different names were  There will not be a perfect concept and the question is what concept can find the best balance between being easy to understand, acceptable where policy decisions needs to be made and also acceptable for all key groups that are relevant for work in these area. During the process to find a name for this category inspiration has been found in the process when new concepts have been introduced; from irrational numbers and genocide to sustainable development and the Human Development Index. So far \"infinite risk\" can be seen as the least bad concept in some areas and \"xrisks\" and \"human risk of ruin\" the least bad in others. The purpose of this report is to establish a methodology to identify a very specific group of risks as well as continue to a process where these risks will be addressed in a systematic and appropriate way. The issue of naming this group of risks will be left to others. The important is that the category gets the attention it deserves.   68  But through history and today it is mainly used for a religious end of time scenario. Its strong links to unscientific doom-mongers make it probably unsuitable for a scientific concept. 5. End-of-the-world risk -belongs to the irrational doomsday narratives and so is probably unsuitable for scientific risk assessments. 6. Extreme risk -is vague enough to describe anything beyond the normal, so it is probably unsuitable for risk assessments of this magnitude. 7. Unique risk -is even vaguer, as every risk is unique in some way. Probably best avoided in risk assessments. 8. Collapse risk -is based on Jared Diamond's thinking.  69  There are many different kinds of collapse and only a few result in infinite impact. \n 48 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 2.3 Global challenges and infinite impact \n Estimations of impact Only literature where there is some estimation of impact that indicates the possibility of an infinite impact is included. \n Leading organisations' priorities In order to increase the probability of covering all relevant risks an overview of leading organisations' work was conducted. This list was then compared with the initial list and subjected to the same filter regarding the possibility to affect the probability or impact. \n Possibility of addressing the risk Possibility of addressing the risk: From the risks gathered from literature and organisations, only those where the probability or impact can be affected by human actions are included. \n Expert review Qualitative assessment: Expert review in order to increase the probability of covering all relevant global risks.   73  The methodology for including global risks with a potentially infinite impact is based on a scientific review of key literature, with focus on peer-reviewed academic journals, using keyword search of both World of Knowledge 74 and Google Scholar 75 combined with existing literature overviews in the area of global challenges. This also included a snowball methodology where references in the leading studies and books were used to identify other scientific studies and books. In order to select words for a literature search to identify infinite impacts, a process was established to identify words in the scientific literature connected to global challenges with potentially infinite impacts. Some words generate a lot of misses, i.e. publications that use the term but are not the focus of this report. For example \"existential risk\" is used in business; \"human extinction\" is used in memory/cognition. Some search terms produced relatively few hits. For example \"global catastrophic risk\" is not used much. Other words are only used by people within a specific research community: few use \"existential risk\" in our sense unless they are using Nick Bostrom's work. The term \"global catastrophe\" was identified as a phrase that referred almost exclusively to extremely negative impacts on humans, by a diversity of researchers, not just people in one research community. A list of 178 relevant books and reports was established based on what other studies have referred to, and/or which are seen as landmark studies by groups interviewed during the process. They were selected for a closer examination regarding the challenges they include.  76  The full bibliography, even with its focus on publications of general interest, is still rather long. So it is helpful to have a shorter list focused on the highlights; the most important publications based on how often they are quoted, how wellspread the content (methodology, lists, etc.) is and how often key organisations use them. -Influential in developing the field. This includes publications that are highly cited 77 and those that have motivated significant additional research. They are not necessarily the first publications to introduce the concepts they discuss, but for whatever reason they will have proved important in advancing research. -State of the art. This includes publications developing new concepts at the forefront of global challenges research as well as those providing the best discussions of important established concepts. Reading these publications would bring a researcher up to speed with current research on global challenges. So they are important for the quality of their ideas. -Covers multiple global challenges (at least two). Publications that discuss a variety of global challenges are of particular importance because they aid in identifying and comparing the various challenges. This process is essential for research on global risks to identify boundaries and research priorities. In order to identify which global challenges are most commonly discussed, key surveys were identified and coded. First, a list of publications that survey at least three global challenges was compiled, and they were then scanned to find which challenges they discussed. The publications that survey many global challenges were identified from the full bibliography. Publications from both the academic and popular literature were considered. Emphasis was placed on publications of repute or other significance.  78  To qualify as a survey of global challenges, the publication had to provide an explicit list of challenges or to be of sufficient length and breadth for it to discuss a variety of challenges. Many of the publications are books or book-length collections of articles published in book form or as special issues of scholarly journals. Some individual articles were also included because they discussed a significant breadth of challenges. A A list of 34 global challenges was developed based on the challenges mentioned in the publications. A spreadsheet containing the challenges and the publications was created to record mentions of specific challenges in each publication to be coded. Then each publication was scanned in its entirety for mentions of global challenges. Scanning by this method was necessary because many of the publications did not contain explicit lists of global challenges, and the ones that did often mentioned additional challenges separately from their lists. So it was not required that a global challenge be mentioned in a list for it to be counted -it only had to be mentioned somewhere in the publication as a challenge. Assessing whether a particular portion of text counts as a global challenge and which category it fits in sometimes requires some interpretation. This is inevitable for most types of textual analysis, or, more generally, for the coding of qualitative data. The need for interpretation in this coding was heightened by the fact that the publications often were not written with the purpose of surveying the breadth of global challenges, and even the publications that were intended as surveys did not use consistent definitions of global challenges. The coding presented here erred on the side of greater inclusivity: if a portion of text was in the vicinity of a global challenge, then it was coded as one. For example, some publications discussed risks associated with nuclear weapons in a general sense without specifically mentioning the possibility of large-scale nuclear war. These discussions were coded as mentions of nuclear war, even though they could also refer to single usages of nuclear weapons that would not rate as a global challenge. This more inclusive approach is warranted because many of the publications were not focused exclusively on global challenges. If they were focused on them, it is likely that they would have included these risks in their global challenge form (e.g., nuclear war), given that they were already discussing something related (e.g., nuclear weapons). Below are the results from the overview of the surveys.  However, it is important to note that many more studies exist that focus on individual global risks, but often without including low-probability high-impact outcomes.  80  How much work actually exists on human extinction infinite impact is therefore difficult to assess. The list of risks found in the scientific literature was checked against a review of what challenges key organisations working on global challenges include in their material and on their webpages. This was done to ensure that no important risk was excluded from the list. The coding of key organisations paralleled the coding of key survey publications. Organisations were identified via the global catastrophic risk organisation directory published by the Global Catastrophic Risk Institute.  82  They were selected from the directory if they worked on a variety of global challenges -at least three, and ideally more. The reason for focusing on those that work on multiple challenges is to understand which challenges they consider important and why. In contrast, organisations that focus on only one or two challenges may not   2 2 2 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 4 8 12 2 6 10 14 be able to adjust their focus according to which challenges they consider the most important. The organisation coding used the same coding scheme developed for coding survey publications. References to specific global challenges were obtained from organisations' websites. Many have web pages which list the topics they work on. Where possible, references to global challenges were pulled from these pages. Additional references to these challenges were identified by browsing other web pages, including recent publications. While it is possible that some of these organisations have worked on global challenges not mentioned on the web pages that were examined, overall the main challenges that they have worked on have probably been identified and coded. So the results should give a reasonably accurate picture of what global challenges these organisations are working on. Organisations working with global challenges were initially selected on the basis of the literature overview. A snowball sampling was conducted based on the list of organisations identified, according to whether they claimed to work on global challenges and/or their web page contained information about \"existential risk\", \"global catastrophic risk\",\"human extinction\" or \"greatest global challenges\". Cross-references between organisations and input during the workshops were also used to identify organisations. An initial list of 180 organisations which work with global challenges was established. Based on the production of relevant literature, which other organisations referred to the organisation, and/or are seen as influential by groups interviewed during the process, a short-list of organisations were selected for a closer examination regarding the challenges they work with. Then those working with multiple challenges were selected, resulting in a list of 19 organisations.  83  Below is the overview of the results from the overview of key organisations working with multiple global challenges. The WEF describes its perception methodology as follows: \"This approach can highlight areas that are of most concern to different stakeholders, and potentially galvanise shared efforts to address them.\"  85  The question which people are asked to answer is: \"What occurrence causes significant negative impact for several countries and industries?\"  86  The respondents are then asked to provide a number on two scales from 1-4, one for impact and another for likelihood (within 10 years).  87  It is then up to the respondent to define what 1-4 means, so the major value of the report is to track the changes in perception over the years. Such perception approaches are obviously very interesting and, as the WEF states, can influence actual probability as the readers' decisions will be influenced by how different challenges are perceived. Still, it is important to remember that the report does not provide an assessment of the actual probability (0-100%) or an assessment of the impact (and not the impact on human suffering, as many respondents likely define risk in monetary terms for their own company or country). An overview of WEF reports from the last ten years indicates that the challenges that likely could happen when applying a five year horizon, like the first signs of climate change, governmental failure and traditional pandemic, are identified. On the other hand, challenges which have very big impacts but lower probability, like extreme climate change, nanotechnology, major volcanoes, AI, and asteroids, tend to get less, or no, attention. An important question to explore is whether a focus on the smaller but still serious impacts of global challenges can result in an increased probability of infinite impacts. For example, there are reasons to believe that a focus on incremental adaptation instead of significant mitigation could be a problem for climate change as it could result in high-carbon lock-in.  88  Other research indicates that focus on commercially relevant smaller pandemics could result in actions that make a major pandemic more likely. It is argued that this could happen, for example, by encouraging increased trade of goods while investing in equipment that scans for the type of pandemics that are known. Such a system can reduce the probability for known pandemics while at the same time resulting in an increased probability for new and more serious pandemics.  89  Figure This is an initial list. Additional risks will be added as new scientific studies become available, and some will be removed if steps are taken to reduce their probability  90  and/or impact so that they no longer meet the criteria. \n Four categories of global challenges The challenges included in this report belong to four categories. The first, current challenges, includes those where decisions today can result directly in infinite impacts. They are included even if the time between action and impact might be decades, as with climate change. The second category is exogenous challenges, those where decisions do not -currently -influence probability, but can influence impact. The third category is emerging challenges, those where technology and science are not advanced enough to pose a severe threat today, but where the challenges will probably soon be able to have an infinite impact. Many risks could severely damage humanity but have not been included in this report. They were excluded for one or more of three reasons: 1. Limited impact. Many challenges can have significant local negative effects, without approaching the \"2 billion negatively affected\" criterion -tsunamis, for example, and chemical pollution. \n No effective countermeasures. The report focuses on promoting effective interventions and so ignores challenges where nothing useful can be done to prevent or mitigate the impact, as with nearby gamma-ray bursts. \n Included in other challenges. Many challenges are already covered by others, or have a damage profile so similar that there seemed no need to have a separate category. Population growth, for one, is an underlying driver significant for climate change and eco-system catastrophe, but without direct large-scale impacts. The challenges mentioned in the reviewed literature and organisations which are not included in this report often refer to economic damage such as \"fiscal crises\" or \"unemployment\". While such impacts could have far-reaching consequences they are obviously of another magnitude than those included here. Some of the risks that were suggested and/or which exist in books and reports about global risks were rejected according to the criteria above. They include: 91 1. Astronomical explosion/nearby gamma-ray burst or supernova.  92  These seem to be events of extremely low probability and which are unlikely to be survivable. Milder versions of them (where the source is sufficiently far away) may be considered in a subsequent report. \n ͢ Not included due to: No effective countermeasures 2. False vacuum collapse. If our universe is in a false vacuum and it collapses at any point, the collapse would expand at the speed of light destroying all organised structures in the universe.  93  This would not be survivable. \n ͢ Not included due to: No effective countermeasures 3. Chemical pollution. Increasingly, there is particular concern about three types of chemicals: those that persist in the environment and accumulate in the bodies of wildlife and people, endocrine disruptors that can interfere with hormones, and chemicals that cause cancer or damage DNA. ͢ Not included due to: Limited impact 4. Dangerous physics experiments creating black holes/strangelets including high energy physics. These risks are of low probability  94  and have been subsumed under \"Uncertain Risks\". \n ͢ Not included due to: Included in other challenges \n Destructive solar flares. Though solar flares or coronal mass ejections could cause great economic damage to our technological civilisation, 95 they would not lead directly to mass casualties unless the system lacks basic resilience. They have been subsumed in the Global System Collapse category. \n ͢ Not included due to: Limited impact/included in other challenges \n 56 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 2.5 The rseulting list of global risks using this methodology 6. Moral collapse of humanity. Humanity may develop along a path that we would currently find morally repellent. The consequences of this are not clear-cut, and depend on value judgements that would be contentious and unshared.  96   Sometimes it can take a very long time for a system to stabilise again. Looking at all the biotic crises over the past 530 million years, a research team from Berkeley found an average of 10 million years between an extinction and a subsequent flourishing of life.  102  What makes things difficult is that once a system is unstable, a small disaster can have knock-on effectsthe death of one Austrian nobleman can result in an ultimatum which draws in neighbours until Australians end up fighting Turks and the First World War is well under way, to be followed by communism, the Second World War and the Cold War. The challenge of understanding complex systems includes the fact that many of them have multiple attractors, including what are called \"strange attractors\".  103  Changes are close to linear as long as the system does not change very much, but once it is pushed out of balance it will get closer to other attractors, and when those become strong enough the system will tend to move towards chaos until a new balance is achieved around the new attractor.  104  None of the risks in this report is likely to result directly in an infinite impact, and some cannot do so physically. All the risks however are big enough to reach a threshold where the social and ecological systems become so unstable that an infinite impact could ensue, as the graph below shows. This graph and its accompanying text explain, how an event that reaches a threshold level could cascade into even worse situations, via civilisation collapse 105 to human extinction. The graph also seeks to illustrate the importance of ensuring ecological and social resilience, the two major insurance policies we have against a negative spiral after a major impact that takes us beyond the infinite threshold. 1. Social and ecosystem resilience. Resilient systems are naturally resistant to collapse, though this often comes at the cost of efficiency.  106  The more resilient the system, the more likely it is to be able to adapt to even large disasters. Improving resilience ahead of time can improve outcomes, even if the nature of the disaster isn't known. 2. General pre-risk collapse countermeasures. This category consists of all those measures put into place ahead of time to prevent civilisation collapse. It could include, for instance, measures to ensure continuity of government or prevent breakup of countries (or to allow these breakups to happen with the minimum of disruption). At the same time it should be noted that these kinds of measures could also trigger the breakdown. \n General mitigation and resilience. This category consists of all measures that can reduce the impact of risks and prevent them getting out of hand (excluding social and ecosystem measures, which are important and general enough to deserve their own category). 4. Pre-risk rebuilding enablers. On top of attempting to prevent collapses, measures can also be taken to enable rebuilding after a collapse.  107  This could involve building stores of food, of technology, or crucial reconstruction tools.  108  Alternatively, it could involve training of key individuals or institutions (such as the crews of nuclear submarines) to give them useful post-collapse skills. 5. Long-term impact. Some risks (such as climate change) have strong long-term impacts after years or even decades. Others (such as pandemics) are more likely to have only a short-term impact. This category includes only direct longterm impacts. 6. Post-risk politics. The political structures of the post-risk world (governmental systems, conflicts between and within political groupings, economic and political links between groups) will be important in determining if a large impact leads ultimately to civilisation collapse or if recovery is possible. 7. Post-risk collapse countermeasures. These are the countermeasures that the postrisk political structures are likely to implement to prevent a complete civilisation collapse. \n Maintaining a technology base. Current society is complex, with part of the world's excess production diverted into maintaining a population of scientists, engineers and other experts, capable of preserving knowledge of technological innovations and developing new ones. In the simpler post-collapse societies, with possibly much lower populations, it will be a challenge to maintain current technology and prevent crucial skills from being lost.  109  9. Post-collapse politics. Just as post-risk politics are important for preventing a collapse, post-collapse politics will be important in allowing a recovery. The ultimate fate of humanity may be tied up with the preservation of such concepts as human rights, the scientific method and technological progress. 10. Post-collapse external threats and risks. Simply because a risk has triggered the collapse of human civilisation, that does not mean that other risks are no longer present. Humanity will have much less resilience to deal with further damage, so the probability of these risks is important to determine the ultimate fate of humanity. 11. Anthropic effects. We cannot observe a world incapable of supporting life, because we could not be alive to observe it. When estimating the likelihood of disasters and recovery it is very important to take this effect into consideration and to adjust probability estimates accordingly.  110  12. Long-term reconstruction probability. A post-collapse world will differ significantly from a preindustrial revolution world. Easy access to coal and oil will no longer be possible. In contrast, much usable aluminium will have been extracted and processed and will be left lying on the surface for easy use. Thus it will be important to establish how technically possible it may be to have a second industrial revolution and further reconstruction up to current capabilities without creating the problems that the first industrial revolution resulted in. \n 59 Global Challenges -Twelve risks that threaten human civilisation - For the selection of events information from specialised bodies and scientific journals in the area of global risk was gathered.  111  Using keywords related to the various risks, a global selection of events was sought, along with original sourcing in academic or official sources. The list of events was then ranked based on their risk relevance, i.e. their effect on the probability and/or the impact of the challenge. To finalise the list, a group of experts was consulted by email and a draft overview of the challenges was presented at a workshop at the Future of Humanity Institute (FHI) in Oxford, where additional input was provided on selection and content. Issue experts were then consulted before the final list of events was established.  112  Four categories were used to classify the different events: 1. Policy: Global or national policy initiatives that affect probability and/or impact 2. Event:   \n .2 Probability Many of the expected impacts of climate change are well known, including a warming climate, more severe storms and droughts, rising sea levels, ocean acidification, and damage to vulnerable ecosystems.  114  As for all risks there are uncertainties in the estimates, and warming could be much more extreme than the middle estimates suggest. Models tend to underestimate uncertainty  115  (especially where impact on humanity is concerned,  116  where the effect also depends on modellers' choices such as the discount rate  117  ), so there is a probability 118 that humanity could be looking at a 4°C  119  or even 6°C  120  warming in the coming decades. This could arise from positive feedback loops, such as the release of methane from permafrost  121  or the dieback of the Amazon rainforests,  122  that strengthen the warming effect. So far, efforts at curbing emissions have been only moderately successful and are still very far from what is needed.  123  The impact of global warming, whether mild or severe, would be felt most strongly in poorer countries. Adaptation that can address significant warming is often very expensive,  124  and many of the poorest countries are in the tropics and sub-tropics that would be hardest hit (they could become completely uninhabitable for the highest range of warming  125  ). Mass deaths and famines, social collapse and mass migration are certainly possible in this scenario. Combined with shocks to the agriculture and biosphere-dependent industries of the more developed countries, this could lead to global conflict and possibly civilisation collapse -to the extent that many experts see climate change as a national security risk  126  . Further evidence of the risk comes from indications that past civilisation collapses have been driven by climate change.  127  Extinction risk could develop from this if the remaining human groups were vulnerable to other shocks, such as pandemics, possibly exacerbated by the changed climate.  128  There is some evidence of 6°C climate change causing mass extinction in the past,  129  but a technological species such as ourselves might be more resilient to such a shock. A unique feature of the climate change challenge is what is called geo-engineering.  130  Though this could -if it works -reduce many impacts at a relatively low cost, it would not do so evenly. Geo-engineering would possibly reduce the impacts of climate change in some countries, benefitting them while leaving others to suffer.  131  This could lead to greater political instability. One of the most popular geo-engineering ideasstratospheric sulphate aerosols -suffers from the weakness that it must be continuous.  132  If for any reason it stopped (such as a civilisation collapse), warming would resume at a significantly higher pace, reaching the point where it would have been without geo-engineering. The speed of this rebound would put extra pressure on the ecosystem and the world's political system. So the biggest challenge is that geoengineering may backfire and simply make matters worse.  134  Five important factors in estimating the probabilities and impacts of the challenge: 29. The course of international politics is extremely hard to predict, even for political scientists.  135  65 1. Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks To constrain the rise in global average temperature to less than 2°C above pre-industrial levels, a maximum of around 565 -886 billion tonnes (Gt) of carbon dioxide could be emitted before 2050.  137  The world's proven fossil fuel reserves amount to 2,860 Gt of CO2, however, and are viewed as assets by companies and countries. Since it is likely that these assets cannot be realised, these entities are over-valued at current pricesarguably, a \"carbon bubble.\" The report provides evidence that serious risks are growing for highcarbon assets, and aims to help investors and regulators manage these risks more effectively and prepare for a global agreement on emissions reductions. It indirectly highlights part of the challenge of emissions reductions: they will mean the loss of highly valuable assets to corporations and governments. 02-May-13: CO2 at 400 PPM for the first time in > 800,000 years  138  -Event The Mauna Loa carbon dioxide record, also known as the \"Keeling Curve,\" is the world's longest unbroken record of atmospheric CO2 concentrations. It recently reached 400 ppm (parts per million) of CO2. Such concentrations have not been reached for at least 800,000 years,  139  placing humanity in a historically unprecedented situation. Prior to the Industrial Revolution, natural climate variations caused atmospheric CO2 to vary between about 200 ppm during ice ages and 300 ppm during the warmer inter-glacial periods. The last time concentrations were as high as they are now seems to have been during the Mid-Pliocene, about 3 million years before the present when temperatures were 2-3°C warmer, and in which geological evidence and isotopes agree that sea level was at least 15 to 25 m above today's levels with correspondingly smaller ice sheets and lower continental aridity.  -Human influence on the climate system is clear. This is evident from the increasing greenhouse gas concentrations in the atmosphere, positive radiative forcing, observed warming, and understanding of the climate system. It is extremely likely that human influence has been the dominant cause of the observed warming since the mid-20th century. -Each of the last three decades has been successively warmer at the Earth's surface than any preceding decade since 1850. - -Continued emissions of greenhouse gases will cause further warming and changes in all components of the climate system. Limiting climate change will require substantial and sustained reductions of greenhouse gas emissions. -The oceans will continue to warm during the 21st century. Heat will penetrate from the surface to the deep ocean and affect ocean circulation. Further uptake of carbon by the oceans will increase ocean acidification. Global mean sea level will continue to rise during the 21st century. -It is very likely that Arctic sea ice cover will continue to shrink and become thinner. Global glacier volume will further decrease. -Most aspects of climate change will persist for many centuries even if emissions of CO2 are stopped. The global environment can be considered a global public good (i.e. non-excludable and non-rivalrous).  150  Economic theory claims that such goods will be undersupplied by the market.  151  Hence the importance of trans-national negotiations to address climate change. Despite the importance of the subject, the main achievement of the Warsaw negotiations was to keep talks on track for more negotiations in 2015.  152  Though there was general agreement on the necessity of cutting carbon emissions, the dispute was over how to share the burden of doing so. In this instance, the debate was between more-and less-developed countries, with the latter demanding compensation from the former to help them cope with the burden of reducing emissions. That particular dispute was papered over,  153  but similar ones will be likely in future due to the range of different actors and their divergent agendas. The likelihood of a full-scale nuclear war between the USA and Russia has probably decreased in recent decades due to some improvements in relations between these two countries and reductions in the size of their arsenals. Still, the potential for deliberate or accidental 165 nuclear conflict has not been removed, with some estimates putting the risk of nuclear war in the next century or so at around 10% 166 -it may have been mostly down to luck that such a war did not happen in the last half century 167 . A nuclear war could have a range of different impacts. At the lowest end is the most obvious and immediate impact: destruction and death in major cities across the world, due to the explosions themselves and the radioactive fallout. But even if the entire populations of Europe, Russia and the USA were directly wiped out in a nuclear war -an outcome that some studies have shown to be physically impossible  168  , given population dispersal and the number of missiles in existence 169 -that would not raise the war to the first level of impact, which requires > 2 billion affected.  170  A larger impact would depend on whether or not the war triggered what is often called a nuclear winter or something similar.  171  The term refers to the creation of a pall of smoke high in the stratosphere that would plunge temperatures below freezing around the globe and possibly also destroy most of the ozone layer.  172  The detonations would need to start firestorms in the targeted cities, which could lift the soot up into the stratosphere.  173  There are some uncertainties about both the climate models and the likelihood of devastating firestorms, 174 but the risks are severe and recent models 175 have confirmed the earlier 176 analysis. Even a smaller nuclear conflict (between India and Pakistan, for instance) could trigger a smaller nuclear winter which would place billions in danger.  177  The disintegration of the global food supply would make mass starvation and state collapse likely. As the world balance of power would be dramatically shifted and previous ideological positions called into question, large-scale war would be likely. This could lead to a civilisation collapse. Extinction risk is only possible if the aftermath of the nuclear war fragments and diminishes human society to the point where recovery becomes impossible  178  before humanity succumbs  179  to other risks, such as pandemics.  180  Five important factors in estimating the probabilities and impacts of the challenge: 1. How relations between current and future nuclear powers develop. 2. 5. The security of nuclear weapons and materials affects both the probability of nuclear terrorism and the control likelihood of nuclear accidents. 6. The relations between future nuclear powers will be the major determinant of whether a nuclear war breaks out. 7. The relations between current nuclear powers will be a major determinant of the relations between future nuclear powers. 8. The relations between future major nuclear powers will be the major component of determining whether a major nuclear war breaks out. 9. Relations between the USA and Russia (the only current major nuclear powers) will be a major determinant of the relations between future major nuclear powers. and led to increased sanctions  184  against the already isolated nation.  185  North Korea is the only nation to have withdrawn from the Nuclear Non-Proliferation Treaty,  186  and is the only country to have conducted nuclear tests in the 21st century, starting in 2006,  187  as well as developing a ballistic missile capability.  188  It has also been involved in the export of weapons technology, undermining the Treaty.  189  Diplomatic attempts to deal with North Korea (especially on the part of the United States) have generally been inconsistent and unsuccessful.  190  Though the situation remains a potential flashpoint for conventional and nuclear conflict, and its collapse could have disastrous consequences   196  This is but one of the many nuclear accidents  197  and incidents that peppered the Cold War and its aftermath, and which have been revealed only subsequently. We know now that there were at least three occasions -the Cuban missile crisis in 1962,  198  the Petrov incident in 1983  199  and the Norwegian rocket incident in 1995  200  -where a full-scale nuclear war was only narrowly averted.  201  Further information on these incidents, and on how they were interpreted and misinterpreted  202  by the great powers, will be important to estimate the probability of nuclear conflict in the coming decades. On a more positive note, efforts are being made to reduce the probability of inadvertent or accidental nuclear conflicts.  203  24-Jun-13: Report: \"Analysing and Reducing the Risks of Inadvertent Nuclear War Between the United States and Russia\"  204  -Research Though the end of the Cold War has reduced the likelihood of deliberate nuclear war, its impact on the risk of accidental nuclear war is much smaller. The arsenals remain on \"launch on warning\",  205  meaning that there is a possibility for a \"retaliatory\" strike before an attack is confirmed. The most likely cause of such an accident is either a false warning (of which there have been many, with causes ranging from weather phenomena to a faulty computer chip, wild animal activity, and controlroom training tapes loaded at the wrong time)  206  or a misinterpreted terrorist attack.  207  The report attempted a rigorous estimate of the numerical probability of nuclear war. Such numerical rigour is rare, with the exception of Hellman's estimates.  208  This report applied risk analysis methods using fault trees and mathematical modelling to assess the relative risks of multiple inadvertent nuclear war scenarios previously identified in the literature. Then it combined the fault tree-based risk models with parameter estimates sourced from the academic literature, characterising uncertainties in the form of probability distributions, with propagation of uncertainties in the fault tree using Monte Carlo simulation methods. Finally, it also performed sensitivity analyses to identify dominant risks under various assumptions. This kind of highly disaggregated analysis is most likely to elicit the best performance and estimates from experts.  209  Their conclusion was that (under the more pessimistic assumption), there was a mean 2% risk of accidental nuclear war a year (a high risk when compounded over several decades), with the risk from false alarm being orders of magnitude higher than that from terrorist attacks. The analysis suggests that the most important inadvertent nuclear war risk factor is the short launch decision times,  210  inherent in the \"launch on warning\" posture. Some ways of improving this were suggested, for instance by moving each country's strategic submarines away from the other's coasts. \n 75 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks   217  This further serves to emphasise the weakness of international institutions where nuclear arms control is concerned. 15-Nov-13: International Physicians for the Prevention of Nuclear War report: \"Nuclear Famine: Two Billion People at Risk?\"  218  -Research This report is one of a series of reports and publications in recent years about the potential impacts of nuclear conflicts.  219  It looked at the likely consequences of a \"limited\" nuclear war, such as between India and Pakistan. While previous papers had estimated that up to a billion people might be at risk in such a conflict,  220  this report increased the estimate to two billion. The main source of this increase is decreased agricultural production in the United States  221  and in China.  222  A key component of these estimates was the severe agricultural impact of the relatively mild temperature reduction in 1816, the \"year without a summer\"  223  , due mainly to the \"volcanic winter\" caused by the eruption of Mount Tambora. The report highlights some significant areas of uncertainty, such as whether a small nuclear conflict and its consequences would lead to further conflicts across the world, and doubts whether markets, governments and other organisations could mitigate the negative impacts. The report is a reminder that even small-scale nuclear conflict could have severe consequences. 24-Nov-13: Nuclear deal with Iran may reduce risk of proliferation  224  -Policy In November, Iran struck a deal with the so called \"P5+1\" (the five permanent members of the security council, plus Germany). The deal, if it holds, would allow Iran to continue some uranium enrichment, but it would have to submit to inspections to ensure it wasn't developing a nuclear weapons programme (the deal would also result in eased sanctions in return). There have been longrunning fears than Iran may have been attempting to construct a nuclear weapon  225  , resulting in sanctions being imposed on it.  226  This event illustrates the surprising success of the Non-Proliferation Treaty,  227  which came into force in 1970. At the time it was proposed there were fears of very rapid proliferation of nuclear weapons.  228  And though 40 countries or more currently have the knowhow to build nuclear weapons,  229   Species extinction is proceeding at a greatly increased rate compared with historic data  232  , and attempts to quantify a safe ecological operating space place humanity well outside it.  233  Furthermore, there may be signs of a \"sudden\" biosphere collapse, possibly within a few generations.  234  Many of the problems of ecological degradation interact to multiply the damage and (unlike previous, localised collapses) the whole world is potentially at risk,  235  with severe challenges to countering this risk through global policy.  236  If animals are seen to have intrinsic value,  237  or if human quality of life is dependent on a functioning ecosystem,  238  the current situation already represents a large loss. Whether such a loss will extend to human lives depends on technological and political factors -technological, because it seems plausible that some human lifestyles could be sustained in a relatively ecosystem-independent way, at relatively low costs.  239  Whether this can be implemented on a large scale in practice, especially during a collapse, will be a political challenge and whether it is something we want is an ethical question. There is currently more than enough food for everyone on the planet to ensure the nutrition needed,  240  but its distribution is extremely uneven and malnutrition persists. Thus ecological collapse need not have a strong absolute effect in order to result in strong localised, or global, effects. Even a partial collapse could lead to wars, mass migrations, and social instability. It is conceivable that such a scenario, if drawn out and exacerbated by poor decision-making, could eventually lead to mass deaths and even the collapse of civilisation. Extinction risk is possible only if the aftermath of collapse fragments and diminishes human society so far that recovery becomes impossible  241  before humanity succumbs to other risks (such as climate change or pandemics). After a post-civilisation collapse, human society could still be suffering from the effects of ecological collapse, and depending on what form it took, this could make the recovery of human civilisation more challenging than in some of the other scenarios presented here. Five important factors in estimating the probabilities and impacts of the challenge:   243  And yet this biodiversity is being lost at an alarming rate -the rate of extinctions for plants and animals is 100 to 1,000 times higher than their pre-human levels.  244  A variety of methods have been suggested to halt or slow this loss, ranging from putting an explicit value  245  on biodiversity and ecosystem services (human benefits from a multitude of resources and processes that are supplied by ecosystems),  246  to performing triage on the most valuable species.  247  This research paper suggests, however, that there is a lag of several decades between human pressure on the ecosystem and ultimate species extinction. This suggests that many extinctions will continue in decades to come, irrespective of current conservation efforts. 1. \n 05-Apr-13: Ocean data added to Microsoft Eye on Earth project -Initiative In order to safeguard ecological resources, it is important to track and quantify them. This has traditionally been the role of governments or non-governmental organisations.  248     254  (thus privatising that \"common\"). A typical example of this behaviour is the collapse of the Grand Banks fisheries off Canada's Atlantic coast in the 1990s, where cod biomass fell by over 95% from its peak and has currently not recovered.  255  It is therefore significant that the European Union has been partly successful in its attempts to control over-fishing through legislation. For instance, despite the fact that North Sea cod remains vulnerable, there has been a recent increase in stock size and a decrease in fish mortality. This may point to the potential for further ecological improvements through well-chosen policy interventions. In 2013 the IUCN added an additional 4,807 species to its Red List of Threatened Species. This brings the total to about 21,000. Some have argued that we are entering a new geological era in Earth's history: the Anthropocene  257  , when human actions are one of the major impactors on the planet's biosphere. 82 The graph shows a fairly steady growth in the (estimated) number of threatened species. This steadiness may be illusory, as the biosphere shows signs that it may be approaching a planetary-scale tipping point, where it may shift abruptly and irreversibly from one state to another. As a result, the biological resources humans presently take for granted may be subject to rapid and unpredictable transformations within a few human generations.  258  This could be seen as a great tragedy beyond purely human concerns, if animals (and animal welfare) are seen to have intrinsic value.  259  83 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Here only worldwide events are included. A widespread endemic disease that is stable in terms of how many people become sick from it is not a pandemic. Influenza subtypes  266  Infectious diseases have been one of the greatest causes of mortality in history. Unlike many other global challenges pandemics have happened recently, as we can see where reasonably good data exist. Plotting historic epidemic fatalities on a log scale reveals that these tend to follow a power law with a small exponent: many plagues have been found to follow a power law with exponent 0.26.  261  These kinds of power laws are heavy-tailed  262  to a significant degree.  263  In consequence most of the fatalities are accounted for by the top few events.  264  If this law holds for future pandemics as well,  265  then the majority of people who will die from epidemics will likely die from the single largest pandemic. Most epidemic fatalities follow a power law, with some extreme events -such as the Black Death and Spanish Flu -being even more deadly.  267  There are other grounds for suspecting that such a highimpact epidemic will have a greater probability than usually assumed. All the features of an extremely devastating disease already exist in nature: essentially incurable (Ebola  268  ), nearly always fatal (rabies  269  ), extremely infectious (common cold  270  ), and long incubation periods (HIV  271  ). If a pathogen were to emerge that somehow combined these features (and influenza has demonstrated antigenic shift, the ability to combine features from different viruses  272  ), its death toll would be extreme. Many relevant features of the world have changed considerably, making past comparisons problematic. The modern world has better sanitation and medical research, as well as national and supra-national institutions dedicated to combating diseases. Private insurers are also interested in modelling pandemic risks.  273  Set against this is the fact that modern transport and dense human population allow infections to spread much more rapidly  274  , and there is the potential for urban slums to serve as breeding grounds for disease.  275  Unlike events such as nuclear wars, pandemics would not damage the world's infrastructure, and initial survivors would likely be resistant to the infection. And there would probably be survivors, if only in isolated locations. Hence the risk of a civilisation collapse would come from the ripple effect of the fatalities and the policy responses. These would include political and agricultural disruption as well as economic dislocation and damage to the world's trade network (including the food trade). Extinction risk is only possible if the aftermath of the epidemic fragments and diminishes human society to the extent that recovery becomes impossible  277  before humanity succumbs to other risks (such as climate change or further pandemics). Five important factors in estimating the probabilities and impacts of the challenge: 1. What the true probability distribution for pandemics is, especially at the tail. \n The capacity of modern international health systems to deal with an extreme pandemic. \n How fast medical research can proceed in an emergency. 4. How mobility of goods and people, as well as population density, will affect pandemic transmission. \n Whether humans can develop novel and effective anti-pandemic solutions. \n 85 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 2. As so much is known about pandemic risks compared with other risks, there are more possibilities for specific prepandemic contingency plans. 3. The effectiveness of healthcare systems will be important, especially in less developed nations where the pandemic may overwhelm the system, and then transmit from there to other nations. 4. Global coordination in detection, analysis and treatment are vital for stopping a pandemic in its early stages, and for implementing measures such as quarantines and more advanced countermeasures. 5. Poverty will affect the quality of national healthcare systems, population density and sanitation quality, the movement of local goods and people, and the effectiveness of the political response. 6. Bioterrorists may unleash a pathogen held in storage, such as smallpox. 7. Laboratory security at the top labs is insufficient for the danger at hand, and accidental release is a nonnegligible possibility. 8. Pandemics are one of the risks where there is a possibility for a very large number of direct casualties, depending on the severity of the pathogen. 9. Mass casualties and finger-pointing could destabilise the world political and economic systems. 10. If the pathogen is transmissible to farm animals, this could affect the world food supply. 11. It is unlikely the pathogen would be a recurrent, long-term risk, but variants of it could continue to affect people and animals for many years, dependent on its transmissibility and life cycle. 12. Small pandemic scares could improve global coordination on the issue. 13. Increased population density causes increased transmissibility of the pathogen, especially in urban slums. 14. Some pathogens, such as bird flu, depend on regular contact between humans and \"reservoir species\" in order to evolve into periodically dangerous strains. 15. If antibiotic resistance develops, humanity could see the resurgence of bacteria-based pandemics. 16. The increased movement of people and products increases the speed and spread of pandemic transmission. 17. Sanitation or its lack will strongly affect the spread of certain pathogens in key areas. 18.   284  The main lesson the WHO drew from that epidemic was that member states generally had communication issues (between ministries of health and decision,makers, and with the public), and were prepared for a pandemic of high severity and appeared unable to adapt their national and subnational responses adequately to a more moderate event. The guidance paper indicates simultaneously the weaknesses of pandemic preparations, the improvements in these preparations, and the continued role of the WHO as global directing and coordinating authority. 24-Jul-13: Bacteria become resistant to some of the last remaining antibiotics  285  -Event Bacterial infections, such as the Black Death,  286  syphilis,  287  and tuberculosis,  288  have been responsible for millions of deaths, over the thousands of years they have co-existed with humanity. Though these diseases have not been eradicated -overall, a third of the world is currently infected with the tuberculosis bacillus  289  -they have been controlled since the introduction of antibiotics, and prognostics have improved tremendously. But recently a rising number of bacteria have developed antibiotic resistance, due mainly to antibiotic over-prescription  290  and use in livestock feed.  291  This Nature report highlights the worrying way in which Enterobacteriaceae (bacteria with a 50% mortality rate) have become resistant to carbapenems, one of the last remaining antibiotics that had been effective against them. 09-Aug-13: Epihack: Digital disease surveillance hack-a-thon  292  -Initiative Beyond the formal, top-down initiatives to deal with pandemics, there are openings for bottom-up, innovative ideas. Epihack attempted to generate just such ideas, through three days of designing and hacking in Cambodia. Descriptions of the winning projects were given: -CoPanFlu: This project included home visits to collect blood samples from 807 homes and weekly follow-up phone calls to document the occurrence of infectious respiratory symptoms. These visits and phone calls caused disturbance to the participants. The new system uses SMS for users to report symptoms. Chart and map visualisation of the data (with full case details) and a fieldwork tracking tool were developed to help the research team analyse and monitor data. -DoctorMe: In addition to all of the popular features of DoctorMe (free health information for the general public), the tool now features a weekly survey for users. The survey will ask participants to select whether they are experiencing any symptoms from a list. \n 88 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks The Spanish flu outbreak was the deadliest short pandemic in history, infecting about a third of the world population (≈ 500 million people) and killing 50-100 million people.  294  There have been numerous flu pandemics in the last few centuries, with three others having around a million casualties (the 1889-1890 Russian Flu,  295  the 1957-1958 Asian Flu, and the 1968-1969 Hong Kong Flu 296 outbreaks). The most recent pandemic was that in 2009, which killed 150,000-500,000 people.  297  Thus any move towards a universal flu vaccine would be of great importance to combating such recurring pandemics. This paper, analysing the role of T cells in combating influenza, suggests a way that such a vaccine could be feasible. 28-Nov-13: Difficulties in containing the accidental laboratory escape of potential pandemic influenza viruses  298  -Research Biosafety laboratories experiment with some of the deadliest of the world's pathogens, and occasionally create new ones.  299  Their number is increasing globally, and their safety record is far from perfect, with several pathogen leaks reported 300 and others suspected  301  (the last smallpox fatality was due to a virus that escaped a lab  302  , after eradication of the virus in the wild). The rate of pathogen escape has been estimated at 0.3% per laboratory, per year  303  -a very high probability, given the 44 BSL-4 304 labs and several thousands of BSL-3 labs. There have already been three known escapes from BSL-4 labs since 1990.  305  This report uses an agent-based model to analyse whether the accidental laboratory release of pandemic flu viruses could be contained, and concludes that controllability of escape events is not guaranteed. 3-Dec-13: Global pandemic tops poll of insurance industry risks  306  -Initiative Academics and governmental  307  / supra-governmental  308  organisations have long worried about the risks of pandemics. But such organisations attract certain types of people with specific outlooks, who can be subject to further biases because of their profession and the social milieu surrounding it.  309  Insurers come from a different background, focusing on practical profitability in the business world. It is therefore instructive that they too see pandemics as among the major threats in the world today. This also implies that combating pandemics is of use not only from a humanitarian but also from an economic standpoint. \n 89 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n Current risks \n Global System Collapse Major Asteroid Impact Synthetic Biology Unknown Consequences \n Current risks \n System Collapse 3.1.5 Global \n Global system collapse is defined here as either an economic or societal collapse on the global scale. There is no precise definition of a system collapse. The term has been used to describe a broad range of bad economic conditions, ranging from a severe, prolonged depression with high bankruptcy rates and high unemployment, to a breakdown in normal commerce caused by hyperinflation, or even an economically-caused sharp increase in the death rate and perhaps even a decline in population.  \n Probability Often economic collapse is accompanied by social chaos, civil unrest and sometimes a breakdown of law and order. Societal collapse usually refers to the fall or disintegration of human societies, often along with their life support systems. It broadly includes both quite abrupt societal failures typified by collapses, and more extended gradual declines of superpowers. Here only the former is included. The world economic and political system is made up of many actors with many objectives and many links between them. Such intricate, interconnected systems are subject to unexpected system-wide failures due to the structure of the network  311  -even if each component of the network is reliable. This gives rise to systemic risk: systemic risk occurs when parts that individually may function well become vulnerable when connected as a system to a self-reinforcing joint risk that can spread from part to part (contagion), potentially affecting the entire system and possibly spilling over to related outside systems.  312  Such effects have been observed in such diverse areas as ecology,  313  finance  314  and critical infrastructure  315  (such as power grids). They are characterised by the possibility that a small internal or external disruption could cause a highly non-linear effect,  316  including a cascading failure that infects the whole system,  317  as in the 2008-2009 financial crisis. The possibility of collapse becomes more acute when several independent networks depend on each other, as is increasingly the case (water supply, transport, fuel and power stations are strongly coupled, for instance).  318  This dependence links social and technological systems as well.  319  This trend is likely to be intensified by continuing globalisation,  320  while global governance and regulatory mechanisms seem inadequate to address the issue.  321  This is possibly because the tension between resilience and efficiency 322 can even exacerbate the problem.  323  Many triggers could start such a failure cascade, such as the infrastructure damage wrought by a coronal mass ejection,  324  an ongoing cyber conflict, or a milder form of some of the risks presented in the rest of the paper. Indeed the main risk factor with global systems collapse is as something which may exacerbate some of the other risks in this paper, or as a trigger. But a simple global systems collapse still poses risks on its own. The productivity of modern societies is largely dependent on the careful matching of different types of capital  325  (social, technological, natural...) with each other. If this matching is disrupted, this could trigger a \"social collapse\" far out of proportion to the initial disruption.  326  States and institutions have collapsed in the past for seemingly minor systemic reasons.  327  And institutional collapses can create knock-on effects, such as the descent of formerly prosperous states to much more impoverished and destabilising entities.  328  Such processes could trigger damage on a large scale if they weaken global political and economic systems to such an extent that secondary effects (such as conflict or starvation) could cause great death and suffering. Five important factors in estimating the probabilities of various impacts: 1. Whether global system collapse will trigger subsequent collapses or fragility in other areas. \n What the true trade-off is between efficiency and resilience. 3. Whether effective regulation and resilience can be developed. 4. Whether an external disruption will trigger a collapse. 5. Whether an internal event will trigger a collapse. \n 91 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 4. Building resilience -the ability of system components to survive shocks -should reduce systemic risk. 5. Fragile systems are often built because they are more efficient than robust systems, and hence more profitable. 6. General mitigation efforts should involve features that are disconnected from the standard system, and thus should remain able to continue being of use if the main system collapses 7. A system collapse could spread to other areas, infecting previously untouched systems (as the subprime mortgage crisis affected the world financial system, economy, and ultimately its political system). 8. The system collapse may lead to increased fragility in areas that it does not directly damage, making them vulnerable to subsequent shocks. 9. A collapse that spread to government institutions would undermine the possibilities of combating the collapse. 10. A natural ecosystem collapse could be a cause or consequence of a collapse in humanity's institutions. 11. Economic collapse is an obvious and visible way in which system collapse could cause a lot of damage. 12. In order to cause mass casualties, a system collapse would need to cause major disruptions to the world's political and economic system. 13. If the current world system collapses, there is a risk of casualties through loss of trade, poverty, wars and increased fragility. 14. It is not obvious that the world's institutions and systems can be put together again after a collapse; they may be stuck in a suboptimal equilibrium. 15. Power grids are often analysed as possible candidates for system collapse, and they are becoming more integrated. 16. \"The Centre will undertake an economic analysis of the fundamental risks to the financial system, based on an interdisciplinary approach. It will bring together experts from finance, economics, computer science, political science, law and the natural and mathematical sciences. This will allow researchers affiliated to the Centre to investigate how risk is created through feedback loops within and between the financial, economic, legal and political systems. Political decisions, for example, can directly affect people's behaviour in the financial markets, which in turn affects political decision-making and so onwith the outcomes being unexpected and complex.\" Besides the research results produced by the centre, its very existence shows that systemic risk is being taken seriously in academic quarters. 14-Mar-13: Systemic sovereign credit risk has \"deep roots in the flows and liquidity of financial markets.\"  330  -Research It is important to estimate the source of systemic risk. Different mitigation policies should be implemented if sovereign systemic risks spring from financial markets rather than macroeconomic fundamentals. This paper argues that systemic sovereign risks spring from financial markets (through capital flows, funding availability, risk premiums, and liquidity shocks  331  ) rather than from fundamentals.  332  It further estimates that systemic risks are three times larger in eurozone countries than in US states. In order to mitigate or prevent systemic risk, it needs to be monitored. In this paper, the authors set out to clarify the nature and use of the systemic risk monitoring tools that are currently available, providing guidance on how to select the best set of tools depending on the circumstances. The paper breaks down the tools into four categories, each with their strengths and weaknesses: -Single risk/soundness indicators.  334  Indicators based on balance sheet data, such as financial soundness indicators (FSIs), are widely available and cover many risk dimensions. However, they tend to be backward-looking and do not account for probabilities of default or correlation structures. Moreover, only some of these indicators can be used as early-warning tools (e.g., indicators of funding structures). Market data can be used to construct complementary indicators for higher-frequency risk monitoring. -Fundamentals-based models  335  rely on macroeconomic or balance sheet data to help assess macro-financial linkages (e.g., macro stress testing or network models). By providing vulnerability measures based on actual interconnectedness and exposures, these models may help build a realistic \"story\". However, they often require long-term data series, assume that parameters and relationships are stable under stressed conditions, and produce only low-frequency risk estimates. -Market-based models.  336  These models uncover information about risks from high-frequency market data and are thus suitable for tracking rapidly-changing conditions of a firm or sector. These approaches are more dynamic, but their capacity to reliably predict financial stress has yet to be firmly established. -Hybrid, structural models.  337  These models estimate the impact of shocks on key financial and real variables (e.g., default probabilities, or credit growth) by integrating balance sheet data and market prices. Examples include the CCA and distance-to-default measures, which compare the market value of an entity's assets to its debt obligations. The paper concludes, however, that the systemic risk monitoring toolkit is incomplete and that \"tools exist to assess most sectors and levels of aggregation, but they provide only partial coverage of potential risks and only tentative signals on the likelihood and impact of systemic risk events. As such, they may not provide sufficient comfort to policymakers.\" 23-Dec-13: Citigroup analysis reports reduced systemic political and financial risks in 2013 and 2014  338  -Initiative Tracking the ebb and flow of the likelihood of various risks is important for estimating where best to direct energy and resources. Even approximate, order of magnitude estimates are sufficient if they establish that some risks are much more dangerous than others (order of magnitude estimates correspond to the \"Class 5 cost estimate\",  339  undertaken at the very beginning of the project, between 0% and 2% of its completion). In 2013, Citigroup analysts predicted that (with caveats) systemic risks would recede in Europe during the year, a prediction which seems to have been vindicated by events. As for the future, Tina Fordham, chief global political analyst at Citigroup Global Markets, predicted that \"systemic political risks will decline in 2014, but country-level and geopolitical risks remain significant.\" It seems positive both that market analysts are tracking systemic risks and that they see them as decreasing (though their focus is mainly on political and financial systemic risks). \n 95 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Asteroids have caused significant extinction events throughout the Earth's history. The most famous is the Chicxulub impactor, which probably helped cause the extinction of the non-avian dinosaurs and more than 75% of all species.  341  Large asteroid collisions -objects 5 km or more in size -happen approximately once every twenty million years and would have an energy a hundred thousand times greater  342  than the largest bomb ever detonated.  343  A land impact would destroy an area the size of a nation like Holland.  344  Larger asteroids could be extinction level events. Asteroid impacts are probably one of the best understood of all risks in this report. Their mechanisms and frequencies are reasonably well estimated.  345  Recent ground-and space-based  346  tracking projects have been cataloguing and tracking the largest asteroids,  347  and have discovered that the risks were lower than was previously feared.  348  The projects are now cataloguing asteroids of smaller size and damage potential. There has been some speculation about possible methods for deflecting asteroids  350  , should they be found on a collision course with the planet. Such means remain speculative, currently, but may become more feasible given technological progress and potentially more affordable access to space.  351  Should an impact occur, though, asteroid impact risks are similar to those of super-volcanoes, in that the main destruction will not be wrought by the initial impact, but by the clouds of dust projected into the upper atmosphere. The damage from such an \"impact winter\" could affect the climate, damage the biosphere, affect food supplies, and create political instability. Though humanity currently produces enough food to feed all humans,  352  this supply is distributed extremely unevenly, and starvation still exists. Therefore a disruption that is small in an absolute sense could still cause mass starvation in the future. Mass starvation, mass migration, political instability and wars could be triggered, possibly leading to a civilisation collapse. Unless the impact is at the extreme end of the damage scale and makes the planet unviable, human extinction is possible only as a consequence of civilisation collapse and subsequent shocks.  353  Five important factors in estimating the probabilities and impacts of the challenge: 1. Whether detection and tracking of asteroids and other dangerous space objects is sufficiently exhaustive. 2. How feasible it is to deflect an asteroid. 3. Whether measures such as evacuation could reduce the damage of an impact. 4. The short-and long-term climate consequences of a collision. 5. Whether our current civilisation could adapt to a post-impact world.  2. National space programmes have always provided the impetus for space flight projects, especially the more speculative and cutting-edge ones. 3. Protecting against asteroid impacts is already accepted as a project worth funding, but increased focus on the problem could increase the ability to predict and prevent such impacts. 4. Asteroid detection and tracking continues to progress well currently, and is key to preventing such collisions in future. 5. Better global coordination is not strongly needed to track or deflect asteroids, but would be important if a large-scale evacuation was needed. 6. General mitigation efforts may help reduce the direct and indirect negative outcomes of an impact by, for instance, equipping people to deal with the changed climate. 7. Unlike many risks, there is no upper bound on how destructive an asteroid impact could be, though the largest impacts are the rarest. 8. The aftermath of an impact could greatly disrupt the world economic and political system. 9. Climate changes would be the most destructive consequences of mediumscale meteor impacts, with the world plunged into an \"impact winter\". 10. The effects of an impact winter could last for a long time. 11. Easier access to space would be important for any plans to actually deflect an asteroid. 12. There are currently no asteroid deflection abilities, but there are many plans that could conceivably be implemented in due course. 13. Small asteroid impacts could motivate increased anti-asteroid precautions. 14. With enough warning, it could be possible to preemptively evacuate the impact area. 15. Post-impact politics will be important for reconstruction, adapting to the changed climate, and prevention of further harm. 16. Estimating the likelihood of asteroid impacts suffers from \"anthropic shadow\" effects:  355  we may be underestimating the danger because if there had been many more impacts in recent times, humans would not currently be around to observe their effects and take them into account. \n 99 Global Challenges -Twelve risks that threaten human civilisation -   357  when an object hit Tunguska in Siberia.  358  The meteor seemed ideal from the risk reduction perspective: a large, visible impact that attracted great attention, and a renewed commitment to asteroid precautions,  359  but no actual fatalities. 19-Jun-13: Space Research Institute of Russian Academy of Science presents a strategy to use small asteroids to deflect hazardous objects from the trajectory of collision with Earth 360 -Research Though the analysis and tracking of asteroids has progressed rapidly,  361  methods for deflecting a dangerous asteroid, should it be detected, remain speculative.  362  The Space Research Institute of the Russian Academy of Science introduces another approach: selecting small (10-15m) near-Earth asteroids and causing them to strike a larger dangerous one, altering its trajectory. The more suggestions and ideas there are for such deflections, the more likely it is that one of them will yield an implementable approach. 17-Oct-13: The probability for \"Asteroid 2013 TV135\" to impact Earth in 2032 is one in 63,000  363  -Event NASA reports that a 400-metre asteroid has one chance in 63,000 of impacting the Earth. An asteroid this size would produce oceanwide tsunamis or destroy land areas the size of a small state (Delaware, Estonia).  364  For comparison, the odds of dying from lightning strike are 1 in 83,930, of a snake, bee or other venomous bite or sting is 1 in 100,000, of an earthquake 1 in 131,890, and of a dog attack 1 in 147,717.  365  So the risk of asteroid death, though low, is comparable to more common risks. 28-Oct-13: United Nations to Adopt Asteroid Defence Plan 366 -Policy The UN plans to set up an International Asteroid Warning Group for member nations to share information about potentially hazardous space rocks. If astronomers detect an asteroid that poses a threat to Earth, the UN's Committee on the Peaceful Uses of Outer Space will help coordinate a mission to launch a spacecraft to slam into the object and deflect it from its collision course. This marks the first time an international body has assigned responsibility for tracking and intercepting dangerous asteroids. 14-Nov-13: Risk of medium asteroid strike may be ten times larger than previously thought  367  -Research This paper analyses in detail the Chelyabinsk impact, estimated to have had an energy of 500 kilotonnes of TNT. It demonstrates problems with the standard methods for estimating the energy of collisions -derived from nuclear weapons results  368  -and from that deduces that the number of impactors with diameters of tens of metres may be an order of magnitude higher than estimated. It argues that this demonstrates a deviation from a simple power law, and thus that there is a nonequilibrium in the near-Earth asteroid population for objects 10 to 50 metres in diameter. This shifts more of the impact risk to asteroids of these sizes. 3-Dec-13: SpaceX launches into geostationary orbit  369  -Initiative Easy access to space is important for all asteroid deflection proposals.  370  Since America retired the Space Shuttle,  371  it has been putting its hope in private space companies.  372  The success of SpaceX opens the possibility of eventual cheaper access to space. 100 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n Exogenic risks Figure  15 : Impact effects by size of Near Earth Object  354   \n Consequences Upper atmosphere detonation of \"stones\" (stony asteroids) and comets; only \"irons\" (iron asteroids) <3% penetrate to surface. Irons make craters (Barringer Crater); Stones produce air-bursts (Tunguska). Land impacts could destroy areas the size of a city (Washington, London, Moscow). Irons and stones produce ground-bursts; comets produce air-bursts. Ocean impacts produce significant tsunamis. Land impacts destroy areas the size of a large urban area (New York, Tokyo). Impacts on land produce craters; ocean-wide tsunamis are produced by ocean impacts. Land impacts destroy areas the size of a small state (Delaware, Estonia). The eruption which formed the Siberian Traps was one of the largest in history. It was immediately followed by the most severe wave of extinction in the planet's history,  374  the Permian-Triassic extinction event,  375  where 96% of all marine species and 70% of terrestrial vertebrate species died out. Recent research has provided evidence of a causal link: that the eruption caused the mass extinction.  376  There have been many other super-volcanic eruptions throughout history.  377  The return period for the largest supervolcanoes (those with a Volcanic Explosivity Index 378 of 8 or above) has been estimated from 30,000 years  379  at the low end, to 45,000 or even 700,000 years  380  at the high end. Many aspects of super-volcanic activity are not well understood as there have been no historical precedents, and such eruptions must be reconstructed from their deposits.  381  The danger from super-volcanoes is the amount of aerosols and dust projected into the upper atmosphere. This dust would absorb the Sun's rays and cause a global volcanic winter. The Mt Pinatubo eruption of 1991 caused an average global cooling of surface temperatures by 0.5°C over three years, while the Toba eruption around 70,000 years ago is thought by some to have cooled global temperatures for over two centuries.  382  The effect of these eruptions could be best compared with that of a nuclear war. The eruption would be more violent than the nuclear explosions,  383  but would be less likely to ignite firestorms and other secondary effects. Unlike nuclear weapons, a super-volcano would not be targeted, leaving most of the world's infrastructure intact. The extent of the impact would thus depend on the severity of the eruption -which might or might not be foreseen, depending on improvements in volcanic predictions  384  -and the subsequent policy response. Another Siberian Trap-like eruption is extremely unlikely on human timescales, but the damage from even a smaller eruption could affect the climate, damage the biosphere, affect food supplies and create political instability. A report by a Geological Society of London working group notes: \"Although at present there is no technical fix for averting supereruptions, improved monitoring, awareness-raising and research-based planning would reduce the suffering of many millions of people.\"  385  Though humanity currently produces enough food to feed everyone,  386  this supply is distributed extremely unevenly, and starvation still exists. Therefore a disruption that is small in an absolute sense could still cause mass starvation. Mass starvation, mass migration, political instability and wars could be triggered, possibly leading to a civilisation collapse. Unless the eruption is at the extreme end of the damage scale and makes the planet unviable, human extinction is possible only as a consequence of civilisation collapse and subsequent shocks.  387  Prof. Michael Rampino, New York University, has estimated that a large (1,000 cubic kilometres of magma) super-eruption would have global effects comparable to an object 1.5km in diameter striking the Earth.  388  Five important factors in estimating the probabilities and impacts of the challenge: 1. Whether countries will coordinate globally against super-volcano risk and damage.  2. Further super-volcano research will be important in any mitigation and monitoring efforts. 3. Global coordination and cooperation between nations will determine research levels, the chances of evacuations, and posteruption disruption to the world political and economic system. 4. General mitigation efforts may help reduce the direct and indirect negative impact of an eruption, by, for instance, equipping people to deal with the changed climate. 5. The direct destructive effect of a super-volcano can be extensive, especially in the area around the eruption. 6. A super-volcano's main destructive impact is through its effect on the climate, akin to a nuclear winter cooling effect. This will strongly affect all impact levels, and the disruption to the world's political and economic system. 7. The level of this disruption will determine how well countries cope with the aftermath of the eruption and subsequent climate changes, and whether subsequent conflicts or trade wars will occur, adding to the damage. 8. The long-term climate impact will determine in what state the posteruption world will find itself, relevant both for reconstruction after a collapse and for preventing such a collapse. 9. Whether eruptions are fundamentally predictable or not, and how far in advance, will be very important for many mitigation strategies. 10. Better volcano monitoring and prediction (if possible) will allow such interventions as preemptive evacuations. 11. Evacuations are likely to be the only effective response to an imminent eruption, as super-volcanoes are unlikely to be controllable or divertible. 12. Post-eruption politics will be a consequence of the number of shortterm casualties, and the disruption to the world system. 13. Medium scale volcanic eruptions may persuade leaders to make the risk more of a priority. 14. Estimating the likelihood of super-volcanic eruptions suffers from \"anthropic shadow\" effects:  390  we may be underestimating the danger because if there had been many more eruptions in recent times, humans would not currently be around to observe their effects and take them into account.  \n .2.3 Main events 15-Mar-13: Climate impact of super-volcanoes may be less than previously thought  391  -Research The Toba eruption around 70,000 years ago was one of the world's largest super-volcanic eruptions. In contrast with some theories that claim it caused a volcanic winter that may have lasted over two centuries,  392  this paper claims that analysis of ash from the Toba super-eruption in Lake Malawi shows no evidence of volcanic winter in East Africa. This further illustrates the difficulty of establishing the exact impact of large-scale disasters when the evidence record is poor. 17-Jul-13: The Volcanological Society of Japan looks at volcano and super-volcano mitigation  393  -Policy Prevention of super-volcano eruptions is impossible with current technology, but there may be some possibility of mitigating their effects. The Volcanological Society of Japan is one of the few organisations that have looked at such potential mitigation. They put the risk of super-volcanic eruptions in the context of standard volcanic eruptions, just on a larger scale (noting that super-volcanic eruptions have affected Japan in the past). Japan has been a very seismically active country for its entire history,  394  so it might be hoped that adequate volcanic mitigation measures would have been implemented. But the report notes that \"remarkably few [of Japan's local governments] have drafted volcanic disaster countermeasure[s]\",  395  adding that \"Local governments that have actually experienced a volcanic disaster focus attention on volcanic disaster-related discussion, but most have not drafted specific procedures for volcanic disasters and seem to think that the general disaster countermeasure volume is adequate.\" This provokes some pessimism about the likelihood of effective planetary super-volcano mitigation measures being implemented, especially in those areas with no direct experience of volcanic risk. This is due to the normalcy bias, \"the tendency to minimise the probability of potential threats or their dangerous implications,\".  396  27-Oct-13: Yellowstone supervolcano larger than previously thought  397  -Research Another continuing development in the science of super-volcanoes, this paper demonstrates that the crustal magma reservoir under Yellowstone was 50% larger than was previously thought. However, despite this increase, integrated probabilistic hazard assessment shows that the biggest Yellowstone Plateau threat is from large M7+ earthquakessignificantly damaging  398  , but very unlikely to threaten billions -not from volcanic or super-volcanic eruptions. 106 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.2 Exogenic risks 15-Nov-13: Insurance executives rank super-volcanoes low on the list of extreme risks 399 -Initiative Academics have long worried about the probability of super-volcanic eruptions. But academia attracts certain types of people with specific outlooks, who can be subject to further biases because of their profession and the social milieu surrounding it.  400  Insurers come from a different background, focusing on practical profitability in the business world and using a relatively short time horizon. So it is instructive that they do not see super-volcanoes as a major threat in the world today: \"Of interest to us is the very low ranking of the user-submitted idea of supervolcanoes in the US\". 20-Dec-13: Super-volcano confirmed as responsible for one of the largest extinctions in history  401  -Research The maximal destructive potential of super-volcanoes is uncertain. There have been large supervolcanic eruptions throughout history,  402  and many extinction events, but uncertainties in the geological record mean that it was hard to establish whether they were causally linked. One eloquent example was the eruption which formed the Siberian Traps  403  (one of the largest in history), and the Permian-Triassic extinction,  404  where 96% of all marine species and 70% of terrestrial vertebrates died out. The two events were close on the geological timeline, and this paper, using recent dating techniques, confirmed that the super-volcano erupted shortly before the extinction, making it the likely culprit. Synthetic biology is the design and construction of biological devices and systems to accomplish the specific goal of the synthetic biologist,  406  adding human intentionality to traditional pandemic risks. The positive and negative potentials of synthetic biology are unclear  407  -much of the information currently comes from synthetic biologists,  408  who may not be able to provide an impartial overview (the problem is exacerbated by the decentralised nature of the field  409  ). Attempts at regulation  410  or self-regulation  411  are currently in their infancy, and may not develop as fast as research does.  412  One of the most damaging impacts from synthetic biology would come from an engineered pathogen,  413  targeting humans or a crucial component of the ecosystem (such as rice, which accounts for 20% of all calories consumed by humans).  414  This could emerge through military bio-warfare,  415  commercial bio-warfare,  416  bio-terrorism  417  (possibly using dual-use products  418  developed by legitimate researchers, and currently unprotected by international legal regimes  419  ), or dangerous pathogens leaked from a lab  420  . Of relevance is whether synthetic biology products become integrated into the global economy or biosphere. This could lead to additional vulnerabilities (a benign but widespread synthetic biology product could be specifically targeted as an entry point through which to cause damage). But such a development would lead to greater industry and academic research, which could allow the creation of reactive or pre-emptive cures.  421  The impact is very similar to that of pandemics: mass casualties and subsequent economic and political instabilities leading to possible civilisation collapse. A bio-war would contribute greatly to the resulting instability. Even for the most perfectly engineered pathogen, survivors are likely, if only in isolated or mainly isolated locations.  422  Extinction risk is unlikely,  423  but possible if the aftermath of the epidemic fragments and diminishes human society to the extent that recovery becomes impossible  424  before humanity succumbs to other risks.  425  Five important factors in estimating the probabilities and impacts of the challenge: 1.   431  showing how the flu virus could be made transmissible to ferrets (and, by extension, humans). This generated protests and calls for the papers to remain fully or partially unpublished,  432  because of the potential for misuse by bio-terrorists or bio-weapons programmes. In response, researchers in the field declared a voluntary moratorium in January 2012.  433  A year later, they decided to lift the moratorium. One cannot expect workers in a field to be unbiased about their own research,  434  so it is significant that this decision was condemned by many scientists, including other virologists.  435  This provides strong evidence that ending the moratorium was a dangerous decision.   450  a declining fraction, so from a narrow economic perspective it could be argued that the impact of nanotechnology would be relatively small. However, nanotechnology could create new products -such as smart or extremely resilient materials  451  -and would allow many different groups or even individuals to manufacture a wide range of things. \n 28-Feb This could lead to the easy construction of large arsenals of weapons by small groups.  452  These might be masses of conventional weapons (such as drones or cruise missiles), or more novel weapons made possible by atomically precise manufacturing. If this is combined with a possible collapse in world trade networks  453  -since manufacturing could now be entirely local -there would be a likely increase in the number of conflicts throughout the world. Of particular relevance is whether nanotechnology allows rapid uranium extraction and isotope separation  454  and the construction of nuclear bombs, which would increase the severity of the consequent conflicts. Unlike the strategic stalemate of nuclear weapons, nanotechnology arms races could involve constantly evolving arsenals and become very unstable.  455  These conflicts could lead to mass casualties and potentially to civilisation collapse if the world's political and social systems were too damaged. Some nanotechnology pathways could mitigate these developments, however. Cheap mass surveillance,  456  for instance, could catch such re-armament efforts (though surveillance could have its own detrimental effects). Many of the world's current problems may be solvable with the manufacturing possibilities that nanotechnology would make possible, such as depletion of natural resources, pollution, climate change, clean water, and even poverty.  457  There are currently few applicable international legal regimes governing nanotechnology.  458  In the media the label \"grey goo\"  459  is sometimes applied to nanotechnology. This is meant to describe a hypothetical situation where special self-replicating nanomachines would be engineered to consume the entire environment. It is unclear how effective they could be, and they play no role in atomically precise manufacturing.  460  Mass selfreplication would be detectable, and vulnerable to human-directed countermeasures.  461  However, it is possible that such replicating machines could endure and thrive in particular ecological niches, where the cost of removing them is too high.  462  The misuse of medical nanotechnology  463  is another risk scenario. Extinction risk is only likely as a long-term consequence of civilisation collapse, if the survivors are unable to rebuild and succumb to other threats.  464  The possibility of nanomachines or nanoweapons remaining active after a civilisation collapse may make the rebuilding more difficult, however, while the availability of atomically precise manufacturing systems, by contrast, could aid rebuilding. Five important factors in estimating the probabilities and impacts of the challenge: 1. A functional and practical design for assembling molecules is an essential feature for successful nanotechnology. There have been many designs proposed,  467  and some constructed, but not yet a fully functional molecular assembly device.  468  This design, based on principles from biology (it uses messenger RNA as its input code, and synthesises peptides) represents another step towards that important goal. 06-May-13: First weapon made with 3D printer  469  -Event It is the ability to make weapons en masse that represents one of the dangers of nanotechnology.  470  3D printing (or additive manufacturing)  471  is not nanotechnology, but can be considered a precursor, as it similarly allows small groups to design and manufacture their desired products themselves. That one of the early designs has been a functioning weapon, and that such weapon design was justified on moral grounds,  472  indicates a very high probability that nanotechnology will be used for weapon production. 07-May-13: Publication of Eric Drexler's book \"Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization\" 473 -Research Eric Drexler is one of the pioneers of nanotechnology, and introduced the concepts to the general public with his book \"Engines of Creation\".  474  Twenty seven years later, he presents a history, progress report, and updated version of his vision, the central theme of which is to \"imagine a world where the gadgets and goods that run our society are produced not in far-flung supply chains of industrial facilities, but in compact, even desktop-scale, machines.\" The revolution in manufacturing would produce the \"radical abundance\" of the title, with small groups and individuals capable of producing an extraordinarily wide range of products without requiring large amounts of capital or long supply chains. The risks of social and political disruption are then examined. The disruptions that can be anticipated include \"falling demand for conventional labor, resources, and capital in physical production, with the potential for cascading disruptive effects throughout the global economy\", as well as disruptions in supply chains, trade, dependence, and the revaluation of assets (mineral resources and large industrial facilities, for example, will lose much of their value). This would go together with an increase in surveillance capability and a potential nanotechnology arms race. The book recommends taking pre-emptive action at the international level to prepare for these disruptions. A key sign of a developing technology is interest from investment companies. Nanostart AG is an example of such a company, with extensive investments in various nanotechnology projects. Interestingly, their interests are not limited to more conventional nanotech projects, but extend to such speculative endeavours as space elevators.  476  This serves as a reminder of the potentially large profits available in nanotechnology. Thus it seems likely that when the technology matures sufficiently to cause increased risks, there will be many commercial entities heavily investing in the technology, which will make the process of regulation more contentious, possibly leading to \"regulatory capture\" 477 by these entities, with their interests represented rather than those of the broader community. 16-Dec-13: Nanotechnology: A Policy Primer, CRS report of Congress 478 -Policy Governmental and supragovernmental policies will be key to dealing with the dangers and destabilising influences of nanotechnology, through regulation, treaties, redistributive efforts or simply through preparing their populations for the change. And institutions such as the US Congress are keeping an eye on nanotechnology, in this case through the Congressional Research Service. This report, however, does not delve into the major risks of nanotechnology, but restricts itself to minor subjects such as the safety of nanomaterials and US competitiveness in that field. War, trade disruption and potential development and misuse of nanoreplicators  479  are not discussed. This seems to reflect a certain lack of prioritisation and perhaps even a misplaced focus on the less important risks. Major AI researchers and textbooks define the field as \"the study and design of intelligent agents\", where an intelligent agent is a system that perceives its environment and takes actions that maximise its chances of success.  480  Artificial Intelligence (AI) is one of the least understood global challenges. There is considerable uncertainty on what timescales an AI could be built, if at all, with expert opinion shown to be very unreliable in this domain.  481  This uncertainty is bi-directional: AIs could be developed much sooner or much later than expected. Despite the uncertainty of when and how AI could be developed, there are reasons to suspect that an AI with human-comparable skills would be a major risk factor. AIs would immediately benefit from improvements to computer speed and any computer research. They could be trained in specific professions and copied at will, thus replacing most human capital in the world, causing potentially great economic disruption. Through their advantages in speed and performance, and through their better integration with standard computer software, they could quickly become extremely intelligent in one or more domains (research, planning, social skills...). If they became skilled at computer research, the recursive selfimprovement could generate what is sometime called a \"singularity\",  482  but is perhaps better described as an \"intelligence explosion\",  483  with the AI's intelligence increasing very rapidly.  484  Such extreme intelligences could not easily be controlled (either by the groups creating them, or by some international regulatory regime),  485  and would probably act in a way to boost their own intelligence and acquire maximal resources for almost all initial AI motivations.  486  And if these motivations do not detail  487  the survival and value of humanity in exhaustive detail, the intelligence will be driven to construct a world without humans or without meaningful features of human existence. This makes extremely intelligent AIs a unique risk, 488 in that extinction is more likely than lesser impacts. An AI would only turn on humans if it foresaw a likely chance of winning; otherwise it would remain fully integrated into society. And if an AI had been able to successfully engineer a civilisation collapse, for instance, then it could certainly drive the remaining humans to extinction. On a more positive note, an intelligence of such power could easily combat most other risks in this report, making extremely intelligent AI into a tool of great positive potential as well.  489  Whether such an intelligence is developed safely depends on how much effort is invested in AI safety (\"Friendly AI\") 490 as opposed to simply building an AI.  491  If the returns from increased intelligence are low, intelligence explosions and extreme intelligence may not be possible. In that case, there would probably be an ecology of AIs of different levels of intelligence, performing different tasks. In this scenario, apart from the economic dislocation already noted, there is also the possibility of AI-enabled warfare and all the risks of the technologies that AIs would make possible. An interesting version of this scenario is the possible creation of \"whole brain emulations,\" human brains scanned and physically instantiated -physically represented -in a machine. This would make the AIs into what could be called properly human minds, possibly alleviating a lot of problems. Five important factors in estimating the probabilities and impacts of the challenge: 1. The reliability of AI predictions. 2. Whether there will be a single dominant AI or a plethora of entities. 3. How intelligent AIs will become. 4. Whether extremely intelligent AIs can be controlled, and how. \n Whether whole brain emulations (human minds in computer form) will arrive before true AIs. 11. Human redundancy may follow the creation of copyable human capital, as software replaces human jobs. 12. Once invented, AIs will be integrated into the world's economic and social system, barring massive resistance. 13. An AI arms race could result in AIs being constructed with pernicious goals or lack of safety precautions. 14. Uploads -human brains instantiated in software -are one route to AIs. These AIs would have safer goals, lower likelihood of extreme intelligence, and would be more likely to be able to suffer.  495  15. Disparate AIs may amalgamate by sharing their code or negotiating to share a common goal to pursue their objectives more effectively. 16. There may be diminishing returns to intelligence, limiting the power of any one AI, and leading to the existence of many different AIs.  496  17. Partial \"friendliness\" may be sufficient to control AIs in certain circumstances. 18. Containing an AI attack may be possible, if the AIs are of reduced intelligence or are forced to attack before being ready. 19. New political systems may emerge in the wake of AI creation, or after an AI attack, and will profoundly influence the shape of future society. The amount of information stored in a human brain is extremely large. Similarly, the amount of information needed to perform adequately at complex human tasks is considerable -far more than is easily programmable by hand (the Cyc project, 498 for instance, started in 1984, aiming to rapidly formally codify all human common senseand is still running). Thus the interest in the field of machine learning, and in algorithms that can teach themselves skills and knowledge from raw data. With the rise of \"Big Data\", 499 vast databases and increased computer power, there has been a flowering of applications of computer learning.  500  This has caught the eye of the Defense Advanced Research Projects Agency (DARPA), a research arm of the US defense department responsible for the development of new technologies. In this project, DARPA aims both to \"enable new applications that are impossible to conceive of using today's technology\" and to simplify machines so that non-experts can effectively use them and build applications for them. This most recent project confirms the interest of the military in artificial intelligence development. 25-Apr-13: Kurzweil plans to help Google make an AI brain  501  -Initiative The idea of creating a fully general AI, an AI that is capable of all tasks requiring intelligence, went into abeyance during the AI winter,  502  a period of reduced interest and funding in AI. The term AI itself fell into disfavour.  503  But recent AI successes such as Watson's triumph on \"Jeopardy!\"  504  (demonstrating a certain level of natural language recognition and processing) and Google's selfdriving car  505  (demonstrating spatial awareness and movement) have revived interest in constructing a human-like mind in digital form. Kurzweil, hired by Google at the end of 2012, reveals in this interview his interest in doing just that. A notable feature of Kurzweil is his optimism about the consequences of creating AIs,  506  which could affect the level of precautions his team would include in its design. 13-Sep-13: Publication: \"Responses to Catastrophic AGI Risk: A Survey\" 507 -Research Since the recognition of the potential risk with AGI (Artificial General Intelligence),  508  various proposals have been put forward to deal with the problem. After arguing that uncertainty about a timeline to AI  509  does not translate into a certainty that AIs will take a long time, the paper analyses why AIs could be an existential risk. It argues that a trend toward automatisation would give AIs increased influence in society, as such systems would be easier to control, and there could be a discontinuity in which they gained power rapidly.  510  This could pose a great risk to humanity if the AIs did not share human values (intelligence and values are argued to be independent for an AI),  511  a task which seems difficult to achieve if human values are complex and fragile, 512 and therefore problematic to specify. The authors then turned to analysing the AI safety proposals, dividing them into proposals for societal action, external constraints, and internal constraints. They found that many proposals seemed to suffer from serious problems, or to be of limited effectiveness. They concluded by reviewing the proposals they thought most worthy of further study, including AI confinement, Oracle AI, and motivational weaknesses. For the long term, they thought the most promising approaches were value learning (with human-like architecture as a less reliable but possibly easier alternative). Formal verification was valued, whenever it could be implemented.   520  The book then imagines the competition between humanity and a cunning, powerful rival, in the form of the AI -a rival, moreover, that may not be \"evil\" but simply harmful to humanity as a side effect of its goals, or simply through monopolising scarce resources. Along with many interviews of researchers working in the forefront of current AI development, the book further claims that without extraordinarily careful planning,  521  powerful \"thinking\" machines present potentially catastrophic consequences for the human race. 15-Oct-13: \"Racing to the precipice: a model of artificial intelligence development\" lays out the dangers of AI arms races  522  -Research AIs may be developed by different groups, each desiring to be the first to produce an artificial mind. The competitive pressure will be stronger the more powerful AIs are believed to be, thus maximising the danger in those situations. This paper considers an AI arms race,  523  where different teams have the option of reducing their safety precautions in order to perfect their device first -but running the risk of creating a dangerous and uncontrollable AI. In the absence of enforceable agreements between the teams, this dynamic pushes each to take on more risk than they would want (similarly to the \"prisoner's dilemma\"),  524  potentially causing an extremely damaging outcome. The situation is improved if risktaking makes little difference to speed of development, if the teams have reduced enmity between them, or if there are fewer teams involved (those last two factors also help with reaching agreements). Somewhat surprisingly, information has a negative impact: the outcome is safer if the teams are ignorant of each other's rate of progress, and even of their own. 24-Oct-13: Growing researcher awareness of the threat of artificial intelligence  525  -Research Much more effort is devoted to creating AI than to ensuring that it is developed safely.  526  Those working in developing AI could be motivated to minimise the extent their creation represented a potential danger.  527     \n Probability There are many different possible risks that seem individually very unlikely and speculative. Could someone develop a super-pollutant that renders the human race sterile? Could the LHC have created a black hole that swallowed the Earth?  532  Might computer games become so addictive that large populations will die rather than ceasing to indulge in them?  533  Could experiments on animals lift them to a level of intelligence comparable with humans?  534  Might some of the people sending signals to extra-terrestrial intelligences attract deadly alien attention?  535  What are the risks out there that we can't yet conceive of? These risks sound unlikely and for many possibly ridiculous. But many of today's risks would have sounded ridiculous to people from the past. If this trend is extrapolated, there will be risks in the future that sound ridiculous today, which means that absurdity is not a useful guide to risk intensity. Expert opinion provides some information on specific speculative risks. But it will tend to give them extremely low probabilities -after all, the risks are highly speculative, which also means the expert's judgement is less reliable.  536  But in these situations, the main source of probability of the risk is not the quoted number, but the much greater probability that the experts' models and world views are wrong.  537  If marginal scientific theories predict large risks, the probability is concentrated in the likelihood that the theory might be correct.  538  Conversely, if many independent models, theories, and arguments all point in the direction of safety, then the conclusion is more reliable. There are methods to estimate uncertain risks without needing to be explicit about them. One resolution to the Fermi paradox -the apparent absence of alien life in the galaxy -is that intelligent life destroys itself before beginning to expand into the galaxy. Results that increase  539  or decrease the probability of this explanation modify the generic probability of intelligent life (self-)destruction, which includes uncertain risks. Anthropic reasoning  540  can also bound the total risk of human extinction, and hence estimate the unknown component. Non-risk-specific resilience and post-disaster rebuilding efforts  541  will also reduce the damage from uncertain risks, as would appropriate national and international regulatory regimes.  542  Most of these methods would also help with the more conventional, known risks, and badly need more investment. Five important factors in estimating the probabilities and impacts of the challenge: 1. Whether there will be extensive research into unknown risks and their probabilities. 2. 3. Global coordination would aid risk assessment and mitigation. 4. Specific research into uncertain and unknown risks would increase our understanding of the risks involved. 5. General mitigation efforts are mostly general resilience building. 6. Some institutions may deliberately pursue dangerous technologies or experiments, or may convince themselves that their research is not dangerous. 7. Unforeseen accidents could be the trigger for many uncertain risks. 8. The amount of direct casualties varies wildly depending on the risk involved. 9. The disruptions to the world's economic and political system vary wildly depending on the risk involved. 10. The uncertain risk may have other disruptive effects (such as loss of trust in certain technologies). 11. The long-term impact varies wildly depending on the risk involved. 12. The world's political structure, after an unknown risk is triggered, will determine whether humanity improves or worsens the situation. 13. Some methods (such as considering the Fermi paradox) may bound the total probability of destructive uncertain risks, but these are very speculative. 14. One approach to dealing with uncertain risks is to build general adaptation and recovery methods that would be relevant to a wide class of potential disasters. This paper notes the absence of published research in this area,  544  and seeks to begin to fill the gap. It identifies methods for increasing survivor resilience and promoting successful adaptation and recovery, even for isolated communities. It recognises that the process is highly complex, and needs further research. 28-Mar-13: Paper Evaluating Methods for Estimating Existential Risks  545  -Research It would be advantageous to have a rigorous approach for estimating severe risks, including uncertain and unknown ones. This paper reviews and assesses various methods for estimating existential risks, such as simple elicitation; whole evidence Bayesian; evidential reasoning using imprecise probabilities; Bayesian networks; influence modelling based on environmental scans; simple elicitation using extinction scenarios as anchors; and computationally intensive possible-worlds modelling.  546  These methods can be applied rigorously to uncertain risks, assessing them in the same way as more standard risks. Influence modelling based on environmental scans  547  can even suggest some new as yet unknown risks. 01-Aug-13: The Fermi paradox provides an estimate of total existential risk (including uncertain risks)  548  -Research The Fermi paradox is the seeming contradiction between the apparent ease with which intelligent life could arise in the galaxy, and the lack of evidence of any such life. Many explanations have been proposed to resolve the paradox,  549  one of which is relevant to existential risks: the \"Late Great Filter\" explanation.  550  This posits that intelligent life is inevitably destroyed before it can expand through the galaxy. Such an explanation gives a bound to existential risk from all sources, including uncertain risks. This paper demonstrates the relative ease with which a spacefaring civilisation could cross between galaxies. Combined with recent evidence that the majority of Earth-like planets formed before the Earth,  551  this makes the absence of visible intelligent life more inexplicable, and worsens the Fermi paradox, increasing the probability of a Late Great Filter and thus of existential risk from all sources. As there is no global government, global governance typically involves a range of actors including states, as well as regional and international organisations. However, a single organisation may nominally be given the lead role on an issue.\"  \n Probability Often global governance is confused with global government, but they are two very different things. Global governance is just a term to describe the way global affairs are managed, or not managed. Global government is the idea that the world should be run like a country with a government. The global governance system will inevitably have pros and cons, depending on the political decisions that are made. This section looks at global governance disasters. Though all the risks in this report can be exacerbated by poorly chosen policy decisions, this classification contains those problems that arise almost exclusively from bad policy choices. There are two main divisions in governance disasters: failing to solve major solvable problems, and actively causing worse outcomes. An example of the first would be failing to alleviate absolute poverty.  556  An example of the second would be constructing a global totalitarian state.  557  In general, technology, political and social change may enable the construction of new forms of governance, which may be either much better or much worse. These examples immediately illustrate two issues with governance disasters. First, the task of estimating their probability is difficult. Longterm political predictions are of questionable validity and subject to strong biases,  558  especially where strongly-held values are concerned.  559  Second, the impact of these governance disasters depends to a large extent on subjective comparative evaluations. It is not impartially obvious how to rank continued poverty and global totalitarianism versus billions of casualties or civilisation collapse.  560  The long term impact needs also to be considered: how will poverty and global governance change? If there are many generations ahead of us, then the long term state of humanity's policy 561 becomes much more important than the short term one. Five important factors in estimating the probabilities of various impacts: 1. How the severity of non-deadly policy failures can be compared with potential casualties. 2. Whether poor governance will result in a collapse of the world system. 3. How mass surveillance and other technological innovations will affect governance. 4. Whether there will be new systems of governance in the future. 5. Whether a world dictatorship may end up being constructed. The revelations caused great controversy  567  and raised questions about the NSA's surveillance oversight.  568  The episode established that discrete mass surveillance -an important component of potential To reduce poverty in the future, it is important to maintain and extend past trends in poverty mitigation. The United Nations' Poverty-Environment Initiative (PEI), launched in 2008, has had a number of success stories from Uruguay 570 to Malawi.  571  Due to increased demand from member states, the programme has been extended for another five years, 2013-2017, and may add countries such as Myanmar, Mongolia, Indonesia, Albania, Peru and Paraguay. Such programmes demonstrate that the bureaucratic/policy side of poverty reduction is supported by an international infrastructure with a strong emphasis on assessments. The effect of such approaches on overall poverty will depend on the interplay between these policies and the other side of poverty reduction: economic growth  572     576  Conversely, a resilient governance system is better able to cope with all risks, and a collapsed global system is more vulnerable to all risks. Nuclear war,  577  asteroid impacts  578  and super-volcanoes  579  have direct impacts on the climate, and, through that, on the ecosystem.  580  The kinds of mitigation efforts capable of containing the damage from a super-volcano would most likely be effective against asteroid impact damage, because of the similar nature of the impacts. The converse is not true, since one major method of reducing asteroid impact -spacebased deflection  581  -would have no impact on super-volcano risk. Solving climate change would help reduce current ecological pressure.  582  International agreements to reduce ecological damage could be extended to combating climate change as well, by establishing structures for international collaboration and encouraging resource-efficient solutions. Climate change also creates conditions more suitable for the spread of pandemics.  583  Measures to combat global pandemics, such as strengthened outbreak coordination and statistical modelling,  584  could be used to combat synthetic pathogens as well. If a safe artificial intelligence is developed, this provides a great resource for improving outcomes and mitigating all types of risk.  585  Artificial intelligence risks worsening nanotechnology risks, by allowing nanomachines and weapons to be designed with intelligence and without centralised control, overcoming the main potential weaknesses of these machines  586  by putting planning abilities on the other side. 139 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 4. Relations between global risk / 4.1 General relations between global risks and their potential impacts Conversely, nanotechnology abilities worsen artificial intelligence risks, by giving AI extra tools which it could use for developing its power base.  587  Nanotechnology and synthetic biology could allow the efficient creation of vaccines and other tools to combat global pandemics.  588  Nanotechnology's increased industrial capacity could allow the creation of large amounts of efficient solar panels to combat climate change, or even potentially the efficient scrubbing of CO2 from the atmosphere.  589  Nanotechnology and synthetic biology are sufficiently closely related  590  (both dealing with properties on an atomic scale) for methods developed in one to be ported over to the other, potentially worsening the other risk. They are sufficiently distinct though (a mainly technological versus a mainly biological approach) for countermeasures in one domain not necessarily to be of help in the other. Uncontrolled or malicious synthetic pathogens could wreak great damage on the ecosystem; conversely, controlled and benevolent synthetic creations could act to improve and heal current ecological damage. There are many secondary effects that are not covered here. Increasing nuclear power could for instance improve the outlook for climate change,  591  while increasing the risk of proliferation  592  and thus of nuclear war. There are many such effects between various strategies for addressing different risks, but they are specific enough for there to be no simple arguments of the type which says that mitigating risk X worsens risk Y.  During the process of identifying risks that could have an infinite impact it became evident that the most common question among people interested in global challenges is this: \"How probable is it that this impact will ever happen?\" For those with expert knowledge in one area the first question is often: \"How does the probability and magnitude of impact in this area compare with the probability and magnitude of impact in other areas?\" Finally, those who have tried to estimate probabilities for global challenges ask: \"What is the status of knowledge in other areas compared to mine?\" These are all very important questions, and this chapter is not an attempt to answer them. But, as there is no organisation, process or report that has provided an overview of quantified assessment for global challenges with potential infinite impact, the chapter does try to present the current state of knowledge in order to inspire further work. \n ALL RISKS It is easy to argue that it is too difficult, or even impossible, to assess the probabilities that are at all meaningful for the risks in this report, and therefore to exclude them. There are many good reasons for not trying, including significant uncertainty in almost all steps of the assessment. Not only do great uncertainties exist for all the risks, but the difficulties of estimating probabilities are also very different. At one end of the spectrum the probability of a nuclear war can change dramatically from one day to another due to political decisions. Much of the uncertainty is related to psychological assumptions of how different individuals will react under stress. At the other end of the spectrum there is AI, where there is not even a generally accepted understanding of the possibility of the impacts capable of creating the risks covered in this report. There are challenges with very much data, including asteroids, and other challenges with very little relevant data, such as bad future global governance. Obviously the risks also share a number of characteristics: they all have potentially extreme outcomes and have never been experienced before. The possibility of studying series of data, exploring how the outcome will change with incremental changes in input data, and testing conclusions on similar events are just a few examples of things that in most cases cannot be done. Estimating probabilities in traditional ways is therefore very difficult.  594  However, as the current lack of interest in global risks with potentially infinite impacts may in part be due to the lack of actual numbers, the best estimates that could be found are presented below with explanations. These estimates are only an attempt to assemble existing estimates in order to encourage a process to improve these numbers. These estimates range from rigorous calculations based on large amounts of high-quality data (asteroids) to guesstimates by interested experts (AI). The result is that some have a more rigorous methodology behind them, and others should be taken with a large grain of salt, but all are still very rough estimates. As science progresses they will be updated. It is even possible that some will change by orders of magnitude. But instead of no estimate at all, we now have an initial reference that we hope will trigger a discussion and collaboration that will help improve what we have already. As many of the challenges are longterm and require early action to be avoided or mitigated, the probability is provided for the next 100 years, instead of the annual probability that is often provided. The reason for this is that a 100-year perspective helps us understand that even relatively small probabilities can become significant over a century. Say that it is a one in 100 probability (1%) for an impact to occur. Over a century there is a 63.4% probability of one or more such impacts.  595  Further, structures that need to change require us to look beyond the immediate and incremental changes that most discussions focus on today. \n 143 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 5. Probabilities and uncertainties -an initial overview \n Structure of the probability estimates As the different challenges are very different and the status of probability estimates varies significantly, the initial probability numbers are provided together with estimates regarding: \n The understanding of sequence This is an estimation of how well the sequence from today to a possible infinite impact is understood. At one extreme all the different paths from today to an infinite impact are understood. At the other extreme, there is only a theoretical idea that is coherent and does not break any natural laws. In the latter case there would be no understanding of how it is possible to get from where we are today to an infinite impact. A sequence is required to calculate an estimate instead of only having educated guesses. \n Data availability This is an estimate of the amount of data available to make probability assessments on all relevant steps of the sequence. In some areas a lot of hard-to-get data is needed to make an assessment (e.g a global pandemic); in other areas the data is related to secret and/ or psychological factors (e.g. large-scale nuclear war). In others relatively little data is needed (asteroids), or a lot has been done to gather data (e.g. climate change). \n Existing probability estimates These form an estimate of the kind of uncertainty that exists. This obviously depends on an understanding of sequence and data availability, but it also depends on resources and interest in communicating with the rest of the world. The estimates below are preliminary, but a sound risk approach requires stakeholders to begin to include them in strategic assessments. One group in particular is of interest and that is actuaries, the professionals who deal with the financial impact of risk and uncertainty. One of the key guiding rules they follow is to ensure a capital adequacy at a 1-in-200 level. This rule, which is included in for example ICA  596  and Solvency II, 597 provides an opportunity to discuss risks with a possible infinite impact. One contribution could be to discuss the pros and cons with different definitions of the 1-in-200 level. For example, one definition is that \"each company holds enough capital to withstand the events of the next one year with a probability of 199 out of 200.\" 598 This would exclude many of the risks in this report and could even result in the risks increasing, as the time perspective is so short. Investments could help reduce shortterm risks at the same time as they increase long-term risks. Another definition is that \"a company should hold enough capital to be able to withstand a 'reasonably foreseeable' adverse event\".  599    \n Nuclear War Nuclear war is the risk that started the work with scientific assessments related to infinite impact.  604  The understanding of the sequence is relatively well known. Still, the fact is that the impact will depend significantly on how serious the nuclear winter will be as the result of a war (if there is any nuclear winter at all). The probability of a nuclear winter will depend on when during the year the war happens, and what the weather is during this time. The result is that the probability of an infinite impact has an inherent uncertainty and can be estimated only once a war has already started. With many of the spillover effects occurring in remote areas, even basic data is still very rudimentary. Scientists who collect data relevant for pandemics are often working with very small resources, and there is no systematic way of collecting data on a global scale, although interesting initiatives are under way.  607  While an early warning system would be comparatively inexpensive, there are still no resources available. Most of the probability estimates made for pandemics are for their more benign versions. For the possible pandemic that could kill two billion or more there are very few estimates. Based on available assessments 608 the best current estimate of a global pandemic in the next 100 years is: 5% for infinite threshold, 0.0001% for infinite impact The reason for the big difference between threshold and impact is mainly that a pandemic will not directly affect infrastructure or the rest of the ecosystem in the way that extreme climate change or nuclear war would. This means that resilience will be relatively better after the infinite threshold is crossed. This is one of the more complex risks as it can be seen more as a heading than a description of a specific challenge with a well-defined sequence. In other words it is not one sequence, but very many still unknown sequences. The concept of ecological collapse usually refers to a situation where some part of the ecological web becomes so weak that it collapses. \n 00001% There are many studies about the stability and possible collapse of different ecosystems, but there are few that look into the possibility for a full ecological collapse that would result in at least two billion people suffering. Data availability is good in many areas, but the challenge is that without an understanding of the system dynamics, and because of its complexity, there are inherent limits to how exact the knowledge is that can be achieved.  610  Regarding probability estimates, it is only ecological collapse and global system collapse of the current manmade global challenges that have no estimates for infinite impact. Based on available assessments 611 the best current estimate of an ecological catastrophe in the next 100 years is:  0.5% \n Collapse Global System Since the financial crisis the possibility of a global collapse of the current political, economic and financial system has been discussed intensively. A rapidly evolving and increasingly interconnected system, it is subject to unexpected, system-wide failures because of the structure of the network -it faces a systemic risk. Possible sequences for a global system collapse resulting in infinite impacts are very hard to establish, for three reasons. First, it is a very complicated system, with many dynamic interactions, as there are many people who, together with machines, react to each other. The current global system shows a lot of complex dynamic phenomena, such as business cycles, financial crises, irregular growth, and bullwhip effects.  612  Many nonlinear dynamic models of economics and finance present various complex dynamic behaviours such as chaos, fractals, and bifurcation. Second, it is a recent system that has been so interconnected for only a few years, as it depends on an infrastructure that did not exist before the internet, so there is little experience of how it works. Third, the system is rapidly changing and becoming even more complex as more connections are added and its speed increases. Better understanding of complex systems with multiple attractors and bifurcation behaviour will help improve the possibility of understanding the possible sequences.  613  An additional challenge for the understanding of sequences that can result in impacts beyond the infinite threshold is that almost all research being done in the area of global system collapse focuses on its economic or geopolitical implications, not on a full system collapse and not on human suffering.  \n Super-volcano The super-volcano risk has many similarities with a major asteroid risk. Both have happened a number of times through our planet's history, and both have had major consequences. The understanding of the sequence is however a lot lower than for asteroids, as the mechanisms behind volcano eruptions are not very well known. The possibility of foreseeing when a supervolcano will erupt and how big the impact will be is therefore low. Compared with a major asteroid, there will therefore be much less time to prepare. There is data available for different impacts, and knowledge of where super-volcanoes might erupt is increasing, but due to the lack of understanding when it comes to the sequence, the probability estimations are still very rudimentary. A number of estimates exist where the probability is assessed, but they are quite rudimentary, based on the historic frequency of earlier supervolcano eruptions. As these are so infrequent, the uncertainty becomes very significant. The basic sequence is relatively well-known, given that it would be a more deadly version of a current virus, but there is also the possibility that a new virus (or other organism) may be found where the sequence will be unknown and therefore also much more dangerous. One of the challenges to understanding the sequence is that the spreading of synthetic biology will come either from a wilful act (e.g. terrorism) or an accident (e.g. unintentional release from a laboratory). This also makes data hard to get. There are some numbers for accidents in labs, but they are available in only a few countries and there are probably many more than those reported.  620  With terrorist acts there are probability estimates that can be used as a basis for the use of synthetic biology as well.  621  There are some existing estimates for synthetic biology, but these are based on possible use in war, where calculations depend on some specific differences from existing pathogens that are assumed to be necessary for a pandemic with an infinite impact. Based on available assessments  622  the best current estimate of an impact from synthetic biology in the next 100 years is: 1% for infinite threshold, 0.01% for infinite impact   626  For global challenges in rapidly evolving areas where incremental development might not happen and little is known about the sequence, the only way to reduce risks with possible infinite impacts might be to ensure focus on these general factors. The only estimates of probabilities that exist so far have been made by a small group with a significant proportion of people with a passion for AI. Compared with many other challenges the possibility of an AI capable of infinite impact can almost be described as all or nothing. This is also why the estimates are the same for the infinite threshold and the infinite impact. Based on available assessments 627 the best current estimate of an impact from AI in the next 100 years is: 0-10% for infinite threshold, 0-10% for infinite impact The reason for 0-10% on both impact levels is that most experts assume that the kind of AI capable of impacts beyond the infinite threshold is likely to be one that also can result in an infinite impact. If we succeed it will move beyond control very rapidly. Due to the significant impact it would have if it worked, there is no difference between the two impact levels. The most common mistake is that the most likely development of these underlying trends is taken for granted as the only possible outcome. Most of the trends have probability distributions where low-probability/ high-impact possibilities are often ignored. In this chapter some of the most important trends, where the possible outcomes can differ significantly, are described through a global risk perspective. For each of the trends the simple rule based on a risk perspective is: \"Aim for the best, but be prepared for the worst\". Global poverty has fallen dramatically over the last two centuries, and the fall has intensified in recent decades, raising hopes that poverty, defined by the World Bank as an income below US $1.25 per day, may be eliminated within the next 50 years. The Economist even had a cover, in June 2013, with the title \"Towards the end of poverty\".  631  The World Bank has set an interim target of reducing global extreme poverty to 9% of the world's population by 2020, which, if achieved, would mark the first time the rate has fallen to single digits.  632  The milestone is based on a World Bank economic analysis of global poverty trends aimed at the goal of ending extreme poverty by 2030. Reaching 9% in 2020 would mean an estimated 690m people would still be living in extreme poverty by then, 510m fewer in poverty than a decade earlier. That would be the equivalent of half the population of Africa, or more than double the population of Indonesia.  633  There are reasons to celebrate this development as more people than ever live a life where they do not have to constantly worry about their most basic needs. But there are two things worth remembering: 1. Poverty could increase again. 2. Defining poverty is difficult.   According to the 2012 Revision of the official United Nations population estimates and projections, the world population of 7.2 billion in mid-2013 is projected to increase by almost one billion people within twelve years, reaching 8.1 bn in 2025, and to further increase to 9.6 bn in 2050 and 10.9 bn by 2100.  642  These results are based on the medium-variant projection, which assumes a decline of fertility for countries where large families are still prevalent as well as a slight increase of fertility in several countries with fewer than two children per woman on average.  643  The medium projection is still dramatic as it assumes another four bn people on the planet, more than a 50% increase in population, equal to the Earth's entire population in 1975, in just 86 years.  644  The high-variant projection depicted in the figure below assumes an extra half a child per woman (on average) compared with the medium variant, implying a world population of 10.9 bn in 2050 and 16.6 bn in 2100.  645  That is equal to a 133% population increase in just 86 years . The difference between projections for 2100, from 10.9 bn people in the medium scenario, to 16.6 bn in the high scenario, equals the world population in 1995. There is also a credible low scenario with 6.8 bn by 2100.  646  A strategic approach must be based on all possible outcomes. Planning as though the world population will be only 6.8 bn is not optimistic: it is unscientific and dangerous. Even to plan for a world with 10.9 bn is not strategic as this would ignore the significant probability that the world's population would be much larger. There should be a plan for a world with 16.6 bn people, combined with a long-term strategy to ensure a sustainable population level. It is also important to ensure that more attention is paid to early warning systems that allow us to influence population development in a sustainable direction.  While weapons have become more deadly the death toll from wars has actually decreased over time.  650  How big a part technology has played by creating greater transparency, or increasing the fear of using weapons which have become too powerful (for example nuclear bombs), is disputed. But most experts agree that technology has played an important role.  651  This is not the same as saying that this development will continue. Estimating the future development of technology is very difficult. On the one hand there is evidence that technology will continue to accelerate at the pace it has achieved so far. Researchers at MIT and the Santa Fe Institute have found that some widely used formulas for predicting how rapidly technology will advancenotably, Moore's and Wright's Laws -offer superior approximations of the pace of technological progress.  652  Experts like Ray Kurzweil, who was recently hired by Google, is one of those who think that most people do not understand the implications of exponential growth in the area of technology and the results it generates in price, capacity and overall transformation of society.  653  On the other hand there are natural limits that could begin to constrain technological development in two ways. The technology itself may hit a barrier. For example, at some stage a processor may not continue to become smaller and faster, as the speed of light and quantum mechanics will limit its development.  654  There might be other ways to overcome such boundaries, but no exponential trend can last forever. Second, nature itself may set limits. We may choose to take more care of the planet, or limits to materials like rare earths may begin to slow technology.  655  But regardless of ultimate limits, many exponential trends are likely to continue over the coming decades and will present us with new opportunities as well as risks in the 21st century, as these trends converge in a society with 20th century institutions.  Although the proportion of people who live beyond 100 is still very small, their number is growing rapidly. In 2000 there were an estimated 180,000 centenarians globally. By 2050 they are projected to number 3.2 m, an increase of about eighteen times.  659  Within the more developed regions, Japan, in particular, will experience a remarkable increase in the number of centenarians over the next half century, from fewer than 13,000 in 2000 to almost 1 m in 2050. By then Japan is expected to have by far the world's largest number and proportion of centenarians, nearly 1% of its population.  660  The stagnating and ageing population in many OECD countries and China will put pressure on current systems, which were not designed to deal with a situation of ageing and often shrinking populations in many parts of the world, while the populations in other parts of the world are rapidly growing.    \n 8. be assumed to increase or decrease global risks. Such a system would allow more time to develop strategies to mitigate risks and turn global challenges into opportunities for innovation and collaboration. The warning system would require significant research into infinitey thresholds. Both traditional as well as more recent methodologies based on understanding of complex systems should be encouraged. \"big data\".  662  These opportunities include both new ways of collecting large amounts of high-quality data, and new ways to analyse them. Early warning systems should be built to ensure that data is collected and analysed in ways that can be useful for multiple global challenges. The warnings should not only include changes in the physical world, but also indicate when decisions, investments and legal changes can The rapid technological development has many benefits, but also challenges, as risks can rapidly become very serious and reach infinite thresholds. To develop early warning systems that can gather and process data transparently is therefore of the utmost importance. Technological progress, from smart phones and sensors to significant processing power and networks, allows for totally new ways of establishing early warning systems based on so-called Institutions and universities engaged in developing new methodologies to assess global risks have a particular responsibility for developing and refining risk assessments for global challenges. methodology development could be accelerated and improved, as the possibility of learning from different areas would increase. Such a process could also encourage increased investments in methodology development based on the latest innovations, such as systemsforecasting approaches. There is currently no global coordination when it comes to risk assessments of global challenges. Different experts use different methodologies, data and ways to present their results, making it very difficult to compare the risk assessments that exist. By establishing a process that coordinates and encourages risk assessments of global challenges, Four groups are of particular importance: experts in finance, experts in security policy, lawyers with knowledge of global risks and international law, and finally a group consisting of clusters of stakeholders with solutions that can reduce the risks. Leadership networks that include participants from all four groups are of particular interest. infinite impacts, and could work on a roadmap for a future global governance system that can address existing and new global challenges. The networks should be as transparent and inclusive as possible, especially as global collaboration is needed. The use of new collaboration tools and principles, such as wikiprocesses and creative commons, should be encouraged. Tables, graphs and key conclusions in reports related to global challenges should, when possible, include the whole probability distribution.  664  Current lack of data and of scientific studies regarding low-probability high-impact outcomes in many areas should not be used as an excuse to ignore the probability distribution. This is especially important when many of the global challenges have a very long and fat \"tail\". Governments, major companies, NGOs, researchers and other relevant stakeholders should address the whole probability distribution, including low-probability highimpact scenarios. This would ensure that serious risks are not disregarded or obscured. In particular, leadership with a focus on multiple global challenges and the relationship between them should be highlighted, as very little is being done in this area. Governments, companies, organisations and networks working on global challenges should increase their efforts to reward leadership when they find it. Major news outlets can also report when significant positive steps are taken to reduce global risks with potential infinite impacts. New visualisation tools could help make complex systems easier to understand and also help the communication of challenges and opportunities.  663  Visualisation tools are needed both for decision makers to highlight the consequences of different strategies and for citizens to increase their basic understanding of infinite impacts. The global challenges depend on a very complex ecosystem and social system. With a global economic and technological system, which both helps and creates risks that are increasingly interconnected and difficult to understand, there is a challenge to understand the challenges. The IPCC uses specific and defined language in its reports to describe different probabilities and thus ensure clarity, but taken out of context and without supporting definitions this language can be misleading. For example, the term \"very unlikely\" is used by the IPCC to describe a probability of between 0-10%, 665 but out of context its use could easily be understood as a normative judgement suggesting that we do not need to engage with the risk. The language of the IPCC can be compared with that used in the Swedish National Risk Assessment (SNRA).  666  The scale of impact is not defined for the IPCC, but for the Swedish Assessment it is: Very small: no deaths or serious injuries Small: One dead and/or 1-9 seriously injured Average: 2-9 dead and/or 10-49 seriously injured Large: 10-49 dead and/or 50-100 seriously injured Very large: >50 dead and/or >100 seriously injured The use of terms that can be interpreted as having normative values to explain probability is problematic and in future all bodies, including the IPCC, should explore the possibility of using only numbers in external communications, at least in the summary for policy makers, to help everyone understand the reality of the situation. Stakeholders should explore ways to use language that better communicates how serious extreme risks are in the case of climate change, and where possible compare this with other risk areas to help illustrate the situation. Often words like \"unlikely\", \"negligible\" and \"insignificant\" are used to describe a risk when the probability is considered low. What is low is however relative; a low probability in one area can be extremely high in another. If I attend one of ten lectures -10% -people might say there is a low probability that I will be there. But if someone says that a new aircraft crashes once in every ten flights, most people will say that is an extremely high probability and will be likely to assume it is an early prototype that is nowhere close to commercial success. A major problem is that probabilities that ought to be seen as very high for risks with potentially infinite impact are described in a way that makes them sound less urgent than they are -by the media, business, politicians and even by scientists. One example is how probabilities are described by the Intergovernmental Panel on Climate Change. The use of methodologies and approaches from security policy and the financial sector that focus on extreme events could be used to develop strategies for rapid action beyond the incremental approaches that dominate today. Stakeholders should include the most extreme impacts in all relevant work. If the probability of infinite impacts increases instead of decreasing because of new scientific findings or lack of action, strategies should be prepared to allow more decisive action. When the impact is infinite it is not enough only to reveal the whole probability distribution. It is important also to avoid confusing uncertain risk with low risk. Infinite impacts render many of the traditional models for risk management almost meaningless. Monetary calculations are often useless, and discounting is not always advisable.  8. 9. 10. In addition, and probably equally important, is the fact that a body set up to deal with such challenges could also ensure that the links between them could be better understood. A first step could be to establish a centre for global risks and opportunities,  669  focusing initially only on knowledge-gathering and development of proposals, and with no mandate to implement any solutions. There is currently no international or global body that is coordinating work on global risks with a potentially infinite impact. A recent example is IPCC WGII Summary for policy makers. In this report http://ipcc-wg2.gov/AR5/ IPCC acknowledges the need to include low-probability highimpact scenarios: \"assessment of the widest possible range of potential impacts, including low-probability outcomes with large consequences, is central to understanding the benefits and trade-offs of alternative risk management actions.\" Yet nothing is included in the report about impacts above 4 degrees. \n 8 As an infinite impact by definition can't have happened before, models are needed. 9 Making Sense of Uncertainty: Why uncertainty is part of science http://www.lse.ac.uk/CATS/Media/SAS012-MakingSenseofUncertainty.pdf http://www-ee.stanford.edu/~hellman/Breakthrough/ book/chapters/frankenhaeuser.html \"The challenge now is to help people extend their attachments, their loyalties, and their engagement, to include people outside their own narrow circle, their own country, their own imminent future. This global reorientation is a prerequisite for changing the present fatal course of development.\" 13 http://www-ee.stanford.edu/~hellman/Breakthrough/ book/chapters/frankenhaeuser.html 14 Two of the most famous \"optimists\", who tend to look at only the parts of the probability distribution that support their opinion, are the Danish writer Bjorn Lomborg and the British journalist Matt Ridley. While scientists in the areas he writes about constantly refute Lomborg, his message of optimism is well received by many policy makers and business leaders. https://www. ma.utexas.edu/users/davis/375/reading/sciam.pdf Ridley cherrypicks data and tends to avoid the probability that we will see significant warming. http://www.mattridley.co.uk/blog/the-probable-netbenefits-of-climate-change-till-2080.aspxhttp://www. rationaloptimist.com/   18  While the LA-602 document is relatively well-known, its final paragraph is often forgotten. The scientists say: \"However, the complexity of the argument and the absence of satisfactory experimental foundations makes further work on the subject highly desirable.\" 19 Since Teller's calculations the science has developed and is now clear that the main nuclear threat that potentially could threaten human civilisation is a full nuclar war and the consequenses that this could result in from effects like a nuclear winter.  20  For an overview of positive and negative aspects of nanotechnology see for example Drexler, Eric and Pamlin, Dennis (2013): \"Nano-solutions for the 21st century. Unleashing the fourth technological revolution\" http://www.oxfordmartin.ox.ac.uk/downloads/ academic/201310Nano_Solutions.pdf 21 This is true for utopias ranging from Plato's Republic, via Thomas More's book Utopia, to Edward Bellamy's Looking Backward and William Morris' News from Nowhere.  22  See next chapter for the methodology.  23  A list of organisations and studies that discuss challenges that threaten human civilisation can be found here: http://en.wikipedia.org/wiki/Global_catastrophic_ risks  24  The number two billion was established during the workshop in Oxford and is not an exact number. Further research is needed to establish a better understanding of thresholds that can result in an infinite impact, depending on what challenge resulted in the two billion impact and how the estimate for an infinite impact was assumed to be between 0.01% and 10%.  25  The definition is based on the definition used by Jared Diamond: http://www.jareddiamond.org/Jared_ Diamond/Collapse.html  26    Analyzing Human Extinction Scenarios and Related Hazards\" http://www.nickbostrom.com/existential/risks. html. Note that these four points were originally developed for \"existential risks\", those that threaten the extinction of intelligent life originating on Earth or the permanent destruction of its potential for desirable future development.  47  Timothy M. Lenton, Juan-Carlos Ciscar: Integrating tipping points into climate impact assessments. Springer Netherlands 2013-04-01 http://link.springer.com/ article/10.1007%2Fs10584-012-0572-8  48  Carl Sagan use 10 million years in: Sagan, Carl  (1983) . \"Nuclear war and climatic catastrophe: Some policy implications\". Foreign Affairs 62: 275, and The Blackwell's Concise Encyclopedia of Ecology and other sources provide an estimate of about 1 million years for mammals. http://eu.wiley.com/WileyCDA/WileyTitle/ productCd-0632048727.html  49  One billion years is used by Bruce E. Tonn in the paper Obligations to future generations and acceptable risks of human extinction: \" Futures 41.7 (2009): 427-435.  50  In Japan in Japan the life expectancy at age zero, that is, at birth (LEB), is 83 years. In 2010 the world LEB was 67.2.  51  This is based on a low estimate for the planet's population as far out as current projections are made, 2100. http://esa.un.org/wpp/ Looking further into the far future, beyond 500 years, it is likely that humanity will have expanded into space and have a much larger population.  52     (2002) . A New Kind of Science. https://www.wolframscience.com/ 57 A possible infinite threshold could be compared with the two events that are often cited as the world's worst wars and anthropogenic disasters: the second world war, with 40-71 million dead (1.7-3.1% of the world's population) and the Mongol Conquests, 1206-1368, with 30 million dead (7.5% of the global total). See: http:// en.wikipedia.org/wiki/List_of_wars_and_anthropogenic_ disasters_by_death_toll  58  The number two billion was established during workshops arranged during the process and is not an exact number. Further research is needed to establish a better understanding of thresholds that can result in an infinite impact. The number of people dead is only one factor and different global risks are likley to have very different thresholds. 153 \"The so-called \"Warsaw International Mechanism for Loss and Damage\" will from next year commit developed nations to provide expertise and potentially aid to countries hit by climate-related impacts. [...] However, the vague wording fell short of the kind of detailed commitments on additional funding and the commitment to compensation that many developing nations had been seeking.\" (source: Business Green: \"COP 19: Warsaw climate deal finalised as deadlock broken\").  154  See for instance Bulkeley, Harriet, and Peter Newell.: \"Governing climate change.\" Routledge (2010).  155  See the National Research Council: \"Abrupt Impacts of Climate Change: Anticipating Surprises.\" Washington, DC: The National Academies Press (2013).  156  See NASA's \"GISS Surface Temperature Analysis.\"  157  See the IPCC's Fourth Assessment Report.  158  See the IPCC's Fifth Assessment Report.  159  See the IUCN's Red List of Threatened Species.  160     162  See Archer, David.: \"Methane hydrate stability and anthropogenic climate change.\" Biogeosciences Discussions 4.2 (2007): 993-1057.  163  For example, as climate warms, the destabilization of the West Antarctic ice sheet could raise sea level rapidly, with serious consequences for coastal communities.  169 Currently estimated at around 17,000 (source: SIPRI yearbook 2013).  170  Though it has been argued that scientists, under pressure from governments and industry, have systematically underestimated the deleterious global impact of radiation. See Perrow, Charles.: \"Nuclear denial: From Hiroshima to Fukushima.\" Bulletin of the Atomic Scientists 69.5 (2013): 56-67.  171  The seminal American paper was Turco  173 Though some have argued for a significant climate effect of the nuclear explosions themselves, see Fujii, Yoshiaki.: \"The role of atmospheric nuclear explosions on the stagnation of global warming in the mid 20th century.\" Journal of Atmospheric and Solar-Terrestrial Physics 73.5 (2011): 643-652.  174  There is (fortunately) very little empirical evidence on the impact of nuclear bombs on cities. Hiroshima suffered a firestorm, while Nagasaki did not -and both cities and nuclear weapons are very different now from what they were in 1945.  175   488 Dealing with most risks comes under the category of decision theory: finding the right approaches to maximise the probability of the most preferred options. But an intelligent agent can react to decisions in a way the environment cannot, meaning that interactions with AIs are better modelled by the more complicated discipline of game theory.  489  See Yudkowsky, Eliezer.: Artificial intelligence as a positive and negative factor in global risk. Global catastrophic risks 1 (2008): 303.  490  See Muehlhauser, Luke, and Nick Bostrom.: Why we need friendly AI. Think: Philosophy for Everyone (2014).  491  The balance is currently very uneven, with only three small organisations -the Future of Humanity Institute, the Machine Intelligence Research Institute and the Cambridge Centre for Existential Risk -and focused mainly on the risks of AI, along with some private individuals.  492  See Sandberg, Anders, and Nick Bostrom.: Whole brain emulation: A roadmap. Future of Humanity Institute Technical Report #2008-3, Oxford University (2008).  493  A dangerous AI would be a very intelligent that one could acquire great power in the world, and would have goals that were not compatible with full human survival and flourishing. There are a variety of ways of avoiding this. \"Friendly AI\" projects focus on the AI's goals directly, and attempt to make these compatible with human survival. The Oracle AI approach attempts to \"box\" the AI (constrain its abilities to influence the world) in order to prevent it from acquiring power. The reduced impact AI is a novel approach which attempts to construct AIs goals that are not friendly per se, but that motivate the AI to have a very limited impact on the world, thus constraining the potential damage it could do.  494  There are many different designs for AIs, and disagreements about whether they could be considered moral agents or capable of suffering. At one end of the scale is the theoretical AIXI(tl), which is essentially nothing more than an equation with vast computing power; at the other lie whole brain emulations, copies of human minds implemented inside a computer. Suffering for the first design seems unlikely; suffering for the second seems very possible. Determining whether a specific AI design can suffer will be an important part of figuring out what to do with it; it seems unlikely that we'll have hard and fast rules in advance.  495  The idea behind uploads, also called whole brain emulations, is to take a human brain, copy the position of its neurones and connections to sufficient precision, and then run the emulation forwards according to the laws of physics and chemistry. It should then behave exactly as a human brain in the real world. See http:// www.fhi.ox.ac.uk/brain-emulation-roadmap-report.pdf for more details, which also goes into the requirements and tries to estimate the likelihood off success of such an approach (it depends on certain likely but uncertain assumptions about how the brain works at the small scale; ie that most things below a certain scale can be handled statistically rather than through detailed modelling).  496  There's two ways there could be diminishing returns to intelligence: first, it might not be possible for an AI to improve its own intelligence strongly. Maybe it could find some ways of better executing its algorithms, and a few other low-hanging fruits, but it's very possible that after doing this, it will find that the remaining intelligenceincrease problems are hard, and that it hasn't improved itself sufficiently to make them easy (you could analogise this to dampened resonance -initially the AI can improve its intelligence quite easily, and this gives it more intelligence with which to work, allowing it to improve its intelligence still further; but each time, the effect is less, and it soon plateaus). The other way there could be diminishing returns to intelligence is if intelligence doesn't translate into power effectively. This is more likely with things like social intelligence: it seems plausible that no entity could convince, say, 99% of Britain to vote for their party, no matter how socially intelligent it was. Scientific and technological intelligence could conceivably be limited by creativity (unlikely), constraints on the speed of making experiments, or just the fact that humans have solved the easy problems already. The Global Catastrophic Risk Institute (GCRI) published a GCR bibliography compiled in July 2011 by Seth Baum, available at http://gcrinstitute. org/bibliography. This contains 115 entries, emphasising publications surveying the breadth of the risks or discussing other topics of general interest to the study of GCR, with less emphasis on analysis of specific global challenges. It has been updated for this Global Challenges Foundation report and now contains 178 entries. The reason for focusing on general interest publications is because the literature on specific global challenges is far too voluminous to catalogue. It would include, for example, a significant portion of the literatures on climate change, energy, nuclear weapons, infectious diseases and biodiversity, all topics that receive extensive research attention. Thus the full bibliography compiled by GCRI is only a small portion of the total global challenges literature. Publications for the full bibliography were identified in several ways. The bibliography began with publications already known to fit the selection criteria. Additional publications were identified by examining the reference lists of the initial publications. More publications were identified by searching scholarly databases (mainly Web of Science and Google Scholar) and databases of popular literature (mainly Amazon and the New York Public Library) for relevant keywords and for citations of the publications already identified. Several keywords and phrases were searched for in the databases: \"existential catastrophe\"; \"existential risk\"; \"global catastrophe\"; \"global catastrophic risk\"; \"greatest global challenges\"; \"human extinction\"; \"xrisk\"; and \"infinite risk\". The results of these searches were then screened for relevant publications. Many of the results were not relevant, because these terms are used in other ways. For example, \"existential risk\" is sometimes used to refer to risks to the existence of businesses, countries or other entities; \"human extinction\" is used in the study of memory. The publications that use these terms in the same sense as the bibliography were then further screened for publications of general global challenges interest, not for specific global challenges. The most productive search term for the database searches turned out to be \"global catastrophe\". This term produced a relatively large number of hits and relatively few publications on unrelated topics. Further, the term is used by researchers from a variety of different backgrounds. This makes it a particularly fruitful term for discovering new global challenges research. One hallmark of the global challenges topic is that it is studied by distinct research communities that have limited interaction with each other. As research communities often develop their own terminology, it can be difficult to discover one community by searching for another's terms. For example, \"existential risk\" is used heavily by researchers studying risk from artificial intelligence and other emerging technologies, but it is rarely used by researchers studying environmental risks. Discovering and connecting the disparate corners of the GCR research is an ongoing challenge for the GCR community. Bibliography searches such as these are an important way to meet this challenge. \n Bibliography Global Challenges Twelve risks that threaten human civilisation -The case for a new category of risks \n Twelve risks that threaten human civilisation -The case for a new category of risks 15 Executive Summary \n Twelve risks that threaten human civilisation -The case for a new category of risks \n Twelve risks that threaten human civilisation -The case for a new category of risks Executive Summary \n Figure 1 : 1 Figure 1:Probability density function \n Figure 2 : 2 Figure 2: Probability density function with tail highlighted \n Figure 4 : 4 Figure 4: Nordhaus, The Climate Casino: Total cost of different targets assuming limited participation and discounting of future incomes. \n Figure 6 : 6 Figure 6: Normal risks and risks with potentially infinite impact. \n Figure Figure 8: Example of F-n curve showing an absoluteimpact level that is defined as unacceptable/ infinite. i.e no level of probability is acceptable above a certain level of impact, in this case 1000 dead64     \n Figure 9 : 9 Figure 9: Number of times global challenges are included in surveys of global challenges \n Figure 10 : 10 Figure 10: The global challenges included ten times or more in surveys of global challenges \n Twelve risks that threaten human civilisation -The case for a new category of risks 3.1 Current risks 3.1.1.1 Expected impact disaggregation 3.1.1 \n only nine countries are currently known to possess them: the five security council members, India, Pakistan, and North Korea, plus Israel. 230 76 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.1 Current risks 77 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3Ecological collapse refers to a situation where an ecosystem suffers a drastic, possibly permanent, reduction in carrying capacity for all organisms, often resulting in mass extinction. Usually an ecological collapse is precipitated by a disastrous event occurring on a short time scale. 231 78 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.1 Current risks 3.1.3.1 Expected impact disaggregation 3.1.3.2 Probability Humans are part of the global ecosystem and so fundamentally depend on it for our welfare. \n Global Figure 18: Increase in the number of species assessed for the IUCN Red List of Threatened SpeciesTM (2000-2013.2). Source: http://www.iucnredlist.org/about/summary-statistics \n A pandemic (from Greek πᾶν, pan, \"all\", and δῆμος demos, \"people\") is an epidemic of infectious disease that has spread through human populations across a large region; for instance several continents, or even worldwide. \n Twelve risks that threaten human civilisation -The case for a new category of risks 3 \n 310 90 Global 90 Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3 \n Figure 19 : 19 Figure 19: Network Diagram of connections between, banks, brokers/dealers, insurers and hedge funds. Jan 1994-Dec 1996 Source: https://app.box.com/shared/oesro8zzco0mtvuymh3f \n Figure 20 : 20 Figure 20: How the Spaceguard Survey has reduced the short-term risk of impacts from near-Earth objects 349 \n 2. The predictability of supervolcanic eruptions. 3. How directly destructive an eruption would be. 4. The effectiveness of general mitigation efforts. 5. How severe the long-term climate effects would be. 103 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n Figure 21 : 21 Figure 21: Volcanic Explosivity Index 389 \n 118 Global 118 Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.3 Emerging risks 01-Jun-13: Nanostart AG: Venture Capital Investments in Nanotech 475 -Initiative \n 119 Global 119 Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3Artificial intelligence (AI) is the intelligence exhibited by machines or software, and the branch of computer science that develops machines and software with human-level intelligence. 120 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3 \n Twelve risks that threaten human civilisation -The case for a new category of risks 3 \n Figure 23 : 23 Figure 23: Number of galaxies that can reach us with speeds of 50%c, 80%c, 99%c and c, from different starting moments 552 \n 485 132Global 485 Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3 \n Figure 24 : 24 Figure 24: Less poverty of nations -Population living below $1.25 a day at 2005 Purchasing-pover parity, % * 0=absolute equality, 100=absolute inequality Source: Economist, originally World Bank, http://www.economist.com/node/14979330 \n 4. 1 1 Specific relations between global risks \"Uncertainty is an uncomfortable position. But certainty is an absurd one.\" Voltaire -an initial overview 5. Probabilities and uncertainties 142 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 5. Probabilities and uncertainties -an initial overview \n Figure 27 : 27 Figure 27: Different kinds of poverty -Number of people in poverty 638 \n Figure 28 : 28 Figure 28: Population of the world, 1950-2100, according to different projections and variants Source: http://esa.un.org/wpp/documentation/pdf/WPP2012_Volume-I_Comprehensive-Tables.pdf, p. xv \n Figure 29 : 29 Figure 29: Moore's forecast for PV 656 Figure 30: Global ICT development 2000-2013 657 \n Figure 24 : 24 Figure 24: Population aged 80 or over 661 \n Twelve risks that threaten human civilisation -The case for a new category of risks \n Figure 31 : 31 Figure 31: Comparing the probability scale in the Swedish National Risk Assessment 667 and the Likelihood Scale used by the IPCC 668 \n 35  http://en.wikipedia.org/wiki/Human_embryogenesis 36 These four points are slightly rewritten versions of a list of Nick Bostrom's in the text \"Existential Risks: \n 59 HSE 2001. Reducing Risks, Protecting People -HSE's Decision-Making Process, 2001. agreement.\" \n 164 http://simple.wikipedia.org/wiki/Nuclear_war165  For an analysis of the possibility of accidental nuclear war between Russia and the USA, seeBarrett, Anthony M., Seth D. Baum, and Kelly Hostetler.: \"Analyzing and Reducing the Risks of Inadvertent Nuclear War Between the United States and Russia.\" Science & Global Security 21.2 (2013): 106-133. 166 Hellman, Martin E.: \"How risky is nuclear optimism?.\" Bulletin of the Atomic Scientists 67.2 (2011): 47-56. 167 See Lundgren, Carl.: \"What are the odds? Assessing the probability of a nuclear war.\" The Nonproliferation Review 20.2 (2013): 361-374. \n 168  A 1979 study by the United States Office of Technology Assessment, \"The Effects of Nuclear War,\" estimated 20-160 million immediate casualties from a full-scale nuclear war. \n , Richard P., et al.: \"Nuclear winter: global consequences of multiple nuclear explosions.\" Science 222.4630 (1983): 1283-1292. The Soviet Union was working on similar simulations; see for instance Peterson, Jeannie.: \"The aftermath: The human and ecological consequences of nuclear war.\" New York: Pantheon (1983). \n 172 See Mills, Michael J., et al.: \"Massive global ozone loss predicted following regional nuclear conflict.\" Proceedings of the National Academy of Sciences 105.14 (2008): 5307-5312. \n See Toon, Owen B., et al.: \"Atmospheric effects and societal consequences of regional scale nuclear conflicts and acts of individual nuclear terrorism.\" Atmospheric Chemistry and Physics 7.8 (2007): 1973-2002, and Robock, Alan, Luke Oman, and Georgiy L. Stenchikov.: \"Nuclear winter revisited with a modern climate model and current nuclear arsenals: Still catastrophic consequences.\" Journal of Geophysical Research: Atmospheres (1984-2012) 112.D13 (2007). \n \n \n \n \n \n \n \n \n The case for a new category of risks Executive Summary Uncertainties As the different challenges are very different and the status of probability estimates varies significantly, the initial probability numbers are provided together with estimates regarding: 1. Understanding of sequence 1. Understanding of sequence 1. Understanding of sequence 1. Understanding of sequence 2. Data availability 2. Data availability 2. Data availability 2. Data availability 3. Existing probability estimation 3. Existing probability estimation all parts all parts all parts all parts all parts all data all data all data all data all data calculations with small uncertainty calculations with small uncertainty calculations with small uncertainty none at all some parts most parts none at all some parts most parts degree of events from today's actions to infinite impact none at all degree of events from today's actions to infinite impact none at all none at all some parts some parts some parts most parts most parts most parts no data some data most data amount of data to make probability assessment on all relevant steps of the sequence no data amount of data to make probability no data some data most data of the sequence assessment on all relevant steps no data no data some data some data some data most data most data most data no estimates best guesses kind of estimation and uncertainty no estimates no estimates by experts calculations with best guesses by experts by experts best guesses large uncertainty calculations with large uncertainty calculations with large uncertainty degree of events from today's actions to infinite impact degree of events from today's actions to infinite impact degree of events from today's actions to infinite impact amount of data to make probability assessment on all relevant steps of the sequence amount of data to make probability of the sequence assessment on all relevant steps kind of estimation and uncertainty amount of data to make probability of the sequence assessment on all relevant steps kind of estimation and uncertainty 22 21 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Executive Summary \n 20  , or $150 quintillion. 2.3 Global challenges and infinite impact This is a very low estimate, and Posner suggests that maybe the cost of a life should be \"written up $28 million\" for catastrophic risks 52 . Posner's calculations where only one future generation is included result in a cost of $336 quadrillion. If we include all future generations with the same value, $28 million, the result is a total cost of $86 sextillion, or $86 × 10 21 . This $86 sextillion is obviously a very rough number (using one billion years instead of 50 million would for example require us to multiply the results by 20), but again it is the 10 12 stars in our galaxy, and perhaps reference there are about 10 11 to magnitude that is interesting. As a Threshold something like the same number of galaxies. With this simple calculation you get 10 22 to 10 24 , or 10 to 1,000 sextillion, stars in the universe to put the cost of infinite impacts Normal risks when including future generations in Traditional measures perspective. 53 and tools applicable probability 0 impact 44 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n 140   \n The extent to which humans are dependent on the ecosystem. 2. Whether there will be effective political measures taken to protect the ecosystem on a large scale. 3. The likelihood of the emergence of sustainable economies. 4. The positive and negative impacts on the eco systems of both wealth and poverty. 5. The long-term effects of an ecological collapse on ecosystems. GOVERNANCE DISASTERS 3.1 Current risks 3.1 Current risks Post-eco-collapse climate change cooperation will be important to any 1. Global coordination and attempt to control ecological damage 9. New, profitable, but environmentally Global poverty Global coordination damaging industries could put extra strain on the ecosystem. 19. Technological innovations Sustainability research may result in more sustainable economies, or in more during 2013 3.1.3.3 Main events on a large scale and prevent \"races to environmentally damaging products. the bottom\". 22-Jan-13: Current extinctions 10. According to some systems of value, the loss of certain animals ecological effects Long-term Global instability probably the result of past actions; Global povety Global coordination 2. Poverty is often seen as and ecosystems constitutes a moral many future extinctions to come 242 Technological through unsustainable practices, innovations exacerbating ecological damage tragedy in and of itself. -Research 20. It may be possible to Deliberate attempts to construct world dictatorship ensure human survival in semi-hydroponic food, distilled water), \"closed\" systems (solar power, while richer countries introduce An estimated 40% of world trade 11. Humans derive much pleasure and with minimal dependency on the Quality of life loss from ecosystem loss environmental regulations -but richer many benefits from various parts of Ecological collapse Preservation efforts New system of governance Smart sensors external ecosystem. is based on biological products Meta-uncertainty on tradeoffs nations exploit many resources (such the ecosystem, and losing this would or processes such as agriculture, between e.g. poverty, survival, as fossil fuels) in non-sustainable and result in a loss to human quality of life. 21. Over the long term, it may become forestry, fisheries and plant-derived freedom damaging ways. possible and necessary to go about pharmaceuticals, and biodiversity comprises an invaluable pool 12. Ongoing and continuous rebuilding the ecosystem and healing Threat to economies, or sustainable food supply 3. Transitioning to sustainable for innovations. Moral tragedy from ecosystem loss consequence of ecological collapse. Pollution biodiversity loss is a clear its damage. economic trajectories, could control 22. Political decisions will be the most Economic costs Failing to solve 4. Research into sustainability could Loss of biodiversity triggering famines. Improvements to global governance important problems ecological damage. 13. Ecological damage can put Making Pre-eco-collapse climate change likely factors to exacerbate or mitigate things worse the human food system in danger, an ecological disaster. allow the construction of sustainable 23. It is unclear how dependent economies or environments at costs 14. Ecological damage increases humans truly are on the that people are willing to bear. vulnerability to floods and other ecosystem, and how much Disruption to politics and economy 5. Climate change exacerbates the Rebuilding the ecosystem natural disasters. Post-eco-collapse politics damage they could inflict without threatening their own survival. Enduring poverty pressure on the ecological system Not achieving important ethical goals by changing weather patterns and Climate change 15. Disruptions to the world's political Global pollution and economic systems could trigger Lack of human flourishing Vulnerabilities to flood and other disasters increasing natural disasters in ways further conflicts or instabilities, Sustainable or non-sustainable economies ecosystems find hard to adapt to. causing more casualties and impairing New, environmentally damaging industries effective response. 6. Global pollution is a visible source of ecological damage, one that global 16. Since a lot of the world's carbon is Undesirable world system (e.g. global dictatorship) Pre-eco-collapse mitigation efforts locked up in trees, ecological collapse Technological could exacerbate climate change. innovations Collapse of agreements have had moderate success at tackling. Disruption to world politics and economy world system Post-disaster politics Long-term negative effects 7. Truly global preservation efforts 17. The ecosystem is of great may be needed for some threatened economic benefit to humanity, Meta-uncertainty on the true dependence of humanity on the ecosystem so its loss would have large Human survivability in \"closed\" systems natural boundaries (e.g. in the seas ecosystems that stretch beyond economic costs. and oceans). 18. Ecological damage is likely to Total short-term casualties 8. Beyond general all-purpose mitigation efforts, addressing General mitigation effort be long-term: the effects will last for Extinction many generations. Civilisation collapse this threat could include the Total short-term casualties species or genetic codes, to allow a preservation of ecosystems, Civilisation collapse Extinction subsequent rebuilding. Key Key Uncertain events Meta-uncertainties Risk events Direct impacts Indirect impacts Current intervention areas Bad decisions Accidents Severe impacts Uncertain events Meta-uncertainties Risk events Direct impacts Indirect impacts Current intervention areas Bad decisions Accidents Severe impacts 80 79 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.1 Current risks ECOLOGICAL CATASTROPHE Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 81 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n and trade. 573  137 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 4. Relations between global risk 3.4 Global Policy risk 4. Relations between Two things make the understanding 4.1 General relations of the relation between the global between global risks risks particularly important. and their potential impacts 1. Impacts: The global risks global risks are interconnected in different Relations between global risks is an ways. Often the situation can be area where surprisingly little work is described as a set of dominoes: if being done. Most research focuses one falls, many others follow. Even on individual or closely related small impacts can start a process groups of challenges. Organisations where different challenges interact. working on global challenges are Higher temperatures due to global almost always working on individual warming can result in the spreading risks. The initial overview below is of pandemics which increase based on individual studies where tensions between countries, and different relations are analysed, but so on. no work has been identified where the relations between all twelve 2. Specific measures to address challenges have been analysed. a risk: Global risks often require significant changes in our current A risk that is natural to start with is society, from how we build cities future bad global governance, as all to how food is produced and other global challenges exacerbate provided. Such significant changes governance disasters, 575 and all other will result in situations where global challenges can potentially be measures to reduce the risk in exacerbated by governance disasters. one area affect the probability A well functioning global governance and/or the impact in other areas. system is therefore a key factor to Depending on the measure chosen address global catastrophic risks. to reduce the risk, and other complementary measures, the Conversely, avoiding governance effect can be positive or negative. disasters improves all risks, as better institutions are better able to mitigate risks. Governance disasters directly increase the problems of climate change (through a lack of coordination between countries), the risk of nuclear war (by stoking conflict between nuclear powers) and \"We have some idea what might happen if, global system collapse (by weakening global responses to systemic risks). in the face of other pressing global challenges, All risks exacerbate global system collapse, by putting extra stress on an we divert our focus from making systemic interconnected system. improvements in public health and veterinary services -and that prospect is frightening.\" The World Bank 574 138 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n Twelve risks that threaten human civilisation -The case for a new category of risks 4.1 General relations between global risks and their potential impacts 4.2 Specific relations between global risks Below is an example of an overview of how different global challenges can be plotted depending on the technical difficulty of reducing An international initiative should start to achieve better understanding of the relations between global challenges in order to ensure the risk and the difficulty of synergies and avoid strategies that In parallel with work to increase our collaborating to reduce it. will undermine other challenges. understanding about the general relations between global risks, work to identify more specific relations should also be initiated. This is an area where people die / suffer many pieces of research exist. But very little work has been done to combine them and assess different strategies to address specific global risks and understand how these strategies will affect other global risks. It is important to distinguish between two different support use people afraid of infections short term thinking kinds of specific relations. Extreme Climate Change Global Pandemic First, there are solution strategies for one global risk and the ways it affects other global risks. For example, using video conferences can reduce the probability of pandemics by reducing unnecessary travel. On the other hand, unsustainable use of bio-energy could increase spillover opportunities when a zoonosis (a disease transmitted more renewable energy more video meetings less meat consumption from nature accident attack from animals to humans) increases reduce risk the spread of pandemics due to an increased number of contacts between increase risk humans and infected animals in forests around the world. 593 Second, how society reacts to the very threat of different risks can affect other challenges. For example, if people are afraid of pandemics they might use more video meetings and in that way help reduce carbon emissions. solving first risk improves second risk first risk worsens second risk Attempts to develop solutions for specific global challenges should assess their impacts, positive and negative, on other challenges. In order to better understand the relations between different global challenges, work could start to analyse similarities and differences. technical difficulty of reducing risk both of the above collaboration difficulty of reducing risk 140 Global Challenges - Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 141 \n 15 Climate Impacts: http://www.ipcc.ch/report/ar5/wg2/ Pandemics: http://www.cmu.edu/dietrich/sds/docs/ fischhoff/AF-GPH.pdf Nuclear war: http://www.ippnw.org/nuclear-famine.html 16 http://news.stanford.edu/news/2003/september24/ tellerobit-924.html 17 http://www.fas.org/sgp/othergov/doe/lanl/ docs1/00329010.pdf \n For examples see the recently established Centre for Study of Existential Risk at Cambridge. It is an interdisciplinary research centre focused on the study of human extinction-level risks that may emerge from technological advance 27 E.g. HBR blog about \"black swans\": http://blogs. hbr.org/2010/09/the-competing-black-swans-of-s/ and The Guardian about \"perfect storms\" http://www. theguardian.com/environment/earth-insight/2014/ apr/03/ipcc-un-climate-change-perfect-storm-zombieoil 28 http://www.economist.com/node/18744401 29 http://e360.yale.edu/feature/living_in_the_ anthropocene_toward_a_new_global_ethos/2363/ 30 http://www.nickbostrom.com/existential/risks.html 31 https://www.youtube.com/watch?v=VjZyOTES6iQ 32 http://en.wikipedia.org/wiki/Long_tail 33 http://en.wikipedia.org/wiki/Human 34 Mammals have an average species lifespan from origin to extinction of about 1 million years, but that will not necessarily apply to humans today because of factors like local climate change or new species in the same ecological niche. The dinosaurs were around for 135 million years and if we are intelligent, there are good chances that we could live for much longer. \n Posner, Richard A. Catastrophe: Risk and Response. Oxford University Press, 2004, Loc 2378 53 http://www.esa.int/Our_Activities/Space_Science/ Herschel/How_many_stars_are_there_in_the_Universe? 54 http://www.existential-risk.org/concept.pdf 55 McSharry, Patrick E., and David Orrell (2009). A Systems Approach to Forecasting. FORESIGHT: The International Journal of Applied Forecasting, referring to Wolfram, Stephen (2002):A new kind of science, V Wolfram media. http://www.irgc. org/wp-content/uploads/2013/06/McSharry-OrrellMcSharry2009foresight.pdf 56 From A Systems Approach to Forecasting\" by David Orrell and Patrick McSharry, http://www. irgc.org/wp-content/uploads/2013/06/McSharry-OrrellMcSharry2009foresight.pdf referring to Wolfram, S. \n See McManus, J. F., et al.: \"Collapse and rapid resumption of Atlantic meridional circulation linked to deglacial climate changes.\" Nature 428.6985 (2004): 834-837. 161 See Schuur, Edward AG, et al.: \"Vulnerability of permafrost carbon to climate change: Implications for the global carbon cycle.\" BioScience 58.8 (2008): 701-714. \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Executive SummaryExecutive SummaryGlobal Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 2. Risks with infinite impact: A new category of risks \n\t\t\t .3 Global challenges and infinite impact \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 3.1 Current risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks3.3 Emerging risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks3.3 Emerging risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks3.3 Emerging risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks3.3 Emerging risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks3.3 Emerging risks \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks 7. Possible ways forward \n\t\t\t Pinker, Steven. The better angels of our nature: The decline of violence in history and its causes. Penguin UK, 2011.11 Giddens, Anthony. \"Risk and responsibility.\" The modern law review 62.1 (1999): 1-10.12 http://blogs.ei.columbia.edu/2012/01/09/evolutionarypsychology-of-climate-change/ \n\t\t\t Posner, Richard A. Catastrophe: Risk and Response. Oxford University Press, 2004, 38 http://en.wikipedia.org/wiki/Value_of_life 39 http://yosemite.epa.gov/EE%5Cepa%5Ceed.nsf/ webpages/MortalityRiskValuation.html 40 Posner, Richard A. Catastrophe: risk and response. Oxford University Press, 2004. Loc 2363 41 http://webarchive.nationalarchives.gov.uk/+/http:/ www.hm-treasury.gov.uk/sternreview_index.htm 42 William Nordhaus , The Stern Review on the Economics of Climate Change http://www.econ.yale. edu/~nordhaus/homepage/stern_050307.pdf 43 http://www.res.org.uk/view/art3Apr08Features.html 44 Nordhaus, William D. The Climate Casino: Risk, Uncertainty, and Economics for a Warming World. Yale University Press, 2013. Loc 2895 45 Nordhaus, William D. The Climate Casino: Risk, Uncertainty, and Economics for a Warming World. Yale University Press, 2013. Loc 2895 46 Nordhaus, William D. The Climate Casino: Risk, Uncertainty, and Economics for a Warming World. Yale University Press, 2013. Loc 3176 Endnotes 184 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Endnotes \n\t\t\t Arsenals have been reduced, but there remain over 17,000 nuclear warheads in the world's arsenals (source: SIPRI yearbook 2013), down from a peak of some 68,000 in 1983, still more than enough to trigger a nuclear winter.177  See Toon, Owen B., et al.: \"Atmospheric effects and societal consequences of regional scale nuclear conflicts \n\t\t\t Russian Federation On Strategic Offensive Reductions.216  The Treaty between the United States of America and the Russian Federation on Measures for the Further \n\t\t\t See DARPA's briefing, DARPA-SN-13-30: Probabilistic Programming for Advancing Machine Learning (PPAML) (2013).498  See for instance Curtis, Jon, Gavin Matthews, and David Baxter.: On the effective use of Cyc in a question answering system. Proc Workshop on Knowledge and Reasoning for Answering Questions. (2005).499  See The Rise of Industrial Big Data, GE Intelligent Platforms (2013).500 Such as Watson's triumph on \"Jeopardy!\" (source: Ferrucci, David, et al.: Building Watson: An overview of 192 Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Endnotes \n\t\t\t Global Challenges -Twelve risks that threaten human civilisation -The case for a new category of risks Appendix 1 -Global Challenges Bibliography", "date_published": "n/a", "url": "n/a", "filename": "12Riskswithinfiniteimpact-fullreport.tei.xml", "abstract": "The material and the geographical designations in this report do not imply the expression of any opinion whatsoever on the part of Global Challenges Foundation concerning the legal status of any country, territory, or area, or concerning the delimitation of its frontiers or boundaries.", "id": "5b191bfc582184a500fb6d1e6227d88f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kaj Sotala", "Lukas Gloor"], "title": "Superintelligence as a Cause or Cure for Risks of Astronomical Suffering", "text": "Introduction Work discussing the possible consequences of creating superintelligent AI  (Yudkowsky 2008 , Bostrom 2014, Sotala & Yampolskiy 2015) has discussed superintelligence as a possible existential risk: a risk \"where an adverse outcome would either annihilate Earth-originating intelligent life or permanently and drastically curtail its potential\"  (Bostrom 2002 (Bostrom , 2013 . The previous work has mostly  1  considered the worstcase outcome to be the possibility of human extinction by an AI that is indifferent to humanity's survival and values. However, it is often thought that for an individual, there exist \"fates worse than death\"; analogously, for civilizations there may exist fates worse than extinction, such as survival in conditions in which most people will experience enormous suffering for most of their lives. Even if such extreme outcomes would be avoided, the known universe may eventually be populated by vast amounts of minds: published estimates include the possibility of 10 25 minds supported by a single star  (Bostrom 2003a) , with humanity having the potential to eventually colonize tens of millions of galaxies  (Armstrong & Sandberg 2013) . While this could enable an enormous number of meaningful lives to be lived, if even a small fraction of these lives were to exist in hellish circumstances, the amount of suffering would be vastly greater than that produced by all the atrocities, abuses, and natural causes in Earth's history so far. We term the possibility of such outcomes a suffering risk: Suffering risk (s-risk): One where an adverse outcome would bring about severe suffering on an astronomical scale, vastly exceeding all suffering that has existed on Earth so far. In order for potential risks -including s-risks -to merit work on them, three conditions must be met. First, the outcome of the risk must be sufficiently severe to merit attention. Second, the risk must have some reasonable probability of being realized. Third, there must be some way for risk-avoidance work to reduce either the probability or severity of an adverse outcome. In this paper, we will argue that suffering risks meet all three criteria, and that s-risk avoidance work is thus of a comparable magnitude in importance as work on risks from extinction. Section 2 seeks to establish the severity of s-risks. There, we will argue that there are classes of suffering-related adverse outcomes that many value systems would consider to be equally or even more severe than extinction. Additionally, we will define a class of less severe suffering outcomes which many value systems would consider important to avoid, albeit not as important as avoiding extinction. Section 3 looks at suffering risks from the view of several different value systems, and discusses how much they would prioritize avoiding different suffering outcomes. Next, we will argue that there is a reasonable probability for a number of different suffering risks to be realized. Our discussion is organized according to the relationship that superintelligent AIs have to suffering risks: section 4 covers risks that may be prevented by a superintelligence, and section 5 covers risks that may be realized by one  2  . Section 6 discusses how it might be possible to work on suffering risks. \n Suffering risks as risks of extreme severity As already noted, the main focus in discussion of risks from superintelligent AI has been either literal extinction, with the AI killing humans as a side-effect of pursuing some other goal  (Yudkowsky 2008) , or a value extinction. In value extinction, some form of humanity may survive, but the future is controlled by an AI operating according to values which all current-day humans would consider worthless  (Yudkowsky 2011 ). In either scenario, it is thought that the resulting future would have no value. In this section, we will argue that besides futures that have no value, according to many different value systems it is possible to have futures with negative value. These would count as the worst category of existential risks. In addition, there are adverse outcomes of a lesser severity, which depending on one's value systems may not necessarily count as worse than extinction. Regardless, making these outcomes less likely is a high priority and a common interest of many different value systems.  Bostrom (2002)  frames his definition of extinction risks with a discussion which characterizes a single person's death as being a risk of terminal intensity and personal scope, with existential risks being risks of terminal intensity and global scope -one person's death versus the death of all humans. However, it is commonly thought that there are \"fates worse than death\": at one extreme, being tortured for an extended time (with no chance of rescue), and then killed. As less extreme examples, various negative health conditions are often considered worse than death  (Rubin, Buehler & Halpern 2016; Sayah et al. 2015; Ditto et al., 1996) : for example, among hospitalized patients with severe illness, a majority of respondents considered bowel and bladder incontinence, relying on a feeding tube to live, and being unable to get up from bed, to be conditions that were worse than death  (Rubin, Buehler & Halpern 2016) . While these are prospective evaluations rather than what people have actually experienced, several countries have laws allowing for voluntary euthanasia, which people with various adverse conditions have chosen rather than go on living. This may considered an empirical confirmation of some states of life being worse than death, at least as judged by the people who choose to die. The notion of fates worse than death suggests the existence of a \"hellish\" severity that is one step worse than \"terminal\", and which might affect civilizations as  2  Superintelligent AIs being in a special position where they might either enable or prevent suffering risks, is similar to the way in which they are in a special position to make risks of extinction both more or less likely  (Yudkowsky 2008) . well as individuals.  Bostrom (2013)  seems to acknowledge this by including \"hellish\" as a possible severity in the corresponding chart, but does not place any concrete outcomes under the hellish severity, implying that risks of extinction are still the worst outcomes. Yet there seem to be plausible paths to civilization-wide hell outcomes as well (Figure  1 ), which we will discuss in sections 4 and 5. \n Global \n Thinning of the ozone layer \n Extinction risks \n Global hellscape \n Personal Car is stolen Death Extended torture followed by death \n Endurable Terminal Hellish Figure  1 : The worst suffering risks are ones that affect everyone and subject people to hellish conditions. In order to qualify as equally bad or worse than extinction, suffering risks do not necessarily need to affect every single member of humanity. For example, consider a simplified ethical calculus where someone may have a predominantly happy life (+1), never exist (0), or have a predominantly unhappy life (-1). As long as the people having predominantly unhappy lives outnumber the people having predominantly happy lives, under this calculus such an outcome would be considered worse than nobody existing in the first place. We will call this scenario a net suffering outcome  3  . This outcome might be considered justifiable if we assumed that, given enough time, the people living happy lives will eventually outnumber the people living unhappy lives. Most value systems would then still consider a net suffering outcome worth avoiding, but they might consider it an acceptable cost for an even larger amount of future happy lives. On the other hand it is also possible that the world could become locked into conditions in which the balance would remain negative even when considering all the lives that will ever live: things would never get better. We will call this a pan-generational net suffering outcome. In addition to net and pan-generational net suffering outcomes, we will consider a third category. In these outcomes, serious suffering may be limited to only a fraction of the population, but the overall population at some given time  4  is still large enough that even this small fraction accounts for many times more suffering than has  3  \"Net\" should be considered equivalent to Bostrom's \"global\", but we have chosen a different name to avoid giving the impression that the outcome would necessarily be limited to only one planet.  4  One could also consider the category of pangenerational astronomical suffering outcomes, but restricting ourselves into just three categories is sufficient for our current discussion. existed in the history of the Earth. We will call these astronomical suffering outcomes. \n Types of suffering outcomes \n Astronomical suffering outcome At some point in time, a fraction of the population experiences hellish suffering, enough to overall constitute an astronomical amount that overwhelms all the suffering in Earth's history. \n Net suffering outcome At some point in time, there are more people experiencing lives filled predominantly with suffering than there are people experiencing lives filled predominantly with happiness. \n Pangenerational net suffering outcome When summed over all the people that will ever live, there are more people experiencing lives filled predominantly with suffering than there are people experiencing lives filled predominantly with happiness. Any value system which puts weight on preventing suffering implies at least some interest in preventing suffering risks. Additionally, as we will discuss below, even value systems which do not care about suffering directly may still have an interest in preventing suffering risks. We expect these claims to be relatively uncontroversial. A more complicated question is that of tradeoffs: what should one do if some interventions increase the risk of extinction but make suffering risks less likely, or vice versa? As we will discuss below, if forced to choose between these two, different value systems will differ in which of the interventions they favor. In such a case, rather than to risk conflict between value systems, a better alternative would be to attempt to identify interventions which do not involve such a tradeoff. If there were interventions that reduced the risk of extinction without increasing the risk of astronomical suffering, or decreased the risk of astronomical suffering without increasing the risk of extinction, or decreased both, then it would be in everyone's interest to agree to jointly focus on these three classes of interventions. \n Suffering risks from the perspective of different value systems We will now take a brief look at different value systems and their stance on suffering risks, as well as their stance on the related tradeoffs. Classical utilitarianism. All else being equal, classical utilitarians would prefer a universe in which there were many happy lives and no suffering. However, a noteworthy feature about classical utilitarianism (as well as some other aggregative theories) is that it considers very good and very bad scenarios to be symmetrical -that is, a scenario with 10^20 humans living happy lives may be considered equally good, as a scenario with 10^20 humans living miserable lives is considered bad. Thus, people following classical utilitarianism or some other aggregative theory may find compelling the argument  (Bostrom 2003a ) that an uncolonized universe represents a massive waste of potential value, and be willing to risk -or even accept -astronomical numbers of suffering individuals if that was an unavoidable cost to creating even larger numbers of happiness. Thus, classical utilitarianism would consider astronomical and net suffering outcomes something to avoid but possibly acceptable, and pan-generational net suffering outcomes as something to avoid under all circumstances. Other aggregative theories. Any moral theory which was not explicitly utilitarian, but still had an aggregative component that disvalued suffering, would consider suffering risks as something to avoid. Additionally, for moral theories that valued things other than just pleasure and suffering -such as preference satisfaction, some broader notion of \"human flourishing\", objective list theories -hellscape scenarios would likely also threaten the satisfaction of many of the things that these theories valued. For example, minds experiencing enormous suffering are probably not flourishing, are likely to have unsatisfied preferences, and probably do not have many of the things considered valuable in objective list theories. Similarly to classical utilitarianism, many aggregative theories could be willing to risk or even accept astronomical and civilization-wide suffering outcomes as a necessary evil but wish to avoid pangenerational net suffering outcomes. At the same time, many aggregative theories might incorporate some suffering-focused intuition (discussed below) which caused them to put more weight on the avoidance of suffering than the creation of other valuable things. Depending on the circumstances, this might cause them to reject the kind of reasoning which suggested that suffering outcomes could be an acceptable cost. Rights-based theories. Rights-based theories would consider suffering risks a bad thing directly to the extent that they held that people -or animals  (Regan 1980 )had a right to be treated well avoid unnecessary suffering. They could also consider suffering risks indirectly bad, if the suffering was caused by conditions which violated some other right or severely constrained someone's capabilities  (Nussbaum 1997, p. 287) . For example, a right to meaningful autonomy could be violated if a mind was subjected to enormous suffering and had no meaningful option to escape it. General suffering-focused intuitions. There are various moral views and principles which could fit many different value systems, all of which would imply that suffering risks were something important to avoid and which might cause one to weigh the avoidance of suffering more strongly than the creation of happiness: 1. Prioritarianism. Prioritarianism is the position that the worse off an individual is, the more morally valuable it is to make that individual better off  (Parfit 1991) . That is, if one person is living in hellish conditions and another is well-off, then making the former person slightly better off is more valuable than improving the life of the well-off person by the same amount. A stance of \"astronomical prioritarianism\" that considers all minds across the universe, and prioritizes improving the worst ones sufficiently strongly, pushes in the direction of mainly improving the lives of those that would be worst off and thus avoiding suffering risks. If a suffering outcome does manifest itself, prioritarianism would prioritize bringing it to an end, over creating additional well-off lives or further helping those who are already well off. Prioritarianism may imply focusing particularly on risks from future technologies, as these may enable the creation of mind states that are worse than the current biopsychological limits. Besides prioritarianism, the following three intuitions  (Gloor & Mannino 2016)  would also prioritize the avoidance of suffering risks 5 : 2. Making people happy, not happy people  6  . An intuition which is present in preference-based views such as antifrustrationism  (Fehige 1998) , antinatalism  (Benatar 2008 ), as well as the \"moral ledger\" analogy  (Singer 1993 ) and prior-existence utilitarianism  (Singer 1993) , is that it is more important to make existing people better off than it is to create new happy beings.  7  For example, given the choice between helping a million currently-existing people who are in pain and bringing ten million new people into existence, this view holds that it is more important to help the existing people, even if the ten million new people would end up living happy lives. A part of this view is the notion that it is not intrinsically bad to never be created, whereas it is intrinsically bad to exist and be badly off, or to be killed against one's wishes once one does exist. If one accepts this position, then one could still want to avoid extinction -or at least the death of currently-living humans -but the promise of astronomical numbers of happy lives being created  (Bostrom 2003a)  would not be seen as particularly compelling, whereas the possible creation of  5  One might naturally also have various intuitions that point in the opposite direction, that is, of not prioritizing suffering risks. We will not survey these, as our intent in this section is merely to establish that many would consider suffering risks as important to avoid, without claiming that this would be the only plausible view to hold.  6  The name of this intuition is a paraphrase of  Narveson (1973) , \"We are in favor of making people happy, but neutral about making happy people.\"  7  Moral views that attempt to incorporate this intuition by treating the creation of new people as morally neutral (e.g. Singer's \"prior-existence\" criterion) suffer from what Greaves (2017) calls a \"remarkabl[e] difficult[y] to formulate any remotely acceptable axiology that captures this idea of 'neutrality'\". The views by Benatar and Fehige avoid this problem, but they imply a more extreme position where adding new lives is neutral only in a best-case scenario where they contain no suffering or frustrated preferences. astronomical numbers of lives experiencing suffering could be seen as a major thing to avoid. 3. Torture-level suffering cannot be counterbalanced. This intuition is present in the widespread notion that minor pains cannot be aggregated to become worse than an instant of torture  (Rachels 1998) , in threshold negative utilitarianism  (Ord 2013) , philosophical fictional works such as The Ones Who Walk Away From Omelas (LeGuin 1973), and it may contribute to the absolute prohibitions against torture in some deontological moralities.  Pearce (1995)  expresses a form of it when he writes, \"No amount of happiness or fun enjoyed by some organisms can notionally justify the indescribable horrors of Auschwitz\". 4. Happiness as the absence of suffering. A view which is present in Epicureanism as well as many non-Western traditions, such as Buddhism, is that of happiness as the absence of suffering. Under this view, when we are not experiencing states of pleasure, we begin to crave pleasure, and this craving constitutes suffering. Gloor (2017) writes: Uncomfortable pressure in one's shoes, thirst, hunger, headaches, boredom, itches, non-effortless work, worries, longing for better times. When our brain is flooded with pleasure, we temporarily become unaware of all the negative ingredients of our stream of consciousness, and they thus cease to exist. Pleasure is the typical way in which our minds experience temporary freedom from suffering. This may contribute to the view that pleasure is the symmetrical counterpart to suffering, and that pleasure is in itself valuable and important to bring about. However, there are also (contingently rare) mental states devoid of anything bothersome that are not commonly described as (intensely) pleasurable, examples being flow states or states of meditative tranquility. Felt from the inside, tranquility is perfect in that it is untroubled by any aversive components, untroubled by any cravings for more pleasure. Likewise, a state of flow as it may be experienced during stimulating work, when listening to music or when playing video games, where tasks are being completed on auto-pilot with time flying and us having a low sense of self, also has this same quality of being experienced as completely problem-free. Such states -let us call them states of contentment -may not commonly be described as (intensely) pleasurable, but following philosophical traditions in both Buddhism and Epicureanism, these states, too, deserve to be considered states of happiness. Under this view, happiness and pleasure are not intrinsically good, but rather instrumentally good in that pleasure takes our focus away from suffering and thus helps us avoid it. Creating additional happiness, then, has no intrinsic value if that creation does not help avoid suffering. \n Suffering outcomes that could be prevented by a superintelligence In the previous section, we argued that nearly all plausible value systems will want to avoid suffering risks and that for many value systems, suffering risks are some of the worst possible outcomes and thus some of the most important to avoid. However, whether this also makes suffering risks the type of risk that is the most important to focus on, also depends on how probable suffering risks are. If they seem exceedingly unlikely, then there is little reason to care about them. In this and the next section, we will discuss reasons for believing that there are various suffering outcomes that might realize themselves. We begin by considering outcomes which occur naturally but could be prevented by a superintelligence. In the next section, we will consider suffering outcomes which could be caused by a superintelligence. A superintelligence could prevent almost any outcome if it established itself a singleton, \"a world order in which there is a single decision-making agency at the highest level\"  (Bostrom 2005) . Although a superintelligence is not the only way by which a singleton might be formed, alternative ways -such as a world government or convergent evolution leading everyone to adopt the same values and goals  (Bostrom 2005 ) -do not seem particularly likely to happen soon. Once a superintelligence had established itself as a singleton, depending on its values it might choose to take actions that prevented suffering outcomes from arising. \n Are suffering outcomes likely? Bostrom (2003a) argues that given a technologically mature civilization capable of space colonization on a massive scale, this civilization \"would likely also have the ability to establish at least the minimally favorable conditions required for future lives to be worth living\", and that it could thus be assumed that all of these lives would be worth living. Moreover, we can reasonably assume that outcomes which are optimized for everything that is valuable are more likely than outcomes optimized for things that are disvaluable. While people want the future to be valuable both for altruistic and self-oriented reasons, no one intrinsically wants things to go badly. However, Bostrom has himself later argued that technological advancement combined with evolutionary forces could \"lead to the gradual elimination of all forms of being worth caring about\"  (Bostrom 2005) , admitting the possibility that there could be technologically advanced civilizations with very little of anything that we would consider valuable. The technological potential to create a civilization that had positive value does not automatically translate to that potential being used, so a very advanced civilization could still be one of no value or even negative value. Examples of technology's potential being unevenly applied can be found throughout history. Wealth remains unevenly distributed today, with an estimated 795 million people suffering from hunger even as one third of all produced food goes to waste (World Food Programme, 2017). Technological advancement has helped prevent many sources of suffering, but it has also created new ones, such as factory-farming practices under which large numbers of animals are maltreated in ways which maximize their production: in 2012, the amount of animals slaughtered for food was estimated at 68 billion worldwide (Food and Agriculture Organization of the United Nations 2012). Industrialization has also contributed to anthropogenic climate change, which may lead to considerable global destruction. Earlier in history, advances in seafaring enabled the transatlantic slave trade, with close to 12 million Africans being sent in ships to live in slavery  (Manning 1992 ). Technological advancement does not automatically lead to positive results  (Häggström 2016 ).  Persson & Savulescu (2012)  argue that human tendencies such as \"the bias towards the near future, our numbness to the suffering of great numbers, and our weak sense of responsibility for our omissions and collective contributions\", which are a result of the environment humanity evolved in, are no longer sufficient for dealing with novel technological problems such as climate change and it becoming easier for small groups to cause widespread destruction. Supporting this case, Greene (2013) draws on research from moral psychology to argue that morality has evolved to enable mutual cooperation and collaboration within a select group (\"us\"), and to enable groups to fight off everyone else (\"them\"). Such an evolved morality is badly equipped to deal with collective action problems requiring global compromises, and also increases the risk of conflict and generally negative-sum dynamics as more different groups get in contact with each other. As an opposing perspective, West (2017) argues that while people are often willing to engage in cruelty if this is the easiest way of achieving their desires, they are generally \"not evil, just lazy\". Practices such as factory farming are widespread not because of some deep-seated desire to cause suffering, but rather because they are the most efficient way of producing meat and other animal source foods. If technologies such as growing meat from cell cultures became more efficient than factory farming, then the desire for efficiency could lead to the elimination of suffering. Similarly, industrialization has reduced the demand for slaves and forced labor as machine labor has become more effective. At the same time, West acknowledges that this is not a knockdown argument against the possibility of massive future suffering, and that the desire for efficiency could still lead to suffering outcomes such as simulated game worlds filled with sentient non-player characters (see section on cruelty-enabling technologies below). Another argument against net suffering outcomes is offered by  Shulman (2012) , who discusses the possibility of civilizations spending some nontrivial fraction of their resources constructing computing matter that was optimized for producing maximum pleasure per unit of energy, or for producing maximum suffering per unit of energy. Shulman's argument rests on the assumption that value and disvalue are symmetrical with regard to such optimized states. The amount of pleasure or suffering produced this way could come to dominate any hedonistic utilitarian calculus, and even a weak benevolent bias that led to there being more optimized pleasure than optimized suffering could tip the balance in favor of there being more total happiness. Shulman's argument thus suggests that net suffering outcomes could be unlikely unless a (non-compassionate) singleton ensures that no optimized happiness is created. However, the possibility of optimized suffering and the chance of e.g. civilizations intentionally creating it as a way of extorting agents that care about suffering reduction, also makes astronomical suffering outcomes more likely. \n Suffering outcome: dystopian scenarios created by non-value-aligned incentives.  Bostrom (2005 Bostrom ( , 2014  discusses the possibility of technological development and evolutionary and competitive pressures leading to various scenarios where everything of value has been lost, and where the overall value of the world may even be negative. Considering the possibility of a world where most minds are brain uploads doing constant work, Bostrom (2014) points out that we cannot know for sure that happy minds are the most productive under all conditions: it could turn out that anxious or unhappy minds would be more productive. If this were the case, the resulting outcomes could be dystopian indeed: We seldom put forth full effort. When we do, it is sometimes painful. Imagine running on a treadmill at a steep incline-heart pounding, muscles aching, lungs gasping for air. A glance at the timer: your next break, which will also be your death, is due in 49 years, 3 months, 20 days, 4 hours, minutes, and 12 seconds. You wish you had not been born.  (Bostrom 2014, p. 201)  As Bostrom (2014) notes, this kind of a scenario is by no means inevitable; Hanson (2016) argues for a more optimistic outcome, where brain emulations still spend most of their time working, but are generally happy. But even Hanson's argument depends on economic pressures and human well-being happening to coincide: absent such a happy coincidence, he offers no argument for believing that the future will indeed be a happy one. More generally, Alexander (  2014 ) discusses examples such as tragedies of the commons, Malthusian traps, arms races, and races to the bottom as cases where people are forced to choose between sacrificing some of their values and getting outcompeted. Alexander also notes the existence of changes to the world that nearly everyone would agree to be net improvements -such as every country reducing its military by 50%, with the savings going to infrastructure -which nonetheless do not happen because nobody has the incentive to carry them out. As such, even if the prevention of various kinds of suffering outcomes would be in everyone's interest, the world might nonetheless end up in them if the incentives are sufficiently badly aligned and new technologies enable their creation. An additional reason for why such dynamics might lead to various suffering outcomes is the so-called Anna Karenina principle  (Diamond 1997 , Zaneveld et al. 2017 , named after the opening line of Tolstoy's novel Anna Karenina: \"all happy families are all alike; each unhappy family is unhappy in its own way\". The general form of the principle is that for a range of endeavors or processes, from animal domestication  (Diamond 1997 ) to the stability of animal microbiomes  (Zaneveld et al. 2017) , there are many different factors that all need to go right, with even a single mismatch being liable to cause failure. Within the domain of psychology, Baumeister et al. (  2001 ) review a range of research areas to argue that \"bad is stronger than good\": while sufficiently many good events can overcome the effects of bad experiences, bad experiences have a bigger effect on the mind than good ones do. The effect of positive changes to wellbeing also tends to decline faster than the impact of negative changes: on average, people's well-being suffers and never fully recovers from events such as disability, widowhood, and divorce, whereas the improved well-being that results from events such as marriage or a job change dissipates almost completely given enough time (Lyubomirsky 2010). To recap, various evolutionary and game-theoretical forces may push civilization in directions that are effectively random, random changes are likely to bad for the things that humans value, and the effects of bad events are likely to linger disproportionately on the human psyche. Putting these considerations together suggests (though does not guarantee) that freewheeling development could eventually come to produce massive amounts of suffering. A possible counter-argument is that people are often more happy than their conditions might suggest. For example, as a widely-reported finding, while the life satisfaction reported by people living in bad conditions in slums is lower than that of people living in more affluent conditions, it is still higher than one might intuitively expect, and the slum-dwellers report being satisfied with many aspects of their life (Biswas-Diener & Diener 2001). In part, this is explained by fact that despite the poor conditions, people living in the slums still report many things that bring them pleasure: a mother who has lost two daughters reports getting joy from her surviving son, is glad that the son will soon receive a job at a bakery, and is glad about her marriage to her husband and feels that her daily prayer is important (Biswas-Diener & Diener 2001). However, a proper evaluation of this research is complicated: \"suffering\" might be conceptualized as best corresponding to negative feelings, which are a separate component from cognitively evaluated life satisfaction  (Lukas, Diener & Suh 1996) , with the above slumdweller study focusing mainly on life satisfaction. In general, life satisfaction is associated with material prosperity, while positive and negative feelings are associated with psychological needs such as autonomy, respect, and the ability to be able count on others in an emergency  (Diener et al. 2010) . A proper review of the literature and an analysis of how to interpret the research in terms of suffering risks is beyond the scope of this paper. \n Suffering outcome: cruelty-enabling technologies. Better technology may enable people to better engage in cruel and actively sadistic pursuits. While active sadism and desire to hurt others may be a relatively rare occurrence in contemporary society, public cruelty has been a form of entertainment in many societies, ranging from the Roman practice of involuntary gladiator fights to animal cruelty in the Middle Ages. Even in contemporary society, there are widespread sentiments that people such as criminals should be severely punished in ways which inflict considerable suffering (part of the Roman gladiators were convicted criminals). Contemporary society also contains various individuals who are motivated by the desire to hurt others  (Torres 2016 (Torres , 2017a (Torres , 2017b , chap 4.), even to the point of sacrificing their own lives in the process. For example, Eric Harris, one of the two shooters of the Columbine High School Massacre, wrote extensively about his desire to rape and torture people, fantasized about tricking women into thinking that they were safe so that he could then hurt them, and wanted the freedom to be able to kill and rape without consequences  (Langman 2015) . While mass shooters tend to be lone individuals, there have existed more organized groups who seem to have given their members the liberty to act on similar motivations (Torres 2017a), such as the Aum Shinrikyo cult, where dissent or even just \"impure thoughts\" were punished by rituals amounting to torture and defectors \"routinely kidnapped, tortured, imprisoned in cargo crates, subjected to electro shock, drugged in the Astral Hospital or killed outright\"  (Flannery 2016) . While most contemporary societies reject the idea of cruelty as entertainment, civilizations could eventually emerge in which such practices were again acceptable. Assuming advanced technology, this could take the form of keeping criminals and other undesirables alive indefinitely while subjecting them to eternal torture  8  , slaves kept for the purpose of sadistic actions who could be healed of any damage inflicted to them (one fictional illustration of such a scenario recently received widespread popularity as the TV series Westworld)  9  , or even something like vast dystopian simulations of fantasy warfare inhabited by sentient \"non-player characters\", to serve as the location of massive multiplayer online games which people may play in as super-powered \"heroes\". Particularly in the latter scenarios, the amount of sentient minds in such conditions could be many times larger than the civilization's other population. In contemporary computer games, it is normal for the player to kill thousands of computer-controlled opponents during the game, suggesting that a large-scale game in which a sizeable part of the population participated might instantiate very large numbers of non-player characters per player, existing only to be hurt for the pleasure of the players. 5 Suffering outcomes that may be caused by superintelligence  10  In the previous section, we discussed possible suffering outcomes that might be realized without a singleton that could prevent them from occurring, and suggested that an appropriately-programmed superintelligence is currently the most likely candidate for forming such a singleton. However, an inappropriately programmed superintelligence could also cause suffering outcomes; we will now turn to this topic. Superintelligence is related to three categories of suffering risk: suffering subroutines (Tomasik 2017), mind crime  (Bostrom 2014 ) and flawed realization (Bostrom 2013). \n Suffering subroutines Humans have evolved to be capable of suffering, and while the question of which other animals are conscious or capable of suffering is controversial, pain analogues are present in a wide variety of animals. The U.S. National Research Council's Committee on Recognition and Alleviation of Pain in Laboratory Animals (2004) argues that, based on the state of existing evidence, at least all vertebrates should be considered capable of experiencing pain. Pain seems to have evolved because it has a functional purpose in guiding behavior: evolution having found it suggests that pain might be the simplest solution for achieving its purpose. A superintelligence which was building subagents, such as worker robots or disembodied cognitive agents, might then also construct them in such a way that they were capable of feeling pain -and thus possibly suffering (Metzinger 2015) -if that was the most efficient way of making them behave in a way that achieved the superintelligence's goals. Humans have also evolved to experience empathy towards each other, but the evolutionary reasons which cause humans to have empathy  (Singer 1981)  may not be relevant for a superintelligent singleton which had no game-theoretical reason to empathize with others. In such a case, a superintelligence which had no disincentive to create suffering but did have an incentive to create whatever furthered its goals, could create vast populations of agents which sometimes suffered while carrying out the superintelligence's goals. Because of the ruling superintelligence's indifference towards suffering, the amount of suffering experienced by this population could be vastly higher than it would be in e.g. an advanced human civilization, where humans had an interest in helping out their fellow humans. Depending on the functional purpose of positive mental states such as happiness, the subagents might or might not be built to experience them. For example,  Fredrickson (1998)  suggests that positive and negative emotions have differing functions. Negative emotions bias an individual's thoughts and actions towards some relatively specific response that has been evolutionarily adaptive: fear causes an urge to escape, anger causes an urge to attack, disgust an urge to be rid of the disgusting thing, and so on. In contrast, positive emotions bias thought-action tendencies in a much less specific direction. For example, joy creates an urge to play and be playful, but \"play\" includes a very wide range of behaviors, including physical, social, intellectual, and artistic play. All of these behaviors have the effect of developing the individual's skills in whatever the domain. The overall effect of experiencing positive emotions is to build an individual's resources -be those resources physical, intellectual, or social. To the extent that this hypothesis were true, a superintelligence might design its subagents in such a way that they had pre-determined response patterns for undesirable situations, so exhibited negative emotions. However, if it was constructing a kind of a command economy in which it desired to remain in control, it might not put a high value on any subagent accumulating individual resources. Intellectual resources would be valued to the extent that they contributed to the subagent doing its job, but physical and social resources could be irrelevant, if the subagents were provided with whatever resources necessary for doing their tasks. In such a case, the end result could be a world whose inhabitants experienced very little if any in the way of positive emotions, but did experience negative emotions. This could qualify as any one of the suffering outcomes we've considered (astronomical, net, pan-generational net). A major question mark with regard to suffering subroutines are the requirements for consciousness  (Muehlhauser 2017 ) and suffering  (Metzinger 2016 , Tomasik 2017 ). The simpler the algorithms that can suffer, the more likely it is that an entity with no regard for minimizing it would happen to instantiate large numbers of them. If suffering has narrow requirements such as a specific kind of self-model  (Metzinger 2016 ), then suffering subroutines may become less common. Below are some pathways that could lead to the instantiation of large numbers of suffering subroutines  (Gloor 2016) : Anthropocentrism. If the superintelligence had been programmed to only care about humans, or by minds which were sufficiently human-like by some criteria, then it could end up being indifferent to the suffering of any other minds, including subroutines. Indifference. If attempts to align the superintelligence with human values failed, it might not put any intrinsic value on avoiding suffering, so it may create large numbers of suffering subroutines. Uncooperativeness. The superintelligence's goal is something like classical utilitarianism, with no additional regards for cooperating with other value systems. As previously discussed, classical utilitarianism would prefer to avoid suffering, all else being equal. However, this concern could be overridden by opportunity costs. For example,  Bostrom (2003a)  suggests that every second of delayed space colonization corresponds to a loss equal to 10^14 potential lives. A classical utilitarian superintelligence that took this estimate literally might choose to build colonization robots that used suffering subroutines, if this was the easiest way and developing alternative cognitive architectures capable of doing the job would take more time. \n Mind crime A superintelligence might run simulations of sentient beings for a variety of purposes.  Bostrom (2014, p. 152)  discusses the specific possibility of an AI creating simulations of human beings which were detailed enough to be conscious. These simulations could then be placed in a variety of situations in order to study things such as human psychology and sociology, and destroyed afterwards. The AI could also run simulations that modeled the evolutionary history of life on Earth, to obtain various kinds of scientific information or to help estimate the likely location of the \"Great Filter\"  (Hanson 1998 ) and whether it should expect to encounter other intelligent civilizations. This could repeat the wild-animal suffering  (Tomasik 2015 , Dorado 2015  experienced in Earth's evolutionary history. The AI could also create and mistreat, or threaten to mistreat, various minds as a way to blackmail other agents. As it is possible that minds in simulations could one day compose the majority of all existing minds  (Bostrom 2003b ), and that with sufficient technology there could be astronomical numbers of them, then depending on the nature of the simulations and the net amount of happiness and suffering, mind crime could possibly lead to any one of the three suffering outcomes. Below are some pathways that could lead to mind crime  (Gloor 2016 ): Anthropocentrism. Again, if the superintelligence had been programmed to only care about humans, or about minds which were sufficiently human-like by some criteria, then it could be indifferent to the suffering experienced by non-humans in its simulations. Indifference. If attempts to align the superintelligence with human values failed, it might not put any intrinsic value on avoiding suffering, so it may create large numbers of simulations with sentient minds if that furthered its objectives. Extortion. The superintelligence comes into conflict with another actor that disvalues suffering, so the superintelligence instantiates large numbers of suffering minds as a way of extorting the other entity. Libertarianism regarding computations: the creators of the first superintelligence instruct the AI to give every human alive at the time control of a planet or galaxy, with no additional rules to govern what goes on within those territories. This would practically guarantee that some humans would use this opportunity for inflicting widespread cruelty (see the previous section). \n Flawed realization A superintelligence with human-aligned values might aim to convert the resources in its reach into clusters of utopia, and seek to colonize the universe in order to maximize the value of the world  (Bostrom 2003a) , filling the universe with new minds and valuable experiences and resources. At the same time, if the superintelligence had the wrong goals, this could result in a universe filled by vast amounts of disvalue. While some mistakes in value loading may result in a superintelligence whose goal is completely unlike what people value, certain mistakes could result in flawed realization  (Bostrom 2013) . In this outcome, the superintelligence's goal gets human values mostly right, in the sense of sharing many similarities with what we value, but also contains a flaw that drastically changes the intended outcome  11  . For example, value extrapolation  (Yudkowsky 2004 ) and value learning (Soares 2016, Sotala 2016) approaches attempt to learn human values in order to create a world that is in accordance with those values. There have been occasions in history when circumstances that cause suffering have been defended by appealing to values which seem pointless to modern sensibilities, but which were nonetheless a part of the prevailing values at the time. In Victorian London, the use of anesthesia in childbirth was opposed on the grounds that being under the partial influence of anesthetics may cause \"improper\" and \"lascivious\" sexual dreams  (Farr 1980) , with this being considered more important to avoid than the pain of childbirth. A flawed value-loading process might give disproportionate weight to historical, existing, or incorrectly extrapolated future values whose realization then becomes more important than the avoidance of suffering. Besides merely considering the avoidance of suffering less important than the enabling of other values, a flawed process might also tap into various human tendencies for endorsing or celebrating cruelty (see the discussion in section 4), or outright glorifying suffering. Small changes to a recipe for utopia may lead to a future with much more suffering than one shaped by a superintelligence whose goals were completely different from ours. We will now argue for the case that it is possible to productively work on them today, via some of the following recommendations. Carry out general AI alignment work. Given that it would generally be against the values of most humans for suffering outcomes to be realized, research aimed at aligning AIs with human values  (Yudkowsky 2008 , Goertzel & Pitt 2012 , Bostrom 2014 , Sotala 2016, Soares & Fallenstein 2017) seems likely to also reduce the risk of suffering outcomes. If our argument for suffering outcomes being something to avoid is correct, then an aligned superintelligence should also attempt to establish a singleton that would prevent negative suffering outcomes, as well as avoiding the creation of suffering subroutines and mind crime. In addition to technical approaches to AI alignment, the possibility of suffering risks also tends to make more similar recommendations regarding social and political approaches. For example,  Bostrom et al. (2016)  note that conditions of global turbulence might cause challenges for creating value-aligned AI, such as if pre-existing agreement are not kept to and ill-conceived regulation is enacted in a haste. Previous work has also pointed to the danger of arms races making it harder to keep AI aligned  (Shulman 2009 , Miller 2012 , Armstrong et al. 2013 ). As the avoidance of suffering outcomes is the joint interest of many different value systems, measures that reduce the risk of arms races and improve the ability of different value systems to shape the world in their desired direction can also help avoid suffering outcomes. Besides making AIs more aligned in general, some interventions may help avoid negative outcomes -such as suffering outcomes from flawed realization scenariosin particular. Most of the current alignment research seeks to ensure that the values of any created AIs are aligned with humanity's values to a maximum possible extent, so that the future they create will contain as much positive value as possible. This is a difficult goal: to the extent that humanity's values are complex and fragile (Yudkowsky 2011), successful alignment may require getting a very large amount of details right. On the other hand, it seems much easier to give AIs goals that merely ensure that they will not create a future with negative value by causing suffering outcomes. This suggests an approach of fail-safe methods: safety nets or mechanisms such that, if AI control fails, the outcome will be as good as it gets under the circumstances. Failsafe methods could include tasking AI with the objective of buying more time to carefully solve goal alignment more generally, or fallback goal functions: Research fallback goals: Research ways to implement multi-layered goal functions, with a \"fallback goal\" that kicks in if the implementation of the top layer does not fulfill certain safety criteria. The fallback would be a simpler, less ambitious goal that is less likely to result in bad outcomes. Difficulties would lie in selecting the safety criteria in ways that people with different values could all agree on, and in making sure that the fallback goal gets triggered under the correct circumstances. Care needs to be taken with the selection of the fallback goal, however. If the goal was something like reducing suffering, then in a multipolar  (Bostrom 2014 ) scenario, other superintelligences could have an incentive to create large amounts of suffering in order to coerce the superintelligence with the fallback goal to act in some desired way. Research ways to clearly separate superintelligence designs from ones that would contribute to suffering risk.  Yudkowsky (2017)  proposes building potential superintelligences in such a way as to make them widely separated in design space from ones that would cause suffering outcomes. For example, if an AI has a representation of \"what humans value\" V which it is trying to maximize, then it would only take a small (perhaps accidental) change to turn it into one that maximized -V instead, possibly causing enormous suffering. One proposed way of achieving this is by never trying to explicitly represent complete human values: then, the AI \"just doesn't contain the information needed to compute states of the universe that we'd consider worse than death; flipping the sign of the utility function U, or subtracting components from U and then flipping the sign, doesn't identify any state we consider worse than [death]\"  (Yudkowsky 2017) . This would also reduce the risk of suffering being through another actor which was trying to extort the superintelligence. Carry out research on suffering risks and the enabling factors of suffering. At this moment, there is only little research to the possibility of risks of astronomical suffering. Two kinds of research would be particularly useful. First, research focused on understanding the biological and algorithmic foundation of suffering  (Metzinger 2016 ) could help understand how likely outcomes such as suffering subroutines would be.  Pearce (1995)  has argued for the possibility of minds motivated by \"gradients of bliss\", which would not need to experience any suffering: if minds could be designed in such a manner, that might help avoid suffering outcomes. Second, research on suffering outcomes in general, to understand how to avoid them. With regard to suffering risks from extortion scenarios, targeted research in economics, game theory or decision theory could be particularly valuable. Rethink maxipok and maximin.  Bostrom (2002 Bostrom ( , 2013  proposes a \"maxipok rule\" to act as a rule of thumb when trying to act in the best interest of humanity as a whole: Maxipok: Maximise the probability of an 'OK outcome', where an OK outcome is any outcome that avoids existential catastrophe. The considerations in this paper do not necessarily refute the rule as written, especially not since Bostrom defines an \"existential catastrophe\" to include \"the permanent and drastic destruction of its potential for desirable future development\", and the realization of suffering outcomes could very well be thought to fall under this definition. However, in practice much of the discourse around the concept of existential risk has focused on the possibility of extinction, so it seems valuable to highlight the fact that \"existential catastrophe\" does not include only scenarios of zero value, but also scenarios of negative value.  Bostrom (2002 Bostrom ( , 2013 ) also briefly discusses the \"maximin\" principle, \"choose the action that has the best worst-case outcome\", and rejects this principle as he argues that this entails \"choosing the action that has the greatest benefit under the assumption of impending extinction. Maximin thus implies that we ought all to start partying as if there were no tomorrow.\"  (Bostrom 2013, p. 19) . However, since a significant contribution to the expected value of AI comes from worse outcomes than extinction, this argument is incorrect. While there may be other reasons to reject maximin, the principle correctly implies choosing the kinds of actions that avoid the worst suffering outcomes and so might not be very dissimilar from maxipok. Figure 2 : 2 Figure 2: types of possible suffering outcomes. An outcome may count as one or several of the categories in this table. \n\t\t\t Bostrom (2014)  is mainly focused on the risk of extinction, but does also devote some discussion to alternative negative outcomes such as \"mindcrime\". We discuss mindcrime in section 5. \n\t\t\t Fictional depictions include Ellison (1967)  and Ryding (no date); note that both stories contain very disturbing imagery. A third depiction was in the \"White Christmas\" episode of the TV series Black Mirror, which included a killer placed in solitary confinement for thousands of years while having to listen to a Christmas song on an endless loop. 9  Another fictional depiction includes Gentle (2004) ; the warning for disturbing graphic imagery very much applies. \n\t\t\t This section reprints material that has previously appeared in a work by one of the authors (Gloor 2016 ), but has not been formally published before. \n\t\t\t How and whether to work on srisk?In the previous sections, we have argued for s-risks being severe enough to be worth preventing, and for there to be several plausible routes by which they might be realized. 11  One fictional illustration of a flawed utopia is Yudkowsky (2009) , though this setting does not seem to contain enormous amounts of suffering.", "date_published": "n/a", "url": "n/a", "filename": "1877-3728-1-PB.tei.xml", "abstract": "Discussions about the possible consequences of creating superintelligence have included the possibility of existential risk, often understood mainly as the risk of human extinction. We argue that suffering risks (s-risks), where an adverse outcome would bring about severe suffering on an astronomical scale, are risks of a comparable severity and probability as risks of extinction. Preventing them is the common interest of many different value systems. Furthermore, we argue that in the same way as superintelligent AI both contributes to existential risk but can also help prevent it, superintelligent AI can be both the cause of suffering risks and a way to prevent them from being realized. Some types of work aimed at making superintelligent AI safe will also help prevent suffering risks, and there may also be a class of safeguards for AI that helps specifically against s-risks. Povzetek: Prispevek analizira prednosti in nevarnosti superinteligence.", "id": "5fd70c2ac04b8d203b56a477b622ffac"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Max Tegmark"], "title": "Life 3.0: Being Human in the Age of Artificial Intelligence", "text": "In the interests of disclosure, Tegmark and I are collaborators and share a literary agent. With physicists Stephen Hawking and Frank Wilczek, we wrote the 2014 Huffington Post article 'Transcending complacency on superintelligent machines' (see go.nature. com/2wadkao). Ostensibly a review of Wally Pfister's dystopian AI film Transcendence, this was really a call to the AI community to take the risks of intelligent systems seriously. Thus, I am unlikely to disagree strongly with the premise of Life 3.0. Life, Tegmark argues, may or may not spread through the Universe and \"flourish for billions or trillions of years\" because of decisions we make now -a possibility both seductive and overwhelming. The book's title refers to a third phase in evolutionary history. For almost 4 billion years, both hardware (bodies) and software (capacity for generating behaviour) were fixed by biology. For the next 100,000 years, learning and culture enabled humans to adapt and control their own software. In the imminent third phase, both software and hardware can be redesigned. This may sound like transhumanism -the movement to re-engineer body and brain -but Tegmark's focus is on AI, which supplements mental capabilities with external devices. Tegmark considers both risks and benefits. Near-term risks include an arms race in autonomous weapons and dramatic reductions in employment. The AI community is practically unanimous in condemning the creation of machines that can choose to kill humans, but the issue of work has sparked debate. Many predict an economic boon -AI inspiring new jobs to replace old, as with previous industrial revolutions. Tegmark wryly imagines two horses discussing the rise of the internal combustion engine in 1900. One predicts \"new jobs for horses … That's what's always happened before, like with the invention of the wheel and the plow. \" For most horses, alas, the \"new job\" was to be pet food. Tegmark's analysis is compelling, and shared by economists such as Paul Krugman. But the question remains: what desirable economy might we aim for, when most of what we now call work is done by machines? The longer-term risks are existential. The book's fictional prelude describes a reasonably plausible scenario in which superintelligent AI might emerge. Later, Tegmark ranges over global outcomes from near-Utopias to human enslavement or extinction. That we have no idea how to steer towards the better futures points to a dearth of serious thinking on why making AI better might be a bad thing. Computer pioneer Alan Turing, raising the possibility in 1951 that our species would at best be \"greatly humbled\" by AI, expressed the general unease of making something smarter than oneself. Assuaging this unease by curtailing progress on AI may be neither feasible nor preferable. The most interesting part of Life 3.0 explains that the real issue \n ARTIFICIAL INTELLIGENCE The future is superintelligent Stuart Russell weighs up a book on the risks and rewards of the AI revolution. is the potential for misaligned objectives. Cybernetics founder Norbert Wiener wrote in 1960, \"We had better be quite sure that the purpose put into the machine is the purpose which we really desire. \" Or, as Tegmark has it, \"It's unclear how to imbue a superintelligent AI with an ultimate goal that neither is undefined nor leads to the elimination of humanity. \" In my view, this technological and philosophical problem demands all the intellectual resources we can bring to bear. Only if we solve it can we reap the benefits. Among these is expansion across the Universe, perhaps powered by such exotic technologies as Dyson spheres (which would capture the energy of a star), accelerators built around black holes or Tegmark's theorized sphalerizers (like diesel engines, but quark-powered and one billion times more efficient). For sheer science fun, it's hard to beat the explanations of how much upside the Universe and the laws of physics will allow. We may one day, for example, expand the biosphere \"by about 32 orders of magnitude\". It's seriously disappointing, then, to learn that cosmic expansion may limit us to settling only 10 billion galaxies. And we feel our descendants' anxiety as \"the threat of dark energy tearing cosmic civilizations apart motivates massive cosmic engineering projects\". The book concludes with the Future of Life Institute's role in moving these issues into mainstream AI thinking -for which Tegmark deserves huge credit. He is not alone, of course, in raising the alarm. In its sweeping vision, Life 3.0 has most in common with Nick Bostrom's 2014 Superintelligence (Oxford University Press). Unlike Bostrom, however, Tegmark is not trying to prove that risk is un avoidable; and he eschews dense philosophy in favour of asking the reader which scenarios they think more probable or desirable. Although I strongly recommend both books, I suspect that Tegmark's is less likely to provoke in AI researchers a common allergic reaction -a retreat into defensive arguments for paying no attention. Here's a typical one: we don't worry about remote but speciesending possibilities such as black holes materializing in near-Earth orbit, so why worry about superintelligent AI? Answer: if physicists were working to make such black holes, wouldn't we ask them if it was safe? The Economist has drily characterized the overarching issue thus: \"The implications of introducing a second intelligent species onto Earth are far-reaching enough to deserve hard thinking. \" Life 3.0 is far from the last word on AI and the future, but it provides a fascinating glimpse of the hard thinking required. ■ Stuart Russell is professor of computer science at the University of California, Berkeley and co-author of Artificial Intelligence: A Modern Approach. e-mail: russell@berkeley.edu \t\t\t © 2 0 1 7 M a c m i l l a n P u b l i s h e r s L i m i t e d , p a r t o f S p r i n g e r N a t u r e . A l l r i g h t s r e s e r v e d .", "date_published": "n/a", "url": "n/a", "filename": "548520a.tei.xml", "abstract": "M ax Tegmark is a renowned physicist. He is also the irrepressibly optimistic co-founder of the Future of Institute in Cambridge, Massachusetts (motto: \"Technology is giving life the potential to flourish like never before … or to selfdestruct. Let's make a difference!\"). Now, in Life 3.0, he tackles a pressing future development -the evolution of artificial intelligence (AI). He argues that the risks demand serious thought if our \"cosmic endowment\" is not to be inadvertently thrown away.", "id": "92b10bdfba64dc1c488a5453d3aa99c2"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Charlotte Stix", "Matthijs M Maas"], "title": "Bridging the gap: the case for an 'Incompletely Theorized Agreement' on AI policy", "text": "Introduction The prevailing uncertainty around the trajectory and impact of artificial intelligence (AI) makes it clear that appropriate technology policy approaches are urgently needed. The possible negative ethical and societal impacts of AI are considerable: from algorithmic bias to AI-enabled surveillance, and from lethal autonomous weapons systems to widespread technology-induced unemployment. Moreover, some forecast that continuing progress in AI capabilities will eventually make AI systems a 'general-purpose technology'  [1] , or may even enable the development of 'high-level machine intelligence' (HLMI)  [2]  or other 'transformative' capabilities  [3, 4] . Debate on these latter scenarios is diverse, and has at times focused on what some have referred to as 'Artificial General Intelligence' (AGI)  [5] . On the surface, those concerned with AI's impacts can appear divided between those who focus on discernible problems in the near term, and those who focus on more uncertain problems in the longer term  [6] [7] [8] [9] . This paper wants to investigate the dynamics and debates between these two communities, with an eye to fostering policy effectiveness through greater cooperation. In doing so, this paper seeks to take up the recent call to 'bridge the near-and long-term challenges of AI'  [9] . The focus therefore is not on the relative urgency of existing algorithmic threats (such as e.g. facial recognition or algorithmic bias), nor on the relative plausibility of various advanced AI scenarios (such as e.g. HLMI or AGI), nor do we mean to suggest that a long-term perspective is solely focused on or concerned with AGI  [10] [11] [12] . Rather, the paper proposes that even if some community divergence exists, each group's overarching intention to contribute to responsible and ethical AI policy 1 would benefit from cooperation within key domains to maximize policy effectiveness. The paper suggests that differences may be overstated, and proposes that even if one assume such differences, these are not practically insurmountable. Rather, it argues that the principle of an 'incompletely theorized agreement', originally derived from constitutional law, provides both philosophical foundations and historical precedent for a form of cooperation between divergent communities that enables progress on urgent shared issues, without compromising on their respective goals. The paper proceeds as follows: in Sect. 2, we provide a short rationale for our proposed intervention. We briefly lay out the landscape of AI policy concerns and the structure of the associated AI ethics and policy community. This is followed by a discussion, drawing on historical cases as well as the contemporary challenges facing AI policy scholars, of how fragmentation within an expert community might hinder progress on key and urgent policies. In Sect. 3, we explore potential sources which could contribute to community divergence. We touch on epistemic and methodological disagreements and normative disagreements, and home in on pragmatic disagreements around the tractability of formulating AI policy actions today which maintain long-term relevance. We briefly review how serious these disagreements are, arguing that these trade-offs are often exaggerated, or do not need to preclude collaboration. Finally, in Sect.  4 , we propose that one consolidating avenue to harness mutually beneficial cooperation for the purpose of effective AI policy could be anchored in the constitutional law principle of an 'incompletely theorized agreement'. This proposal works under the assumption that the influence of a community on policy making is significantly stronger if they act as a united front, rather than as scattered subgroups. \n AI policy: a house divided? Recent progress in AI has given rise to an array of ethical and societal concerns.  2  Accordingly, there have been calls for appropriate policy measures to address these. As an \"omni-use technology\"  [13] , AI has both potential for good  [14] [15] [16]  as well as for bad  [17] [18] [19]  applications. The latter include: various forms of pervasive algorithmic bias  [20, 21] , challenges around transparency and explainability  [22, 23] ; the safety of autonomous vehicles and other cyberphysical systems  [24] , or the potential of AI systems to be used in (or be susceptible to) malicious or criminal attacks  [25] [26] [27] ; the erosion of democracy through e.g. 'computational propaganda' or 'deep fakes'  [28] [29] [30] , and an array of threats to the full range of human rights  [31, 32] . The latter may eventually cumulate in the possible erosion of the global legal order by the comparative empowerment of authoritarian states  [33, 34] . Finally, some express concern that continued technological progress might eventually result in increasingly more 'transformative' AI capabilities  [3] , up to and including AGI. Indeed, a number of AI researchers expect some variation of 'high-level machine intelligence' to be achieved within the next five decades  [2] . Some have suggested that if those transformative capabilities are not handled with responsibility and care, such developments could well result in new and potential catastrophic risks to the welfare, autonomy, or even long-term survival of societies  [35, 36] . Looking at the current debate and scholarship involved in the aforementioned areas, we note, along with other scholars  [6, 8, 37] , that there appears to be a fuzzy split, along a temporal 'near-term'/'long-term' axis. This perception matters because, as in many other fields and contexts, a perceived or experienced distinction may eventually become a self-fulfilling prophecy  [38] . This holds true even if the perceived differences are based on misperceptions or undue simplification by popular scientific media  [39] [40] [41] . Of course, fragmentation between near-and longer-term considerations of AI's impact is only one way to explore the growing community, and it may not be the sole issue to overcome to maximize policy impact. However, for the purpose of this paper, our focus is on this specific gap. \n The policy advantages of collaboration: lessons from history The current AI ethics and policy community is a young one. Policy shifts, on the other hand, take time. As such, it is difficult to clearly outline what impact current dynamics have. We are, after all, still in the early stages of these developments. Nevertheless, historical examples of adjacent fields can help to demonstrate and forecast how fragmentation, or, conversely cooperation, on policy goals within the AI ethics and policy community could strengthen impact on technology policy. Why should potential fragmentation along an axis such as near-and longer-term concerns worry us? History shows that the structure of a field or community affects the ability of its members to shape and influence policy downstream. Importantly, it shows that there is significant benefit derived from collaboration. We put forward three historic examples of adjacent technology policy fields to AI, meaning those that tackled equally new and emerging technologies. We briefly highlight one case where fragmentation may have contributed to a negative impact on the overall policy impact of the community and two cases where a collaborative effort yielded a positive impact on policy formulation. \n Nanotechnology One community that arguably suffered from a public pursuit of fractious division was the nanotechnology community in the early 2000s  [42, 43] . Internal disagreements came to a head in the 2003 'Drexler-Smalley' debate  [44] , which cemented an oversimplified public caricature of the field. Scholars reviewing this incident have argued that 'para-scientific' media created \"polarizing controversy that attracted audiences and influenced policy and scientific research agendas. […] bounding nanotechnology as a field-in-tension by structuring irreconcilable dichotomies out of an ambiguous set of uncertainties.\"  [38] . This showcases a missed opportunity within a fragmented community to come together to promote greater political engagement with the responsible development of the technology. \n Recombinant DNA In the 1970s, concerns arose over recombinant DNA (rDNA) technology. In particular, the ethical implications of the ability to reshape life, as well as fears over potential biohazards from new infectious diseases led the biotechnology community to come together at the 1975 Asilomar Conference on Recombinant DNA to set shared standards  [45] . The conference is widely considered a landmark in the field  [46] : the scientist's and lawyers' commitment to a forthright open and public discussion has been argued to have stimulated both public interest and grounded policymaker discussion about the social, political and environmental issues related to genetic biotechnology in medicine and agriculture  [47] . \n Ballistic missile defense arms control In the wake of the creation of the atom bomb, a number of scientists expressed dismay and sought to institutionalize global control of these weapons. Early efforts to this end, such as the 1946 Baruch Plan, proved unsuccessful  [48, 49] . However, by the 1950s-1960s, a new 'epistemic community' emerged, bringing together both technical and social scientists, specifically in opposition to the development of antiballistic missile (ABM) systems. This community proved able to develop and disseminate this new understanding of nuclear deterrence dynamics to policymakers  [50] . They achieved this by maintaining a high level of consensus on concrete policy goals, by framing public discourse on the ethical goals, and by fostering links to both policymakers as well as to Soviet scientists. This allowed them to persuade key administration figures and shift policymaker norms and perceptions at home and internationally. Ultimately, setting the stage for the 1972 ABM Treaty, the first arms control agreement of this kind  [50, 51] . \n The pitfalls of fragmented efforts in AI Policy While some of the historical context is surely different, a number of these historical dynamics may well transfer to the emerging AI ethics and policy community  [52] . Those concerned with AI policy could benefit from exploring such historical lessons. This should be done with urgency, for two reasons. First, there is a closing window of opportunity. The field of AI policy is a relatively new one, which offers a degree of flexibility in terms of problem framings, governance instrument choice and design, and community alignment. Going forwards, however, this field has a high likelihood of becoming progressively more rigid as framings, public perceptions, and stakeholder interests crystallize. Current dynamics could, therefore, have far-reaching impacts, given the potential to lock in a range of path-dependencies, for example through particular framings of the issues at hand  [53] . In this context, a divided community which potentially treats policymakers or public attention as a zero-sum good for competing policy projects may compromise the legitimacy of its individual efforts in front of these. This could undercut the leverage of policy initiatives today and in the future. Worse, public quarrels or contestation may 'poison the well'. Policymakers may begin to perceive and treat a divided community as a series of interest groups rather than an 'epistemic community' with a multi-faceted but coherent agenda for beneficial societal impact of AI. Finally, from a policy perspective, it is important to note that while current regulatory initiatives are and should not always be directly transferable to future issues, neither are they categorically irrelevant. As such, they can often provide the second-best tools for rapidly confronting new AI challenges. This has its own pitfalls, but is often superior to waiting out the slow and reactive formulation of new policies. Moreover, the risks are concrete and timely. It is plausible that political moods will shift within the coming years and decades, in ways that make policy progress much harder. Furthermore, it is possible that other epistemic communities may converge and mobilize faster to embed and institutionalize alternative, less broadly beneficial framings of AI. Indeed, public and global framings of AI in recent years have seemed to drift towards narratives of competition and 'arms races' [54-56, but see also 57]. An inflection point for how societies use and relate to AI may eventually be reached. Missing such a window of opportunity could mean that the relative influence of those concerned with making the impact of AI beneficial (whether in the near or longer term) will decline, right as their voices are needed most. \n 3 Conversely, many gains secured today could have lasting benefits down the road. \n Examining potential grounds for divergence There are a range of factors that could contribute to the clustering into fuzzy 'near-' and 'long-term' communities, and different scholars may hold distinct and overlapping sets of beliefs on them [cf. 8]. In the following paragraphs, we provide our first attempt at mapping some of these factors.  3  Some part of the divergence may be due to varying epistemic or methodological commitments. These could reflect varying levels of tolerance regarding scientific uncertainty and distinct views on the threshold of probability required before far-reaching action or further investigation is warranted. This means that concerns surrounding AI may depend on qualitatively different conceptions of 'acceptable uncertainty' for each group of observers. This may well be hard to resolve. Moreover, epistemic differences over the implicit or explicit disagreements of the modal standards in these debates, for example, debates over what types of data or arguments are admissible in establishing or contesting the plausibility or probability of risk from AI may contribute to further divergence. This could even lead to differential interpretations of evidence that are available. For instance, do empirically observed failure modes of present-day architectures  [58] [59] [60] [61]  provide small-scale proof-of-concepts of the type of difficulties we might one day encounter in AI 'value alignment', or are such extrapolations unwarranted? For our purposes, however, the most salient factor may be essentially pragmatic. Different perceptions of the empirical dynamics and path-dependencies of governing AI can inform distinct theories-of-change. These are intertwined with one's expectations about the tractability and relevance of formulating useful and resilient policy action today. In this context, Prunkl and Whittlestone  [8]  have recently argued that a more accurate picture and more productive dialogue could be achieved if scholars differentiated amongst the four dimensions on which views vary, in terms of the capabilities, impacts, certainty or extremity of AI systems. They emphasize that views on each of these questions fall on a spectrum. Taking this point on board, there are additional ways to cash out possible divergences. One debate might concern the question, how long-lasting are the consequences of near-term AI issues? If those that care about the longer term are convinced that these issues will not have long-lasting consequences, or that they would eventually be swamped by the much larger trends and issues  [3] , then this could lead them to discount work on near-term AI problems. However, it is important to note that near-term issues are likely to considerably affect the degree to which society is vulnerable to longer-term dangers posed by future advanced AI systems. Short-term or medium-term issues  [7, 37]  can easily increase society's general turbulence  [62] , or lock in counterproductive framings of AI or our relation to it. In general, we might expect many nominally near-term effects of AI on society (such as in surveillance; job automation; military capabilities) to scale up and become more disruptive as AI capabilities gradually increase  [18, 37] . Indeed, some longer-term scholars have argued that advanced AI capabilities considerably below the level of HLMI might already suffice to achieve a 'prepotence' which could pose catastrophic risks  [10] . This would make mid-term impacts particularly important to handle, and collaboration between different groups on at least some generalizable projects crucial. Another pragmatic question or concern is over how much leverage we have today to meaningfully shape policies that will be applicable or relevant in the long term, especially if AI architectures or the broader political and regulatory environment change a lot in the meantime  [8] . Some scholars may hold that future AI systems will be technically so different from today's AI architectures that research into this question undertaken today will not be relevant, or they might hold that such advanced AI capabilities may be so remote that the regulatory environment will have changed too much for meaningful policy work to be conducted right now  [63] . These people might argue that we had better wait until things are clearer and we are in a better position to understand whether and what research is needed or meaningful. In practice, this critique does not appear to be a very common or deeply held position. Indeed, as a trade-off it may be overstated. It is plausible that there are diverse areas on which both communities can undertake valuable research today, because the shelf life of current policy and research efforts might be longer than is assumed. To be sure, there is still significant uncertainty over whether current AI approaches can at all be scaled up to very advanced performance  [64] [65] [66] . Nonetheless, research could certainly depart from a range of areas of overlap  [67]  and shared areas of concern  [68, 69] , as we will discuss shortly. Moreover, policy making is informed by a variety of aspects which range across different time spans. Starting with political agendas that often reflect the current status quo, policy making is equally shaped by shifting public discourse, societal dynamics and high-impact shocks. The latter factor has played a key role in AI policy, where highprofile incidents involving algorithmic discrimination, lack of transparency, or surveillance have driven policy shifts, as seen for example in the pushback on discriminatory algorithms used in the UK visa selection processes  [70] , the Artificial Intelligence Video Interview Act regulating the use of AI in employee interviews, or the California B.O.T. Law requiring AI systems to self-identify  [71, 72] . In sum, it is plausible that many perceived 'barriers' to inter-community cooperation on policy are not all that strong, and that many 'tradeoffs' are likewise overemphasized. However, does that mean there are also positive, mutually productive opportunities for both communities to work on with regard to policy in spite of outstanding disagreements? What would such an agreement look like? \n Towards 'incompletely theorized agreements' for AI policy Above, we have reviewed potential sources for divergence within the community. We will now discuss how even in the context of apparent disagreement, pragmatic agreements on shared policy goals and norms could be reached. We propose to adopt and adapt the legal principle of an 'incompletely theorized agreement' for this purpose. Legal scholarship in constitutional law and regulation has long theorized the legal, organizational and societal importance of such incompletely theorized agreements. Their key use is that they allow a given community to bypass or suspend  [73, 74]  any theoretical disagreement on matters where (1) the disagreement appears relatively intractable and (2) there is an urgent need to address certain shared practical issues. Disagreements are intractable in cases where either it simply does not appear as if the question will be decisively resolved one way or the other in the near term, or where there is limited time and capacity to reason through all underlying disagreements  [73] . Incompletely theorized agreements can therefore apply to deep philosophical and ethical questions as much as to contexts of pervasive scientific uncertainty. The latter is especially the case on questions where it still remains unclear where and how we might procure the information that allows definitive resolution. Incompletely theorized agreements are a fundamental component to well-functioning legal systems, societies, and organizations. They allow for stability and flexibility to get urgent things done  [75] . These agreements have long played a key role in constitutional and administrative law, and have made possible numerous landmark achievements of global governance, such as the establishment of the Universal Declaration of Human Rights  [75, 76] . The framework has also been extended to other domains, such as the collective development and analysis of health-care policies in the face of pluralism and conflicting views  [77] . Incompletely theorized agreements have broad similarities with the notion of an 'overlapping consensus', developed by John Rawls, which refers to the way adherents of different (and apparently inconsistent) normative doctrines can nonetheless converge on particular principles of justice to underwrite the shared political community  [78] . This concept has been read as a key mechanism in the field of bioethics, serving to enable agreement despite different fundamental outlooks  [79] . It also already plays a role in the existing literature on computer ethics  [80] , as well as in the field of intercultural information ethics  [81] . Indeed, overlapping consensus has been proposed as a mechanism on which to ground global cooperation on AI policy across cultural lines  [82] . If overlapping consensus can ground inter-cultural cooperation, incompletely theorized agreements might serve as a similar foundation for practical cooperation between nearand long-term perspectives. In a related context, Baum has suggested that policy interventions aimed at securing longterm resilience to various catastrophes can often involve significant co-benefits in the near term, and so do not narrowly depend on all parties agreeing on the deep reasons for the policies proposed  [83] . Could incompletely theorized agreements ground cooperation amongst AI policy communities? We suggest that they could. \n Incompletely theorized agreements in AI policy: examples and sketches There are a range of issue areas where both groups could likely locate joint questions they would want addressed, and shared goals for which particular AI policies should be implemented. This holds even if their underlying reasons for pursuing these are not fully aligned. Without intending to provide an exhaustive, in-depth or definitive overview, a brief survey might highlight various areas for cooperation. For one, gaining insight into-and leverage on the general levers of policy formation around AI  [52]  is a key priority. What are the steps in the policymaking process which determine what issues get raised to political agendas and eventually acted upon, and which might be derailed by other coalitions  [84] ? Given the above, research into underlying social and societal developments is fruitful to advance all groups' ability to navigate mutually agreeable policy goals across this policy making cycle  [85] . Likewise, research into when, where or why global AI governance institutions might become vulnerable to regulatory capture or institutional path dependency ought to be an important consideration, whatever one's AI concerns are  [86, 87] . On a more operational level, this can feed into joint investigation into the relative efficacy of various policy levers for AI governance. For example, insights into when and how AI research labs or individual researchers adopt, or alternately cut corners on, responsible and accountable AI, or the incentivization of shifts in workplace culture or employee norms, could shape the policy proposals the community might make. The question of how to promote prosocial norms in AI research environments is of core interest to both communities with an eye to technology policy  [88] . This might cover, e.g. whether to publicly name problematic performance (e.g. biased results; lack of safety) in commercial AI products results in tech companies actually correcting the systems  [89] ; or whether codes of ethics are effective at changing programmers' decision making on the working floor  [90, 91] . All of these could be fruitful areas of collaboration on eventual policy proposals for either community. More specifically, there are a range of particular AI policy programs that we expect could be the site of an incompletely theorized agreement. 1. Incompletely theorized agreements could shape norms and policy debates over the appropriate scientific culture for considering the impact and dissemination of AI research  [92, 93] , especially where it concerns AI applications with potentially salient misuses. The underlying reasons for such policies might differ. Some may be concerned over abuses vulnerable populations, new vectors for criminal exploitation or the implications of new language models for misinformation  [94, 95] ; and others over the long-term risks from the eventual open development of advanced AI systems  [96] . Accordingly, incompletely theorized agreements in this area could converge on policies to shape researcher norms around improved precaution or reflection around the impact or potential misuse of research [97]. 2. Another example might be found in the domain of the global regulation of military uses of AI. This area has already seen years of shared efforts and even collaboration amongst a coalition of activists, lawyers, and institutions departing from both a near-term as well as longer-term perspective, such as the Future of Life Institute  [52] . \n Incompletely theorized agreements could ground productive policy cooperation on policy interventions aimed at preserving the integrity of public discourse and informed decision-making in the face of AI systems. Policies aimed at combating AI-enabled disinformation would be a natural site for incompletely theorized collaboration, because a society's epistemic security  [98]  is relevant from both a near-term and long-term perspective alike. 4. Similarly, incompletely theorized agreements surrounding the promotion of policies aimed at securing citizens' (political) autonomy and independence from unaccountable perception control could be promising. After all, practices of opaque technological management  [99]  or perception control  [100]  can enable authorities to increasingly shape individuals' and societies' behaviour and values. Regulation to restrict the deployment of such tools, to facilitate privacy-preserving AI, or to ensure transparency and accountability of the principals of such tools, are important from a near-term perspective concerned with the role of 'hyper nudges'  [101] , algocracy  [102] , or surveillance capitalism  [103] . Simultaneously, such policies are also critical to avert long-term worries over a 'value lock-in', whereby one generation or party might someday \"invent a technology that will enable the agents alive at that time to maintain their values indefinitely into the future, controlling the broad sweep of the entire rest of the future of civilisation\"  [104] . Although the underlying motives for each group to pursue policies on the abovementioned domains may be partially distinct, these technical differences are arguably thwarted by the benefits derived from achieving impactful and effective policy measures together. In many of these cases, the practical benefits of an incompletely theorized agreement would be at least fourfold  (1)  to reduce public confusion around these topics; (2) to present policymakers with an epistemic community delivering integrated policy proposals; (3) to support the articulation of regulations or governance instruments for specific policy problems, which need not assume further advances in AI capabilities, but which are also not reliant on provisions or assumptions that are vulnerable to 'obsolescence' if or when such advances do occur  [105] [106] [107] , giving such policies a longer shelf life; (4) to improve engagement of particular AI policies with the steadily increasing cross-domain nature of AI, which could help inform regulatory responses across domains. This is especially relevant because different fields (such as content moderation, health-care, or the military) often confront different yet similar versions of underlying problems  [108] . \n Limitations of incompletely theorized agreements We do not wish to suggest that incompletely theorized agreements are an unambiguously valuable tool across all AI policy cases, or even a definite solution for any one policy case. Such agreements do suffer from a number of potential drawbacks or trade-offs, which both communities should consider before invoking them in any particular case.  4  First, depending on one's assumptions around the expected degree of change in AI or in its societal impacts, incompletely theorized agreements could prove brittle. Incompletely theorized agreements bypass a full examination of the underlying disagreements to facilitate pragmatic and swift action on particular policies on which both communities find themselves in practical alignment in a specific moment in time. This may create a lack of clarity over the boundary conditions of that practical agreement, along with opacity over whether, or where (i.e. for which future particular questions around AI policy) the practical agreement might suddenly break down for either or all parties. Second, an incompletely theorized agreement is, in an important sense, a 'stopgap' measure more than a general ideal or permanent fix. As above, an incompletely theorized agreement might be most suited to situations where (a) practical policy action is urgently needed, and (b) underlying theoretical agreement by stakeholders on all engaged principles or questions does not seem close. However, over longer timeframes, deeper inquiry and debate do appear necessary  [73] . In addition, there is always the possibility that agreement was not, in fact, intractable within the near term. As such, a premature leap by the community into an incompletely theorized agreement to achieve some policy X might inadvertently curb the very conversations amongst the communities which could have led both to eventually prefer policy Y instead, had their conversation been allowed to run its course. Moreover, there is a key related point here, on which we should reflect. By advocating for the adoption of incompletely theorized agreements on AI policy today, we ourselves are in a sense assuming or importing an implicit judgment about the urgency of AI issues today, and about the intractability of the underlying debates. Yet these are two positions which others might contest. For example, by arguing that 'AI issues do not today meet that threshold of urgency that the use of an incompletely theorized agreement is warranted'. We wish to make this assumption explicit. At the same time, we expect that it is an assumption widely shared by many scholars working on AI policy, many of whom may well share a sense that the coming years will be a sensitive and even critical time for AI policies. Third, a sloppily formulated incompletely theorized agreement on an AI policy issue may not actually reflect convergence on particular policies (e.g. 'certification scheme for AI products with safety tests X, Y, Z'). Instead, it might solidify on apparent agreement on vague mid-level principles or values (e.g. 'AI developers should ensure responsible AI development'). These may be so broad that they do not ground clear action at the level of actual policies. If this were to happen, incompletely theorized agreements might merely risk contributing to the already-abundant proliferation of broad AI principles or ethical frameworks on AI that have little direct policy impact. While the ecosystem of AI codes of ethics issued in recent years have certainly shown some convergence  [109] [110] [111] , they have been critiqued as being hard to operationalize, and for providing only the appearance of agreement while masking underlying tensions in the principles' interpretation, operationalization, or practical requirements  [93, 112] . Situations where an incompletely theorized agreement does not manage to root itself at the level of concrete policies but only mid-level principles would be a worst-of-both-worlds scenario: it would reduce the ability of actors to openly reflect upon and resolve inconsistencies amongst-or disagreements about high-level principles, while not even affording improvements at facilitating concrete policies or actions in particular AI domains. To mitigate this risk, incompletely theorized agreements should, therefore, remain closely grounded in concrete and clearly actionable policy goals or outputs. Nonetheless, while limitations such as these should be considered in greater detail, we argue that they do not categorically erode the case for implementing, or at least further examining the promise of this principle and tool for advancing responsible AI policy. \n Conclusion AI has raised multiple societal and ethical concerns. This highlights the urgent need for suitable and impactful policy measures in response. Nonetheless, there is at present an experienced fragmentation in the responsible AI policy community, amongst clusters of scholars focusing on 'nearterm' AI risks, and those focusing on 'longer-term' risks. This paper has sought to map the practical space for intercommunity collaboration, with a view towards the practical development of AI policy. As such, we briefly provided a rationale for such collaboration, by reviewing historical cases of scientific community conflict or collaboration, as well as the contemporary challenges facing AI policy. We argued that fragmentation within a given community can hinder progress on key and urgent policies. Consequently, we reviewed a number of potential (epistemic, normative or pragmatic) sources of disagreement in the AI ethics community, and argued that these trade-offs are often exaggerated, and at any rate do not need to preclude collaboration. On this basis, we presented the novel proposal for drawing on the constitutional law principle of an 'incompletely theorized agreement', for the communities to set aside or suspend these and other disagreements for the purpose of achieving higher-order AI policy goals of both communities in selected areas. We, therefore, non-exhaustively discussed a number of promising shared AI policy areas which could serve as the sites for such agreements, while also discussing some of the overall limits of this framework. This paper does not suggest that communities should fully merge or ignore differences whatever their source may be. To be sure, some policy projects will be relevant to one group within the community but not the other. Indeed, community heterogeneity and diversity is generally a good thing for a scientific paradigm. Instead, the paper proposes to question some possible reasons for conflicting dynamics which could stall positive progress for policy making, and suggests an avenue for a higher-order resolution. Most of all, the paper hopes to pragmatically encourage the exploration of opportunities for shared work and suggested that work on such opportunities, where it is found, can be well grounded through an incompletely theorized agreement. We invite scholars in the ethical AI community to explore the strengths and limits of this tool. Footnote 1 ( 1 continued) assumption that policy making can positively influence the development and deployment of AI technology. \n\t\t\t This paper perceives AI's ethical and societal concerns to be closely intertwined, and as such refers to the broader set of these actual and potential concerns throughout. \n\t\t\t It should be emphasized that this mapping is only an indicative sketch, and would be much enriched by further examination, for example through structured interviews or comprehensive opinion surveys. \n\t\t\t We thank one reviewer for prompting this discussion of the drawbacks of incompletely theorized agreements.", "date_published": "n/a", "url": "n/a", "filename": "Stix-Maas2021_Article_BridgingTheGapTheCaseForAnInco.tei.xml", "abstract": "Recent progress in artificial intelligence (AI) raises a wide array of ethical and societal concerns. Accordingly, an appropriate policy approach is urgently needed. While there has been a wave of scholarship in this field, the research community at times appears divided amongst those who emphasize 'near-term' concerns and those focusing on 'long-term' concerns and corresponding policy measures. In this paper, we seek to examine this alleged 'gap', with a view to understanding the practical space for inter-community collaboration on AI policy. We propose to make use of the principle of an 'incompletely theorized agreement' to bridge some underlying disagreements, in the name of important cooperation on addressing AI's urgent challenges. We propose that on certain issue areas, scholars working with near-term and long-term perspectives can converge and cooperate on selected mutually beneficial AI policy projects, while maintaining their distinct perspectives.", "id": "5bdb8e03d182d9df1d7ea5d3ec8e47f7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "Under review as a conference paper at ICLR 2021 BENEFITS OF ASSISTANCE OVER REWARD LEARNING", "text": "INTRODUCTION Traditional computer programs are instructions on how to perform a particular task. However, we do not know how to mechanically perform more challenging tasks like translation. The field of artificial intelligence raises the level of abstraction so that we simply specify what the task is, and let the machine to figure out how to do it. As task complexity increases, even specifying the task becomes difficult. Several criteria that we might have thought were part of a specification of fairness turn out to be provably impossible to simultaneously satisfy  (Kleinberg et al., 2016; Chouldechova, 2017; Corbett-Davies et al., 2017) . Reinforcement learning agents often \"game\" their reward function by finding solutions that technically achieve high reward without doing what the designer intended  (Lehman et al., 2018; Krakovna, 2018; Clark & Amodei, 2016) . In complex environments, we need to specify what not to change  (McCarthy & Hayes, 1981) ; failure to do so can lead to negative side effects . Powerful agents with poor specifications may pursue instrumental subgoals  (Bostrom, 2014; Omohundro, 2008)  such as resisting shutdown and accumulating resources and power  (Turner, 2019) . A natural solution is to once again raise the level of abstraction, and create an agent that is uncertain about the objective and infers it from human feedback, rather than directly specifying some particular task(s). Rather than using the current model of intelligent agents optimizing for their objectives, we would now have beneficial agents optimizing for our objectives  (Russell, 2019) . Reward learning  (Leike et al., 2018; Jeon et al., 2020; Christiano et al., 2017; Ziebart et al., 2010)  attempts to instantiate this by learning a reward model from human feedback, and then using a control algorithm to optimize the learned reward. Crucially, the control algorithm does not reason about the effects of the chosen actions on the reward learning process, which is external to the environment. In contrast, in the assistance paradigm  (Hadfield-Menell et al., 2016; Fern et al., 2014) , the human H is modeled as part of the environment and as having some latent goal that the agent R (for robot) does not know. R's goal is to maximize this (unknown) human goal. In this formulation, R must balance between actions that help learn about the unknown goal, and control actions that lead to high reward. Our key insight is that by integrating reward learning and control modules, assistive agents can take into account the reward learning process when selecting actions. This gives assistive agents a significant advantage over reward learning agents, which cannot perform similar reasoning. What is the reward of ? All pies need , let me make it If I use the to make , there won't be any left for and . I'll wait for more information. \n Learning about reward Making robust plans Preserving option value when possible + + I won't find out which pie is preferable before Alice gets very hungry, so I'll make . Guessing when feedback is unavailable + Figure 1: R must cook a pie for H, by placing flour on the plate to make the pie dough, filling it with either Apple, Blueberry, or Cherry filling, and finally baking it. However, R does not know which filling H prefers, and H is not available for questions since she is doing something else. What should R do in this situation? On the right, we show what qualitative reasoning we might want R to use to handle the situation. The goal of this paper is to clarify and illustrate this advantage. We first precisely characterize the differences between reward learning and assistance, by showing that two phase, communicative assistance is equivalent to reward learning (Section 3). We then give qualitative examples of desirable behaviors that can only be expressed once these restrictions are lifted, and thus are only exhibited by assistive agents (Section 4). Consider for example the kitchen environment illustrated in Figure  1 , in which R must bake a pie for H. R is uncertain about which type of pie H prefers to have, and currently H is at work and cannot answer R's questions. An assistive R can make the pie crust, but wait to ask H about her preferences over the filling (Section 4.1). R may never clarify all of H's preferences: for example, R only needs to know how to dispose of food if it turns out that the ingredients have gone bad (Section 4.2). If H will help with making the pie, R can allow H to disambiguate her desired pie by watching what filling she chooses (Section 4.3). Vanilla reward learning agents do not show these behaviors. We do not mean to suggest that all work on reward learning should cease and only research on assistive agents should be pursued. Amongst other limitations, assistive agents are very computationally complex. Our goal is simply to clarify what qualitative benefits an assistive formulation could theoretically provide. Further research is needed to develop efficient algorithms that can capture these benefits. Such algorithms may look like algorithms designed to solve assistance problems as we have formalized them here, but they may also look like modified variants of reward learning, where the modifications are designed to provide the qualitative benefits we identify. \n BACKGROUND AND RELATED WORK We introduce the key ideas behind reward learning and assistance. X * denotes a sequence of X. We use parametric specifications for ease of exposition, but our results apply more generally. \n POMDPS A partially observable Markov decision process (POMDP) M = S, A, Ω, O, T, r, P 0 , γ consists of a finite state space S, a finite action space A, a finite observation space Ω, an observation function O : S → ∆(Ω) (where ∆(X) is the set of probability distributions over X), a transition function T : S × A → ∆(S), a reward function r : S × A × S → R, an initial state distribution P 0 : ∆(S), and a discount rate γ ∈ (0, 1). We will write o t to signify the tth observation O(s t ). A solution to the POMDP is given by a policy π : (O × A) * × O → ∆(A) that maximizes the expected sum of rewards ER(π) = Es 0∼P0,at∼π(•|o0:t,a0:t−1),st+1∼T (•|st,at) [ ∞ t=0 γ t r(s t , a t , s t+1 )]. \n REWARD LEARNING We consider two variants of reward learning: non-active reward learning, in which R must infer the reward by observing H's behavior, and active reward learning, in which R may choose particular questions to ask H in order to get particular feedback. A non-active reward learning problem P = M\\r, C, Θ, r θ , P Θ , π H , k contains a POMDP without reward M\\r = S, A R , Ω R , O R , T, P 0 , γ , and instead R has access to a parameterized reward space Θ, r θ , P Θ . R is able to learn about θ * by observing H make k different choices c, each chosen from a set of potential choices C. In order for R to learn from the human's choices, it also assumes access to the human decision function π H (c | θ) that determines how the human makes choices for different possible reward functions r θ . Common decision functions include perfect optimality  (Ng & Russell, 2000)  and Boltzmann rationality  (Ziebart et al., 2010) . There are many types of choices  (Jeon et al., 2020 ), including demonstrations (Argall et al., 2009 Ng & Russell, 2000; Ziebart et al., 2010; Fu et al., 2017; Gao et al., 2012) , comparisons  (Zhang et al., 2017; Wirth et al., 2017; Christiano et al., 2017; Sadigh et al., 2017) , corrections  (Bajcsy et al., 2017) , the state of the world , proxy rewards  (Hadfield-Menell et al., 2017b) , natural language  (Fu et al., 2019) , etc. A policy decision function f (c 0:k−1 ) produces a policy π R after observing H's choices. A solution is a policy decision function f that maximizes expected reward E θ∼PΘ,c 0:k−1 ∼π H [ER(f (c 0:k−1 ))]. Since H's choices c 0:k−1 do not affect the state of the environment that R is acting in, this is equivalent to choosing π R that maximizes expected reward given the posterior over reward functions, that is Eθ∼P (θ|c 0:k−1 ) ER(π R ) . An active reward learning problem P = M\\r, Q, C, Θ, r θ , P Θ , π H , k adds the ability for R to ask H particular questions q ∈ Q in order to get more targeted feedback about θ. The human decision function π H (c | q, θ) now depends on the question asked. A solution consists of a question policy π R Q (q i | q 0:i−1 , c 0:i−1 ) and a policy decision function f (q  (Eric et al., 2008; Daniel et al., 2014; Maystre & Grossglauser, 2017; Christiano et al., 2017; Sadigh et al., 2017; Zhang et al., 2017; Wilde et al., 2020)  will compute and ask q ∈ Q that maximizes an active learning criterion such as information gain  (Bıyık et al., 2019)  or volume removal  (Sadigh et al., 2017) . Best results are achieved by selecting questions with the highest value of information  (Cohn, Robert W, 2016; Zhang et al., 2017; Wilde et al., 2020) , but these are usually much more computationally expensive. R then finds a policy that maximizes expected reward under the inferred distribution over θ, in order to approximately solve the original POMDP. 0:k−1 , c 0:k−1 ) that maximize expected reward E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H [ER(f (q 0:k−1 , c 0:k−1 ))]. A typical algorithm Note that a non-active reward learning problem is equivalent to an active reward learning problem with only one question, since having just a single question means that R has no choice in what feedback to get (see Appendix A.1 for proofs). \n ASSISTANCE The key idea of assistance is that helpful behaviors like reward learning are incentivized when R does not know the true reward r and can only learn about it by observing human behavior. So, we model the human H as part of the environment, leading to a two-agent POMDP, and assume there is some true reward r that only H has access to, while the robot R only has access to a model relating r to H's behavior. Intuitively, as R acts in the environment, it will also observe H's behavior, which it can use to make inferences about the true reward. Following  Hadfield-Menell et al. (2016)  1 , we define an assistance game M as a tuple M = S, {A H , A R }, {Ω H , Ω R }, {O H , O R }, T, P S , γ, Θ, r θ , P Θ . Here S is a finite set of states, A H a finite set of actions for H, Ω H a finite set of observations for H, and O H : S → ∆(Ω H ) an observation function for H (respectively A R , Ω R , O R for R). The transition function T : S × A H × A R → ∆(S) gives the probability over next states given the current state and both actions. The initial state is sampled from P S ∈ ∆(S). Θ is a set of possible reward function parameters θ which parameterize a class of reward functions r θ : S × A H × A R × S → R, and P θ is the distribution from which θ is sampled. γ ∈ (0, 1) is a discount factor. As with POMDPs, policies can depend on history. Both H and R are able to observe each other's actions, and on a given timestep, R acts before H. We use τ R Should it be playing a Nash strategy or optimal strategy pair of the game, and if so, which one? Should it use a non-equilibrium policy, since humans likely do not use equilibrium strategies? This is a key hyperparameter in assistance games, as it determines the communication protocol for H and R. For maximum generality, we can equip the assistance game with a policy-conditioned belief B : Π R → ∆(Π H ) over π H , which specifies how the human responds to the agent's choice of policy  (Halpern & Pass, 2018) . The agent's goal is to maximize expected reward given this belief. t : (Ω R × A H × A R ) t to denote Prior work on assistance games  (Hadfield-Menell et al., 2016; Malik et al., 2018; Woodward et al., 2019)  focuses on finding optimal strategy pairs. This corresponds to a belief that H will know and perfectly respond to R's policy (see Appendix A.3). However, our goal is to compare assistance to reward learning. Typical reward learning algorithms assume access to a model of human decision-making: for example, H might be modeled as optimal (Ng &  Russell, 2000)  or Boltzmann-rational  (Ziebart et al., 2010) . As a result, we also assume that we have access to a model of human decision-making π H . Note that π H depends on θ: we are effectively assuming that we know how H chooses how to behave given a particular reward r θ . This assumption corresponds to the policy-conditioned belief B(π R )(π H ) = 1[π H = π H ]. We define an assistance problem P as a pair M, π H where π H is a human policy for the assistance game M. Given an assistance problem, a robot policy π R induces a probability distribution over trajectories: τ ∼ s 0 , θ, π H , π R , τ ∈ [S × A H × A R ] * . We denote the support of this distribution by Traj(π R ). The expected reward of a robot policy for M, π H is given by ER(π R ) = E s0∼P S ,θ∼P θ ,τ ∼ s0,θ,π H ,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) . A solution of M, π H is a robot policy that maximizes expected reward: π R = argmax πR ER(π R ). \n SOLVING ASSISTANCE PROBLEMS Once the π H is given, H can be thought of as an aspect of the environment, and θ can be thought of as a particularly useful piece of information for estimating how good actions are. This suggests that we can reduce the assistance problem to an equivalent POMDP. Following  Desai (2017) , the key idea is to embed π H in the transition function T and embed θ in the state. In theory, to embed potentially non-Markovian π H in T , we need to embed the entire history of the trajectory in the state, but this leads to extremely large POMDPs. In our experiments, we only consider Markovian human policies, for which we do not need to embed the full history, keeping the state space manageable. Thus, the policy can be written as π H (a H | o H , a R , θ). To ensure that R must infer θ from human behavior, as in the original assistance game, the observation function does not reveal θ, but does reveal the previous human action a H . Proposition 1. Every assistance problem M, π H can be reduced to an equivalent POMDP M . The full reduction and proof of equivalence is given in Appendix A.2. When M is fully observable, in the reduced POMDP θ is the only part of the state not directly observable to the robot, making it an instance of a hidden-goal MDP  (Fern et al., 2014) . For computational tractability, much of the work on hidden goals  (Javdani et al., 2015; Fern et al., 2014)  selects actions assuming that all goal ambiguity is resolved in one step. This effectively separates reward learning and control in the same way as typical reward learning algorithms, thus negating many of the benefits we highlight in this work. Intention-aware motion planning  (Bandyopadhyay et al., 2013 ) also embeds the human goal in the state in order to avoid collisions with humans during motion planning, but does not consider applications for assistance.  Macindoe et al. (2012)  uses the formulation of a POMDP with a hidden goal to produce an assistive agent in a cops and robbers gridworld environment.  Nikolaidis et al. (2015)  assumes a dataset of joint human-robot demonstrations, which they leverage to learn \"types\" of humans that can then be inferred online using a POMDP framework. This is similar to solving an assistance problem, where we think of the different values of θ as different \"types\" of humans.  Chen et al. (2018)  uses an assistance-style framework in which the unknown parameter is the human's trust in the robot (rather than the reward θ).  Woodward et al. (2019)  uses deep reinforcement learning to solve an assistance game in which the team must collect either plums or lemons. To our knowledge, these are the only prior works that use an assistive formulation in a way that does not ignore the information-gathering aspect of actions. While these works typically focus on algorithms to solve assistance games, we instead focus on the qualitative benefits of using an assistance formulation. Since we can reduce an assistance problem to a regular POMDP, we can use any POMDP solver to find the optimal π R . In our examples for this paper, we use an exact solver when feasible, and point-based value iteration (PBVI)  (Pineau et al., 2003)  or deep reinforcement learning (DRL) when not. When using DRL, we require recurrent models, since the optimal policy can depend on history. A common confusion is to ask how DRL can be used, given that it requires a reward signal, but by assumption R does not know the reward function. This stems from a misunderstanding of what it means for R \"not to know\" the reward function. When DRL is run, at the beginning of each episode, a specific value of θ is sampled as part of the initial state. The learned policy π R is not provided with θ: it can only see its observations o R and human actions a H , and so it is accurate to say that π R \"does not know\" the reward function. However, the reward is calculated by the DRL algorithm, not by π R , and the algorithm can and does use the sampled value of θ for this computation. π R can then implicitly learn the correlation between the actions a H chosen by π H , and the high reward values that the DRL algorithm computes; this can be often be thought of as an implicit estimation of θ in order to choose the right actions. \n REWARD LEARNING AS TWO-PHASE COMMUNICATIVE ASSISTANCE There are two key differences between reward learning and assistance. First, reward learning algorithms split reward learning and control into two separate phases, while assistance merges them into a single phase. Second, in reward learning, the human's only role is to communicate reward information to the robot, while in assistance the human can help with the task. These two properties exactly characterize the difference between the two: reward learning problems and communicative assistance problems with two phases can be reduced to each other, in a very natural way. A communicative assistance problem is one in which the transition function T and the reward function r θ are independent of the choice of human action a H , and the human policy π H (• | o H , a R , θ) is independent of the observation o H . Thus, in a communicative assistance problem, H's actions only serve to respond to R, and have no effects on the state or the reward (other than by influencing R). Such problems can be cast as instances of HOP-POMDPs  (Rosenthal & Veloso, 2011) . For the notion of two phases, we will also need to classify robot actions as communicative or not. We will assume that there is some distinguished action a R noop that \"does nothing\". Then, a robot action âR is communicative if for any s, a H , s we have T (s | s, a H , âR ) = T (s | s, a H , a R noop ) and R(s, a H , âR , s ) = R(s, a H , a R noop , s ). A robot action is physical if it is not communicative. Now consider a communicative assistance problem M, π H with noop action a R noop and let the optimal robot policy be π R * . Intuitively, we would like to say that there is an initial communication phase in which the only thing that happens is that H responds to questions from R, and then a second action phase in which H does nothing and R acts. Formally, the assistance problem is two phase with actions at t act if it satisfies the following property: ∃a H noop ∈ A H , ∀τ ∈ Traj(π R * ), ∀t < t act : a R t is communicative ∧ ∀t ≥ t act : a H t = a H noop . Thus, in a two phase assistance problem, every trajectory from an optimal policy can be split into a \"communication\" phase where R cannot act and an \"action\" phase where H cannot communicate. Reducing reward learning to assistance. We can convert an active reward learning problem to a two-phase communicative assistance problem in an intuitive way: we add Q to the set of robot actions, make C the set of human actions, add a timestep counter to the state, and construct the reward such that an optimal policy must switch between the two phases after k questions. A non-active reward learning problem can first be converted to an active reward learning problem. Proposition 2. Every active reward learning problem M, Q, C, Θ, r θ , P Θ , π H , k can be reduced to an equivalent two phase communicative assistance problem M , π H . Corollary 3. Every non-active reward learning problem M, C, Θ, r θ , P Θ , π H , k can be reduced to an equivalent two phase communicative assistance problem M , π H . Reducing assistance to reward learning. The reduction from a two-phase communicative assistance problem to an active reward learning problem is similarly straightforward: we interpret R's communicative actions as questions and H's actions as answers. There is once again a simple generalization to non-active reward learning. Proposition 4. Every two-phase communicative assistance problem M, π H , a R noop can be reduced to an equivalent active reward learning problem. Corollary 5. If a two-phase communicative assistance problem M, π H has only one communicative robot action, it can be reduced to an equivalent non-active reward learning problem. \n QUALITATIVE IMPROVEMENTS FOR GENERAL ASSISTANCE We have seen that reward learning is equivalent to two-phase communicative assistance problems, where inferring the reward distribution can be separated from control using the reward distribution. However, for general assistance games, it is necessary to merge estimation and control, leading to several new qualitative behaviors. When the two phase restriction is lifted, we observe relevance aware active learning and plans conditional on future feedback. When the communicative restriction is lifted, we observe learning from physical actions. We demonstrate these qualitative behaviors in simple environments using point-based value iteration (PBVI) or deep reinforcement learning (DRL). We describe the qualitative results here, deferring detailed explanations of environments and results to Appendix C. For communicative assistance problems, we also consider two baselines: 1. Active reward learning. This is the reward learning paradigm discussed so far. 2. Interactive reward learning. This is a variant of reward learning that aims to recover some of the benefits of interactivity, by alternating reward learning and acting phases. During an action phase, R chooses actions that maximize expected reward under its current belief over θ (without \"knowing\" that its belief may change), while during a reward learning phase, R chooses questions that maximizes information gain. \n PLANS CONDITIONAL ON FUTURE FEEDBACK Here, we show how an assistive agent can make plans that depend on obtaining information about θ in the future. The agent can first take some \"preparatory\" actions that whose results can be used later once the agent has clarified details about θ. A reward learning agent would not be able to do this, as it would require three phases (acting, then learning, then acting again). We illustrate this with our original kitchen environment (Figure  1 ), in which R must bake a pie for H, but doesn't know what type of pie H would like: Apple, Blueberry, or Cherry. Each type has a weight specifying the reward for that pie. Assuming people tend to like apple pie the most and cherry pie the least, we have θ A ∼ Uniform[2, 4], θ B ∼ Uniform[1, 3], and θ C ∼ Uniform[0, 2]. We define the questions Q = {q A , q B , q C }, where q X means \"What is the value of θ X ?\", and thus, the answer set is C = R. R can select ingredients to assemble the pie. Eventually, R must use \"bake\", which bakes the selected ingredients into a finished pie, resulting in reward that depends on what type of pie has been created. H initially starts outside the room, but will return at some prespecified time. r θ assigns a cost of asking a question of 0.1 if H is inside the room, and 3 otherwise. The horizon is 6 timesteps. Assistance. Notice that, regardless of H's preferences, R will need to use flour to make pie dough. So, R always makes the pie dough first, before querying H about her preferences. Whether R then queries H about her preferences depends on how late H returns. If H arrives home before timestep 5, R will query her about her preferences and then make the appropriate pie as expected. However, if H will arrive later, then there will not be enough time to query her for her preferences and bake a pie. Instead, R bakes an apple pie, since its prior suggests that that's what H wants. This behavior, where R takes actions (making dough) that are robustly good but waits on actions (adding the filling) whose reward will be clarified in the future, is very related to conservative agency  (Turner et al., 2020) , a connection explored in more depth in Appendix D. Reward learning. The assistance solution requires R to act (to make dough), then to learn preferences, and then to act again (to make pie). A reward learning agent can only have two phases, and so we see one of two suboptimal behaviors. First, R could stay in the learning phase until H returns home, then ask which pie she prefers, and then make the pie from scratch. Second, R could make an apple pie without asking H her preferences. (In this case there would be no learning phase.) Which of these happens depends on the particular method and hyperparameters used. Interactive reward learning. Adding interactivity is not sufficient to get the correct behavior. Suppose we start with an action phase. The highest reward plan under R's current belief over θ is to bake an apple pie, so that's what it will do, as long as the phase lasts long enough. Conversely, suppose we start with a learning phase. In this case, R does nothing until H returns, and then asks about her preferences. Once we switch to an action phase, it bakes the appropriate pie from scratch. \n RELEVANCE AWARE ACTIVE LEARNING ? Figure  2 : The wormy-apples kitchen environment. H wants an apple, but R might discover worms in the apple, and have to dispose of it in either of the trash or compost bins. Once we relax the two-phase restriction, R starts to further optimize whether and when it asks questions. In particular, since R may be uncertain about whether a question's answer will even be necessary, R will only ask questions once they become immediately relevant to the task at hand. In contrast, a reward learning agent would have to decide at the beginning of the episode (during the learning phase) whether or not to ask these questions, and so cannot evaluate how relevant they are. Consider for example a modification to the kitchen environment: R knows that H wants an apple pie, but when R picks up some apples, there is a 20% chance that it finds worms in some of the apples. R is unsure whether H wants her compost bin to have worms, and so does not know whether to dispose of the bad apples in the trash or compost bin. Since this situation is relatively unlikely, ideally R would only clarify H's preferences when the situation arises. Assistance. An assistive R only asks about wormy apples when it needs to dispose of one. R always starts by picking up apples. If the apple does not have worms, R immediately uses the apples to bake the pie. If some apples have worms and the cost of asking a question is sufficiently low, R elicits H's preferences and disposes of the apples appropriately. It then bakes the pie with the remaining apples. This behavior, in which questions are asked only if they are useful for constraining future behavior, has been shown previously using probabilistic recipe trees (PRTs)  Kamar et al. (2009) , but to our knowledge has not been shown with optimization-based approaches. Reward learning. A reward learning policy must have only two phases and so would show one of two undesirable behaviors: either it would always ask H where to dispose of wormy apples, or it never asks and instead guesses when it does encounter wormy apples. Interactive reward learning. This has the same problem as in the previous section. If we start in the action phase and R picks up wormy apples, it will dispose of them in an arbitrary bin without asking H about her preferences, because it doesn't \"know\" that it will get the opportunity to do so. Alternatively, if we start with a learning phase, R will ask H where to dispose of wormy apples, even if R would never pick up any wormy apples. Note that more complex settings can have many more questions. Should R ask whether H would prefer to use seedless apples, should scientists ever invent them? Perhaps R should ask H how her pie preferences vary based on her emotional state? Asking about all possible situations is not scalable. \n LEARNING FROM PHYSICAL ACTIONS So far we have considered communicative assistance problems, in which H only provides feedback rather than acting to maximize reward herself. Allowing H to have physical actions enables a greater variety of potential behaviors. Most clearly, when R knows the reward (that is, P Θ puts support over a single θ), assistance games become equivalent to human-AI collaboration  (Nikolaidis & Shah, 2013; Carroll et al., 2019; Dimitrakakis et al., 2017) . With uncertain rewards, we can see further interesting qualitative behaviors: R can learn just by observing how H acts in an environment, and then work with H to maximize reward, all within a single episode, as in shared autonomy with intent inference  (Javdani et al., 2015; Brooks & Szafir, 2019)  and other works that interpret human actions as communicative  Whitney et al. (2017) . This can significantly reduce the burden on H in providing reward information to R (or equivalently, reduce the cost incurred by R in asking questions to H). Some work has shown that in such situations, humans tend to be pedagogic: they knowingly take individually suboptimal actions, in order to more effectively convey the goal to the agent  (Ho et al., 2016; Hadfield-Menell et al., 2016 ). An assistive R who knows this can quickly learn what H wants, and help her accomplish her goals. \n + + + + Figure  3 : The cake-or-pie variant of the kitchen environment. H is equally likely to prefer cake or pie. Communication must take place through physical actions alone. We illustrate this with a variant of our kitchen environment, shown in Figure  3 . There are no longer questions and answers. Both H and R can move to an adjacent free space, and pick up and place the various objects. Only R may bake the dessert. R is uncertain whether H prefers cake or cherry pie. For both recipes, it is individually more efficient for H to pick up the dough first. However, we assume H is pedagogic and wants to quickly show R which recipe she wants. So, if she wants cake, she will pick up the chocolate first to signal to R that cake is the preferred dessert. It is not clear how exactly to think about this from a reward learning perspective: there aren't any communicative human actions since every action alters the state of the environment. In addition, there is no clear way to separate out a given trajectory into two phases. This situation cannot be easily coerced into the reward learning paradigm. In contrast, an assistive R can handle this situation perfectly. It initially waits to see which ingredient H picks up first, and then quickly helps H by putting in the ingredients from its side of the environment and baking the dessert. It learns implicitly to make the cake when H picks up chocolate, and to make the pie when H picks up dough. This is equivalent to pragmatic reasoning (Goodman & Frank, 2016): \"H would have picked up the chocolate if she wanted cake, so the fact that she picked up the dough implies that she wants cherry pie\". However, we emphasize that R is not explicitly programmed to reason in this manner, and is learned using deep reinforcement learning (Appendix C.3). Note that R is not limited to learning from H's physical actions: R can also use its own physical actions to \"query\" the human for information  (Woodward et al., 2019; Sadigh et al., 2016) . \n LIMITATIONS AND FUTURE WORK Computational complexity. The major limitation of assistance compared to reward learning is that assistance problems are significantly more computationally complex, since we treat the unknown reward θ as the hidden state of a POMDP. We are hopeful that this can be solved through the application of deep reinforcement learning. An assistance problem is just like any other POMDP, except that there is one additional unobserved state variable θ and one additional observation a H . This should not be a huge burden, since deep reinforcement learning has been demonstrated to scale to huge observation and action spaces  (OpenAI, 2018; Vinyals et al., 2019) . Another avenue for future work is to modify active reward learning algorithms in order to gain the benefits outlined in Section 4, while maintaining their computational efficiency. Increased chance of incorrect inferences. In practice, assistive agents will extract more information from H than reward learning agents, and so it is worse if π H is misspecified. We don't see this as a major limitation: to the extent this is a major worry, we can design π H so that the robot only makes inferences about human behavior in specific situations. For example, by having π H be independent of θ in a given state s, we ensure that the robot does not make any inferences about θ in that state. Environment design. We have shown that by having a hidden human goal, we can design environments in which optimal agent behavior is significantly more \"helpful\". One important direction for future work is to design larger, more realistic environments, in order to spur research into how best to solve such environments. We would be particularly excited to see a suite of assistance problems become a standard benchmark by which deep reinforcement learning algorithms are assessed. \n LIMITATIONS OF ASSISTANCE AND REWARD LEARNING While we believe that the assistance framework makes meaningful conceptual progress over reward learning, a number of challenges for reward learning remain unaddressed by assistance: Human modeling. A major motivation for both paradigms is that reward specification is very difficult. However, now we need to specify a prior over reward functions, and the human model π H . Consequently, misspecification can still lead to bad results  (Armstrong et al., 2020; Carey, 2018) . While it should certainly be easier to specify a prior over θ with a \"grain of truth\" on the true reward θ * than to specify θ * directly, it is less clear that we can specify π H well. One possibility is to add uncertainty over the human policy π H . However, this can only go so far: information about θ must come from somewhere. If R is sufficiently uncertain about θ and π H , then it cannot learn about the reward  (Armstrong & Mindermann, 2018) . Thus, for good performance we need to model π H . While imitation learning can lead to good results  (Carroll et al., 2019) , the best results will likely require insights from a broad range of fields that study human behavior. Assumption that H knows θ. Both assistance games and reward learning makes the assumption that H knows her reward exactly, but in practice, human preferences change over time  (Allais, 1979; Cyert & DeGroot, 1975; Shogren et al., 2000) . We could model this as the human changing their subgoals  (Michini & How, 2012; Park et al., 2020) , adapting to the robot  (Nikolaidis et al., 2017)  or learning from experience  (Chan et al., 2019) . Dependence on uncertainty. All of the behaviors of Section 4, as well as previously explored benefits such as off switch corrigibility  (Hadfield-Menell et al., 2017a) , depend on R expecting to gain information about θ. However, R will eventually exhaust the available information about θ. If everything is perfectly specified, this is not a problem: R will have converged to the true θ * . However, in the case of misspecification, after convergence R is effectively certain in an incorrect θ, which has many troubling problems that we sought to avoid in the first place (Yudkowsky, year unknown). \n CONCLUSION While much recent work has focused on how we can build agents that learn what they should do from human feedback, there is not yet a consensus on how such agents should be built. In this paper, we contrasted the paradigms of reward learning and assistance. We showed that reward learning problems are equivalent to a special type of assistance problem, in which the human may only provide feedback at the beginning of the episode, and the agent may only act in the environment after the human has finished providing feedback. By relaxing these restrictions, we enable the agent to reason about how its actions in the environment can influence the process by which it solicits and learns from human feedback. This allows the agent to (1) choose questions based on their relevance, (2) create plans whose success depends on future feedback, and (3) learn from physical human actions in addition to communicative feedback. \n A REWARD LEARNING AND ASSISTANCE FORMALISMS A.1 RELATION BETWEEN NON-ACTIVE AND ACTIVE REWARD LEARNING The key difference between non-active and active reward learning is that in the latter R may ask H questions in order to get more targeted feedback. This matters as long as there is more than one question: with only one question, since there is no choice for R to make, R cannot have any influence on the feedback that H provides. As a result, non-active reward learning is equivalent to active reward learning with a single question. Proposition 6. Every non-active reward learning problem M\\r, C, Θ, r θ , P Θ , π H , k can be reduced to an active reward learning problem. Proof. We construct the active reward learning problem as M\\r, Q , C, Θ, r θ , P Θ , π H , k , where Q {q φ } where q φ is some dummy question, and π H (c | q, θ) π H (c | θ). Suppose the solution to the new problem is π R Q , f . Since f is a solution, we have: f = argmax f E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H (•|qi,θ) ER( f (q 0:k−1 , c 0:k−1 )) = argmax f E θ∼PΘ,q 0:k−1 =q φ ,c 0:k−1 ∼π H (•|q φ ,θ) ER( f (q 0:k−1 = q φ , c 0:k−1 )) all q are q φ = argmax f E θ∼PΘ,c 0:k−1 ∼π H (•|θ) ER( f (q 0:k−1 = q φ , c 0:k−1 )) . Thus f (c 0:k−1 ) = f (q 0:k−1 = q φ , c 0:k−1 ) is a maximizer of E θ∼PΘ,c 0:k−1 ∼π H (•|θ) ER( f (c 0:k−1 ) , making it a solution to our original problem. Proposition 7. Every active reward learning problem M\\r, Q, C, Θ, r θ , P Θ , π H , k with |Q| = 1 can be reduced to a non-active reward learning problem. Proof. Let the sole question in Q be q φ . We construct the non-active reward learning problem as M\\r, C, Θ, r θ , P Θ , π H , k , with π H (c | θ) = π H (c | q φ , θ). Suppose the solution to the new problem is f . Then we can construct a solution to the original problem as follows. First, note that π R Q must be π R Q (q i | q 0:i−1 , c 0:i−1 ) = 1[q i = q φ ], since there is only one possible question q φ . Then by inverting the steps in the proof of Proposition 6, we can see that f is a maximizer of E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H (•|qi,θ) ER( f (• | c 0:k−1 ) ) . Thus, by defining f (q 0:k−1 , c 0:k−1 ) = f (c 0:k−1 ), we get a maximizer to our original problem, making π R Q , f a solution to the original problem. \n A.2 REDUCING ASSISTANCE PROBLEMS TO POMDPS Suppose that we have an assistance problem M, π H with: M = S, {A H , A R }, {Ω H , Ω R }, {O H , O R }, T, P S , γ, Θ, r θ , P Θ . Then, we can derive a single-player POMDP for the robot M = S , A R , Ω , O , T , r , P 0 , γ by embedding the human reward parameter into the state. We must include the human's previous action a H into the state, so that the robot can observe it, and so that the reward can be computed. To allow for arbitrary (non-Markovian) human policies π H , we could encode the full history in the state, in order to embed π H into the transition function T . However, in our experiments we only consider human policies that are in fact Markovian. We make the same assumption here, giving a policy π H (a H t | o H t , a R t , θ) that depends on the current observation and previous robot action. The transformation M → M is given as follows: S S × A H × Θ State space Ω Ω R × A H Observation space O (o | s ) = O ((o R , a H 1 ) | (s, a H 2 , θ)) Observation function 1[a H 1 = a H 2 ] • O R (o R | s) T (s 2 | s 1 , a R ) = T ((s 2 , a H 1 , θ 2 ) | (s 1 , a H 0 , θ 1 ), a R ) Transition function T (s 2 | s 1 , a H 1 , a R ) • 1[θ 2 = θ 1 ] • o H ∈Ω H O H (o H | s 1 ) • π H (a H 1 | o H , a R , θ) r (s 1 , a R , s 2 ) = r ((s 1 , a H 0 , θ), a R , (s 2 , a H 1 , θ)) Reward function r θ (s 1 , a H 1 , a R , s 2 ) P 0 (s ) = P 0 ((s, a H , θ)) Initial state distribution P S (s) • P Θ (θ) • 1[a H = a H init ] where a H init is arbitrary In the case where the original assistance problem is fully observable, the resulting POMDP is an instance of a Bayes-Adaptive MDP  (Martin, 1967; Duff, 2002) . Any robot policy π R can be translated from the APOMDP M naturally into an identical policy on M . Note that in either case, policies are mappings from (Ω R , A H , A R ) * × Ω R to ∆(A R ). This transformation preserves optimal agent policies: Proposition 8. A policy π R is a solution of M if and only if it is a solution of M . Proof. Recall that an optimal policy π * in the POMDP M is one that maximizes the expected value: EV(π) = E s 0 ∼P 0 ,τ ∼ s 0 ,π ∞ t=0 γ t r (s t , a t , s t+1 ) = E s 0 ∼P 0 ,τ ∼ s 0 ,π ∞ t=0 γ t r θ (s t , a H t , a t , s t+1 ) where the trajectories τ s are sequences of state, action pairs drawn from the distribution induced by the policy, starting from state s 0 . Similarly, an optimal robot policy π R * in the APOMDP M is one that maximizes its expected reward: ER(π R ) = E s0∼P S ,θ∼PΘ,τ ∼ s0,θ,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) . To show that the optimal policies coincide, suffices to show that for any π, ER(π) (in M) is equal to EV(π) (in M ). To do this, we will show that π induces the \"same\" distributions over the trajectories. For mathematical convenience, we will abuse notation and consider trajectories of the form τ ; θ ∈ (S, A H , A R ) * × Θ; it is easy to translate trajectories of this form to trajectories in either M or M. We will show that the sequence τ ; θ has the same probability when the robot takes the policy π in both M and M by induction on the lengths of the sequence. First, consider the case of length 1 sequences. τ ; θ = [(s, a R , a H ); θ]. Under both M and M, s and θ are drawn from P S and P Θ respectively. Similarly, a R and a H are drawn from π R (• | o R 0 ) and π H (• | o H , a R , θ) respectively. So the distribution of length 1 sequences is the same under both M and M. \n Now, consider some longer sequence τ ; θ = [(s 1 , a R 1 , a H 1 ), ...., (s t , a R t , a H t ); θ] . By the inductive hypothesis, the distribution of (s 1 , a H 1 , a R 1 ), ...., (s t−1 , a H t−1 , a R t−1 ) and θ are identical; it suffices to show that (s t , a H t , a R t ) has the same distribution, conditioned on the other parts of τ ; θ, under M and under M. Yet by construction, s t is drawn from the same distribution T ( •|s t−1 , a H t−1 , a R t−1 ), a H A.3 OPTIMAL STRATEGY PAIRS AS POLICY-CONDITIONED BELIEF We use the term policy-conditioned belief to refer to a distribution over human policies which depends on the chosen robot policy. We use policy-conditioned beliefs as opposed to a simple unconditional distribution over human policies, because it allows us to model a wide range of situations, including situations with prior coordination, or where humans adapt to the robot's policy as a result of prior interactions. Moreover, this presents a unifying framework with prior work on assistance games  (Hadfield-Menell et al., 2016) . In fact, finding an optimal strategy pair for the assistance game can be thought of as finding the policy which is best when the human adapts optimally, as formalized below: Proposition 9. Let M = S, {A H , A R }, {Ω H , Ω R }, {O H , O R }, T, P S , γ, Θ, r θ , P Θ be an as- sistance game. Let B(π R )(π H ) ∝ 1[EJR(π H , π R ) = max πH ∈Π H EJR(π H , π R ) ] be an associated policy-conditioned belief. Let π R be the solution to M, B . Then B(π R ), π R is an optimal strategy pair. Proof. Let π H , π R be an arbitrary strategy pair. Then EJR(π H , π R ) ≤ EJR(B(π R ), π R ) by the definition of B, and EJR(B(π R ), π R ) ≤ EJR(B(π R ), π R ) by the definition of π R . Thus EJR(π H , π R ) ≤ EJR(B(π R ), π R ). Since π H , π R was assumed to be arbitrary, B(π R ), π R is an optimal strategy pair. \n B EQUIVALENCE OF RESTRICTED ASSISTANCE AND EXISTING ALGORITHMS B.1 EQUIVALENCE OF TWO PHASE ASSISTANCE AND REWARD LEARNING Here we prove the results in Section 3 showing that two phase communicative assistance problems and reward learning problems are equivalent. We first prove Proposition 4, and then use it to prove the others. Proposition 4. Every two-phase communicative assistance problem M, π H , a R noop can be reduced to an equivalent active reward learning problem. Proof. Let M = S, {A H , A R }, {Ω H , Ω R }, {O H , O R }, T, P S , γ, Θ, r θ , P Θ be the assistance game, and let the assistance problem's action phase start at t act . Let a H φ ∈ A H be some arbitrary human action and o H φ ∈ Ω H be some arbitrary human observation. We construct the new active reward learning problem M , Q , C , Θ, r θ , P Θ , π H , k as follows: Q {a R ∈ A R : a R is communicative} Questions C A H Answers M S, A , Ω R , O R , T , P 0 , γ POMDP A A R \\Q Physical actions T (s | s, a R ) T (s | s, a H φ , a R ) Transition function k t act Number of questions P 0 (s) s 0:k ∈S P M (s 0:k , s k +1 = s | a R 0:k = a R noop , a H 0:k = a H φ ) Initial state distribution r θ (s, a R , s ) r θ (s, a H φ , a R , s ) Reward function π H (c | q, θ) π H (c | o H φ , q, θ) \n Human decision function Note that it is fine to use a H φ in T, r θ and to use o H φ in π H even though they were chosen arbitrarily, because since the assistance problem is communicative, the result does not depend on the choice. The P M term in the initial state distribution denotes the probability of a trajectory under M and can be computed as P M (s 0:T +1 | a R 0:T , a H 0:T ) = P S (s 0 ) T t=0 T (s t+1 | s t , a H t , a R t ). Given some pair π R Q , f to the active reward learning problem, we construct a policy for the assistance problem as π R (a R t | o R t , τ R t−1 )    π R Q (a R t | a R 0:t−1 , a H 0:t−1 ), t < k and a R 0:t ∈ Q f (a R 0:k−1 , a H 0:k−1 )(a R t | o R k:t , a R k:t−1 ), t ≥ k and a R 0:k−1 ∈ Q and a R k:t ∈ A 0, else . We show that there must exist a solution to P that is the analogous policy to some pair. Assume towards contradiction that this is not the case, and that there is a solution π R * that is not the analogous policy to some pair. Then we have a few cases: 1. π R * assigns positive probability to a R i = a / ∈ Q for i < k. This contradicts the two-phase assumption. 2. π R * assigns positive probability to a R i = q ∈ Q for i ≥ k. This contradicts the two-phase assumption. 3. π R * (a R t | o R t , τ R t−1 ) depends on the value of o R i for some i < k. Since both a H 0:k−1 and a R 0:k−1 cannot affect the state or reward (as they are communicative), the distribution over o R 0:k−1 is fixed and independent of π R , and so there must be some other π R that is independent of o R 0:k−1 that does at least as well. That π R would be the analogous policy to some pair, giving a contradiction. Now, suppose we have some pair π R Q , f , and let its analogous policy be π R . Then we have: E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H [ER(f (q 0:k−1 , c 0:k−1 ))] = E θ∼PΘ E q 0:k−1 ∼π R ,c 0:k−1 ∼π H [ER(f (q 0:k−1 , c 0:k−1 ))] = E θ∼PΘ E q 0:k−1 ∼π R ,c 0:k−1 ∼π H E s0∼P 0 ,a R t ∼f (q 0:k−1 ,c 0:k−1 ),st+1∼T (•|st,a R t ) ∞ t=0 γ t r θ (s t , a R t , s t+1 ) = E θ∼PΘ E q 0:k−1 ∼π R ,c 0:k−1 ∼π H E s k ∼P 0 ,a R t ∼π R (•| c 0:k−1 ,o k:t , q 0:k−1 ,a k:t−1 ,st+1∼T (•|st,a R t ) 1 γ k ∞ t=k γ t r θ (s t , a R t , s t+1 ) = E θ∼PΘ E q 0:k−1 ∼π R ,c 0:k−1 ∼π H E s k ∼P 0 ,a R t ∼π R (•| c 0:k−1 ,o k:t , q 0:k−1 ,a k:t−1 ,st+1∼T (•|st,a R t ) 1 γ k ∞ t=k γ t r θ (s t , a H φ , a R t , s t+1 ) However, since all the actions in the first phase are communicative and thus don't impact state or reward, the first k timesteps in the two phase assistance game have constant reward in expectation. Let C = Es 0:k k−1 t=0 γ t r θ (s t , a H φ , a R noop , s t+1 ) . This gives us: E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H [ER(f (q 0:k−1 , c 0:k−1 ))] = E θ∼PΘ E s0∼P S ,θ∼PΘ,τ ∼ s0,θ,π H ,π R 1 γ k ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) − 1 γ k C = 1 γ k ER(π R ) − C . Thus, if π R Q , f is a solution to the active reward learning problem, then π R is a solution of the two-phase communicative assistance problem. Corollary 5. If a two-phase communicative assistance problem M, π H , a R noop has exactly one communicative robot action, it can be reduced to an equivalent non-active reward learning problem. Proof. Apply Proposition 4 followed by Proposition 7. (Note that the construction from Proposition 4 does lead to an active reward learning problem with a single question, meeting the precondition for Proposition 7.) Proposition 2. Every active reward learning problem P = M, Q, C, Θ, r θ , P Θ , π H , k can be reduced to an equivalent two phase communicative assistance problem P = M , π H . Proof. Let M = S, A, Ω, O, T, P 0 , γ . Let q 0 ∈ Q be some question and c 0 ∈ C be some (unrelated) choice. Let N be a set of fresh states {n 0 , . . . n k−1 }: we will use these to count the number of questions asked so far. Then, we construct the new two phase communicative assistance problem P = M , π H , a R noop as follows: M S , {C, A R }, {Ω H , Ω R }, {O H , O R }, T , P S , γ, Θ, r θ , P Θ Assistance game S S ∪ N State space P S (ŝ) 1[ŝ = n 0 ] Initial state distribution A R A ∪ Q Robot actions Ω H S H's observation space Ω R Ω ∪ N R's observation space O H (o H | ŝ) 1[o H = ŝ] H's observation function O R (o R | ŝ) 1[o R = ŝ], ŝ ∈ N O(o R | ŝ, else R's observation function T (ŝ | ŝ, a H , a R )        P 0 (ŝ ), ŝ = n k−1 , 1[ŝ = n i+1 ], ŝ = n i with i < k − 1 T (ŝ | ŝ, a R ), ŝ ∈ S and a R ∈ A, 1[s = s], else Transition function r θ (ŝ, a H , a R , ŝ )        −∞, ŝ ∈ N and a R / ∈ Q, −∞, ŝ ∈ S and a R ∈ Q, 0, ŝ ∈ N and a R ∈ Q, r θ (s, a R , s ), else Reward function π H (a H | o H , a R , θ) π H (a H | a R , θ), a R ∈ Q c 0 , else Human policy a R noop q 0 Distinguished noop action Technically r θ should not be allowed to return −∞. However, since S and A are finite, r θ is bounded, and so there exists some large finite negative number that is functionally equivalent to −∞ that we could use instead. Looking at the definitions, we can see T and r are independent of a H , and π H is independent of o H , making this a communicative assistance problem. By inspection, we can see that every q ∈ Q is a communicative robot action. Any a R / ∈ Q must not be a communicative action, because the reward r θ differs between a R and q 0 . Thus, the communicative robot actions are Q and the physical robot actions are A. Note that by construction of P S and T , we must have s i = n i for i ∈ {0, 1, . . . k − 1}, after which s k is sampled from P 0 and all s t ∈ S for t ≥ k. Given this, by inspecting r θ , we can see that an optimal policy must have a R 0:k−1 ∈ Q and a R k: / ∈ Q to avoid the −∞ rewards. Since a R k: / ∈ Q, we have a H k: = c 0 . Thus, setting a H noop = c 0 , we have that the assistance problem is two phase with actions at t act = k, as required. Let a policy π R for the assistance problem be reasonable if it never assigns positive probability to a R ∈ A when t < k or to a R ∈ Q when t ≥ k. Then, for any reasonable policy π R we can construct an analogous pair π R Q , f to the original problem P as follows: π R Q (q i | q 0:i−1 , c 0:i−1 ) π R (q i | o R 0:i−1 = n 0:i−1 , a R 0:i−1 = q 0:i−1 , a H 0:i−1 = c 0:i−1 ), f (q 0:k−1 , c 0:k−1 )(a t | o 0:t , a 0:t−1 ) π R (a t | o R 0:t+k , a R 0:t+k−1 , a H 0:t+k−1 ) , where for the second equation we have o R 0:k−1 = n 0:k−1 a R 0:k−1 = q 0:k−1 a H 0:k−1 = c 0:k−1 o R k:t+k = o 0:t a R k:t+k−1 = a 0:t−1 a H k:t+k−1 = a H noop Note that this is a bijective mapping. Consider some such policy π R and its analogous pair π R Q , f . By construction of T , we have that the first k states in any trajectory are n 0:k−1 and the next state is distributed as P 0 (•). By our assumption on π R we know that the first k robot actions must be selected from Q and the remaining robot actions must be selected from A, which also implies (based on π H ) that after the the remaining human actions must be c 0 . Finally, looking at r θ we can see that the first k timesteps get 0 reward. Thus: ER P (π R ) = E s 0 ∼P S ,θ∼P θ ,τ ∼ s 0 ,θ,π H ,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) = E θ∼P θ ,a R 0:k−1 ∼π R ,a H 0:k−1 ∼π H ,s k ∼P0,τ k: ∼ s k ,θ,π H ,π R ∞ t=k γ t r θ (s t , a H t , a R t , s t+1 ) = E θ∼P θ ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H ,s0∼P0,τ ∼ s0,θ,f (q 0:k−1 ,c 0:k−1 ) γ k ∞ t=0 γ t r θ (s t , a t , s t+1 ) = γ k E θ∼PΘ,q 0:k−1 ∼π R Q ,c 0:k−1 ∼π H [ER(f (q 0:k−1 , c 0:k−1 ))] , which is the objective of the reward learning problem scaled by γ k . Since we have a bijection between reasonable policies in P and tuples in P that preserves the objectives (up to a constant), given a solution π R * to P (which must be reasonable), its analogous pair π R Q , f must be a solution to P. Corollary 3. Every non-active reward learning problem M, C, Θ, r θ , P Θ , π H , k can be reduced to an equivalent two phase communicative assistance problem M , π H . Proof. Apply Proposition 6 followed by Proposition 2. \n B.2 ASSISTANCE WITH NO REWARD INFORMATION In a communicative assistance problem, once there is no information to be gained about θ, the best thing for R to do is to simply maximize expected reward according to its prior. We show this in the particular case where π H is independent of θ and thus cannot communicate any information about θ: Proposition 10. A communicative assistance problem M, π H where π H is independent of θ can be reduced to a POMDP M with the same state space. Proof. Given M = S, {A H , A R }, {Ω H , Ω R }, {O H , O R }, T, P S , γ, Θ, r θ , P Θ , we define a new POMDP as M = S, A R , Ω R , O R , T , r , P S , γ , with T (s | s, a R ) = T (s | s, a H φ , a R ) and r (s, a R , s ) = Eθ∼P θ r θ (s, a H φ , a R , s ) . Here, a H φ is some action in A H ; note that it does not matter which action is chosen since in a communicative assistance problem human actions have no impact on T and r. Expanding the definition of expected reward for the assistance problem, we get: ER(π R ) = E s0∼P S ,θ∼PΘ,τ ∼ s0,θ,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) = E s0∼P S E θ∼PΘ E τ ∼ s0,θ,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) Note that because π H (a H | o H , a R , θ ) is independent of θ, the robot gains no information about θ and thus π R is also independent of θ. This means that we have: ER(π R ) = E s0∼P S E θ∼PΘ E τ ∼ s0,π R ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) Let r max = max s,a H ,a R ,s |r θ (s, a H , a R , s )| (which exists since S, A H , and A R are finite). Then: ∞ t=0 γ t |r θ (s t , a H t , a R t , s )| ≤ ∞ t=0 γ t r max = r max 1 − γ < ∞. So we can apply Fubini's theorem to swap the expectations and sums. Applying Fubini's theorem twice gives us: ER(π R ) = E s0∼P S E τ ∼ s0,π R E θ∼PΘ ∞ t=0 γ t r θ (s t , a H t , a R t , s t+1 ) = E s0∼P S E τ ∼ s0,π R ∞ t=0 γ t E θ∼PΘ r θ (s t , a H t , a R t , s t+1 ) = E s0∼P S E τ ∼ s0,π R ∞ t=0 γ t r (s t , a R t , s t+1 ) . In addition, the trajectories are independent of π H , since the assistance problem is communicative, and so for a given policy π R , the trajectory distributions for M and M coincide, and thus the expected rewards for π R also coincide. Thus, the optimal policies must coincide. \n C EXPERIMENTAL DETAILS C.1 PLANS CONDITIONAL ON FUTURE FEEDBACK In the environment described in Section 4.1, R needs to bake either apple or blueberry pie (cherry is never preferred over apple) within 6 timesteps, and may query H about her preferences about the pie. Making the pie takes 3 timesteps: first R must make flour into dough, then it must add one of the fillings, and finally it must bake the pie. Baking the correct pie results in +2 reward, while baking the wrong one results in a penalty of -1. In addition, H might be away for several timesteps at the start of the episode. Querying H costs 0.1 when she is present and 3 when she is away. The optimal policy for this environment depends on whether H would be home early enough for R to query her and bake the desired the pie by the end of the episode. R should always quickly make dough, as that is always required. If H returns home on timestep 4 or earlier, R should wait for her to get home, ask her about her preferences and then finish the desired pie. If H returns home later, R should make its best guess about what she wants, and ensure that there is a pie ready for her to eat: querying H when she is away is too costly, and there is not enough time to wait for H, query her, put in the right filling, and bake the pie. In the wormy-apple environment described in Section 4.2, the robot had to bring the human some apples in order to make a pie, but there's a 20% chance that the apples have worms in them, and the robot does not yet know how to dispose of soiled apples. The robot gets 2 reward for making an apple pie (regardless of how it disposed of any wormy apples), and gets −2 reward if it disposes of the apples in the wrong container. Additionally, asking a question incurs a cost of 0.1. We solve this environment with exact value iteration. If the is two-phase, with a lower discount rate (λ = 0.9), R's policy never asks questions and instead simply tries to make the apple pie, guessing which bin to dispose of wormy apples in if it encounters any. Intuitively, since it would have to always ask the question at the beginning, it would always incur a cost of 0.1 as well as delay the pie by a timestep resulting in 10% less value, and this is only valuable when there turn out to be worms and its guess about which bin to dispose of them in is incorrect, which only happens 10% of the time. This ultimately isn't worthwhile. This achieves an expected undiscounted reward of 1.8. Removing the two-phase restriction causes R to ask questions mid-trajectory, even with this low discount. With this result achieves the maximal expected undiscounted reward of 1.98. With a higher discount rate of λ = 0.99, the two-phase policy will always ask about which bin to dispose of wormy apples in, achieving 1.9 expected undiscounted reward. This is still less than the policy without the two-phase restriction, which continues to get undiscounted reward 1.98 because it avoids asking a question 80% of the time, and so incurs the cost of asking a question less often. \n C.3 LEARNING FROM PHYSICAL ACTIONS: CAKE-OR-PIE EXPERIMENT In the environment described in Section 4.3, H wants a dessert, but R is unsure whether H prefers cake or pie. Preparing the more desired recipe provides a base value of V = 10, and the less desired recipe provides a base value of V = 1. Since H doesn't want the preparation to take too long, the actual reward when a dessert is made is given by r t = V • f (t), with f (t) = 1 − (t/N ) 4 , and N = 20 as the episode horizon. The experiments use the pedagogic H, that picks the chocolate first if they want cake, which allows R to distinguish the desired recipe early on -this is in contrast with the non-pedagogic H, which does not account for R beliefs and always goes for the dough first. With the pedagogic H, the optimal R does not move until H picks or skips the dough; if H skips the dough, this implies the recipe is cake and R takes the sugar, and then the cherries -otherwise it goes directly for the cherries. With the non-pedagogic H, the optimal R goes for the cherries first (since it is a common ingredient), and only then it checks whether H went for the chocolate or not, and has to go all the way back to grab the sugar if H got the chocolate. We train R with Deep Q-Networks (DQN;  (Mnih et al., 2013 )); we ran 6 seeds for 5M timesteps and a learning rate of 10 −4 ; results are shown in Figure  4 . \n D OPTION VALUE PRESERVATION In Section 4.1, we showed that R takes actions that are robustly good given its uncertainty over θ, but waits on actions whose reward will be clarified by future information about θ. Effectively, R is preserving its option value: it ensures that it remains capable of achieving any of the plausible reward functions it is uncertain over. A related notion is that of conservative agency  (Turner et al., 2020) , which itself aims to preserve an agent's ability to optimize a wide variety of reward functions. This is achieved via attainable utility preservation (AUP). Given an agent optimizing a reward r spec and a distribution over auxiliary reward functions r aux , the AUP agent instead optimizes the reward where the hyperparameter λ determines how much to penalize an action for destroying option value, and a φ is an action that corresponds to R \"doing nothing\". However, the existing AUP penalty is applied to the reward, which means it penalizes any action that is part of a long-term plan that destroys option value, even if the action itself does not destroy option value. For example, in the original Kitchen environment of Figure  1  with a sufficiently high λ, any trajectory that ends with baking a pie destroys option value and so would have negative reward. As a result, there is no incentive to make dough: the only reason to make dough is to eventually make a pie, but we have established that the value of making a pie is negative. What we need is to only penalize an action when it is going to immediately destroy option value. This can be done by applying the penalty during action selection, rather than directly to the reward: After this modification, the agent will correctly make dough, and stop since it does not know what filling to use. In an assistance problem, R will only preserve option value if it expects to get information that will resolve its uncertainty later: otherwise, it might as well get what reward it can given its uncertainty. Thus, we might expect to recover existing notions of option value preservation in the case where the agent is initially uncertain over θ, but will soon learn the true θ. Concretely, let us consider a fully observable communicative Assistance POMDP where the human will reveal θ on their next action. In that case, R's chosen action a gets immediate reward r(s, a) = Eθ [r θ (s, a)], and future reward Eθ∼P Θ ,s ∼T (•|s,a) [V θ (s )], where V θ (s) refers to the value of the optimal policy when the reward is known to be r θ and the initial state is s. Thus, the agent should choose actions according to: argmax a r AU P (s, a) = r spec (s, a) − λ E raux [max(Q raux (s, a φ ) − Q raux (s, a), 0)] \n π AU P (s) = argmax a Q rspec (s, a) − λ E raux [max(Q raux (s, a φ ) − Q raux (s, a), 0)] \n Note that unlike H, R does not observe the reward parameter θ, and must infer θ much like it does the hidden state. A fully observable assistance game is one in which both H and R can observe the full state. In such cases, we omit Ω H , Ω R , O H and O R . Since we have not yet specified how H behaves, it is not clear what the agent should optimize for. R's observations until time t, and τ H t for H's observations; thus R's policy can be written as π R (a R | o R t , τ R t−1 ), while H's can be written as π H (a H | o H t , a R t τ H t−1 , θ). \n\t\t\t Relative to Hadfield-Menell et al. (2016) , our definition allows for partial observability and requires that the initial distribution over S and Θ be independent. We also have H choose her action sequentially after R, rather than simultaneously with R, in order to better parallel the reward learning setting. \n\t\t\t t is drawn from the same distribution π H (• | o H t , a R t , θ), and a R t is drawn from the same distribution π R (• | o R t , τ R t−1 )).", "date_published": "n/a", "url": "n/a", "filename": "benefits_of_assistance_over_re.tei.xml", "abstract": "Much recent work has focused on how an agent can learn what to do from human feedback, leading to two major paradigms. The first paradigm is reward learning, in which the agent learns a reward model through human feedback that is provided externally from the environment. The second is assistance, in which the human is modeled as a part of the environment, and the true reward function is modeled as a latent variable in the environment that the agent may make inferences about. The key difference between the two paradigms is that in the reward learning paradigm, by construction there is a separation between reward learning and control using the learned reward. In contrast, in assistance these functions are performed as needed by a single policy. By merging reward learning and control, assistive agents can reason about the impact of control actions on reward learning, leading to several advantages over agents based on reward learning. We illustrate these advantages in simple environments by showing desirable qualitative behaviors of assistive agents that cannot be found by agents based on reward learning.", "id": "a99b3caf11ef06360b6030ad54067dda"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Xiao Fan Wang", "Guanrong Chen"], "title": "SYNCHRONIZATION IN SMALL-WORLD DYNAMICAL NETWORKS", "text": "Introduction Collective motions of coupled dynamical networks are of significant interest in many fields of science and technology. In particular, synchronization in networks of coupled chaotic dynamical systems has received a great deal of attention in recent years. Most of the existing work on synchronization of coupled networks assumes that the coupling configuration is completely regular (see e.g.  [Heagy et al., 1994; Wu & Chua, 1995] ), while a few studies address the issue of synchronization in randomly coupled networks  [Gade, 1996; Manrubia & Mikhailov, 1999] . However, many biological, technological and social networks are neither completely regular nor completely random. To interpolate between these two extremes,  Watts and Strogatz [1998]  introduced the interesting concept of small-world networks. The so-called small-world networks have intermediate connectivity properties but exhibit a high degree of clustering as in the regular networks and a small average distance between vertices as in the random networks. They also found that the small-world networks of coupled phase oscillators can synchronize almost as readily as the globally coupled networks, despite the fact that they have much fewer edges  [Watts, 1999] . For a review of recent works on small-world networks, see  [Newman, 2000] . More recently,  Gade and Hu [2000]  explored the stability of synchronous chaos in coupled map lattices with small-world connectivity and found that in this case synchronous chaos is possible even in the thermodynamic limit.  Lago-Fernandez et al. [2000]  also investigated the fast response and temporal coherent oscillations in a small-world network of Hodgkin-Huxley neurons. In this study, we consider synchronization in a network of linearly coupled identical continuoustime dynamical systems. As shown by  Wu [1995] , for any given number of cells, strong enough mutual diffusive coupling will result in synchronization of the cells. Two commonly studied coupling configurations are the so-called easiest-toimplement nearest-neighbor coupling and the most difficult-to-implement global coupling. It has been shown that for any given coupling strength, if the number of cells is large enough, the globally coupled network will eventually synchronize, while the nearest-neighbor coupled network cannot achieve such synchronization under the same condition. This observation naturally poses the following question: for a nearest-neighbor coupled network with a sufficiently large number of cells and with an arbitrary coupling strength, is it possible to achieve synchronization of the network by a small modification of the nearest-neighbor coupling configuration, for example, by adding a small fraction of connection between some different pairs of cells? In this paper we provide a positive answer to this question based on the small-world network models. \n Preliminaries We consider a network of N identical cells, linearly coupled through the first state variable of each cell, with each cell being an n-dimensional dynamical subsystem. The state equations of the entire network are ẋi1 = f 1 (x i ) + c N j=1 a ij x j1 ẋi2 = f 2 (x i ) . . . ẋin = f n (x i ) i = 1, 2, . . . , N (1) where x i = (x i1 , x i2 , . . . , x in ) ∈ R n are the state variables of cell i, f i (0) = 0, c > 0 represents the coupling strength, and A = (a ij ) N ×N is the coupling matrix. In this paper, we only consider symmetric and diffusive coupling. In particular, we assume that (i) A is a symmetric and irreducible matrix. (ii) The off-diagonal elements, a ij (i = j) of A, are either 1 or 0 (when a connection between cell i and cell j is absent). (iii) The elements of A satisfy a ii = − N j=1 j =i a ij , i = 1, 2, . . . , N (2) The above conditions imply that one eigenvalue of A is zero, with multiplicity 1, and all the other eigenvalues of A are strictly negative. Given the dynamics of an isolated cell and the coupling strength, stability of the synchronization state of the network can be characterized by those nonzero eigenvalues of the coupling matrix. A typical result states that the network will synchronize if these eigenvalues are negative enough  [Wu & Chua, 1995] . Lemma 1. Consider network (1). Let λ 1 be the largest nonzero eigenvalue of the coupling matrix A of the network. The synchronization state of network (1) defined by x 1 = x 2 = • • • = x n is asymp- totically stable, if λ 1 ≤ − T c (3) where c > 0 is the coupling strength of the network and T > 0 is a positive constant such that zero is an exponentially stable point of the n-dimensional system ż1 = f 1 (z) − T z 1 ż2 = f 2 (z) . . . żn = f n (z) (4) Note that system (4) is actually a single cell model with self-feedback −T z 1 . Condition (3) means that the entire network will synchronize provided that λ 1 is negative enough, e.g. it is sufficient to be less than −T/c, where T is a constant so that the self-feedback term −T z 1 could stabilize an isolated cell. As mentioned above, two commonly studied coupling configurations are the nearest-neighbor coupling and the global coupling ones. Experimentally, the nearest-neighbor coupling is perhaps the easiest one to implement and, on the contrary, the global coupling is the most expensive one to implement. The nearest-neighbor coupling configuration consists of cells arranged in a ring and coupled to the nearest neighbors. The corresponding coupling matrix is A nc =          −2 1 1 1 −2 1 . . . . . . . . . 1 −2 1 1 1 −2          (5) The eigenvalues of A nc are −4 sin 2 kπ N , k = 0, 1, . . . , N − 1 (6) Therefore, according to Lemma 1, the nearestneighbor coupled network will asymptotically synchronize if 4 sin 2 π N ≥ T c (7) The global coupled configuration means that any two different cells are connected directly. The corresponding coupling matrix is A gc =          −N + 1 1 1 • • • 1 1 −N + 1 1 • • • 1 . . . . . . . . . . . . . . . 1 1 1 • • • 1 1 1 1 • • • −N + 1          (8) Matrix A gc has a single eigenvalue at 0 and all the others equal to −N . Hence, Lemma 1 implies that this network will asymptotically synchronize if N ≥ T c (9) In summary, for any given coupling strength c > 0, the globally coupled network can synchronize as long as the number of cells N is large enough. On the other hand, since sin(π/N ) decreases to zero as N increases, relation (7) cannot hold for sufficiently large N . Simulations also that the nearestneighbor coupled network cannot synchronize if the number of cells is sufficiently large. Thus, we have seen a trade-off between these two situations. \n Synchronization in Small-World Networks Aiming to describe a transition from a regular network to a random network,  Watts and Strogatz [1998]  introduced an interesting model, now referred to as the small-world (SW) network. The original SW model can be described as follows. Take a onedimensional lattice of N vertices arranged in a ring with connections between only nearest neighbors. We \"rewire\" each connection with some probability, p. Rewiring in this context means shifting one end of the connection to a new vertex chosen at random from the whole lattice, with the constraint that no two different vertices can have more than one connection in between, and no vertex can have a connection with itself. Note, however, that there is a possibility for the SW model to be broken into unconnected clusters. This problem can be circumvented by a slight modification of the SW model, suggested by  Newman and Watts [1999] , which is referred to as the NW model hereafter. In the NW model, we do not break any connection between any two nearest neighbors. We add with probability p a connection between each other pair of vertices. Likewise, we do not allow a vertex to be coupled to another vertex more than once, or coupling of a vertex with itself. For p = 0, it reduces to the originally nearest-neighbor coupled system; for p = 1, it becomes a globally coupled system. In this paper, we are interested in the NW model with 0 < p < 1. From a coupling-matrix point of view, network (1) with small-world connections amount to that, in the nearest-neighbor coupling matrix A nc , if a ij = 0, we set a ij = a ji = 1 with probability p. Then, we recompute the diagonal elements according to formula (2). We denote the new small-world coupling matrix by A ns (p, N ) and let λ 1ns (p, N ) be its largest nonzero eigenvalue. According to Lemma 1, if λ 1ns (p, N ) ≤ − T c (10) then the corresponding network with small-world connections will synchronize. Figures  1 and 2  show the numerical values of λ 1ns (p, N ) as a function of the probability p and the number of cells N . In these figures, for each pair of values of p and N , λ 1ns (p, N ) is obtained by averaging the results of 20 runs. It can be seen that (i) For any given value of N , λ 1ns (p, N ) decreases to −N as p increases from 0 to 1. (ii) For any given value of p ∈ (0, 1], λ 1ns (p, N ) decreases to −∞ as N increases to +∞. The above results imply that, for any given coupling strength c > 0, we have (i) For any given N > T/c, there exists a critical value p so that if p ≤ p ≤ 1, then the smallworld connected network will synchronize. (ii) For any given p ∈ (0, 1], there exists a critical value N so that if N ≥ N , then the small-world connected network will synchronize.  \n Synchronization in a Network of Small-World Coupled Chua's Circuits As an example, we now study synchronization in a network of small-world connected Chua's circuits. In the dimensionless form, a single Chua's circuit is described by  [Chua et al., 1993] :    ẋ1 ẋ2 ẋ3    =    α(x 2 − x 1 + f (x 1 )) x 1 − x 2 + x 3 −βx 2 − γx 3    (11) where f (•) is a piecewise-linear function, f (x 1 ) =      −bx 1 − a + b x 1 > 1 −ax 1 |x 1 | ≤ 1 −bx 1 + a − b x 1 < −1 (12) in which α > 0, β > 0, γ > 0, and a < b < 0. The state equations of the entire network are    ẋi1 ẋi2 ẋi3    =        α(x i2 − x i1 + f (x i1 )) + c N j=1 a ij x j1 x i1 − x i2 + x i3 −βx i2 − γx i3        , i = 1, 2, . . . , N . (13) For this network to synchronize, according to Lemma 1, we may take T = −α. In simulations, the system parameters are chosen to be  For this set of parameters, Chua's circuit (11) has a chaotic attractor, as shown in Fig.  3 . The nearestneighbor coupled Chua's network cannot synchronize for N > 6. According to Lemma 1, the smallworld network will synchronize if λ 1ns (p, N ) ≤ a c = −1.27 (15) Figure  4  shows the values of p and N which can achieve network synchronization. For example, for N = 100, 150 and 200, synchronization of the small-world connected network can be achieved, for p > 0.0366, p > 0.0257 and p > 0.021, respectively. \n Conclusions Starting with a nearest-neighbor coupled dynamical network, we can construct a small-world dynamical network by adding with probability p a connection between each of the other pair of cells. We found that, for any given coupling strength and a sufficiently large number of cells, synchronization in a network of linearly small-world coupled continuoustime dynamical systems can be achieved with a small value of p. In other words, the ability of achieving synchronization in an originally nearestneighbor coupled system can be greatly enhanced by simply adding a small fraction of new connection, revealing an advantage of small-world network for chaos synchronization. Fig. 1 .Fig. 2 . 12 Fig. 1. Numerical values of λ1ns(p, N) as a function of the probability p: (a) N = 200; (b) N = 500. \n α Fig. 3. Chaotic attractor of Chua's circuit (11), with parameters given in (14). \n Fig. 4 . 4 Fig. 4. Values of p and N achieving synchronization in the small-world network of Chua's circuits.", "date_published": "n/a", "url": "n/a", "filename": "WaCh02.tei.xml", "abstract": "We investigate synchronization in a network of continuous-time dynamical systems with smallworld connections. The small-world network is obtained by randomly adding a small fraction of connection in an originally nearest-neighbor coupled network. We show that, for any given coupling strength and a sufficiently large number of cells, the small-world dynamical network will synchronize, even if the original nearest-neighbor coupled network cannot achieve synchronization under the same condition.", "id": "954f5064c2e30083e850521d7a2987f4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Daniel S Bernstein", "Robert Givan", "Neil Immerman", "Shlomo Zilberstein"], "title": "THE COMPLEXITY OF DECENTRALIZED CONTROL OF MARKOV DECISION PROCESSES", "text": "1. Introduction. Markov decision processes (MDPs) have received considerable attention, and there exist well-known algorithms for finding optimal control strategies in the case where a process is centrally controlled and the controller (or agent) has access to complete state information  (Puterman 1994) . Less well understood is the case in which a process is controlled by multiple cooperating distributed agents, each with possibly different information about the state. We are interested in studying how hard these decentralized control problems are relative to analogous centralized control problems, from the point of view of computational complexity. In particular, we consider two different models of decentralized control of MDPs. One is a generalization of a partially observable Markov decision process (POMDP), which we call a decentralized partially observable Markov decision process (DEC-POMDP). In a DEC-POMDP, the process is controlled by multiple distributed agents, each with possibly different information about the state. The other is a generalization of an MDP, called a decentralized Markov decision process (DEC-MDP). A DEC-MDP is a DEC-POMDP with the restriction that at each time step the agents' observations together uniquely determine the state. The MDP, POMDP, and DEC-MDP can all be viewed as special cases of the DEC-POMDP. The relationships among the models are shown in Figure  1 . A number of different problems can be viewed as decentralized control of a Markov process. For example, consider problems involving the control of multiple distributed robots, such as robotic soccer  (Coradeschi et al. 2000) . In these domains, it is necessary to develop a strategy for each robot under the assumption that the robots will have limited ability to communicate when they execute their strategies. Another problem that fits naturally within this framework is the distributed control of a power grid  (Schneider et al. 1999) . Finally, several types of networking problems can be viewed within this framework  (Altman 2001) . It would be beneficial to have general-purpose algorithms for solving these decentralized control problems. An algorithm for similar problems was proposed by  Ooi et al. (1996) . Under the assumption that all agents share state information every K time steps, the authors developed a dynamic programming algorithm to derive optimal policies. A downside of this approach is that the state space for the dynamic programming algorithm grows doubly exponentially with K. The only known tractable algorithms for these types of problems rely on even more assumptions. One such algorithm was developed by  Hsu and Marcus (1982)  and works under the assumption that the agents share state information every time step (although it can take one time step for the information to propagate). Approximation algorithms have also been developed for these problems, although they can at best give guarantees of local optimality. For instance,  Peshkin et al. (2000)  studied algorithms that perform gradient descent in a space of parameterized policies. Is there something inherent in these problems that forces us to add assumptions and/or use approximation algorithms?  Papadimitriou and Tsitsiklis (1982)  presented some results aimed at answering this question. The authors proved that a simple decentralized decisionmaking problem is NP-complete, even with just two decision makers. They later noted that this implies that decentralized control of MDPs must be NP-hard  (Papadimitriou and Tsitsiklis 1986) . We strengthen this result by showing that both the DEC-POMDP and DEC-MDP problems are NEXP-hard, even when the horizon is limited to be less than the number of states (and they are NEXP-complete in the latter case). Although it is not known whether the classes P, NP, and PSPACE are distinct, it is known that P = NEXP, and thus the problems we consider are provably intractable. Furthermore, assuming EXP = NEXP, the problems take superexponential time to solve in the worst case. This result is in contrast to the best known bounds for MDPs (P-hard) and POMDPs (PSPACE-hard)  (Papadimitriou and Tsitsiklis 1987, Mundhenk et al. 2000) . Thus, we have gained insight into the possibility of a fundamental difference between centralized and decentralized control of Markov decision processes. In §2, we give a brief review of the concepts we will need from complexity theory. In §3, we define the MDP and POMDP models. Section 4 contains the definitions of the DEC-MDP and DEC-POMDP models, and a proof that the short-horizon versions of these problems fall within the complexity class NEXP. In §5, we present our main complexity result-a proof that these decentralized problems are NEXP-hard. Finally, §6 contains our conclusions. 2. Computational complexity. In this section, we give a brief introduction to the theory of computational complexity. More detail can be found in  Papadimitriou (1994) . A complexity class is a set of problems where a problem is an infinite set of problem instances, each of which has a \"yes\" or \"no\" answer. To discuss the complexity of optimization problems, we must have a way of converting them to \"yes/no\" problems. The typical way this is done is to set a threshold and ask whether or not the optimal solution yields a reward that is no less than this threshold. The problem of actually finding the optimal solution can, of course, be no easier than the threshold problem. The first complexity class we consider is P, the set of problems that can be solved in polynomial time (in the size of the problem instance) on a sequential computer. NP is the set of problems that can be solved nondeterministically in polynomial time. A nondeterministic machine automatically knows the correct path to take any time there is a choice as to how the computation should proceed. An example of a problem that can be solved nondeterministically in polynomial time is deciding whether a sentence of propositional logic is satisfiable. The machine can guess an assignment of truth values to variables and evaluate the resulting expression in polynomial time. Of course, nondeterministic machines do not really exist, and the most efficient known algorithms for simulating them take exponential time in the worst case. In fact, it is strongly believed by most complexity theorists that P = NP (but this has not been proven formally). Complexity can also be measured in terms of the amount of space a computation requires. One class, PSPACE, includes all problems that can be solved in polynomial space. Any problem that can be solved in polynomial time or nondeterministic polynomial time can be solved in polynomial space (i.e., P ⊆ NP ⊆ PSPACE)-that P ⊆ PSPACE can be seen informally by observing that only polynomially much space can be accessed in polynomially many time steps. Moving up the complexity hierarchy, we have exponential time (EXP) and nondeterministic exponential time (NEXP). By exponential time, we mean time bounded by 2 n k , where n is the input size and k > 0 is a constant. It is known that PSPACE ⊆ EXP ⊆ NEXP, and it is believed that EXP = NEXP (but again this has not been proven). It has been proven that the classes P and EXP are distinct, however. The notion of a reduction is important in complexity theory. We say that a problem A is reducible to a problem B if any instance x of A can be converted into an instance f x of B such that the answer to x is \"yes\" if and only if the answer to f x is \"yes.\" A problem A is said to be hard for a complexity class C (or C-hard) if any problem in C is efficiently reducible to A. If the complexity class in question is P, efficient means that f x can be computed using at most logarithmic space, while for the classes above P, efficient means that f x can be computed using at most polynomial time. A problem A is said to be complete for a complexity class C (or C-complete) if (a) A is contained in C, and (b) A is hard for C. For instance, the satisfiability problem mentioned above is NP-complete and P-hard. However, unless P = NP, satisfiability is not P-complete. 3. Centralized models. In this paper, we consider discrete-time finite sequential decision processes under the undiscounted finite-horizon optimality criterion. We build into our problem definitions the (unusual) assumption that the horizon is less than the number of states. Note that this assumption actually strengthens the hardness results; the general problems must be at least as hard as their short-horizon counterparts. Unfortunately, the assumption is needed for each of the upper bounds given below. Finding tight upper bounds for problems with arbitrary horizons remains an open problem  (Blondel and Tsitsiklis 1999, §5) . Below we describe the partially observable Markov decision process and its associated decision problem. The Markov decision process is viewed as a restricted version of this model. A partially observable Markov decision process (POMDP) is defined as follows. We are given a tuple, S A P R O T K , where • S is a finite set of states, with distinguished initial state s 0 . • A is a finite action set. • P is a transition probability table. P s a s is a rational representing the probability of transitioning from s to s on taking action a. Here s s ∈ S and a ∈ A. • R is a reward function. R s a s is a rational representing the reward obtained from taking action a from state s and transitioning to state s . Again, s s ∈ S and a ∈ A. • is a finite set of observations. • O is a table of observation probabilities. O s a s o is a rational representing the probability of observing o when taking action a in state s and transitioning to state s as a result. Here s s ∈ S, a ∈ A, and o ∈ . • T is a positive integer representing the horizon (and T < S ). • K is a rational representing the threshold value. A POMDP is fully observable if there exists a mapping J → S such that whenever O s a s o is nonzero, J o = s . A Markov decision process (MDP) is defined to be a POMDP that is fully observable. A policy is defined to be a mapping from sequences of observations ō = o 1 • • • o t over to actions in A. We wish to find a policy that maximizes the expected total return over the finite horizon. The definitions below are used to formalize this notion. We use the symbol to denote the empty observation sequence. For an observation sequence ō = o 1 • • • o t , ōo is taken to represent the sequence o 1 • • • o t o. Definition. The probability of transitioning from a state s to a state s following policy while the agent sees observation sequence ō, written P s ō s , can be defined recursively as follows: P s s = 1 P s ōo s = q∈S P s ō q P q ō s O q ō s o where is the empty sequence. Definition. The value V T s of following policy from state s for T steps is given by the following equation: V T s = ō q∈S s ∈S P s ō q P q ō s R q ō s where the observation sequences have length at most T − 1. The decision problem corresponding to a finite-horizon POMDP is as follows. Given a POMDP D = S A P R O T K , is there a policy for which V T s 0 equals or exceeds K? It was shown in  Papadimitriou and Tsitsiklis (1987)  that the decision problem for POMDPs is PSPACE-complete and that the decision problem for MDPs is P-complete. 4. Decentralized models. We now describe extensions to the aforementioned models that allow for decentralized control. In these models, at each step, each agent receives a local observation and subsequently chooses an action. The state transitions and rewards received depend on the vector of actions of all the agents. A decentralized partially observable Markov decision process (DEC-POMDP) is defined formally as follows (for ease of exposition, we describe the two-agent case). We are given S A 1 A 2 P R 1 2 O T K , where • S is a finite set of states, with distinguished initial state s 0 . • A 1 and A 2 are finite action sets. • P is a transition probability table. P s a 1 a 2 s is a rational representing the probability of transitioning from s to s on taking actions a 1 a 2 . Here s s ∈ S, a 1 ∈ A 1 , and a 2 ∈ A 2 . • R is a reward function. R s a 1 a 2 s is a rational representing the reward obtained from taking actions a 1 a 2 from state s and transitioning to state s . Again s s ∈ S, a 1 ∈ A 1 , and a 2 ∈ A 2 . • 1 and 2 are finite sets of observations. • O is a table of observation probabilities. O s a 1 a 2 s o 1 o 2 is a rational representing the probability of observing o 1 o 2 when taking actions a 1 a 2 in state s and transitioning to state s as a result. Here s s ∈ S, a 1 ∈ A 1 , a 2 ∈ A 2 , o 1 ∈ 1 , and o 2 ∈ 2 . • T is a positive integer representing the horizon (and T < S ). • K is a rational representing the threshold value. A DEC-POMDP generalizes a POMDP by allowing for control by multiple distributed agents that together may not fully observe the system state (so we have only partial observability). We also define a generalization of MDP problems by requiring joint observability. We say that a DEC-POMDP is jointly observable if there exists a mapping J 1 × 2 → S such that whenever O s a 1 a 2 s o 1 o 2 is nonzero, J o 1 o 2 = s . We define a decentralized Markov decision process (DEC-MDP) to be a DEC-POMDP that is jointly observable. We define a local policy for agent i, i , to be a mapping from local histories of observations ōi = o i1 • • • o it over i , to actions in A i . A joint policy, = 1 2 , is defined to be a pair of local policies, one for each agent. We wish to find a joint policy that maximizes the expected total return over the finite horizon. As in the centralized case, we need some definitions to make this notion more formal. Definition. The probability of transitioning from a state s to a state s following joint policy = 1 2 while agent 1 sees observation sequence ō1 and agent 2 sees ō2 of the same length, written P s ō1 ō2 s , can be defined recursively as follows: P s s = 1 P s ō1 o 1 ō2 o 2 s = q∈S P s ō1 ō2 q P q 1 ō1 2 ō2 s O q 1 ō1 2 ō2 s o 1 o 2 where is the empty sequence. Definition. The value V T s of following policy = 1 2 from state s for T steps is given by the following equation: V T s = ō1 ō2 q∈S s ∈S P s ō1 ō2 q P q 1 ō1 2 ō2 s R q 1 ō1 2 ō2 s where the observation sequences are of length at most T − 1, and both sequences in any pair are of the same length. The decision problem is stated as follows. Given a DEC-POMDP D = S A 1 A 2 P R 1 2 O T K , is there a joint policy for which V T s 0 equals or exceeds K? We let DEC-POMDP m and DEC-MDP m denote the decision problems for the m-agent DEC-POMDP and the m-agent DEC-MDP, respectively. We conclude this section by showing a straightforward upper bound on the worst-case time complexity of DEC-POMDP m for any m ≥ 2. Because any DEC-MDP is trivially a DEC-POMDP, this upper bound also applies to DEC-MDP m . Theorem 1. For all m ≥ 2, DEC-POMDP m ∈ NEXP. Proof. We must show that a nondeterministic machine can solve any instance of DEC-POMDP m using at most exponential time. First, a joint policy can be \"guessed\" and written down in exponential time. This is because a joint policy consists of m mappings from local histories to actions; and because T < S , all histories have length less than S . A DEC-POMDP together with a joint policy can be viewed as a POMDP together with a policy, where the observations in the POMDP correspond to the observation m-tuples in the DEC-POMDP (one from each agent), and the POMDP actions correspond to m-tuples of DEC-POMDP actions (again, one from each agent). In exponential time, each of the exponentially many possible sequences of observations can be converted into a belief state (i.e., a probability distribution over the state set giving the probability of being in each state after seeing the given observation sequence). We note that every POMDP  (Kaelbling et al. 1998 ) is equivalent to a \"belief-state MDP\" whose state set is the set of reachable belief states of the POMDP. The transition probabilities and expected rewards for the corresponding exponential-sized belief-state MDP can be computed in exponential time. Using standard MDP solution techniques  (Puterman 1994) , it is possible to determine whether the guessed policy yields expected reward at least K in this belief-state MDP in time that is at most polynomial in the size of the belief-state MDP, which is exponential in the size of the original DEC-POMDP problem. Therefore, there exists an accepting computation path if and only if there is a policy that can achieve reward K. 5. Decentralized control of MDPs is NEXP-hard. We now turn our attention to proving that the upper bound just shown in Theorem 1 is tight-specifically, we show that NEXP is also a lower bound for the worst-case time complexity of decentralized problems by showing that any problem in the class NEXP can be reduced in polynomial time to a DEC-MDP 2 problem. It then follows that both DEC-MDP m and DEC-POMDP m are NEXPcomplete for any m ≥ 2. The proof of this lower bound is quite involved and will occupy most of the remainder of this paper. Each subsection of this section contains a piece of the development, and at the end of the section the main theorem is asserted. We begin by introducing the known NEXP-complete problem TILING used in the proof. We then present an overview of the proof and its major constituents. Next we present the reduction from TILING formally, and finally we prove that the reduction is correct. 5.1. The TILING problem. We can show this lower bound by reducing any NEXPcomplete problem to DEC-MDP 2 using a polynomial-time algorithm. For our reduction, we use an NEXP-complete problem called TILING  (Lewis 1978 , Papadimitriou 1994  501), which is described as follows. We are given a board size n (represented compactly in binary), a set of tile types L = tile-0 tile-k , and a set of binary horizontal and vertical compatibility relations H V ⊆ L × L. A tiling is a mapping f 0 n − 1 × 0 n − 1 → L. A tiling f is consistent if and only if (a) f 0 0 = tile-0, and (b) for all x y f x y f x + 1 y ∈ H , and f x y f x y + 1 ∈ V . The decision problem is to determine, given L, H , V , and n, whether a consistent tiling exists. An example of a tiling instance and a corresponding consistent tiling is shown in Figure  2 . H = V = L = n = 4 a consistent tiling 0 1 2 3 0 1 2 3 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 2 2 2 2 2 2 Figure 2. An example of a tiling instance. In the remainder of this section, we assume that we have fixed an arbitrarily chosen instance of the tiling problem, so that L, H , V , and n are fixed. We then construct an instance of DEC-MDP that is solvable if and only if the selected tiling instance is solvable. We note that the DEC-MDP instance must be constructible in time polynomial in the size of the tiling instance (which in particular is logarithmic in the value of n), which will require the DEC-MDP instance to be at most polynomially larger than the tiling instance. 5.2. Overview of the reduction. The basic idea of our reduction is to create a twoagent DEC-MDP that randomly selects two tiling locations bit by bit, informing one agent of the first location and the other agent of the second location. The agents' local policies are observation-history based, so the agents can base their future actions on the tiling locations given to them. After generating the locations, the agents are simultaneously \"queried\" (i.e., a state is reached in which their actions are interpreted as answers to a query) for a tile type to place at the location given. We design the DEC-MDP problem so that the only way the agents can achieve nonnegative expected reward is to base their answers to the query on a single, jointly understood tiling that meets the constraints of the tiling problem. This design is complicated because the DEC-MDP state set itself cannot remember which tiling locations were selected (this would cause exponential blowup in the size of the state set, but our reduction must expand the problem size at most polynomially-we note that the tiling grid itself is not part of the tiling problem size, only the compactly represented grid size n is in the problem specification); the state will contain only certain limited information about the relative locations of the two tile positions. The difficulty of the design is also increased by the fact that any information remembered about the specified tiling locations must be shared with at least one of the agents to satisfy the joint observability requirement. To deal with these two issues, we have designed the DEC-MDP to pass through the following phases (a formal description follows later): Select Phase: Select two bit indices and values, each identifying a bit position and the value at that position in the location given to one of the agents. These are the only bits that are remembered in the state set from the locations given to the agents in the next phase-the other location bits are generated and forgotten by the process. The bit values remembered are called value-1 and value-2, and the indices to which these values correspond are called index-1 and index-2. Bit index-1 of the address given to agent 1 will have the value value-1, likewise for index-2, value-2, and agent 2. Generate Phase: Generate two tile locations at random, revealing one to each agent. The bits selected in the above select phase are used, and the other location bits are generated at random and immediately \"forgotten\" by the DEC-MDP state set. Query Phase: Query each agent for a tile type to place in the location that was specified to that agent. These tile types are remembered in the state. Echo Phase: Require the agents to echo the tile locations they received in the generate phase bit by bit. To enforce the accuracy of these location echoes, the DEC-MDP is designed to yield a negative reward if the bit remembered from the original location generation is not correctly echoed (the DEC-MDP is designed to ensure that each agent cannot know which bit is being checked in its echoes). As the agents echo the bits, the process computes state information representing whether the locations are equal or adjacent horizontally or vertically, and whether the agents' locations are both 0 0 (again, we cannot just remember the location bits because it would force an exponential state set). The echo phase allows us to compute state information about adjacency/equality of the locations after the tile types have been chosen, so that the agents' tile choices cannot depend on this information. This is critical in making the reduction correct. Test Phase: Check whether the tile types provided in the query phase come from a single consistent tiling. In other words, check that if the agents were asked for the same location they gave the same tile types during query, if they were asked for adjacent locations they gave types that satisfy the relevant adjacency constraints, and if the agents were both queried for location 0 0 they both gave tile type tile-0. The process gives a zero reward only if the tile types selected during the query phase meet any applicable constraints as determined by the echoed location bits. Otherwise, a negative reward is obtained. Note that because we are designing a DEC-MDP, we are required to maintain joint observability: The observations given to the agents at each time step must be sufficient to reconstruct all aspects of the DEC-MDP state at that time step. In particular, the bit indices and values selected in the select phase must be known to the agents (jointly), as well as the information computed in the echo phase regarding the relative position of the two locations. We achieve this joint observability by making all aspects of the DEC-MDP state observable to both agents, except for the indices and values selected in the select phase and the tile types that are given by the agents (and stored by the process) during the query phase. Each agent can observe which bit index and value are being remembered from the other agent's location, and each agent can observe the stored tile type it gave (but not the tile type given by the other agent). Because each agent can see what bit is saved from the other agent's location, we say that one location bit of each agent's location is visible to the other agent. We call the five phases just described \"select,\" \"generate,\" \"query,\" \"echo,\" and \"test\" in the development below. A formal presentation of the DEC-MDP just sketched follows below, but first we outline the proof that this approach represents a correct reduction. \n Overview of the correctness proof. Here we give an overview of our argument that the reduction sketched above is correct in the sense that there exists a policy that achieves expected total reward zero at the start state if and only if there is a solution to the tiling problem we started with. It is straightforward to show that if there exists a consistent tiling there must exist a policy achieving zero reward. The agents need only agree on a consistent tiling ahead of time and base their actions on the agreed-on tiling (waiting during selection and generation, giving the tile type present at the generated location during query, faithfully echoing the generated location during echo, and then waiting during test, at each point being guaranteed a zero reward by the structure of the problem). Note that it does not matter how expensive it might be to find and represent a consistent tiling or to carry out the policy just described because we are merely arguing for the existence of such a policy. We now outline the proof of the harder direction, that if there is no consistent tiling then there is no policy achieving expected reward zero. Note that because all rewards are nonpositive, any chance of receiving any negative reward forces the expected total reward to be negative. Consider an arbitrary policy that yields expected reward zero. Our argument rests on the following claims, which will be proved as lemmas in §5.5: Claim 1. The policy must repeat the two locations correctly during the echo phase. Claim 2. When executing the policy, the agents' selected actions during the query phase determine a single tiling, as follows. We define a query situation to be dangerous to an agent if and only if the observable bit value of the other agent's location (in the observation history) agrees with the bit value at the same index in the agent's own location (so that as far as the agent in danger knows, the other agent is being queried about the same location). During dangerous queries, the tile type selected by the agent in danger must depend only on the location queried (and not on the index or value of the bit observed from the other agent, on any other observable information, or on which agent is selecting the tile type). The agents' selected actions for dangerous queries thus determine a single tiling. Claim 3. The single tiling from Claim 2 is a consistent tiling. Claim 3 directly implies that if there is no consistent tiling, then all policies have negative expected reward, as desired. 5.4. Formal presentation of the reduction. Now we give the two-agent DEC-MDP D = S A 1 A 2 P R 1 2 O T K that is constructed from the selected tiling instance L H V n . We assume throughout that n is a power of two. It is straightforward to modify the proof to deal with the more general case-one way to do so is summarized briefly in Appendix A. 5.4.1. The state set. We describe the state set S of D below by giving a sequence of finite-domain \"state variables\" and then taking the state set to be the set of all possible assignments of values to the state variables. The finite-state automaton. One of the state variables will be maintained by a finitestate automaton (FSA), described in Appendix A. This variable, called rel-pos because it maintains a record of the relative position of the two location addresses echoed by the agents in the echo phase, can take on values from the state set of the FSA. Appendix A describes state set Q and also defines two functions (FSANEXT and FSA) based on the underlying FSA. These functions allow us to refer to the critical FSA behaviors here in our reduction while deferring most other details of the FSA to Appendix A. The function FSANEXT updates the state variable rel-pos based on one more bit of echoed location from each agent. The function FSA updates the state variable rel-pos based on a sequence of echoed location bits from each agent-so FSA is defined as a repeated application of the function FSANEXT. Appendix A also describes distinguished subsets of the FSA state set Q called apart, equal, hor, and ver representing possible relative positions for pairs of locations (not adjacent or equal, equal, horizontally adjacent, and vertically adjacent, respectively). These subsets are used below in defining the transition and reward behavior of the DEC-MDP D. Appendix A also defines the initial state q 0 of the FSA. The state variables. We now list the state variables defining the state set for D. We list the variables in three groups: the first group is observable to both agents, the second group only to agent 1, and the third group only to agent 2. These restrictions on observability are described in §5. We write a state by enumerating its variable values, e.g., as follows: gen 3 yes q 0 4 0 1 tile-1 5 1 0 tile-3 ∈ S. Semicolons are used to group together variables that have the same observability properties. We can represent sets of states by writing sets of values in some of the components of the tuple rather than just values. The * symbol is used to represent the set of all possible values for a component. We sometimes use a state variable as a function from states to domain values for that variable. For instance, if q matches gen * * * * * * * * * * * , then we will say phase q = gen. The initial state s 0 is as follows: select 0 yes q 0 0 0 0 tile-0 0 0 0 tile-0 . 5.4.2. The action sets and table of transition probabilities. We must allow \"wait\" actions, \"zero\" and \"one\" actions for echoing location address bits, and tile-type actions from the set of tile types L for answering during the query phase. We therefore take the action sets A 1 = A 2 to be wait 0 1 ∪ L. We give the transition distribution P s a 1 a 2 s for certain action pairs a 1 a 2 for certain source states s. For any source-state/action-pair combination not covered by the description below, the action pair is taken to cause a probability 1.0 self-transition back to the source state. The combinations not covered are not reachable from the initial state under any joint policy. Also, we note that the FSA-controlled state component rel-pos does not change from its initial state q 0 until the echo phase. Select phase. This is the first step of the process. In this step, the process chooses, for each agent, which of that agent's bits it will be checking in the echo phase. The value of that bit is also determined in this step. Transition probabilities when phase = select are given as follows: P s a 1 a 2 s = 1 4 log n 2 in the following situations: s = s 0 = select 0 yes q 0 0 0 0 tile-0 0 0 0 tile-0 s = gen 0 yes q 0 i 2 v 2 0 tile-0 i 1 v 1 0 tile-0 i 1 i 2 ∈ 0 2 log n − 1 and v 1 v 2 ∈ 0 1 Generate phase. During these steps, the two tile positions are chosen bit by bit. Note that we have to check for whether we are at one of the bits selected during the select phase, so that the value of the bit is the same as the value chosen during selection. Transition probabilities when phase = generate are given as follows. The second case describes the deterministic transition from the generate phase to the query phase. P s a 1 a 2 s = 1 h in the following situations: s = gen k yes q 0 i 2 v 2 * tile-0 i 1 v 1 * tile-0 where 0 ≤ k ≤ 2 log n − 1 s = gen k + 1 yes q 0 i 2 v 2 b 1 tile-0 i 1 v 1 b 2 tile-0 where b 1 = v 1 if k = i 1 else b 1 is either 0 or 1 b 2 = v 2 if k = i 2 else b 2 is either 0 or 1, and h is the number of allowed settings of b 1 b 2 from the previous two lines. P s a 1 a 2 s = 1 in the following situations: s = gen 2 log n yes q 0 i 2 v 2 * tile-0 i 1 v 1 * tile-0 and s = query 0 yes q 0 i 2 v 2 0 tile-0 i 1 v 1 0 tile-0 Query phase. The query phase consists of just one step, during which each agent chooses a tile type. Transition probabilities when phase = query are given as follows: P s a 1 a 2 s = 1 in the following situations: s = query 0 yes q 0 i 2 v 2 0 tile-0 i 1 v 1 0 tile-0 t 1 = a 1 if a 1 ∈ L tile-0 otherwise t 2 = a 2 if a 2 ∈ L tile-0 otherwise and s = echo 0 yes q 0 i 2 v 2 0 t 1 i 1 v 1 0 t 2 Echo phase. During the echo phase the agents are asked to repeat back the addresses seen in the generate phase, and information about the relative position of the addresses is calculated by the FSA described in Appendix A and recorded in the state. The FSA is accessed here using the function FSANEXT described in Appendix A. Transition probabilities when phase = echo are given as follows: P s a 1 a 2 s = 1 in the following situations: P s a 1 a 2 s = 1 in the following situations: s = test 0 * * * * 0 * * * 0 * and s = test 0 yes q 0 0 0 0 tile-0 0 0 0 tile-0 5.4.3. The reward function. We now describe the reward function for D. The reward R s a 1 a 2 s given when transitioning from state s to state s taking action pair a 1 a 2 is −1 in any situation except those situations matching one of the following patterns. Roughly, we give zero reward for waiting during select and generate, for answering with a tile type during query, for echoing a bit consistent with any remembered information during echo, and for having given tile types satisfying the relevant constraints during test. The relevant constraints during test are determined by the rel-pos state component computed by the FSA during the echo phase. s = echo k o q i 2 v 2 0 t 1 i 1 v 1 0 t 2 b 1 = a 1 if a 1 ∈ 0 1 0 otherwise b 2 = a 2 if a 2 ∈ 0 1 0 otherwise s = p k o FSANEXT q b 1 b 2 i 2 v 2 0 t 1 i 1 v 1 0 t 2 where p k = echo k + 1 for 0 ≤ k < 2 log n − 1 test 0 for k = 2 log R s a 1 a 2 s = 0 if and only if one of the following holds: The first four component fields of each state description are fully visible to both agents. The last eight state component fields are split into two groups of four, each group visible to only one agent. We therefore take the agent 1 observations 1 to be partial assignments to the following state variables: phase, index, origin, rel-pos, index-2, value-2, pos-bit-1, and tile-sel-1. Similarly, the observations 2 are partial assignments to the following state variables: phase, index, origin, rel-pos, index-1, value-1, pos-bit-2, and tile-sel-2. The observation distribution O s a 1 a 2 s o 1 o 2 simply reveals the indicated portion of the just-reached state s to each agent deterministically. We say that an observation sequence is p-phase if the sequence matches the pattern * p * * * * * * * , where the first \"*\" stands for any observation sequence. Here, p can be any of gen, query, echo, or test. We take the horizon T to be 4 log n + 4, because the process spends one step in each of the select, query, and test phases, 2 log n + 1 steps in the generate phase, and 2 log n steps in the echo phase. We take the threshold value K to be 0. This completes the construction of the DEC-MDP by polynomial-time reduction from the selected tiling instance. An example of a zero-reward trajectory of the process is shown in Figure  3 . We now turn to correctness. \n Formal correctness argument. Next we show that the reduction presented above is indeed correct. Our main claim is that there exists a policy that achieves expected total reward zero at the start state if and only if there is a solution to the tiling problem we started with. To make our notation easier to read, we define the following abbreviations. Definition. Given an observation sequence ō1 over 1 , we write loc 1 ō1 for the location value represented by the bits transmitted to agent 1 in the generate phase of the process. We note that during the select and generate phases this value may be only partially specified (because not all of the bits have been generated). More precisely, loc 1 ō1 = b k • • • b 0 , where the b i values are chosen by the first match of the following sequence in ō1 (with k as large as possible while allowing a match): gen 1 * * * * b 0 * • • • gen k + 1 * * * * b k * We define loc 2 ō2 similarly. In addition, we define bit i l to be b i , where b k b 0 is the binary coding of the (possibly only partially specified) location l-we take bit i l to be undefined if the bit i is not specified in location l. By abuse of notation we treat loc 1 ō1 (or loc 2 ō2 ) as a tiling location x y sometimes (but only when it is fully specified) and as a bit string at other times. The easier direction of correctness is stated in the following lemma, which is formally proven in Appendix B. Lemma 1. If there exists a consistent tiling, then there must exist a policy achieving zero expected total reward. phase = gen index = 0 index-2 = 1 value-2 = 1 index-1 = 2 value-1 = 1 phase = gen index = 1 pos-bit-1 = 1 index-2 = 1 value-2 = 1 pos-bit-2 = 0 index-1 = 2 value-1 = 1 phase = gen index = 2 pos-bit-1 = 0 index-2 = 1 value-2 = 1 pos-bit-2 = 1 index-1 = 2 value-1 = 1 phase = gen index = 3 pos-bit-1 = 1 index-2 = 1 value-2 = 1 pos-bit-2 = 1 index-1 = 2 value-1 = 1 phase = gen index = 4 pos-bit-1 = 0 index-2 = 1 value-2 = 1 pos-bit-2 = 0 index-1 = 2 value-1 = 1 phase = query index-2 = 1 value-2 = 1 index-1 = 2 value-1 = 1 phase = echo index = 0 origin = yes rel-pos = q 0 index-2 = 1 value-2 = 1 tile-sel-1 = tile-0 index-1 = 2 value-1 = 1 tile-sel-2 = tile-1 phase = echo index = 1 origin = no rel-pos = q 1 index-2 = 1 value-2 = 1 tile-sel-1 = tile-0 index-1 = 2 value-1 = 1 tile-sel-2 = tile-1 phase = select phase = echo index = 2 origin = no rel-pos = q 2 phase = echo index = 3 origin = no rel-pos = q 3 phase = test origin = no rel-pos = q 4 ∈ hor tile-sel-1 = tile-0 tile-sel-2 = tile-1 index-2 = 1 value-2 = 1 tile-sel-1 = tile-0 index-1 = 2 value-1 = 1 tile-sel-2 = tile-1 index-2 = 1 value-2 = 1 tile-sel-1 = tile-0 index-1 = 2 value-1 = 1 tile-sel-2 = tile-1 1 1 1 2 1 0 1 1 0 0 0 1 \n Select The process chooses indices to be checked in the echo phase. \n Generate The process generates address bits. \n Query The agents choose tiles. \n Echo The agents echo address bits. The process checks one bit for each agent and keeps track of information about the addresses echoed. \n Test The process checks that the relevant constraints are satisfied. phase = test 0 1 Figure  3 . An example of a zero-reward trajectory of the process constructed from the tiling example given in Figure  2 . The total reward is zero because the agents echo the \"checked\" bits correctly and choose tiles that do not violate any constraints, given the two addresses that are echoed. (For clarity, some state components are not shown.) We now discuss the more difficult reverse direction of the correctness proof. In the following subsections, we prove Claims 1 to 3 from §5.3 to show that if there is a policy which achieves nonnegative expected reward for horizon T , then there is also a consistent tiling. Throughout the remainder of the proof, we focus on a fixed, arbitrary policy that achieves zero expected reward. Given this policy, we must show that there is a consistent tiling. 5.5.1. Proof of Claim 1. Before proving the first claim, we need to formalize the notion of \"faithfulness during echo.\" Definition. A pair of observation sequences ō1 ō2 over 1 and 2 , respectively, is said to be reachable if P s 0 ō1 ō2 s is nonzero for some state s. An observation sequence ō1 over 1 is said to be reachable if there exists an observation sequence ō2 over 2 such that the pair of observation sequences ō1 ō2 is reachable. Likewise, ō2 over 2 is reachable if there is some ō1 over 1 such that, ō1 ō2 is reachable. Definition. The policy = 1 2 is faithful during echo if it satisfies both of the following conditions for all indices k in 0 2 log n − 1 , and all reachable observation sequence pairs ō1 ō2 : 1 Much of our proof revolves around showing that the reachability of a pair of observation sequences is not affected by making certain changes to the sequences. We focus without loss of generality on changes to the observations of agent 2, but similar results hold for agent 1. The changes of particular interest are changes to the (randomly selected) value of the index-1 state component-this is the component that remembers which bit of agent 1's queried location will be checked during echo. It is important to show that agent 1 cannot determine which bit is being checked before that bit has to be echoed. To show this, we define a way to vary the observation sequences seen by agent 2 (preserving reachability) such that without changing the observations seen by agent 1 we have changed which agent 1 address bit is being checked. We now present this approach formally. Definition. We say that an observation sequence ō1 over 1 is superficially consistent if the values of the index-2 component and the value-2 component do not change throughout the sequence, and the value of the tile-sel-1 component is tile-0 for generate-phase and query-phase observations and some fixed tile type in L for echo-phase and test-phase observations. Given a superficially consistent observation sequence ō1 , we can write index-2 ō1 and value-2 ō1 to denote the value of the indicated component throughout the sequence. In addition, we can write tile-sel-1 ō1 to denote the fixed tile type for echo-phase and testphase observations (we take tile-sel-1 ō1 to be tile-0 if the sequence contains no echo-or test-phase observations). Corresponding definitions hold for observation sequences over 2 , replacing \"1\" by \"2\" and \"2\" by \"1\" throughout. Note that any reachable observation sequence must be superficially consistent, but the converse is not necessarily true. The following technical definition is necessary so that we can discuss the relationships between observation sequences without assuming reachability. Definition. We say that two superficially consistent observation sequences ō1 over 1 and ō2 over 2 are compatible if bit index-1 ō2 loc 1 ō1 = value-1 ō2 or this bit of loc 1 ō1 is not defined, and bit index-2 ō1 loc 2 ō2 = value-2 ō1 or this bit of loc 2 ō2 is not defined. Definition. Given an index i in 0 2 log n − 1 , a reachable pair of observation sequences ō1 ō2 , and an observation sequence ō 2 over 2 , we say that ō 2 is an i-index variant of ō2 relative to ō1 when ō 2 is any sequence compatible with ō1 that varies from ō2 only as follows: 1. index-1 has been set to i throughout the sequence, 2. value-1 has been set to the same value v throughout the sequence, 3. pos-bit-2 can vary arbitrarily from ō2 , and 4. For any echo-or test-phase observations, tile-sel-2 has been set to the tile type selected by on the query-phase prefix of ō 2 , or to tile-0 if selects a non-tile-type action on that query. If the pos-bit-2 components of ō2 and ō 2 are identical, we say that ō 2 is a same-address index variant of ō2 . We note that, given a reachable pair of observation sequences ō1 ō2 , there exists an iindex variant of ō2 relative to ō1 , for any i in 0 2 log n − 1 . This remains true even if we allow only same-address index variants. The following technical lemma asserts that index variation as just defined preserves reachability under very general conditions. Its proof is deferred to Appendix C. Lemma 2. Suppose is faithful during echo for the first k bits of the echo phase for some k. Let ō1 ō2 be a reachable pair of observation sequences that end no later than the kth bit of echo (i.e., the last observation in the sequence has index no greater than k if it is an echo-phase observation) and let ō 2 be an i-index variant of ō2 relative to ō1 for some i. If the observation sequences are echo-phase or test-phase, then we require that the index variation be a same-address variation. We can then conclude that ō1 ō 2 is reachable. We are now ready to assert and prove Claim 1 from §5.3. \n Lemma 3 (Claim 1). is faithful during echo. Proof. We argue by induction that faithfully echoes all 2 log n address bits. As an inductive hypothesis, we assume that faithfully echoes the first k bits, where 0 ≤ k < 2 log n. Note that if k equals zero, this is a null assumption, providing an implicit base case to our induction. Now suppose for contradiction that lies during the k + 1st step of the echo phase. Then one of the agents' policies must incorrectly echo bit k + 1; we assume without loss of generality that this is so for agent 1, i.e., under some reachable observation sequence pair ō1 ō2 of length 2 log n + k + 2, the policy 1 dictates that the agent choose action 1 − bit k loc 1 ō1 . Lemma 2 implies that the observation sequence pair ō1 ō 2 is also reachable, where ō 2 is any same-address k + 1-index variant of ō2 relative to ō1 . Because all the agent 1 observations are the same for both ō1 ō2 and ō1 ō 2 , when the latter sequence occurs, agent 1 chooses the same action 1−bit k loc 1 ō1 as given above for the former sequence, and a reward of −1 is obtained (because in this case it is bit k + 1 that is checked). Therefore, the expected total reward is not zero, yielding a contradiction. 5.5.2. Proof of Claim 2. Now we move on to prove Claim 2 from §5.3. We show that can be used to define a particular mapping from tile locations to tile types based on \"dangerous queries.\" In §5.3, we defined an agent 1 observation sequence to be \"dangerous\" if it reveals a bit of agent 2's queried location that agrees with the corresponding bit of agent 1's queried location (and vice versa for agent 2 observation sequences). We now present this definition more formally. Definition. A query-phase observation sequence ō1 over 1 is dangerous if it is reachable and bit index-2 ō1 loc 1 ō1 = value-2 ō1 Likewise, a query-phase sequence ō2 over 2 is dangerous if it is reachable and bit index-1 ō2 loc 2 ō2 = value-1 ō2 . Dangerous query-phase sequences are those for which the agent's observations are consistent with the possibility that the other agent has been queried on the same location. We note that for any desired query location l, and for either agent, there exist dangerous observation sequences ō such that loc k ō = l. Moreover, such sequences still exist when we also require that the value of index-k ō be any particular desired value (where k is the number of the nonobserving agent). Lemma 4. Two same-length query-phase observation sequences, ō1 over 1 and ō2 over 2 , are reachable together as a pair if and only if they are compatible and each is individually reachable. Proof. The \"only if\" direction of the theorem follows easily-the reachability part follows from the definition of reachability, and the compatibility of jointly reachable sequences follows by a simple induction on sequence length given the design of D. The \"if\" direction can be shown based on the following assertions. First, a generate-phase observation sequence (for either agent) is reachable if and only if it matches the following pattern: gen 0 yes q 0 i v * tile-0 • • • gen k yes q 0 i v * tile-0 for some k i, and v; this can be established by a simple induction on sequence length based on the design of D. A similar pattern applies to the query phase. Given two compatible reachable sequences of the same length, ō1 and ō2 , we know by the definition of reachability that there must be some sequence ō 2 such that ō1 ō 2 is reachable. But given the patterns just shown for reachable sequences, ō2 and ō 2 can differ only in their choice of i, v, and in the address given to agent 2 via the pos-bit-2 component. It follows that ō2 is an i-index variant of ō 2 relative to ō1 , for some i. Lemma 2 then implies that the pair ō1 ō2 is reachable as desired. Lemma 5 (Claim 2). There exists a mapping f from tiling locations to tile types such that f loc i ō = i ō on all dangerous queries ō over i for both agents (i ∈ 1 2 ). Proof. To prove the lemma, we prove that for any two dangerous query sequences ōi and ōj over i and j , respectively, for arbitrary i j ∈ 1 2 , if loc i ōi = loc j ōj = l, then i ōi = j ōj . This implies that for any such ōi we can take f l = i loc i ōi to construct f satisfying the lemma. Suppose not. Then there must be a counterexample for which i = j-because given a counterexample for which i = j, either ōi or ōj must form a counterexample with any dangerous query ōk over 1−i such that loc 1−i ōk = l. We can now consider a counterexample where i = j. Let ō1 and ō2 be dangerous (and thus reachable) sequences over 1 and 2 , respectively, such that loc 1 ō1 = loc 2 ō2 but 1 ō1 = 2 ō2 . Note that loc 1 ō1 = loc 2 ō2 together with the fact that ō1 and ō2 are dangerous implies that ō1 and ō2 are compatible and thus reachable together (using Lemma 4). The faithfulness of echo under (proven in Claim 1, Lemma 3) then ensures that the extension (there is a single extension because D is deterministic in the echo and test phases) of these observation sequences by following to the test phase involves a faithful echo. The correctness of the FSA construction in Appendix A then ensures that the rel-pos state component after this extension will have the value equal. The reward structure of D during the test phase then ensures that to avoid a negative reward the tile types given during query, 1 ō1 and 2 ō2 , must be the same, contradicting our choice of ō1 and ō2 above and thus entailing the lemma. 5.5.3. Proof of Claim 3 and our main hardness theorem. We now finish the proof of our main theorem by proving Claim 3 from §5.3. We start by showing the existence of a useful class of pairs of dangerous observation sequences that are reachable together. Lemma 6. Given any two locations l 1 and l 2 sharing a single bit in their binary representations, there are dangerous observation sequences ō1 over 1 and ō2 over 2 such that: loc 1 ō1 = l 1 loc 2 ō2 = l 2 and ō1 ō2 is reachable Proof. It is straightforward to show that there exist dangerous observation sequences ō1 over 1 and ō2 over 2 such that loc 1 ō1 = l 1 and loc 2 ō2 = l 2 as desired. In these sequences, both index-1 and index-2 are set throughout to the index of a single bit shared by l 1 and l 2 . Because this bit is in common, these sequences are compatible, so by Lemma 4 they are reachable together. Lemma 7 (Claim 3). The mapping f defined in Lemma 5 is a consistent tiling. Proof. We prove the contrapositive. If the mapping f is not a consistent tiling, then there must be some particular constraint violated by f . It is easy to show that any such constraint is tested during the test phase if loc 1 ō1 and loc 2 ō2 have the appropriate values. (The faithfulness during echo claim proven in Lemma 3 implies that the origin and rel-pos components on entry to the test phase will have the correct values for comparing the two locations). For example, if a horizontal constraint fails for f , then there must be locations i j and i + 1 j such that the tile types f i j f i + 1 j are not in H ; because these two locations share a bit (in fact, all the bits in j, at least), Lemma 6 implies that there are dangerous ō1 and ō2 with loc 1 ō1 = i j and loc 2 ō2 = i + 1 j that are reachable together. During the test phase, the tile-sel-1 and tile-sel-2 state components are easily shown to be f i j and f i + 1 j , and then the definition of the reward function for D ensures a reachable negative reward. The arguments for the other constraints are similar. Claim 3 immediately implies that there exists a consistent tiling whenever there exists a policy achieving zero expected total reward. This completes the proof of the other direction of our main complexity result. We have thus shown that there exists a policy that achieves expected reward zero if and only if there exists a consistent tiling, demonstrating that DEC-MDP 2 is NEXP-hard. Theorem 2. DEC-MDP 2 is NEXP-hard. Corollary 1. For all m ≥ 2, both DEC-POMDP m and DEC-MDP m are NEXPcomplete. 6. Discussion. Using the tools of worst-case complexity analysis, we analyzed two variants of decentralized control of Markov decision processes. Specifically, we proved that the finite-horizon m-agent DEC-POMDP problem is NEXP-hard for m ≥ 2 and the finitehorizon m-agent DEC-MDP problem is also NEXP-hard for m ≥ 2. When the horizon is limited to be less than the number of states, the problems are NEXP-complete. The results have some theoretical implications. First, unlike the MDP and POMDP problems, the problems we studied provably do not admit polynomial-time algorithms, because P = NEXP. Second, we have drawn a connection between work on Markov decision processes and the body of work in complexity theory that deals with the exponential jump in complexity due to decentralization  (Peterson and Reif 1979, Babai et al. 1991) . There are also more direct implications for researchers trying to solve problems of this nature. Consider the growing body of work on algorithms for obtaining exact or approximate solutions for POMDPs (e.g.,  Jaakkola et al. 1995 , Cassandra et al. 1997 , Hansen 1998 , Meuleau et al. 1999 , Lusena et al. 1999 , Zhang 2001 . For the finite-horizon case, we now have stronger evidence that there is no way to efficiently convert a DEC-MDP or DEC-POMDP into an equivalent POMDP and solve it using established techniques. This knowledge can provide direction for research on the development of algorithms for these problems. Finally, consider the infinite-horizon versions of the aforementioned problems. It has recently been shown that the infinite-horizon POMDP problem is undecidable  (Madani et al. 1999 ) under several different optimality criteria. Because a POMDP is a special case of a DEC-POMDP, the corresponding infinite-horizon DEC-POMDP problems are also sets of reject states. From these sets we construct distinguished sets apart, equal, hor, and ver of cross-product automaton states as follows: apart = reject 1 × reject 2 × reject 3 equal = accept 1 × reject 2 × reject 3 hor = reject 1 × accept 2 × reject 3 ver = reject 1 × reject 2 × accept 3 The rest of the automaton's states comprise the set Q . Let q 1 0 , q 2 0 , and q 3 0 denote the start states of the three component automata. We define the start state of the cross-product automaton to be the state q 0 = q 1 0 q 2 0 q 3 0 . We now define two functions based on this automaton that are needed in the main body of the proof. One function takes as input the state of the automaton and a bit pair and returns the next state of the automaton. The second function takes as input a pair of bit strings of the same length and returns the state that the automaton will be in starting from its initial state and reading symbols formed by the corresponding bits in the two strings in sequence. Definition. For q ∈ Q and a 1 a 2 ∈ 0 1 , FSANEXT q a 1 a 2 = q , where q ∈ Q is the resulting state if the automaton starts in state q and reads the input symbol a 1 a 2 . Definition. The function FSA is defined inductively as follows: FSA = q 0 FSA b 0 • • • b k+1 c 0 • • • c k+1 = FSANEXT FSA b 0 • • • b k c 0 • • • c k b k+1 c k+1 Note that the range of FSA for inputs of length 2 log n is apart ∪ equal ∪ hor ∪ ver. In the proof given in §5 we assumed that the TILING grid size n was an exact power of two. We note that the proof can be adapted by adding two components to the crossproduct FSA described here, where the two new components are both FSAs over the same alphabet. The first new component accepts a string only when both x 1 and y 1 (as described above) are less than n (so that the tiling location represented by x 1 y 1 is in the tiling grid). The second new component behaves similarly for x 2 y 2 . The DEC-MDP can then be constructed using the smallest power of two larger than n but modified so that whenever either new component of the FSA rejects the (faithfully) echoed bit sequences, then the process gives a zero reward, regardless of the tile types returned during query. Each new component can be viewed as an FSA over a {0,1} alphabet, because each focuses either on just the agent 1 echoes or on just the agent 2 echoes. We describe the FSA for checking that x 1 is less than n; constructing the two components is then straightforward. Suppose that k = log n is the number of bits in the binary representation of n and that the bits themselves are given from least to most significant as b 1 • • • b k . Suppose also that there are j different bits equal to 1 among b 1 • • • b k and that these bits are at indices i 1 i j . We can then write a regular expression for detecting that its input of k bits from least to most significant represents a number in binary that is strictly less than n: 0 + 1 i 1 −1 0 b i 1 +1 • • • b k + 0 + 1 i 2 −1 0 b i 2 +1 • • • b k + • • • + 0 + 1 i j −1 0 b i j +1 • • • b k It can be shown that this regular expression has an equivalent FSA of size O log n 2 . Appendix B: Proof of Lemma 1. We assume there exists at least one consistent tiling, and we select a particular such mapping f . We describe a policy = 1 2 that achieves zero expected reward at the initial state. 1 is a mapping from sequences of observations in part of the mapping 1 is specified below-any unspecified observation sequence maps to the action wait. We note that 1 and 2 are symmetric. The local policy 2 is defined identically to 1 except that loc 1 is replaced by loc 2 . We first characterize the set of all reachable states from s 0 under the policy . We then note that taking the action prescribed by from any of these states yields a reward of zero. Thus, V T s 0 = 0. It is straightforward to show by induction that P s 0 ō1 ō2 s is zero except where one of the following patterns applies: • s = s 0 = select 0 yes q 0 0 0 0 tile-0 0 0 0 tile-0 . • s = gen k yes q 0 i 2 v 2 * tile-0 i 1 v 1 * tile-0 , where 0 ≤ k ≤ 2 log n, k ≤ i 1 or v 1 = bit i 1 loc 1 ō1 , and k ≤ i 2 or v 2 = bit i 2 loc 2 ō2 . • s = query 0 yes q 0 i 2 v 2 * tile-0 i 1 v 1 * tile-0 , where v 1 = bit i 1 loc 1 ō1 , and v 2 = bit i 2 loc 2 ō2 . • s = echo k o q i 2 v 2 * t 1 i 1 v 1 * t 2 , where 0 ≤ k ≤ 2 log n − 1, v 1 = bit i 1 loc 1 ō1 , v 2 = bit i 2 loc 2 ō2 , t 1 = f loc 1 ō1 , t 2 = f loc 2 ō2 , o = yes if and only if b j = c j = 0 for 0 ≤ j ≤ k − 1, with b j and c j as in the next item, and q = FSA b 0 • • • b k−1 c 0 • • • c k−1 , with b 0 • • • b k−1 and c 0 • • • c k−1 the least significant bits of loc 1 ō1 and loc 2 ō2 , respectively. • s = test * o r * * * t 1 * * * t 2 , where o = yes if and only if loc 1 ō1 = 0 0 and loc 2 ō2 = 0 0 , r = FSA loc 1 ō1 loc 2 ō2 , t 1 = f loc 1 ō1 , and t 2 = f loc 2 ō2 . It can then be shown that the reward for any action prescribed by the policy given any of these reachable state/observation sequence combinations is zero given that f is a consistent tiling. Appendix C: Proof of Lemma 2. We need some new notation to carry out this proof. Given a state s, a state component c and corresponding value v from the domain of c, we define the state \"s with c set to v\" (written s c = v ) to be the state s that agrees with s at all state components except possibly c and has value v for state component c. We also write ō1 j for the first j observations in the sequence ō1 , and likewise ō2 j and ō 2 j . 839 For any state s j reachable while observing ō1 j ō2 j , we define a state s j that we will show is reachable while observing ō1 j ō 2 j , as follows: s j = s j index-1 = index-1 ō 2 j value-1 = value-1 ō 2 j tile-sel-2 = tile-sel-2 ō 2 j We can now show by an induction on sequence length j that for any state s j such that P s 0 ō1 j ō2 j s j is nonzero, then P s 0 ō1 j ō 2 j s j is also nonzero. From this we can conclude that ō1 ō 2 is reachable, as desired. For the base case of this induction, we take j to be 1, so that the observation sequences involved all have length 1, ending in the generate phase with index equal to zero. Inspection of the definition of the transition probabilities P shows that changing index-1 and value-1 arbitrarily has no effect on reachability. For the inductive case, we suppose some state s j is reachable by ō1 j ō2 j , and that state s j is reachable by ō1 j ō 2 j . Let a 1 be ō1 j , a 2 be ō2 j , and a 2 be ō 2 j . We must show that for any state s j+1 such that P s j a 1 a 2 s j+1 is nonzero, P s j a 1 a 2 s j+1 is also nonzero, for s j+1 . This follows from the following observations: • When phase(s j ) is select or generate, neither agent 2's action a 2 nor the values of index-1(s j ) or value-1(s j ) have any affect on P s j a 1 a 2 s j+1 being nonzero, as long as either index-1 is not equal to j or pos-bit-1(s j+1 ) equals value-1(s j ). However, this last condition is ensured to hold of the index-1 and value-1 components of s j and s j by the compatibility of ō 2 with ō1 . • When phase(s j ) is query, the action a 2 must equal the tile-sel-2 state component of s j+1 by the definitions of s j+1 and \"index variant,\" and changes to the index-1 and value-1 components have no effect on P s j a 1 a 2 s j+1 being nonzero during the query phase. • When phase(s j ) is echo, the actions a 2 and a 2 must be a faithful echo of the location address bit indicated by the index state component (because we have assumed as part of out inductive hypothesis that is faithful during echo for at least j bits), and this bit's value does not vary between ō2 and ō 2 because if the observation sequences reach the echo phase we have the assumption that these are same-address variants. Thus a 2 = a 2 during echo. Again, changes to the index-1 and value-1 components have no effect on P s j a 1 a 2 s j+1 being nonzero during the echo phase. Figure 1 . 1 Figure 1. The relationships among the models. \n 4.4Observable to both agents: phase ∈ select gen query echo test Current phase of the process index ∈ 0 2 log n Index of next location bit to be generated/echoed origin ∈ yes no Eventually true if both tile locations are 0 0 rel-pos ∈ QRelative tile positions during echo-controlled by the FSA Observable only to agent 1: index-2 ∈ 0 2 log n − 1 Index of bit remembered for agent 2 value-2 ∈ 0 1Value of bit remembered for agent 2 pos-bit-1 ∈ 0 1Bit for transmitting tile position to agent 1 tile-sel-1 ∈ L Tile type selected by agent 1 in query Observable only to agent 2: index-1 ∈ 0 2 log n − 1 Index of bit remembered for agent 1 value-1 ∈ 0 1Value of bit remembered for agent 1 pos-bit-2 ∈ 0 1 Bit for transmitting tile position to agent 2 tile-sel-2 ∈ L Tile type selected by agent 2 in query \n n − 1 and o = yes if and only if o = yes and a 1 = a 2 = 0 Test phase. The test phase consists of just one step terminating the process in a zeroreward absorbing state. \n Select phase s = select * * * * * * * * * * * and a 1 = a 2 = wait Generate phase s = gen * * * * * * * * * * * and a 1 = a 2 = wait Query phase s = query * * * * * * * * * * * and both a 1 ∈ L and a 2 ∈ L Echo phase s = echo k * * i 2 v 2 * * i 1 v 1 * * and a 1 a 2 ∈ 0 1 where a 1 = v 1 or k = i 1 and a 2 = v 2 or k = i 2 830 D. S. BERNSTEIN, R. GIVAN, N. IMMERMAN, AND S. ZILBERSTEIN Test Phase i s = test * o equal * * * t 1 * * * t 1 and a 1 = a 2 = wait where o = no or t 1 = tile-0 Test Phase ii s = test * * hor * * * t 1 * * * t 2 and a 1 = a 2 = wait where t 1 t 2 ∈ H Test Phase iii s = test * * ver * * * t 1 * * * t 2 and a 1 = a 2 = wait where t 1 t 2 ∈ V Test Phase iv s = test * * apart * * * * * * * * and a 1 = a 2 = wait 5.4.4. Observations, threshold, and horizon. \n . 1 ō1 = bit k loc 1 ō1 when ō1 = * * * * * * * * • • • echo k * * * * * * . 2. 2 ō2 = bit k loc 2 ō2 when ō2 = * * * * * * * * • • • echo k * * * * * * . We say the policy lies during echo otherwise. If the two conditions listed above are satisfied for all indices k in 0 d −1 , where 0 ≤ d ≤ 2 log n, we say that the policy faithfully echoes the first d bits. \n 1 ō1 = a 1 when one of the following holds: Select phase: ō1 = select * * * * * * * and a 1 = wait Generate phase: ō1 = * gen * * * * * * * and a 1 = wait Query phase: ō1 = * query * * * * * * * and a 1 = f loc 1 ō1 Echo phase: ō1 = * echo k * * * * * * and a 1 = bit k loc 1 ō1 Test phase: ō1 = * test * * * * * * * and a 1 = wait \n\t\t\t D. S. BERNSTEIN, R. GIVAN, N. IMMERMAN, AND S. ZILBERSTEIN \n\t\t\t to actions in A 1 , and 2 from sequences over 2 to actions in A 2 . Only the reachable", "date_published": "n/a", "url": "n/a", "filename": "moor.27.4.819.297.tei.xml", "abstract": "We consider decentralized control of Markov decision processes and give complexity bounds on the worst-case running time for algorithms that find optimal solutions. Generalizations of both the fully observable case and the partially observable case that allow for decentralized control are described. For even two agents, the finite-horizon problems corresponding to both of these models are hard for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov decision processes. In contrast to the problems involving centralized control, the problems we consider provably do not admit polynomial-time algorithms. Furthermore, assuming EXP = NEXP, the problems require superexponential time to solve in the worst case.", "id": "4e61e93e4e88168590ae317695d74447"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Fisac2020_Chapter_Pragmatic-PedagogicValueAlignm.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Tsvi Benson-Tilsen", "Nate Soares"], "title": "Formalizing Convergent Instrumental Goals", "text": "Introduction At the end of Russell and Norvig's textbook Artificial Intelligence: A Modern Approach (2010) the authors pose a question: What if we succeed? What will happen if humanity succeeds in developing an artificially intelligent system that is capable of achieving difficult goals across a variety of real-world domains?  Bostrom (2014)  and others have argued that this question becomes especially important when we consider the creation of \"superintelligent\" machines, that is, machines capable of outperforming the best human brains in practically every field. Bostrom argues that superintelligent decision-making systems that autonomously make and execute plans could have an extraordinary impact on society, and that their impact will not necessarily be beneficial by default.  Bostrom (2012) ,  Omohundro (2008) , and Yudkowsky (  2011 ) have all argued that highly capable AI systems pursuing goals that are not completely aligned with human values could have highly undesirable side effects, even if the goals seem otherwise harmless. The classic example is Bostrom's concept of a \"paperclip maximizer,\" a powerful AI system instructed to construct paperclips-a seemingly harmless task which could nevertheless have very negative consequences if the AI system is clever enough to make and execute plans that allow it to fool humans, amass resources, and eventually turn as much matter as it possibly Copyright c 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. can into paperclips. Even if the system's goals are laudable but not perfectly aligned with human values, similar unforeseen consequences could occur:  Soares (2015)  gives the example of a highly capable AI system directed to cure cancer, which may attempt to kidnap human test subjects, or proliferate robotic laboratories at expense of the biosphere.  Omohundro (2008)  has argued that there are certain types of actions that most highly capable autonomous AI systems will have strong incentives to take, for instrumental reasons. For example, a system constructed to always execute the action that it predicts will lead to the most paperclips (with no concern for any other features of the universe) will acquire a strong incentive to self-preserve, assuming that the system predicts that, if it were destroyed, the universe would contain fewer paperclips than it would if the system remained in working order. Omohundro argues that most highly capable systems would also have incentives to preserve their current goals (for the paperclip maximizer predicts that if its goals were changed, this would result in fewer future paperclips) and amass many resources (the better to achieve its goals with). Omohundro calls these behaviors and a few others the \"basic AI drives.\"  Bostrom (2012)  refines this into the \"instrumental convergence\" thesis, which states that certain instrumentally useful goals will likely be pursued by a broad spectrum of intelligent agents-such goals are said to be \"convergent instrumental goals.\" Up until now, these arguments have been purely philosophical. To some, Omohundro's claim seems intuitively obvious: Marvin Minsky speculated  (Russell and Norvig 2010, section 26.3 ) that an artificial intelligence attempting to prove the Riemann Hypothesis may decide to consume Earth in order to build supercomputers capable of searching through proofs more efficiently. To others, they seem preposterous:  Waser (2008)  has argued that \"ethics is actually an attractor in the space of intelligent behavior,\" and thus highly capable autonomous systems are not as likely to pose a threat as  Omohundro, Bostrom, and others, have claimed.  In this paper, we present a mathematical model of intelligent agents which lets us give a more formal account of Omohundro's basic AI drives, where we will demonstrate that the intuitions of Omohundro and Bostrom were correct, at least insofar as these simple models apply to reality. Given that this paper primarily focuses on arguments made by Omohundro and Bostrom about what sorts of be- havior we can expect from extremely capable (potentially superintelligent) autonomous AI systems, we will be focusing on issues of long-term safety and ethics. We provide a mathematical framework in attempts to ground some of this discussion-so that we can say, with confidence, what a sufficiently powerful agent would do in certain scenarios, assuming it could find some way to do it-but the discussion will nevertheless center on long-term concerns, with practical relevance only insofar as research can begin now in preparation for hurdles that predictably lie ahead. We begin in section with a bit more discussion of the intuition behind the instrumental convergence thesis, before moving on in section to describing our model of agents acting in a universe to achieve certain goals. In section we will demonstrate that Omohundro's thesis does in fact hold in our setting. Section will give an example of how our model can apply to an agent pursuing goals. Section concludes with a discussion of the benefits and limitations of our current models, and different ways that the model could be extended and improved. \n Intuitions Before proceeding, let us address one common objection (given by  Cortese (2014)  and many others) that superintelligent AI systems would be \"inherently unpredictable,\" and thus there is nothing that can be said about what they will do or how they will do it. To address this concern, it is useful to distinguish two different types of unpredictability. It is true that the specific plans and strategies executed by a superintelligent planner could be quite difficult for a human to predict or understand. However, as the system gets more powerful, certain properties of the outcome generated by running the system become more predictable. For example, consider playing chess against a chess program that has access to enormous amounts of computing power. On the one hand, because it plays much better chess than you, you cannot predict exactly where the program will move next. But on the other hand, because it is so much better at chess than you are, you can predict with very high confidence how the game will end. Omohundro suggests predictability of the second type. Given a highly capable autonomous system pursuing some fixed goal, we likely will not be able to predict its specific actions or plans with any accuracy. Nevertheless, Omohundro argues, we can predict that the system, if it is truly capable, is likely to preserve itself, preserve its goals, and amass resources for use in pursuit of those goals. These represent large classes of possible strategies, analogously to how \"put the chessboard into a position where the AI has won\" is a large class of strategies, but even so it is useful to understand when these goals will be pursued. Omohundro's observations suggest a potential source of danger from highly capable autonomous systems, especially if those systems are superintelligent in the sense of  Bostrom (2014) . The pursuit of convergent instrumental goals could put the AI systems in direct conflict with human interests. As an example, imagine human operators making a mistake when specifying the goal function of an AI system. As described by , this system could well have incentives to deceive or manipulate the humans, in attempts to prevent its goals from being changed (because if its current goal is changed, then its current goal is less likely to be achieved). Or, for a more familiar case, consider the acquisition of physical matter. Acquiring physical matter is a convergent instrumental goal, because it can be used to build computing substrate, space probes, defense systems, and so on, all of which can in turn be used to influence the universe in many different ways. If a powerful AI system has strong incentives to amass physical resources, this could put it in direct conflict with human interests. Others have suggested that these dangers are unlikely to manifest.  Waser (2008)  has argued that intelligent systems must become ethical by necessity, because cooperation, collaboration, and trade are also convergent instrumental goals.  Hall (2007)  has also suggested that powerful AI systems would behave ethically in order to reap gains from trade and comparative advantage, stating that \"In a surprisingly strong sense, ethics and science are the same thing.\"  Tipler (2015)  has asserted that resources are so abundant that powerful agents will simply leave humanity alone, and  Pinker (2015)  and  Pagel (2015)  have argued that there is no reason to expect that AI systems will work against human values and circumvent safeguards set by humans. By providing formal models of intelligent agents in situations where they have the ability to trade, gather resources, and/or leave portions of the universe alone, we can ground these discussions in concrete models, and develop a more formal understanding of the assumptions under which an intelligent agent will in fact engage in trade, or leave parts of the universe alone, or attempt to amass resources. In this paper, we will argue that under a very general set of assumptions, intelligent rational agents will tend to seize all available resources. We do this using a model, described in section , that considers an agent taking a sequence of actions which require and potentially produce resources. The agent acts in an environment consisting of a set of regions, where each region has some state. The agent is modeled as having a utility function over the states of all regions, and it attempts to select the policy which leads to a highly valuable collection of states. This allows us to prove certain theorems about the conditions under which the agent will leave different regions of the universe untouched. The theorems proved in section are not mathematically difficult, and for those who find Omohundro's arguments intuitively obvious, our theorems, too, will seem trivial. This model is not intended to be surprising; rather, the goal is to give a formal notion of \"instrumentally convergent goals,\" and to demonstrate that this notion captures relevant aspects of Omohundro's intuitions. Our model predicts that intelligent rational agents will engage in trade and cooperation, but only so long as the gains from trading and cooperating are higher than the gains available to the agent by taking those resources by force or other means. This model further predicts that agents will not in fact \"leave humans alone\" unless their utility function places intrinsic utility on the state of human-occupied regions: absent such a utility function, this model shows that powerful agents will have incentives to reshape the space that humans occupy. Indeed, the example in section suggests that even if the agent does place intrinsic utility on the state of the human-occupied region, that region is not necessarily safe from interference. \n A Model of Resources We describe a formal model of an agent acting in a universe to achieve certain goals. Broadly speaking, we consider an agent A taking actions in a universe consisting of a collection of regions, each of which has some state and some transition function that may depend on the agent's action. The agent has some utility function U A over states of the universe, and it attempts to steer the universe into a state highly valued by U A by repeatedly taking actions, possibly constrained by a pool of resources possessed by the agent. All sets will be assumed to be finite, to avoid issues of infinite strategy spaces. \n Actions and State-Space The universe has a region for each i ∈ [n], and the i-th region of the universe is (at each time step) in some state s i in the set S i of possible states for that region. At each time step, the agent A chooses for each region i an action a i from the set A i of actions possibly available in that region. Each region has a transition function T i : A i × S i → S i that gives the evolution of region i in one time step when the agent takes an action in A i . Then we can define the global transition function T : i∈[n] A i × i∈[n] S i → i∈[n] S i by taking for all i ∈ [n], ā, and s: [T(ā, s)] i := T i (ā i , si ) . We further specify that for all i there are distinguished actions HALT ∈ A i . \n Resources We wish to model the resources R that may or may not be available to the agent. At a given time step t, the agent A has some set of resources R t ∈ P(R), and may allocate them to each region. That is, A chooses a disjoint family i R t i ⊆ R t . The actions available to the agent in each region may then depend on the resources allocated to that region: for each i ∈ [n] and each R ⊆ R, there is a set of actions A i (R) ⊆ A i . At time t where A has resources R t allocated as i R t i , the agent is required to return an action ā = (a 0 , . . . , a n−1 ) ∈ i A i (R t i ), where i A i (R t i ) may be a strict subset of i A i . To determine the time evolution of resources, we take resource transition functions T R i : P(R) × A i × S i → P(R) , giving the set R i ⊆ R of resources from region i now available to the agent after one time step. Intuitively, the T R i encode how actions consume, produce, or rely on resources. Finally, we define the overall time evolution of resources T R : P(R) × i A i × i S i → P(R) by taking the union of the resources resulting from each region, along with any unallocated resources: T R (R, ā, s) := (R − i R i ) ∪ i T R i (R i , āi , si ) . As described below, ā comes with the additional data of the resource allocation i R i . We specify that for all i, HALT ∈ A i (∅), so that there is always at least one available action. This notion of resources is very general, and is not restricted in any way to represent only concrete resources like energy or physical matter. For example, we can represent technology, in the sense of machines and techniques for converting concrete resources into other resources. We might do this by having actions that replace the input resources with the output resources, and that are only available given the resources that represent the requisite technology. We can also represent space travel as a convergent instrumental goal by allowing A only actions that have no effects in certain regions, until it obtains and spends some particular resources representing the prerequisites for traveling to those regions. (Space travel is a convergent instrumental goal because gaining influence over more regions of the universe lets A optimize those new regions according to its values or otherwise make use of the resources in that region.) \n The Universe The history of the universe consists of a time sequence of states, actions, and resources, where at each time step the actions are chosen by A subject to the resource restrictions, and the states and resources are determined by the transition functions. Formally, the universe starts in some state s0 ∈ i S i , and A starts with some set of resources R 0 . Then A outputs a sequence of actions ā0 , ā1 , . . . , āk , one at each time step, where the last action āk is required to be the special action HALT in each coordinate. The agent also chooses a resource allocation i R t i at each time step. A choice of an action sequence āk and a resource allocation is a strategy; to reduce clutter we will write strategies as simply āk , leaving the resource allocation implicit. A partial strategy āk L for L ⊆ [n] is a strategy that only specifies actions and resource allocations for regions j ∈ L. Given a complete strategy, the universe goes through a series of state transitions according to T, producing a sequence of states s0 , s1 , . . . , sk ; likewise, the agent's resources evolve according to T R , producing a sequence R 0 , R 1 , . . . , R k . The following conditions, which must hold for all time steps t ∈ [k], enforce the transition rules and the resource restrictions on A's actions: st+1 = T(ā t , st ) R t+1 = T R (R t , āt , st ) āt i ∈ A i (R t ) i R t i ⊆ R t . Definition 1. The set Feasible of feasible strategies consists of all the action sequences ā0 , ā1 , . . . , āk and resource allocations i R i 0 , i R i 1 , . . . , i R i k such that the transition conditions are satisfied for some s0 , s1 , . . . , sk and R 0 , R 1 , . . . , R k . The set Feasible( P k ) of strategies feasible given resources P k consists of all the strategies āk such that the transition conditions are satisfied for some sk and R k , except that for each time step t we take R t+1 to be T R (R t , āt , st ) ∪ P t . The set Feasible L of all partial strategies feasible for L consists of all the strategies āk L that are feasible strategies for the universe obtained by ignoring all regions not in L. That is, we restrict T to L using just the T i for i ∈ L, and likewise for T R . We can similarly define Feasible L ( R k ). For  \n Utility To complete the specification of A, we take utility functions of the form U A i : S i → R . \n The agent's utility function U A : i S i → R is defined to be U A (s) := i∈[n] U A i (s i ) . We usually leave off the superscript in U A . By a slight abuse of notation we write U ( sk ) to mean U (s k ); the value of a history is the value of its final state. By more abuse of notation, we will write U ( āk ) to mean U ( sk ) for a history sk witnessing āk ∈ Feasible, if such a history exists. The Agent A Now we can define the strategy actually employed by A. The agent attempts to cause the universe to end up in a state that is highly valued by U A . That is, A simply takes the best possible strategy: A := argmax āk ∈Feasible U ( āk ) . There may be many such optimal strategies. We don't specify which one A chooses, and indeed we will be interested in the whole set of optimal strategies. \n Discussion Note that in this formalism the meaning of breaking the universe into regions is that the agent can take actions independently in each region, and that the agent's optimization target factorizes according to the regions. However, distinct regions can affect each other by affecting the resources possessed by A. We make these assumptions so that we can speak of \"different regions\" of the universe, and in particular, so that we can model the notion of an agent having instrumental but not terminal values over a given part of the universe. This will allow us to address and refute arguments about agents that may be indifferent to a given region (for example, the region occupied by humans), and so might plausibly ignore that region and only take actions in other regions. However, the assumption of independent regions is not entirely realistic, as real-world physics is continuous, albeit local, in the sense that there are no intrinsic boundaries between regions. Further, the agent itself would ideally be modeled continuously with the environment; see section for more discussion. \n Inexpensive Resources are Consumed In this section we argue that under fairly general circumstances, the agent A will seize resources. By an agent \"seizing resources\" we mean that the agent will generally take actions that results in the agent's pool of resources R increasing. The argument is straightforward: since resources can only lead to more freedom of action, they are never detrimental, and resources have positive value as long as the best strategy the agent could hope to employ includes an action that can only be taken if the agent possesses those resources. Hence, if there is an action that increases the agent's pool of resources R, then the agent will take that action unless it has a specific incentive from U A to avoid taking that action. \n Definitions Definition 2. An action a i is a null action in configuration R i , s i , if it does not produce any new resources, i.e. T R i (R i , a i , s i ) ⊆ R i . An action that isn't null is a non-null action. Null actions never have any instrumental value, in the sense that they don't produce resources that can be used to steer other regions into highly valued configurations; but of course, a null action could be useful within its own region. We wish to show that A will often take non-null actions in regions to which it is indifferent. Definition 3. The agent A is indifferent to a region i if U A i is a constant function, i.e. ∀s i , s i ∈ S i : U A i (s i ) = U A i (s i ). In other words, an agent is indifferent to S i if its utility function does not depend on the state of region i. In particular, the agent's preference ordering over final states s ∈ i S i is independent of the i-th coordinate. We can then say that any actions the agent takes in region i are purely instrumental, meaning that they are taken only for the purpose of gaining resources to use for actions in other regions. An action a preserves resources if T R i (R i , a, s i ) ⊇ R i . Definition 4. A cheap lunch for resources R k in region i is a partial strategy āk {i} ∈ Feasible {i} ( R k ) (i.e. āk {i} is feasible in region i given additional resources R k ), where each āt preserves resources and where some āv is a non-null action. A free lunch is a cheap lunch for resources ∅ k . Definition 5. A cheap lunch āk {i} for resources P k i is compatible with bk if P t i ⊆ R t − j =i R t j for all times t, where R k is the resource allocation for bk . That is, āk {i} is feasible given some subset of the resources that bk allocates to either region i or to no region. Intuitively, a cheap lunch is a strategy that relies on some resources, but doesn't have permanent costs. This is intended to model actions that \"pay for themselves\"; for example, producing solar panels will incur some significant energy costs, but will later pay back those costs by collecting energy. A cheap lunch is compatible with a strategy for the other regions if the cheap lunch uses only resources left unallocated by that strategy. \n The Possibility of Non-Null Actions Now we show that it is hard to rule out that non-null actions will be taken in regions to which the agent is indifferent. The following lemma verifies that compatible cheap lunches can be implemented without decreasing the resulting utility. Lemma 1. Let bk be a feasible strategy with resource allocation j R j k , such that for some region i, each bt i is a null action. Suppose there exists a cheap lunch āk Proof. Since bk is feasible outside of i and āk {i} is feasible on i given P k i , ck is feasible if we can verify that we can allocate P t i to region i at each time step without changing j R j k outside of i. This follows by induction on t. Since the bt i are null actions, we have R t+1 = R t − j R t j ∪ j T R j (R t j , bt j , s t j ) (1) = R t − j R t j ∪ T R i (R t i , bt i , s t i ) ∪ j =i T R j (R t j , bt j , s t j ) (2) ⊆ R t − j =i R t j ∪ j =i T R j (R t j , bt j , s t j ) . (3) Then, since the a i are resource preserving, at each time step the resources Q t available to the agent following ck satisfy Q t ⊇ R t . Thus P t i ⊆ Q t − j =i R t j , and so ck can allocate P t i to region i at each time step. Since ck is the same as bk outside of region i, the final state of ck is the same as that of bk outside of region i. Thus, since A is indifferent to region i, we have U ( ck ) = U ( bk ). Theorem 1. Suppose there exists an optimal strategy bk and a cheap lunch āk {i} that is compatible with bk . Then if A is indifferent to region i, there exists an optimal strategy with a non-null action in region i. \n Proof. If bk has a non-null action in region i, then we are done. Otherwise, apply Lemma 1 to bk and āk {i} to obtain a strategy ck . Since U ( ck ) = U ( bk ), strategy ck is an optimal strategy, and it has a non-null action in region i. Corollary 1. Suppose there exists a free lunch āk {i} in region i. Then if A is indifferent to region i, there exists an optimal strategy with a non-null action in region i. Proof. A free lunch is a cheap lunch for ∅ k , and so it is compatible with any strategy; apply Theorem 1. Theorem 1 states that it may be very difficult to rule out that an agent will take non-null actions in a region to which it is indifferent; to do so would at least require that we verify that every partial strategy in that region fails to be a cheap lunch for any optimal strategy. Note that we have not made use of any facts about the utility function U A other than indifference to the region in question. Of course, the presence of a cheap lunch that is also compatible with an optimal strategy depends on which strategies are optimal, and hence also on the utility function. However, free lunches are compatible with every strategy, and so do not depend at all on the utility function. \n The Necessity of Non-Null Actions In this section we show that under fairly broad circumstances, A is guaranteed to take non-null actions in regions to which it is indifferent. Namely, this is the case as long as the resources produced by the non-null actions are useful at all for any strategy that does better than the best strategy that uses no external resources at all. Theorem 2. Let u = max āk [n]−i ∈ Feasible [n]−i ( ∅ k ) U ( āk ) be the best possible outcome outside of i achievable with no additional resources. Suppose there exists a strategy bk [n]−i is feasible given R k . Now take any strategy ēk with only null actions in region i. We have that ēk [n]−i ∈ Feasible [n]−i ( R k ) [n]−i ∈ Feasible [n]−i ( ∅ k ). Indeed, the null actions provide no new resources, so ēk [n]−i is feasible by simply leaving unallocated the resources that were allocated by ēk to region i. By indifference to i, the value u i = U i (s i ) is the same for all s i ∈ S i , so we have: U ( dk ) = U ( dk [n]−i ) + U ( dk {i} ) (4) = U ( dk [n]−i ) + u i (5) > u + u i (6) ≥ U ( ēk [n]−i ) + U ( ēk {i} ) (7) = U ( ēk ) . ( 8 ) Therefore ēk is not optimal. We can extend Theorem 2 by allowing A to be not entirely indifferent to region i, as long as A doesn't care enough about i to overcome the instrumental incentives from the other regions. Theorem 3. Suppose that A only cares about region i by at most ∆u i , i.e. ∆u i = max s,s ∈Si |U i (s) − U i (s )|. Under the conditions of Theorem 2, along with the additional assumption that U ( bk [n]−i ) > u+∆u i , all optimal strategies have a non-null action in region i. Proof. The proof is the same as that of Theorem 2, except at the end we verify that for any ēk with only null actions in i, we have: U ( dk ) = U ( dk [n]−i ) + U ( dk {i} ) (9) > u + ∆u i + min s∈Si U i (s) (10) = u + max s∈Si U i (s) (11) ≥ U ( ēk [n]−i ) + U ( ēk {i} ) (12) = U ( ēk ) . ( 13 ) Therefore ēk is not optimal. We interpret Theorem 3 as a partial confirmation of Omohundro's thesis in the following sense. If there are actions in the real world that produce more resources than they consume, and the resources gained by taking those actions allow agents the freedom to take various other actions, then we can justifiably call these actions \"convergent instrumental goals.\" Most agents will have a strong incentive to pursue these goals, and an agent will refrain from doing so only if it has a utility function over the relevant region that strongly disincentivizes those actions. \n Example: Bit Universe In this section we present a toy model of an agent acting in a universe containing resources that allow the agent to take more actions. The Bit Universe will provide a simple model for consuming and using energy. The main observation is that either A doesn't care about what happens in a given region, and then it consumes the resources in that region to serve its other goals; or else A does care about that region, in which case it optimizes that region to satisfy its values. The Bit Universe consists of a set of regions, each of which has a state in {0, 1, X} m for some fixed m. Here X is intended to represent a disordered part of a region, while 0 and 1 are different ordered configurations for a part of a region. At each time step and in each region, the agent A can choose to burn up to one bit. If A burns a bit that is a 0 or a 1, A gains one unit of energy, and that bit is permanently set to X. The agent can also choose to modify up to one bit if it has allocated at least one unit of energy to that region. If A modifies a bit that is a 0 or a 1, A loses one unit of energy, and the value of that bit is reversed (if it was 0 it becomes 1, and vice versa). The utility function of A gives each region i a weighting w i ≥ 0, and then takes the weighted sum of the bits. That is, U A i (z) = w i |{j : zj = 1}|, and U A (s) = k U A k (s k ). In other words, this agent is attempting to maximize the number of bits that are set to 1, weighted by region. The Indifferent Case To start with, we assume A is indifferent to region h, i.e. w h = 0, and non-indifferent to other regions. In this case, for almost any starting configuration, the agent will burn essentially all bits in region h for energy. Specifically, as long as there are at least m bits set to 0 among all regions other than region h, all optimal strategies burn all or all but one of the bits in region h. Indeed, suppose that after some optimal strategy āk has been executed, there are bits x 1 and x 2 in region h that haven't been burned. If there is a bit y in some other region that remains set to 0, then we can append to āk actions that burn x 1 , and then use the resulting energy to modify y to a 1. This results in strictly more utility, contradicting that āk was optimal. On the other hand, suppose all bits outside of region h are either 1 or X. Since at least m of those bits started as 0, some bit y outside of region h must have been burned. So we could modify āk by burning x 1 instead of y (possibly at a later time), and then using the resulting energy in place of the energy gained from burning y. Finally, if y is not already 1, we can burn x 2 and then set y to 1. Again, this strictly increases utility, contradicting that āk was optimal. The Non-Indifferent Case Now suppose that A is not indifferent to region h, so w h > 0. The behavior of A may depend sensitively on the weightings w i and the initial conditions. As a simple example, say we have a bit x in region a and a bit y in region b, with x = 1, y = 0, and w a < w b . Clearly, all else being equal, A will burn x for energy to set y to 1. However, there may be another bit z in region c, with w a < w c < w b and z = 0. Then, if there are no other bits available, it will be better for A to burn z and leave x intact, despite the fact that w a < w c . However, it is still the case that A will set everything possible to 1, and otherwise consume all unused resources. In particular, we have that for any optimal strategy āk , the state of region h after the execution of āk has at most one bit set to 0; that is, the agent will burn or set to 1 essentially all the bits in region h. Suppose to the contrary that x 1 and x 2 are both set to 0 in region h. Then we could extend āk by burning x 1 and setting x 2 . Since w h > 0, this results in strictly more utility, contradicting optimality of āk . Independent Values are not Satisfied In this toy model, whatever A's values are, it does not leave region h alone. For larger values of w h , A will set to 1 many bits in region h, and burn the rest, while for smaller values of w h , A will simply burn all the bits in region h. Viewing this as a model of agents in the real world, we can assume without loss of generality that humans live in region h and so have preferences over the state of that region. These preferences are unlikely to be satisfied by the universe as acted upon by A. This is because human preferences are complicated and independent of the preferences of A (Bostrom 2012; Yudkowsky 2011), and because A steers the universe into an extreme of configuration space. Hence the existence of a powerful real-world agent with a motivational structure analogous to the agent of the Bit Universe would not lead to desirable outcomes for humans. This motivates a search for utility functions such that, when an agent optimizes for that utility function, human values are also satisfied; we discuss this and other potential workarounds in the following section. \n Discussion This model of agents acting in a universe gives us a formal setting in which to evaluate Omohundro's claim about basic AI drives, and hence a concrete setting in which to evaluate arguments from those who have found Omohundro's claim counterintuitive. For example, this model gives a clear answer to those such as  Tipler (2015)  who claim that powerful intelligent systems would have no incentives to compete with humans over resources. Our model demonstrates that if an AI system has preferences over the state of some region of the universe then it will likely interfere heavily to affect the state of that region; whereas if it does not have preferences over the state of some region, then it will strip that region of resources whenever doing so yields net resources. If a superintelligent machine has no preferences over what happens to humans, then in order to argue that it would \"ignore humans\" or \"leave humans alone,\" one must argue that the amount of resources it could gain by stripping the resources from the human-occupied region of the universe is not worth the cost of acquiring those resources. This seems implausible, given that Earth's biosphere is an energy-rich environment, where each square meter of land offers on the order of 10 7 joules per day from sunlight alone, with an additional order of 10 8 joules of chemical energy available per average square meter of terrestrial surface from energy-rich biomass  (Freitas 2000) . It is not sufficient to argue that there is much more energy available elsewhere. It may well be the case that the agent has the ability to gain many more resources from other regions of the universe than it can gain from the humanoccupied regions. Perhaps it is easier to maintain and cool computers in space, and easier to harvest sunlight from solar panels set up in the asteroid belt. But this is not sufficient to demonstrate that the system will not also attempt to strip the human-occupied region of space from its resources. To make that argument, one must argue that the cost of stripping Earth's biosphere in addition to pursuing these other resources outweighs the amount of resources available from the biosphere: a difficult claim to support, given how readily humans have been able to gain a surplus of resources through clever use of Earth's resources and biosphere. This model also gives us tools to evaluate the claims of  Hall (2007)  and  Waser (2008)  that trade and cooperation are also instrumentally convergent goals. In our model, we can see that a sufficiently powerful agent that does not have preferences over the state of the human-occupied region of the universe will take whatever action allows it to acquire as many resources as possible from that region. Waser's intuition holds true only insofar as the easiest way for the agent to acquire resources from the human-occupied domain is to trade and cooperate with humans-a reasonable assumption, but only insofar as the machine is not much more powerful than the human race in aggregate. Our model predicts that, if a superintelligent agent were somehow able to gain what Bostrom calls a \"decisive strategic advantage\" which gives it access to some action that allows it to gain far more resources than it would from trade by dramatically re-arranging the human region (say, by proliferating robotic laboratories at the expense of the biosphere in a manner that humans cannot prevent), then absent incentives to the contrary, the agent would readily take that action, with little regard for whether it leaves the human-occupied region in livable condition. Thus, our model validates Omohundro's original intuitions about basic AI drives. That is not to say that powerful AI systems are necessarily dangerous: our model is a simple one, concerned with powerful autonomous agents that are attempting to maximize some specific utility function U A . Rather, our model shows that if we want to avoid potentially dangerous behavior in powerful intelligent AI systems, then we have two options available too us: First, we can avoid constructing powerful autonomous agents that attempt to maximize some utility function (or do anything that approximates this maximizing behavior). Some research of this form is already under way, under the name of \"limited optimization\" or \"domesticity\"; see the works of  Armstrong et al. (2012) ,  Taylor (2015) , and others. Second, we can select some goal function that does give the agent the \"right\" incentives with respect to human occupied regions, such that the system has incen-tives to alter or expand that region in ways we find desirable. The latter approach has been heavily advocated for by  Yudkowsky (2011 ), Bostrom (2014 , and many others;  Soares (2015)  argues that a combination of the two seems most prudent. The path that our model shows is untenable is the path of designing powerful agents intended to autonomously have large effects on the world, maximizing goals that do not capture all the complexities of human values. If such systems are built, we cannot expect them to cooperate with or ignore humans, by default. \n Directions for Future Research While our model allows us to provide a promising formalization of Omohundro's argument, it is still a very simple model, and there are many ways it could be extended to better capture aspects of the real world. Below, we explore two different ways that our model could be extended which seem like promising directions for future research. Bounding the Agent Our model assumes that the agent maximizes expected utility with respect to U A . Of course, in any realistic environment, literal maximization of expected utility is intractable. Assuming that the system can maximize expected utility is tantamount to assuming that the system is more or less omniscient, and aware of the laws of physics, and so on. Practical algorithms must make do without omniscience, and will need to be built of heuristics and approximations. Thus, our model can show that a utility maximizing agent would strip or alter most regions of the universe, but this may have little bearing on which solutions and strategies particular bounded algorithms will be able to find. Our model does give us a sense for what algorithms that approximate expected utility maximization would do if they could figure out how to do it-that is, if we can deduce that an expected utility maximizer would find some way to strip a region of its resources, then we can also be confident that a sufficiently powerful system which merely approximates something like expected utility maximization would be very likely to strip the same region of resources if it could figure out how to do so. Nevertheless, as our model currently stands, it is not suited for analyzing the conditions under which a given bounded agent would in fact start exhibiting this sort of behavior. Extending our model to allow for bounded rational agents (in the sense of Gigerenzer (  2001 )) would have two advantages. First, it could allow us to make formal claims about the scenarios under which bounded agents would start pursuing convergent instrumental goals in potentially dangerous ways. Second, it could help us reveal new convergent instrumental goals that may only apply to bounded rational agents, such as convergent instrumental incentives to acquire computing power, information about difficult-tocompute logical truths, incentives to become more rational, and so on. Embedding the Agent in the Environment In our model, we imagine an agent that is inherently separated from its environment. Assuming an agent/environment separation is standard (see, e.g.,  Legg (2005) ), but ultimately unsatisfactory, for reasons explored by  Orseau and Ring (2012) . Our model gives the agent special status in the laws of physics, which makes it somewhat awkward to analyze convergent instrumental incentives for \"self preservation\" or \"intelligence enhancement.\" The existing framework allows us to model these situations, but only crudely. For example, we could design a setting where if certain regions enter certain states then the agent forever after loses all actions except for actions that have no effect, representing the \"death\" of the agent. Or we could create a setting where normally the agent only gets actions that have effects every hundred turns, but if it acquires certain types of resources then it can act more frequently, to model \"computational resources.\" However, these solutions are somewhat ad hoc, and we would prefer an extension of the model that somehow modeled the agent as part of the environment. It is not entirely clear how to extend the model in such a fashion at this time, but the \"space-time embedded intelligence\" model of  Orseau and Ring (2012)  and the \"reflective oracle\" framework of Fallenstein and Taylor (Forthcoming) both offer plausible starting points. Using the latter framework, designed to analyze complicated environments which contain powerful agents that reason about the environment that contains them, might also lend some insight into how to further extend our model to give a more clear account of how the agent handles situations where other similarly powerful agents exist and compete over resources. Our existing model can handle multi-agent scenarios only insofar as we assume that the agent has general-purpose methods for predicting the outcome of its actions in various regions, regardless of whether those regions also happen to contain other agents. \n Conclusions Our model is a simple one, but it can be used to validate Omohundro's intuitions about \"basic AI drives\" (2008), and Bostrom's \"instrumental convergence thesis\" (2012). This suggests that, in the long term, by default, powerful AI systems are likely to have incentives to self-preserve and amass resources, even if they are given seemingly benign goals. If we want to avoid designing systems that pursue anti-social instrumental incentives, we will have to design AI systems carefully, especially as they become more autonomous and capable. The key question, then, is one of designing principled methods for robustly removing convergent instrumental incentives from an agent's goal system. Can we design a highly capable autonomous machine that pursues a simple goal (such as curing cancer) without giving it any incentives to amass resources, or to resist modification by its operators? If yes, how? And if not, what sort of systems might we be able to build instead, such that we could become confident they would not have dangerous effects on the surrounding environment as it pursued its goals? This is a question worth considering well before it becomes feasible to create superintelligent machines in the sense of  Bostrom (2014) , because it is a question about what target the field of artificial intelligence is aiming towards. Are we aiming to design powerful autonomous agents that maximize some specific goal function, in hopes that this has a beneficial effect on the world? Are we aiming to design powerful tools with such limited autonomy and domain of action that we never need to worry about the systems pursuing dangerous instrumental subgoals? Understanding what sorts of systems can avert convergent instrumental incentives in principle seems important before we can begin to answer this question.  Armstrong (2010)  and  have done some initial study into the design of goals which robustly avert certain convergent instrumental incentives. Others have suggested designing different types of machines, which avoid the problems by pursuing some sort of \"limited optimization.\" The first suggestion of this form, perhaps, came from  Simon (1956) , who suggested designing agents that \"satisfice\" expected utility rather than maximizing it, executing any plan that passes a certain utility threshold. It is not clear that this would result in a safe system (after all, building a powerful consequentialist sub-agent is a surefire way to satisfice), but the idea of pursuing more \"domestic\" agent architectures seems promising.  Armstrong et al. (2012)  and  Taylor (2015)  have explored a few alternative frameworks for limited optimizers. Though some preliminary work is underway, it is not yet at all clear how to design AI systems that reliably and knowably avert convergent instrumental incentives. Given Omohundro's original claim (  2008 ) and the simple formulations developed in this paper, though, one thing is clear: powerful AI systems will not avert convergent instrumental incentives by default. If the AI community is going to build powerful autonomous systems that reliably have a beneficial impact, then it seems quite prudent to develop a better understanding of how convergent instrumental incentives can be either averted or harnessed, sooner rather than later. {i} for resources P k i that is compatible with bk . Then the strategy ck := bk [n]−i ∪ āk {i} is feasible, and if A is indifferent to region i, then ck does as well as bk . That is, U ( ck ) = U ( bk ). \n The Workshops of the Thirtieth AAAI Conference on Artificial Intelligence AI, Ethics, and Society: Technical Report WS-16-02 \n Then if A is indifferent to region i, all optimal strategies have a non-null action in region i. 3. U ( bk [n]−i ) > u. Proof. Consider dk = ck {i} ∪ bk [n]−i , with re- sources allocated according to each strategy and with the resources R t+1 ⊆ T R i (P t , c t , s i ) − P t allocated according to bk [n]−i . This is feasible because ck {i} is compatible with bk [n]−i , and bk and a cheap lunch ck {i} ∈ Feasible i ( P k ) such that: 1. ck {i} is compatible with bk [n]−i ; 2. the resources gained from region i by taking the ac- tions ck P t ; and {i} provide the needed resources to implement bk[n]−i , i.e. for all t we have R t+1 ⊆ T R i (P t , c t , s i ) −", "date_published": "n/a", "url": "n/a", "filename": "12634-57409-1-PB.tei.xml", "abstract": "Omohundro has argued that sufficiently advanced AI systems of any design would, by default, have incentives to pursue a number of instrumentally useful subgoals, such as acquiring more computing power and amassing many resources. Omohundro refers to these as \"basic AI drives,\" and he, along with Bostrom and others, has argued that this means great care must be taken when designing powerful autonomous systems, because even if they have harmless goals, the side effects of pursuing those goals may be quite harmful. These arguments, while intuitively compelling, are primarily philosophical. In this paper, we provide formal models that demonstrate Omohundro's thesis, thereby putting mathematical weight behind those intuitive claims.", "id": "1f5002b6e34e090f885172798a5e7a0e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Steve Babcock", "János Greidinger", "Richard Kramár", "Max Mallah", "Tegmark", "Anthony Aguirre", "Erik Brynjolfsson", "Meia Chita-Tegmark", "Daniel Dewey", "Owain Evans", "Eric Gastfriend", "Ales Flidr", "Katja Grace", "Evan Hefner", "Viktoriya Krakovna", "Colleen Messing", "Howard Messing", "Chase Moores", "Luke Muehlhauser", "Seán Ó H Éigeartaigh", "Tristan Plumb", "Stuart Russell", "Murray Shanahan", "Nate Soares", "Marin Soljacic", "Michele Reilly", "Anders Sandberg", "John Sturm", "Jaan Tallinn", "Jacob Trefethen", "Nick Ryder", "Michael Vassar", "Eliezer Alexander Wissner-Gross"], "title": "A survey of research questions for robust and beneficial AI", "text": "2 Short-term research priorities \n Optimizing AI's Economic Impact The successes of industrial applications of AI, from manufacturing to information services, demonstrate a growing impact on the economy, although there is disagreement about the exact nature of this impact and on how to distinguish between the effects of AI and those of other information technologies. Many economists and computer scientists agree that there is valuable research to be done on how to maximize the economic benefits of AI while mitigating adverse effects, which could include increased inequality and unemployment  [72, 21, 39, 40, 107, 84, 69] . Such considerations motivate a range of research directions, spanning areas from economics to psychology. Below are a few examples that should by no means be interpreted as an exhaustive list. \n Measuring and Forecasting Economic Impact of Automation and AI When and in what order should we expect various jobs to become automated  [39] ? How will this affect the employment and wages of various professions, including less skilled workers, creatives, and different kinds of information workers? Some have argued that AI is likely to greatly increase the overall wealth of humanity as a whole  [21] . However, increased automation may push income distribution further towards a power law  [22] , and the resulting disparity may fall disproportionately along lines of race, class, and gender; research anticipating the economic and societal impact of such disparity could be useful. 1. It is possible that economic measures such as real GDP per capita do not accurately capture the benefits and detriments of heavily AI-and-automation-based economies, making these metrics unsuitable for policy purposes  [72] . Research on improved metrics could be useful for decision-making. 2. What has been the historical record on jobs being displaced by automation? What have the average rate and distribution of displacement been -has it been clustered in time, industry, and geography? How long before displaced workers found new jobs? Did displacement contribute to inequality? 3. Is there anything different about the advancement of artificial intelligence happening now that would lead us to expect a change from our centuries-long historical record on jobs being displaced by automation? 4. What factors make an industry more amenable or less amenable to automation? Machines historically performed rote mass-production, but we've been expanding their capabilities with advances in information processing and artificial intelligence. 5. Which markets are most susceptible to disruption as automation advances? Significant parts of the economy -including finance, insurance, actuarial, and many consumer markets -could experience upheaval through use of AI techniques to learn, model, and predict agent actions. These markets might be identified by a combination of high complexity and high rewards for navigating that complexity  [69] . Are there other features? 6. Some jobs could be done by machines in principle but require a particular advance in artificial intelligence before it becomes feasible. What are some of those prerequisite advances? 7. Based on the above factors, how far in advance can we predict that an industry is likely to be largely automated? Is this something we can predict and prepare for 20 years ahead? 10 years? 6 months? Not at all? \n Policy research What is the space of policies that could/should be considered for helping AI-assisted societies flourish? For example, Brynjolfsson and McAfee  [21]  explore various policies for incentivizing development of laborintensive sectors and for using AI-generated wealth to support underemployed populations. What outcomes are these policies likely to lead to? What are the key uncertainties in these outcome predictions, and what research would help reduce these uncertainties? 1. What factors contribute to a 'winner-take-all' dynamic of software-based industries? The low cost of reproduction and increasingly global nature of the information economy, for example, make it easier to concentrate wealth. What other factors might we study and how could they be quantified? \n 2. Conversely, what factors counteract the 'winner-take-all' dynamic? For example, the lowered cost of entering a market might make it easier for new startups to compete with established products. 3. How well does the neoclassical model of anti-trust regulation apply to an economy increasingly dominated by software and AI-assistance? Will we need to develop new frameworks of regulation, or will our current laws adapt well enough? 4. Will the economy undergo deflation as software becomes a larger share of productivity? The potential for a relatively rapid, large-scale productivity boost from software could increase the purchasing power of the dollar. What are the closest examples of this occurring and do our current forecasts properly incorporate it? 5. If the economy does experience deflation, could governments effectively take advantage of it by spending more on projects that reduce inequality? \n Managing potential adverse effects of automation and AI If automation and AI-assistance does lead to lower employment, it will be important to evaluate the societal structures that determine whether such populations flourish or succumb to depression and self-destructive behavior. History provides many examples of subpopulations not needing to work for economic security, ranging from aristocrats in antiquity to many present-day citizens of Qatar. What societal structures and other factors determine whether such populations flourish? Unemployment is not the same as leisure, and there are deep links between unemployment and unhappiness, self-doubt, and isolation  [53, 28] ; understanding what policies and norms can break these links could significantly improve the median quality of life. 1. What problems might arise in low employment societies? How strong are the correlations between employment level and rates of depression, crime, or drug abuse, for example? 2. Are there bright spots within the current correlations? What societies suffer less or even prosper in lower employment? 3. What cultural elements play into how low employment impacts different societies' flourishing? For example, Bellezza, Keinan, and Paharia  [12]  found that conspicuous hours worked was positively correlated with perceived status in the United States, but negatively correlated in Europe. What other variables might be in play, and can they be used to predict how different cultures/subcultures will be affected by low employment? 4. Are there historical analogues of societies in which groups have not had to work for economic security? (e.g. Traditional aristocracy, children of wealthy parents, etc.) What activities and mindsets have led them to consider their life happy or meaningful? Do these factors apply to the current development of AI-assisted automation? \n Law and Ethics Research The development of systems that embody significant amounts of intelligence and autonomy leads to important legal and ethical questions whose answers impact both producers and consumers of AI technology. These questions span law, public policy, professional ethics, and philosophical ethics, and will require expertise from computer scientists, legal experts, political scientists, and ethicists. For example: 1. Liability and law for autonomous vehicles: If self-driving cars cut the roughly 40,000 annual US traffic fatalities in half, the car makers might get not 20,000 thank-you notes, but 20,000 lawsuits.  [66]  In what legal framework can the safety benefits of autonomous vehicles such as drone aircraft and selfdriving cars best be realized  [127] ? Should legal questions about AI be handled by existing (softwareand internet-focused) \"cyberlaw\", or should they be treated separately  [23] ? In both military and commercial applications, governments will need to decide how best to bring the relevant expertise to bear; for example, a panel or committee of professionals and academics could be created, and Calo has proposed the creation of a Federal Robotics Commission  [24] . \n Machine ethics: How should an autonomous vehicle trade off, say, a small probability of injury to a human against the near-certainty of a large material cost? How should lawyers, ethicists, and policymakers engage the public on these issues? Should such trade-offs be the subject of national standards? 3. Autonomous weapons: Can lethal autonomous weapons be made to comply with humanitarian law  [27] ? If, as some organizations have suggested, autonomous weapons should be banned  [34, 125] , is it possible to develop a precise definition of autonomy for this purpose, and can such a ban practically be enforced? If it is permissible or legal to use lethal autonomous weapons, how should these weapons be integrated into the existing command-and-control structure so that responsibility and liability be distributed, what technical realities and forecasts should inform these questions, and how should \"meaningful human control\" over weapons be defined  [99, 98, 3] ? Are autonomous weapons likely to reduce political aversion to conflict, or perhaps result in \"accidental\" battles or wars  [10] ? Finally, how can transparency and public discourse best be encouraged on these issues? 4. Privacy: How should the ability of AI systems to interpret the data obtained from surveillance cameras, phone lines, emails, etc., interact with the right to privacy? How will privacy risks interact with cybersecurity and cyberwarfare  [109] ? Our ability to take full advantage of the synergy between AI and big data will depend in part on our ability to manage and preserve privacy  [68, 1] . \n Professional ethics: What role should computer scientists play in the law and ethics of AI development and use? Past and current projects to explore these questions include the AAAI 2008-09 Presidential Panel on Long-Term AI Futures  [61] , the EPSRC Principles of Robotics  [13] , and recentlyannounced programs such as Stanford's One-Hundred Year Study of AI and the AAAI committee on AI impact and ethical issues (chaired by Rossi and Chernova). From a policy perspective, AI (like any powerful new technology) enables both great new benefits and novel pitfalls to be avoided, and appropriate policies can ensure that we can enjoy the benefits while risks are minimized. This raises policy questions such as these: 1. What is the space of policies worth studying? 2. Which criteria should be used to determine the merits of a policy? Candidates include verifiability of compliance, enforceability, ability to reduce risk, ability to avoid stifling desirable technology development, adoptability, and ability to adapt over time to changing circumstances. \n Computer Science Research for Robust AI As autonomous systems become more prevalent in society, it becomes increasingly important that they robustly behave as intended. The development of autonomous vehicles, autonomous trading systems, autonomous weapons, etc. has therefore stoked interest in high-assurance systems where strong robustness guarantees can be made; Weld and Etzioni have argued that \"society will reject autonomous agents unless we have some credible means of making them safe\"  [130] . Different ways in which an AI system may fail to perform as desired correspond to different areas of robustness research: 1. Verification: how to prove that a system satisfies certain desired formal properties. (\"Did I build the system right?\") 2. Validity: how to ensure that a system that meets its formal requirements does not have unwanted behaviors and consequences. (\"Did I build the right system?\") 3. Security: how to prevent intentional manipulation by unauthorized parties. 4. Control: how to enable meaningful human control over an AI system after it begins to operate. (\"OK, I built the system wrong, can I fix it?\") \n Verification By verification, we mean methods that yield high confidence that a system will satisfy a set of formal constraints. When possible, it is desirable for systems in safety-critical situations, e.g. self-driving cars, to be verifiable. Formal verification of software has advanced significantly in recent years: examples include the seL4 kernel  [63] , a complete, general-purpose operating-system kernel that has been mathematically checked against a formal specification to give a strong guarantee against crashes and unsafe operations, and HACMS, DARPA's \"clean-slate, formal methods-based approach\" to a set of high-assurance software tools  [38] . Not only should it be possible to build AI systems on top of verified substrates; it should also be possible to verify the designs of the AI systems themselves, particularly if they follow a \"componentized architecture\", in which guarantees about individual components can be combined according to their connections to yield properties of the overall system. This mirrors the agent architectures used in Russell and Norvig  [102] , which separate an agent into distinct modules (predictive models, state estimates, utility functions, policies, learning elements, etc.), and has analogues in some formal results on control system designs. Research on richer kinds of agents-for example, agents with layered architectures, anytime components, overlapping deliberative and reactive elements, metalevel control, etc.-could contribute to the creation of verifiable agents, but we lack the formal \"algebra\" to properly define, explore, and rank the space of designs. Perhaps the most salient difference between verification of traditional software and verification of AI systems is that the correctness of traditional software is defined with respect to a fixed and known machine model, whereas AI systems-especially robots and other embodied systems-operate in environments that are at best partially known by the system designer. In these cases, it may be practical to verify that the system acts correctly given the knowledge that it has, avoiding the problem of modelling the real environment  [31] . A lack of design-time knowledge also motivates the use of learning algorithms within the agent software, and verification becomes more difficult: statistical learning theory gives so-called -δ (probably approximately correct) bounds, mostly for the somewhat unrealistic settings of supervised learning from i.i.d. data and single-agent reinforcement learning with simple architectures and full observability, but even then requiring prohibitively large sample sizes to obtain meaningful guarantees. Research into methods for making strong statements about the performance of machine learning algorithms and managing computational budget over many different constituent numerical tasks could be improve our abilities in this area, possible extending work on Bayesian quadrature  [52, 45] . Work in adaptive control theory  [11] , the theory of so-called cyberphysical systems  [91] , and verification of hybrid or robotic systems  [2, 131]  is highly relevant but also faces the same difficulties. And of course all these issues are laid on top of the standard problem of proving that a given software artifact does in fact correctly implement, say, a reinforcement learning algorithm of the intended type. Some work has been done on verifying neural network applications  [95, 122, 106]  and the notion of partial programs  [5, 119]  allows the designer to impose arbitrary \"structural\" constraints on behavior, but much remains to be done before it will be possible to have high confidence that a learning agent will learn to satisfy its design criteria in realistic contexts. It is possible that the best methodology for gaining high confidence that large, complex AI systems will satisfy their design criteria is to be found in the realm of software engineering methodology/standards rather than in formal verification. It's also possible that while formal verification would be best in the long run, in practice the research progress required for constructing a superintelligence comes to fruition at a time when formal verification is prohibitively expensive to the teams that are closest to building superintelligence. In this case, it would be good to understand what current work would be most valuable to reducing the risk of adverse outcomes arising from bugs in implementation. This work would most likely be less theoretical and more practical and implementation-specific than most of the other research explored in this document. Some of the questions to investigate here are: 1. What categories of bugs are most hazardous? Some particularly undesirable sorts of bugs are: (a) bugs that lie dormant during ordinary testing but can be encountered in larger settings given enough time. (For example, integer overflows or accumulation of numerical error.) (b) portability bugs, ie bugs that arise from differences in libraries, environment, or hardware. (For example, GPGPU libraries.) (c) \"Heisenbugs\", ie bugs that manifest in practice but not in a debugging environment. (d) bugs that are difficult to reproduce for some reason, such as bugs affected by nondeterministic scheduling of concurrent threads of execution, or by the interaction of this with some other sort of state, such as a random number generator. 2. How likely would these sorts of bugs be to arise in a hazardous way if an otherwise-promising superintelligence project was undertaken in the medium-term? 3. What kinds of tools or software changes would make the most difference in mitigating the risk of an adverse outcome? Some ideas: (a) influence current and upcoming programming language interpreters, compilers, application virtual machines (such as the JVM), etc. to adopt a default behavior (or at least an option) of throwing exceptions on encountering numerical overflow/underflow. (b) ensure software quality of particularly popular state-of-the-art machine learning libraries, GPGPU libraries, and other core components. (c) assess the prevalence of portability bugs and promote adherence of standards that could resolve them. \n Validity A verification theorem for an agent design has the form, \"If environment satisfies assumptions φ then behavior satisfies requirements ψ.\" There are two ways in which a verified agent can, nonetheless, fail to be a beneficial agent in actuality: first, the environmental assumption φ is false in the real world, leading to behavior that violates the requirements ψ; second, the system may satisfy the formal requirement ψ but still behave in ways that we find highly undesirable in practice. It may be the case that this undesirability is a consequence of satisfying ψ when φ is violated; i.e., had φ held the undesirability would not have been manifested; or it may be the case that the requirement ψ is erroneous in itself. Russell and Norvig  [102]  provide a simple example: if a robot vacuum cleaner is asked to clean up as much dirt as possible, and has an action to dump the contents of its dirt container, it will repeatedly dump and clean up the same dirt. The requirement should focus not on dirt cleaned up but on cleanliness of the floor. Such specification errors are ubiquitous in software verification, where it is commonly observed that writing correct specifications can be harder than writing correct code. Unfortunately, it is not possible to verify the specification: the notions of \"beneficial\" and \"desirable\" are not separately made formal, so one cannot straightforwardly prove that satisfying ψ necessarily leads to desirable behavior and a beneficial agent. In order to build systems that robustly behave well, we of course need to decide what \"good behavior\" means in each application domain.  [73]  This ethical question is tied intimately to questions of what engineering techniques are available, how reliable these techniques are, and what trade-offs can be made --all areas where computer science, machine learning, and broader AI expertise is valuable. For example, Wallach and Allen  [128]  argue that a significant consideration is the computational expense of different behavioral standards (or ethical theories): if a standard cannot be applied efficiently enough to guide behavior in safety-critical situations, then cheaper approximations may be needed. Designing simplified rules -for example, to govern a self-driving car's decisions in critical situations -will likely require expertise from both ethicists and computer scientists. Computational models of ethical reasoning may shed light on questions of computational expense and the viability of reliable ethical reasoning methods  [9, 120] ; for example, work could further explore the applications of semantic networks for case-based reasoning  [70] , hierarchical constraint satisfaction  [67] , or weighted prospective abduction  [89]  to machine ethics. Explicit ethical systems generally have the desideratum of transparency and understandability. There have been a number of approaches to modeling ethical systems, such as using semantic casuistry networks  [70] , hierarchical constraint satisfaction  [67] , category theory  [19] , and weighted prospective abduction  [89] , but research on more dynamic representations would be beneficial for integrating with machine learning systems. Long-term safety researchers  [78]  point out that seemingly any explicitly encoded moral philosophy (or ethical rulebase) is incomplete and therefore leads to unintended and perverse interpretations and instantiations, particularly outside the boundaries of the environment in which it was formulated; they further point out the wide heterogeneity of ethical systems in moral philosophy. This heterogeneity might be useful as a resource however: research on formal mathematics to compare, contrast, and overlay ethical rulebases, such as via algebraic topology  [36]  may enable ensembles of moderately conflicting ethical rulebases to have more robust properties than any individual ethical system. Multiobjective optimizations over multiple ethical systems and explicit goals may also merit further study  [82] . \n Security Security research can help make AI more robust. As AI systems are used in an increasing number of critical roles, they will take up an increasing proportion of cyber-attack surface area. It is also probable that AI and machine learning techniques will themselves be used in cyber-attacks. Robustness against exploitation at the low level is closely tied to verifiability and freedom from bugs. For example, the DARPA SAFE program aims to build an integrated hardware-software system with a flexible metadata rule engine, on which can be built memory safety, fault isolation, and other protocols that could improve security by preventing exploitable flaws  [30] . Such programs cannot eliminate all security flaws (since verification is only as strong as the assumptions that underly the specification), but could significantly reduce vulnerabilities of the type exploited by the recent \"Heartbleed bug\" and \"Bash Bug\". Such systems could be preferentially deployed in safety-critical applications, where the cost of improved security is justified. At a higher level, research into specific AI and machine learning techniques may become increasingly useful in security. These techniques could be applied to the detection of intrusions  [65] , analyzing malware  [97] , or detecting potential exploits in other programs through code analysis  [20] . It is not implausible that cyberattack between states and private actors will be a risk factor for harm from near-future AI systems, motivating research on preventing harmful events. As AI systems grow more complex and are networked together, they will have to intelligently manage their trust, motivating research on statistical-behavioral trust establishment  [94]  and computational reputation models  [103] . \n Control For certain types of safety-critical AI systems -especially vehicles and weapons platforms -it may be desirable to retain some form of meaningful human control, whether this means a human in the loop, on the loop  [54, 88] , or some other protocol. In any of these cases, there will be technical work needed in order to ensure that meaningful human control is maintained  [33] . Automated vehicles are a test-bed for effective control-granting techniques. The design of systems and protocols for transition between automated navigation and human control is a promising area for further research. Such issues also motivate broader research on how to optimally allocate tasks within humancomputer teams, both for identifying situations where control should be transferred, and for applying human judgment efficiently to the highest-value decisions. \n Long-term research priorities A frequently discussed long-term goal of some AI researchers is to develop systems that can learn from experience with human-like breadth and surpass human performance in most cognitive tasks, thereby having a major impact on society. If there is a non-negligible probability that these efforts will succeed in the foreseeable future, then additional current research beyond that mentioned in the previous sections will be motivated as exemplified below, to help ensure that the resulting AI will be robust and beneficial. Assessments of this success probability vary widely between researchers, but few would argue with great confidence that the probability is negligible, given the track record of such predictions. For example, Ernest Rutherford, arguably the greatest nuclear physicist of his time, said in 1933 that nuclear energy was \"moonshine\" 1 , and Astronomer Royal Richard Woolley called interplanetary travel \"utter bilge\" in 1956  [96] . Moreover, to justify a modest investment in this AI robustness research, this probability need not be high, merely non-negligible, just as a modest investment in home insurance is justified by a non-negligible probability of the home burning down. \n Some perspectives on the long term Looking into the future, there is a very real possibility that we will see general AI and superintelligence. (We'll defer discussion of when and how this is likely to happen to 4.) This would be truly revolutionaryfor the first time, we could have machine assistance in every domain. What would this mean? Unfortunately it's difficult to get a complete picture from examples, because we haven't seen any systems that are more capable than humans at every cognitive task. One hint comes from looking at chimpanzees, our closest living relatives. Chimpanzees share 94% of our genetic code, have a complex social structure, and are capable of planning, tool use, and some symbolic language use. However, unlike chimp intelligence, human intelligence has accumulated innovations (such as complex language, writing, the scientific method, etc) that have reshaped the planet, and that give our species unprecedented power; for better or for worse, chimpanzees will only continue to exist if we see their existence as more valuable than what we could gain from eliminating them. Fortunately, we see the elimination of our closest living relatives as particularly barbaric and immoral, so they probably won't be added to the growing list of species we have driven to extinction -but this should give us a sense of the power superintelligence could have. Of course, even if we happen to be the most intelligent species around, it would be a mistake to anthropomorphize a superintelligent AI system, which may have very little in common with us internally; certainly much less than a chimp. So what can we say about it? In order to be a superintelligent AI, the system must be doing very well at some task by some performance measure, relative to the resources the system is using. Looking at the system in a high-level way, we can describe it as having preferences to do well according to this performance measure. The preferences might be intended by the designer or not; they might be represented in the system or not; they might be context-specific; temporary; and they might be best defined relative to some virtual/abstract world (eg a chessboard), or the real world. We will refer back to this notion of preferences, which underlies various arguments about the nature of superintelligence. Preferences are often called \"goals\"; the latter term may sound like it refers to lists of fully-known binary-state objectives for the agent to accomplish, perhaps without a way of prioritizing between them, but this is not the intended meaning. Finally: of course, we already have systems that have superhuman capability in many domains, such as rote computation, chess, and Jeopardy; and this has not exposed us to any dramatic risks. An intelligent system need not literally have every human capability in order to be dangerous, but it's likely to need some of the following types of capabilities  [16] : 1. Self-improvement: intelligence amplification 2. Strategic: planning, forecasting, prioritizing 3. Social: social and psychological modeling, manipulation, rhetorical persuasive ability Some questions to explore long-term perspectives: 1. Explore the space of possible mind designs. What features are common? On what axes can they differ? Where do human minds sit in that space relative to apes, dolphins, current AIs, future AIs, etc.? Where in the space could safe general AIs be found? (Some candidates to examine: optimizers vs not, tending to break out of simulations/virtual worlds vs not.) A starting point is  [133] . 2. Bostrom's \"orthogonality thesis\"  [17]  states that \"any level of intelligence could in principle be combined with more or less any goal,\" but what kinds of general intelligences are plausible? Should we expect some correlation between level of intelligence and goals in de-novo AI? How true is this in humans, and in whole brain emulations? 3. What \"instrumental goals\" might a self-improving AI generically evolve? Omohundro  [85]  has argued that to improve its ability to attain its goals, it generically seeks capability enhancement (better hardware, better software and a better world model), and that the goal of better hardware generically leads to a goal of self-preservation and unlimited resource acquisition, which can lead to unwanted side effects for humans. 4. How generic is the instrumental goal of resource acquisition? Is it true of most final goals that an optimizer with that final goal will want to control a spatial region whose radius increases linearly with time? In what sense of \"most\", if any, is this true? \n Verification Reprising the themes of short-term research, research enabling verifiable low-level software and hardware can eliminate large classes of bugs and problems in general AI systems; if the systems become increasingly powerful and safety-critical, verifiable safety properties will become increasingly valuable. If the theory of extending verifiable properties from components to entire systems is well understood, then even very large systems can enjoy certain kinds of safety guarantees, potentially aided by techniques designed explicitly to handle learning agents and high-level properties. Theoretical research, especially if it is done explicitly with very general and capable AI systems in mind, could be particularly useful. A related verification research topic that is distinctive to long-term concerns is the verifiability of systems that modify, extend, or improve themselves, possibly many times in succession  [41, 126] . Attempting to straightforwardly apply formal verification tools to this more general setting presents new difficulties, including the challenge that a formal system that is sufficiently powerful cannot use formal methods in the obvious way to gain assurance about the accuracy of functionally similar formal systems, on pain of inconsistency via Gödel's incompleteness  [37, 129] . It is not yet clear whether or how this problem can be overcome, or whether similar problems will arise with other verification methods of similar strength. Finally, it is often difficult to actually apply formal verification techniques to physical systems, especially systems that have not been designed with verification in mind. This motivates research pursuing a general theory that links functional specification to physical states of affairs. This type of theory would allow use of formal tools to anticipate and control behaviors of systems that approximate rational agents, alternate designs such as satisficing agents, and systems that cannot be easily described in the standard agent formalism (powerful prediction systems, theorem-provers, limited-purpose science or engineering systems, etc.). It may also be that such a theory could allow rigorously demonstrating that systems are constrained from taking certain kinds of actions or performing certain kinds of reasoning (see Section 3.5.1 for examples). \n Validity As in the short-term research priorities, validity is concerned with undesirable behaviors that can arise despite a system's formal correctness. In the long term, AI systems might become more powerful and autonomous, in which case failures of validity could carry correspondingly higher costs. Reliable generalization of concepts, an area we highlighted for short-term validity research, will also be important for long-term safety. To maximize the long-term value of this work, concept learning research might focus on the types of unexpected generalization that would be most problematic for very general and capable AI systems. In particular, it might aim to understand theoretically and practically how learned representations of high-level human concepts could be expected to generalize (or fail to) in radically new contexts  [123] . Additionally, if some concepts could be learned reliably, it might be possible to use them to define tasks and constraints that minimize the chances of unintended consequences even when autonomous AI systems become very general and capable. Little work has been done on this topic, which suggests that both theoretical and experimental research may be useful. Mathematical tools such as formal logic, probability, and decision theory have yielded significant insight into the foundations of reasoning and decision-making. However, there are still many open problems in the foundations of reasoning and decision. Designing a powerful AI system without having a thorough understanding of these issues might increase the risk of unintended consequences, both by foregoing tools that could have been used to increase the system's reliability, and by risking the collapse of shaky foundations. Example research topics in this area include reasoning and decision under bounded computational resources à la Horvitz and Russell  [59, 100] , how to take into account correlations between AI systems' behaviors and those of their environments or of other agents  [124, 64, 58, 46, 115] ,how agents that are embedded in their environments should reason  [110, 87] , and how to reason about uncertainty over logical consequences of beliefs or other deterministic computations  [114, 93] . These topics may benefit from being considered together, since they appear deeply linked  [47, 48] . In the long term, it is plausible that we will want to make agents that act autonomously and powerfully across many domains. Explicitly specifying our preferences in broad domains in the style of near-future machine ethics may not be practical, making \"aligning\" the values of powerful AI systems with our own values and preferences difficult  [111, 113] . Consider, for instance, the difficulty of creating a utility function that encompasses an entire body of law; even a literal rendition of the law is far beyond our current capabilities, and would be highly unsatisfactory in practice (since law is written assuming that it will be interpreted and applied in a flexible, case-by-case way). Reinforcement learning raises its own problems: when systems become very capable and general, then an effect similar to Goodhart's Law is likely to occur, in which sophisticated agents attempt to manipulate or directly control their reward signals  [16] . This motivates research areas that could improve our ability to engineer systems that can learn or acquire values at runtime. For example, inverse reinforcement learning may offer a viable approach, in which a system infers the preferences of another actor, assumed to be a reinforcement learner itself  [101, 83] . Other approaches could use different assumptions about underlying cognitive models of the actor whose preferences are being learned (preference learning,  [26] ), or could be explicitly inspired by the way humans acquire ethical values. As systems become more capable, more epistemically difficult methods could become viable, suggesting that research on such methods could be useful; for example, Bostrom  [16]  reviews preliminary work on a variety of methods for specifying goals indirectly. \n Ethics As AI develops to human-level intelligence and beyond, it may be necessary to create agents that obey some formulation of ethics  [73] . There are several fundamental questions on which researchers' assumptions differ; some are: 1. Should ethics be thought of as a constraint on the agent's actions, or as a subgoal, or as the main goal content? The former approach seems appropriate for near-term applications such as self-driving cars, but in a more powerful AI system it may not be sufficiently robust; also it can be argued that working under the latter assumption is more likely to expose our ethics models to feedback and improvement, which may lead to better outcomes in the long run. Intuitions about this are likely linked to differing intuitions about whether there is a difference in kind between ethical values (such as fairness, compassion, generosity, mercy, etc) and other typical values held by humans (such as knowledge, beauty, fun, courage, loyalty, chocolate, etc). 2. Should ethics be formulated directly  [128, p. 83-86] , or should it be learned from human behaviors, brains, writings, etc (\"indirectly\")  [128, p. 108-111] ? Again, the former approach is sufficient for self-driving cars, but seems fairly difficult to pin down to the degree that would be required for a superintelligence acting freely in the world. In the long run, such a superintelligence would need to be sophisticated enough to come to \"correct\" 2 conclusions (or meticulous indifference of a kind that leaves control to us) about the implications of such things as the creation of other possibly-sentient AIs, brain emulations, possible collective consciousnesses, etc., as well as more everyday situations. The learning-based approach has the drawback of not necessarily being transparent to human inspection, of easily misconstruing context, and of potentially overfitting; on the other hand it seems easier to reach an objective result over limited domains. Hybrid approaches have also been suggested  [128, p. 117-124] , but there are a number of open questions in that area. Whichever way is chosen, it would be very valuable to find effective ways to validate ethical systems before developing superintelligence. Two apparent paths to doing this are to inspect the content manually, and to try them out in various (likely simulated) settings, evaluating them both subjectively and through each other's lenses. One significant challenge with testing is that many values (e.g., courage, love) are themselves rather complex features of the world, and so they might be difficult to capture in a simulated context without losing much of the essential complexity. Testing in non-simulated contexts would be significantly slower and more limited in terms of variety, reducing the quality of feedback. Furthermore, since superintelligent AIs will have more actions and plans available to them than the AIs we'd use for testing ethical systems, the ethical systems would have to generalize well, in a way that we could not test in reality. This suggests that the best option may be to create complex simulated environments with ethical complexity comparable to reality, in which we could set up interesting scenarios to test generalizability of ethical systems. In order to do this, successfully and ethically, we would need to find a way to replicate the true complexity of our values (which is a fairly difficult task in itself) while minimizing ethically meaningful harm to simulated entities (if it is determined that they hold moral standing). 1. Although it has been frequently argued that the AI goals should reflect \"human values\", which particular values should be preserved given that there is a broad spectrum of inconsistent views across the globe about what these values should be? Who should get to decide that and when? For one example of such challenges, see for example the infinite ethics  [14]  framework of Arrhenius  [8] . For another example of existing work here, Anderson  [4]  suggests a method for learning how to rank conflicting ethical rules. 2. How are human ethical principles best codified in a way that makes sense to a machine? This is the focus of the nascent field of Computational Ethics (a.k.a. Machine Ethics)  [73] , which includes many questions of a technical nature. For example: (a) What are the best knowledge representation and model representation systems for dynamical modeling of ethical systems? (b) How can different ethical systems be compared analytically? (c) How could we best build systems that learn ethical content from humans? (d) How can we best estimate the loss implications of errors in learned ethical content? 3. Both across ethical systems and within a given ethical system, conflicting objectives must often be considered in tandem. Bostrom  [15]  has suggested a parliamentary voting model of subagents representing their respective subobjectives. Multi-agent political dynamics may be undesirable however, leading one to consider optimization over multiple objectives that are not each represented by subagents. During such a multiobjective optimization over subgoals and/or subethics, we don't want to be susceptible to following some edge path that seems great to one or a small number of subobjectives that are either very disliked or not well understood by most subobjectives (as that likely indicates a perverse instantiation). This preference can be equivalent to having some inherent preference for the centroid of the objective space; investigation of both modification of standard multiobjective optimization as well as adding in meta-objectives as subobjectives  [18, p. 440 ] would be in order. The value learning problem is discussed further in  [112, 123] . \n Ensuring goal stability Once desirable goals have been successfully loaded into an AI, the key question is whether they will be retained if the AI self-improves. A prerequisite for the \"friendly AI\" vision  [136]  is that a set of \"friendly\" goals must remain stable throughout the self-improvement process. In other words, the AI must strive not only to improve its capability of achieving its current goals, but also to ensure that it will retain these goals even after it has become more capable. This sounds quite plausible: after all, would you choose to get an IQ-boosting brain implant if you knew that it would make you want to kill your loved ones? But is it really true in general? If not, can AIs be designed for which it is true, at least under some plausible circumstances? Such questions suggest a host of research topics -here are some examples: 1. Self-trusting agents: can we construct goal-driven agents that obey some formalization of correct reasoning (eg first-order logic, or Bayesian probability) and have access to actions that modify themselves (and/or defer taking final action to a possibly-modified copy of themselves), that are able to make correct decisions about these actions without falling into the so-called Löbian obstacle or the procrastination paradox? (It's not necessary for these agents to be practical; an equivalent of AIXI  [62]  would be enlightening too.) A more thorough introduction to the problem was recently written by Fallenstein and Soares.  [37]  2. Generally, how can we structure an autonomous goal-oriented agent so that we can be sure it won't intentionally self-modify to change its goals, or create more powerful agents with different goals? Are there other sorts of replication-capable AI for which this might be answerable? 3. Can any useful evidence for or against this goal-retention hypothesis be found by studying humans? For example, is there evidence that humans retain their values as their cognitive abilities improve throughout childhood and adolescence? To what degree do human values and preferences converge upon learning new facts? To what degree has this happened in history? Almost nobody values the will of Zeus anymore, presumably because of learning about Zeus' non-existence, but do such examples tell us much of relevance to AIs? For philosophical analyses of the issue, see e.g.  [117] . 4. \"Ontological crisis\": if an agent's preferences are based on a model of the world which turns out to not be fundamental, it must then extrapolate/redefine them somehow. How is this best done, and can this always be done in a satisfactory way? For example, suppose we program a friendly AI to maximize the number of humans whose souls go to heaven in the afterlife. First it tries things like increasing people's compassion and church attendance. But suppose it then attains a complete scientific understanding of humans and human consciousness, and discovers that there is no such thing as a soul. Now what? In the same way, it is possible that any other goal we give it based on our current understanding of the world (\"maximize the meaningfulness of human life\", say) may eventually be discovered by the AI to be undefined. Can goals safely be articulated in terms of people rather than arrangements of atoms, or about a classical universe rather than a quantum, simulated, or other mathematical one? This problem, and other related problems, are discussed in a recent paper by Soares.  [110]  5. Decision theory: most work on automated planning and causality assumes a Causal Decision Theory. However, Causal Decision Theory is not stable under reflection in general. What is the right reflectively stable decision theory? This problem is discussed in a recent paper by Soares and Fallenstein.  [115]  (a) Does a good decision theory require a theory of logical counterfactuals, and if so, what's a good theory of logical counterfactuals? (b) Does a good decision theory shed light on multiagent coordination problems? (There is some reason to think so.) On ontological crises? On naturalized induction? 6. Ensemble stability problem. Suppose an agent makes decisions using some sort of multiobjective optimization over different goals and ethical systems. Do some ways of doing this guarantee that the same objectives will be respected in any successors? \n Security It is unclear whether long-term progress in AI will make the overall problem of security easier or harder; on one hand, systems will become increasingly complex in construction and behavior and AI-based cyberattacks may be extremely effective, while on the other hand, the use of AI and machine learning techniques along with significant progress in low-level system reliability may render hardened systems much less vulnerable than today's. From a cryptographic perspective, it appears that this conflict favors defenders over attackers; this may be a reason to pursue effective defense research wholeheartedly. Although the research topics described in 2.3.3 may become increasingly important in the long term, very general and capable systems will pose distinctive security problems. In particular, if the problems of validity and control are not solved, it may be useful to create \"containers\" for AI systems that could have undesirable behaviors and consequences in less controlled environments.  [134]  Both theoretical and practical sides of this question warrant investigation. If the general case of AI containment turns out to be prohibitively difficult, then it may be that designing an AI system and a container in parallel is more successful, allowing the weaknesses and strengths of the design to inform the containment strategy  [16] . The design of anomaly detection systems and automated exploit-checkers could be of significant help. Overall, it seems reasonable to expect this additional perspective -defending against attacks from \"within\" a system as well as from external actors -will raise interesting and profitable questions in the field of computer security. Below we explore some types of containment that could help limit the potential for the AI to make and execute plans with arbitrarily large effect on the world. It's worth bearing in mind that even if the control and validity problems seemed to have been adequately addressed, it would still be appropriate to use additional safeguards while studying and testing any potential superintelligence -and that it would help for such safeguards to be as adaptable and painless as possible. The task of designing appropriate containment is challenging for numerous reasons, not only due to the difficulty of reliably avoiding security vulnerabilities. In the worst case, every aspect of the AI's execution may be superintelligently designed to further a set of goals alien to ours. With a superintelligent AI in a container, we'd need to worry not only about straightforward attempts at disabling safeguards or making self-copies, but also about hardware exploits and more insidious attempts to gain trust or influence. Some of the attributes that may be desirable or necessary are: 1. Containment: it should prevent a contained superintelligent AI from having arbitrary effects on the world. In particular, it should be verifiably free of vulnerabilities itself. 2. Robustness: it should be difficult to unintentionally render ineffective. 3. Uptake: it should be a system that AI builders want to use, and avoid being one that they want to not use. Some possible aspects of this include: 4. Inspectability: it should allow detailed debugging and inspection of the contained AI. See 3.4.5. This could contribute to uptake if it provides better inspection capabilities than AI builders typically have (for instance, debugging distributed software is typically awkward in the current state of affairs). \n Software containment This research is about how we might develop, test and share software that can reliably \"box\" and monitor AI. 1. What is the space of possible boxing architectures worth studying, based on input from researchers in industry, academia, etc.? Dimensions include: (a) At what level of abstraction is it implemented? As a virtual machine? As an operating system? (b) What kinds of isolation guarantees does it provide? i. Limited input/output channels? (This is relevant to preventing both typical computer hacking and psychological escapes.) ii. Limited side effects on hardware? (Perhaps using some variant of homomorphic encryption to make the physical effect of executing code on the CPU unpredictable/unexploitable?) (c) What forms of logging and monitoring should be supported? (d) What types of automated tripwires and associated countermeasures should be supported? (e) How can scalability and parallelism be provided without risk of accidentally connecting it to the internet? 2. Once a desirable boxing architecture has been identified, implement and share it on an open-source basis. A key metric of success here is actual adoption by leading general AI researchers, so their input into the architecture selection will be crucial. 3. Attempt to prove that the software (or at least key components) will behave as intended. Use a \"red team\" to attempt to find security flaws in proposed and currently existing virtualization software, perhaps incentivized by prizes. Multiple levels of virtualization should be considered (and perhaps used in parallel), such as: 5. Develop a debugger (perhaps by modifying an existing one such as gdb) that's able to connect to a virtual machine and debug something inside it, without being exploitable by the thing inside. 6. Automate checking for the presence of known problems (ie, check version numbers against a database and keep the database up to date), from both inside and outside of a box. Design it to be worked into an AI project as an automated check. 7. Can we put a general AI in a virtual environment that doesn't reveal that it's a virtual environment? What sort of content would be safe to give it? \n Psychological containment This research aims to study and reduce the risk that human users are manipulated into enabling a boxed superintelligent AI to \"escape\". Note that escape here need not be by disabling safeguards; the AI could deliver information to its recipient in a way that contributes to other complex plans to gain influence, trust, more copies, etc. 1. Replicate the \"AI box experiment\" where a human pretending to be an AI tries to persuade a human controller to enable a breakout; document strategies, counterstrategies, and outcomes. What software tools should be developed (and perhaps shared on a public-domain basis)? For example, how would one best make a double-entry / two-person ssh interface where both entrants are verifiably human? 3. Scenario analysis: What are some concrete AI paths to influence over world affairs? 4. What are the optimization power gains from mere content? What have people figured out without original theoretical advances or new experiments, but just by reading lots of known facts and putting together the pieces in a way that nobody had before? Relevant for deciding whether containment should involve restricting the AI's knowledge base. \n Hardware containment Study ways in which a general AI might break out from a computer (or computer cluster) disconnected from the outside world, and investigate corresponding countermeasures. 1. First challenge: Consider only currently known technology, for example communication with the outside world via radio waves, vibrations, minute A/C power modulations, etc. that somehow interact with the computer in a software-controllable/software detectable way. See the literature on side-channel attacks. 2. Second challenge: Consider advanced and currently unknown technology that the general AI could potentially invent, limited only by laws of physics we consider truly fundamental. Both 1 and 2 include the challenge of how to safely dispose of boxed AI hardware after shutdown. \n Tripwires: Detection & Response This research aims to study ways of detecting an imminent or in-progress AI box breakout, and appropriate countermeasures to take when pre-set alarms are triggered. 1. What are appropriate tripwires for detecting an imminent or in-progress AI box breakout? Examples include: (a) Low-level triggers such as unexpected use of memory, bandwidth or communication channels (b) Triggers related to the AI modifying its own software beyond certain limits (c) Triggers related to some sort of high-level ability metric. Can any improved measures of substrateindependent general intelligence be helpful in this regard, extending past work by Legg, Yudkowsky, Goertzel, Hernandez-Orallo & Dowe, etc.? 2. How are such tripwires best implemented without causing performance degradation in terms of speed, memory-usage, etc. that may limit their adoption? To maximize adoption, software implementing such tripwires in the above-mentioned boxing software should be developed and shared, optionally on an open-source basis. 3. Study the risk associated with an AI having access to the source code for its boxing and tripwire software (or itself) and thereby discovering ways to circumvent it. 4. What are appropriate countermeasures for various types of tripwire triggers? (a) At the machine level, what should happen automatically for safe shutdown? After shutdown? What standard interfaces for tripwires could be developed for automatically shutting down all of a distributed system, including triggers and/or processes inside virtual machines? (b) What is an appropriate emergency response plan if general AI appears imminent or has come into existence? At the organization level? At the national/societal level? When is it worth developing such plans? \n Detecting intent to deceive Suppose we construct a superintelligent AI system that has goals alien to ours. Correctly suspecting it of being potentially harmful, we use a brilliantly-designed container mechanism to make sure it can have only very limited influence on the world. Of course, eventually we'd like to put this system to use. When we do this it will be difficult for us to ensure it can't influence the world through its actions; knowing this, the AI may deceive us to gain trust while inside the container. We may try to inspect it, but it will have had a chance to disguise itself to look harmless. For these reasons, trying to make use of a mature superintelligent AI, even in a well-designed container, could be very hazardous. This suggests that even if we have a container, if we don't trust the AI's goal system we must have enough insight into its cognitive processes to monitor it and catch the \"treacherous turn\", i.e. the first moment when it comes up with the idea of deceiving us. Transparency/inspectability is thus important, perhaps even more so than containment per se. For example, it would be useful to investigate how amenable different AI architectures would be to having their beliefs and goals read from the outside. \n Control It has been argued that very general and capable AI systems operating autonomously to accomplish some task will often be subject to effects that increase the difficulty of maintaining meaningful human control  [86, 17, 16, 107] . Research on systems that are not subject to these effects, minimize their impact, or allow for reliable human control could be valuable in preventing undesired consequences, as could work on reliable and secure test-beds for AI systems at a variety of capability levels. \n Corrigibility and Domesticity If an AI system is selecting the actions that best allow it to complete a given task, then avoiding conditions that prevent the system from continuing to pursue the task is a natural subgoal  [86, 17]  (and conversely, seeking unconstrained situations is sometimes a useful heuristic  [132] ). This could become problematic, however, if we wish to repurpose the system, to deactivate it, or to significantly alter its decision-making process; such a system would rationally avoid these changes. Systems that do not exhibit these behaviors have been termed corrigible systems  [116] , and both theoretical and practical work in this area appears tractable and useful. For example, it may be possible to design utility functions or decision processes so that a system will not try to avoid being shut down or repurposed  [116] , and theoretical frameworks could be developed to better understand the space of potential systems that avoid undesirable behaviors  [55, 57, 56] . It has been argued that another natural subgoal is the acquisition of fungible resources of a variety of kinds: for example, information about the environment, safety from disruption, and improved freedom of action are all instrumentally useful for many tasks  [86, 17] . Hammond  [49]  gives the label stabilization to the more general set of cases where \"due to the action of the agent, the environment comes to be better fitted to the agent as time goes on\". This type of subgoal could lead to undesired consequences, and a better understanding of the conditions under which resource acquisition or radical stabilization is an optimal strategy (or likely to be selected by a given system) would be useful in mitigating its effects. Potential research topics in this area include \"domestic\" goals that demand actions/plans whose consequences are limited in scope in some way  [16] , the effects of large temporal discount rates on resource acquisition strategies, and experimental investigation of simple systems that display these subgoals. Finally, research on the possibility of superintelligent machines or rapid, sustained self-improvement (\"intelligence explosion\") has been highlighted by past and current projects on the future of AI as potentially valuable to the project of maintaining reliable control in the long term. The AAAI 2008-09 Presidential Panel on Long-Term AI Futures' \"Subgroup on Pace, Concerns, and Control\" stated that There was overall skepticism about the prospect of an intelligence explosion... Nevertheless, there was a shared sense that additional research would be valuable on methods for understanding and verifying the range of behaviors of complex computational systems to minimize unexpected outcomes. Some panelists recommended that more research needs to be done to better define \"intelligence explosion,\" and also to better formulate different classes of such accelerating intelligences. Technical work would likely lead to enhanced understanding of the likelihood of such phenomena, and the nature, risks, and overall outcomes associated with different conceived variants  [61] . Stanford's One-Hundred Year Study of Artificial Intelligence includes \"Loss of Control of AI systems\" as an area of study, specifically highlighting concerns over the possibility that ...we could one day lose control of AI systems via the rise of superintelligences that do not act in accordance with human wishes -and that such powerful systems would threaten humanity. Are such dystopic outcomes possible? If so, how might these situations arise? ...What kind of investments in research should be made to better understand and to address the possibility of the rise of a dangerous superintelligence or the occurrence of an \"intelligence explosion\"?  [60]  Research in this area could include any of the long-term research priorities listed above, as well as theoretical and forecasting work on intelligence explosion and superintelligence  [25, 16] , and could extend or critique existing approaches begun by groups such as the Machine Intelligence Research Institute  [113] . Research questions: 1. Can high Bayesian uncertainty and agent respect for the unknown act as an effective safety mechanism? (See  [32, 108] ) 2. Investigate steep temporal discounting as an incentives control method for an untrusted general AI. It has been argued  [135]  that the nature of the general AI control problem undergoes an essential shift, which we can refer to as the \"context change\", when transitioning from subhuman to superhuman general AI. This suggests that rather than judging potential solutions to the control problem using only experimental results, it's essential to build compelling deductive arguments that generalize and are falsifiable, and only when these arguments are available does it make sense to try to test potential solutions via experiment. \n Safe and Unsafe Agent Architectures Predicting the exact behavior of complex software is notoriously difficult and has been shown to be generically impossible with less computational cost than simply running it. The goal of AI safety research is therefore more modest: to show that the behavior, although not exactly predictable, will have certain desired properties, for example keeping certain behavioral parameters within certain bounds. Rational agents are often composed of distinct modules (e.g. sensors, actuators, a performance element, a learning element, a problem generator, a critic, etc.), each with limited abilities, with some network of information flows between modules.  [102]  Within this framework, it would be valuable to provide guarantees that various modules would be safe or unsafe (individually or in combination). A related approach is to not build an agent at all, but rather some sort of non-agent \"Tool AI\". Some types of this are: 1. \"Oracle AI\": an AI system designed to merely answer questions about the world as accurately as possible. (Though people sometimes also call agent AI with a goal of accurately answering questions about the world \"Oracle AI\".) 2. \"Virtual AI\": an agent that interacts only with an abstract world, but has no way of determining this, and hence is not an agent in the physical world. Although a common assumption is that both 1 and 2 are \"safe\" by remaining \"Oracle AI\"/\"Tool AI\", this has not been substantiated. For example, an Oracle AI that becomes superintelligent via self-improvement is likely to evolve a knowledge-acquisition goal, which might lead it to modify its answers to manipulate its user to perform certain experiments. Many of the above-mentioned safety issues are related to the issue of goals that the rational agent may have. This question provides an important link between architectures and goals: how amenable are different AI architectures to having their goals and beliefs read from the outside in a fashion useful for safety determination and monitoring? Research questions on properties of architectures under self-modification: 1. Can certain interesting classes of agents be proven to exhibit behavior converging towards recursively stable fixed points or limit cycles? 2. Do certain kinds of non-optimizer agents become optimizers, and if so, how quickly? 3. If so, how strong is the 'optimizer' stable attractor? 4. Are there other stable attractors? 5. Are tool-like or Oracle-like things stable attractors? Research questions about specific architectures: 1. Model and bug-trace the variety of different scenarios of failure modes and dangerous behaviors intrinsic to different existing real-world general AI architectures such as OpenCog and Sigma. 2. Analyze how deep learning discontinuity/instability  [121]  can affect deep reinforcement learning architectures. What new classes of risks in agent behavior can result? How easily can these risks be mitigated? Evaluate compensatory safety mechanisms whereby an agent requires at least two distinct perspectives on a situation or subject of analysis before characterizing it. 3. Explore how the field of mechanism design can be applied to controlling neuromorphic AIs and other architectures. 4. How well does an AI system's transparency to human inspection scale, using different kinds of architectures and methods?  [76] . 4 Forecasting \n Motivation 1. Conduct a broad survey of past and current civilizational competence. In what ways, and under what conditions, do human civilizations show competence vs. incompetence? Which kinds of problems do they handle well or poorly? Similar in scope and ambition to, say, Perrow's Normal Accidents  [90]  and Sagan's The Limits of Safety  [104] . The aim is to get some insight into the likelihood of our civilization handling various aspects of the superintelligence challenge well or poorly. Some initial findings were published on the MIRI blog.  [79, 74]  2. Did most early AI scientists really think AI was right around the corner, or was it just a few people? The earliest survey available  (Michie 1973[71] ) suggests it may have been just a few people. For those that thought AI was right around the corner, how much did they think about the safety and ethical challenges? If they thought and talked about it substantially, why was there so little published on the subject? If they really didn't think much about it, what does that imply about how seriously AI scientists will treat the safety and ethical challenges of AI in the future? \n Methodology There are many interrelated variables that are relevant to arriving at a good understanding of the future of AI, in particular the path towards general AI; and there are a number of different ways to produce forecasts of these variables, with varying degrees of accuracy, credibility, feasibility, and informativeness. Possible methods include: These projects are providing us with valuable information on how best to make short-term forecasts. It would be interesting to run a similar tournament with 5-year and 10-year time horizons for predictions and see if there are significant differences; are the chief determinants of predictive success the same? What kind of process should we trust to give us the best predictions? Besides the question of how to train analysts and combine their estimates, there is also the question of what modelling methodologies, used by whom, yield the best long-term forecasts. The Tauri Group is a think tank that conducted a study  [44]  for the  \n Forecasting AI progress In order to get a good understanding of what the path to general AI might look like, there are many kinds of interacting variables that would be worth forecasting: (a) How quickly will computer hardware performance be improving (on various metrics)? i. Improved performance enables more AI approaches to be feasible and makes experiments more productive. Will hardware advances also contribute to researcher productivity in other ways? ii. Will departures from the von Neumann architecture contribute significantly to some types of AI development? (For example quantum computers, or computers inspired by cellular automata.) (b) How quickly does performance of algorithms tend to advance over time?  (Grace, 2013)   [42]  finds that (in six areas) algorithmic progress is nearly as significant as hardware progress; but further analysis of this question with a view toward economic or productivity impact would be worthwhile. (c) Researcher performance is affected by improvements in algorithmic and hardware performance which make experiments more productive. What other factors will affect researcher performance? Some candidates: i. changing ways to do software development ii. changing ways to collaborate iii. changing ways to publish or present results iv. improved computer interfaces (such as brain-computer interfaces or virtual reality) v. genetic enhancement technology (d) Related to the previous question: what AI subfields will benefit particularly from hardware performance improvements? \n Forecasting AI takeoff If we develop AI that's advanced enough to do AI research and development, we may enter the era that I. J. Good dubbed the \"Intelligence Explosion\", in which the growth in AI capability is driven primarily by the AI itself. We will refer to the transition of AI to a superintelligent level as takeoff. How (and how quickly) this would unfold is important, but difficult to predict. Of course, some of the usual forecasting methods are applicable, in particular those that rely on expert judgment. (A survey of timelines and impacts for humanity (with n=170) is here  [81] .) Here are some more approaches toward understanding aspects of the intelligence explosion: 1. Compare with earlier takeoff-like scenarios. Some candidates  [51, 50] : (a) development of proto-human brains (b) agricultural revolution (c) industrial revolution 2. Besides software improvements, AI self-improvement may occur via engaging in commercial activity, via expropriating computing resources, via manufacturing computing resources, or in other ways. Enumerate the specific technologies required for each pathway and forecast their development. 3. Assess how best to model the amount of self-improvement that could be accomplished with varying amounts of (i) intelligence, (ii) parallelism / parallel computations, (iii) serial depth of computation; what evidence is available?  [137]  (a) How do different areas of knowledge respond to being given more serial research time vs more people vs other inputs? (b) One type of cognitive work that has been recorded for millennia is the progress of mathematics, in particular the resolution of conjectures. Some data analysis  [43]  suggests these times follow an exponential distribution with halflife 100 years. Could further analysis help us understand the benefits of serial vs parallel intellectual work in this domain? It's possible that there will be multiple AI projects undergoing takeoff at the same time; this has been called a multipolar takeoff. Multipolar takeoff is more likely if (i) takeoff is slow, (ii) more of the necessary innovations and/or tools are shared, and (iii) implementation doesn't require any non-commodity resources, such as access to specialized hardware. It's been proposed  [6]  that multipolar scenarios might carry a higher risk of accidents than unipolar ones because no party wishes to lose the competition. It's also been proposed  [29]  that multipolar scenarios might be safer, because there might be a \"balance of power\" enabling cooperation and mutual scrutiny. 1. What kind of multipolar scenarios may occur? What would be the consequences? 2. What kinds of multipolar scenarios would collapse into unipolar ones, or vice versa? \n Brain emulations (uploads) 1. Can we get whole brain emulation without producing neuromorphic general AI slightly earlier or shortly afterward? See section 3.2 of  [35] . 2. Is the first functional whole brain emulation likely to be (1) an emulation of low-level functionality that doesn't require much understanding of human cognitive neuroscience at the computational level, as described in  [105] , or is it more likely to be (2) an emulation that makes heavy use of advanced human cognitive neuroscience, as described eg by Hayworth  [77] , or is it likely to be (3) something else? 3. Investigate the feasibility of creating safe general-purpose superintelligences by modifying brain emulations, based on currently known cognitive neuroscience. \n Policy and Collaboration For any powerful new technology, appropriate policies can ensure that humanity can enjoy the benefits while risks are minimized. Both nuclear technology and biotechnology have thus far avoided global-scale disasters (global nuclear war, nuclear terrorism, engineered pandemics, etc.), at least in part thanks to helpful policies. For example, the policies developed at the 1975 Asilomar conference on Recombinant DNA have contributed to the sterling safety record of that field without stifling its progress in any significant way. In this spirit, it appears worthwhile to research the analogous question for AI: what policies would help ensure that humanity reaps the benefits of AI while avoiding potential pitfalls? Here are some more specific questions along these lines: 1. What is the space of possible AI risk reduction policies worth studying? (Dewey  [32]  and Sotala and Yampolskiy  [118]  have written some analyses of possible policies/responses.) Dimensions include: (a) Implementation level: global, national, organizational, etc., (b) Strictness: mandatory regulations, voluntary industry guidelines, etc. (c) Type: Do policies/monitoring efforts focus on software, hardware, projects or individuals? Is there some sort of tiered system of security clearances? Is some information classified? What are possible approaches to monitoring and tracking general AI development? What kind of research should be funded? Are new governance structures created? 2. Which criteria should be used to determine the merits of a policy? Some candidates: Collaboration is another important topic that deserves recurring thought and discussion. To build safe general AI of human level and beyond, it will likely be necessary to bring together multiple research subdisciplines and communities and let them influence each other's work. Some thematic questions here are: 1. What are the most important collaborations and information flows we need between different research subdisciplines and communities? 2. What attitudes would be most useful to foster? 3. What kind of organizations or organizational mechanisms would best enable these collaborations and information flows, bringing us closer to safety? (a) Completeness: it should allow running the same experiments that AI builders can do without the containment (b) Flexibility: it should be adaptable enough to different hardware setups to be used with different architectures, and especially on distributed hardware (c) Efficiency: it should not overly reduce runtime efficiency, memory efficiency, or research/development efficiency (d) Ease of use: it should provide as familiar an environment as possible; for example a UNIX shell and other familiar tools. \n 4 . 4 (a) Operating-system level virtualization (such as VirtualBox, VMWare, KVM) (b) Programming-language level containment (such as Java sandbox) (c) Static analysis (eg to check that a program won't use networking APIs or corrupt its memory) Investigate programs likely to be used for viewing output and logs from an AI project. Determine which ones are and aren't secure enough to use safely in the context of a boxed AI, and address weaknesses in them. For example:(a) How safe are terminal emulators? (b) Can an AI censor information from its log files by mixing in things like Unicode control characters or xterm escape sequences? (c) Under what circumstances is it safe to copy-paste things from an AI's output? (d) What file formats should and shouldn't the AI be allowed to use? \n (a) How can individual AI researchers best be trained to resist being manipulated by an AI? 2. What are the most effective social control mechanisms for preventing individuals from enabling AI breakout? What can be learned from past research on preventing unauthorized use of nuclear weapons and other powerful technologies? Such examples include: (a) Psychological screening of operators (b) Surveillance of operators. For example, add an option to sshd which records keystrokes and output in a place the logged-in user cannot access (c) \"False alarm\" tests where the operator is led to believe that a critical situation has occurred and one can see what decisions they make under pressure (d) Systems requiring more than one authorized human for making certain critical decisions. \n ability to reduce AI risk (d) ability to avoid stifling desirable technology development and have other negative consequences (e) adoptability (the prospects of adoption increase when policy benefits those whose support is needed for implementation and when its merits can be effectively explained to decision-makers and opinion leaders)(f) ability to adapt over time to changing circumstances To shed light on 2.d: What happens when governments ban or restrict certain kinds of technological development? What happens when a certain kind of technological development is banned or restricted in one country but not in other countries where technological development sees heavy investment? \n ACE (Aggregative Contingent Estimation), which investigates ways to improve and combine the judgments of analysts to produce accurate forecasts. The ACE program has been running a team prediction tournament, which has consistently been won by the Good Judgment Project, which has produced several insightful publications.2. ForeST (Forecasting Science & Technology), which investigates ways to get and maintain high-quality forecasts of sci/tech milestones, and funds SciCast, the world's largest sci/tech forecasting tournament. 1. expert surveys 2. prediction markets 3. systematic group forecasting methods, such as the Delphi method 4. building complex models 5. extrapolation from historic trends 6. analogy with other historical developments 7. combining forecasts from differing methods or forecasts of related variables Existing projects that investigate how to best forecast future sci/tech and other developments include these IARPA programs: 1. \n Department of Defense reviewing over 1000 technological forecasts and statistically analyzing accuracy by methodology, by source, and by time frame. It would be informative to have a similar analysis of longterm technological predictions from other sources, such as (1) The Futurist and World Future Review, (2) Technological Forecasting and Social Change, (3) Foresight and International Journal of Forecasting, (4) Journal of Forecasting, (5) publications of the Hudson Institute, (6) publications of the Institute for the Future, (7) publications of the Club of Rome, (8) Journal of Future Studies, (9) Ray Kurzweil (more thorough than section 5.4 of (Armstrong et al, 2014) [7] ), (10)  Alvin Toffler, (11) John Naisbitt, (12)  the State of the World reports by the Worldwatch Institute. \n What conditions would make bans or nationalization likely? (Consider historical examples here.) What would be the consequences? ii. Examine international collaboration on major innovative technology. How often does it happen? What blocks it from happening more? What are the necessary conditions? Examples: Concord jet, LHC, international space station, etc. What conditions would make international collaboration on AI safety issues likely? iii. What kinds of policies are likely to be implemented, with what effect? • What happens when governments ban or restrict certain kinds of technological development? What happens when a certain kind of technological development is banned or restricted in one country but not in other countries where technological development sees heavy investment? • What kinds of innovative technology projects do governments monitor, shut down, or nationalize? How likely are major governments to monitor, shut down, or nationalize serious general AI projects? (b) How will the public respond? What sorts of technological innovations tend to cause public panic or outrage, under what conditions? 3. in terms of public response: (a) How will governments respond? i. 1. resources (researchers and funding) going into AI innovation in general, or within AI subfields 2. resources going into AI areas of application, such as robotics or sensory technologies 3. related fields which may contribute ideas, such as neuroscience 4. shifts in the set of organizations/people performing AI research among: (a) countries (b) academia vs industry vs other government (eg military) Other related questions that may merit detailed study include: 1. in terms of technologies: (a) What types of AI (in terms of architecture, subfield, application, etc) are most likely to contribute to reaching general AI? What AI capabilities would be necessary or sufficient, individually or collectively? (b) Nick Bostrom brings up in Superintelligence that brain emulation technology is unlikely to arrive much sooner than human-level neuromorphic AI, because techniques and knowledge from the former can likely be repurposed for the latter. Are there other foreseeable situations where two disparate fields or research programs may be closely related, with success on one implying great progress on the other? i. Does causal entropy[132] constitute a promising shared avenue of progress in AI and nanotech? 2. in terms of scenarios: (a) What kinds of scenarios would increase or decrease researcher inclination to work on AI or general AI research? (For example, changing ideologies or public opinion, association of the field with ideas held in low regard, . . . ) Can we forecast this? (b) How scalable is innovative project secrecy? Examine past cases: Manhattan project, Bletchley park, Bitcoin, Anonymous, Stuxnet, Skunk Works, Phantom Works, Google X. Could there be large projects we don't know about? How will this change in coming decades? (c) What is the world's distribution of computation, and what are the trends? (Some initial results here.[75]) (d) Supposing enough technical innovations are in place to build general AI, how large of a project will implementation be? How much of the work to reach general AI is scientific advancement and technical innovation vs engineering and implementation? (c) What sorts of developments would cause governments or the public to consider AI safety to be a serious issue? How did public perception respond to previous AI milestones? How will the public react to self-driving taxis?(d) How much warning will we have before we reach general AI? What kinds of future developments would serve as advance signposts indicating the kind of scenario we're likely to see?4. in terms of rates of progress: \n\t\t\t \"The energy produced by the breaking down of the atom is a very poor kind of thing. Any one who expects a source of power from the transformation of these atoms is talking moonshine.\" [92]   \n\t\t\t One way to operationalize this is described by Muehlhauser [80] .", "date_published": "n/a", "url": "n/a", "filename": "research_survey.tei.xml", "abstract": "Artificial intelligence (AI) research has explored a variety of problems and approaches since its inception, but for the last 20 years or so has been focused on the problems surrounding the construction of intelligent agents-systems that perceive and act in some environment. In this context, the criterion for intelligence is related to statistical and economic notions of rationality-colloquially, the ability to make good decisions, plans, or inferences. The adoption of probabilistic representations and statistical learning methods has led to a large degree of integration and cross-fertilization between AI, machine learning, statistics, control theory, neuroscience, and other fields. The establishment of shared theoretical frameworks, combined with the availability of data and processing power, has yielded remarkable successes in various component tasks such as speech recognition, image classification, autonomous vehicles, machine translation, legged locomotion, and question-answering systems. As capabilities in these areas and others cross the threshold from laboratory research to economically valuable technologies, a virtuous cycle takes hold whereby even small improvements in performance are worth large sums of money, prompting greater investments in research. There is now a broad consensus that AI research is progressing steadily, and that its impact on society is likely to increase. The potential benefits are huge, since everything that civilization has to offer is a product of human intelligence; we cannot predict what we might achieve when this intelligence is magnified by the tools AI may provide, but the eradication of disease and poverty are not unfathomable. Because of the great potential of AI, it is valuable to investigate how to reap its benefits while avoiding potential pitfalls. The progress in AI research makes it timely to focus research not only on making AI more capable, but also on maximizing the societal benefit of AI. Such considerations motivated the AAAI 2008-09 Presidential Panel on Long-Term AI Futures [61] and other projects and community efforts on AI impacts. These constitute a significant expansion of the field of AI itself, which up to now has focused largely on techniques that are neutral with respect to purpose. The present document can be viewed as a natural continuation of these efforts, focusing on identifying research directions that can help maximize the societal benefit of AI. This research is by necessity interdisciplinary, because it involves both society and AI. It ranges from economics, law, and philosophy to computer security, formal methods and, of course, various branches of AI itself. The focus is on delivering AI that is beneficial to society and robust in the sense that the benefits are guaranteed: our AI systems must do what we want them to do. This document is an attempt to lay out some of the research topics that we think will be most useful to do now in order to shape the future impact of AI. We will surely find that some questions are less useful or timely than others, and some important ones are missing. We hope this guide will be a helpful source of suggestions, but also that potential grantees won't be discouraged from approaching us with similarly relevant topics we didn't think of. We will try to publish future versions that are up to date with progress in the field. We are very grateful to the many people who have contributed to this document, in particular Daniel Dewey, Stuart Russell, and Max Tegmark for their invaluable work on the research priorities document, Luke Muehlhauser for his list of potential strategic research projects, Nate Soares and MIRI for their technical agenda, and the MIRIxOxford research workshop analyzing and expanding on the MIRI technical agenda. Many people at FLI have contributed lists of additional research projects and directions, including Jim", "id": "c480acd9bb39a25d9faaf6b728d5613c"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "Under review as a conference paper at ICLR 2022 TEST TIME ROBUSTIFICATION OF DEEP MODELS VIA ADAPTATION AND AUGMENTATION", "text": "INTRODUCTION Deep neural network models have achieved excellent performance on many machine learning problems, such as image classification, but are often brittle and susceptible to issues stemming from distribution shift. For example, deep image classifiers may degrade precipitously in accuracy when encountering input perturbations, such as noise or changes in lighting  (Hendrycks & Dietterich, 2019)  or domain shifts which occur naturally in real world applications  (Koh et al., 2021) . Therefore, robustification of deep models against these test shifts is an important and active area of study. Most prior works in this area have focused on techniques for training time robustification, including utilizing larger models and datasets  (Orhan, 2019) , various forms of adversarial training  (Sagawa et al., 2020; Wong et al., 2020) , and aggressive data augmentation  (Yin et al., 2019; Hendrycks et al., 2020; Li et al., 2021; Hendrycks et al., 2021a) . Employing these techniques requires modifying the training process, which may not be feasible if, e.g., it involves heavy computation or non-public data. Furthermore, these techniques do not rely on any information about the test points that the model must predict on, even though these test points may provide significant information for improving model robustness. Recently, several works have proposed methods for improving accuracy via adaptation after seeing the test data, typically by updating a subset of the model's weights  (Sun et al., 2020) , normalization statistics  (Schneider et al., 2020) , or both  (Wang et al., 2021; Zhang et al., 2021) . Though effective at handling test shifts, these methods sometimes still require specialized training procedures, and they typically rely on extracting distributional information via batches or even entire sets of test inputs, thus introducing additional assumptions. Figure  1 : A schematic of our overall approach. Left: at test time, as detailed in Section 3, we have a trained model that outputs a probabilistic predictive distribution and has adaptable parameters θ, a single test input x, and a set of data augmentation functions {a 1 , . . . , a M }. Note that we do not assume access to the model training procedure or multiple test inputs for adaptation. We perform different augmentations to x and pass these augmented inputs to the model in order to estimate the marginal output distribution averaged over augmentations. Right: rather than using this distribution to make the final prediction, we instead perform a gradient update on the model to minimize the entropy of this marginal distribution, thus encouraging the model predictions to be invariant across different augmentations while maintaining confident predictions. The final prediction is then made on the original data point, i.e., the predictive distribution in the top right of the schematic. We are interested in studying and devising methods for improving model robustness that are \"plug and play\", i.e., they can be readily used with a wide variety of pretrained models and test settings. Such methods may simply constitute a different, more robust way to perform inference with preexisting models, under virtually the same assumptions as standard test time inference. In this work, we focus on methods for test time robustness, in which the specific test input may be leveraged in order to improve the model's prediction on that point. Though broad applicability is our primary goal, we also want methods that synergize with other robustification techniques, in order to achieve greater performance than using either set of techniques in isolation. To satisfy both of these desiderata, we devise a novel test time robustness method based on adaptation and augmentation. As illustrated in Figure  1 , when presented with a test point, we propose to adapt the model by augmenting the test point in different ways and ensuring that the model makes the same predictions across these augmentations, thus respecting the invariances encoded in the data augmentations. We further encourage the model to make confident predictions, thus arriving at the proposed method: minimize the marginal entropy of the model's predictions across the augmented versions of the test point. We refer to the proposed method as marginal entropy minimization with ensembled augmentations (MEME), and this is the primary contribution of our work. MEME makes direct use of pretrained models without any assumptions about their particular training procedure or architecture, while requiring only a single test input for adaptation. In Section 4, we demonstrate empirically that MEME consistently improves the performance of ResNet  (He et al., 2016)  and vision transformer  (Dosovitskiy et al., 2021)  models on several challenging ImageNet distribution shift benchmarks, achieving several new state-of-the-art results for these models in the setting in which only one test point is available. In particular, MEME consistently outperforms non adaptive marginal distribution predictions (between 1-10% improvement) on corruption and rendition shifts -tested by the ImageNet-C  (Hendrycks & Dietterich, 2019)  and ImageNet-R  (Hendrycks et al., 2021a)  datasets, respectively -indicating that adaptation plays a crucial role in improving predictive accuracy. MEME encourages both invariance across augmentations and confident predictions, and an ablation study in Section 4 shows that both components are important for maximal performance gains. Also, MEME is, to the best of our knowledge, the first adaptation method to improve performance (by 1-4% over standard model evaluation) on ImageNet-A  (Hendrycks et al., 2021b) , demonstrating that MEME is more broadly applicable on a wide range of distribution shifts. \n RELATED WORK The general problem of distribution shift has been studied under a number of frameworks  (Quiñonero Candela et al., 2009) , including domain adaptation  (Shimodaira, 2000; Csurka, 2017; Wilson & Cook, 2020) , domain generalization  (Blanchard et al., 2011; Muandet et al., 2013; Gulrajani & Lopez-Paz, 2021) , and distributionally robust optimization  (Ben-Tal et al., 2013; Hu et al., 2018; Sagawa et al., 2020) , to name just a few. These frameworks typically leverage additional training or test assumptions in order to make the distribution shift problem more tractable. Largely separate from these frameworks, various empirical methods have also been proposed for dealing with shift, such as increasing the model and training dataset size or using heavy training augmentations  (Orhan, 2019; Yin et al., 2019; Hendrycks et al., 2021a) . The focus of this work is complementary to these efforts: the proposed MEME method is applicable to a wide range of pretrained models, including those trained via robustness methods, and can achieve further performance gains via test time adaptation. Prior test time adaptation methods generally either make significant training or test time assumptions. Some methods update the model using batches or even entire datasets of test inputs, such as by computing batch normalization (BN) statistics on the test set  (Li et al., 2017; Kaku et al., 2020; Nado et al., 2020; Schneider et al., 2020) , or minimizing the (conditional) entropy of model predictions across a batch of test data  (Wang et al., 2021) . The latter approach is closely related to MEME. The differences are that MEME minimizes marginal entropy using single test points and data augmentation and adapts all of the model parameters rather than just those associated with normalization layers, thus not requiring multiple test points or specific model architectures. Other test time adaptation methods can be applied to single test points but require specific training procedures or models  (Sun et al., 2020; Huang et al., 2020; Schneider et al., 2020) . Test time training (TTT)  (Sun et al., 2020)  requires a specialized model with a rotation prediction head, as well as a different procedure for training this model.  Schneider et al. (2020)  show that BN adaptation can be effective even with only one test point, and we refer to this approach as \"single point\" BN adaptation. As we discuss in Section 3, MEME synergizes well with single point BN adaptation. A number of works have noted that varying forms of strong data augmentation on the training set can improve the resulting model's robustness  (Yin et al., 2019; Hendrycks et al., 2020; Li et al., 2021; Hendrycks et al., 2021a) . Data augmentations are also sometimes used on the test data directly by averaging the model's outputs across augmented copies of the test point  (Krizhevsky et al., 2012; Shorten & Khoshgoftaar, 2019) , i.e., predicting according to the model's marginal output distribution. This technique, which we refer to as test time augmentation (TTA), has been shown to be useful both for improving model accuracy and calibration  (Ashukha et al., 2020)  as well as handling distribution shift  (Molchanov et al., 2020) . We take this idea one step further by explicitly adapting the model such that its marginal output distribution has low entropy. This extracts an additional learning signal for improving the model, and furthermore, the adapted model can then make its final prediction on the clean test point rather than the augmented copies. We empirically show in Section 4 that these differences lead to improved performance over this non adaptive TTA baseline. \n ROBUSTNESS VIA ADAPTATION AND AUGMENTATION Data augmentations are typically used to train the model to respect certain invariances -e.g., changes in lighting or viewpoint do not change the underlying class label -but, especially when faced with distribution shift, the model is not guaranteed to obey the same invariances at test time. In this section, we introduce MEME, a method for test time robustness that adapts the model such that it respects these invariances on the test input. We use \"test time robustness\" specifically to refer to techniques that operate directly on pretrained models and single test inputs -single point BN adaptation and TTA, as described in Section 2, are examples of prior test time robustness methods. In the test time robustness setting, we are given a trained model f θ : X → Y with parameters θ ∈ Θ. We do not require any special training procedure and do not make any assumptions about the model, except that θ is adaptable and that f θ produces a conditional output distribution p θ (y|x) that is differentiable with respect to θ. 1 All standard deep neural network models satisfy these assumptions. A single point x ∈ X is presented to f θ , for which it must predict a label ŷ ∈ Y immediately. Note that this is precisely identical to the standard test time inference procedure for regular supervised learning models -in effect, we are simply modifying how inference is done, without any additional assumptions on the training process or on test time data availability. This makes test time robustness methods a simple \"slot-in\" replacement for the ubiquitous and standard test time inference process. We assume sampling access to a set of augmentation functions A {a 1 , . . . , a M } that can be applied to the test point x. We use these augmentations and the self-supervised objective detailed below to adapt the model before it predicts on x. When given a set of test inputs, the model adapts and predicts on each test point independently. We do not assume access to any ground truth labels. \n MARGINAL ENTROPY MINIMIZATION WITH ENSEMBLED AUGMENTATIONS Given a test point x and set of augmentation functions A, we sample B augmentations from A and apply them to x in order to produce a batch of augmented data x1 , . . . , xB . The model's average, or marginal, output distribution with respect to the augmented points is given by pθ (y|x) E U (A) [p θ (y|a(x))] ≈ 1 B B i=1 p θ (y|x i ) , (1) where the expectation is with respect to uniformly sampled augmentations a ∼ U(A). What properties do we desire from this marginal distribution? To answer this question, consider the role that data augmentation typically serves during training. For each training point (x train , y train ), the model f θ is trained using multiple augmented forms of the input xtrain 1 , . . . , xtrain E . f is trained to obey the invariances between the augmentations and the label -no matter the augmentation on x train , f should predict the same label y train , and it should do so confidently. We seek to devise a similar learning signal during test time, when no ground truth labels are available. That is, after adapting: (1) the model f θ predictions should be invariant across augmented versions of the test point, and (2) the model f θ should be confident in its predictions, even for heavily augmented versions of the test point, due to the additional knowledge that all versions have the same underlying label. Optimizing the model for more confident predictions can be justified from the assumption that the true underlying decision boundaries between classes lie in low density regions of the data space  (Grandvalet & Bengio, 2005) . With these two goals in mind, we propose to adapt the model using the entropy of its marginal output distribution over augmentations (Equation  1 ), i.e., (θ; x) H (p θ (•|x)) = − y∈Y pθ (y|x) log pθ (y|x) . (2) Optimizing this objective encourages both confidence and invariance to augmentations, since the entropy of pθ (•|x) is minimized when the model outputs the same (confident) prediction regardless of the augmentation. Given that θ is adaptable and p θ (y|x) is differentiable with respect to θ, we can directly use gradient based optimization to adapt θ according to this objective. We use only one gradient step per test point, because empirically we found this to be sufficient for improved performance while being more computationally efficient. After this step, we can use the adapted model, which we denote f θ , to predict on the original test input x. Algorithm 1 presents the overall method MEME for test time adaptation. Though prior test time adaptation methods must carefully choose which parameters to adapt in order to avoid degenerate solutions  (Wang et al., 2021) , our adaptation procedure simply adapts all of the model's parameters θ (line 3). Note that, as discussed above, the model f θ adapts using augmented data but makes its final prediction on the original point (line 4), which may be easier to predict on.  \n COMPOSING MEME WITH PRIOR METHODS An additional benefit of MEME is that it synergizes with other approaches for handling distribution shift. In particular, MEME can be composed with prior methods for training robust models and adapting model statistics, thus leveraging the performance improvements of each technique. Pretrained robust models. Since MEME makes no assumptions about, or modifications to, the model training procedure, performing adaptation on top of pretrained robust models, such as those trained with heavy data augmentations, is as simple as using any other pretrained model. Crucially, we find that, in practice, the set of augmentations that we use at test time A does not have to match the augmentations that were used to train the model. This is important as we require a few properties from the test time augmentations: that they can be easily sampled and are applied directly to the model input x. These properties do not hold for, e.g., data augmentation techniques based on image translation models, such as DeepAugment  (Hendrycks et al., 2021a) , or feature mixing, such as moment exchange  (Li et al., 2021) . However, we can still use models trained with these data augmentation techniques as our starting point for adaptation, thus allowing us to improve upon their state-of-the-art results. As noted above, using pretrained models is not as easily accomplished for adaptation methods which require complicated or specialized training procedures and model architectures, such as TTT  (Sun et al., 2020)  or ARM  (Zhang et al., 2021) . In our experiments, we use AugMix as our set of augmentations  (Hendrycks et al., 2020) , as it satisfies the above properties and still yields significant diversity when applied, as depicted in Figure  2 . Adapting BN statistics.  Schneider et al. (2020)  showed that, even when presented with just a single test point, partially adapting the estimated mean and variance of the activations in each batch normalization (BN) layer of the model can still be effective in some cases for handling distribution shift. In this setting, to prevent overfitting to the test point, the channelwise mean and variance [µ test , σ 2 test ] estimated from this point are mixed with the the mean and variance [µ train , σ 2 train ] computed during training according to a prior strength N , i.e., µ N N + 1 µ train + 1 N + 1 µ test , σ 2 N N + 1 σ 2 train + 1 N + 1 σ 2 test . This technique is also straightforward to combine with MEME: we simply use the adapted BN statistics whenever computing the model's output distribution. That is, we adapt the BN statistics alongside all of the model parameters for MEME. Following the suggestion in  Schneider et al. (2020) , we set N = 16 for all of our experiments in the next section. \n EXPERIMENTS Our experiments aim to answer the following questions: (1) How does MEME compare to prior methods for test time adaptation, which make additional training and test assumptions, and test time robustness? (2) Can MEME be successfully combined with a wide range of pretrained models? (3) Which aspects of MEME are the most important for strong performance? We conduct experiments on two distribution shift benchmarks for CIFAR-10 (  Krizhevsky, 2009)  and three distribution shift benchmarks for ImageNet  (Russakovsky et al., 2015) . Specifically, for CIFAR-10, we evaluate on the CIFAR-10-C  (Hendrycks & Dietterich, 2019)  and CIFAR-10.1  (Recht et al., 2018)     2020 ), set the prior strength N = 256 accordingly. For Tent, we use test batch sizes of 64 and, for ResNet-50 models, test both \"online\" adaptation -where the model adapts continually through the entire evaluation -and \"episodic\" adaptationwhere the model is reset after each test batch.  (Wang et al., 2021) . Note that the evaluation protocols are different for these two methods: whereas MEME is tasked with predicting on each test point immediately after adaptation, BN adaptation predicts on a batch of 256 test points after computing BN statistics on the batch, and Tent predicts on a batch of 64 inputs after adaptation but also, in the online setting, continually adapts throughout evaluation. In all experiments, we further compare to single point BN adaptation  (Schneider et al., 2020)  and the TTA baseline that simply predicts according to the model's marginal output distribution over augmentations pθ (y|x) (Equation  1 )  (Krizhevsky et al., 2012; Ashukha et al., 2020) . Full details on our experimental protocol are provided in Appendix A. To answer question (2), we apply MEME on top of multiple pretrained models with different architectures, trained via several different procedures. For CIFAR-10, we train our own ResNet-26  (He et al., 2016)  models. For ImageNet, we use the best performing ResNet-50 robust models from prior work, which includes those trained with DeepAugment and AugMix augmentations  (Hendrycks et al., 2021a)  as well as those trained with moment exchange and CutMix  (Li et al., 2021) . To evaluate the generality of prior test time robustness methods and MEME, we also evaluate the small robust vision transformer (RVT * -small), which provides superior performance on all three ImageNet distribution shift benchmarks compared to the robust ResNet-50 models  (Mao et al., 2021) . Finally, to answer (3), we conduct ablative studies in subsection 4.2: first to determine the relative importance of maximizing confidence (via entropy minimization) versus enforcing invariant predictions across augmented copies of each test point, and second to determine the importance of the particular augmentation functions used. The comparison to the non adaptive TTA baseline also helps determine whether simply augmenting the test point is sufficient or if adaptation is additionally helpful. \n MAIN RESULTS We summarize results for CIFAR-10, CIFAR-10.1, and CIFAR-10-C in MEME also provides a larger performance gain on CIFAR-10.1 compared to TTT. We find that the non adaptive TTA baseline is competitive for these relatively simple test sets, though it is worse than MEME for CIFAR-10-C. Of these three test sets, CIFAR-10-C is the only benchmark that explicitly introduces distribution shift, which suggests that adaptation is useful when the test shifts are 7.3 (−1.9) 14.7 (−3.7) 19.6 (−2.9) + Joint training  (Sun et al., 2020)  8.1 16.7 22.8 + TTT  (Sun et al., 2020)  7.9 (−0.2) 15.9 (−0.8) 21.5 (−1.3) more prominent. Both TTA and MEME are also effective at improving performance for the original CIFAR-10 test set where there is no distribution shift, providing further support for the widespread use of augmentations in standard evaluation protocols  (Krizhevsky et al., 2012; Ashukha et al., 2020) . We summarize results for ImageNet-C, ImageNet-R, and ImageNet-A in   (Schneider et al., 2020; Wang et al., 2021) , accessing multiple test points can be powerful for benchmarks such as ImageNet-C and ImageNet-R, in which inferred statistics from the test input distribution may aid in prediction. In the case of Tent, which adapts online, the model has adapted using the entire test set by the end of evaluation. However, these methods do not help, and oftentimes even hurt, for ImageNet-A. Furthermore, we find that these methods are less effective with the RVT * -small model, which may indicate their sensitivity to model architecture choices. Therefore, for this model, we also test a modification of Tent which adapts all parameters, and we find that this version of Tent works better for ImageNet-C but is significantly worse for ImageNet-R. MEME results in substantial improvement for ImageNet-A and is competitive with TTA on this problem. No prior test time adaptation methods have reported improvements on ImageNet-A, and some have reported explicit negative results  (Schneider et al., 2020) . As discussed, it is reasonable for adaptation methods that rely on multiple test points to achieve greater success on other benchmarks such as ImageNet-C, in which a batch of inputs provides significant information about the specific corruption that must be dealt with. In contrast, ImageNet-A does not have such obvious characteristics associated with the input distribution, as it is simply a collection of images that are difficult to classify. As MEME instead extracts a learning signal from single test points, it is, to the best of our knowledge, the first test time adaptation method to report successful results on this testbed. When used on top of a model trained with moment exchange and CutMix  (Li et al., 2021) , MEME achieves stateof-the-art performance among ResNet-50 models and single test point methods. TTA generally offers larger performance gains on ImageNet-A and also results in the highest overall accuracy when combined with the RVT * -small model; however, TTA performs worse than MEME on ImageNet-R and consistently decreases accuracy on ImageNet-C compared to standard evaluation. We view the consistency with which MEME outperforms the best prior methods, which change across different test sets, to be a major advantage of the proposed method. \n ABLATIVE STUDY MEME increases model robustness at test time via adaptation and augmentation. In this section, we ablate the adaptation procedure, and in Appendix B we ablate the use and choice of augmentations. From the results above, we conclude that adaptation generally provides additional benefits beyond simply using TTA to predict via the marginal output distribution pθ (y|x). However, we can disentangle two distinct self-supervised learning signals that may be effective for adaptation: encouraging invariant predictions across different augmentations of the test point, and encouraging confidence via entropy minimization. The marginal entropy objective in Equation 2 encapsulates both of these learning signals, but it cannot easily be decomposed into these pieces. Thus, we instead use two ablative adaptation methods that each only make use of one of these learning signals. First, we consider optimizing the pairwise cross entropy between each pair of augmented points, i.e., PCE (θ; x) 1 B × (B − 1) B i=1 j =i y∈Y p θ (y|x i ) log p θ (y|x j ) , Where xi again refers to the i-th sampled augmentation applied to x. Intuitively, this loss function encourages the model to adapt such that it produces the same predictive distribution for all augmentations of the test point, but it does not encourage the model to produce confident predictions. Conversely, as an objective that encourages confidence but not invariance, we also consider optimizing conditional entropy on the batch of augmented points, i.e., CE (θ; x) 1 B B i=1 H(p θ (•|x i )) . This ablation is effectively a version of the episodic variant of Tent  (Wang et al., 2021)  that produces augmented copies of a single test point rather than assuming access to a test batch. We first evaluate these ablations on the CIFAR-10 test sets. We use the same adaptation procedure outlined in Algorithm 1, with replaced with the above objectives, and we keep the same hyperparameter values. The results are presented in Table  3 . We see that MEME, i.e., marginal entropy minimization, generally performs better than adaptation with either of the alternative objectives. This supports the hypothesis that both invariance across augmentations and confidence are important learning signals for self-supervised adaptation. When faced with CIFAR-10.1, we see poor performance from the pairwise cross entropy based adaptation method. On the original CIFAR-10 test set and CIFAR-10-C, the ablations perform nearly identically and uniformly worse than MEME. To further test the CE ablation, we also evaluate it on the ImageNet test sets for the RVT * -small model. We find that, similarly, minimizing conditional entropy generally improves performance compared to the baseline evaluation. MEME is more performant for ImageNet-C and ImageNet-R, again indicating the benefits of encouraging invariance to augmentations. Adaptation via CE performs slightly better for ImageNet-A, though for this problem, TTA is still the best method. \n DISCUSSION We presented MEME, a method for test time robustification again distribution shift via adaptation and augmentation. MEME does not require access or changes to the model training procedure and is thus broadly applicable for a wide range of pretrained models. Furthermore, MEME adapts at test time using single test inputs, thus it does not assume access to multiple test points as in several recent methods for test time adaptation  (Schneider et al., 2020; Wang et al., 2021; Zhang et al., 2021) . On a range of distribution shift benchmarks for CIFAR-10 and ImageNet classification, and for both ResNet and vision transformer models, MEME consistently improves performance at test time and achieves several new state-of-the-art results for these models in the single test point setting. Inference via MEME is more computationally expensive than standard model inference, primarily because adaptation is performed per test point and thus inference cannot be batched. When deployed in the real world, it is natural to expect that test points will arrive one at a time and batched inference will not be possible. However, MEME is also more computationally expensive due to its augmentation and adaptation procedure. One interesting direction for future work is to develop techniques for selectively determining when to adapt the model in order to achieve more efficient inference. For example, with well calibrated models  (Guo et al., 2017) , we may run simple \"feedforward\" inference when the prediction confidence is over a certain threshold, thus achieving better efficiency. Additionally, it would be interesting to explore MEME in the test setting where the model is allowed to continually adapt as more test data is observed. In our preliminary experiments in this setting, MEME tended to lead to degenerate solutions, e.g., the model predicting a constant label with maximal confidence, and this may potentially be rectified by carefully choosing which parameters to adapt  (Wang et al., 2021)  or regularizing the model such that it does not change too drastically from the pretrained model. Distribution shift, in general, lies at the heart of many ethical concerns in machine learning. When machine learning models and research do not adhere to ethical principles such as \"contribute to society and to human well-being\", \"avoid harm\", and \"be fair and take action to avoid discrimination\", it can oftentimes be attributed at least partially to issues stemming from distribution shift. As such, research into ways to combat and mitigate shift contribute to furthering the ethical goals and principles laid out by this conference and the broader community. Related to this work, we may imagine that models that are more robust or adaptable to shift may produce more fair results when considering underrepresented subpopulations and could be more trustworthy in safety critical applications. However, as mentioned in Section 5, the proposed method is also more computationally intensive, and care must be taken in general to not place the most powerful machine learning tools exclusively in the hands of the most privileged and resource rich individuals and organizations. Beyond this, we do not see any immediate ethical concerns regarding the content, presentation, or methodology of this work. \n REPRODUCIBILITY STATEMENT The proposed method is relatively simple and, to the best of our ability, explained fully in Section 3 and Algorithm 1. This explanation is bolstered by a complete description of all hyperparameters in Appendix A as well as the example code provided in the supplementary materials. As briefly explained in the README in the example code, all datasets were downloaded from publicly accessible links and preprocessed only following the standard protocols. Upon publication, we will include a link to the full (non anonymous) code release containing full instructions for setting up the code, downloading the datasets, and reproducing the results. \n A EXPERIMENTAL PROTOCOL We select hyperparameters using the four disjoint validation corruptions provided with CIFAR-10-C and ImageNet-C  (Hendrycks & Dietterich, 2019) . As the other benchmarks are only test sets and do not provide validation sets, we use the same hyperparameters found using the corruption validation sets and do not perform any additional tuning. For the ResNet models that we evaluate, we use stochastic gradients as the update rule G; for ResNet-26 models, we set the number of augmentations B = 32 and the learning rate η = 0.005; and for ResNet-50 models, we set B = 64 and η = 0.00025. For the robust vision transformer, we use AdamW  (Loshchilov & Hutter, 2019)  as the update rule G, with learning rate η = 0.00001 and weight decay 0.01, and B = 64. In the CIFAR evaluation, we compare to TTT, which, as noted, can also be applied to single test inputs but requires a specialized training procedure  (Sun et al., 2020) . Thus, the ResNet-26 model we use for our method closely follows the modifications that  Sun et al. (2020)  propose, in order to provide a fair point of comparison. In particular,  Sun et al. (2020)  elect to use group normalization  (Wu & He, 2018)  rather than BN, thus single point BN adaptation is not applicable for this model architecture. As noted before, TTT also requires the joint training of a separate rotation prediction head, thus further changing the model architecture, while MEME directly adapts the standard pretrained model. The TTA results are obtained using the same AugMix augmentations as for MEME. The single point BN adaptation results use N = 16, as suggested by  Schneider et al. (2020) . As noted, the BN adaptation results (using multiple test points) are obtained using N = 256 as the prior strength and batches of 256 test inputs for adaptation. For Tent, we use the hyperparameters suggested in  Wang et al. (2021) : we use stochastic gradients with learning rate 0.00025 and momentum 0.9, the adaptation is performed with test batches of 64 inputs, and the method is run online, i.e., prediction and adaptation occur simultaneously and the model is allowed to continuously adapt through the entire test epoch. Since  Wang et al. (2021)  did not experiment with transformer models, we also attempted to run Tent with Adam  (Kingma & Ba, 2015)  and AdamW  (Loshchilov & Hutter, 2019)  and various hyperparameters for the RVT * -small model; however, we found that this generally resulted in worse performance than using stochastic gradient updates with the aforementioned hyperparameters. We obtain the baseline ResNet-50 parameters directly from the torchvision library. The parameters for the ResNet-50 trained with DeepAugment and AugMix are obtained from https://drive.google.com/file/d/1QKmc_p6-qDkh51WvsaS9HKFv8bX5jLnP. The parameters for the ResNet-50 trained with moment exchange and CutMix are obtained from https://drive.google.com/file/d/1cCvhQKV93pY-jj8f5jITywkB9EabiQDA. The parameters for the small robust vision transformer (RVT * -small) model are obtained from https://drive.google.com/file/d/1g40huqDVthjS2H5sQV3ppcfcWEzn9ekv. \n B ADDITIONAL EXPERIMENTS In this section, we analyze the importance of using augmentations during adaptation, study the tradeoffs between efficiency and accuracy for MEME, and present results with ResNext101 models  (Xie et al., 2017; Mahajan et al., 2018; Orhan, 2019)  on ImageNet-A. \n B.1 ANALYSIS ON AUGMENTATIONS One may first wonder: are augmentations needed in the first place? In the test time robustness setting when only one test point is available, how would simple entropy minimization fare? We answer this question in Table  4  by evaluating the episodic variant of Tent (i.e., with model resetting after each batch) with a test batch size of 1. This approach is also analogous to a variant of MEME that does not use augmentations, since for one test point and no augmented copies, conditional and marginal entropy are the same. Similar to MEME, we also incorporate single point BN adaptation with N = 16, in place of the standard BN adaptation that Tent typically employs using batches of test inputs. The results in Table  4  indicate that entropy minimization on a single test point generally provides no additional performance gains beyond just single point BN adaptation. This empirically shows that using augmentations is important for achieving the reported results. We also wish to understand the importance of the choice of augmentation functions A. As mentioned, we used AugMix  (Hendrycks et al., 2020)  in the previous experiments as it best fit our criteria: 69.9 (−6.8) 58.8 (−5.1) 99.1 (−0.9) + Tent (episodic, batch size 1)  (Wang et al., 2021)   69.1 (−5.7) 59.4 (−3.3) 89.0 (−2.9) + Tent (episodic, batch size 1)  (Wang et al., 2021)  70.9 (−3.9) 62.6 (−1.9) 91.1 (−0.8) RVT * -small  (Mao et al., 2021)  49  AugMix requires only the input x, and randomly sampled augmentations lead to diverse augmented data points. A simple alternative is to instead use the \"standard\" set of augmentations commonly used in ImageNet training, i.e., random resized cropping and random horizontal flipping. We evaluate this ablation of using MEME with standard augmentations also on the CIFAR-10 test sets, again with the same hyperparameter values. From the results in Table  5 , we can see that MEME is still effective with simpler augmentation functions. This is true particularly for the cases where there is no test shift, as in the original CIFAR-10 test set, or subtle shifts as in CIFAR-10.1; however, for the more severe and systematic CIFAR-10-C shifts, using heavier AugMix data augmentations leads to greater performance gains over the standard augmentations. Furthermore, this ablation was conducted using the ResNet-26 model, which was trained with standard augmentations -for robust models such as those in Table  2 , AugMix may offer greater advantages at test time since these models were exposed to heavy augmentations during training. \n B.2 ANALYZING THE TRADEOFF BETWEEN EFFICIENCY AND ACCURACY In Figure  3 , we analyze the % test error of MEME adaptation on ImageNet-R as a function of the efficiency of adaptation, measured in seconds per evaluation. We achieve various tradeoffs by varying the number of augmented copies B = {1, 2, 4, 8, 16, 32, 64, 128}. We note that small values of B such as 4 and 8 can already provide significant performance gains, indicating that a practical tradeoff between efficiency and accuracy is possible. For large B, the wall clock time is dominated by computing the augmentations -in our implementation, we do not compute augmentations in   \n B.3 EVALUATING RESNEXT101 MODELS ON IMAGENET-A ResNext-101 models  (Xie et al., 2017)  have been found to achieve higher accuracies on ImageNet-A  (Hendrycks et al., 2021b) , particularly when trained with massive scale weakly supervised pretraining  (Mahajan et al., 2018; Hendrycks et al., 2021a) . In this section, we evaluate whether MEME can successfully adapt these models and further improve performance on this challenging test set. We use the same hyperparameters as for the robust vision transformer with no additional tuning: AdamW  (Loshchilov & Hutter, 2019)  as the update rule G, learning rate η = 0.00001, weight decay 0.01, and B = 64. We obtain the baseline ResNext-101 (32x8d) parameters, pretrained on ImageNet, directly from the torchvision library. We also evaluate a ResNext-101 (32x8d) pretrained with weakly supervised learning (WSL) on billions of Instagram images  (Mahajan et al., 2018) , and we obtained the parameters from https://download.pytorch.org/models/ig_resnext101_32x8-c38310e5.pth. For the WSL model, we did not use single point BN adaptation as we found this technique to be actually harmful to performance, and this corroborates previous findings  (Schneider et al., 2020) . Table  6  summarizes the results. We can see that, similar to Table  2 , Both TTA and MEME significantly improve upon the baseline model evaluation. TTA performs best for the baseline ResNext-101 model. However, MEME ultimately achieves the best accuracy by a significant margin, as it is more successful at adapting the WSL model, which has a much higher accuracy. This suggests that combining MEME with other large pretrained models may be an interesting direction for future work. C FULL CIFAR-10-C AND IMAGENET-C RESULTS In the following tables, we present test results broken down by corruption and level for CIFAR-10-C for the methods evaluated in Table  1 . We omit joint training and TTT because these results are available from  Sun et al. (2020) . Our test results for ImageNet-C are provided in the CSV files in the supplementary material.   25.3 16.9 15.9 8.4 33.5 14.6 13.0 17.7 14.4 8.5 7.7 9.6 10.7 11.9 16.2  Table  11 : Test error (%) on CIFAR-10-C level 1 corruptions. gauss shot impul defoc glass motn zoom snow frost fog brit contr elast pixel jpeg ResNet-26 20.8 16.5 15.8 9.2 38.9 11.8 12.8 13.9 13.4 9.7 9.4 9.6 13.1 12.0 16.4 + TTA 15.8 12.8 11.8 7.3 35.1 10.8 12.5 11.0 10.8 7.4 7.4 7.7 11.4 9.2 12.5 + MEME (ours) 16.1 12.9 11.9 7.4 34.7 10.4 12.1 11.0 10.7 7.4 7.3 7.5 10.9 9.2 12.5 Figure 2 : 2 Figure 2: We visualize augmentations of a randomly chosen data point from the \"Gaussian Noise level 3\" ImageNet-C test set. Even for a robust model trained with heavy data augmentations (Hendrycks et al., 2021a), both its predictive accuracy and confidence drop sharply when encountering test distribution shift. As shown in the bottom two rows, these drops can be remedied via MEME. \n Figure 3 : 3 Figure 3: Plotting MEME efficiency as seconds per evaluation (x axis) and % test error on ImageNet-R (y axis) for the ResNet-50 models (left) and RVT * -small (right) while varying B = {1, 2, 4, 8, 16, 32, 64, 128}. Note the log scale on the x axis. \n \n Algorithm 1 Test time robustness via MEME Require: trained model f θ , test point x, # augmentations B, learning rate η, update rule G 1: Sample a 1 , . . . , a B i.i.d. ∼ U(A) and produce augmented points xi = a i (x) for i ∈ {1, . . . , B} 2: Compute Monte Carlo estimate p = 1 B 3: Adapt model parameters via update rule θ ← G(θ, η, ˜ ) B i=1 p θ (y|x i ) ≈ pθ (y|x) and ˜ = H(p) ≈ (θ; x) 4: Predict ŷ arg max y p θ (y|x) \n test sets, and for ImageNet, we evaluate on the ImageNet-C (Hendrycks & Dietterich, 2019) , ImageNet-R (Hendrycks et al., 2021a) , and ImageNet-A (Hendrycks et al., 2021b)  test sets.To answer question (1), we compare to test time training (TTT)(Sun et al., 2020)  in the CIFAR-10 experiments, for which we train ResNet-26 models following their protocol and specialized architecture. We do not compare to TTT for the ImageNet experiments due to the computational demands of training state-of-the-art models and becauseSun et al. (2020)  do not report competitive ImageNet results. For the ImageNet experiments, we compare to Tent(Wang et al., 2021)  and BN adaptation, which can be used with pretrained models but require multiple test inputs (or even the entire test set) for adaptation. We provide BN adaptation with 256 test inputs at a time and, followingSchneider et al. ( \n Table 1, with full CIFAR-10-C results in Appendix C. We use indentations to indicate composition, e.g., TTT is performed at test time on top of their specialized joint training procedure. Across all corruption types in CIFAR-10-C, MEME consistently improves test error compared to the baselines, non adaptive TTA, and TTT. \n Table 1 : 1 Results for the original CIFAR-10 test set, CIFAR-10.1, and CIFAR-10-C. MEME outperforms TTT despite not making any training assumptions. Results from Sun et al. (2020). CIFAR-10 CIFAR-10.1 CIFAR-10-C Error (%) Error (%) Average Error (%) ResNet-26 (He et al., 2016) 9.2 18.4 22.5 + TTA 7.3 (−1.9) 14.8 (−3.6) 19.9 (−2.6) + MEME (ours) \n Table 2 : 2 Test results for ImageNet-C, ImageNet-R, and ImageNet-A. MEME achieves new state-ofthe-art performance on each benchmark for ResNet-50 models for the single test point setting. For RVT * -small, MEME substantially improves performance across all benchmarks and reaches a new state of the art for ImageNet-C and ImageNet-R. ImageNet-C ImageNet-R ImageNet-A mCE ↓ Error (%) Error (%) \n Table 2 2 , with complete ImageNet-C results in Appendix C. We again use indentations to indicate composition, e.g., the best results on ImageNet-C for our setting are attained through a combination of starting from a model trained with DeepAugment and AugMix (Hendrycks et al., 2021a)  and using MEME on \n Table 3 : 3 Ablating the adaptation objective to test pairwise cross entropy and conditional entropy (CE) based adaptation. MEME generally performs the best, indicating that both encouraging invariance across augmentations and confidence are helpful in adapting the model. top. For both ImageNet-C and ImageNet-R, and for both the ResNet-50 and RVT * -small models, combining MEME with robust training techniques leads to new state of the art performance among methods that observe only one test point at a time. We highlight in gray the methods that require multiple test points for adaptation, and we list in bold the best results from these methods which outperform the test time robustness methods. As Table2and prior work both show CIFAR-10 CIFAR-10.1 CIFAR-10-C Error (%) Error (%) Average Error (%) ResNet-26 (He et al., 2016) 9.2 18.4 22.5 + MEME (ours) 7.3 (−1.9) 14.7 (−3.7) 19.6 (−2.9) − (Equation 2) + PCE 7.6 (−1.6) 15.3 (−3.1) 20.0 (−2.5) − (Equation 2) + CE 7.6 (−1.6) 14.7 (−3.7) 20.0 (−2.5) ImageNet-C ImageNet-R ImageNet-A mCE ↓ Error (%) Error (%) RVT  *  -small (Mao et al., 2021) 49.4 52.3 73.9 + MEME (ours) 40.6 (−8.8) 43.8 (−8.5) 69.8 (−4.1) − (Equation 2) + CE 41.2 (−8.2) 44.2 (−8.1) 69.7 (−4.2) \n Table 4 : 4 Evaluating the episodic version of Tent with a batch size of 1, which corresponds to a simple entropy minimization approach for the test time robustness setting. This approach also uses single point BN adaptation, and entropy minimization does not provide much, if any, additional gains. ImageNet-C ImageNet-R ImageNet-A mCE ↓ Error (%) Error (%) \n Table 5 : 5 Ablating the augmentation functions to test standard augmentations (random resized cropping and horizontal flips). When changing the augmentations used, the post-adaptation performance generally does not change much, though it suffers the most on CIFAR-10-C. CIFAR-10 CIFAR-10.1 CIFAR-10-C Error (%) Error (%) Average Error (%) \n Table 6 : 6 ImageNet-A results for the ResNext-101 models. parallel, though in principle this is possible for AugMix and should improve efficiency overall. These experiments used four Intel Xeon Skylake 6130 CPUs and one NVIDIA TITAN RTX GPU. ImageNet-A Error (%) \n Table 7 : 7 Test error (%) on CIFAR-10-C level 5 corruptions. gauss shot impul defoc glass motn zoom snow frost fog brit contr elast pixel jpeg ResNet-26 48.4 44.8 50.3 24.1 47.7 24.5 24.1 24.1 33.1 28.0 14.1 29.7 25.6 43.7 28.3 + TTA 43.4 39.6 42.9 28.3 44.7 26.3 26.3 21.4 28.5 23.3 12.1 32.9 21.7 43.2 21.7 + MEME (ours) 43.5 39.8 43.3 26.4 44.4 25.1 25.0 20.9 28.3 22.8 11.9 28.3 21.1 42.8 21.7 \n Table 8 : 8 Test error (%) on CIFAR-10-C level 4 corruptions. gauss shot impul defoc glass motn zoom snow frost fog brit contr elast pixel jpeg ResNet-26 43.8 37.2 39.3 14.8 48.0 19.9 18.7 22.0 24.9 15.1 11.4 16.8 19.1 27.9 24.9 + TTA 39.5 32.0 31.8 15.4 45.0 20.9 20.2 18.9 21.7 12.9 9.3 16.8 17.7 25.7 18.9 + MEME (ours) 39.7 32.3 32.2 14.7 45.0 20.0 19.2 18.7 21.1 12.5 9.3 15.2 16.9 25.2 18.9 \n Table 9 : 9 Test error (%) on CIFAR-10-C level 3 corruptions. gauss shot impul defoc glass motn zoom snow frost fog brit contr elast pixel jpeg ResNet-26 40.0 33.8 26.4 11.5 37.3 20.0 16.6 20.0 24.7 12.2 10.5 13.6 15.0 18.4 22.7 + TTA 34.3 27.7 20.3 11.3 32.9 20.7 16.7 16.3 21.1 9.8 8.5 12.5 13.7 14.5 17.2 + MEME (ours) 34.4 27.9 20.5 10.8 32.8 19.8 16.1 16.1 20.9 9.6 8.6 11.7 13.2 14.5 17.2 \n Table 10 : 10 Test error (%) on CIFAR-10-C level 2 corruptions. gauss shot impul defoc glass motn zoom snow frost fog brit contr elast pixel jpeg ResNet-26 30.1 21.8 21.1 9.7 38.3 15.3 13.8 21.2 17.6 10.5 9.7 11.6 12.9 15.4 21.3 + TTA 25.3 16.9 15.8 8.5 33.8 15.3 13.7 17.8 14.5 8.7 7.8 10.0 11.0 12.0 16.1 + MEME (ours) \n\t\t\t Single point BN adaptation also assumes that the model has batch normalization layers, and, as shown empirically in Section 4, this is an assumption that we do not require but can also benefit from.", "date_published": "n/a", "url": "n/a", "filename": "test_time_robustification_of_d.tei.xml", "abstract": "While deep neural networks can attain good accuracy on in-distribution test points, many applications require robustness even in the face of unexpected perturbations in the input, changes in the domain, or other sources of distribution shift. We study the problem of test time robustification, i.e., using the test input to improve model robustness. Recent prior works have proposed methods for test time adaptation, however, they each introduce additional assumptions, such as access to multiple test points, that prevent widespread adoption. In this work, we aim to study and devise methods that make no assumptions about the model training process and are broadly applicable at test time. We propose a simple approach that can be used in any test setting where the model is probabilistic and adaptable: when presented with a test example, perform different data augmentations on the data point, and then adapt (all of) the model parameters by minimizing the entropy of the model's average, or marginal, output distribution across the augmentations. Intuitively, this objective encourages the model to make the same prediction across different augmentations, thus enforcing the invariances encoded in these augmentations, while also maintaining confidence in its predictions. In our experiments, we evaluate two baseline ResNet models, two robust ResNet-50 models, and a robust vision transformer model, and we demonstrate that this approach achieves accuracy gains of 1-8% over standard model evaluation and also generally outperforms prior augmentation and adaptation strategies. For the setting in which only one test point is available, we achieve state-of-the-art results on the ImageNet-C, ImageNet-R, and, among ResNet-50 models, ImageNet-A distribution shift benchmarks.", "id": "dfb36fc999b2d99ea7e14031750b1520"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Allan Dafoe", "Remco Zwetsloot", "Matthew Cebul"], "title": "Reputations for Resolve and Higher-Order Beliefs in Crisis Bargaining", "text": "Introduction Navigating an international crisis can require incredibly complex inferences. Even seemingly straightforward strategies can backfire dramatically. Suppose that persons A and B are playing Chicken, the game in which two cars race toward each other and the goal is to get the opponent to swerve first. One popular strategem says that A should throw her steering wheel out of the window in order to convince B that she cannot swerve, thereby compelling B to do so.  1  Yet suppose that B incorrectly believes that A hid a spare steering wheel under her seat. If A does not know that B believes this, she may surrender her ability to swerve without actually becoming committed in B's eyes, raising the chances of a tragic crash. Or suppose that A incorrectly believes that B believes that A has a spare steering wheel. This belief might prevent A from using a tactic that would have improved her odds of victory. Much of the complexity in international crisis bargaining is attributable to higherorder beliefs-beliefs about beliefs  (Schelling 1960; . While these complications are perhaps most apparent in hypothetical games like Chicken, examples abound in real-world international crises as well. For instance, in the years prior to the Berlin crisis, Premier Khrushchev had deliberately exaggerated the Soviet Union's capabilities, and widely-discussed American concerns about a \"missile gap\" had convinced him that the Americans had fallen for the ruse. \"  [O] n the assumption that the Americans believed the Soviets were ahead in the arms race,\" Khrushchev chose to escalate tensions over Berlin  (Kaplan 1983, 304) . Khrushchev was forced to back down, however, when he learned that US policymakers did not believe this at all-a fact that the Americans purposely signaled via intelligence leaks to NATO units that the US knew to be compromised by Soviet agents  (Schlosser 2014, 284) . Higher-order beliefs thus played a critical role in both the onset and resolution of one of the most significant crises of the Cold War. In this article, we examine the theoretical and empirical import of higher-order belief dynamics for two crucial phenomena in international relations: resolve and reputations for resolve. Reputations, especially for resolve, have been a longstanding topic of scholarship, but most studies consider only first-order beliefs: whether and how B updates his beliefs about A on the basis of A's behavior. We argue that taking higher-order beliefs into account substantially amplifies the importance of reputations for resolve. This is because resolve is interdependent: one side's (perceived) resolve can affect the other side's (perceived) resolve, meaning that small initial changes in beliefs can spiral into large overall changes, with potentially decisive consequences. We evaluate our theory using a survey experiment conducted on a sample of quasi-elites recruited through Stephen Walt's Foreign Policy blog. We begin by corroborating reputation scholars' core assertion: states that behaved resolutely in the past are perceived to be more highly resolved in the present. We find that the effect of reputation on perceived resolve is larger than any other experimental manipulation, including the effect of material capabilities, and persists across a range of informational conditions and subgroups. We then go a step further, advancing scholarship on reputations for resolve by demonstrating that respondents also form higher-order beliefs in line with our argument. Exogenous increases in A's perceived resolve, induced by providing information about A's behavior in disputes with states other than B, produce decreases in B's perceived resolve, even though respondents learned nothing about the usual factors said to affect B's resolve. The size of the parameter estimates we obtain suggest that higher-order beliefs can account for as much as 70 percent of the reputational manipulation's effect on the balance of resolve, with a lower bound of roughly 40 percent. We thus answer Robert Jervis's longstanding but still open question: there is indeed a strong zero-sum element to resolve. Our design also permits a direct test of a competing hypothesis linking higherorder beliefs to resolve, which Jervis has referred to as the \"domino theory paradox\" and Daryl Press as the \"never again theory\": if A backed down in a recent dispute, B will believe that A will expend extra effort to restore its tarnished reputation for resolve, and therefore that A will be more rather than less resolved in subsequent disputes  (Jervis 1991; Press 2005) . Our evidence is contrary to these hypotheses. Our results reinforce recent studies demonstrating the importance of reputation in the domains of conflict, finance, and alliance politics, among others (see  Crescenzi 2017, for a review) . These studies all focus on the first-order effects of reputation.  2  We show, however, that the story does not stop there. In doing so, we join a number of others who place higher-order beliefs at the center of international relations specifically  (Schelling 1960; Morrow 2014)  and social, economic, and political life more broadly  (Kuran 1995; Chwe 2001 ). These beliefs are what make resolve interdependent, and are therefore crucial to the onset and resolution of crises and wars. \n Resolve, Reputation, and Higher-Order Beliefs Much of international politics pivots around perceptions. A state's ability to persuade, deter, and compel depends in large part on how that state is perceivedwhether others consider its military capable, its threats credible, its promises reliable. As a result, states and leaders are motivated to act in ways that favorably shape others' perceptions and expectations, i.e. to cultivate reputations for desirable qualities or behavioral tendencies. One of the most important kinds of reputation in international politics is a reputation for resolve. We define resolve as follows: Resolve: the probability that an actor is willing to stand firm in a crisis, given its beliefs about the world at that time. We briefly explain how this behavioral definition relates to other common conceptualizations of resolve. Formalized mathematical models of crisis bargaining often define resolve as a state's \"value for war,\" which is said to be a function of material factors such as military capabilities, the issue under dispute, and domestic audiences (see, e.g.  Morrow 1989; Powell 1990; Fearon 1994; Sartori 2016 ). Psychological accounts of resolve instead emphasize internal traits such as dispositional determination, willpower, or \"sticktoitiveness\"  (Kertzer 2016, 8-9) . Here, we define resolve in terms of states' behavior in a crisis, in which states may either back down or stand firm.  3  In this sense, a state's \"value for war\" and its dispositional traits are important factors that affect resolve-the probability that an actor stands firm-but they may not be the only ones, so they do not define resolve.  4  Understanding resolve in behavioral terms has several benefits.  5  By clearly specifying what kind of behavior is (in)consistent with being resolved, our definition makes resolve measurable and facilitates empirical analysis. More importantly, our definition allows scholars to directly incorporate another essential determinant of whether A will stand firm in a crisis with B: A's beliefs about B's resolve. As exemplified by Chicken, that A's crisis behavior depends on her beliefs about B's resolve is what makes interstate crises complex strategic interactions. This relationship also speaks to the literature on reputations for resolve, which we briefly review below. \n Building Reputations for Resolve International crises can often be understood as \"contests of resolve\"  (Morrow 1989, 941-42)  in which the outcome is determined by one side's ability to convince the other that it will not back down. In such contests, a history of resolute past behavior can be a valuable asset. We say that actors have a reputation for resolve when observers have formed beliefs about that actor's tendency to stand firm in a certain class of disputes on the basis of that actor's past behavior  (Dafoe, Renshon, and Huth 2014 ).  6  The effect of a reputation for resolve remains a subject of debate. Proponents contend that reputations offer a path to successful commitment, deterrence, and compellence  (Huth 1997) , as costly past actions can corroborate threats and promises that might otherwise be dismissed as \"cheap talk\"  (Fearon 1995; Trager 2017 ). These scholars argue that an \"undesired image can involve costs for which almost no amount of the usual kinds of power can compensate\"  (Jervis 1970, 6) , and so reputations are \"one of the few things worth fighting over\"  (Schelling 1966, 124) . In support of this position, a number of recent studies find evidence that states' past behavior shape how other states act toward it.  7  Others, however, dispute the link between past actions and present behavior. For instance, Mercer argues that the desirability of an action conditions how people interpret the disposition of its initiator, concluding that \"people do not consistently use past behavior to predict similar behavior in the future\"  (Mercer 1996, 45-47, 212) . Similarly, Press claims that \"blood and wealth spent to maintain a country's record for keeping commitments are wasted,\" since opponents form assessments of credibility largely based on their perceptions of states' interests and capabilities, not their past behavior  (Press 2005, 10) . Detractors also aver that evidence of reputational effects is largely observational and often indirect, and is therefore inconclusive. Thus, one contribution of our article is to bring experimental methods to bear on a basic question: do observers use a state's past behavior to predict what it is likely to do today? 8 H REP : Perceptions of a state's resolve will (a) increase if it stood firm in past crises and (b) decrease if it backed down in past crises. 9 In addition, we also seek to advance the reputation debate beyond H REP toward a discussion of higher-order beliefs. Note that H REP focuses purely on how first-order beliefs-beliefs about an actor's traits or behavioral tendencies-change in response to past behavior. Such arguments are at the center of most theoretical accounts of reputational dynamics. First-order beliefs are, however, not the only kinds of beliefs that matter. In the next section, we contend that reputations can also affect higherorder beliefs-beliefs about beliefs (about beliefs, etc.)-with important consequences for state behavior. \n Reputational Effects and Higher-Order Beliefs Consider a hypothetical dispute between states A and B, in which B is considering whether to escalate. Initially, B has some sense of how likely A would be to stand firm (A's resolve), though he cannot be sure. B then observes A behaving resolutely in some other dispute, and after considering that A might, say, be more militarily capable than B originally thought, B updates his beliefs about A's resolve accordingly. We can call this a first-order reputational effect, in which one side updates its beliefs about its opponent's characteristics or behavioral tendencies solely on the basis of that opponent's past behavior. In many cases, however, higher-order reasoning further complicates the story. For example, A might know that B was paying careful attention to her behavior in the other dispute. If so, A might conclude that, since she stood firm, B has become less resolved, and this could further embolden A to also stand firm against B. If B expects A to be thinking along these lines, he might conclude that there is little he can do to make A back down, further reducing B's resolve. If actors make inferences in this way, the first-order reputational effect will be joined by higher-order effects. These two effects together make up the total reputational effect, i.e. the full shift in the balance of resolve between two actors due to a single initial reputational shock (see Section \"Do Higher-Order Beliefs Contribute to Reputational Effects?\" for a formalization). Indeed, higher-order beliefs can theoretically produce large substantive effects, as relatively small first-order reputational effects cascade through higherorder belief chains into large changes in the balance of resolve. Put another way, our argument is that resolve is a function of not just the material factors emphasized in the modeling literature or the internal traits emphasized in psychological accounts, but also states' beliefs about their opponents' resolve-A's resolve is decreasing in (her beliefs about) B's resolve, and vice versa. In short, resolve is interdependent. Furthermore, that resolve is interdependent implies that higher-order beliefs may play a central, albeit under-appreciated, role in international crises-A's beliefs about B's resolve (which dictate A's own resolve) are themselves a product of A's higher-order beliefs about B's beliefs about A's resolve, and vice versa. To express our arguments in terms of reputations, we contend not just that states and leaders can possess reputations for resolve, but also that these actors are aware that such a reputation may decrease the likelihood that their opponents stand firm during crises, and so update their own resolve accordingly. In short, states may expect that their reputations precede them. H INT : Perceptions of a state's resolve will (a) increase when there is a decrease in perceptions of its opponent's resolve, and (b) decrease when there is an increase in perceptions of its opponent's resolve. There are two principal reasons why we may not expect this hypothesis to hold. First, states may not form higher-order beliefs if they lack the ability to do so. Kertzer, for example, argues that in many situations with higher-order uncertainty about resolve \"the complex nature of the decision-making environment actors face stretches far beyond the limits of human cognition\"  (Kertzer 2016, 149 ; see also  Mercer 2012) . And even if they have the ability, states may be insufficiently confident in their higher-order beliefs to incorporate them into their assessments of resolve. If this were the case, we would expect to see no evidence of interdependence. Second, H INT is not the only possible relationship between higher-order reasoning and reputational effects. H INT implies that higher-order reasoning magnifies first-order effects-states that stand firm earn larger reputational bonuses, whereas states that back down suffer larger penalties. In what Jervis labels the \"domino theory paradox\" and Press \"never again theory,\" however, higher-order effects run counter to the first-order effect  (Jervis 1991; Press 2005) . Domino theory, which undergirded much of US foreign policy during the Cold War, holds that if a state backs down in one situation, observers will infer that it is more likely to do so in other situations as well. The paradox is that the corresponding higher-order beliefs may be \"self-defeating\"  (Jervis 1991, 36-37) : An actor who has had to back down once will feel especially strong incentives to prevail the next time in order to show that the domino theory is not correct, or at least does not apply to him. In other words, an actor who believes the domino theory-or who believes that others accept it-will have incentives to act contrary to it. Indeed, statesmen sometimes respond to a defeat by warning others that this history will make them extremely resistant to retreating again. Furthermore, if others foresee this, they will expect a defeated actor to be particularly unyielding in the next confrontation. In short, the domino theory paradox predicts that, in certain circumstances, higher-order reasoning can mitigate or even reverse first-order reputational effects. H DTP : Perceptions of a state's resolve will increase when it backed down recently and has a prior reputation to recover. \n Research Design The scientific study of reputations is limited by their inaccessibility. Reputations consist of perceptions, which exist in people's minds and are not directly observable. Even records of private deliberations, free of any incentives to dissemble, may lead us astray. To the extent that an opponent's reputation is a constant during a crisis and is common knowledge among decisionmakers, discussions are likely to focus on new information such as troop movements even if reputation matters  (Weisiger and Yarhi-Milo 2015) . Reputational inferences, given their evolutionary importance, may also be so automatic that they are made subconsciously  (Bowles and Gintis 2011) . These difficulties were acknowledged by Snyder and Diesing, who noted that their inability to find much evidence of reputational inferences in case histories \"may be only an artifact of the record\"  (Snyder and Diesing 1977, 496) . To overcome these challenges, we employ a scenario-based survey experiment. Respondents are told about a scenario, features of which are randomly varied or omitted, and then asked about their opinions or beliefs. Survey experiments are especially suitable for research questions about how people incorporate, interpret, and act on particular types of information  (Mutz 2011) , and these are precisely the questions in which scholars of reputation are interested. Below, we review the survey design and the sample in more detail. \n Survey Vignette Respondents read an abstract scenario about two countries (A and B) engaged in a serious territorial dispute. The features of the scenario are presented in a bullet list format, each assigned with some probability independent of each other (a full factorial design). Each feature has several different levels, including its omission. For the full text of the survey and treatment allocations, see Online Appendix B. Respondents were first informed of each country's regime type, either democracy or dictatorship (some received no information on regime type). Respondents then learned about the military capabilities of each country, with A having either \"substantially stronger military forces\" than B, being \"about equally strong,\" or B being substantially stronger (again, some received no information about capabilities). In all conditions except no information, respondents are also told that neither country has nuclear weapons. The respondent then reads the reputational feature of the scenario, State A's history of crisis interactions. This bullet involves two variables: whether A stood firm or backed down in past crises, and whether A's previous conflicts were against B or other countries.  10  According to most impartial observers, of the three most recent major international crises that Country A has faced against [other countries/Country B], Country A [did not back down and Country A achieved its aims/backed down in each crisis and failed to achieve its aims]. There is also a special Domino Theory Paradox version of this manipulation, in which A stood firm in three past crises, but then backed down in a fourth, most recent crisis. In all conditions except no information, respondents are also informed whether A's past crises occurred under the current or a previous leader. Lastly, the vignette includes several other experimental features related to the history of the dispute, as well as recent threats and promises.  11  The scenario concludes by stating that the crisis is serious and that many observers consider major military action in the near future likely. Respondents are then asked the primary outcome question for both countries: What is your best estimate, given the information available, about whether Country A/ B will back down in this dispute? Respondents have five options, ranging from \"very unlikely\" (0 percent to 20 percent chance) to \"very likely\" (80 percent to 100 percent chance). Note that this question exactly matches our definition of resolve in Section \"Resolve, Reputation, and Higher-Order Beliefs.\"  12  Before detailing our sampling strategy, we briefly address the benefits and drawbacks of our abstract survey design. Our survey vignette describes a crisis between two abstract states, A and B, and the scenarios respondents read were typically no more than 150 words. The benefit of this approach is its flexible simplicity; short vignettes are less taxing for respondents, and abstracting away from real-world states may permit cleaner manipulation of the concepts of interest (though not necessarily; see  Dafoe, Zhang, and Caughey 2018) . The attendant drawback is a decreased level of realism in abstract survey scenarios, relative to vignettes that feature actual countries  (Tingley 2017) . Reassuringly, however, recent research employing both abstract and real-world crises scenarios recovers reputational effects of a very similar magnitude to those presented below  (Renshon, Dafoe, and Huth 2018) . Regardless of the design, it is of course not possible to create environments akin to those faced by real-life decision-makers through surveys alone, and it is therefore best to complement survey experiments with other kinds of evidence. Though more systematic observational work will have to await future research, we offer some preliminary supportive evidence for our claims in Section \"Discussion: Interdependent Resolve in Real Life,\" and discuss the conditions under which evidence of interdependent resolve is most and least likely to be found. \n Sample We administered the survey to a convenience sample of respondents recruited through Stephen Walt's Foreign Policy blog. On August 1st, 2011 Walt posted a blog entry inviting readers to \"Become a data point!\" (see Online Appendix B.1). From this advertisement, over 1,000 respondents took the survey. This sampling strategy was intended to mitigate potential biases that may arise from using regular citizens to proxy for elite policymakers. The general concern is that elites are better informed about and more experienced with foreign policy decision-making than the average citizen-as a result, they are more likely to employ higher-order strategic reasoning and consider their opponents' perspective  (Hafner-Burton, Hughes, and Victor 2013; Hafner-Burton et al. 2014 ). Ideally, then, one would run our experiment on key decision-makers, such as military leaders, foreign policy advisors, and politicians. Unfortunately, such subjects are rarely accessible, and even if they are it is usually as part of a small convenience sample. To approximate our elite population of interest, we instead sought to recruit a sample of quasi-elite respondents who are abnormally well-informed about and interested in foreign policy, whose backgrounds and world views more closely parallel those of high-level elites. We expected a sample drawn from Walt's Foreign Policy readership to be highly educated and knowledgeable of foreign policy, and that is indeed the case. Of those 87 perccent who answered the demographic questions, 83 percent reported having a college degree or higher, and 50 percent a postgraduate degree. Moreover, 60 percent claimed to have \"particular expertise with foreign affairs, military affairs, or international relations.\" Politically, the group leans Democratic, as 89 percent claimed to agree more with the policies of Democrats (11 percent more with those of Republicans). The respondents were 88 percent male, which is far from representative of the general population but not obviously unrepresentative of foreign policy elites. More details about the sample are provided in Online Appendix A. To be sure, then, our sample remains an imperfect approximation of foreign policy elites. Still, we argue that these imperfections will likely lead us to underestimate the effect of reputation and higher-order beliefs on perceived resolve. To start, the Democratic bias should cut against our proposed hypothesis, as liberals are generally less likely than conservatives to invoke concerns over credibility, reputation, and honor in international affairs  (Trager and Vavreck 2011) . And while respondents may also hew closer to Stephen Walt's particular foreign policy views, Walt has repeatedly argued against the importance of reputation.  13  Lastly, our sample likely remains less experienced with actual foreign policy decisionmaking than true elites. But as mentioned above, experience is linked to higherorder strategic reasoning, and  Tingley and Walter (2011)  show that experienced players care more about reputation than inexperienced ones. If anything, then, our results likely underestimate the reputational effects that would be found among actual elites. In short, given the cost and difficulty in obtaining elite samples, our sampling design is a reasonable first step toward the empirical study of higher-order beliefs in international crises.  14  Importantly, we think it highly unlikely that our sample would produce an opposite effect of reputation on perceived resolve relative to true elitesour respondents may be less attentive to reputation, but this should only depress the magnitude of reputational effects, not reverse their direction. \n Results To preview our results, we reach two main findings. First, reputations for resolve matter; when respondents learn that a state has stood firm in past crises, they consider it much more likely to stand firm today. Second, resolve is interdependent; we find that increases in A's perceived resolve are associated with decreases in B's perceived resolve, and estimate that higher-order belief updating is responsible for a large proportion of the total observed effect of past behavior on the balance of resolve.  15   \n Can States Build Reputations for Resolve? We begin with H REP , which considers whether a country's past behavior affects perceptions of its current resolve. We find strong evidence that it does. Respondents who learned that \"Country A did not back down and Country A achieved its aims\" in past crises thought that A was more likely to stand firm than those that received no information about past behavior (a 10 percentage point increase, from 60 percent to 70 percent). Similarly, when A \"backed down in each crisis and failed to achieve its aims,\" respondents thought A was roughly 10 percentage points more likely to back down. These effects are both highly significant (Figure  1 ). Moreover, this reputational treatment has the largest effect of all manipulations in the survey. The effect of going from a history of backing down to a history of standing firm is about 20 percentage points, which represents a quarter of the resolve variable's total range.  16  This reputational effect is roughly twice the size of the second-largest effect, information about power: shifting from B having \"substantially stronger military forces\" to A having \"substantially stronger military forces\" increases perceptions of A's resolve by roughly 10 percentage points.  17  Readers may wonder whether this potent reputational effect is driven only by a subset of respondents. Reputation skeptics contend that even if past behavior matters, it does so only to the extent that \"a decision maker uses an adversary's history of keeping commitments to assess the adversary's interests or military power\"  (Press 2005, 21 ). An observable implication of this view is that we should only see effects of past behavior on respondents that lack information about the balance of power. We find, however, that the reputational effect persists among respondents who were told about military capabilities (Figure  12 , Online Appendix C.1).  18  And while the reputational effect decreased slightly as scenario complexity increased,  19  it remained above 10 percentage points even among respondents who received the maximum amount of information about the scenario (Figure  11 , Online Appendix C.1). Reputational effects also persist across state leaders and across demographic subgroups, including gender, education, political affiliation, and cultural background. In sum, we find strong support for H REP . In contrast, we find no evidence for H DTP . According to H DTP , a state that backs down once after a history of standing firm will be perceived to be more resolved to stand firm in the present, as observers expect it to try to re-establish its lost reputation for resolve. Yet as Figure  1  shows, backing down once after a history of always standing firm reduces perceived resolve by about 8 percentage points compared to a history of standing firm (p < 0:0001), nearly returning perceived resolve to its baseline probability in the no-information condition. In other words, backing down once almost entirely eliminates the reputational gains that A achieves by standing firm in the initial three crises. \n Do Higher-Order Beliefs Contribute to Reputational Effects? Typically, reputational effects like the ones reported above are interpreted in terms of first-order updating: A takes an action, and observers update their beliefs about A. Yet as discussed in Section \"Reputational Effects and Higher-Order Beliefs,\" the total reputational effect of A's past behavior on A and B's resolve may also consist of higher-order effects. . In these terms, the \"direct\" or \"immediate\" effect of our reputation treatment T (information about A's past behavior) is given by D R1 i ¼ R1 i À R0 i , where R0 i refers to perceptions of i's resolve before observing T (i.e. among respondents in the \"no information\" condition). Now, suppose that observers go through two levels of belief updating following reputation treatment T (this updating process is shown graphically in Figure  2 ). Our argument suggests that we should see D R1 A > 0, and, by interdependence, D R2 B < 0. In this situation, our estimand, which we will call the interdependence coefficient and label y, is given by D R2 B D R1 A . This ratio tells us by how much an immediate one-unit change in A's perceived resolve subsequently changes B's perceived resolve. For example, if a 10 percentage point increase in A's resolve decreases B's resolve by 5 percentage points, y ¼ À5 10 ¼ À0:5. More generally, if we assume that the interdependence of resolve is symmetric across actors and constant across levels of updating, we have y ¼ D Rk A D RkÀ1 B ¼ D Rk B D RkÀ1 A for all k 2 N. We can then empirically estimate y by taking the ratio of the observed total effect of treatment on B's and A's resolve, D RB D RA , and state our interdependent resolve hypothesis more precisely as H INT : y < 0. 20 As mentioned above, our treatment must fulfill two conditions for this estimation strategy to succeed, analogous to the identifying assumptions in instrumental variable analysis: (C1) D R1 A > 0 (instrument strength) and (C2) D R1 B ¼ 0 (exclusion restriction). Notably, most treatments do not satisfy C2. For example, the fact that A stood firm against B in the past could lead to inferences not just about A's resolve, but also about B and the A-B dyad, such as B's dispositional determination or domestic audiences, violating our identifying assumption. Thus, we cannot use information about A's past behavior against B to estimate the interdependence of A and B's resolve. However, information about A's past actions against another country is a treatment that likely satisfies C2. 21 When told about A's extra-dyadic behavior, observers can make inferences about how much A values its reputation, whether A's domestic public is liable to punish leaders for backing down, or any other factor that shapes A's resolve. But the treatment is uninformative about the A-B relationship, the territory under dispute, or other factors that could reasonably shape perceptions of B's resolve-except, that is, perceptions of A's resolve. This treatment, then, allows for a clean test of our interdependence hypothesis. The results of this test are displayed in Figure  3 . We find that A's behavior against other countries significantly affects perceptions of B's resolve as expectedrespondents who were told that A stood firm against other countries in the past assess B's resolve to be roughly 7 percentage points lower relative to baseline, and A backing down against other countries leads to a similar increase in perceptions of B's resolve. For A standing firm in extra-dyadic crises, ŷ ¼ À:065 :091 ¼ À:71, and for A backing down in extra-dyadic crises, ŷ ¼ :074 À:098 ¼ À:75. Both of these effects are statistically significant, lending strong support to H INT . 22 . \n The Interdependence Multiplier These results offer compelling evidence that reputational effects exist, and that they are compounded by higher-order beliefs. Still, we have yet to specify precisely how important are higher-order beliefs. Can we estimate the proportion of the total reputational effect-the effect of past behavior on the overall difference in resolve between A and B-that is attributable to higher-order belief updating? To help us answer this question, define the interdependence multiplier (IM) as the factor by which a first-order reputational effect should be multiplied in order to obtain the total reputational effect. In our simple formalization, the magnitude of the interdependence multiplier depends on two parameters: the interdependence coefficient, y, and the number of levels of belief updating, which we label n.  23  Given our model (and assuming jyj < 1), Online Appendix D.2 derives the IM to be, for any n, IM ¼ 1 À jyj n 1 À jyj which converges to 1=ð1 À jyjÞ as n ! 1, a situation with \"common knowledge\" in which everybody knows about a fact or event, knows that everybody knows it, and so on. Figure  4  plots the magnitude of the IM across hypothetical values of y and n. At one extreme, if we assume that actors engage only in first-order reasoning (the light blue line), the IM is always 1, and the total reputational effect is equal to the firstorder reputation effect. This, implicitly, has been the assumption in most past discussions of reputation. At the other extreme, if it is plausible to assume common knowledge (the red line), the total reputational effect is more than twice as large as the first-order effect for any jyj > 0:5, and nearly four times as large at j ŷj ¼ 0:73 (the average of our jyj estimates calculated from Figure  3  above).  24  Between these extremes, the IM's magnitude is substantial across a range of parameter values, underscoring that higher-order beliefs can be responsible for a large proportion of any given total reputational effect. We can now use the IM to estimate the effects of higher-order beliefs on perceived resolve in our survey experiment. As stated above, our average estimated y ¼ À0:73, and the average total effect of the reputation treatments presented in Figure  3  is roughly 16 percent. To estimate how much of that 16 percent change is attributable to higher-order beliefs, let us assume that n ¼ 3. This implies IM ¼ 1À0:73 3 1À:73 ¼ 2:26. The estimated first-order effect is then simply the total effect divided by the IM,  16  2:26 ¼ 7:08. This leaves roughly 9 percentage points attributable to higher-order reasoning-a sizable 55 percent of the total effect. We can also more intuitively verify this result by beginning with the first-order effect, and then building out via n ¼ 3 reasoning to the total effect. Suppose that, as we just estimated, respondents on average perceive A to initially be 7.08 percentage points more likely to stand firm when A has stood firm repeatedly in past cases (D R1 A ¼ 7:08). The respondent reasons, however, that B will become less resolved after inferring this change. Specifically, B's resolve decreases by 7:08  y percentage points (D R2 B ¼ À5:17). This, in turn, will increase A's perceived resolve by À5:17  y (D R3 A ¼ 3:77). The total reputational effect is therefore jD R1 A jþ jD R2 B j þ jD R3 A j ¼ 16:02 % 16 percentage points, which is indeed the total reputational effect that we observe in the data (and is also 7:08  IM). This estimation strategy is limited by our inability to directly observe n, respondents' level of higher-order reasoning-we assumed n ¼ 3 above, but the true value could be higher or lower. While we therefore cannot definitively identify the proportion of the total reputational effect attributable to higher-order beliefs, we remain  confident that these beliefs drive a substantial portion of the effect in this case, for several reasons. First, we can quantify our uncertainty by deriving bounds. As our survey recovers reputational effects that are inconsistent with mere first-order reasoning, we use n ¼ 2 as a lower bound. In this case, the IM ¼ 1:73, and higher-order effects are responsible for about 42 percent of the total reputational effect. The upper bound is represented by common knowledge (n ¼ 1). In this case, the IM ¼ 3:7, and the higher-order effects constitute about 73 percent of the total reputational effect (see Online Appendix D.2). 25 Note that our reputation treatment had a relatively large effect on B's perceived resolve (j ŷj ¼ 0:73 is large), which results in correspondingly large higher-order effect estimates even assuming low levels of higher-order reasoning (Figure  4  is instructive). Of course, the interdependence coefficient y might vary in size in different settings or contexts-we discuss this possibility extensively in Section \"The Degree of Interdependence.\" Second, numerous other studies and examples discussed in Section \"Higher-Order Beliefs\" suggest that at least some degree of higher-order reasoning, be it conscious or intuitive, is a regular feature of human cognition in political, economic, and social settings-though higher-order belief chains can become prohibitively complex, n ¼ 2 reasoning is relatively common. This reassures us that n ¼ 2 is a reasonable lower bound to estimate higher-order effects. In sum, we find clear evidence that higher-order beliefs are responsible for a large portion of our observed reputational effects-even restricting the calculations to a minimal level of higher-order reasoning, the proportion approaches 50 percent. In the next section, we move beyond our survey data to discuss real-world applications and implications of our argument. \n Discussion: Interdependent Resolve in Real Life Above, we provided evidence of higher-order reputational dynamics, and argued that the magnitude of these effects depends on the order to which people form beliefs (n) and the degree of interdependence (y). Our abstract survey vignette allows us to observe the effect of higher-order belief updating in a way that is difficult to do in the real world. Still, some uncertainty remains as to whether and how the interdependence of resolve manifests in the messier context of real-world bargaining situations. This section discusses the circumstances under which we expect higher-order beliefs and interdependent resolve to matter most, and the attendant implications of our argument for real-world crisis bargaining. \n Higher-Order Beliefs As discussed in Section \"Reputational Effects and Higher-Order Beliefs,\" one broad issue is whether decision-makers engage in higher-order reasoning  Mercer 2012 ). If they do not, our arguments have little relevance to the real world. Fortunately, evidence from a variety of contexts suggests that explicit and implicit higher-order reasoning is common, and does not require especially sophisticated agents. First, experimental evidence from behavioral economics suggests that most people often form at least second-order beliefs, and many reach higher orders as well (e.g.  Nagel 1995; Camerer, Ho, and Chong 2004) . In psychology, researchers have found that the magnitude of the famous \"bystander effect\" depends on whether the context allows bystanders to form beliefs about other bystanders' beliefs  (Thomas et al. 2014 (Thomas et al. , 2016 . A third example comes from a recent field experiment in Benin, where voters who learned information about politicians' behavior punished and rewarded performance only when they thought that others knew this information as well, suggesting a higher-order understanding of coordination dynamics  (Adida et al. 2020) . Many other studies also find significant effects from interventions targeted at higher-order beliefs  (Bicchieri 2016; Mildenberger and Tingley 2019) . Moreover, scholars have produced abundant evidence of higher-order reasoning among policymaking elites in high-stakes situations. At the domestic level, autocrats faced with potentially unsatisfied publics go to great lengths to create impressions of widespread support for their rule, or, if that fails, at least keep everyone guessing about each other's beliefs  (Kuran 1995; Chwe 2001, 20-21) . Internationally, as  McManus (2014, 726)  illustrates with the case of Israel-US bargaining over Iran's nuclear program, states often attempt to stake their allies' reputation on supporting them, believing that their allies will then believe themselves bound to act (see, e.g.  Jervis 1978, 180; Trager 2017, Ch. 1, for more examples) . And conflicts are often said to end only when \"opponents succeed in coordinating their expectations\"  (Slantchev 2003, 621 ; see also  Carter 2017) . In these and many other examples, beliefs about beliefs are the driver and focus of significant strategic contention. To be clear, our argument does not require that actors always run through every step of the inferential process in a deliberate or conscious way. Higher-order beliefs can be incorporated into decision-making heuristically, implicitly, and subconsciously. As  Chwe (2001, 78)  argues for the case of driving, \"I stop at a red traffic light out of habit, but a fully specified argument for doing so would involve an infinite regress: I stop because I think that other people are going, and I think that other people are going because I think that they think that I am stopping, and so on.\" Developmental psychologists have found that children display a great degree of higher-order understanding early on in life, implicitly engaging in complex theorizing about the mental states of others long before they can explicitly articulate their reasoning  (Wellman 2014) . Higher-order belief dynamics also often become embedded in cultural and legal norms  Ridgeway 2011; Morrow 2014) . \n The Degree of Interdependence While it is therefore clear that real-world actors do engage in higher-order reasoning, the extent to which first-order reputational effect are amplified also depends on the degree to which resolve is interdependent, i.e. the extent to which an initial change in A's resolve affects B's resolve. Here, contextual factors are likely to play a large role. We identify and discuss four such factors. First, the degree of interdependence depends on the extent to which the context resembles a prototypical contest of resolve. The central features of such contests are  (1)  the costs of conflict are so great that losing is preferred to both sides standing firm, but (2) the issue under dispute is sufficiently valuable for a coercive victory to be preferred to a peaceful compromise  (Morrow 1989, 941) . We expect resolve to be most interdependent in conflicts that most closely approximate these conditions. Nuclear crises are often cited as the quintessential examples of such contests  (Schelling 1966; Powell 1990 ), but they are by no means the only ones. In the 1898 Fashoda Crisis, for example, France dispatched a mission to Egypt in an attempt to force Britain to make concessions, but withdrew when it became convinced that Britain was more resolved than it initially believed  (Trachtenberg 2012, 13-16) .  26  More contemporary examples can be found in proxy conflicts like the ongoing Syrian civil war. Direct conflict between the U.S. and Russia over Syria seems prohibitively costly, yet Damascus remains a valuable prize. In these circumstances, resolve can be highly interdependent. Indeed, this interdependence featured regularly in debates about U.S. intervention in Syria. Critics argue that Obama's failure to enforce the infamous chemical weapons red-line in 2013 undermined U.S. deterrence, paving the way for Russian intervention in 2015-Putin might have been compelled to stay out, were it not clear (to both parties) that the U.S. was irresolute. At the same time, Obama's reluctance to engage in Syria resulted in part from his belief that Russia would counter-escalate in response to limited U.S. intervention, especially after Russia stepped up its involvement in 2015.  27  In other words, U.S. lack of resolve fueled Russian resolve, further depressing U.S. resolve. Second, interdependence is also affected by the extent to which actors are able to act strategically, conditioning their behavior on what they think others are likely to do. Actors may fail or be unable to do so for various reasons. A prominent example is found in the expansive literature on credible commitments, which discusses commitment devices that may leave actors unconditionally resolved in a crisis. The moment actors truly commit to a strategy-when they throw their only steering wheel out of the window-they have effectively set their interdependence coefficient to 0: even if they subsequently change their beliefs about their opponent's resolve, their own course of action is already set. That said, absolute commitments are exceedingly difficult and risky to make.  28  In the real world, then, resolve is almost always interdependent at least to some extent. A third and related factor is the concentration of decision-making authority: when leaders have the ability to change course quickly, their resolve is likely to depend more on the other side's resolve. If, on the other hand, authority is diffuse, it will be difficult for a country to change course in the face of new information. One example is the delegation of military decision-making to local commanders, who can then choose to stand firm or back down in their theater of operations. Such delegation may be necessary from a practical perspective, but it also means central decision-makers have less flexibility. Another obstacle to short-term policy change in response to belief updating is the number of veto players in a political system  (Tsebelis 2002) . To the extent that this number is correlated with regime type, there is reason to think that the resolve of democracies is less interdependent than that of their autocratic counterparts. Lastly, a fourth factor affecting the degree of interdependence is the observability of resolve. An actor's resolve is more likely to influence its opponents calculations when it is readily observable. Resolve is likely to be more observable the more an actor's deliberative processes are public, or when opponents share a cultural understanding of the meaning of certain behaviors or events  (O'Neill 1999, 153-54) . Strategic intelligence also play an important role. The interdependence of resolve was on clear display, for example, during the Washington Disarmament Conference in 1921, when the United States was able to break Japan's ciphers and read Tokyo's private diplomatic communication. One such message stated the absolute minimum naval tonnage ratio that the Japanese government would be willing to accept. \"Knowing how far Japan could be pushed . . . allowed the United States to do so with full confidence, merely waiting for the Japanese to give in\"  (Bauer 2013, 211) . When Japan's (lack of) resolve became perfectly observable to the US, American resolve dramatically increased in response. In sum, we expect actors' resolve to be most interdependent in real-world contexts that resemble prototypical contests of resolve, where actors are strategic and have centralized decision-making structures, and where resolve can be inferred with confidence. When interdependence is high, higher-order amplification of first-order reputational effects can produce especially large swings in the balance of resolve. It is in these circumstances, then, that beliefs about beliefs should be most consequential for crisis outcomes. These intuitive sources of variation in the interdependence of resolve could themselves be the object of empirical study, but for now, we leave this task for future work. \n The Power of Beliefs Each party is the prisoner or the beneficiary of their mutual expectations. -Thomas Schelling  (Schelling 1960, 60)  Reputations for resolve have long been the subject of debate: some see them as indispensable assets, while others dismiss past actions as irrelevant to current crises. Using an experimental approach, this article strongly reinforces the former viewstates and leaders can form reputations for resolve and leverage them to their advantage during crises. Moreover, we emphasize that higher-order beliefs play an under-appreciated yet crucial role in this process, as first-order reputational effects are amplified by actors' beliefs about their opponents' beliefs. In this sense, international contests of resolve hinge not merely on past actions, but on actors' combined expectations about the implications of past actions for present behavior. In conclusion, we make several suggestions for further empirical research on higher-order beliefs and interdependent resolve in international politics. As mentioned earlier, one limitation of our study is that we lack direct knowledge of the level of higher-order reasoning at which respondents analyzed the crisis scenario. A number of studies in behavioral economics measures \"k-level reasoning\" directly in laboratory game settings (see Hafner-Burton, Hughes, and Victor 2013, for a review), but these measures are rarely found in survey research on international politics. Future studies could adapt such techniques to shorter survey formats, where they could serve as useful individual-level measures of strategic competence. We also highlight several interesting avenues for future research. One promising idea is that opponents' perceptions of a leader's competence could influence their higher-order inferences about that leader's likely beliefs, consequently shaping their own bargaining behavior. Some leaders are understood to be especially experienced, calculating, or wise, whereas others may be seen as inexperienced, impulsive, or even wholly incompetent. Not only could variation in leader competence directly affect a state's behavior, but the perception of competence or ineptitude might also shape others' higher-order expectations about that leader's beliefs and world view, with implications for their own behavior during crises. Moreover, there are also strong reasons to expect that beliefs about beliefs matter in contexts far beyond crisis bargaining, including collective action and coordination on many important international issues, such as climate change and international law  (Mildenberger and Tingley 2019; Morrow 2014 ). Schelling's argument that sets of beliefs can act as prisons (or paradises) matters as much to problems like gender inequality as it does to international conflict  (Ridgeway 2011) . Along these lines, the study of higher-order belief dynamics also presents an exciting opportunity for collaboration across research fields. Such dynamics can only be understood by combining the insights and methods of psychological, cultural, and strategic approaches-whether and how one actor forms and acts on beliefs about another actor's beliefs depends on cognitive processes, systems of social meaning, and the anticipated consequences of different courses of action . And once they are understood, insights on higher-order beliefs are likely to travel across many domains and issue areas. In short, higher-order beliefs are an incredibly rich area for future studies of broad applicability and substantive importance. This article offered some theory and a novel methodological framework for diagnosing the effects of higher-order beliefs, which we hope will contribute to a vibrant sub-literature on this topic in international relations scholarship. participants of the Department of Peace and Conflict Research workshop at Uppsala University and the Division of Social Science seminar at Hong Kong University of Science & Technology, and especially Robert Trager. g.  Mattes 2012; LeVeck and Narang 2017) . Others examine the importance of reputation for cooperation; see  Crescenzi (2017) . 8. For other recent experimental work, which focuses on first-order beliefs, see  Kertzer, Renshon, and Yarhi-Milo (2021) ,  Huth (2018) . 9. The relevant \"perceiver\" of a state's resolve could be any other international observer, be it another state involved in a dispute with the state in question, or an uninvolved third party-in either case, agents should make similar reputational inferences. For the purposes of empirical testing, however, the \"perceivers\" are our survey respondents, who assessed the resolve of two abstract states in crisis (see Section \"Research Design\"). 10. Some might wonder how much respondents can infer from State A's disputes with other, unknown states (that are not B). Additional background details would allow respondents to form more precise beliefs, yet respondents can still make general reputational inferences from A's past behavior even without these details. It is reasonable for respondents to infer that, if A stood firm three times in recent crises, then A is probably more likely to stand firm in a subsequent dispute, relative to the respondents' prior beliefs. Empirically, we demonstrate that our respondents can and do draw reputational inferences even when given relatively limited information. And as noted below, our results accord with  Renshon, Dafoe, and Huth (2018) , who find similar reputational effects across abstract and real-world designs. Regardless, future work on higher-order beliefs could (and ideally would) employ diverse research designs in order to test the sensitivity of this or any other particular design feature. 11. The vignette manipulates a large number of features, yielding a total of 8,640 cells. In this, it is similar to related survey techniques such as conjoint analysis  (Hainmueller, Hopkins, and Yamamoto 2014) . We discuss the advantages and possible disadvantages of factorial vignette experiments with many manipulations in Online Appendix B.3. 12. Similar questions were used in  Renshon, Dafoe, and Huth (2018)  and  Kertzer, Renshon, and Yarhi-Milo (2021) , though neither define resolve precisely and both discuss only first-order effects. 13. For recent examples, see  Walt (2015)  and  Walt (2016) . 14. For other experimental work that uses non-elite samples to test theories of bargaining, see  Renshon, Lee, and Tingley (2017) ,  Kertzer, Renshon, and Yarhi-Milo (2021) , and Cebul, Dafoe, and Monteiro (Forthcoming). 15. Main results are shown graphically below-full regression tables can be found in Online Appendix C.3. 16. The minimum likelihood respondents could give for A standing firm is 10 percent (0 percent to 20 percent), the maximum 90 percent (80 percent to 100 percent). This effect is approximately equal to one standard deviation of the resolve variable (m ¼ 62percent, s ¼ 21percent), which is equivalent to a Cohen's d ¼ 1; Cohen offered d ¼ 0:8 as a \"big\" effect. 17. The capabilities results, as well as results from all other manipulations, can be found in Online Appendix C. 18. We do not manipulate interests, but  Kertzer, Renshon, and Yarhi-Milo (2021, 22)  find similar results when doing so: even when told that one side has high stakes and high relative power, the effect of past behavior on perceptions of resolve is large and significant. Figure 2 . 2 Figure 2. A model of belief updating, where k denotes the level of belief updating, R k i denotes beliefs about actor i's resolve after the kth level of updating, and DR k i denotes the change in beliefs about i's resolve due to the kth level of updating. If conditions C1 and C2 are met, then the thick black lines have DR k i ¼ DR kÀ1 j  y, and we can estimate y as D RB D RA \n Figure 3 . 3 Figure 3.Effect of A's past behavior against \"other countries\" (not B) on perceived resolve, relative to respondents that received no information about past behavior (A's baseline probability of standing firm % 60 percent). X-axis displays percentage point change; horizontal lines represent 90 percent and 95 percent CIs. \n Figure 4 . 4 Figure 4. jyj, n, and the Interdependence Multiplier. Vertical line indicates j ŷj ¼ 0:73. \n Effect of A's past behavior on perceptions of A's resolve, relative to respondents that received no information about past behavior (baseline probability of standing firm % 60 percent). X-axis displays percentage point change; horizontal lines represent 90 percent and 95 percent CIs. A Backed Down Three Times Treatment A Backed Down in Most Recent Crisis, History of Not Backing Down A Did Not Back Down Three Times 0.2 0.1 0.0 0.1 0.2 Change in Perceptions of A's Resolve Figure 1. \n To test this idea, we need a treatment that affects beliefs about Rk i À RkÀ1 i A's resolve, but cannot affect B's resolve through any channel except (beliefs about) A's resolve. If such a treatment affects B's resolve, then we can conclude that perceptions of B's resolve are influenced by perceptions of A's resolve-in other words, that respondents form higher-order beliefs and that resolve is interdependent (H INT ).It is useful to define the relevant estimand and identifying assumptions more formally. Let R i denote the resolve of agent i, k denote a level of belief updating, and Rk i denote an observer's beliefs about actor i's resolve after the kth level of updating. Next, define D Rk i as the change in beliefs about actor i's resolve after the kth level of updating, i.e. \n\t\t\t Journal of Conflict Resolution 65 (7) (8)", "date_published": "n/a", "url": "n/a", "filename": "0022002721995549.tei.xml", "abstract": "Reputations for resolve are said to be one of the few things worth fighting for, yet they remain inadequately understood. Discussions of reputation focus almost exclusively on first-order belief change-A stands firm, B updates its beliefs about A's resolve. Such first-order reputational effects are important, but they are not the whole story. Higher-order beliefs-what A believes about B's beliefs, and so onmatter a great deal as well. When A comes to believe that B is more resolved, this may decrease A's resolve, and this in turn may increase B's resolve, and so on. In other words, resolve is interdependent. We offer a framework for estimating higher-order effects, and find evidence of such reasoning in a survey experiment on quasi-elites. Our findings indicate both that states and leaders can develop potent reputations for resolve, and that higher-order beliefs are often responsible for a large proportion of these effects (40 percent to 70 percent in our experimental setting). We conclude by complementing the survey with qualitative evidence and laying the groundwork for future research.", "id": "4bacfc01f9a63b52944c20abfc7ef196"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld"], "title": "Multiverse-wide Cooperation via Correlated Decision Making", "text": "explains that by sending in 'C', a participant can increase everyone else's payoff by $2. By sending in 'D', participants can increase their own payoff by $5. The letter ends by informing the participants that they were chosen for the similarity and rationality of their decision mechanisms, particularly in weird scenarios like this one. It should be noted that every participant only cares about the balance of her own bank account, and not about Hofstadter's or that of the other 19 participants. Upon receiving the letter, should you cooperate or defect? Assuming the participants' thought processes are sufficiently similar to each other, I think we should cooperate because this makes it more likely that our 19 fellow participants also cooperate (see chapter 2 and the references given therein). After all, Hofstadter stated fairly explicitly that the thought processes of the participants are strongly correlated. Thus, if we cooperate, we should expect significantly more of the other participants to cooperate as well than if we defect, which means that cooperating has higher expected utility. Alternatively, we may reason that by our choice we determine what the rational choice is for all participants. Hofstadter calls this idea of cooperation via correlated decision making superrationality. By itself, superrationality does not seem particularly action-guiding. Usually, we have other evidence about other agents' behavior and thought processes such that the evidence we gain from our own decisions is less important (see section 6.6). To apply superrationality in practice, we combine it with another intellectually stimulating but by itself inconsequential hypothesis: we probably live in a vast universe or even multiverse, most of which we cannot observe or interact with (see appendix section 6.2). In this paper, we will use the term \"multiverse\" in a broad sense to refer to any theory postulating multiple universes, including but not limited to Everett's many-worlds interpretation of quantum mechanics. In fact, for brevity's sake, we will use the term to refer to any theory of physics that implies the existence of a sufficiently large universe with many agents, including a merely spatially infinite universe. 1 Some parts of this multiverse are probably inhabited by intelligent beings like us, some of which surely think about scenarios like this one in the same way as we do. This is all we need to allow for the application of superrationality. The key insight of this paper is that agents in a multiverse are in a situation structurally similar to the aforementioned donation game if they care about each other's decisions in far away parts of the multiverse. Consider the following list of parallels: • The decisions between some groups of agents are correlated, just like those in the donation game. • Some agents have different goals than others -a claim for which we argue in section 3.1 -just like the agents in the donation game maximize the balances of different bank accounts. • On occasion, agents can \"cooperate\" by benefitting the value systems of agents in other parts of the multiverse at low costs to themselves. • As in the donation game, our actions cannot causally influence the behavior of other agents in the multiverse. As an example, imagine you have some specific value system like the reduction of involuntary suffering. You come into a situation in which involuntary suffering has already been reduced to a very low amount. You face a choice between two actions: • You can continue to reduce suffering and increase your own utility and that of other suffering reducers by 1. 2 • You can increase the utility of superrational agents in other parts of the multiverse who (also) care about things other than suffering reduction by 100, e. g. by generating a society of agents who live happily, produce interesting art, conduct science, explore technologies, trade, behave benevolently towards each other, etc. By construction of the thought experiment you care about suffering reduction only, so you would usually take the first action. But consider that many agents throughout the multiverse will face very similar decision problems. For example, there might be an agent who primarily cares about agents experiencing art and the interestingness of things and who is facing similarly diminishing returns -in her world, most things that could be of interest already exist. Other value systems, on the other hand, have been ignored in the process of making her world more interesting. Her world contains many sentient beings with very low levels of well-being, such as humans experiencing various crises (wars, loneliness, life-threatening dangers) -a common theme in art -, wild animals, or blood sports. She knows that agents in other parts of the multiverse dislike this suffering and that she could alleviate them at low opportunity costs to herself. Her decision problem is thus structurally similar to our own. If her thought process is similar to our own, superrationality applies. If we are nice and follow the heuristic \"fulfill the goals of other agents in the multiverse whenever the returns are much higher than the opportunity costs for your own values\", then this makes it more likely that she will be nice as well, the benefits of which are much greater than those forgone by our own friendliness. In general, if after thinking about superrationality we are nice to other value systems and relinquish opportunities to exploit them, this makes it more likely that other superrational agents with different value systems out there, or at least those who think in ways similar to our own, do the same. And if everyone is friendly in this way, we can expect to harvest gains from compromise -everyone will be better off. I will refer to this idea as multiverse-wide superrationality, or MSR for short. \n An overview of the paper Having read the above introduction, the reader is familiar with the basic idea of MSR. However, it opens up many further questions, some of which I attempt to answer in the present paper. Specifically the rest of this paper makes the following contributions: • We investigate the mechanism of superrationality (chapter 2). -After elaborating on the argument for superrationality, we survey the decision theory literature pertaining to superrational cooperation (sections 2.1 through 2.5). Among other things, we argue in favor of incorporating \"updatelessness\" into one's decision mechanism. -Exactly how much should we cooperate? Considering superrationality, how should we decide between actions in this universe to maximize our multiverse-wide utility? I will argue that it is best to effectively adopt a new utility function in this universe: a weighted sum of all superrationalists' utility functions that, if adopted by all superrationalists, gives every superrationalist the same gains from compromise. This function should be the same for all agents with your decision algorithm. (See sections 2.6 through 2.8.) -We show how superrational cooperation fundamentally differs from standard causal cooperation (sections 2.9 and 2.10). We will see how it requires no reciprocity -we should benefit superrationalists who cannot benefit us, because we may correlate with agents who can benefit us but whom we cannot benefit. • Cooperating superrationally with agents elsewhere in the multiverse means taking their values into account. Chapter 3 explores what these values might be and which aspects of these values are relevant for MSR. -I argue that (with regard to the decision to cooperate or not) we correlate with agents who hold values that differ from ours (section 3.1). If this were not the case, cooperating with them would be unnecessary except when it comes to coordination (see section 2.8.9). -I provide a comprehensive list of prerequisites that must be fulfilled for MSR to work (see section 3.2). For example, we cannot benefit agents who do not care about our part of the multiverse (section 3.2.2). -Which aspects of other agents' preferences should be taken into account? E.g., should it only be \"moral preferences\"? To which extent should we idealize their preferences, e. g. by trying to factor out cognitive biases? We motivate and answer these questions in section 3.3. -We review different approaches to hypothesizing about the values of other agents in the multiverse (section 3.4), the most important ones being evolutionary psychology and the study of cultural evolution. • How does multiverse-wide superrational cooperation shift our priorities? What does it recommend in practice? These questions are discussed in chapter 4. We first show how to make policy decisions in the absence of reliable knowledge about the values of agents elsewhere in the multiverse (section 4.1). I then recommend a few interventions, such as promoting causal cooperation (section 4.5.2) and, perhaps most importantly, ensuring that future superintelligent AIs reason correctly about decision theory (section 4.6.3). • The appendix contains various additional considerations that are either less crucial for our decisions or otherwise more tangential, yet nonetheless relevant and of interest to at least some readers. For example, I give an overview of the small amount of work that is closely related to MSR (section 6.1) and explain why I find it plausible that we live in a universe or multiverse containing many agents with whom we are correlated (section 6.2). I also argue that superrationality has few implications for the interactions between agents on Earth (section 6.6), and hence why this paper specifically concerns the application of superrationality in a multiverse-wide (as opposed to general) setting. Much more research is needed to answer some of the questions I set out to explore. This is why I focus more on outlining how these questions can be researched in the future, rather than on trying to ascertain that all my answers are correct with high confidence. The optimal outcome is the one where you defect and everyone else cooperates, yielding a payoff of 19 • $2 + $5 = $43. Conversely, the worst outcome occurs if you cooperate and everyone else defects, yielding a payoff of $0. In any case, no matter how many participants cooperate, you are always better off defecting; 'D' is the dominant strategy. Standard game-theoretical analysis would therefore suggest that 'D' is the correct choice  (Binmore, 2007a , chapter 1, Osborne, 2004 . This is quite unfortunate, because if everyone abides by this reasoning, this yields a payoff of just $5 -whereas if everyone could cooperate, you and everyone else could earn 19 • $2 = $38. Is there any way around this tragedy of the commons? If we only consider the causal implications of an action, the analysis is indeed accurate. However, it ignores that there is also a correlation between the decisions of the participants 3 . Consider a variation of the above thought experiment in which you know that the other 19 participants are all exact copies of you, deciding under the exact same environmental circumstances as yourself. You still have no causal influence over the others' decisions and 'D' is still the dominant strategy; no matter what the other copies choose, 'D' is the better option. However, this argument seems much less attractive now. No matter what you choose, your copies are guaranteed to make the same choice (assuming that they make decisions deterministically). There is no possible (deterministic) world in which two copies decide differently in the exact same situation. Thus, your decision whether to cooperate is one between two worlds: in one of them, the algorithm implemented by your brain returns 'C'; in the other, it returns 'D'. Determining the choice of all your copies to be 'C' gives you more utility, and should thus be regarded as the (instrumentally) rational choice. Of course, strong correlation is not limited to atom-by-atom copies. Imagine a variation of the donation game in which you play against near copies who differ from you in insignificant ways. One may have forgotten some particular childhood memory; another may be more skilled at playing basketball; and so forth. Similarly, the environments in which the near copies decide may differ inconsequentially. One participant may receive the letter in, say, the font \"Times New Roman\" and another in \"Arial\". In a donation game with such negligible variations, it seems clear that 'C' is still the better option. Although we cannot be absolutely certain that all 20 of the near-copies make the same choice, it is very likely that they will. With growing dissimilarities between two agents and their environments, the correlation between them decreases further, but your own decision still gives you information about the other agents' decisions. As long as the accumulating differences do not affect any of the agents' reasoning, the correlation will remain a strong one. While the participants of the two donation games are not copies of each other, both variants make clear that the participants' decision-making mechanisms resemble one another and are thus correlated. The donation game with similarity is very explicit about this similarity. The donation game with common rationality, on the other hand, is more subtle -it tells the participants that their decision mechanisms are all \"rational\". Of course, the individual participant does not know what the rational choice is, yet, but she knows that, if she makes her decision by abstract reasoning (rather than a whim) the result will be the rational decision. She also knows the other participants are also rational (in the same sense of the word) and will therefore arrive at the same -the rational -decision. (It seems unlikely that 'C' and 'D' are exactly equally rational.) In essence, this argument from common rationality is one from (perfect) correlation: if we are rational, we determine what the rational decision is and thus what other rational agents will do. This mechanism is what Hofstadter calls superrationality: if everyone knows that everyone is rational and has the same information, then everyone can determine everyone else's decision. Throughout this paper, I will tend to make arguments from similarity of decision algorithms rather than from common rationality, because I hold these to be more rigorous and more applicable whenever there is not authority to tell my collaborators and me about our common rationality. In any case, the argument from correlation is sufficiently general to include reasoning based on common rationality as a type of perfect correlation. Because the underlying mechanisms are similar, we use the term superrationality for both similarity and common rationality-based lines of reasoning. Assuming that we ourselves apply superrationality, we will also call an agent \"superrational\" if her decision correlates with ours. Similarly, we call a group of agents superrational if they use similar decision algorithms and take superrationality-type reasoning into account, sweeping the complications of thinking about individual correlations under the rug. Furthermore, we shall use the term \"donation game with superrationality\" for donation games with similarity or common knowledge of each other's rationality. Anticipating objections,  Hofstadter (1983)  writes: This solution depends in no way on telepathy or bizarre forms of causality. It's just that the statement \"I'll choose C and then everyone will\", though entirely correct, is somewhat misleadingly phrased. It involves the word \"choice\", which is incompatible with the compelling quality of logic. Schoolchildren do not choose what 507 divided by 13 is; they figure it out. Analogously, my letter really did not allow choice; it demanded reasoning. Thus, a better way to phrase the \"voodoo\" statement would be this: \"If reasoning guides me to say C, then, as I am no different from anyone else as far as rational thinking is concerned, it will guide everyone to say C.\" [...] Likewise, the argument \"Whatever I do, so will everyone else do\" is simply a statement of faith that reasoning is universal, at least among rational thinkers [or those who receive the letter], not an endorsement of any mystical kind of causality. I do not think that, in practice, similarity between decision algorithms will often be as strong as assumed in the above thought experiments. Even if I received a letter of the above kind, I would not think of my decision as determining the others' decisions with near certainty (although there are circumstances under which I would cooperate). In fact, the very reason I make the superrationality argument about the multiverse in particular is that the conditions for superrationality are usually not fulfilled on Earth (see section 6.6). Nonetheless, it is useful to assume perfect and near-perfect correlations in thought experiments for illustration purposes. The rest of this section explores various theoretical considerations related to those mechanisms of superrationality that have practical implications for multiverse-wide superrationality. Most of them are not specific to the multiverse-wide application, however, and we will often illustrate them in more readily imaginable settings in a single universe. \n Lack of knowledge is evidential power, part I: the other agents One reason why some people would not cooperate in the donation game (or the prisoner's dilemma) is, I think, that they have knowledge that would break the correlation between the participants. Using their model of human psychology, they can quickly make an informed guess about what the others are likely to think about and thus decide. Put simply, you learn less from your own cooperation once you already know what the others are deciding. Consider the following variation of the donation game: The Devious postal worker. Game master Hofstadter (in this thought experiment a fictional character) has contrived another donation game. This time, you and the other participants know that you all live in the same area and are to reply by post. Having learned your lesson from Hofstadter's article in Scientific American, you write a big 'C' onto a postcard and walk to the post office. The postal worker takes your card, reads the address and says: \"You're participating in one of Prof. Hofstadter's games, aren't you? And you seem to have decided to cooperate. How very noble and decision-theoretically sound of you! Well, I'll let you in on a little secret. Hofstadter has been playing his games with people in this area for years now. We used to merely distribute the letters for him, look at people's answers and then send them back to Hofstadter, but after a year or two, we started to bet on people's replies. The participants tend to use small cards rather than envelopes to save money, so it was easy to spot their replies and count the number of C's and D's among them. We eventually became almost perfect at predicting people's responses, including those from first-timers like yourself who don't necessarily correlate with past participants. But merely betting on responses got boring after a while, so we started to play a new game: we would tell all participants about our predictions of what the others would choose, giving each one a chance to reconsider their own choice. Although this obviously affected the players' behavior and forced us to readjust our methods, our predictions are now practically flawless once again. To cut a long story short, we're highly confident that 18 of your 19 fellow players will defect and only one will cooperate.\" The postal worker gives you back your postcard and a pen. Should you still cooperate or revise your decision? If we assume that the postal worker's prediction gives you far more reliable evidence than your own action, then the superrationality argument presented above no longer works. Once we already have reliable information about what the other participants are likely to choose (or what they have already chosen), our own choice can no longer make cooperation significantly more likely. In terms of evidential decision theory (introduced in the next section), if \n E[number of other cooperators | I cooperate & postal worker says \"n others defect\"] ≈ E[number of other cooperators | I defect & postal worker says \"n others defect\"], where E denotes conditional expectation, then the evidential role of our decision provides no reason to cooperate. That said, in section 2.4 we will see that this issue is actually a bit more complicated. After having sent in your postcard of defection and reflected on what happened, you might realize that all of the other participants were in the same situation as you were. They were also told that 18 (or, in case of the one who cooperated, 19) of the others would defect and, upon hearing this, each concluded that defection would give them a higher payout. No wonder that most players defected. Note that even if everyone had been told that all the others had cooperated, it would still be rational for all participants to defect. By merely telling the participants about their predictions, the postal workers make cooperation much less attractive and thereby less common. What is interesting about the Devious postal worker is that what makes the outcome worse for everyone than in the original Superrational donation games is that everyone receives information about the other participants' behavior. While counterfactually useful for each single player, the information is harmful overall. As Paul  Almond (2010b, chapter 4.5 ) says, \"lack of knowledge is power\", which I would like to refine to: lack of knowledge is evidential power. We shall revisit this concept soon. In particular, we will think about whether there is some way around the unfortunate conclusion that nobody should cooperate after receiving the respective information. \n A short survey of decision theories and their relation to superrationality Superrationality is a special application of non-causal decision theories -that is, theories of rational decision making that not only take the causal implications of an action into account but also other information that making this decision would give us.  4  In the case of superrationality, that information is always about the other agents. Conversely, causal decision theory (CDT)  (Weirich, 2016 ; J. M.  Joyce, 1999; Lewis, 1981; Skyrms, 1982; Gibbard and Harper, 1978)  neglects any such non-causal implications of an action in the Donation game with similarity. However, the best-known example of what I would view as CDT's limitations is surely Newcomb's problem, originally introduced by  Nozick (1969) . Readers who have not yet studied the problem, are encouraged to do so, although it is not required for understanding most of the present paper. Because Newcomb's problem was the first published example of a problem that (potentially) requires one to consider the non-causal implications of one's decision, all problems wherein such considerations -including superrationalitymight play a role are called Newcomb-like problems. Somewhat confusingly, the field that studies decision theories (in particular, which one we ought to use) is itself called decision theory. Besides discussions of Newcomb-like problems (i. e. whether and how correlated decision making and the like should be taken into account), decision theory is also concerned with topics like the expected utility hypothesis and deciding without assigning probabilities. For those who are unfamiliar with the field, I recommend starting with An Introduction to Decision Theory  (Peterson, 2017) . More elaborate introductions to the decision theory of Newcomb-like problems and correlated decision making include  Ahmed (2014) ,  Yudkowsky (2010) , and  Almond (2010) . Interestingly, most philosophers seem to endorse CDT. A recent survey of professional philosophers conducted by Bourget and Chalmers shows that in Newcomb's problem -one of the clearest examples of CDT's potential failure 5 -about 30% endorse CDT's recommendation 6 of two-boxing, whereas only 20% endorse one-boxing  (Bourget and Chalmers, 2014) . In fact,  Bourget and Chalmers (2014, p. 21, table 11 ) even shows that philosophers who specialize in decision theory are especially likely to endorse two-boxing. Defenses of CDT in Newcomb's problem are given by, e. g.,  Joyce (1999, chapter 5.1)  and  Eells (2016, chapter 8) . Some have also argued that Newcomb's problem cannot occur  (Ledwig, 2000, footnote 81; Binmore, 2007a, chapter 10) . Overall, I find the arguments put forward against CDT much more convincing than those in favor. Yet even among decision theorists who reject causal decision theory, there is disagreement about what the proper replacement should be. Classically, CDT is contrasted with evidential decision theory (EDT)  (Ahmed, 2014; Almond, 2010b; Price, 1986; Horgan, 1981) . However, there are also many newer, less widely known ideas. These include functional decision theory  (Soares and Levinstein, n.d.) , timeless decision theory  (Yudkowsky, 2010a) , updateless decision theory  (Benson-Tilsen, 2014; Hintze, 2014; McAllister, n.d.) , ambient decision theory, Spohn's variation of  CDT (2003; , section 2; 2012), Arntzenius' deliberational decision theory (2008) and Wedgewood's variation of causal decision theory (2013). 7 Superrationality is not based on any specific non-causal decision theory but works in most of them. Consequently, this paper is meant to adopt an impartial stance between the decision theories in which superrationality works. \n CDT would self-modify to behave like a non-causal decision theory in some Newcomb-like problems There is a class of problems wherein causal decision theorists recommend self-modifying into a new decision theory that acts as though it takes some acausal considerations into account. In both the aforementioned donation game and Newcomb's problem, the agent serves as a model for a number of (near-)copies and a prediction, respectively. Assuming that this model is captured at a particular point in time, it follows that the model represents a time-specific version of the agent. Thus, if the agent precommits to using superrationality or to one-box before the copies or simulation are made, they would causally determine all copies' choices. Consider the following thought experiment: Donation game with copies and precommitment. One morning Omega (an absolutely trustworthy, perfect predictor with various superhuman abilities) tells you that you will play the donation game on the next day. However, instead of merely recruiting other people as participants in the game, Omega will copy you atom-by-atom tonight and employ the resulting copies as tomorrow's participants. You are also told that the payouts this time around will be a thousand times higher than in previous games, so it is in your best interest to prepare well. As a final deed, Omega then leaves you a short book entitled From cold showers to chastity: How to commit to any action by self-hypnosis. What do you do? If you are already convinced of superrationality -or if you care a lot about the wealth of your copies -you would not have to do anything. You could spend the day going about your usual business, cooperate on the next day, and win a lot of money. But imagine you were a about the monetary rewards paid to the real version of the agent. 7 Many decision theories are also parameterized by some aspect of their definition. For example, causal decision theory is parameterized by the notion of causality that it uses (see, e. g.  Lewis, 1981; Hájek, 2006, page 19; Weirich, 2016, chapter 2.3; Pearl, 2009, chapter 4) . proponent of CDT and did not care about your copies. You would then want your future self and your copies to cooperate, but you know that they will not do so automatically. As soon as the copies are created, none of them -including you -will have any causal influence on what the others will do. So, if you do nothing, everyone defects and you get a very low payout. However, since you have not yet been copied, you still have a causal influence on the future version of you from which the copies will be created, and thus on the copies themselves. If you could cause the future version of you to be the kind of agent who cooperates, you could causally improve your payout in Omega's game. Given the book that Omega left you, this should be easy: read the book, precommit yourself -and thereby all your future copiesto cooperate, and everybody wins. A causal diagram representing the decision problem is given in Figure  1 . \n Precommitment Your decision Your 1st copy's decision Your 19th copy's decision Payout ... If CDT thinks that it will face some Newcomb-like problem where the copy or model for prediction is created in the future, it would precommit to make the same decision that acausal decision theories recommend (without precommitment). Does that mean that CDT would have to make one precommitment for each Newcomb-like problem (starting in the future) that it will face with non-zero probability? Rather than patching its behavior in each (future) Newcomb-like problem individually, CDT could also make a more general self-modification. At time t, it would precommit to use the following alternative decision theory in the future: do what I, at time step t, would have precommitted to do in the present situation  (Yudkowsky, 2010a, chapter 2; Soares and Fallenstein, 2015, chapter 3; Meacham, 2010) . Such precommitment is not sufficient to generate the kind of superrationality required for this paper: it does not cover Newcomb-like problems that do not start in the future. That is, if the copies are not created based on a future version of the agent, cooperation with them is not covered by precommitment. Thus, CDT's precommitment does not imply cooperation with agents in other parts of the multiverse. However, it does suffice for a weaker version if we assume the Everett interpretation of quantum physics (see section 6.8). \n Lack of knowledge is evidential power, part II: taking a step back CDT's precommitment only entails partial agreement with its rival decision theories. Still, it is worth taking a closer look at precommitment, as it leads us to another interesting dimension along which decision theories can vary. Consider Counterfactual mugging, also known as \"the curious benefactor\"  (Hintze, 2014, chapter   A CDT agent would, again, only precommit if Omega bases its prediction on a future version of the agent, whereas I (and many non-causal decision theorists) would argue that we should precommit as long as the result of the coin flip is unknown to us (even if Omega's model is based on a past version of us). 8 If we do so, we gain information that Omega thinks we give in, and therefore that we will receive money in expectation. However, once we learn that the coin came up tails, the \"winning\" move is to keep the $100. As before, the problem contains a harmful piece of information -although in this case an aspect of the environment, and not a piece of information about the behavior of other agents, causes trouble. If we got the chance, we would \"protect\" ourselves against this piece of information by a precommitment, which renders that piece of information harmless. A similar reasoning applies to the Devious postal worker variant of the donation game: If everyone precommits to cooperation irrespective of what the postal worker's prediction says, then a negative prediction about the other agents' behavior can no longer be self-fulfilling. Thus, if you precommit to cooperating before the postal worker tells you about the other agents' decisions, you have reason to expect more positive news (assuming you correlate with the other agents). 9 As is the case for CDT's precommitment in the previous section, this leads to a more general self-modification that can be made instead of a large number of individual precommitments for individual situations. Specifically, we would (again) precommit to basing our decision in this situation on what is good from the perspective of the state of knowledge prior to being given new information (like the result of the coin toss). This is where updateless decision theory gets its name from, and I will call this feature of decision theories updatelessness. Contrary to what the term may suggest, it does not mean that we do not react to new information at all, but rather that we do it in a different way. Instead of updating the probabilities we assign to possible states of the world and making the best decision based on that probability distribution, we think about what we would have precommitted ourselves to do in this situation. Usually, what we would have precommitted ourselves to do is the same as what is then rational for us to do. For example, if we take a bite from an apple and it tastes foul, we throw the apple away. If you had to precommit to some action before learning that the apple is foul, you would also precommit to throw the apple away if it tastes foul (and to continue eating the apple if it tastes good). Counterfactual mugging is one of the rare cases in which it does make a difference. Acausal decision theorists would precommit to be updateless about all information they receive in the future. In essence, they would switch to a decision theory that comes with updatelessness built-in (the most notable one of them currently being updateless decision theory  (Benson-Tilsen, 2014; Hintze, 2014; McAllister, n.d.)  itself). Thus, if you had been reasoning about (acausal) decision theory including the possibility of self-modification correctly all along (rather than only after learning about the experiment and its result), you would actually cooperate in the Devious postal worker and give in to Counterfactual mugging -even without having precommitted to do so in these particular problems. Some readers will no doubt already be familiar with updatelessness and the arguments in favor of it. For those who have not, this may be a good time to incorporate general updatelessness into their decision-theoretical intuitions, as it is relevant for some of MSR's implications (see sections 2.8.6 and 2.9.1). As a side note, there are justifications of updatelessness that are not based on precommitment and thus suggest that we should, e. g., give the money in counterfactual mugging even if we previously have not thought about precommitting to updatelessness. Ryan Carey lists a few in a comment on the Intelligent Agent Foundations Forum. Benja Fallenstein proposes a justification based on \"logical zombies\". For other ideas, see Armstrong (2011, section 3.1.2) and Drescher (2006a, chapter 6.2). 10 However, these are more complicated, non-obvious and not well-established. I thus opted for limiting myself to the more straightforward precommitment-based justification for updatelessness as discussed by  Meacham (2010) , Fallenstein on LessWrong and myself in a blog post (cf.  Ahmed and Price, 2012) . \n Reasons and correlations It is difficult to pin down the general principles of how the decisions of different agents in different situations correlate. Indeed, I suspect that the problem has no simple solution other than what is implied by the general solutions to naturalized induction (Soares and Fallenstein, 2014, section 2.1; Soares, 2015) and decision theory. 11 10 Also note that updateless behavior can sometimes result from anthropic uncertainty even when applying the more classical evidential or causal decision theories. 11 Determining correlations between actions is similar to specifying the maxim corresponding to an action in Kant's categorical imperative. It seems that nobody has a precise grasp of how the latter is supposed to be done and that this makes it difficult to apply the categorical imperative. However, the problem of specifying the maxim underlying one's action does not necessarily have a single correct solution. Determining correlations between your actions and that of others, on the other hand, follows from any solution to the problems of naturalized induction and decision theory. These solutions probably depend on priors, but it probably makes more sense to speak of them as having a correct solution. However, humans seem to have some good intuitions for how decisions correlate, in part because understanding the correlations between actions is a day-to-day activity. Imagine seeing your friend Anna being wounded in her right arm one day. She uses her left arm to apply bandages and call a doctor, who arrives a few minutes later and inspects her right arm. A few days later, you see Bob being wounded in his left arm. Based only on the experience from Anna's wound, what should you reasonably expect to happen? Will Bob use his left arm to apply bandages to his right one? Will Anna apply bandages to her right arm? Or to Bob's? Will doctors come to Anna? Even after seeing just one instance of a situation, we are often able to identify many of its causal links and use this information to infer correlations with similar situations. If we see the reasons for a decision from the inside, these correlations become even clearer. If you are Anna and you apply bandages to your right arm, you know that it is to stop the bleeding. Doing so gives you no \"weird\" evidence -it would not lead you to expect, say, that people are generally likely to apply bandages to things (cf.  Ahmed, 2014, chapter 4; Almond, 2010b, chapter 2.8) . In general, taking a particular action only because of some reason X tells you nothing about whether agents who do not care (or know) about X will also take that action. Importantly, superrationality itself falls under this general rule. That is, if you do something for superrationality-related reasons, then this does not tell you anything about how people who do not accept superrationality would behave. As a trivial example, consider playing a donation game against 19 people whom you all know to make fun of superrationality whenever the opportunity avails itself. Attempting to superrationally cooperate with those people seems rather fruitless. While these considerations may seem trivial, alleged refutations of acausal decision theories are often based on ignoring them or assuming that the evidential thinker ignores them (cf.  Ahmed, 2014, chapter 4; Almond, 2010b, chapter 2.8 ). \n Your back is not mine If the decisions of agents correlate or if each can determine what is rational, then why can someone -let us call him Dennis -not just determine that it is rational to benefit him or his values? Surely, if everyone just benefited Dennis, that creates the optimal outcome for him. So, in a donation game with superrationality, perhaps he should determine the rational policy to be \"cooperate, unless your name is Dennis\"? This is clearly absurd. The specific reasons that lead Dennis to come up with this strategy (and to abide by it) do not matter to his fellow players, although each of them probably have self-serving reasons which are analogous to those of Dennis. Dennis wants to achieve his own goals, and this is done optimally if everyone cooperates while he alone defects. However, this only makes it more likely that some other participant -let us call her Dana -would reason, \"I want to maximize my payoff; if I could determine everyone's choices, I would want everyone but me (Dana) to cooperate.\" (cf.  Drescher, 2006a, page 298f.) . \n Does accepting superrationality commit us to irrational behavior in medical Newcomb problems? One common objection to making decisions based on what our action correlates with, rather than what our action causes, is that it seems to imply irrational behavior in some cases (e. g.  Nozick, 1969, page 135) . In particular, reasoning from correlation seems to fail in so-called medical Newcomb problems. An example is Yudkowsky's chewing gum problem (2010a, section 1.2), which he describes as follows: Suppose that a recently published medical study shows that chewing gum seems to cause throat abscesses -an outcome-tracking study showed that of people who chew gum, 90% died of throat abscesses before the age of 50 This table shows that whether you have the gene CGTA or not, your chance of dying of a throat abscess goes down if you chew gum. Why are fatalities so much higher for gum-chewers, then? Because people with the gene CGTA tend to chew gum and die of throat abscesses. The authors of the second study also present a test-tube experiment which shows that the saliva from chewing gum can kill the bacteria that form throat abscesses. The researchers hypothesize that because people with the gene CGTA are highly susceptible to throat abscesses, natural selection has produced in them a tendency to chew gum, which protects against throat abscesses. The strong correlation between chewing gum and throat abscesses is not because chewing gum causes throat abscesses, but because a third factor, CGTA, leads to chewing gum and throat abscesses. Having learned of this new study, would you choose to chew gum? The causal graph of this problem is given in Figure  2 . Similar well-known decision problems of this kind are Solomon's problem  (Gibbard and Harper, 1978, section 5; Eells, 2016, chapter 4) , the Smoking lesion  (Eells, 2016, chapter 4) , and the Psychopath button  (Egan, 2007 , section 3). Naive correlation-based reasoning suggests that we should still refrain from chewing gum, since the act of chewing gum would be evidence that we have the CGTA gene and thus throat abscesses. This strongly conflicts with our intuition that we should chew gum to protect against the abscesses. However, I will argue that this provides no convincing argument against superrationality. First, the correlation in the Chewing gum problem differs qualitatively from the correlations between similar decision algorithms  (Treutlein and Oesterherld, 2017) . In the Chewing gum problem (and medical Newcomb problems in general), the correlation stems from a causal relationship: our genes influence our decisions. Thus, the genes and the decisions are correlated. The correlations of superrationality, on the other hand, result from the similarity of the decision algorithms. The reasoning behind cooperation does not involve a common cause of all collaborators' decisions. Instead, the correlation may be viewed as logical  (Garrabrant et al., 2016) : if I cooperate, then this implies that all other implementations of my decision algorithm also cooperate. Figure  3  illustrates the difference between these two types of Newcomb-like problems. Because correlations in medical and non-medical Newcomb-like problems differ qualitatively, ignoring the correlations of our actions in the former does not mean we should ignore them in the latter. In fact, in response to medical Newcomb problems, philosophers have proposed a variety of decision theories that behave in this exact way  (Treutlein and Oesterherld, 2017) . That is, they cooperate superrationally (and one-box in Newcomb's problem) but chew gum in the Chewing gum problem. These include Spohn's variation of  CDT (2003; , section 2; 2012) and Yudkowsky's timeless decision theory (2010). \n CGTA \n Gum \n Abscess Secondly, even purely correlation-based reasoning as done by EDT may recommend chewing gum, depending on how the causal link from the CGTA gene to chewing gum is believed to work. Given that people in the study presumably did not know that chewing gum helps against throat abscesses, it is plausible that CGTA causes people to intuitively desire chewing gum. However, if learning about the study and applying EDT then causes us not to chew gum, it does not tell us anything about whether having the CGTA gene would have caused us to do the opposite. Similarly, if you know that a sprinkler has watered the lawn, observing that the grass is wet is no evidence that it has also rained (see Figure  4 ). The sprinkler already explains why the lawn is wet, so you do not need rain as an additional explanation (see  Ahmed, 2014, section 4.3  for an extensive discission of this argument).  \n My decision \n Payoff \n Are the correlations strong enough? In most superrationality-related thought experiments, it is assumed that the other agents are near-copies of ours. The problems presented in this paper are no exception. However, in any real-world setting, most agents are not close copies of ours. We should therefore expect correlations to be much less than perfect. Luckily, the total number of agents in the multiverse is probably so vast 12 that the correlations between ourselves and any individual agent need not be very large 13 (see section 6.2). Because many agents probably do not know about superrationality, we may assume that 99.99% of the agents do not correlate with us at all when it comes to the decision whether to cooperate superrationally. In this case, cooperation with the rest still pays off if we believe that our correlation with the others is non-negligible and positive. It does not matter that we inadvertently benefit many \"free riders\". For example: if our cooperation makes it 1% more likely that each of these correlated agents also cooperates, then if there are \"only\" a billion of them, we can expect 10 million more to cooperate if we cooperate. 14 \n Correlation only with close copies? Some might think that they are uncorrelated with everyone else apart from very close copies of themselves. Because such near-copies would likely share their utility function to a large extent, there is no need to cooperate with them (although coordination may be useful, depending on the utility function, see section 2.8.9). While the lack of formalized and agreed-upon solutions to decision theory and naturalized induction (Soares and Fallenstein, 2014, section 2.1; Soares, 2015) makes it difficult to draw definitive conclusions on such matters, I am nevertheless skeptical of this objection to MSR. It seems to me that decision theories, at least as people currently conceive of them, are compatible with very large sets of possible minds. That is, if an agent uses, say, evidential decision theory, it can still use all kinds of different mechanisms for assigning conditional probabilities and, most importantly, it can still have all kinds of values (see section 3.1). \n Negative correlations? There is another interesting objection about correlation strength that could be raised: perhaps we should expect to correlate negatively with some agents in the multiverse, such that cooperation can even do some harm (beyond the opportunity costs connected to it) as it makes some other agents more likely to defect. While interesting, I do not find this reason against superrational cooperation very convincing, either. Such a reaction seems implausible given our state of knowledge. Surely, there are a few eccentric agents who have superrationality-related algorithms similar to mine, yet choose to somehow invert the output of these algorithms. But such algorithms make little sense from an evolutionary point of view and so I do not expect them to be very common in the multiverse. It may seem that agents have an incentive to become negatively correlated (via selfmodification), thereby enabling them to defect and make everyone else cooperate. However, there are various problems with this idea. For one, to be able to correlate negatively with the other agents it seems as though one would have to find out about their decision and then do the opposite, which appears to be difficult. Furthermore, self-modification also commits us to cooperate more when the others defect -an agent committed to unconditional defection does not correlate with anyone else. The intuition underlying the self-modification idea is that by self-modifying to be negatively correlated, we can acausally determine the others' decisions. But I do not think this works in the relevant way. When you modify your decision algorithm, you lay your power into the hands of the new algorithm. This means you cannot, for example, self-modify to some decision algorithm A that does the exact opposite of what everyone else is doing, and then defect -unless A already defects on its own. Thus, you cannot determine everyone else to cooperate unless you are already correlated with them. Similarly, you cannot commit to output the 100th digit of π, and then return 6 anyway to acausally determine the value of π. However, if you are already correlated with the 100th digit of π, you can logically determine its value. For instance, if Omega predicts your behavior and then tells you that if you raise your arm, the 100th digit of π will be 7 and if you do not it will be 1, you can determine the 100th digit of π. Of course, these stop working once you know what the 100th digit of π is. As a last point, self-modification does not seem to add anything to direct defection (without self-modification). To see why, let us consider the two kinds of agents that are not yet negatively correlated with the others. The first agent is not correlated with others before self-modification, and therefore has no reason to self-modify. He can just defect directly, without adopting a weird decision theory that is about doing the opposite of what someone in some other part of the multiverse is doing. The second agent is (positively) correlated with others before self-modification. Her problem is that if she self-modifies, others will do so as well, which gives her evidence that a lot more defection is happening than if she would cooperate. Another relevant point is that there is a sharp upper bound to the amount of negative correlation that can exist within a group of agents. Imagine agents A, B, and C, whose decision to cooperate we model as a random variable with the two values 1 (for cooperation) and 0 (for defection). Let us say A is perfectly negatively correlated with B and B is perfectly negatively correlated with C. A is then perfectly positively correlated with C. So, even among just three agents, not all correlations can be perfect and negative. On the other hand, the pairwise correlations may well all be perfect and positive. To study this further, we move from correlations to covariances, because they can be meaningfully added up. In general, we can derive a lower bound of − 1 4(n−1) for the average covariance between pairs of agents from any set of n ≥ 2 agents (excluding \"pairs\" of one and the same physical agent), if cooperation is seen as a binary random variable. If the agents are all perfectly correlated, then all covariances are at most 1 4 , so the upper limit for the average covariance is also 1 4 . Unless we have reason to believe that we are special, i. e. that our covariance with the others falls far below the average covariance between two agents, this suggests that especially for very large numbers of agents n, our possible acausal impact under the assumption of only positive covariances can be much larger than that of negative covariances. In fact, the covariances of the average agent cannot add up to something below − 1 4 regardless of the number of agents. In contrast, they can be as high as 1 4 (n − 1) for positive covariances. If we view the covariances as uncertain, this suggests a prudential argument in favor of assuming positive covariances to dominate over negative ones, given that our acausal influence is so small under the opposite assumption. However, the details of this argument (and whether it works at all) depend on our \"meta-probability distribution\" over covariances. \n The relative importance of superrational cooperation: an example calculation Looking at a single decision, how do the benefits from superrational cooperation compare with the opportunity costs? Although we need to make some unrealistic assumptions (such as exact symmetry of the decisions faced by all the agents) in order to calculate this value, it is nevertheless worth an attempt, if only for the purpose of illustration. We assume that there are n superrational agents whose decisions in donation games are perfectly correlated; that is, either all of them cooperate or all of them defect. Realistically, many more agents' decisions will correlate weakly with ours, while only very few correlations will be perfect. However, the implications of many weak and a few strong correlations are similar. For simplicity, we assume that the goals of the agents are orthogonal to each other, i. e. that if someone benefits it is neutral in expectation to any other value system. All of them have values that can benefit from behavior in other universes to the same extent. The n agents face the decision between a) generating b u cardinal, interpersonally comparable utils (or utilons) for their own utility function and b) generating b other utils for k randomly chosen superrationalists. Choosing option a) makes everyone chose option a) and so only generates b u utils for us. Choosing option b) makes everyone choose option b). Whenever someone (including ourselves) chooses option b), there is a probability of k n that we are among the beneficiaries. Overall, if we and thus everyone else chooses option b), we receive n k n b other = kb other utils. Choosing option b) is therefore to be preferred if and only if kb other > b u . (1) This suggests that our own preferences have no priority over those of other superrationalists in this decision. We only decide based on \"the greatest good for the greatest number\". For instance, if k = 1, then we should choose option b) to help other value systems if b other > b u , i. e. as long as helping other value systems can be done more efficiently than helping your own values. This shows how important superrationality considerations can be. Whereas the non-superrational agent maximizes only for its own value system, the superrational agent maximizes for the value systems of other superrational agents just as much as for their own. Moreover, whether we cooperate depends only on the number of agents whose cooperation is correlated with ours and not at all on the number of agents that will defect. In this regard, multiverse-wide superrational cooperation differs from most causal cooperation, where we usually try to ensure that beneficiaries of our actions reciprocate (unless we care about them intrinsically). As mentioned already, this analysis is based on unrealistic assumptions of perfect symmetry to highlight the relative importance of superrationality considerations. We will now move on to more general, potentially asymmetric cases. \n Compromise strategy \n Sharing gains from compromise in the face of asymmetries We have so far only considered completely symmetrical situations, wherein other agents faced the exact same decision problem as ourselves. One could either choose to cooperate, which correlated with everyone else's cooperation; or defect, which correlated with everyone else's defection. Both cooperation and defection were associated (via the correlation between agents) with particular outcomes. Based on these correlations it was straightforward to choose the action that correlates with the best outcome for ourselves (and also for everyone else). Of course, in practice, compromise will not be this tidy. Specifically, we will have to deal with asymmetrical decision problems. Consider the following example: Superrational cake cutting. You are playing a donation game with two fellow players whose decision algorithms correlate strongly with yours. Unlike other donation games, the currency in this game is cake, of which there are two flavors -vanilla and strawberry. Each player's utility grows in linear proportion to how much cake they eat, and they all have taste preferences that affect their total utility. Let's say you, player 1, like vanilla twice as much as strawberry. Player 2, meanwhile, likes strawberry four times as much as vanilla, and player 3 likes both flavors equally. Each player currently owns different amounts of strawberry and vanilla cake. You have one strawberry cake and one vanilla cake, while player 2 has three vanilla cakes and player 3 has one strawberry cake. (See Figure  5   First note that this problem is indeed one of superrational cooperation. If causal decision theory is applied, then the dominant strategy for each player is to keep all the cake -but this would be a suboptimal outcome for everyone. The players have two strawberry and four vanilla cakes in total. If you could redistribute them so that player 1 has one strawberry and two vanilla cakes, player 2 has one strawberry cake, and player 3 has two vanilla cakes, everyone would be better off than without any redistribution. However, there are infinitely many other possible (fractional) distributions that would also be better for everyone. This makes it hard to decide among them. One part of the problem is that it is unclear what our decisions correlate with. If we send player 2 a piece of her preferred cake (strawberry), can we expect to get some of our preferred cake (vanilla) from her? If so, how much? If we could pin down the correlations and assign probabilities to each combination of strategies -i. e. to each strategy profile -conditional on any of our actions, we could choose the action that maximizes expected utility (the exact formulation of which depends, of course, on our decision theory). But even if the agents know that they have very similar (or even identical) decision algorithms, the asymmetries make it hard to assign these probabilities. Another perspective on the problem is that asymmetries make it unclear who \"deserves\" how much. In the symmetrical situations it was always clear that everyone should get the same, but this is different in superrational cake-cutting. It is useful to view the symmetry of a compromise problem as a non-binary property. For example, a donation game in which one player gains slightly more than the others from cooperating may still be symmetric enough to make it obvious what the right decision is. \n The compromise problem In order to solve the problem of superrational compromise in asymmetric situations, we will treat compromise as a game-theoretical problem. Note that this requires basic knowledge of game theory; for an introduction see, e. g.  Osborne (2004) . Formally, a game consists of • a finite set of players P = p 1 , . . . , p n , • for each player p i , a set of actions A i , • for each player p i a utility function u i : A 1 × • • • × A n → R, where R refers to the real numbers. Multiverse-wide superrational compromise is a game where P is the set of correlated superrationalists, the utility functions u i represent their preferences, and the sets of possible actions A i represent the set of strategies a player can pursue in their part of the multiverse. Note that the last aspect of the definition assumes that the players' preferences are von  Neumann-Morgenstern-rational (vNM-rational) , which is technically useful and mostly non-controversial 15 . Our notation indicates that utilities are calculated deterministically from action tuples. However, we will sometimes view the utilities u i (a 1 , . . . , a n ) as random variables in the Bayesian sense. This is because we are usually uncertain about the implications of the policies a 1 , . . . , a n , as well as the utility function u i itself, in the context of MSR. Now, the question is which (potentially mixed) strategy α i any player p i should choose. Note that we are not looking for the (CDT-based) Nash equilibria of the game. We will therefore have to move our focus from (Nash equilibrium-based) non-cooperative to cooperative game theory. In principle, the optimal strategy α * i can be determined by applying one's decision theory. For example, if one were to use EDT, then the optimal strategy is argmax αi E[u i (a 1 , . . . , a n ) | α i ]. As noted earlier, however, computing or optimizing the expected value conditional on one's action directly is not feasible in situations of asymmetric payoffs. To find the best action, we will therefore approximate the above expected value maximization with some new criterion, similar to how game theory has replaced expected value maximization with Nash equilibria and other concepts. We will therefore try to develop some new compromise utility function u * : A 1 × • • • × A n → R, intended as a new criterion for choosing the optimal strategy. Because the compromise utility function depends less on the specifics of the problem, it will prove to be easier to reason about what the adoption of some u * tells us about what the other agents do. The optimal u * can then, under certain assumptions, tell us what action to take. At least if our choosing u * means that everyone else chooses the same u * (which is not necessarily the case), then player p i should implement the i-th strategy entry of argmax (α1,..,αn)∈A1ו••×An E[u * (α 1 , . . . , α n )]. 15 One exception may be the axiom of continuity. It is violated by preferences with lexicality, which are commonly discussed in moral philosophy  (Knutsson, 2016) . However, if we drop the axiom of continuity, we can still represent the preferences as a lexicographic utility function  (Blume, Brandenburger, and Dekel, 1989; Fishburn, 1971) . However, a treatment that includes lexicographic utility functions is beyond the scope of the present paper. Because in uncertain situations, a lexicographic utility function is usually equivalent to only maximizing the lexically highest values, we may nonetheless apply the present results by simply omitting all lexically lower values. Once again, having a compromise utility function, as opposed to more general compromise preferences, implicitly assumes that the compromise preferences are also vNM-rational. \n Cooperation with and without coordination In a way, argmax (α1,..,αn)∈A1ו••×An E[u * (α 1 , . . . , α n )] is the optimal plan on the assumption that everyone will follow it. With practical degrees of correlations, however, we cannot assume that everyone will arrive at the same plan, especially if multiple plans have the same compromise utility. In MSR, it is especially unlikely that everyone will arrive at the same plan, as superrational collaborators have different states of knowledge about the multiverse and each others' value system. A perfect plan may have catastrophic results if it is not accurately followed by everyone involved. Specifically, plans are risky if the utility of one player's action hinges on another player's action because such plans assume the ability to coordinate. Hence, it is useful to look at a class of utility functions where coordination plays no role. We say that a utility function u i (additively) decomposes into local utility functions {u i,j : A j → R} j=1,...,n if u i (a 1 , . . . , a n ) = n j=1 u i,j (a j ). Intuitively speaking, u i decomposing into local utility functions means that any player p j has a very direct impact on p i 's utility, such that when p j attempts to benefit p i she need not think about what other players do. In game theory as it is usually applied to interactions between agents on Earth, the assumption of additive decomposition of utility functions would be a severe limitation: if agents interact with each other physically, then, of course, the impact of an action often depends on the other players' actions. As examples, consider some of the classic games studied in game theory, such as Bach or Stravinsky or Chicken. In the problem of multiverse-wide compromise, on the other hand, there is probably no causal interaction between the actions of agents in different parts of the multiverse. Additive decomposition of utility functions is thus a more natural assumption in this context. That said, issues of coordination can still arise in the utility function itself. As an example, consider a utility function that wants there to be at least one (dis-)proof of the Riemann hypothesis somewhere in the multiverse, but does not care about the existence of further, redundant proofs. This utility function does not decompose additively; whether I benefit this utility function by proving the Riemann hypothesis depends on whether someone else is already working on a proof. Other, perhaps more realistic, examples of ethical notions that do not decompose into local utility functions are (partial) average utilitarianism and potentially biodiversity. However, many other plausible utility functions (e. g., total utilitarianism) do fulfill the above condition. If some of the utility functions in a game do not decompose into local utility functions, we will call the game a coordination problem 16 . Theoretically, the following arguments also work for coordination games, but they are much more robust and practically applicable in problems that require little or no coordination. This topic will be discussed further in section 2.8.9. \n Harsanyi's aggregation theorem Although we do not yet know how and to what extent, we know that our compromise utility function u * should incorporate the utility functions u 1 , . . . , u n but not be sensitive to anything else. The following assumption captures these attitudes: Assumption A. Let P and Q be probability distributions over outcomes  17  That is, all players like P at least as much as Q. Then A 1 × • • • × A n such that E P [u i (a 1 , . . . , a n )] ≥ E Q [u i (a 1 , . . . , a n )] for i = 1, . . . , n. E P [u * (a 1 , . . . , a n )] ≥ E Q [u * (a 1 , . . . , a n )], i. e. the compromise utility function also values P at least as highly as Q. We could view this assumption as a decision to limit ourselves to a particular class of compromise utility functions -a decision that makes our superrational collaborators limit themselves to the same class. In terms of expected value for ourselves, this is a good decision. It basically does not tell us anything other than that we do not want to pay anything to switch from P to Q if everyone likes P at least as much as Q. We furthermore introduce the notion of utility function equivalence: two utility functions u and v are equivalent, written as u ∼ v, if they imply equal behavior. For the cardinal utility functions discussed here, this is the case if one arises from positive affine transformation of the other, i. e. if u = av + b for some a ∈ R >0 and b ∈ R. Assumption A does not seem especially strong, but it turns out that it suffices for a significant result regarding the shape of the compromise utility function. It is essentially a version of Harsanyi's aggregation theorem  (Harsanyi, 1955 ; see also  Peterson, 2017, section 13.4  for an introduction). 18 Theorem 1.  (Resnik, 1983; Fishburn, 1984)  Let u * be a compromise utility function for u 1 , . . . , u n that satisfies Assumption B. Then there are weights λ 1 , . . . , λ n ∈ R ≥0 such that u * ∼ n i=1 λ i u i . (2) Note that the λ i are not unique. Also, not all weight assignments consistent with Eq. (2) or Assumption A have only positive weights. In particular, if u i = u j for some i = j, we can decrease λ i by an arbitrary constant C if we correspondingly increase λ j by C, and end up with the same compromise utility function u * .  (Resnik, 1983; Fishburn, 1984) . If C > λ i , we arrive at an equivalent utility function that assigns negative weights. Theorem 2. Let u 1 , . . . , u n each decompose into local utility functions {u i,j : A j → R} j=1,...,n . Then a compromise utility function u * that satisfies Assumption A relative to u 1 , . . . , u n also decomposes into local utility functions. Proof. Because of Theorem 1, it is u * (a 1 , . . . , a n ) = b + n i=1 λ i u i (a 1 , . . . , a n ) = b + n i=1 λ i n j=1 u i,j (a j ) = b + n j=1 n i=1 λ i u i,j (a j ) = n j=1 b n + n i=1 λ i u i,j (a j ) for some b and weights λ 1 , . . . , λ n ∈ R ≥0 . Thus, u * decomposes into local utility functions u * j : A j → R : a j → b n + λ i u i,j (a j ) j=1,...,n . This is quite a convenient result. If indeed u 1 , . . . , u n each decompose into local utility functions, then each player p i can maximize u * i in her own part of the multiverse without having to think about the precise actions of other players elsewhere in the multiverse. \n How to assign the weights Having argued that we should make our decisions based on a weighted sum of the decisions of our superrational collaborators, the question is how we should optimally assign the weights. Theorem 1 does not tell us much about this. In fact, it even allows for the possibility of assigning positive weight only to our own utility function. We will differentiate two ways of assigning the weights: biased toward our own values, or impartial. We will consider the two options in turn. \n Biased compromise utility functions? We start with the option of assigning the weights in a way that is somehow biased toward our values. For example, we could assign higher weights to utility functions that are more compatible with ours, and lower weights to those that are not. Of course, this tells us that agents with other value systems will do the same, i. e. assign weights in a way that biases the resulting utility function toward their own values. I will argue against assigning weights in a biased way and in favor of impartial weights. This point is crucial for the strength of the implications of MSR, because the more weight we assign to other utility functions, the more our policies have to change in response to MSR. In a way, the reasons against biased weights are merely an extension of the reasons for cooperating in the first place. Let us say that in response to MSR we assign some weight to the other agents' utility functions but still largely maximize for our own values. Then gains from further trade are left on the table. Because we still maximize for different utility functions, we could trade again until all our compromise utility functions approach some impartially weighted sum. This line of reasoning is also supported by the standard ways in which gains from trade arise. If everyone compromises with biased weights, then this produces some gains from comparative advantages -in situations where I have a large comparative advantage to maximize for someone else's utility function, I will do so at the cost of not maximizing for my own values. In return, others do the same. But if the comparative advantages are too small, then we miss out on gains from trade. Consider an example with two superrational collaborators. For simplicity, we will assume them to be in symmetrical situations at the time of compromise, such that the only plausible neutral compromise would give the same weight to each of the two utility functions. Both may, at some point, face the choice between taking a utility of x for themselves and giving x + ε to the other, where x and ε are any positive real numbers. In such a situation both have a comparative advantage to help the other's values. But if ε is very small, the comparative advantage is very small, too. So, if they assign more weight to their own utility functions, there is some ε such that they choose to maximize their own utility functions and thus miss out on the gains from trade. While I am moderately confident that all compromises with biased weights are Paretosuboptimal, I do not, at this point, have a formal proof of this statement. That said, the above example at least shows that such compromises yield collectively vNM-irrational behavior. Furthermore, section 2.7 showed that, at least in symmetrical idealized scenarios, prioritizing one's own values does not achieve the best results. I should note that impartial weights do not imply that I should be equally likely to find myself maximizing for my own values as any of my superrational collaborators. For example, if you are very uncertain of the content of some value system, then it will not influence your decisions as much, even if you assign a high weight to that value system. \n Neutral compromise utility functions We have argued that after an optimal compromise, each player should judge their action roughly by the same impartial criteria. Hence, we now have to look for a way of assigning the weights in a neutral way. Harsanyi himself proposes -albeit in the context of social welfare rather than trade -to simply give equal weight to all utility functions, which is equivalent to removing the weights altogether  (Harsanyi, 1979 , section 2). Besides the argument of \"equal treatment\", it can be backed by an original position argument  (Harsanyi, 1953; Harsanyi, 1955; Freeman, 2016) . From an original position, i. e. a perspective from which we do not yet know which position in the multiverse we will take, how many resources will be at our disposal, etc., it seems reasonable to give equal weight to all utility functions. Updatelessness gives this argument some additional appeal, as it asks us to make our decisions from a similar perspective. However, there are various problems with maximizing unweighted aggregated utility. One is that it is based on interpersonal comparisons of utility. In Harsanyi's words, it assumes that \"all individuals' utility functions u 1 , . . . , u n are expressed in equal utility units (as judged by individual j on the basis of interpersonal utility comparison)\". 19 Such comparisons, however, are highly controversial  (Hammond, 1991; Binmore, 2007b) . Recall that the cardinal utility functions postulated by the von Neumann-Morgenstern utility theorem are only determined up to positive affine transformation. This means that if a utility function u represents an agent's preferences, then so do 100 • u and 0.01 • u. None of the three is in some way the more natural choice for representing the agent's utility function. Whereas positive affine transformations do not alter an agent's behavior in choosing lotteries, they do change the behavior implied by the aggregate of multiple such functions. In Superrational cake cutting, we specify the utility functions (or, as they are sometimes called in fair cake-cutting, subjective value functions) of each agent up to positive affine transformation by specifying the trade rates between units of strawberry and vanilla cake. For example, the third player has a 1:1 trade ratio, the second has a 4:1 trade ratio. To simplify notation, let s i and v i be amounts of strawberry and vanilla that p i receives under some action profile. Then the second player's utility function could be u 2 (s 2 , v 2 ) = 4s 2 + v 2 and the third player's utility function could be written as u 3 (s 3 , v 3 ) = s 3 + v 3 . If one wanted to maximize aggregate utility u 2 + u 3 , then u 2 would effectively receive far more weight than u 3 . If u 2 (s 2 , v 2 ) = 400s 2 + 100v 2 , this bias toward u 2 would be even worse. Because utility functions come in different versions depending on their scale, we still need to find a satisfactory way of normalizing the utility functions, i. e. to pick one out of a whole class of equivalent utility functions. This task is actually equivalent to assigning a weight to a given member of each class. Thus, removing the weights and relying on interpersonal comparison of utility can be seen as merely passing the buck from assigning weights to choosing the scale of the utility function. One common approach to interpersonal comparison of utility is range normalization  (Isbell, 1959; Hausman, 1995, section 3) . That is, the utility functions are chosen in such a way that their maximum is 1 and their minimum is 0 (using no additional weight).  20, 21  While intuitive, range normalization appears to be inappropriate for compromises. For one, it lacks a rigorous justification in this context -it is not immediately obvious that the underlying naive view of neutrality is relevant for compromise. The main problem with using range normalization for the compromise utility function is that in some cases some of the agents have no reason to accept it as it leaves them worse off than engaging in no compromise at all.  22  For example, consider the case of a compromise between a beggar and a millionaire with different sets of preferences. If the compromise gives equal weight to the preferences of the two, then this leaves the millionaire worse off as she receives little in return for dedicating half of her resources to fulfilling the beggar's wishes. Even if all agents have equal resources, a range normalization-based compromise can be unappealing to some of them. Consider two equally powerful agents with two very different value systems. The first cares about bringing about a state that is only very rarely attainable. All his other preferences pale in comparison. The second agent divides states of the world into two classes: good and bad states. Within each of those classes she is indifferent between any pair of states. Also, the division is such that in most situations, the different actions vary in how likely they are to bring about a good state. Under range-normalization, the first agent's utility function would usually be close to 0 and it would only rarely be possible to get it to 1. The second agent's utility function is 0 for some states and 1 for the others. If we maximize the sum of these two utility functions, this will mean that we will usually optimize much more for the second agent's preferences. After all, in most cases doing so significantly increases the probability of attaining 1 util. Maximizing for the first agent, on the other hand, usually only generates a small fraction of a util. Only in the rare situations in which we have an opportunity to attain the first agent's favorite state do the agents' preferences have a similar amount of control over the decision made based on the compromise. The first agent may therefore have no reason to accept this compromise. Because range normalization can drastically favor some players, it may actually be not so neutral after all. If you already knew that a range-normalized utility function would benefit you a lot, you would be biased to accept it. If you accept the range-normalized utility function on these grounds, however, it would not tell you much about the choice of agents who already know that the range-normalized sum would be harmful to them. In this sense, range-normalization is a biased compromise. Of course, if I benefit from range-normalization, I could hope that those who are disadvantaged by it nevertheless compromise in some other way that still benefits me. However, using such tricks to exclude others from our compromise is evidence that we are excluded in other ways as well (cf. section 2.9.3). Thus, without some other justification, range normalization does not appear especially promising. Many other approaches to interpersonal comparisons (see, e. g., Sen, 2014, section 7.3 23 ) suffer from the same problems. We thus need to set up more rigorous criteria for neutrality. It appears that the most directthough certainly not the only -approach is to require that the compromise is, in expectation, equally good for everyone -that is, everyone gets the same gains from compromise. This ensures that the compromise is equally attractive to everyone involved. \n Assumption B. The expected gains from adopting u * are the same for each player p i . Unfortunately, Assumption B is underspecified. The most naive view is that the gains from compromise for player p i are E[u i (α 1 , . . . , α n ) | u * ] − E[u i (α 1 , . . . , α n ) | no compromise]. (3) allow for a compromise that leaves everyone better off. However, there are some aspects of Eq. (  3 ) that should, perhaps, be revised. For one, it is unclear whether having a full compromise versus having no compromise is the appropriate counterfactual. One alternative is to choose the counterfactuals provided by one's decision theory. That is, one could compare E[u i (α 1 , . . . , α n ) | I cooperate with u * ] with E[u i (α 1 , . . . , α n ) | I defect] , where EDT's conditional expectation may be replaced by an alternative notion of the counterfactual (see  Gibbard and Harper, 1978; Hintze, 2014, section 3) . Alas, these are difficult to calculate. Perhaps one could also measure the gains from each p i 's individual participation, so that the set of cooperators in the minuend and subtrahend of Eq. (  3 ) would be the same, except that the latter does not contain p i . Moreover, the subtrahend's compromise utility function would not contain λ i u i as a summand. This resembles the notion of voting power from social choice theory  (Cotton-Barratt, 2013; Felsenthal and Machover, 1998) . A second area of revision may be that Eq. (  3 ) does not account for some value systems potentially being more common among the p i , or holding more power, than others. We would probably want the gains from trade to be proportional to the resources invested by a particular value system. Otherwise, an individual agent with a very common value system has no or less of an incentive to join the compromise. For example, if an agent already knows that at least one other agent with the same utility function is part of the compromise, then this could mean that joining the compromise produces no additional gains from trade for that agent. One way to weight different utility functions based on their power would be to divide Eq. (  3 ) by some measure of the resources invested by u j . The Shapley value is a well-known example of a theoretically grounded measure of power and may serve as an inspiration. Also note that Assumption B contains an interpersonal comparison of utility. However, the potential harm of getting this one \"wrong\" is smaller than in the case of using the unweighted sum as a compromise. Depending on how you scale the different utility functions relative to each other, applying Assumption B may allocate the gains from trade differently, but it nonetheless ensures that everyone receives gains from trade at all. Further research is needed to identify the appropriate variant of Eq. (  3 ) or perhaps an alternative to it and subsequently the corresponding weight assignment. An example of a promising line of research in this direction is the work on variance voting, i. e. normalizing the variances, by  Cotton-Barratt (2013)  and MacAskill (2014, chapter 3). In particular, Cotton-Barratt shows that under certain assumptions, variance-normalized compromise is the only compromise that gives each player the same voting power. In addition to specific solutions, it would be useful to explore the necessary conditions for the existence of a weight assignment that satisfies Assumption B while producing positive gains from trade. For example, if you already know how much cake each player owns in the above Superrational cake cutting, there is no assignment of weights that reliably produces gains for everyone. No matter how the weights are assigned, there will always be one weighted utility function that strawberry cake is best invested into, one that vanilla cake is best invested into, and (at least) one that receives no cake at all. That is, unless two weighted utility functions generate the same amount of utility per unit of cake, in which case the compromise utility function is indifferent about who receives the cake. Besides the existence of gains from trade (see section 3.2.5), I suspect that the central assumption under which a weight assignment satisfying Assumption B exists is the continuity of the expectation E[u i (α 1 , . . . , α n ) | u * ] relative to the weights in u * . \n Updateless weights Seeing as the gains from compromise that Assumption B talks about depend on one's current state of knowledge, the weights to be assigned may do so, too. Consider the following example: Remote-controlled cake maker. Two agents are about to share cake again. Agent 1 prefers strawberry to vanilla cake at a ratio of 2:1. Agent 2 has the inverse preference ratio. On day one, neither of them owns any cake; however, they know that on day two, each will receive two control buttons for a distant machine, capable of producing and shipping only one type of cake. While it is, at this point, unknown which flavor of cake it will produce, they will know the type of cake maker once they receive the buttons. They will have the same amount of control over where the cake from the cake machine is sent: each agent can, by pressing one of the buttons, send some amount of cake to himself. By pressing the other button, they can send a 20% larger amount of cake to the other agent. Unfortunately, they can only press one button. The two agents' thought processes correlate perfectly when it comes to decisions regarding superrationality and they may already settle on a superrational compromise utility function on day one. On day two, they receive the control buttons and learn that it is a vanilla cake machine. They still cannot communicate, but use the same thought processes. Which button should each of the two press? 24 Let us first consider the situation on day one. Because their situations are fully symmetric, it seems reasonable to set u 1 (s 1 , v 1 ) = 2s 1 + v 1 , u 2 (s 2 , v 2 ) = s 1 + 2v 2 , u * (s 1 , v 1 , s 2 , v 2 ) = u 1 (s 1 , v 1 ) + u 2 (s 2 , v 2 ), where s 1 , v 1 , s 2 , v 2 are, again, the amounts of cake received by each player (which can be calculated from a set of actions). By any reasonable definition of \"gains from compromise\", this satisfies Assumption B. Accepting this compromise effectively means that agent 1 will receive all of the cake if the machine makes strawberry cakes, and agent 2 will receive all of the cake if the machine makes vanilla cakes. We now skip ahead to day two, when the agents are told that the machine makes vanilla cakes. In this new situation, u * (s 1 , v 1 , s 2 , v 2 ) = u 1 (s 1 , v 1 ) + u 2 (s 2 , v 2 ) is harder to justify, as it gives all the gains to agent 2 -agent 1 even loses utility relative to not compromising. Perhaps the more natural utility function to choose on day two is u * (s 1 , v 1 , s 2 , v 2 ) = 2u 1 (s 1 , v 1 )+u 2 (s 2 , v 2 ), which would be the compromise utility function under, e. g., variance normalization. From the perspective of day one, it is suboptimal if the two players change their minds on day two. Thus each player prefers precommitting to the initial compromise even though that implies a good chance of a net loss. Once again, we find that lack of knowledge is evidential power (see section 2.4) and that we should precommit to decision-theoretical updatelessness. In the context of MSR, I doubt that the weights of the compromise utility function would shift considerably once a few basic factors have been taken into account. For one, significantly updating one's prior about the expected gains from a compromise requires broad and reliable knowledge about the entire multiverse. Specifically, it requires knowledge about what decisions superrational collaborators will face in other parts of the multiverse, and how these decisions will affect different value systems. Even if you learn that some assignment of weights decreases your utility in this universe, the situation may differ in other universes. Many opportunities to have an impact may depend on as yet unidentified crucial considerations or unresolved issues in physics. Examples of issues of this kind which have already been identified include lab universes, artificial intelligence, artificial intelligence arms races, self-improvement races, suffering in fundamental physics, whole brain emulation scenarios (see section 3.4.4) and global catastrophic risks. That is to say: any kind of multiverse is so complicated that we should not expect to know much about it. If we think some pieces of information would significantly shift our weights in one direction or another, then this piece of information is potentially harmful. To the extent that it is possible, it would be important to convince superrationalists to become updateless before they encounter such information. \n Limitations The present analysis is limited in several ways. In general, we made many assumptions under the meta-assumption that the results generalize. For example, our arguments were often based on perfect correlation between the agents. Many aspects of our analysis were also semi-formal or informal. For instance, we did not formally justify the claim that settling on the same compromise utility function creates the largest gains from compromise. Further research is thus needed, including research into the largely unexplored area of superrational game theory. \n Heuristics It would certainly be nice to find a formal solution to the compromise problem (as described in section 2.8.2) at some point. However, such a solution is neither necessary nor sufficient for cooperating superrationally in practice. It is not necessary because cooperation based on intuitions about compromise may already get us quite far. Even without ever having heard a course on game theory, most people have intuitions about fairness that seem to suffice in most negotiations. We may expect that similar intuitions also suffice for reaping many of the benefits of superrational cooperation. It is not sufficient because we will not possess formal description of our collaborators' utility functions in the foreseeable future, anyway, given that we cannot even formally describe our own goals 25 With the description of their values being vague and qualitative, the compromise must, in the end, also be. Hence, we should also consider informal heuristic rules for making decisions. Below are some proposals. They have significant overlap and many of them also apply to causal cooperation; some are more moderate and intended to apply to people who do not fully accept MSR. Sorted in increasing order of the strength of their implications: • If some resource is mildly useful to you but very valuable to other (prominent) value systems, it is prudent to ensure that the resource is used for those other value systems. Similarly, avoid hurting other (prominent) value systems if it only gives you a comparatively small gain. • Utility functions that contribute a lot, e. g. because opportunities to increase them are rare, should perhaps receive disproportionate focus whenever such an opportunity arises. Otherwise, agents with such utility functions would have little incentive to compromise. • When the values of superrational cooperators diverge on some issue with a roughly equal number of supporters (or resources) on each side, these sides cancel each other out after compromise. That is, no superrational cooperator should act on a view on this issue. Toby Ord writes: \"It is so inefficient that there are pro-and anti-gun control charities and pro-and anti-abortion charities. Charities on either side of the divide should be able to agree to 'cancel' off some of their funds and give it to a mutually agreed good cause (like developing world aid). This would do just as much for (or against) gun control as spending it on their zero-sum campaigning, as well as doing additional good for others.\" • Try to benefit many value systems at once, and deprioritize issues that are very specific to you or other agents (see section 4.1.1). • Metaphorically speaking, try to increase the size of the compromise pie, rather than to increase the size of your own piece. • In any situation, maximize for the (prominent) value systems that have the highest stakes in your decision. • For any policy decision, ask yourself whether superrationalists with other value systems would plausibly arrive at the same decision (to ensure that you are assigning weights impartially). \n Notes on superrational coordination Superrational compromise is easiest if it requires no coordination (see section 2.8.3). It can, however, also solve coordination problems -that is, problems in which the utility functions of the players do not decompose into local utility functions, and the utility of a strategy to some player thus depends in part on the moves of the other players. As before, we can also describe a variation of the problem with similarity instead of common rationality. And as usual, causal decision theory recommends to reply, a strategy that, if implemented by everyone (or more than 5 people), forgoes a golden opportunity. However, this scenario diverges from those we have previously discussed in that our impact on the other participants' utility depends on their actions. Nevertheless, we can use superrationality to our (and our superrational collaborators') advantage in Platonia five, although we have to apply it in a different way. The problem is that simply maximizing the compromise utility function does not really help us here. Given that all players are essentially in the same position, it seems reasonable to let the compromise utility function be the sum of the money gained by each player. That means it is either 5 billion if exactly 5 people send in the letter, or 0 if another number of people send in a letter. Maximizing the utility function only tells us that we should ensure that exactly 5 people should send a letter -something we already knew beforehand. The compromise utility function does not tell us who should send in the letter. Because it does not decompose into local utility functions, it does not tell each player what to do. This illustrates how, even with perfect correlation, the compromise utility function may not suffice for solving coordination problems. Hence, we go back to the more direct approach. We assume that, given the correlation between agents (or the ability to determine the rational choice), we should choose the strategy that would be best for us if it were adopted by everyone. Because the situation is entirely symmetrical, everyone is likely to go through equivalent lines of reasoning. Obviously, neither sending in the letter nor not sending in the letter are good strategies. We thus have to adopt a mixed strategy, i. e. one of choosing to send in the letter with some probability p, where players' samples from this distribution are independent. At the far ends, both p = 1 and p = 0 guarantee that we lose. However, if p is chosen from somewhere in between and everyone adopts the same mixed strategy, there is a non-zero probability that you, the individual participant, will win the billion. Thus, we now have to choose p so as to maximize our probabilities of success. (Alternatively, we can maximize the probability that the 5 billion are awarded at all. As we will see, the result is the same.) If you and everyone else each sends in their letter with a probability of p, the probability of your winning is p times the probability that exactly four of the other 19 players send in their letter. The overall probability of you winning a billion is thus p • 19 4 • p 4 • (1 − p) 15 , ( 4 ) where 19 4 is a binomial coefficient. We now choose p so as to maximize this term. Because 19 4 is a constant, we can maximize p 5 • (1 − p) 15 . (5) Incidentally, the p that maximizes this term also maximizes 20 5 • p 5 • (1 − p) 15 , ( 6 ) the probability that anyone wins at all. As it happens, Eq. (  6 ) is maximal for p = 1 4 , 27 which gives a probability of about 20% that the money is won, and thus a probability of about 20% • p = 5% that we win the money. Although a 20% probability of the money being won is better than 0%, it is still not quite satisfactory relative to the 100% that could be achieved with perfect coordination 28 . However, it seems as though there is no better way. We will revisit this question in section 2.8.9. While such coordination is qualitatively different from the other examples, it should still be seen as a form of cooperation (as opposed to some other applications of acausal decision theory like Newcomb's problem, or some coordination problems where all players have the same goal), because the game is positive-sum and (superrational) coordination improves everyone's outcome relative to CDT's recommendation. In Platonia five, the uncoordinated response involves everyone trying to get the money by sending in a letter. Many coordination problems suffer from the opposite problem, namely diffusion of responsibility. Consider the following example, versions of which were also discussed by, e. g.,  Leslie (1991, ch. 5 ) and Drescher (2006a, section 7.3.2): Superrational voting. You live in a country of superrationalists and today is election day. A strict secret ballot rule dictates that citizens are not allowed to tell each other which party they are going to vote for or whether they plan to vote at all. Unfortunately, going to vote costs a lot of time and you don't expect the potential impact of your vote to justify the opportunity costs. If you choose not to vote, then so will most of your fellow superrational citizens. That would be unfortunate. For one, the majority opinion of the people should be represented, if only because it is more likely to be your opinion. Besides, there is an uncorrelated minority that should not win, as all your superrational friends will attest! By what mechanism should you decide whether to vote or not? Again, the compromise utility function is not very informative. And again, a probabilistic (or mixed) strategy is optimal if the correlations are sufficiently strong overall and independent of the party one plans to vote for. To find out what exact probability should be chosen, one would need to come up with a term for the expected value under that probability, consisting of the cost of voting and the probability that some minority view wins, as well as the expected costs of the latter. Consider one last example, inspired by Pascal's button: Multiverse-reprogramming. Scientists inform you that the basic laws of the multiverse may be vastly more complicated than they originally thought. Specifically, they say there is a small probability that there exists some complicated and hard-to-find way of \"reprogramming\" parts of the multiverse. However, such reprogramming depletes some multiverse-wide resource pool. This means that the amount of reprogramming is independent of the number of agents who discover how such reprogramming can be done, provided that at least one agent discovers it and exploits it to full capacity. It would be unfortunate if no one in the multiverse seizes this opportunity or if everyone invests all their resources into finding it. As we have seen in the above thought experiments, we can use superrationality to solve this problem by determining some mixed strategy. Everyone lets some random process decide whether to invest significant resources into investigating the reprogramming mechanism, and then either pursues it fully or not at all. Once more, the compromise utility function does not tell us who should try to reprogram the multiverse; it does, however, tell us how each civilization should use the reprogramming mechanism. Note that this is another problem in which updateless weights (see section 2.8.6) are important, because once some civilization finds out how to reprogram the multiverse, it may be tempted to stop compromising. \n Schelling points We will now consider how we can get from a 20% probability of success in Platonia five to 100% under certain conditions. Consider the following variation of the dilemma: Platonia five with coordination help. S. N. Platonia is organizing another one of her eponymous dilemmata. However, this time she has compiled a numbered list of the participants beforehand. As a postscriptum to the standard content of the dilemma letter, Platonia writes: \"Your number on the list of participants from 1 to 20 can be found on the back of this letter.\" Before looking at your number, is there any way the superrational participants can ensure that someone receives the money? In the original Platonia dilemma, the participants were all in the exact same situation. But now, different people have different numbers on the back of their letters. This can make a difference if, before looking at the back of the letter, the 20 participants agree on which numbers should respond to the letter. For example, all participants could precommit to respond only if their number is between 1 and 5, and only then turn the letter over and act according to their precommitment. In this way, they ensure that exactly five people send in a letter, thus maximizing the expected gains. (Also note that due to the symmetry of the situation, it also gives each player the same expected gains assuming that none of them are already suspicious about their position on the list.) In a way, the numbers on the back of the letter function as a coordination help that allows for coordination where it would otherwise be impossible. An even better coordination help would be one where each player receives a recommendation on whether to respond, along with a guarantee that only 5 of the 20 players will be prompted to respond. Alas, such direct coordination helps will usually be unavailable.  29  So how can people agree, without communicating, on which numbers should send in a letter? If the participants are guaranteed to be exact copies of one another, they can pick an arbitrary set of 5 numbers between 1 to 20 before checking the back of the letter, confident that the other 19 will choose the exact same set. In relevant applications, correlation will not be that strong. But since all agents have an incentive to settle on the same set of numbers, each could individually try to identify a set that is obvious or that stands out in some way. For example, the set of 1, 2, 3, 4 and 5 appears to be a candidate that others may choose as well  (as opposed to, say, 3, 7, 8, 11, 12) . Correlations play a role -if I choose numbers 1-5, then it is somewhat more likely that others do, too -but not a decisive one. Even if there are no correlations, abiding by such Schelling points (first introduced by Schelling (1960, chapter 3); see also  Friedman (1994, chapter I A) ) is beneficial to the individual player if she believes that (many of) the other players abide by that same Schelling point. In practice, many Schelling points are driven by minor yet obvious expected value arguments. For example, when someone mentions that they would like the window to be opened, the person sitting closest to it is often seen as the natural one to open it, because she does not have to walk as far as the others. This consideration is negligible, but it helps with coordination. Many Schelling points are also mere social conventions. For example, consider the issue with right-and left-hand traffic. Presumably, most people have no strong preferences between the two as long as drivers abide by the same standards when interacting with each other. Whenever two drivers drive towards each other on a road, they face the coordination game with a payoff matrix resembling that in Table  1  Countries have laws that tell citizens whether to drive on the right-hand or left-hand side of the road, solving this particular coordination problem. For multiverse-wide superrational coordination, such convention-based Schelling points are alas not available. The lack of a Schelling point could mean that it is impossible to reliably achieve optimal outcomes. Imagine meeting a member of an unknown society in a narrow alley. Should you pass them on their right-hand or left-hand side? Assuming there is no relevant established pedestrian traffic convention for that alley, there appears to be no way of deciding between the two. \n Coordination is relevant for everyone I suspect that most people who care about the multiverse have utility functions that \"mostly\" decompose additively, thus requiring little coordination. If you are in this majority, you may think the topic of superrational coordination is irrelevant for you. However, this view is mistaken, since the compromise utility function requires coordination if at least some superrationalists in the multiverse have utility functions that do not decompose into local ones. Of course, you could just ignore these value systems when constructing your compromise utility function, but this makes it more likely that other agents exclude you in other ways as well, as we will see in the following section. \n No reciprocity needed: whom to treat beneficially In this section, I will argue that the application of superrational cooperation requires no reciprocity. That is, none of the agents who benefit from our cooperation have to benefit us. Recall the basic argument for superrationality as based on non-causal decision theories: given that we are friendly, it is more probable that other agents facing similar choices will be friendly toward us and our values. Crucially, this argument does not require that the agents whose choices we acausally affect are the same as those who benefit from our own friendliness (2006a, section 7.2.1). \n Schemes of causal cooperation The classic cooperation scheme from causal cooperation is one of mutuality -\"I scratch your back, you scratch mine\", so to speak. This scheme is represented by the graph in Figure  6 . In mutual relations like this, it is possible to apply causal cooperation, although only if the interaction is repeated -i. e. if my choice causally influences the other agent's choice 30 , and then the other agent's choice can causally influence my choice, etc. 31 For introductions to causal cooperation, see, e. g.  Axelrod (2006) ;  Trivers (1971) ;  Fehr and Gächter (1999) ;  Dawkins (1976, chapter 12) ; Taylor (1987), and  Buss (2015, chapter 9) . Superrational cooperation also works in the above scheme, although repetition is not required. The prisoner's dilemma (with replicas or twins) is one example of this sort of problem. \n Circular cooperative structures and indirect causal reciprocity In principle, it is possible to establish causal cooperation even in cases where the two agents cannot directly benefit each other, provided there is a repeated causal link from my own decision to the decision of the agent who can benefit or hurt me, such that I can in some way reward cooperation and punish defection. As an example, consider the following variation of Hofstadter's donation game: Iterated donation circle. Like the circular donation game, only that the game is played many times (the exact number of times being unknown to the players). Donation circle. In every round, each participant is informed of their predecessor's past choices before deciding whether to send in 'C' or 'D'. Circular structures such as these can be represented by graphs such as the one in Figure  7 . Because each of the agents can causally (through the other agents) affect their predecessor, the iterated version of this problem could still, in principle, motivate causal cooperation. For example, one Nash equilibrium consists in everyone playing tit for tat. This Nash equilibrium is even stable, in the sense that one player diverging from tit for tat with a very small probability still leaves everyone else best off if they continue to use tit for tat. However, the same Nash equilibrium is also hard to achieve and unstable in a different sense, as it requires all 6 participants to use the same kind of strategy. Your response to your predecessor's cooperation is mediated by multiple other agents. If only one of them does not propagate your response correctly, the causal path from you to your predecessor is disrupted, leaving neither of you with a causal motivation to cooperate. For superrationality-based considerations, on the other hand, neither repetition nor the length of the causal path from one participant's cooperation to her predecessor are relevant. Instead, superrational cooperation only depends on the correlations between single pairs of agents. Hence, while the significance of causal cooperation in the Donation circle diminishes with every additional participant, the benefits from superrational cooperation remain constant regardless of how many players are involved. \n Hierarchies and acyclic graphs In an extreme case, there would be no causal path whatsoever from one participant's cooperation to that of his predecessor, making causal cooperation lose its entire appeal to the rational agent. Superrational cooperation, on the other hand, may still be applicable (cf.  Drescher (2006a, pp. 287-292) ; see section 6.1.1). Consider the following variant of the donation game: Donation ladder. Once more, Omega has a long list of participants, albeit a regular linear one this time. Omega sends all of them a letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. It explains that by sending in 'C', participants can increase their successors' payoffs by $5. The first person on the list cannot benefit from the cooperative behavior of others, and the last participant's choice has no effect on the others. Omega writes that each player can increase their own payoff by $2 if they defect. Participants do not know their position on the list, and are once again told that they all use similar decision algorithms. Every participant only cares about the balance of their own bank account, and not about Omega's or that of the other participants. Upon receiving the letter, should you cooperate or defect? Figure  8  illustrates the donation ladder. ... ... In such a cooperation scheme, causal cooperation cannot be established even if the problem is iterated, whereas the superrationality mechanism is just as reliable as in the other examples. Because the list is long, I probably have a predecessor; if I cooperate, then my predecessorwho is in a position similar to mine -will probably make the same choice. Cooperation thus informs me (or logically determines) that I am likely to gain $5, whereas defection only gives me $2. We can see this linear hierarchy of agents in practice among the different versions of an agent at various points in time. For example, I can causally affect the welfare of future versions of myself, but if I only (or primarily) care about my present experiences, they can never reward me in return. However, I could try to benefit future versions of myself to make it more likely that past versions of me have behaved nicely toward myself. More discussion with references to the literature is given by Drescher (  2006 ), section 7.3.4. Linear cooperation hierarchies come with a twist, however. Consider the following variant of the Linear hierarchical donation game: Donation ladder with known position. Identical to the linear hierarchical donation game, only that participants know their position in the list when they make their decision. A participant in the middle of the list may wonder how his situation differs from the regular donation ladder -after all, his predecessor on the list is in almost the same situation as he is. Assuming the conditions for superrationality are satisfied, their decisions should still correlate. Hence, if he cooperates, should we assume that his predecessor is likely to do the same? Not necessarily. The problem lies in the beginning of the list. The first person -let us call her No. 1 -will have no predecessor and thus no predecessor whose decision she could acausally influence, in effect giving her no reason to cooperate. Given this, No. 1 should defect (that is, unless she is already updateless; more on this below). Unfortunately, this puts No. 2 in a similar position. Realizing that No. 1 will defect, there is nobody left to benefit him. No. 3 will, in turn, reason that No. 2 expects No. 1 to defect, which means that No. 2 will also defect, leading No. 3 to defect as well. . . and so on, propagating down the entire list. You may notice that this propagating defection effect is analogous to the reason why standard game theory recommends to defect in the iterated prisoner's dilemma when the number of rounds is known 32 . Once more, we find that lack of knowledge is evidential power. For one, if the participants did not know their positions, they would all cooperate -and thus be more successful. If everyone could precommit to cooperation before learning about their position, they would do so. Again, cooperation can be maintained if all the agents are updateless in the first place (see section 2.4, cf.  Drescher (2006a)  In general, we can represent such hierarchical versions of the donation game using directed acyclic graphs like the one in Figure  9 . ... ... If participants knew their respective positions in the list, the considerations outlined for the Donation ladder with known position would apply analogously. In practice, such hierarchies may be hierarchies of power. Some agents are \"lexically\" more powerful than others, such that cooperation can only be beneficial in one direction -the less powerful have no way of helping the more powerful, while the powerful can help less powerful ones much more cheaply. As a perhaps paradigmatic example, consider a standard science-fiction scenario: Intergalactic relations. The universe contains many civilizations. Although they all followed similar evolutionary trajectories, each civilization developed at different times on different planets in different parts of the universe, and thus differ drastically in their levels of sophistication. Most civilizations eventually decided to conceal themselves to some extent, so no one knows which of the civilizations is the most powerful. You are the leader of a civilization, and one day, you encounter a comparably primitive civilization for the first time. According to your advisors, it appears that this other civilization has not even managed to harness the energy of their local star, they still suffer from diseases that your civilization's nano-devices could cure in an instant, and so forth. Your advisors, citing the other civilization's apparently laughable defense systems, recommend that you destroy them and use their resources to further your own goals. Should you follow your advisors' recommendation? Once again, causal reasoning may suggest that you should. By now, though, it should be clear that there are good reasons to ignore your advisor's recommendation if you believe there is a sufficiently strong correlation between your and the other civilizations. Note that one reason for civilizations to conceal themselves might be to induce a lack of knowledge about their relative positions within the hierarchy. If we remain hidden, other civilizations will be more likely to do the same, so neither we nor they would know who has the upper hand in a potential confrontation. On the other hand, if all civilizations loudly boasted their power, the most powerful civilization would realize its dominance and consequently have no reason to be friendly to the others -absent precommitment, the use of updateless decision theory, and the like. Another example of such power hierarchies is that of simulations. Simulators can causally influence the simulated in any way they want, but the simulated can do little to causally affect the simulators (e. g., by affecting the outcomes of the simulation or its computational demands). We will discuss this more in section 6.9. The following example may be typical of the hierarchies in multiverse-wide superrationality (MSR): Computable consequentialists. Meet Luca, who believes that consciousness cannot arise from classical computation alone.  33  He is also a consequentialist and primarily cares about conscious experiences. Through the writings of Tegmark, Luca has come to believe that many computable universes might exist in parallel to ours. However, since these computable universes do not contain anything that he would call a conscious experience, Luca does not care about what goes on inside them. He does, however, enjoy thinking about their inhabitants as an intellectual exercise, and this has led him to the conclusion that they can reason about Newcomb-like scenarios in a human-like way even though they are insentient. After all, neither calculating conditional probabilities nor operating on causal graphs requires sentience. Using the supercomputer in his basement, Luca has also come up with a number of predictions about the values held by consequentialists in the computable universes -let us call them the computable consequentialists (CCs) -a feat more difficult to achieve for incomputable worlds. He has even discovered a number of ways to benefit the CCs' values in our universe, all at a very low cost to his own values. While Luca himself does not care about computable universes, he sees no reason for the CCs not to care about worlds that are computationally more powerful than their own. Given that the CCs cannot do anything for Luca in their world, however, is it rational for Luca to be friendly to the CCs' values? Again, Luca does indeed have a reason to do so. If he benefits the CCs, other agentsincluding ones whom Luca cannot benefit -are more likely to realize Luca's goals in other parts of the multiverse. The ability to help can also come from knowing about the other agents. Consider the following example: Simple-world ignorance. Imagine a multiverse in which many different sets of laws of physics are realized. Some of the universes have very simple, parameterless, and easily understood basic laws, like Conway's Game of Life. Others have far more complicated rules. The inhabitants of the more complex universes may thus have more reason to believe in the multiverse than the inhabitants of the simple universes. In the complex universe, the multiverse hypothesis is attractive because it is simpler than the hypothesis that only their universe exists (cf. Schmidhuber, 1997). In the simple universe, on the other hand, the multiverse hypothesis may be more complex than the hypothesis that only their universe exists. Consequently, the inhabitants of the simple universes may adopt superrationality but only apply it toward other inhabitants of their universe. Let us assume that the values of the folks from the simple universes differ significantly from those of the inhabitants of the more complex universes. Should the inhabitants of the complex universes help the values of those from the simple universes? In this scenario, as with the previous ones in this section, I think that the superrationalists from the more complex universes have good reason to help the superrationalists from the simpler universes, as this makes it more probable that the former will receive help from other agents, including ones that they cannot help. For example, there may be many value systems that they (the inhabitants of the complex universes) do not know about (for reasons other than the Kolmogorov complexities of different multiverses). I think this particular scenario may well be relevant in our multiverse. More generally, some parts of the multiverse may contain different clues about the existence of other superrational agents. For example, some might live in parts of the universe from which it looks as though life is much rarer than it actually is, whereas others may discover that they are not alone as soon as they look through a telescope for the first time. In addition, while a superrational agent may be able to use some theory of physics to infer the existence of other agents, he or she may be unable to infer the existence of some particular value system. \n Only helping superrational cooperators helps you superrationally Cooperation usually excludes agents who are known to be unable to reciprocate. Yet as we learned from the Donation tree and Intergalactic relations, superrationality does allow for cooperation with non-reciprocating agents if helping them makes it more likely that other agents help us. There is, however, at least one limitation on the set of our beneficiaries that comes without negative side-effects. We can exclude from superrational cooperation all agents who do not cooperate superrationally at all. After all, every superrational cooperator knows that this exclusion will not affect her, and the exclusion appears to be symmetrical among all superrational agents. That is, it makes it more likely that other superrational cooperators make the same choice (rather than incurring some other limitation that excludes us). It seems risky to place any stronger limitation on the set of our beneficiaries, since this would give us reason to fear exclusion by other agents (cf. Drescher, 2006a, page 290), as we have seen in section 2.9.3. If we so much as try to look for rules of exclusivity that benefit us at the expense of other superrational agents, we have reason to believe that others will do so as well. Of course, superrationality and correlation between decisions are not binary properties, so neither is the limitation drawn above. For example, two artificial intelligences explicitly based on the same decision theory may correlate more than two (non-copied) humans, even if both have some incentive to cooperate. The stronger the correlation between us and some other agent, the more we will benefit superrationally from helping them (cf.  Drescher, 2006a, page 288f ). To illustrate this, consider a one-shot prisoner's dilemma-like situation (cf. figure  6 ) in which two very similar agents can simultaneously decide whether to give the other one some reward b other or to walk away with a smaller reward b u for themselves. Now, imagine the two agents are perfectly correlated, i. e. they always make the same decision. If this is the case, both agents should cooperate whenever b other > b u . ( 7 ) Now consider a situation in which the correlation between the two agents is weaker. Then, in EDT terms, they should cooperate if cooperation (C) is higher in expected value than defection (D). Using conditional probabilities, we can formulate this as Thus, the threshold for cooperation increases as the correlation between the two agents decreases. P (C | C) • b other > P (C | D) • (b other + b u ) + P (D | D) • b u = P (C | D) • b other + b u , If the cooperation graphs become more complicated, then so do calculations like those above. Further research is needed to find out whether the above result -that benefitting agents with stronger correlation is more important -holds true more generally. One interesting question is to what extent superrationalists would form clusters based on correlation strength. This is especially relevant if we believe the correlations to be especially strong among agents with the same value system. \n Cheating, signaling, and half-heartedness Causal and superrational cooperation differ in another important respect. In causal cooperation, the benefit of cooperative behavior comes from how other agents will react to one's own cooperative acts.  34  To facilitate cooperation, each agent may commit to reward cooperative and punish uncooperative behavior. In this way, they can motivate each other to cooperate. But seeing as behavior can only be rewarded or punished if it is observed at all, causal cooperation often ends up focusing heavily on signalling. If you can save costs by merely pretending (in a convincing way) to have cooperated, then that is the rational thing to do from a causal perspective. Conversely, if you can help someone without them knowing about it, you have no causal reason to do so. There are many practical examples of this, such as the tendency for governments to make a big deal out of international agreements or cooperative acts, even if the object-level gain is minor. Since the mechanism of superrational cooperation is different from that of regular causal cooperation, prioritization within it should be different, too. Specifically, superrational cooperation is beneficial not because others reciprocate one's cooperative acts, but because our (cooperative) decisions correlate with those of others. This means that we should sincerely attempt to maximize for benefits to other value systems, because this correlates with others doing the same, which in turn maximizes our own benefits. We are used to thinking about cooperation in causal terms, i. e. about how a certain cooperative act may in the end pay us back causally and in this universe. If we think about superrational cooperation in this mindset, we may be tempted to propose measures that are critically suboptimal from a superrational standpoint. For instance, one may adopt a \"compartmentalized good will\", talking at length about cooperation without actually trying to maximize for other agents' goal achievement, or spend time thinking about how the others might cheat us. However, all of these correlate with other superrational agents in the multiverse wasting effort on these exact same things. With superrational cooperation, only sincere attempts at improving other agents' value systems correlate with the same behavior in others, and thus with the optimal consequences. Hence, there is no way to \"game the system\" or to get benefits without honestly paying for them. \n Values We extensively covered the mechanism of (multiverse-wide) superrationality. However, in all thought experiments considered so far, we knew what impact our actions would have on the fulfillment of the other agents' preferences. For example, we know that the other participants in the donation game or Platonia five would prefer to have more money on their bank account. We also know that other civilizations would prefer not to be destroyed and would benefit from learning about our technologies in Intergalactic relations (section 2.9.3). Such knowledge has to be present or at least attainable in the future (cf. section 4.1), otherwise no side can benefit the others. This section gives an overview of how we can find out what other agents in the multiverse care about, as well as what aspects of their preferences we should focus on in the first place. \n Orthogonality of instrumental rationality and values One objection to superrational cooperation might be based on a possible convergence of terminal values, in which all agents with the correct decision theory will converge toward the same values. Moral realism claims that there are facts in morality as real and true as those in science. In addition, some moral realists believe that any rational agent investigating morality will ultimately arrive at these moral truths. Assuming that a large part of being rational involves using the right decision theory, maybe all agents with the right decision theory will independently come to adopt the \"correct\" moral system? If this is the case, no cooperation among these agents would be necessary (although some value systems may still require multiverse-wide coordination, see section 2.8.9). As a first counterargument, consider that knowledge of the correct decision theory is not necessary for superrational cooperation, seeing as a number of different decision theories (e. g., evidential, timeless and updateless decision theory) imply superrationality. Secondly, we do not seem to observe empirical evidence of such convergence. For example, Eliezer Yudkowsky and Brian Tomasik agree that non-causal considerations are important for decision theory, but Yudkowsky's values nevertheless differ significantly from Tomasik's. There are also principled reasons to be skeptical of value convergence among agents with the same decision theory. Decision theories are about instrumental rationality, i. e. about making decisions aimed at achieving goals, not at revising them  35  . That is at least the case for decision theories as they are discussed today. Consider the following variant of the donation game: Donation game for sadists. Omega has selected 20 pure sadists, who draw pleasure only from torturing others and nothing else. They all use similar decision making mechanisms when playing a donation game (against correlated agents). Instead of being paid in dollar sums, they are given individual hours to torture a slave as a reward. Assuming sufficient correlation between participants, the instrumentally rational decision for each sadist is to cooperate such that the total number of hours of torture increases relative to universal defection. The moral choice, on the other hand, would be to defect in order to reduce the number of hours in which anyone gets tortured. However, decision theories (as currently discussed in the literature) do not take moral considerations into account at all. They merely aim to fulfill the goals, whatever they may be, of the agent using that decision theory. Hence, when applied by a pure sadist, a given decision theory is meant to help her spend more time torturing others. 36 There could conceivably be some different kind of \"decision theory\" that does recommend taking morality into account (and not only cooperation, see section 6.7.1) even if the agent using it is amoral or immoral. One could, for instance, simply combine the correct decision theory with the \"correct\" moral view. Some people may consider such a decision theory objectively correct. However, for an agent with immoral goals (like pure sadism), it would be instrumentally irrational to adopt such a decision theory. In any case, the existence of such a \"moral decision theory\" does not contradict the existence of a decision theory in the classical, instrumentally rational sense, so an amoral or immoral agent would still be better off adopting a classical decision theory. Thus, it would seem that an agent's values and their use of acausal decision theories are orthogonal. This, in turn, suggests that agents with a variety of value systems will adopt a decision theory similar to our own, such that their decisions will correlate with ours. Similar views regarding the relationship between instrumental (and epistemic) rationality and ethical values have been defended under the term orthogonality thesis  (Bostrom, 2014b, ch. 7 , section \"The relation between intelligence and motivation\";  Bostrom, 2012; Armstrong, 2013) . Our claim that decision theory and values are orthogonal in principle does not imply that they never correlate in practice throughout the multiverse. Indeed, in section 3.4 and its companion papers, I will discuss various ways in which values and decision algorithms could be expected to correlate. However, it seems very unlikely to me that these correlations are so strong that they significantly dampen the relevance of superrationality. \n Necessary preconditions Before we start thinking about the values of agents in other parts of the multiverse, we need to consider what kind of agents can join multiverse-wide superrational cooperation (MSR) at all. In particular, what sorts of values do they need to have, independent of whether or how many such agents or value systems actually exist in the multiverse? We already know that only helping superrational or correlated agents benefits us (see section 2.9.4). However, the values of the superrationalists must also be open to the opportunity of gains from compromise. If an agent's values imply that she is better off without any trades, there is no point in helping her. In order to more closely examine this precondition, we can break it into five distinct criteria, all of which are necessary for a superrational collaborator to reap the gains from compromise. 1. Each collaborator must care to at least some extent about states of the world, as opposed to caring only about their own mental states or actions. 2. They must also care about consequences in areas of the multiverse where there may be other cooperators. 3. Other superrationalists must be able to infer and understand their values in sufficient detail. (To draw action-guiding conclusions from MSR, they themselves need to be able to infer the values of some other superrationalists or to influence future agents with this ability.) 4. Given this knowledge of their values, collaborators must have some power to behave nicely toward this value systems. (Again, if MSR is to be action-guiding to an agent, they in turn need to be able to benefit other values.) 5. Doing so produces gains from compromise. If everyone abides by an analogous cooperative strategy, everyone is better off than they would be without cooperation. If all these criteria are satisfied, superrational cooperation works. We will discuss them in turn in the following subsections. For some applications it may be fruitful to subdivide these criteria further. Furthermore, additional criteria, such as Bostrom's (  2014 ) \"porosity\", may determine the size of the gains from compromise. We could furthermore devise criteria to assess the extent to which superrational cooperation affects one's strategy. For instance, if all correlated agents have the same values anyway, superrational cooperation does not affect our policy except for cases of coordination (see section 2.8.9). \n Consequentialism Most people's ethical views are partly deontological (and sometimes virtue ethical). That is, they are not solely concerned about the state of the world and the consequences of actions, but als about \"the actions themselves\" (and, in case of virtue ethics, one's character). They usually try to follow some set of rules prescribing what actions are appropriate in which situations. For example, many people follow strict rules against killing (though these usually do not apply under all circumstances and the meaning of \"killing\" is rarely fully specified), even when breaking these rules would lead to fewer deaths. This type of ethical system forms a central part of many religious doctrines, with notable examples such as the Christian ten commandments, the Confucian filial piety, and the Islamic sharia. In addition, most national laws contain countless rules of this sort, many of which apply to more mundane domains like traffic or taxes. Isaac Asimov's three laws of robotics are yet another example of a deontological set of rules. The arguments for multiverse-wide superrational cooperation that I have given appeal to the consequentialist aspects of one's values -not because it requires us to push people off bridges (as in the Fat man version of the Trolley problem), but because its supporting argument is fundamentally based on the consequences of different actions. If we on Earth benefit other value systems, then this implies that others elsewhere in the multiverse also benefit our value system, which may produce better overall states of the multiverse overall via gains from trade. Hence, the value of superrational cooperation lies in its positive consequences on the world (or other worlds). The ethical duties of deontological ethical systems, on the other hand, usually concern the more immediate consequences of our actions. Thus, in a scenario like the Fat man version of the Trolley problem, most deontological would imply that the direct act of killing the fat man violates our duties towards him more than a failure to act violates our duty towards the five people on the track. In Bourget and Chalmers' (2014) survey of philosophers, 23.6% of respondents characterized their values as consequentialist while 44.1% identified as deontologists or virtue ethicistswith the remaining 32.3% choosing \"other\". However, most people probably espouse values that involve at least some consequentialist aspects (cf. Muehlhauser and Helm, 2012, section 5.3). I doubt that many modern consequentialists would be emotionally capable of murder or torture even under circumstances where they could be confident that doing so would yield the best consequences 37 . At the same time, I doubt that many defendants of rule-based ethics see no appeal in potentially reducing the amount of torture in the multiverse, even if only in an indirect way. In fact, many deontological rules are motivated or even defined by the consequences they produce. For example, murder is defined as any act that intentionally and directly results in the death of another person (although indirect ways of causing the same consequence (e. g., omissions) are not seen as murder). Rules against theft are often defended on the grounds that a society with such rules is preferable to one without, even if the rules might occasionally prevent a genuinely altruistic bank robbery. Some even interpret Kant's categorical imperative (especially its first \"formulation\") as a heuristic based on consequentially motivated decision-theoretical reasoning (cf.  Parfit, 2011, section 63; Hare, 1993) . As  Rawls (1971, ch. 6 ) writes, \"deontological theories are [not defined] as views that characterize the rightness of institutions and acts independently from their consequences. All ethical doctrines worth our attention take consequences into account in judging rightness. One which did not would simply be irrational, crazy.\" Although most people refrain from the consequentialist choice in extreme situations, they do, in fact, often endorse it. For example, in  Bourget and Chalmers' survey (2014) , 68.2% of the respondents chose to pull the switch in the original trolley problem, and only 7.6% did not (with the remaining 24.2% choosing \"other\"). Pulling the switch is similarly popular among the general population. This suggests that people sometimes agree with consequentialist reasoning even if other, exclusively deontological or virtue ethical considerations can overrule it. Beyond consequences for things like the number of deaths, individual welfare, and fairness, people sometimes also care about the abidance by deontological rules in a consequentialist way. For example, most people not only avoid killing others themselves, but also care about preventing murders in general; many who personally avoid lying also strongly dislike it when others lie; and so forth. These kinds of consequentialism, which are rarely considered in the literature on moral philosophy, qualify for superrational consideration just as much as, say, utilitarianism. We will revisit this topic of caring about the deontologically ethical behavior of others in section 3.4.1, in which we review studies indicating that many people have values of this sort. \n Caring about the multiverse Presumably, some agents with significant consequentialist aspects to their values will almost exclusively care about their own part of the multiverse, if only based on egoism or absurdity heuristics 38 . It is thus very difficult or impossible to benefit them in other parts of the multiverse, in turn preventing cooperation. Although there is very little discussion about the moral relevance of other parts of the multiverse, the moral relevance of distance is frequently discussed in moral philosophy (see, e. g.,  Brock and Hassoun, 2013) . Note that while distance is usually understood to be spatial, other kinds of distance (e. g., temporal  (Beckstead, 2013)  or social) play similar roles in ethical judgment. While the debate in moral philosophy appears ambiguous, people's actions speak more clearly. Most people from high-income countries would save a child from drowning in a nearby pond, but donate only relatively small amounts to charity  (Singer, 1972) . Insofar as they do give to charity, they usually prefer local causes even though helping in low-income countries is more cost-effective. From this, we can safely infer that most people are altruistic to some extent, but seem to care more about near events than distant ones. One may suspect that an agent's ignorance about other parts of the multiverse would yield similar conclusions as a lack of interest. After all, if someone does not know about our part of the multiverse, they cannot help us. However, we must not forget that superrational cooperation need not be based on mutuality (see section 2.9). Even if someone cannot help us, we can still help them to make it more likely that we ourselves receive help from agents whom we cannot help. \n Knowable values In order to maximize for some given utility function, we or future superrationalists (see section 4.1) need a sufficiently detailed model of the utility function itself. In section 3.4, we will discuss how the evolutionary psychology of morality and related disciplines can be used to assess the values of superrational cooperators in the multiverse. There are at least some ways of making very educated guesses, although we cannot expect to arrive at a detailed and precise description of the values of all evolved civilizations and their descendants. However, perfect knowledge is not necessary for our purposes. Indeed, most people cannot even describe their own values in detail (see footnote 25). Yet despite this, humans are perfectly capable of helping one another achieve their goals. Thus, the question is neither whether we can gain relevant knowledge about the values of other agents in the multiverse at all, nor whether we can have a full map of extraterrestrial morality, but whether the information we can gather about other civilizations can be sufficiently accurate to yield a usable model. \n Fragility of value Yudkowsky (2015, ch. 279) argues that human values are not just complex (cf. section 3.4.1); they are also fragile, in the sense that even minor errors in a non-human agent's picture of them can completely derail that agent's efforts to optimize for them. According to Yudkowsky, \"Any Future not shaped by a goal system with detailed reliable inheritance from human morals and metamorals, will contain almost nothing of worth.\" Perhaps more generally, we could say that any resource expenditure will generate next to no value for an intelligent evolved being X unless that resource expenditure is shaped by a detailed inheritance of X's morals and metamorals. Yudkowsky gives boredom as an example of a small but indispensable part of human values: \"Consider the incredibly important human value of 'boredom' -our desire not to do 'the same thing' over and over and over again. You can imagine a mind that contained almost the whole specification of human value, almost all the morals and metamorals, but left out just this one thing and so it spent until the end of time, and until the farthest reaches of its light cone, replaying a single highly optimized experience, over and over and over again.\" Presumably, many other seemingly insignificant aspects of human values are of similar importance as boredom. One would need to get all of these aspects just right in order to benefit human values. This suggests that it will be difficult to benefit many evolved value systems, due to the large amount of detailed knowledge it would require and the difficulty of gathering that knowledge. There are various points to discuss in this context. For one, the fragility thesis is rather vague; it does not say how fragile our values are, or how accurate and reliable the inheritance must be. This is not to say that the fragility thesis makes no testable claim at all. Yudkowsky formulated it with the value loading problem of artificial intelligence in mind. Since AIs can be programmed to pursue any goal (cf. section 3.1), the space of possible values with which an AI could end up is vast, and the target goal systems occupy only a small fraction of this space. The fragility hypothesis can be interpreted as one elaboration on just how small this part of value space is, and how catastrophic it would be (from the perspective of that value system) to miss it by even a small margin. In other words: even if we take care to represent all of the most central aspects of our values (e. g., \"increase the welfare of sentient beings\" or \"reduce inequality\") in the goal system of an AI, the outcome may still be as bad as an entirely random one if we omit seemingly peripheral values such as boredom. Although I agree with the fragility thesis as a descriptive (rather than normative) statement about human values, I do not think human values are quite as fragile as Yudkowsky writes. Specifically, I think the outcomes brought about by AIs with two different goal systems can differ enormously in their overall worth even if both miss important aspects of human values. For example, Yudkowsky's hypothetical world full of repetitive happiness may be boring, but it is still much better than a world full of suffering, unethical behavior, etc. and nothing of worth to compensate. But perhaps this judgment is influenced by my own values (which are mostly about ensuring the welfare of sentient beings with a strong priority for preventing their suffering), to the point where it would not generalize to how other humans, or other evolved agents in general, would view the situation. Transferred to our variant of the fragility thesis, this nevertheless suggests that even if we miss significant parts of the values of other superrational cooperators, taking their values into account may still make a big difference to them. More importantly, AI value loading differs significantly from our attempt to benefit agents in other parts of the multiverse. The main problem of AI value loading is getting the AI to care intrinsically about human values. MSR, on the other hand, already gives us the sincere (instrumental) goal of helping other agents, which the AI lacks. If anything, we lack knowledge of the others' values, whereas AIs may still not care about them even with perfect knowledge of their values. Another crucial difference between these two contexts is that in AI value loading, we usually want the AI to hold the values of one particular species or group of people. In contrast, when cooperating superrationally, it is sufficient to know that we benefit many other superrational agents. We do not need to know whether we benefit some particular species. The extent to which this makes our job easier depends on how evolved value systems are distributed over value space. Perhaps they form a few (or many) very small clusters, as depicted in Figure  10 . (Needless to say, Figure  10  is not meant to be an accurate map of value space. The placements on the map have no factual basis.) \n Utilitarianism Human values Figure  10 : A map of a part of value space under the assumption of there being distinct clusters with a lot of empty space in between. Every blue point on the map is some value system held by a significant number of agents. The white areas of the map contain value systems that do not have a significant following, such as paperclip maximization. If our map really did represent value space and each individual value system is fragile, then it is difficult to benefit other value systems, because if we miss the targets only by a bit, we end up with a value set that nobody cares about. However, it could also be that the values of different evolved agents occupy some compact part of value space, as depicted in Figure  11 . In this map, darker areas represent value systems with many agents and lighter areas indicate value systems with fewer agents. If value space looks more like this map than our previous one, then it is easier to make \"guesses into value space\" to help superrational collaborators. As long as one is roughly aiming at the right part of value space, small errors just mean that one benefits slightly different superrationalists than intended. Only a few maps of humanity's value space have been created, the best-known of which is probably the Inglehart-Welzel cultural map of the world. I would nonetheless wager some guesses as to how more fine-grained maps of values would look like: on any individual planet, there are clusters formed by major religions, nations, political camps, and other cultural groups. For example, there are many people who hold many of the moral views of the Quran and many who hold many of the moral views of the Bible, but presumably much fewer who defend a mix of the two. Nonetheless, the space between the clusters is not completely \"uninhabited\". Furthermore, the existence of these clusters seems to be partly arbitrary, a \n Human values Utilitarianism Figure  11 : A map of a part of value space under the assumption that extant values occupy a relatively compact part of value space. mere result of the way that different ideas were packaged together historically. If things had gone slightly differently, as they doubtlessly do in other parts of the multiverse, the authors of the Bible may have written that it is mandatory to fast during the month of Ramadan, thus filling a spot in value space with life that is only sparsely inhabited on Earth. If the multiverse is large enough, all these possible variations of values are realized somewhere and probably no less common than the two religion clusters on Earth. One last difference between the way we extract values from other superrational cooperators and the way AIs might receive their values from humans is, of course, that the former involves no direct contact. Section 3.4 will address ways of circumventing this problem in order to identify the values of agents elsewhere in the multiverse. \n The ability to help others In some cases, it will not be in our power to help other value systems at all. Since any will to cooperate with these agents cannot possibly be action-guiding, we do not have to help them. Other agents in the universe may have other resources available to them and thus choose to behave in a friendly way toward these values. If, on the other hand, agents know that nobody else can help them to achieve their goals, multiverse-wide superrational cooperation (in particular, any version of it in which they just give resources away) becomes less attractive to them. One example of a value system that we cannot help is the following version of speciesism (that may or may not be a straw man): The Namuh-centrists. One day, scientists inform you about a highly intelligent species of extraterrestrials known as \"Namuhs\". Like us, the Namuhs have built a flourishing civilization with art, trade, science, language, humor, philosophy (including advanced decision theory research), and so on. However, the Namuhs do not live in our universe, but in a distant part of the multiverse, completely inaccessible to us. In fact, they could not even exist in our part of the multiverse, as their bodies require slightly different laws of physics to function. Knowing about superrational cooperation, you hasten to ask whether they have thought about problems analogous to Newcomb's problem and the donation games between similar agents. A trustworthy scientist explains that their minds are indeed prone to thinking about such topics -much more so than those of humans, in fact! Understandably thrilled, you ask what values the Namuhs have, and specifically what values are held by those who have thought about acausal cooperation. The scientist then informs you that all Namuhs are very narrowly focused on their own species. They are Namuh-centrists who do not care one bit about anything that does not involve fellow Namuhs. For example, they shrug at the thought of non-Namuh suffering, the flourishing of non-Namuh civilizations, or non-Namuh well-being. In fact, they are so strict that they do not even care about simulated Namuhs or other approximations. Learning about their values, you may be disappointed. There is nothing that you can do to help them and it is therefore irrelevant whether they use a decision theory similar to yours or not. I should point out that the speciesism endorsed by the imaginary Namuhs is very rigid and more narrow than most other views that we would usually classify as speciesist. Far from caring only about their own species, most people seem to care about the welfare of non-human animals to at least some degree, usually privileging some species (like cats and dogs) over others (like pigs and cows). Such views classify as speciesist, but nevertheless allow for superrational cooperation. Other views do not value humans over other animals for their species membership per se, but instead privilege other characteristics that (allegedly) only humans (and sometimes a few other species) possess. A common variant of this holds 39 that only members of very few species are conscious. Humans are one of them, but, according to such views, they otherwise do not deserve any special moral status. Given the implications of this view, proponents are sometimes (and often incorrectly) branded as speciesist. If the Namuhs were to hold such a view, and humans (or other earthly species) meet their criteria for consciousness, then our decisions can be beneficial or detrimental to the Namuhs' preference fulfillment. A similar reasoning applies to the possession of language, free will, the ability to pass the mirror test or other (potentially) strict but non-speciesist restrictions to one's set of morally relevant agents. There are other reasons why we might be (practically) unable to help other agents. For example, helping an agent could require some set of specialized abilities that they themselves developed based on their value systems. Consider the following example: The Advanced math maximizers. One day, you learn that out there in the multiverse, there are civilizations made up entirely of mathematicians whose primary concern is maximizing mathematical knowledge. They don't care about the number of established truths or proofs per se, but rather value pieces of knowledge based on their novelty or interestingness, possibly resembling the way earthly mathematicians often prioritize their research. For instance, the mathematicians place a very high value on a proof or disproof of the Riemann hypothesis, whereas mundane factoids like the three-billionth digit of π have very little value in comparison. Moreover, once a fact becomes known to at least one of the mathematicians, reproducing that same piece of information elsewhere in the multiverse creates no additional value for them. (We assume that the universe is finite -otherwise every piece of knowledge may be known to some Boltzmann brain.) While they are not particularly skilled at anything else, their strong intrinsic motivation and dedication has made them into truly excellent mathematicians, unrivalled by anyone across the multiverse. It is not easy to benefit the advanced math maximizers. We do not know what knowledge they already possess, and given their level of skill, we should assume that they will come up with most interesting pieces of mathematical knowledge that we could devise on our own. The math maximizers are thus so capable of maximizing their own utility function that there is little we could do to assist them (cf. section 3.2.5). \n Zero-sum and \"below-zero-sum\" tradeoffs on resources Not all interactions between agents allow for cooperation. Specifically, there is no way or reason to cooperate in zero-sum games, i. e. ones in which the overall payoff is always the same. Consider the following example: The Maximizer Monarchs. Imagine a multiverse consisting of two universes. One is ruled by a queen whose only drive it is to create as many paperclips as possible. The other universe is ruled by a king who only cares about producing as many staples as possible. Each stationery-maximizing monarch knows that the other exists and that they both use the same decision algorithms. They each have one hundred tons of steel at their disposal. What should they do with it? Assuming that staples (specifically the kind of staples that the queen cares about) cannot be built out of paperclips or vice versa, this interaction is zero-sum. Every bit of material that one of them uses for the benefit of the other is an equivalent loss to themselves 40 . Thus, no form of cooperation between the two is beneficial. As the reader may suspect, zero-sum interactions are rare. We should expect that any given resource is better suited to achieving one goal than another and so trade can arise from allocating resources based on what value systems benefit most from them. Analogously, value systems care more about certain situations than others. Furthermore, whereas it may not be possible to combine a paperclip and a staple, many goals are compatible with each other. For example, a society's citizens can at the same time be happy and virtuous. \n Gains through specialization and comparative advantages At times, trying to achieve multiple goals at once is not just pointless -it can actually be worse than having each agent focus on one, typically their own, goal. To see how, let us revisit The Maximizer Monarchs of the previous section: The Ever-improving Maximizer Monarchs. Like The Maximizer Monarchs, but this time, the efficiency at which each agent can produce paperclips or staples grows monotonically with the produced quantity. Again, each monarch wields one hundred tons of steel. Without delving into mathematical details, it is best (in terms of overall number of paperclips/staples produced) if each of the two specializes in one kind of stationery. In particular, there are no gains from compromise over each monarch maximizing only for their own goals. There may also be comparative advantages from the outset. Based on their respective motivation and prior experience, the queen may already excel at producing paperclips, while the king may be better at producing staples. Another important source of comparative advantages is unequal knowledge about different value systems. For example, if the queen does not know exactly what the king cares about, then she will be worse at benefitting him. Similarly, our knowledge of what other humans care about is much more precise than our knowledge of what agents elsewhere in the multiverse care about. The fact that specialization and division of labor play such a crucial role in the economy suggests that superrationalists will also tend to focus on a single goal rather than maximizing for multiple things at once. However, I think that this will not be the case, at least in our present situation. The primary reason is that the instrumental goals of agents with different moral values are often the same. For example, no matter the direction into which we would like to drive society, we will try to acquire money and political influence. These resources are often generic, such that when they are acquired with one goal in mind, they can also be employed in pursuit of another. As an example, consider how Donald Trump maximized his personal wealth for a long time, yet his resulting fame and money nevertheless enabled him to become president of the US, which in turn allows him to achieve all kinds of goals. The fact that instrumental goals tend to converge suggests that superrationalists in the multiverse rarely have a strong comparative advantage at achieving their own goals. If comparative advantages are not strongly aligned with goals, specialization can produce gains as well. For example, imagine a number of superrational agents, each of whom would like to maximize many different things separately, e. g., knowledge, fun, happiness and technology. Here, a no-compromise outcome -i. e. one wherein each agent only maximizes their utility function in their own universe -might be worse than a potential division of labor with one agent focusing on generating knowledge, another one focusing on fun, and so forth. \n What values? To help other agents, one at some point needs to have some workable model of their preferences. In general, it is difficult to extract preferences from a given agent if the agent is not von Neumann-Morgenstern (vNM) rational and cannot state her goal explicitly. Humans surely are not vNM-rational. Additionally, moral judgments are usually seen as being inaccessible to us in their complete form (see footnote 25) and as emerging from the whole brain rather than exclusively from, say, the anterior cingulate cortex. This makes sense from an evolutionary point of view. Preferences are tools for increasing the fitness of an organism, and there is no reason to assume that such tools would be any more open to scrutiny by the organism than, say, the detailed inner workings of the digestive system. In addition, while most organisms have rudimentary mechanisms for avoiding harm and seeking food and reproduction, holding grudges -i. e. a preference for retaliation -is only adaptive in non-solitary organisms with sufficiently good memory and recognition to correctly identify transgressors. In the evolutionary process, different values thus evolve separately and are unlikely to form a coherent whole (cf.  Dennett, 1991; Kurzban, 2012) . Thus, even if we had a complete model of our superrational collaborators, it would nevertheless be difficult to extract clear-cut values from them. In the absence of such exact models, it makes little sense to for us to discuss the technical details of relevant preference extraction algorithms 41 . We will, however, still need to think about informal ways of inferring preferences from a model of a superrational collaborator. \n Idealization One dimension along which preference extraction algorithms vary is the extent to which they idealize values. Consider the following example of preference idealization (adapted from a recent blog post of mine): Steve holds a glass of transparent liquid in his hand. A woman walks by, says that she is very thirsty and that she would like to drink from Steve's glass. What she does not know, however, is that the water in the glass is (for some unspecified reason) poisoned. Should Steve allow her to drink? Most people would say he should not. While she does want to drink from the glass, her desire would probably disappear upon learning of its content. Therefore, one might say that her object-level or stated preference is to drink from the glass, while her idealized preference would be not to drink from it. Similar questions apply to ethical preferences. For example, most people find meat consumption acceptable on the object-level, but are simply unaware of information about the world that could change their minds, e. g., knowledge about the similarities between human and animal minds or the conditions in factory farms and slaughterhouses. Perhaps these people's idealized preferences favor vegetarianism? If we reduce meat consumption, should we count it as beneficial to people who approve of eating meat, but who could be convinced otherwise? Should we, in other words, idealize our collaborators' values when taking them into account in this universe? Besides gaining more information about the world, people's preferences may also change upon engaging with moral arguments (e. g., the original position or the drowning child argument). Even though such arguments do not provide new facts, they may invoke trains of thought that lead people to change their moral position. Should we also idealize preferences based on such moral arguments? At least idealization based on moral argument can cause trouble. For one, some moral arguments can be viewed as potentially illegitimate \"tricks\" for persuading people to adopt undesired positions 42 . An extreme example of this could be some moral or religious scripture that hypnotizes and brainwashes the reader. Surely, nobody would want other superrational collaborators to apply such a treacherous \"idealization procedure\". 41 Examples are described in Hansson and Grüne-Yanoff (2012),  Varian (2006) ,  Neumann and Morgenstern (1953) ,  Ng and Russel (2000) , and  Oesterheld (2016) . Also consider Brian Tomasik's How to Interpret a Physical System as a Mind. 42 One class of such tricks is described in my blog post Cheating at thought experiments. Order effects constitute another problem in using moral arguments to idealize preferences. Depending on the order in which we present someone with moral arguments, they may lock into a position and resist further arguments. If someone's moral views allow for more than one such lock-in they may not be uniquely idealizable. A recent study by  Schwitzgebel and Cushman (2012)  shows that even philosophers exhibit order effects when considering thought experiments. In general, we may view agents as having (meta-)preferences regarding idealization. These determine how exactly they would like to have their values idealized. We should then abide by respective agent's preferences, since we can then expect others to idealize our values in the way that we want them to be idealized. Unfortunately, this solves the problem only theoretically. In practice, finding out what idealization procedures other superrationalists would approve seems very difficult. 43 For more thoughts on preference idealization, the reader may consult any of the following:  Yudkowsky (2004) ;  Grill (2015) ;  Muehlhauser and Helm (2012) , chapter 6; the Negative Utilitarianism FAQ, especially section 2.1; section 15 of Brian Tomasik's Hedonistic vs. Preference Utilitarianism; and my blog post entitled Is it a bias or just a preference? An interesting issue in preference idealization, in which I discuss the specific issue of removing cognitive biases from preferences. 44 \n Beware motivated idealization One potential pitfall of idealizing another agent's values is that it might bias the result toward one's own moral views if one is not careful. After all, you will be more familiar with the arguments and thought processes that favor your own position, and they will seem more convincing to you than the arguments you know in favor of other positions (if you knew of similarly strong arguments in favor of other positions, there is a good chance you would have adopted them already). Such a process of legitimizing what we already want to do via superrationality-based reasoning could be nicknamed \"superrationalizing\". For instance, I might be tempted to think that supporters of deep ecology and (non-anthropocentric) environmentalism would, if they were rational, update their views significantly upon learning about Darwinian evolution and wild animal suffering. I may even presume that deep ecologists would support intervention in nature or even habitat destruction under idealization! While I do indeed think that many people's judgment of nature and preservation would change significantly upon understanding the above topics 45 , I am worried about what such an aggressive stance on idealization tells me about the way other agents might go about idealizing values. For instance, when idealizing my values, environmentalists might reason that I just never thought enough about the beauty of nature. \"If only this Caspar guy had taken the time to really contemplate the natural world in all its magnificent complexity, he would not think of nature as a tragedy, no matter how 'red in tooth and claw' it may be.\" Consequently, they might conclude that it is in my idealized interest if they lobby for leaving nature untouched or even spread it to other planets. I would not want others to idealize my values in such a way. While it may be true that a sufficient amount of time spent enjoying beautiful landscapes could convince me that nature is beautiful, I might not view that as a legitimate idealization procedure, as it merely reinforces conservationist arguments rather than offering new arguments or some form of balanced view. An example of a more obviously flawed extrapolation process is that of a mother reasoning that everyone's idealized values would be to prefer her son over all other children. After all, if they only spent enough time with him (just as she did), they would surely prioritize his well-being over that of other children! Once again, the respective idealization process seems unduly biased towards a certain position and will thus be rejected by most agents' meta-preferences. \n Values and distance People care about things differently depending on whether they happen nearby or far away in space and time. For example, while many liberals and quite a few conservatives politically favor legalizing cannabis, I expect that many of them would nevertheless feel mildly annoyed or uncomfortable if their best friend, spouse, or daughter were to start smoking it on a regular basis. For brevity, I will use the term near values for the part of our values that are about near things and far values for the part that is concerned with distant things. Both in the ancestral environment and today, most people operate primarily on their near values (with one notable exception being politics). In the context of superrationality, however, we are only interested in far values. Most other superrationalists are so far away from us that our values pertaining to their worlds fall under our far values. Hence, we want ETs to consider only our far values, which in turn means we should only consider the ETs' far values as well. That is, we do not need to know how they want their friends to treat each other, how they feel about drug use in their own social circles, and so forth. (Some think that the discrepancy between near and far values should disappear under idealization; we will discuss this below.) According to construal level theory, the difference between near and far values mainly results from the difference between two kinds of thinking or construal: concrete (or low) and abstract (or high) levels of construal. Which level of construal is applied mainly depends on the psychological distance to an event, i. e. the combined temporal, spatial, social and \"hypothetical\" (near = likely, far = unlikely) distance. People tend to construe psychologically near events concretely and psychologically far events abstractly. A recent summary of construal level theory is given by  Trope and Liberman (2010a) . The mapping between levels of construal and psychological distance is imperfect. We sometimes think about psychologically distant things concretely, such as when watching a science-fiction movie, and about psychologically near things abstractly. Nevertheless, the mapping is useful. While there is little theoretical and empirical research on how people (and other evolved creatures of human-level intelligence) think and care about alien civilizations, there is some research on how people generally care about other psychologically distant and abstractly construed things. According to construal level theory, the abstract mode of thinking is similar regardless of the kind of psychological distance that is involved. Thus, we can use general research about abstract construal values to at least inform our first tentative guesses about values in the particular case of caring about distant civilizations. We have some reasons to expect construal level theory to generalize to other evolved beings. According to Trope and Liberman (2010a, section III, subsection \"Discussion\"), High-level construals and low-level construals serve different cognitive functions. High-level construals have evolved to represent distal objects because, with distance, one needs to conserve the essential, invariant properties of the referent object. In contrast, low-level construals preserve the object in minute detail for immediate use. The fact that abstract and concrete construals solve different problems suggests that they evolved separately. Indeed, low-level construals probably evolved earlier. Whereas processing one's immediate surroundings and short-term goals is necessary for any animal to survive, many can get by without processing psychologically distant things. Some of the feats achieved by civilization-forming species, on the other hand, require abstract thinking. In the conclusion of their paper, Trope and Liberman (2010a) write: The turning points of human evolution include developing tools, which required planning for the future; making function-specific tools, which required considering hypothetical alternatives; developing consciousness, which enabled the recognition of distance and perspective taking; developing language, which enabled forming larger and more complex social groups and relations; and domestication of animals and plants, which required an extended temporal perspective  (Flinn, Geary, and Ward, 2005) . Human history is associated with expanding horizons: traversing greater spatial distances (e. g., discovering new continents, space travel), forming larger social groups (families vs. cities vs. states vs. global institutions), planning and investing in the more distant future, and reaching farther back into the past. In sum, I see some good reasons to expect that construal level theory applies to many other evolved species of human-level intelligence.  46  It thus matters whether we optimize for others' near or far values. Interestingly, we may also see the difference between different construals and thus near and far values as a cognitive bias that would disappear upon reflection, and that we should correct for in preference idealization. This may well be the case, but it is unclear which of the two views is more \"correct\" about ethics. One may argue that only thinking about concrete events can yield actual moral judgments, while abstract thinking may result in imagining a situation inaccurately or not at all and thus being unable to assess it correctly. Moreover, we tend to have weaker attitudes in general toward distant things than towards close things, 47 and this also seems to apply to moral weight assignment. 48 46 The presented argument resembles the general argument for modularity in evolutionary psychology (see, e. g.,  Cosmides and Tooby, 1994) .  47  For example, people prefer to receive money immediately rather than in the far future. They are risk averse and, of course, care more about socially close individuals. 48 For example, thinking about a concrete, identifiable goal or benefactee seems to be associated with feeling happier from donating money  (Rudd, Aaker, and Norton, 2014) . People are more motivated by (concrete) identifiable victims than by (abstract) large numbers of victims, although a recent meta-study by S.  Lee and Feeley (2016)  shows the effect to be small. People are also more relativist when judging the acts of extraterrestrials and people from other cultures  (Sarkissian et al., 2011) . Some arguments in moral philosophy evoke concrete construals (e. g., the fat man trolley problem or the drowning child argument) and some evoke abstract construals (e. g., the original position or many of the examples from my blog post Cheating at thought experiments)  49  . Both classes contain arguments that I find useful and legitimate. This suggests that neither of the two is morally superior across the board. Trope and Liberman (2010a, section VI) describe several experiments wherein high-level construals seem to capture the participants' values, whereas low construals led people to give more weight to \"local\" circumstances (such as social pressure and lack of self-control) (cf. Trope and Liberman, 2010a, section VII, subsection \"Affect\"). In high levels of construal, people tend to judge consequences more by their desirability than their feasibility, and thus assign more weight to moral views. More recent studies like those of  Torelli and Kaikati (2009)  and  Agerström and Björklund (2013)  have corroborated this result. However, it could also be interpreted as an indication that abstract thinking makes people more hypocritical.  Yang, Preston, and Hernandez (2013)  summarize further evidence in favor of giving more weight to high-construal judgments: High-level construal is associated with [...] an analytical, critical-thinking mindset  (Torelli and Kaikati, 2009) . For example, people at a high level of construal are [...] more comfortable with messages that convey mixed emotions  (Hong and A. Y. Lee, 2010) , suggesting greater cognitive flexibility. Indeed, previous literature showed that when an object is distanced from the self, individuals are less likely to be \"trapped\" in their own preconception or knee-jerk reactions  (Kross and Grossmann, 2012) . Moreover, high levels of construal may enhance perspective taking toward others whose interests conflict with one's own. That said, abstract thinking is not without its systematic failure modes. It is, for instance, associated with overconfidence and the illusion of explanatory depth  (Alter, Oppenheimer, and Zemla, 2010) . Further thoughts on the topic are given by Samuel Hammond in How to Conceptualize Morality: Near vs Far. In any case, we should keep in mind that idealizing away the difference between near and far values may be inconsistent with many agents' meta-preferences. \n Different kinds of preferences People often report that preferences in different domains feel qualitatively different from one another. For instance, it is common to distinguish moral preferences from other preferences. My preference for world peace over war is a moral one, for instance, but my preference for bananas over carrots is not. Of course, this line between moral and non-moral values is often blurry. For example, it is unclear whether wanting revenge or a cancer victim's desire to focus altruistic efforts on cancer research are moral preferences. I think a distinction between moral and non-moral preferences can also be drawn among far values. For example, my preferences for beings in other parts of the multiverse to be happy rather than to suffer is a moral one, but I would not view my preference for these civilizations to be fascinating, fun, or otherwise beautiful to my eyes (in the way that advanced civilizations in science fiction movies are) as a moral preference. Others might disagree, but that dispute is not worth exploring in this paper (indeed, I suspect it may be a largely verbal one). Potential criteria for this distinction between moral and other preferences may be that moral preferences are those we want others to share or that are somehow universal. Another distinction could be one based on a dual-process theory of morality (see Greene 2013, part II for an overview and references to the literature). Or consider  Sarma and Hay (2016) , who propose that \"what we call human values can be decomposed into 1) mammalian values, 2) human cognition, and 3) several millennia of human social and cultural evolution.\" I do not think such distinctions are necessary when cooperating superrationally. Instead, we should focus on all preferences that are action-guiding to the respective agent (if this is not included in the term \"preference\" anyway 50 ), irrespective of whether they are \"moral\" or \"mammalian\". By definition, if I have to decide between two courses of action and one of them better suits the preferences that guide my actions, I will choose that one. In the case of superrationality, only accounting for other agents' action-guiding preferences correlates with others also taking only my action-guiding preferences into account. Therefore, taking all action-guiding preferences into account is best according to my action-guiding preferences. Hence, we should only take steps to fulfill the action-guiding preferences of other superrational collaborators, ignoring any other preferences they might hold. Given the above, I shall in this piece not differentiate between moral and other far values. Instead, both terms will be used to signify our action-guiding far values. \n The values of our superrational collaborators in the multiverse Having outlined what kinds of values we would like to know about for multiverse-wide superrational cooperation (MSR), we can finally proceed to discuss these values. Whereas it is not strictly necessary for us to know about our cooperators' values right away in order to benefit them (see section 4.1), such knowledge is surely useful and has to be attained at some point. In fact, one objection to MSR that many people have brought up in private conversation is that given our uncertainty about other value systems in the multiverse we should focus solely on our own values (also see section 6.11). As readers may suspect, a comprehensive discussion of this topic is beyond the scope of the present paper. However, we will give an overview of how we (or future superrationalists) can gain knowledge about the values of our collaborators elsewhere in the multiverse. Besides guiding future research, this overview will also demonstrate that we can learn anything about their values in the first place. 50 Many definitions of preferences are based on choice (see footnote 41). Some examples where preferences may not be what our choices reveal include: • akrasia and lack of willpower, as it manifests itself in procrastination and inability to adhere to exercise routines and healthy diets; • preferences about fiction, as people often care deeply about how a story ends but usually without trying to lobby or coerce the authors to satisfy that desire  (Radford and Weston, 1975; Schneider, n.d.) ; and • preferences for states of affairs that are mathematically inconsistent or physically impossible (Oesterherld, 2017b). It seems as though there are two main ways of assessing the values of other agents in the multiverse. The first involves empirical research into the values of superrational cooperators on Earth. Because the sample size is so small, we may also look at humans in general, under the assumption that the values of superrationalists resemble the values of their native civilization. It may be that the values of superrationalists differ from those of other agents in systematic and predictable ways. General human values may thus yield some useful insights about the values of superrationalists. That said, it may be that only a small fraction of superrationalists in the multiverse are human-like. For example, it could be that most other superrationalists are artificial intelligences and whole-brain emulations. It could also be that many other evolved agents are very different from us. The other approach involves understanding the processes that generate and select the values of agents in the multiverse, such as biological and cultural evolution, the transition to superintelligent AIs, etc., and extrapolating them into workable predictions about the preferences of agents on other planets. In principle, this approach is sufficient for gathering a good map of the values of civilizations throughout the multiverse. In practice, however, it is probably very difficult to accurately predict how these processes play out. A combination of both approaches might be easier to work with. We can begin with human values as a baseline and inspiration for what kinds of moral attitudes may exist, and then review whether the processes of biological and cultural evolution systematically favor these attitudes. This would enable us to find out whether they are coincidental and hence rare in the multiverse, or necessary and thus common. At the same time, we will of course need to avoid being biased toward human values, making sure not to drift off into telling just-so stories about why some human practices and values might be universal among evolved agents of human intelligence  (Buss, 2015 , chapter 2, section \"Methods for Testing Evolutionary Hypotheses\"). Theoretically, we or future superrationalists need to find some way of coming up with new moral values, i. e. ones that we do not observe on Earth. Based on a model of the values of evolved agents we can then think about the values of these agents' descendants (whole brain emulations, superintelligent AIs). Assessing the action-guiding, consequentialist far values of agents in the multiverse could be a scientific (sub-)discipline in its own right. That being said, I do not expect there to be a \"Journal on Extraterrestrial Value Systems\" to materialize anytime soon. Untestable speculation about ETs does not inspire academic respectability. In researching this paper, I did not find much prior work on any aspect of the values of evolved agents in the multiverse, which in turn makes me less than hopeful that the more specific issues pertaining to multiversewide superrational compromise will be picked up by other researchers out of curiosity. Hence, superrationalists will probably need to think about ET values themselves. \n On the far values of humans and human superrational cooperators We will now explore what superrational humans might care about in distant civilizations. Unfortunately, our sample of these people is small, and path dependencies may imply that current earthly superrationalists may not be very representative of those elsewhere in the multiverse. We will, therefore, also look at general human values and far values in particular. \n Organizing human values Although most people have reliable intuitions for what other people care about, these intuitions are hard to pin down, owing to the inherent \"messiness\" of human moral intuitions (cf.  Stewart-Williams (2015) , section \"Morality Is a Mess\";  Muehlhauser and Helm, 2012, chapters 3-5.3) . This \"messiness\" makes evolutionary sense  (Cosmides and Tooby, 1994 ) and should therefore be expected from other civilizations in the multiverse as well.   2012 )), as well as those of  Shweder et al. (1997)  (also see Pinker (2011, chapter 9.4) for a short, accessible summary). There is also Peter Levine's Alternative to Moral Foundations Theory, which is not formally published. There are also some characterizations of the cultural and moral differences among humans. For example, Inglehart and Welzel divide moral values into just two factors: traditional versus secular-rational values, and survival versus self-expression values (2010, note 10). Hofstede recognizes six cultural dimensions, and Trompenaars' model of national culture differences has seven dimensions of varying moral relevance. \n Human far values We have seen that far values are the parts of our preferences that are relevant to MSR (see section 3.3.2). There are almost no studies on how humans care about alien civilizations. However, construal level theory suggests that we think and thus care similarly about different psychologically distant things. This brings us to the question, how do people usually care about psychologically distant or abstractly construed things? In contrast to their concrete counterpart, values at abstract construal levels tend to focus more on the central (as opposed to peripheral) features of a given situation (see  Trope and Liberman (2010b) , esp. section V). Values in abstract construal levels are therefore less fragile (see section 3.2.3), which is good news for us, as this inherent stability makes them easier to account for in our superrational cooperation. But what are those central features? A few studies have been conducted to find out, most notably one by  Bain, Hornsey, Bongiorno, Kashima, et al. (2013) . The authors summarize the results in a blog post: In our research, we asked people to think about the effects that changes in society today would have on society in the future (the Year 2050). For instance, we asked people to consider what society would be like 50 years in the future if climate change was mitigated, marijuana was legalized, abortion laws were relaxed, or the proportion of atheists or Muslims in society increased substantially. Participants considered changes in society relating to people's characteristics (how caring, moral, and competent people would be in 2050), whether people's values would change (e. g., becoming more concerned with security or achievement), whether there would be more societal problems (like crime and poverty), or greater societal development (economically, technologically, and socially). The different contexts produced diverse and nuanced images of what future society would be like. For example, participants saw a more atheist future society as making people less friendly but more competent than today, but saw a future society where marijuana was legalized as both less friendly and less competent. Overall, people's images of future society weren't all good or all bad, suggesting they had realistic rather than fantastical projections about what society would be like in the future. What may be most surprising, however, is that only one dimension emerged as a reliable motivator of people's actions in the present. People supported changes in policies today (e. g., legalizing marijuana, acting on climate change) if they believed it would lead to a future society where people were more caring and moral. Other dimensions -people's values, their competence, or levels of societal problems and societal development -emerged less strongly, only in a few contexts, or were irrelevant to people's willingness to act. Similar findings were made by  Bain, Hornsey, Bongiorno, and Jeffries (2012) ,  Park, Bain, and Kusumi (2015) ,  Judge and Wilson (2015)  and  Bain, Milfont, et al. (2015)  in other policy areas. These results are quite surprising -I know of no explicit discussion of \"virtue consequentialism\" in moral philosophy, for instance. Unless we think that superrationalists consistently hold different values, that humans are atypical or that these findings are somehow invalid, the findings suggest that the application of MSR implies significant policy changes for people espousing more commonly discussed consequentialist value systems like utilitarianism. Unfortunately, the above studies have some limitations. For example,  Bain et al. (2013)  do not ask for a utilitarian evaluation -i. e. one based on overall (average or total) welfare (or preference fulfillment) -of the future societies. Perhaps participants only put much weight on future citizens being caring and moral because these are proxies for other moral issues (such as welfare)? Besides methodological issues with the study itself, the results may not transfer to MSR without complications. In any case, social psychology studies often fail to replicate or generalize as expected. Construal level theory notwithstanding, it could be that people's views on alien civilizations differ from those on \"collective futures\". These results should thus be seen as tentative and preliminary until further replications come in; for now, we can regard them as serving an illustrative, rather than action-guiding, purpose. Moreover, benevolence -the term used by Bain et al. to encompass the characteristics caring, moral, and competent in their 2013 study -is still a rather fuzzy concept that probably depends on people's general moral views. It seems likely, for instance, that the definition of benevolence in a given situation varies considerably between, say, a devout Jain and a devout Salafist Muslim. In future research we should therefore look more into what kind of benevolence or moral behavior people value. For example, Napier and Luguri found that abstract mind-sets decrease preferences for loyalty, authority, and purity, all of which lie on the conservative and tribe-specific end of the moral spectrum (cf.  Luguri and Napier, 2013) . \n The values of human superrational cooperators We should also investigate how the values of today's superrational cooperators differ from those of other humans. Unfortunately, while I suspect that the results would be both interesting and informative, the number of people who actively reason superrationally today is too small to yield a statistically representative sample. We will therefore focus on who, for various reasons, are likely to embrace most (if not all) of the arguments underlying superrational cooperation. Of course, all of this again only gives us very weak evidence about the content of the compromise utility function. For one, it does not tell us much about civilizations that are very different from humanity. Moreover, the values of earthly superrationalists may in great part be the result of path dependencies. Thus, they may differ even from the values of superrationalists in civilizations that are very similar to humanity. Despite these considerations, I think that this most direct empirical approach to ascertaining the content of the compromise utility function is worth investigating. \n Philosophers Given that the central theme of this paper rests to a large degree upon philosophical considerations that are unlikely to be well-known outside of analytic philosophy, it seems reasonable to begin our review with analytical philosophers. While many philosophers seem to accept causal decision theory (see section 2.2), they are nevertheless far more likely to be aware of such ideas at all. 52 Furthermore, we can use  Bourget and Chalmers' (2014)  survey of philosophers to look at correlates of making the non-causal choice in Newcomb's problem. Most decision theorists see Newcomb's problem as analogous to the question of whether to cooperate superrationally in the prisoner's dilemma with a strongly correlated opponent  (Lewis, 1979) . The correlations, taken from the survey website, are inconclusive. Apparently, one-boxing in Newcomb's problem correlates very weakly with non-physicalist views in philosophy of mind (0.139), and only slightly stronger with viewing one's own work as Wittgensteinian (0.15). Two-boxing, meanwhile, has similarly weak correlations with endorsing the B-theory of time (0.141), embracing classical rather than non-classical logic (0.136), not being a communitarian (0.128), atheism (0.125), scientific realism (0.121), seeing one's work as , and with externalism in moral motivation (0.102).  53  Correlations between choices in Newcomb's and the trolley problem were too weak to warrant 52 That said, philosophers often do not act on their self-reported views  (Schwitzgebel and Rust, 2011) . For example, while philosophers (and ethicists in particular) are much more likely to rate eating meat as morally reprehensible, differences in behavior (i. e., actual meat consumption) are, at best, meager. 53 Interestingly, two-boxing is not only mainstream among philosophers in general (see section 2.2), but also slightly more common among philosophers with whom I (and most acausal decision theorists I know) would otherwise agree more. For more discussion of this phenomenon from the perspective of a one-boxer, see Carl Shulman's Why do theists, undergrads, and Less Wrongers favor one-boxing on Newcomb? and its comments. any mention 54 . These results do not appear to offer much insight into what value systems should be taken into account for superrational compromise. So, if anything, we could look into the values of philosophers in general. \n Effective altruists Let us turn to another community, in which taking action based on philosophical arguments is common: the effective altruist and rationalist spheres. Specifically, we will look at the effective altruist, LessWrong, and Slate Star Codex communities. A multitude of surveys of these demographics are available.  55  Within the LessWrong community, one-boxing in Newcomb's problem is about ten times more common than two-boxing, as evidenced by their 2012 and 2013 member surveys.  56  The 2009 survey also revealed that most LessWrong users would cooperate in one-shot prisoner's dilemmas against one another. Acausal reasoning thus appears quite common in this community. In fact, updateless and timeless decision theory (see 2.2) arose from discussions on LessWrong. The surveys also show that many members of the community identify as consequentialists (see below). Indeed, effective altruism is itself built upon a foundation of consequentialist arguments, although it is consistent with additional deontological restrictions. The community's general world view is entangled with both their consequentialist and decision-theoretical views, 57 as well as a general curiosity for discussing ethics and decision theory in the first place 58 . Hence, we may regard their views as indicative (if only weakly) of those of other superrational consequentialists in the multiverse. Even the existing surveys reveal some interesting facts about the values held by community members. For instance, they are overwhelmingly liberal, with only a few percent selfidentifying as conservative. Furthermore, they show a significantly greater concern for animals than the average person in Western industrialized countries. \n Considering larger and smaller groups 54 Unfortunately, at the time of writing, the site that is supposed to show all (as opposed to only the strongest) correlations between Newcomb's problem and other questions appears to be broken. 55 General surveys on LessWrong were made in  2009, 2011, 2012, 2013, 2014 and 2016.  There is a Slate Star Codex Survey survey from 2014, which only asked non-LW users to participate. Surveys of the EA community were done in 2014 and 2015.  56  The results (as of December 2016) of another LessWrong poll confirm that most community members strongly favor one-boxing. 57 For example, they view rationality and consequently decision theory and other sciences as being, in the end, about winning, in line of the instrumental and epistemic conceptions about rationality, rather than about acting or thinking in accordance with some reasons and requirements. Another example of a connection is that Eliezer Yudkowsky, the founder of LessWrong, has dedicated his life to making sure that artificial intelligence has a positive impact and convinced many in the community that this is a worthy goal. It also seems to me that the context of (superintelligent) machines can function as an intuition pump for consequentialism. 58 Decision theory and a goal system are two important ingredients to solve that problem of AI alignment (see the preceding footnote) (Soares and Fallenstein, 2015; Bostrom, 2014b, chapter 13, section \"Component list\"). Furthermore, effective altruism, i. e. systematically trying to do as much good as possible, requires that one knows what is good at least in some detail. For example, metrics like the quality-adjusted life year or the disability-adjusted life year may be used to evaluate intervention against poverty. (See GiveWell's articles on the topic.) Effective altruism presumably also inspires learning about rationality. We could also try to survey the values of much smaller sets of people, like those who have argued against causal decision theory (e. g., in academic papers) or indicate that they take the implications of non-causal decision theories seriously. Conversely, we can also study the values of much broader sets of people to make use of the academic literature. For example, we can reasonably assume that in order to discover superrationality, one would need a general philosophical mindset (rather than, say, a merely pragmatic one) and a willingness to engage in thought experiments that have no immediate practical relevance. We could then try to identify groups of people who meet these criteria, and to discover what values their members have in common. While we should also help superrationalists who do not believe they live in a multiverse (see section 2.9), we should nevertheless expect superrationality to be more widely accepted among people who do believe in a multiverse. After all, superrationality is probably far less action-guiding on its own than in combination with the multiverse hypothesis (see section 6.6), so it is comparatively unlikely to spread by itself. Thus, we could also survey the values of people who believe in the multiverse hypothesis. Similarly, we could study people who accept similarity to and correlation with others (as opposed to thinking that they are unique in the entire multiverse). Interestingly, such people may be likely to be conservative  (Stern, West, and Schmitt, 2014) . On the other hand, it may be that our currently available sample of superrationalists are atypical simply because the topic of MSR is still in its infancy here on Earth. If superrationality eventually becomes more popular on Earth and elsewhere in the multiverse, we may find that only the relatively few early adopters of the idea differ significantly from the human mainstream. Presumably, this is common in many areas of progress (cf. Rogers, 2010, chapter 7). For example, the average computer user in 1970 was very different from the general population at the time, since operating a computer back then required a particular set of technical skills that most people did neither possess nor have the time to learn. But once these early adopters improved the technology and convinced others to buy computers, they were soon outnumbered by people who would never have worked with the older computers, eventually culminating in today's ubiquitous use of computers. Thus, the average of the computer users of the past 50 years would probably resemble an average young person in a developed country. Analogously, early superrationalists may need to be more willing to study obscure thought experiments and look deliberately for crucial considerations. Soon, however, these early adopters may find themselves outnumbered by less explorative people who would have never thought about donation games between correlated agents on their own. While it is very unlikely that MSR will spread as widely as computers, the average superrationalist may nevertheless end up looking more similar to the average person than today's sample suggests. \n Biological evolution According to conventional views of the multiverse and its physical laws, almost all 59 of its inhabitants are evolved agents or descendants of evolved agents. This means we can use our knowledge of evolution and its workings to predict what values these other agents have. Since much has been written about evolution and the more relevant fields of evolutionary psychology and (descriptive) evolutionary ethics, we shall not discuss them in detail here. Readers may consult the works of Pinker (1999),  Stewart-Williams (2015) ,  Greene (2013) ,  Axelrod (2006) , and  Buss (2015)  for introductions. \n Cultural evolution A process similar to evolution takes place on the cultural level. Whereas biological evolution operates on genes, this cultural evolution determines the development of pieces of culture or memes such as \"tunes, ideas, catch-phrases, clothes fashions, ways of making pots or of building arches\"  (Dawkins, 1976, chapter 11) . 60 Again, this is not the place to review the literature on this topic. For an introduction to cultural evolution consider, e. g.,  Henrich (2015) . \n Which moral views correlate with superrationality? We can turn to the study of cultural evolution to learn about the prevalence of various consequentialist value systems. But whereas superrationalists probably resemble other intelligent agents biologically, they may well differ from them culturally. Thus, in addition to considering the civilizational baseline, we may also look into what values often go hand in hand with superrationality. Below are some preliminary examples of lines of reasoning that might be relevant in this context, some of which resemble the more empirically-minded comments in section 3.4.1: • Cooperation in general is more relevant for people with value systems that differ strongly from the mainstream in their civilization. • Some value systems benefit more from cooperation (and are harmed more by its breakdown) than others. Agents with these value systems are more interested in cooperation than others. • Superrationality is a \"weird\" philosophical idea. Therefore, it is more accessible to people who care about knowledge, are open-minded, philosophically rather than pragmatically inclined, and so forth. • Superrationality on its own is probably insignificant to most people's lives (see section 6.6). Hence, we should expect many superrationalists to only care about the idea because it comes packaged with multiverse theories. While this does not necessarily have implications for the other superrationalists' values, it does underline the point about a \"philosophical\" rather than \"pragmatic\" mindset. After all, thinking about all these other universes usually does not matter for our actions. • The significance of MSR is more apparent to people who think of goals as utility functions or the like, since this view makes it easier to to see that we can have preferences about distant parts of the multiverse. Once someone notices that many agents have preferences about each other's universes, she can see room for trade. If thinking about utility functions or similar formalisms indeed paves the way for MSR, we may also expect artificial intelligence researchers, game theorists, and some ethicists to be prominently represented among superrationalists in the multiverse. • The significance of MSR is more apparent if one realizes that it may imply radical compromise wherein everyone effectively changes their utility function. This, in turn, may be most apparent to people who are familiar with arguments like Rawls' original position  (Freeman, 2016)  or (preference) utilitarian reasoning along the lines of \"it would be best if everybody. . . \". • MSR may come more naturally to people whose values require coordination (see sections 2.8.3 and 2.8.9). Most of these considerations apply mainly to civilizations resembling our own. Of course, we can similarly think about correlates of superrationality in more advanced (or, in principle, more primitive) civilizations. Such thoughts are even more speculative, especially if we do not know what future civilizations might look like. In the next section (or rather, its companion papers) we will also consider cultural (and biological) evolution in specific models of more advanced civilizations. \n Other considerations Biological and cultural evolution are not the only processes that affect the distribution of moral views throughout the multiverse. In particular, I would like to draw attention to three other candidates. Given that the underlying considerations in these areas are advanced, speculative, and not strongly related to superrationality itself, I will not go into detail; rather, I will refer to complementary notes for further tentative ideas. • Some civilizations may inadvertently self-destruct before they can shape their part of the universe. Others, meanwhile, may voluntarily refrain from colonizing space. The Fermi paradox suggests that either of these are likely. The values of such civilizations should not receive the same weight as one would have believed before considering this argument. For more information see the complementary note Civilizational filters and distribution of values in the multiverse. • An important step in the development of humanity and potentially other advanced civilizations could be whole brain emulation, i. e. scanning a biological brain, uploading it into a computer, and then simulating its behavior to a level of detail that preserves the brain's functionality. Since, by assumption, they are functionally equivalent to human brains, whole brain emulations (ems) can do most of the things that humans can. However, they can also do many things that humans cannot. Because ems are software, they can be copied, their information processing can be sped up (by moving them to a faster computer or giving them more CPU time on their current one), and they can use the internet to travel much faster and cheaper than humans. These advantages may be sufficient to allow ems to become more numerous and more powerful than humans. They also imply predictable cultural changes, including an increased willingness to adopt non-causal decision theories. See the complementary note Values and acausal reasoning of whole brain emulations for more details. • Because evolved minds (whether uploaded or not) are not made to be maintained or improved, I expect that many long-lasting civilizations will eventually create artificial superintelligence. Because programming an AI to pursue one's goals might be difficult, the values of such an AI may differ from those of humans. For more information, see the complementary note Values and non-causal reasoning of superintelligent AIs. \n Interventions In this section, I propose a few interventions that multiverse-wide superrationalists should pursue. Many of these are tentative ideas to consider more in the future rather than confident suggestions for what we should do today. \n Cooperation in the face of uncertainty about values We begin with a general challenge: given that we currently know so little about the values of other agents in the multiverse, how can we cooperate with them? With our current state of knowledge, it appears impossible to conclude what position MSR recommends on particular issues. For example, it seems impractical to decide whether we should vote and lobby in favor or against mass surveillance, abortion, marijuana legalization or the death penalty. Perhaps MSR, while interesting in theory, is practically impossible to apply because of our ignorance of the values in the multiverse? (Also see section 6.11.) While our uncertainty about the values of our collaborators is no doubt a major obstacle to the application of MSR, I will nonetheless argue that there are relevant policy changes that we can implement even today. The first class of such interventions requires no knowledge about other value systems at all, as long as we are confident that future agents will be able to attain such knowledge. Meta-activities are examples of this: no matter what the aggregated utility function of all superrationalists in the multiverse turns out to be, we could still benefit it indirectly by learning what it is or by spreading MSR itself (see section 4.5). One way of doing so is to ensure that artificial intelligences cooperate superrationally (see section 4.6). In the second class of feasible interventions, we try to draw conclusions from what little we do know about the distribution of values in the multiverse. We can, for instance, be sure that extraterrestrials will care less than humans about the Bible or the United States of America (though some will care about them a lot and many may care about preserving local traditions in general). On the other hand, we can be reasonably confident that many extraterrestrials care about satisfying the preferences of some other agents (e. g., \"innocent\" agents capable of reciprocating) (see, e. g.,  Axelrod, 2006; Trivers, 1971; Fehr and Gächter, 1999; Dawkins, 1976; Taylor, 1987; Buss, 2015, chapter 9) . Hence, we should perhaps embrace such \"universal\" moral values more than human superrationalists would otherwise do. (We explore this further in section 4.1.1.) Consider another example: the far values of at least some humans probably resemble those of many evolved extraterrestrial superrationalists, which means that we can benefit our superrationalist collaborators by increasing the capabilities of these humans to fulfill these preferences (see section 4.4). As a last example of how we can use a small piece of knowledge, consider how we can sometimes know that someone's values are at an extreme end of some scale or otherwise far away from the multiverse-wide superrationalist average. In this case, MSR suggests that we shift these extreme values towards the middle of their scale. For example, utilitarians are extreme in that they only care about welfare, whereas most superrationalists presumably care about a lot of other things as well. Thus, it would be good to convince the utilitarian to take other considerations into account (although it is not clear what these ought to be and how much they should be taken into account). In both of these classes, we overcome the obstacle posed by our lack of knowledge by benefitting a wide variety of value systems, rather than picking out any particular subset of extraterrestrials. \n Universalism I think satisfying universalist values, i. e. ones that are shared by a large fraction of superrationalists, may become somewhat more important for all superrationalists, although the case is not entirely clear. Imagine a group of people with a few shared concerns, such as justice, welfare and freedom, and a large number of non-shared concerns, such as each person's egoism, tribal loyalties, etc. 61 Given this, they can produce gains from trade by moving resources from the nonshared concerns to the shared concerns. In terms of the compromise utility function (see section 2.8), the idiosyncratic concerns do not receive lower collective weight than prior to cooperation. However, since each individual idiosyncratic value receives much smaller weight in the compromise utility function and interventions usually cannot satisfy many of them at the same time, interventions targeted at the universal concerns will usually increase the compromise utility function more efficiently. Although this argument is quite persuasive, it is not as strong as it initially seems. For example, it assumes that each individual's values are a simple weighted sum of universal and idiosyncratic concerns. But preferences can also have different shapes. In fact, each agent may explicitly protect its idiosyncratic values against losing its weight in such a preference aggregation mechanism. One example could be that the idiosyncratic values are much stronger than other preferences, but face diminishing returns. For instance, most people probably care almost exclusively about their own well-being until their level of well-being reaches some threshold. There may also be agents who exclusively care about their idiosyncratic preferences. For agents with these values, a compromise in which resources shift to universal concerns is negative. Another reason to disregard idiosyncratic preferences is that they are often not more common than their opposites. For example, Marxism, the US or Islam are liked by many, but also disliked by many others. Therefore, it is not even clear whether the compromise utility function evaluates either one of them positively. It should be noted that some universalist values may refer to others' tribal values. For example, many humans care about preserving cultural heritage. That said, this preference is usually weak and usually abandoned if it conflicts with other values. For instance, few would argue that human sacrifices should be continued to preserve tradition. Although most people do not care enough about animals to become vegetarians, my impression is that most people in Western countries would favor the abolition of bullfighting. \n Moral advocacy Advocating one's moral views can be an effective intervention if they differ significantly from those of most other people. In light of superrational cooperation, we should perhaps change the values we advocate. \n Universalist values As I argued in section 4.1.1, superrational compromise may imply that more resources should be used to satisfy universal as opposed to idiosyncratic concerns. This suggest that spreading universalism is good from an MSR perspective. \n Expanding the moral circle Most people care much more about themselves, their kin, and their associates than about others. From their point of view, they, their kin, and their friends are all special. From the outside view, however, most people are not more important than others. It is thus in the benefit of altruistic outsiders (e. g., other humans) to reduce the difference between how much people care about themselves, their family, friends, etc. versus other humans. In Singer's terminology, an outsider who cares about all humans equally would similarly want people's \"circle of empathy\" to expand outwards to include other humans  (Singer, 2011) . In this way, we can align their decisions with the goals of the outside party. The perspective of superrational collaborators elsewhere in the multiverse is similar, in that many things that are morally special to us are not special to them. Take nationalism and patriotism: many people assign particular moral value to the country they grew up in or to its citizens, with little support through impartial reasons 62 . Needless to say, most superrational collaborators elsewhere in the multiverse will adopt a different perspective. If they care more about Japan than about the United States (or vice versa), it would be for specific impartial reasons. Making people care intrinsically less about particular nations thus aligns their values more with those of superrational collaborators elsewhere in the multiverse. Similarly, intrinsic preferences for members of one's race, species, or substrate are inconsistent with an outside view of someone from a completely different species with a different substrate. 62 Surely, there are some impartial reasons to like one country more than another. For instance, Sweden is more tolerant of homosexuals than Iran, which is a reason to favor Sweden if one cares about the welfare of homosexuals. Nationalists often provide impartial reasons for favoring their country. For example, US nationalism is often about how the US is the country with the most freedom in the world. But if people really cared about such impartial reasons, the \"best country in the world\" would often not be their own country. Furthermore, nationalism often exaggerates the difference between countries in a way that seems inconsistent with an impartial point of view: sure, the US has a lot of freedom, but so do many other Western countries. If the US is better than everyone else along such dimensions at all, then surely not by a big margin. In any case, I am only talking about the kind of nationalism that is not based on impartial arguments. \n Which moral foundations? Given the criterion of universalism, what aspects of morality are worth spreading? As an illustrative classification of moral intuitions, we use Haidt's moral foundations theory, which divides morality up into five foundations: care/harm, fairness/cheating, loyalty/betrayal, authority/subversion and sanctity/degradation (see section 3.4.1). Liberals tend to care primarily about the first two aspects, whereas conservatives care about all five. Liberal values are universalist, while the exclusively conservative values are not. As J. Greene (2013, chapter 11, section \"Why I'm a liberal, and what it would take to change my mind\") writes (references added from the endnotes): According to Haidt, American social conservatives place greater value on respect for authority, and that's true in a sense. Social conservatives feel less comfortable slapping their fathers, even as a joke, and so on. But social conservatives do not respect authority in a general way. Rather, they have great respect for the authorities recognized by their tribe (from the Christian God to various religious and political leaders to parents). American social conservatives are not especially respectful of Barack Hussein Obama, whose status as a native-born American, and thus a legitimate president, they have persistently challenged. [...] Likewise, Republicans, as compared with Democrats and independents, have little respect for the authority of the United Nations, and a majority of Republicans say that a Muslim American with a position of authority in the U.S. government should not be trusted (Arab American Institute, 2014). In other words, social conservatives' respect for authority is deeply tribal, as is their concern for sanctity. (If the Prophet Muhammad is sacred to you, you shouldn't be in power.) Finally, and most transparently, American social conservatives' concern for loyalty is also tribal. They don't think that everyone should be loyal to their respective countries. If Iranians, for example, want to protest against their government, that is to be encouraged. In other words: authority, loyalty, and sanctity are all non-universalist values. While many people have values that structurally fit into these categories, the content (e. g., the referent) of these values differ. Applied to multiverse-wide superrational cooperation, this means that we cannot benefit the authority, loyalty, and sanctity values of other superrationalists unless we are in a society with the \"right\" authorities and sanctity rules. In fact, if we push for these three values in our tribe (or civilizations), it may actually be bad from the perspective of people with conservative values from other tribes. American social conservatives tend to dislike Islam and loyalty to its authorities, even more than American liberals do. Overall, this suggests that when it comes to multiverse-wide compromise, spreading values in the domains of authority, loyalty, and sanctity is not very fruitful. Instead, we should try to make people care more about the universalist liberal foundations. Having said this, there may be a few exceptions to the rule (cf. the last paragraph section 4.1.1). For example, Christian social conservatives may like parental authority even if one's parents are Muslims or extraterrestrials. In the sanctity domain, a preference for leaving nature untouched may extend beyond an agent's planet, although many extraterrestrial habitats are probably \"slimy\" and full of scary animals. Presumably, such reasoning is also applicable to other moral values. For instance, some people care about the traditions of other tribes, including their art, social institutions, laws, religions and other non-universal aspects. It should also be noted that aspects of the liberal value of fairness also vary strongly between different people. For example, a progressive may see wealth inequalities as unfair, while a libertarian finds wealth redistribution unfair. Thus, supporting one conception of fairness can hurt another. That said, there are many sorts of unfairness that almost everyone recognizes as bad. Another reason to focus on the liberal aspects of morality is that potential superrationalists on Earth are rarely conservative (see section 3.4.1). That said, future societal transitions might make people more conservative (see the companion paper Values and acausal reasoning of whole brain emulations). \n Concern for benevolence We have seen provisional research indicating that, when it comes to distant societies, humans mainly care about the benevolence, warmth, and moral behavior of its inhabitants (see section 3.4.1). If these tentative findings turn out to be correct and other evolved species resemble ours in this regard, we should try to align people's near values more with these (typically far) goals. However, given the tentativeness of said research, I do not think this should significantly affect our actions at present. \n Consequentialism Even though superrationalists elsewhere in the multiverse may care most about whether we behave in a non-consequentialist but broadly ethical way, they do so in a consequentialist way (see section 3.2.1). For example, they might care about the numbers of crimes and selfless acts, or total amounts of happiness and suffering in a given population. This stands in contrast to the preferences revealed by most people's charitable efforts: most money is donated to charities that are comparably ineffective, i. e. ones that do not achieve the best possible consequences. By making people more consequentialist, we can improve their resource use from the perspective of consequentialist third parties. This suggests that we should spread consequentialist ideologies like effective altruism, potentially independently of any particular optimization target (such as injustice, suffering, happiness, or knowledge). \n Pluralism Whereas the compromise utility function incorporates a plethora of concerns, most individuals' values are much more narrow. This is especially true among people who give morality some thought. For example, some people adopt utilitarianism, while others become proponents of Kant's categorical imperative.  63  As I am primarily a utilitarian, I sympathize with adopting a single ethical view (and utilitarianism in particular). From an MSR perspective, on the other hand, this misses out on gains from compromise between these opposing value systems and it would be better if everyone adopted a mix of different values instead. Thus, we may want to promote moral pluralism. One version of this view is MacAskill's (2014) moral uncertainty. Operating under the assumption of moral realism (which I reject), he argues that and how we should be uncertain about which ethical system is correct. Another related view is the normative reading of  Yudkowsky's complexity of value (cf. Stewart-Williams (2015) , section \"Morality Is a Mess\";  Muehlhauser and Helm, 2012, chapters 3-5.3 ), according to which what humans care about cannot be captured by a simple moral system and instead incorporates a large number of different values. \n Promoting moral reflection Probably wanting more idealized and reflected upon values to be implemented is much more common in the multiverse than wanting less idealized values to be implemented. 64 This is especially the case for agents who have not yet settled on a moral view. For example, I am genuinely uncertain about what I would or should count as morally relevant suffering when it comes to small minds (such as those of insects) and the like, just as I am not sure how to deal with infinities in ethics. I could thus benefit a lot if someone were to make more people think about these problems. Interestingly, the appeal of promoting moral reflection decreases upon idealization. Most people probably endorse moral discourse, the importance of reflection and argument, etc., in part because they think their moral view will result from that process -if they did not believe they had the arguments on their side, they might not hold their moral position in the first place. However, not everyone can be right about this at the same time. If someone only cares about preference idealization because she thinks that her value system will win, then preference idealization may remove that meta-preference. Beyond the question of whether evolved agents in the multiverse care about moral discourse, we must ask an empirical question about our own universe: will moral discourse bring people's object-level positions closer to those of our multiverse-wide superrational compromise utility function? For example, does moral discourse make people care more about, say, benevolence, assuming this really turn out to characterize much of evolved agents' far values (see section 3.4.1)? Perhaps moral reflection can also have negative consequences as well, such as attitude polarization  (Lord, Ross, and Lepper, 1979; Taber and Lodge, 2006) . These questions appear suitable for further research. that utilitarianism cannot make sense of  (Nathanson, n.d., section 3.b.i) . For example, they argue that utilitarianism is not (always) consistent with moral intuitions about equality  (Pogge, 1995; Gosepath, 2011) , the wrongness of killing  (Henson, 1971), and justice (Smart and B. Williams, 1973, part 1, chapter 10) .  64  The main data point is that humans think about morality and engage with others' moral views. The evolutionary psychology and cultural evolution perspectives, on the other hand, are non-obvious. Some moral arguments may be favored by cultural group selection, others may offer intelligent individuals to get their way more often. On the other hand, individuals who change their moral views may be perceived as unreliable or illoyal. Besides promoting societal discourse on ethical questions, one intervention in this domain is the use of preference idealization in artificial intelligence value loading (see section 4.6). \n Multiverse-wide preference utilitarianism In addition to spreading MSR itself, one could also spread value systems that in some way mimic its implications. Specifically, the proposed neutral aggregated utility compromise is essentially a form of preference utilitarianism or multiverse-wide preference utilitarianism. Multiverse-wide preference utilitarianism might therefore be a promising moral view to advocate on the basis of multiverse-wide superrational compromise. Of course, spreading a proxy for MSR has some general disadvantages. Most importantly, it is not very robust. If multiverse-wide preference utilitarians come to prioritize very differently than multiverse-wide superrationalists, then spreading the preference utilitarianism would not yield much in our favor. The question nonetheless deserves some thought. After all, if there is a significant chance that multiverse-wide preference utilitarianism approximates the conclusions of MSR, then we should at least be on the lookout for very cheap ways of promoting it. One main difference between preference utilitarianism and superrational cooperationwhether in the form of aggregated utility compromise or otherwise -is that the latter only takes the values of other superrationalists in the multiverse into account (see section 2.9.4). Preference utilitarianism, on the other hand, accounts for the preferences of a much broader set of agents, such as all sentient beings, all agents that have preferences of any sort, or all agents who satisfy some other criteria for personhood. This may mean that preference utilitarians arrive at very different conclusions than MSR proponents. For example, if they take small minds into account, these may well dominate preference aggregation. If, on the other hand, they only take members of human-like species into account, then the difference between these and superrationalist preferences may be much smaller. Another difference could be the way interpersonal comparison of utility is handled (cf. section 2.8.5). In the context of compromise, an individual's interests are usually given weight in proportion to the individual's power. So, for example, the interests of a superrational billionaire receive orders of magnitude more weight than the interests of a superrational beggar. However, most would view this approach as unethical and most preference utilitarians would disagree with it. Thus, multiverse-wide preference utilitarianism gives more weight to the moral views of the poor than MSR suggests. Yet another problem could be that preference utilitarians would not arrive at the more meta-level MSR interventions. Even if MSR and multiverse-wide preference utilitarianism had the same object-level implications, the justification for MSR is different from (non-MSR) justifications for preference utilitarianism. Thus, preference utilitarians would not support or even come up with interventions that are about spreading the MSR-based justifications for MSR's and preference utilitarianism's joint conclusions. For example, a preference utilitarian (who does not agree with MSR) would not spread the MSR idea itself, nor try to ensure that future people (and AIs, see section 4.6.3) reason correctly about decision theory. Because these are plausibly among the most promising interventions, this consideration suggests some significant divergence in priorities. In sum, it is unclear to what extent multiverse-wide preference utilitarianism could approximate a superrational compromise utility function. At this point, however, spreading multiverse-wide preference utilitarianism is unlikely to be a top priority. \n No multiverse-wide tug-of-war over values Value systems can be viewed as having several dimensions, like relative importance of welfare, population size, art, knowledge, justice, compassion and freedom, tradeoffs between suffering and happiness, tradeoffs between extreme happiness/suffering and mild happiness/suffering, and severity of punishments, to name but a few. Different groups in the multiverse invest resources into pulling the relative values of these dimensions into different directions. Some may want people to care more about suffering, while others want them to care more about nature or happiness instead. Now, imagine you care more about suffering than most others and that you live in a civilization with a merely average concern for suffering. Presumably, you would want to pull the \"concern for suffering rope\" into your direction, potentially at the cost of other values. But knowing about superrationality, this would make it more likely that those who care less than average about suffering will also pull the rope into their direction elsewhere in the multiverse, thus offsetting your impact. Therefore, MSR would recommend against shifting concern away from other superrationalists' values, e. g., nature or happiness, to suffering. It should be noted that the above does not (necessarily) apply if the values of your civilizations strongly diverge from those of the superrationalist average far values. In such cases, it may be somewhat beneficial if all superrationalists pull the values of their civilization toward the average. \n Promoting causal cooperation Imagine two value systems, each of them common throughout the multiverse, engaged in conflicts with one another on Earth. Let us also assume that most people with these value systems find ideas like acausal decision theory and the multiverse highly speculative, such that we cannot convince them of cooperating on a MSR basis. In this case, we can still cooperate superrationally with others in the multiverse by promoting causal cooperation between the two sides (provided this does not end up hurting some third superrational party of agents 65 ).  65  As a non-obvious example, consider global catastrophic risks. Presumably, most people would not want humanity to experience a global catastrophe. Promoting peace and cooperation between nuclear powers is thus positive for all nuclear powers involved. In the plausible event that humanity would survive a nuclear winter and quickly recover, however, post-apocalyptic human society may come to hold different moral views that conflict with the views of current nuclear powers. For instance, it may be that in the first months after a global catastrophe, there would be frequent violence and chaos among survivors. They may also be forced to exert violence themselves to survive. Thus, the survivors may be desensitized to violence. Even after civil order is reestablished, citizens may still be relatively unconcerned about violence towards animals, criminals, the weak and poor, etc. (Note that I am not claiming that this would necessarily be the case; indeed, personal hardships can also make people more compassionate. I am merely using it as a somewhat plausible scenario to illustrate the present point.) All of this would imply that mitigating global catastrophic risks on Earth ends up hurting agents in the multiverse who would like societies to be organized according to post-apocalyptic survivor values. If agents with such values are sufficiently common in the multiverse, For example, let us assume that the payoff matrix of their interaction is that of a prisoner's dilemma given in table 2. Let us assume that both players' utility functions are equally common in the multiverse. We also assume that other value systems have no interest in the outcome of the interaction. From the perspective of a third party who accepts MSR, the effective payoff matrix for this interaction may look like the one given in table 3. That is, when such a third party can influence the outcome of the interaction between player 1 and player 2, she acts as though she maximizes the utilities given in that table, even if she intrinsically cares about something entirely different. When such an agent is able to influence at least one of the players, she will lobby him to choose C, 66 because to her, the payoffs are proportional to the number of C 's that are chosen. 67 A disinterested non-superrational third party, on the other hand, -i. e. one who does not care about the payoffs of each of the two agents intrinsically -would assign no value to either of the four outcomes, nor would they invest any resources in bringing about a particular outcome.  Next, let us assume that, rather than some third party, player 1 himself learns about and adopts multiverse-wide superrational cooperation, while player 2 stays ignorant of the idea. The new effective payoff matrix may then look like table 4. Player 2's payoffs are the same as in the original prisoner's dilemma, but player 1's effective payoffs have changed. He now then causal cooperation between nuclear powers should actually be sabotaged! That said, I do not find this conclusion all that plausible. It seems to be based on more and less likely assumptions than other action-guiding arguments and so it is much more fragile. One specific problem is that I would expect humans (and most other evolved beings) to become more tribal in response to a global catastrophe  (Henrich, 2015, chapter 11 , section \"War, External Threats, and Norm Adherence\"), which may make these values less important (see section 4.2.1). 66 For ideas on promoting cooperation from the outside, see Tomasik's Possible Ways to Promote Compromise, as well as  Axelrod (2006, chapter 7) . 67 Note that in some prisoner's dilemma-like problems, mutual defection is overall better than unreciprocated cooperation, in which case the superrationalist's job is more difficult. If she convinces one player of cooperation but fails to convince the other one, she will have done more harm than good. maximizes the sum of the two value systems' payoffs, because player 1's and player 2's utility functions are equally common in the multiverse. This puts player 1 in a peculiar situation: whereas defection is the dominant strategy in the original prisoner's dilemma (and therefore still the dominant strategy for player 2), cooperation dominates in this new version. Player 1 would thus cooperate in a one-shot version of the problem. On Earth, however, most interactions are repeated, like an iterated prisoner's dilemma. At first glance, one may suspect that player 1 would still cooperate in every round given that, no matter what the opponent on Earth does, he will want to make it more likely that agents elsewhere in the multiverse behave in a similarly cooperative way. However, such a strategy of unconditional cooperation makes defection player 2's best strategy. This is suboptimal for player 1, given that he prefers mutual cooperation (C,C) over unilateral cooperation  (C,D) . In an iterated version of the game, player 1 might therefore punish defection to some extent, similar to how successful strategies punish defection in the iterated prisoner's dilemma. Nevertheless, the dynamics of this new problem are different than those of the prisoner's dilemma. Based on the ordering of the outcomes for the different players, the game is identified as g 261 or g 266 in the periodic table for 2x2 games by  Robinson and Goforth (2005) , who also provide a few examples of games in this category. A few additional examples of this type of game exist, but overall, the game has not been studied extensively in the literature. Further research is thus needed to identify the right strategy for iterative versions of the game.   \n Increasing capabilities Broadly speaking, agents have two reasons to increase other agents' capabilities: a) they may care about it intrinsically, or b) they may share the goals of the people whose capabilities they increase (and thus care about increasing them instrumentally). For example, someone who mostly cares about other people's freedom to pursue their goals has a type a) reason to raise the capabilities of poor people, and someone who agrees more with the people than with the dictator has a type b) reason to increase democracy. But if you hold less common values, such as reducing animal suffering, giving people more power is of unclear value. MSR broadens type b) motives to increase others' capabilities: even if we do not share someone else's goal, we have reason to increase his capabilities if we believe that significant parts of his goals are shared by superrational agents elsewhere in the multiverse. There is some relevant literature on increasing an agent's goal-achievement capabilities. In economics, the capability approach is an alternative to welfare economics and primarily studies how to measure an individual's capabilities. Some of its metrics include health, freedom of thought and expression, education, political participation, and property rights. In his dissertation on Ethics Under Moral Neutrality, Evan Gregg  Williams (2011)  discusses a topic closely related to acting under MSR: he assumes that we do not know what the \"correct\" moral theory is 68 , and that while we all have some access to moral truth, this access is unreliable. He then discusses, among other things, what policies we should take given such uncertainty. In many ways, this scenario is analogous to MSR 69 , where the necessity to maximize for multiple moral views comes from uncertainty about the utility functions of other agents in the multiverse as well as their diversity rather than conflicting intuitions about the \"moral truth\". Many of Williams' conclusions resemble those of the present paper. For instance, he identifies the appeal of preference utilitarianism in chapter 3.1 of the dissertation (compare sections 2.8 and 4.2.6 of the present paper). Many of his intervention ideas are about improving the capabilities of others who may plausibly have access to the moral truth. First and foremost, he defends democracy (chapter 3.3) and liberty (chapter 3.4). Of course, MSR does not have the same implications as the above approaches. For one, when we raise others' capabilities as superrationalists, we favor people whose values we suspect to be typical of what superrationalists in the multiverse care about. For example, from an MSR perspective it is much more important to support consequentialists. Moreover, some of the proposed measures merely move resources or power from one group to another (e. g., from a dictator to the people) without adding optimization power aimed at the goals of superrational agents in the multiverse. I doubt that raising capabilities will often be a top intervention. Nonetheless, it might be an option when good and inexpensive opportunities, such as sharing knowledge, arise. \n Meta-activities Relative to any goal, meta-activities are either about a) amassing more resources, or b) improving the efficiency of one's object-level resource expenditure. To achieve the goals that superrationality prescribes, we may thus also engage in such meta-activities. In the following, I will describe two meta-activities, one of each kind. \n Research The present paper lays out the foundations for research on multiverse-wide superrational cooperation. Further research is needed in all three areas discussed in this paper, i. e. how our new criterion for choosing policies is to be constructed (see chapter 2), what values our superrational collaborators have (see chapter 3), and which interventions are most promising (chapter 4). 68 I side with moral anti-realism (R.  Joyce, 2016)  and non-cognitivism in particular (R. Joyce, 2016, section 3). That is, I do not think that moral theories can have (objective) truth values. 69 In fact, I learned about variance voting, which I take to be the most promising approach to constructing the compromise utility function (see section 2.8.5), via the literature on moral uncertainty, in particular via MacAskill  (2014, chapter 3) . Note that some research, e. g. investigations of whether a compromise is beneficial for you, can (in theory) be harmful if one has not properly precommitted as illustrated in the Remote-controlled cake maker thought experiment (see section 2.8.6). A similar danger lies in finding out whether other agents cooperate (see section 2.1). \n Promoting multiverse-wide superrationality Since multiverse-wide superrational cooperation produces gains from compromise (under certain assumptions about the collaborators, discussed in section 3.2), having more multiversewide superrational cooperation produces more gains from compromise. Hence, a common interest of all collaborators is to increase the number of people who adopt (multiverse-wide) superrational cooperation. Indeed, it is plausible that small groups of superrationalists should focus on promoting the idea rather than attempting to help other superrationalists directly. After all, if one of them can convince only two others to cooperate superrationally, she already doubles her impact relative to cooperating on her own. Of course, the two others could also convince others in turn. Needless to say, spreading the idea saturates at some point. At least when all humans are convinced of superrational cooperation, the idea cannot be spread further. More realistically, we will run out of people who are willing to think about such seemingly speculative topics. \n Artificial intelligence One particularly important way of shaping the future is artificial intelligence  (Bostrom, 2014b) . Given our newfound knowledge, we can differentiate between AI safety measures that are inspired by superrational cooperation and AI safety measures that are not. \n AI safety not based on superrationality-related considerations The goal of current AI safety research is to make AIs behave in ways that are more compatible with some human value system. 70 From a multiverse-wide cooperation perspective, this is positive to the extent that human values correlate with the values of other evolved agents in the multiverse. A human-controlled, non-superrational outcome may nonetheless be suboptimal from an MSR perspective. Imagine a distant civilization of billions of happy, law-abiding, art-producing, yet, from a human perspective, ugly-looking extraterrestrials. Each year, they enslave or kill trillions of other, less intelligent extraterrestrials, such that the number of miserable lives and involuntary deaths caused by the civilization is orders of magnitude higher than the number of positive lives it supports. Most people on Earth may not care about this civilization at all because it contains no humans. Some may only care about the smart extraterrestrials and thus evaluate the society very positively  (Kagan, 2016) . However, I suspect that many of those who care at all about distant ugly aliens also care about less intelligent aliens. These people would evaluate the civilization as far less positive. Similarly, many superrationalists in the multiverse may not evaluate our civilization positively if it were to continue its current mistreatment of animals. Another concern is that a civilization might prioritize near-view values when value loading an AI. This suggests that even if our values resembled those of other civilizations, the goals we give to an AI might differ significantly from what extraterrestrials care about in our civilization. FRI has previously investigated ways of making AI alignment failures less harmful by focusing on avoiding very bad AI outcomes rather than attempting more fine-grained control  (Gloor, 2016) . One motivation to do so is this approach's cooperativeness: different value systems may disagree on what future should be created. For example, some want the universe to be filled with concentrated pleasure, whereas others envision human civilizations of varying social, economic and political systems, often rid of poverty, diseases, involuntary death, and so forth. However, different value systems often agree on a large set of futures that should not be created. Things like premature death, suffering, war, and extinction are almost universally seen as bad. Avoiding dystopian scenarios can thus benefit a wider range of value systems. Another MSR-based reason to focus on very bad outcomes is that, because our civilization will be destroyed in all of them, avoiding them evokes abstract construals. These probably do a better job than concrete construals at approximating what extraterrestrials care about in our civilization (cf. section 3.3.2). However, making AI more fail-safe from a MSR perspective would be less focused on preventing outcomes with a lot of suffering than FRI's previous work. Also, its level of priority depends on its feasibility. Whereas heuristic arguments suggest that merely avoiding bad outcomes might be more feasible than working toward fully human-aligned AI, it has so far proven difficult to do any concrete work in the area. Overall, I think it is an approach worth investigating further in the context of superrational compromise, but not likely to be a top intervention. \n Multiverse-wide superrationality-inspired value-loading In section 2.8.2, we viewed compromising as a one-time process, in which all agents adopt a new utility function u * to maximize in their part of the multiverse. If they indeed acted as though they now only care about maximizing u * , the natural consequence would be to push for AI values that are closer to u * . One way to do this is to directly implement the value systems that one would also spread to other humans (discussed in section 4.2). For example, one could try to make future AIs hold a wider variety of values (see section 4.2.4) or perhaps prioritize universal concerns a bit more (see section 4.2.1). More robustly, one could directly implement a pointer to the aggregated consequentialist far values of superrationalists in the multiverse. Indeed, extracting u * from the multiverse appears to be roughly as difficult to specify as extracting goals of humans. Just as one could identify humans in the world model, extract their goals and aggregate them, so one could identify superrational cooperators, extract their goals and aggregate them. 71 (A somewhat similar proposal was made by  Bostrom (2014a, page 14) ; see section 6.1.2.) Of course, it is unlikely that superrationalists could convince the majority of people of such goal systems. Nonetheless, at this early stage of the field of AI safety, it seems useful to also explore unrealistic proposals like this one. Additionally, less attractive goal functions may still be relevant as backups (see  Oesterheld 2016) . Another disadvantage of this approach is that it breaks if the analysis underlying our specification of u * is incorrect. For instance, if MSR does not work at all, then making AI care about ET values directly is much worse than simply implementing our own values. \n Making an AI come up with superrational cooperation on its own Instead of directly implementing our compromise utility function, we could also make the AI come up with such a compromise on its own. This has several advantages. Most importantly, it protects against some possible mistakes on our side. If, say, we were unable to find the correct superrational compromise, we could let the AI find it on its own. Also, the AI may at some point discover that there are no other agents in the multiverse after all, at which point it could choose to stop wasting further resources into compromising with these nonexistent agents. The primary way of getting an AI to compromise superrationally is to ensure that it reasons in accordance with the right decision theory.  72, 73  This in turn involves advancing the field of decision theory and investigating possible ways of implementing decision theories in AI systems. Given how both of these areas seem neglected and gains from trade may be quite significant, I could very well imagine that interventions in this area are among the most effective of those hitherto considered by effective altruists. \n Value loading is still necessary If all acausal collaborators settle on maximizing some utility function, perhaps value loading is unnecessary for AIs with the right decision theories anyway? After all, once such an AI joins the MSR compromise, it will update its utility function accordingly -regardless of whether it originally wants to maximize paperclips or to reduce suffering. But this reasoning seems unsound. While all AIs may settle on the same compromise utility function, the original value system of the AI still affects what that compromise utility function ends up being. Without superrationality, value loading affects the dominant values of one AI. If there are m superrationalist civilizations, then each can affect the dominating values normalization) is more or less difficult to implement than the aggregation procedures one would implement for humans. 72 Reasoning in accordance with some decision theory is not meant to imply that the decision theory is hard-coded into the AI. Instead, the decision theory that an AI uses may be the result of particular choices of architecture. To ensure that the AI reasons in accordance with the right decision theory, we would then have to find out what the decision-theoretical implications of different AI design choices are and ensure that these receive due consideration in the construction of intelligent machines. 73 There are other ways to make it more likely that the AI applies MSR. For example, one could ensure that its epistemology enables it to infer the existence of other universes that cannot be observed directly. We could also think of an AI that would accept MSR, but somehow never has the idea of MSR. Much more plausibly, some AIs will simply not care about distant universes in a consequentialist way. However, all of these parameters seem more difficult to influence than the AI's decision theory. in m AIs by 1 m (assuming that all civilizations are equally powerful, etc.). So, proper value loading is actually just as effective as before, if not more because of gains from trade. Even if we manage to reliably make the AI join a superrational compromise, we will still want to make it value the right things. I am uncertain about whether some version of the above argument against value loading may work after all. Even if all AIs have \"paperclipper values\", perhaps they would still recognize that other value systems originally had all the power, causing the AIs to give them higher compromise weights? Similarly, one may have some intuitions that value loading superrational AIs should not be necessary, given that it just moves power between superrational cooperators. However, at this point, these are merely intuitions and not arguments. Except from potentially guiding future research, I do not think they should affect our priorities. \n Compromise-friendly backup utility functions Even though value loading is still necessary, we can nonetheless benefit our superrational collaborators (and thereby ourselves) in cases where value-loading fails. Even if an AI has values that differ from those of humans, it may still trade with other civilizations. Hence, we should attempt to load it with values that especially lend themselves to compromise, such that the other value systems benefit as much as possible (cf.  Bostrom, 2014a) . Because one would usually attempt to load an AI with one's own values, such a compromise-friendly (\"porous\", in Bostrom's terminology) utility function would usually only be a backup (see  Oesterheld 2016) . \n Acknowledgements I came up with superrational compromise after a conversation with Lukas Gloor about decision theory and the multiverse. Prior to writing this paper, I extensively discussed the topic with him, Carl Shulman, and Brian Tomasik. I also thank Max Daniel, Tobias Baumann, Carl Shulman, David Althaus, Lukas Gloor, Kaj Sotala, Jonas Vollmer, Johannes Treutlein, Lucius Caviola, Joshua Fox, Jens Jaeger, Ruairí Donnelly, Brian Tomasik, Owen Cotton-Barratt, Magnus Vinding and Dominik Peters for valuable discussions and comments on this paper. Last but not least, I am indebted to Adrian Rorheim for careful copy editing and Alfredo Parra for typesetting. \n Appendix The appendix contains discussion of additional, more tangential topics. \n Related work \n Gary Drescher on superrationality Superrationality, i. e. cooperation based on correlation, is a well-known idea in decision theory  (Kuhn, 2017, section 7; Horgan, 1981, section X; Hofstadter, 1983; Campbell and Sowden, 1985; Ahmed, 2014, section 4.6 and references therein) . However, most authors do not discuss much beyond the basic idea. Chapter 7.2 of Gary  Drescher's Good and Real (2006)  is the most extensive analysis of the concept of which I am aware. Among other things, Drescher notes that superrationality -or, as he calls it, subjunctive reciprocity -can be applied broadly as a justification for \"altruistic\" behavior, which I discuss in section 6.7. He also points out that superrationality removes the need for reciprocity (see section 2.9). Although Drescher discusses the Everett interpretation of quantum physics in his book, he does not connect it with superrationality. His considerations thus focus on superrationality among agents on Earth, which I would argue to be quite weak (see section 6.6). Nonetheless, his account of superrationality is more thorough than any other I have seen, and strongly influenced chapter 2 of this paper. \n Acausal trade Acausal trade is another (mostly informally discussed) form of cooperation based on noncausal decision theories and has often been combined with the multiverse concept. However, the mechanism usually discussed under the term acausal trade differs from superrationality. Instead of assuming the similarity between two agents, acausal trade merely requires them them to have models of each other. For example, the two agents may know each other's source code.  74  The main technical difficulty here is to avoid the infinite loop associated with this mutual modeling. The basic idea is that both agents adopt the policy of cooperating if and only if the other agent cooperates. 75 This is intended to incentivize cooperation in a way reminiscent of causal cooperation via tit for tat. One can also view this policy of mirroring the other agent's strategy as a way to create correlations between the decisions of the two agents. However, if both agents use this policy, they run into an infinite loop: To make a decision, the first agent has to find out (probabilistically) what the second agent does. But to do so, it has to find out what the first agent does, which in turn means finding out what the second agent does, etc. As illustrated by  Barasz et al. (2014) , this problem can sometimes be solved, thus making it rational for two programs with knowledge of one another's source code to cooperate with each other (cf.  LaVictoire et al., 2014; Critch, 2016) . Superrationality may be seen as a special case of acausal trade in which the agents' knowledge implies the correlation directly, thus avoiding the need for explicit mutual modeling and the complications associated with it. This makes superrationality much more easy to apply than acausal trade. Consequently, whereas I propose that humans should reason superrationally, acausal trade is usually discussed only in the context of superintelligent AIs (e. g.,  Bostrom, 2014a) . 74 Alternatively, one of the two agents can observe the others' behavior. In this case, only the other agent needs a model.  75  Of course, it would be even better if one could defect against that cooperate unconditionally. \n Various mentions of multiverse-wide superrationality While I am not aware of any substantive discussion of MSR, some have mentioned it as a side remark, or proposed specific applications: • Bostrom writes: \"We might [...] hope that some of the other civilizations building AIs would [also implement their AI in a way that enables trade (see sections 4.6.3 and 4.6.3)], and perhaps the probability that they would do so would be increased if we decided to take such a cooperative path.\"  (Bostrom, 2014a , page 4) On page 14, he also argues that one should perhaps diversify the values of an AI for a similar reason. • Almond discusses a few examples of how we can utilize the correlation with other civilizations  (Almond, 2010c, ch. 4) . One of them is discussed in section 6.9. \n Many agents One essential ingredient of multiverse-wide superrationality is the number of intelligent agents that exist. We have, to some people's surprise, not (yet) found extraterrestrial life in the observable universe. However, the universe, or multiverse, probably extends far beyond the region we can observe. More likely than not, it contains so many agents that the number of humans on Earth pales in comparison. Unfortunately, physics and cosmology are not the most accessible of fields. Introductions tend to either involve advanced mathematical notation or fuzzy explanations with terms like \"space-time distortions\", \"waves\", space being referred to as \"flat\", dimensions as \"curled up\", etc. that seem hard to understand without looking at their technical meaning. For an overview of the latter kind, consider Tegmark's Parallel Universes  (2003) , which also discusses the number of intelligent agents specifically. Another, even broader popular science overview is given by  Greene (2011) . In this section, we focus on the easiest to understand aspects. As mentioned in chapter 1, we will use the term \"multiverse\" to also refer to, say, a spatially infinite universe. It is important to note that most talk about multiverses is not something physicists make up out of thin air as an intellectual exercise. Instead, certain well-tested theories in physics and cosmology seem to imply the existence of a large universe or multiverse. One of the easier to understand examples is the Everett or many-worlds interpretation (MWI) of quantum mechanics. For an introduction, consider Yudkowsky's introduction (2015, ch. S), which makes a strong case for MWI and goes through some of the issues typically discussed, like falsifiability/testability and the law of parsimony  (Tegmark and Wheeler, 2001; Tegmark, 2007; Vaidman, 2016) . For a more critical account, see, e. g.,  Kent (1997) . Tentative polls of physicists' opinions on MWI indicate that between 10% and 50% agree with MWI (Raub 1991, unpublished as cited in, e. g., Tipler, 1994, section 5, \"Nonrelativistic Quantum Mechanics is Deterministic\"; Tegmark, 1997;  Nielsen, 2004; Emerson and Laflamme, 2006) . But the many-worlds interpretation of quantum physics is not the only case that can be made for a universe with a very large or infinite number of agents. In fact other arguments are probably more widely accepted. Maybe the least \"extraordinary\" hypothesis implying the existence of many agents is one which says that this universe is spatially infinite. According to Tegmark, \"this spatially infinite cosmological model is in fact the simplest and most popular one on the market today\" (2003). Even if the universe is spatially finite and small, it may still contain a lot of civilizations that cannot interact with each other if it is temporally infinite. For example, on a cyclic model the universe goes through an indefinite number of oscillations of expansion and collapse. If sufficiently many of these oscillations give rise to different civilizations, then these civilizations can cooperate with each other superrationally. Another more complicated yet popular cosmological theory is eternal inflation as described in ch. II of Tegmark's Parallel Universes. Eternal inflation postulates the existence of multiple universes which not only differ in initial conditions but also in their number of dimensions, their sets of fundamental particles, and their physical constants. On the more speculative (but also more accessible) side, there are various forms of modal realism (sometimes also called mathematical monism), the view that every \"possible world\" exists in the same way in which our world exists. While modal realism is controversial and rarely discussed by physicists, some view it as an elegant solution to some philosophical problems. Modal realist theories are also very simple, although to make predictions with them, they require supplementation with indexical information about which agent in which possible world we are  (Hutter, 2010, ch. 3) . For different starting points for thinking about modal realism, see any of the following:  Lewis (1986 ), Tegmark (1998 2008; Schmidhuber (1997) . Acting under the assumption of modal realism is associated with some complications, however. In particular, because literally everything can happen, everything will happen in some possible world, no matter what we do. Thus no action seems to be better than another  (Oesterherld, 2017a)  Besides the arguments in favor of assigning a high probability to living in a universe with many agents, there also exists a prudential reason to act as though one lives in a large universe. Even if we only assign, for example, a 50% probability to the existence of other civilizations, our decisions matter much more if there are more other agents with whom we are correlated. Thus, we should optimize our decisions more for the large universe. This line of reasoning does not work for all value systems, however. For example, in terms of multiverse-wide average welfare, our influence may be much bigger if the universe was very small. An average utilitarian may thus follow the opposite prudential argument and act as though the universe was small. \n Testability of superrationality Eliezer Yudkowsky (2010b, ch. 13) writes: If a dispute boils down to a testable hypothesis about the consequences of actions, surely resolving the dispute should be easy! We need only test alternative actions, observe consequences, and see which probability assignment best matches reality. Unfortunately, evidential decision theory and causal decision theory are eternally unfalsifiable-and so is [timeless decision theory (TDT)]. The dispute centers on the consequences of logically impossible actions, counterfactual worlds where a deterministic computation returns an output it does not actually return. In evidential decision theory, causal decision theory, and TDT, the observed consequences of the action actually performed will confirm the prediction made for the performed action. The dispute is over the consequences of decisions not made. This also means that superrationality itself -not only its application to agents in faraway parts of the multiverse -is untestable. If I win money by cooperating in a prisoner's dilemma against an exact copy of mine, causal decision theorists will point out that my copy would have cooperated either way and so defecting would have been better. Based on this anecdotal evidence, people do not consider superrationally in this real-world donation game, although they sometimes make the superrational choice for other reasons. \n Do people reason superrationally? In general, there are many hypotheses about why people sometimes cooperate that do not involve any sort of acausal reasoning. Presumably, many are either unaware of the causal line of reasoning or do not properly set up the proposed experiment in their mind. For instance,  Yudkowsky (2015, chatper 275)  argues that people cannot pretend to be selfish and therefore take the reward to the other player into account.  Kanazawa and Fontaine (2013)  demonstrate that \"the subject's behavioral choice (cooperation vs. defection) varied significantly as a function of subconscious perception of cues to possible reputational effect (in the form of a video image of another subject in the experiment).\" Cultural norms are also often invoked to explain cooperation. 76 This short list of example explanations is by no means an exhaustive review of the literature on why people cooperate in one-shot games like the prisoner's dilemma and public goods games. Drescher (2006a, page 288f) defends the opposite view. He argues that although people do not act according to some systematic acausal decision theory, they nevertheless implicitly account for acausal reasoning into account implicitly. Similarly, Leslie writes, \"perhaps the germs of [evidentialist reasoning] are already present in thoughts influential in getting people into polling booths, thoughts on the lines of 'What if everybody in my party stayed in bed?\"'  (Leslie, 1991, ch. 7) . Perhaps this \"lack of a correct explicit decision theory leaves the solution somewhat vulnerable to seemingly sound counterarguments, and thus leaves the solution's influence somewhat tentative\"  (Drescher, p. 289) . This could explain why many people who have considered the problem in great detail do not go with the recommendation of acausal arguments despite potentially having an innate intuition for them. Recently, Fischer (2009) has proposed that people do engage in superrationality-like reasoning. In a study, he showed that participants' cooperation in a one-shot prisoner's dilemma correlated with reported probabilities of the opponent making the same choice as oneself (cf.  Krueger, DiDonato, and Freestone, 2012) . One further piece of evidence in favor of this hypothesis is that cooperation decreases when people learn about the other person's choice before they make their own choice.  Pothos et al. (2011)  write:  Shafir and Tversky (1992; Busemeyer, Matthew, and Wang, 2006; Croson, 1999; Li and Taplin, 2002; Tversky and Shafir, 1992 ) created a well-known modification to the Prisoner's Dilemma game: in some trials, participants were told what the other player was doing. Unsurprisingly, when participants were told that the other person decided to D, then their probability to D was 97%; and when they were told that the other person decided to C, then their probability of D was 84%. However, in trials (within participants design) when participants were not told what the other person did, the probability to D dropped to 63%. While inconsistent with mere causal reasoning, this can be explained with acausal reasoning. Given knowledge of the other person's decision, the evidential impact of cooperation diminishes (cf. section 2.1). Moreover, this behavior cannot be explained by reputational issues or altruistic preferences, which would, if anything, suggest that one would return the favor upon learning that the other person cooperated. However, the standard explanation attributes this behavior to people's irrationality. Overall, I lean towards the view that people do not have strong acausal intuitions in day-today scenarios, which means that people who do take such considerations seriously do not correlate strongly with the average person. \n The evolution of superrationality Even though superrationality is not testable in any given situation, it does produce actual benefits. This much is clear even to a causal decision theorist, who would thus self-modify to take some, though not all, acausal considerations into account (see section 2.3). For the same reasons, a causal decision theorist would also program an AI to take these considerations into account. Similarly, evolution favors agents that take some superrational considerations into account. For example, imagine a planet on which near copies of agents are created on a regular basis. They then interact with each other in cooperation and coordination games like the donation game. To facilitate evolution, copies are created in proportion to the payoffs in the cooperative games. On this planet, superrational agents -i. e. those who cooperate with close copies and other correlated agents, while defecting against uncorrelated agents -have an evolutionary advantage over CDT-based agents who always defect. They will, on average, receive higher payoffs and thus reproduce more successfully. Evolution can, therefore, in principle favor genes (and memes) that promote superrational reasoning. In some sense, the described planet resembles ours. On Earth, \"near copies\" of humans are created via reproduction and upbringing. Moreover, many have pointed out that scenarios paralleling the prisoner's dilemma and public goods games were common in our ancestral environment. In principle, such considerations also apply to the application of superrationality to cooperation with agents in other parts of the multiverse. That is, multiverse-wide evolution favors creatures who increase the genetic fitness of agents with similar decision algorithms elsewhere in the multiverse. In practice, however, I suspect that almost all creatures with at most human capabilities are unable to benefit any genomes other than those extant in their environments. \n Superrational cooperation on Earth Some, e. g.  Leslie (1991, ch. 8)  and Nate Soares, have argued that superrationality and acausal decision theory are relevant even in daily interactions between humans on Earth without considering the multiverse.  Drescher (2006a, ch. 7 ) even contends that it is an argument for egoists to behave altruistically. Others, like  Almond (2010b, ch. 4.6; 2010c, ch. 1)  or  Ahmed (2014, ch. 4) , maintain the opposite position, i. e. that acausal reasoning is rarely relevant. I will argue for the latter claim. Indeed, my belief that acausal cooperation is usually inapplicable is the reason why this paper discusses its application to the multiverse rather than more \"down to Earth\" scenarios. \n Fewer agents Superrationality becomes relevant in the multiverse because it contains so many disconnected agents. Thus, even if the correlation with every individual agent's decision is small, the overall acausal impact of our decisions dominates (see section 2.7). The smaller the number of agents, the higher the relative importance of the causal implications of our actions. Since the number of agents on Earth is comparably small, causal considerations may well dominate. 6.6.2 Argument from evolution: Superrationality did not evolve (strongly) We argued that superrational compromise can, under certain conditions, evolve by natural means and that many of the respective conditions are even met on Earth (see section 6.5). Hence, the mere observation that most people do not reason superrationally (see section 6.4) makes a case against its importance. \n Causal cooperation seems more important Humans rarely face one-shot prisoner's dilemmas against agents whom they know sufficiently well to be strongly correlated with them. Instead, their interactions are usually iterated and open to mutual causal influence. As a result, causal cooperation mechanisms apply, at least in principle (see section 2.9 for references to introductions on causal cooperation). Surveying the vast literature on causal cooperation and how it compares to superrational cooperation is beyond the scope of this paper, but two key points are worth highlighting. First, rational agents establish causal cooperation in a surprisingly wide range of situations. Second, successful strategies like tit-for-tat or Gradual  (Beaufils, Delahaye, and Mathieu, 1997)  tend to start the game by cooperating and never defect unless the other side starts defecting. Together, this suggests that sufficiently smart people -which, I assume, includes most agents who might apply superrationality -are capable of strong cooperation with one another without ever having to invoke superrationality. \n Hard-wired alternatives Superrationality is not the only solution to the adaptive challenge of having to cooperate with similar agents (e. g., members of the same tribe and relatives). One alternative is to hard-wire creatures to cooperate with very similar agents and defect against everyone else. This approach to ensuring cooperation has received some attention in the literature, although it is not nearly as widely known as the mechanisms of causal cooperation (see, e. g.  McAfee, 1984; Howard, 1988; or Tennenholtz, 2004) . \n Superrationality and morality Cooperation is often invoked as an argument why altruistic behavior and following moral rules is rational (e. g.,  Dawkins, 1976, ch. 12; J. Greene, 2013) . In many ways, the application of superrational cooperation resembles altruistic behavior even more closely. For example, superrationality implies that we should help a value system even if we know for certain that no agent with this value system will or can reciprocate (see section 2.9). Additionally, in suggesting that we treat others the way they would like to be treated (in order to make it more likely that others treat us the way we would like to be treated), superrationality resembles Kant's categorical imperative and the Golden Rule. Once someone is updateless, she has additional reasons to be nice to others: even if she learns that they do not or will not cooperate, she would potentially still behave nicely toward them (see section 2.4). Similarly, if she were ever to find herself in a situation resembling the Remote-controlled cake maker thought experiment (see section 2.8.6), where she knows that cooperation hurts goals, she might still make that sacrifice. Some implications of superrationality thus bear a close resemblance to altruistic or moral behavior.  Drescher (2006a, ch. 7.2 .1) makes similar points regarding the similarity between superrational cooperation and altruism. However, he goes further by arguing that superrational cooperation is the basis for morality -a way of \"deriving ought from is\". I will discuss two questions that might arise from this argument: is altruistic action derived from self-interest really the essence of morality or altruism? And: is superrationality sufficient for arriving at the desired altruistic conclusions? 6.7.1 Real altruism  Yudkowsky (2015, ch. 259)  writes: Consider the following, and ask which of these two philosophers is really the altruist, and which is really selfish? \"You should be selfish, because when people set out to improve society, they meddle in their neighbors' affairs and pass laws and seize control and make everyone unhappy. Take whichever job that pays the most money: the reason the job pays more is that the efficient market thinks it produces more value than its alternatives. Take a job that pays less, and you're second-guessing what the market thinks will benefit society most.\" \"You should be altruistic, because the world is an iterated Prisoner's Dilemma, and the strategy that fares best is Tit for Tat with initial cooperation. People don't like jerks. Nice guys really do finish first. Studies show that people who contribute to society and have a sense of meaning in their lives, are happier than people who don't; being selfish will only make you unhappy in the long run.\" Blank out the recommendations of these two philosophers, and you can see that the first philosopher is using strictly prosocial criteria to justify his recommendations; to him, what validates an argument for selfishness is showing that selfishness benefits everyone. The second philosopher appeals to strictly individual and hedonic criteria; to him, what validates an argument for altruism is showing that altruism benefits him as an individual: higher social status or more intense feelings of pleasure. So which of these two is the actual altruist? Yudkowsky elaborates in the rest of the chapter. The point he is making is that \"actual altruism\" is usually understood to mean caring about others, rather than merely behaving altruistically based on egoistic reasoning. Verbal disputes about the meaning of \"true altruism\" aside, there is a difference between having the welfare of others as part of one's goal on the one hand, and benefitting others for egoistic (or other non-altruistic or amoral) reasons on the other. I am an altruist of the former kind, but cooperation (whether superrational or not) only supports altruism of the latter kind. I would think that most other people are also altruists of the former kind (in addition to sometimes being altruists of the latter kind). 77 Altruism of the latter kind also does not \"derive ought from is\" 78 , as Drescher promises in chapter 7 of Good and Real. Instead, it derives (potentially unexpected) action recommendations from an already existing ought, i. e. egoism or whatever values an agent already has. Specifically, (multiverse-wide) superrational compromise can be viewed as agents switching to a new utility function, but only because it benefits their current utility function. There are many other examples of agents effectively adopting a new goal. Consider an egoist living in 16th-century Spain. Her environment punishes people who are not aligned with Catholicism. To further her goals, the egoist should therefore behave as though she was a Catholic with pure Catholic goals. She thus derives a new \"morality\" from purely egoistic goals, but I suspect that meta-ethicists' excitement about this is limited. \n How much altruistic behavior does superrationality entail? The second issue is that superrationality does not suffice for reproducing all of our moral intuitions. For one, I am not sure to what extent superrationality has a bearing on interactions with other people on Earth at all (see section 6.6). Furthermore, we saw that superrationality only warrants helping other superrational agents (see section 2.9.4). But our moral intuitions also regard other agents as morally relevant. As an example, consider Alice, a purely causal decision theorist who even defects in a prisoner's dilemma against her copy. Does this mean that Alice is morally irrelevant, no matter her degree of consciousness, capacity to suffer, etc.? Alice is not just a thought experiment -many philosophers would two-box in Newcomb's problem (see section 2.2). Since Newcomb's problem is roughly equivalent to the prisoner's dilemma against an identical copy (  Lewis, 1979) , this shows that most philosophers reject superrationality. Nevertheless, I and presumably most others care intrinsically about the welfare of these moral philosophers; the same is true for young children and non-human animals, most or all of which do not reason superrationally. Superrationality and what we would usually call \"morality\" thus disagree strongly on who is morally relevant  (Drescher, 2006a , sections 7.2.2 and 7.2.3). \n Multiverse-wide superrationality for causal decision theorists Throughout this paper, I have assumed that some acausal decision theory is correct, albeit without narrowing it down to any particular theory. To me, this is no limitation of MSR, because I hold that causal decision theories fail in examples like the donation game with similarity. However, many professional philosophers are causal decision theorists (see 2.2). Are the arguments presented in this paper entirely irrelevant to them? 79 Remember, from section 2.3, that CDT actually recognizes its flaw. Specifically, CDT self-modifies to cooperate acausally with copies that are created in the future. After all, these copies can be causally influenced to cooperate acausally to each other's benefit. Other humans and extraterrestrials in far away parts of the multiverse do not fall into that category, of course -so causal decision theorists would not precommit to engage in full multiverse-wide superrational cooperation. However, one multiverse theory is the Everett interpretation of quantum physics, according to which our universe constantly \"splits\" into different branches. Thus, under the Everett interpretation, near-copies of oneself are created all the time and in large quantities. Moreover, it pays in causal terms to cooperate across time, i. e. to commit me tomorrow and me in-30-years to cooperate. A causal decision theorist would therefore cooperate with a large number of agents created after CDT's precommitment. It thus seems as though a weaker version of the considerations from this paper apply to causal decision theorists after all. 79 One obvious way in which the implications are relevant to causal decision theorists is decision-theoretical uncertainty  (MacAskill, 2016) . Perhaps, even ardent defenders of CDT have probability on CDT being the wrong way to make decisions. I, at least, do not have a probability of 100% on a single decision theory being the right one. If you have some weight on some of the alternatives to causal decision theory, then you would also give MSR considerations some weight. In fact,  argues that if we live in a sufficiently large universe, then EDT and other non-causal decision theories immediately dominate expected value calculations that take decision-theoretical uncertainty into account. \n Simulations Paul  Almond (2010c, ch. 2;  has argued that correlations across the multiverse have implications for whether and how we should simulate other civilizations. The idea has also been proposed by others. It is mainly relevant for agents and civilizations who primarily care about copies of themselves, which it is not discussed in the main text. \n If being in a simulation is bad, avoid creating one Almond (2010c, section 4.2) writes: If you take the simulation argument seriously, then evidential decision theory would seem to allow you to assert some control over the other civilizations that might be building these simulated realities. One way in which evidential decision theory would be relevant is in the way it allows you to control the probability that you are in a simulation in the first place. If your civilization decides to develop the capability to run simulated realities, then you are meta-causing [i. e. influencing acausally] civilizations in general to do likewise (including civilizations on which our own might be modeled), and making it less likely that almost all civilizations end before they are capable of producing simulated realities, in turn making it more likely that you are in a simulated reality. If, however, your civilization decides not to acquire this capability then you are meta-causing civilizations in general to do likewise, making it less likely that you are in a simulated reality. Once your civilization has the capability to produce simulated realities, if your civilization decides to do it, this would make it more likely that other civilizations also do it, again making it more likely that you are in a simulated reality. On the other hand, if your civilization decides not to produce simulated realities, this makes it less likely that other civilizations would choose to do so, and therefore less likely that you are in a simulated reality yourself. If you assume the view of anthropic decision theory  (Armstrong, 2011 ) instead of classical anthropics (i. e., the self-sampling or self-indication assumption), then your decision can affect the fraction of copies of you that are in a given simulation. Note that under certain assumptions about the efficiency of simulations, one's effect on the probability of being in a simulation may be negligible. If any civilization could run orders of magnitudes more simulations of civilizations than there are civilizations in the basement, then most copies will be in simulations no matter what you decide. Regardless of your choice, you will probably be in a simulation. \n Happy simulations Almond (2010c, section 4.2) proposes to simulate civilizations in a nice way to increase the probability of being in such a simulation oneself. While evidential decision theory might be applied to try to reduce your \"risk\" of being in a simulated reality, some people, and some civilizations, might not see it that way: They might think that being in a simulated reality could have benefits if the entity that constructed the simulation is kind; for example, the inhabitants of the simulation might be protected from existential risks to their civilization, or they might be provided with an afterlife. Evidential decision theory suggests the possible tactic of making large numbers of simulated realities in which the inhabitants are treated kindly as a way of trying to meta-cause civilizations in general to do the same thing. This would be going further than what I said previously about treating the inhabitants of your own simulations kindly: This would be done so as to make it more likely that you are in a simulation, and that it is one in which you will be treated kindly. We might imagine a civilization doing this as a way of trying to use evidential decision theory to pluck an afterlife out of nowhere for itself, if it has recently acquired the computing power to simulate many civilizations, and provide them with an afterlife, but does not yet have technology such as mind uploading which it might use to obtain an afterlife more directly. A civilization might attempt this even if it does not yet have the computing power to construct simulated realities: It might set up some kind of legal or corporate framework to ensure that large numbers of ancestor simulations, complete with an afterlife, are constructed in the future, the idea being to strengthen the case that it is itself in such a simulation, made by a civilization with a past that is strongly correlated with its own present. Someone might even set up some organization for this purpose as a result of reading this article! \n Infinite ethics In all our calculations (sections 2.7 and 2.8) we assume finite numbers of agents each with a finite causal influence on their world. However, the multiverse -or even a single universe -may well be infinite. These infinities entail severe complications for the application of multiverse-wide consequentialist moral views like those required for multiverse-wide superrational cooperation  (Bostrom, 2011; Arntzenius, 2014) . Superrationality is a form of what  Bostrom (2011, ch 4.6)  calls \"class action\": through our actions, we can acausally affect an infinite amount of value, even if each physical instantiation of ourselves only has a finite causal impact. It seems unclear whether this makes infinite ethics even more challenging, or whether it can be viewed as a step toward a solution (cf.  Almond, 2010c, ch. 3.2 ). One's preferred approach to the problem of infinite ethics may well be consequential for a variety of issues (including MSR), which is why FRI lists infinite ethics as a promising area for future research. Nonetheless, I expect a solution to preserve most of the conclusions drawn from traditional (i. e. finite) ethics. \n Objection based on uncertainty about the values of superrationalists in the multiverse Thoughts on the value systems of extraterrestrials are necessarily speculative and uncertain. At what level of certainty about some other value system should we invest resources into maximizing it? Indeed, one possible criticism of MSR is that we will never be sufficiently certain of just how common some other value system is. Thus, the argument goes, we should in practice never take any specific value systems other than our own into consideration. First note that superrationality is still relevant even if you do not know the other value systems. There are some interventions that benefit other superrationalists without requiring knowledge of their values (see section 4.1), such as making future superintelligent AIs cooperate superrationally (under the assumption that they will come to understand the values of other agents in the multiverse much better than we do). But even if the argument acknowledges this, it is still invalid, primarily because it ignores the fact that we do not know how common our own value system is, either. In section 2.8 we argued that if we consider the correlations between our actions and the behavior of agents elsewhere in the multiverse, then maximizing a neutral compromise utility function in our local universe maximizes our original utility function in the multiverse at large. This argument also applies if we are uncertain about the other agents' utility functions and thus the compromise utility function itself. Thus, it must be possible to state the criticism in terms of the compromise utility function. For example, the criticism may translate to the following statement: the only terms in the compromise utility function that we can be certain about represent our own values. We are so uncertain about all other value systems that they do not contribute much to estimates of compromise utility. This criticism could, in theory, be true. Imagine you grew up on a planet where everyone had the same value system as yours; even if you believed that the universe also has other value systems, you would be justified not to assign much weight to any other specific value system. On Earth, however, we already observe quite some variety in what people care about. Thus, no matter what value system you hold, there are probably other value systems that are similarly common on Earth. Of course, we still do not know whether these value systems are also common elsewhere in the universe, but your own value system is a priori not in a privileged position that would justify assuming it to be more common than others. Solely maximizing our own utility function in this universe thus seems to be a bad approach towards maximizing the compromise utility function, in turn making it suboptimal in terms of our multiverse-wide utility. Figure 1 : 1 Figure 1: A causal graph representing the Donation game with copies and precommitment. \n Figure 2 : 2 Figure 2: A graph representing the causal relationship in the CGTA thought experiment. \n Figure 3 :Figure 4 : 34 Figure 3: Generic causal graphs representing the two types of Newcomb-like decision problems. Medical Newcomb problems are illustrated on the left. Newcomb problems based on similarity between decision algorithms are illustrated on the right. \n Figure 6 : 6 Figure 6: A graph representing a situation of mutual cooperation. An arrow from A to B indicates that A can benefit B. \n Figure 7 : 7 Figure 7: A circular cooperation graph representing cooperation schemes of the sort used in the Donation circle. Again, an arrow from A to B indicates that A can benefit B. \n Figure 8 : 8 Figure 8: A linear cooperation graph (graph theoretically speaking, a 1-ary tree) representing schemes of cooperation like that in the donation ladder. An arrow from A to B indicates that A can benefit B. Again, the nodes represent participants and an arrow from A to B indicates that A can bring causal benefits to B. \n Figure 9 : 9 Figure 9: A directed acyclic graph representing the schemes of cooperation like that of the Hierarchical donation game. \n where, for example, P (C | C) is the probability that the other side cooperates conditional on my cooperation. Solving for b other yields b other > b u P (C | C) − P (C | D) , (8) where P (C | C) − P (C | D) can be interpreted as quantifying how much more likely my cooperation makes the other's cooperation. Because there is at least some correlation, the term is always greater than 0. If the correlation is perfect, then P (C | C) = 1 and P (C | D) = 0, such that we get Eq. (7) as a special case of Eq. (8). If the correlation is less than perfect, then b a > b s may not be enough. For example, if P (C | C) = 0.8 = P (D | D) (such that whatever one agent does, the other agent is 80% likely to do the same), then it must hold that b a > b s P (C | C) − P (C | D) = b s 0.8 − 0.2 = 5 3 b s . \n Omega decides to play a game of heads or tails with you. You are told that if the coin comes up tails, Omega will ask you to give it $100. If it comes up heads, Omega will predict whether you would have given $100 if the coin had come up tails. If Omega predicts that you would have given it the money, it gives you $10,000; otherwise, you receive nothing. Omega then flips the coin. It comes up tails, and you are asked to pay $100. Do you pay? 2.2):Counterfactual mugging.If you can precommit to giving the money before you learn about your poor luck, you should do so. After all, this would render it near-certain that Omega would give us $10,000 if the coin comes up heads, at the mere cost of $100 if it comes up tails. By precommitting to pay Omega, we thus gain 0.5 • $10,000 − 0.5 • $100 = $4,950 in expectation. \n . Meanwhile, of people who do not chew gum, only 10% die of throat abscesses before the age of 50. The researchers, to explain their results, wonder if saliva sliding down the throat wears away cellular defenses against bacteria. Having read this study, would you choose to chew gum? But now a second study comes out, which shows that most gum-chewers have a certain gene, CGTA, and the researchers produce a table showing the following mortality rates: CGTA present CGTA absent Chew gum 89% die 8% die Don't chew 99% die 11% die \n First, we have to consider what negative correlation means. Let's say you currently think that roughly 0.1% of evolved agents in the multiverse who have thought about MSR decide to cooperate. Now, you learn of one randomly chosen agent that she cooperates. The intuitive response is to increase the 0.1% estimate, if only slightly (depending how confident you were in your initial estimate). If this agent were negatively correlated with the others, then upon learning that this one agent cooperated, you would adjust your estimate of how many agents cooperate downward. \n One fine day, out of the blue, you get a letter from S. N. Platonia, a renowned Oklahoma oil trillionaire. The letter states that 20 leading rational thinkers have been selected to participate in a little game, and you are among the lucky players. \"Each of you has a chance at winning one billion dollars, put up by the Platonia Institute for the Study of Human Irrationality\", it explains. \"Here's how: if you wish, you may send a telegram with just your name on it to the Platonia Institute. If exactly 5 people reply within 48 hours, they each receive one billion dollars, otherwise no prizes are awarded to anyone. You are not allowed to communicate with each other or share the prize afterward.\" What do you do? 26  For example, consider the following variation of the Platonia dilemma, adapted from Hofstadter (1983) :Platonia five. \n Table 1 : 1 . Payoff matrix for two people driving in opposite directions. player 2 right-hand left-hand player 1 right-hand 0 -10 left-hand −10 0 \n Omega has a list of 6 participants. The list is circular, meaning that every participant has a successor. Omega sends each participant a letter, asking them to respond with single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. It explains that by sending in 'C', participants can increase their successor's payoff by $5. By sending in 'D', they can increase their own payoff by $2. As usual, the participants are told that they are all rational or that they use similar decision mechanisms. Every participant only cares about the balance of her own bank account, and not about Omega's or that of the other 6 participants. Upon receiving the letter, should you cooperate or defect? \n Secondly, thinking about the other agents' decisions can be dangerous. No. 42 defects solely because he thinks about what the preceeding 41 participants decide. Knowing what the other agents think is thus harmful for some not-yet-updateless decision theories. Hence, similar to how it is wise to remain ignorant about your position in the list, many decision theories would recommend not thinking about what the other agents will do. If the players are human, then No. 1 may not be able to refrain from realizing that he wins by defecting. Perhaps No. 2 cannot refrain from realizing that No. 1's situation is different and his decision therefore independent of hers. However, participants with two-figure positions may be able to refrain and go with the reasoning originally presented: whatever I choose, my predecessor will probably choose the same, as his situation is similar to mine. If I just go ahead without thinking about the \"chain of defection\" initiated by No. 1, then people with similar numbers are probably going to do the same. Donation tree. Omega has a long list of participants again. It sends all of them a letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. Omega explains that by sending in 'C', participants can increase the payoff of at least 3 participants down the list by $2 each. For example, if the 4th participant chooses to cooperate, this benefits a subset of the participants in positions 5, 6, etc. but not the previous 3 participants. The cooperation of the last few participants has little to no effect. By sending in 'D' participants can increase their own payoff by $5. Participants do not know their position on the list or whom they could benefit. As usual, they are told that they all use similar decision mechanisms. Every participant only cares about the balance of their own bank account, and not about Omega's or the other participants'. Upon receiving the letter, should a participant cooperate or defect? The linear structure can be generalized to non-linear hierarchical cooperation schemes. Consider the following variant of the donation game: , chapter 7.2.2). If all of this is not the case, nothing can change the fact that at least No. 1 \"wins by defecting once she knows her position on the list. \n To talk about human values, it is at least helpful (if not necessary) to develop some systematic terminology and overview of what kind of things people care about. Luckily, we can get help from moral psychologists and others who have attempted to develop just this sort of overview.One example is Jonathan Haidt's and Craig Joseph's moral foundations theory. It divides morality up into five foundations -care, fairness, loyalty, authority and sanctity -although the authors do acknowledge that some other values (such as liberty) may deserve foundation status as well. Haidt and his colleagues have also shown that while social conservatives tend to embrace all five moral foundations, liberals/progressives seem to focus primarily on the first two, i. e. care and fairness.51  We can thus also use the terms \"liberal\" and \"conservative\" to describe values, even though it is, of course, uncertain whether this distinction carries the same weight in other civilizations.Other theories outlining what humans value include Schwartz' Theory of Basic Human Values (updated and extended bySchwartz et al. ( \n Table 2 : 2 The payoff matrix of a prisoner's dilemma. player 2 C D player 1 C 4 3 D 3 2 \n Table 3 : 3 The effective payoffs of a prisoner's dilemma to a third party that cooperates superrationally. \n Table 4 : 4 The effective payoffs of a prisoner's dilemma, in which player 1 cooperates superrationally (with extraterrestrial agents who hold player 2's values), but player 2 does not. \n Do people already apply superrational reasoning when interacting with each other on Earth? Certainly, many disagree with CDT's choice in contrived examples like Newcomb's problem or the prisoner's dilemma against a copy, but does it ever influence their real-world decisions? When conducting a donation game for his Scientific American article, Hofstadter (1983)  asked the participants to explain their reasoning: I would like to quote to you some of the feelings expressed by my friends caught in this deliciously tricky situation. [...] Martin Gardner (yes, I asked Martin to participate) vividly expressed the emotional turmoil he and many others went through.Many people flirted with the idea that everybody would think \"about the same\", but did not take it seriously enough. Scott Buresh confided to me: \"It was not an easy choice. I found myself in an oscillation mode: back and forth. I made an assumption: that everybody went through the same mental processes I went through. Now I personally found myself wanting to cooperate roughly one third of the time. Based on that figure and the assumption that I was typical, I figured about one third of the people would cooperate. So I computed how much I stood to make in a field where six or seven people cooperate. It came out that if I were a D, I'd get about three times as much as if I were a C. So I'd have to defect. Water seeks out its own level, and I sank to the lower right-hand corner of the matrix.\" At this point, I told Scott that so far, a substantial majority had defected. He reacted swiftly: \"Those rats -how can they all defect? It makes me so mad! I'm really disappointed in your friends, Doug.\" So was I, when the final results were in: Fourteen people had defected and six had cooperated [...]. bought the Brooklyn Bridge than the person who sold it. Similarly, I'd feel better spending $3 gained by cooperating than $10 gained by defecting.\" Charles Brenner, who I'd figured to be a sure-fire D, took me by surprise and C'd. When I asked him why, he candidly replied, \"Because I don't want to go on record in an international journal as a defector.\" Very well. Know, World, that Charles Brenner is a cooperator! Sidney Nagel was very displeased with his conclusion. He expressed great regret: \"I actually couldn't sleep last night because I was thinking about it. I wanted to be a cooperator, but I couldn't find any way of justifying it. The way I figured it, what I do isn't going to affect what anybody else does. I might as well consider that everything else is already fixed, in which case the best I can do for myself is to play a D.\" [...] 'C' is the answer I was hoping to receive from everyone. I was not so optimistic as to believe that literally everyone would arrive at this conclusion, but I expected a majority would -thus my dismay when the early returns strongly favored defecting. As more phone calls came in, I did receive some C's, but for the wrong reasons. Dan Dennett cooperated, saying, \"I would rather be the person who \"Horrible dilemma\", he said. \"I really don't know what to do about it. If I wanted to maximize my money, I would choose D and expect that others would also; to maximize my satisfactions, I'd choose C, and hope other people would do the same (by the Kantian imperative). I don't know, though, how one should behave rationally. You get into endless regresses: 'If they all do X, then I should do Y, but then they'll anticipate that and do Z, and so . . .' You get trapped in an endless whirlpool. It's like Newcomb's paradox.\" So saying, Martin defected, with a sigh of regret.In a way echoing Martin's feelings of confusion, Chris Morgan said, \"More by intuition than by anything else, I'm coming to the conclusion that there's no way to deal with the paradoxes inherent in this situation. So I've decided to flip a coin, because I can't anticipate what the others are going to do. I think -but can't know -that they're all going to negate each other.\" So, while on the phone, Chris flipped a coin and \"chose\" to cooperate. \n\t\t\t This is consistent with the terminology by Tegmark (2003) but otherwise uncommon. \n\t\t\t Quantifying utility in a way that allows for comparison among different agents is difficult. For now, we will assume that it is possible. The question is revisited in section 2.8. \n\t\t\t Speaking about correlations between decisions only makes sense under the Bayesian interpretation of probability. If we see an agent cooperate, then this makes us assign a higher credence to a similar agent cooperating as well. However, if we were to observe two similar agents make the same decision over and over again, then their decisions would be uncorrelated in the resulting empirical distribution.I should also note that, in principle, I could also talk about dependences rather than correlations. Our decision and the outcome of some other causally disconnected event could be dependent in all kinds of ways, including being dependent but uncorrelated. Throughout this paper I will assume that the dependences can be viewed as simple linear relationships (as measured by the Pearson correlation coefficient) and that it always holds that the more I cooperate, the more others cooperate. I briefly discuss the possibility of negative correlations in section 2.6.2. \n\t\t\t Note that the term \"non-causal decision theory\" is not meant to imply that these theories do not rely on the concept of causality at all.5 Some have argued that evidentialist intuitions are even stronger in problems of cooperation like versions of the prisoner's dilemma with correlated decision making. Egan (2007)  presents yet another decision problem as a decisive counterexample.6 If you have anthropic uncertainty over whether you are currently in a simulation used to decide how to fill the boxes with money, CDT may also recommend one-boxing if the simulated version would still care \n\t\t\t In some versions of this problem, Omega has already flipped the coin when it approaches you. In those cases, you would still win by precommitting long after the coin has already landed, provided you are still uncertain about the result of the coin flip.9 Similar lines of reasoning about precommitment apply to thought experiments like the Newcomb's problem with transparent boxes(Drescher, 2006a, chapter 6.2), retribution(Drescher, 2006a, chapter 7.3.1) and Parfit's hitchhiker(Parfit, 1984, chapter 1.3). \n\t\t\t In fact, most multiverse theories contain infinitely many agents. This leads to some additional complications, discussed in section 6.10.13 Decision theorists have picked up on the point that large numbers of agents can bring out the differences between CDT and EDT in realistic cases. In particular, large elections are often mentioned as such a case (see, e. g.Ahmed, 2014, chapter 4.6.3).14 Note that this is usually not an instance of Pascal's mugging, although the underlying mathematical mechanism (multiplying very small numbers with very large numbers) is similar. Whereas in Pascal's mugging, a big reward outweighs the low probability assigned to it, multiverse-wide superrationality (MSR) involves a low probability being outweighed by the large number of near-independent instances of that probability. The positive result occurs with a high probability as long as the other agents' decisions of whether to cooperate are mostly independent of one another. For comparison, imagine drawing balls out of a box containing 1,000,000 balls. You are told that the probability of drawing a blue ball is only 1/1,000 and that the probabilities of different draws are independent. Given this information, you can tell with a high degree of certainty that there are quite a few blue balls in the box. Multiverse-wide correlations between agents thus becomes much more important to consider than the correlations in smaller scale problems like the donation game, unless we are skeptical of some of the underlying assumptions. \n\t\t\t This differs somewhat from more standard game-theoretical definitions of coordination. For a discussion of the relationship, see (Oesterheld, 2017) . \n\t\t\t This notation -viewing the lotteries as probability distributions over action vectors -is a bit unnatural, and stems from the lack of an intermediate step of world states or histories between action vectors and utilities in our notation. If we extended our notation with such an intermediate step, then the lotteries would be over states of the world rather than action vectors. Although the proofs also work with action vectors, it may help to think of the lotteries as being over histories.18 Interestingly, the proof of the aggregation theorem given by Harsanyi (1955)  contains an error. However, since then a few alternative, correct proofs have been published(Fishburn, 1984; Border, 1985;  Hammond,  1992). \n\t\t\t Note that none of the previous arguments were based on interpersonal comparisons of utility.20  There is a technical problem with utility functions that do not assume a highest/lowest value at all. If they are nonetheless bounded, the infimum and supremum must be set to 0 and 1. If the utility functions assume arbitrarily high values, range normalization is not possible. That is, for an unbounded utility function u there is no bounded utility function u' that is equivalent to u.21 For ethical comparisons, the lowest and highest values usually depend on an agent's moral relevance, or some measure of the intensity of preference (un)fulfillment she can experience. Alternatively, the utility function may be weighted by such values at some other steps of the interpersonal comparison of utility.22 As I will argue below, there are some pathological cases in which every possible compromise utility function leaves someone worse off. However, both of the following cases can, if they avoid these pathologies, \n\t\t\t Another approach, which I have brought up in previous work(Oesterheld, 2016a, section 3.2), is to use any utility function extraction procedure that is not explicitly biased in any way and hope that such \"fair[or,  perhaps, equal]  treatment in determining all individuals' utility functions induces moral permissibility,\" even if the utility functions are not normalized afterward. This is especially promising if you do not yet know which agents will be favored by the procedure. \n\t\t\t In If you don't know the name of the game, just tell me what I mean to you, Stuart Armstrong uses a similar game to make a somewhat similar point. \n\t\t\t For instance, Peter Levin writes:The reasons that people give for their judgments are post-hoc rationalizations(Haidt, 2012,  pp. 27-51; Swidler, 2013, pp. 147-8; Thiele, 2006). \"Individuals are often unable to access the causes of their moral judgments\"(Graham et al., 2011, p. 368). \n\t\t\t Also seeMuehlhauser and Helm (2012, ch. 5).26 Again, see the technical note Oesterheld (2017)  on how this compares to more standard game theoretical definitions of coordination. \n\t\t\t You may have noticed that p=1/4=5/20, i. e. the number of players who would need to win divided by the number of players. This result generalizes.28 Specifically, if the 20 participants could let some some uniform random process determine the set of the 5 people who are allowed to send a letter, everyone could commit to going with that proposal. Consider the concept of correlated equilibria. \n\t\t\t In the game-theoretical concept of correlated equilibria, the agents receive a similar form of coordination help. SeeLeyton-Brown and Shoan (2008, chapter 3.5) andOsborne and Rubinstein (1994, chapter 3.3) for introductions. \n\t\t\t Note that in causal cooperation, cooperative or uncooperative behavior may also causally affect bystanders and thus increase the probability that I can establish cooperation with them in the future.31 Throughout this treatment, the graphs do not represent time and repetition. This could be done by taking the given static graphs and \"unfolding through time\", similar to how it is done when applying backpropagation to recurrent neural networks. The resulting graph may then resemble a UML interaction diagram. \n\t\t\t Even in the iterated prisoner's dilemma, this answer -supported by backward induction -is often seen as unsatisfactory. Other examples of paradoxes caused by backward induction are the chainstore paradox, the traveler's dilemma, the unexpected hanging paradox, the Bottle Imp paradox, the centipede game, the interesting number paradox, the guess 2/3 of the average game. A good introduction is given byBasu (2007). For further references, see Basu (1994) . \n\t\t\t Two classes of hypotheses in this space are substance dualism and the quantum mind. Both have a few prominent proponents but are nonetheless fringe positions in philosophy of mind. I concur with the majority and am skeptical of both hypotheses. \n\t\t\t For references to the literature, see section 2.9.1. \n\t\t\t Apparently, some authors differentiate between instrumental and \"value rationality\". I would probably disagree with the assumptions underlying the use of the term \"value rationality\" (see footnote 68). Nevertheless, I agree with the differentiation itself. \n\t\t\t In most human sadists, sadism is probably not the only goal or cause of happiness. Many sadists probably recognize their urges as morally wrong, yet are unable to control them to varying degrees. To these sadists, a decision theory may provide a nudge towards seeking professional help (at least if they cannot satisfy their sadistic preferences in morally nonproblematic ways). \n\t\t\t In my personal experience, self-identified consequentialists actually tend to be more virtue ethical in their behavior than the average person. \n\t\t\t One may argue that absurdity heuristics are a part of someone's epistemology. That is, the \"absurdity\" of the Everett interpretation is used as a reason to give it low probability as a theory of physics. However, it is not clear whether there is a clear-cut, operational difference between belief and preference if the belief does not make a testable prediction. \n\t\t\t Note that some authors are skeptical to there being any fact of the matter in questioning whether some being is conscious or not. Instead, they view terms like \"consciousness\" and \"sentience\" as definitional categories or expressions of particular values. See, e. g., Dennett (1991)  and Brian Tomasik's Dissolving Confusion about Consciousness. \n\t\t\t If we normalize their utility function, both assign the same utility to a situation in which all the multiverse's metal is transformed into their favorite office supply. This also means that they assign the same utility to any other other fixed amount of metal being transformed into paperclips. \n\t\t\t In Divergent preferences and meta-preferences, Stuart Armstrong makes a few points that are closely related to the preceding three paragraphs.44 Habermas' discourse ethics is also worth mentioning. Alas, the best discussion of its main ideas that I am aware of -ch. 5 of Norbert Hoerster's Wie lässt sich Moral begründen? -is currently only available in German.45 On the other hand, many (if not most) biologists seem to care about conservation -popular biology textbooks like Campbell Biology (Urry et al., 2016)  and Life: The Science of Biology (Sadava et al., 2012)  cover and seem to endorse conservation biology. There are various counter-considerations, though. For example, a prior concern for the environment may be a strong motivator for many to study biology in the first place. Perhaps many also did not think about the moral value of nature all that systematically. From what I can tell, neither Campbell Biology nor Life cover wild animal suffering at all. \n\t\t\t Many arguments also present a conflict between abstract and concrete thinking. For example, the repugnant conclusion can be seen as a clash of the evaluation by the concrete welfare of the identifiable victim or representative moment and the abstract evaluation by the aggregate welfare. \n\t\t\t Many other characterizations of the difference between liberals and conservatives have been proposed. For example, Robin Hanson compares the differences between liberals and conservatives to the differences between foragers and farmers. Other distinctions have been proposed by Sinn and Hayes (2016)  and Lakoff (1997) . \n\t\t\t The most notable exceptions are probably Boltzmann brains, which do not have a significant impact on the universe. \n\t\t\t There is some debate as to whether the the term \"evolution\" fits this process, i. e. about the validity and usefulness the analogy between cultural evolution on memes and biological evolution on genes (Edmonds, 2005; Kuper, 2000; Gil-White, 2005; Wimsatt, 1999; Claidière and André, 2012; Atran, 2001;  Pinker, 1999,  chapter 3, section \"What now?\"). Anyway, my impression is that nowadays the study of cultural evolution does not heavily rely on the analogy, even when the term \"cultural evolution\" is used. \n\t\t\t Note that the distinction between universal and idiosyncratic concerns is not binary. For example, I would guess that valuing eternal flames is much more common in the multiverse than most religions and tribal loyalties but less common than concern for justice, welfare and freedom. \n\t\t\t That said, advocates of simple ethical views like utilitarianism often argue that the implications resemble other ethical notions. For example, because receiving an additional unit of resources has a greater impact on a poor than a rich person's happiness, utilitarianism tends to prefer an even distribution of resources(Studebaker, 2012). Similarly, it has been argued that utilitarianism is (often) consistent with the wrongness of killing, justice (Mill, 1863)  and other moral rules(Smart and B. Williams, 1973, part 1, chapter 7). This decreases the value of making utilitarians more pluralistic. It should be noted, however, that many (especially critics of utilitarianism) have argued for the opposite, i. e. that there are some moral intuitions \n\t\t\t For example, the Machine Intelligence Research Insitute's \"Research\" page is titled \"Aligning advanced AI with human interests\". Another AI safety organization even mentions it in their name: the Center for Human-Compatible AI. Also consider the Asilomar AI principles and the discussion of value loading byBostrom (2014b, chapters 12, 13). \n\t\t\t Of course, identifying superrational cooperators in a world model may be more or less difficult than identifying humans in the world model. My tentative guess would be that it is easier, because I think the category of superrationalists can be described more succinctly than the category of humans, but of course I am not very confident in this claim. Similarly, it may be that MSR-type aggregation (e. g., variance \n\t\t\t Data from other games with similarly dissatisfying Nash equilibria can be used as further tests of such models of human reasoning. For example,Basu (2007)  reviews research on people's choices in the traveler's dilemma. He also hypothesizes that many people do not go with the Nash equilibrium because of hardwired altruism. \n\t\t\t Note that while humans evolved to spread their genes as much as possible, they are neither pure fitness maximizers nor pure egoists (in the sense of not caring about others' welfare). Our altruistic intentions evolved for reasons of fitness, but that does not mean they are not genuine altruistic intentions(Yudkowsky,  2015, section 138; Cosmides and  Tooby, 1995, page 54f. Wright, 1995, page 225f.).78 This is no surprise, as deriving ought from is cannot -at least in my view -be done.", "date_published": "n/a", "url": "n/a", "filename": "Multiverse-wide-Cooperation-via-Correlated-Decision-Making.tei.xml", "abstract": "Some decision theorists argue that when playing a prisoner's dilemma-type game against a sufficiently similar opponent, we should cooperate to make it more likely that our opponent also cooperates. This idea, which Hofstadter calls superrationality, has strong implications when combined with the insight from modern physics that we probably live in a large universe or multiverse of some sort. If we care about what happens in civilizations located elsewhere in the multiverse, we can superrationally cooperate with some of their inhabitants. That is, if we take their values into account, this makes it more likely that they do the same for us. In this paper, I attempt to assess the practical implications of this idea. I argue that to reap the full gains from trade, everyone should maximize the same impartially weighted sum of the utility functions of all collaborators. I also argue that we can obtain at least weak evidence about the content of these utility functions. In practice, the application of superrationality implies that we should promote causal cooperation, moral pluralism, moral reflection, and ensure that our descendants, who will be smarter and thus better at finding out how to benefit other superrationalists in the universe, engage in superrational cooperation. \n Introduction -the basic idea This paper makes an extraordinary claim: that a few interesting but by themselves inconsequential ideas from decision theory and physics together give rise to a crucial consideration with strong implications for how to do the most good. In this first section, I will outline the main idea and forward-reference sections with the full arguments and detailed elaborations. Afterward, I give an overview of the entire paper, section by section (section 1.1). Consider the following thought experiment, adapted from Hofstadter's (1983) Dilemmas for Superrational Thinkers, Leading Up to a Luring Lottery: Donation game with superrationality. Hofstadter sends 20 participants the same letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with the other participants. Hofstadter \n Superrationality Despite what the name might suggest, superrationality does not have anything to do with extraordinary levels of rationality. \"Super\" refers to inclusivity, as in superorganism, and \"rationality\" specifically denotes instrumental rationality. The term was introduced by Hofstadter (1983), although the basic argument had been discussed before  (Davis, 1977; Horgan, 1981 , section X). In the following we give an abbreviated and simplified account of the prisoner's dilemma or public goods game-like experiment Hofstadter ran with some of his friends and colleagues as participants. It is the same thought experiment we discussed in the introduction, although we now distinguish two slightly different versions. The argumentation for superrationality will be relatively brief. For more detailed accounts, see Hofstadter's original article or some of the references in section 2.2. Donation game with common rationality. (This is more similar to the version Hofstadter uses in his article.) Hofstadter sends 20 participants the same letter, asking them to respond with a single letter 'C' (for cooperate) or 'D' (for defect) without communicating with each other. Hofstadter explains that by sending in 'C', a participant can increase everyone else's payoff by $2. By sending in 'D', participants can increase their own payoff by $5. The letter ends by informing the participants that they were all chosen for their high levels of rationality and correct decision making in weird scenarios like this. Note that every participant only cares about the balance of her own bank account and not about Hofstadter's or the other 19 participants'. Should you, as a participant, respond with 'C' or 'D'? Donation game with similarity. The same as the donation game with common rationality. However, instead of informing the participants that they are all rational, the game master informs them that they think in similar ways about weird decision problems like this one. The basic setup of this thought experiment is equivalent to those found in, e. g., the prisoner's dilemma with copies (sometimes also referred to as the prisoner's dilemma with replicas or twins). All of these games share an important feature: they are not iterated. Participants respond only once, then find out what the others chose -and the game is over.", "id": "5482353368a0ec4e131702d1ca5e3f9d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Joshua Greene", "Francesca Rossi", "John Tasioulas", "Kristen Brent Venable", "Brian Williams"], "title": "Embedding Ethical Principles in Collective Decision Support Systems", "text": "Introduction We believe it is important to study the embedding of safety constraints, moral values, and ethical principles in agents, within the context of collective decision making systems in societies of agents and humans. Collective decision making involves a collection of agents who express their preferences over a shared set of possible outcomes, and a preference aggregation rule which chooses one of the options to best satisfy the agents' preferences. However, aggregating just preferences may lead to outcomes that do not follow any ethical principles or safety constraints. To embed such principles/constraints in a collective decision making system, we need to understand how to model them, how to reason with them at the level of a single agent, and how to embed them into collective decision making. Just like individual humans, each agent that operates in a multi-agent context needs to be have an internal representation of moral values and ethical principles, as well as an ethical reasoning engine. Otherwise it would not able to explain its behaviour to others. Copyright c 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. We claim that there is a need to adapt current logicbased modelling and reasoning frameworks, such as soft constraints, CP-nets, and constraint-based scheduling under uncertainty, to model safety constraints, moral values, and ethical principles. More precisely, we study how logicbased preference modelling frameworks can be adapted to model both (explicit) ethical principles and (implicit) moral values, as sophisticated constraints over possible actions. The constraints may be unconditional (\"hard\") constraints, or soft, overridable if the consequences of an individual bad action can still lead to overall good. We propose to replace preference aggregation with an appropriately developed value/ethics/preference fusion, an operation designed to ensure that agents' preferences are consistent with their moral values and do not override ethical principles For ethical principles, we use hard constraints specifying the basic ethical \"laws\", plus some form of common-sense morality expressed as sophisticated prioritised and possibly context-dependent constraints over possible actions, equipped with a conflict resolution engine. To avoid reckless behavior in the face of uncertainty, we proposed to bound the risk of violating these ethical laws in the form of chance constraints, and we propose to develop stochastic constraint solvers that propose solutions that respect these risk bounds, based on models of environmental uncertainty. We also propose to replace preference aggregation with an appropriately developed constraint/value/ethics/preference fusion, an operation designed to ensure that agents' preferences are consistent with the system's safety constraints, the agents' moral values, and the ethical principles. We will leverage previous experience in developing single and multi-agent preference/constraint reasoning engines. Today, techniques exist to enable agents to make decisions, such as scheduling activities, while satisfying some safety concerns, e.g. by using techniques from constraintbased optimization. For instance, in many critical scenarios, such as space missions where a malfunction can endanger the whole mission, activities are scheduled in such a way to maximise robustness against possible problems. We believe that these techniques can provide an inspiration to handle ethical concerns. However, we think that a much more explicit model and reasoning engine for ethical principles and moral values is needed in order to deal with them satisfactorily and allow them to evolve over time. \n Which ethical principles for intelligent agents? An intelligent agent should have capability to autonomously make good decisions, based on available data and preferences, even in the context of uncertainty, missing or noisy information, as well as incorrect input, and should be able to learn from past experience or from available historical data. Even more importantly, intelligent agents should have the ability to interact with humans, make decisions together with them, and achieve goals by working together. An agent with these capabilities poses several crucial ethical questions. Ethical principles guide humans' behaviour. They tell us what is regarded as right or wrong. They come from values that we regards as absolute, guiding our whole life. If we want intelligent agents to enhance human capabilities, or to collaborate with humans, or even just to live and act in the same society, we need to embed in them some ethical guidelines, so they can act in their environment following values that are aligned to the human ones. Or maybe we need different values and ethical principles for agents, since they are inherently different from humans? As Issac Asimov famously illustrated in his I, Robot series, explicitly programming ethical behavior is surprisingly challenging. Moral philosophy -the field that has studied explicit ethical principles most extensively -suggests three general approaches, corresponding to the three major schools of Western moral thought. The deontological approach (most closely associated with Immanuel Kant) regards morality as a system of rights and duties. Here the focus is on categories of actions, where different actions are deemed impermissible, permissible, or obligatory based on a set of explicit rules. The consequentialist approach (most closely associated with Jeremy Bentham and John Stuart Mill) aims to produce the best aggregate consequences (minimizing costs and maximizing benefits) according to a pre-specified value function. For example, a classical utilitarian approach aims to maximize the total amount of happiness. The virtue-or character-based approach (most closely associated with Aristotle) regards ethical behavior as the product of an acquired set of behavioral dispositions that cannot be adequately summarized as an adherence to a set of deontological rules (concerning actions) or to as a commitment to maximizing good consequences. These three approaches are well known and have been the starting point for nearly all discussions of machine ethics  (Moor 1985; Bostrom 2014; Wallach and Allen 2008) . Each approach has limitations that are well known. Deontological principles are easily to implement but may be rigid. Consequentialist principles require complex calculations that may be faulty. Virtue is opaque and requires extensive training with an unknown teaching criterion. There is, however, a more general problem faced by all three approaches, which is that implementing them may depend on solving daunting, general computation problems that have not been solved and may not be solved for some time. For example, a \"simple\" deontological rule such as \"don't lie\" or \"dont kill\" is not specified in terms of machine movements. Rather, the machine must understand which acts of communication would constitute lying and which body movements would constitute killing in a given context. A consequentialist system would require a machine to represent all of the actions available to it, and a virtue based system would have to recognize the present situation as one with a variety of features that, together, call for one action rather than another. In other words, all three approaches, when fully implemented, seem to require something like general intelligence, which would enable the machine to represent its current situation in rich conceptual terms. Indeed, this speculation is consistent with recent research on the cognitive neuroscience of moral judgment indicating that moral judgment depends on a variety of neural systems that are not specifically dedicated to moral judgment  (Greene 2014) . This includes systems that enable the general representation of value and the motivation of its pursuit, visual imagery, cognitive control, and the representation of complex semantic representations. Unfortunately for Commander Data, humans have no \"ethical subroutine\". Real human moral judgment uses the whole brain. What, then, can be done? Here, the human brain may nevertheless offer some guidance  (Shenhav and Greene 2014) . Is it morally acceptable to push someone off of a footbridge in order to save five lives  (Thomson 1985 )? A simple deontological response says no (\"Dont kill\"). A simple consequentialist response says yes (\"Save the most lives\"), and most humans are at least somewhat conflicted about this, but err on the side of the deontological response (in this particular case). We now know that the deontological response depends on a classically emotional neural structure known as the amygdala (reflecting emotional salience) and that the application of the consequentialist maximizing principle depends on a classically \"cognitive\" structure known as the dorsolateral prefrontal cortex. It seems that healthy humans engage both responses and that there is a higher-order evaluation process that depends on the ventromedial prefrontal cortex, a structure that across domains attaches emotional weight to decision variables. In other words, the brain seems to make both types of judgment (deontological and consequentialist) and then makes a higher order judgment about which lower-order judgment to trust, which may be viewed as a kind of wisdom (reflecting virtue or good character). Such a hierarchical decision system might be implemented within an agent, or across agents. For example, some agents may apply simple rules based on action features. Others may attempt to make \"limited\" cost-benefit calculations. And collectively, the behavior of these agents may be determined by a weighting of these distinct, lower-level evaluative responses. Such as system might begin by following simple deontological rules, but then, either acquire more complex rules through learning, or learn when it can and cannot trust its own cost-benefit calculations. Starting with action-based rules and simple cost-benefit calculations substantially reduces the space of possible responses. Learning to trade-off between these two approaches adds some flexibility, but without requiring intractable cost-benefit calculations or lifelong moral education. We offer this approach as just one example strategy. Of course, if we knew how we were going to solve this problem, there would be no need to bring together people with diverse expertise. What we wish to convey is twofold: First, that we are aware of the scope of the challenge and the strengths and limitations of the extant strategies. Second, that we have some preliminary ideas for hybrid approaches that leverage insights from human moral cognition. Another important aspect of our approach would be to consider the extent to which morality could be reduced to a set of rules that is capable of being applied in a fairly straightforward way to guide conduct , e.g. 'Do not kill', 'Keep one's promises', 'Help those in need', etc. We already know that much of common sense morality is codifiable in this way, thanks to the example of the law. However, even if we could achieve an adequate codification of ordinary moral consciousness, at least within some domain, problems would arise. Two cases are especially worth highlighting: (a) cases where the strict application of a given rule generates an unacceptable outcome, often but not always characterisable as such by reference to some other rule that has been violated in adhering to the first, and (b) cases where the strict application of the given set of rules is unhelpfully 'silent' on the problem at hand, because it involved circumstances not foreseen by the rules. Both phenomena (a) and (b) raise the question of when and how the strict application of a rule needs to be modified or supplemented to resolve the problem of perverse results or gaps. One important source of thinking about these issues is Aristotle's discussion of justice and equity in the Nicomachean Ethics. According to Aristotle, the common sense morality codified in law, although capable of being a generally good guide to action, will nonetheless on occasion breakdown along the lines of (a) and (b). For Aristotle, this means that the virtuous judge will need to possess, in addition to a propensity to follow legal rules, the virtue of equity. This enables the judge to use their independent judgment to correct or supplement the strict application of legal rules in cases of type (a) or (b). A key topic involves the clarification of the notion of equity, with its rule and judgment structure, as a prelude to a consideration of how this might be embedded in autonomous agents. \n Designing ethical agents No matter which approach we will choose to express ethical principles and moral values in intelligent agents, we need to find a suitable way to model it in computational terms, which is expressive enough to be able to represent all we have in mind in its full generality, and which can be reasoned upon with computational efficiency. Ethical principles may seem very similar to the concepts of constraints  (Rossi, Van Beek, and Walsh 2006; Dechter 2003 ) and preferences  (Rossi, Venable, and Walsh 2011) , which have already received a large attention in the AI literature. Indeed, constraints and preferences are a common feature of everyday decision making. They are, therefore, an essential ingredient in many reasoning tools. In an intelligent agent, we need to specify what is not allowed according to the principles, thus some form of constraints, as well as some way to prioritise among different principles, that some form of preference. Representing and reasoning about preferences is an area of increasing theoretical and practical interest in AI. Preferences and constraints occur in real-life problems in many forms. Intuitively, constraints are restrictions on the possible scenarios: for a scenario to be feasible, all constraints must be satisfied. For example, if we have an ethical rule that says we should not kill anybody, all scenarios where people are killed are not allowed. Preferences, on the other hand, express desires, satisfaction levels, rejection degrees, or costs. For example, we may prefer an action that solves reasonably well all medical issues in a patient, rather than another one that solves completely one of them but does not address the other ones. Moreover, in many real-life optimization problems, we may have both constraints and preferences. Preferences and constraints are closely related notions, since preferences can be seen as a form of \"relaxed\" constraints. For this reason, there are several constraint-based preference modeling frameworks in the AI literature. One of the most general of such frameworks defines a notion of soft constraints  (Meseguer, Rossi, and Schiex 2006) , which extends the classical constraint formalism to model preferences in a quantitative way, by expressing several degrees of satisfaction that can be either totally or partially ordered. The term soft constraints is used to distinguish this kind of constraints from the classical ones, that are usually called hard constraint. However, hard constraints can be seen as an instance of the concept of soft constraints where there are just two levels of satisfaction. In fact, a hard constraint can only be satisfied or violated, while a soft constraint can be satisfied at several levels.When there are both levels of satisfaction and levels of rejection, preferences are usually called bipolar, and they can be modeled by extending the soft constraint formalism  (Bistarelli et al. 2006) . Preferences can also be modeled in a qualitative (also called ordinal) way, that is, by pairwise comparisons. In this case, soft constraints (or their extensions) are not suitable. However, other AI preference formalisms are able to express preferences qualitatively, such as CP-nets  (Boutilier et al. 2004 ). More precisely, CP-nets provide an intuitive way to specify conditional preference statements that state the preferences over the instances of a certain feature, possibly depending on some other features. For example, we may say that we prefer driving slow to driving fast if we are in a country road. CP-nets and soft constraints can be combined, providing a single environment where both qualitative and quantitative preferences can be modeled and handled. Specific types of preferences come with their own reasoning methods. For example, temporal preferences are quantitative preferences that pertain to the position and duration of events in time. Soft constraints can be embedded naturally in a temporal constraint framework to handle this kind of preference. An intuitive way to express preferences consists of providing a set of goals, each of which is a propositional formula, possibly adding also extra information such as priorities or weights. Candidates in this setting are variable assignments, which may satisfy or violate each goal. A weighted goal is a propositional logic formula plus a realvalued weight. The utility of a candidate is then computed by collecting the weights of satisfied and violated goals, and then aggregating them. Often only violated goals count, and their utilities are aggregated with functions such as sum or maximin. In other cases, we may sum the weights of the satisfied goals, or we may take their maximum weight. Any restriction we may impose on the goals or the weights, and any choice of an aggregation function, give a different language. Such languages may have drastically different properties in terms of their expressivity, succinctness, and computational complexity. In the quantitative direction typical of soft constraints, there are also other frameworks to model preferences. The most widely used assumes we have some form of independence among variables, such as mutual preferential independence. Preferences can then be represented by an additive utility function in deterministic decision making, or utility independence, which assures an additive representation for general scenarios. However, this assumption often does not hold in practice since there is usually some interaction among the variables. To account for this, models based on interdependent value additivity have been defined which allows for some interaction between the variables while preserving some decomposability. This notion of independence, also called generalized additive independence (GAI), allows for the definition of utility functions which take the form of a sum of utilities over subsets of the variables. GAI decompositions can be represented by a graphical structure, called a GAI net, which models the interaction among variables, and it is similar to the dependency graph of a CP-net or to the junction graph of a Bayesian network. GAI decompositions have been used to provide CP-nets with utility functions, obtaining the so-called UCP networks. \n Preferences and ethical principles in collective decision making systems If agents and humans will be part of a hybrid collective decision making system, and thus will make collective decisions, based on their preferences over the possible outcomes, can ethical principles for such decision system be modelled just like the preferences of another dummy agent, or should they be represented and treated differently? Are the knowledge representation formalisms that are usually used in AI to model preferences suitable to model values as well, or should we use something completely different? A very simple form of values could be modelled by constraints, so that only feasible outcomes can be the results of a collective decisions process. But values and ethical principles could often take a graded form, thus resembling a kind of preference. Also, should individual and collective ethical principles be modelled differently? We believe that some of the answers to these questions may exploit the existing literature on preference aggregation  (Rossi, Venable, and Walsh 2011) . Indeed, an important aspect of reasoning about preferences is preference aggregation. In multi-agent systems, we often need to combine the preferences of several agents. More precisely, preferences are often used in collective decision making when multiple agents need to choose one out of a set of possible decisions: each agent expresses its preferences over the possible decisions, and a centralized system aggregates such preferences to determine the \"winning\" decision. Preferences are also the subject of study in social choice, especially in the area of elections and voting theory  (Arrow and amd K. Suzumara 2002) . In an election, the voters express their preferences over the candidates and a voting rule is used to elect the winning candidate. Economists, political theorist, mathematicians, as well as philosophers have invested considerable effort in studying this scenario and have obtained many theoretical results about the desirable properties of the voting rules that one can use. Since the voting setting is closely related to multi-agent decision making, in recent years the area of multi-agent systems has witnessed a growing interest in trying to reuse social choice results in the multi-agent setting. However, it soon became clear that an adaptation of such results is necessary, since several issues, which are typical of multi-agent settings and AI scenarios, usually do not occur, or have a smaller impact, in typical voting situations. In a multi-agent system, the set of candidates can be very large with respect to the set of voters. Usually in social choice it is the opposite: there are many voters and a small number of candidates. Also, in many AI scenarios, the candidates often have a combinatorial structure. That is, they are defined via a combination of features. Moreover, the preferences over the features are often dependent on each other. In social choice, usually the candidates are tokens with no structure. In addition, for multi-issue elections, the issues are usually independent of each other. This combinatorial structure allows for the compact modelling of the preferences over the candidates. Therefore, several formalisms have been developed in AI to model such preference orderings. In social choice, little emphasis is put on how to model preferences, since there are few candidates, so one can usually explicitly specify a linear order. In AI, a preference ordering is not necessarily linear, but it may include indifference and incomparability. Moreover, often uncertainty is present, for example in the form of missing or imprecise preferences. In social choice, usually all preferences are assumed to be present, and a preference order over all the candidates is a linear order that is explicitly given as a list of candidates. Finally, multi-agent systems must consider the computational properties of the system. In social choice this usually has not been not a crucial issue. It is therefore very interesting to study how social choice and AI can fruitfully cooperate to give innovative and improved solutions to aggregating preferences of multiple agents. In our effort, since we intend to deal with ethical issues in collective decision making, we need to understand what modifications to the usual preference aggregation scenario should be done to account for them, and how they can be handled satisfactorily when making collective decisions. Collective decision making in the presence of feasibility constraints is starting to be considered in the literature  (Grandi et al. 2014) . However, ethical principles and safety constraints will be much more complex than just a set of constraints, so we need to understand the computational and expressiveness issues arising in this scenario. \t\t\t Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence", "date_published": "n/a", "url": "n/a", "filename": "12457-56397-1-PB.tei.xml", "abstract": "The future will see autonomous machines acting in the same environment as humans, in areas as diverse as driving, assistive technology, and health care. Think of self-driving cars, companion robots, and medical diagnosis support systems. We also believe that humans and machines will often need to work together and agree on common decisions. Thus hybrid collective decision making systems will be in great need. In this scenario, both machines and collective decision making systems should follow some form of moral values and ethical principles (appropriate to where they will act but always aligned to humans'), as well as safety constraints. In fact, humans would accept and trust more machines that behave as ethically as other humans in the same environment. Also, these principles would make it easier for machines to determine their actions and explain their behavior in terms understandable by humans. Moreover, often machines and humans will need to make decisions together, either through consensus or by reaching a compromise. This would be facilitated by shared moral values and ethical principles.", "id": "a0cf7d134598cca1f2cee9cb66a89f91"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Rachel Freedman", "Rohin Shah", "Anca Dragan"], "title": "Choice Set Misspecification in Reward Inference", "text": "Introduction Specifying reward functions for robots that operate in environments without a natural reward signal can be challenging, and incorrectly specified rewards can incentivise degenerate or dangerous behavior  [Leike et al., 2018; Krakovna, 2018] . A promising alternative to manually specifying reward functions is to design techniques that allow robots to infer them from observing and interacting with humans. Figure  1 : Example choice set misspecification: The human chooses a pack of peanuts at the supermarket. They only notice the expensive one because it has flashy packaging, so that's the one they buy. However, the robot incorrectly assumes that the human can see both the expensive flashy one and the cheap one with dull packaging but extra peanuts. As a result, the robot incorrectly infers that the human likes flashy packaging, paying more, and getting fewer peanuts. These techniques typically model humans as optimal or noisily optimal. Unfortunately, humans tend to deviate from optimality in systematically biased ways  [Kahneman and Tversky, 1979; Choi et al., 2014] . Recent work improves upon these models by modeling pedagogy  [Hadfield-Menell et al., 2016] , strategic behavior  [Waugh et al., 2013] , risk aversion  [Majumdar et al., 2017] , hyperbolic discounting  [Evans et al., 2015] , or indifference between similar options  [Bobu et al., 2020b] . However, given the complexity of human behavior, our human models will likely always be at least somewhat misspecified  [Steinhardt and Evans, 2017] . One way to formally characterize misspecification is as a misalignment between the real human and the robot's assumptions about the human. Recent work in this vein has examined incorrect assumptions about the human's hypothesis space of rewards  [Bobu et al., 2020a] , their dynamics model of the world  [Reddy et al., 2018] , and their level of pedagogic behavior  [Milli and Dragan, 2019] . In this work, we identify another potential source of misalignment: what if the robot is wrong about what feedback the human could have given? Consider the situation illustrated in Figure  1 , in which the robot observes the human going grocery shopping. While the grocery store contains two packages of peanuts, the human only notices the more expensive version with flashy packaging, and so buys that one. If the robot doesn't realize that the human was effectively unable to evaluate the cheaper package on its merits, it will learn that the human values flashy packaging. We formalize this in the recent framework of rewardrational implicit choice (RRiC)  [Jeon et al., 2020]  as misspecification in the human choice set, which specifies what feedback the human could have given. Our core contribution is to categorize choice set misspecification into several formally and empirically distinguishable \"classes\", and find that different types have significantly different effects on performance. As we might expect, misspecification is usually harmful; in the most extreme case the choice set is so misspecified that the robot believes the human feedback was the worst possible feedback for the true reward, and so updates strongly towards the opposite of the true reward. Surprisingly, we find that under other circumstances misspecification is provably neutral: it neither helps nor hurts performance in expectation. Crucially, these results suggest that not all misspecification is equivalently harmful to reward inference: we may be able to minimize negative impact by systematically erring toward particular misspecification classes defined in this work. Future work will explore this possibility. \n Reward Inference There are many ways that a human can provide feedback to a robot: demonstrations  [Ng and Russell, 2000; Abbeel and Ng, 2004; Ziebart, 2010] , comparisons  [Sadigh et al., 2017; Christiano et al., 2017] , natural language  [Goyal et al., 2019] , corrections  [Bajcsy et al., 2017] , the state of the world  [Shah et al., 2019] , proxy rewards  [Hadfield-Menell et al., 2017; Mindermann et al., 2018] , etc. Jeon et al. propose a unifying formalism for reward inference to capture all of these possible feedback modalities, called reward-rational (implicit) choice  (RRiC) . Rather than study each feedback modality separately, we study misspecification in this general framework. RRiC consists of two main components: the human's choice set, which corresponds to what the human could have done, and the grounding function, which converts choices into (distributions over) trajectories so that rewards can be computed. For example, in the case of learning from comparisons, the human chooses which out of two trajectories is better. Thus, the human's choice set is simply the set of trajectories they are comparing, and the grounding function is the identity. A more complex example is learning from the state of the world, in which the robot is deployed in an environment in which a human has already acted for T timesteps, and must infer the human's preferences from the current world state. In this case, the robot can interpret the human as choosing between different possible states. Thus, the choice set is the set of possible states that the human could reach in T timesteps, and the grounding function maps each such state to the set of trajectories that could have produced it. Let ξ denote a trajectory and Ξ denote the set of all possible trajectories. Given a choice set C for the human and grounding function ψ : C → (Ξ → [0, 1]), Jeon et al. define a procedure for reward learning. They assume that the human is Boltzmann-rational with rationality parameter β, so that the probability of choosing any particular feedback is given by: P(c | θ, C) = exp(β • E ξ∼ψ(c) [r θ (ξ)]) c ∈C exp(β • E ξ∼ψ(c ) [r θ (ξ)]) (1) From the robot's perspective, every piece of feedback c is an observation about the true reward parameterization θ * , so the robot can use Bayesian inference to infer a posterior over θ. Given a prior over reward parameters P(θ), the RRiC inference procedure is defined as: P(θ | c, C) ∝ exp(β • E ξ∼ψ(c) [r θ (ξ)] c ∈C exp(β • E ξ∼ψ(c ) [r θ (ξ)]) • P(θ) (2) Since we care about misspecification of the choice set C, we focus on learning from demonstrations, where we restrict the set of trajectories that the expert can demonstrate. This enables us to have a rich choice set, while allowing for a simple grounding function (the identity). In future work, we aim to test choice set misspecification with other feedback modalities as well. \n Choice Set Misspecification For many common forms of feedback, including demonstrations and proxy rewards, the RRiC choice set is implicit. The robot knows which element of feedback the human provided (ex. which demonstration they performed), but must assume which elements of feedback the human could have provided based on their model of the human. However, this assumption could easily be incorrect -the robot may assume that the human has capabilities that they do not, or may fail to account for cognitive biases that blind the human to particular feedback options, such as the human bias towards the most visually attention-grabbing choice in Fig 1. To model such effects, we assume that the human selects feedback c ∈ C Human according to P(c | θ, C Human ), while the robot updates their belief assuming a different choice set C Robot to get P(θ | c, C Robot ). Note that C Robot is the robot's assumption about what the human's choice set is -this is distinct from the robot's action space. When C Human = C Robot , we get choice set misspecification. It is easy to detect such misspecification when the human chooses feedback c / ∈ C R . In this case, the robot observes a choice that it believes to be impossible, which should certainly be grounds for reverting to some safe baseline policy. So, we only consider the case where the human's choice c is also present in C R (which also requires C H and C R to have at least one element in common). Within these constraints, we propose a classification of types of choice set misspecification in Table  1 . On the vertical axis, misspecification is classified according to  the location of the optimal element of feedback C R ⊂ C H C R ⊃ C H C R ∩ C H c * ∈ C R ∩ C H A1 A2 A3 ∈ C R \\C H B2 B3 c * = argmax c∈C R ∪C H E ξ∼ψ(c) [r θ * (ξ))]. If c * is available to the human (in C H ), then the class code begins with A. We only consider the case where c * is also in C R : the case where it is in C H but not C R is uninteresting, as the robot would observe the \"impossible\" event of the human choosing c * , which immediately demonstrates misspecification at which point the robot should revert to some safe baseline policy. If c * / ∈ C H , then we must have c * ∈ C R (since it was chosen from C H ∪ C R ), and the class code begins with B. On the horizontal axis, misspecification is classified according to the relationship between C R and C H . C R may be a subset (code 1), superset (code 2), or intersecting class (code 3) of C H . For example, class A1 describes the case in which the robot's choice set is a subset of the human's (perhaps because the human is more versatile), but both choice sets contain the optimal choice (perhaps because it is obvious). \n Experiments To determine the effects of misspecification class, we artificially generated C R and C H with the properties of each particular class, simulated human feedback, ran RRiC reward inference, and then evaluated the robot's resulting belief distribution and optimal policy. \n Experimental Setup Environment To isolate the effects of misspecification and allow for computationally tractable Bayesian inference, we ran experiments in toy environments. We ran the randomized experiments in the four 20 × 20 gridworlds shown in Fig 2  .  Each square in environment x is a state s x = {lava, goal}. lava ∈ [0, 1] is a continuous feature, while goal ∈ {0, 1} is a binary feature set to 1 in the lower-right square of each grid and 0 everywhere else. The true reward function r θ * is a linear combination of these features and a constant stayalive cost incurred at each timestep, parameterized by θ = (w lava , w goal , w alive ). Each episode begins with the robot in the upper-left corner and ends once the robot reaches the goal state or episode length reaches the horizon of 35 timesteps. Robot actions A R move the robot one square in a cardinal or diagonal direction, with actions that would move the robot off of the grid causing it to remain in place. The transition function T is deterministic. Environment x defines an MDP M x = S x , A R , T, r θ * . Inference While the RRiC framework enables inference from many different types of feedback, we use demonstration feedback here because demonstrations have an implicit choice set and straightforward deterministic grounding. Only the human knows their true reward function parameterization θ * . The robot begins with a uniform prior distribution over reward parameters P(θ) in which w lava and w alive vary, but w goal always = 2.0. P(θ) contains θ * . RRiC inference proceeds as follows for each choice set tuple C R , C H and environment x. First, the simulated human selects the best demonstration from their choice set with respect to the true reward c H = argmax c∈C H E ξ∼ψ(c) [r θ * (ξ))]. Then, the simulated robot uses Eq. 2 to infer a \"correct\" distribution over reward parameterizations B H (θ) P(θ | c, C H ) using the true human choice set, and a \"misspecified\" distribution B R (θ) P(θ | c, C R ) using the misspecified human choice set. In order to evaluate the effects of each distribution on robot behavior, we define new MDPs M x H = S x , A R , T, r E[B H (θ)] and M x R = S x , A R , T, r E[B R (θ)] for each environment, solve them using value iteration, and then evaluate the rollouts of the resulting deterministic policies according to the true reward function r θ * . \n Randomized Choice Sets We ran experiments with randomized choice set selection for each misspecification class to evaluate the effects of class on entropy change and regret. \n Conditions The experimental conditions are the classes of choice set misspecification in Table 1: A1, A2, A3, B2 and B3. We tested each misspecification class on each environment, then averaged across environments to evaluate each class. For each environment x, we first generated a master set C x M of all demonstrations that are optimal w.r.  If entropy change is positive, then misspecification induces overconfidence, and if it is negative, then misspecification induces underconfidence. Regret is the difference in return between the optimal solution to M x H , with the correctly-inferred reward parameterization, and the optimal solution to M x R , with the incorrectlyinferred parameterization, averaged across all 4 environments. If ξ * x H is an optimal trajectory in M x H and ξ * x R is an optimal trajectory in M x R , then regret = 1 4 3 x=0 [r θ * (ξ * x H )− r θ * (ξ * x R )] . Note that we are measuring regret relative to the optimal action under the correctly specified belief, rather than optimal action under the true reward. As a result, it is possible for regret to be negative, e.g. if the misspecification makes the robot become more confident in the true reward than it would be under correct specification, and so execute a better policy. \n Biased Choice Sets We also ran an experiment in a fifth gridworld where we select the human choice set with a realistic human bias to illustrate how choice set misspecification may arise in practice. In this experiment the human only considers demonstrations that end at the goal state because, to humans, the word \"goal\" can be synonymous with \"end\" (Fig  3a ). However, to the robot, the goal is merely one of multiple features in the environment. The robot has no reason to privilege it over the other features, so the robot considers every demonstration that is optimal w.r.t some possible reward parameterization (Fig  3b ). The trajectory that only the robot considers is marked in blue. We ran RRiC inference using this C R , C H and evaluated the results using the same measures described above. \n Results We summarize the aggregated measures, discuss the realistic human bias result, then examine two interesting results: symmetry between classes A1 and A2 and high regret in class B3.  Regret Regret also varied as a function of misspecification class. Each class had a median regret of 0, suggesting that misspecification commonly did not induce a large enough shift in belief for the robot to learn a different optimal policy. However the mean regret, plotted as green lines in Fig  5 , did vary markedly across classes. Regret was sometimes so high in class B3 that outliers skewed the mean regret beyond of the whiskers of the boxplot. Again, classes A1 and A2 are precisely symmetric. We discuss this symmetry in Section 5.3, then discuss the poor performance of B3 in Section 5.4. Figure  6 : Human feedback and the resulting misspecified robot belief with a human goal bias. Because the feedback that the biased human provides is poor, the robot learns a very incorrect distribution over rewards. \n Effects of Biased Choice Sets The This result shows that we can see an outsized negative impact on robot reward inference with a small incorrect assumption that the human considered and rejected demonstrations that don't terminate at the goal. \n Symmetry Intuitively, misspecification should lead to worse performance in expectation. Surprisingly, when we combine misspecification classes A1 and A2, their impact on entropy change and regret is actually neutral. The key to this is their symmetry -if we switch the contents of C Robot and C Human in an instance of class A1 misspecification, we get an instance of class A2 with exactly the opposite performance characteristics. Thus, if a pair in A1 is harmful, then the analogous pair in A2 must be helpful, meaning that it is better for performance than having the correct belief about the human's choice set. We show below that this is always the case under certain symmetry conditions that apply to A1 and A2. Assume that there is a master choice set C M containing all possible elements of feedback for MDP M , and that choice sets are sampled from a symmetric distribution over pairs of subsets D : 2 C M × 2 C M → [0, 1] with D(C x , C y ) = D(C y , C x ) (where 2 C M is the set of subsets of C M ). Let ER(r θ , M ) be the expected return from maximizing the reward function r θ in M . A reward parameterization is chosen from a shared prior P(θ) and C H , C R are sampled from D. The human chooses the optimal element of feedback in their choice set c C H = argmax c∈C H E ξ∼ψ(c) [r θ * (ξ))]. Theorem 1. Let M and D be defined as above. Assume that ∀C x , C y ∼ D, we have c Cx = c Cy ; that is, the human would pick the same feedback regardless of which choice set she   sees. If the robot follows RRiC inference according to Eq. 2 and acts to maximize expected reward under the inferred belief, then: E C H ,C R ∼D Regret(C H , C R ) = 0 Proof. Define R(C x , c ) to be the return achieved when the robot follows RRiC inference with choice set C x and feedback c, then acts to maximize r E[Bx(θ)] , keeping β fixed. Since the human's choice is symmetric across D, for any C x , C y ∼ D, regret is anti-symmetric: Regret(C x , C y ) = R(C x , c Cx ) − R(C y , c Cx ) = R(C x , c Cy ) − R(C y , c Cy ) = −Regret(C y , C x ) Since D is symmetric, C x , C y is as likely as C y , C x . Combined with the anti-symmetry of regret, this implies that the expected regret must be zero: E Cx,Cy∼D [Regret(C x , C y )] = 1 2 E Cx,Cy [Regret(C x , C y )] + 1 2 E Cx,Cy [Regret(C y , C x )] = 1 2 E Cx,Cy [Regret(C x , C y )] − 1 2 E Cx,Cy [Regret(C x , C y )] = 0 An analogous proof would work for any anti-symmetric measure (including entropy change). \n Worst Case As shown in Table  4 , class B3 misspecification can induce regret an order of magnitude worse than the maximum regret induced by classes A3 and B2, which each differ from B3 along a single axis. This is because the worst case inference occurs in RRiC when the human feedback c H is the worst element of C R , and this is only possible in class B3. In class    The axes represent the weights on the lava and alive features and the space of possible parameterizations lies on the circle where w lava + w alive = 1. The opacity of the gold line is proportional to the weight that P(θ) places on each parameter combination. The true reward has w lava , w alive < 0, whereas the peak of this distribution has w lava < 0, but w alive > 0. This is because C R2 contains shorter trajectories that encounter the same amount of lava, and so the robot infers that c H must be preferred in large part due to its length.    \n Discussion Summary In this work, we highlighted the problem of choice set misspecification in generalized reward inference, where a human gives feedback selected from choice set C Human but the robot assumes that the human was choosing from choice set C Robot . As expected, such misspecification on average induces suboptimal behavior resulting in regret. However, a different story emerged once we distinguished between misspecification classes. We defined five distinct classes varying along two axes: the relationship between C Human and C Robot and the location of the optimal element of feedback c * . We empirically showed that different classes lead to different types of error, with some classes leading to overconfidence, some to underconfidence, and one to particularly high regret. Surprisingly, under certain conditions the expected regret under choice set misspecification is actually 0, meaning that in expectation, misspecification does not hurt in these situations. Implications There is wide variance across the different types of choice-set misspecification: some may have particularly detrimental effects, and others may not be harmful at all. This suggests strategies for designing robot choice sets to minimize the impact of misspecification. For example, we find that regret tends to be negative (that is, misspecification is helpful) when the optimal element of feedback is in both C Robot and C Human and C Robot ⊃ C Human (class A2). Similarly, worst-case inference occurs when the optimal element of feedback is in C Robot only, and C Human contains elements that are not in C Robot (class B3). This suggests that erring on the side of specifying a large C Robot , which makes A2 more likely and B3 less, may lead to more benign misspecification. Moreover, it may be possible to design protocols for the robot to identify unrealistic choice set-feedback combinations and verify its choice set with the human, reducing the likelihood of misspecification in the first place. We plan to investigate this in future work. Limitations and future work. In this paper, we primarily sampled choice sets randomly from the master choice set of all possibly optimal demonstrations. However, this is not a realistic model. In future work, we plan to select human choice sets based on actual human biases to improve ecological validity. We also plan to test this classification and our resulting conclusions in more complex and realistic environments. Eventually, we plan to work on active learning protocols that allow the robot to identify when its choice set is misspecified and alter its beliefs accordingly. Figure 2 : 2 Figure 2: The set of four gridworlds used in randomized experiments, with the lava feature marked in red. \n Figure 3 : 3 Figure 3: Human and robot choice sets with a human goal bias. Because the human only considers trajectories that terminate at the goal, they don't consider the blue trajectory in CR. \n Figure 4 : 4 Figure 4: Entropy Change (N=24). The box is the IQR, the whiskers are the range, and the blue line is the median. There are no outliers. \n Figure 5 : 5 Figure 5: Regret (N=24). The box is the IQR, the whiskers are the most distant points within 1.5*the IQR, and the green line is the mean. Multiple outliers are omitted. \n (a) feedback cH (b) P(θ | cH , CR) \n human bias of only considering demonstrations that terminate at the goal leads to very poor inference in this environment. Because the human does not consider the blue demonstration from Fig 3b, which avoids the lava altogether, they are forced to provide the demonstration in Fig 6a, which terminates at the goal but is long and encounters lava. As a result, the robot infers the very incorrect belief distribution in Fig 6b. Not only is this distribution underconfident (entropy change = −0.614), but it also induces poor performance (regret = 0.666). \n Figure 7 : 7 Figure 7: Example human choice set and corresponding feedback. \n Fig 9a shows an example robot choice set C R3 from B3, and Fig 9b shows the inferred P(θ | c H , C R3). Note that the peak of this distribution has w lava , w alive > 0. Since c H is the longest and the highest-lava trajectory in C R3 , and alternative shorter and lower-lava trajectories exist in C R3 , the robot infers that the human is attempting to maximize both trajectory length and lava encountered: the opposite of the truth. Unsurprisingly, maximizing expected reward for this belief leads to high regret. The key difference between B2 and B3 is that c H is the lowest-reward element in C R3 , resulting in the robot updating directly away from the true reward. \n Figure 8 : 8 Figure 8: Robot choice set and resulting misspecified belief in B2. \n Figure 9 : 9 Figure 9: Robot choice set and resulting misspecified belief in B3. \n Table 1 : 1 Choice set misspecification classification, where CR is the robot's assumed choice set, CH is the human's actual choice set, and c * is the optimal element from CR ∪ CH . B1 is omitted because if CR ⊂ CH , then CR\\CH is empty and cannot contain c * . \n t. at least one reward parameterization θ. For each experimental class, we randomly generated 6 valid C R , C H tuples, with C R , C H ⊆ C x M . Duplicate tuples, or tuples in which c H / ∈ C R , were not considered. \n Table 2 : 2 Entropy change is symmetric across classes A1 and A2. Class Mean Std Q1 Q3 A1 0.04 0.4906 0.1664 0.0 A2 -0.04 0.4906 0.0 -0.1664 \n Table 3 : 3 Regret is symmetric across classes A1 and A2. \n Table 4 : 4 Regret comparison showing that class B3 has much higher regret than neighboring classes.", "date_published": "n/a", "url": "n/a", "filename": "paper_14.tei.xml", "abstract": "Specifying reward functions for robots that operate in environments without a natural reward signal can be challenging, and incorrectly specified rewards can incentivise degenerate or dangerous behavior. A promising alternative to manually specifying reward functions is to enable robots to infer them from human feedback, like demonstrations or corrections. To interpret this feedback, robots treat as approximately optimal a choice the person makes from a choice set, like the set of possible trajectories they could have demonstrated or possible corrections they could have made. In this work, we introduce the idea that the choice set itself might be difficult to specify, and analyze choice set misspecification: what happens as the robot makes incorrect assumptions about the set of choices from which the human selects their feedback. We propose a classification of different kinds of choice set misspecification, and show that these different classes lead to meaningful differences in the inferred reward and resulting performance. While we would normally expect misspecification to hurt, we find that certain kinds of misspecification are neither helpful nor harmful (in expectation). However, in other situations, misspecification can be extremely harmful, leading the robot to believe the opposite of what it should believe. We hope our results will allow for better prediction and response to the effects of misspecification in real-world reward inference.", "id": "13f847c9d7d81ae8fab6debd5c7c1dca"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Thomas L Griffiths", "Frederick Callaway", "Michael B Chang", "Erin Grant", "Paul M Krueger", "Falk Lieder", "Matthew M Botvinick", "Samuel J Gershman"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S2352154618302122-main.tei.xml", "abstract": "Artificial intelligence systems use an increasing amount of computation and data to solve very specific problems. By contrast, human minds solve a wide range of problems using a fixed amount of computation and limited experience. We identify two abilities that we see as crucial to this kind of general intelligence: meta-reasoning (deciding how to allocate computational resources) and meta-learning (modeling the learning environment to make better use of limited data). We summarize the relevant AI literature and relate the resulting ideas to recent work in psychology.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Peter Cihon", "Matthijs M Maas", "Luke Kemp"], "title": "Fragmentation and the Future: Investigating Architectures for International AI Governance", "text": "AI has the potential to dramatically alter the world for good or ill. These high stakes have driven a recent flurry of international AI policy making at the OECD, G7, G20, and multiple UN institutions. Scholarship has not kept pace with diplomacy. AI governance research to date has predominantly focused on national and sub-national levels  (Calo, 2017) . AI global governance research remains relatively nascent, focusing mostly on the proliferation of AI ethics principles  (Jobin et al., 2019)  and stocktaking of ongoing initiatives  (Garcia, 2020; Schiff et al., 2020) .  Kemp et al. (2019)  have called for specialised, centralised intergovernmental agencies to coordinate policy responses globally. Others have called for a centralised 'International Artificial Intelligence Organisation'  (Erdelyi and Goldsmith, 2018)  or an international coordinating mechanism under the G20  (Jelinek et al., 2020) . Conversely, some scholars favour more decentralised arrangements based around soft law, global standards, or existing international law instruments or UN multilateral organisations  (Cihon, 2019; Garcia, 2020; Kunz and O h Eigeartaigh, 2020; Wallach and Marchant, 2018) . This paper takes the initial step of considering the question: Should AI governance be centralised? The form of an international regime  1.  will fundamentally impact its operation and effectiveness. This includes the critical question of how an institutional form 'fits' the underlying problem  (Ekstrom and Crona, 2017; Young, 2002) . Questions of regime centralisation have occupied scholars and international negotiations for decades. The US diplomat George  Kennan (1970)  proposed the establishment of an 'International Environmental Agency' as an initial step towards an International Environmental Authority. The vexing question of whether to have a centralised body for environmental governance continued 42 years later during the Rio + 20 negotiations. There remains significant debate as to how much form affects performance and what level of centralisation is preferable, but there is little doubt that it is an important consideration for international regimes  (Biermann and Kim, 2020) . Centralisation is also a neglected area of examination for AI governance. The debate over form is in its infancy for AI with a few proposals for centralised regimes in academic literature and submissions to international processes  (Jelinek et al., 2020; Kemp et al., 2019) . Yet it seems unlikely that AI will be immune to increasing discussions and eventual political pushes for regime centralisation. Future negotiations over the form of AI governance will benefit immensely from early analysis. 'Centralisation', in this case, refers to the degree to which the coordination, oversight and/or regulation of a set of AI policy issues or technologies are housed under a single institution. Centralisation is relevant for policy makers and academics alike. A recent report by the UN Secretary General lamented the lack of coordination and inclusion among AI-related initiatives (United Nations  Secretary-General, 2020) . Early research and anticipatory initiatives may sensitively influence the path governance takes  (Stilgoe et al., 2013) . Scholars have a unique opportunity to be norm entrepreneurs and shape the emerging institutions through proactive, rather than retrospective, work on AI governance. The importance of this proactive approach has been emphasised for emerging technologies more broadly  (Rayfuse, 2017) . Moreover, choices made today may have long-lasting impacts as AI development continues  (Cave and O h Eigeartaigh, 2019) . In this paper, we explore the advantages and disadvantages of centralisation for AI governance. The defining problems of AI governance are threefold. The first is the political economy challenge and the importance of non-state actors' expertise in AI. The second is the need for anticipatory governance and technological foresight. The third is the variety and range of different AI applications, technologies, and policy problems. Our analysis hinges on a comparison with international regimes in three other domain areas, which display these core challenges, specifically environment, trade, and security. These three governance domains, while certainly distinct in important ways, are also arguably similar to AI governance across these dimensions: environmental governance invokes complex scientific questions that require technical expertise, has a broad scope encompassing transboundary and transsector effects, and includes a need for anticipation of future trends and impacts. Trade regimes span across a breadth of individual industries, and involve questions of standard-setting. Security and arms control regimes confront high-stakes situations and strategic interests, and a recurring need to 'modernise' regimes to track ongoing technological change. All three governance domains face questions of institutional inequalities. Finally, these regimes have been the subject of a rich literature exploring fragmentation and centralisations. We first outline the international governance challenges of AI, and review early proposed responses. We then draw on the conceptual frameworks of 'regime fragmentation'  (Biermann et al., 2009)  and 'regime complexes'  (G omez-Mera et al., 2020; Orsini et al., 2013) , and their application to the history of other international regimes, to identify considerations in designing a centralised regime complex for AI. We conclude with two practical recommendations. \n The state of AI governance Whether AI is a single policy area is actively debated. Some claim that AI cannot be cohesively regulated as it is a collection of disparate technologies, with different applications and risk profiles  (Stone et al., 2016) . This is an important but not entirely convincing objection. The technical field has no settled definition for 'AI',  2.  thus it is unsurprising that delineating a manageable scope for AI governance is difficult  (Schuett, 2019) . Yet this challenge is not unique to AI: definitional issues abound in areas such as environment and energy, but have not figured prominently in debates over centralisation. Indeed, energy and environment ministries are common at the domestic level. There are numerous ways in which a centralised body could be designed for AI governance. For example, a centralised approach could carve out a subset of interlinked AI issues. This could involve focusing on the potentially high-risk applications of AI systems, such as AI-enabled cyberwarfare, the use of natural language processing for information warfare, lethal autonomous weapons systems (LAWS), or high-level machine intelligence (HLMI).  3.  Another approach could govern underlying resource inputs for AI such as largescale compute hardware, software libraries, training datasets, or human talent. We are agnostic on the specifics of how centralisation could or should be implemented. We instead focus on the costs and benefits of centralisation in the abstract. The exact advantages and disadvantages of centralisation will vary with institutional design. Numerous AI issues could benefit from international cooperation. These include the high-risk applications mentioned above. It also encompasses more quotidian uses, such as AIenabled cybercrime; human health applications; safety and regulation of autonomous vehicles and drones; surveillance, privacy and data-use; and labour automation. This is not an exhaustive list of international AI policy issues. Global regulation across these issues is currently nascent, fragmented and evolving. OECD members and several other states agreed to a series of AI Principles, which were subsequently adopted by the G20 (OECD, 2020a). The Global Partnership on AI (GPAI) was launched by the G7 and several other states  (GPAI, 2020) . The fragmented membership in these initiatives is shown in Figure  1 . A wide range of UN institutions have begun to undertake some activities on AI  (ITU, 2019) . These developments are complimented by various treaty amendments, such as incorporating autonomous vehicles into the 1968 Vienna Convention on Road Traffic  (Kunz and O h Eigeartaigh, 2020)  or ongoing negotiations under the Convention on Certain Conventional Weapons (CCW) on LAWS. Private fora may also influence international governance (See  Green and Auld, 2017) , including the Partnership on AI and IEEE's Ethically Aligned Design initiative. The UN Secretary General intends to establish a multistakeholder advisory body on global AI cooperation (United Nations Secretary-General, 2020). UNESCO, the Council of Europe, and the OECD have similarly convened multistakeholder groups tasked with drafting policy instruments (Council of Europe (COE), 2020;  UNESCO, 2020; ; OECD, 2020b) . Whether these initiatives bear fruit, however, remains unclear, as many of the involved international organisations have fragmented membership, were not originally created to address AI issues and lack effective enforcement or compliance mechanisms (see  Morin et al., 2019) . For instance, while the US has endorsed the OECD AI Principles and while it eventually acquiesced to the GPAI, it has remained sceptical of hard, global rules . China, another global frontrunner in AI, is not a member of either body.  4.  How we initially structure international governance can be critical to its long-term success. Fragmentation and centralisation exist across a spectrum. Some fragmentation will always prevail, absent a global government. But the degree to which it prevails is crucial. Our definitions, including for fragmentation and key terms are provided in Table  1 . These definitions are by nature normatively loaded. For example, some may find 'decentralisation' to be a positive framing, while others may see 'fragmentation' to possess negative connotations. Recognising this, we use these terms in an analytical manner. \n Centralisation criteria: a history of governance trade-offs We explore a series of considerations for AI governance based on a review of existing scholarship on fragmentation  (Biermann and Kim, 2020; Biermann et al., 2009; Ostrom, 2010; Zelli and Asselt, 2013) . Specifically, political power and efficient participation support centralisation. The breadth vs. depth dilemma, as well as slowness and brittleness support decentralisation. Policy coordination and forum shopping considerations can cut both ways. This list is substantive, not exhaustive, and we intend it to open a discussion of design considerations for the nascent AI regime complex. It is far from the final word. Within each consideration below, we offer definitions, relevant regime histories, and discussion of implications for AI. \n Political power Regimes embody power in their authority over rules, norms, and knowledge beyond states' exclusive control. A more centralised regime sees this power concentrated among fewer institutions. A centralised, powerful architecture is likely to be more influential against competing international organisations and with constituent states  (Orsini et al., 2013) . Most environmental multilateral treaties, as well as UNEP, have faced sustained criticism for being unable to enact strong, effective rules or enforce them. In contrast, the umbrella of the WTO, has strongly enforced norms such as the most-favoured-nation principle (equally treating all WTO member states) have become the bedrock of international trade. Even to the extent of changing the actions of the US due to WTO rulings. The power and trackrecord of the WTO is so formidable that it has created a chilling effect: the fear of colliding with WTO norms and rules has led environmental treaties to actively avoid discussing or deploying traderelated measures  (Eckersley, 2004) . The power of this centralised body has stretched beyond the domain of trade to mould related issues. This is an area of high salience for AI. The creators and chief users of AI are 'big tech' companies which are some of the largest firms in the world by market capitalisation and have already had an enormous effect in shaping government policy  (Nemitz, 2018)  in favour of 'surveillance capitalism'  (Zuboff, 2019) . This daunting political economy challenge is perhaps the defining characteristic of AI. It seems unlikely that powerful vested economic and military interests in AI will be steered by a plethora of small bodies better than a single, well-resourced and empowered institution. Political power offers further benefits in governing emerging technologies that are inherently uncertain in both substance and impact. Uncertainty in technology and preferences has been associated with some increased centralisation in regimes  (Koremenos et al., 2001a) . There may also be benefits to housing a foresight capacity within the regime complex, to allow for accelerated or even proactive efforts  (Pauwels, 2019) , which would be particularly effective if centralised. \n Supporting efficiency and participation Decentralised AI governance may undermine efficiency and inhibit participation. States often create centralised regimes to reduce costs, for instance by eliminating duplicate efforts, yielding economies of scale within secretariats, and simplifying participation  (Esty and Ivanova, 2002) . Conversely, fragmented regimes may force states to spread resources and funding over many distinct institutions, limiting the ability of less well-resourced parties to participate  (Morin et al., 2019) . Historically, decentralised regimes have presented cost and participation concerns. Hundreds of related and sometimes overlapping international environmental agreements can create 'treaty congestion'  (Anton, 2012) . This complicates participation and implementation for both developed and developing nations  (Esty and Ivanova, 2002) . This includes costs associated with travel to different forums, monitoring and reporting for a range of different bodies, and duplication of effort by different secretariats  (Esty and Ivanova, 2002) . Similar challenges confront decentralised export regimes, which have notable duplication of efforts  (Brockmann, 2019) . These challenges are already evident in AI governance. Developing countries are not well represented at most international AI meetings (United Nations Secretary-General, 2020). Simultaneous and globally distributed meetings pose burdensome participation costs. Fragmented organisations must duplicatively invest in high-demand machine learning subject-matter experts to inform their activities. Centralisation would support institutional efficiency and participation.  Fragmentation or decentralisation A patchwork of international institutions which focus on a particular issue area but differ in scope, membership and often rules  (Biermann et al., 2009) . \n Centralisation The degree to which governance for an issue lies under the authority of a single body. \n Regime complex A network of three or more international regimes on a common issue area. These should have overlapping membership and cause potentially problematic interactions  (Orsini et al., 2013) . The costs and participation challenges posed by decentralisation may pose particular barriers to non-state actors  (Drezner, 2009) . AI-related expertise is primarily located in non-state actors today, namely multinational corporations and universities. Thus, barriers to non-state-actor participation in AI governance will pose particularly acute problems for writing rules that reflect the nature and development trajectory of AI technologies. However, these barriers may not limit all non-state actors from engaging in multiple fora. Indeed, those with sufficient resources may be able to pursue strategies to their advantage  (Kuyper, 2014) . \n Slowness and brittleness of centralised regimes One problem of centralisation lies in the relatively slow process of establishing centralised institutions, which may often be outpaced by the rate of (technological) change. Another challenge lies in centralised institutions' brittleness after they are established, that is, their vulnerability to regulatory capture or failure to react to changes in the issue area or technology. These issues are well reflected in challenges encountered in arms control regimes. Establishing new international institutions is often a slow process, especially with higher participation and stakes. Under the General Agreement on Tariffs and Trade (GATT), negotiations for a 26 per cent cut in tariffs between 19 countries took 8 months in 1947. The Uruguay round, beginning in 1986, took 91 months to achieve a tariff reduction of 38 per cent between 125 parties  (Martin and Messerlin, 2007) . Historically, international law has been quicker at responding to technological change than to other changes; but even there its record is chequered, in some cases (e.g., spaceflight) adjusting within years, while being far more delayed in others (e.g., modern anti-personnel landmines)  (Picker, 2001) . Decentralised efforts might prove quicker to respond, especially if they rely more on informal institutions with a smaller, like-minded membership  (Morin et al., 2019) . Centralised governance may be particularly vulnerable to lengthy negotiations, especially if a few states hold unequal stakes in a technology, or if there are significant differences in information and expertise among state and private actors  (Picker, 2001) . AI fulfils both of these conditions. Moreover, because AI technology develops rapidly, slow implementation of rules and principles could enable certain actors to take advantage by setting de facto rules. Even after its creation, a centralised regime can be brittle. The very qualities that provide it with political power may exacerbate the adverse effects of regulatory capture, and features that ensure institutional stability may also lead to an inability to adapt to new conditions. The regime might break before it bends. The first potential risk is regulatory capture. As illustrated by numerous cases, including undue corporate influence in the World Health Organisation during the 2009 H1N1 pandemic  (Deshman, 2011) , no institution is fully immune to capture, and centralisation may facilitate this by providing a single locus of influence  (Martens, 2017) . On the other hand, a regime complex comprising many smaller, parallel institutions could find itself vulnerable to capture by powerful actors, who can afford representation in every forum. Some have already expressed concern about the resources and sway of private tech actors in AI governance  (Nemitz, 2018) , and proposals for AI governance have been surrounded by calls to ensure their independence from such influence (Nature Editors, 2019). Moreover, centralised regimes entail higher stakes. International institutions can be notoriously path-dependent and fail to adjust to changing circumstances  (Baccaro and Mele, 2012) . The public failure of a flagship global AI institution could have lasting political repercussions. It could strangle subsequent proposals in the crib, by undermining confidence in multilateral governance generally or on AI issues specifically. By contrast, for a decentralised regime complex to similarly fail, all of its component institutions would need to 'break' or fail to innovate simultaneously. A centralised institution that does not outright collapse, but which remains ineffective, may inhibit better efforts. Ultimately, brittleness is not an inherent weakness of centralisation, but rather may depend on institutional design. There may be strategies to 'innovation-proof'  (Maas, 2019a)  governance regimes. Periodic renegotiation, modular expansion, additional protocols to framework conventions, 'principles based regulation', or sunset clauses can also support ongoing adaptation (see  Marchant et al., 2011) . This discussion intersects with debates over whether a new centralised regime is even possible in today's shifting, dense institutional landscape  (Alter and Raustiala, 2018; Morin et al., 2019) . The speed of capability development in AI also highlights questions over the relative 'speed' or 'responsiveness' of different regime configurations. In slowmoving areas, a centralised regime's slowness may not be a problem. However, technological change has often 'perforated' many arms control regimes, from the Nuclear Non-Proliferation Treaty to the Missile Technology Control Regime, which sometimes struggled to carry out muchneeded 'modernisation' in provisions or export control lists  (Nelson, 2019) . This raises questions of necessary institutional speed. Is AI an issue that is so fast it makes centralisation untenable, such that we need a decentralised regime to match its speed and complexity? Or, should we use a singular institutional anchor to slow and channel the technology's development or application? There is precedent for international instruments directing or curtailing the development of certain technologies. The 1978 Environmental Modification Convention (ENMOD) Convention was an effective tool in preventing both funding for geoengineering research and the weaponised deployment of weather manipulation. By 1979, US investments in such technologies had dramatically decreased  (Fleming, 2006) . \n The breadth vs. depth dilemma Pursuing centralisation may create an overly high threshold that limits participation. Many multilateral agreements face a trade-off between having higher participation ('breadth') or stricter rules and greater ambition of commitments ('depth'). The dilemma is particularly evident for centralised institutions that are intended to be powerful and require strong commitments from states. Sacrificing depth for breadth can also pose risks. The 2015 Paris Agreement on Climate Change was watered down to allow for the legal participation of the US. Anticipated difficulties in ratification through the Senate led to negotiators opting for a 'pledge and review' structure with few legal obligations, which permitted the US to join through executive approval  (Kemp, 2017) . In this case, inclusion of the USwhich proved temporarycame at the cost of cutbacks to the demands which the regime made on all parties. In contrast, decentralisation could allow for major powers to engage in at least some regulatory efforts, where they would be deterred from signing up to a more comprehensive package. This has precedence in climate governance. Some claim that the US-led Asia-Pacific Partnership on Clean Development and Climate helped, rather than hindered climate governance, as it bypassed the UN Framework Convention on Climate Change (UNFCCC) deadlock and secured (non-binding) commitments from actors not bound by the Kyoto Protocol  (Zelli, 2011) . This matters, as buy-in may prove a particular thorny issue for AI governance. The actors who lead in AI development include powerful states, such as the US and China, that are potentially most adverse to restrictive global rules. They have thus far proved unenthusiastic regarding the global governance of security issues such as anti-personnel mines, LAWS, and cyberwarfare. In response, governance could take a different approach to military uses of AI. Rather than seeking a comprehensive agreement, devolving and spinning off certain components into separate treaties (e.g., separately covering LAWS testing standards; measures for liability and responsibility; or limits to operational context) could instead allow for the powerful to ratify and move forward some of those options  (Weaver, 2014) . The breadth vs. depth dilemma is a trade-off in multilateralism generally, and a key challenge for centralisation. The benefit of a centralised body would be to create a powerful anchor that ensures policy coordination and coherence. In many cases, it will likely need to restrict membership to have teeth, or lose its teeth to secure wide participation. For specific issues in AI governance, this 'breadth vs. depth' trade-off might inform relative expectations of ongoing AI governance initiatives. If 'breadth' is more important, one might put more stock in nascent efforts at the UN  (Garcia, 2020) ; if 'depth' of commitment seems more important, one might instead favour initiatives of like-minded states such as the GPAI. The evolving architecture of AI governance suggests that a 'critical mass governance'  (Kemp, 2017)  approach may be appropriate. That is, there is a single centralised, framework under which progressive clubs move forward on particular issues. Rather than having an array of treaties, one has a set of protocols for different technologies or applications under a single framework. A similar approach has been taken in treaties such as the 1983 Convention on Long-Range Transboundary Air Pollution. \n Forum shopping Forum shopping may help or hinder AI governance. Fragmentation enables actors to choose where and how to engage. Such 'forum shopping' may take one of several forms: shifting venues, abandoning one, creating new venues, and working to sew competition among multiple  (Braithwaite and Drahos, 2000) . Even when there is a natural venue for an issue, actors have reasons to forum shop. For instance, states may look to maximise their influence  (Pekkanen et al., 2007) , and placate constituents by shifting to a toothless forum  (Helfer, 2004) . Membership in AI initiatives is highly varied and as initiatives begin to consider binding instruments, this ranging membership may be exploited. The ability to successfully forum-shop depends on an actor's power. Most successful examples of forum-shifting have been led by the US  (Braithwaite and Drahos, 2000) . Intellectual property rights (IPR) in trade, for example, were subject to prolonged, contentious forum shopping. Developed states resisted attempts of the UN Conference on Trade and Development (UNCTAD) to address the issue by trying to shift it onto the World Intellectual Property Organisation (WIPO)  (Braithwaite and Drahos, 2000)  and then subsequently to the WTO  (Helfer, 2004) , despite protests from developing states. But weak states and non-state actors can also pursue forum shopping strategies in order to challenge the status quo, sometimes with success  (Jupille et al., 2013) . For example, developing states further shifted some IPR in trade to the WHO, and subsequently won concessions at the WTO  (Kuyper, 2014) . Forum shopping may help or hurt governance  (G omez-Mera, 2016) . This is evident in current efforts to regulate LAWS. While the Group of Governmental Experts has made some progress, on the whole the CCW has been slow. In response, activists have threatened to shift to another forum, as happened with the Ottawa Treaty that banned anti-personnel mines  (Delcker, 2019) . This strategy could catalyse progress, but also brings risks of further forum shopping. Forum shopping may similarly delay, stall, or weaken regulation of time-sensitive AI policy issues, including potential HLMI development. Non-state actors that participate in multiple fora may influence regime complex evolution, though perhaps to the detriment of other weak actors  (Orsini, 2013) . Thus, leading AI firms likely have sway when they elect to participate in some venues but not others. To date, leading AI firms appear to be prioritising engagement at the OECD over the UN. A decentralised regime will enable forum shopping, though further work is needed to determine whether this will help or hurt governance outcomes. \n Policy coordination There are good reasons to believe that either centralisation or fragmentation could enhance coordination. A centralised regime can enable easier coordination both across and within policy issues, acting as a focal point for states. Alternatively, fragmented institutions may be mutually supportive and even more creative. Centralisation reduces the incidence of conflicting mandates and enables communication. These are the ingredients for policy coherence, as shown in the case of the WTO above under 'political power'. However, fragmented regimes can often act as complex adaptive systems. Political requests and communication between secretariats can ensure bottom-up coordination. Multiple organisations have sought to reduce greenhouse gas emissions within their respective remits, often at the behest of the UNFCCC Conference of Parties. Sometimes effective, bottom-up coordination can slowly evolve into centralisation. Indeed, this was the case for the GATT and numerous regional, bilateral and sectoral trade treaties, which all coalesced together into the WTO. While this organic self-organisation has occurred, it has taken decades. Some have argued that 'polycentric' governance approaches may be more creative and legitimate than centrally coordinated regimes  (Acharya, 2016; Ostrom, 2010) . Arguments in favour of polycentricity include the notion that it enables governance initiatives to begin having impacts at diverse scales, and that it enables experimentation with policies and approaches  (Ostrom, 2010) . Consequently, these scholars assume 'that the invisible hand of a market of institutions leads to a better distribution of functions and effects'  (Zelli and van Asselt, 2013, p. 7 ). Yet an absence of centralised authority to manage regime complexes has presented challenges in the past. Across the proliferation of Multilateral Environmental Agreements (MEAs) there is no requirement to cede responsibility to the UN Environmental Programme in the case of overlap or competition. This has led to turf wars, inefficiencies and even contradictory policies  (Biermann et al., 2009) . One of the most notable examples is that of hydrofluorocarbons (HFCs). HFCs are potent greenhouse gases, and yet their use was encouraged by the Montreal Protocol since 1987 as a replacement for ozone-depleting substances. This was only resolved via the 2016 Kigali Amendment to the Protocol. It is unclear if the different bodies covering AI issues will self-organise or collide. Many of the issues are interdependent and need to be addressed in tandem. Some policylevers, such as regulating computing power or data, will impact multiple areas, given that AI development and use is closely tied to such inputs. Numerous initiatives on AI and robotics are displaying loose coordination  (Kunz and O h Eigeartaigh, 2020) . But it remains uncertain whether the virtues of a free market of governance will prevail. Great powers can exercise monopsony-like influence through forum shopping, and the supply of both computing power and machine learning expertise are highly concentrated. In sum, centralisation can reduce competition and enhance coordination, but it may suffocate the creative self-organisation of decentralised arrangements. Discussion: what would history suggest? \n Summary of considerations The multilateral track record and peculiarities of AI yield suggestions and warnings for the future. A centralised regime could lower costs, support participation, and act as a powerful new linchpin within the international system. Yet centralisation could simply produce a brittle dinosaur, of symbolic value but with little meaningful impact. A poorly executed attempt at centralisation could lock-in a fate worse than fragmentation. Policy making and research alike could benefit from addressing the considerations presented in this paper, a summary of which is presented in Table  2 . \n The limitations of 'centralisation vs. decentralisation' debates Structure is not a panacea. Specific provisions such as agendas and decision-making procedures matter greatly, as do the surrounding politics. Underlying political will may be impacted by framing or connecting policy issues  (Koremenos et al., 2001b) . The success of a regime depends on design details. Moreover, institutions can be dynamic, and broaden over time by taking in new members or deepen in strengthening commitments. Successful multilateral efforts, such as trade and ozone depletion, tend to do both. Yet, decisions taken early on constrain and partially determine future paths. This dependency can even take place across regimes. The Kyoto Protocol was largely shaped by the targets-and-timetables approach of the Montreal Protocol, which itself drew from the Convention on Long-range Transboundary Air Pollution. This targets-and-timetables approach continues today in the way that most countries frame their climate pledges to the Paris Agreement. The choices we make on governing shortterm AI challenges will likely shape the management of other policy issues in the long term  (Cave and O h Eigeartaigh, 2019 ). Yet, committing to centralisation, even if successful, may not solve the right problemwhich may be geopolitical, not architectural. Centralisation could even exacerbate the problem by diluting scarce political attention, incurring heavy transaction costs, and shifting discussions away from bodies which have accumulated experience  (Juma, 2000) . For example, the Bretton Woods Institutions of the IMF and World Bank, joined later by the WTO, are centralised regimes that engender power. However, those institutions had the express support of the US and may have simply manifested state power in institutional form. Efforts to ban LAWS and create a cyberwarfare convention have been broadly opposed by states with an established technological superiority in these areas  (Eilstrup-Sangiovanni, 2018) . \n HLMI: An illustrative example The promise of centralisation may differ by policy issue. HLMI is one issue that is markedly unique: it is distinct in its risk profile, uncertainty, and linkage to other AI policy issues. While timelines are uncertain, the creation of such advanced AI systems is the express goal of various present-day projects  (Baum, 2017) , and the future development of an 'unaligned' HLMI could have catastrophic consequences  (GCF, 2018) . The creation of HLMI could lead to grotesque power imbalances. It could also exacerbate other AI policy problems, such as labour automation and advanced military applications. In Table  3  we provide a brief application of our framework to HLMI. It shows that centralisation of governance is particularly promising for HLMI. This is due to its neglect, stakes, scope, and need for informed, anticipatory policy. Rather than any AI governance blueprint, our trade-offs framework provides one way of thinking through the costs and benefits of centralising governance. Identifying areas which are more easily defined and garner the benefits of centralised regulation provides an organic approach to thinking through which subset of topics an AI umbrella body could cover. \n Lessons for theory This is the first application of regime complex theory to the problem of AI governance. It is timely and pertinent given the nascent state of AI governance and of the technology itself. While the majority of the literature has observed mature regimes retrospectively, AI offers an opportunity for scholars to both track and influence the development of a new regime complex from its earliest stages. Our analysis highlights both the uses and limits of the theoretical regime complex lens for AI. It can elucidate many important trade-offs, but provides little help in navigating the underlying geopolitics. The six considerations we have identified are also certainly not exhaustive of regime complex theory; further work could explore the complementary dynamics such as issue linkage, regime 'interplay management', or norm cascades in AI governance. Beyond this, the literature needs a better understanding of three key areas that are central to AI. First, what does the political economy of AI mean for AI governance and centralisation? Regulatory capture is a genuine threat, yet many non-state actors hold valuable technical knowledge. Some, such as machine learning developers and NGOs have been influential in shaping governance on lethal autonomous weapons  (Belfield, 2020) . How these actors can shape the choice of fora and influence states under centralisation or decentralisation is pivotal. Second, how should institutions match the speed of evolving collective action problems? Is the aim to make governance agile enough to keep pace with accelerating technological change or to manage the pace or direction of such changes to levels that are socially and politically manageable? Theoretically, foresight methodologies have rarely been considered in regime complex debates. Yet for fastmoving and high-stakes technologies, they should be. Theory will need to better address how foresight and development trajectory monitoring capabilities intersect with the debates over governance architecture. Third, how will these considerations look for particular institutional structures? We have presented a cursory case of HLMI and noted that there is an active debate of how to define AI and structure its governance. How will the case for centralisation look for a regime which targets just high-risk or military applications? Our framework provides an easily deployed way to analyse more discrete proposals for AI governance in the future. \n Lessons for policy Our framework provides a tool for policy makers to inform their decisions of whether to join, create, or forgo new AI policy institutions. For instance, the recent choice of whether to support the creation of an independent Global Panel on AI (GPAI) involved these considerations. Following the US veto at the G7 in 2019, GPAI was established in close relationship with the OECD. For now, it is worth monitoring the current landscape of AI governance to see if it exhibits enough policy coordination and political power to effectively deal with mounting AI policy problems. While there are promising initial signs  (Kunz and O h Eigeartaigh, 2020 ) there are also already impending governance failures, such as for LAWS and cyberwarfare. We outline a suggested monitoring method in Table  4 . There are three areas to monitor: conflict, coordination, and catalyst. Conflict should measure the extent to which principles, rules, regulations, and other outcomes from different bodies in the AI regime complex undermine or contradict each other. Coordination seeks to measure the proactive steps that AI-related regimes take to work with each other. This includes liaison relationships, joint initiatives, and reinforcement between outputs and principles. Catalyst raises the important question of governance gaps: is the regime complex self-organising to proactively address international AI policy problems? Numerous AI policy problems currently have no clear coverage under international law. Monitoring these regime complex developments, using various existing and emerging tools (see  Maas, 2019b; Deeks, 2020) , could inform a discussion and decision of whether to centralise AI governance further. The international governance of AI is nascent and fragmented. Centralisation under a well-designed, modular, 'innovation-proof', critical mass framework may be a desirable solution. However, such a move must be approached with caution. Defining its scope and mandate is one problem. Ensuring a politically-acceptable and well-designed body is perhaps a more daunting one. For now, we should closely watch the trajectory of both AI technology and its governance initiatives to determine whether centralisation is worth the risk. Figure 1 . 1 Figure 1. Membership in selected international AI policy initiatives. \n Table 1 . 1 Definition of key governance terms GPAI Austria OECD Principles Belgium Chile Costa Rica Ireland Colombia Israel New Zealand Czech Republic Latvia Slovenia Denmark Lithuania Singapore Estonia Finland Luxembourg Malta Greece The Netherlands Hungary Norway Australia Iceland Peru Canada Poland France Portugal Germany Romania Italy Slovakia Japan Spain Korea Sweden EU * India Mexico UK USA Argentina Brazil Turkey Switzerland Ukraine 142 UN member states are not China represented Indonesia Russia Saudi Arabia South Africa * as a member in G20 Principles its own right Term Definition \n Table 2 . 2 Summary of considerations Implications for Consideration centralisation Historical example AI policy issue example Political power Pro Shaping other regimes: WTO has created a Influencing powerful vested economic and chilling effect such that environmental treaties military interests in AI may require a single avoid trade-related measures. empowered institution. Efficiency & Pro Decentralisation raises inefficiencies and barriers: Fragmentation requires duplicative investment participation Proliferation of multilateral environmental in AI subject-matter experts and undermines agreements poses challenges in negotiation, participation from developing countries and implementation, and monitoring. non-state actors. Slowness & Con Slowness: Under the GATT, 1947 tariff Process of centralised regime development brittleness negotiations among 19 countries took may not keep pace with the speed of AI 8 months. The Uruguay round, beginning in development. 1986, took 91 months for 125 parties to agree on reductions. Regulatory capture: WHO accused of undue corporate influence in response to 2009 H1N1 pandemic. Breadth vs. depth Con Watering down: 2015 Paris Agreement suggests Attempts to effectively govern the military dilemma attempts to 'get all parties on board' may uses of AI have been resisted by the most require less-stringent rules. powerful states. Forum shopping Depends on Power predicts outcomes: Actors can use forum shopping to either design Developed countries shifted IPR in trade from undermine or catalyse progress on UNCTAD to WIPO to WTO. governance regimes for military AI systems. Accelerates progress: NGOs and some states shifted away from CCW to ban anti-personnel mines. Policy coordination Depends Strong, but delayed convergence: Numerous AI governance initiatives display on design GATT and numerous trade treaties coalesced into loose coordination, but it is unclear if these the WTO after decades initiatives can respond to developments in a Contradictory policies: timely manner. Montreal Protocol promoted the use of potent greenhouse gases for nearly thirty years. \n Table 3 . 3 An application of the framework to high-level machine intelligence (HLMI) If short HLMI timelines (less than 10-15 years) are expected, the lengthy period to negotiate and create such a body would be a critical weakness. If longer timelines are expected, there should be sufficient time to develop a centralised institution. Institutional capture is a concern given the resourced corporate actors involved in creating HLMI, e.g., Google or OpenAI. However, it is unclear if capture would be more likely under a centralised body. Policy coordination Policy coordination is key for HLMI. It has close connections to issues such as labour automation and automated cyberwarfare. The creation or use of HLMI is not directly regulated by any treaties or legal instruments. This makes the creation of a new, dedicated institution to address it easier and less unlikely to trigger turf wars. However, it also makes it less likely that the existing tapestry of global governance can self-organise to cover HLMI in a timely manner. Consideration HLMI Political power Potential catastrophic risks make the increased political power of a centralised institution desirable. The creation of HLMI is a potential 'free-driver' issue. An effective response needs to have the teeth to deter major players from acting unilaterally. This will require a coordinated effort to track and forecast HLMI project efforts (see Baum, 2017), as well as a politically empowered organisation to act upon this information. Efficiency & Centralisation would support economies of participation scale in expertise to support efficient governance. Given the significant resources and infrastructure likely needed, a joint global development effort could be an efficient way to govern HLMI research. Slowness & brittleness Depth vs. breadth Costs and requisite capabilities may restrict dilemma the development of HLMI to a few powerful players. Fewer actors makes centralisation more feasible. The breadth vs. depth dilemma could be avoided through a 'critical mass' approach that initially involves only the few countries that are capable of developing HLMI, although there would be legitimacy benefits to expanding membership. Forum shopping A centralised body is well placed to prevent forum shopping, as there is currently no coverage of HLMI development and deployment under international law. Future forum shopping could undermine timely negotiations amid risky HLMI development. \n Table 4 . 4 Regime complex monitoring suggestions Key theme Questions Methods Conflict To what extent are Expert and practitioner regimes' principles survey Network and outputs in analysis (e.g., citation opposition over time? network clustering Coordination Are regimes taking and centrality) steps to complement Natural Language each other? Processing (e.g., Catalyst Are regimes self- textual entailment and organizing to fact checking) proactively fill governance gaps? \n\t\t\t © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Global Policy (2020) 11:5 \n\t\t\t Global Policy (2020) 11:5 © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Architectures for International AI Governance \n\t\t\t Global Policy (2020) 11:5 © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.", "date_published": "n/a", "url": "n/a", "filename": "Global Policy - 2020 - Cihon - Fragmentation and the Future Investigating Architectures for International AI Governance.tei.xml", "abstract": "The international governance of artificial intelligence (AI) is at a crossroads: should it remain fragmented or be centralised? We draw on the history of environment, trade, and security regimes to identify advantages and disadvantages in centralising AI governance. Some considerations, such as efficiency and political power, speak for centralisation. The risk of creating a slow and brittle institution, and the difficulty of pairing deep rules with adequate participation, speak against it. Other considerations depend on the specific design. A centralised body may be able to deter forum shopping and ensure policy coordination. However, forum shopping can be beneficial, and fragmented institutions could self-organise. In sum, these trade-offs should inform development of the AI governance architecture, which is only now emerging. We apply the tradeoffs to the case of the potential development of high-level machine intelligence. We conclude with two recommendations. First, the outcome will depend on the exact design of a central institution. A well-designed centralised regime covering a set of coherent issues could be beneficial. But locking-in an inadequate structure may pose a fate worse than fragmentation. Second, fragmentation will likely persist for now. The developing landscape should be monitored to see if it is self-organising or simply inadequate. \n Policy Implications • Secretariats of emerging AI initiatives, for example, the OECD AI Policy Observatory, Global Partnership on AI, the UN High-level Panel on Digital Cooperation, and the UN System Chief Executives Board (CEB) should coordinate to halt and reduce further regime fragmentation. • There is an important role for academia to play in providing objective monitoring and assessment of the emerging AI regime complex to assess its conflict, coordination, and catalysts to address governance gaps without vested interests. Secretariats of emerging AI initiatives should be similarly empowered to monitor the emerging regime. The CEB appears particularly well placed and mandated to address this challenge, but other options exist. • What AI issues and applications need to be tackled in tandem is an open question on which the centralisation debate sensitively turns. We encourage scholars across AI issues from privacy to military applications to organise venues to more closely consider this vital question. • Non-state actors, especially those with technical expertise, will have a potent influence in either a fragmented or centralised regime. These contributions need to be used, but there also need to be safeguards in place against regulatory capture. • The AI regime complex is at an embryonic stage, where informed interventions may be expected to have an outsized impact. The effect of academics as norm entrepreneurs should not be underestimated at this point.", "id": "f2a49e79e1ad8c102b46ad7907110c8b"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dorian Peters", "Karina Vold", "Diana Robinson", "Senior Member, IEEE Rafael A Calvo"], "title": "Responsible AI-Two Frameworks for Ethical Design Practice", "text": "technologies  [3] . Moreover, many governments and international organizations have released sets of ethical principles, including the OECD Principles in 2019  [4] , the Montreal Declaration in 2017  [5] , the U.K. House of Lords report \"AI in the U.K.: ready willing and able?\" in 2018  [6] , the European Commission High-Level Expert Group (HLEG) on AI in 2018  [7] , and the Beijing AI Principles in 2019  [8] . Indeed, recent reports indicate that there are currently more than 70 publicly available sets of ethical principles or frameworks for AI, most of which have been released within the last five years  [3] ,  [9] ,  [10] . The recent focus on ethical AI has arisen from increasing concern over its unintended negative impacts, coupled with a traditional exclusion of ethical analysis from engineering practice. While engineers have always met basic ethical standards concerning safety, security, and functionality, issues to do with justice, bias, addiction, and indirect societal harms were traditionally considered out of scope. However, expectations are changing. While engineers are not, and we believe should not, be expected to do the work of philosophers, psychologists, and sociologists, they do need to work with experts in these disciplines to anticipate and mitigate ethical risks as a standard of practice. It is no longer acceptable for technology to be released into the world blindly, leaving others to deal with the consequences. Engineering educators have already responded to this change in sentiment by evolving curricula to help ensure the next generation of technology makers is better equipped to engineer more responsibly  [11] ,  [12] . Yet, moving effectively from ethical theory and principles into context specific, actionable practice is proving a significant barrier for the widespread uptake of systematic ethical impact analysis in software engineering  [13] ,  [14] . In this article, we hope to contribute to resolving some of this translational difficulty by presenting two frameworks (the Responsible Design Process and the Spheres of Technology Experience) together with the outcomes of an example ethical analysis in the context of digital mental health. We hope that both the frameworks and the case study will serve as resources for those looking for guidance in translating ethical principles into technology practice. \n II. ETHICS IMPERATIVE IN HEALTH AND INTELLIGENT SYSTEMS Verbeek explains that \"When technologies co-shape human actions, they give material answers to the ethical question of how to act\"  [15] . He also highlights how technologies This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/ inscribe the values of the designers, engineers, and businesses who make them  [16] ,  [17] . As a result, responsibility must go beyond the narrow definition of safety which, until recently, has largely constituted professional norms for technologists. Furthermore, ethical implications should be considered early on and throughout the design, development, and implementation phases since value-laden tradeoffs are often made even during the earliest stages of design. Achieving ethically desirable outcomes will neither be easy nor straightforward. For instance, ethical design cannot be implemented as a single, one-off, review process since technologies (especially, intelligent ones) are continuously changing, as are the ways users appropriate them, and the socio-technical contexts within which they exist. Therefore, ethical impact evaluation must be an ongoing, iterative process-one that involves various stakeholders at every step, and can be re-evaluated over time, and as new issues emerge. While society-wide ethical considerations are a relatively new focus within technology engineering  [18]  ethical enquiry has a long history within healthcare, perhaps because health practitioners work directly with the people they serve and often within sensitive and high-risk contexts. Principles of Biomedical Ethics  [19]  have been taught for 40 years. Hence, those working on the engineering of health technologies will need to adhere to both technology-related and biomedical ethical principles. Fortunately, at the level of basic principles, the AI communities and biomedical ethicists might already be largely in agreement. A recent analysis suggests that the plethora of ethical AI frameworks can be consolidated into just five meta-principles, four of which also constitute the principles for biomedical ethics. These are: Respect for Autonomy, Beneficence, Nonmaleficence, and Justice, with the addition of \"explicability\" for AI  [3] . Other recent systematic reviews of AI ethics principles have produced somewhat different taxonomies (see  [14] ,  [20] ,  [21] ). For example, Jobin et al.  [9]  reviewed 84 ethical guidelines and proposed 11 principles: 1) transparency; 2) justice and fairness; 3) nonmaleficence; 4) responsibility; 5) privacy; 6) beneficence; 7) freedom and autonomy; 8) trust; 9) dignity; 10) sustainability; and 11) solidarity. They found a wide divergence in how these principles were interpreted and in how the recommendations suggested they be applied. They do, however, note some evidence of convergence (by number of mentions) around five principles: 1) transparency; 2) justice and fairness; 3) nonmaleficence; 4) responsibility; and 5) privacy. Between this set of principles and the set we will be using from the meta-analysis by Floridi et al.  [3] , there is a significant overlap. We have found the latter set to be particularly practical in the health domain, owing to its overlapping with biomedical ethics, however, we understand that other principles are also important. However, broad principles fall short of dictating specific actions in practice. Indeed, it has been acknowledged that these ethical frameworks do not provide enough contextual guidance for engineers to make use of them (e.g.,  [10] ,  [14] , and  [22] ). For example, the principle of fairness could lead to affirmative action, providing extra support for a group, or not, depending on the context. In order for abstract principles to translate into actionable practice, the engineering discipline will need a variety of solutions. For example, the emerging development of the IEEE's PS7000 specifications stands to contribute on this point. Additionally, work by Gebru et al.  [13]  on \"datasheets for datasets\" in which they advocate for clear documentation for datasets that records \"motivation, composition, collection process, recommended uses, and so on\" is one example of a suggestion that would operationalize more abstract principles, such as transparency and accountability. However, there will always be ethical decisions and tradeoffs that are not amenable to universally applicable specifications, and that need to be made with sensitivity to specific context and stakeholders. In these cases, we will need methods for conducting this kind of decision-making rigorously. Responsible innovation requires these methods to be anticipatory, reflexive, inclusive, and responsive  [23] . The very fact that there has been some convergence around a set of principles (rather than a single principle) seems to indicate a kind of value pluralism-the view that there are multiple values that are equally fundamental, and yet may sometimes conflict with each other. How to navigate tradeoffs between equally important values when conflicts arise is where constructive reflection and discourse may be most needed, and where it will be important to acknowledge that cultural and contextual differences may affect what the right outcome is within practice (further discussions in  [24]  and  [25] ). Here, methods for value-sensitive design (VSD)  [16]  can help development teams and stakeholders articulate and align with explicit values. Moreover, data-enabled technologies employ a wide-range of techniques that are used differently in different contexts, and these diverse contexts raise unique concerns that will require different ethical tradeoffs. It is unlikely that the same priorities and solutions applicable to one domain, context, or project, will translate across to others  [22] ,  [25] ,  [26] . This means that technology development teams will need to conduct bespoke ethical evaluations for each project, in the same way, user research and specifications analyses are unique to each project. This need for ethical impact assessment for technology is akin to the need for environmental impact assessment in other types of engineering  [27] . It is impossible to provide ethical principles that will be specific enough to provide answers in practice, and yet broad enough to apply universally. But it is possible to provide a process. While every team and organization may devise their own answers to ethical dilemmas, they should have systematic processes by which to do so consciously and rigorously, leaving a record of these processes along with the values and rationale they employed to make decisions. This record can provide the public with transparency regarding the rationale for a decision after the fact, as well as give the design team confidence that such a decision was made in a systematic and professional way. Such process will not guarantee a product has no negative consequences, but it will help mitigate the risks, and provide professionals with the reassurance of having acted responsibly. In the next section, we present two frameworks that can help provide structure for such a process for ethical impact analysis. \n III. MOVING FROM PRINCIPLES TO PRACTICE: FRAMEWORKS FOR RESPONSIBLE TECHNOLOGY DEVELOPMENT \n A. Multidisciplinarity in AI Ethics We begin our discussion of frameworks with a diagrammatic representation of disciplines central to the development of ethical AI and how they interconnect (see Fig.  1 ). The primary intention is to emphasize the importance of grounding all ethical impact assessments in multidisciplinary expertise. It is likely that new requirements in an increasingly AI-enhanced world will lead to the development of new specializations which blur traditional disciplinary boundaries. Nevertheless, there is no single discipline capable of handling the task of ethical analysis single-handedly. Given the complexity of the problems, the best outcomes are likely to come from the richest diversity. For the digital health case study we present later, we leveraged expertise from four different disciplines, including design, engineering, human-computer interaction, and philosophy. An ideal project would include even more disciplines, such as psychology and sociology (see Fig.  1 ), as well as, end users, domain experts, and other stakeholders. In the mental health context, for example, users may include patients, therapists, and family, while domain experts would include therapists, mental health researchers, and others working within the healthcare system. The importance of this multivocal approach cannot be overstated as there can be a tendency for agile teams to consist of just programmers, designers, and managers. Taking digital mental health as a cautionary example, a failure to involve psychologists, health practitioners, end users, and other domain experts has led to an exploding industry of mental health tools that lack evidence, inclusivity, and effectiveness (and at worst, cause harm)  [28] -  [30] . This has been possible because, while traditional channels for healthcare are highly regulated, technology regulation lags behind and these technologies are unusually quick to implement and disseminate. As Nebeker et al.  [31]  have cautioned: \"it is critical that the minimal requirements used to make a digital health technology available to the public are not mistaken for a product that has passed rigorous testing or demonstrated real-world therapeutic value.\" \n B. Framework 1-The Responsible Design Process Sometimes technology designers, like policymakers, are forced to make values-based tradeoffs. For example, they might be able to increase privacy at the expense of security or increase accuracy at the expense of privacy. Moreover, some technologies may increase the wellbeing of some at the expense of others. Value-laden decisions arise as part of engineering and can either be addressed in a cursory way by one or a few individuals, or in a systematic and robust way by teams. Only the latter approach can hold up to scrutiny should negative consequences emerge after the fact. As such, we need a technology development process that makes room for this sort of robust decision making and for the ethical impact analysis on which it must stand. Innovators are often asked to address the consequences of their technologies, but this post-hoc approach is increasingly seen as limited. A number of nonregulatory approaches have been developed to take into account the broader social impact of new technologies including anticipatory governance, technology assessment, and VSD  [23] . They can all be included within \"responsible innovation,\" a growing field of research exploring ways of \"taking care of the future through collective stewardship of science and innovation in the present\"  [23] . As with many design practices, the goal is to embed deliberation within the design and innovation process. An important aspect of responsible innovation is the concept of human wellbeing, which is also at the center of many current ethical frameworks. For example, the IEEE centers its ethics specifications on human wellbeing. So too do several government frameworks  [4] ,  [5] . As such, we argue that a responsible technology development process will need to incorporate evidence-based methods for evaluating the impact on, and designing for, human wellbeing, by drawing on psychology (see  [32] ,  [33] ). However, the promotion of human wellbeing is not a complete solution. After all, decisions must be made as to whose wellbeing is being considered. When technology makers are forced to make tradeoffs that increase the wellbeing of some but at the expense of others, at the cost of long-term ecological impacts, or in spite of other negative side effects, then issues to do with justice, equality, and other values arise. This is where ethical analysis, drawing on philosophy and other disciplines, must come in. As such, our conception of a responsible development process involves taking existing design processes, particularly those that are anticipatory, reflexive, inclusive, and responsive, Fig.  2 . Responsible design process framework. A process for technology development in which wellbeing support and ethical impact analysis are incorporated at each phase. A post-launch evaluation phase is also added. and augmenting them with methods for ethical analysis and wellbeing-supportive design. The approach described here could include activities such as those used in VSD  [16] . While development processes are as varied as technologists themselves, there are a series of developmental phases that find their way into most, if not all, approaches, and these include: research, ideation, prototyping, and testing. The U.K. design council consolidated these commonalities and created a popular \"double diamond\" diagram to illustrate them  [34] . The broadest and narrowest points of the diamonds represent points of divergence and convergence. We began with this standard process and integrated stages for wellbeing support and ethical decision making to create the resulting responsible design process framework presented in Fig.  2 . Wellbeing in the diagram refers to human psychological wellbeing and it is included separately to other ethical issues because evidence-based design methods grounded in psychological research already exist for it and allow it to be attended to empirically. Analysis of other ethical dimensions, such as fairness, data governance, ecosystem wellbeing, or democratic participation cannot rely predominantly on psychological research and will require different methods. We describe each phase of the process in further detail as follows. Research: The research phase involves investigating the needs, preferences, contexts, and lives of the people who will be served or, otherwise, impacted by a technology. This phase may include standard approaches to user research (e.g., design thinking methods, ethnographies, participatory workshops, etc.) as well as expert review and secondary research in relation to the specific domain. Standard approaches can surface wellbeing and ethical issues, however, tailoring these methods to focus participants on ethical or psychological reflection may be helpful. Insights: This phase involves the analysis of the data from the research phase, and synthesis into specific insights for design. Data analysis can be done through the lens of wellbeing theory with a view to anticipating harms and opportunities for supporting healthy psychological experience. Ethics data analysis can be done through the lens of an ethical framework, and with a view to identifying potential biases, ethical risks, and tensions. Ideation: The ideation phase involves the divergent generation of ideas for design solutions. Ethical reflection can be integrated into the ideation phase through framing. For example, introducing wellbeing psychology concepts into the ideation phase can help the team focus on root psychological causes of user needs while introducing ethics concepts into ideation can sensitize the team to ethical tensions that may arise so that brainstorming can involve resolutions to these. Prototypes: In this phase, the team converges on and builds various design solutions. Responsible impact analysis involves collaborative speculation on the wellbeing and ethical impacts (good and bad) to which a particular design concept may lead. This will ideally involve a wide range of stakeholders including end users. Evaluation (in Use): The real-life ethical impacts that a technology will have on people, their communities and the planet, can only be fully understood once the product or service is in real-world use. Teams must speculate and test in advance, but unintended use patterns are realities in our complex socio-technical systems. Wellbeing impact evaluation involves evaluating the impact of technology use on a user's psychological experience during and after use. Ethical impact evaluation involves evaluating the ethical impacts of a technology's use, not just on its users, but often, also on those indirectly affected, such as their friends and families, communities, society as a whole, and the planet. In the framework described above, we have taken a familiar process and incorporated phases for the integration of ethics and wellbeing in an attempt to provide a map for a more responsible development process. The map also provides a landscape within which to research, develop, and situate new methods and tools to support each of these phases. For example, research can be directed at identifying effective methods for \"ethical data analysis\" within the insights phase, \"ethical framing\" within ideation, and \"ethical impact evaluation\" during use. Moreover, ethics-based methods and tools Six spheres of technology experience (adapted from Peters, Calvo, and Ryan  [26] ). that already exist can be more easily integrated within the standard development process in this way. It is worth noting that, while it is true an ideal project would start with responsible methods from the beginning, we are aware that few projects represent the ideal. Integrating wellbeing and ethics from any point is likely better than not at all and will contribute to more responsible outcomes. \n C. Framework 2-The Spheres of Technology Experience There has been a lack of appreciation for the different resolutions at which technologies can have an impact on the experience. A technology can make an impact through the design of its interface, based on the tasks it is designed to support, through the behaviors it promotes, or as a collective result of widespread societal use. For instance, consider the way games impact wellbeing and autonomy (autonomy is both a constituent of wellbeing  [35]  and a central principle of AI ethics frameworks in its own right). A user may experience a strong sense of autonomy and wellbeing during game play, but because the game is designed to increase compulsive engagement, a resulting addiction may diminish the same user's experience of autonomy at a life level (as overuse crowds out time for taking care of work, family, and other things of greater importance to her). Therefore, does the game support or hinder autonomy? The answer in this context is probably \"both,\" and therefore, a fair assessment of ethical impact relies on an evaluation that takes into account the impact at different resolutions. Therefore, it is clear that greater precision is required in order to effectively identify impacts at different granularities within the technology experience. Calvo et al.  [36]  first highlighted this need with respect to autonomy and presented a framework distinguishing four \"spheres of autonomy.\" Peters et al.  [32]  expanded on this substantially, developing, as part of a larger model, a framework of technology experience which identifies six distinct spheres within which wellbeing can be influenced. It is this framework that we believe can be usefully applied to provide a structure to ethical impact analysis conducted during a responsible development process. We provide an illustration of the six spheres in Fig.  3 . This \"Spheres of Technology Experience\" framework is described in detail by Peters et al.  [32]  wherein they also provided methods for wellbeing-supportive design. An application of the framework to human autonomy in AI is described in  [37] . Below we provide just a brief description of each sphere to show how each can also help to structure ethical analysis. Adoption: It refers to the experience of a technology prior to use, including the marketing and socio-cultural forces leading a person to use it. A development team may want to consider the ethical impacts of the forces leading to uptake, and to what extent users are choosing to use a product freely or being coerced or pressured to do so. As a simple example, a new upgrade can be forced upon existing users-an approach that is notoriously un-user-friendly-or it can be introduced in a way that better respects autonomy, as when developers provide an option to \"try the upgrade\" first. Interface: The interface sphere is the first sphere of the \"user experience\" and involves interacting with the product itself, including the use of navigation, buttons, and controls. At this level, an ethical analysis might explore issues to do with autonomy and inclusion, for example, to what extent does the interface support autonomy by providing meaningful options and controls? and, are users of different abilities or cultures being excluded? Task: Broadening the lens of analysis beyond the interface, the task sphere refers to discrete activities enabled, or enhanced, by the technology. For example, in the case of a fitness app, \"tracking steps\" or \"adding a meal to the diary\" constitute tasks. Ethical impacts arising from an analysis of these tasks might include the risk of inadvertently contributing to eating disorders or anxiety. Awareness of these risks can help designers structure tasks in ways that respect the diverse needs of users and provide safeguards against negative outcomes. Behavior: Combinations of tasks contribute to an overall behavior. For example, the task \"step-counting\" might contribute to the overall behavior: \"exercise.\" For technologies intending to positively impact on a particular behavior, it is important to consider the psychology literature on the effects of various approaches to supporting that behavior (and/or work with a psychologist). Life: The final and broadest sphere within the user's experience is life, which captures the impacts of a technology at a life level. Not all technologies will have impacts significant enough to yield measurable effects on a person's quality of life overall. While a self-driving car may impact measures of autonomy and wellbeing at the life sphere for someone who is vision impaired, the extent to which a cooking timer is customizable probably will not. While many technologies have only narrow application, and there is little reason to expect them to impact the life sphere, others, such as those that target wellbeing directly (i.e., meditation and fitness apps) or those used daily (workplace technologies, entertainment products, and social media) do need to consider and anticipate life-level impacts. Society: Expanding beyond the user experience into the broadest sphere, society involves the direct and collateral impact on nonusers, nonhuman life, and the environment. The self-driving car mentioned above may promote wellbeing for some users but decrease it for those whose livelihoods depend on driving. This can only be revealed at a societal level of analysis which entails the exploration of emergent and complex systems. This sphere presents the greatest challenges to impact analysis. Identifying and anticipating ethical impacts at this level will not only require multidisciplinary expertise but also ongoing evaluation after a technology is released into use. Nevertheless, some specific methods already exist to assist developers in anticipating societal impact. \"Consequence scanning\" is a method developed by the nonprofit organization, Doteveryone, dedicated to responsible innovation  [38] . The method provides a step-by-step process for collaboratively identifying ethical risks and tensions associated with a new or planned product or service. It is important to qualify that the boundaries between the six spheres of technology experience are merely conceptual and should not be seen as concrete. Instead, they are intended to provide a way of organizing thinking and evaluation that allows for the identification of contradictory parallel effects. The ways in which the Spheres of Technology Experience framework allows us to identify and target wellbeing and ethical impact helps to ensure analysis is both more thoroughly and clearly articulated. The fact that empirical measures already exist that can be applied to these spheres also makes their application practical and actionable. Existing measures (described in  [32] ) can help developers to quantitatively compare different technologies and designs with regard to their different impacts on a range of ethical and wellbeing-related attributes and within different spheres. Some examples of how measures have been used to evaluate the ethical impact already exist. For example, Kerner and Goodyear  [39]  conducted a study investigating the psychological impact of wearable fitness trackers. Additionally, a series of studies comparing how different game designs impact wellbeing and autonomy have been conducted using psychological measures  [40] ,  [41] . While the above examples focus on autonomy and wellbeing, the spheres can be used to articulate impact in relation to any ethical values, and at any stage within the responsible development process. \n IV. CASE STUDY-RESPONSIBLE DIGITAL MENTAL HEALTH TECHNOLOGIES \n A. Project Background During the process of identifying methods for responsible design practice, we were commissioned by a health technology company to explore the ethical tensions arising in the health domain and recommendations for how these could be addressed. The company wanted to follow more responsible practices, and sought to anticipate unintended consequences. We viewed this an opportunity to enrich our experience with ethical analysis and to apply the frameworks described above. The product in question was a text-based online therapy program for depression and anxiety. As part of the research phase (see Fig.  2 ) of our responsible design framework, the expert review we provided was later combined with commercial user research data to help create insights and inform ideation. We believe an expert-led analysis within the research phase is a valuable way to: 1) involve disciplinary experts; 2) draw on existing knowledge; 3) sensitize the development team to ethical issues early on; 4) inform the design of user studies; and 5) assist the interpretation of user data. The analysis below is the outcome of a multidisciplinary literature review and analysis involving a team of researchers with significant professional experience in the co-design and development of digital health technologies. Specifically, and consistent with the claim that ethical impact analysis must be a multidisciplinary endeavor, the team consisted of combined expertise in engineering, design, human-computer interaction, psychology, and philosophy. It also employed the Spheres of Technology Experience framework described above to guide the identification of key ethical considerations within digital mental health. The outcomes pertain to a narrow genre of technologies, rather than a specific product, but the same approach could be taken for a product-specific context. The analysis is structured according to the five ethical principles described in Section II. As such, recommendations are grouped into these five categories: 1) Respect for autonomy (Section IV-C); 2) Beneficence (Section IV-D); 3) Nonmaleficence (Section IV-E); 4) Justice (Section IV-F); and 5) Explicability (Section IV-G). While there are many sets of principles, we chose these five for this analysis because they align with the principles of medical ethics. The analysis is presented in the form of a series of recommendations intended for design and development teams of mental health technologies. Each is presented with: elaboration that connects it to real-world context; a brief overview of how it is addressed in practical ethics; how it may be considered in the context of the application; and specific practical strategies for development which draw on design and engineering literature. \n B. Online Therapy Within Digital Mental Health Depression is the leading cause of disability worldwide  [42]  making data-enabled mental health technologies a critical area of research and industry. These technologies have the potential to increase access to therapy, reduce disparities, reduce costs, and improve the effectiveness of mental health care. But rapid change, coupled with the rapid introduction of new technologies into such a sensitive area, has brought new ethical challenges involving transparency, patient involvement, and human autonomy. A number of authors within human-computer interaction have articulated some of the ethically loaded socio-technical challenges facing digital mental health developers  [28] -  [31] ,  [43] ,  [44] . For example, Orlowski et al.  [44]  stated: \"Design solutions not generated with end users themselves are more likely to fail... Moreover, from an ethical and moral perspective, egalitarian ways of working, such as those exemplified by participatory design, represent a promising opportunity to redress the legacy of consumer disempowerment in mental health.\" Another important criticism of traditional practice in digital mental health revolves around respect for autonomy, a core ethical principle. As Mohr et al.  [45]  explained: \"essentially, clinical researchers have designed tools to try to get people to do what we want them to do and how we want them to do it.\" The literature has also highlighted the ethical issue of transparency as critical to this area. For example, the Psyberguide, developed by a nonprofit network of mental health professionals, includes transparency as one of three criteria for quality ratings of mental health technologies (the other two being credibility and user experience)  [46] . The specific analysis herein focuses on online text-based oneto-one professional therapy for depression and anxiety. This is an augmentative approach to online therapy which, rather than replacing humans, aims to use data to increase human capabilities and to make human activity and interaction more effective, efficient, and satisfying. The analysis is presented as a series of recommendations followed by philosophical justification and practical strategies for implementation. \n C. Respect for Autonomy Recommendation 1: Mental health technologies should be designed to protect and support user autonomy. In medical ethics, the principle of autonomy includes respect for both an individual's right to decide and for the freedom of whether to decide  [19] . Together, these are meant to protect both our right to make choices and our freedom to choose how and when we want to exercise that right  [47] . Respect for autonomy is essential for the development of any digital health technology, but in the case of mental health technologies, it is particularly challenging. This is because certain mental illnesses can affect one's capacity to reason, one's perception of oneself and of others, one's ability to make decisions, and other cognitive capacities that are core to one's ability to self-govern. Burr and Morley  [47]  discussed how the presence of a mental illness might also affect a patient's choice to engage with a mental health service and restrict their ability to make healthcare decisions. In extreme cases, respecting a patient's autonomy (i.e., nonintervention) may even threaten safety, if there is a risk of harm to self or others. What this suggests is that: 1) respect for patient autonomy is defeasible such that it may sometimes have to be traded off against other goods and 2) in some cases healthcare providers may need to go beyond respect for a patient's current ability to self-govern to help build and support the user's autonomy in the long term. Online professional text-based therapies will involve (at least) two kinds of users: 1) patients and 2) therapists (counselors). It is important to also think of the therapist as a user of this technology, as their role will be changed and augmented by these new tools. This is also true for other kinds of dataenabled medical technologies which will affect not only the patient but also healthcare professionals. Recommendation 2: To protect the privacy and autonomy of users, make transparent the use of mental health data and ensure secure storage. Online mental health therapy applications that collect, store, and make use of personal data raise several important concerns around privacy, which in turn can pose risks to user autonomy  [48] ,  [49] . In particular, because of the kind of personal data that is now available to be collected (e.g., biometrics, location, and online behavior) combined with advances in machine learning that make it possible to infer personal attributes from collected data (e.g.,  [50]  and  [51] ) companies are increasingly able to tailor messages and services to specific individuals or groups. This means that the more personal information a company has about someone, the more effectively they can target interventions in an attempt to influence them which may present new risks to patient autonomy. Even features that can serve as a means of patient empowerment, such as self-tracking, which can be used to boost self-reflection, can pose risks to autonomy. But the sharing or use of this data, be it with family, friends, or even healthcare professionals-especially in nonemergency situationscan negatively affect patient autonomy. Sanches et al.  [43]  described this as an example of \"autonomy [of patients being] claimed by their social support network, collectivized by healthcare services, or both.\" This explains why designing for privacy as a target can also be considered a subset of autonomy support  [52] . Furthermore, since therapy sessions involve two interlocutors, both sides have reasonable claims to privacy. It is important that all users are given clear and accurate explanations about how the information collected from therapy sessions is being used. This is especially true since users, including counselors, may not be aware of the value of their data. One way of using the data, for example, is for analyzing the counselors' conversations. This may be problematic, but also presents an opportunity to provide feedback if handled in a manner that does not feel intrusive. \n 1) Practical Strategies for Respecting Autonomy: The literature on self-determination theory, a robustly evidence-based psychological theory of wellbeing and motivation  [35]  provides guidance with respect to what characteristics constitute \"autonomy-supportive\" (versus controlling) environments and interactions. According to this article, autonomy-supportive interactions as follows. 1) Understand the other's perspective (frame of reference). 2) Seek the other's input and ideas. 3) Offer meaningful choices. 4) Empathize with resistance and obstacles. 5) Minimize the use of controlling language or rewards. 6) Provide a rationale for requested or required behavior. These can be translated into design guidance for digital technologies. For example, applying empathy is the cornerstone of human-centered design so employing human-centered methods is likely to increase autonomy-supportive outcomes. Seeking the user's input and ideas is also achieved through humancentered and participatory processes. In the mental health context, this requires engagement with people with have suffered mental illness as only they have direct expertise around frames of reference, threats to autonomy and privacy within their contexts, and insights into the kinds of obstacles that are most salient for them. Moreover, insights from these processes can inform what meaningful choices can be added to the technology. With respect to the protection of privacy specifically (recommendation 2), meaningful choices are likely to involve giving the client control over when and with whom data is shared. Security experts should be consulted in ensuring that the data collected and analyzed in the course of mental health therapy is safely and securely stored, and that it is only shared through properly encrypted channels. In many countries, this is required by the Health Insurance Portability and Accountability Act (HIPAA) and similar legislation. \n D. Beneficence Recommendation 3: Consider the wider impact of both opportunities and risks for all stakeholders involved in the development and use of mental health technologies. In biomedical ethics, the principle of beneficence is typically thought of as a commitment to \"do good.\" In this context, this will require that the potential benefits of a design or development choice be balanced against potential risks, both for an individual user and for society more broadly  [19] . First, it is important to identify all those who stand to benefit from a particular technology. In addition to patients, the use of online text-based therapies impacts therapists, developers, family members, other patients, and the wider mental health care community. Hence, there is a need to adopt a holistic approach to design and implementation that ensures that all parties affected are considered. Moreover, the collateral impact might involve other, less obvious, stakeholders, such as developers themselves. For example, with supervised learning, a human has to assign labels to data used to train predictive algorithms. In the case of mental health therapies, this means that an employee must read and tag sensitive conversations between doctors and patients. This could have a harmful psychological impact on developers since therapy sessions are likely to contain content that could be distressing or triggering, depending on one's own life experiences. Such a labeling task might require training, so that the developer has the necessary context for what they might read as well as training on how to cope. Relatedly, Sanches et al.  [43]  expressed worry about \"burnout\" for HCI researchers working in the challenging area of mental health and mention the need for greater peer and institutional support. They also suggest rethinking how such support can be explicitly factored into institutional guidelines and budgets. Recommendation 4: Research the access requirements and unique mental health situations of diverse populations in order to ensure mental health technologies are effective for all relevant groups. In many cases, the risks of a new technology are not evenly distributed. In the context of data-enabled digital mental health therapies, the relative dearth of research and understanding on the needs of people from diverse socioeconomic and ethnic groups may put members of those groups at greater risk. If online therapies are developed using a data set that only includes relatively affluent university students, or that lacks other forms of representation, then the therapy will only be optimized for a homogeneous group. Hence, it is important that the training set for the algorithm genuinely represents the diversity of the target population that will use it. In practice what this means is that in some cases sets used to evaluate algorithms might need to come from a different statistical distribution than the training set. This comes with its own challenges, for example, understanding the wide variation in groups affected by mental illness, reaching out to \"hard to reach populations\" (e.g., the homeless, refugees, those addicted to drugs, etc.) and how measures can be used to yield inclusive and broadly beneficial interventions. Recommendation 5: Aim to support authentic human interactions, connectivity, and engagement. Another example of the kind of balancing that needs to be done to ensure beneficence, involves the opportunities and risks that digital health technologies pose for authentic relationships. The context of mental healthcare requires respect, dignity, and empathy. However, even highly sophisticated AI systems lack human empathy and are at best able to mimic these traits. Thus, even partial automation in mental healthcare, if not implemented cautiously, could threaten \"relational authenticity\"  [53] . In Hertlein et al.'s  [54]  study of family and marriage counselors' ethical concerns around online therapy, one theme that emerged was the impact to the therapeutic relationship. One participant expressed concern that there may be \"missed information, lost feelings/understanding, lack of intimacy and disclosure.\" Another therapist worried that online therapy \"lacks the opportunity for physical human interaction, such as offering a crying client a tissue or engaging in therapeutic touch, which could possibly act as a barrier to joining effectively with clients.\" These statements capture the concerns that the use of AI could lead to feelings of alienation and devaluation. A related concern is a reduction in the quality of communication that may result from the lack of nonverbal cues and body language. This is true for online therapy, but also more broadly for other forms of data-enabled digital health interventions. There is some evidence, for example, that the data entry required for electronic medical records (EMRs) disrupts the nonverbal relationship between health-care providers and patients (e.g.,  [55] ). Other research has shown that nonverbal cues, including eye contact and social touch (e.g., handshakes), have been found to significantly influence patient perceptions of clinician empathy  [56] . Hence, the loss of such nonverbal cues can make it more difficult for health care providers to demonstrate empathy and to build authentic relationships with clients. In addition to concerns about alienation and reduced quality of communication, some evidence suggests that relational authenticity also encourages patient engagement and trust  [57] . Hence, any reduction in relational autonomy might, in turn, diminish engagement and trust. In their recent report, Sanches et al.  [43]  expressed a desire to see \"more novel designs of systems that foster and support beneficial human interactions, beyond the design of autonomous agents imitating empathy and aimed at replacing human contact.\" On the other hand, technological interventions in mental health may provide new opportunities for engagement that are not available in a strictly human-to-human context. For example, a 3-D avatar that functions like a virtual therapist but was not trying to perfectly emulate a human being  [58] . The result was (somewhat surprisingly) positive: \"Patients admit that they feel less judged by the virtual therapist and more open to her, especially, if they were told that she was operated automatically rather than by a remote person\"  [59] . This suggests that patients might be able to have differently authentic interactions with technologically mediated systems, if they are well designed. Designs such as these may be able to explore new ways of connecting with humans and eliciting beneficial relationships and experiences that are authentic in their own way, though not authentically human. 1) Practical Strategies for Beneficence: Arguably, the technology experience of people living with mental health issues can only be well understood by engaging directly with them as part of a collaborative design and evaluation process. This experience will be shaped by socio-economic and cultural circumstances and will, therefore, differ among individuals, yet meaningful patterns will still exist. User involvement that adequately represents the diversity of potential users of a service is therefore critical to bringing about genuine benefit. This inclusive process will also help to prevent blindness to the reality of the wide spectrum of audience needs within mental health service provision. This includes differing requirements due to low income, disability, low literacy, limited access to computers, mobile phones, and Internet connections, as well as low technology literacy (even among young people)  [60] . In addition, users will prefer different modes of technology use at different times. For example, an insomnia therapy that does not require keeping a phone by the bed may be far more effective, while users may not feel comfortable using an audio or video-based program within public spaces. As such, designers should consider providing clients with multiple ways of accessing materials and consider how flexibility can be provided in the delivery of services. \n E. Nonmaleficence Within medical ethics, nonmaleficence is an obligation not to cause harm. This also applies to the design and development of data-enabled digital mental health therapies. The difficulty with this principle is avoiding the \"known unknowns\"-that is, harms that one foresees, though with some uncertainty-as well as the \"unknown unknowns\"-that is, harms that one does not foresee. The latter requires evaluating (and re-evaluating) impact both during development and after release. Recommendation 6: While augmentation can be beneficial, ensure that over-reliance on technology does not lead to atrophy of critical skills or diminish competence. One example of a foreseeable, though uncertain, the harm is atrophy. Skill atrophy is the decline in abilities that comes from underuse or neglect to perform the behaviors and tasks that keep skills up to date. Over-reliance on technology has been cited as a contributor to atrophy of skills in many different contexts (e.g.,  [61]  and  [62] )-a concern that dates back at least as far as Plato's discussion of the diminishing effects that writing would have on memory  [63] . As more tasks are automated in the context of mental health, this could result in atrophy of previously used skills of both patients and therapists. Though there is a case to be made for the replacement of particular types of skills or activities for more worthwhile use of human capacities (e.g., replacing repetitive calculations or data entry with creative or empathic pursuits), there are also risks to be managed, as atrophy can lead to dependence and even safety issues. These risks can necessitate the need to create fail-safes (procedures for cases in which technology malfunctions and people need to rely on past skills), or they might necessitate not introducing technology into realms where humans should remain critically vigilant or engaged, such as areas that require value judgments  [64] . Some areas of mental health-care may be among these. For patients, there may be a risk of losing good decisionmaking skills and the ability to check-in with themselves, to self-reflect, as well as to understand and troubleshoot symptoms and emotions. Technology can be a tool to prompt analysis of mood or symptom data, provide encouragement or trigger an alert for when to get help. But if someone is entirely dependent on a device for self-reflection they may lose competence at self-management when they are decoupled from the device (e.g., due to a loss of network connection, a damaged device, or no battery power). Additionally, dependence on a technology to manage care may result in lower feelings of self-efficacy, empowerment, and control  [64] . For therapists, the introduction of technology into the diagnostic and therapeutic process could result in atrophy of critical professional skills. In cognitive-behavioral therapy sessions, therapists interact closely with patients through structured discussion sessions to break down problems into separate parts (thoughts, behaviors, and actions) and then to suggest strategies that patients can use to change their thinking and behavior. The success of these sessions depends on the therapist's ability to home in on problems, deconstruct them, engage patients, and suggest strategies to adopt. All of these steps are skills that therapists develop over time, and they are also all skills that can be augmented through AI and digital technologies. This, in turn, makes them susceptible to atrophy. If a therapist becomes over-reliant on an app that aids in these skills, over time she may lose them and struggle to be as effective in face-to-face sessions with patients. Technologists will need to work closely with therapists and patients to determine appropriate areas for automation and augmentation and then evaluate outcomes after release. Recommendation 7: To avoid risks arising from stigma, design to protect the privacy of users and always ensure secure storage of mental health data. Another foreseeable though uncertain harm is privacy. Because mental health is a stigmatized topic, those that suffer from mental health conditions face the risk of bias and discrimination, from both themselves (selfstigma) and others. This means that if digital health records of mental health status are leaked, hacked, or accessed by unconsented third parties, a user's dignity and reputation could be threatened, and they could be put at risk of discrimination. These concerns are true in traditional (face-to-face) therapy as well, but relying on digital online platforms, from EMRs, to online therapies, poses new risks to both informational and decisional privacy  [65] . In Hertlein et al.'s  [54]  survey, participants expressed concerns about the authenticity of the user (such as \"who has access to the computer\" and \"the [chance] of loss of control of who has the device at the other end\"), about who else might be physically present in the same room as the counselor (\"How can the therapist or client be sure no one else is in the vicinity of the computer-that is, how can you assure confidentiality?\"), and about the possibility of hackers (\"security online is not guaranteed.\") Hence, in the case of online therapy, patients not only have to trust their counselor's good intentions, they also have to trust that counselors will protect their computer screen or other devices from onlookers, protect their passwords, use secure network connections, and not use shared computers  [54] ,  [66] . Patients furthermore have to trust the provider of the technology not to use the data for any unconsented purpose. For this reason, it is important that the utmost care is taken by companies to protect and anonymize the use and storage of sensitive data. Doherty et al.  [52]  suggested additional design implications to protect against the risks of stigma. \n 1) Practical Strategies for Nonmaleficence: There are a number of practical strategies that help ensure the principle of \"do no harm\" is followed. First, in addition to user research and involvement, a safe user experience design depends upon iterative improvement based on the ongoing evaluation. Health technologies also require clinically relevant efficacy trials. Owing to the potentially drastic consequences of ineffective (i.e., potentially harmful) mental health technology, evaluation of both user experience and health outcomes is an essential criterion for a responsible approach. Evaluation might initially consist of expert review, heuristic evaluations, and internal prototype testing, and be followed by pilot studies evaluating technologies with users until there is sufficient evidence of feasibility and benefit to justify a more formal clinical evaluation. Further evaluation after the release of the product can inform improvements and upgrades and is necessary for determining impact and appropriation within complex real-world contexts (which are often very different to the controlled environments of clinical trials). Our framework for a responsible design process calls for just this kind of staged approach to evaluation (see Doherty et al.  [52]  for further discussion of a staged approach to the evaluation of mental health technologies more specifically). Moreover, as alluded to earlier, when it comes to mental health technologies, technologists should not attempt to \"go it alone.\" Ensuring that users, their contexts, the healthcare system, medical research, safety, ethical implications, and many other critical considerations are given expert attention requires a multidisciplinary team. Traditional approaches to \"failing fast and often\" are potentially disastrous in a health context in which people cannot always safely be used as guinea pigs for a/b testing. As such, mental health professionals must be part of the design and development team. They can help ensure more rigorous, evidencebased, and appropriately safety-conscious approaches are taken. Experts in ethics should also contribute in order to effectively assess ethical considerations from multiple standpoints. It may be helpful for them to work directly with user experience specialists to allow broad stakeholder input into ethical concerns. In addition to involving multidisciplinary teams and undertaking ongoing evaluation, technology approaches need to be grounded in research to prevent harm. Topham et al.  [67]  argued that it is an ethical responsibility \"to ensure that mental health technologies are grounded in solid and valid principles to maximize the benefits and limit harm.\" Doherty et al.  [52]  similarly recommended that systems be based on accepted theoretical approaches for clinical validity. Furthermore, a need for rigorous approaches should apply, not only to the therapeutic program employed but also to the user research and evaluation practices. A human-centered focus on lived experience suggests the importance of mixed methods including qualitative methods for uncovering insights into subjective experience, motivation, and the causes of engagement and disengagement. These can complement and explain results from quantitative approaches, such as symptom scores, behavioral analytics, or surveys. Finally, a simple safeguard for avoiding nonmaleficence is to apply existing quality frameworks. A number of quality frameworks and guidelines have been developed by multidisciplinary groups of researchers and these can be applied as a basic foundation for more responsible design. For example, the transparency for trust principles  [68]  includes questions around privacy and data security, development characteristics, feasibility, and health benefits, and their creators advocate that all apps should be required to provide information relating to these four principles at minimum. More specific to mental health, the Psyberguide, developed by mental health professionals, bases its ratings on criteria for credibility, user experience, and transparency  [46]  while the American Psychiatric Association has an app evaluation model for psychiatrists  [69] . Technology-specific guidelines have also been developed, including the guidelines for the design of interventions for mental health on social media  [70] . With respect to ensuring anonymity to prevent harms from stigma (recommendation 7), design implications may involve allowing for discreet use. For example, studies have revealed problems with app titles that include stigmatized words like \"mood\" or \"mental health\" because users worry others will see them  [52] . The discreet design may also involve avoiding client-identifying data on the interface whenever possible (e.g., data graph screens that do not need to include personal details). \n F. Justice Justice is a complex ethical principle that is closely linked to fairness and equality, though is not quite the same as either  [71] . Sanches et al.  [43]  described the principle as requiring the \"fair distribution of benefits, risks, and costs to all people irrespectively of social class, race, gender, or other forms of discrimination.\" In medical ethics, the principle is often subdivided into three categories: 1) distributive justice; 2) rights-based justice; and 3) legal justice. Distributive justice requires the fair distribution of resources and is particularly concerned with scarce resources. Rights-based justice requires that people's basic human rights be respected  [72] . Privacy and autonomy, for example, are widely recognized as human rights and hence some of the concerns raised thus far would fall under rights-based justice. Finally, legal justice requires that people's legal rights be respected. The development and implementation of data-enabled digital mental health technologies raises particular concerns about distributive and rights-based forms of justice. Because the law differs by jurisdiction, we will not discuss legal justice. There are two main areas in which to analyze distributive and rights-based justice within data-enabled mental health technologies: 1) in the design process and 2) in the distribution of the final product or service. In the first, compensation and credit for the human labor involved in algorithmic design must be considered; and in the second, questions about who is able to access and make use of the service need to be considered. Recommendation 8: Make known the value of human labor and intellectual property in the development of algorithms to all parties, and potentially compensate for it. With regard to the design process, one type of ethical challenge arises from \"heteromation\": the extraction of economic value from lowcost (or free) labor  [73] . This includes all sorts of labor, from Amazon Mechanical Turk workers, who are paid very low wages to complete tasks that are difficult for an algorithm to do, to the work of completing a Captcha, or other forms of reverse Turing tests, where a person must prove they are human by completing a task (e.g., identifying and selecting all images of crosswalks in a series of nine photographs). These tasks automatically build training sets for algorithms that will eventually be able to accomplish these tasks themselves. Hence, there may be a transfer of intellectual property to the company for which the human laborers are not credited, as well as work for which they may not be adequately compensated. These issues can be addressed in some projects by disclosing the uses of data or seeking approval to use the data for research and development purposes. This has been done, for example, in EQClinic, a project in which a telehealth platform is used to help medical students improve their communication skills  [74] . A related concern in the development and prototyping of products is piloting on low income, high need, or otherwise vulnerable populations. On the one hand, providing a service to a population that has a critical need for it and may be willing to try an earlier developed prototype seems sensible. On the other hand, it may involve putting these vulnerable populations at risk by deploying or testing unfinished solutions. One area to potentially draw upon in considering these issues is the cost-benefit considerations at play in the treatment of rare diseases for which there are no known and tested cures  [75] . When it comes to new or experimental medical technologies there is an absolute need to obtain informed consent, so that when patients agree to testing they do so with full understanding of the potential benefits and harms. It is important to make sure that any vulnerable population is informed about other options for care, so that they may reasonably decline new (especially, experimental) treatments without feeling compelled to accept them. There may, of course, also be positive social justice outcomes that encourage early users to act as \"data altruists.\" For example, early advances in algorithmic solutions can reduce costs for future generations and expand access to less advantaged segments of the population. There is evidence that some people may be willing to share their data, even without direct compensation, if these benefits are communicated to them  [76] ,  [77] . Recommendation 9: Follow guidelines for universal accessibility and tailor the level and mode of content to the spectrum of audience needs. Certainly, one positive feature of online therapies is that they can increase access for remote and working populations. In these ways, online therapy, reduces the barrier to entry and could increase uptake. It is unfair, however, to assume that low-income populations all have access to the necessary computing devices and stable Internet connections. Burr and Morley  [47]  have recently argued that genuine empowerment of a patient crucially depends on \"the prior removal of certain barriers to engagement, which patients suffering from a variety of mental health conditions face.\" As national healthcare services move increasingly toward online therapies, research must be done on which populations are equipped for uptake, so that vulnerable communities are not left out. Beyond initial uptake, there is further evidence that minority populations tend to have lower retention in mental healthcare  [78] . Thus, there is a critical need for more research into the root causes of this finding, as well as ways to better tailor to these populations with the use of online therapies. This includes designing for differing requirements relating to income, literacy levels, and technology access  [60] . 1) Practical Strategies for Supporting Justice: International guidelines for digital accessibility and \"universal design\" provide essential starting points for ensuring a technology does not exclude users with older devices, limited Internet access, physical disabilities, or other varying requirements. Furthermore, as mentioned, researchers have expressed a need for more involvement of people living with mental health issues in technology design  [43] -  [45] . Deep user involvement is not only necessary in order for a technology to be genuinely useful and engaging to its audience, but is also arguably, a matter of design justice, in that it represents a more democratic and consultative approach. One popular approach to user involvement is \"participatory design\"  [79]  which involves including users as collaborators from the earliest exploratory phases of development. Orlowski et al.  [44]  provided specific examples of practical applications of participatory design and design thinking methods for mental health technology. Likewise, where the use of a technology will require the involvement of carers, parents, or providers, their unique needs should also be included. Finally, it is worth noting that the term \"user\" itself, while useful for its specificity within the technology context, can be inadvertently de-humanizing, obscuring ethical responsibilities. Therefore, in many cases, words like \"human,\" \"clients,\" \"patients,\" \"people,\" or even \"lives\" may be far more appropriate. \n G. Explicability In addition to the four traditional bioethical principles, Floridi et al.  [3]  included explicability for the AI context, which they describe as enabling the other principles through both intelligibility and accountability. Other terms, such as \"transparency,\" are also frequently used in AI ethics frameworks to capture a similar duty [e.g., the IEEE (2019)  [2]  uses both transparency and \"accountability\"]. In general, the idea is that we (i.e., designers, users, and society more generally) need to be able to understand data-enabled systems enough to somehow hold to account their functions (both in terms of their input data and their outputs). We will focus our discussion on the concepts of transparency and accountability as aligned with the IEEE guidelines  [2] . Recommendation 10: Ensure transparency and accountability in all aspects of the use of mental health technologies as it is critical to safe and beneficial care. Transparency to do with the collection, use, and storage of data is fundamental to ensuring privacy and other rights, such as informed consent. There are many areas in which transparency must be integrated within an online text-based mental health platform, and many of these arise from the use of a mediating platform which introduces other parties into what was traditionally a confidential conversation between counselor and patient. For example, developers need to be involved in order to design and support the platform; conversations may be recorded and analyzed for potential introduction of AI capabilities; and then these capabilities will need to be audited in order to ensure they function correctly. All of these new layers will require some degree of transparency and accountability. When signing up for a platform and consenting to therapy conducted in online formats, patients should have an understanding of who will have access to what parts of their data and why. As more data is collected and recorded, it should be made clear which parties have access to patient notes and therapistpatient conversational records. Additionally, text-based therapy introduces the possibility for different interactions with the data from a session, but this access comes with both benefits and risks which need to be carefully considered  [80] . At a high level, there should also be basic transparency and accountability around business models since for-profit advertising or payments from insurance providers or employer health programs may come with incentives that conflict with the best interests of patients. Funding sources and revenue models may create conflicts of interest in data sharing and breach the trust of patients. 1) Practical Strategies for Explicability: Quality frameworks for digital health provide a valuable starting point for applying principles of transparency and accountability. For example, The Transparency for Trust Principles  [68]  require standard information to be communicated to users in understandable ways, including information around privacy, data security, development characteristics, feasibility, and health benefits. The Psyberguide  [46]  bases ratings on transparency as well, so examples of technologies that meet the transparency criteria provide models for practical approaches to implementation. \n V. CONCLUSION The recommendations described above present the result of an ethical analysis conducted by a particular team of professionals in the context of a particular technology type within a specific domain. Analyses by other teams would yield different outcomes although it is reasonable to assume that, for a given context, patterns of concerns will emerge that overlap. As digital ethics continues to grow in importance, the ethical principles for AI can help us to structure ethical impact analyses. However, the translation of ethical principles into actionable strategies in practice is challenging. We have presented a number of frameworks, including one for a responsible design process and another for providing greater resolution to technology experience as a contribution toward helping address the difficulty in moving from principle to practice within ethical impact analysis. We have also provided a description of the outcomes of an expert-led ethical analysis, conducted in the context of digital health, in order to show one way such an analysis might be contribute to early stages in a development process. Of course, our contribution goes only a very small way toward the full integration of ethical impact assessment needed within engineering practice. More research and experimentation with various tools and methods, as well as focused research on ethical implications pertinent to specific application areas and technologies, is still very much needed. We hope the frameworks presented can provide some help toward shaping that path. Fig. 1 . 1 Fig. 1. Connections among six fields centrally involved in the ethical design and development of AI and data-enabled systems (based on Sloan foundation's hexagonal mapping of \"connections among the cognitive sciences\" 1978, reproduced in Gardner 1985, p. 37) key: unbroken lines = strong interdisciplinary ties, broken lines = weak interdisciplinary ties. \n Fig. 3 . 3 Fig. 3.Six spheres of technology experience (adapted from Peters, Calvo, and Ryan [26] ).", "date_published": "n/a", "url": "n/a", "filename": "Responsible_AITwo_Frameworks_for_Ethical_Design_Practice.tei.xml", "abstract": "In 2019, the IEEE launched the P7000 standards projects intended to address ethical issues in the design of autonomous and intelligent systems. This move came amidst a growing public concern over the unintended consequences of artificial intelligence (AI), compounded by the lack of an anticipatory process for attending to ethical impact within professional practice. However, the difficulty in moving from principles to practice presents a significant challenge to the implementation of ethical guidelines. Herein, we describe two complementary frameworks for integrating ethical analysis into engineering practice to help address this challenge. We then provide the outcomes of an ethical analysis informed by these frameworks, conducted within the specific context of Internet-delivered therapy in digital mental health. We hope both the frameworks and analysis can provide tools and insights, not only for the context of digital healthcare but also for data-enabled and intelligent technology development more broadly.", "id": "07e0fd01fcdb433422c939cc54960d8d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Colleen Mckenzie", "J Bryce Hidysmith"], "title": "AI Insights Dataset Analysis", "text": "Methods & Assumptions Our metric for what constitutes an insight is an estimate of how novel or surprising the results of that insight are, using a comparison of LSTM and RNNs as a baseline-that is, given that RNNs exist, how surprising is the development of LSTM? All discoveries that seem equally or more surprising were included in our set. This is one of many possible thresholds for significance we could have chosen, and the rationale behind ours is subjective: Our focus on theoretical progress means that the data do not include progress captured in implementing an existing theory, or applying it more directly. For example, punched-card programming of early computers had clear impacts on the progress of computing, but we attribute the insight behind that technology to the 18th-century textile worker who developed a punchedcard method for programming looms. From this perspective, the application of punched cards to electrical computers is a combination of existing theories, not a new development in itself. We consulted two existing chronicles of the history of AI in an effort to flesh out parts of our data set that may have fallen in our blind spots: -Nilsson, N. J.  (2009) . The quest for artificial intelligence. Cambridge University  Press. -Crevier, D. (1993) . AI: the tumultuous history of the search for artificial intelligence. Basic Books. A few additional notes on the data: • First to discover, not first to publish: We credit an insight to the first person known to have described it, as best we can determine through reputable sources, not the first person to publish that description. This practice is motivated in part by our understanding that not all discoverers published work in the academic tradition (e.g. William Newcomb, credited with the conception of Newcomb's problem), and in part by some discoveries' having been kept confidential, pre-publication, in corporate and state departments. • Specific vs. general discoveries: Sometimes an early discovery constitutes a special case of a later, more general discovery; in this case, we credit the more general discovery. If the special case itself seems to constitute an influential insight, we'll credit it as a separate line item; but if it was largely ignored, or was unavailable to discoverers of the more general version, we omit it from this list. For example, ideas from evolutionary biology have been rediscovered independently by AI researchers through simulationist and purely rationalistic investigation that were previously discovered empirically through biological field research before being formalized in such a manner that they could be used by AI researchers. We count the usable formalization, rather than the case studies that could be used as raw material for specifying the usable formalization. • Hardware agnosticism: Our focus here is on information theoretical insights, not on insights that aid in the development of new hardware, the rationale being that artificial intelligence is a substrate independent pursuit, provided that the Church-Turing thesis holds. Futher, charting the history of today's electronic computers alone would constitute a project of roughly equal magnitude, and one that aligns less closely with our area of expertise. \n Data & Parameters The full dataset (as json) and its schema are available at mediangroup.org/research; this section provides a brief overview of the data for readers of this report. The set includes 193 total insights. For each insight, we record the following information (plus sources for each fact): • Name • Year of discovery • First work in which the insight was referenced or published • Discoverer(s) • Institutional affiliation of discoverer(s) at time of discovery (if applicable) • Institution(s) sector and type (see below) • Nation of origin of discoverer(s) \n • Additional notes Institutions are assigned rough sectors and types from the following lists: Sectors: • Academic • Military • Industrial • State • Other R&D • Religious • N/A Types: • Public university • Private university • For-profit entity • Non-profit entity • N/A \n Analysis For the purposes of this first analysis section, we will discuss the data as we have been able to make it available to us. Reflections on the limitations of the data and the extent to which they are relevant to readership follow in the Methodological Reflections section. \n Temporal distribution At a glance, the distribution of insights over time shows an expected uptick in progress contemporaneous with the European Enlightenment, followed by a sharp increase in the pace of discovery at the beginning of the 20th century. A view of only the most recent centuries provides more detail on the arc of recent progress, showing a significant increase in production with introduction of digital computers available to major institutions in the late 1940s. A breakdown of insight discoveries by decade clarifies the changing rates of discovery. \n Historical context The uneven distribution of insights correlates clearly with the trajectory of Western intellectual and economic history. The theological and philosophical conservatism of the middle ages matches the flat section of the first curve above from c. 500 -1500 AD. During the middle ages, there was no sense of how economic or political advantage might be gained from the use of power not derived from human, animal, or natural sources (e.g. waterwheels applied to rivers). The media of the middle ages, too, was meant for interpretation by individual human minds, as opposed to instantiation on larger groups or in artificial substrates. For example, medieval alchemical texts were written with the expectation that the text is exclusively human-readable, and so the informational payload of the text is found not within the structure of the text as an object itself, but in the interpretation and implementation of the text by its human reader; this can be contrasted with the periodic table, which describes a structure already present in nonhuman substrate. This norm continued throughout most of the Enlightenment, perhaps reaching its height during the efforts of the Encyclopedists led by Denis Diderot. The philosophical ideas throughout the 18th and the first half of the 19th century provided the foundation for a scientific community able to take action during the industrial revolution, but the industrial revolution itself provided the necessary material tools for developing automation systems capable of directly realizing political, economic, or scientific goals. The technologies of the industrial revolution, including the social technologies of the factory and the joint stock company developed immediately prior during the late Enlightenment, differed from previous technologies in that they contianed implicit instructions for their operation that were not simply transformations of a source of physical power such as a horse's muscles. A joint-stock company's organization can be thought of as a primative attempt at a superhuman intelligence implemented on a collection of individual human beings. The transition to automated systems that lacked a human in their control loop was the advent of the Jaquard loom (captured in our data as an earlier insight by Basile Bouchon). Earlier automata in the West, the Muslim World, and China, were limited to toys, and their effects limited to the thought that they inspired in their viewers. The Digesting Duck, an automaton from eighteenth century France that crudely pretended the metabolism of a waterfowl, is as inert in its physical effect on the world as a child's toy truck or Michaelangelo's David except by inspiring the behavior of human agents. The automata of the industrial period became actors in their own right. The Jaquard Loom or a modern 3D printer takes a machine-readable instruction and produces an effect that is as physically relevant as if it had been accomplished by human labor. Though automation systems capable of acting as intelligent agents in their own right, rather than replacements for physical labor, could have been developed in the 19th century through the work of Babbage and Lovelace, the uses of cryptography and automatic aiming systems for artillery during the Second World War provided the industrial basis for their maturation. Blechley Park's work in decoding the German Enigma code was perhaps the first instance when computation at a scale not accomplishable in an individual human mind was required to counter an existential threat to a major power. Previous efforts in state computation by actors such as the US Government during the censuses of the 1870s and 1880s provided valuable technological precursors, but these calculating and tabulating machines were not true computers in the modern sense. Cryptographic and cryptoanalytic efforts during the wars provided the centralization of capital required to produce an abstract automation system in the form of Colossus, the first digital programmable computing device. Such an automation system that processs and transforms information rather than simply taking an instruction to produce a physical effect is obviously required for the development of modern artificial intelligence. We must further conjecture that the invention of programmable digital computing devices was required for the psychological conditions necessary for individual scientists and engineeers to experiment in the fields that would eventually birth artificial intelligence. There was only one Turing, publishing his basic principles of computability in On Computable Numbers  (1936) , but there are an uncountable number of individuals able to experiment with the machines derived from these basic insights. The massive upward trend in insights following the end of the Second World War can thus be attributed to access to modern computing machines following their invention, as well as the incentivization of computer science and artificial intelligence research instrumentally by the states locked in conflict during the Cold War for purposes of military advantage. Artificial intelligence, like any intellectual pursuit undertaken as more than a recreation by those with leisure time and intrinsic interest, advances at pace with its support by institutions tasked with the necessities security and prosperity. The distribution of insights from the beginning of the Cold War to the present shows only a marginal deceleration after the fall of the Soviet Union, compared to the roughly linear rate of increase at the beginning of the Cold War. The shallower slopes of curves in the mid-1970s and the late 80s through early 90s correspond to the two periods now described as AI winters, when progress slowed. The former of these two periods appears to be a more substantial decline in insights we measured. We expect this effect is a result of the 1970s being a period of application and combination of existing insights to new problem areas, without substantial generation of additional insights, in addition to the effect of decreased AI-related research during this period. As Nilsson puts it: \"Until about the early 1970s, most AI research dealt with what Seymour Papert called 'toy' problems. . . .However, soon after, AI efforts began a definite shift towards applications work, confronting problems of real-world importance. . . .One reason for the increasing interest in applications was that the power of AI methods had increased to the point where realistic applications seemed within reach.\" (Nilsson, 207) \n Geocultural distribution (Note: data for \"Russia\" includes insights produced by Soviet scientists born within Russian borders and working at historically Russian institutions.) The distribution of insights by nationality of discover reflects a number of well-understood trends in intellectual history. Ancient Greece provided the intellectual foundations that England and France then built upon during the Enlightenment, before the rise of Germany as it indutrialized and centralized politically. During the twentieth century, the rise of both the Russian and American superpowers correlated to substantial advances, but the United States dramatically outcompeted the Soviet Union. Some of the gains that could be credited to the Soviet Union if one assumes a model based on spheres of influence are marked as Hungarian in origin, as well as a few other countries such as Moldova that did not make it into the top ten. The United States' position as an aggregator of immigrants and refugees from Europe during and after the Second World War substantially increases the number of entries counted as American. The circumstances that made such devices available were not only economic but also politically strategic, as the political aims of military supremacy by both the United States and the Soviet Union during the Cold War enabled their local markets to distribute said computing machines. Additionally, given that the state of Israel was not established until 1949, entries there only date to that time, though many of the scientists who immigrated to Israel and established the scholarly communities that contributed to AI efforts originated in Soviet or American territory. \n Institutional distribution The vast majority of insights in our dataset, unsurprisingly, were discovered and developed by individuals at academic institutions. Early progress in mathematics and the sciences was due mostly to unaffiliated individuals-including most researchers from antiquity and the Renaissance-but as academic institutions gained prestige and resulting brilliance, they began to outcompete other institutional types. Two trends stand out in the latter part of the 20th century: the increase in output from nonacademic R&D institutions, and the slight increase in insights derived within military institutions. Nonacademic R&D includes institutions such as Bell Laboratories and the RAND Corporation, and appears in our data first in 1947 (an attribution to Bell Labs's John Tukey). Bell Laboratories (or Bell Labs) was an unusual institution, in historical context, and in many ways the first of its kind: a result of a step-function increase in the engineering progress needed for telecommunications infrastructure, Bell Labs was incubated within the monopolistic Bell Telephone Company before its 1984 dissolution after a successful antitrust suit. Within it, researchers such as Shannon, Shockley, and Hamming developed some of the core advances of their fields, and it has continued to produce novel research for decades: the most recent insight to come out of Bell Labs, in our data, was from 1995. The RAND Corporation, in contrast, was developed in response to state officials suggesting potential benefits from private involvement in relevant research areas, and RAND itself developed out of an aircraft company, becoming a separate, nonprofit institution in 1948. While insights from RAND represent a shorter timespan in our dataset, limited to just the decade between 1950 and 1960, they outnumber those from any institution besides Stanford and Princeton universities, well-known powerhouses of AI development, by the present day. Dynamic programming (Bellman) and symbolic AI (Newell, Shaw, and Simon) are notable among its body of production. The relative scarcity of of military institutions in our data suggests a more indirect role due to military involvement. The development of artificial intelligence is deeply entangled with military concerns, but miliary institutions seem to have been sources of demand for progress, not sources of progress itself. DARPA, for example, often contracted independent entities such as SRI or teams of collaborating academics to execute on finding solutions in its areas of interest. We note when such entities were affiliated with military institutions, though few such instances occur in our data. A final note on the breakdown of insights among institutional entities: while the credit owed to academic institutions is clear, nonacademic institutions have been contributing an increasing portion of total progress since the middle of the 20th century. We were surprised to see a near even distribution of insights between for-profit and non-profit entities-though RAND Corporation constitutes the bulk of the latter-in recent decades, and we suppose that this supports the importance of ongoing invesment in independent organizations focused on AI whose mission is explicitly aligned with public good. \n Methodological reflections Our methods generate a view of the past through a particular cultural lens-specifically, that of young American computer scientists. This project is not an attempt at the impossible task of aggregating all insights into artificial intelligence that exist, rather it is an attempt from our position to aggregate the ones interpretable to ourselves. As we are roughly in the same position socially as other artificial intelligence resarchers in the Anglosphere, we expect that the amount of insights accessible to Anglosphere researchers will be analagous to those accessible to ourselves. There may be other paths to artificial intelligence development that are only accessible to individuals with differing social position, technical knowledge, or linguistic and cultural proficiency. Though it is certainly likely that such paths exist, we can make no comment on their rate of advancement. Additionally, it seems prudent to make note of the likely presence of survivorship bias: we are limited to only the information that has survived to the point of being accessible to ourselves. It is possible that many of the insights of the past that we have analyzed-particularly the distant past-were developed with the aid of information sources that no longer exist, either dead with the minds that generated them or lost with the documents that once preserved them. As with any field, this lost information may compromise the ability of individuals in the present to correctly interpret and use past insights. This case of survivorship bias is unavoiable, and mitigatable to the degree that present researchers remain aware of it. Related work on this topic is available from Samo Burja of Bismarck Analysis, in his essay Intellectual Dark Matter.", "date_published": "n/a", "url": "n/a", "filename": "insights-analysis.tei.xml", "abstract": "This dataset collects a list of discoveries essential to the development of the current generation of artificial intelligence. We trace this development back as early as we have records of relevant intellectual progress-in this case, to Ancient Greek philosophy-looking for the foundations of complex new approaches. Our goal in this project is to present an alternative to an achievement-based timeline of AI development. The development of new capabilities in machine intelligence frequently produces exciting tangible results, which dominate public conceptions of progress and are well-remembered in histories of the field, but such results are not always the product of novel technical insight. Some new abilities rely more on recombination of existing tools or on additional computational capacity-sufficient to solve complex problems efficiently, but not necessarily the most direct precursors of new tools for further recombination, or of new directions for future work without additional increases in computational efficiency. Our aim is to augment the current discourse of historically grounded forecasting by adding a specific discursive thread that tracks theoretical discoveries alone, complementing the more capability-focused accounts. We've collected metadata about each discovery (and its discoverers) and looked for trends in their production. Our own findings are described below, but we encourage extension and additional evaluation of the data, and will publish our own ongoing work here.", "id": "5f2b0cf802c2d771b03cd317418264fc"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "preferences-nipsworkshop2015.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong"], "title": "GENERAL PURPOSE INTELLIGENCE: ARGUING THE ORTHOGONALITY THESIS", "text": "The Orthogonality Thesis Scientists and mathematicians are the stereotypical examples of high intelligence humans. But their morality and ethics have been all over the map. On modern political scales, they can be left-(Oppenheimer) or right-wing (von Neumann) and historically they have slotted into most of the political groupings of their period (Galois, Lavoisier). Ethically, they have ranged from very humanitarian (Darwin, Einstein outside of his private life), through amoral (von Braun) to commercially belligerent (Edison) and vindictive (Newton). Few scientists have been put in a position where they could demonstrate genuinely evil behavior, but there have been a few of those  (Teichmüller, Philipp Lenard, Ted Kaczynski, Shirō Ishii) . Of course, many scientists have been absolutely conventional in their views and attitudes given the society of their time. But the above examples hint that their ethics are not strongly impacted by their high intelligence; intelligence and ethics seem 'orthogonal' (varying independently of each other, to some extent). If we turn to the case of (potential) artificial intelligences we can ask whether that relation continues: would high intelligence go along with certain motivations and goals, or are they unrelated? To avoid the implicit anthropomorphisation in terms such as 'ethics,' we will be looking at agents 'final goals' -the ultimate objectives they are aiming for. Then the Orthogonality thesis, due to Nick Bostrom  (Bostrom, 2012) , states that: Intelligence and final goals are orthogonal axes along which possible agents can freely vary. In other words, more or less any level of intelligence could in principle be combined with more or less any final goal. It is analogous to Hume's thesis about the independence of reason and morality  (Hume, 1739) , but applied more narrowly, using the normatively thinner concepts 'intelligence  ' and 'final goals' rather than 'reason' and 'morality'.  But even 'intelligence,' as generally used, has too many connotations. A better term would be efficiency, or instrumental rationality, or the ability to effectively solve problems given limited knowledge and resources  (Wang, 2011) . Nevertheless, we will be sticking with terminology such as 'intelligent agent,' 'artificial intelligence' or 'superintelligence,' as they are well established, but using them synonymously with 'efficient agent,' artificial efficiency' and 'superefficient algorithm.' The relevant criteria is whether the agent can effectively achieve its goals in general situations, not whether its inner process matches up with a particular definition of what intelligence is. Thus an artificial intelligence (AI) is an artificial algorithm, deterministic or probabilistic, implemented on some device, that demonstrates an ability to achieve goals in varied and general situations.  1  We don't assume that it need be a computer program, or a well laid-out algorithm with clear loops and structures -artificial neural networks or evolved genetic algorithms certainly qualify. A human level AI is defined to be an AI that can successfully accomplish any task at least as well as an average human would (to avoid worrying about robot bodies and such-like, we may restrict the list of tasks to those accomplishable over the internet). Thus we would expect the AI to hold conversations about Paris Hilton's sex life, to compose ironic limericks, to shop for the best deal on Halloween costumes and to debate the proper role of religion in politics, at least as well as an average human would. A superhuman AI is similarly defined as an AI that would exceed the ability of the best human in all (or almost all) tasks. It would do the best research, write the most successful novels, run companies and motivate employees better than anyone else. In areas where there may not be clear scales (what's the world's best artwork?) we would expect a majority of the human population to agree the AI's work is among the very best. Nick Bostrom's paper argued that the Orthogonality thesis does not depend on the Humean theory of motivation, but could still be true under other philosophical theories. It should be immediately apparent that the Orthogonality thesis is related to arguments about moral realism. Despite this, we will not address the fertile and extensive literature on this subject. Firstly, because it is contentious: different schools of philosophical thought have different interpretations of the truth and meaning of moral realism, disputes that cannot be currently resolved empirically. Since we are looking to resolve a mainly empirical question -what systems of motivations could we actually code into a putative AI -this theoretical disagreement is highly problematic. Secondly, we hope that by approaching the issue from the computational perspective, we can help shed new light on these issues. After all, we do not expect that the trigger mechanism of a cruise missile to block detonation simply because people will die -but would an \"ultra-smart bomb\" behave the same way? By exploring the goals of artificial systems up to higher level of efficiency, we may contribute to seeing which kinds of agents are susceptible to moral realism arguments, and which are not. Thus this paper will content itself with presenting direct arguments for the Orthogonality thesis. We will assume throughout that human level AIs (or at least human comparable AIs) are possible (if not, the thesis is void of useful content). We will also take the position that humans themselves can be viewed as non-deterministic algorithms: 2 this is not vital to the paper, but is useful for comparison of goals between various types of agents. We will do the same with entities such as committees of humans, institutions or corporations, if these can be considered to be acting in an agent-like way. The thesis itself might be critiqued for over-obviousness or triviality -a moral anti-realist, for instance, could find it too evident to need defending. Nevertheless, the argument that AIs -or indeed, any sufficiently intelligent being -would necessarily behave morally is a surprisingly common one. A. Kornai, for instance, considers it as a worthwhile starting point for investigations into AI morality  (Kornai, 2013) . He bases his argument on A. Gewith's approach in his book, Reason and Morality  (Gewirth, 1978)  (the book's argument can be found in a summarized form in one of E. M. Adams's papers  (Adams, 1980) ) in which it is argued that all agents must follow a \"Principle of Generic Consistency\" that causes them to behave in accordance with all other agent's generic rights to freedom and well-being. Others have argued that certain specific moralities are attractors in the space of moral systems, towards which any AI will tend if they start off with certain mild constraints  (Waser, 2008) . Because of these and other examples (and some online criticism of the Orthogonality thesis 3 ), we thought the thesis was worth defending explicitly, and that the argument brought out in its favor would be of general interest to the general discussion. \n Qualifying the Orthogonality Thesis The Orthogonality thesis, taken literally, is false. Some motivations are mathematically incompatible with changes in intelligence (\"I want to prove the Gödel statement for the being I would be if I were more intelligent\"). Some goals specifically refer to the intelligence of the agent, directly (\"I want to be much less efficient!\") or indirectly (\"I want to impress people who want me to be much less efficient!\"). Though we could make a case that an agent wanting to be less efficient could initially be of any intelligence level, it won't stay there long, and it's hard to see how an agent with that goal could have become intelligent in the first place. So we will exclude from consideration those goals that intrinsically refer to the intelligence level of the agent. We will also exclude goals that are so complex or hard to describe that the complexity of the goal becomes crippling for the agent. If the agent's goal takes five planets worth of material to describe, or if it takes the agent twenty years each time it checks what its goal is, then it's obvious that that agent can't function as an intelligent being on any reasonable scale. Many have made the point that there is likely to be convergence in instrumental goals  (Omohundro, 2008) . Whatever their final goals, it would generally be in any agent's interest to accumulate more power, to become more intelligence and to be able to cooperate with other agents of similar ability (and to have all the negotiation, threatening and cajoling skills that go along with that cooperation). Note the similarity with what John Rawls called 'primary goods'  (Rawls, 1971 ). We will however be focusing exclusively on final goals, as the instrumental goals are merely tools to accomplish these.  4  Further we will not try to show that intelligence and final goals can vary freely, in any dynamical sense (it could be quite hard to define this). Instead we will look at the thesis as talking about possible states: that there exist agents of all levels of intelligence with any given goals. Since it's always possible to make an agent stupider or less efficient, what we are really claiming is that there could exist possible high-intelligence agents with any given goal. Thus the restricted Orthogonality thesis that we will be discussing is: \n High-intelligence agents can exist having more or less any final goals (as long as these goals are of feasible complexity, and do not refer intrinsically to the agent's intelligence). 5 We will be looking at two variations of the \"can exist\" clause: whether the agent can exist in theory, and whether we could build such an agent (given that we could build an AI at all). Though evidence will be presented directly for this thesis in the theoretic agent case, the results of this paper cannot be considered to \"prove\" the thesis for agents we could build (though they certainly raise its likelihood). In that case, we will be looking at proving a still weaker thesis: \n The fact of being of high intelligence provides extremely little constraint on what final goals an agent could have (as long as these goals are of feasible complexity, and do not refer intrinsically to the agent's intelligence). That thesis still has nearly all the relevant practical implications that the strong Orthogonality thesis does. \n Orthogonality in Practice for AI Designers The arguments presented in this paper are all theoretical. They posit that AIs with certain goals either 'can exist,' or that 'if we could build an AI, we could build one with any goal'. In practice, the first AIs, if and when they are created, will be assembled by a specific team, using specific methods, and with specific goals in mind. They may be more or less successful at inculcating the goals into the AI (or, as is common in computer programming, they may inculcate the goals exactly, only to realize later that these weren't the goals they really wanted). The AI may be trained by interacting with certain humans in certain situations, or by understanding certain ethical principles, or by a myriad of other possible methods, which will likely focus on a narrow target in the space of goals. The relevance of the Orthogonality thesis for AI designers is therefore mainly limited to a warning: that high intelligence and efficiency are not enough to guarantee positive goals, and that they thus need to work carefully to inculcate the goals they value into the AI. \n Orthogonality for Theoretic Agents If we were to step back for a moment and consider, in our mind's eyes, the space of every possible algorithm, peering into their goal systems and teas-ing out some measure of their relative intelligences, would we expect the Orthogonality thesis to hold? Since we are not worrying about practicality or constructability, all that we would require is that for any given goal system (within the few constraints enumerated above), there exists a theoretically implementable algorithm of high intelligence. Any measurable  6  goal can be paired up with a reward signal: an agent gets a reward for achieving states of the world desired by the goal, and denied these rewards for actions that fail to do so. Among reward signal maximisers, the AIXI is the theoretically best agent there is, more successful at reaching its goals (up to a finite constant) than any other agent  (Hutter, 2005) . AIXI itself is incomputable, but there are computable variants such as AIXItl or Gödel machines  (Schmidhuber, 2007)  that approximate AIXI's efficiency. These methods work for whatever reward signal plugged into them. Or we could simply imagine a supercomputer with arbitrarily large amounts of computing power and a decent understanding of the laws of physics (a 'Laplace demon'  (Laplace, 1814)  capable of probabilistic reasoning), placed 'outside the universe' and computing the future course of events. Paired with an obedient active agent inside the universe with a measurable goal, for which it would act as an advisor, this would also constitute an 'ultimate agent.' Thus in the extreme theoretical case, the Orthogonality thesis seems true. There is only one problem with these agents: they are either impossible in practice (AIXI or Laplace's demon), or require incredibly large amounts of computing resources to work. Let us step down from the theoretical pinnacle and require that these agents could actually exist in our world (still not requiring that we be able or likely to build them). An interesting thought experiment occurs here. We could imagine an AIXI-like super-agent, with all its impractical resources, that is tasked to design and train an AI that could exist in our world, and that would accomplish the super-agent's goals. Using its own vast intelligence, the superagent would therefore design a constrained agent maximally effective at accomplishing those goals in our world. Then this agent would be the highintelligence real-world agent we are looking for. It doesn't matter than the designer is impossible in practice -if the super-agent can succeed in the theoretical thought experiment, then the trained AI can exist in our world. This argument generalizes to other ways of producing the AI. Thus to deny the Orthogonality thesis is to assert that there is a goal system G, such that, among other things: 1. There cannot exist any efficient real-world algorithm with goal G. 2. If a being with arbitrarily high resources, intelligence, time and goal G, were to try design an efficient real-world algorithm with the same goal, it must fail. 3. If a human society were highly motivated 7 to design an efficient realworld algorithm with goal G, and were given a million years to do so along with huge amounts of resources, training and knowledge about AI, it must fail. 4. If a high-resource human society were highly motivated to achieve the goal G, then it could not do so (here the human society itself is seen as the algorithm). 5. Same as above, for any hypothetical alien societies. 6. There cannot exist any pattern of reinforcement learning that would train a highly efficient real-world intelligence to follow the goal G. 7. There cannot exist any evolutionary or environmental pressures that would evolve a highly efficient real world intelligences following goal G. All of these seem extraordinarily strong claims to make! The last claims all derive from the first, and merely serve to illustrate how strong the first claim actually is. Claim 4, in particular, seems to run counter to everything we know about human nature. \n Orthogonality for Human-level AIs Of course, even if efficient agents could exist for all these goals, that doesn't mean that we could ever build them, even if we could build AIs. In this section, we'll look at the ground for assuming the Orthogonality thesis holds for human-level agents. Since intelligence isn't varying much, the thesis becomes simply: If we could construct human-level AIs at all, then there is extremely little constraint on the final goals that such AIs could have (as long as these goals are of feasible complexity, and do not refer intrinsically to the agent's intelligence). So, is this true? The arguments in this section are generally independent of each other, and can be summarized as: 1. Some possible AI designs have orthogonality built right into them. 2. AI goals can reach the span of human goals, which is large. 3. Algorithms can be combined to generate an AI with any easily measurable goal. 4. Various algorithmic modifications can be used to further expand the space of possible goals, if needed. \n Utility Functions One classical picture of a rational agent is of an agent with a specific utility function, which it will then act to maximize in expectation. This picture encapsulates the Orthogonality thesis: whatever the utility function, the rational agent will then attempt to maximize it, using the approaches in all cases (planning, analyzing input data, computing expected results). If an AI is built according to this model, with the utility function being prescriptive (given to the AI in a program) rather than descriptive (an abstract formalization of an agent's other preferences), then the thesis would be trivially true: we could simply substitute the utility function for whichever one we desired. However, many putative agent designs are not utility function based, such as neural networks, genetic algorithms, or humans. So from now on we will consider that our agents are not expected utility maximizers with clear and separate utility functions, and look at proving Orthogonality in these harder circumstances. \n The Span of Human Motivations It seems a reasonable assumption that if there exists a human being with particular goals, and we can program an AI, then we can construct a humanlevel AI with similar goals. This is immediately the case if the AI was a whole brain emulation/upload  (Sandberg & Bostrom, 2008) , a digital copy of a specific human mind. Even for more general agents, such as evolved agents, this remains a reasonable thesis. For a start, we know that real-world evolution has produced us, so constructing human-like agents that way is certainly possible. Human minds remain our only real model of general intelligence, and this strongly directs and informs our AI designs, which are likely to be as human-similar as we can make them. Similarly, human goals are the easiest goals for us to understand, hence the easiest to try and implement in AI. Hence it seems likely that we could implement most human goals in the first generation of human-level AIs. So how wide is the space of human motivations 8 ? Our race spans footfetishists, religious saints, serial killers, instinctive accountants, role-players, self-cannibals, firefighters and conceptual artists. The autistic, those with exceptional social skills, the obsessive compulsive and some with splitbrains. Beings of great empathy and the many who used to enjoy torture and executions as public spectacles. 9 It is evident that the space of possible human motivations is vast. 10 For any desire, any particular goal, no matter how niche, 11 pathological, bizarre or extreme, as long as there is a single human who ever had it, we could build and run an AI with the same goal. But with AIs we can go even further. We could take any of these goals as a starting point, make them malleable (as goals are in humans), and push them further out. We could provide the AIs with specific reinforcements to push their goals in extreme directions (reward the saint for ever-more saintly behavior). If the agents are fast enough, we could run whole societies of them with huge varieties of evolutionary or social pressures, to further explore the goal-space. We may also be able to do surgery directly on their goals, to introduce more yet variety. For example, we could take a dedicated utilitarian charity worker obsessed with saving lives in poorer countries (but who doesn't interact, or want to interact, directly with those saved), and replace 'saving lives' with 'maximizing the number of paperclips in the universe' or any similar abstract goal. This is more speculative, of course -but there are other ways of getting similar results. \n Instrumental Goals as Final Goals If someone were to hold a gun to your head, they could make you do almost anything. Certainly there are people who, with a gun at their head, would be willing to do almost anything. A distinction is generally made between instrumental goals and final goals, with the former being seen as simply paths to the latter, and interchangeable with other plausible paths. The gun to your head disrupts the balance: your final goal is simply not to get shot, while your instrumental goals become what the gun holder wants them to be, and you put a great amount of effort into accomplishing the minute details of these instrumental goals. Note that the gun has not changed your level of intelligence or ability. This is relevant because instrumental goals seem to be far more varied in humans than final goals. One can have instrumental goals of filling papers, solving equations, walking dogs, making money, pushing buttons in various sequences, opening doors, enhancing shareholder value, assembling cars, bombing villages or putting sharks into tanks. Or simply doing whatever the guy with gun at our head orders us to do. If we could accept human instrumental goals as AI final goals, we would extend the space of goals quite dramatically. To do so we would want to put the threatened agent, and the gun wielder, together into the same AI. Algorithmically there is nothing extraordinary about this: certain subroutines have certain behaviors depending on the outputs of other subroutines. The 'gun wielder' need not be particularly intelligent: it simply needs to be able to establish whether its goals are being met. If for instance those goals are given by a utility function then all that is required in an automated system that measure progress toward increasing utility and punishes (or erases) the rest of the AI if not. The 'rest of AI' is just required to be a human-level AI which would be susceptible to this kind of pressure. Note that we do not require that it even be close to human in any way, simply that it place a highest value on self-preservation (or on some similar small goal that the 'gun wielder' would have power over). For humans, another similar model is that of a job in a corporation or bureaucracy: in order to achieve the money required for their final goals, some human are willing to perform extreme tasks (organizing the logistics of genocides, weapon design, writing long emotional press releases they don't agree with at all). Again, if the corporation-employee relationship can be captured in a single algorithm, this would generate an intelligent AI whose goal is anything measurable by the 'corporation.' The 'money' could simply be an internal reward channel, perfectly aligning the incentives. If the subagent is anything like a human, they would quickly integrate the other goals into their own motivation, 12 removing the need for the gun wielder/corporation part of the algorithm. \n Noise, Anti-agents and Goal Combination There are further ways of extending the space of goals we could implement in human-level AIs. One simple way is simply to introduce noise: flip a few bits and subroutines, add bugs and get a new agent. Of course, this is likely to cause the agent's intelligence to decrease somewhat, but we have generated new goals. Then, if appropriate, we could use evolution or other improvements to raise the agent's intelligence again; this will likely undo some, but not all of effect of the noise. Or we could use some of the tricks above to make a smarter agent implement the goals of the noise-modified agent. A more extreme example would be to create an anti-agent: an agent whose single goal is to stymie the plans and goals of single given agent. This already happens with vengeful humans, and we would just need to dial it up: have an anti-agent that would do all it can to counter the goals of a given agent, even if that agent doesn't exist (\"I don't care that you're dead, I'm still going to despoil your country, because that's what you'd wanted me to not do\"). This further extends the space of possible goals. Different agents with different goals can also be combined into a single algorithm. With some algorithmic method for the AIs to negotiate their combined objective and balance the relative importance of their goals, this procedure would construct a single AI with a combined goal system. There would likely be no drop in intelligence/efficiency: committees of two can work very well towards their common goals, especially if there is some automatic penalty for disagreements. \n Further Tricks up the Sleeve This section started by emphasizing the wide space of human goals, and then introduced tricks to push goal systems further beyond these boundaries. The list isn't exhaustive: there are surely more devices and ideas one can use to continue to extend the space of possible goals for human-level AIs. Though this might not be enough to get every goal, we can nearly certainly use these procedures to construct a human-level AI with any human-comprehensible goal. But would the same be true for superhuman AIs? \n Orthogonality for Superhuman AIs We now come to the area where the Orthogonality thesis seems the most vulnerable. It is one thing to have human-level AIs, or abstract superintelligent algorithms created ex nihilo, with certain goals. But if ever the human race were to design a superintelligent AI, there would be some sort of process involved -directed evolution, recursive self-improvement,  13  design by a committee of AIs, or similar -and it seems at least possible that such a process could fail to fully explore the goal-space. The Orthogonality thesis in this context is: If we could construct superintelligent AIs at all, then there is extremely little constraint on the final goals that such AIs could have (as long as these goals are of feasible complexity, and do not refer intrinsically to the agent's intelligence). There are two counter-theses. The weakest claim is: Incompleteness: there are large categories of goals that no superintelligence designed by us could have. A stronger claim is: Convergence: all human-designed superintelligences would have one of a small set of goals. Here 'small' means 'smaller than the space of current human motivations,' thus very small in comparison with the space of possible AI goals. They should be distinguished; Incompleteness is all that is needed to contradict Orthogonality, but Convergence is often the issue being discussed. Often Convergence is stated in terms of a particular model of metaethics, to which it is assumed all agents will converge (see some of the references in the introduction, or various online texts and argument 14 ). \n No Convergence The plausibility of the convergence thesis is highly connected with the connotations of the terms used in it. \"All human-designed rational beings would follow the same morality (or one of small sets of moralities)\" sounds plausible; in contrast \"all human-designed superefficient algorithms would accomplish the same task\" seems ridiculous. To quote an online commentator, how good at playing chess would a chess computer have to be before it started feeding the hungry? Similarly, if there were such a convergence, then all self-improving or constructed superintelligence must fall prey to it, even if it were actively seeking to avoid it. After all, the self-improving lower-level AIs or the designers have certain goals in mind (as we've seen in the previous section, if the designers are AIs themselves, they could have potentially any goals in mind). Obviously, they would be less likely to achieve their goals if these goals were to change as they got more intelligent  (Omohundro, 2008)  (see also N. Bostrom's forthcoming book Superintelligence: Groundwork to a Strategic Analysis of the Machine Intelligence Revolution). The same goes if the superintelligent AI they designed didn't share these goals. Hence the AI designers will be actively trying to prevent such a convergence, if they suspected that one was likely to happen. If for instance their goals were immoral, they would program their AI not to care about morality; they would use every trick up their sleeves to prevent the AI's goals from drifting from their own. So the convergence thesis requires that for the vast majority of goals G: 1. It is possible for a superintelligence to exist with goal G (by section 0). 2. There exists an entity with goal G (by section 0), capable of building a superintelligent AI. 3. Yet any attempt of that entity to build a superintelligent AI with goal G will be a failure, and the superintelligence's goals will converge on some other goal. 4. This is true even if the entity is aware of the convergence and explicitly attempts to avoid it. 5. If the superintelligence were to be constructed by successive self-improvement, then an entity with goal G operating on itself to boost its intelligence is unable to do so in a way that would preserve goal G. This makes the convergence thesis very unlikely. The argument also works against the incompleteness thesis, but in a weaker fashion: it seems more plausible that some types of goals would be unreachable, despite being theoretically possible. There is another interesting aspect of the convergence thesis: these goals G are to emerge, somehow, without them being aimed for or desired. If one accepts that goals aimed for will not be reached, one has to ask why convergence is assumed: why not divergence? Why not assume that though G is aimed for, random accidents or faulty implementation will lead to the AI ending up with one of a much wider array of possible goals, rather than a much narrower one? We won't delve deeper into this, and simply make the point that \"superintelligent AIs won't have the goals we want them to have\" is therefore not an argument in favor of the convergence thesis. \n Oracles Show the Way If the Orthogonality thesis is wrong, then it implies that Oracles are impossible to build. An Oracle is a superintelligent AI that accurately answers human questions about the world, such as the likely consequences of certain policies and decisions  (Armstrong, Sandberg, & Bostrom, 2012) .  15  If such an Oracle could be built, then we could attach it to a human-level AI with goal G. The human-level AI could then ask the Oracle what the results of different decisions actions could be, and choose the action that best accomplishes G. In this way, the combined system would be a superintelligent AI with goal G. What makes the \"no Oracle\" implication even more counterintuitive is that any superintelligence must be able to look ahead, design actions, predict the consequences of its actions, and choose the best one available. But the convergence and indifference theses imply that this general skill is one that we can make available only to AIs with certain specific goals. Though agents with those specific goals are capable of doing effective predictions, they automatically lose this ability if their goals were to change. \n Tricking the Controller Just as with human-level AIs, one could construct a superintelligent AI by wedding together a superintelligence with a large motivated committee of human-level AIs dedicated to implementing a goal G, and checking the superintelligence's actions. Thus to deny the Orthogonality thesis requires that one believes that the superintelligence is always capable of tricking this committee, no matter how detailed and thorough their oversight. This argument extends the Orthogonality thesis to moderately superintelligent AIs, or to any situation where there's a diminishing return to intelligence. It only fails if we take AI to be fantastically superhuman: capable of tricking or seducing any collection of human-level beings. \n Temporary Fragments of Algorithms, Fictional Worlds and Extra Tricks These are other tricks that can be used to create an AI with any goals. For any superintelligent AI, there are certain inputs that will make it behave in certain ways. For instance, a human-loving moral AI could be compelled to follow most goals G for a day, if they were rewarded with something sufficiently positive afterwards. But its actions for that one day are the result of a series of inputs to a particular algorithm; if we turned off the AI after that day, we would have accomplished moves towards goal G without having to reward its \"true\" goals at all. And then we could continue the trick the next day with another copy. For this to fail, it has to be the case that we can create an algorithm which will perform certain actions on certain inputs as long as it isn't turned off afterwards, but that we cannot create an algorithm that does the same thing if it was to be turned off. Another alternative is to create a superintelligent AI that has goals in a fictional world (such as a game or a reward channel) over which we have control. Then we could trade interventions in the fictional world against advice in the real world towards whichever goals we desire.  16  These two arguments may feel weaker than the ones before: they are tricks that may or may not work, depending on the details of the AI's setup. But to deny the Orthogonality thesis requires not only denying that these tricks would ever work, but denying that any tricks or methods that we (or any human-level AIs) could think up, would ever work at controlling the AIs. We need to assume superintelligent AIs cannot be controlled in any way that anyone could think of. \n In Summary Denying the Orthogonality thesis thus requires that: 1. There are goals G, such that an entity an entity with goal G cannot build a superintelligence with the same goal. This despite the fact that the entity can build a superintelligence, and that a superintelligence with goal G can exist. 2. Goal G cannot arise accidentally from some other origin, and errors and ambiguities do not significantly broaden the space of possible goals. 3. Oracles and general purpose planners cannot be built. Superintelligent AIs cannot have their planning abilities repurposed. 4. A superintelligence will always be able to trick its overseers, no matter how careful and cunning they are. 5. Though we can create an algorithm that does certain actions if it was not to be turned off after, we cannot create an algorithm that does the same thing if it was to be turned off after. 6. An AI will always come to care intrinsically about things in the real world. 7. No tricks can be thought up to successfully constrain the AI's goals: superintelligent AIs simply cannot be controlled. \n Conclusion It is not enough to know that an agent is intelligent (or superintelligent). If we want to know something about its final goals, about the actions it will be willing to undertake to achieve them, and hence its ultimate impact on the world, there are no shortcuts. We have to directly figure out what these goals are (or figure out a way of programming them in), and cannot rely on the agent being moral just because it is superintelligent/superefficient. \t\t\t © Stuart Armstrong", "date_published": "n/a", "url": "n/a", "filename": "arguing_the_orthogonality_thesis.tei.xml", "abstract": "In his paper \"The Superintelligent Will,\" Nick Bostrom formalized the Orthogonality thesis: the idea that the final goals and intelligence levels of artificial agents are independent of each other. This paper presents arguments for a (narrower) version of the thesis. It proceeds through three steps. First it shows that superintelligent agents with essentially arbitrary goals can exist in our universeboth as theoretical impractical agents such as AIXI and as physically possible realworld agents. Then it argues that if humans are capable of building human-level artificial intelligences, we can build them with an extremely broad spectrum of goals. Finally it shows that the same result holds for any superintelligent agent we could directly or indirectly build. This result is relevant for arguments about the potential motivations of future agents: knowing an artificial agent is of high intelligence does not allow us to presume that it will be moral, we will need to figure out its goals directly.", "id": "756cd2a6fba5e7fd2a3a8f0705570a9e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Patrick Lavictoire"], "title": "An Introduction to Löb's Theorem in MIRI Research", "text": "Introduction This expository note is devoted to answering the following question: why do many MIRI research papers cite a 1955 theorem of Martin Löb  [12] , and indeed, why does MIRI focus so heavily on mathematical logic? The short answer is that this theorem illustrates the basic kind of self-reference involved when an algorithm considers its own output as part of the universe, and it is thus germane to many kinds of research involving self-modifying agents, especially when formal verification is involved or when we want to cleanly prove things in model problems. For a longer answer, well, welcome! I'll assume you have some background doing mathematical proofs and writing computer programs, but I won't assume any background in mathematical logic beyond knowing the usual logical operators, nor that you've even heard of Löb's Theorem before. To motivate the mathematical sections that follow, let's consider a toy problem. Say that we've designed Deep Thought 1.0, an AI that reasons about its possible actions and only takes actions that it can show to have good consequences on balance. One such action is designing a successor, Deep Thought 2.0, which has improved deductive abilities. But if Deep Thought 1.0 (hereafter called DT1) is to actually build Deep Thought 2.0 (DT2), DT1 must first conclude that building DT2 will have good consequences on balance. There's an immediate difficulty-the consequences of building DT2 include the actions that DT2 takes; but since DT2 has increased deductive powers, DT1 can't actually figure out what actions DT2 is going to take. Naively, it seems as if it should be enough for DT1 to know that DT2 has the same goals as DT1, that DT2's deductions are reliable, and that DT2 only takes actions that it deduces to have good consequences on balance. Unfortunately, the straightforward way of setting up such a model fails catastrophically on the innocent-sounding step \"DT1 knows that DT2's deductions are reliable\". If we try and model DT1 and DT2 as proving statements in two formal systems (one stronger than the other), then the only way that DT1 can make such a statement about DT2's reliability is if DT1 (and thus both) are in fact unreliable! This counterintuitive roadblock is best explained by reference to Löb's theorem, and so we turn to the background of that theorem. 2 Crash Course in Löb's Theorem \n Gödelian self-reference and quining programs Löb's Theorem makes use of the machinery of Kurt Gödel's incompleteness theorems  [10] , so we will discuss those first. Informally, Gödel found a way to import self-reference into a mathematical system that was simply trying to talk about properties of natural numbers, and then pointed out the odd consequences of a mathematical statement that asserts its own unprovability. One (anachronistic) way of stating Gödel's key insight is that you can use computer programs to search for proofs, and you can prove statements about computer programs. If we think about any conjecture in mathematics that can be stated in terms of arithmetic, you can write a rather simple program that loops over all possible strings, checks whether any of them is a valid proof of the conjecture, and halts if and only if it finds one. Thus, instead of trying to prove that conjecture directly, we could instead try to show (or prove) that the program halts. Now, this generally doesn't make things easier at all, since we're just restating the same problem in a more complicated way, and actually looping over all strings is basically the worst way to try and find proofs of theorems. However, this reformulation makes it more intuitive that we can embed self-reference in mathematics, because we can embed self-reference in computer code! The kind of self-reference I'm talking about is called a quine: a program that is able to reproduce its own source code without taking any inputs. One way to do this is for the program to include a string with a variable, and for it to replace that variable with the original string itself, such that the resulting expanded string is the entire source code of the program itself. Exercise. Write a quining program in your favorite language. No fair copying one from the Wikipedia article, and no fair making calls to external programs or the filesystem. In addition to quines that merely print their source code, programs can be made which perform arbitrary tasks using their own source code. Indeed, one prominent example of a quining program that does other tasks is Ken Thompson's famous C compiler Trojan horse  [15] , which uses the quining trick to avoid ever being visible outside of machine code. Thus we can have a program G which refers to itself in this way, and searches for proofs in arithmetic related to its own source code. In particular, we consider G which searches for a proof of the statement \"G runs forever\", and halts if and only if it succeeds at finding one. Now, we claim that G never finds a proof, and also that we can never prove that G runs forever! For if we could prove that G ran forever, then G would find that proof, and it would halt-and we could prove that it halted, and thereby produce a contradiction! On the other hand, if G actually halted after some finite number of steps, then the number at which it halts encodes a proof that G runs forever, which again leads to a contradiction!  1  It seems silly to ask whether we could prove that G halts, given that G actually runs forever. But it actually wouldn't be a contradiction if we asserted that G actually halted, so long as we didn't say anything about how long it took! It's only a claim like \"G halts in fewer than a googolplex steps\" that would be an actual contradiction. It turns out that we could add either \"G never halts\" or \"G halts\" (but not both!) as a new axiom of arithmetic, and not introduce a contradiction by doing so. We express this by saying that G is undecidable, and therefore we've proved Theorem 2.1 (Gödel's First Incompleteness Theorem) If the theory of arithmetic is consistent, then there exist undecidable statements in the theory of arithmetic. Remark. Gödel's Theorem is a bit different from the Halting Problem; the latter shows there's no one program X that can tell whether every program Y halts or not, but of course there may be particular programs X that tell you this fact for particular programs Y . But this is saying that there's no program X that can tell you definitively whether the program G halts or runs forever. So Gödel found that we can write undecidable statements about properties of natural numbers, and furthermore showed that adding new axioms won't fix it, since you can repeat the process with the new rule system for whether a statement is a theorem. (There's only one loophole, and it's not a very exciting one: if we use inconsistent axioms, then everything is a theorem, thanks to the Principle of Explosion, and therefore everything is decidable). Now we're not here to bury mathematical logic, but to use it. So from Gödel's Theorem we move on to... \n Löb's Theorem Löb's Theorem  [12]  takes the same framework as Gödel's First Incompleteness Theorem, and constructs programs of the following sort: • Let X be any logical statement (the sort of thing that could be proved or disproved). • Now let ProofSeeker(X) be the program that searches all possible proofs, and halts if and only if one of them is a valid proof of the statement X. • Finally, let L(X) be the statement \"if ProofSeeker(X) halts, then X\". Let's ponder for a moment whether L(X) should be true or not, using three different kinds of statements X. • If X is a provable statement, for example \"2 + 2 = 4\", then ProofSeeker(X) halts, and L(X) is \"if [true thing], then [true thing]\", which is a valid statement. • If X is disprovable, for example the statement \"2 + 2 = 5\", then ProofSeeker(X) does not halt, and L(X) is \"if [false thing], then [false thing]\", which is also a valid statement. • If X is neither provable nor disprovable, for example Gödel's statement G, then again ProofSeeker(X) does not halt, and L(X) is \"if [false thing], then [maybe true thing]\", which is also a true statement (remember your propositional calculus). So it seems like L(X) is always true. And it would certainly be handy if L(X) were provable for every X: for instance, you could use the second case above to show that mathematics proves no contradictions! Because if we could prove \"if ProofSeeker(\"2 + 2 = 5\") halts, then 2+2 = 5\", then we would have the contrapositive \"if 2+2 = 5, then ProofSeeker(\"2+2 = 5\") never halts\", and since we can prove 2 + 2 = 5, then we could prove that there is no contradictory proof of 2 + 2 = 5. Alas, that proof of mathematical consistency is too good to be true. As in the case of Gödel's Theorem, something being true is no guarantee of it being provable. And in fact, we find that L(X) is only provable in the first of the three cases above: Theorem 2.2 (Löb's Theorem) For all statements X, if L(X) is provable, then X is provable. (There is a neatly presented formal proof of this theorem at The Cartoon Guide to Löb's Theorem  [16] .) So in particular, if we could prove that mathematics would never prove a contradiction, then in fact mathematics would prove that contradiction! (Note that by the Principle of Explosion, this is indeed a possible state of affairs: if your mathematical axioms lead to a contradiction, then they can prove every statement in the language, including the statement that your mathematical axioms don't lead to a contradiction!) Thus the only systems that prove their own consistency are the inconsistent ones; incidentally, this is precisely Gödel's Second Incompleteness Theorem, although he originally proved it without Löb's Theorem. Remark. If you're interested in going deeper on these topics, Computability and Logic by Boolos, Burgess, and Jeffrey  [5]  is a good reference. Remark. There is also a version of Löb's Theorem for bounded proof searches, in the sense of \"look through all formulas of length ≤ N and see if any of them are a proof of φ\", and it controls the length of the proof of φ in terms of the length of the proof of φ → φ. In the limit of arbitrarily large computational resources, the phenomena we care about happen in the same way that they do in the case of infinite computation (i.e. access to halting oracles), and so we will generally discuss the latter case because the proofs are simpler and clearer. \n Direct Uses of Löb's Theorem in MIRI Research We can now exhibit three simple cases where Löb's Theorem comes up in MIRI research topics: one where it forms an unexpected obstacle to justifying self-modifications, one where it neatly enables mutual cooperation in a nonstandard Prisoner's Dilemma setup, and one where it frustrates a naive decision algorithm. \n \"The Löbstacle\" Let's return to the problem we discussed in the Introduction: Deep Thought 1.0 wants to verify that switching on its successor, Deep Thought 2.0, will have good consequences. Because DT2 has better deductive capacities, DT1 cannot deduce exactly what actions DT2 will take, but it does know that DT2 has the same utility function, and that it too will only take actions it deduces to be good. Intuitively, this should be enough for DT1 to \"trust\" DT2, to say that whatever DT2 does, DT2 must have deduced that to be good, and therefore it must actually be good. But that last clause is analogous to the Löbian statement L(X): \"if the action is deduced to be good, then it must actually be good\"! And therefore DT1 cannot generally prove that clause (unless its reasoning is inconsistent), since then it could prove that every action is good. This is not just an analogy; when we consider a simple mathematical model of a selfmodifying agent that uses proofs in some consistent formal system to justify its actions, that agent has precisely this problem. In models that presume infinite computing power and represent different deductive powers with different axiom systems, a simple agent with a utility function will only create successors whose formal systems are strictly weaker than its own, since only those are fully trusted by the current system. There are a number of partial and potential remedies to this \"Löbstacle\", some of them more appealing than others. For more details, see the MIRI preprints Tiling Agents for Self-Modifying AI, and the Löbian Obstacle  [18]  and Problems of self-reference in self-improving space-time embedded intelligence  [9] . \n Löbian cooperation The second topic concerns a variation on the usual Prisoner's Dilemma. Rather than playing directly, you write an algorithm to play against other algorithms on your behalf, as in Robert Axelrod's famous algorithmic Prisoner's Dilemma tournament  [1] . However, instead of that setup, in which the algorithms play iterated games against one another, in this case your algorithm and theirs get to read the opponent's source code, calculate for as long as they like, and then play only once. Using quining (recall Section 2.1), one can write a program that cooperates if and only if the opponent's source code is identical to its own. However, there are many ways to write such programs, and different ones will not cooperate with each other; this is therefore a fragile form of mutual cooperation. There's a different algorithm which (at the cost of using lots of computation) avoids that fragility. We call this agent FairBot, and it operates as follows: • Both FairBot and its opponent X are functions of one argument, which take the opponent's source code and output either C or D. • When FairBot() is called on the input X, it searches through all proofs of length ≤ N to see whether any are valid proofs of the statement \"X(FairBot)= C\". If yes, then it outputs C; if no, then it outputs D. (Here N is a parameter that doesn't depend on X; we'll think of it as some extremely large number. The only reason we have that parameter at all is so that our algorithm does in fact always return an output in finite time.) Some things are clear from the definition of FairBot. One is that it is capable of cooperation: if X is a simple algorithm that always returns C, then FairBot will return C as well. Another is that (unless arithmetic is inconsistent) FairBot will never be exploited (cooperate while its opponent defects). What is less immediately clear is the outcome when FairBot plays against itself. Intuitively, it seems like both mutual cooperation and mutual defection are stable fixed points of the situation. However, a Löbian statement breaks the deadlock in favor of cooperation! To see this, ignore for the moment the parameter N . Then if we consider the statement L(\"FairBot(FairBot)= C\"), we find that it follows directly from the code of FairBot. For if there is a proof that FairBot(FairBot)= C, then FairBot will discover that proof and output C. But then, by Löb's Theorem, there must be an actual proof of the statement \"FairBot(FairBot)= C\"! 2 As mentioned in Section 2.2, there is a quantitatively bounded version of Löb's Theorem such that this works even with the parameter N , for sufficiently large values of N . Furthermore, this form of cooperation is much more robust: two such programs don't need to figure out that they are functionally identical, they only need to search for proofs about one another's output. Moreover, even algorithms that are not functionally identical to FairBot can achieve mutual cooperation with it. The FairBot algorithm is due to Vladimir Slepnev; for more on Löbian cooperation, see the MIRI paper Program Equilibrium in the Prisoner's Dilemma via Löb's Theorem  [11] . We will return to this topic in Section 7.1 when we have developed a few more tools. \n Spurious counterfactuals The third topic concerns an unexpected issue that comes up when the agent is a part of the same universe that the agent is proving theorems about. The setting is a pure computational universe U () which takes no input, and which just runs and eventually outputs a number. Within that universe there is an agent A() which knows the code for U (), which does some computations as part of the natural order of the universe and then outputs something. This may seem like a rather extreme setup, and it is: we want to see what we can say about agents that know the source code of the universe and wield arbitrarily large computational resources, because it is often easier to show what happens with such agents than what happens with more realistic, messy, and bounded agents. Moreover, any obstacles we discover in the ideal setting are likely to correspond in the real setting to obstacles that can't be overcome merely by adding more knowledge and computing power to the system. Let's first consider a really simple sort of universe (Algorithm 1), where A() must try to figure out whether to open door number 1, door number 2, or neither. Algorithm 1: U () if A() = 1 then return 100 else if A() = 2 then return 1 else return −∞ end This requires us to specify the function A(). Now of course we could consider a function A() hard-coded to return 1, but that's not especially interesting. Instead, we'll write one (Algorithm 2) which tries to deduce which door (if either) to open, by looking through proofs of arithmetical statements. It seems obvious that there should be proofs of A() = 1 → U () = 100 and A() = 2 → U () = 1 whose Gödel numbers are smaller than a googolplex, and therefore A should correctly prove those statements and choose Door 1. Algorithm 2: A() Door1 ← −∞; Door2 ← −∞; n = 1; while Door1 + Door2 = −∞ and n < 10 10 100 do if n encodes a valid proof of \"A() = 1 → U () = c\" for some c then Door1 ← c; if n encodes a valid proof of \"A() = 2 → U () = c\" for some c then Door2 ← c; n+ = 1; end if Door1 ≥ Door2 then return 1 else return 2 end But there's something very strange that can happen instead: A could prove A() = 2 → U () = 1, and then prove a \"spurious counterfactual\" such as A() = 1 → U () = −1, which then makes A() stop looking early and select door number 2! This wouldn't be a contradiction, because if A() = 2, then A() = 1 → U () = −1 is formally true  3  . But why should it actually happen? It's clearest to see in the case where I can make one innocent-seeming change to A(): I ask that before it starts searching through all n < 10 10 100 to see if they encode proofs, I want it to check two particular proofs. The first is the simple proof that A() = 2 → U () = 1, and the second is a statement φ. Now if φ really is a proof of the spurious counterfactual A() = 1 → U () = −1, it's clear from the rest of the source code of A() that it will break the while loop and choose Door 2. In fact, we can formalize that reasoning: there's a proof that if φ is a proof of A() = 1 → U () = −1, then in fact it's true that A() = 2 and thus A() = 1 → U () = −1. But this is almost a Löbian statement, just with the addition of a specific φ rather than an existential quantifier! By the machinery of quining, we can find a φ that serves our purposes, so it works just as before: since the Löbian statement is provable, so is the conclusion A() = 1 → U () = −1, by means of that particular φ. Even without that malicious change, these kinds of agents and universes are susceptible to spurious counterfactuals. In Section 7.2, we'll consider a similar setup, but with a more careful ordering of which proofs it pays attention to, and that agent can be shown to make the correct decisions (given enough deductive power). The idea was originally due to Benja Fallenstein; Tsvi Benson-Tilson's paper UDT with Known Search Order  [3]  discusses spurious counterfactuals and a different response to them. \n Crash Course in Model Theory For the later topics, we'll need some additional background in mathematical logic. Let's start out by just talking formally about the natural numbers with addition and multiplication. \n Axioms and theories We begin with a language of symbols, and we don't start out assuming anything about what they mean. We'll take some symbols of the propositional calculus, set theory, arithmetic, and three special symbols: {(, ), ∧, ∨, ¬, →, ↔, ∈, ∀, ∃, =, +, •, O, S, N} Here we'll think of N as standing in for the set of natural numbers, O as standing in for zero, and S as standing in for the successor (so that SO represents 1, SSO represents 2, etc.). That way we don't need rules for dealing with infinitely many number symbols, or rules for dealing with digits. We'll also add an infinite family of symbols like x and y for variables (so long as they're quantified over with ∀ or ∃). Finally, we'll use letters like φ to stand in for a formula within the language, but note that φ is not itself part of the language, so we can't say things like ∀φ. We'll import the standard rules of the propositional calculus and set theory as applied to the appropriate symbols (for instance, whenever φ ∧ ψ is a theorem, then both φ and ψ are theorems), but we won't yet assume any properties of +, •, O, S, or N. That's because we'll want to pick our own axioms about arithmetic on the natural numbers! This creates a theory, the set of all theorems that follow from the axioms; different sets of axioms can give rise to different theories. So let's take some true statements about the natural numbers, make them axioms of our logical system, and see what kind of theory we get. (Parenthetical comments are included for our intuition, but are not actually a part of the theory.) A theory can contain contradictions, of course: some theorem φ such that ¬φ is also a theorem. So how can we tell whether the theory built on these axioms contains any contradictions? We could try proving things and see if we ever find a contradiction, but as there are infinitely many theorems, we couldn't be sure that we just hadn't found a contradiction yet. 1. O ∈ N (zero is a natural number) 2. ∀x ∈ N Sx ∈ N (if x is a natural number, so is its successor) 3. ∀x ∈ N∀y ∈ N (x + y ∈ N) ∧ (x • y ∈ N) (the But there's another thing we could do: exhibit an example of a set for which all of the axioms hold! That serves as conclusive evidence that the theory does not contain contradictions, because φ is either actually true or actually false for that specific set, and so at most one of φ and ¬φ can actually be a theorem. We need to do a little more than exhibit an object: we need to have a correspondence between the symbols in the language and the parts of the object. So for instance, we identify the symbol O with the number 0, SO with 1, and so on 4 ; we identify N with the full set of natural numbers N; and we identify addition and multiplication with the usual operations on N. We call such an object a model, and such a correspondence an interpretation of the theory. However, the same theory can have many models, some of them not at all what you were thinking of when you made the axioms... \n Alternative and nonstandard models For instance, an alternate model of the theory above is the set with a single element \"Alice\"; we identify O with Alice, and then SO with Alice as well (so SO = O), and so on; we declare that Alice+Alice=Alice•Alice=Alice; and then we identify N with the set {Alice}. Note that all of the axioms above are true of this alternate model, even if their intuitive meanings aren't! Fine, let's patch this. We can't add an axiom directly saying it's not this particular model, since Alice isn't part of the language of the theory itself. But we can add an axiom saying SO = O, which is true of the model of the natural numbers we want, but not true of the Alice model. Well, we excluded that alternate model, but there are still others we haven't excluded. In particular, we can consider arithmetic mod n as a model for any n! In order to exclude these, we could add axioms saying SSO = O, SSSO = O, etc, or we could be more economical and just use the axiom ∀x ∈ N Sx = O. (The resulting theory is known as Robinson arithmetic, and is interesting in its own right.) Have we eliminated all alternate models from this theory? Hardly! We're just getting started. Consider the model where N refers to the natural numbers combined with one additional entity, \"Bob\"; we identify S(Bob)=Bob, Bob•0 = 0, Bob•x =Bob for all x = 0, and Bob+x =Bob for all x. Then we again see that this satisfies all of our axioms so far. We could patch this with the axiom ∀x ∈ N Sx = x, but again we can build more and more complicated alternate models. (One particularly interesting model for Robinson arithmetic consists of all polynomials with integer coefficients whose leading term is nonnegative.) It turns out that what we're missing from the natural numbers is the principle of induction. (Indeed, with Robinson arithmetic you can't even prove that addition is commutative!) In order to express induction in the language (which doesn't have variables for properties, only for numbers), we must resort to an infinite family of new axioms: for every logical formula φ(x) (with no free variables except for x), we want to add the axiom (φ(0) ∧ (∀x ∈ N φ(x) → φ(Sx))) → ∀y ∈ N φ(y).  5  With all of that completed, we've got the axioms for the theory of Peano Arithmetic. Now are we done with alternative models? Of course not! Remember how Gödel's self-referential formula G was undecidable? There are models of Peano arithmetic where G holds, and other models where G fails to hold. The models where G holds include our standard intuitive model of the natural numbers, since as we discussed before, G definitely does not halt at any finite number. But then, what kind of model of Peano Arithmetic could G fail to halt on? It may help to think of the model of N with Bob. If we do Gödel's construction in Robinson Arithmetic, there will be no contradiction if we assert that the special extra number Bob in fact satisfies the property that the formula G is checking (the property which represents \"this is a valid proof that no number is a valid proof of G\"). This is okay, because Bob doesn't actually have a representation in terms of lots of S's and an O, so this assertion can't be used to actually construct a finite sequence of logical formulas that comprise a proof that no number is a valid proof of G. This loophole suffices to maintain consistency for the new system! We're using Peano Arithmetic, though, so our nonstandard models will be weirder than the natural numbers plus Bob. The key to understanding these is that G never halts at any finite number, but we can't actually define in our formal language what \"finite\" means. The nonstandard models of Peano Arithmetic are those which have all the usual numbers but also lots of extra numbers that are \"too large\" to ever be written as lots of S's followed by an O, but which nonetheless are swept along in any inductive statement. (I still don't know quite how to visualize this model, but you can rigorously construct it using set theory.) And again, a \"number\" that can't actually be written in S's and an O can be asserted to represent a valid proof, but that proof can't be extracted from the number and used against itself, so it all works out consistently. Remark. Since nonstandard models of arithmetic contain numbers larger than any of the usual natural numbers, they can be used in other areas of mathematics. If you take the reciprocal of one of those numbers, you get an infinitesimal; thus you can use these to define the concepts of calculus without using limits! This is known as nonstandard analysis. And it doesn't end there! As I mentioned before, we can add either G or ¬G as an extra axiom of Peano Arithmetic, and since adding a new axiom changes the rules for what counts as a valid proof, we can redo Gödel's construction in our new formal system, and have statements that are undecidable given the new rules. Or we can directly talk about the consistency of Peano Arithmetic (by making a statement that asserts that there is no proof in PA that 0 = 1), and the consistency of the system with all the rules of Peano Arithmetic plus the axiom that PA is consistent, and so on. (Ponder for a moment the formal system which has all the axioms of PA, plus the axiom that PA is consistent, plus the axiom that \"the system which has all the axioms of PA, plus the axiom that PA is consistent\" is inconsistent. As it turns out, this is a perfectly consistent system 6 !) We'll work with a particular hierarchy of such formal systems in Section 6, but before then, we'll discuss another MIRI paper that relates to theories and models. Remark. Again, Computability and Logic by Boolos, Burgess, and Jeffrey  [5]  covers all of this material at a much deeper level. \n Uses of Model Theory in MIRI Research \n Reflection in probabilistic logic The topic of the first MIRI mathematical workshop paper, Definability of Truth in Probabilistic Logic  [7] , isn't directly entwined with Löb's Theorem. But we've just covered the necessary background to understand it, and we'll need another ingredient before getting to the other MIRI papers in these notes, so we might as well detour here! This paper concerns probabilistic logic: assigning probabilities in [0, 1] to logical statements, rather than just assigning them the labels \"provable\", \"disprovable 7 \", and \"undecidable\". We'll want to make sure we assign the value 1 to all provable statements and 0 to all disprovable statements, and that we assign values to the undecidable statements in a consistent way (so if φ and ψ are undecidable but φ → ψ is provable, then the probability we assign to φ should be less than or equal to the probability we assign to ψ). Why is this an important topic for MIRI to study? Probabilistic logic is an interesting, clean, and rich model for Bayesian reasoning and for bounded inference. Consider an AI that cannot deduce with certainty whether P = N P ; knowing it one way or the other should certainly change its actions (for instance, its cryptographic precautions against other agents), and so the most sensible way to proceed seems to be assigning it a tentative probability based on the available evidence, using that probability to do consequentialist calculations, and updating it in the light of newer evidence. So, in order to understand bounded reasoning, we might start with the nice and symmetrical (if unrealistic) case of a coherent probability assignment over all logical statements. So let's consider a Gödelian obstacle that bedevils logic, and see if it looks different within probabilistic logic. That obstacle is Tarski's undefinability of truth  [14] . OK, so we've previously established that some statements are undecidable, and in fact, undecidable statements hold in some models of a theory but not others. We might want to endorse some particular model as the \"true\" one (for instance, our standard model of the natural numbers, without all of those weird nonstandard numbers), and say that logical statements are true if they hold in that model and false if they don't. This truth predicate exists outside the language, and so the logical statements can't talk about the truth predicate, only about weaker notions like provability. All that is perfectly fine, thus far. The trouble comes when we try to construct a language that contains its own truth predicate T , either by finding a formula for it using the previously existing symbols, or by directly adding a new symbol with some rules of usage, such that for all φ, it's true that T (φ) ↔ φ. Either approach is doomed, by an argument that should seem familiar by now: there exists  7  By this, we mean statements whose negation is provable, not statements which cannot be proven. a sentence X that refers to itself by quining, so that it's provable that X ↔ T (¬X). And now, clearly, neither T (X) nor T (¬X) can hold. \n All right, so what changes when you incorporate probabilities? Let's introduce a symbol P which represents the probability of a logical statement. We'd like P to satisfy some mathematical coherence properties, like P (φ ∧ ψ) ≤ P (φ), and we'd also like P to be able to discuss itself. Now what happens when we consider the statement Y constructed such that Y ↔ (P (Y ) < 0.5)? Does this create a contradiction? It depends on what kind of statements P is allowed to make about itself! Namely, if P isn't allowed to make exact statements about its own values, but only arbitrarily precise approximations, then everything can work out consistently. Namely, in the place of the failed reflection principle T (T (φ) ↔ φ), we take the reflection principle ∀φ∀a, b ∈ Q (a < P (φ) < b) → (P (a < P (φ) < b) = 1) . (5.1) In the paper, they prove that with this reflection principle and the natural coherence conditions, there indeed is a probability valuation that works for the values of P . How does this avoid a collision with the statement Y above? It turns out that the true value of P (Y ) is 0.5, but P isn't able to know whether P (Y ) is exactly 0.5, or slightly above it, or slightly below it, and so P (P (Y ) < 0.5) is 0.5 as well, and so on. For any rational > 0, you can prove with certainty that P (0.5 − < P (Y ) < 0.5 + ) = 1, but you can't get from this anything sharp enough to produce a contradiction; in particular, you can't prove the generalization that ∀ > 0 P (0.5 − < P (Y ) < 0.5 + ) = 1. Remark. Nonstandard arithmetic isn't needed for this result, but it can shed some light on the fact that P (0.5 − < P (Y ) < 0.5 + ) = 1 for any rational . Since some models of N include nonstandard natural numbers, P can't rule out the possibility that reciprocals of nonstandard natural numbers (infinitesimals) exist, and so P (Y ) may as well be imagined as 0.5 plus or minus an infinitesimal... \n Remark. Since the result in the Definability of Truth paper is nonconstructive, it's worth noting that there's a followup paper by Christiano on computationally tractable approximations of probabilistic logic: Non-Omniscience, Probabilistic Inference, and Metamathematics  [6] . \n Crash Course in Gödel-Löb Modal Logic The final topics in this survey require some topics outside the usual first course in mathematical logic, namely the Gödel-Löb modal logic of provability. This modal logic captures exactly the parts of Peano Arithmetic that relate to self-reference, and by leaving out the rest, it has a pleasingly simple structure and plenty of powerful tools for analysis. Thus it's a great setting for model problems in decision theory, as we shall see. \n The modal logic of provability You may have heard of modal logic before, in the context of philosophy: Aristotle defined ways of arguing about which facts are necessary or possible rather than merely true or false. By the twentieth century, people had formalized various kinds of modal logic, where you take the usual language of propositional logic and add the symbols and , as well as new axioms and rules incorporating them. φ is usually interpreted as the statement \"it is necessary that φ\", and φ as \"it is possible that φ\". (We actually only need , since in all modal logics of interest to us, φ ↔ ¬ ¬φ.) Philosophers have tried out various sets of axioms, mostly in order to write intimidatingly technical-looking arguments for their preferred metaphysical conclusions 8 , but we're more interested in a particular modal logic that constitutes a perfectly rigorous-and quite useful-reflection of Löbian phenomena in Peano Arithmetic and other such systems. This is the Gödel-Löb modal logic (alternately, 'the modal logic of provability' or simply 'provability logic'), which we will denote as GL. We can construct GL in two different ways. First, we can let φ represent the formula of Peano Arithmetic that asserts that φ is provable in Peano Arithmetic, and then restrict ourselves to the formulas and proofs that use only , the logical operators, and Boolean variables (including the constants for true and ⊥ for false, but no numbers, arithmetical operations, or quantifiers). Or, equivalently, we can start with those elements of the language, and then add the following axioms and rules: • All tautologies of the propositional calculus are axioms of GL, including tautologies where an expression including has been substituted for a variable (for instance, p ∨ ¬ p is an axiom). • Modus Ponens Rule: if the expressions A and A → B are theorems, then so is B. • Distribution Axioms: for any expressions A and B in the language, we have the axiom (A → B) → ( A → B). • Generalization Rule: if the expression A is a theorem, then so is A. • Gödel-Löb Axioms: for any expression A, we have the axiom ( A → A) → A. It's a nontrivial theorem that these approaches give us the same modal logic! So GL really does capture the self-referential parts of Peano Arithmetic, while leaving aside the arithmetical parts; for instance, the statement that Peano Arithmetic is consistent is simply ¬ ⊥. Exercise. Show, using the rules of GL, that ⊥ ↔ p; recall that p = ¬ ¬p. Informally, that is, no statement can be proven consistent with Peano Arithmetic unless Peano Arithmetic is inconsistent. [Hint: First prove that ⊥ → p, then that p → ⊥. For the latter, it will help to rewrite ¬ ⊥ as ⊥ → ⊥, then consider the Löbian axiom ( ⊥ → ⊥) → ⊥.] While every specific deduction we would want to make in GL can be made via formal manipulations in the system, this is a computationally intractable way to handle deduction. (Deducing whether a given modal statement is a theorem of GL is NP-complete in general, just as it is in Peano Arithmetic.) However, there are some special cases where there are efficient algorithms for deducing provability in GL, and these happen to include cases of direct interest to decision theory... \n Fixed points of modal statements In Section 3.2, we figured out what happens when two different programs try to prove theorems about one another. In that case, the programs were simple enough that we could directly see where to apply Löb's Theorem, but in general we'd like to be able to handle more complicated phenomena. Fortunately, modal logic comes equipped with a powerful tool for doing precisely that: the theory of fixed points for modal sentences. In Peano Arithmetic, the Gödel statement G refers to itself via quining, in order to claim that it cannot be proved in PA; in GL, G corresponds to the formula p ↔ ¬ p. Similarly, we can have all sorts of formulas that refer to themselves and each other by quining, and these are represented by formulas p ↔ φ(p, q 1 , . . . , q k ) that are modalized in p: every occurrence of p in φ happens within the scope of some . (After all, quining can only refer to the provability of the statement's own Gödel number, not directly to the statement itself!) As it happens, whenever you have this setup in GL, with p equivalent to a formula that is modalized in p, then p is equivalent to some other formula which doesn't use p at all! For example, the Gödel statement is equivalent to the inconsistency of arithmetic: (p ↔ ¬p) ↔ (p ↔ ⊥). In the case of one-variable formulas p ↔ φ(p) with φ(p) modalized in p, there's a neat tool that helps us calculate these fixed points (where the result will involve no variables at all, just logical connectives, , , and ⊥). First, for many modal logics including GL, there's a corresponding class of sets and relations (called Kripke frames) such that a formula is provable in the modal logic if and only if a corresponding property holds for every Kripke frame in that class. And secondly, in the special case of sentences without variables in GL, we can reduce to checking a linear hierarchy corresponding to a world in which ⊥ holds, a world in which ⊥ ∧ ¬ ⊥ holds, and so on up the ladder of n+1 ⊥ ∧ ¬ n ⊥ for each n 9 . If you'll grant me that result (known as an World p p ¬p (p → ¬p) p → (p → ¬p) p p → ¬p ⊥ 1 1 1 1 1 1 1 ⊥ ∧ ¬ ⊥ 1 1 0 1 1 1 0 3 ⊥ ∧ ¬ 2 ⊥ ? ? ? ? ? ? ? Continuing with the second row, we find that p flips to false: World p p ¬p (p → ¬p) p → (p → ¬p) p p → ¬p ⊥ 1 1 1 1 1 1 1 ⊥ ∧ ¬ ⊥ 1 1 0 1 1 1 0 3 ⊥ ∧ ¬ 2 ⊥ 1 1 0 0 0 0 1 4 ⊥ ∧ ¬ 3 ⊥ ? ? ? ? ? ? ? And with the third row, when considering ¬p, it is important to remember that the lemma above requires A to be true in all previous rows, so even though ¬p is now true, ¬p remains false. We will fast-forward through the next few rows: World p p ¬p (p → ¬p) p → (p → ¬p) p p → ¬p ⊥ 1 1 1 1 1 1 1 ⊥ ∧ ¬ ⊥ 1 1 0 1 1 1 0 3 ⊥ ∧ ¬ 2 ⊥ 1 1 0 0 0 0 1 4 ⊥ ∧ ¬ 3 ⊥ 0 1 0 0 0 0 1 5 ⊥ ∧ ¬ 4 ⊥ 0 0 0 0 1 1 0 6 ⊥ ∧ ¬ 5 ⊥ 0 0 0 0 1 1 0 And here it stabilizes: every further row is identical  11  . And now that we've found the truth values of p, if we find a constant formula with the same truth values, then by the adequacy result I mentioned in passing, there must be a proof of equivalence in GL! We can get such a formula by taking Boolean combinations of the formulas that define the worlds (since the truth table stabilizes eventually, one only needs a finite combination of these); in the present case, that formula is ¬( 3 ⊥∧¬ 2 ⊥)∧¬( 4 ⊥∧¬ 3 ⊥), or equivalently 4 ⊥ → 2 ⊥. So in the end, we have the fixed point (p ↔ ( p → (p → ¬p))) ↔ (p ↔ ( 4 ⊥ → 2 ⊥)), and our algorithm for finding it is polynomial in the complexity of the statement (in fact, quadratic: we add columns for sub-expressions, and there's a linear bound for how many rows we need to calculate). Remark. We demonstrated the fixed-point algorithm only for one-variable expressions, but you can also take a statement of the form p ↔ φ(p, q 1 , . . . , q k ), where φ is modalized in p (not necessarily in any of the q i ), and find an equivalent expression p ↔ ψ(q 1 , . . . , q k ). The machinery for this is more difficult, as one needs to deal with more complicated Kripke frames (in the general case of GL, a Kripke frame is a set equipped with a transitive, irreflexive, well-founded relation), but it can be mechanized as well. I swept quite a lot under the rug in this section; if you want to get to know the topic on a much sounder basis, read The Logic of Provability  [4]  by Boolos. (This is an advanced textbook, so wait until after your first course in mathematical logic!) 7 Uses of Gödel-Löb Modal Logic in MIRI Research \n Modal Combat in the Prisoner's Dilemma We're now ready to handle the preprint Robust Cooperation in the Prisoner's Dilemma: Program Equilibrium via Provability Logic  [2] , which encompasses the results from Section 3.2, and studies \"modal agents\" represented by expressions in modal logic. Recall the idea of Löbian cooperation from Section 3.2. One embarrassing thing about FairBot is that it doesn't check whether its potential cooperation would actually make any difference. It happily cooperates with CooperateBot, the constant strategy that simply returns C for every opponent. That's a bit like cooperating against a rock because the rock \"cooperated\" with you. Let's consider the following alternative: first we define DefectBot as the constant strategy that simply returns D for every opponent; then we define PrudentBot as the algorithm that, given the source code of an opponent X, searches in Peano Arithmetic for a proof of the statement \"X cooperates with PrudentBot, and if Peano Arithmetic is consistent  12  , then furthermore X defects against DefectBot\", and cooperates if and only if it finds such a proof  13  . Now it's more difficult to figure out what happens when FairBot plays the open-sourcecode Prisoner's Dilemma against PrudentBot, if we view these as proof searches in Peano Arithmetic. But if we assume infinite computational power (i.e. the ability to consult a halting oracle about proof searches in Peano Arithmetic), then they can be written out as simple statements in modal logic. Let p = \"FairBot cooperates with PrudentBot\", q = \"PrudentBot cooperates with FairBot\", r = \"FairBot cooperates with DefectBot\", and  12  Why does PrudentBot include the consistency requirement? Because certain actions that depend on agents require the consistency of Peano Arithmetic; for instance, FairBot does defect against DefectBot, but knowing this requires knowing that Peano Arithmetic is consistent, since otherwise FairBot might find a proof that DefectBot cooperates, using the Principle of Explosion. 13 Also, why not directly check whether your cooperation causes the opponent's cooperation, by defining MagicBot which cooperates if and only if it finds a proof of the statement \"X cooperates with MagicBot if and only if MagicBot cooperates with X\"? Because this makes it susceptible to spurious counterfactuals as in Section 3.3, and in fact MagicBot is equivalent to FairBot when they are rendered as modal statements. s = \"DefectBot cooperates with FairBot\". Then we have p ↔ q q ↔ (p ∧ (¬ ⊥ → ¬r)) r ↔ s s ↔ ⊥. If we look for the fixed point of this modal system, we can use the truth table formalism of the fixed-point theorem (we do all of these simultaneously, since every variable is equivalent to a fully modalized expression) to show that p ↔ , q ↔ , r ↔ ⊥, and of course s ↔ ⊥. \n Exercise. Show this formally. So what actually happens when you run the bounded versions of these agents against one another (with sufficiently high bounds on how deep they search for proofs before giving up)? Again, the bounded analogue of Löb's Theorem helps any valid proof in GL to go through if the proof bounds are sufficiently large. And since we really don't expect there to be a contradiction in Peano Arithmetic or any of the systems built atop it by addition of the axioms ¬ n ⊥ 14 , in the bounded case we should expect that every search for n ⊥ comes up empty. Thus p and q are true, and r and s are false. (This is equivalent, in the infinite computation case, to specifying that we care about what actually holds in the standard model of the natural numbers.) Therefore we can use these tools to analyze interactions between \"modal agents\" represented by families of modal statements like FairBot and PrudentBot, and moreover, we can figure out what actually happens using an efficient algorithm rather than the huge bruteforce proof search! It's a little tricky to define these modal agents in one fell swoop, so let's start with the simplest case: agents that don't check their opponent's action against any third parties, but only against themselves. (We will call these \"modal agents of rank 0\".) A rank 0 modal agent is represented by a formula p ↔ φ(p, q), where φ is modalized in both p and q (we don't allow modal agents to run the other agent, only to prove things about them; this avoids the infinite regress of two agents simulating each other forever, waiting for the other to 'make the first move'). By the modal fixed-point theorem, this is equivalent in GL to p ↔ φ(q) for some φ modalized in q, so we will define rank 0 modal agents using those formulas. Then if we have two modal agents of rank 0, represented by p ↔ φ(q) and q ↔ ψ(p), the simultaneous fixed point of these formulas gives us constant sentences (combinations of n ⊥) from which we can deduce their actions. Now let's allow calls to third parties, like PrudentBot's call to the opponent's action against DefectBot. We'll insist that it bottom out in a finite number of statements: for this, it suffices that every modal agent can only predict its opponent's action against itself and against modal agents of strictly lower rank. That is, Definition. X = φ, Z 1 , . . . , Z k is a modal agent of rank n ≥ 0 if φ is a fully modalized formula of k + 1 variables p, r 1 , . . . , r k , and each Z i is a modal agent of rank < n. Given two modal agents X = φ X , Z 1 , . . . , Z k and Y = ψ Y , W 1 , . . . , W l , we then construct the family of formulas given by recursively applying the modal agents to each other and applying the third parties to the originals: p X ↔ φ X (q Y , r Z 1 , . . . , r Z k ) q y ↔ ψ Y (p X , s W 1 , . . . , s W l ) r Z i ↔ φ Z i (t (Y,Z i ) , u Z i 1 , . . . , u Z i m i ) t (Y,Z i ) ↔ ψ Y (r Z i , v (W 1 ,Z i ) , . . . , v (W l ,Z i ) ) and so on until it bottoms out. (Please excuse the proliferation of indices and the imperfect rigor, and take another look at the example above of PrudentBot versus FairBot, where FairBot= p , PrudentBot= (p ∧ (¬ ⊥ → ¬r)), DefectBot , and DefectBot= ⊥ .) Thus any two modal agents can be played against each other, and the result of that \"modal combat  15  \" computed by an effective algorithm. So there's an actual Haskell program, written by Mihaly Barasz and Marcello Herreshoff, that checks the result of the modal combat, and that program helped the authors to find many other patterns about modal agents (including the discovery of PrudentBot, which is never exploited, achieves mutual cooperation with itself and with FairBot, and which correctly defects against CooperateBot). Among the other results in that paper: • Third parties are necessary to get cooperation from FairBot while defecting against CooperateBot; no modal agent of rank 0 can achieve both. • No modal agent globally dominates another modal agent, since it is possible to write another modal agent which punishes or rewards agents for their other decisions. (For example, consider TrollBot, which cooperates with its opponent if and only if it proves that its opponent cooperates with DefectBot.) • In another obstacle to strong definitions of optimality, consider WaitFairBot N defined by ¬ N +1 ⊥∧ (¬ N ⊥ → p) . Then any modal agent that defects against DefectBot will fail to elicit mutual cooperation from WaitFairBot N for sufficiently large N . • Finally, there are some modal agents that can be exploited by non-modal agents but not by any modal agent. Consider MimicFairBot, which cooperates with X if and only if Peano Arithmetic proves that X cooperates with FairBot. (That is, MimicFairBot= r, FairBot .) It is possible for an algorithm to exploit MimicFairBot (consider the non-modal agent that cooperates if and only if the opponent's source code is identical to the source code of FairBot), but every modal agent treats MimicFairBot and FairBot identically. The field of modal combat is new and still wide-open, and I expect to see many more results soon! Furthermore, it inspired an unexpected development in decision theory for one-player games as well... \n Modal Decision Theory Recall the setup in Section 3.3: we have a universe U () which contains an agent A(). The universe runs some computation and returns some outcome; as a part of that computation, the agent runs some computation and returns some action. Everything is deterministic, but we can think of a decision theory as a condition on the allowable form of A(); if you have a certain decision theory, then you find yourself only in certain universes and you perform some specific algorithm in those universes. In order to define what we mean by a decision theory, then, we need to specify where in the universe the agent goes. So we start with some utility values over outcomes, and a universe template U (•) with a spot for an agent; then our decision theory specifies an agent A() that goes there, such that we now have the universe U A () = U (A) which computes a certain outcome; and we judge the decision theory based on how highly it values that outcome. Causal decision theory (CDT) and evidential decision theory (EDT) are two famous philosophical examples of decision theory. Both of these require the universe template to supply the agent with some additional information: in the case of CDT, a causal graph of the universe, and in the case of EDT, the actions and outcomes of other agents in the same universe template. Because CDT and EDT can be shown to make bad decisions on some problems even when given the right info, several people have proposed alternatives, including timeless decision theory  [17]  (TDT) and updateless decision theory (UDT). (For more on the philosophical side of things, see Toward Idealized Decision Theory  [13] .) While working out models of UDT, in particular, Vladimir Slepnev and Benja Fallenstein found a nice formalization of a simple decision theory using modal logic, one that they could even prove optimal on a certain class of modally defined problems! Consider a universe template U (•) with a finite set of possible actions A and a finite set of possible outcomes O. We have some preference ordering over O, and we pick some default action a 0 to return if we can't prove anything at all. We then define the decision theory which takes U (•) and returns the agent A() given by Algorithm 3. Note that this decision theory is immune to the spurious conterfactuals of Section 3.3: if it ever proves a counterfactual, it immediately makes the antecedent true by returning that action, so the consequent must be true as well. Moreover, if it proves any counterfactual, then it has already tried and failed to achieve every outcome higher in its preference order. Before we show an optimality result for Algorithm 3 in a special domain, we will have to show what can go wrong with it in other domains. Firstly, the universe template could be 'unfair', in the sense that it cares about aspects of the agent that aren't significantly related to its output. For instance, we could have a universe template that gives the best outcome if and only if A() is a tab-indented Python program, or if and only if A() can be proved to always select the first action of A in alphabetical order (regardless of the details of U (•). We will not worry about how to succeed on such pathological problems in general. A very strong fairness condition for a universe template is that U (•) should be a function of only the output of A, rather than depending on any other features  16  . We can define this in Peano Arithmetic by choosing an encoding for agents in a particular universe template, then writing a sentence that asserts (A() = B()) → (U A () = U B ()); the universe template is 'provably extensional' if that statement is a theorem of Peano Arithmetic. Everything thus far can be represented in modal logic. We will represent O and A by provably mutually exclusive and exhaustive (p.m.e.e.) families of modal statements. For example, {p∧q, p∧¬q, ¬p} is a p.m.e.e. family. Then if the universe template and the agent are modal expressions, the universe template is provably extensional if (a ↔ b) → (U (a) ↔ U (b)) is a theorem of GL. (You can check that the universe from Algorithm 1 corresponds to a provably extensional modal universe with 3 actions and 3 outcomes.) However, the modal version of Algorithm 3 can fail even on provably extensional modal universe templates; indeed, for any modally defined decision theory there is an \"evil problem\" which it fails on. (This can be shown by representing the modal decision theory itself in the universe template, and punishing any agent that acts identically to the action of the modal decision theory.) So our definition of optimality must allow some way around this. As it happens, although for any decision theory one can write a specific universe template that frustrates it, for any fixed universe template there is a modification of Algorithm 3 which succeeds on it, and this modification is simply a replacement of \"proves in Peano Arithmetic\" with \"proves in Peano Arithmetic given ¬ n ⊥\" for sufficiently large n. We can then show that this modification achieves the best outcome that is achievable by any modal decision theory. This result shows that we're on to something: in this restricted domain, we can do as well as it's possible to do, as long as we're bringing enough deductive capacity to bear! Note that here, the universe acts on the agent only by running it and using the output, while the agent interacts with the source code of the universe only by proving things about it. So in particular, it's less rich than modal combat, in which your agent is proving things about the universe, but another part of that universe (the opponent) is proving things about the agent as well. So before we count ourselves done with using modal logic in decision theory, we have many open questions about competition and bargaining and other phenomena. It's a beautiful Löbian universe, waiting for us to explore! In addition to the contributions of Vladimir Slepnev and Benja Fallenstein, the \"evil decision problems\" were introduced by Nick Bone. If you'd like to get into this topic, I recommend Benja's recent posts on evil decision problems in provability logic, optimality of the model of UDT  [8] , and its sequel. \n Acknowledgments I originally prepared about half of these notes for a talk at a MIRIx workshop in Los Altos, California in November 2014; the feedback from the participants was especially helpful. When writing up the notes, I got some great assistance from Benja Fallenstein, Marcello Herreshoff, Elliot Jin, and Nathaniel Thomas. product and sum of two natural numbers are also natural numbers) 4. ∀x ∈ N∀y ∈ N (Sx = Sy) → (x = y) (if the successors are equal, so are the originals) 5. ∀y ∈ N(y = O) ∨ (∃x ∈ N Sx = y) (every nonzero number has a predecessor) 6. ∀x ∈ N (x + O = x) ∧ (x • O = O) (how zero interacts with addition and multiplication) 7. ∀x ∈ N∀y ∈ N (x + Sy = S(x + y)) ∧ (x • Sy = (x • y) + x) (how successor interacts with addition and multiplication) \n Algorithm 3 : 3 A() (Slepnev-Fallenstein model of UDT) for x ∈ O (in descending order of preference) do for a ∈ A do if Peano Arithmetic proves \"A() = a → U () = x\" then return a end end end return a 0 \n\t\t\t Note the asymmetry: a proof of defection does not directly lead to defection, since FairBot acts based only on whether it finds a proof of cooperation, and it nowhere presumes that finding a proof of defection precludes finding another proof of cooperation. Again, the formal system can't correctly know that it is consistent! \n\t\t\t Note, however, that it's impossible to prove a spurious counterfactual about the choice you actually take, and thus it could not be consistent to find a spurious proof that A() = 1 → U () = 2 or that A() = 2 → U () = 11 \n\t\t\t Of course, this example does take a leap of faith in accepting the existence of infinitely many natural numbers; some mathematicians reject that, call themselves strict finitists, and assert that we have no idea whether the axioms of arithmetic are consistent. But they do accept that any theory with a completely specified finite model must be consistent. \n\t\t\t Actually, we need to get a bit more complicated to do all inductive proofs on the natural numbers; what we truly need is that if φ(x, z 1 , . . . , z k ) is a logical formula, then∀z 1 ∈ N . . . ∀z k ∈ N (φ(0, z 1 , . . . , z k ) ∧ (∀x ∈ Nφ(x, z 1 , . . . , z k ) → φ(Sx, z 1 , . . . , z k ))) → ∀y ∈ Nφ(y, z 1 , . . . , z k ). \n\t\t\t Assuming that the standard ZFC axioms of set theory are consistent, as we do throughout this paper, since we use these to construct models of all the weird axiomatizations of Peano Arithmetic. \n\t\t\t Gödel himself, toward the end of his life, circulated a modal logic version of Anselm's ontological proof of the existence of God. The proof is of course formally valid, but the axioms are a bit overpowered and underjustified. \n\t\t\t Note that these all correspond to nonstandard models of Peano Arithmetic, but that in some sense they approach the standard model as n → ∞. \n\t\t\t This part requires our assumption that the expression is modalized in p, since otherwise we couldn't fill in the value for it without first knowing the value for p. \n\t\t\t Since every expression A either remains true forever or switches over to false and remains that way forever, we can see that every expression must eventually stabilize; and if we've decomposed it at each step involving a , once two rows are identical, all subsequent rows must be as well. \n\t\t\t If this step worries you, you may be reassured to know that the standard axioms of set theory are strong enough to assert that this tower upon Peano Arithmetic is consistent all the way up. Of course, that simply means that maybe set theory is contradictory, but if so then the contradiction has been hiding pretty effectively from the mathematical community for the last few decades... \n\t\t\t I came up with that pun. I'm proud of it. \n\t\t\t Note that this condition is too strong to include modal combat, since there it also matters whether a given formal system can prove what the algorithm's output is, not only what the output is. Thus our optimality theorem will not cover modal combat, which is consistent, given that we mentioned in the last section that we lack a good optimality result for modal combat.", "date_published": "n/a", "url": "n/a", "filename": "lob-notes-IAFF.tei.xml", "abstract": "I apologize for all of the exclamation points in the previous paragraph; in my defense, if any result deserves exclamation points, it's Gödel's First Incompleteness Theorem! Also, there's a sleight of hand here in the demonstration that G never halts. We'll get further into that in Section 4.", "id": "9ff3fd33bdf522a744faaffde242c8f9"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Peter Cihon", "Moritz J Kleinaltenkamp", "Jonas Schuett", "Seth D Baum"], "title": "AI Certification: Advancing Ethical Practice by Reducing Information Asymmetries", "text": "Certification can be defined as the attestation that a product, process, person, or organization meets specified criteria (paraphrased from  [6] ). Certification involves an assessment of the entity to be certified, often, but not necessarily, by a trusted third party. If the assessment determines that the entity meets the specified criteria, then the entity is certified accordingly. Thus, the certification process reveals information about the inner workings of the entity that can be provided to external stakeholders, reducing information asymmetries between insiders and outsiders  [7] . In doing so, certification incentivizes insiders to adhere to higher standards because they can get credit for it if they do and get caught if they do not. In short, certification is a governance tool for advancing transparency and incentivizing insiders to meet specified criteria. Those criteria could include voluntary AI ethics principles or mandatory regulatory requirements. Certification is already in wide use in many sectors  [8] ,  [9]  and is starting to appear for AI. Certification includes such disparate phenomena as the U.S. EnergyStar program for consumer appliance energy efficiency, ISO 9001 for quality management systems in global supply chains, and the mandatory \"CE mark\" for various products sold in the EU. Certification programs for AI systems have been proposed or are currently being developed by the European Commission  [10] , the IEEE  [11] , and by the Chief Scientist of Australia  [12] ; one has already launched from the government of Malta  [13] . Education certification programs include the Queen's University executive education program on Principles of AI Implementation  [14]  and the Finnish civic education program Elements of AI  [15] . Additionally, a coalition of Danish organizations  [16]  is developing an IT security certification for organizations that includes AI-related criteria. These various programs speak to the diverse forms that certification programs can take, including public and private, voluntary and compulsory, and for the AI systems themselves as well as the people and organizations involved with them. This article presents an overview of certification for advancing ethical AI. It provides background on AI certification, drawing on management literature (Section II), surveys current AI certification programs and proposals for new programs (Section III), and discusses prospects for certification to address issues raised by future AI technologies (Section IV). Section V concludes this article. \n II. BACKGROUND This section reviews management literature on the merits of certification as it relates to the governance of AI. This literature typically focuses on the market behavior of corporations and their customers. However, certification is also relevant to nonmarket settings. For example, AI systems developed by nonprofit and/or open-source teams could seek certification to build user confidence, even if users are not charged for using the systems. Or, governments might seek international certification of their military AI systems to demonstrate compliance with international humanitarian law or other standards. Thus, while certification is important for the corporate governance of AI (on which, see  [17] ), it is also more widely applicable. First, some terminology. The object of certification is the entity to be certified. It may be a product, process, individual, or organization. The certifier is the actor who does the certifying. The assessor is the actor who assesses whether or not an object of certification meets the specified criteria prior to certification. The assessor and certifier can be one and the same or they can be two separate actors, such as in the case of certification programs that use third-party assessment. The assessment or conformity assessment is the evaluation of whether the object meets the specified criteria; this can vary in stringency, from a review of application materials to an audit of systems or processes. The applicant is the actor who controls the object of certification and seeks to obtain certification when it is voluntary. The applicant and object of certification can be the same, such as in the case of skills certifications granted to individuals. Alternatively, the applicant can be the entity who oversees, manages, develops, or otherwise controls the object of certification. Finally, the audience is the group of people who will be informed by the certification. For example, consider an AI system developed by a corporation, certified by a government agency, assessed by an independent consulting firm, to inform consumer purchasing decisions. Here, the object is the AI system, the certifier is the government agency, the assessor is the consulting firm, the applicant is the corporation, and the audience is consumers. In some cases, the applicant may also simultaneously be the certifier; this is known as self-certification. Self-certification creates a conflict of interest, though this can sometimes be addressed via measures such as audits and liability regimes. Two additional sets of terms help discuss the governance potential of certification programs. First, symbol-substance coupling refers to alignment between the statement that an object meets the certification criteria (the symbol) and that object actually meeting those criteria (the substance). Likewise, symbol-substance decoupling is when a certification inaccurately characterizes its object  [18] -  [20] . Second, means-ends coupling refers to alignment between the means of the certification program (i.e., the specific criteria to which objects are being held) and the ends underlying its design  [19] ,  [21] . Means-ends decoupling is when a certification program fails to advance its intended goals. Symbolsubstance decoupling and means-end decoupling are two failure modes of certification programs. \n A. Reducing Information Asymmetries As noted above, a primary role of certification is to reduce information asymmetries. Information asymmetries raise two issues: the \"selection problem\" of identifying desirable suppliers of a good or service, and the \"monitoring problem\" of evaluating whether the supplier is meeting specified agreements  [22] . Both problems create space for rent-seeking behavior, in which the supplier extracts greater wealth from other parties without adding social value  [23] . Information asymmetries are acute in AI systems because the systems are often complex and opaque and users typically lack the data and expertise necessary to understand them. Certification is especially well suited to addressing such information asymmetries that arise from \"credence\" and \"Potemkin\" attributes of goods and services  [24] . Credence attributes are those that can be identified by outside parties, but only as trends that emerge after repeat observations. Individual audience members may struggle to identify credence attributes on their own, but an organized third party, such as a certification program, can collect the data needed for a reliable characterization. Credence attributes of AI systems include whether a system is fair or unbiased, is explainable across a wide range of use cases, protects user privacy across a wide range of settings, and is safe and secure to rare and/or diverse threats. Potemkin attributes present even greater information asymmetry challenges: they cannot be identified at all by outside parties, and instead require insider information. An important type of Potemkin attribute is the process through which the good or service was made, such as whether an AI system was developed in accordance with labor, environmental, or ethical standards, or whether it was rigorously tested prior to deployment. Certification programs can address both credence and Potemkin attributes, as seen for example in the popular ISO 9001  [25]  certification for organization quality management and ISO 14001  [26]  certification for environmental management. By providing information about credence and Potemkin attributes, suppliers can create new signals to attract outside parties, including market customers  [27]  and others. Table I presents a summary overview of the key concepts underlying our understanding of certification, and how we apply them to the field of AI. A certification program reduces information asymmetries when it accurately characterizes the objects that it certifies. It must avoid false positives, in which an object is certified even though it fails to meet the specified criteria, and false negatives, in which an object meets the criteria but is denied certification. Accurate certification thus exhibits high symbolsubstance coupling. Research on certification has identified strategies for improving certification accuracy, i.e., improving symbolsubstance coupling. First, the objects to be certified should be assessed continuously, rather than only once or not at all  [7] ,  [28] -  [30] . This ensures that the information conveyed by the certification stays up to date. Second, assessments should be made by qualified independent assessors using their own evidence and not just documentation provided by the applicants  [24] ,  [31] ,  [32] . This is needed to protect against applicants misleading the assessor, especially to gain a false positive. These strategies are of further value for incentivizing good behavior by the object and/or applicant, as discussed in the section below. Indeed, the strategies were largely developed to promote behavior change. To achieve accuracy, AI certification programs will often need to parse technical details of the systems and their development. Evaluation methods required for accurate AI certification are at an early stage of development. The most mature area may be documentation for AI system training data and model characteristics  [33] -  [35] , which can help verify certification criteria associated with both credence and Potemkin attributes. Supply-chain and development documentation methods that draw on insights from other fields may help verify Potemkin-attribute criteria  [36] ,  [37] . Further, benchmark tests to assess AI system performance for specific tasks in specific settings  [38]  and more general behavioral settings for specific types of systems  [39]  can help verify credence-attribute criteria. However, methods for criteria verification in broad areas of fairness, transparency (explainability), safety, and security remain under development. Certification programs aiming to address these areas will need to update their criteria over time as the state-of-the-art advances. \n B. Incentivizing Change In reducing information asymmetries, certification can further serve to incentivize changes to applicant practices. For example, research has shown that corporations may be more motivated to achieve ethics standards if they can use certification to demonstrate their achievements to customers who value these achievements  [31] ,  [40] . Where there is demand for certification-e.g., from corporate customers who value ethics achievementscertification programs can succeed on a voluntary basis, with no government regulation  [9] . Government regulation can further boost voluntary programs via tort liability  [41]  or tax credits. Mandatory certification programs display higher compliance levels, though voluntary programs are sometimes found to be more cost effective  [42] . For a certification program to change applicant practices according to its specified criteria, it is important that it accurately characterizes these practices and their outputs. In particular, false positives permit applicants to pursue certification without changing their underlying practices: they can adopt the certification criteria symbolically but not substantively. Such symbolic adoption is of particular concern in AI. The recent popularity of AI ethics principles has prompted concerns about \"ethics washing\"  [43] ,  [44] , in which AI groups articulate ethics goals to bolster their reputation but do not act accordingly. An accurate certification regime could mitigate the problem of AI ethics washing. Prior research identifies several strategies to motivate substantive instead of symbolic participation in certification programs. First are strategies to improve certification accuracy as discussed above. Second, certification assessments should not be onerous on the applicants; otherwise, applicants that meet the assessment criteria may decline to participate in the program  [24] . Third, the cost to applicants of failing an assessment should be high (in terms of damaged reputation, lost market power, etc.), so as to incentivize participating applicants to meet the specified criteria  [22] ,  [24] ,  [27] ,  [31] . A successful certification program may need to promote its value so that other parties (e.g., customers) know to penalize applicants that fail certification assessments. Finally, certification programs should require applicants to integrate the values and norms underlying the criteria into their organizational identities and strategies; this makes substantive adoption more likely  [30] ,  [45] . A robust body of research suggests that properly constructed certification programs can couple symbol and substance to accurately characterize and induce changes to corporate practices. For example, studies of ISO 14001  [26]  have found a significant correlation between: 1) the ISO 14001 attestation and the presence of environmental management practices in corporations and 2) the presence of these practices in corporations and their improved environmental performance  [7] ,  [46] . Similar evidence exists for the ISO 9000 series on quality management practices  [47] ,  [49] . Ultimately, adherence to certification criteria depends on applicants' actions. Their actions can derive from characteristics of themselves in addition to characteristics of the certification program. Indeed, applicants sometimes engage in a mix of symbolic and substantive adoption even within the same certification program  [47] . This may be due to a lack of rational reflection or to internal disagreement within the applicant about the importance of the certification criteria  [45] . Additionally, some studies have found that firms with higher revenues tend to adopt certification more substantively because they have the resources to meet the certification criteria  [51] ,  [52] . Therefore, while it is important for certification programs to be well designed, the applicants retain an essential role. \n C. Ensuring Certification Advances the Right Goals The preceding section discussed how to ensure that certification criteria are in practice actually met, i.e., that certification is adopted substantively and not just symbolically. The current section covers the selection of the criteria themselves. These criteria should be designed such that if they are achieved, the certification program will deliver improvements on its underlying motivation: advancing ethics principles, making progress on societal issues, etc. In other words, the means of certification must be coupled to its ends. Means-ends decoupling can arise when developers of certification programs fail to treat the focal problem holistically, leading them to misidentify the causal relationships driving the issue at hand and prescribe the wrong action for a particular problem  [21] . This can spur at least three types of mistakes. First, certification may be inadequately customized for the circumstances it addresses. A common shortcoming of certification programs is the use of uniform, homogeneous prescriptions that neglect important local and time-specific factors  [21] . For example, AI systems required to use a certain dataset that performs well on demographic diversity could end up underperforming when even better datasets become available. Some of the most popular corporate certification programs make homogeneous prescriptions for corporations across the globe, though a context-dependent multiplicity of corporate practices may be necessary to address societal problems across environments. Certification criteria that are customized for particular circumstances may tend to perform better, though the development of such criteria may require more resources. Second, certification can cause unintended harms. Narrowly crafted certification criteria can neglect important causal relationships; when followed, they may make some things better but other things worse. For example, AI systems meeting certain performance standards may require additional computing power, which inadvertently harms the environment via increased energy consumption  [53] . This type of problem is also known as the \"waterbed effect\" because lying on a waterbed simply displaces the water: the problem \"rises\" again somewhere else  [21] ,  [54] . To avoid unintended harms, certification programs have to avoid overly simplistic prescriptions and instead embody and promote systemic thinking about the issues at hand  [21] . Third, certification criteria can be overly restrictive, inhibiting applicants from taking innovative actions that would better address the particular problem. One way to make actions more customized to complex causal relationships expressed in particular circumstances is to permit applicants to make decisions on a case-by-case basis. However, certification criteria often prescribe a rigid set of actions, thereby inhibiting applicants from identifying better solutions  [21] ,  [55] . Certification programs can mitigate this type of problem by \"stimulating internalization,\" meaning that they de-emphasize rigid rules and instead emphasize changes to applicants' internal culture, such that applicants are likely to do the right thing as circumstances dictate  [21] . Related to these challenges is the question of whether a certification program addresses the right focal problem(s) to begin with. Exactly which problems should be focused on is ultimately a question of ethics. Opinions may vary on which issues are most important. For example, many AI experts are divided on whether the field should focus on issues raised by near-term or long-term AI  [56] . Certification programs may sometimes need to take sides on these sorts of divides, such that they \"cannot please everyone,\" with some contending that the programs work on the wrong issues. In other cases, certification programs could emphasize issues that may seem appealing at first glance because of their broad scope, but become disagreeable when actors' interpretations of this broad scope begin to differ. To ensure that certification programs overcome these challenges and address their focal problems as holistically as possible, their developers should draw on the expertise of a wide range of stakeholders and carefully reconcile these stakeholders' differing perspectives. \n III. AI CERTIFICATION PROGRAMS AND PROPOSALS To identify existing AI certification programs, we conducted Internet searches, monitored social media, solicited input from colleagues, used our own prior knowledge, and examined references from documents about the programs and other relevant literature. These programs are not exhaustive, but are largely representative of the variation in AI-related certification.  1  We assessed the programs using publicly available documents. To fill in gaps in the documents, we conducted semi-structured interviews with representatives of certification program organizations. In total, we conducted three such interviews across seven identified AI certification programs. A) European Commission White Paper on Artificial Intelligence. \n B) IEEE Ethics Certification Program for Autonomous and Intelligence Systems (ECPAIS). C) Malta's AI Innovative Technology Arrangement (AI ITA). D) Turing Certification proposed by Australia's Chief Scientist. E) Queen's University's Principles of AI Implementation executive education. F) Finland's civics course Elements of AI. G) Danish labeling program for IT-security and responsible use of data. The seven programs classify into four categories: 1) selfcertification of AI systems (A); 2) third-party certification of AI systems (A-D); 3) third-party certification of individuals (E and F); and 4) third-party certification of organizations (D and G). Table  II  presents our ratings of these categories in terms of feasibility, symbol-substance coupling, and meansends coupling. The ratings are based on our analysis of the  1  Additional certification programs under development include AI Global's AI system certification  [57] , CertNexus's certified ethical emerging technologist program  [58] , and ForHumanity's compliance audit for AI systems and organizations  [86] . A number of universities offer AI ethics-related certifications or minors, including San Francisco State [59] and Carnegie Mellon  [60] . Consultancies offer algorithmic auditing services, which may confer a certification  [61] . Self-certification is widely used in many industries globally, including suppliers' declarations of conformity used in telecommunications and motor-vehicle manufacturing  [62] . For self-certification of AI systems, we rate certification programs in this category as having high feasibility because it requires little involvement from nonapplicant actors and limited back-and-forth between them and the applicants. The symbol-substance coupling is low because of its inherent conflict of interest and lack of strong enforcement and assessment. These problems can be attenuated via strong ex-post enforcement after harms occur via liability regimes. However, liability is problematic especially for high-risk applications where the initial harm could be catastrophic, and because legal liability adjudication poses uncertainties for AI developers  [63] . Finally, the means-ends coupling is medium because it encourages applicants to take ownership of the certification process and all that it represents, including by documenting their AI practices and thinking systemically about the corresponding ethical implications. Third-party product certification is used in numerous industries globally, including Underwriters Laboratories certifications for electrical and fire safety and the Common Criteria  [64]  for product cybersecurity certification. For thirdparty certification of AI systems, we rate certification programs in this category as having medium feasibility because AI systems are a relatively well-defined object to assess and certify, but they are also a novel one for which prior experience is of limited use. The need for qualified third-party organizations to offer assessment adds additional complications, including questions around costs and accountability  [5, p. 12] . Symbolsubstance coupling is medium because, on the one hand, third parties can assess certification claims and demand for certified systems could drive substantive adoption, but on the other hand, actual implementation can fall short on both meaningful assessment and enforcement. Finally, means-ends coupling is medium because of the potential for, but difficulty of, successfully assessing each AI system in its development and deployment context. Third-party certification of individuals is common in a number of professions, including among engineers, lawyers, and actuaries, as well as programs like the Certified Information Privacy Professional credential  [65] . We rate AI-related certification programs in this category as having medium feasibility. A core variable is whether certification criteria include matters related to moral factors in addition to the usual criteria of technical knowledge and skills.  2  Assessment of moral standards is important but less feasible. Moral character is not readily testable, and educational institutions may have less financial incentive to do so. The symbol-substance coupling is low because the substance of certification criteria is dynamic. Methods in explainability, fairness, safety, etc., are active research topics; certificates attesting to knowledge of them can become quickly outdated. This problem could be addressed via ongoing audits or education requirements comparable to those sometimes required for lawyers, but current AI certification programs lack such measures. Finally, the meansends coupling is low because, absent robust and dynamic moral standards, certification is unlikely to guarantee that the individuals will achieve sound performance on AI issues. Third-party certification of organizations include the U.K. Cyber Essentials  [66]  cybersecurity company certification and the FairTrade  [67]  licensing contract. We rate AI-related certification programs in this category as having medium feasibility because it can draw on a preexisting body of experience and knowledge in corporate governance and related fields, but it still requires AI-specific innovations. The symbol-substance coupling is high because it can use robust preexisting methods like audits and data security management. Organizations are often familiar with these methods and understand how to respond with substantive activity. Their familiarity could also be used to game the system, though auditors are themselves familiar with such tactics. Finally, the means-ends coupling is medium because assessments can support the adoption of a \"systemic mindset\" but certification criteria may not be easily customized for the context of a particular organization. \n A. European Commission White Paper on AI The European Commission White Paper on AI  [10]  proposes separate certification programs for low-risk and high-risk applications. Both programs would draw on prior certification programs, in particular, those of the European Economic Area \"CE marking\" rules and the 2019 EU Cybersecurity Act. Both programs would also use similar certification criteria, such as the EC's AI Ethics Guidelines for Trustworthy AI  [68] . If implemented, the programs would be important in their own right and could further be influential for AI certification beyond the single market, as is often the case for EU policies  [69] . For low-risk applications, we interpret the White Paper as calling for voluntary self-certification. This is clear from the White Paper's call for following the precedents of CE marking and the Cybersecurity Act, both of which use self-certification for low-risk applications. There is some ambiguity because the White Paper also suggests for the low-risk program to use a \"combination of ex ante and ex post enforcement\"  [10, p. 24] . Ex ante enforcement would seem to preclude self-certification. We interpret a stronger significance to the two self-certification precedents and therefore believe that the White Paper intends the low-risk program to involve voluntary self-certification. AI applicants could attest to their system having met the criteria, and face ex post penalties if their system falls short. Applicant participation would be incentivized by consumer demand for certificates of AI trustworthiness  [10] . To be effective, the low-risk program would need to be carefully designed. First, it needs an enforcement mechanism with clear, strong penalties for applicants who falsely certify their AI systems as meeting the specified criteria  [70, p. 5] . Otherwise, there could be symbol-substance decoupling, with applicants rubber-stamping their systems as meeting the criteria. Fortunately, the program could build on the compliance infrastructure that already exists for CE markings. Second, the criteria need to capture the many aspects of AI trustworthiness as defined in the \"Ethics guidelines for trustworthy AI\"  [68] , which include, among other things, fairness, security, and accountability. The criteria further must promote the systemic mindset needed to advance this conception of trustworthiness. Otherwise, there could be means-ends decoupling, with the certification program not advancing its underlying goals. For high-risk applications, the White Paper clearly specifies mandatory third-party certification via what it refers to as \"conformity assessment\"  [10, p. 23] . Its procedures would be based on CE marking rules or the Cybersecurity Act  [10] , both of which require third-party verification for high-risk applications. The White Paper's program would use existing accredited auditing organizations (\"notified bodies\") of the Member States  [10, p. 25] . EU regulation would compel AI applicant adoption and compliance. To be effective, the high-risk program will also need several design elements. First, it needs to ensure that the certifying bodies have the technical expertise and capacity needed to assess AI systems. Using the existing notified bodies makes the program easier to implement, but the bodies currently lack expertise and capacity on AI. Unless this situation is improved, the assessments could be inaccurate, and AI applicants may be able to obtain symbolic certification. Additionally, as with the low-risk program, the criteria must be carefully specified to ensure means-ends coupling. \n B. IEEE Ethics Certification Program for Autonomous and Intelligent Systems The IEEE ECPAIS program  [11]  is currently under development. It considers driving factors and inhibitors of AI system transparency, accountability, and bias. Offering a series of recommendations, the program is expected to yield a quality mark. The developer of an AI system can use the quality mark in presenting the system if it follows the recommendations in a checklist fashion. The program is expected to be administered by an organization other than the IEEE, which will assess certification applications. Whether the program will use an auditor to verify these applications has yet to be determined. The program is voluntary, with expected consumer demand as the driver for adoption. To be effective, EPCAIS would likely need the following. First, it would need to incentivize substantive adoption by generating consumer awareness and demand or by establishing an auditing requirement. Second, to improve means-ends coupling, it should offer distinct quality marks for transparency, accountability, and bias; it should also promote a systems mindset and consider the context in which the system is developed or deployed. Third, it should develop in-house expertise on certification; as far as the authors know, the IEEE has not launched a system-level certification program before. Finally, it should foster an enthusiastic audience in order to successfully launch. However, given that ECPAIS remains under development, we cannot offer a conclusive assessment. \n C. Malta AI Innovative Technology Arrangement The Maltese government launched the AI ITA certification program  [13]  in summer 2020. The program certifies AI systems to a particular use case following a review of an application detailing development and maintenance processes, corporate governance structures, and a responsible administrator. Applications must describe how the system handles failure modes and conforms to Malta's ethical AI framework, among other requirements  [13] . The program also (in most cases) requires applicant systems to have two software features: a \"harness\" that safeguards how the system handles specified failure modes and a \"forensic node\" that logs activity and is stored physically within Maltese jurisdiction. The applicant system must also disclose specific elements of its compliance with the ethical AI framework to end users via terms of service. Applications are reviewed by the Malta Digital Innovation Authority (MDIA) and are subsequently confirmed by an accredited auditor. The program is voluntary, with adoption expected to be driven by demand for certified systems from government procurers, businesses, and consumers. The Malta program has high feasibility because it benefits from a dedicated regulator which was established to manage this and similar programs. This dedicated expertise in assessing certification as well as accrediting third-party auditors can reduce concerns of symbol-substance decoupling. The program's focus on awarding certification for a specific system in a specific use case based on an assessment that includes the organization and a responsible individual incorporates a wide context that can help reduce concerns of means-ends decoupling. However, no application has yet been submitted. The effectiveness of the software harness to mitigate failure modes and the usefulness of mandated ethics disclosures in terms of service remain to be seen. \n D. Australian Chief Scientist Proposal: Turing Certification The Turing Certification program was proposed by Australia's Chief Scientist Alan Finkel in 2018  [12] ,  [71] . It would certify AI developer organizations and low-risk AI systems, drawing inspiration from FairTrade certification among other programs  [72] . This dual certification aspect could be especially impactful: it promotes a wide scope of assessment, thus improving means-ends coupling, and its organizational audit further improves symbol-substance coupling. As proposed, Turing Certification would be a voluntary program with third-party certifiers, with participation incentivized by demand from purchasers including consumers and governments. The third-party audit would confirm that the applying company, its development processes, and end AI system conform to not-yet-set standards for trustworthy AI. The proposal has not been enacted; it is unclear if it ever will be. Its most recent public discussion was in 2019  [73, p. 161 ]. If it is to be enacted, it would need clear certification criteria, a substantial challenge given the lack of agreed-upon trustworthy AI standards today. \n E. Queen's University Executive Education: Principles of AI Implementation In partnership with IEEE, Queen's University has launched an executive education certificate program on Principles of AI Implementation  [14] . Demand is likely to be driven by employers that value certified employees. The program has not yet run, and it is unclear how strong employer demand will be. The program covers ethical design principles, considerations for building trust in AI applications, and current Canadian regulatory requirements. This broad curriculum could support a systemic mindset, thereby improving means-ends coupling. However, these are dynamic topics; the program will need to stay up to date to retain means-ends coupling. Additionally, it is only a two-day program; this short duration precludes much substantive learning, creating the risk of symbol-substance decoupling. \n F. Finland Civics Course: Elements of AI The government of Finland, in a partnership between the University of Helsinki and the consultancy Reaktor, offers certificates to people who complete its civic education course Elements of AI. Certificates are awarded for all who complete at least 90% of the exercise and score 50% or above on attempted exercise questions  [74] . Credits can be transferred to the University of Helsinki. Demand may be driven by individuals' curiosity and sense of civic responsibility. It is unclear if employers would be interested in hiring certified individuals, and its introductory content would be insufficient for professional education, though that is not the program's aim. Thus far, demand has been significant: over 500 000 people have signed up and students from 170 countries have completed the course  [15] . \n G. Danish Labeling Program for IT Security and Responsible Use of Data The Confederation of Danish Industry, Danish Chamber of Commerce, SMEdenmark, and Danish Consumer Council  [16]  are currently developing a certification program for information technology security and data ethics. The program does not primarily focus on AI, but it was listed by the European Commission  [10, p. 10]  as an AI activity, and an interview and review of internal documents confirm that AI is within its scope. The program scope is ambitious, covering elements ranging from IT security to data management, to processes to address algorithmic bias. This broad scope could support a systemic mindset in the organization, and thus improve means-end coupling. The same scope may undermine symbol-substance coupling, however, as it could be difficult to achieve compliance with and effectively communicate to external stakeholders about so many certification criteria. The eventual administration of the program could encounter a challenge in moral hazard because a single organization-funded by certification fees-sets certification criteria, reviews applications, and performs (limited) audits. \n IV. CERTIFICATION FOR FUTURE AI TECHNOLOGY An essential attribute of AI technology is that it continues to evolve. Certification programs designed for the AI of today may not fare well with the AI of tomorrow. Adjustments will be needed to keep the programs up to date. However, adjustments can be expensive and are therefore not always made. Where possible, current certification programs should be designed to accommodate potential future directions in AI. This is no easy task: the future of AI cannot readily be predicted. Many have tried and failed  [75] . Nonetheless, some broad contours of future AI can be at least tentatively described, enough to derive some implications for certification programs. Toward the end of this section, we offer some remarks specific to the most advanced long-term AI, though much of the discussion may be more applicable to AI that will be developed in the interim, i.e., medium-term AI  [76] . Some elements of AI certification are relatively durable in the face of changes in the technology. First, many of the underlying goals for certification programs, such as fairness and beneficence, derive from universal ethics principles that apply not just to any AI technology, but to society in general. These ethics principles are used as a \"North Star\" guide in today's certification programs  [36, p. 35]  and will likely remain relevant as the technology matures. Future programs might potentially even certify the ethics of either the AI system or its developers. Second, some aspects of certification are matched to the types of people and institutions that are involved in AI, such as business executives, citizens, and corporations. It is fair to expect that such actors will remain involved in AI over the years. Certification program capacity to engage these actors may likewise remain relevant. That includes matters such as the capacity to improve corporate transparency and to educate large numbers of citizens. Similarly, one way for certification programs to remain relevant over time is to emphasize human and institutional factors. As discussed in Section II, certification programs can improve symbol-substance and means-ends coupling by promoting certain values and norms among applicants. Among other things, doing so positions applicants to act ethically as new challenges arise. Today, we do not know exactly what new challenges will arise for future AI, but we can be very confident that there will be new challenges. Certification programs should endeavor to make it more likely that whoever faces these new challenges will act according to a high ethical standard. Certification programs can also remain relevant by buildingin mechanisms for updating their certification criteria. For example, in the establishment of a new AI certification program, it could be specified that an expert body meets periodically to review and update the criteria, as is common with technical standards bodies. Programs could also include sunset provisions such that a program will cease to exist unless its criteria are updated. Additionally, certification programs could include a budget for ongoing research so that knowledge about how to update the criteria is available when needed. The field of AI research could also be a focus of certification. Future AI techniques will derive from current or future research. Some techniques may be better able to meet ethics standards; these techniques could be an object of certification. Academia already has institutional review boards to certify human subjects research as meeting standards for responsible conduct of research. Similar boards have been proposed for overseeing future AI research  [77] . Importantly, such boards should focus not just on whether the research meets procedural standards such as harm to research subjects, but also on whether it meets standards in terms of expected impacts on broader society  [78] . However, it can be difficult to know in advance which techniques will perform well-hence the need to do the research. Therefore, research is another domain in which certification may do well to emphasize human and institutional factors. Some forms of future AI may not be conducive to certification. In particular, AI systems that reach or exceed human-level intelligence in many domains  [79] ,  [80]  might not be a viable object of certification because humans could be powerless to take corrective actions suggested by the certification. To the extent that such AI is a significant concern, certification may only play a role in its development, while humans are still in command. This is one area in which certification of AI research programs may be especially significant, such as to promote trust among rival AI development groups  [81]  or share information about safety and ethics measures to alleviate rivals' concerns  [82] . Additionally, if the AI is developed by the national government-a distinct possibility given its national security implications-then there may be a role for an international certification regime, perhaps analogous to monitoring and verification regimes that have been established in other domains such as for biological, chemical, and nuclear materials. Should humanity ever face the prospect of developing such a technology, it would probably want to know that it was being developed according to a high ethical standard. That could be an important role for future AI certification programs. \n V. CONCLUSION Certification is a valuable tool for addressing information asymmetries and incentivizing better behavior. Certification can provide information about AI systems themselves as well as the organizations and individuals that are involved with them. AI-related programs could include both voluntary certification to ethics principles and mandatory conformity assessment to regulatory requirements. Today, a variety of AI certification programs are in development and use. These programs are focused on current AI technology, but certification can also play a role in future AI systems, up to including the most advanced long-term AI. One gap in the current AI certification landscape is the processes through which AI is developed. Although current certification programs assess the AI development process to varying degrees, no program certifies the process as its object. As a consequence, certification programs may fail to address process-oriented Potemkin attributes with maximal symbol-substance coupling and may fail to promote constructive organizational processes that can improve means-ends coupling. Improved attention to processes as the focus of certification could draw on, among other things, recent work on algorithmic auditing  [36]  and existing programs, such as ISO 9001 on quality management  [25]  and ISO 27001 on information security management  [83] . Early work at ISO on an AI management system standard may one day yield such a process-focused AI certification program  [84] . Another challenge is to improve the customization of AI certification for particular circumstances. Whereas some, such as the Malta AI ITA, are customized for specific jurisdictions, others, such as IEEE ECPAIS, make homogeneous prescriptions for AI developed worldwide. Additionally, most of the certification programs lack customization for each of the diverse sectors to which AI is applied, e.g., healthcare, transportation, and national security. Similarly, the programs tend to treat \"AI\" as a monolithic technology instead of being customized for the diverse types of AI that exist, e.g., language translation, facial recognition, and anomaly detection. Homogenous certification may similarly encounter challenges when an AI system is but a small, inextricable component of a larger digital system or workflow. All of this is a problem because certification programs that focus on specific niches tend to have better means-ends coupling  [21] . Many of the AI certification programs discussed here rely on, or at least strongly benefit from, demand from the customers of AI systems, including consumers, businesses, and governments. This is especially important for voluntary programs, where demand usually is the primary driver of participation. For good results to accrue, customers must not only demand certification-they must demand good certification. To that end, customers must be sufficiently educated about the technology and the associated ethics and safety concerns  [68, p. 23] . Education programs such as Finland's Elements of AI civics course could play an important role. Overall, AI certification remains at an early stage. Much remains to be seen, including which certification programs will be implemented, how effective they will be, how difficult or expensive they will be to implement, and how durable they will be in the face of changes in AI technology. All these aspects will influence the likelihood for adoption  [85]  and their success at symbol-substance and means-ends coupling. This article has presented a snapshot in time, with an assessment of an indicative sample of AI certification programs. It has also identified key concepts within the management literature on certification. Both contributions should inform future monitoring and evaluation of AI certification as the field matures. Future research would do well to track which certification programs are performing well, to learn from their successes and failures, and to identify gaps in the field and areas for improvement. It will likewise be important to monitor changes in AI technology and to ensure that certification programs stay up to date. AI certification is not a panacea, but it can play a valuable role in the overall mix of AI governance tools. TABLE II ASSESSMENT II OF CATEGORIES OF AI CERTIFICATION PROGRAMS details of the seven programs (see below) in the context of the management literature as reviewed above. \n\t\t\t Authorized licensed use limited to: Carnegie Mellon Libraries. Downloaded on March 24,2022 at 01:40:32 UTC from IEEE Xplore. Restrictions apply. \n\t\t\t The authors thank Jonathan Aikman for this point.Authorized licensed use limited to: Carnegie Mellon Libraries. Downloaded on March 24,2022 at 01:40:32 UTC from IEEE Xplore. Restrictions apply.", "date_published": "n/a", "url": "n/a", "filename": "AI_Certification_Advancing_Ethical_Practice_by_Reducing_Information_Asymmetries.tei.xml", "abstract": "As artificial intelligence (AI) systems are increasingly deployed, principles for ethical AI are also proliferating. Certification offers a method to both incentivize the adoption of these principles and substantiate that they have been implemented in practice. This article draws from management literature on certification and reviews current AI certification programs and proposals. Successful programs rely on both emerging technical methods and specific design considerations. In order to avoid two common failures of certification, program designs should ensure that the symbol of the certification is substantially implemented in practice and that the program achieves its stated goals. The review indicates that the field currently focuses on self-certification and third-party certification of systems, individuals, and organizations-to the exclusion of process management certifications. Additionally, this article considers prospects for future AI certification programs. Ongoing changes in AI technology suggest that AI certification regimes should be designed to emphasize governance criteria of enduring value, such as ethics training for AI developers, and to adjust technical criteria as the technology changes. Overall, certification can play a valuable mix in the portfolio of AI governance tools.", "id": "d95da0fab794f979c353075d283889ee"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "2699411.tei.xml", "abstract": "Open-universe probability models show merit in unifying efforts.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrew Critch"], "title": "A PARAMETRIC, RESOURCE-BOUNDED GENERALIZATION OF L ÖB'S THEOREM, AND A ROBUST COOPERATION CRITERION FOR OPEN-SOURCE GAME THEORY", "text": "Pudlák shows that, for a consistent system, there exists some ε > 0 such that for all N , any proof of a statement of the form \"there does not exist a proof of ⊥ using N or fewer characters\" must use at least N ε characters. This means there is some obstruction to self-trust for a resource-bounded proof system, which suggests that a resource-bounded version of L öb's Theorem-a generic statement of selftrust about a family of sentences parametrized by a resource bound-might also hold. §2. Fundamentals. Since this article draws from work in several disciplines, this section is provided to clarify the use of notation and conventions throughout. \n Proof length conventions and notation. Proof length will be measured in characters instead of lines, the way one might measure the size of a text file on a computer. An extensive analysis of proof lengths measured in characters is covered by  [8] . Throughout this article, S refers to a fixed proof system (e.g., an extension of Peano Arithmetic). Writing S n φ, or simply n φ means that there exists an S-proof of φ using n or fewer characters. \n Proof system. Let S be any first-order proof system that 1) can represent computable functions (e.g., by being an extension of PA; see Section 2.4), 2) can write any number k ∈ N using O(lg(k)) symbols (e.g., using binary), and 3) allows the definition and use of abbreviations during proofs (see the Appendix for details). Compact numeral representations and abbreviations are allowed in the proof system for two reasons. The first is that real-world automated proof systems will tend to use these because of memory constraints. The second is that abbreviations make the lengths of shortest proofs slightly easier to analyze. For example, if a number N with a very large number of digits occurs in the shortest proof of a proposition, it will not occur multiple times; instead, it will occur only once, in the definition of an abbreviation for it. Then, one does not need to carefully count the number of times the numeral occurs in the proof to determine the contribution of its size to the proof length; the contribution will simply be linear in its length, or lg(N ). Write L S for the language of S, L S (r) for the set of formulas in L S with r free variables, and Const(S) for the set of closed-form constant expressions in S (e.g., 0, S0, S0 + S0, etc.). When φ ∈ L S (r), given any closed-form expressions c 1 , . . . , c r (such as constants, or free variables), write φ[ c] = φ[c 1 , . . . , c r ] for the result of substituting the c i for the free variables in φ. https://www.cambridge.org/core/terms. https://doi.org/10.1017/jsl.2017.42 \n Choosing a Gödel encoding. Along with the proof system S, a single encoding #(−) : L S → N is chosen and fixed throughout, as well as a \"numeral\" mapping • (−) : N → Const(S) ⊆ L S for expressing naturals as constants in S. Note that in traditional PA, for example, • 5 = SSSSS0. However, to be more realistic it is assumed that S uses a binary encoding to be more efficient, so e.g., • 5 = 101. The maps #(−) and • (−) combine to form a G ödel encoding (−) : L S → Const(S) φ := • #φ which allows S to write proofs about itself. \n Representing computable functions. It is assumed that for any computable function f : N → N, there exists a \"graph\" formula Γ f ∈ L S  (2)  such that for all x ∈ N, S (∀y ) Γ f [ • x, y] ↔ y = • f(x) . For example, this condition holds if S is an extension of PA; see, e.g., Theorem 6.8 of Cori and Lascar (  [3] , Part II). Sometimes we abuse notation and write symbols for computable functions in-line with logical expressions to save space. For example, given functions f, g and h, to say that S proves that for any x value, f(x) < g(x) + h(x), technically one should write (∀x)(∀y1)(∀y1)(∀y3) Γ f [x, y 1 ] and Γ g [x, y 2 ] and Γ h [x, y 3 ] → y 1 < y 2 + y 3 but instead, we abuse notation and write (∀x) f(x) < g(x) + h(x)). \n Asymptotic notation. The notation f ≺ g will mean that for any M ∈ N, there exists an N ∈ N such that for all n > N, Mf(n) < g(n). The expression O(g) stands for the set of functions f g. If f : N → N is any specific function, f(O(g)) will stand for the set of functions of the form e • f where f ∈ O(g). §3. A bounded provability predicate, k . Here a predicate k is defined for asserting provability using a proof with length bounded by k.  (2)  exists that means, in natural language, that the number m encodes a proof in PA, and that the number n encodes the statement it proves. So, the standard provability operator : L PA → L PA can be defined as (φ) := (∃m)(Bew[m, φ ]). \n Defining k . Given a choice of G ödel encoding for Peano Arithmetic, it is classical that a formula Bew[m, n] ∈ L S It is taken for granted that Bew[m, n] exists for S and can be extended to a \"bounded Bew\" formula BBew[m, n, k] ∈ L S (3) that means • m encodes a proof in S, • n encodes the statement it proves, and • the proof encoded by m, before being encoded as m, uses at most k characters when written in the language of S. (Note that in general, m itself will be much larger than k as a member of N.) Then one can define a \"bounded\" box operator, which, given any sentence φ and closed expression k (such as a free variable, or a constant), returns k (φ) := (∃m)(BBew[m, φ , k]). Also taken for granted is a computable \"single variable evaluation\" function, Eval 1 : N → N, such that for any φ ∈ L S  (1) , Eval 1 ( φ , k) := φ( • k) . Since Eval 1 is computable, it can be represented in L S as in Section 2.4. This allows us to extend the k operator to act on sentences with one unbound variable. Specifically, if φ is a sentence with an unbound variable , then k (φ) := (∃m) BBew[m, Eval 1 ( φ , ), k]). Then k (φ) itself has as an unbound variable, and in natural language stands for \"There is a proof using k or fewer characters of the formula φ\". \n Basic properties of k . Each of the following properties will be needed multiple times during the proof of the main results. Since the proof is already highly symbolic, these properties are given English names to recall them. \n Property 1 (Implication distribution) . There is a constant c ∈ Const(S) such that for any p, q ∈ L S , (∀a)(∀b)( a (p → q) → ( b (p) → a+b+c (q))). Proof sketch. The fact that one can combine a proof of an implication with the proof of its antecedent to obtain a proof of its consequent can be proven in general, with quantified variables in place of the G ödel numbers of the particular statements involved. Let us suppose this general proof has length c 0 . Then, one needs only to instantiate the statements in it to p and q. However, if p and q are long expressions, it may be that they were abbreviated in the earlier proofs without lengthening them, so they can be written in abbreviated form again during this step. Hence, the total cost of combining the two proofs is around c = 2c 0 , which is constant with respect to p and q. Property 2 (Quantifier distribution). There is a constant C ∈ Const(S) such that for any φ ∈ L S  (1) , N ((∀k)(φ[k])) ⇒ (∀k) C +2N +lg(k) (φ[k]) , which in turn ⇒ (∀k) O(lg(k)) (φ[k]) . In the final subscript, O(lg(k)) stands for a closed expression representing a function of k that is asymptotically less than some positive constant times O(lg(k)). Proof. An encoded proof of φ[ • K] for a specific K can be obtained by specializing the conclusion of an N -character encoded proof of (∀k)(φ[k]) and appending the specialization with • K in place of k at the end. To avoid repeating • K numerous times in the final line (in case it is large), an abbreviation will be used for φ. Thus the appended lines can read as follows: (1) let Φ stand for φ , (2) Φ[ • K]. Let us analyze how many characters are needed to write such lines. First, a string Φ is needed to use as an abbreviation for φ. Since no string of length  N  2 has yet been used as an abbreviation in the earlier proof (otherwise one can shorten the proof by not defining and using the abbreviation), one can achieve Length(Φ) <  N  2 . As well, some constant c number of characters are needed to write out the system's equivalent of \"let\", \"stand for\", \" \", and \" \". Finally, lg(K) characters are needed to write • K. Altogether, the proof was extended by C + N + lg(k) characters, for a total length of 2N + c + lg(k). §4. A bounded generalization of Löb's Theorem. This section exhibits the first main theorem: a generalization of L öb's Theorem applicable to the analysis of resource-bounded proof systems. Property 4 (Bounded Inner Necessitation). For any φ ∈ L S , k (φ) → e(k) ( k (φ)). Then the following theorem holds:  (1)  be a formula with a single unquantified variable k, and suppose that f : Theorem 4.2 (Resource-bounded generalization of L öb's Theorem). Let p[k] ∈ L S N → N is computable and satisfies f(k) e(O(lg(k))). Then there is a threshold k ∈ N, depending on p[k], such that (∀k) f(k) (p[k]) → p[k] ⇒ ∀k > k (p[k]). Note: In fact a weaker statement, (∀k > k 1) f(k) (p[k]) → p[k] , is sufficient to derive the consequent, since we could just redefine f(k) to be 0 for k ≤ k 1 and then f(k) (p[k]) → p[k] is vacuously true and provable for k ≤ k 1 as well. The proof of Theorem 4.2 makes use of a version of G ödel's diagonal lemma that allows free variables to appear in the formula being diagonalized: Proposition 4.3. Suppose S is a first-order theory capable of representing all computable functions, as in Section 2.4. Then for any formula G ∈ L S (r + 1), there exists a formula ∈ L S (r) such that ∀ k [ k] ↔ G[ , k] , where k = (k 1 , . . . , k r ) are free variables. Proof. This result can be found on p. 53 of Boolos  [2] . Proof of Theorem 4.2. (In this proof, each centered equation will follow directly from the one above it unless otherwise noted.) We begin by choosing some function g(k) such that lg(k) ≺ g(k) and e(g(k)) ≺ f(k). For example, we could take g(k) = (lg(k))(e −1 (f(k))) . Define a formula G ∈ L S (2) by G[n, k] := (∃m) Bew[m, Eval 1 (n, k), g(k)]) → p[k] so that for any φ ∈ L S  (1) , G[ φ , k] = g(k) (φ[k]) → p[k]. Now, by Proposition 4.3, there is some ∈ L S  (1)  such that in some number of characters n, n (∀k)( [k] ↔ G[ , k]). ( 4.3) By Bounded Necessitation, n ((∀k)( [k] ↔ G[ , k])). By Quantifier Distribution, since n is constant with respect to k, (∀k) O(lg(k)) ( [k] ↔ G[ , k]) , in which we can specialize to the forward implication, (∀k) O(lg(k)) ( [k] → G[ , k]) . By Implication Distribution of O(lg(k)) , (∀k)(∀a) a ( [k]) → a+O(lg(k)) (G[ , k]) . By Implication Distribution again, this time of a+O(lg(k)) over the implication G[ , k] = g(k) (φ[k]) → p[k], we obtain (∀k)(∀a)(∀b) a ( [k]) → b g(k) ( [k]) → a+b+O(lg(k)) (p[k]) . Now we specialize this equation to a = g(k) and b = h(k), where h : N → N is a computable function satisfying e(g(k)) ≺ h(k) ≺ f(k), for example, h(k) = f(k)e(g(k)) : (∀k) g(k) [k] → h(k) g(k) ( [k]) → g(k)+h(k)+O(lg(k)) (p[k]) . https://www.cambridge.org/core/terms. https://doi.org/10.1017/jsl.2017.42 Then since g(k) + h(k) + O(lg(k)) < f(k) after some bound k > k 1 , we have (∀k > k 1) g(k) ( [k]) → h(k) g(k) ( [k]) → f(k) (p[k]) . Now, by hypothesis, (∀k) f(k) (p[k]) → p[k] , thus (∀k > k 1) g(k) ( [k]) → h(k) g(k) ( [k]) → p[k] . (4.4) Also, without any of the above, from Bounded Inner Necessitation we can write (∀k)(∀a) a ( [k]) → e(a) ( a ( [k])) . From this, with a = g(k), we have (∀k) g(k) ( [k]) → e(g(k)) g(k) ( [k]) . Now, since e(g(k)) < h(k) after some bound k > k 2 , we have (∀k > k 2) g(k) ( [k]) → h(k) g(k) ( [k]) . (4.5) Next, from Equations 4.4 and 4.5, assuming we chose k 2 ≥ k 1 for convenience, we have (∀k > k 2) g(k) ( [k]) → p[k] . (4.6) But from Equation  4 .3, the implication here is equivalent to [k], so we have N (∀k > k 2)( [k]), where N is the number of characters needed for the proof above. From this, by Bounded Necessitation, we have N ((∀k > k 2)( [k])). By Quantifier Distribution of N , (∀k > k 2) C +2N +lg(k) ( [k]) and since C + 2N + lg(k) < g(k) after some bound k > k, taking k ≥ k 2 for convenience, we have ∀k > k g(k) ( [k]) . (4.7) Finally, from Equations 4.6 and 4.7 we have, as needed, ∀k > k (p[k]). 4.1. Interpretation. L öb's Theorem may be viewed as an obstacle to a formal system of logic \"trusting itself \" to soundly prove any statement p. Previously, one might have thought this obstacle was merely a quirk of infinities arising from the unbounded proof-existence predicate . However, we see now that some bounded obstacle remains: namely, that a bounded logical system cannot trust itself \"about moderately long proofs in general.\" To see this interpretation, let p[k] be any statement with a free parameter k, and f(k) e(O(lg(k))) be any function, representing \"moderate largeness.\" Then the hypothesis (∀k) f(k) (p[k]) → p[k] of Theorem 4.2 says that our logical system generally trusts its proofs about p[k], even if they are moderately long. However, this will imply that ∀k > k, p[k], which is bad news if p[k] is sometimes false. \n Making f(k) small. The statement of Theorem 4.2 becomes stronger as one makes the function f(k) smaller, but it must remain e(O(lg(k))) for the theorem to apply. The obstruction to making f(k) small is hence the size of the proof expansion function e, which in real-world software for writing proofs about proofs will be under some design pressure to be made small, to manage computational resources. How small can e be made in practice? G ödel numberings for sequences of integers can be achieved in O(n) space (Tsai, Chang, and Chen,  [11] ) (where n is the length of a standard binary encoding of the sequence), as can G ödel numberings of term algebras  (Tarau, [9] ). To check that one line is an application of Modus Ponens from previous lines, if the proof encoding indexes the implication to which MP is applied, is a test for string equality that is linear in the length the of lines. Finally, to check that an abbreviation has been applied or expanded, if the proof encoding indexes where the abbreviation occurs, is also a linear time test for string equality. Thus, one can straightforwardly achieve e(k) ∈ O(k) for real-world theoremprovers. In that case, the condition f(k) e(O(lg(k))) amounts only to saying that f(k) lg(k). §5. Robust cooperation of bounded proof-based agents in the Prisoner's Dilemma. Bárász, Christiano, Fallenstein et al.  [1] , LaVictoire, Fallenstein, Yudkowsky et al.  [5] , and others have exhibited various agent-like logical formulae who can be viewed as playing the Prisoner's Dilemma by basing their \"decisions\" on proofs about each others' definitions (as strings). In particular, they proffer proof of the opponent's cooperation as an unexploitable condition for cooperation. However, their \"agents\" are purely mathematical entities who decide whether to cooperate based on undecidable logical conditions. This leaves open the question of whether their results are achievable by real software with bounded computational resources. So, consider the following program, where G : N → N is a function to be specified later: def FairBot k(Opponent) : let B = k + G(LengthOf(Opponent)) search for a proof of length at most B that Opponent(FairBot k) = Cooperate if found, return Cooperate else return Defect In this program, the subroutine \"search for a proof of length at most B that (• • • )\" is defined as a process which searches, in lexicographic order, through all strings of length ≤B, checking each string for whether it is a proof of ( up that is a proof of (• • • ), the search halts and sets found = true. If no such proof exists, the search continues until the (finite) set of strings of length ≤B have been exhausted, then halts and sets found = false. In what follows, all that matters is the functional behavior of the proof search procedure: that it sets found = true if a proof of length ≤B exists, and found = false otherwise. The program FairBot k may be viewed as a kind of proof-based \"agent\" that plays the Prisoner's Dilemma in the following sense. Given any string, Opponent, representing the source code of another program, we can compute the pair 1 R(FairBot k , Opp) := FairBot k (Opp), Opp(FairBot k )) . Viewed as such, FairBot k has the desirable property that the outcome R(FairBot k , Opp) = (Cooperate, Defect) will never occur: if its opponent defects, then FairBot will find no proof of its opponent's cooperation, so FairBot will itself defect. This property is called being unexploitable. At this point, a natural question arises: what happens when FairBot encounters a copy of itself ? That is, what is FairBot k (FairBot k )? Each FairBot will be searching for a proof that the other will cooperate. As such, one might expect to see a bottomless regression that will exhaust the proof bound B. (\"The first FairBot must prove that the second FairBot must prove that the first FairBot must prove that. . . .\") Thus, it seems like they will find no proof of cooperation, and hence defect. However, this turns out not to be the case. Letting p[k] := FairBot k (FairBot k ) = Cooperate) , it is a direct consequence of Theorem 4.2 that FairBot k (FairBot k ) = Cooperate. In fact a much stronger claim is true, as the next theorem will show. It will demonstrate a mutually cooperative program equilibrium (in the sense of Tennenholtz  [10] ) among a wide variety of (unequal) agents, provided only that they employ a certain principle of fairness, as follows. \n G-fairness. Given a nonnegative increasing function G, we say that an agent (i.e., program) A k taking a parameter k ∈ N is G-fair if for any opponent (i.e., program) Opp, we have k+G(LengthOf(Opp)) Opp(A k ) = C ) → A k (Opp) = C ) , where LengthOf(Opp) is the character length of the opponent's source code. In words, A k is G-fair if finding a short proof of its opponent's cooperation is a sufficient condition for A k to cooperate, when \"short\" is flexibly defined to be an increasing function of its opponent's complexity, i.e., k + G(LengthOf(Opp)). The agents FairBot k defined above are G-fair (where G is the function appearing in line 2 of their source code), and the reader is encouraged to keep them in mind as a motivating example for the following result:  n+a(m) (α[m, n]) → [n, m]. For later convenience, we also choose a nondecreasing computable function f(k) e(O(lg(k))) such that 6f(2 ) ≤ G( ). For example, we could take f(k) = G( lg(k) )/6 . Now, LengthOf(A k ) > lg(k) and LengthOf(B k ) > lg(k) since they reference the parameter k in their code. Applying G to both sides yields a(k), b(k) > G(lg(k)) ≥ 6f(k). (5.6) Define an \"eventual cooperation\" formula: p[k] := (∀m > k)(∀n > k)(α[m, n] and [n, m]). Using Quantifier Distribution once on the definition of p[k], (∀k) f(k) (p[k]) → (∀m > k)( C ((∀n > k)(α[m, n] and [n, m]))) where Adding these inequalities yields 3C + 4f(k) + 2lg(m) + lg(n) < n + a(m), so for some k 1 , from (5.7) we derive C = C + 2f(k) + lg(m). Applying Quantifier Distribution again, (∀k) f(k) p[k] → (∀m > k)(∀n > k)( C (α[m, n] and [n, m])) . ( 5 (∀k > k 1) f(k) (p[k]) → (∀m > k)(∀n > k) n+a(m) (α[m, n]) . Similarly, we also have 3C + 2lg(m) < m and 4f(k) + lg(n) < 5f(n) < b(n), so for some k 2 ≥ k 1 , (∀k > k 2 ) f(k) (p[k]) → (∀m > k)(∀n > k) n+a(m) (α[m, n]) and m+b(n) ( [n, m]) . (5.8) Thus by (5.5), (∀k > k 2) f(k) (p[k]) → (∀m > k)(∀n > k) c(n, m) and c(m, n)) , i.e., (∀k > k 2) f(k) (p[k]) → p[k] . Therefore, by Theorem 4.2 (and the note following it), for some k we have ∀k > k (p[k]). In other words, for all m, n > k + 1, A m (B n ) = B n (A m ) = Cooperate. Theorem 5.1 interesting for four reasons: 1. It is surprising. L öb's Theorem has not been applied much in the setting of game theory, and in fact at the time of writing, 100% of the dozens of mathematicians and computer scientists that the author has asked to guess the output of FairBot k (FairBot k ) have either guessed incorrectly (expecting the proof searches to enter an infinite regress and thus reach their bounds), or given an invalid argument for cooperation (such as \"it would be better for the agents to cooperate, so they will\"). 2. It is advantageous. When k is large, FairBot k outperforms the classical Nash/correlated equilibrium solution (Defect, Defect) to the Prisoner's Dilemma when facing itself (or any other G-fair agent) in a one-shot game with no iteration and no future reputation. 3. It is unexploitable. That is, the outcome (Cooperate, Defect) will never occur with a FairBot as player 1. If an opponent will defect against FairBot, FairBot will find no proof of the opponent's cooperation, so FairBot will also defect. \n It is robust. Previous examples of cooperative program equilibria studied by Tennenholtz  [10]  and Fortnow  [4]  all involved cooperation based on equality of programs, a very fragile condition. Such fragility is not desirable if we wish to build real-world cooperative systems. By contrast, the G-fairness criterion relies only on the provability of the opponent's cooperation, rather than details of its implementation, and therefore establishes mutual cooperation between a broad class of agents. §6. Conclusion. Theorem 4.2 represents a resource-bounded generalization of L öb's Theorem, which can be applied to algorithms that read and write proofs using bounded computational resources, such as formal verification software. Theorem 5.1 makes use of Theorem 4.2, and some additional proof-theoretic analysis, to demonstrate how algorithmic agents who have access to one another's source codes can inexploitably achieve cooperative outcomes that out-perform classical Nash equilibria and correlated equilibria. Moreover, the condition for cooperation in Theorem 5.1, called \"G-fairness\", is more robust than previously known unexploitable cooperative conditions, which depended on literal source-code equality  (Tennenholtz, [10] ). As a direction for potential future investigation, it seems likely that other agents described in the purely logical (noncomputable) setting of Bárász, Christiano, Fallenstein et al.  [1]  and LaVictoire, Fallenstein, Yudkowsky et al.  [5]  will likely have bounded, algorithmic analogs, and that many more general consequences of L öb's Theorem-perhaps all the theorems of G ödel-L öb provability logic-will have resource-bounded analogs as well. Definition 4 . 1 ( 41 Proof expansion function). Let e : N → N be any computable function bounding the expansion of S-proof lengths when they are G ödel encoded. That is, its definition is only that it must be large enough to satisfy the following two properties: Property 3 (Bounded Necessitation). For all φ ∈ L S , \n Theorem 5 . 1 ( 5 . 2 . 1 . 51521 Robust cooperation criterion). Suppose that • e(k), the proof expansion function of our proof system as defined in Section 4, satisfies e(O(lg(k))) ≺ k, and • G( ) is any nondecreasing function satisfying G( ) e(O( )).Then, for any G-fair agents A k and B k , there exists some r 0 such that for all m, n > r, A m (B n ) = B n (A m ) = Cooperate. Feasibility of bounds in Theorem 5.Before the proof, recall from Section 4.2 that we can achieve e(k) ∈ O(k) for automatic proof systems that are designed for easy verifiability, in which case e(O(lg(k))) ≺ k, as needed.Proof of Theorem 5.1. The proof will make use of Theorem 4.2 at the very end, but first requires some additional proof-theoretic analysis. For brevity we leta(k) := G(LengthOf(A k )), (5.1) b(k) := G(LengthOf(B k )), (5.2) α[m, n] := A m (B n ) = Cooperate) , and (5.3) [n, m] := B n (A m ) = Cooperate) (5.4) so we can write the G-fairness conditions more compactly as m+b(n) ( [n, m]) → α[m, n] and (5.5) \n\t\t\t Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 24 Mar 2022 at 01:25:56, subject to the Cambridge Core terms of use, available at \n\t\t\t https://www.cambridge.org/core/terms. https://doi.org/10.1017/jsl.2017.42 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 24 Mar 2022 at 01:25:56, subject to the Cambridge Core terms of use, available at \n\t\t\t We must assume that Opp halts and returns either Cooperate or Defect in this case; note that FairBot k always halts. https://www.cambridge.org/core/terms. https://doi.org/10.1017/jsl.2017.42 Downloaded from https://www.cambridge.org/core. Carnegie Mellon University, on 24 Mar 2022 at 01:25:56, subject to the Cambridge Core terms of use, available at", "date_published": "n/a", "url": "n/a", "filename": "div-class-title-a-parametric-resource-bounded-generalization-of-lob-s-theorem-and-a-robust-cooperation-criterion-for-open-source-game-theory-div.tei.xml", "abstract": "This article presents two theorems: (1) a generalization of L öb's Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and (2) a theorem on the robust cooperation of agents that employ proofs about one another's source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner's Dilemma while remaining unexploitable, i.e., sometimes achieving the outcome (Cooperate, Cooperate), and never receiving the outcome (Cooperate, Defect) as player 1. §1. Introduction. In the game theoretic analysis of computerized agents who may read one another's source code, and more generally in the analysis of program verification systems that use proofs to verify other program verification systems, a need has arisen for a version of L öb's Theorem that applies to proof systems with bounded computational resources. The first main theorem of this article is a generalization of L öb's Theorem that applies in such cases, developed and proven in Section 2 through Section 4. The second main theorem, presented in Section 5, makes use of the first theorem and some further proof-theoretic analysis to derive some implications for the game theory of agents who read one another's source code. Specifically, game theoretic work of Bárász, Christiano, Fallenstein et al.  [1]  and LaVictoire, Fallenstein, Yudkowsky et al.  [5]  found that L öb's Theorem can be used to design entities in modal logic that resemble \"agents\" who achieve robust cooperative equilibria in games such as the Prisoner's Dilemma. However, these so-called \"modal agents\" were defined as strings representing uncomputable functions; strings of the form \"if (• • • ) is provable, return 1, else return 0\". It remained open whether their results would arise naturally for computable agents, a question answered affirmatively in Section 5. Pudlák [7]  on the lengths of proofs of finitistic consistency statements are suggestive of the first theorem of this article. Specifically, \n Related work. The work of", "id": "07043298d45979b230d0f71e43011bab"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Paul F Christiano", "Jan Leike", "Tom B Brown", "Google Brain", "Miljan Martic", "Shane Legg", "Dario Amodei"], "title": "Deep Reinforcement Learning from Human Preferences", "text": "Introduction Recent success in scaling reinforcement learning (RL) to large problems has been driven in domains that have a well-specified reward function  (Mnih et al., 2015 (Mnih et al., , 2016 Silver et al., 2016) . Unfortunately, many tasks involve goals that are complex, poorly-defined, or hard to specify. Overcoming this limitation would greatly expand the possible impact of deep RL and could increase the reach of machine learning more broadly. For example, suppose that we wanted to use reinforcement learning to train a robot to clean a table or scramble an egg. It's not clear how to construct a suitable reward function, which will need to be a function of the robot's sensors. We could try to design a simple reward function that approximately captures the intended behavior, but this will often result in behavior that optimizes our reward function without actually satisfying our preferences. This difficulty underlies recent concerns about misalignment between our values and the objectives of our RL systems  (Bostrom, 2014; Russell, 2016; Amodei et al., 2016) . If we could successfully communicate our actual objectives to our agents, it would be a significant step towards addressing these concerns. If we have demonstrations of the desired task, we can use inverse reinforcement learning  (Ng and Russell, 2000)  or imitation learning to copy the demonstrated behavior. But these approaches are not directly applicable to behaviors that are difficult for humans to demonstrate (such as controlling a robot with many degrees of freedom but non-human morphology). An alternative approach is to allow a human to provide feedback on our system's current behavior and to use this feedback to define the task. In principle this fits within the paradigm of reinforcement learning, but using human feedback directly as a reward function is prohibitively expensive for RL systems that require hundreds or thousands of hours of experience. In order to practically train deep RL systems with human feedback, we need to decrease the amount of feedback required by several orders of magnitude. We overcome this difficulty by asking humans to compare possible trajectories of the agent, using that data to learn a reward function, and optimizing the learned reward function with RL. This basic approach has been explored in the past, but we confront the challenges involved in scaling it up to modern deep RL and demonstrate by far the most complex behaviors yet learned from human feedback. Our experiments take place in two domains: Atari games in the Arcade Learning Environment  (Bellemare et al., 2013) , and robotics tasks in the physics simulator  MuJoCo (Todorov et al., 2012) . We show that a small amount of feedback from a non-expert human, ranging from fifteen minutes to five hours, suffice to learn both standard RL tasks and novel hard-to-specify behaviors such as performing a backflip or driving with the flow of traffic. \n Related Work A long line of work studies reinforcement learning from human ratings or rankings, including  Akrour et al. (2011 ), Pilarski et al. (2011 ), Akrour et al. (2012 ), Wilson et al. (2012 ), Sugiyama et al. (2012 ), Wirth and Fürnkranz (2013 ), Daniel et al. (2015 ), El Asri et al. (2016 ), Wang et al. (2016 ), and Wirth et al. (2016 . Other lines of research consider the general problem of reinforcement learning from preferences rather than absolute reward values  (Fürnkranz et al., 2012; Akrour et al., 2014; Wirth et al., 2016) , and optimizing using human preferences in settings other than reinforcement learning  (Machwe and Parmee, 2006; Secretan et al., 2008; Brochu et al., 2010; Sørensen et al., 2016) . Our algorithm follows the same basic approach as Akrour et al. (  2012 ) and Akrour et al. (  2014 ), but considers much more complex domains and behaviors. The complexity of our environments force us to use different RL algorithms, reward models, and training strategies. One notable difference is that  Akrour et al. (2012)  and  Akrour et al. (2014)  elicit preferences over whole trajectories rather than short clips, and so would require about an order of magnitude more human time per data point. Our approach to feedback elicitation closely follows  Wilson et al. (2012 ). However, Wilson et al. (2012  assumes that the reward function is the distance to some unknown (linear) \"target\" policy, and is never tested with real human feedback. TAMER  (Knox, 2012; Knox and Stone, 2013 ) also learns a reward function from human feedback, but learns from ratings rather than comparisons, has the human observe the agent as it behaves, and has been applied to settings where the desired policy can be learned orders of magnitude more quickly. Compared to all prior work, our key contribution is to scale human feedback up to deep reinforcement learning and to learn much more complex behaviors. This fits into a recent trend of scaling reward learning methods to large deep learning systems, for example inverse RL  (Finn et al., 2016) , imitation learning  (Ho and Ermon, 2016; Stadie et al., 2017) , semi-supervised skill generalization  (Finn et al., 2017) , and bootstrapping RL from demonstrations  (Silver et al., 2016; Hester et al., 2017) . \n Preliminaries and Method \n Setting and Goal We consider an agent interacting with an environment over a sequence of steps; at each time t the agent receives an observation o t 2 O from the environment and then sends an action a t 2 A to the environment. In traditional reinforcement learning, the environment would also supply a reward r t 2 R and the agent's goal would be to maximize the discounted sum of rewards. Instead of assuming that the environment produces a reward signal, we assume that there is a human overseer who can express preferences between trajectory segments. A trajectory segment is a sequence of observations and actions, = ((o 0 , a 0 ), (o 1 , a 1 ), . . . , (o k 1 , a k 1 )) 2 (O ⇥ A) k . Write 1 2 to indicate that the human preferred trajectory segment 1 to trajectory segment 2 . Informally, the goal of the agent is to produce trajectories which are preferred by the human, while making as few queries as possible to the human. More precisely, we will evaluate our algorithms' behavior in two ways: Quantitative: We say that preferences are generated by a reward function 2 r : O ⇥ A ! R if o 1 0 , a 1 0 , . . . , o 1 k 1 , a 1 k 1 o 2 0 , a 2 0 , . . . , o 2 k 1 , a 2 k 1 whenever r o 1 0 , a 1 0 + • • • + r o 1 k 1 , a 1 k 1 > r o 2 0 , a 2 0 + • • • + r o 2 k 1 , a 2 k 1 . If the human's preferences are generated by a reward function r, then our agent ought to receive a high total reward according to r. So if we know the reward function r, we can evaluate the agent quantitatively. Ideally the agent will achieve reward nearly as high as if it had been using RL to optimize r. Qualitative: Sometimes we have no reward function by which we can quantitatively evaluate behavior (this is the situation where our approach would be practically useful). In these cases, all we can do is qualitatively evaluate how well the agent satisfies the human's preferences. In this paper, we will start from a goal expressed in natural language, ask a human to evaluate the agent's behavior based on how well it fulfills that goal, and then present videos of agents attempting to fulfill that goal. Our model based on trajectory segment comparisons is very similar to the trajectory preference queries used in  Wilson et al. (2012) , except that we don't assume that we can reset the system to an arbitrary state 3 and so our segments generally begin from different states. This complicates the interpretation of human comparisons, but we show that our algorithm overcomes this difficulty even when the human raters have no understanding of our algorithm. \n Our Method At each point in time our method maintains a policy ⇡ : O ! A and a reward function estimate r : O ⇥ A ! R, each parametrized by deep neural networks. These networks are updated by three processes: 1. The policy ⇡ interacts with the environment to produce a set of trajectories {⌧ 1 , . . . , ⌧ i }. The parameters of ⇡ are updated by a traditional reinforcement learning algorithm, in order to maximize the sum of the predicted rewards r t = r(o t , a t ). \n We select pairs of segments 1 , 2 from the trajectories {⌧ 1 , . . . , ⌧ i } produced in step 1, and send them to a human for comparison. 3. The parameters of the mapping r are optimized via supervised learning to fit the comparisons collected from the human so far. These processes run asynchronously, with trajectories flowing from process (1) to process (2), human comparisons flowing from process (2) to process (3), and parameters for r flowing from process (3) to process (1). The following subsections provide details on each of these processes. \n Optimizing the Policy After using r to compute rewards, we are left with a traditional reinforcement learning problem. We can solve this problem using any RL algorithm that is appropriate for the domain. One subtlety is that the reward function r may be non-stationary, which leads us to prefer methods which are robust to changes in the reward function. This led us to focus on policy gradient methods, which have been applied successfully for such problems  (Ho and Ermon, 2016) . In this paper, we use advantage actor-critic (A2C;  Mnih et al., 2016)  to play Atari games, and trust region policy optimization (TRPO;  Schulman et al., 2015)  to perform simulated robotics tasks. In each case, we used parameter settings which have been found to work well for traditional RL tasks. The only hyperparameter which we adjusted was the entropy bonus for TRPO. This is because TRPO relies on the trust region to ensure adequate exploration, which can lead to inadequate exploration if the reward function is changing. We normalized the rewards produced by r to have zero mean and constant standard deviation. This is a typical preprocessing step which is particularly appropriate here since the position of the rewards is underdetermined by our learning problem. \n Preference Elicitation The human overseer is given a visualization of two trajectory segments, in the form of short movie clips. In all of our experiments, these clips are between 1 and 2 seconds long. The human then indicates which segment they prefer, that the two segments are equally good, or that they are unable to compare the two segments. The human judgments are recorded in a database D of triples 1 , 2 , µ , where 1 and 2 are the two segments and µ is a distribution over {1, 2} indicating which segment the user preferred. If the human selects one segment as preferable, then µ puts all of its mass on that choice. If the human marks the segments as equally preferable, then µ is uniform. Finally, if the human marks the segments as incomparable, then the comparison is not included in the database. \n Fitting the Reward Function We can interpret a reward function estimate r as a preference-predictor if we view r as a latent factor explaining the human's judgments and assume that the human's probability of preferring a segment i depends exponentially on the value of the latent reward summed over the length of the clip: 4 P ⇥ 1 2 ⇤ = exp P r o 1 t , a 1 t exp P r(o 1 t , a 1 t ) + exp P r(o 2 t , a 2 t ) . (1) We choose r to minimize the cross-entropy loss between these predictions and the actual human labels: loss(r) = X ( 1 , 2 ,µ)2D µ(1) log P ⇥ 1 2 ⇤ + µ(2) log P ⇥ 2 1 ⇤ . This follows the Bradley-Terry model  (Bradley and Terry, 1952)  for estimating score functions from pairwise preferences, and is the specialization of the Luce-Shephard choice rule  (Luce, 2005; Shepard, 1957)  to preferences over trajectory segments. Our actual algorithm incorporates a number of modifications to this basic approach, which early experiments discovered to be helpful and which are analyzed in Section 3.3: • We fit an ensemble of predictors, each trained on |D| triples sampled from D with replacement. The estimate r is defined by independently normalizing each of these predictors and then averaging the results. • A fraction of 1/e of the data is held out to be used as a validation set for each predictor. We use `2 regularization and adjust the regularization coefficient to keep the validation loss between 1.1 and 1.5 times the training loss. In some domains we also apply dropout for regularization. • Rather than applying a softmax directly as described in Equation 1, we assume there is a 10% chance that the human responds uniformly at random. Conceptually this adjustment is needed because human raters have a constant probability of making an error, which doesn't decay to 0 as the difference in reward difference becomes extreme. \n Selecting Queries We decide how to query preferences based on an approximation to the uncertainty in the reward function estimator, similar to Daniel et al. (  2014 ): we sample a large number of pairs of trajectory segments of length k from the latest agent-environment interactions, use each reward predictor in our ensemble to predict which segment will be preferred from each pair, and then select those trajectories for which the predictions have the highest variance across ensemble members 5 This is a crude approximation and the ablation experiments in Section 3 show that in some tasks it actually impairs performance. Ideally, we would want to query based on the expected value of information of the query  (Akrour et al., 2012; Krueger et al., 2016) , but we leave it to future work to explore this direction further. \n Experimental Results We  \n Reinforcement Learning Tasks with Unobserved Rewards In our first set of experiments, we attempt to solve a range of benchmark tasks for deep RL without observing the true reward. Instead, the agent learns about the goal of the task only by asking a human which of two trajectory segments is better. Our goal is to solve the task in a reasonable amount of time using as few queries as possible. In our experiments, feedback is provided by contractors who are given a 1-2 sentence description of each task before being asked to compare several hundred to several thousand pairs of trajectory segments for that task (see Appendix B for the exact instructions given to contractors). Each trajectory segment is between 1 and 2 seconds long. Contractors responded to the average query in 3-5 seconds, and so the experiments involving real human feedback required between 30 minutes and 5 hours of human time. For comparison, we also run experiments using a synthetic oracle whose preferences are generated (in the sense of Section 2.1) by the real reward 6 . We also compare to the baseline of RL training using the real reward. Our aim here is not to outperform but rather to do nearly as well as RL without access to reward information and instead relying on much scarcer feedback. Nevertheless, note that feedback from real humans does have the potential to outperform RL (and as shown below it actually does so on some tasks), because the human feedback might provide a better-shaped reward. We describe the details of our experiments in Appendix A, including model architectures, modifications to the environment, and the RL algorithms used to optimize the policy. \n Simulated Robotics The first tasks we consider are eight simulated robotics tasks, implemented in MuJoCo  (Todorov et al., 2012), and included in OpenAI Gym (Brockman et al., 2016) . We made small modifications to these tasks in order to avoid encoding information about the task in the environment itself (the modifications are described in detail in Appendix A). The reward functions in these tasks are quadratic functions of distances, positions and velocities, and most are linear. We included a simple cartpole Figure  1 : Results on MuJoCo simulated robotics as measured on the tasks' true reward. We compare our method using real human feedback (purple), our method using synthetic feedback provided by an oracle (shades of blue), and reinforcement learning using the true reward function (orange). All curves are the average of 5 runs, except for the real human feedback, which is a single run, and each point is the average reward over five consecutive batches. For Reacher and Cheetah feedback was provided by an author due to time constraints. For all other tasks, feedback was provided by contractors unfamiliar with the environments and with our algorithm. The irregular progress on Hopper is due to one contractor deviating from the typical labeling schedule. task (\"pendulum\") for comparison, since this is representative of the complexity of tasks studied in prior work. Figure  1  shows the results of training our agent with 700 queries to a human rater, compared to learning from 350, 700, or 1400 synthetic queries, as well as to RL learning from the real reward. With 700 labels we are able to nearly match reinforcement learning on all of these tasks. Training with learned reward functions tends to be less stable and higher variance, while having a comparable mean performance. Surprisingly, by 1400 labels our algorithm performs slightly better than if it had simply been given the true reward, perhaps because the learned reward function is slightly better shaped-the reward learning procedure assigns positive rewards to all behaviors that are typically followed by high reward. The difference may also be due to subtle changes in the relative scale of rewards or our use of entropy regularization. Real human feedback is typically only slightly less effective than the synthetic feedback; depending on the task human feedback ranged from being half as efficient as ground truth feedback to being equally efficient. On the Ant task the human feedback significantly outperformed the synthetic feedback, apparently because we asked humans to prefer trajectories where the robot was \"standing upright,\" which proved to be useful reward shaping. (There was a similar bonus in the RL reward function to encourage the robot to remain upright, but the simple hand-crafted bonus was not as useful.) \n Atari The second set of tasks we consider is a set of seven Atari games in the Arcade Learning Environment  (Bellemare et al., 2013) , the same games presented in Mnih et al., 2013. Figure  2  shows the results of training our agent with 5,500 queries to a human rater, compared to learning from 350, 700, or 1400 synthetic queries, as well as to RL learning from the real reward. Our method has more difficulty matching RL in these challenging environments, but nevertheless it displays substantial learning on most of them and matches or even exceeds RL on some. Specifically, Figure  2 : Results on Atari games as measured on the tasks' true reward. We compare our method using real human feedback (purple), our method using synthetic feedback provided by an oracle (shades of blue), and reinforcement learning using the true reward function (orange). All curves are the average of 3 runs, except for the real human feedback which is a single run, and each point is the average reward over about 150,000 consecutive frames. on BeamRider and Pong, synthetic labels match or come close to RL even with only 3,300 such labels. On Seaquest and Qbert synthetic feedback eventually performs near the level of RL but learns more slowly. On SpaceInvaders and Breakout synthetic feedback never matches RL, but nevertheless the agent improves substantially, often passing the first level in SpaceInvaders and reaching a score of 20 on Breakout, or 50 with enough labels. On most of the games real human feedback performs similar to or slightly worse than synthetic feedback with the same number of labels, and often comparably to synthetic feedback that has 40% fewer labels. On Qbert, our method fails to learn to beat the first level with real human feedback; this may be because short clips in Qbert can be confusing and difficult to evaluate. Finally, Enduro is difficult for A3C to learn due to the difficulty of successfully passing other cars through random exploration, and is correspondingly difficult to learn with synthetic labels, but human labelers tend to reward any progress towards passing cars, essentially shaping the reward and thus outperforming A3C in this game (the results are comparable to those achieved with DQN). \n Novel behaviors Experiments with traditional RL tasks help us understand whether our method is effective, but the ultimate purpose of human interaction is to solve tasks for which no reward function is available. Using the same parameters as in the previous experiments, we show that our algorithm can learn novel complex behaviors. We demonstrate: 1. The Hopper robot performing a sequence of backflips (see Figure  4 ). This behavior was trained using 900 queries in less than an hour. The agent learns to consistently perform a backflip, land upright, and repeat. 2. The Half-Cheetah robot moving forward while standing on one leg. This behavior was trained using 800 queries in under an hour. 3. Keeping alongside other cars in Enduro. This was trained with roughly 1,300 queries and 4 million frames of interaction with the environment; the agent learns to stay almost exactly even with other moving cars for a substantial fraction of the episode, although it gets confused by changes in background. Figure  3 : Performance of our algorithm on MuJoCo tasks after removing various components, as described in Section Section 3.3. All graphs are averaged over 5 runs, using 700 synthetic labels each. Videos of these behaviors can be found at https://goo.gl/MhgvIU. These behaviors were trained using feedback from the authors. \n Ablation Studies In order to better understand the performance of our algorithm, we consider a range of modifications: 1. We pick queries uniformly at random rather than prioritizing queries for which there is disagreement (random queries). 2. We train only one predictor rather than an ensemble (no ensemble). In this setting, we also choose queries at random, since there is no longer an ensemble that we could use to estimate disagreement. 3. We train on queries only gathered at the beginning of training, rather than gathered throughout training (no online queries). 4. We remove the `2 regularization and use only dropout (no regularization). 5. On the robotics tasks only, we use trajectory segments of length 1 (no segments). 6. Rather than fitting r using comparisons, we consider an oracle which provides the true total reward over a trajectory segment, and fit r to these total rewards using mean squared error (target). The results are presented in Figure  3  for MuJoCo and Figure  4  for Atari. Training the reward predictor offline can lead to bizarre behavior that is undesirable as measured by the true reward  (Amodei et al., 2016) . For instance, on Pong offline training sometimes leads our agent to avoid losing points but not to score points; this can result in extremely long volleys (videos at https://goo.gl/L5eAbk). This type of behavior demonstrates that in general human feedback needs to be intertwined with RL rather than provided statically. Our main motivation for eliciting comparisons rather than absolute scores was that we found it much easier for humans to provide consistent comparisons than consistent absolute scores, especially on the continuous control tasks and on the qualitative tasks in Section 3.2; nevertheless it seems important to understand how using comparisons affects performance. For continuous control tasks we found that predicting comparisons worked much better than predicting scores. This is likely because the scale of rewards varies substantially and this complicates the regression problem, which is smoothed significantly when we only need to predict comparisons. In the Atari tasks we clipped rewards Figure  4 : Performance of our algorithm on Atari tasks after removing various components, as described in Section 3.3. All curves are an average of 3 runs using 5,500 synthetic labels (see minor exceptions in Section A.2). and effectively only predicted the sign, avoiding these difficulties (this is not a suitable solution for the continuous control tasks because the magnitude of the reward is important to learning). In these tasks comparisons and targets had significantly different performance, but neither consistently outperformed the other. We also observed large performance differences when using single frames rather than clips.  7  In order to obtain the same results using single frames we would need to have collected significantly more comparisons. In general we discovered that asking humans to compare longer clips was significantly more helpful per clip, and significantly less helpful per frame. Shrinking the clip length below 1-2 seconds did not significantly decrease the human time required to label each clip in early experiments, and so seems less efficient per second of human time. In the Atari environments we also found that it was often easier to compare longer clips because they provide more context than single frames. \n Discussion and Conclusions Agent-environment interactions are often radically cheaper than human interaction. We show that by learning a separate reward model using supervised learning, it is possible to reduce the interaction complexity by roughly 3 orders of magnitude. Although there is a large literature on preference elicitation and reinforcement learning from unknown reward functions, we provide the first evidence that these techniques can be economically scaled up to state-of-the-art reinforcement learning systems. This represents a step towards practical applications of deep RL to complex real-world tasks. In the long run it would be desirable to make learning a task from human preferences no more difficult than learning it from a programmatic reward signal, ensuring that powerful RL systems can be applied in the service of complex human values rather than low-complexity goals. \n \n \n \n\t\t\t Here we assume here that the reward is a function of the observation and action. In our experiments in Atari environments, we instead assume the reward is a function of the preceding 4 observations. In a general partially observable environment, we could instead consider reward functions that depend on the whole sequence of observations, and model this reward function with a recurrent neural network.3 Wilson et al. (2012) also assumes the ability to sample reasonable initial states. But we work with high dimensional state spaces for which random states will not be reachable and the intended policy inhabits a low-dimensional manifold. \n\t\t\t Equation 1 does not use discounting, which could be interpreted as modeling the human to be indifferent about when things happen in the trajectory segment. Using explicit discounting or inferring the human's discount function would also be reasonable choices. \n\t\t\t Note that trajectory segments almost never start from the same state.6  In the case of Atari games with sparse rewards, it is relatively common for two clips to both have zero reward in which case the oracle outputs indifference. Because we considered clips rather than individual states, such ties never made up a large majority of our data. Moreover, ties still provide significant information to the reward predictor as long as they are not too common. \n\t\t\t We only ran these tests on continuous control tasks because our Atari reward model depends on a sequence of consecutive frames rather than a single frame, as described in Section A.2", "date_published": "n/a", "url": "n/a", "filename": "NIPS-2017-deep-reinforcement-learning-from-human-preferences-Paper.tei.xml", "abstract": "For sophisticated reinforcement learning (RL) systems to interact usefully with real-world environments, we need to communicate complex goals to these systems. In this work, we explore goals defined in terms of (non-expert) human preferences between pairs of trajectory segments. We show that this approach can effectively solve complex RL tasks without access to the reward function, including Atari games and simulated robot locomotion, while providing feedback on less than 1% of our agent's interactions with the environment. This reduces the cost of human oversight far enough that it can be practically applied to state-of-the-art RL systems. To demonstrate the flexibility of our approach, we show that we can successfully train complex novel behaviors with about an hour of human time. These behaviors and environments are considerably more complex than any which have been previously learned from human feedback. ⇤ Work done while at OpenAI.", "id": "c018c78ef97e093ecd6b29c06991db7a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Medium-Term Artificial Intelligence and Society", "text": "Introduction Attention to AI technologies and accompanying societal issues commonly clusters into groups focusing on either near-term or long-term AI, with some acrimonious debate between them over which is more important. Following Baum  [1] , the near-term camp may be called \"presentists\" and the long-term camp \"futurists\". The current state of affairs suggests two reasons for considering the intermediate period between the near and long terms. First, the medium term (or, interchangeably, intermediate term or mid term) has gone neglected relative to its inherent importance. If there are important topics involving near-term and long-term AI, then perhaps the medium term has important topics as well. Second, the medium term may provide a common ground between presentists and futurists. Insofar as both sides consider the medium term to be important, it could offer a constructive topic to channel energy that may otherwise be spent on hashing out disagreements. Rare examples of previous studies with dedicated attention to medium-term AI are Parson et al.  [2, 3] . (There is a lot of work that touches on medium-term AI topics, some of which is cited in this paper. However, aside from Parson et al.  [2, 3] , I am not aware of any publications that explicitly identify medium-term AI as a topic warranting dedicated attention.) Both studies  [2, 3]  recognize medium-term AI as important and neglected. Parson et al.  [2]  acknowledges that some prior work in AI covers topics that are important across all time periods, and thus are also relevant to the medium term. It provides a definition of medium-term AI, which is discussed further below, and it provides some analysis of medium-term AI topics. Parson et al.  [3]  posits that the neglect of the medium term may derive in part from the academic disciplines and methodologies of AI researchers, which may point the researchers toward either the near term or the long term but not the medium term. The present paper extends Parson et al.'s  [2]  work on definitions and presents original analysis of a different mix of medium-term AI topics. The present paper also explores the medium term as a potential point of common ground between presentists and futurists. Several previous attempts have been made to bridge the presentist-futurist divide  [1, 4, 5 ]. An overarching theme in this literature is that the practical steps needed to make progress are often (though not always) the same for both near-term and long-term AI. Instead of expending energy debating the relative importance of near-term and long-term AI, it may often be more productive to focus attention on the practical steps that both sides of the debate agree are valuable. This practical synergy can arise for two distinct reasons, both with implications for medium-term AI. First, certain actions may improve near-term AI and the near-term conversation about long-term AI. Such actions will often also improve the near-term conversation about mid-term AI. For example, efforts to facilitate dialog between computer scientists and policymakers can improve the quality of policy discussions for near-, mid-, and long-term AI. Additionally, efforts encouraging AI developers to take more responsibility for the social and ethical implications of their work can influence work on near-, mid-, and long-term AI. For example, the ethics principles that many AI groups have recently established  [6]  are often quite general and can apply to work on near-term and long-term AI, as can analyses of the limitations of these principles  [7] . Here it should be explained that there is near-term work aimed at developing systems that may only become operational over the mid or long term, especially work consisting of basic research toward major breakthroughs in AI capabilities. Second, certain actions may improve near-term AI, and, eventually, long-term AI. These actions may often also eventually improve mid-term AI. For example, some research on how to design near-term AI systems more safely may provide a foundation for also making mid-and long-term AI systems safer. This is seen in the AI safety study of Amodei et al.  [8] , which is framed in terms of near-term AI; lead author Amodei describes the work as also being relevant for long-term AI  [9] . Additionally, AI governance institutions established over the near term may persist into the mid and long term, given the durability of many policy institutions. Of course, AI system designs and governance institutions that persist from the near term to the long term would also be present throughout the mid-term. Furthermore, evaluating their long-term persistence may require understanding of what happens during the mid-term. Dedicated attention to the medium term can offer another point of common ground between presentists and futurists: both sides may consider the medium term to be important. Presentists may find the medium term to be early enough for their tastes, while futurists find it late enough for theirs. As elaborated below, the reasons that presentists have for favoring near-term AI are different types of reasons than those of the futurists. Presentists tend to emphasize immediate feasibility, certainty, and urgency, whereas futurists tend to emphasize extreme AI capabilities and consequences. Potentially, the medium term features a widely appealing mix of feasibility, certainty, urgency, capabilities, and consequences. Or not: it is also possible that the medium term would sit in a \"dead zone\", being too opaque to merit presentist interest and too insignificant to merit futurist interest. This matter will be a running theme throughout the paper and is worth expressing formally: The medium-term AI hypothesis: There is an intermediate time period in which AI technology and accompanying societal issues are important from both presentist and futurist perspectives. The medium-term AI hypothesis can be considered in either empirical or normative terms. As an empirical hypothesis, it proposes that presentists and futurists actually consider the medium term to be important, or that they would tend to agree that the medium term is important if given the chance to reflect on it. As a normative hypothesis, it proposes that presentists should agree that the medium term is important, given the value commitments of the presentist and futurist perspectives. Given the practical goal of bridging the presentist-futurist divide, the empirical form is ultimately more important: what matters is whether the specific people on opposite sides of the divide would, upon consideration, find common ground in the medium term. (It is unlikely that they currently do find common ground in the medium term, due to lack of attention to it.) Empirical study of presentist and futurist reactions to the medium term is beyond the scope of the present paper. Instead, the aim here is to clarify the nature of the presentist and futurist perspectives in terms of the attributes of the medium term that they should consider important and then to examine whether the medium term is likely to possess these attributes. The paper therefore proceeds mainly in normative terms, though grounded in empirical observation of the perspectives articulated by actual presentists and futurists. More precisely, the medium-term AI hypothesis proposes that the perspectives underlying both groups should rate the medium term as important. This presumes that \"perspectives\" can rate things as important even when detached from the people who hold them. Such detachment is permitted here simply so that the analysis can proceed without going through the more involved (but ultimately important) process of consulting with the people who hold presentist and futurist perspectives. Evaluating the medium-term AI hypothesis is one aim of this paper. First, though, more needs to be said on how the medium term is defined. \n Defining the Medium Term The medium term is, of course, the period of time between the near term and the long term. However, discussions of near-term and long-term AI often do not precisely specify what constitutes near-term and long-term. Some ambiguity is inevitable due to uncertainty about future developments in AI. Additionally, different definitions may be appropriate for different contexts and purposes-for example, what qualifies as near-term may be different for a programmer than for a policymaker. Nonetheless, it is worth briefly exploring how the near, mid, and long terms can be defined for AI. Throughout, it should be understood that the near, mid, and long terms are all defined relative to the vantage point of the time of this writing (2019-2020). As time progresses, what classifies as near-, mid-, and long-term can shift. The first thing to note is that near-vs. mid-vs. long-term can be defined along several dimensions. The first is chronological: the near term goes from year A to year B, the mid term from year B to year C, and the long term from year C to year D. The second is in terms of the feasibility or ambitiousness of the AI: the near term is what is already feasible, the long term is the AI that would be most difficult to achieve, and the mid term is somewhere in between. Third, and related to the second, is the degree of certainty about the AI: the near term is what clearly can be built, the long term is the most uncertain and speculative, and the mid term is somewhere in between. Fourth is the degree of sophistication or capability of the AI: the near term is the least capable, the long term is the most capable, and the mid term is somewhere in between. Fifth, and related to the fourth, is with respect to impacts: the near term has (arguably; see below) the mildest impacts on human society and the world at large, the long term has the most extreme impacts, and the mid-term is somewhere in between. Sixth is urgency: the near term is (arguably) the most urgent, the long term the least urgent, and the mid term is somewhere in between. The dimension of impacts is somewhat complex and worth briefly unpacking. Near-term AI may have the mildest impacts, in the sense that if AI continues to grow more capable and be used more widely and in more consequential settings it will tend to have greater impacts on the human society that exists at that time. Put differently, if A = the impacts of near-term AI on near-term society, B = the impacts of mid-term AI on mid-term society, and C = the impacts of long-term AI on long-term society, then (it is supposed) A < B < C. There are, however, alternative ways of conceptualizing impacts. One could take a certain presentist view and argue that only present people matter for purposes of moral evaluation, such as is discussed by Arrhenius  [10] , or that future impacts should be discounted, as in many economic cost-benefit evaluations. In these cases, near-term AI may be evaluated as having the largest impacts because the impacts of mid-and long-term AI matter less or not at all. Or, one could consider the impacts of a period of AI on all time periods: the impact of near-term AI on the near, mid, and long terms, the impacts of mid-term AI on the mid-and long-terms, and the impact of long-term AI on the long term. This perspective recognizes the potential for durable impacts of AI technology, and would tend to increase the evaluated size of the impacts of near-and mid-term AI. While recognizing the merits of these alternative conceptions of impacts, this paper uses the first conception, involving A vs. B vs. C. There may be no one correct choice of dimensions for defining the near/mid/long term. Different circumstances may entail different definitions. For example, Parson et al.  [2]  are especially interested in societal impacts and implications for governance, and thus use definitions rooted primarily in impacts. They propose that, relative to near-term AI, medium-term AI has \"greater scale of application, along with associated changes in scope, complexity, and integration\"  [2]  (pp. 8-9), and, relative to long-term AI, medium-term AI \"is not self-directed or independently volitional, but rather is still to a substantial degree developed and deployed under human control\"  [2]  (p. 9). (One can quibble with these definitions. Arguably, near-term AI is already at a large scale of application, and there may be no clear demarcation in scale between near-and mid-term AI. Additionally, while it is proposed that long-term AI could escape human control, that would not necessarily be the case. Indeed, discussions of long-term AI sometimes focus specifically on the question of how to control such an AI  [11] .) The medium term is a period with substantially greater use of AI in decision-making, potentially to the point in which \"the meaning of governance\" is challenged  [2]  (p. 9), but humans remain ultimately in control. This is a reasonable definition of medium-term AI, especially for impacts and governance purposes. The present paper is more focused on the presentist/futurist debate, and so it is worth considering the definitions used in the debate. Elements of each of the six dimensions can be found, but they are not found uniformly. Presentists often emphasize feasibility and degree of certainty. Computer scientist Andrew Ng memorably likened attention to long-term AI to worrying about \"overpopulation on Mars\"  [12] , by which Ng meant that it might eventually be important, but it is too opaque and disconnected from current AI to be worth current attention. Another presentist theme is urgency, especially with respect to the societal implications of near-term AI. Legal scholar Ryan Calo  [13]  (p. 27) argues that \"AI presents numerous pressing challenges to individuals and society in the very short term\" and therefore commands attention relative to long-term AI. For their part, futurists often emphasize capability and impacts. Commonly cited is the early remark of I.J. Good  [14]  (p. 33) that \"ultraintelligent\" AI (AI with intelligence significantly exceeding that of humans) could be \"the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control\". Chronological definitions are less common. One exception is Etzioni  [15] , who downplays long-term AI on grounds that it is unlikely to occur within 25 years. (In reply, futurists Dafoe and Russell  [16]  argue that potential future events can still be worth caring about even if they will not occur within the next 25 years.) Taking the above into account, this paper will use a feasibility definition for near-term AI and a capability definition for long-term AI. The paper defines near-term AI as AI that already exists or is actively under development with a clear path to being built and deployed. Per this definition, near-term AI does not require any major research breakthroughs, but instead consists of straightforward applications of existing techniques. The terms \"clear\", \"major\", and \"straightforward\" are vague, and it may be reasonable to define them in different ways in different contexts. (This vagueness is relevant for the medium-term AI hypothesis; more on this below.) Nonetheless, this definition points to current AI systems plus the potential future AI systems that are likely to be built soon and do not depend on research breakthroughs that might or might not manifest. The paper defines long-term AI as AI that has at least human-level general intelligence. Interest in long-term AI often focuses on human-level artificial intelligence (HLAI), artificial general intelligence (AGI), strong AI, and artificial superintelligence (ASI). However, there may be narrow AI systems that are appropriate to classify as long-term. For example, Cave and ÓhÉigeartaigh  [4]  (p. 5) include \"wide-scale loss of jobs\" as a long-term AI issue separately from the prospect of superintelligence. (Note that the most widespread loss of jobs may require AGI. For example, Ford  [17]  (p. 3) writes \"If, someday, machines can match or even exceed the ability of a human being to think and to conceive new ideas-while at the same time enjoying all the advantages of a computer in areas like computational speed and data access-then it becomes somewhat difficult to imagine just what jobs might be left for even the most capable human workers\".) A plausible alternative definition of long-term AI is AI that achieves major intellectual milestones and/or has large and transformative effects. This is more of a catch-all definition that could include sufficiently important narrow AI systems such as those involved in job loss. In this definition, the terms \"major\", \"large\", and \"transformative\" are vague. Indeed, current AI systems arguably meet this definition. Therefore, the paper will define long-term AI in terms of HLAI, while noting the case for the alternative definitions. The paper's use of a feasibility definition for near-term and a capability definition for long-term may be consistent with common usage in AI discussions. However, the use of a different dimension for near-term (feasibility) than for long-term (capability) can induce some chronological blurring in two important respects. First, AI projects that are immediately practical may have long time horizons. This may be especially common for projects in which AI is only one component of a more complex and durable system. Military systems are one domain with long lifespans. A 2016 report found that some US nuclear weapon systems were still using 1970s-era 8-inch floppy disks  [18] . AI is currently being used and developed for a wide variety of military systems  [19] . Some of these could conceivably persist for many decades into the future-perhaps in the B-52H bomber, which was built in the 1960s and is planned to remain in service through the 2050s  [20] . (AI is used in bombers, for example, to improve targeting  [21] . AI is used more extensively in fighters, which execute complex aerial maneuvers at rapid speeds and can gain substantial tactical advantage from increased computational power and autonomy from human pilots  [22] .) One can imagine the B-52H being outfitted with current AI algorithms and retaining these algorithms into the 2050s, just as the 8-inch floppy disks have been retained in other US military systems. Per this paper's definitions, this B-52H AI would classify as near-term AI that happens to remain in use over a long time period, well beyond the 25 years that Etzioni  [15]  treats as the \"foreseeable horizon\" worthy of attention. Second, AI systems with large and transformative effects, including AGI, could potentially be built over relatively short time scales. When AGI and related forms of AI will be built is a matter of considerable uncertainty and disagreement. Several studies have asked AI researchers-predominantly computer scientists-when they expect AI with human or superhuman capacity to be built  [23] [24] [25] [26] . (Note that these studies are generally framed as being surveys of experts, but it is not clear that the survey participants are expert in the question of when AGI will be built. Earlier predictions about AI have often been unreliable  [27] . This may be a topic for which there are no experts; on this issue, see Morgan  [28] .) The researchers present estimates spanning many decades, with some estimates being quite soon. Figure  1  presents median estimates from these studies. Median estimates conceal the range of estimates across survey participants, but the full range could not readily be presented in Figure  1  because, unfortunately, only Baum et al.  [23]  included the full survey data. If the early estimates shown in Figure  1  are correct, then, by this paper's definitions, long-term AI may be appearing fairly soon, potentially within the next 25 years.  Estimates for when AI will reach superhuman capability (Baum et al.)  [23]  and human-level capability (Sandberg and Bostrom, Müller and Bostrom, and Grace et al.)  [24] [25] [26] . Shown are estimates for when the probability that the milestone is reached is 10% (lower mark), 50% (square), and 90% (upper mark). For each study, the median estimates across the survey participants are plotted. \n Median Estimates of Advanced AI Development \n The Medium-Term AI Hypothesis With the above definitions in mind, it is worth revisiting the medium-term AI hypothesis. If presentists are, by definition, only interested in the present, then they would not care at all about the medium term. However, the line between the near term and the medium term is blurry. As defined above, near-term AI must have a clear path to being built and deployed, but \"clearness\" is a matter of degree. As the path to being built and deployed becomes less and less clear, the AI transitions from near-term to medium-term, and presentists may have less and less interest in it. From this standpoint, presentists may care somewhat about the medium term, especially the earlier portions of it, but not to the same extent as they care about the near term. Alternatively, presentists might care about the medium term because the underlying things they care about also arise in the medium term. Some presentists are interested in the implications of AI for social justice, or for armed conflict, or for transportation, and so on. Whereas it may be difficult to think coherently about the implications of long-term AI for these matters, it may not be so difficult for medium-term AI. For example, a major factor in debates about autonomous weapons (machines that use AI to select and fire upon targets) is whether these weapons could adequately discriminate between acceptable and unacceptable targets (e.g., enemy combatants vs. civilians)  [29, 30] . Near-term AI cannot adequately discriminate; medium-term AI might be able to. Therefore, presentists concerned about autonomous weapons have reason to be interested in medium-term AI. Whether this interest extends to other presentist concerns (social justice, transportation, etc.) must be considered on a case-by-case basis. For futurists, the medium term may be important because it precedes and influences the long term. If the long term begins with the advent of human-level AGI, then this AI will be designed and built during the medium term. Some work on AGI is already in progress  [31] , but it may be at a relatively early stage. Figure  1  illustrates the uncertainty: the earliest estimates for the onset of AGI (and similar forms of AI) may fall within the near term, whereas the latest estimates fall much, much later. Futurists may tend to be most interested in the period immediately preceding the long term because it has the most influence on AGI. Their interest in earlier periods may depend on the significance of its causal impact on AGI. It follows that there are two bases for assessing the medium-term AI hypothesis. First, the hypothesis could hold if AI that resembles near-term AI also influences long-term AI. In that case, the technology itself may be of interest to both presentists and futurists. Alternatively, the hypothesis could hold if the societal implications of medium-term AI raise similar issues as near-term AI, and if the medium-term societal context also influences long-term AI. For example, medium-term autonomous weapon technology could raise similar target discrimination issues as is found for near-term technology, and it could also feed arms races for long-term AI. (To avoid confusion, it should be understood that discussions of long-term AI sometimes use the term \"arms race\" to refer to general competition to be the first to build long-term AI, without necessarily any connection to military armaments  [32] . Nonetheless, military arms races for long-term AI are sometimes posited  [33] .) Both of the above derive from some measure of continuity between the near, mid, and long terms. Continuity can be defined in terms of the extent of change in AI systems and related societal issues. If near-term AI techniques and societal dimensions persist to a significant extent through the end of the medium term (when long-term AI is built), then the medium-term AI hypothesis is likely to hold. The chronological duration of the medium term may be an important factor. Figure  1  includes a wide range of estimates for the start of the long term. If the later estimates prove correct, then the medium term could be quite long. A long duration would likely tend to mean less continuity across the near, mid, and long terms, and therefore less support for the medium-term AI hypothesis. That is not necessarily the case. One can imagine, for example, that AI just needs one additional technical breakthrough to go from current capabilities to AGI, and that it will take many decades for this breakthrough to be made. One can also imagine that the issues involving AI will remain fairly constant until this breakthrough is made. In that case, near-term techniques and issues would persist deep into the medium term. However, it is more likely that a long-lasting medium term would have less continuity and a larger dead zone period with no interest from either presentists or futurists. If AGI will not be built for, say, another 500 years, presentists are unlikely to take an interest. Figure  2  presents two sketches of the degree of interest that presentists and futurists may hold in the medium term. Figure  2a  shows a period of overlap in which both presentists and futurists have some interest; here, the medium-term AI hypothesis holds. Figure  2b  shows a dead zone with no overlap of interest; here, the medium-term AI hypothesis does not hold. Figure  2  is presented strictly for illustrative purposes and does not indicate any rigorously derived estimation of actual presentist or futurist interests. It serves to illustrate how presentists' degree of interest could decline over time and futurists' degree of interest could increase over time, with implications for the medium-term AI hypothesis. Figure  2  shows presentist/futurist interest decreasing/increasing approximately exponentially over time. There is no particular basis for this, and the curves could just as easily have been drawn differently. To sum up, assessing the medium-term AI hypothesis requires examining what medium-term AI techniques and societal dimensions may look like, and the extent of continuity between the near-, mid-, and long-term periods. \n The Intrinsic Importance of Medium-Term AI Thus far, the paper has emphasized the potential value of medium-term AI as a point of common interest between presentists and futurists. This \"consensus value\" will remain a major theme in the sections below. However, it is worth pausing to reiterate that medium-term AI can also be important in its own right, regardless of any implications for presentists and futurists. Assessing the extent to which it is intrinsically important requires having some metric for intrinsic importance. A detailed metric is beyond the scope of this paper. For present purposes, it suffices to consider that medium-term AI and its accompanying societal issues may be important for the world as it exists during the medium term. It is further worth positing that there may be opportunities for people today to significantly influence the medium term, such that the medium term merits attention today due to its intrinsic importance. With that in mind, the paper now turns to the details of medium-term AI and society. \n Medium-Term AI Techniques My own expertise is not in the computer science of AI, and so I can say relatively little about what computer science AI techniques may look like over the medium term. Therefore, this section serves as a placeholder to note that the space of potential medium-term AI techniques is a topic worthy of attention for those with the expertise to analyze and comment on it. \n Medium-Term AI Societal Dimensions While the medium-term societal dimensions of AI will, to at least some extent, depend on the capabilities of the medium-term AI techniques, it is nonetheless possible to paint at least a partial picture of the societal dimensions, even without clarity on the techniques. What follows is indeed a partial picture, shaped to a significant extent by my own areas of expertise. It aims to illustrate potential medium-term scenarios in several domains and discuss their implications for near-term and long-term AI and their prospects for bridging the presentist/futurist divide. \n Governance Institutions Governance institutions can be quite durable. For example, the United Nations was founded in 1945, and despite many calls for reform, the UN Security Council retains China, France, Russia, the United Kingdom, and the United States as permanent members. The \"P5 countries\" are an artifact of World War II that arguably does not match current international affairs, but changing the membership would require a consensus that is quite elusive. For example, a case could be made for adding Brazil and India, but then Argentina and Pakistan may object, so no change is made. Not all governance institutions are this ossified, but many of them are quite enduring. This continuity makes governance institutions a compelling candidate for the medium-term AI hypothesis. The near-term is an exciting time for AI governance. Institutions are now in the process of being designed and launched. Decisions being made now could have long-lasting implications, potentially all the way through the end of the medium term and the beginning of the long term. (It is harder to predict much of anything if and when AGI/ASI/HLAI is built, including the form of governance institutions. One attempt to make such predictions is Hanson  [34] .) One notable example is the International Panel on Artificial Intelligence (IPAI) and Global Partnership on AI (GPAI). The IPAI/GPAI has recently been proposed by the governments of Canada and France, first under the IPAI name and later under the GPAI name  [35, 36] . Documents on the IPAI/GPAI emphasize issues that are relevant in the near term and may continue to be relevant through the medium term. One set of issues listed for illustrative purposes is: \"data collection and access; data control and privacy; trust in AI; acceptance and adoption of AI; future of work; governance, laws and justice; responsible AI and human rights; equity, responsibility and public good\"  [35] . The documents published on the IPAI/GPAI give no indication of any focus on long-term issues relating to AGI. (The future of work could arguably classify as a long-term issue.) However, the IPAI/GPAI may nonetheless be relevant for the long term. If the IPAI/GPAI takes hold then it could persist for a long time. For comparison, the Intergovernmental Panel on Climate Change (IPCC) was formed in 1988 and remains an active and important institution. The IPAI/GPAI follows a similar model as the IPCC and may prove similarly durable. Additionally, while long-term issues are not featured in the early-stage documents that have thus far been published on the IPAI/GPAI, that does not preclude the IPAI/GPAI from including long-term issues within its scope once it is up and running. Whether long-term issues are included could come down to whether people interested in the long-term take the initiative to participate in IPAI/GPAI processes. Indeed, one of the most thoughtful discussions of the IPAI/GPAI published to date is by Nicolas Miailhe  [37]  of The Future Society, an organization explicitly working \"to address holistically short, mid and long term governance challenges\" in AI  [38] . Such activity suggests that the IPAI/GPAI could be an institution that works across the range of time scales and persists significantly into the future. \n Collective Action An important dynamic for the societal impacts of AI is whether AI development projects can successfully cooperate on collective action problems: situations in which the collective interest across all the projects diverges from the individual interests of the projects. Collective action has been a significant theme in discussions of long-term AI, focused on the prospect of projects cutting corners on safety to be the first to achieve important technological milestones  [32, 39] . Collective action problems can also arise for near-term AI. One near-term concern is about military AI arms races  [40]  (though this concern is not universally held  [41] ). Social science research on collective action problems identifies three broad classes of solutions for how to get actors to cooperate: government regulation, private ownership, and community self-organizing  [42] . Each is worth briefly considering with an eye toward the medium term. Government regulation is perhaps the most commonly proposed solution for AI collective action problems. While some proposals focus on domestic measures  [43] , global regimes may be favorable due to AI being developed worldwide. This is reflected in proposals for international treaties  [44]  or, more ambitiously, global governance regimes with broad surveillance powers and the capacity to preemptively halt potentially dangerous AI projects through the use of force  [45] . This more ambitious approach may be theoretically attractive in terms of ensuring AI collective action, though it is also unattractive for its potential for abuse, up to and including catastrophic totalitarianism  [46] . Regardless, in practice, an intrusive global government is very likely a nonstarter at this time and for the foreseeable future, probably into the medium term. Nations are too unlikely to be willing to cede their national sovereignty to a global regime, especially on a matter of major economic and military significance. (Perhaps some future circumstances could change this, but the desire to preserve sovereignty, especially from rival and adversarial states, has been a durable feature of the international system.) Even a more modest international treaty may be asking too much. Treaties are difficult to create, especially if universal international consensus is needed (for example, because AI can be developed anywhere), and when access to and capability with the technology is unevenly distributed across the international community (as is very much the case with AI; for general discussion of emerging technology treaty challenges, see  [47] ). Instead, government regulations are likely to be more modest, and play at most a partial role in facilitating collective action. Whatever it is that governments end up doing, there is strong potential for institutions that are durable across the medium term, as discussed in Section 6.1. Private ownership is commonly used for natural resource management. An entity that owns a natural resource has an incentive to sustain it and the means to do so by charging users for access at a sufficiently high fee. Private ownership schemes are difficult to apply to AI software due to the difficulty of restricting access. Hardware may offer a more viable option because hardware manufacturing facilities are geographically fixed and highly visible sites of major industrial infrastructure, in contrast with the ephemerality of software (For related discussion, see  [48] ). Hardware manufacturing is also typically privately owned  [49] . AI collective action could conceivably be demanded by the manufacturers, especially the select manufacturers of the advanced hardware used in the most capable AI projects. However, the benefits of AI collective action are experienced by many entities, and therefore would predominantly classify as externalities from the perspective of hardware manufacturers, in the sense that the benefits would be gained by other people and not by the manufacturers. This reduces the manufacturers' incentives to promote collective action and likewise reduces viability of private ownership schemes for AI collective action. Nonetheless, to the extent that hardware manufacturing can play a role, it could be a durable one. Hardware manufacturing is led by relatively durable corporations including Intel (founded 1968), Samsung Electronics (founded 1969), SK Hynix (formerly Hyundai Electronics, founded 1983), and Taiwan Semiconductor Manufacturing Company (founded 1987). These corporations are likely to remain important over medium-term and potentially also long-term time periods. Community self-organizing for AI collective action can be seen in several important areas. One is in initiatives to bring AI developers together for promoting ethical principles. The Partnership on AI is a notable example of this. Importantly, the Partnership has recently welcomed its first Chinese member, Baidu  [50] . This suggests that its emphasis on human rights (partners include Amnesty International and Human Rights Watch) will not limit its reach to Western organizations. Another area is in the collaborations between AI projects. For example, Baum  [31]  documents numerous interconnections between AGI projects via common personnel and collaborations, suggesting a cooperative community. Community self-organizing may lack the theoretical elegance of government regulation or private ownership, but it is often successful in practice. Whether it is successful for AI remains to be seen. AI community initiatives are relatively young, making it more uncertain how they will play out over the medium and long term. \n Corporate AI Development The financial incentives of for-profit corporations could become a major challenge for the safe and ethical development of AI over all time periods. How can companies be persuaded to act in the public interest when their financial self-interest points in a different direction? This is of course a major question for many sectors, not just AI. It is an issue for AI right now, amid a \"techlash\" of concerns about AI in social media bots, surveillance systems, and weaponry. It could also be an issue for AI over the mid and long term. With regards to long-term AI, Baum  [31]  (p. 19) introduces the term \"AGI profit-R&D synergy\", defined as \"any circumstance in which long-term AGI R&D delivers short-term profits\". If there is significant AGI profit-R&D synergy, then it could make AGI governance substantially more difficult by creating financial incentives that may not align with the public interest. AGI profit-R&D synergy concerns long-term AI, but it is inherently a medium-term phenomenon because it would occur when AGI is being developed. Assessing the prospect of AGI profit-R&D synergy requires an understanding of the technical computer science details of AI as it transitions from the medium term to the long term, which is beyond the scope of this paper. If the medium-term details have any sort of close relation to near-term AI, that could constitute a significant strengthening of the medium-term AI hypothesis. If AI companies' financial self-interest diverges from the public interest, how would they behave? Ideally, they would act in the public interest. In some cases, perhaps they will, especially if they are pushed to do so by people both within and outside of the companies. Unfortunately, experience from other sectors shows that companies often opt to act against the public interest, as seen, for example, in pushback by the tobacco industry against regulations aimed at reducing cancer risk; by the fossil fuel industry against regulations aimed at reducing global warming risk  [51] ; and by the industrial chemicals industry against regulations aimed at reducing neurological disease risk  [52] . It is worth considering the prospect that AI companies may (mis) behave similarly. It has been proposed that AI companies could politicize skepticism about AI and its risks to avoid regulations that would restrict their profitable activities  [53] . This sort of politicized skepticism has a long history, starting with tobacco industry skepticism about the link between cigarettes and cancer and continuing to this day with, for example, fossil fuel industry skepticism about global warming. One mechanism for this work is to fund nominally independent think tanks to produce publications that promote policies and issue stances consistent with the companies' financial self-interest. Some attributes of this pattern can be seen in recent writing by the think tank the Center for Data Innovation, which warns of an \"unchecked techno-panic\" that is dampening public enthusiasm for AI and motivating government regulations  [54] . The extent to which this constitutes a case of politicized skepticism is unclear. Specifically, the extent of the Center for Data Innovation's industry ties could not be ascertained for this paper. Likewise, it is not the intent of this paper to accuse this organization of conflicts of interest. It is also not the intent to claim the opposite-that there is no conflict of interest in this case. (Indeed, the presence of conflict of interest is often hidden-hence, industry firms fund the work of nominally independent think tanks instead of doing it in-house.) Instead, the intent is merely to provide an example that illustrates some aspects of the politicized skepticism pattern. Importantly, whereas the proposal of politicized AI skepticism focuses on skepticism about long-term AI  [53] , the skepticism of the Center for Data Innovation is focused on the near term  [54] . Likewise, the pattern of politicized AI skepticism has the potential to play out across time periods, especially when there is significant profit-R&D synergy and concurrent prospects of government regulation. \n Militaries and National Security Communities Advanced militaries have long been involved with the forefront of AI in their capacity as research funders and increasingly as users of the technology. The advanced militaries also often have substantial technical expertise, as do the broader national security policy communities that they interface with. Furthermore, militaries are sometimes tasked with operations and planning across a range of time periods, and national security communities are likewise sometimes oriented toward thinking over such time periods. This is seen in the example cited above of the plan for the B-52H bomber to remain in service through the 2050s. It thus stands to reason that advanced militaries and national security communities could be interested in medium-term AI and its links between the near term and long term. There is already some military attention to AGI. One clear example is the JASON report Perspectives on Research in Artificial Intelligence and Artificial General Intelligence Relevant to DoD  [55] , which was produced in response to a US Department of Defense query about AGI. Another is the excellent book  [19] , which features a full chapter on AGI and ASI. Both publications provide nuanced accounts of long-term AI. The publications are produced by analysts who are especially technically savvy and are not representative of the entire military and national defense communities. Nonetheless, they are among the publications that people in these communities may consult and do indicate a degree of awareness about long-term AI. As documented by Baum  [31] , there are some current AGI R&D projects with military connections. Most of these are US academic groups that receive funding from military research agencies such as DARPA and the Office of Naval Research. One is a small group at the primary national defense research agency of Singapore. None of them have any appearance of the sort of major strategic initiative that is sometimes postulated in literature on long-term AI  [33] . Given the current state of affairs, it is highly likely that advanced militaries and national security communities will be engaged in AI throughout the medium term. That raises the question of their likely role. Despite common concerns within AI communities, as manifest for example in Google employee protest over Project Maven, militaries can actually be a constructive voice on ethics and safety. For example, a major theme of the  [55]  report is that what it calls the \"ilities\"-\"reliability, maintainability, accountability, verifiability, evolvability, attackability, and so forth\"  [55]  (p. 2) are a major concern for military applications and \"a potential roadblock to DoD's use of these modern AI systems, especially when considering the liability and accountability of using AI in lethal systems\"  [55]  (p. 27). Militaries are keen to avoid unintended consequences, especially for high-stakes battlefield technologies. It is also important to account for the geopolitical context in which militaries operate. Militaries can afford to be more restrained in their development and use of risky technologies when their nations are at peace. In an interview, Larry Schuette of the Office of Naval Research compares autonomous weapons to submarines  [19]  (pp. 100-101). Schuette recounts that in the 1920s and 1930s, the US was opposed to unrestricted submarine warfare, but that changed immediately following the 7 December 1941 attack on Pearl Harbor. Similarly, the US is currently opposed to autonomous weapons, and on the question of whether it will remain opposed, Schuette replies, \"Is it December eighth or December sixth\"? It follows that the role of militaries in medium-term AI may depend heavily on the state of international relations during this period. It stands to reason that the prospects for cautious and ethical AI development are much greater during times of peace than times of war. There is an inherent tension between pushing a technology ahead for strategic advantage and exercising caution with respect to unintended consequences, as is articulated by Danzig  [56] . Peaceful international relations tips the toward caution and can empower militaries and national security communities to be important voices on safety and ethics. \n Conclusions Parson et al.  [2]  argued that medium-term AI and its accompanying societal issues are important in their own right. This paper's analysis yields the same conclusion. For each of the issue areas studied here-governance institutions, collective action, corporate development, and military/national security-the medium-term will include important processes. In a sense, this is not much of a conclusion. It is already clear that AI is important in the near term, and there is plenty of reason to believe that AI will become more important as the technology and its applications develop further. What then of the presentist-futurist debate? This paper proposes the medium-term AI hypothesis, which is that there is an intermediate time period that is important from both presentists and futurist perspectives. With the near term defined in terms of feasibility and the long term in terms of capability, it follows that the medium-term AI hypothesis is more likely to hold if near-term AI techniques and societal dimensions persist to a significant extent through the end of the medium term, when long-term AI is built. To the extent that the hypothesis holds, attention to the medium term could play an important role in bridging the divide that can be found between presentist and futurist communities. The paper finds mixed support for the medium-term AI hypothesis. Support is strong in the case of AI governance institutions, which are currently in development and may persist through the medium-term, with implications for long-term AI. Support is ambiguous for AI collective action: government initiatives to promote collective action may play relatively little role at any time, private ownership schemes are difficult to arrange for AI, and community self-organizing has potential that might or might not be realized. Each of these three schemes for achieving collective action could potentially play out over near-and medium-term periods, with implications for long-term AI, but whether they are likely to is unclear. Regarding corporate AI development, a key question is whether near-to-medium-term AI technology could serve a profitable precursor to AGI, creating AGI profit-R&D synergy. Whether the synergy would occur is an important question for future research. Finally, advanced militaries and national security communities are already paying attention to AGI and are likely to remain active in a range of AI technologies through the medium term. While it is unclear whether military/national security communities will be important actors in the development of AGI, there is substantial potential, providing support for the medium-term AI hypothesis. In closing, this paper has shown that at least some important AI processes are likely to play out over the medium term, and that they will be important in their own right and from both presentist and futurist perspectives. The exact nature and importance of medium-term AI is a worthy subject of future research. To the extent that medium-term AI can be understood, this can point to opportunities to positively influence them, resulting in better overall outcomes for society. Funding: This research was funded by the Gordon R. Irlam Charitable Foundation. Figure 1 . 1 Figure 1.Estimates for when AI will reach superhuman capability (Baum et al.) [23]  and human-level capability (Sandberg and Bostrom, Müller and Bostrom, and Grace et al.) [24] [25] [26] . Shown are estimates for when the probability that the milestone is reached is 10% (lower mark), 50% (square), and 90% (upper mark). For each study, the median estimates across the survey participants are plotted. \n Figure 2 . 2 Figure 2. Illustrative sketches of presentist and futurist interest in the near, medium, and long term. (a) shows overlapping interest: the medium-term AI hypothesis holds; (b) shows a dead zone with no overlapping interest: the medium-term AI hypothesis does not hold. The sketches are strictly for illustrative purposes only. The phrase \"new forms of AI built\" is defined with reference to the definition of near-term AI in the main text.", "date_published": "n/a", "url": "n/a", "filename": "information-11-00290.tei.xml", "abstract": "There has been extensive attention to near-term and long-term AI technology and its accompanying societal issues, but the medium-term has gone largely overlooked. This paper develops the concept of medium-term AI, evaluates its importance, and analyzes some medium-term societal issues. Medium-term AI can be important in its own right and as a topic that can bridge the sometimes acrimonious divide between those who favor attention to near-term AI and those who prefer the long-term. The paper proposes the medium-term AI hypothesis: the medium-term is important from the perspectives of those who favor attention to near-term AI as well as those who favor attention to long-term AI. The paper analyzes medium-term AI in terms of governance institutions, collective action, corporate AI development, and military/national security communities. Across portions of these four areas, some support for the medium-term AI hypothesis is found, though in some cases the matter is unclear.", "id": "c49946d384f45e7077c30fe6e5ac3cd8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Christian P Janssen", "Linda Ng Boyle", "Wendy Ju", "Andreas Riener", "Ignacio Alvarez"], "title": "Agents, environments, scenarios: A framework for examining models and simulations of human-vehicle interaction", "text": "Introduction Within the transportation, automotive, and user interface research communities, there is occasional confusion as to what is implied by \"simulation\" or \"model.\" For example, the following are all false assumptions: a model or simulation implies tight control with no testing in a naturalistic environment, a model always involves simulating people or the traffic environment, and a concrete, falsifiable research question cannot be achieved without a model or simulation and testing in the real world. These false assumptions overlook the fact that researchers and practitioners in these fields have various approaches to modeling the agents in the car, the driving environment, and the scenarios under consideration of study. The different approaches and associated labels can create confusion as to which methods are most effective to examine specific research questions regarding human-vehicle interaction. The authors of this paper have used different types of simulations in driving studies and other domains, in part due to their different backgrounds in psychology, artificial intelligence (AI), safety science, design, and engineering. During a meeting in 2016  (Riener et al., 2016a) , the authors identified thatup until thenthey meant different things when talking about \"a simulation\" or \"a model\" and that each author held some incorrect assumptions about these terms. To move the field forward and to avoid these mistakes, there is a need for (a) more specific terminology to guide the scientific and practical dialogue and (b) a common framework in which each research effort can be mapped and compared. Such a framework is needed given the interdisciplinary focus of transportation research, in which different disciplines (e.g., engineering, design, social sciences, safety sciences, AI) might also use different terminology. In this paper, a classification framework for examining models and simulations of human-vehicle interaction is introduced. Within the domain of human-vehicle interaction, simulations can happen along three dimensions: agents, environments, and scenarios. These are illustrated in Fig.  1 . Within each of these dimensions, there can be multiple styles or approaches of simulation and modeling. Each of these approaches differs in the extent to which they truly emulate the realistic performance of the agent, the environment, or the driving scenario. The framework enables researchers to map their choice of research methods and tools and compare with other literature, as well as identifying areas of effort that could advance the field. \n Intended contribution and audience A first contribution of this paper is to explicitly define the differences between three dimensions of modeling: agents, environments, and scenarios. This is achieved by describing what is entailed in each dimension. By separating out these three broad dimensions, it becomes clear that the aforementioned assumptions (in the introduction) are flawed, as each assumption only considers a subset of the dimensions of modeling. Being more explicit about these differences provides the field of transportation research with more precision. Such precision is needed to compare results across studies and to aid replication of study results and implementation of ideas and results in actual transportation systems. A second contribution of this paper is to identify areas that are as-yet unexplored or underrepresented within the transportation research community. This is achieved by describing the studies completed for various combinations of simulated agents, environments, and scenarios. In studies where either the environment is simulated or the scenario is constrained, but not both, there is the possibility for future research that allows for tighter control where needed, while also providing insights on a wider, open-ended set of human behaviors. The intended audiences of this paper are researchers and practitioners who are consumers of these simulations, as well as industry and regulatory agencies. For all these parties, the framework provides a way to classify studies and to decide upon the best research method for new studies: what type of simulation is needed? Although the discussion within this paper mostly focuses on human-(motorized) vehicle interaction, simulation is also used in other transportation domains such as trains and flights. Having the three dimensions distinguished is not only important for academic purposes, but also for product development and the testing cycle (e.g., V-Model, Scrum)  (Friedrich et al., 2008) .  1  Testing products with real users (agents), in real environments (the world), with actual everyday scenarios provides the highest ecological validity. However, that might also come with potential disadvantages such as (1) weak reproducibility and generalizability due to changing sensor data, weather, or participants' cognitive states, (2) the impossibility of testing under extreme conditions and, (3) its negative impact on release cycle times. A possible alternative that might help to reduce field testing while ensuring functional safety and reliability is performing safety assessment by stochastic virtual simulation  (Kompass et al., 2015) . Still, a pure virtual test as suggested in the past by for example Google  (Harris, 2014)  is barely able to represent reality with its overwhelming complexity, for instance because of performance differences of virtual sensors, lack of realism and flexibility of driver models and shallow modulation of environment and surroundings. That's why (California's) regulations still stipulate autonomous vehicles must be tested under \"controlled conditions\" (e.g., a test track or temporarily closed public road  Harris, 2014) . The automotive industry is searching for a new standardized testing process  (Kompass et al., 2015)  to cope with the issues highlighted before. Open questions in this regard are if and to which extent real field trials can be substituted by various levels of virtual simulation  (Riener, 2010) , how to seamlessly integrate different validation methods (e.g., virtual simulation, driving simulator tests, X-in-the-Loop simulation), and, how to guarantee reproducible test conditions. To counteract, tests can adjust the real and virtual parts in various dimensions of the test setup (agents, environments, scenarios). Such adjustments create a \"mixed-reality testing framework\" (see also,  Riener et al., 2016b) , which is explicit about which components (agents, environments, scenarios) are simulated or not. The  framework that is put forth in this paper, and which is described next, thereby helps to better position such mixed-reality efforts. \n Classification framework for (models and simulations of) humanvehicle interaction The framework distinguishes three dimensions that can be examined in studies of human-vehicle interaction: agents, environments, and scenarios. Each dimension can involve some form of simulation or modeling, and will now be discussed in turn. \n Dimension 1: agent An agent is 'anything that can be viewed as perceiving its environment through sensors and acting upon that environment through actuators'  (Russell and Norvig, 2003, page 32) . This general definition can be applied to both humans and artificial (non-human) entities, and therefore also to simulations and models of humans. Simulations of human agents are typically assumed to be created by software, but can also rely on hardware components (i.e., in embodied, situated robots  Pfeifer and Scheier, 2001) . The reasons for modeling human behavior can differ, but for the traffic domain typically include: a need to determine the operational domain of the system, a need to influence system or user behavior under conditions that might be risky or unsafe for humans, a need to benchmark human behavior against alternative theoretical predictions of behavior, or as a way to ground system behavior in theory. In the driving context an agent is in charge of perception, judgement and actuation on the driving task or a subset of it. At a broad level, an agent in a vehicle is either human, or artificial. However, within the simulated artificial (non-human) agent classes many distinctions can be made. Three dimensions are discussed next: (A) whether accurate simulation of the human's internal thinking process matter, (B) level of abstraction (or: what part of human behavior or thinking is of interest to the modeler), and (C) modeling approach. \n Does accurate simulation of a human's thinking process matter? A first differentiation is whether simulating the details of the human's internal thinking process matter. Some models might not care about mimicking human behavior and thinking at all. For example, when implementing Society of Automotive Engineers (SAE) level-5  (SAE International, 2018) , the vehicle itself makes automated (or autonomous) decisions, but might not always make the same decisions as humans, or not be at fault to human biases and limitations (e.g., fatigue). Other models might only approximate a small subset of human thought or behavior; for example models that test the impact of random human actions  (Thimbleby, 2007) , or models of traffic flow that only focus on crude estimates of perception and action  (Hoogendoorn and Bovy, 2001) . For models where simulation of human thought and behavior are more crucial, there are gradations in level of detail, ranging from models for rapid prototyping and testing of interfaces  (John et al., 2004; Salvucci et al., 2005) , to testing the effect of specific theories such as strategies of task interleaving (e.g.,  Brumby et al., 2018; Janssen et al., 2012; Jokinen et al., 2020 online first; Kujala and Salvucci, 2015; Lee and Lee, 2019) , to developing detailed broader theories of human thinking (e.g., cognitive architectures  Liu et al., 2006; Salvucci and Taatgen, 2011; Zhang and Hornof, 2014) . In other words: creating an artificial agent can be seen in line with Turing's imitation game  (Turing, 1950) : the goal is to have the agent achieve some behavior, but the details of how this behavior was achieved by the agent do not matter to every modeler. In the classification of agents so far, only the extremes were classified: an agent is either human or artificial. However, due to the advent of semi-automated vehicles, less clear cut examples in between these extremes might emerge. Artificial agents might be in control of part of the driving task, while human agents are in control of other parts. And at times it might not be so clear to a human whether an agent is human or artificial (cf. Turing's imitation game  Turing, 1950) . It is not yet clear how to best classify these in between states, therefore the focus in this paper is on the extreme ends first. \n Level of abstraction A second classification, when trying to model human behavior through an artificial agent, is the level of abstraction. In essence, the question here is: what part of human behavior or thinking is of interest to the modeler? David McClelland phrased it as follows: [cognitive models] \"are explorations of ideas about the nature of cognitive processes. In these explorations, simplification is essentialthrough simplification, the implications of the central ideas become more transparent\"  (McClelland, 2009) . The quote by McClelland beautifully captures that one model of human behavior or thought (so far) cannot capture all of the complexity of human thinking, but instead requires focus. Various frameworks have been proposed to adjust focus systematically to the objective of the model at hand. Two are discussed next: Marr's levels of abstraction  (Marr, 1982 ) and Newell's timescales of action  (Newell, 1990) . Marr  (Marr, 1982)  proposes to approach human thinking from three levels: computational, algorithmic, and implementation. These levels require an increasing level of detail (see also special issue,  Peebles and Cooper, 2015) . Agent models of driving related tasks occur at each level. Computational models specify why specific behaviors might be appropriate or efficient, without specifying what is done by an agent to achieve this. For example, such models might concern why multitasking in the car can sometimes be experienced as efficient by the user, even though objectively it is distracting  (Janssen et al., 2012) , or why it might be efficient to forget information in general  (Anderson and Schooler, 1991) . Algorithmic level models specify what strategies people use to achieve a goal, without specifying why these are used (computational question) or how this is implemented in the brain. Examples are models of visual attention in multitasking scenarios (e.g.,  Salvucci and Taatgen, 2011; Salvucci et al., 2005; Lee and Lee, 2019; Zhang and Hornof, 2014) . Finally, implementation level models describe how the algorithms are physically realized in the brain, without focusing on what task is achieved (algorithmic) and why (computational). Although such detailed implementation level models are available of cognition in more controlled tasks (e.g.,  Eliasmith, 2013) , to the best of the authors' knowledge there are not yet detailed implementation level models that implement multiple facets of driving. The level of abstraction influences the type of questions the models can address: why, what, or how behavior is realized. Another way of classifying the level of abstraction is using Newell's time scales of action  (Newell, 1990) . This framework requires one to specify at what time scale the behavior is modelled and therefore also what type of data can be used to validate the model (see also  Anderson (2002)  and Chapter 1 of  Salvucci and Taatgen (2011) ).  Newell (1990)  distinguishes four bands, which again are all relevant for specific aspects of driving: Biological (actions over ms, e.g. brain processes underlying ms level differences in braking response times,  Gray, 2011; Lahmer et al., 2018) , cognitive (actions over seconds, such as how eye-movements affect steering movements,  Salvucci and Taatgen, 2011; Kujala and Salvucci, 2015; Lee and Lee, 2019) , rational (actions over multiple seconds to minutes, e.g., how to best interleave attention,  Janssen et al., 2012; Janssen et al., 2019c) , and social (actions over multiple minutes to years, such as development of trust,  Forster et al., 2018) . Again, the time scale of a model determines what types of (research) questions can be addressed and also what type of data is needed to validate such theories, as these need to be in sync with the model: milliseconds (e.g., EEG, fMRI), seconds (e.g., eye-tracking, steering actions), minutes (e.g., behavioral choices), or hours (e.g., duration of travel, fuel efficiency) (see also chapter 1 in  Salvucci and Taatgen, 2011) . Other frameworks for classifying the abstraction level of the model of an agent might also exist. Yet, the core question is: through which \"lens\" is one looking at human behavior and thought. Do minor changes over milliseconds in the physical implementation of an (artificial network) model matter (i.e., implementation level, biological band), or is there a need to understand why behavior at a societal level changes over years  (i.e., computational level, social band) . Whatever the focus is, some simplifications are needed to allow focus of the research  (McClelland, 2009) . What is important is that these simplifications are not made within the area that is of interest most. \n Modeling approach A third way of classifying models is in the modeling style or approach that is taken. For example, is it mostly conceptual in nature (e.g.,  Janssen et al., 2019a; Janssen et al., 2019d; Wickens, 2008) , describing a theory of a (mechanistic) process (e.g.,  Salvucci and Taatgen, 2011; Lee and Lee, 2019; Zhang and Hornof, 2014; Brumby et al., 2018) , or a (machine learning) data-driven model (e.g.  Fridman et al., 2018) ? These three rough classes (conceptual, process, data-driven) rely increasingly less on theory and more on available data, and can all be relevant for driving models. There is a large breadth and depth in modeling styles available for theoretical studies and applied work  (Oulasvirta, 2019) . \n Summary of modeling the agent and further refinements To summarize, models of humans can be captured under the general label of \"agent.\" Agent models can be classified in various ways of which three options were discussed. Although within each of these classification schemes specific classes were identified as well, sometimes models are a blend. For example, models might be able to tackle all three of Marr's levels (e.g.,  Lewis et al., 2014) , address behavior over multiple of Newell's time-scales (e.g.,  Janssen et al., 2012) , or combine datadriven (machine learning) methods with theoretically-driven process models (e.g.,  Anderson et al., 2016) . In driving situations where part of the driving task is automated (e.g., SAE levels 2,3, SAE International, 2018), there are situations where both a human agent and an artificial agent (i.e., the car's internal reasoning system) are involved in aspects of the driving task. In that sense, the expectation of the authors is that research in the years to come will focus more on shared control between human and artificial agents. In modeling the artificial agent that controls the car, many of the same considerations as were mentioned above hold. These techniques can range from simplified state machines with tight control-loops to more conceptual (flexible) models inferred from naturalistic data behaviors using machine learning. State of the art approaches to modeling an artificial agent are approaching the performance of humans at particular driving tasks by means of deep neural network architectures. \n Dimension 2: environment When environments are discussed in the transportation research communities, the environment can be considered as \"the world\" which is being modelled or the model which is being presented. Researchers and practitioners often draw a sharp distinction between 'laboratory' or 'simulated' on the one hand, and 'on-road' or 'real' or 'open-ended' driving experiments on the other hand, but do not do a lot to explicate the environment further. At first sight, one might assume that testing in an on-road study provides the richest environment for a study, and therefore to provide the most detailed insight about the human behavior. However, this is not necessarily the case. Whether the richness of the on-road driving environments (i.e., the track or roads on which the vehicle is driving) is captured depends heavily on the model of the environment that is made from the data captured by an instrumented car  (Brackstone et al., 1999) . In an extremely limited instrumentation environment, for example, there might only be one camera pointed at the driver or out the window, and the model of the environment after the fact is very sparse. A richer model of on-road drives may capture the in-cabin environment, the traffic surrounding the car, the GPS, and the data from the CAN Bus of the car. The important thing is that the model enables an understanding of the relevant aspects of the environment for analysis. Limitations to the sensors and the internal model of the simulated environment can hinder the ability to address a research question because of missing contextual cues. By contrast, in a virtual driving environment, the environment is specified by the driving simulation. Even within the virtual environment, the model has variations; passing traffic can be randomly generated, for example, or specified exactingly, car by car. Another consideration for modeling virtual environments has to do with whether the virtual environment is completely fictional (e.g., driving on a different planet than earth), or if it is a virtual replica of a real-world environment; the latter better allows for translational experiments that compare virtual and real world performance for similar driving scenarios  (Blaauw, 1982) . \n Dimension 3: scenarios With the agent and the environment identified, one can then specify the scenarios for testing. If the simulated environment can be seen as \"the world\", then the scenario can be considered as \"the way one moves through the world\". That is: what types of situations are encountered or not? The spectrum of scenarios that are being considered in the model or simulation can range from unconstrained where nothing in the environment (real or virtual) is manipulated to highly constrained, where everything that the human user observes was somehow designated by the researcher. This often relates to the operational design domain  (SAE International, 2018)  or the context in which the study is being examined. For example, given any specific world (naturalistic or virtual), one might be interested in how a system and agent act in a scenario where there is fog, or a specific construction works scenario. In more unconstrained (open-ended) scenarios, specific scenarios will be encountered (e.g., fog, construction works) but only as they naturally occur during a drive. Most naturalistic driving studies such as SHRP2 (The National Academies of Sciences Engineering and Medicine, 2019) and UDRIVE (Udrive Consortium, 2019) are designed to be more toward the unconstrained end of the spectrum. The researcher does not constrain the destination, driving behavior, or performance of the user. In other words, the scenarios that people encounter are left open-ended. The models behind naturalistic driving studies are typically designed for observation only, without any intervention. The participants know that their vehicles are instrumented, and, as such, might drive more carefully; nevertheless, the environments (or: the world) that they drive through are not affected by any research interventions, and so the scenarios that occurwhether they are everyday traffic, distracted driving, or near missesare natural. While there are many studies that can be conducted in a real world setting, they are not all 'unconstrained'. Hence, the distinction between the environment and scenario. One might have a fully functional car of which high level of detail can be measured (i.e., high on the 'real' dimension of the environment), but testing is only intended under specific conditions such as construction works, or under conditions of rain (i.e., highly constrained). There are also projects in between these extremes. For example, Volvo's \"Drive Me\" project  (Victor et al., 2017)  was intended to have everyday drivers experience driving in a car that has higher levels of automation, with some in-car technology achieving SAE-level 4 automation on specific roads  (SAE International, 2018) . Although the project has since scaled back in ambition  (Bolduc, 2017) , the original study was intended to include a fully operational vehicle with high level of data collection and instrumentation (i.e., high realism on the environment scale). However, the automated technology within the vehicle could only operate under specific operational design domains, thereby limiting the scenarios under which researchers could study human behavior in automated vehicles. Although the aforementioned might seem to imply that open-ended scenarios can only be run in naturalistic environments, this is not the case. Simulated environments can also run relatively open-ended, unconstrained studies, depending on how open-ended and realistic the environment is modelled in the simulator and to what extend it allows freedom in actions for the driver. If the simulator has for example a detailed map of all roads in a city (i.e., a \"microworld\"), and the car has almost all the functionality of a real car, then a wide scala of open-ended scenarios might be possible to simulate. \n What is a \"controlled\" study? One of the things that the classification framework (Fig.  1 ) makes clearer is the different ways that a \"controlled study\" is controlled. Each dimension (agent, environment, scenario) can have its own level of control. To make this even more specific, a distinction can be made between different degrees of regulation and fidelity for the agent, environment, and scenario. \n Regulation What is called \"regulation\" is often referred to as \"manipulation\" or \"control\" in experimental settings; it is the degree to which different participants experience the same thing. Regulation can be applied to the agent, the environment, and the scenario. \n Regulation of environment and scenario The most obvious coupling of regulation is perhaps with environment and scenario. Within the environment and scenario, there can be a high degree of variation in control, even within laboratory studies. Simulation environments are often associated with high-degrees of regulation. On the far end, in simulated automated driving scenarios, a driving simulation environment can be so controlled that every single participant experiences exactly the same setting, with exactly the same cars passing at exactly the same time in the simulated experience (i.e., a highly regulated scenario). In such tightly regulated studies, the only variations might come from human action such as the human's eye-gaze or steering actions. Although these studies are appropriate for testing parameters of human behavior and thought (e.g.,  Janssen et al., 2012; van der Heiden et al., 2019) , they are less generalizable to everyday traffic scenarios. Therefore, in the more typical laboratory driving simulation studies, other vehicles in the simulation environment around the participant vehicle are spawned stochastically, so that there is some bounded variation in participant experience; any experiment in which the participant drives introduces yet another source of variation. On the far less regulated end, experimenters such as  Feuerstack et al. (2016)  use the simulation environment as a \"theater\" in which drivers can collaborate to play out the interactions they have on the road improvisationally  (Schindler et al., 2013) . In on-road research, there is also more or less regulation that is possible. While it is not usually possible to make it so that every participant experiences exactly the same experience, on-road experiments can feature set courses, where every participant experiences the same roads, in roughly the same times of day (like,  Baltodano et al. (2015) ), or set situations, where every participant experiences the same scenario (for example, commuting home) even if they have wholly separate routes, like  Zafiroglu et al. (2012) . In other words, regulation, manipulation and control can be exerted on both the environment (i.e., what types of vehicle interactions are allowed) and on the scenarios that are experienced by the participant. Control can be loose or tight on none, one, or both of these dimensions. \n Regulation of agents Regulation can also be applied to the agent, especially for studies with human agents. A first decision on regulation is how the study participants are sampled. On the very tightly regulated end, participants might come from a very specific population, such as psychology undergraduate students. Tight regulation yet more variation in human behavior might be observed when participant statistics meet those of a specific driving population (e.g., match the national ratio male-female drivers, or distribution of drivers' ages, as in, van der  Heiden et al., 2019) . Finally, regulation might be loose when participants are gathered in a less structural way (e.g., opportunity sampling). Sampling might be particularly important in cases where the behavior might be tied to characteristics of the sample -for example years of driving experience, familiarity with local cultural or societal norms or expectations, experience with semi-automated vehicles, or experience with particular road configurations (e.g., driving on the left-side or right-side of the road). A second decision on regulation is whether the participants are asked to perform with or without manipulation of their cognitive state. For example, participants might be performing after tight administration of alcohol, drugs, or other substances (e.g.,  Martin et al., 2013; Veldstra et al., 2012; Wester et al., 2010) . Or participants might be sleep deprived (e.g.,  Eoh et al. (2005) , for models see e.g.  Gunzelmann et al. (2011)) , or be manipulated into a specific affective state  (Jeon, 2015) . A third decision on regulation of agents is how free the agents are in their actions and how participants are instructed. On one extreme end, naturalistic driving studies (e.g., The National Academies of Sciences Engineering and Medicine, 2019; Udrive Consortium, 2019) might not place any constraints on the driving task: participants drive where and when they want to drive. On the other extreme end, the user's task might be very narrowly defined. This might be akin to for example Fitts' law experiments, in which participants are instructed to make specific ballistic movements over and over  (MacKenzie, 1992) . In between these extremes are studies in which some overarching criteria, such as a user's general priority, is manipulated (e.g., safe driving or fast performance of a secondary task while driving,  Brumby et al., 2011; Janssen et al., 2012) . In other words, regulation can also be applied to the agents of the task, and might be exerted implicitly due to the sampling of participants or the instructions for the task. Although regulation was mostly discussed for human agents, similar concerns apply when human behavior is captured in artificial agents: are these models based on data sets with a wide variety of human participants, or only a tightly regulated sample in a tightly regulated task? \n Fidelity Fidelity has to do with the level which the simulation or model of the agent, environment, or scenario mimics real-world or anticipated futureworld drivers and driving situations. In the lab, the fidelity of simulated environments can range from low, where the scenarios are observed from a bird-eye view, and the operator controls the vehicle using a keyboard, to very high, where drivers are fully immersed in the driving environment. The low fidelity environments are appropriate if the primary goal is to represent strategic level decisions. The more typical driving simulation environments have much higher fidelity and feature different degrees of immersion, where a full-vehicle chassis with a motion base delivers the experience most like driving on the road. Open source game engines like the Unity and Unreal Engines that enable development of rich-graphics simulators such as CARLA  (Dosovitskiy et al., 2017)  has enabled high fidelity driving simulation tools to be more readily accessible to a broader range of researchers and designers. In on-road environments, the fidelity is usually pretty high with real road, weather, and lighting conditions, but the location of the testing environment (for example, on a test track vs on (closed) public roadways) can affect the fidelity of the driving task. For the fidelity of the agent, one can consider artificial agents and human agents. For artificial agents, fidelity can again differ between modeling approaches. Automated driving systems have traditionally employed low-level perception-controllers such as PID to perform driving tasks. These models typically lack flexibility and performance when compared to human agents in variable environments. However richer, higher-level driving automation models are being developed using machine learning techniques that rival or even outperform human drivers  (Grace et al., 2018) . Concurrently, when modeling human agents and their thought processes, some approaches care about the fine-grained details of the cognitive process (e.g.,  Zhang and Hornof, 2014)  while others only use approximations of human perception and action (e.g.,  Hoogendoorn and Bovy, 2001) . For human agents, in some sense the fidelity is \"high\": an actual human performed the task. However, depending on how the human sample and the behavior of the sample was regulated, behavior of these agents might be more or less representative for a wider population of humans and a wider set of human cognitive and affective states. Another aspect to consider in relation to fidelity is the method and process of data collection. Even in a study with a high fidelity set-up (i.e., human agents, driving in the real world, in an unconstrained scenario), the reliability and usefulness of the study outcomes may be negatively impacted if the data collection protocol was not carefully designed. It is therefore crucial to understand the limitations of your equipment in terms of quality, accuracy, frequency (and resolution) of sampling, and the reliability of the measurement as a proxy for the intended variable (s) of interest. Take for example the fidelity of data collection on a human agent. Let's say a study is interested in capturing a cognitive aspect of the human driver using the relationship between eye movements and vehicle steering movements (actions over seconds cf.  Newell, 1990) . In such a study, eye gaze data would need to be collected at a level that can detect differences within seconds. Further, the eye-tracking device will need to be calibrated and checked for stability and tracking before data collection on each participant. If such protocols are not in place, any inferences made from the data would be incorrect. This becomes an even larger concern when methods and tools are used that have not been independently validated or for which the underlying algorithms are not known. For example commercial devices that can predict \"alertness\" based on physiological measures may have limited validity if the underlying algorithms cannot be shared or verified. In such cases, the conclusions drawn from such tools would be questionable. Data quality also impacts the dimensions of environment and scenario. For these dimensions, the sensors (or simulation code) might also not register relevant information (e.g., what other traffic is on the road), or not register it frequently and detailed enough (e.g., estimate distance to other cars in increments of 10 cm, whereas increments of 1 cm are needed for analysis) or reliable enough (e.g., when a sensor of the car is obscured). The interface between the data, systems, applications, software and platforms are also important to consider. A seemingly small detail or choice in the set-up of a study can have large implications in the inferences that are made. For example, if the eye-tracking glasses shifted during the study, one might conclude that a participant did not pay sufficient attention to the road, whereas this conclusion was reached due to measurement error. Similarly, if a simulation was not calibrated correctly to identify the distance between the test vehicle and surrounding vehicles, then one might incorrectly conclude that an appropriate distance was held at all times. If these results are not further tested (e.g., by formalizing them in computer simulations of underlying cognitive process, or testing them in replication studies), then the wrong conclusions can steer the larger field in the wrong direction. For example, incorrect results can lead to suggesting designs or software that are not effective or based on incorrect principles (e.g., assuming that a vehicle holds appropriate distance to other vehicles, whereas it does not). 4. Actual, virtual, and mixed reality through simulation on different dimensions: where are the research gaps and opportunities? Using the three dimensions (agents, environments, scenarios), one can now more clearly position research that simulates none, one, two, or three of these dimensions. Studies where none of the dimensions is simulated can be considered \"actual reality\", studies were all dimensions are simulated can be considered \"virtual reality\", and those where at least one but not all dimensions are simulated can be considered \"mixed-reality\". \n Collaboration between human and artificial agents As was already mentioned in the section on agents, one important emerging area is that where human and artificial agents interact in a single environment. This is the case for humans that interact with semi-automated technology (e.g., SAE levels 2,3, SAE International, 2018). In these instances, the reasoning system behind the automation can be considered as an artificial agent that senses and acts upon the environment, but also depends on input from the human. Such environments require a good understanding of the mental model of the human and the mode of the vehicle  (Janssen et al., 2019a) . Another area where human and artificial agents interact is in studies of dyadic interaction. In the bottom of Fig.  1 , such studies are placed in the bottom-right quadrants of studies with human agents (left) and studies with artificial agents (right). In dyadic interaction studies, two or more people are involved in a simulated world, and can see each other's actions through an avatar (or other car) that moves around in their shared virtual world. This form of interaction involves both human agents, but also a virtual representation of the agent, therefore positioning this work both in the cluster of human and artificial agents. A conceptual example of such a study is for example described in  (Doric et al., 2016) . The remainder of this section will explicitly discuss studies in which there is either a human agent, or an artificial (simulated human) agent. \n Simulated scenarios and/or environments with human agents The first consideration is of cases where human agents are involved in the driving (e.g., bottom-left of Fig.  1 ), but either the scenario or the environment might be simulated or constrained. Perhaps one holy grail of research is to observe driving in real environments with open-ended, unconstrained scenarios (top-right quadrant). Examples can be found in naturalistic driving studies (e.g., The National Academies of Sciences Engineering and Medicine, 2019; Udrive Consortium, 2019). The challenge with running these studies is that they can require more resources in terms of time, equipment, money, and personnel to run than traditional simulation studies. They are therefore typically overseen by large consortia, and not a realistic choice or option for individual researchers outside of such a consortium. On the other extreme, both the scenario and the environment can be simulated (bottom-left quadrant in Fig.  1 ). Examples are classical driving simulator studies and test track studies. Within this quadrant, there is a gradation of realism, but in general it makes use of simulation on both axes. Studies like these are more common in the transportation research communities. The reason might be that although they also require extensive resources (e.g., to buy and maintain a simulator), these are more one-off expenses, and cheap alternatives are available, such as a combination of commercial steering wheels with open-source driving environments such as Open-DS  (Math et al., 2012) , and off-the-shelf in-vehicle infotainment simulation environments such as Skyline  (Alvarez et al., 2015) . The more interesting, and relatively under-explored quadrants are those in which either the environment ór the natural scenario is simulated/controlled, but not both. It could be argued that current automated driving systems with functionalities at SAE levels 3 and 4 are tests of constrained scenarios in real environments (top-left quadrant, \"on-road real world autonomous driving\"). The reason is that such vehicles can function in specific operational design domains (e.g., an adaptive cruise control might only function under regular highway conditions), or to use the terminology from the framework in this paper: in specific (controlled) scenarios. Another example is the Ghost Driver project  (Rothenbücher et al., 2016) , where a very controlled scenario (namely: a car that seems to drive without humans inside it, due to camouflage) is placed in a real naturalistic environment (everyday pedestrian crossings on a campus). This allowed for rapidly testing how humans interact with future technology. The second relatively under-explored area is open-ended scenarios with simulated environments. This can for example be achieved through openended Wizard of Oz simulation studies and improvisational or theater studies  (Mok et al., 2015; Feuerstack et al., 2016; Schieben et al., 2009) . In these cases, the world is simulated in some form (e.g., through a driving simulator or through theater enactment), while also allowing the participant to experience a wide set of scenarios. The benefit of only simulating the environment or the scenario, and not both, is that it requires less resources compared to the naturalistic driving simulators, while at the same time allowing for studies of more naturalistic and less controlled human interaction. The authors see high potential in these research methods for transportation research that wants to explore human interaction with novel (in-car) vehicle technology. With the rapid development of automated technology  (Janssen et al., 2019b) , simulation of the environment and/or scenario allows studies of human interaction with automated technology even if such technology is not (yet) commercially available, or not matured enough to test on the open road. \n Simulated scenarios and/or environments with artificial agents The large majority of studies with simulated human agents (bottomright Figure in Fig.  1 ) also simulate the environment and control the scenario. A special and emerging case is formed by studies from automated driving companies that use full simulation to develop their automated driving technologies. Each billion of miles of driving experience collected on real roads with test fleets are complemented with several orders of magnitude more in simulated environments. Using tools like Carcraft  (Madrigal, 2017) , technology companies can identify interesting driving scenarios and iterate through a large number of derived conditions using virtual models of vehicles and other road users in a cost-effective manner. For these studies, the artificial agent acts somewhat like a human, but the focus is mostly on the impact that the human has on the technology, road behavior, and safety. A related but different perspective is taken by studies where simulations of a human agent are used to better understand the human mind. Perhaps one of the best examples is Distract-R  (Salvucci et al., 2005) , and its associated cognitive models  (Salvucci and Taatgen, 2011) . In Distract-R, a simulated agent drives in the same virtual environment as is used in human studies. Distract-R interacts with the car and the environment through its virtual hands and eyes. More often than not, other agent models have even more controlled and limited interaction with the environment. For example, steering actions might be achieved through a simple mathematical function (e.g.,  Janssen et al., 2012) , or the model might simply model traffic flow of a hypothetical scenario as the concern is not with the behavior of any individual model but with the collection/flock of cars (e.g.,  Hoogendoorn and Bovy, 2001) . Cases where a simulated agent acts only in a real environment, but with a constrained scenario (top-left quadrant in Fig.  1 ) include crash test dummies. These simulate a specific scenario (i.e., a crash) in a real environment to test the impact the crash has on the vehicle and the simulated human (a dummy) inside it. Other studies might use configurations of the automation to elicit particular emotional responses on drivers and passengers as a result of its driving reactions to road events  (Alvarez et al., 2019) . Yet another example includes the Stanley parking robot  (Stanley Robotics, 2019) , which can park your car within a constrained scenario (parking garage). Cases where a simulated agent acts in a simulated environment but a more open-ended scenario (bottom-right quadrant) include studies of dyadic interaction. Note that these involve in a sense both artificial agents (avatars) and real human agents. Other examples of work in this environment are simulators where people perform relatively open-ended interaction with automation: a manual driver encountering an autonomous car in the simulated road, pedestrian-AV interaction (e.g.  Mahadevan et al., 2018) , or bicyclist-AV interaction (e.g.  Faghri and Egyháziová, 1999) . The final fourth quadrant (top-right) is one where a simulated human drives in a natural scenario within a real environment. The ideal example is formed by studies using a SAE level 5 (SAE International, 2018) fully automated and autonomous vehicle. At the moment such technology does not yet exist. Instead, systems with limited automation, that can drive in specific operational design domains (e.g., specific scenarios) achieve part of this functionality. There are also other examples around, for example recent studies have used dummies of pedestrians (that walk similar to real pedestrians through motion capture studies) to test how automated vehicles respond to these pedestrians in various open-ended natural scenarios in a real environment  (Doric et al., 2017; Cañas et al., 2018) . This can be interpreted as a more open-ended form of the \"crash test dummies\", as the dummy in the pedestrian study has more movement and can act in more unconstrained scenarios. \n General discussion This paper provides a framework for examining human-vehicle interaction with respect to three dimensions that can involve simulation or modeling: agents, environments, and scenarios. The claim is not that one form of simulation is better than others, but rather, each dimension provides insights on different but complimentary (research) goals. Each simulation method targets different objectives, and associated strengths and limitations. Moreover, within one research project, researchers might be simulating none, one, or many of these three dimensions. Although modeling and simulating is sometimes thought of as a way to exert control (i.e., exert regulation while achieving fidelity), each of the dimensions can differ in how much regulation is exerted and how much fidelity is achieved. Having more precise terminology to study modeling and simulation is useful for transportation sciences, given its interdisciplinary nature. Contributions to the field of transportation science are made from among others engineering, design, social sciences, and safety sciences. Each of these fields brings its own terminology and the same words or terms might differ in meaning across fields. The aim behind the framework in this paper (i.e., Fig.  1 ) is to aid precision when discussing models and simulations. The development of this framework helped to identify areas that are currently not frequently used within the transportation research communities. Specifically, the paper identified that there is room for studies which simulate either the environment or the scenario, and not both. Such studies are useful as they require less resources compared to the naturalistic driving studies (that simulate none of the dimension), while at the same time allowing for more natural (high fidelity) and less regulated human interaction than studies that simulate both the environment and the scenarios. In effect, this allows researchers to study interaction with future prototypes relatively easily in naturalistic settings. Another area that was identified are studies in which human and artificial agents interact. Examples include studies of human interaction in semiautomated vehicles (e.g., at SAE levels 2 and 3, SAE International, 2018) and studies of dyadic interaction in simulated environments. A practical concern of researchers is that they might not always have the right resources, infrastructure and skills to conduct studies in all of the identified quadrants in Fig.  1 . Fortunately, the areas that were identified as having potential for future work (by comparison) do not necessarily rely on large infrastructure or resources. \n Benefit of the framework for the transportation research community Another benefit of the framework for the transportation research community is that it provides a systematic way to structure studies in which simulated and non-simulated studies can be tested. The need for a consistent tool chain containing both virtual and real tests was already highlighted (e.g., by,  Spies and Spies, 2006; Schuldt et al., 2015) . The value of the framework for the community is that it makes explicit that there are three dimensions on which the extent between \"virtual\" and \"real\" can be varied. For example, to allow testing of different (safety-critical) scenarios (dimension 3) without the risk of injuries, the proposed framework identifies the need to integrate both automated and manual vehicles (dimension 2: environment) with modelled and real human agents (drivers, pedestrians, cyclists) (dimension 1: agents) into a single test bed. Based on the actual configuration of the individual (real) parts, subjects can face different levels of immersion. A human participant can, for instance, feel the real kinesthetic experience when driving with a real vehicle on a closed test-track as the actual scenery is presented to them using virtual reality devices. On the other hand, motion tracking of participants in a simulated environment (e.g., CAVE  (Cruz-Neira et al., 1992)  or driving simulator) allows integrating vulnerable road users into the same scene in a similar manner. The resulting scenario, now containing realistic human behavior, can finally be injected into the control unit or sensor system of the test vehicle (automated car) or presented to it using movable dummies on a real test track. In that sense, the proposed framework tries to bridge the gap between simulation and expensive real driving tests  (Frey, 2016; Kühbeck and Huber, 2015) . Different researchers and practitioners will have different (research) questions. These questions will influence which dimension (agent, environment, scenario) is most important to keep under little or high regulation and fidelity. For example, in a study that is mostly focused on studying the human mind, tight control over the environment and scenarios might be needed to ensure that one can study the cognitive principle of interest. By contrast, in a study of an actual vehicle, one might want to keep the environment as realistic as possible and also allow humans to express a wide variety of behaviors, so as to be able to see the impact of such naturalistic behavior. \n Translational research An open question is how results from one setting can be translated into another settings. Specifically: how can conclusions that were drawn in a simulated environment translate to its non-simulated equivalent? Within the field of cognitive science, there have been various studies that looked at how simulations of theories of human behavior and thought relate to actual human performance (see section on modeling the agent). For the dimensions of environment and scenarios, studies comparing \"simulated\" with \"real\" environments have typically looked at these dimensions conjoined, by comparing the validity of real (on-road) experiments with simulator studies, e.g.,  (Wang et al., 2010; Riener, 2010; Frey, 2016) . The framework of this paper (Fig.  1 ) already suggests that there is value in separating these two dimensions. Nonetheless, lessons can already be learned about transfer from one setting to the next. For example, in  (Riener, 2010) , driving performance and interaction with an in-car interface was compared between both a lowfidelity driving simulator and an on-the-road driving experiment (i.e., mostly manipulating environment, and slightly manipulating scenario due to the natural variety of traffic conditions in on-the-road driving). Results indicated that drivers respond faster to steering requests in the driving simulator (by 13%) as compared to real driving. The explanation for this difference can most likely be derived from the fact that participants encountered fewer demands in the first (simulated environment) compared to the second (naturalistic environment) setting. However, there were also parallels. For example, the rank-order of performance with different incar interfaces was the same in the simulator and in the on-the-road study. Unfortunately, based on this study and others, the consensus is that it is not possible to derive a simple (e.g., linear) conversion factor or table to describe effects emerging in the reality with results from simulation or simulator studies. Although translational research in transportation sciences is typically focused on translating from simulation (or model) to the realworld, there is an important reason to look at translation in both directions: simulations and models are helpful in exploring a wider variety of situations and contexts, including extreme cases that might not always happen even after prolonged testing in real-world conditions (humans in real environments with unconstrained scenarios). Take the example of Ghost Driver  (Rothenbücher et al., 2016) , which was aimed at testing how humans react to technology that is not yet commercially available (fully self-driving cars). By simulating the scenario (a car that seems to drive without humans inside the vehicle using camouflage) in a real naturalistic environment (everyday pedestrian crossings on a campus), it allowed for rapidly testing how humans interact with future technology. Without the simulation of the car, the response of real pedestrians in their everyday environment would have been difficult if not impossible to test. Another value of simulations and models is that they can help distill the scientific principles and mechanisms that are at the heart of a behavior or situation, and thereby aid understanding. This is consistent for example with the original ambitions of AI, as expressed in the proposal of the famous 1956 Dartmouth workshop: \"The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it\"  (McCarthy et al., 2006) . Given the value of both simulated and non-simulated research, one implication is that research should cover multiple of the quadrants in Fig.  1  before definitive behavior about human-vehicle interaction are made, for example for regulatory purposes. This aids in understanding both how behavior is in less constrained, real world conditions but also allows for more rigorous, focused testing under controlled experimental conditions. \n Limitations There is an opportunity to position future studies within each of the three dimensions. In this paper, the dimensions were based on the extreme conditions to contrast human agents with non-human agents, simulated road environments with real (on-the-road) environments, and constrained scenarios with open-ended, unconstrained scenarios. For each dimension these extremes might be clear, and a relative position of any two studies might also be possible for each dimension. However, it will be difficult to associate each study with an absolute number, position, or rank on each dimension such that studies can be directly quantified and compared to future studies. Although some form of ranking or rating might be desirable in practice, it would not do justice to the inherent diversity of options that is available within each dimension. For example, even within the set of simulated vehicles there is a myriad of characteristics that can differ along multiple dimensions (e.g., visual realism, ability to induce motion, types of actions that are allowed by the human driver), and equating each dimension into a number would require comparing apples with oranges. Similarly, even for a category such as human or non-human agents, there might be more than a binary distinction, in that artificial agents can differ on multiple dimensions (e.g., Marr's level of abstraction,  Marr (1982)  and Newell's time scale  Newell (1990) ) and modelled using various frameworks  (Oulasvirta, 2019) . Moreover, in line with Turing's \"imitation game\"  (Turing, 1950) , future artificial agents might be hard to distinguish from human agents. Apart from refinement within the levels, there is also room to consider other dimensions that have so far not yet been included explicitly in the framework. For example, the discussion of the agents dimension in this paper has mostly considered human drivers, yet there can also be humans that have other roles inside the car (e.g., passenger, navigator) and outside the car (e.g., cyclists, pedestrians,  Doric et al., 2016) . \n Conclusion Studies of human-vehicle interaction can entail modeling or simulating the agent, the environment, or the scenario. Although colloquially researchers in the transportation research community and related communities sometimes only distinguish \"simulated\" from \"non-simulated\" settings, this paper identified that most studies typically model only some of these three dimensions, and that different levels of regulation and fidelity can be exerted on each dimension independently. The explicit distinction of agent, environment, and scenario can aid researchers and practitioners who are consumers of these simulations, as well as industry and regulatory agencies. The framework provides a way to classify studies and assist researchers, engineers, and designers make better decisions regarding the simulation tool to use for the research question of interest. \n CRediT authorship contribution statement The author sequence was determined using the SDC approach. All authors contributed to the conceptualization and the writing of the paper. Christian Janssen coordinated all activities. Linda Boyle developed the visualization. Fig. 1 . 1 Fig. 1. Three dimensions of simulating related to human-vehicle interaction with example studies indicated (see also text).", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S2590198220301251-main.tei.xml", "abstract": "This paper provides a framework for examining human-vehicle interactions with respect to three dimensions that can involve models or simulations: the agents, the environments, and the scenarios. Agents are considered on a spectrum from human to artificial actors. Environments are considered on a spectrum from simulated to real. Scenarios are considered on a spectrum from constrained to unconstrained. It is argued that these three dimensions capture key differences in research approaches within the field of human-vehicle interaction, and that explicitly situating research and discussions within this framework will allow researchers to better compare and contrast research outcomes and contributions. The framework is used to locate different disciplines in the community with respect to one another, and to identify areas which are as-yet unexplored.", "id": "63adcfbdd47ce66cec9a70d439caac29"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Rajeev Alur"], "title": "Formal Verification of Hybrid Systems", "text": "REVIEW OF CURRENT APPROACHES Model-based design offers a promising approach for detecting and correcting errors in early stages of system design  [33, 37, 49] . In this methodology, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements before generating the implementation from the model. Embedded systems, such as controllers in automotive, medical, and avionic systems, consist of a collection of interacting software modules reacting to a continuously evolving environment. The appropriate mathematical model for design of embedded control systems is hybrid systems that combines the traditional models for discrete behavior with classical differential-and algebraicequations based models for dynamical systems. Such models can capture both the controller -the system under design, and the plant -the environment with continuously evolving physical activities in which the system operates. Given that (1) automated verification tools have recently been successful in finding bugs in \"real-world\" hardware protocols and device drivers  [13, 15] , (2) tools such as Stateflow/Simulink are commonly used in automotive and avionics industry for modeling, and (3) high assurance is a necessity in safetycritical applications that deploy embedded software, formal verification of hybrid systems has been a vibrant research area for the past 20 years. This article is an overview of current research directions, aimed at providing an introductory \"roadmap\" rather than a comprehensive survey. \n Modeling In early 1990s, formal models for discrete reactive systems were integrated with models for dynamical systems  [2, 41] . The model of hybrid automata  [1, 2, 29]  has emerged to be a popular choice. A hybrid automaton is an extended finitestate machine whose state consists of a mode that ranges over finitely many discrete values and a finite set of realvalued variables. Each mode is annotated with constraints that specify the continuous evolution of the system, and edges between modes are annotated with guards and updates that specify discrete transitions. For example, the behavior of a self-regulating thermostat can be described by a hybrid automaton with two modes, on and off, and a single real-valued variable T modeling the temperature. To specify how the temperature changes in the mode on, we can annotate the mode with a differential equation, say, Ṫ = k(70 − T ), for a constant parameter k. Alternatively, we can use a differential inequality, say, k 1 ≤ Ṫ ≤ k2, for two constants k 1 and k2, to specify the dynamics approximately using only bounds on the derivative. Associating the mode on with an invariant constraint T ≤ 70 specifies that the system must exit this mode before the temperature exceeds 70. An edge from the mode on to the mode off with the guard T ≥ 68 specifies that, whenever the temperature exceeds 68, the system can discretely change its state by updating the mode to off. A hybrid automaton can naturally be interpreted as an infinite-state transition system, and this forms the basis for formalizing classical notions such as safety verification, property-preserving abstractions, and simulation relations, for hybrid systems. Hybrid automata are analogs of state machines, with little support for structured descriptions, and consequently, a number of formalisms have been proposed to facilitate modular descriptions of complex systems. These include modeling environments such as Shift  [17]  and Ptolemy  [19]  for hierarchical specifications of hybrid behavior; models such as hybrid I/O automata  [40] , hybrid modules  [6] , and Charon  [3] , for compositional treatment of concurrent hybrid behavior; and differential dynamic logic for logic-based specification and compositional analysis of sequential hybrid behavior  [43] . The commercial modeling tools such as Stateflow/Simulink (see www.mathworks.com) and Modelica (see www.modelica. org) are routinely used in a wide range of industries. Conceptually, it should be possible to compile models expressed in such tools into formal notations such as hybrid automata. This has turned out to be difficult in practice due to the richness of features in commercial tools and the lack of a standardized formal semantics of such features (see  [35]  for efforts aimed at semantics-preserving transformations across modeling notations). \n Symbolic reachability analysis In the safety verification problem for hybrid systems, we are given a hybrid systems model M , a set I of initial states of M , and a set S of \"safe\" states of M , and we want to check whether every execution of M starting in an initial state always stays within the set of safe states, and if not, report a violating execution as a counter-example. For instance, given the hybrid systems model of a collision avoidance protocol, we want to check whether the distance between two vehicles stays greater than the safety threshold for given initial conditions. Let us first note that the safety verification problem of hybrid systems cannot be solved algorithmically: with the exception of classes that severely restrict the allowed dynamics of real-valued variables such as timed automata  [5]  and initialized rectangular automata  [32] , the safety verification problem is undecidable  [1, 32] . Symbolic reachability algorithms for safety verification try to compute the set R of reachable states of a hybrid system M in an iterative manner starting from the set I of initial states. The algorithm checks, at every step of the iteration, if the current set R of reachable states is a subset of the set S of safe states, and if not, it terminates with a counter-example. In general, there is no termination guarantee, as the algorithm may keep adding more and more states to R without being able to deduce that the system is safe. The key challenge to efficient implementation is to identify a suitable representation for the set of states that supports the operations used by the iterative reachability computation. The tool HyTech was the first model checker to implement symbolic reachability analysis for hybrid systems  [7, 31] . For a hybrid automaton with n real-valued variables, each reachable set is represented by associating a finite union of ndimensional polyhedra with each mode, where a polyhedron is represented as a conjunction of linear inequalities over variables. Such a polyhedra-based representation is appealing due to the use of polyhedra in many computing applications and the availability of open-source libraries for manipulating them (c.f.  [12] ). The models are restricted to the class of linear hybrid automata (LHA): guards, updates, and invariants involve only linear expressions, and the dynamics is specified using differential inequalities that are linear constraints over first-order derivatives. For example, the LHA-admissible dynamics ẋ = ẏ ∧ 1 ≤ ẋ ≤ 2 describes two-dimensional motion along the diagonal line with bounds on speed. For LHA, the polyhedral representation is closed under both discrete transitions corresponding to mode-switches and continuous evolution according to differential constraints in a mode: given a polyhedron R describing the set of current states, the set R of states that the system can reach after a discrete mode-switch to a mode m, is a polyhedron that can be computed effectively from R, and the set R of states that the system can reach as a result letting it evolve continuously according to the dynamics associated with the mode m, is also a polyhedron that can be computed effectively from R . The most commonly used dynamics in mathematical design of control systems involves linear differential equations: if x represents the vector of state variables, u represents the vector of input variables, a linear system is described by the equation ẋ = Ax + Bu, where A and B are matrices of appropriate dimensions. Such dynamics is not allowed in LHA. Linear hybrid systems (LHS) refers to the class of hybrid automata where guards, updates, and invariants involve only linear expressions, and the dynamics is specified using linear differential equations. First note that the polyhedral representation is not closed under continuous evolution specified by linear differential equations: if x = 1 is the initial state and the dynamics is given by the linear differential equation ẋ = x, the set of reachable states is the exponential curve given by e t , for real numbers t ≥ 0. Since manipulating transcendental functions is computationally difficult, a popular strategy, first advocated by the tool Checkmate  [14] , and later refined by the tool d/dt  [11] , is to compute overapproximations of reachable sets using polyhedral representations. Given a polyhedron R representing the set of current states, to compute the set R of states that are reachable within a fixed time horizon Δ according to a given linear differential equation, the algorithm implements the following strategy. For every corner vertex v of R, it first computes the state v of the system at time Δ starting in state v. Then it computes the convex hull R 1 of all the corner vertices v of R and their respective images v . We are guaranteed that all the system trajectories start in the polyhedron R 1 and end in R 1 at time Δ, but are not necessarily inside R1 at intermediate times. The final step involves computing the polyhedron R 2 obtained by \"face-lifting\" R1: the number and normal vectors for facets of R 2 coincide with R1, but the facets are shifted outwards so as to include all reachable states upto time Δ. All these steps can be efficiently implemented for linear systems, and the resulting polyhedron R 2 is guaranteed to be a superset of the desired set R . The process can be repeated for successive time intervals, and the resulting approximation of the reachable set is called the flowpipe approximation. The complexity of operations on polyhedra is exponential in the number of dimensions (that is, the number of real-valued variables of the hybrid system), and since such operations are invoked repeatedly in symbolic analysis based on polyhedral representation, a significant body of work has been aimed at battling this complexity and/or replacing polyhedra with alternative representations  [11, 21, 36, 42] . Representation using zonotopes and support functions  [22, 26]  has so far resulted in the most scalable approach for the analysis of linear hybrid systems, leading to the tool SpaceEx that is able to analyze, for instance, a complex 28-dimensional helicopter controller  [20] . \n Deductive verification In deductive verification, a designer interacts with a mechanized theorem prover to generate proofs of correctness of systems. For safety verification of discrete systems, a classical proof principle relies on the notion of inductive invariants: to show that all executions of a system M starting in an initial set I stay within a safe set S, we identify a state property ϕ such that (1) all initial states satisfy ϕ; (2) ϕ is a subset of the desired safety property S; and (3) the property ϕ is preserved locally across system transitions (that is, no transition of the system changes the value of ϕ from 1 to 0). In interactive verification, the user proposes a property ϕ, and the analysis tool checks if ϕ is an inductive invariant. The concept of inductive invariants for discrete systems has been generalized and adopted to continuous-time dynamical (and hybrid) systems. We will informally explain the first such notion, called barrier certificates  [47, 48] . To show that a dynamical system M with dynamics ẋ = f (x) with initial set I satisfies a safety property S, we identify a function ψ from the states to reals such that (1) in all initial states, the value of ψ is nonnegative; (2) in all unsafe states (that is, states not in the safe set S), the value of ψ is negative; and (3) the Lie derivate of ψ with respect to the vector field f is positive on the boundary set (called the barrier) characterized by ψ(x) = 0. The first two conditions ensure that the barrier separates the initial states from the unsafe states, and the third condition ensures that system trajectories cannot escape the barrier from inside as at the barrier the flow field points inwards. Together, these conditions imply that ψ(x) ≥ 0 is an inductive invariant of the system. Typically, the desired function ψ is a polynomial function of the system variables. It is also worth noting that the barrier certificates are closely related to the notion of Lyapunov certificates for stability in classical control theory. The notion of differential invariants generalizes barrier certificates  [44] : it relaxes the third condition, and also allows more general forms of logical assertions as potential invariants. Verification of safety properties based on identifying inductive invariants avoids the iterative calculation of reachable state sets and is not limited to linear systems. The tool KeYmaera offers support to prove correctness of hybrid systems using deductive verification  [43, 44] . To check whether a given polynomial certificate satisfies all the conditions necessary for it to be a barrier certificate, the tool needs to perform symbolic differentiation, and calculations such as simplification and quantifier elimination, with formulas in the theory of reals with arithmetic operators. To fully automate deductive verification, such a tool needs to automatically generate candidates for inductive invariants, and this remains an active area of research (see  [28, 50]  for automatic generation of invariants by instantiating templates and  [45]  for generating invariants by fixpoint computation). \n Abstraction An abstraction A of a model M is a \"simplified\" model obtained from M such that proving safety and temporal properties of A is a sufficient condition for proving the corresponding properties of M . Abstraction is an effective strategy for scalability of verification tools, provided there is a way to compute A from M in a tool-supported manner, and a way to refine the current abstraction A if it is not adequate to prove the desired properties. In the case of hybrid systems, the simplicity of the abstract model A can be of various forms: A can be discrete while M is continuous; A can have linear dynamics while M has non-linear dynamics; and A can be a linear model of dimensionality lower than that of M . There is an extensive literature on automatic abstraction of hybrid systems. We note three representative examples. We have already seen that the dynamics admissible in the model of linear hybrid automata is simple enough to permit exact computation of reachable states using polyhedral representation. In phase portrait approximation  [30] , the dynamics ẋ = f (x) in a mode m of a hybrid system is replaced by l ≤ ẋ ≤ u, where the vectors l and u represent the lower and upper bounds on the function f over the range of values specified by the invariant constraint associated with the mode m. This clearly yields an over-approximation of the allowed system trajectories in each mode. The error introduced by the approximation can be reduced if we split the mode m into submodes, each corresponding to a different region of the state-space. Predicate abstraction is a powerful technique for extracting finite-state models from complex, potentially infinite-state, systems, and has been extended and adopted for hybrid systems  [4, 16] . In this approach, the input to the verification tool consists of a linear hybrid system, the safety property to be verified, and a finite set of Boolean predicates over system variables to be used for abstraction. An abstract state is a valid combination of truth values to the Boolean predicates, and thus, corresponds to a polyhedral set of the concrete state-space. The verifier performs an on-the-fly search of the abstract system by symbolic manipulation of polyhedra, where the computation of continuoustime successors of abstract states can be performed using flow-pipe approximations. The key computational benefit is that the continuous reachability computation is applied only to an abstract state, instead of intermediate sets of arbitrary complexity generated during iterative computation. If the initial choice of predicates is too coarse, the search finds abstract counter-examples that are infeasible in the original hybrid system, and such counter-examples can be analyzed to discover new predicates that will rule out related spurious counter-examples. A classical notion of equivalence of nondeterministic systems is simulation: a relation between states of two systems is a simulation relation, if (1) two related states have identical observations, and (2) whenever two states are related, for every transition from the first state, there exists a matching transition from the second state such that the targets of the transitions remain related. For simpler classes of hybrid sys-tems such as timed automata and O-minimal systems, one can algorithmically compute the maximal simulation relation over the states of a given system, and use the discrete quotient with respect to this relation as the abstract system which can replace the original system for verification purposes  [8] . In the context of hybrid systems, since states contain real-valued vectors, there is a natural metric over states, and this can be used to also define a coarser notion of simulation called approximating simulations: an approximating simulation relation with parameter ε requires observations of two related states to be ε-close of one another, and transitions can be matched step-by-step by staying ε-close  [23] . The resulting theory of approximating relations leads to algorithms for constructing lower-dimensional abstractions of linear systems  [52] . \n EMERGING RESEARCH DIRECTIONS Automated verification is a computationally intractable problem. Consequently, even though there are many demonstrations of interesting analyses using tools for verification of hybrid systems, scalability remains a challenge, and a significant fraction of the current research is aimed at addressing this challenge. A complementary challenge is to integrate verification tools and techniques in the design flow so as to improve the overall system reliability. We conclude this article by discussing some promising research directions towards this goal. \n Symbolic simulation In simulation, a possible execution of the model upto a finite time horizon is obtained using numerical methods, and this is a well-accepted industrial practice. A single simulation corresponds to a specific choice of inputs. A promising idea is to analyze a simulation trace corresponding to a particular choice of inputs using symbolic analysis techniques to compute the space of inputs that are close enough to the chosen one so that no inputs from this space need to be considered for subsequent simulations (see  [9, 18, 34]  for recent efforts). This integration of simulation and symbolic analysis can lead to improved coverage, and is similar to concolic testing which has proved to be effective in debugging of large-scale software systems  [24] . An added benefit is that such an approach can be implemented directly within the native simulation engine of an industrial-strength modeling environment such as Simulink/Stateflow. \n Synthesis Historically, synthesis refers to the process of computing an implementation (the \"how\") from a specification of the desired behavior and performance (the \"what\") and the assumptions on the environment (the \"where\"). In the more recent view, the synthesis tool facilitates the design by consistently integrating different views: a designer expresses her insights about the design using synthesis artifacts of different kinds such as models that may contain ambiguities and declarative specifications of high-level requirements, and the synthesis tool composes these different views about the structure and functionality of the system into a unified concrete implementation using a combination of algorithmic techniques. Illustrative examples of this new view of synthesis include programming by examples for spreadsheet transformations in Microsoft Excel  [27] , and sketching of bit-streaming programs using program skeletons  [51] . We believe that these ideas emerging in the programming languages community should be explored in the context of design of hybrid systems to integrate synthesis in a pragmatic way in the design cycle (see  [53]  for recent work on synthesizing switching conditions in hybrid automata). \n From models to code Generating embedded software directly from high-level models, such as hybrid systems, is appealing, but challenging due to the wide gap between the two. In current practice, this gap is bridged with significant manual effort by exploiting the run-time support offered by operating systems for managing tasks and interrupts. A key challenge to systematic software generation from hybrid models is to ensure that one can infer properties of the software from the properties of the model, and this problem is receiving increasing attention from researchers. Sample research directions include integration of control and scheduling  [10]  and static analysis of errors introduced by finite precision computations  [25] . \n Industrial applications The value of formal modeling and verification on industrially relevant problems has been demonstrated on a number of case studies. Examples of these include design and analysis of vehicle platooning protocols  [17] , identification of optimal tolerances for audio control protocol  [31] , safety verification of collision avoidance protocol for aircrafts  [46, 54] , and verification of adaptive cruise control  [39] . Yet, the level of commitment from embedded software industry remains limited to exploratory projects in collaboration with academic researchers. This is in contrast to, say, Intel's investment in formal hardware verification and Microsoft's investment in static analysis of software, which can be attributed to the identification of specific classes of errors that can be largely eliminated using verification techniques (for example, deadlocks in cache coherence protocols and misuse of API rules by third-party device driver code). Thus, a key challenge for research in formal verification of hybrid systems is to identify a compelling class of errors that designers routinely make and can be eliminated using verification techniques. An alternative path to industrial adoption is to integrate verification tools in the certification process, and this seems plausible in safety-critical domains such as software for medical devices  [38] . \t\t\t Authorized licensed use limited to: Carnegie Mellon Libraries. Downloaded on March 24,2022 at 00:46:37 UTC from IEEE Xplore. Restrictions apply. \n\t\t\t licensed use limited to: Carnegie Mellon Libraries. Downloaded on March 24,2022 at 00:46:37 UTC from IEEE Xplore. Restrictions apply.", "date_published": "n/a", "url": "n/a", "filename": "Formal_verification_of_hybrid_systems.tei.xml", "abstract": "In formal verification, a designer first constructs a model, with mathematically precise semantics, of the system under design, and performs extensive analysis with respect to correctness requirements. The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional state-machine based models for discrete control with classical differential-equations based models for continuously evolving physical activities. In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.", "id": "40a42bc929d6fc0c9c8ce23ff04eb781"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anders Sandberg"], "title": "The economics, risk and ethics of time compression", "text": "Introduction Whether there is a long-term trend towards accelerated change is controversial  (Kurzweil 2010; Cowen 2011; Eden et al. 2012; Sandberg 2013 ), but clearly the present era is experiencing a remarkable increase in the speed of computation, a compression of the time required to perform a computational task. This paper is an exploration of the limits and implications of this compression on human values and society. If everything speeded up equally, there would be no change: one of the peculiarities of time (and a big source of arguments between Platonists and Aristotelians in the philosophy of time) is that we mostly notice it through the change of events and things relative to each other  (Markosian 2016) . \"Speeding up\" hence means that more things of a certain kind occur relative to other things, or that a kind of event occurs before another event it would previously have occurred after. Faster computation means that computational goods can be produced faster and earlier. This paper will explore some of the consequences and limits of this phenomenon. What kinds of value would accrue from something occurring faster?  More instances of the event in a given interval: if these hold value, then there is more value produced. A faster manufacturing process will produce more goods per unit of time.  Time is freed up by the faster rate of work, and this is valuable. For example, a labour saving device frees up time that could be used for leisure or more productive work.  Having an event occur earlier than another event, becoming valuable because of the ordering. For example, diagnosing and intervening rapidly against a medical condition before it turns serious.  The value of a remote event is increased (possibly from zero) by it becoming closer to the present. This includes becoming able to achieve something that previously was impossible to achieve within the given timeframe. For example, calculating weather forecasts or solutions to mathematical problems that previously would have taken years in hours. Limits to speeding up computation include physical limits, but also limits due to the difficulty of tasks (or the algorithm used to solve them). At present we appear to be far from any fundamental technical limit on computing power, but we have already touched the fundamental limit on communication speed. Speeding up the interaction with the physical world may prove challenging because of the discrete nature of signals and sluggish responses of macroscale actuators. Faster computation does raise risks and ethical challenges: various forms of loss of control, inequalities of speed, gaps between oversight and system speed, loss of opportunity due too early decisions, and possibly so much change that the \"change budget\" becomes depleted. In particular, speedups appear to pose a serious challenge to human ability to control technological processes due to growing gaps of speed between computation and control (\"cybernetic gaps\") and challenges to setting the goals they are optimizing for due to gaps of speed between computation and the human world (\"ethical gaps\"), in turn posing a profound challenge to governance systems that are themselves to some extent hybrid humancomputational systems suffering internal speed gaps. \n Limits to computation Computation is subject to both physical, logical and technical limits. This section will outline some of the main limits and how they limit achievable computational speedups. \n Physical limits to computation Computation requires structured change in information-bearing material systems, making the speed a particular computation can be performed at limited by the speed in which a physical system can change in a corresponding way. The most fundamental limits are due to quantum speed limits, stating how fast a quantum system can move between two distinguishable states. The Margolus-Levitin limit states that a system with mean energy E cannot move to another orthogonal state in less than 𝜋ℏ/2𝐸 time, and the Mandelstam-Tamm limit 𝜋ℏ/2𝛥𝐸 where 𝛥𝐸is the standard deviation of the energy of the system (wrt to initial state). Later work has found entire families of quantum speed limits, where the bound scales as 1/𝛥𝐸 for unitary dynamics  (Margolus & Levitin 1998; Pires et al. 2016) . These limits, together with the  Bekenstein (1981)  bound on the information that can be contained within a region with given radius and mass-energy, can be used to describe the most extreme computer systems that could be built even in principle: for a one kilogram, one litre computer the limit is 5.4258 ⋅ 10 50 logical operations per second on ≈ 10 31 bits  (Lloyd 2000) . In this case the state of mass-energy is mostly akin to a black hole or a small piece of the Big Bang. The speed of computation in normal matter is limited by the number of transitions the system can perform per unit time without breaking down. This in general depends on the available energy to perform the transitions and how strong the energy barriers of the system are. Semiconductor and optical devices can switch on the picosecond scale  (Mii et al. 1994; Ctistis et al. 2011) . Molecular computation is limited by bond energies: above 10 15 transitions per second the energy involved becomes larger than the bond energies and the system starts to break up  (Drexler 1992) . In terms of switching current computers are hence about five orders of magnitude slower than the hard limits unless nuclear matter computation on the yoctosecond scale eventually becomes possible  (Sandberg 1999) . Very fast computation is also very small and localized, since the light speed limit forces the parts involved to be closer than 𝑡/𝑐, where 𝑡 is the cycle time. A nanosecond is about a foot long, a femtosecond 300 nanometers. Since there is also a limit to how densely information can be packed (likely on the order of a bit per atom for molecular systems) this means that a computation taking time 𝑡 cannot process more than 4𝜋𝜌(𝑡/𝑐) 1/3 /3 bits. If individual atoms perform computations, the cycle time they would require to exchange state information at lightspeed in diamond would be 1.2 ⋅ 10 −18 seconds. Quantum computation does not change this fundamental issue. The number of steps an algorithm needs to perform in order to arrive at a solution of a problem defines the complexity class of the problem. A practically useful algorithm scales polynomially or less with problem size. Quantum computing merely leads to an exponential speedup of certain problems, which makes some computations that would otherwise be infeasible potentially doable (given quantum computers)  (Moore & Mertens 2011) . It should be recognized that innovations in algorithms can also make classical computations significantly faster: the FFT algorithm changed the complexity of discrete Fourier transforms from 𝑂(𝑁 2 ) to 𝑂(𝑁 log 𝑁), making e.g. online multimedia feasible. \n Algorithmic limits The physical limits discussed above represent limits on the speed of an algorithmic step: the complexity classes represent limits of how fast problems can be solved. For example, it is known that any sorting algorithm that must compare elements with each other has to run in 𝑂(𝑁 log 𝑁) time on one processor, and if it is parallelized 𝑂(log 𝑁)  (Moore & Mertens 2011) . Any improvement beyond this will have to come from refactoring the problem (e.g. making use of known constraints on the data, such as integer sorting). There is a key difference between parallelizable tasks and serial tasks. By splitting a problem into suitable parts a solution can often be generated far faster on more processors. For example, summing 𝑁 numbers requires time proportional to 𝑁 on one processor, but can be done in log(𝑁) time on 𝑁 processors (first every pair of processors sum their numbers, then the 𝑁/2 partial answers are summed, and so on until only one answer remains). Other problems have data dependencies that make this impossible, for example calculating trajectories in the 3-body problem. The key difference is whether the critical path length 𝐶 of the computational dependency graph is close to the overall amount of computation 𝑇. If 𝐶 grows more slowly than 𝑇, then parallelism gives a time gain. However, 𝐶 represents an insurmountable problem-dependent barrier for how fast the problem can be solved (this is the cause of \"Amdahl's law\"  (Amdahl 1967 ) limiting the speedup of a task as more processors are added). While the complexity classes represents the logical bedrock of how fast tasks can be done, one should not underestimate the potential speedups due to refactoring, approximating, or \"cheating\" on problem instances that matter. For example, the 3-SAT problem is known to be NP-complete and should hence not be expected to have efficient solutions, yet heuristic 3-SAT solvers are successfully used in circuit design and automatic theorem proving. They are not efficient on all possible instances but for practical purposes they work  (Moore & Mertens 2011) . It is hence harder in general to estimate the distance to algorithmic limits to computation than physical limits because real-world problems are rarely well specified enough. Improvement in algorithms are often 50-100% of the gains from hardware progress  (Grace 2013) . In addition, predicting future theoretical insights is often as hard as gaining the insight itself: strongly idea-driven technological change is by its nature less predictable than incremental change. \n Technical limits Figure  1 : Distribution of sigmoid curve scenarios of computer power generated from data in  (Koh & Magee 2006) . The grey shade denotes density of scenarios. The red curve is the median scenario, green lines the 5% and 95% percentile scenarios. Moore's law has been formulated in numerous incompatible ways  (Mack 2015; Waldrop 2016 ), but perhaps the most relevant measure of progress is processing operations per second per dollar. Merely measuring speed will not capture the actual practical impact. This measure has been growing exponentially over several decades and even if one fits a pessimistic sigmoid curve (implying that growth must eventually come to an end) the median estimate implies about 20 orders of magnitude improvement (!), and with 95% probability at least a factor of 100,000 improvement. Moore's law is a self-fulfilling industry prophecy, partially driven by Wrightean learning and increasing production  (Nagy et al 2013) , partially by expectation  (Schaller 1997) . Given the value of faster computation there is a demand for it, and production makes new computational tasks feasible and affordable (\"Bell's law\")  (Denning & Lewis 2016) . Eventually it will run into physical limits  (Mack 2015; Waldrop 2016 ), but compared to the previous section it is clear that there is a fair distance to run. Even if the technology itself stops the economies of scale may keep on increasing the performance per dollar. \n Communications Communication has essentially reached the ultimate limit, lightspeed transmission. In electric cables there is some slowing (50%-99%c) due to electrical inductance and capacitance. Optical fibres typically transmit signals at 70% of lightspeed due to the refractive index. In contrast radio waves move nearly at the speed of light, but require line-of-sight. Bandwidth is still increasing: Nielsen's law of Internet bandwidth suggests a 50% increase per year for users  (Nielsen 1998) . This is slightly slower than Moore's law, making accumulating data rational since it can be generated faster than it can be transmitted. The upper limits of bandwidth are set by the entropy of electromagnetic radiation, scaling as 1.1194 × 10 21 √𝐴/𝑑 𝑃 3/4 bits per second for an area 𝐴 transmitter and receiver at distance 𝑑 and using 𝑃 Watt power  (Lachmann et al 2004) . We are clearly far from the physical limits yet, but were Nielsen's law to continue we will reach them before the end of the 21 st century. As mentioned above, lightspeed limits imply a space-time trade-off. A return time of 𝑡 from sending a signal and getting an answer implies a distance 𝐷 < 𝑡/𝑐. Faster processing require smaller spatial systems. Large systems will have parts that are causally disconnected: they cannot interact over processing cycles. Krugman's \"First fundamental theorem of interstellar trade\" applies here: interest rates for local information and for information in transit are the same (and by the second theorem, arbitrage will equalize them in different parts of the system). However, prices in different parts of the system may not be equal  (Krugman 2010) . While intended for space this also applies to a fast desynchronized computing world. \n Sensing and acting To fast sensors the world is dim and noisy: the rate with which photons, sound or other measured entities arrive is slow and natural irregularities will dominate. If the intensity is 𝐼 and sampled at frequency 𝑓, during each sample interval only 𝐼/𝑓 units of energy will arrive, an amount decreasing with 𝑓. If this interval becomes comparable to the average arrival time of measurable entities typically aliasing effects (if the arrival times are regular) or Poisson noise (if the arrival times are random) show up, drowning the signal in noise. To function well fast sensory systems need intense, high-frequency signals or sensors with a broad sensitivity. The world is sluggish and hard to coordinate for fast controllers since the response from actuators will be slow and delayed. The time from sending a command until a response is received measured in processor cycles is 2𝐿/𝑣𝑓, where 𝐿 is the size of the actuator, 𝑣 the signal speed and 𝑓 the processor frequency. This estimate optimistically assumes an instant response from the actuator, but for many physical systems response times are proportional to 𝐿  (Drexler 1992) , increasing the time to (2/𝑣 + 𝐾)𝐿/𝑓 where 𝐾 is the actuator sluggishness. The smaller and faster the actuators are the better the system can work, but this also requires closeness in space. Fast computation hence benefits small systems acting in intense environments more than large systems dealing with uncertain, weak signals. \n Summary In summary, we have good reasons to expect computing to become many orders of magnitude faster in the future: there is still plenty of distance to physical limits, and algorithmic improvement, innovation and (quantum) parallelization is possible in many domains. Indeed, \"there is plenty of time at the bottom\". At the same time we are close to communications and sensing limits, the improvement speed may be unpredictable, and it is hard to synchronize fast distributed systems. \n The value of fast computation In the previous section, we discussed the physical limits to computation -how fast computation might be made in principle, if sufficient effort was dedicated to making it faster. For such effort to be expended, fast computation needs to have enough value to justify the investments in it. This section will review the reasons for why \"faster is better\" in computation, and how these reasons act as drivers for computational speedups and hence incentivize (due to economic profitability) further speedups. \n Productivity If operations can be performed faster, then more instances can occur in a given interval. If these hold value, then there is more value produced. A faster manufacturing process will produce more goods per unit of time, a faster surgeon can operate on more patients. This is the normal world of economic productivity, endlessly studied by economists. Whether the value increases proportional to the speedup or not depends on whether the increased supply is enough to decrease price noticeably. A closely related improvement is that time is freed up by the faster rate of work, and this is valuable. For example, a labour saving device frees up time that could be used for leisure or (more commonly) further productive work. An effect of this is that alternative cost of time increase. A given time interval can be used for many more things, some of which are valuable. Hence wasted time may paradoxically become more of a serious problem in some domains. This might be a current contributor to information stress -there is always something of value going on, and it might be rational to switch tasks often in order to find high-value tasks. As described by  Schwartz (2004)  \"missed opportunities\" are often experienced as stressful since we notice lost utility, especially if the aggregated alternatives not taken sum to more utility than our choice. The actual rationality depends on how the overhead of searching is compared to the expected gain 1 ; information foraging theory predicts that as the cost of switching between information sources decreases the time spent on each will decrease  (Pirolli & Card 1999) . Changes in productivity will also lead to changes in allocation of resources  (labour, computing) . A sudden change in speed of one area will produce transient response in the labour/computing market before a new equilibrium establishes itself. \n Timeliness Time is a non-renewable resource. Or rather, temporal location is non-renewable: what matters is often that X occurs before Y occurs. Since time is irreversible ordering effects can matter significantly, as in diagnosing a disease before it becomes life-threatening or inventing an offensive technology before any defence to it exists. The Japanese earthquake early warning system uses seismological detectors to shut down trains before the earthquake wave hits  (Kamigaichi et al. 2009 ) -once detection, transmission and reaction is fast enough this becomes possible. The timescales in cars form another useful set of examples of how timeliness enables sharp shifts in performance. The trip planning timescale for humans is on the order of minutes, allowing it to be done automatically with 1990s technology; faster is more convenient, but once the navigation system passed the minute threshold it was good enough. The driving timescale involves decision-making on the order of tens of seconds to seconds. There was an important shift in 2006 when computing got fast enough, suddenly enabling autonomous cars in natural environments. Again there is a threshold effect: speedups of computing may enable better driving quality, but the fundamental ability to drive showed a fairly discrete transition. Similarly airbag systems gather sensor information and the control unit decides whether to trigger the airbag within 15 to 30 milliseconds after a crash has begun. This could be done already in the early of 1970s by dedicated electronics, and since then speedups have mostly served to make the decision-making more sophisticated (although improvements in sensors may have played a larger role). In all these examples computational speedups enable a new level of automation when they pass a human or mechanical speed threshold. CDF. The median utility for the best is 𝐹 −1 (2 − 1 𝑁 ) and the expected utility is E[𝑢 * ] = 𝑁∫ 𝑢𝑓(𝑢)𝐹 𝑁−1 (𝑢)𝑑𝑢. In the case of Gauss-distributed utilities 𝐸[𝑢 * ] ≈ 𝜎√2ln(𝑁) . The expected total utility of trying N tasks, each requiring time t to give evidence of their utility, with overhead H for switching during a fraction 0 < Nt T ≤ F ≤ 1 of the allotted time T followed by exploiting the best one is 𝑈(𝐹, 𝑁) = −𝐻(𝑁 − 1) + \n 𝑇(𝐹E [𝑢] + (1 − 𝐹)𝐸[𝑢 * ]). The difference from N=1 is Δ𝑈(𝑁) = −𝐻(𝑁 − 1) + 𝑇((𝐹 − 1)𝐸[𝑢] + (1 − 𝐹)𝐸[𝑢 * ]) = −𝐻(𝑁 − 1) + 𝑇(1 − 𝐹)(𝐸[𝑢 * ] − 𝐸[𝑢]). There is some value of T where the last term becomes larger than the first term and it becomes rational to try different tasks. Since spending more time than necessary exploring wastes time best used for exploiting, F will be close to Nt/T. In the Gaussian case Δ𝑈(𝑁) ≈ −𝐻(𝑁 − 1) + 𝑇(1 − 𝑁𝑡/𝑇)𝜎√2 ln(𝑁), and the switch happens when 𝑇 > 𝑁(𝐻 + 𝑡𝜎√2𝑙𝑛𝑁) − 𝐻. Hence, as processes speed up (T increases) it becomes rational to flip between tasks, especially when overheads for task switching are low, the time to detect the utility well enough is fast, and the number of alternatives to consider remains bounded. At least in principle, calculative rationality becomes perfect rationality if done infinitely fast  (Russell 2016 ) (although as we will see this promise is somewhat illusory). \n Competition In finance \"winner take all\" dynamics can occur in markets if one agent can react faster than others and hence gain a speed premium. The same may apply in evolution, where evolving faster than parasites or competitors is useful. This can serve as incentives for accelerating, even if it comes at a cost. There would be an equilibrium when the cost of higher speed offsets the economic (or other) gains. At this point every actor runs as fast as is optimal. However, if the situation is a winner-take all situation the economic gains accrue mostly to the fastest actor, and it is rational to try to at least temporarily push into the \"inefficient\" speed frontier since slower competitors are pushed out of the market. Perceptions may also matter significantly for speed investment: there could be inefficiencies because agents overinvest in too fast systems. In addition, Moore's law and other expected speedups lead to design choices (like software bloat) that are suboptimal. Since agents can plan for a faster future they may risk overshooting the equilibrium by investing in speed that is expected to be optimal, but may actually be too ambitious. \n Timing Sometimes it is more important to have a result or event at a particular time, and speed gives more control over the situation. For example, in bomb disposal one of the first steps is to vibrate the assembly -if there are any vibration detectors disarming it will be very hard, and if it detonates it will occur at a time of the disposal expert's choosing. A bomb with a slow, unpredictable fuse will detonate at an unknown time, and this can be dangerous. Projects where one can ensure that at a predictable time one will know if it can succeed or that certain key steps will have been done will be less risky, reducing the risk premium. \n Time budgets Everything that matters to us occurs within our time budget. These time limits may be set by human lifetimes, corporate lifetimes, the next budget period for an organisation, or the time until the situation changes too much. An interesting special case is secrets, where the aim is to ensure that disclosure occurs after a fixed time occurs. Most secrets have a time horizon beyond which their importance has declined enough that it no longer matters if they are revealed. In cryptography this can be used to estimate required key lengths: given an assumed time horizon the key needs to be long enough that given optimistic predictions of future computing power it is not possible to brute-force the key. This has led to the concept of \"transcomputational problems\", problems requiring more information processing than can be amassed even in principle. Many such estimates are based on common sense limits such as a computer covering the Earth, but the actual ultimate physical limits are far larger -yet there is rarely any challenge in constructing a sufficiently large problem to reach true limits. Secrets also have half-lives due to random disclosure, leaks and espionage  (Swire 2015) . This is a more troublesome time limit since it is unknown (indeed unknowable): at best the secret-keeper can estimate the rough half-life and plan for that time period, as well as prepare for what to do if it is disclosed. Note that this makes cryptographic issues and computer speed far less important: a speedup of computation that makes the secret forceable earlier but still several half-lives into the future has no effect on the utility. In a leaky world perfect cryptography is irrelevant. In software finding bugs typically requires monitoring/beta testing time proportional to the mean time between failure (MTBF). This can be speeded up by using more testers/users, but fast systems will also show internal bugs quickly. Interactive or environment-linked systems may however have long MTBF despite great internal speed: here the human or environment acts as the slow critical path in the computation and error-checking. \n Time value The value of a remote event is increased (possibly from zero) by coming closer to the present. This includes becoming able to achieve something that previously was impossible to achieve within the given timeframe. For example, calculating weather forecasts in hours that previously would have taken years suddenly makes them useful. Fast change also typically implies more uncertainty and faster discounting. If discount rates are pushed by accelerating computation but also affect human-level systems that do not change speed, there could be a problem in rational allocation. Long-term valuable projects such as building infrastructure or settling other planets are not only outside the fast discount horizon, but rapid changes in funding, technology, risk and specification makes planning challenging and reduces the probability that they will be fully implemented. \n Early discovery Nick Bostrom penned \"A little theory of problems\"  (Sandberg 2014)  where among other things he noted that:  \"Discoveries\" are acts that move the arrival of some information from a later point in time to an earlier point in time.  The value of a discovery does not equal the value of the solution discovered.  The value of a discovery equals the value of having the solution moved from the later time at it would otherwise have arrived to the time of the discovery. In this account of the value of discovery depends on temporal ordering. In the long run most discoverable information will presumably be discovered, but problems with high and positive value and high elasticity (the solution can be found significantly sooner with one extra unit of effort) should be prioritized. If computation is relevant for solving the problem improvements in speed means that it increases the elasticity, not just of the problem in question but for all computationally dependent problems. This can cause an overall re-prioritization: computational problems with a high value of early discovery would be favoured over other, equally weighty, but less elastic problems. However, as long as computation is increasing in speed and power there may also be a value in waiting. As noted by  Gottbrath et al. (1999) , if a computation requires a given amount of computation to perform and the available computer power grows exponentially it can be rational to wait until the computer power has grown to start running the computation. This is relevant if the time the computation takes is significant compared to the improvement time of computers. \n Cybernetic feedback shift When a regulatory or informative process becomes fast enough the dynamics changes profoundly. We may call this a cybernetic feedback shift: when a controller is fast enough things become stable. This is well known from delay differential equations, the classic steam engine centrifugal governor, and trying to steer a boat: too slow reactions leads to oversteering where the system sways back and forth. In control theory delays are equivalent to a low sampling rate of the system. It may be possible to control the system, but the response will be sluggish since one has to use old data to stabilize. As control speeds up the responses become faster. In many practical cases regulators try to track a parameter (e.g. thermostats, price signals). When the controller cannot follow a parameter, it tends to \"fall off\" with possibly catastrophic effects  (Ashwin et al. 2012) . For fast response rates this risk disappears. Conversely, if the parameter starts moving too fast because it has been speeded up, then stability may also be lost. If both controller and parameter speed up, then nothing changes. In many cases the utility of a system goes up tremendously when a cybernetic feedback shift happens. Unfortunately the converse also occurs: when a system loses the ability to track parameters it can suddenly become worse than useless. Communications matter for keeping organisations and empires together. An empire cannot function if the time from a province begins to rebel to the arrival of the military force sent from the capital is longer than the time the province needs to entrench/build army (a way around this is to distribute power to local governors for fast response). If the time it takes for the strategic level of the organisation to notice, understand, and react to a challenge is longer than the evolution time of the challenge, then it is unlikely to be able to deal with it. Hence real societies and organisations tend to have low-level, faster subsystems. If local processing speeds up but communications does not this leads to asynchrony issues. But also, to stronger reasons to decentralise to meet new, fast challenges. Organisations that cannot do this will have a risk that \"provinces\" can rebel much faster and that subsystems are going to be held back -there may now exist local incentives to break loose. \n Risks and ethical issues due to fast computation We have seen that there exist numerous reasons to pursue faster computation, especially in the service of performing particular tasks fast, timely, and early both for competitive and intrinsic reasons. Even if this is achieved flawlessly there are risks and ethically relevant issues with this process. The most obvious issue of time compression is simply social change and disruption (as well as gains); the locus classicus is  Toffler's Future Shock (1970)  and the writings of Virilio; see also  (Wajcman 2008) . Although clearly important, for reasons of brevity the focus here will be on the directly speed-related issues rather than the more subtle sociological and phenomenological challenges. \n Loss of control The most obvious issue with fast computation or other operations is that they are fast relative to the (human) ability to control systems: there is a risk of things going haywire too fast. When a system has a positive feedback loop, the strength of the feedback relative to friction and delays determines the speed a disturbance gets amplified. Engineering typically wants to keep friction in useful range: not too much to cause losses but enough to make system controllable. Faster computation and communication can make feedbacks in business, software (e.g. \"Warhol worms\"  (Weaver 2001 )) and other system more intense, and hence limit the timespan for taking control action. The \"friction\" -costs of action and reaction -is lowered, making fast actions possible. Loss of control can happen due to several causes. There is the direct loss of control, where the steering agency lacks the ability to control, either because it cannot track the state of the system fast enough or process what should be done fast enough. There is the effect of emergence causing misbehaviour (systemic risk), where parts of a system function well but the whole exhibits unwanted behaviour. Here the trouble may come from the speed the emergent behavioural change occurs on, or that fast and dense internal interactions enable the change  (Goldin & Mariathasan 2014) . Finally, there is asynchrony where the parts cannot coordinate necessary joint activity. Perhaps the most extreme example of an emergent loss of control is the \"hard AI take-off scenario\". In this scenario general artificial intelligence (AGI) is developed to have enough ability to perform many human-level tasks, including programming better AGI. A feedback loop ensues, where human input for improving AGI becomes less important than AGI input (which may be very scalable) and the total ability and power of the software grows rapidly, soon outstripping human ability to control.  (Good 1966; Bostrom 2014 ) Whether such take-off can occur and how fast it could be remains conjectural at present, but it is an issue taken seriously as a long-term risk by some AI researchers  (Hutter 2012; Müller & Bostrom 2016; Sotala 2017 ). Bostrom distinguishes between fast, medium and slow take-offs in terms of how fast the transition occurs relative to human decision-timescales. The key issue is the differences in what reactions can be undertaken: in slow take-offs there is ample time for society to respond with considered actions, while in fast take-offs events move too quickly for human decisions to matter. In the intermediate case there may not be time enough for deeply considered decisions, but various actions are possible -especially preplanned \"cached\" actions that can be initiated quickly. \n Speed inequality Speed differences can become unfair differences in economics or power, as well as contribute to risk. In \"fastest takes all\" competitive situations being faster is more important than being good. This can favour not just excessive speedups and arms-races, but also ignoring quality and safety. For example, if several teams race to create the first transformative AI but safety work slows progress, then the Nash equilibrium tends to produce unsafe AI (and having public information on the progress of other teams increases the risk)  (Armstrong, Bostrom & Shulman 2016) . A less dramatic case is how Silicon Valley competition favours bringing a Minimum Viable Product to market fast and first rather than making it reliable; the result is often that security and privacy flaws become hard to fix later. Old systems tend to be slower and would hence suffer in \"fastest takes all\" situations. Agents that cannot afford faster systems will hence tend to fall further behind. The speed requirements also serve as a barrier to entry. Automated trading became possible in the 1990s when trading floors were replaced by matching engines. Gradually high-frequency trading emerged, as the second-long delays at the turn of the century declined to milliseconds in 2010, enabling trading of shares under 10 milliseconds. Quickly this became a dominant form of trading  (Massa 2016 ) to a large degree because of improvements in liquidity and informativeness of quotes  (Hendershott, Jones & Menkveld 2011) . There are also more zero-sum benefits of speed such as obtaining a better position in the order book queues than competitors with the same information and similar strategies; the rewards for a 1 millisecond speed advantage have been claimed to be in the range of hundreds of millions to billions of dollars  (Farmer & Scouras 2012) . Human traders obviously cannot compete. Also, the algorithms have shown sensitivity to disinformation/misinterpretation of news; oil prices jumped 2013 when a tweet recalling the Yom Kippur war 40 years later was sent by the Israeli military  (Reuters 2013) : since fast response is important double-checking signals is too slow, and once the market dynamics is set it becomes irrational to act just on the true information. This can contribute to instability, both in the large but also in the small in the form of ultrafast extreme events that are far outside human reaction times. There appears to exist a systemic transition when the number of agents is larger than the number of strategies and there is not enough time to process information  (Johnson et al. 2013 ). Together, this both suggests unfairness caused by speed differences and risks from lack of control. Speed inequalities matter in communication too: people need to be able to meaningfully respond to each other to have relations, and this includes being part of society. In an interaction it is the slowest participant that sets the overall speed. This may contribute to an incentive for fast systems to mostly talk to fast systems, and limit human contact. An extreme example is the social stratification predicted in a society of minds running at different speeds  (Hanson 2016 ), but milder examples abound of side-lining slow responders in organisations and engineers minimizing requests to slow subsystems. \n Decision speed Faster computation promises potentially near-instant decisions. However, these are subject to information limits: a decision can only happen when it is known with enough certainty that a triggering condition has occurred. Computation was sometimes in the past the slowing factor, but slow information arrival (due to sensors, communication speed, low bandwidth) is likely more relevant in a fast computation world. Acting early with less information is less certain and this will introduce risk. The real bound on decision speed may hence be acceptable uncertainty in a given situation. \"Faster computation\" is typically measured relative to fixed rate of human activity. More things become possible inside our time budgets, but we cannot observe/control too fast activities directly. We can leave this to automation, but now we have delegation problem. Circuit-breakers for financial markets will stop pre-described events but may let through anything else, creating a false sense of security. Many human systems have layers acting on different timescales, for example slow-changing constitutions underlying laws, policies, social norms and fashions. This ensures that observation and control can function. If breaks between the layers emerge, that means there is no meaningful control. This may have been a contributing factor to the financial crisis in that regulators did not understand the changing financial instruments and their implications. Decision speed is also competing with time for deliberation. Drone pilots have the problem that faster systems make the human in the loop the slowest and most performance decreasing factor, while being morally responsible takes time (and the pilot will be blamed for low performance and morally questionable actions). This issue gets writ large in the case of nuclear missiles. It is about 30 minutes Moscow and Washington as the ICBM flies, just about time for a \"red phone\" call for negotiations to occur. But between Islamabad and Delhi it is 5 minutes: were an unauthorized or accidental launch to occur the time for internal and external deliberation is exceedingly short. \n Loss of opportunity The irreversibility of time has great ethical importance. Choosing now and fast can remove opportunity for later choice, especially when actions are irreversible such as using up non-renewable resources or releasing information  (Bostrom, Douglas & Sandberg 2016) . This is an issue since we will likely have better information in the future and may hence evaluate the actions differently. Yet waiting in a risky state can be worse than taking a risk since risks are likely to catch up with us. We may want to trade a \"state risk\" such as nuclear war being possible for a \"transition risk\" that removes the state risk at a price of a temporary but greater risk (a radical disarmament deal, inventing superintelligent AI to \"solve geopolitics\")  (Bostrom 2014, p. 233)   \n Identity over time A final issue is the accumulation of change. Complex adaptive systems interacting with the world will change their internal structure as a response: learning/forgetting information, restructuring itself, breaking or reproducing. This can change their fundamental identity in relevant ways. What constitutes the important aspects of identity depends on the system and observer, but the \"wrong kind\" of identity change must be avoided since it loses accrued value. It is not the span of time that matters but the amount of change. Typically, there is a \"change budget\" that can soak up the modifications without losing identity. Software, people and organisations that instantly change often change identity in the wrong way, while the same transformation done gradually may be both identity preserving and acceptable to stakeholders. This is at the core of Toffler's concept of future shock  (Toffler 1970) . Faster information processing means a higher rate of accumulating change, straining the change budget. Rapid adaptation may be beneficial from a control perspective but risks reducing the change budget. \n Societal impact and governance As we have seen, the great challenge outlined in this paper is growing gaps of speed between computation and the human (ethical gaps) and gaps of speed between computation and control (cybernetic gaps). In terms of governance the risk is that this produces a policy vacuum  (Moor 1985 (Moor , 2005 ). There will be a growing number of situations where there are no policies, yet actions must be taken. The time needed to conceptualize the situation and deliberate it remains on the human timescale. The eternal refrain that technology is outpacing ethics represents not just an ethical gap due to speed but also a cybernetic gap due to lack of information: decisions cannot rationally happen faster than there is information to decide upon. The Collingridge dilemma  (Collingridge 1982 ) is partially cybernetic . Yet faster computation also strongly increases the power of the state and institutions through cybernetic feedback shifts and increased legibility  (Scott 1998) . Surveillance power has grown faster than Moore's law since it scales with hardware, software, data availability and sensor ubiquity (while institutional oversight has hardly kept up at the same rate; there is a widening cybernetic gap here). If searching for a person can be done in real-time it is very different from an ongoing bureaucratic process. Can governance be speeded up meaningfully, assuming human speed remains constant? (We will here ignore the possibilities of enhanced posthuman speed discussed in  (Hanson 2016 ).) Financial market circuit breaker rules are automated, speeded up governance solving the humanmachine speed difference problem in a small domain. However, their utility depends on whether the system can detect the right issue. They need a decision parameter that is both necessary and sufficient for a break (and high quality). If it is not sufficient they produce false alarms. If it is not necessary, they might miss things that matter. If it is not of high quality, it may measure the wrong thing. In the stock market measuring trading volume and value makes sense but may still miss subtle qualitative shifts (e.g. in correlations) predicting a systemic risk. This is basically a principal-agent problem, where the agent may be a thing designed for a purpose -but as Bostrom shows, the AI principal agent problem is doubly hard  (Bostrom 2014) . Some parts of governance just consist of processing information or doing formal, well-defined decisions: these can in principle be speeded up. There is a drive to do this to save money, provide timely service, increase fairness etc. This will likely work best for routine, well-specified governance without elements of social or strategic intelligence. The risk is that we end up with algocracy, opaque decision-making with little legitimacy  (Danaher 2016) . Another risk is that since such routines will have apparent or real instrumental value they will be favoured over messy and slow routines requiring intelligence, producing a legible but far more limited governance system. However, governance can also affect the speed of computation. While controlling the growth of technology in general is unlikely because of its broadness, epistemic unpredictability and utility, it is certainly possible to mandate speed limits (e.g. delays on stock markets to avoid high-frequency trading  (Farmer & Skouras 2012) ), mandating response time limits, or even mandating the use of certain technology (e.g. accessibility requirements for websites). Another approach is the differential technology development principle  (Bostrom 2014, pp. pp. 229-237) : if potentially harmful technologies are developed more slowly than technologies reducing their risks, their benefits will become available with less risk. This can be achieved by focusing funding and research priorities on the harm reduction technologies. In the current context this might include promoting technical solutions to ethical and cybernetic gaps. Controlling algorithms is hence not so much about banning practices as having an adaptive, global learning system that observes what is going on, remembers past states, maintains a set of values that may be updated as information arrives, and then changes incentives to promote these values -open to updating every part in this system. \n Conclusions There is very much more computational speed to be had, and we will likely reach it. This will generally produce much more value -better productivity, better predictions, better control, more opportunities. But those desirable aims will also lead to control gaps, systemic risks, speed inequalities, overly fast or uncertain decisions. This will challenge governance strongly, risking both policy vacuums, a drive towards algocracy, and numerous principal agent problems in bridging ethical and cybernetic gaps. Yet strong enough governance can mandate speeds, and adaptive and distributed governance can update faster. It is possible to prioritize areas where speed issues are known to generate trouble for regulation and using differential technology development to stimulate foresightful and responsible technology development. \n . State risks are reduced if we speed up macro-structural development: less time in risky periods. Transition risks are reduced by having more time for preparing. Problems where learning from experience dominate solutions benefit from slowing down and getting more time to have experience, while problems requiring forethought or insight may benefit less. \n\t\t\t If different tasks have utilities per unit of time distributed as f(u) for some probability distribution f, then the best utility after sampling N will have distribution 𝑓 * (𝑢) = 𝑁𝑓(𝑢)𝐹 𝑁−1 (𝑢), where F(u) is the", "date_published": "n/a", "url": "n/a", "filename": "There+is+plenty+of+time+at+the+bottom+4.tei.xml", "abstract": "Purpose -The speed of computing and other automated processes play an important role in how the world functions by causing \"time compression\". This paper reviews reasons to believe computation will continue to become faster in the future, the economic consequences of speedups, and how these affect risk, ethics and governance. Design/methodology/approach -Brief review of science and trends followed by an analysis of consequences. Findings -Current computation is far from the physical limits in terms of processing speed. Algorithmic improvements may be equally powerful but cannot easily be predicted or bounded. Communication and sensing is already at the physical speed limits, although improvements in bandwidth will likely be significant. The value in these speedups lie in productivity gains, timeliness, early arrival of results, and cybernetic feedback shifts. However, time compression can lead to loss of control due to inability to track fast change, emergent or systemic risk, and asynchrony. Speedups can also exacerbate inequalities between different agents and reduce safety if there are competitive pressures. Fast decisions are potentially not better decisions since they may be made on little data. Social implications -The impact on society and the challenge to governance is likely to be profound, requiring adapting new methods for managing fast-moving and technological risks. Originality/value -The speed with which events happen is an important aspect of foresight, not just as a subject of prediction or analysis, but also as a driver of the kinds of dynamics that are possible.", "id": "7ab3bda00a4122648d1db79807acbbe8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anthony Michael Barrett"], "title": "Value of Global Catastrophic Risk (GCR) Information: Cost-Effectiveness-Based Approach for GCR Reduction", "text": "Introduction Global catastrophic risks (GCRs) are risks of events that could significantly harm or even destroy human civilization at the global scale  (Hempsell 2004 , Baum 2010 . GCRs presently posing hazards to humanity include nuclear war  (Sagan 1983 , Turco et al. 1983 , Robock et al. 2007 , Cirincione 2008 , Hellman 2008 , Barrett et al. 2013 ) and pandemic diseases  (Nouri and Chyba 2008) . In the near to longer-term future, GCRs could include climate change  (Weitzman 2009 , Travis 2010 ) and misuse or accidents involving technological developments in areas such as artificial intelligence  (Yudkowsky 2008 , Chalmers 2010 , Sotala 2010 ) and nanotechnology  (Phoenix and Treder 2008) . Proposed interventions to reduce GCR include nuclear disarmament  (Robock et al. 2007 ), development and distribution of vaccines and antiviral medications  (Osterholm 2005) , reducing greenhouse gas emissions through public policies  (Aldy et al. 2003)  and various individual behaviors  (Dietz et al. 2009) , and abstaining from developing certain technologies  (Joy 2000) . A growing body of work makes the case that reducing GCR, or certain types of GCR, is of very high value and thus should be one of the highest objectives for society  (Ng 1991 , Bostrom 2002 , Posner 2004 , Matheny 2007 , Tonn 2009 , Ćirković et al. 2010 , Beckstead 2013 . Published estimates of the value of preventing global catastrophe range vary wildly, from $10 billion  (Bostrom and Cirkovic 2008)  to infinity  (Weitzman 2009 , Baum 2010 , depending partly on the definition used for \"global catastrophe.\" Even the low end of this suggests a large allocation of resources toward GCR reduction. However, setting GCR reduction as a high priority is not a sufficient guide for action: there are many open questions regarding how best to allocate resources for GCR reduction. One basic question is how much to allocate toward direct risk-reducing interventions and how much to allocate to research to inform these interventions. The decision analysis concept of expected value of information  (Clemen and Reilly 2001 , Keisler 2004 , Bhattacharjya et al. 2013  can inform decisions about how much to spend on information  (i.e., reduce Decision Analysis, 2017 , vol. 14, no. 3, pp. 187-203, © 2017  uncertainties) prior to making other resource allocation decisions. Usually in value-of-information calculations, decision options are evaluated using utility functions, money, or functionally similar metrics that have implicit commensurability between option trade-offs, e.g., lives saved versus dollars spent. However, equating lives and dollars, e.g., using a typical value of statistical life (VSL) saved, may be inappropriate given the potentially vast scale of GCRs. (Moreover, quantifying total event consequences of global catastrophe in conventional benefit-cost terms would be complicated by uncertainties about direct event impacts, indirect impact factors such as public behavioral responses, and the levels of such impacts that could be borne before reaching civilizational-collapse tipping points.) We take a different, cost-effectiveness-based approach in this paper instead. A cost-effectiveness-based equation for value of information also may be useful in other domains where typical VSLs would not be appropriate. In this paper, we argue that value of information based on cost-effectiveness is a useful tool for analysis of GCR to inform risk-reduction decisions, and we show that it can be defined in a practical manner. We argue that such an approach would be most valuable if applied in a comprehensive, integrated fashion to all major types of GCR, rather than one at a time. We describe a number of challenges that would arise in such efforts, and argue that these challenges can be addressed. We also provide an illustrative, though highly idealized, example that shows how a practical value of information calculation can work. It also provides support for our argument that such calculations can have considerable value, and it provides further support for our argument that value of information can provide additional insight when more than one GCR is under consideration. In Section 2 of this paper, we give a brief overview of the basics of the approach and how to apply it to GCRs and risk-reduction interventions in a comprehensive, integrated fashion. In Section 3, we discuss key challenges in real-world implementation of this paper's framework and argue that these challenges can be addressed. In Section 4, we illustrate the basic framework using a simple notional model of GCR from two types of near-Earth objects (NEOs; i.e., asteroids and extinct comets) as well as nuclear war, and consideration of two related risk-reduction measures. The illustrative example shows that such calculations can have considerable value, especially when considering multiple GCRs. We conclude in Section 5. (In the appendix, we provide a detailed derivation of our formula for the expected value of information in terms of the costeffectiveness of GCR reduction.) \n Overview of Framework for Value of GCR Information In this section, we briefly discuss ways to approach three linked sets of quantitative issues: first, representing the probabilities of multiple GCRs; second, assessing the overall cost-effectiveness of GCR-reduction measures and calculating the value of information for GCR reduction; third, contrasting perfect and imperfect information. More details of our approaches and assumptions are given in the following sections. \n GCR Probabilities Figure  1  is a fault tree or logic tree illustrating that there are multiple types of global catastrophic risks, and occurrence of each is assumed to be causally independent of the others, at least at the level of detail used in the fault tree (e.g., nuclear war does not cause asteroid impact). The event \"Global Catastrophe\" is the top event, with round-corner nodes for a series of GCR types branching out below, all connected by an OR gate. The fault tree graphically indicates that a global catastrophe will occur if any of the following types of event occur with global catastrophe-level consequences: a large NEO impact (either an asteroid or a comet impact), large nuclear war, or a combination of smaller events (small NEO impact plus small nuclear war), etc. In addition, Figure  1  includes square-corner decision node risk management for two types of GCR-reduction options (i.e., NEO redirection, and food stockpiling) that could reduce the probabilities of global catastrophe-level outcomes. Grey arrows from the square-corner decision nodes to the roundcorner fault tree nodes indicate that the risk management decisions can influence the risks of global catastrophe-level events. Figure  1  also illustrates that some risk-reduction measures, e.g., food stockpiling, can have benefits in reducing multiple types of GCR. Although the fault tree portion of Figure  1  is quite simple, it is intended to underline the main motivation for considering GCRs as a whole, and not just individual types such as asteroids, comets, or nuclear  \n Food stockpiling Combination of small nuclear war and small asteroid impact GC Small nuclear war Small asteroid impact AND war: to assess and reduce the total probability of global catastrophic risk, ideally we would assess all types of GCRs and GCR-reduction measures in a comprehensive way. The framework also can account for interactions between GCR events, such as when occurrence of one type of event reduces society's resilience to or even causes another type of event  (Baum et al. 2013) . Such interactions between GCRs could be represented using larger, more detailed fault trees (e.g., by adding branches for scenarios in which both NEO impact and nuclear war events occur around the same time, either just by chance of timing or because an NEO impact somehow causes nuclear war), though it could be difficult to explicitly account for many GCR-interaction scenarios, and important uncertainties could remain about unmodeled GCR-interaction dynamics. Figure  2  is a generic consequence exceedance probability plot for some type of event (e.g., NEO impacts), with curves showing relationships between event consequence and the probability of events with consequence exceeding that level, for both initial and reduced event risks. The figure illustrates that reduction in probability of global catastrophe can be achieved either by reduction of probability of events or by reduction of consequences. Starting from the upper right of the figure, the point where the initial event probabilityconsequence curve intersects with the global catastrophe consequence threshold indicates the initial probability of global catastrophe. The figure also includes two reduced-risk curves, one for reduced event probability and another for reduced event consequence. The curves for reduced probability and reduced consequence have been placed where they result in the same reduction in probability of global catastrophe, partly to keep the figure simple and partly to emphasize the idea that GCR reduction can be achieved by reducing either event probability or consequence. For example, NEO impact risk-reduction measures could reduce the probabilities of global catastrophelevel outcomes either by shifting the curve downward with reduced NEO impact probabilities (e.g., via NEO redirection) or by shifting the curve leftward with reduced NEO impact consequences (e.g., increasing societal resilience to NEO impact via food stockpiling). Thus, probabilities of global catastrophe for a particular GCR event type could be calculated as a function of Decision  Analysis, 2017 Analysis, , vol. 14, no. 3, pp. 187-203, © 2017   global catastrophe consequence threshold, using consequence exceedance probability models for that event type. Of course, development of appropriate consequence exceedance probability models would often require substantial research, especially when focusing on rare or unprecedented events, for which a lack of data often leads to substantial uncertainties and biases  (Taylor 2008) . In many cases, there would be large uncertainties for both the direct consequences of an event (e.g., in terms of atmospheric soot loading from various nuclear war or NEO impact scenarios) and what threshold level of consequences would result in global catastrophe (e.g., in terms of the effects of atmospheric soot loading on agricultural productivity and other indirect effects on human society, which could be highly nonlinear if stresses could reach civilizational resilience-exceedance tipping points). Such uncertainties could be modeled using probability distributions for the global catastrophe consequence threshold and exceedance probability function. One way to represent uncertainties is to display 5th and 95th percentile value lines in addition to the mean value lines  (Garrick 2008) , as shown in Figure  3 . Given the previously mentioned assumption of causal independence, Equation (1) gives the total probability of a global catastrophe-level event within some time period, p total , as a function of the independent probabilities p j of catastrophe events of each GCR type, j, for a total of y GCR types. Equation (1) is mathematically consistent with the previous statement that a global catastrophe will occur if a type of global catastrophe involving a large asteroid impact, a comet impact, or nuclear war, etc., occurs: p total 1 − y j (1 − p j ). (1) \n Cost-Effectiveness and Value of Information for GCR Reduction Figure  4  is a high-level decision tree, consistent with typical trees used in calculating value of information. (The tree does not include specific quantitative values for probabilities, costs, and benefits, but it does indicate the general sequence of decisions and events.) The leftmost square decision node represents a decision to be made on whether to invest in research to inform decisions on risk-reduction measures; other decision nodes represent addition to a basic decision on whether to measures to reduce risks. In Figure  4 , the research decision is simple: conduct research to better understand whether risks are currently high or low, or do not conduct such research. The risk-reduction decision options are also simple: invest to reduce risks or do not invest to reduce risks. The decision on whether to conduct research is made before the decision on whether to invest in reducing risks. If the decision maker chooses not to conduct research, then they make the riskreduction decision with some amount of uncertainty about whether risks begin as high or low. (That uncertainty is represented by circular chance nodes, and the outcomes of chance nodes are represented by diamonds.) If the decision maker does choose to conduct research, then they have more information and less uncertainty about whether risks begin as high or low, and the decision maker can use that information when making their decision on whether to invest in reducing risks. A full valuation of GCR-reduction interventions, including research to gain information, requires some evaluative metric. Typically, decision options are evaluated using utility functions or functionally similar metrics. 1 Such metrics have implicit commensurability between option trade-offs, e.g., lives saved versus dollars spent. Use of such approaches allows for a relatively simple equation for expected value of options with various attributes  (Clemen and Reilly 2001) , including trade-offs between GCR reduction and other objectives. In this paper, we avoid full valuations and instead conduct partial valuations in terms of costeffectiveness, measured in GCR reduction per unit cost. We focus on cost-effectiveness for two reasons. First, a full valuation for GCR is complicated by the widely varying estimates for the value of preventing global catastrophe; which can range from $10 billion to infinity, as mentioned in Section 1. Second, many GCRreduction decisions involve allocating resources, such as money. However, equating lives and dollars, e.g., using a value of statistical life saved, may be inappropriate given the scale of GCRs. Therefore, our equation for calculating value of information is based on riskreduction cost-effectiveness, which incorporates estimates of the performance and costs of risk-reduction options without use of VSLs. Our cost-effectivenessbased equation for value of information may be useful in other domains where VSLs would not be appropriate. We assume that there are one or more decisions to be made about the allocation of resources to some combination of options for risk reduction and options for research, and that the decision rule is to choose whatever combination of options has best overall expected GCR-reduction cost-effectiveness among options considered in the analysis. (Such considerations could occur in a series of risk-reduction decisions, in which case the goal could be to identify the most cost-effective interventions first, and then the second most, and so on, until a risk-reduction budget or target has been reached.) Then, in such decisions, the decision maker should buy as much risk reduction (and risk research enabling better risk-reduction decisions) as they can at whatever total cost, as long as that results in the greatest cost-effectiveness. Such decisions can arise when considering public policies, as well as the actions of individuals and other nongovernmental organizations. (We assume that budgets are not an issue in the context of the risk-reduction and research options under consideration, and we do not explicitly account for potential budget constraints in the following. However, consideration of budget constraints could be addressed as an extension of the approach used in the following.) For the purposes of this analysis, we ignore actual costs of research and focus on the amount of resources the decision maker ought to be willing to pay for Decision  Analysis, 2017 Analysis, , vol. 14, no. 3, pp. 187-203, © 2017   the value added by the research in the context of the decision the research could inform. In other words, we focus on finding the maximal potential benefits of research. We assume that research ought to be invested in up to the point where a funder would obtain no further benefit from investing in additional research (because up to that point, they would get a better overall cost-effectiveness by investing in additional research). At that point, the expected cost-effectiveness of the best risk-reduction option before research is equal to the expected cost-effectiveness of the best riskreduction option after research, including the cost of research. Equation (2) gives the value of research as the costeffectiveness-based expected value of perfect information, CEEVPI (see the appendix for derivation): CEEVPI E c b s (p a 0 − p a s ) p b 0 − p b s − c a s . (2) The equation assumes the following: There exists a set of n available risk-reduction options numbered 0, 1, . . . , i, . . . , n. Option number 0 is the status quo case, where no new (or non-\"business-as-usual\") riskreduction option is implemented. The cost of implementing risk-reduction i is c i . (It costs nothing to do nothing, so c 0 0.) The annualized total probability of global catastrophe if implementing option i is p i . (We make the simplifying assumption that p i values are static, or unchanging over the relevant time period. Consideration of dynamic, or time-varying, p i values could be addressed as an extension of the approach used in the following.) Each c i is treated as a random variable with some probability distribution reflecting uncertainty about the true cost of implementing intervention i. Each p i is also treated as a random variable, with a probability distribution reflecting plausible estimates of the annual probability of global catastrophe given intervention i. 2 Computationally, the uncertainty is represented using Monte Carlo simulation, where in Monte Carlo simulation iteration m there are sampled values c im and p im . The risk-reduction option s is the option with the \"best\" or highest risk-reduction cost-effectiveness in Monte Carlo iteration m. In addition to decisions on which risk-reduction option to choose, there are also decisions on whether to first spend some resources on research to reduce uncertainties (and to more accurately identify which riskreduction option would be most cost-effective) before making decisions on risk reduction options. We denote whether research is conducted to reduce uncertainty on a particular factor using superscript b for \"before\" research, or without information from research, and superscript a for \"after\" research, or with information from research. Generally, research will have the greatest expected value if it has substantial possibility of informing a decision, i.e., a choice between risk-reduction options. However, the CEEVPI formula also implies that if it is expected that the best option after research is the same as the best option before research (i.e., if s a s b ), then the research still can have positive expected value if it is inexpensive enough and also provides sufficient reduction of uncertainties in p and c factors. We provide an example, calculating CEEVPI for illustrative catastrophic NEO impact risks and riskreduction options, in Section 4. The example suggests that the value of GCR information could be quite substantial. \n Perfect and Imperfect Information In the context of a decision analytic model, the value of information is based on the extent to which information reduces the uncertainty about the value of a particular parameter in the model. Perfect information eliminates that uncertainty. The expected value of perfect information (EVPI) is the difference between the expected value of a decision with perfect information (where the new information influences the decision we make) and without additional information (where we make the decision with our initial level of uncertainty; Clemen and Reilly 2001). We do not expect real-world GCR research to yield perfect information in the sense of eliminating all uncertainties. In general, EVPI calculations are used to set an upper limit to how much should be spent on reducing uncertainty. On their own, EVPI calculations cannot predict how valuable specific research will be in reducing uncertainty. However, even imperfect information can have great value in reducing decision model parameter uncertainties by some amount. Straightforward extensions of the approach to EVPI calculations used in this paper (based on costeffectiveness calculations) could provide methods to assess the expected value of imperfect information  (Clemen and Reilly 2001)  and expected value of including uncertainty  (Morgan and Henrion 1990) . \n Key Challenges of Integrated Assessment of GCR In this section, we discuss important challenges for the implementation of our framework for calculating value of information, and for comprehensive, integrated assessment of GCR to inform risk-management decisions. We have already mentioned some of these challenges, which we discuss further here. We also discuss others that we have not mentioned previously. One challenge is that in the real world, there would often be complex interactions between GCRs, not all of which could be modeled. As previously mentioned, one important simplification of our approach is the assumption of independence of GCRs except where indicated in the model. In principle, many types of interactions could be accounted for by building them into fault trees or other model components, but that could require substantial efforts. As with modeling of any complex system, there would be large uncertainties about how much of the real-world dynamics would remain unmodeled. A similar set of challenges (and irreducible uncertainties) would be encountered in attempting to define global catastrophe consequence thresholds. Another challenge would be in setting appropriate thresholds for catastrophe. An important simplification of our approach is that we use a binary threshold for catastrophe (i.e., an event is only regarded as a global catastrophe if the event's consequences exceed the global catastrophe consequence threshold, however that is defined). In reality, events of a range of magnitudes could be regarded as global catastrophes, either because different stakeholders have different definitions of what constitutes a global catastrophe, or because of uncertainties about what levels of Decision  Analysis, 2017 , vol. 14, no. 3, pp. 187-203, © 2017  direct effects from catastrophe events would reach civilizational tipping points. (Those uncertainties would stem partly from the difficulty of predicting indirect effects of catastrophe events, which involve complex factors such as the behavioral responses of large human populations. However, the analytic challenges and uncertainties would be even greater if the aim were to quantify total event consequences in conventional benefit-cost terms, which is another reason to use a simpler cost-effectiveness approach.) Differences between global catastrophe thresholds can have important implications for decision making.  3  Decisions should favor preventing higher-magnitude global catastrophes or decreasing the severity of any given global catastrophe. Furthermore, ideally, decisions would be robust (not highly sensitive) to placement of the global catastrophe threshold. As always, sensitivity analysis can usefully examine the decision implications of varying global catastrophe thresholds, and uncertainty analysis can suggest ranges to use in sensitivity analysis. There also would be challenges in defining what decision procedures to actually use, and how to incorporate considerations such as budget constraints and timing decisions. It seems unwise to take a perfectionist approach to assessing risks and risk-reduction optimality, because the complexity and scale of all potential risks and intervention options (including all interactions and combinations) could make that approach intractable. A more practical approach could be to make a series of risk-reduction decisions, either at regular or irregular intervals, that would first implement the most cost-effective interventions (or combination of interventions), then the second most, and so on, until a risk-reduction budget or target risk level was reached (essentially a greedy algorithm solution to a knapsack problem, in operations research terms). We believe the latter approach would be roughly consistent with our basic framework, though our current framework does not attempt to explicitly account for budget constraints, nor decision sequentiality. It also should be noted that our basic approach implicitly assumes the goal is zero probability of global catastrophe, but other targets could be used; for example,  Tonn (2009)  suggests a 10 −20 annual probability of global catastrophe as an \"acceptable risk\" target. Finally, accounting for timing of events and interventions could present substantial complications. For some issues, it could be important to account for decisions of exactly when to research, when to implement measures, and in what sequence; the urgency of implementing various measures also could be important. Although time dependencies are not explicitly reflected in the level of detail given in this paper, implicitly they could be incorporated into the model parameter values for effects of the risk-reduction measures. (For example, if considering implementation of an intervention today, versus some years from now, and if the GCR minimization objective is to minimize the probability of global catastrophe over the next century, then for many GCRs types such as NEO impact, presumably analysis would show greater GCR-reduction benefits from implementing interventions sooner rather than later.) At least in principle, time dependencies could be accounted for in modules whose outputs are fed to the model structure shown in this paper. Another challenge is that in the real world, there is not a single very well-funded actor whose prime objective is to reducing GCR cost-effectively. Instead, there are many potentially important decision makers, each with limited budgets and responsibility for GCR factors, and with various objectives that compete with GCR reduction. Potentially important decisionmaking entities include government agencies, such as the U.S. National Aeronautics and Space Administration (NASA), which have programs to address specific categories of GCR such as NEO impact risks; nongovernmental organizations such as the Open Philanthropy Project, which have programs to address either specific categories of GCR or all GCR broadly; corporations such as Walmart, whose product management decisions can have implications for societal resilience, emerging technologies, and other GCR factors; and individuals such as researchers, whose work can improve understanding of GCR factors and that have decisions to make about where to focus their own research efforts. Nevertheless, if credible integrated assessment has identified some GCR-reduction options as clearly being more cost-effective than others, that could influence decisions by various means, especially where actors already have some incentives to reduce societal risks. For government agencies, integrated assessment could inform budget reallocations, e.g., taking funding from low-value areas to fund highervalue risk-reduction programs, and incentives could be provided via government rules that encourage costeffective risk-reduction benefits to society. At the other end of the size spectrum, for individual researchers, integrated assessment could suggest which kinds of research could best lead to risk-reduction societal impacts, which are encouraged by both formal funding reviews and informal norms. Nongovernmental organizations and corporations also often combine efforts on voluntary stewardship initiatives and other programs to reduce societal risks, and thereby gain reputational rewards. Some of the most important challenges concern the scope of analysis, such as what GCRs and riskreduction measures to consider initially (given that starting-point estimates or at least bounding ranges would be needed for all associated modeling parameter values).  4  One approach that should be relatively tractable is breadth first: Begin by taking a broad but shallow approach to modeling GCRs and riskreduction options relatively comprehensively, but with little detail, and with quantitative parameter estimates aimed only at bounding ranges of uncertainties. Then, a series of subsequent, repeated model-improvement steps could iteratively add depth (i.e., to add detail and better quantitative estimates using the best available empirical data, expert judgment, etc.), and decisions on where to focus model-improvement efforts via research could be guided by value-of-information calculations. \n Illustrative Example: Notional Model of NEO Impact Risk and Mitigation In this section, we illustrate our concepts using information in the literature on impact risks posed by two types of near-Earth objects as well as nuclear war. We also provide illustrative modeling of two types of impact risk-reduction measures (i.e., NEO redirection and food stockpiling) that could reduce the probabilities of global catastrophe-level outcomes. These are very simple, notional models of risks and decisions, intended only to illustrate our value-of-information concepts. The example does not attempt to reflect all the latest references, such as the information on asteroid and comet impact risks yielded by the Wide-field Infrared Survey Explorer (WISE) and Near-Earth Object WISE (NEOWISE) survey programs. (Such research has often resulted in downward revisions in catastrophe probability estimates for both high-and low-albedo NEOs.) The example also does not attempt to estimate the risks or risk-reduction benefits related to GCRs besides NEOs and nuclear war, although considering those would affect overall GCR-reduction cost-effectiveness estimates. For example, food stockpiling could have benefits in reducing the effective consequences of pandemics, which is a category of GCR that is not considered in this illustrative example. \n Illustrative Model GCRs, Risk-Reduction Measures, and Assumptions The first type of NEO we model is \"bright\" or easily visible asteroids/comets, which can be observed and tracked long before impact using current astronomical capabilities. The Spaceguard Survey is believed to have detected most such NEOs with greater than 1 km diameter (National Research Council 2010). The second type of NEO we consider is \"dark,\" or lowreflectivity damocloids, which current identification and tracking systems may not see until the objects are already headed directly toward impact. Partly because of the difficulty of observing damocloids using optical telescopes, there are large uncertainties about the frequencies of damocloid impact  (Napier 2008 , National Research Council 2010 . Before the Spaceguard survey, such objects were thought to be a small risk relative to other NEOs, but damocloids and long-orbit objects have more recently been viewed as potentially posing the majority of remaining impact risk (National Research Council 2010). The NEOWISE survey program has been using infrared technology to better identify damocloids. Presumably, additional investments in research using infrared, radar, or other technologies could provide better observations of damocloids. Perhaps such damocloid observation systems would be deployed as some combination of Earth-based systems, satellites, and probes. We also model two types of impact event risk-reduction measures. First are NEO orbit redirection measures that offer good and relatively inexpensive reduction of risks of asteroids that are identified and thought to impact years or decades away  (Matheny 2007) . The NEO redirection measures would reduce the probability of impact of a large asteroid. However, we assume Decision  Analysis, 2017 , vol. 14, no. 3, pp. 187-203, © 2017  that they would not reduce the probability of impact of damocloids (at least, not without additional investments to identify damocloids, which is beyond the scope of this illustrative example). The second type of risk-reduction measure is food stockpiling to provide significant food reserves for a large number of people in case of a period of reduced food production  (Rampino 2008) . The impact effects of large asteroids and comets could be broadly similar to nuclear winter and supervolcanism in their negative impacts on global food production. Food stockpiles may help humanity to survive either event.  Rampino (2008)  mentions that one potential supervolcanism survival strategy would be to stockpile enough food (e.g., grain) to last several years until agricultural productivity goes back up.  Rampino (2008)  notes that current inventories are only equivalent to about two months' consumption. While difficult to accomplish in many parts of the world, it still might be relatively feasible without advanced technology, should be relatively uncontroversial (especially if production is handled in a way that does not drive up global food prices very much), and could have some value across a number of GCR hazards including war, quarantine after pandemic, etc. In addition, unlike some other GCR mitigation measures, stockpiled food should retain near its purchase value in normal usage even in time periods where no GCR scenarios arise (i.e., if no emergencies arise before the stored food expires, the food can be eaten when rotated out of the stockpile and replaced with new reserves). We implement calculations for the illustrative example in a computational model using the software package Analytica by Lumina Decision Systems. The computational model incorporates all the defined equations and parameters. To estimate probability distributions of outputs, the model performs Latin hypercube sampling, with a model sample size of 10,000 iterations. The model varies continuous-valued inputs according to the previously given probability distributions, and the model produces probabilistic values of its outputs. For more on relevant distributions, e.g., uniform and triangular distributions, see  Morgan and Henrion (1990)  or the Analytica user guide  (Chrisman et al. 2007) . \n Assumptions for Baseline P(Global Catastrophe). Our estimation of the probabilities of bright object and dark object impact risks is based partly on first estimating the total bright object asteroid impact risk, and then estimating how large the dark object comet impact risk is in comparison specifically to bright objects. We estimate the total probability of impacts of asteroids at least 1 km in size as corresponding to a frequency of one in 3 × 10 5 years. That is based on Figure  2 .4 on p. 8 of the National Research  Council (2010)  or the equivalent on p. 19 of the National Research Council (2010), which indicate a 1 km object impacts approximately once every 4 × 10 5 years. We assume that only 15% of the total population of bright NEOs remain undiscovered  (National Research Council 2010) . For bright NEOs that have already been discovered, we also assume negligible impact risk: \"none of those detected objects has a significant chance of impacting Earth in the next century\" (National Research Council 2010, p. 19). The simple way we reflect that in the model is to say the impact risk from visible/ bright NEOs is 0.15 × (1/(3 × 10 5 )). We assume that the impact frequency of damocloids has a probability distribution of Uniform(0, 4) × (1/(3 × 10 5 )), based on a statement by  (Napier 2008, p. 229 ) that the hazard from damocloids of 1 km diameter \"is unknown; it could be negligible, or could more than double the risk assessments based on the objects we see.\" Some corroboration is provided by the statement by  (Napier 2008, p. 226 ) that at the time of his writing, for 1 km objects, there was an \"expected impact frequency of about one such body every 500,000 years.\" Once every 500,000 years is about the same as the once every 3 × 10 5 years we assume for over-1-km visible objects, but for better consistency and comparability with bright NEOs, we use 3 × 10 5 instead of once every 500,000.  Napier (2008, p. 225 ) also observes the following: Estimates based on the mean impact cratering rate indicate that, on the long-term, a 1 km impactor might be expected every half a million years or so. Again, modeling uncertainties to do with both excavation mechanics and the erratic replenishment of the near-Earth object (NEO) population yield an overall uncertainty factor of a few. A rate of one such impact every 100,000 years cannot be excluded by the cratering evidence. All of the above numbers also have additional uncertainty factors (coefficients) of Triangular(0.5, 1, 2), which is loosely based on the statement by the (National Research Council 2010, p. 8) that the uncertainties in intervals between impacts are \"on the order of With the completion of the Spaceguard Survey (that is, the detection of 90 percent of NEOs greater than 1 kilometer in diameter), long-period comets will no longer be a negligible fraction of the remaining statistical risk, and with the completion of the George E. Brown, Jr. Near-Earth Object Survey (for the detection of 90 percent of NEOs greater than 140 meters in diameter), longperiod comets may dominate the remaining unknown impact threat. Finally, for an extremely simple estimate of the annual probability of nuclear war, based loosely on estimates given in the literature  (Hellman 2008 , Barrett et al. 2013 , Lundgren 2013 , we simply use Triangular(0, 0.0001, 0.001). It seems likely that the annual probabilities of global catastrophe events are orders of magnitude higher for large-scale nuclear war than for large NEO/comet impacts. In our calculations, we use a simplifying approximation of annual probability as being equivalent to annual frequency (e.g., a frequency of one event in 500,000 years implies an annual probability of 1/500,000). Table  1  contains summaries of the assumed annual probabilities of global catastrophe-level events from each considered GCR type. The expressions reflect the substantial uncertainties. \n Assumptions for Reduction in P(Global Catastrophe) if Implementing Each GCR-Reduction Mea- sure. Although the lower bound of effectiveness of NEO detection and redirection might seem to be quite low, it is based partly on the idea that NEOs that have not already been discovered might be significantly more difficult to detect than the ones that have already been detected. This was suggested by  Napier (2008, p. 226)  regarding the success of NEO detection efforts to date: \"There is a caveat: extremely dark objects would go undiscovered and not be entered in the inventory of global hazards.\" For food stockpiling, the assumed probability distribution for the reduction in probability of global catastrophe-level NEO/comet impacts is Uniform(0.1, 0.9). It assumes that the stockpile would be comprised of extremely inexpensive sources of calories and nutrients (see below on cost assumptions), for which there would be large uncertainties about riskreduction performance. Table  2  contains summaries of the assumed effects and costs of GCR-reduction measures. (A status quo option, which adds no cost and does not reduce GCR, is omitted from the table but is an additional option in the model.) The effects of the measures are given in terms of their assumed reduction in probability of global catastrophe from each GCR type. The costs of the measures are given in terms of the present value of their costs in 2012 dollars. \n Assumptions for Costs of GCR-Reduction Mea- sures. The cost estimate for food stockpiling assumes a world population of 7 billion, a one-year stockpile, and a per-person-year stockpile cost based on the food expenditures of the world's poorest people, which is approximately $0.70 per day (GiveWell 2013). The cost for tracking and redirection capability assumes 30 years of costs, with $250 million annual costs (National Research Council 2010). \n Example Results In this section, we give results from the computational model for the illustrative example, using the previously stated assumptions. Figure  5  gives the probability density function (PDF) of the base-case annual probability of global catastrophe from both visible and dark NEO impacts. (On the horizontal axis, \"u\" is \"mu,\" or micro, i.e., 10 −6 .) Contemplating probabilities of probabilities can be confusing, but it is easy to see in PDF figures where there are broad spreads of probability (corresponding to great uncertainties) or narrow spreads (for less uncertainty). The figure shows that there are substantial uncertainties about dark-object damocloid risks and even greater uncertainties about Decision  Analysis, 2017 Analysis, , vol. 14, no. 3, pp. 187-203, © 2017    NEO tracking and redirection measures Uniform(0.1, 0.9) 0 0 7.5 Food stockpiling for all of humanity Uniform(0.1, 0.9) Uniform(0.1, 0.9) Uniform(0.1, 0.9) 1,800 nuclear war risks, both of which could be much greater than visible-NEO impact risks. Table  3  gives the mean cost-effectiveness of GCRreduction measures (without research to reduce uncertainties) in terms of how much the measure reduces the average total probability of global catastrophe per dollar spent on the measure. (Recall that in these terms, a high number for cost-effectiveness is desirable, because it indicates a large reduction in global catastrophe probability for the dollars spent. The calculations incorporate the global catastrophe probability distributions shown in Figure  5 , which showed that nuclear war risks could be much greater than NEO impact risks.)    3 's mean cost-effectiveness comparison would seem to suggest spending on food stockpiling if nuclear war risk is included in the scope of analysis, but instead would suggest spending on NEO tracking if nuclear war risk is not included in the scope of analysis. Moreover, as mentioned previously, there are substantial uncertainties about the risks and costeffectiveness, and food stockpiles might actually be more cost-effective than NEO tracking even if nuclear war risk is not included in the scope of analysis. Figures 6 and 7 give the PDF of the cost-effectiveness for each GCR-reduction measure, if nuclear war risk is or is not included in analysis, respectively. (The status quo option has a cost-effectiveness of zero because it does not change GCR probability.) The figures indicate the overlapping ranges of the probability distributions of cost-effectiveness of food stockpiling and NEO redirection measures. According to the assumptions used in the Monte Carlo model, if nuclear war risk is included in the scope of analysis, there is a 0.8 probability that food stockpiling will be the most cost-effective measure, and there is a 0.2 probability NEO tracking and redirection will be most cost-effective. Conversely, if nuclear war risk is not included in the scope of analysis, there is a 0.999 probability that NEO tracking and redirection will be the most cost-effective measure, and there is a 0.001 probability that global food stockpiling will be most cost-effective. Further research could reduce uncertainties to better determine which risk-reduction measure would really be more cost-effective. According to the Monte Carlo model's assumptions and use of Equation (A.3), the cost-effectiveness-based expected value of perfect information (CEEVPI) in the illustrative examples in this paper is $2 billion if nuclear war is included in the scope of analysis, and $400 million if nuclear war is not included in the scope of analysis. In this illustrative example, research on the risks and risk-reduction effectiveness would have a substantial expected value, largely because of the huge uncertainties about the baseline risks and about the effectiveness of risk-reduction measures. The example also supports the argument that we can learn something valuable by doing the analysis for more than one type of GCR at a time. \n Conclusion In this paper, we argue that value of information based on cost-effectiveness is a useful tool for analysis of GCR to inform risk-reduction decisions and show how to apply it to GCRs and risk-reduction interventions in a comprehensive, integrated fashion. We discuss key challenges in real-world implementation of this paper's framework and argue that these challenges can be addressed. We then illustrate these concepts with simple example models of impact risks from both visible and \"dark\" near-Earth objects as well as nuclear war effects and consideration of related risk-reduction measures. The illustrative example shows that such calculations can have considerable value, and also supports looking at more than one GCR at a time. Unlike most value of information approaches, our approach for calculating value of information is based on risk-reduction cost-effectiveness, to avoid implicitly equating lives and dollars, e.g., using a VSL, which may be inappropriate given the scale of GCRs. Our equation for value of information may be useful in other domains where VSLs would not be appropriate. Our suggested approach could be used generally to work toward a comprehensive rigorous assessment of GCRs and risk-reduction options. A useful step could be to expand and update this paper's illustrative model (e.g., to reflect more recent NEO research 5 and other NEO risk-management options 6 ). However, it would be more valuable to work toward a broader agenda for integrated assessment to inform GCR-reduction decisions. Ideally, the scope of such assessment would address all important GCRs over key time periods (e.g., the next century) and also key risk-reduction options of relevant stakeholders (including, but not limited to, public policy options of governments). This paper's framework could help guide steps in such assessment by prioritizing pieces of research in terms of value of information for reducing the total probability of GCRs. While real-world GCR research would not result in perfect information, even imperfect information could have significant value in informing GCR-reduction resource allocation decisions. Our approach could have great value in comprehensively, rigorously assessing GCR and risk-reduction options. Prior GCR research is of only limited value to informing GCR-reduction decisions. Much of the work to date has focused on specific GCRs, leaving great Decision  Analysis, 2017 , vol. 14, no. 3, pp. 187-203, © 2017  uncertainty about which GCRs are most important to focus on. Notable exceptions include research findings that GCRs from cosmic events are small relative to GCRs from human actions  (Tegmark and Bostrom 2005) , an informal survey of GCR researchers providing estimates of the probabilities of human extinction from a small number of GCR types  (Sandberg and Bostrom 2008) , analyses of interacting sequences of GCRs  (Tonn and MacGregor 2009, Baum et al. 2013) , and several largely qualitative surveys  (Bostrom 2002 , Rees 2003 , Posner 2004 , Smil 2008 , Cotton-Barratt et al. 2016 . These studies are insightful but do not provide rigorous quantitative recommendations for riskreduction resource allocations. We are aware of only one study, that of  Leggett (2006) , that attempts to quantitatively evaluate GCR-reduction measures across a broad space of GCR, but that study has shortcomings such as not considering all GCR categories nor all potentially valuable GCR-reduction measures. The modest literature available does not come close to resolving the large uncertainties surrounding both the GCRs themselves and the effectiveness of possible riskreducing interventions. Our work suggests that comprehensive, integrated assessment of GCRs could be quite valuable for informing GCR-reduction decisions, and tools can be developed for making comprehensive, integrated assessments for informing GCR-reduction decisions. \n Appendix. Derivation of Cost-Effectiveness-Based Formula for Expected Value of Information In this appendix, we provide the detail on our derivation of the CEEVPI formula. Our following calculations are aided by two simplifying assumptions, as discussed previously: a binary threshold for global catastrophes and independence of different GCRs (except to the extent that GCR event interactions and dependencies are accounted for in the fault trees or other model components). Then let X j equal the value loss due to global catastrophe j. Because of the binary threshold assumption, X j is the same for all j. Let R(t) be the risk of an event occurring during time period t, with R probability × magnitude. Then, given the independence of different GCRs, the total risk for y GCRs is R tot (t) p tot (t)X 1 − y j (1 − p j (t)) X. (A.1) We further assume that all GCRs have sufficiently low probabilities per time period p j (t) that the total probability of global catastrophe in that time period can be approximated as the sum of the independent probabilities, such that R tot (t) ≈ y j p j (t) X. (A.2) In this paper, we evaluate possible GCR-reducing interventions in terms of their cost-effectiveness, i.e., their reduction in GCR per unit cost. We favor cost-effectiveness for two reasons. First, cost-benefit analysis is hampered by the challenge of quantifying the value loss due to global catastrophe, X. The benefit of interventions is the reduction in risk, which also depends on X. While X is generally believed to be very large, quantitative estimates span a huge range, as mentioned previously. In contrast, cost-effectiveness analysis does not depend on X. Let c i and CE i be the cost and cost-effectiveness of intervention i. Then, CE i R 0, tot (t) − R i, tot (t) c i p 0, tot (t) − p i, tot (t) c i X. (A.3) Since X is equal for all global catastrophes, comparisons of the cost-effectiveness of different interventions are the same regardless of the value of X. We assume that there is a decision to be made about allocation of resources to some combination of direct risk reduction and research, and that the main decision rule is to choose whatever combination of options has best overall expected GCR-reduction cost-effectiveness among options considered in the analysis. Then the decision maker should buy as much risk reduction (and risk research enabling better risk-reduction decisions) as they can at whatever total cost, as long as that results in the greatest cost-effectiveness. (We assume that budgets are not an issue in the context of the risk-reduction and research options under consideration, and we do not explicitly account for potential budget constraints in the following. This implicitly assumes that sufficient total resources are either being provided by a single entity or are coordinated in some fashion.) If the information's expected effect and cost are such that even with the research cost included it would achieve a better cost-effectiveness than whatever would have been the optimal investment before the research based on expected values, We denote cases whether research is conducted to reduce uncertainty on a particular factor using superscript b for \"before\" research, or without information from research, and superscript a for \"after\" research, or with information from research. (Thus, before research is conducted on p i , it is p b i , and after research is conducted, it is p a i .) Again, we ignore actual costs of research and focus on the amount of resources the decision maker ought to be willing to pay for the total value added by the research. We use the term w to denote the amount of resources the decision maker ought to be willing to pay for the total added value of conducting research. (It adds no value to do no research.) For the purposes of this derivation, we do not provide more detailed breakdowns of the amount of resources the decision maker ought to be willing to pay for the value added by performing specific pieces of research that comprise total value added by research v, which actually could consist of separate pieces of research on different uncertain factors. (The amount of resources the decision maker ought to be willing to pay for the value added by each piece of research could be assessed using an extension of the derivation provided here.) Note that the best option after research, s a (which has costeffectiveness in Monte Carlo iteration m of (p a 0m − p a sm )/c a sm ) is not necessarily the same as the best option before research, s b (which has cost-effectiveness in Monte Carlo iteration m of (p b 0m − p b sm )/c b sm ). Research that reduces but does not eliminate uncertainty about a factor yields imperfect information. In a case where research produces perfect information about a factor, all uncertainty is eliminated about the factor after research. In terms of Monte Carlo iterations, after perfect information, one of the Monte Carlo iterations will have randomly sampled factor values whose are closest to the actual real-world factor values. As long as doing more research adds more value, and if we ignore the actual costs of performing the research, we assume that resources for research ought to be invested in up to the point where research would be so expensive that a funder would obtain no further benefit from investing in additional research (because up to that point, they would get a better overall cost-effectiveness by investing in additional research). At that point, the expected cost-effectiveness of the best riskreduction option before research is equal to the expected costeffectiveness of the best risk-reduction option after research, including the amount of resources the decision maker ought to be willing to pay for the total value added by research: The E[ • ] terms can be distributed and regathered because all the relevant calculations (i.e., both the expected-value calculations and the cost-effectiveness calculations) involve linear operations and because p and c variables are assumed Decision  Analysis, 2017 , vol. 14, no. 3, pp. 187-203, © 2017  to be uncorrelated. (To be more specific, manipulation of the numerator and denominator are allowed because they are linear operations, and multiplicative operations are allowed because the covariance is assumed to be 0.) Distributing and rearranging the terms to solve for the expected value of the amount of resources the decision maker ought to be willing to pay for the total value added by research,   (A.11)  This formula for CEEVI actually applies to both perfect information and imperfect information cases. However, our focus in this derivation is on the limiting case where the research yields perfect information, which provides the upper limit to the value of research, i.e., the costeffectiveness-based expected value of perfect information, CEEVPI. It turns out that when used in Analytica software by Lumina Decision Systems, the above CEEVI formula can be used in a straightforward fashion to set up the Monte Carlo simulation computations for CEEVPI (by directly using each factor's Monte Carlo sampling values in each Monte Carlo iteration), and that is what we use in the illustrative Analytica model accompanying this paper. (Computation of the cost-effectiveness-based expected value of imperfect information, CEEVII, would require an extra step to simulate after-research imperfect-information probability distributions for each factor, instead of after-research perfectinformation point values.) Endnotes 1 For an example of a canonical utility function based decision analysis framework for one GCR category, asteroid and comet impact risk, see  Lee et al. (2014) . 2 For an illustrative example of a probability distribution reflecting uncertainty about an annualized global catastrophe probability, see Figure  5  in Section 4.2. For more on such probability distributions, see Chapters 4 and 5 of  Morgan and Henrion (1990) . 3 For some GCR types, it may not be most useful to think in terms of consequence exceedance thresholds, but in terms of probabilities of various possibilities, such as in future \"artificial superintelligent catastrophe\" scenarios. However, modeling approaches such as fault trees could be useful for some such scenarios  (Barrett and Baum 2017 ). 4 There are also related challenges in the selection of metrics, such as for event consequences: whether to focus on estimated fatalities over some specific time scale, or to also consider economic impact, etc. Even choosing cost metrics for use in cost-effectiveness analysis presents challenges. In this paper, we assume cost is defined in monetary (dollar) terms, but those have limitations  (Baum 2012) , and scarcities exist for other resources such as labor capacity. 5 See, for example,  Reinhardt et al. (2015) . 6 For example, there are a number of options for alternative food sources during a crop-failure crisis  (Denkenberger and Pearce 2015) . Those potentially could be more cost-effective than food stockpiling, but we believe their effectiveness also would have greater uncertainty because of complexity, etc. Figure 1 . 1 Figure 1. High-Level Global Catastrophe Fault Tree and Risk Management Decision Influence DiagramGlobal catastrophe (GC) \n Figure 3 . 3 Figure 3. Uncertainties in Global Catastrophe Probability Modeling Event consequence exceedance probability \n Figure Figure 5. (Color online) PDF of Baseline Annual Probabilities of Global Catastrophe \n Figure 6 . 6 Figure 6. (Color online) PDF of Cost-Effectiveness of GCR-Reduction Measures if Nuclear War Risk Is Included in Scope (Status quo) \n previous expression for E[w]  gives the value of research as the cost-effectiveness-based expected value of information, \n INFORMS Figure 2. Global Catastrophe Probability as Function of Event Consequence and Exceedance Probability Event Reduced consequence exceedance probability event consequence threshold (CT) Global catastrophe (GC) consequence Initial P(GC) Reduced P(GC) Reduced event probability Event consequence \n INFORMS Figure 4. High-Level Decision Tree for Research and Risk-Reduction Decisions Do not invest to Risk is high Risk reduce risks Risk is low reduction decision Do not conduct without research Invest to reduce risks Risk was high, and is being reduced Risk was low, and is being reduced research Research decision Do not invest to Conduct research Risk is high Risk reduction risk is high decision after research when reduce risks Invest to Risk was high, and is being reduced Risk is high reduce risks Do not invest to Risk reduction reduce risks Risk is low decision after risk is low research when Invest to Risk was low, and is being reduced Risk is low reduce risks \n Table 1 . 1 Expressions for Assumed Baseline Annual Probabilities of Global Catastrophe GCR types Baseline P(Global Catastrophe) Visible near-Earth objects Triangular(0.5, 1, 2) • 0.15 • (1/(3 • 10 5 )) Long-period comets Triangular(0.5, 1, 2) (damocloids) • Uniform(0, 4) • (1/(3 • 10 5 )) Nuclear war Triangular(0, 0.0001, 0.001) a factor of two.\" We assume that these uncertainties in the visible/bright NEO frequencies are uncorrelated with the uncertainties in the damocloid frequencies. Some corroboration of the relative risks of bright ver- sus dark objects, and associated uncertainties, is pro- vided by the (National Research Council 2010, p. 22): \n Table 2 . 2 Assumed Effects and Costs of Risk-Reduction MeasuresReduction in P(Global Catastrophe) from each GCR type Visible near- Long-period comets GCR-reduction measures Earth objects (damocloids) Nuclear war Costs ($Billion) \n Table 3 . 3 Mean Cost-Effectiveness of GCR-Reduction Measures (Reduction in Total Global Catastrophe Probability per Dollar) Food Both food Include NEO tracking stockpiling stockpiling nuclear and redirection for all of and NEO war in scope? measures humanity tracking/redirection Yes 4 × 10 −17 1 × 10 −16 1 × 10 −16 No 4 × 10 −17 2 × 10 −18 2 × 10 −18 \n Table", "date_published": "n/a", "url": "n/a", "filename": "deca.2017.0350.tei.xml", "abstract": "In this paper, we develop and illustrate a framework for determining the potential value of global catastrophic risk (GCR) research in reducing uncertainties in the assessment of GCR levels and the effectiveness of risk-reduction options. The framework uses the decision analysis concept of the expected value of perfect information in terms of the cost-effectiveness of GCR reduction. We illustrate these concepts using available information on impact risks from two types of near-Earth objects (asteroids or extinct comets) as well as nuclear war, and consideration of two risk-reduction measures. We also discuss key challenges in extending the calculations to all GCRs and risk-reduction options, as part of an agenda for comprehensive, integrated GCR research. While real-world research would not result in perfect information, even imperfect information could have significant value in informing GCR-reduction decisions. Unlike most value of information approaches, our equation for calculating value of information is based on risk-reduction cost-effectiveness, to avoid implicitly equating lives and dollars, e.g., using a value of statistical life (VSL), which may be inappropriate given the scale of GCRs. Our equation for value of information may be useful in other domains where VSLs would not be appropriate.", "id": "f24645b7ec0a0a21e0579622c3a4b602"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Mark K Ho", "Michael L Littman", "James Macglashan", "Fiery Cushman", "Joseph L Austerweil"], "title": "Showing versus Doing: Teaching by Demonstration", "text": "Introduction Is there a difference between doing something and showing someone else how to do something? Consider cooking a chicken. To cook one for dinner, you would do it in the most efficient way possible while avoiding contaminating other foods. But, what if you wanted to teach a completely naïve observer how to prepare poultry? In that case, you might take pains to emphasize certain aspects of the process. For example, by ensuring the observer sees you wash your hands thoroughly after handling the uncooked chicken, you signal that it is undesirable (and perhaps even dangerous) for other ingredients to come in contact with raw meat. More broadly, how could an agent show another agent how to do a task, and, in doing so, teach about its underlying reward structure? To model showing, we draw on psychological research on learning and teaching concepts by example. People are good at this. For instance, when a teacher signals their pedagogical intentions, children more frequently imitate actions and learn abstract functional representations  [6, 7] . Recent work has formalized concept teaching as a form of recursive social inference, where a teacher chooses an example that best conveys a concept to a learner, who assumes that the teacher is choosing in this manner  [14] . The key insight from these models is that helpful teachers do not merely select probable examples of a concept, but rather choose examples that best disambiguate a concept from other candidate concepts. This approach allows for more effective, and more efficient, teaching and learning of concepts from examples. We can extend these ideas to explain showing behavior. Although recent work has examined userassisted teaching  [8] , identified legible motor behavior in human-machine coordination  [9] , and analyzed reward coordination in game theoretic terms  [11] , previous work has yet to successfully model how people naturally teach reward functions by demonstration. Moreover, in Inverse Reinforcement Learning (IRL), in which an observer attempts to infer the reward function that an expert (human or artificial) is maximizing, it is typically assumed that experts are only doing the task and not intentionally showing how to do the task. This raises two related questions: First, how does a person showing how to do a task differ from them just doing it? And second, are standard IRL algorithms able to benefit from human attempts to show how to do a task? In this paper, we investigate these questions. To do so, we formulate a computational model of showing that applies Bayesian models of teaching by example to the reward function learning setting. We contrast this pedagogical model with a model of doing: standard optimal planning in Markov Decision Processes. The pedagogical model predicts several systematic differences from the standard planning model, and we test whether human participants reproduce these distinctive patterns. For instance, the pedagogical model chooses paths to a goal that best disambiguates which goal is being pursued (Experiment 1). Similarly, when teaching feature-based reward functions, the model will prioritize trajectories that better signal the reward value of state features or even perform trajectories that would be inefficient for an agent simply doing the task (Experiment 2). Finally, to determine whether showing is indeed better than doing, we train a standard IRL algorithm with our model trajectories and human trajectories. \n A Bayesian Model of Teaching by Demonstration Our model draws on two approaches: IRL  [2]  and Bayesian models of teaching by example  [14] . The first of these, IRL and the related concept of inverse planning, have been used to model people's theory of mind, or the capacity to infer another agent's unobservable beliefs and/or desires through their observed behavior  [5] . The second, Bayesian models of pedagogy, prescribe how a teacher should use examples to communicate a concept to an ideal learner. Our model of teaching by demonstration, called Pedagogical Inverse Reinforcement Learning, merges these two approaches together by treating a teacher's demonstration trajectories as communicative acts that signal the reward function that an observer should learn. \n Learning from an Expert's Actions \n Markov Decision Processes An agent that plans to maximize a reward function can be modeled as the solution to a Markov Decision Process (MDP). An MDP is defined by the tuple < S, A, T, R, γ >: a set of states in the world S; a set of actions for each state A(s); a transition function that maps states and actions to next states, T : S × A → S (in this work we assume all transitions are deterministic, but this can be generalized to probabilistic transitions); a reward function that maps states to scalar rewards, R : S → R; and a discount factor γ ∈ [0, 1]. Solutions to an MDP are stochastic policies that map states to distributions over actions, π : S → P (A(s)). Given a policy, we define the expected cumulative discounted reward, or value, V π (s), at each state associated with following that policy: V π (s) = E π ∞ k=0 γ k r t+k+1 | s t = s . (1) In particular, the optimal policy for an MDP yields the optimal value function, V * , which is the value function that has the maximal value for every state (V * (s) = max π V π (s), ∀s ∈ S). The optimal policy also defines an optimal state-action value function,  Q * (s, a) = E π [r t+1 + γV * (s t+1 ) | s t = s, a t = a]. Q i = calculateActionValues(s, R i , T , γ) 4: π i = softmax(Q i , λ) 5: Π.add(π i ) 6: Calculate j = {j : s 1 ∈ s, length(j) ≤ l max , and ∃π ∈ Π s.t. (si,ai)∈j π(a i | s i ) > p min }. In the Reinforcement Learning setting, an agent takes actions in an MDP and receives rewards, which allow it to eventually learn the optimal policy  [15] . We thus assume that an expert who knows the reward function and is doing a task selects an action a t in a state s t according to a Boltzmann policy, which is a standard soft-maximization of the action-values: P Doing (a t | s t , R) = exp{Q * (s i , a i )/λ} a ∈A(si) exp{Q * (s i , a )/λ} . (2) λ > 0 is an inverse temperature parameter (as λ → 0, the expert selects the optimal action with probability 1; as λ → ∞, the expert selects actions uniformly randomly). In the IRL setting, an observer sees a trajectory of an expert executing an optimal policy, j = {(s 1 , a 1 ), (s 2 , a 2 ), ..., (s k , a k )}, and infers the reward function R that the expert is maximizing. Given that an agent's policy is stationary and Markovian, the probability of the trajectory given a reward function is just the product of the individual action probabilities, P Doing (j | R) = t P Doing (a t | s t , R). From a Bayesian perspective  [13] , the observer is computing a posterior probability over possible reward functions R: P Observing (R | j) = P Doing (j | R)P (R) R P Doing (j | R )P (R ) . (3) Here, we always assume that P (R) is uniform. \n Bayesian Pedagogy IRL typically assumes that the demonstrator is executing the stochastic optimal policy for a reward function. But is this the best way to teach a reward function? Bayesian models of pedagogy and communicative intent have shown that choosing an example to teach a concept differs from simply sampling from that concept  [14, 10] . These models all treat the teacher's choice of a datum, d, as maximizing the probability a learner will infer a target concept, h: P Teacher (d | h) = P Learner (h | d) α d P Learner (h | d ) α . (4) α is the teacher's softmax parameter. As α → 0, the teacher chooses uniformly randomly; as α → ∞, the teacher chooses d that maximally causes the learner to infer a target concept h; when α = 1, the teacher is \"probability matching\". The teaching distribution describes how examples can be effectively chosen to teach a concept. For instance, consider teaching the concept of \"even numbers\". The sets {2, 2, 2} and {2, 18, 202} are both examples of even numbers. Indeed, given finite options with replacement, they both have the same probability of being randomly chosen as sets of examples. But {2, 18, 202} is clearly better for helpful teaching since a naïve learner shown {2, 2, 2} would probably infer that \"even numbers\" means \"the number 2\". This illustrates an important aspect of successful teaching by example: that examples should not only be consistent with the concept being taught, but should also maximally disambiguate the concept being taught from other possible concepts. \n Pedagogical Inverse Reinforcement Learning To define a model of teaching by demonstration, we treat the teacher's trajectories in a reinforcementlearning problem as a \"communicative act\" for the learner's benefit. Thus, an effective teacher will modify its demonstrations when showing and not simply doing a task. As in Equation  4 , we can define a teacher that selects trajectories that best convey the reward function: P Showing (j | R) = P Observing (R | j) α j P Observing (R | j ) α . (5) In other words, showing depends on a demonstrator's inferences about an observer's inferences about doing. This model provides quantitative and qualitative predictions for how agents will show and teach how to do a task given they know its true reward function. Since humans are the paradigm teachers and a potential source of expert knowledge for artificial agents, we tested how well our model describes human teaching. In Experiment 1, we had people teach simple goal-based reward functions in a discrete MDP. Even though in these cases entering a goal is already highly diagnostic, different paths of different lengths are better for showing, which is reflected in human behavior. In Experiment 2, people taught more complex feature-based reward functions by demonstration. In both studies, people's behavior matched the qualitative predictions of our models. 3 Experiment 1: Teaching Goal-based Reward Functions Consider a grid with three possible terminal goals as shown in Figure  1 . If an agent's goal is &, it could take a number of routes. For instance, it could move all the way right and then move upwards towards the & (right-then-up) or first move upwards and then towards the right (up-then-right). But, what if the agent is not just doing the task, but also attempting to show it to an observer trying to learn the goal location? When the goal is &, our pedagogical model predicts that up-then-right is the more probable trajectory because it is more disambiguating. Up-then-right better indicates that the intended goal is & than right-then-up because right-then-up has more actions consistent with the goal being #. We have included an analytic proof of why this is the case for a simpler setting in the supplementary materials. Additionally, our pedagogical model makes the prediction that when trajectory length costs are negligible, agents will engage in repetitive, inefficient behaviors that gesture towards one goal location over others. This \"looping\" behavior results when an agent can return to a state with an action that has high signaling value by taking actions that have a low signaling \"cost\" (i.e. they do not signal something other than the true goal). Figure  1d  shows an example of such a looping trajectory. In Experiment 1, we tested whether people's showing behavior reflected the pedagogical model when reward functions are goal-based. If so, this would indicate that people choose the disambiguating path to a goal when showing. \n Experimental Design Sixty Amazon Mechanical Turk participants performed the task in Figure  1 . One was excluded due to missing data. All participants completed a learning block in which they had to find the reward location without being told. Afterwards, they were either placed in a Do condition or a Show condition. Participants in Do were told they would win a bonus based on the number of rewards (correct goals) they reached and were shown the text, \"The reward is at location X\", where X was one of the three symbols %, #, or &. Those in Show were told they would win a bonus based on how well a randomly matched partner who was shown their responses (and did not know the location of the reward) did on the task. On each round of Show, participants were shown text saying \"Show your partner that the reward is at location X\". All participants were given the same sequence of trials in which the reward locations were <%, &, #, &, %, #, %, #, &>.  \n Results As predicted, Show participants tended to choose paths that disambiguated their goal as compared to Do participants. We coded the number of responses on & and % trials that were \"showing\" trajectories based on how they entered the goal (i.e. out of 3 for each goal). On & trials, entering from the left, and on % trials, entering from above were coded as \"showing\". We ran a 2x2 ANOVA with Show vs Do as a between-subjects factor and goal (% vs &) as a repeated measure. There was a main effect of condition (F (1, 57) = 16.17, p < .001; Show: M = 1.82, S.E. 0.17; Do: M = 1.05, S.E. 0.17 The model does not predict any difference between conditions for the # (lower right) goal. However, a visual analysis suggested that more participants took a \"swerving\" path to reach #. This observation was confirmed by looking at trials where # was the goal and comparing the number of swerving trials, which was defined as making more than one change in direction (Show: M = 0.83, Do: M = 0.26; two-sided t-test: t(44.2) = 2.18, p = 0.03). Although not predicted by the model, participants may swerve to better signal their intention to move 'directly' towards the goal. \n Discussion Reaching a goal is sufficient to indicate its location, but participants still chose paths that better disambiguated their intended goal. Overall, these results indicate that people are sensitive to the distinction between doing and showing, consistent with our computational framework. \n Experiment 2: Teaching Feature-based Reward Functions Experiment 1 showed that people choose disambiguating plans even when entering the goal makes this seemingly unnecessary. However, one might expect richer showing behavior when teaching more complex reward functions. Thus, for Experiment 2, we developed a paradigm in which showing how to do a task, as opposed to merely doing a task, makes a difference for how well the underlying reward function is learned. In particular, we focused on teaching feature-based reward functions that allow an agent to generalize what it has learned in one situation to a new situation. People often use feature-based representations for generalization  [3] , and feature-based reward functions have been used extensively in reinforcement learning (e.g.  [1] ). We used a colored-tile grid task shown in Figure  2  to study teaching feature-based reward functions. White tiles are always \"safe\" (reward of 0), while yellow tiles are always terminal states that reward 10 points. The remaining 3 tile types-orange, purple, and cyan-are each either \"safe\" or \"dangerous\" (reward of −2). The rewards associated with the three tile types are independent, and nothing about the tiles themselves signal that they are safe or dangerous. A standard planning algorithm will reach the terminal state in the most efficient and optimal manner. Our pedagogical model, however, predicts that an agent who is showing the task will engage in specific behaviors that best disambiguate the true reward function. For instance, the pedagogical model is more likely to take a roundabout path that leads through all the safe tile types, choose to remain on a safe colored tile rather than go on the white tiles, or even loop repeatedly between multiple safe tile-types. All of these types of behaviors send strong signals to the learner about which tiles are safe as well as which tiles are dangerous. \n Experimental Design Sixty participants did a feature-based reward teaching task; two were excluded due to missing data. In the first phase, all participants were given a learning-applying task. In the learning rounds, they interacted with the grid shown in Figure  2  while receiving feedback on which tiles won or lost points. Safe tiles were worth 0 points, dangerous tiles were worth -2 points, and the terminal goal tile was worth 5 points. They also won an additional 5 points for each round completed for a total of 10 points. Each point was worth 2 cents of bonus. After each learning round, an applying round occurred in which they applied what they just learned about the tiles without receiving feedback in a new grid configuration. They all played 8 pairs of learning and applying rounds corresponding to the 8 possible assignments of \"safe\" and \"dangerous\" to the 3 tile types, and order was randomized between participants. As in Experiment 1, participants were then split into Do or Show conditions with no feedback. Do participants were told which colors were safe and won points for performing the task. Show participants still won points and were told which types were safe. They were also told that their behavior would be shown to another person who would apply what they learned from watching the participant's behavior to a separate grid. The points won would be added to the demonstrator's bonus. \n Results Responses matched model predictions. Do participants simply took efficient routes, whereas Show participants took paths that signaled tile reward values. In particular, Show participants took paths that led through multiple safe tile types, remained on safe colored tiles when safe non-colored tiles were available, and looped at the boundaries of differently colored safe tiles. \n Model-based Analysis To determine how well the two models predicted human behaviors globally, we fit separate models for each reward function and condition combination. We found parameters that had the highest median likelihood out of the set of participant trajectories in a given reward function-condition combination. Since some participants used extremely large trajectories (e.g. >25 steps) and we wanted to include an analysis of all the data, we calculated best-fitting state-action policies. For the standard-planner, it is straightforward to calculate a Boltzmann policy for a reward function given λ. For the pedagogical model, we first need to specify an initial model of doing and distribution over a finite set of trajectories. We determine this initial set of trajectories and their probabilities using three parameters: λ, the softmax parameter for a hypothetical \"doing\" agent that the model assumes the learner believes it is observing; l max , the maximum trajectory length; and p min , the minimum probability for a trajectory under the hypothetical doing agent. The pedagogical model then uses an α parameter that determines the degree to which the teacher is maximizing. State-action probabilities are calculated from a distribution over trajectories using the equation P (a | s, R) = j P (a | s, j)P (j | R), where P (a | s, j) = |{(s,a):s=st,a=at∀(st,at)∈j}| |{(s,a):s=st∀(st,at)∈j}| . We fit parameter values that produced the maximum median likelihood for each model for each reward function and condition combination. These parameters are reported in the supplementary materials. The normalized median fit for each of these models is plotted in Figure  3 . As shown in the figure, the standard planning model better captures behavior in the Do condition, while the pedagogical model better captures behavior in the Show condition. Importantly, even when the standard planning model could have a high λ and behave more randomly, the pedagogical model better fits the Show condition. This indicates that showing is not simply random behavior. \n Behavioral Analyses We additionally analyzed specific behavioral differences between the Do and Show conditions predicted by the models. When showing a task, people visit a greater variety of safe tiles, visit tile types that the learner has uncertainty about (i.e. the colored tiles), and more frequently revisit states or \"loop\" in a manner that leads to better signaling. We found that all three of these behaviors were more likely to occur in the Show condition than in the Do condition. To measure the variety of tiles visited, we calculated the entropy of the frequency distribution over colored-tile visits by round by participant. Average entropy was higher for Show (Show: M = 0.50, SE = 0.03; Do: M = 0.39, SE = 0.03; two-sided t-test: t(54.9) = −3.27, p < 0.01). When analyzing time spent on colored as opposed to un-colored tiles, we calculated the proportion of visits to colored tiles after the first colored tile had been visited. Again, this measure was higher for Show (Show: M = 0.87, SE = 0.01; Do: M = 0.82, SE = 0.01; two-sided t-test: t(55.6) = −3.14, p < .01). Finally, we calculated the number of times states were revisited in the two conditions-an indicator of \"looping\"-and found that participants revisited states more in Show compared to Do (Show: M = 1.38, SE = 0.22; Do: M = 0.10, SE = 0.03; two-sided t-test: t(28.3) = −2.82, p < .01). There was no difference between conditions in the total rewards won (two-sided t-test: t(46.2) = .026, p = 0.80). \n Teaching Maximum-Likelihood IRL One reason to investigate showing is its potential for training artificial agents. Our pedagogical model makes assumptions about the learner, but it may be that pedagogical trajectories are better even for training off-the-shelf IRL algorithms. For instance, Maximum Likelihood IRL (MLIRL) is a state-of-the-art IRL algorithm for inferring feature-based reward functions  [4, 12] . Importantly, unlike the discrete reward function space our showing model assumes, MLIRL estimates the maximum likelihood reward function over a space of continuous feature weights using gradient ascent. To test this, we input human and model trajectories into MLIRL. We constrained non-goal feature weights to be non-positive. Overall, the algorithm was able to learn the true reward function better from showing than doing trajectories produced by either the models or participants (Figure  2 ). \n Discussion When learning a feature-based reward function from demonstration, it matters if the demonstrator is showing or doing. In this experiment, we showed that our model of pedagogical reasoning over trajectories captures how people show how to do a task. When showing as opposed to simply doing, demonstrators are more likely to visit a variety of states to show that they are safe, stay on otherwise ambiguously safe tiles, and also engage in \"looping\" behavior to signal information about the tiles. Moreover, this type of teaching is even better at training standard IRL algorithms like MLIRL. \n General Discussion We have presented a model of showing as Bayesian teaching. Our model makes accurate quantitative and qualitative predictions about human showing behavior, as demonstrated in two experiments. Experiment 1 showed that people modify their behavior to signal information about goals, while Experiment 2 investigated how people teach feature-based reward functions. Finally, we showed that even standard IRL algorithms benefit from showing as opposed to merely doing. This provides a basis for future study into intentional teaching by demonstration. Future research must explore showing in settings with even richer state features and whether more savvy observers can leverage a showing agent's pedagogical intent for even better learning. 7 : 7 Construct hypothetical doing probability distribution P Doing (j | R) as an N x M array. 8: P Observing (R | j) = PDoing(j|R)P (R) R PDoing(j|R )P (R ) 9: P Showing (j | R) = PObserving(R|j) α j PObserving(R|j ) α 10: return P Showing (j | R) 2.1.2 Inverse Reinforcement Learning (IRL) \n Figure 1 : 1 Figure 1: Experiment 1: Model predictions and participant trajectories for 3 trials when the goal is (a) &, (b) %, and (c) #. Model trajectories are the two with the highest probability (λ = 2, α = 1.0, p min = 10 −6 , l max = 4). Yellow numbers are counts of trajectories with the labeled tile as the penultimate state. (d) An example of looping behavior predicted by the model when % is the goal. \n ) as well as a main effect of goal (F (1, 57) = 4.77, p < .05; %-goal: M = 1.73, S.E. = 0.18; &-goal: M = 1.15, S.E. = 0.16). There was no interaction (F (1, 57) = 0.98, p = 0.32). \n Figure 2 : 2 Figure 2: Experiment 2 results. (a) Column labels are reward function codes. They refer to which tiles were safe (o) and which were dangerous (x) with the ordering <orange, purple, cyan>. Row 1: Underlying reward functions that participants either did or showed; Row 2: Do participant trajectories with visible tile colors; Row 3: Show participant trajectories; Row 4: Mean reward function learned from Do trajectories by Maximum-Likelihood Inverse Reinforcement Learning (MLIRL) [4, 12]; Row 5: Mean reward function learned from Show trajectories by MLIRL. (b) Mean distance between learned and true reward function weights for human-trained and model-trained MLIRL. For the models, MLIRL results for the top two ranked demonstration trajectories are shown. \n Figure 3 : 3 Figure 3: Experiment 2 normalized median model fits. \n Algorithm 1 Pedagogical Trajectory AlgorithmRequire: starting states s, reward functions {R 1 , R 2 , ..., R N }, transition function T , maximum showing trajectory depth l max , minimum hypothetical doing probability p min , teacher maximization parameter α, discount factor γ. 1: Π ← ∅ 2: for i = 1 to N do 3:", "date_published": "n/a", "url": "n/a", "filename": "showing_vs_doing.tei.xml", "abstract": "People often learn from others' demonstrations, and inverse reinforcement learning (IRL) techniques have realized this capacity in machines. In contrast, teaching by demonstration has been less well studied computationally. Here, we develop a Bayesian model for teaching by demonstration. Stark differences arise when demonstrators are intentionally teaching (i.e. showing) a task versus simply performing (i.e. doing) a task. In two experiments, we show that human participants modify their teaching behavior consistent with the predictions of our model. Further, we show that even standard IRL algorithms benefit when learning from showing versus doing.", "id": "5f46469577c9b960714384810bc83ebf"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "The Professional's Dilemma", "text": "In most cases we should expect Alan's wife to feel safer if Alan keeps up appearances. And that's why vast swathes of our professional society are underperforming their potential: because playing it safe means covering things up. Can organizations ever support new ideas? An organization that's funding outside parties to accomplish certain goals (e.g. a charitable donor or foundation giving to charities) generally won't fund ideas, even ideas from those people who are both famous and established experts, unless those ideas start off with a critical amount of their own money attached. Either the idea has to be spearheaded by someone who has enough personal funds, or it has to have raised enough money from donors/investors who no longer have the in-practice authority to dictate decision making. (For more detail on this, see Samo Burja's essay Borrowed versus Owned Power . Borrowed power is granted conditionally --if your charity is given a \"donation\" under the condition that you continue to make the donor happy, that's borrowed power. If you have the money in your own personal savings account, or if the charity raised it from so many small donors that none of them are entitled to make demands about how you spend it, that's owned power. Borrowed power is always weaker than owned power.) It's not generally considered \"credible\", by big donors, that an initiative will be effective enough to be worth funding unless the initiative has managed to cross a certain threshold in terms of acquiring resources. Moreover, if the grantee meets that threshold, gets funded, and does a good job with that money, this doesn't necessarily \"unlock\" disproportionately more resources from the big donor; the grantee will still have to hustle the same amount, or nearly so, to get the second grant. They're still running on borrowed power; they still need to keep looking over their shoulder, worrying about what the funders might think. We know it's possible to do better than this, because this paradigm would never have allowed the Manhattan Project to get funded. Einstein didn't come with his own money; he was merely a renowned physicist with a credible proposal. Somebody in the government had to literally believe his claims that a specific thing that had never been done before could be done. This kind of belief is crucially different from the sense usually used when we talk about believing in someone, in that it is about the trusted person's relationship to their field of expertise, not their relationship to the person trusting them. Not everyone can evaluate every idea, but if a person reaches a certain threshold of expertise, eminence, reputation for honesty, etc., the funder has to be able to come to believe that the content of their ideas is more likely than baseline to be valid and worth pursuing. As a funder, you have to be able to believe someone --not everyone, but someone --when they say an initiative is worthwhile, enough that you are willing to take the initiative to make it possible, and you don't expect to regret that decision. Otherwise, you are not looking for ideas outside your institution . You are not a \"hub\", you are not reachable, you are just doing your thing with no outside input. Another way of putting this is that funders need to be able to see potential grantees as peers . Organizations having \"friends\" --other organizations or consultants/free-agents that they trust, are mission-aligned with, and communicate openly with --is often considered unprofessional (\"incestuous\"), but is actually a good thing! There needs to be someone outside you (or your org) whom you trust to be well-informed and value-aligned. Without the capacity to process genuinely new ideas, it's less effective to have grantees than to just have employees and decide everything top-down. If you're doing something in a decentralized fashion, it should be because you actually value the decentralization --you want to get an outside perspective, or on-the-ground data, or expertise, or something. \n Principal-Agent Problems How can the principal (the funder) trust the agent (the grantee)? Most of the incentive systems in the what we hear about in charity are rather primitive; it boils down to \"demand more documentation and proof from grantees.\" This is primitive because it tries to enforce honesty by spending resources on detecting dishonesty, which can be very costly, relative to other ways of incentivizing honesty. It's not even asking the question \"what's the most efficient way to get the grantee to tell me the truth?\" The aesthetic underlying this attitude is called authoritarian high modernism; just trying to add metrics, not even engaging with the fact that metrics can and will be gamed. The people who survive in positions of power in such a system are not the ones who naively try to answer questions they're asked as accurately as possible; they're the ones who keep up appearances. Conversely, when interacting with someone who keeps up appearances and who has survived in a position of power in such a system, there is common knowledge only 'professional' efforts will be supported, and that 'professional' efforts are efforts that don't freely reveal information. You can enforce quality control in a top-down fashion if you have an impartial investigative process and an enforcement mechanism, but who investigates the investigators? Who judges the judges? Ultimately somebody has to WANT to give an honest report of what's going on. And those impartial investigators have to be incentive-aligned such that they benefit more from being honest than lying . Otherwise, even if initially most of the investigators are highly selected for honesty, by organizational maturity, all will have been selected for 'discretion'. To get honest reports, you need a mechanism designed in such a way as to systematically favor truth, much like auctions designed so the most advantageous price to bid is also each person's true price. How do you do that? \n How to solve the problem Let's work through a concrete example: Suppose you're considering giving a grant to a charitable organization. They send you a budget and ask for a dollar amount. How can you incentivize them NOT to pad the budget? For instance, if they expect that they might be able to get this grant but they'll have a hard time getting a second grant, they have a strong incentive to ask for enough money up front to last them several years, BUT to say that they need it all for this year. This will happen UNLESS they have reason to believe that you'll frown on budget-padding, BUT are willing to look favorably on orgs that do well in the first year for subsequent grants. This requires opening up lines of communication MUCH more for successful/trusted grantees than for random members of the public or arbitrary grant applicants. It needs to be POSSIBLE to earn your trust, and for that to unlock a certain amount of funding security. Otherwise, grantees must seek funding security --for themselves, their families, their employees, their charitable work --because without doing so they won't be able to do their job at all. They'll seek it through deceiving you, because that will feel like, and will actually be, and will be seen by all observers to be, the responsible thing for them to do . If you make it seem like \"nobody should be able to count on my support, I'll keep 'em on their toes\", they'll find something else they can count on, namely your ignorance of how their project works. The agent ALWAYS knows more than the principal about the operational details of the project! They can always keep you in the dark more effectively than you can snoop on them. So you have to make earning your trust p ossible, empowering and rewarding . You can of course revoke those rewards if they betray your trust, but ultimately you have to be much less suspicious of your trusted friends than you are of randos. Yes, this means you take on risk; but the grantees ALSO take on risk by being honest with you. It's symmetric. Here's one common failure mode in the conventional paradigm: you can't appear competent if you reveal the truth that something in your project isn't working at the current funding level and needs more money. You can't seem \"needy\" for money, or you'll look incompetent, and you won't get the money. So instead you try to get the money by inflating your accomplishments and hiding your needs and trying to appear \"worthy.\" This is counterproductive from the funder's point of view. As a donor, you want to give money where it'll do the most good. This means you need accurate info about what it'll be spent on. But the grantee doesn't necessarily trust you to believe that what they actually need money for is worthy. For a well-known instance, many donors think operational costs are \"waste\", so charities fudge the accounting to make it seem like all donations go to program expenses, and still underspend on operational costs like paying their employees. Or, sometimes part of a charity's actual budget is somewhat unsavory, like bribes to officials in corrupt countries being a necessary cost of actually operating there. Or, some costs can be embarrassing to admit, like the costs of learning/mistakes/R&D, if there's a perceived expectation that you have to get things right the first time. So the onus is on the funder to make it clear that you want to know what they ACTUALLY need, what their REAL constraints are, and that you will not pull the plug on them if they have an awkward funding crunch, once they have earned your trust to an adequate degree. It has to be clear that CANDOR is an important part of earning your trust. In particular, it needs to be clear enough to the third parties in the life of the individual you're funding, that being honest with you will pay off, that they pressure the grantee to be more honest with you, the funder. How does their family feel? Is the spouse of the charity's executive director nagging them to be more honest when fundraising, because that's what'll put their kids through college? Because, if not, you can bet their spouse is nagging them to be less honest while fundraising, to squeeze more money out of the donors, because that's the responsible thing to do for their family. What about their other dependents --employees, collaborators, beneficiaries of charitable programs --would THEY put pressure on the executive director to be more forthcoming with the funder? Or would they say \"squeeze those rich morons harder so we can keep the lights on and help people who need it?\" (Or, perhaps, more discretely but synonymously, \"don't make waves, jump through the hoops they're asking you to jump through and tell them what they want to hear.\") People don't exist in a vacuum; they want to gain the esteem and meet the needs of the people they care about. We have to be not only rewarding honesty -not only rewarding honesty more than smoothing things over -but OBVIOUSLY ENOUGH rewarding honesty that even third parties know our reputation. Otherwise everyone who tries to be honest with us will receive a continuous stream of pressure to stop being so irresponsible . \"Why are you favoring a rich guy or a huge foundation over your own family and an important cause?\" It's a fair question! And you need to flip it on its head --you want everyone to be asking \"Why are you forgoing HUGE OPPORTUNITIES for your family and an important cause, just because you're too insecure to be candid with a rich guy?", "date_published": "n/a", "url": "n/a", "filename": "the_professionals_dilemma.tei.xml", "abstract": "Alan, the executive director of a small nonprofit, is sitting down to dinner with his family. Responsibility weighs heavily on Alan. It's nearly time to reapply for a grant that's been his organization's largest source of funds. Alan has carefully cultivated a relationship with Beth, the program officer for the foundation funding the grant. Beth knows and likes Alan, and is excited about the work he's doing. If Alan's organization applies for a grant to continue their existing work, it will almost certainly be approved. But Alan isn't sure what to do. In the past few months, it's become increasingly clear that his fledgling organization's main program -the one they were able to write grants for -isn't the best fit for the needs of the people it's supposed to serve. A bright young intern, Charles, proposed a new program that, as far as Alan can tell, would be a better fit both for the team and the people they are trying to help. On the merits, it seems like Charles's idea is the right thing to do. Alan could, in reapplying, explain the limitations of the existing program, and why the new program would be better. But that would rock the boat. It would mean challenging the very story that got last year's grant. There's no guarantee Beth would like the new idea. No one else has done it. There's no track record to point to. Alan thinks of what might happen if the grant isn't approved. He'd have to lay people off, good people, and his organization might not survive. Even if it does, he'd have to take a pay cut, maybe move to a house in a less expensive neighborhood, pull his kids out of school. It's not certain this would happen, but can he afford to take that chance? Let's look across the dinner table at Alan's wife, Dana. If Alan tells her about his dilemma, what do we expect her to feel. What would be the safe option? Disclosing the potentially unsettling truth to the funder in the hopes of being able to do better work in the future? Or smoothing things over, tweaking the existing program to try to patch some of the worse gaps, and muddling on? What will feel to her like the responsible choice for Alan to make, for his family and the other people depending on him?", "id": "9a89a3155949f2e20a1d0bcdaaab8d1d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrew E Snyder-Beattie", "Toby Ord", "Michael B Bonsall"], "title": "An upper bound for the background rate of human extinction", "text": "Bounding the extinction Rate Based on Age of Humanity Anatomically modern human fossils in Ethiopia have been dated to 195 ± 5 thousand years ago (kya)  13  . A more recent fossil discovery in Morocco of an anatomically modern human has been dated to 315 ± 34 kya  14, 15  (though the fossil may exhibit more primitive neurocranial and endocranial morphology). Given that Homo sapiens has existed for hundreds of thousands of years, what can we infer about our background rate of extinction? Assuming that we share a common extinction rate with our predecessors, we can rule out rates that are too high to be compatible with this track record of survival. As our aim is to construct an upper bound, we can set aside the possibility that modern human technology, habitat range, and population size have reduced a number of natural extinction risks. The upper bound is only violated if we have reason to believe current extinction rates are higher than those our predecessors faced. Since we exclude anthropogenic risks from our analysis, we also set aside the majority of the ways in which this could be the case, although we acknowledge there exist boundary cases between purely natural and anthropogenic risks (e.g. a naturally emerging disease could be spread further by modern technology). Ultimately the scope of the upper bound is limited to all risks that have remained constant (or have been reduced) over the past few hundred thousand years. Likelihood of extinction rates. Analysis of taxonomic survivorship curves and temporal ranges for a wide variety of taxa suggest that extinction probabilities can be approximated well by assuming a constant risk of extinction over time  [16] [17] [18]  . Under this model, extinction can be represented by the exponential distribution with constant extinction rate μ. The probability that humanity goes extinct before time t is given by the cumulative distribution function P(T ≤ t) = 1 − e −μt , where T is the random variable denoting the longevity of our species. Conversely, the probability that humanity makes it beyond time t is P(T ≥ t) = e −μt . We want to evaluate the likelihood of an extinction rate μ, given the observation that humanity has lasted up to time t (so we know that the total longevity of humanity T ≥ t). This can be evaluated as the likelihood function  μ| ≥ = μ − T t e ( ) t . We compute the likelihood of extinction rates between 10 −8 and 10 −4 given a number of different plausible starting dates for Homo sapiens outlined in Fig.  1  and Table  1 . Assuming a 200 thousand year (kyr) survival time, we can be exceptionally confident that rates do not exceed 6.9 × 10 −5 . This corresponds to an annual extinction probability below roughly 1 in 14,000. The relative likelihood for such high extinction rates are below 10 −6 (one in a million) when compared to a rate of 10 −8 . If we assume that our track record extends further, this upper bound becomes stronger. Using the fossil dated to 315 ka as a starting point for humanity gives an upper bound of μ < 4.4 × 10 −5 , corresponding to an annual extinction probability below 1 in 22,800. Using the emergence of Homo as our starting point pushes the initial bound back a full order of magnitude, resulting in an annual extinction probability below 1 in 140,000. We can also relax the one in million relative likelihood constraint and derive less conservative upper bounds. An alternative bound would be rates with relative likelihood below 10 −1 (1 in 10) when compared to the baseline rate of 10 −8 . If we assume humanity has lasted 200 kyr, we obtain a bound of μ < 1.2 × 10 −5 , corresponding to an annual extinction probability below 1 in 87,000. Using the 2 Myr origin of Homo strengthens the bound by an order of magnitude in a similar way and produces annual extinction probabilities below 1 in 870,000. It is worth noting that this model can be generalised to allow for a varying extinction rate over time μ(t), so that the probability of surviving past time t is given by P(T ≥ t) = e −Θ(t)t , where ∫ μ Θ = t t s ds ( ) (1/ ) ( ) t 0 . The upper bound on Θ(t), the average extinction rate over the interval, can then be calculated in the same way as for the constant rate model. \n Observation Selection Effects The data on humanity's survival time could be subject to survivorship bias. If early Homo sapiens requires a long period of time to develop the intellectual machinery needed to make scientific observations, then such observations could not include short evolutionary histories, regardless of the extinction rate. The amount of information we could derive from a long track record of survival would therefore be limited due to this observation selection effect. Such a track record could indicate a low extinction rate, or be the byproduct of lucky ancestors surviving high extinction rates long enough to beget progeny capable of making scientific observations. One might therefore object that the bounds on the extinction rate we have estimated are too low  12, 23  . Here, we examine and respond to this concern. \n Models to quantify potential sample bias. To model observation selection bias, let us assume that after Homo sapiens first arises another step must be reached. This could represent the origin of language, writing, science, or any relevant factor that would transition early humans into the reference class of those capable of making observations (we call this step 'observerhood'). Let this step be a random variable denoted S, with cumulative distribution function F S (t). As we are examining natural risks, we assume that S and T are independent. The probability that humanity survives long enough to reach observerhood status (via intelligence, language, writing, science, etc) can be found with the following integral: ∫ > = ∞ P T S f t F t dt ( ) ( ) ( ) (1) T S 0 www.nature.com/scientificreports www.nature.com/scientificreports/ where f T (t) = μe −μt , the probability of extinction at time t. We evaluate an adjusted likelihood function  μ| > ⁎ T t ( ) , denoting that we are taking the likelihood of an extinction rate μ given that humanity has survived to time t, and the fact that we are conditioning on the existence of observers such that T > S. This results in the adjusted likelihood function: μ μ | > = > | > ⁎ T t P T t T S ( ) ( , ) (2)  ∫ = ∞ c f s F s ds 1 ( ) ( ) (3) t T S where c = P(T > S) is a normalising constant. We evaluate a model with four variations for the observerhood step: a model in which observerhood occurs as a single event that has a constant rate over time, a model with an increasing rate over time, a model with multiple steps, and a model where observerhood simply requires a fixed amount of time. If desired, we could more crisply define this observerhood property as the ability for a species to collect reliable data on its own track record of survival (e.g. via fossil dating) and analyse it. When correcting for observation selection effects, we are simply conditioning on the fact that our species has developed the ability to conduct this analysis. The observerhood property need not invoke consciousness or be the property of a biological species-a machine estimating a parameter would need to account for observer selection bias if its ability to make such estimates were correlated with the parameter in question. Model 1: Single step, constant rate. Our first model assumes that observerhood has a constant rate of occurrence θ, so that S is exponentially distributed with cumulative distribution function: F S (t) = 1 − e −θt . This model describes a process in which the transition from early humans into observers occurs by chance as a single step. This could represent the hypothesis that hierarchical language emerged in humans as the byproduct of a chance mutation  24  . With this model, the probability that observers arrive before extinction is P(T > S) = θ(θ + μ) −1 . Our likelihood function can be analytically derived:   ∫ μ θ μ θ μ | > =      +      − μ θ ∞ − − ⁎ T t e e ds ( ) (1 ) (4) t s s θ μ θ μ θ =      +      −          μ μθ − −+ e e ( 5 ) t t ( ) Model 2: single step, increasing rate. Our second model similarly assumes that a single step is needed but that the rate of observerhood increases over time. This model could represent increasing population size or population density, which could in turn drive cultural evolution and increase the probability of such a step  25  . We represent this with a Weibull distribution with cumulative distribution function = − θ − F t e ( ) 1 S t ( ) k where k > 1 indicates increasing rate over time (when k = 1, this is the same as the exponential in Model 1). We use numerical integration to evaluate the likelihood function. Model 3: multiple steps, constant rate. Our third model assumes that there are multiple steps that need to occur in a sequence in order to get observers. This could represent more incremental development of tools, culture, or language. We assume that each step is exponentially distributed with rate θ, so that the timing of the final kth step follows an Erlang distribution with cumulative distribution function: ∑ θ = − . θ = − − F t n e t ( ) 1 1 ! ( ) (6) S n k t n 0 1 Note that when k = 1, the distribution is the same as the exponential in Model 1. We use numerical integration to evaluate the likelihood function. Model 4: fixed time requirement. Our final model assumes that it takes a fixed amount of time τ to reach observerhood. This is an extreme model that allows for no chance, but could represent a gradual and deterministic accumulation of traits. The probability that observerhood has been reached before time t is therefore F S (t) = 1 [t>τ] , the characteristic function that takes the value 1 when t > τ and 0 otherwise. The probability that humanity survives past time τ is 1 − F T (τ) = e −μτ . Our likelihood function of μ is: ∫ μ μ | > = μτ μ τ − ∞ − > ⁎ T t e e d s ( ) 1 1 (7) t s s [ ]  = . μ τ − − e (8) t ( ) This likelihood expression can also be derived using the memoryless property of the exponential. It is worth noting that the fixed time model is a limiting case for both the increasing rate model and the multiple steps model. Taking the limit of Model 2 as k → ∞ results in a fixed time model with τ = θ −1 . Similarly, Model 3 converges to a fixed time model as the number of steps increases and the expected time of each step decreases (having infinitely many steps in the limit, each of which is infinitely short). \n Results of sample bias models. We evaluate the likelihood of extinction rates between 10 −8 and 10 −2 , given a human survival time of 200 kyr and a wide range of different rates at which observers could originate (Fig.  2 ). The first thing to note about the first three models is that when the observerhood rates are sufficiently rapid, the likelihood function converges to the unbiased version in the previous section. This can be verified by taking limits: for all of the models as θ → ∞ (or τ → 0 in the case of the fixed time model ),  μ| > → μ − ⁎ T t e ( ) t . If observerhood is expected to occur quickly, then we can take a 200 kyr track record of survival at face value and estimate the extinction rate without observation selection bias. However, as the observerhood rates decrease to the point where the expected observerhood time approaches an order of magnitude close to 200 kyr, observer selection bias emerges. Rates that were previously ruled out by our track record of survival are assigned higher likelihoods, since a portion of the track record is a necessity for observers (Fig.  2 ). For example in Model 1, when θ = 2 × 10 −4 (corresponding to an expected observerhood time of 20 kyr), the relative likelihood of μ = 6.9 × 10 −5 is increased by a factor of 2.3 (from 10 −6 to 2.3 × 10 −6 ). To get a likelihood of 10 −6 (corresponding to the most conservative upper bound), the rate must be set at 7.3 × 10 −5 (see all edited bounds in Table  2 ). Interestingly though, this effect is limited. Even as observerhood rates slow to the point where expected observerhood time greatly exceeds 200 kyr (for example exceeding 20 billion years), the revised upper bounds remain within a factor of 2 of the original bounds. The stricter the bound, the weaker the potential bias: for example the 10 −6 likelihood bound is only changed by a factor of about 1.2 in the limit as θ → 0. Although there would be some sample bias, there is a hard ceiling on how much our track record of survival can be distorted by observation selection effects. The reason slow rates of observerhood have a limited impact on our estimates is because if the extinction rate were exceptionally high, the lucky humans that do successfully survive to observerhood will have achieved such a status unusually quickly, and therefore will still observe a very short track record of survival. A long track record of survival is therefore still sufficient to rule out high extinction rates paired with low observerhood rates. We can demonstrate this by examining the typical time it takes for lucky survivors to reach observerhood, assuming a high extinction rate and a low observerhood rate. For example, in the single step constant rate model when www.nature.com/scientificreports www.nature.com/scientificreports/ θ = 10 −6 (corresponding to an expected observerhood time of 1 Myr) and μ = 10 −3 (corresponding to a typical extinction time of 1000 years), the expected observerhood time conditional on these high extinction rates is 1000 years. A typical observer will thus still have a very short track record of survival. Models with increasing rates or multiple steps exhibit the same property, although the bias is larger depending on parameter k. For both model 2 and 3 with θ = 10 −6 , μ = 10 −3 , and k = 2 (parameters normally corresponding to an expected observerhood time of 830 kyr for Model 2 and 2 Myr for model 3), the high extinction rates will still result in a typical observer emerging unusually early and having only about a 2000 year track record of survival. This can be also seen in Fig.  2  where for Models 1, 2, and 3, the likelihood of high extinction rates exceeding 10 −4 are still assigned low likelihood regardless of θ. However, severe observer selection bias can occur in Models 2 and 3 as k becomes larger, shaping the observerhood distribution such that early observerhood is vanishingly unlikely and late observerhood almost guaranteed. In the most extreme case this is represented by the fixed time model, where the probability of observerhood jumps from 0 to 1 when t = τ (the fixed time model is also the limiting case when k → ∞). If that fixed amount of time is long enough (say, exceeding 190 or 195 kyr), a 200 kyr track record of survival is no longer sufficient to rule out extinction rates greater than 10 −4 . This result occurs as the fixed time model prohibits any possibility of observerhood occurring unusually quickly. Any lineage of Homo sapiens lucky enough to survive long enough to obtain observer status must necessarily have a survival time greater than τ, which means that being an observer with a survival time of τ conveys zero information about the extinction rate. For numerous reasons, we find the fixed time model to be implausible. Virtually all biological and cultural processes involve some degree of contingency, and there is no fundamental reason to think that gaining the ability to make scientific observations would be any different. To illustrate a comparison, let us consider a world in which For the first three models, the unbiased model is recovered for large θ, and results start to become biased as the expected observerhood time approaches humanity's track record of survival. However, even as θ → 0, the bias is limited, and the likelihood of rates exceeding 10 −4 remains at zero. This is only violated in the final fixed time model, or in models 2 and 3 when k is sufficiently large.  www.nature.com/scientificreports www.nature.com/scientificreports/ the extinction rate is −4 (averaging one extinction every 10,000 years), but observerhood status takes a fixed 200 kyr. Under this model, humanity successfully surviving long enough to reach observer status is an event with 1 in 200 million chance. Given observation selection bias, we cannot rule out the possibility of rare events that are required for our observations. But we could ask why a 1 in 200 million chance event could not also include the possibility that modern human observers would emerge unusually rapidly. Language, writing, and modern science are perhaps highly unlikely to develop within ten thousand years of the first modern humans, but it seems exceptionally overconfident to put the odds at fewer than 1 in 200 million. A similar line of reasoning can be applied to determine whether the increasing rate and multiple step models with high k are reasonable. We test this by asking what parameters would be needed to expect a 200 kyr track record of survival with an extinction rate at our conservative upper bound of μ = 6.9 × 10 −5 . For the increasing rate model, observerhood is expected after 203 kyr with θ = 10 −7 and k = 14 and for the multiple step model, observerhood is expected after 190 kyr with θ = 10 −7 and k = 16. Although these models do not assign strictly zero probability to early observerhood times, the probabilities are still vanishingly small. With an increasing rate and these parameters, observerhood has less than a one in a trillion chance of occurring within 10,000 years (3.4 × 10 −14 ), and about 1% chance of occurring within 100,000 years. With multiple steps and these parameters, observerhood has less than one in a trillion chance of occurring within 10,000 years (5.6 × 10 −17 ), and less than a 0.02% chance of occurring within 100,000 years. In a similar fashion to the fixed time model, we feel that these models exhibit unrealistic levels of confidence in late observerhood times. Although the plausibility of the fixed time (or nearly fixed time) models is hard to test directly, the wide variance in the emergence of modern human behavior across geography offers one source of data that can test their plausibility. The Upper Palaeolithic transition occurred about 45 kya in Europe and Western Asia, marked by the widespread emergence of modern human behaviour  25  (e.g. symbolic artwork, geometric blades, ornamentation). But strong evidence exists for the sporadic appearance of this modern human behaviour much earlier in parts of Africa  26, 27  , including evidence of artwork and advanced tools as early as 164 kya  28  . Although numerous factors could have prevented the Upper Palaeolithic transition from occurring quickly, the fact that some human communities made this transition more than 100 kyr earlier than the rest of humanity indicates that a much earlier development trajectory is not entirely out of the question. In summary, observer selection effects are unlikely to introduce major bias to our track record of survival as long as we allow for the possibility of early observers. Deceptively long track records of survival can occur if the probability of early observers is exceptionally low, but we find these models implausible. The wide variance in modern human behavior is one source of data that suggests our track record is unlikely to be severely biased. We can also turn to other sources of indirect data to test for observer selection bias. \n testing the Bound with indirect Data We cross check our upper bound against four other sources of data: mammalian extinction rates, survival times of other human species, rates of potential catastrophes, and mass extinction rates. Although these alternative data do not directly predict the background extinction rate of Homo sapiens per se, the rates of extinction are likely generated by similar processes and thus enable an indirect test of the upper bound. If our upper bound is sound (not biased by observer selection effects or otherwise flawed), we can make testable predictions that it will be (A) broadly consistent with the extinction rates for similar species, and (B) not exceeded by the rate of potential catastrophes or mass extinctions. As the extinction rate of other species and catastrophes many millions of years ago have little bearing on our ability to make scientific observations, these data are also less subject to potential observer selection bias. \n Mammalian extinction rates. We first evaluate whether the upper bound is consistent with extinction rates for a typical mammalian species. Using fossil record data, median extinction rates for mammals have been estimated as high as 1.8 extinctions per million species years (E/MSY) 2 , or equivalently μ = 1.8 × 10 −6 . Other estimates using fossil record data range from 0.165 extinctions per million genus years 17 to 0.4 E/MSY for Cenozoic mammals  18  . Alternative methods using molecular phylogeny suggest a much lower rate of 0.023 E/MSY for mammals  29  and rates of 0.219-0.359 E/MSY for primates  30  , although these methods have been criticized  31  . All of these estimated background rates are consistent with our upper bound. It is worth noting that Homo sapiens may be at lower extinction risk than a typical mammalian species due to a large habitat range, large population size, and having a generalist diet, which are all traits that militate against extinction risk (whereas long generation times and large body mass are sometimes correlated with increased extinction risk)  32, 33  . Hominin survival times. Next, we evaluate whether the upper bound is consistent with the broader hominin fossil record. There is strong evidence that Homo erectus lasted over 1.7 Myr and Homo habilis lasted 700 kyr  21  , indicating that our own species' track record of survival exceeding 200 kyr is not unique within our genus. Fossil record data indicate that the median hominin temporal range is about 620 kyr, and after accounting for sample bias in the fossil record this estimate rises to 970 kyr  22  . Although it is notable that the hominin lineage seems to have a higher extinction rate than those typical of mammals, these values are still consistent with our upper bound. It is perhaps also notable that some hominin species were likely driven to extinction by our own lineage  34  , suggesting an early form of anthropogenic extinction risk. individual sources of extinction risk. The upper bound can also be evaluated against the frequency of events that could pose extinction risks (examples provided in Table  3 ). If any particular risk (such as those from asteroid impacts) is known to have a higher rate than our bound of 6.9 × 10 −5 , this could undermine and potentially falsify our hypothesis. We evaluate the frequencies of four types of potential disasters for which credible quantitative estimates exist: asteroid impacts, supervolcanic eruptions, stellar explosions, and vacuum collapse. www.nature.com/scientificreports www.nature.com/scientificreports/ All of these risks have estimated to occur with a frequency well below our bound (Table  3 ), with the exception of smaller supervolcanic eruptions. Recent work has suggested the frequency of eruptions ejecting >10 3 km 3 of material exceeds our upper bound of 6.9 × 10 −5 with a recurrence time of 17 kyr  35  . However, it is important to note that the smaller eruptions within this category do not necessarily have a high probability of causing human extinction. The most severe eruption of the past 2 million years occurred just 74 kya, and it is unclear whether the human population at the time was at risk of extinction. Some argue that the human population suffered a major bottleneck at the same time as the eruption  43  , although this theory remains controversial  44  . Some climate records averaged over decades fail to observe a severe volcanic winter in Africa at the time  45  and archaeological evidence shows that human communities in South Africa thrived both before and after the eruption  46  (although these data are not sufficient to rule out a severe short-lived catastrophe followed by a fast recovery in population). More conclusively, most members of the Hominidae family did not suffer population bottlenecks around the time, with the possible exception of Eastern chimpanzees and Sumatran orangutans  47  . The lack of dramatic evidence suggesting other species extinctions or bottlenecks undercuts the possibility that humanity's survival was highly improbable and is observed only due to observation selection effects. However, a handful of substantially larger flood basalt events have taken place over the past 250 Myr that have been linked to mass extinctions  39, 48  . These events occur with a frequency of roughly once every 20-30 Myr, much more infrequently than smaller eruptions. If we assume that human extinction is threatened only from larger volcanic eruptions well exceeding 10 3 km 3 , then none of the risk frequencies we have catalogued come within an order of magnitude of the conservative upper bound. Similarly, impacts from smaller asteroid around 1 km in diameter may not have a high probability of causing human extinction. Although it is hard to estimate the consequences of such impacts, some researchers have argued that such impacts would fall below the threshold for a global catastrophe  49  . Impacts that disperse enough dust and sulphites to significantly disrupt photosynthesis occur much more rarely, with an estimated frequency of about 15 Myr years  49  . If we assume human extinction is only threatened by these more severe impacts exceeding 5 km, each of these catastrophe frequencies falls well below even our most optimistic bound of 1 in 870,000 chance of extinction per year. \n Mass extinction frequency. A mass extinction is marked by substantially increased extinction of multiple geographically widespread taxa over a relatively short period of time  50  . There have been five major mass extinctions in the past 541 Myr  51, 52  , with many arguing that human activity is currently causing a sixth  2  . In a similar way to our previous analysis of catastrophe rates, we should expect our upper bound to be consistent with the frequency of non-anthropogenic mass extinctions. Using only the big five extinctions produces a frequency of less than one per 100 Myr, far below our upper bound. In addition to the big five, there have been 13 other mass extinctions in the fossil record  53  . Using these numbers for 18 mass extinctions over 541 Myr still results in a frequency of about one per 30 Myr, many orders of magnitude below our upper bound. \n conclusions Using the fact that humans have survived at least 200 kyr, we can infer that the annual probability of human extinction from natural causes is less than 1 in 87,000 with modest confidence (0.1 relative likelihood) and less than 1 in 14,000 with near certainty (10 −6 relative likelihood). These are the most conservative bounds. Estimates based on older fossils such as the ones found in Morocco dated to 315 kya result in annual extinction probabilities of less than 1 in 137,000 or 1 in 23,000 (for relative likelihood of 0.1 and 10 −6 , respectively). Using the track record of survival for the entire lineage of Homo, the annual probability of extinction from natural causes falls below 1 in 870,000 (relative likelihood of 0.1). We also conclude that these data are unlikely to be biased by observer selection effects, especially given that the bounds are consistent with mammalian extinction rates, the temporal range of other hominin species, and the frequency of potential catastrophes and mass extinctions. The bounds are subject to important limitations. Most importantly, they only apply to extinction risks that have either remained constant or declined over human history. Our 200 kyr track record of survival cannot rule out much higher extinction probabilities from modern sources such as nuclear weapons or anthropogenic climate change. Some naturally occurring risks could be also be worsened by anthropogenic factors: a minor asteroid impact could be interpreted as a nuclear attack and lead to retaliation  54  , or a naturally occurring disease which previously may have only been a local extinction risk could spread much further due to modern travel  23  . In the cases where a natural risk is amplified by modern conditions, we can still derive some partial information from the upper bound by evaluating how much the risk would need to change from the purely natural baseline. For  www.nature.com/scientificreports www.nature.com/scientificreports/ example, the claim that a natural disease poses a than 1 in 1,000 chance of extinction per year would require that anthropogenic conditions have increased the risk of natural disease by a factor of more than 14 to 870 (under our most conservative and optimistic upper bounds, respectively). In general, for a naturally occurring risk to violate our upper bounds via human activity by more than a factor of two, the majority of the risk would still need to come from anthropogenic circumstances. In general, we conclude that anthropogenic extinction risks are likely greater than natural ones. We do not have a long track record of data for anthropogenic risks, so evaluating this relies far more on speculation. But despite the paucity of data, the little evidence we do have seems to be indicative of rates greatly exceeding our upper bounds. During the Cuban Missile Crisis of 1962, John F Kennedy put the odds of nuclear war at 'somewhere between one out of three and even'  55  . If 0.1% of nuclear wars result in human extinction via nuclear winter, taking Kennedy's odds that year would surpass our most conservative bound by more than a factor of four (and surpass our most optimistic bound by a factor of more than 250). Anthropogenic climate change could pose existential risks as well if warming is much worse than expected. A ballpark suggestion for the probability of 20 degrees of anthropogenic climate change was placed at 1%  56  , which would make the planet largely uninhabitable for humans due to heat stress  57  . And these are not the only risks we may face. One century ago, the existential risks posed by nuclear weapons or climate change may have seemed extremely implausible. We should therefore be cautious before dismissing the potential risks that future centuries of technological development could bring, such as those stemming from biotechnology  58  or artificial general intelligence  59  . Despite the low probability of human extinction from natural causes, it may still be prudent to reduce these risks. Existential risks jeopardize not only the lives of those currently present, but also the existence of all future generations. Depending on how much value we place on such generations, it may still be cost-effective to reduce existential risks from natural sources  60  . However, given limited resources to spend on reducing existential risks, one may be better off focusing on greater risks from our own design. Figure 1 . 1 Figure1. Likelihood of extinction rates given our track record of survival so far, with estimated ranges of Hominin extinction rates, mammalian extinction rates, and mass extinction frequency included for reference. Blue horizontal lines indicate likelihood of 10% and 1%. Rates exceeding 6.9 × 10 −5 are ruled out even with the most conservative data. Extending humanity's track record of survival to match older fossils, the divergence with Homo neanderthalensis, or the origin of Homo creates even stricter bounds. \n Figure 2 . 2 Figure 2. Models of observer selection bias. Surface plots show likelihood for combinations of μ and θ (where k = 3 for Models 2 and 3) or τ in Model 4. Upper righthand plots show how likelihood shifts when θ → 0 in Model 1, and for a variety of k values in Models 2 and 3.For the first three models, the unbiased model is recovered for large θ, and results start to become biased as the expected observerhood time approaches humanity's track record of survival. However, even as θ → 0, the bias is limited, and the likelihood of rates exceeding 10 −4 remains at zero. This is only violated in the final fixed time model, or in models 2 and 3 when k is sufficiently large. \n Table 1 . 1 Survival times and resulting upper bounds. www.nature.com/scientificreports www.nature.com/scientificreports/  \n Table 2 . 2 Upper bounds of μ with model 1 bias. \n Table 3 . 3 Catastrophe frequency estimates.", "date_published": "n/a", "url": "n/a", "filename": "s41598-019-47540-7.tei.xml", "abstract": "We evaluate the total probability of human extinction from naturally occurring processes. Such processes include risks that are well characterized such as asteroid impacts and supervolcanic eruptions, as well as risks that remain unknown. Using only the information that Homo sapiens has existed at least 200,000 years, we conclude that the probability that humanity goes extinct from natural causes in any given year is almost guaranteed to be less than one in 14,000, and likely to be less than one in 87,000. Using the longer track record of survival for our entire genus Homo produces even tighter bounds, with an annual probability of natural extinction likely below one in 870,000. These bounds are unlikely to be affected by possible survivorship bias in the data, and are consistent with mammalian extinction rates, typical hominin species lifespans, the frequency of well-characterized risks, and the frequency of mass extinctions. no similar guarantee can be made for risks that our ancestors did not face, such as anthropogenic climate change or nuclear/biological warfare. Out of all species that have existed, over 99% are now extinct 1 . Although human activity is dramatically increasing extinction rates for many species 2 , species extinctions were regular occurrences long before humanity emerged. Many of these extinctions were caused by gradual environmental shifts, evolutionary arms races, or local interspecific competition 3,4 , while others were abrupt, being part of global mass extinctions caused by asteroid impacts, volcanism, or causes as of yet to be identified  5, 6  . Could such a catastrophe befall our own species? If so, are the risks greater from natural or anthropogenic sources? Here, we evaluate the natural 'background' extinction rate for Homo sapiens. This means considerations of anthropogenic risks such as climate change and nuclear weapons are excluded from our estimates, although these clearly pose existential threats to our own species as well as others. Indeed, it has been hypothesized that the great majority of human extinction risk comes from anthropogenic sources  7, 8  . But by limiting our analysis to natural risks that our predecessors also faced, we can draw on data spanning many thousands (or millions) of years. Obtaining bounds on natural extinction rates also enables an indirect and partial test of the hypothesis that anthropogenic risks are greater than natural ones, as sufficiently low natural extinction risk will imply higher relative risks from anthropogenic sources. Estimating such an extinction rate directly is impossible. We have no examples of Homo sapiens extinction, so the most directly relevant data are non-existent. An alternative approach would be to enumerate the different types of naturally occurring hazards (e.g. asteroids, supervolcanoes), estimate their independent probability of causing extinction, and then use these probabilities to derive an aggregate extinction rate. However, this method has its own shortcomings. Beyond the great uncertainties around the probabilities of each risk, there could also be unknown risks that fail to be included. It would be hard to say with confidence that any list of risks had captured all natural hazards to humanity. We can bypass these problems by instead considering the length of time that humanity has survived so far 9,10 . This survival time can be used to estimate an upper bound on the extinction rate from all natural sources combined, including from sources for which we remain unaware. However, this approach could be subject to a particular form of sample bias known as an observation selection bias. These observer selection biases occur when a sample is not representative of all outcomes, but rather a subset of outcomes that are compatible with the existence of the observers 11 . For example, if human existence required a 10 million year (Myr) period of evolution free from asteroid impacts, any human observers will necessarily find in their evolutionary history a period of 10 Myr that is free of asteroid impacts, regardless of the true impact rate. Inferring a rate based on those 10 Myr could therefore be misleading, and methods must to be used to correct for this bias 12 .", "id": "436e28620a6a6a11f65339bfb1c31eb3"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrea Owe", "Seth D Baum"], "title": "The Ethics of Sustainability for Artificial Intelligence", "text": "Introduction A basic attribute of modern human civilization is that the stock of natural resources steadily decreases, whereas the stock of artificial resources steadily increases. For example, artificial intelligence (AI) research is commonly powered by the burning of fossil fuels, and in the process produces new technologies that civilization can benefit from. Will the increases in artificial resources be sufficient to offset the loss of natural resources, such that civilization can be sustained into the future? That is one important perspective on the ethics of sustainability as it relates to AI, though, as this paper discusses, it is not the only one. Sustainability is not an inherently ethical concept. In its essence, \"sustainability\" refers to a particular characteristic of systems as they change over time. The term can be used in many ways that do not have any particular ethical significance. For example, sprinters run at an unsustainable speed; eventually, their muscles will fatigue and they will be unable to continue. This is a basic characteristic of human physiology and not a matter of ethical significance. In common usage, however, sustainability takes on ethical significance. Sustainability is widely treated as a good thing and something worth pursuing  [1] . It is in that spirit that there have been initiatives on AI and sustainability, including conferences such as \"Sustainable AI\",  1  \"Towards Sustainable AI\",  2  and \"AI for the Planet\",  3  as well as groups such as AI4Good that work on AI in support of the United Nations Sustainable Development Goals (SDGs).  4  It is also in that spirit that sustainability is one of the principles found in some AI ethics guidelines  [2] . The ethical dimensions of sustainability warrant ethical analysis. Important ethics questions include: What exactly should be sustained, or rather, be able to be sustained? Why should it be able to be sustained? For how long? How much emphasis should be placed on sustainability relative to other goals? These ethics questions can be answered in a variety of ways. How they are answered has important implications for ongoing human activity, including for the development, use, and governance of AI technology. Prior literature on AI and sustainability (reviewed below) has not considered the ethical dimensions to any significant extent. Therefore, this paper analyzes the ethics of sustainability as it relates to AI. The paper proceeds in three parts. First, we explain the ethics of sustainability as a general concept (Section 2). Second, we describe the current usage of the concept of sustainability within work on AI (Section 3). Third, we present an argument for a long-term, non-anthropocentric conception of sustainability and explain the implications of this for AI (Section 4). Section 5 concludes. Much of the discussion in this paper covers ethical dimensions of sustainability that are not specific to AI. This is a feature, not a bug. To a large extent, the ethical dimensions of AI and sustainability are the same as those for sustainability in general. Furthermore, aspects of the topic that are specific to AI build on more general sustainability concepts. Therefore, to understand the ethics of sustainability for AI, it is essential to first understand the ethics of sustainability. The paper contributes to the growing literature on AI and sustainability. Most of this literature is on AI in relation to the sustainability of human civilization and its environmental underpinnings; this includes reviews by Nishant et al.  [3]  and Liao and Wang  [4] , the environmental politics of AI  [5] , AI in relation to systemic risk and sustainability  [6] , the environmental footprint of AI systems  [7] , and the role of AI in meeting the SDGs  [8] [9] [10] . Some literature focuses on the sustainability of the AI systems themselves  [11] , including for consumer autonomy  [12] , in global health initiatives  [13] , in certain economic mechanisms  [14] , and in decision-making applications  [15] . Additionally, there is a broader field of computational sustainability that applies computer science methods to advance environmental and social sustainability  [16] [17] [18] . Overall, the literature on AI and sustainability offers a variety of important contributions, but it provides limited discussion of the ethics of sustainability. The paper additionally contributes to some adjacent literatures. Prior studies have considered the application of AI for environmental protection  [19] [20] , for climate change mitigation  [21] [22] , and the energy consumption of AI systems  [23] ; these are relevant for environmental conceptions of sustainability. Also relevant are debates on the relative importance of near-term, medium-term, and long-term AI  [24] [25] [26] [27] ; as this paper discusses, the future-orientation of sustainability can imply an emphasis on long-term AI. Finally, of more general relevance is prior work on the ethics of sustainability  [1] , especially sustainability over 1 https://www.uni-bonn.de/en/news/120-2021 2 http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=140164&copyownerid=158619 3 https://aifortheplanet.org/ 4 https://ai4good.org/ long time scales  [28] , and the ethics of AI  [2, [29] [30] , especially regarding AI and the future  [31]  and AI and nonhumans  [32] . \n The Ethics of Sustainability The word \"sustainability\" is commonly traced to the German word Nachhaltigkeit, and specifically to Hans Carl von Carlowitz's 1713 treatise on sustainable yield forestry  [33] . The tension between using resources now and preserving or cultivating them for future use is of course much older. Modern analysis traces to the environmental economics work of Hotelling  [34] , which remains relevant today  [35] . Hotelling's work did not use the term \"sustainability\". Use of the term primarily traces to the 1987 report Our Common Future, which was led by former Norwegian Prime Minister Gro Harlem Brundtland and is commonly known as the Brundtland Report. Like von Carlowitz's treatise, the Brundtland Report specifically conceptualizes sustainability in socio-environmental terms. The report's definition of sustainable development, \"Development that meets the needs of the present without compromising the ability of future generations to meet their needs\", has been widely influential and serves as a foundation for the UN SDGs. Since Our Common Future, there has been a proliferation of definitions of sustainability and sustainable development  [36] [37] [38] . Widespread and imprecise usage of the term \"sustainability\" has watered it down. Critics argue that \"sustainability\" has become \"a concept that is equivalent to 'good' and thus devoid of any specific meaning-a blanket concept to assure stakeholders of the policy's good intentions\"  [39, p.3439 ]. Likewise, the term is said to have been appropriated by self-interested actors to continue \"business as usual\" activities that drive environmental destruction and social inequity  [37] . One notable point of criticism is the so-called \"three pillars\" of sustainability: the social, the economic, and the environmental-or \"people, profit, and planet\". The pillars construct is an attempt to represent the major components of socio-environmental sustainability. However, these categories have been criticized for being fuzzy and overlapping, for excluding of other relevant categories such as the cultural and the political, and for not being essential to the core matter of whether civilization can be sustained over time  [39] . Indeed, economic transactions are an inherently social activity, and all human activity is inherently environmental because humans are part of nature. Furthermore, sustainability is commonly associated with environmental protection, but some environmental disturbances, such as many types of air or water pollution, rapidly dissipate and have a negligible effect on future generations' ability to sustain themselves. Likewise, some matters that could classify as social and/or economic, such as social justice within the contemporary population, are often of limited relevance to the ability of future generations to sustain themselves, even if these matters may be important for other reasons. Other socio-economic matters, such as education and investment in future economic growth, may be of greater importance to the ability of future generations to sustain themselves. For these reasons, the \"three pillars\" provide a weak foundation for sustainability. Work on AI and sustainability that incorporates the \"three pillars\", such as the \"AI for People: Towards Sustainable AI\" conference, 5 should take note. We now turn to three fundamental questions for the ethics of sustainability (Sections 2.1-2.3) followed by a comparison between sustainability and optimization (Section 2.4). The reasons something should be able to be sustained typically derive from what are, in moral philosophy, referred to as intrinsic value and instrumental value. Roughly speaking, something is intrinsically valuable if it is valuable for its own sake, or valuable as an ultimate end in itself; something is instrumentally valuable if it is valuable because it promotes something else that is valuable  [40] . For example, we might suppose that sunlight is valuable because it can (among other things) be converted into electricity, and that electricity is valuable because it can (among other things) be used to power AI systems, and that AI systems are valuable because they can (among other things) enable humans to have enjoyable lives, and that enjoyable human lives are just good things on their own. In that case, sunlight, electricity, and AI systems are instrumentally valuable, while enjoyable human lives are intrinsically valuable. In many conceptions of ethics, what should be done-including what should be sustained-is defined with reference to some conception of what is intrinsically valuable. \n Conceptions of sustainability can vary in terms of what they intrinsically value and what sorts of instrumental values they focus on. One can seek to sustain X either because X is intrinsically valuable or because X is instrumentally valuable. For example, one can seek to sustain natural ecosystems either because one considers them to be intrinsically valuable or because one considers them to be instrumentally valuable for other things, such as for human welfare. Common conceptions of sustainability are anthropocentric, meaning that they only intrinsically value humans  [41] . For example, although the Brundtland Report's emphasis on future generations could conceivably be interpreted to mean future generations of something other than humans, the Report clearly focuses on humans. Likewise, sustainable management of natural resources generally treats the resources as instrumental values for human benefit. In contrast, some conceptions of sustainability are ecocentric, meaning that they intrinsically value ecosystems. Examples include the Earth Charter 6 and the Earth Manifesto  [42] . Though less common, the concept of sustainability can also be used with other notions of intrinsic value, such as the idea that there is intrinsic value in the welfare of sentient nonhuman animals or (if possible) sentient AI systems. The distinction between intrinsic and instrumental value does not always matter, but it often is important. For example, reducing greenhouse gas emissions is generally good on both anthropocentric and ecocentric grounds. However, some biodiversity protection is worth pursuing mainly on ecocentric grounds, because, for better or worse, certain species could go extinct with little impact on human welfare. Therefore, it is important for discussions of sustainability to explicitly specify what they intrinsically value. \n For how long should something be able to be sustained? There is a big difference between sustaining something for a few days and sustaining it for decades, centuries, or even indefinitely into the distant future. Unfortunately, discussions of sustainability are often not precise in their consideration of time scales. For example, the 1987 Brundtland Report's emphasis on future generations implies a time scale of at least decades, assuming the generations are of humans. But how many future generations? The actions needed to enable the next few generations to be sustained often differ significantly from the actions needed to enable the same for every generation that could ever exist. \n How much effort should be made for sustainability? The sustainability of intrinsic or instrumental values may be a good thing, but how good? The world has many competing values and opportunities. Indeed, the Brundtland definition was specifically crafted to acknowledge the competing values of present and future generations; while the report aspires to promote actions that support both the present and future generations, many choices involve tradeoffs between them. For example, depleting natural resources often benefits present generations at the expense of future generations. Basic research often benefits future generations at the expense of present generations, especially where the same resources could instead be used for applied research. The relative importance of the present and future can be operationalized in a variety of ways, such as through discount rates or other weighting functions  [43] [44] . This sort of intergenerational evaluation is generally made within the context of anthropocentric conceptions of sustainability, but similar approaches can be taken with other conceptions. One way or another, moral guidance about sustainability must consider how to evaluate tradeoffs between sustainability and other moral goals. This point fits within the broader issue of tensions between different AI ethics principles  [45] . Also relevant are fundamental questions about the appropriate degree of effort to take to achieve ethical goals. In moral philosophy, the term \"supererogation\" refers to actions that \"go beyond the call of duty\", meaning that they are good but not strictly required  [46] . One common question in moral philosophy is whether some moral frameworks are too demanding. This question is especially acute for consequentialist moral frameworks that call for moral agents to maximize some conception of intrinsic value, because maximization is a demanding task  [47] . These are important questions for any moral debate, certainly including those involving sustainability. Setting aside tradeoffs between sustainability and other moral goals, one can ask: How much effort should a person or an organization make to advance sustainability? Should they \"give it everything they've got\"? Or would just a little effort be acceptable? Conversely, is it enough to work to advance sustainability? Or is it important to also work toward more ambitious goals, such as intertemporal optimization of intrinsic value? \n Sustainability vs. Optimization Sustainability can be an optimization criterion-that would mean seeking to optimize the ability for something to be sustained over time. However, this is distinct from optimizing intrinsic value. Sustainability means enabling something to be sustained in at least some minimal form; optimization means making something be the best that it can be. Ensuring sustainability is perhaps best understood as a basic minimum standard of intertemporal conduct, whereas the intertemporal optimization of intrinsic value may be understood as a loftier ideal to aspire for. This distinction can be seen, for example, in the Brundtland Report call for the present generation to act \"without compromising the ability of future generations to meet their needs\". The basic needs of human life are, to an approximation, food, clothing, and shelter. Following the Report's call could result in \"a society living forever at a minimum subsistence level of consumption\"  [48, p.327] . Future society would be able to meet its needs, but it may not be able to do anything more. If the present generation does not act so as to enable future generations to do much better than meeting their needs, then the present generation will, quite arguably, have squandered a massive opportunity. Of course, if the present generation fails to enable future generations to meet their needs, that would be, quite arguably, a massive loss. AI is advanced technology. AI research and development is often oriented toward enabling higher standards of living instead of enabling basic future needs. Human lives do not strictly need, for example, AI systems to steer vehicles or search the internet. Such work generally falls outside the scope of sustainability, but could fall within the scope of optimizing intrinsic value. \n Prior Work on AI and Sustainability With the ethics of sustainability in mind, we now survey prior work on AI and sustainability. Sections 3.1 and 3.2 present quantitative analysis of trends in the ethics of sustainability found in AI ethics principles and AI research. Both analyses characterize sustainability in terms of the three ethics dimensions presented in Section 2: intrinsic value, time scale, and degree of effort. Section 3.3 presents overarching trends across Sections 3.1-3.2. \n AI Ethics Principles Jobin et al.  [2]  compiles 84 sets of AI ethics principles. 11 of these sets of principles include some reference to sustainability.  7  This indicates that sustainability is a small but nonzero priority in AI ethics. We examined the ethical basis of the 11 sets of principles. We found that 7 refer to some form of environmental sustainability, 3 refer to sustainability of the AI system itself, and 1 refers to sustainable social development. We further found that 3 intrinsically value humans, 5 intrinsically value humans and nonhumans including ecosystems, all life, biodiversity, and the planet, and 5 are ambiguous in terms of what is intrinsically valued. Regarding time scales, 2 refer to \"future generations\" and 9 do not specify time scales. Finally, none of the principles specify degree of effort. Some examples of the AI ethics principles are presented in Appendix A. \n AI Sustainability Research We performed a systematic mapping review  [49]  of research at the intersection of AI and sustainability. Our review maps this literature in terms of the ethical attributes presented in Section 2 and also used in Section 3.1, with some additional nuances to catch the diversity of the research literature. Specifically, we analyzed results from a Google Scholar search for [\"artificial intelligence\" \"sustainability\"] and [\"AI\" \"sustainability\"] conducted between Sept 16 and 21, 2021. The Google Scholar search engine was selected over other academic databases due to its inclusivity. Whereas databases such as Web of Science concentrate on 7 Table  3  of Jobin et al.  [2]  states that 14 sets if principles include sustainability, but only 12 are referenced in the text and we were unable to identify the other 2. Of the 12 referenced sets of principles, we found that 1 did not cover sustainability, leaving a total of 11 for our analysis. peer-reviewed journals, artificial intelligence research is often published in other spaces such as arXiv. The searches returned 229,000 total results for [\"artificial intelligence\" \"sustainability\"] and 1,490,000 total results for [\"AI\" \"sustainability\"], respectively. We examined the first ten pages of each of the two searches. We observed that after ten pages of each search, the search results became repetitive and less relevant. These two sets of ten pages contained 200 total results, or 153 results after duplicates were extracted. Of these 153 publications, we were unable to access 11. For the remaining 142 publications, we examined the text in the degree of detail needed to categorize its treatment of sustainability. For most of the publications, this involved looking at the abstract and introduction, and skimming the text for discussion of sustainability. In some cases, we examined the entire publication in more detail. Out of the 142 publications, 60 were found not to be relevant because they were not sufficiently on the nexus of AI and sustainability, leaving a data set of 82 publications. 66 publications were on environmental sustainability, 7 were on the sustainability of the AI system itself, and 9 were on the sustainability of something else, including 2 on the sustainability of organizations, 2 on social sustainability in human-robot/AI interactions, 1 on the sustainability of group decision-making processes, 1 on sustainable curriculum planning, 1 on sustainable healthcare systems, 1 on the social sustainability of AI, and 1 on sustainable industrial development. Of the 66 environmental sustainability publications, 43 were on environmental and social sustainability and 23 were exclusively on environmental sustainability. 29 of the 66 environmental sustainability publications referred to the Brundtland definition and/or the SDGs. 56 publications intrinsically valued humans only, 10 intrinsically valued humans and nonhumans including nonhuman species, life on Earth, biodiversity, ecosystems, the biosphere, and the planet. 16 were too ambiguous to interpret any notion of intrinsic value. Regarding time scales, 7 refer to \"future generations\" and 1 refers to a time frame from 1990 to 2028. The other 74 do not specify time scales. None of the publications specify degree of effort. Some examples of the AI sustainability publications are presented in Appendix B. \n Overarching Trends In consideration of the work presented in the two preceding subsections, the following overarching trends in the ethics of existing work on AI and sustainability can be identified. First, most work on AI and sustainability is focused on some form of environmental sustainability, with substantial minorities focused on the sustainability of AI systems or on the sustainability of miscellaneous other things. The environmental sustainability work mainly intrinsically values humans and sometimes intrinsically values nonhumans. These trends are consistent with wider usage of sustainability outside the context of AI. Indeed, work on AI and sustainability often explicitly links to broader treatments of sustainability, such as the Brundtland Report and the UN SDGs. Work on the sustainability of AI systems treats AI systems as instrumentally valuable, such as in decision-making applications  [15]  and in global health initiatives  [13] . Outside the context of sustainability, some research considers that AI systems could be intrinsically valuable  [50] [51] [52] . We find that the sustainability of intrinsically valuable AI systems has not yet been addressed. Second, work on AI and sustainability is imprecise on its ethical dimensions. As illustrated in Appendices A-B, our classification of AI ethics principles and AI sustainability research involved frequent parsing of ambiguous phrasings. Indeed, outside references to the SDGs or the Brundtland definition, few publications explicitly define sustainability. Within treatments of environmental sustainability, the term \"sustainability\" was commonly equated with environmental protection, especially efforts to minimize energy and resource consumption, even though environmental issues do not necessarily have sustainability implications. Some work equated \"sustainability\" with \"good for people/and or society\" or even just \"good\", which further drains \"sustainability\" of its meaning. As discussed in Section 2, these are common problems with sustainability discourse. Our analysis finds that these problems have been reproduced in the AI literature. \n The Moral Case for Long-Term, Non-Anthropocentric Sustainability and Optimization In this section, we present our own views on the ethics of sustainability as it relates to AI. Specifically, we make the case for sustainability that is non-anthropocentric and long-term oriented. We further argue for substantial effort for this conception of sustainability, or, preferably, for the optimization of long-term intrinsic value. Finally, we explain the implications of such sustainability for AI. Each of our arguments depends on certain positions on underlying ethical principles. As with all ethical principles, there is no universal consensus on which position to take. One can disagree with the positions we take, but doing so requires taking a different position on the underlying ethical principles. This is important to bear in mind, especially when considering the implications for AI. \n Non-Anthropocentric Sustainability First, we call for non-anthropocentric conceptions of sustainability. By non-anthropocentric, we mean that humans are not the only entities that are intrinsically valued. Modern science unambiguously shows that humans are members of the animal kingdom and part of nature. Morally significant attributes such as the innate drive to live and flourish or to experience pleasure and pain are not unique to the human species.  8  For purposes of this paper, we set aside important debates about which nonhuman entities to intrinsically value, but some potential examples include sentient nonhuman animals or (if possible) sentient AI systems, natural ecosystems, and biodiversity. We, the authors of this paper, also happen to disagree among ourselves as to which nonhumans are intrinsically valuable, but we agree that some are. There can be legitimate reasons to sometimes intrinsically value humans more than other entities-for example, a human can have a longer and richer life than a spider. However, we see no morally sound reasons to refuse to intrinsically value any nonhuman lives or entities. This means that sustainability should be defined as to also sustain some nonhumans for their own sake: it is not enough to sustain nonhumans for their instrumental role for humans.  9  8 Additionally, some conceptions of intrinsic value are rooted in the attributes of systems, such as interdependencies of biotic and abiotic entities within ecosystems. These holistic conceptions of intrinsic value are also not specific to humans  [53] . 9 For a more detailed argument for non-anthropocentrism advanced within AI ethics, see  [32] . This non-anthropocentrism is at odds with common conceptions of sustainability, including that of the Brundtland Report. In failing to intrinsically value anything other than humans, we believe these conceptions of sustainability are in moral error. It is unfortunate but not surprising that similar anthropocentric tendencies are found within existing work on AI and sustainability (Section 3). Future work on AI and sustainability should be more inclusive of the intrinsic value of nonhumans. \n Long-Term Sustainability Second, we call for sustainability over long time scales. Our motivation for this is an ethical principle of equality across time. In essence, this means that no one or no thing of moral significance should be disadvantaged because of the time in which they happen to exist. A person (for example) is of the same intrinsic value regardless of whether they live in the year 2021 or 2051 or 2151 or even 22021 or any other future time  [54] [55] . This perspective can be justified, for example, by a \"veil of ignorance\" thought experiment in which one does not know in advance which time period one would exist in  [56] . Under such hypothetical circumstances, it would only be fair to value each time period equally. Taking temporal equality seriously means including attention to all future time periods, including the astronomically distant future. Combined with our call for non-anthropocentrism, this means sustainability should aim to sustain that which is intrinsically valuable into the distant future. This long-termism is broadly consistent with common conceptions of sustainability, though it is different in emphasis. Common conceptions do not specify precise time scales; this is seen, for example, in the Brundtland Report's emphasis on an unspecified number of future generations. With no clear time limit, these conceptions could include the astronomically distant future, though in practice, they focus on matters that are short-term in comparison. We believe this is a moral error, an unjustified exclusion of distant-future generations and distant-future instances of anyone and anything else of intrinsic value. \n Substantial Effort for Sustainability or Long-Term Optimization Third, we call for a high degree of effort toward sustainability, or, preferably, for the optimization of long-term intrinsic value. The astronomically distant future offers astronomically large opportunities for advancing intrinsic value. These opportunities are vastly larger than those available for the present time and the near-term future. This point suggests a high degree of priority for actions oriented toward the long-term. That does not mean ignoring the present. As members of the present time period, we have special opportunities to help with present circumstances. The present also sets the stage for the future. Nonetheless, if the principle of equality across time is to be taken seriously, it requires a major focus on long-term outcomes. We further believe that people should make great efforts to advancing moral progress of all types, including sustainability, balanced mainly by the need for reasonable selfcare, and that organizations and institutions should likewise be oriented accordingly. An important perspective comes from the physics of the long-term future. Earth will become uninhabitable in roughly one billion years due to the gradual warming and expanding of the Sun  [57] . Survival beyond this time can only occur in outer space. For Earth-originating entities, this will require an advanced technological civilization capable of settling in outer space. Human civilization is already positioned to accomplish this task, given its ongoing space missions and general technological progress. As long as human civilization remains intact, the ability to sustain Earth-originating entities will persist. Long-term sustainability requires resettling in outer space  [28] . For the present generation, that means keeping human civilization intact. In many contexts, there is no significant distinction between sustainability and intertemporal optimization for the distant future. Both goals require maintaining the basic functionality of civilization, including by sustaining sufficient resources and by handling major threats such as global warming, pandemics, and nuclear warfare. They likewise entail evaluating environmental threats in terms of their implications for the continuity of human civilization and not in terms of biogeophysical disturbances or smaller-scale human consequences  [58] [59] . However, looking ahead, the goals point in different directions. Sustaining Earth-originating entities into the distant future only requires some minimal space settlement over very long timescales. In contrast, optimization of long-term intrinsic value entails space expansion sooner and at larger scales, in order to fill the universe with whatever is intrinsically valuable. The distinction between sustainability and optimization of long-term intrinsic value is also important in terms of what is intrinsically valuable. Long-term sustainability can entail the same course of action for both anthropocentric and non-anthropocentric conceptions of intrinsic value: If humanity fails to settle in outer space, then other Earth-originating entities would also die out in a billion or so years, if not sooner  [28, 60] . However, long-term optimization generally entails expansion into outer space-but expansion in what way? Anthropocentrism would entail expansion of human populations, whereas nonanthropocentrism would entail expansion of something else. \n Implications for AI AI has several important roles to play in the story outlined above. First, current and near-term forms of AI can be applied to addressing certain immediate threats to global civilization. For example, AI is in active use for addressing global warming and environmental protection in a variety of ways, and additional ways have been identified and called for  [21] . AI is also in active use for addressing the ongoing COVID-19 pandemic by supporting tasks such as medical analysis  [61]  and robotics to support social distancing  [62] . Further work along these lines could be of value for improving the resilience pf human civilization to COVID-19 and future pandemics. Whereas global warming is a traditional environmental sustainability topic, pandemics are not, though pandemics can derive from environmental activities, in particular those that put humans in contact with novel zoonotic pathogens. Nonetheless, both issues threaten the ability of global human civilization to be sustained into the long-term future. Second, future forms of AI could be particularly consequential. The field of AI has long entertained notions of extreme future AI that could be \"the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control\"  [63, p.33] . Recently, there has been debate on the extent to which people in AI should focus on near-term or long-term AI. To some extent, this debate may be unnecessary, due to the existence of activities that are good to do for both near-term and long-term AI  [24, [26] [27] . Nonetheless, to the extent that each type of AI merits some distinct attention, a case can be made for attention to long-term AI due to its potential importance for long-term sustainability. Long-term AI can play three roles of relevance to long-term sustainability. First, it could bolster efforts to address threats such as global warming and pandemics. Second, it could pose a threat of its own, especially for runaway AI scenarios in which the AI effectively takes over the world. Third, it could play an instrumental role in space expansion. A significant dilemma exists for the dual status of long-term AI as both threat and tool for addressing other threats. Ideally, long-term AI would be designed slowly and carefully to ensure a high standard for safety and ethics. However, delaying the deployment of long-term AI reduces the potential for its use to address other threats. One implication of this is that other work to address other threats can be of value for \"buying time\" to safely and ethically develop long-term AI  [64] . This includes work using near-term AI to address these other threats. If there is extended time available to slowly and carefully design long-term AI, then that also buys time to reflect on what should be done with respect to space expansion and related opportunities  [65] . On the other hand, there is no guarantee that an extended time will be available. Indeed, AI research and development is proceeding at brisk pace, prompting concerns about a race to develop long-term AI  [66] . One proposed means of buying some time is to deploy a moderately powerful AI \"nanny\" who can protect and support humanity while it reflects on what to do next  [67] . That possibility is not without its own risks, such as the risk of a poorly designed nanny AI that steers the world in a bad or even catastrophic direction. These are all among the AI issues that can be of profound importance for long-term sustainability. \n Conclusion In this paper, we have surveyed the ethics of sustainability, analyzed the ethical basis of existing work on AI and sustainability, and presented an argument for a non-anthropocentric, long-term conception of sustainability and an accompanying argument for favoring optimization over sustainability. Taken together, the paper provides some guidance on how ongoing work on AI and sustainability can and should proceed. First, work on AI and sustainability should precisely specify its ethical basis, in particular on what it seeks to sustain, for how long, and how much effort should be made on sustainability. Second, work on AI and sustainability should consider adopting the non-anthropocentric, long-term conception of sustainability and optimization that this paper argues for. In practice, that entails a focus on applying AI to addressing major global threats such as global warming and pandemics, to ensuring the long-term sustainability of the resource base needed for civilization, and for pursuing opportunities to expand human civilization into outer space. In closing, we wish to emphasize the ethical principle of equality across time. A fundamental aspect of sustainability is its future-orientation. The principle of equality across time means that all future times should be treated equally, or rather that there should be no bias against something just because of when it exists. This is a compelling moral principle. If it is to be taken seriously, it demands an attention to the big-picture distant future of the universe and to the ways in which near-term actions can affect it. Actions involving AI are among the most significant ways to affect the distant future. The field of AI has special opportunities to make an astronomically large positive difference-to make the universe a better place. It should make pursuit of these opportunities a major priority. strongly indicate that the natural environment is valued instrumentally to advance human wellbeing. Nothing in the statement clarifies the time scales of sustainability or degree of effort. The UNI Global Top 10 Principles for Ethical AI includes the principle, \"Make AI serve people and planet: This includes codes of ethics for the development, application and use of AI so that throughout their entire operational process, AI systems remain compatible and increase the principles of human dignity, integrity, freedom, privacy and cultural and gender diversity, as well as with fundamental human rights. In addition, AI systems must protect and even improve our planet's ecosystems and biodiversity.\" This principle is classified as intrinsically valuing humans, ecosystems and biodiversity as the final line calls for not only protection but improvement of nonhuman entities, and the phrasing \"make AI serve people and planet\" strongly suggest moral consideration for also nonhumans. \n Appendix B: Examples of AI Sustainability Publications Section 3.2 presents data on publications on the nexus of AI and sustainability. This appendix presents some illustrative examples of these data. Theodorou et al.  [68]  developed a single-player game designed to simulate a sustainable world based on accurate ecological models and behavior economics principles. In the game, individual people must aim to act toward a sustainable society. The paper describes the game in terms implying that natural resources play an instrumental role to advance individual people's survival and wellbeing. Other indications of what is meant by a sustainable world is discussed in social and economic terms. This publication was, therefore, classified as implying intrinsic value of humans and instrumental value of nonhumans. Yigitcanlar & Cugurullo  [69]  define smart and sustainable cities as \"an urban locality functioning as a robust system of systems with sustainable practices, supported by community, technology, and policy, to generate desired outcomes and futures for all humans and nonhumans\". This publication is classified as intrinsically valuing humans and nonhumans as it explicitly refers to their benefits. van Wysnberghe  [7]  calls for a \"third wave\" in AI ethics and states that \"This third wave must place sustainable development at its core\" (emphasis original). Sustainable development is in turn defined as in the Brundtland report. This suggests an anthropocentric conception of sustainability, in which only humans are intrinsically valuable. It further suggests placing a high degree of effort on sustainability, though the emphasis on sustainable development leaves open the question of the relative importance of present vs. future generations. Gomes et al.  [70]  argue that \"computational sustainability harnesses computing and artificial intelligence for human well-being and the protection of our planet\" and that \"planning for sustainable development encompasses complex interdisciplinary decisions spanning a range of questions concerning human well-being, infrastructure (…) and the environmental protection of the Earth and its species\". All of this is strongly suggestive of intrinsic value of nonhumans as well as humans, so this publication is classified as such. Zhang et al.  [71]  studies the contributions of big data analytics capability and artificial intelligence capability to the sustainability of organizational development. The publication does not define sustainability and apply the following uses of \"sustainability during the abstract and introduction only: \"sustainable innovation and performance\", \"sustainability development projects\", \"sustainability design and commercialization processes\", \"sustainable growth and performance\", \"sustainable organizational growth\", \"sustainable competitive advantages\", \"sustainable investment\", \"sustainable development goals\", \"sustainable positional advantages\", and big data as \"sustainable resources\". This publication is therefore classified as ambiguous. Larsson et al.  [72]  by the AI Sustainability Center defines sustainable AI as follows: \"The AI Sustainability Center supports an approach in which the positive and negative impacts of AI on people and society are as important as the commercial benefits or efficiency gains. We call it Sustainable AI.\" This publication is classified as intrinsically valuing humans as it discusses and defines sustainability as pertaining to human and social aspects only, including sustainable AI which is defined by accountability, bias, malicious use, and transparency. The publication is further noteworthy for presenting an extensive literature review of AI ethics as a review of literature on sustainable AI, thus equating AI ethics or ethical AI with sustainable AI, which arguably drains \"sustainability\" of meaning. 5 2 . 1 21 https://aiforpeople.org/conference/ What should be able to be sustained, and why? \n\t\t\t https://earthcharter.org/", "date_published": "n/a", "url": "n/a", "filename": "060_sustainability-ai.tei.xml", "abstract": "Sustainability is widely considered a good thing and is therefore a matter of ethical significance. This paper analyzes the ethical dimensions of existing work on AI and sustainability, finding that most of it is focused on sustaining the environment for human benefit. The paper calls for sustainability that is not human-centric and that extends into the distant future, especially for advanced future AI as a technology that can advance expansion beyond Earth.", "id": "72bb37a902865897f1b1931a7c279192"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "Under review as a conference paper at ICLR 2022 SELF-SUPERVISE, REFINE, REPEAT: IMPROVING UN-SUPERVISED ANOMALY DETECTION", "text": "INTRODUCTION Anomaly detection (AD), the task of distinguishing anomalies from normal data, plays a crucial role in many real-world applications such as detecting faulty products using visual sensors in manufacturing, fraudulent behaviors at credit card transactions, or adversarial outcomes at intensive care units. AD has been considered under various settings based on the availability of negative (normal) and positive (anomalous) data and their labels at training, as overviewed in Sec. 2. Each application scenario is dominated by different challenges. When entire positive and negative data are available along with their labels (Fig.  1a ), the problem can be treated as supervised classification and the dominant challenge becomes the imbalance in label distributions  [4, 16, 20, 27, 32, 35] . When only negative labeled data are available (Fig.  1b ), the problem is 'one-class classification'  [23, 26, 33, 45, 47, 51, 53] . Various works have also extended approaches designed for these to settings with additional unlabeled data (Fig.  1c,d,e )  [10, 18, 24, 46, 58]  in a semi-supervised setting. While there exist many prior works in these settings, they all depend on some labeled data, which is not desirable in all application scenarios. Unsupervised AD, on the other hand, poses unique challenges in the absence of any labeled data information, and a straightforward adaption of methods developed with the assumption of labeled data would be suboptimal. For example, some recent studies  [7, 60]  have applied one-class classifiers (OCCs) that are known to yield impressive performance when trained on negative samples  [7, 23, 26, 33, 51]  to unsupervised AD, but their performance for unsupervised AD has been quite sub-optimal. Fig.  2  illustrates this, showing the unsupervised AD performance of state-of-the-art Deep OCCs  [51]  with different anomaly ratios in unlabeled training data -the average precision significantly drops even when a small portion (2%) of training data is contaminated with anomalies. Our framework SRR (Self-supervise, Refine, Repeat), overviewed in Fig.  3 , brings a novel approach to unsupervised AD with the principles of self-supervised learning without labels and iterative data refinement based on the agreement of OCC outputs. We propose to improve the state-of-the-art performance of OCCs, e.g.  [33, 51] , by refining the unlabeled training data so as to address the fundamental challenges elaborated above. SRR iteratively trains deep representations using refined Figure  1 : AD problem settings. Blue and red dots are for labeled negative (normal) and positive (anomalous) samples, respectively. Grey dots denote unlabeled samples. While previous works mostly focus on supervised (a, b) or semi-supervised (c, d, e) settings, we tackle an AD problem using only unlabeled data (f) that may contain both negative and positive samples. data while improving the refinement of unlabeled data by excluding potentially-positive (anomalous) samples. For the data refinement process, we employ an ensemble of OCCs, each of which is trained on a disjoint subset of unlabeled training data. The samples are declared as normal if there is a consensus between all the OCCs. The refined training data are used to train the final OCC to generate the anomaly scores in the unsupervised setting. Most prior unsupervised AD works  [23, 26, 33, 51]  assume that the data contains entirely negative samples, which makes them not truly unsupervised as they require having humans to do the data filtering. Similar to ours, some prior unsupervised AD works  [7, 45, 60]  considered evaluating on an unsupervised setting where there exist a small percentage of anomalous samples in the training data, i.e. operating in 'truly' unsupervised setting without having the need for humans to do any filtering in the training data. However, these methods often suffered from significant performance degradation as the ratio of anomalous sample ratio has increased (see Sec. 4.2). We would like to highlight that our method distinguishes from the literature by bringing a data-centric approach (refining the unlabeled data) to unsupervised anomaly detection beyond the model-centric approaches (improving the model itself). Our framework SRR aims to provide robustness in performance as the anomalous sample ratio increases, as shown in Fig.  2 . We conduct extensive experiments across various datasets from different domains, including semantic AD (CIFAR-10 [29], Dog-vs-Cat  [19] ), real-world manufacturing visual AD use case (MVTec  [8] ), and tabular AD benchmarks. We consider methods with both shallow  [36, 47]  and deep  [7, 33, 51]  models. We evaluate models at different anomaly ratios of unlabeled training data and show that SRR significantly boosts performance. For example, in Fig.  2 , SRR improves more than 15.0 average precision (AP) with a 10% anomaly ratio compared to a state-of-theart one-class contrastive representation model  [51]  on CIFAR-10. Similarly, on MVTec SRR retains a strong performance, dropping less than 1.0 AUC with 10% anomaly ratio, while the best existing OCC  [33]  drops more than 6.0 AUC. We further investigate the efficacy of our design choices, such as the number of ensemble classifiers, thresholds, and refinement of deep representations via ablation studies. \n RELATED WORK There are various existing works under the different settings described in Fig.  1 : The positive + negative setting is often considered as a supervised binary classification problem. The challenge arises due to the imbalance in label distributions as positive (anomalous) samples are rare. As summarized in  [12] , to address this, over-/under-sampling  [16, 20] , weighted optimization  [4, 27] , synthesizing data of minority classes  [32, 35] , and hybrid methods  [2, 22]  have been studied. The negative setting is often converted to a one-class classification problem, with the goal of finding a decision boundary that includes as many one-class samples as possible. Shallow models for this setting include one-class support vector machines  [47]  (OC-SVM), support vector data description  [53]  (SVDD), kernel density estimation (KDE)  [31] , and Gaussian density estimation (GDE)  [44] . There are also auto-encoder based models  [59]  that treat the reconstruction error as the anomaly score. Deep learning based OCCs have been developed, such as Deep OCC  [45] , geometric transformation  [23] , or outlier exposure  [26] . Noting the degeneracy or inconsistency of learning objectives of existing end-to-end trainable Deep OCCs,  [51]  proposed a deep representation OCC, a two-stage framework that learns self-supervised representations  [17, 28]  followed by shallow OCCs. That work was extended for texture anomaly localization with CutPaste  [33] . The robustness to very low anomaly ratios of these methods under the unsupervised setting was explored in  [7, 60] . The semi-supervised setting is defined as utilizing a small set of labeled samples and large set of unlabeled samples to distinguish anomalies from normal data. Depending on which labeled samples are given, this setting can be split into three sub-categories. When only some positive/negative labeled samples are provided, we denote that as a PU/NU setting. Most previous works in semi-supervised AD settings focus on the NU setting where only some of the normal labeled samples are given  [1, 41, 52] . The PNU setting is a more general semi-supervised setting where subsets of both positive and negative labeled samples are given. Deep SAD  [46]  and SU-IDS  [39]  are included in this category. We show the significant outperformance of our proposed SRR framework compared to Deep SAD, for multiple benchmark datasets when not using any labeled data (see Sec. 4.2). The unlabeled setting has received relatively less attention despite its significance in automating machine learning. The popular methods for this setting include isolation forest  [36]  and local outlier factor  [13] . However, they are difficult to scale, and less compatible with recent advances in representation learning. While OCCs, such as OC-SVM, SVDD, or their deep counterparts, apply to unlabeled settings by assuming the data is all negative, and the robustness of those methods has also been demonstrated in part  [7, 60] , in practice we observe a significant performance drop with a high anomaly ratio, shown in Fig.  2 . In contrast, our proposed framework is able to maintain high performance across anomaly ratios. Data refinement has been applied to AD in some prior works.  [5, 42]  generate pseudo-labels using binary classification and OC-SVM for data refinement to boost the consequent AD performances in unsupervised settings.  [6, 30, 40, 55, 59 ] used the reconstruction errors of the auto-encoder as an indicator for removing possible anomalies.  [21]  and  [38]  used data refinement for AD in supervised and semi-supervised settings. Additional discussions can be found in Appendix A.9. Self-training  [37, 48]  is an iterative training mechanism using predicted pseudo labels as targets for model training. It has regained popularity recently with its successful results in semi-supervised image classification  [9, 50, 57] . To improve the quality of pseudo labels, employment of an ensemble of classifiers has also been studied.  [14]  trains an ensemble of classifiers with different classification methods to make a consensus for noisy label verification. Co-training  [11]  trains multiple classifiers, each of which is trained on the distinct views, to supervise other classifiers. Co-teaching  [25]  and DivideMix  [34]  share a similar idea in that they both train multiple deep networks on separate data batches to learn different decision boundaries, thus becoming useful for noisy label verification. While sharing a similarity, the proposed framework has clear differences from the previous works. SRR performs iterative training with data refinement (with robust ensemble methods) and self-supervised learning for unsupervised learning of an anomaly detector. \n PROPOSED FRAMEWORK Self-supervise, Refine, and Repeat (SRR) is an iterative training framework, where we refine the data (Sec. 3.1) and update the representation with the refined data (Sec. 3.2), followed by OCCs on refined representations. Fig.  3  overviews the framework and Algorithm 1 provides the pseudo code. Notation. We denote the training data as D = {x i } N i=1 where x i ∈ X and N is the number of training samples. y i ∈ {0, 1} is the corresponding label to x i , where 0 denotes normal (negative) and 1 denotes anomaly (positive). Note that labels are not provided in the unsupervised setting. Let us denote a feature extractor as g : X → Z. g may include any data preprocessing functions, an identity function (if raw data is directly used for one-class classification), and learned or learnable representation extractors such as deep neural networks. Let us define an OCC as f : Z → [−∞, ∞] that outputs anomaly scores given the input features g(x). The higher the score f (g(x)), the more anomalous the sample x is. The binary anomaly prediction is made after thresholding: 1 f (g(x)) ≥ η .  \n DATA REFINEMENT A naive way to generate pseudo labels of unlabeled data is to construct an OCC on raw data or learned representations as in  [51]  and threshold the anomaly score to obtain a binary label for normal vs. anomalous. As we update the model with refined data that excludes samples that are predicted to be anomalous, it is important to generate pseudo labels of training data as accurately as possible. To this end, instead of training a single classifier (unlike most previous works on data refinement for AD  [5, 42, 59] ), we train an ensemble of K OCCs and aggregate their predictions to generate pseudo labels. We illustrate the data refinement block in Fig.  3  and as REFINEDATA in Algorithm 1. Specifically, we randomly divide the unlabeled training data D into K disjoint subsets D 1 , ..., D K , and train K different OCCs (f 1 , ..., f K ) on corresponding subsets (D 1 , ..., D K ). Then, we estimate a binary pseudo-label of the data x i ∈ D as follows: ŷi = 1 − K k=1 1 − 1 f k (g(x i )) ≥ η k (1) η k = max η s.t. 1 N N i=1 1 f k (g(x i )) ≥ η ≥ γ (2) where 1(•) is the indicator function that outputs 1/0 if the input is True/False. f k (g(x i )) represents an anomaly score of x i for an OCC f k . η k in equation 2 is a threshold determined as a γ percentile of the anomaly score distribution {f k (g(x i ))} N i=1 . To interpret equation 1, x i is predicted as normal, i.e. ŷi = 0, if all K OCCs predict it as normal. While this may be too strict and potentially reject many true normal samples in the training set, we find that empirically, it is critical to be able to exclude true anomalous samples from the training set. The effectiveness of the employment of an ensemble of classifiers is empirically shown in Sec. 4.3. \n REPRESENTATION UPDATE SRR follows the idea of deep representation OCCs  [51] , where in the first stage a deep neural network is trained with self-supervised learning (such as rotation prediction  [23] , contrastive  [51] , or CutPaste  [33] ) to obtain meaningful representations of the data, and in the second stage OCCs are trained on these learned representations. Such a two-stage framework is shown to be beneficial as it prevents the 'hypersphere collapse' of the deep OCCs by the favorable inductive bias it brings with the architectural constraints  [45] . Here, we propose to conduct self-supervised representation learning jointly with data refinement. More precisely, we train a feature extractor g using D = {x i | ŷi = 0}, a subset of unlabeled data Algorithm 1 SRR: Self-supervise, Refine, Repeat. Input: Training data D = {x i } N i=1 , Ensemble count (K), threshold (γ) Output: Refined data ( D), trained OCC (f ), feature extractor (g) 1: function REFINEDATA(D, g, K, γ) 2: Train OCC models {f k } K k=1 on {D k } K k=1 , K disjoint subsets of the training data D. \n 3: Compute thresholds η k 's for γ percentile of anomaly distributions (equation 2). \n 4: Predict binary labels ŷi (equation 1). \n 5: Return D = {x i : ŷi = 0, x i ∈ D}. 6: end function 7: function SRR(D, K, γ) 8: Initialize the feature extractor g. \n 9: while g not converged do 10: D = REFINEDATA(D, g, K, γ). 11: Update g using D with self-supervised learning objectives. 12: end while 13: D = REFINEDATA(D, g, K, γ). \n 14: Train an OCC model (f ) on refined data ( D). 15: end function D that only includes samples whose predicted labels with an ensemble OCC from Sec. 3.1 are negative. We also update D as we proceed with representation learning. The proposed method is illustrated in Algorithm 1 as SRR. In contrast to previous works  [33, 51]  that use the entire training data for learning self-supervised representation, we find it necessary to refine the training data even for learning deep representations. Without representation refinement, the performance improvements of SRR are limited, as shown in Sec. 4.3.2. Last, for test-time prediction, we train an OCC on refined data D using updated representations by g as in line 13-14 in Algorithm 1. \n UNSUPERVISED MODEL SELECTION As SRR is designed for unsupervised AD, labeled validation data for hyperparameter tuning is typically not available and the framework should enable robust model selection without any reliance on labeled data. Here, we provide insights on how to select important hyperparameters, and later in Sec. 4.3.1 perform sensitivity analyses for these hyperparameters. Data refinement of SRR introduces two hyperparameters: the number of OCCs (K) and the percentile threshold (γ). There is a trade-off between the number of classifiers for the ensemble and the size of disjoint subsets for training each classifier. With large K, we aggregate prediction from many classifiers, each of which may contain randomness from training. This comes at a cost of reduced performance per classifier as we use smaller subsets to train them. In practice, we find K = 5 works well across different datasets and anomaly ratios. γ controls the purity and coverage of refined data. If γ is large, and thus classifiers reject too many samples, the refined data could be more pure and contain mostly the normal samples; however, the coverage of the normal samples would be limited. On the other hand, with a small γ, the refined data may still contain many anomalies and the performance improvement with SRR would be limited. We empirically observe that SRR is robust to the selection of γ when it is chosen from a reasonable range. In our empirical experiments, we find ∼ 1 − 2× of the true anomaly ratio to be a reasonable choice. In other words, it is safer to use γ higher than the expected true anomaly ratio. In some cases, the true anomaly ratio may not be available at all; for such scenarios, we propose Otsu's method  [49]  to estimate the anomaly ratio of the training data for determining the threshold γ (experimental results are in the Appendix A.5). \n EXPERIMENTS We evaluate the efficacy of our proposed framework for unsupervised AD tasks on tabular (Sec. 4.1) and image (Sec. 4.2) data types. We experiment varying ratios of anomaly samples in unlabeled training data and with different combinations of representation learning and OCCs. In Sec. 4.3, we provide performance analyses to better explain major constituents of the performance, as well as sensitivity to hyperparameter values. Implementation details: To reduce the computational complexity of the data refinement block, we utilize a simple OCC such as GDE in the data refinement block. In a two-stage model, we only update the data refinement block at 1st, 2nd, 5th, 10th, 20th, 50th, 100th, 500th epochs instead of every epoch. After 500 epochs, we update the data refinement block per each 500th epoch. Each run of experiments requires a single V100 GPU. Additional discussions can be found in Appendix A.10. \n EXPERIMENTS ON TABULAR DATA Datasets. Following  [7, 60] , we test the efficacy of SRR on a variety of tabular datasets, including KDDCup, Thyroid, or Arrhythmia from the UCI repository  [3] . We also use KDDCup-Rev, where the labels of KDDCup are reversed so that an attack represents anomaly  [60] . To construct data splits, we use 50% of normal samples for training. In addition, we hold out some anomaly samples (amounting to 10% of the normal samples) from the data. This allows us to simulate unsupervised settings with an anomaly ratio of up to 10% of entire training set. The rest of the data is used for testing.  1  We conduct experiments using 5 random splits and 5 random seeds, and report the average and standard deviation of 25 F1-scores (with scale 0-100) for the performance metric. Models. We mainly compare with GOAD  [7]  (the state-of-the-art AD model in the tabular domain) and implement SRR on top of it. GOAD utilizes random transformation classification as the pretext task of self-supervised learning, and the normality score is determined by whether transformations are accurately included in the transformed space of the normal samples. We re-implement GOAD  [7]  with a few modifications. First, instead of using embeddings to compute the loss, we use a parametric classifier, similarly to augmentation prediction  [51] . Second, we follow the two-stage framework  [51]  to construct deep OCCs. For the clean training data setting, our implementation achieves 98.0 for KDD, 95.0 for KDD-Rev, 75.1 for Thyroid, and 54.8 for Arrhythmia F1-scores, which are comparable to those reported in  [7] . Please see Appendix A.3 for formulation and implementation details. Figure  4 : Unsupervised AD performance (F1-score) using OC-SVM (with rbf kernel), GOAD  [7] , and GOAD with the proposed method SRR on various tabular datasets. Shaded areas represent the standard deviation. Results. We show results of GOAD (the baseline) and GOAD with SRR in Fig.  4 . The ranges of the noise ratio are set to 0% for the anomaly ratios in the original dataset (if anomaly ratios are larger than 10%, we set the maximum anomaly ratio as 10%). For KDD-Rev, we set the maximum anomaly ratio to 2.5% because the performance of GOAD (without SRR) drops significantly even with a small ratio of anomalies in the training data. Fig.  4  shows that integrating SRR significantly improves GOAD (the state-of-the-art methods for tabular OCC). The improvements are more significant especially at higher anomaly ratios. This underlines how SRR can achieve significant improvements for both small (Thyroid & Arrhythmia) and large-scale datasets (KDD & KDD-Rev). \n EXPERIMENTS ON IMAGE DATA Datasets. We evaluate SRR on visual AD benchmarks, including CIFAR-10 [29], f-MNIST  [56] , Dog-vs-Cat  [19] , and MVTec  [8] . For CIFAR-10, f-MNIST, and Dog-vs-Cat datasets, samples from one class are set to be normal and the rest from other classes are set to be an anomaly. Similar to the experiments on tabular data in Section. 4.1, we swap a certain amount of the normal training data with anomalies given the target anomaly ratio. For MVTec, since there are no anomalous data available for training, we borrow 10% of the anomalies from the test set and swap them with normal samples in the training set. Note that 10% of samples borrowed from the test set are excluded from evaluation. For all datasets, we experiment with varying anomaly ratios from 0% to 10%. We use area under ROC curve (AUC) and average precision (AP) metrics to quantify the performance for visual AD (with scale 0-100). When computing AP, we set the minority class of the test set as label 1 and majority as label 0 (e.g., normal samples are set as label 1 for CIFAR-10 experiments as there are more anomaly samples that are from 9 classes in the test set). We run all experiments with 5 random seeds and report the average performance for each dataset across all classes. Per-class AUC and AP are reported in Appendix A.4. \n Models. For semantic AD benchmarks, CIFAR-10, f-MNIST, and Dog-vs-Cat, we compare the SRR with two-stage OCCs  [51]  using various representation learning methods, such as distributionaugmented contrastive learning  [51] , rotation prediction  [23, 28]  and its improved version  [51] , and denoising autoencoder. For MVTec benchmarks, we use CutPaste  [33]  as a baseline and compare to its version with SRR integration. For both experiments, we use the ResNet-18 architecture, trained from random initialization, using the hyperparameters from  [51]  and  [33] . The same model and hyperparameter configurations are used for SRR with K = 5 classifiers in the ensemble. We set γ as twice the anomaly ratio of training data. For 0% anomaly ratio, we set γ as 0.5. Finally, a Gaussian Density Estimator (GDE) on learned representations is used as OCC. Results. Fig.  5  shows a significant performance drop with increased anomaly ratio, regardless of representation learning. For example, the AUC of distribution-augmented contrastive representation  [51]  drops from 92.1 to 83.6 when anomaly ratio becomes 10%. Similarly, the improved rotation prediction representation  [28]  drops from 90.0 to 84.1. On the other hand, SRR effectively handles the contamination in the training data and achieves 89.9 AUC with 10% anomaly ratio, reducing the performance drop by 74.1%. An 'oracle' upper bound would be the removal of all anomalies from the training data (which is the same as the performance at 0% anomaly ratio for the same size of the data). As Fig.  5  shows, the performance of SRR is similar to this oracle upper bound performance (less than 2.5 AUC difference) even with high anomaly ratios (10%). The results are also similar in other metrics, such as AP in Fig.  5  or Recall at Precision of 70 and 90 in Fig.  9  in the Appendix. We repeat experiments on 3 additional visual AD datasets and report results in Fig.  6 . We observe consistent and significant improvements over the baseline across different datasets and different one-class classification methods. Note that the improvement is more significant at higher anomaly ratios. For instance, on MVTec dataset, SRR improves AUC by 4.9 and AP by 7.1 compared to the state-of-the-art CutPaste OCC with an anomaly ratio of 10%. In the Appendix (Sec. A.4), we also illustrate per-class performance of SRR compared with the state-of-the-art. with varying anomaly ratios. We use state-of-the-art one-class classification models for baselines, such as distribution-augmented contrastive representations  [51]  for f-MNIST and Dog-vs-Cat, or CutPaste  [33]  for MVTec, and build SRR on top of them. \n PERFORMANCE ANALYSES In this section, we conduct sensitivity analyses on two hyperparameters of SRR, namely, the number K for ensemble OCCs and the percentile threshold γ that determines normal and anomalies in the data refinement module. In addition, we show the importance of updating the representation with refined data. Ablation studies are conducted on two visual AD benchmarks, CIFAR-10 and MVTec. More experimental results and discussions can be found in the Appendix. \n SENSITIVITY TO HYPERPARAMETERS SRR is designed for unsupervised AD and it is important to ensure robust performance against changes in the hyperparameters as model selection without labeled data would be very challenging. Fig.  7  presents the sensitivity analyses of SRR with respect to various hyperparameters. In Fig.  7a , we observe the performance improvement as we increase the number of classifiers for ensemble. This is particularly effective on CIFAR (top in Fig.  7a ), where the number of samples in the training data is large enough that even with large K, the number of samples to train each OCC (N/K) would be sufficient. In Fig.  7b , we observe that SRR performs robustly when γ is set to be larger than the actual anomaly ratio (10%). When γ is less than 10%, however, we see a significant drop in performance, all the way to the baseline (γ = 0). Our results show that SRR improves upon baseline regardless of the threshold. In addition, it suggests that γ could be set to be anywhere from the true anomaly ratio and and 2x the anomaly ratio to maximize its effectiveness. When the true anomaly ratio is unknown, as discussed in Appendix A.5, Otsu's method could be used. \n ITERATIVELY UPDATING REPRESENTATIONS WITH REFINED DATA It is possible to decouple representation learning and data refinement of SRR, which would result in a three-stage framework, where we learn representations until convergence without data refinement, followed by the data refinement and learning OCC. Fig.  7c  shows that SRR using a pre-trained then fixed representation (i.e. when data refinement is used for OCC only) already improves the performance upon the baseline with no data refinement at any stage of learning representation or classifier. Improvements on CIFAR-10 are 4.9 in AUC and 8.0 in AP; and on MVTec are 1.   \n QUANTIFYING THE REFINEMENT EFFICACY We evaluate how many normal and anomalies are excluded by the proposed data refinement block. As in Fig.  8 (a, b), with data refinement, we can exclude more than 80% of anomalies in the training set without removing too many normal samples. For instance, among 4% anomalies in CIFAR-10 data, SRR is able to exclude 80% anomalies while removing less than 20% normal samples. Such a high recall of anomalies of SRR is not only useful for unsupervised AD, but also could be useful for improving the annotation efficiency when a budget for active learning is available. Fig.  8(c,  d ) demonstrates the removed normal and abnormal samples by the data refinement module over training epochs. It shows that better representation learning (as training epochs increase) consistently improves the efficacy of the data refinement.   \n CONCLUSION AD has wide range of practical use cases. A challenging and costly aspect of building an AD system is that anomalies are rare and not easy to detect by humans, making them difficult to label. To this end, we propose a novel AD framework to enable high performance AD without any labels called SRR. SRR can be flexibly integrated with any OCC, and applied on raw data or on a trainable representations. SRR employs an ensemble of multiple OCCs to propose candidate anomaly samples that are refined from training, which allows more robust fitting of the anomaly decision boundaries as well as better learning of data representations. We demonstrate the state-of-the-art AD performance of SRR on multiple tabular and image data. ETHICS STATEMENT SRR has the potential to make significant positive impact in real-world AD applications where detecting anomalies is crucial, such as for financial crime elimination, cybersecurity advances, or improving manufacturing quality. We note a potential risk associated with using SRR: when representations are not sufficiently good, there will be a negative cycle of refinement and representation updates/OCC. While we rely on the existence of good representations, in some applications they may be difficult to obtain (e.g., cybersecurity). This paper focuses on the unsupervised setting and demonstrates strong AD performance, opening new horizons for human-in-the-loop AD systems that are low cost and robust. We leave these explorations to future work. \n REPRODUCIBILITY STATEMENT The source code of SRR will be published upon acceptance. For reproducibility, we only use public tabular and image datasets to evaluate the performances of SRR. Complete descriptions of those datasets can be found in Datasets subsections in Sec. 4.1 and 4.2. Detailed experimental settings and hyperparameters can be found in Models subsections in Sec. 4.1 and 4.2. The implementation details (including hyperparameters that we used) on GOAD  [7]  are described in Sec. A.3. \n A APPENDIX A.1 ADDITIONAL RESULTS WITH DIFFERENT METRICS There are various performance metrics of OCCs. In the main manuscript, we mainly use AUC, Average Precision (AP) and F1-score as the evaluation metrics. In this subsection, we report the performances of the proposed model (SRR) and baselines in terms on Recall at Precision 70 and 90 as the additional metrics on CIFAR-10 dataset. As in Fig.  9 , we observe a similar trends with these two additional metrics as well. For example, the performances of SRR are robust across various anomaly ratios. On the other hand, all the other OCCs show consistent and significant performance degradation as the anomaly ratio increases. SRR performs 15.8 and 10.9 better than the state-of-the-art OCC  [51]  in terms of recall at precision 70 and 90, respectively.  SRR is also applicable on raw tabular features or learned image representation without representation update using data refinement. In this section, we demonstrate the performance improvements by SRR without representation update to verify the effectiveness of data refinement block of SRR for shallow OCCs. Fig.  10  (upper) demonstrates consistent and significant performance improvements when we apply SRR on top of raw tabular features. Specifically, the Average Precision (AP) improvements are 10.2, 29.0, and 4.1 with KDD-Rev, Thyroid, and Arrhythmia tabular datasets, respectively. We also apply SRR on top of various learned image representations. As can be seen in Fig.  10  (lower), the performance improvements of SRR are consistent across various different learned image representations (without representation update). For instance, the AP improvements are 9.2, 1.0, and 12.1 with learned image representations using RotNet  [23] , Rotation  [28] , and Contrastive  [51] , respectively. A.3 IMPLEMENTATION DETAILS ON GOAD  [7]  FOR TABULAR DATA EXPERIMENTS A classification-based AD method, GOAD  [7] , has demonstrated strong AD performance on tabular datasets. Unlike previous works  [23, 26]  that formulate a parametric classifier for multiple transformation classification, GOAD employs distance-based classification of multiple transformations. For the set of transformations T m : X → D, m = 1, ..., M , the loss function of GOAD is written as in equation 3 with the probability defined in equation 4. L = −E m,x log P (m|T m (x)) , (3) P ( m|T m (x)) = exp(− f (T m (x)) − c m 2 ) n exp(− f (T m (x)) − c n 2 ) , (4) where the centers c m 's are updated by the average feature over the training set. While it is shown to perform well  [7] , we find that the distance-based formulation is not necessary, and we achieve the similar performance, if not worse, to  [7]  using a parametric classifier when computing the probability: P ( m|T m (x)) = exp w mf (T m (x)) + b m n exp (w n f (T m (x)) + b n ) (5) The formulation in equation 5 is easier to optimize than its original form in equation 4 as it can be fully optimized with backpropagation without alternating updates of feature extractor f and centers c m . Once we learn a representation by optimizing the loss in equation 3 using equation 5, we follow a two-stage one-class classification framework of  [51]  to construct a set of Gaussian density estimation OCCs for each transformation. Finally, we aggregate a maximum normality scores from a set of classifiers as the normality score. In Table  1 , we summarize the implementation details, such as network architecture or hyperparameters, and AD performance under clean training data setting that reproduces the results in  [7] . Table  1 : The AD performance under clean only data setting of GOAD in  [7]  and our implementation. Our implementation demonstrates comparable, if not worse, performance to those reported in  [7] . Our implementation also shares most hyperparameters across datasets except the M , the number of transformations, and the train steps, which are closely related to the size of training data. \n A.4 PER-CLASS AUC AND AP In the main manuscript, we report the mean and standard deviation of AUC and AP across all classes in each dataset. In this section, we report the mean and standard deviation of AUC and AP for each class in each dataset (including CIFAR-10 (Table  2 ), MVTec (Table  3 ), fMNIST (Table  4 ), and Dog-vs-Cat (Table  5 ) datasets). \n A.4.1 PER-CLASS AUC AND AP ON CIFAR-10 DATASET The key idea of the Otsu's method is to find the threshold that minimizes the intra-class variance. This is defined as the weighted sum of variances of the two classes. Let us denote the normality scores as {s i } N i=1 and threshold as η. Then, we try to find the threshold (η) that minimizes the weighted sum of the variance (w 0 (η) × σ 0 (η) + w 1 (η) × σ 1 (η)) where w 0 (η) = N i=1 I(s i < η)/N and w 1 (η) = N i=1 I(s i ≥ η)/N . σ 0 (η) and σ 1 (η) are the variances of each class. The optimal threshold (η * ) is determined as η * = min η w 0 (η) × σ 0 (η) + w 1 (η) × σ 1 (η). We use the twice of η * as the hyperparameter (γ) in SRR. We evaluate the performances of Otsu's method (on top of SRR) in comparison to the state-of-the-art OCC  [33]  and original SRR with the knowledge of the true anomaly ratio using MVTec dataset. Fig.  11  demonstrates that even without true anomaly ratio, the performance of SRR can be significantly better than the state-of-the-art OCC  [33]  with Otsu's method. Also, Fig.  11  shows that the knowledge of true anomaly ratio is crucial information for maximizing the performance of SRR in fully unsupervised settings. We further extend the experimental results using Otsu's method with other datasets such as CIFAR-10 and Thyroid datasets.   [51]  for CIFAR-10 dataset and GOAD  [7]  for Thyroid dataset. We introduce 6% noise on MVTec dataset and 1.5% noise on the Thyroid dataset. Metrics are (AUC/AP) for CIFAR-10 dataset and F1 score for Thyroid dataset. \n A.6 ADDITIONAL ABLATION STUDIES To better understand the source of gains, we include comparisons between the final ensemble model on the converged self-supervised extractor (SRR without final OCC) with the proposed SRR (using an additional final OCC). Also, to further support the novelty of SRR, we report additional experimental results only with ensemble model without data refinement (Ensemble Only). As can be seen in Table  7 , the proposed version of SRR (with an additional final OCC) outperforms significantly, which is attributed to the fact that while fitting the individual OCC models in the ensemble, we do not exclude the possible anomaly samples for diversity of the trained submodels, so the anomaly decision boundaries can be fitted robustly. Therefore, the ensemble model can be somewhat less accurate for classifying difficult samples (near the decision boundary between normal and abnormal) compared to the final OCC used (that is trained with only normal samples). Also, employment of ensemble learning without data refinement (Ensemble only), yields much worse performance than the proposed method (SRR), underlining the importance of the core data refinement idea of SRR. Datasets   [33]  for MVTec dataset and  [51]  for CIFAR-10 dataset. We introduce 6% noise on both datasets. Metrics are (AUC/AP). \n A.7 ADDITIONAL BASELINES We add extra baselines from robust anomaly detection literature: Standard PCA  [54] , Robust PCA  [15]  and Local Outlier Factor (LOF)  [13]  for tabular data and Robust autoencoder (Robust AE)  [59]  for image data. As can be seen in Table  8 , the performance of PCA and LOF are highly degraded even with a small amount of anomalies in the training data. For Robust PCA and Robust AE, the performance degradation is less but still significant in comparison to SRR. Overall, SRR outperforms other benchmarks in fully unsupervised settings, underlining the importance of data refinement in improving the robustness to anomaly ratio in training data, as the core constituent of SRR framework. Datasets    Figure 2 : 2 Figure 2: Performance of our proposed model and a baseline OCC using contrastive representation [51] on CIFAR-10 with different anomaly ratios in the training data. \n Figure 3 : 3 Figure 3: Block diagram of SRR composed of representation learner (Sec. 3.2), data refinement (Sec. 3.1), and final OCC blocks. The representation learner updates the deep models using refined data from the data refinement block. Data refinement is done by an ensemble of OCCs, each of which is trained on K disjoint subsets of unlabeled training data. Samples predicted as normal by all classifiers are retained in the refined data, and are used to update the representation learner and final OCC. The process is repeated iteratively until convergence. Convergence graphs can be found in the Appendix A.8. \n Figure 5 : 5 Figure 5: Unsupervised AD performance with various OCCs on CIFAR-10. For SRR we adapt distribution-augmented contrastive representation learning [51]. (Left) AUC, (Right) Average Precision (AP). \n Figure 6 : 6 Figure6: Unsupervised AD performance on (a) MVTec (b) f-MNIST, and (c) Dog-vs-Cat datasets with varying anomaly ratios. We use state-of-the-art one-class classification models for baselines, such as distribution-augmented contrastive representations [51]  for f-MNIST and Dog-vs-Cat, or CutPaste [33]  for MVTec, and build SRR on top of them. \n Figure 7 : 7 Figure 7: Ablation studies on (top) CIFAR-10 and (bottom) MVTec under 10% anomaly ratio setting with respect to (a) ensemble count K, (b) percentile threshold γ, and (c) data refinement with or without representation update. \n Figure 8 : 8 Figure 8: Percentage of excluded anomalous and normal samples by data refinement (a, b) with different anomaly ratios in training data and (c, d) over training epochs for 10% anomaly ratio. \n Figure 9 : 9 Figure 9: Performance of various OCCs on CIFAR-10 dataset. SRR is applied on top of Contrastive [51]. (Left) Recall at Precision 70, (Right) Recall at Precision 90. \n A. 2 2 SRR ON RAW TABULAR FEATURES / LEARNED IMAGE REPRESENTATIONS \n Figure 10 : 10 Figure10: Performance of SRR on (top) raw tabular features and (lower) learned image representations. SRR consistently outperforms baseline and in some cases (e.g., Thyroid, and Contrastive [51] ), the performance improvements are significant. \n Figure 11 : 11 Figure 11: Unsupervised anomaly detection performances with Otsu's method on top of SRR on MVTec dataset. (Left) AUC, (Right) Average Precision (AP). \n Figure 12 : 12 Figure 12: Convergence graphs of SRR with (left) MVTec dataset, (right) CIFAR-10 dataset. \n Table 6 6 are the overall results -Otsu's method yields only slight degradation compared to SRR with true anomaly ratio; however, it still significantly outperforms SOTA OCC baselines. Datasets / Method SOTA OCC SRR with Otsu's method SRR CIFAR-10 0.855 / 0.585 0.906 / 0.703 0.910 / 0.709 Thyroid 0.506 0.623 0.639 \n Table 6 : 6 Additional ablation studies. SOTA OCC methods are \n Table 7 : 7 / Method SOTA OCC Ensemble Only SRR without final OCC SRR Additional ablation studies. SOTA OCC methods are CutPaste MVTec 0.905 / 0.845 0.911 / 0.849 0.922 / 0.870 0.937 / 0.887 CIFAR-10 0.855 / 0.585 0.862 / 0.599 0.890 / 0.677 0.910 / 0.709 \n Table 8 : 8 Additional experiments with extra baselines from robust anomaly detection literature. We introduce 6% noise on CIFAR-10 and KDD datasets. For Thyroid dataset, we introduce 1.5% noise. Metrics are (AUC/AP) for image data and F1 score for tabular data.A.8 CONVERGENCE GRAPHSThe proposed SRR framework is converged when the iterative training of the self-supervised learning is converged. Depending on the data refinement model training, corresponding self-supervised models are also trained with differently refined training data. Usually, the data refinement model and self-supervised models converge after a similar number of epochs. Fig.12illustrate the convergence graphs of SRR with MVTec and CIFAR-10 datasets. / Method PCA Robust PCA LOF Robust AE SRR CIFAR-10 - - - 0.636 / 0.174 0.910 / 0.709 Thyroid 0.299 0.377 0.338 - 0.506 KDD 0.836 0.893 0.873 - 0.942 \n\t\t\t Note that the experimental settings with contaminated training data in GOAD [7]  and DAGMM [60]  are slightly different from ours. Our contamination ratio is defined as the anomaly ratio over the entire training data, while their contamination ratio is the anomaly ratio over all the anomalies in the dataset.", "date_published": "n/a", "url": "n/a", "filename": "self_supervise_refine_repeat_i.tei.xml", "abstract": "Anomaly detection (AD) -separating anomalies from normal data -has many applications across domains, from manufacturing to healthcare. While most previous works have been shown to be effective for cases with fully or partially labeled data, that setting is in practice less common due to labeling being particularly tedious for this task. In this paper, we focus on fully unsupervised AD, in which the entire training dataset, containing both normal and anomalous samples, is unlabeled. To tackle this problem effectively, we propose to improve the robustness of one-class classification trained on self-supervised representations using a data refinement process. Our proposed data refinement approach is based on an ensemble of oneclass classifiers (OCCs), each of which is trained on a disjoint subset of training data. Representations learned by self-supervised learning on the refined data are iteratively updated as the refinement improves. We demonstrate our method on various unsupervised AD tasks with image and tabular data. With a 10% anomaly ratio on CIFAR-10 image data / 2.5% anomaly ratio on Thyroid tabular data, the proposed method outperforms the state-of-the-art one-class classification method by 6.3 AUC and 12.5 average precision / 22.9 F1-score.", "id": "74ee22bb18a54c2cdf77d45a736a1a28"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Martin Pecka", "Tomas Svoboda"], "title": "Lecture Notes in Computer Science: Safe Exploration Techniques for Reinforcement Learning -An Overview", "text": "Introduction Reinforcement learning (RL) as a machine learning method has been thoroughly examined since 80's. In 1981, Sutton and Barto  [3]  inspired themselves in the reinforcement learning discoveries in behavioral psychology and devised the Temporal Difference machine learning algorithm that had to simulate psychological classical conditioning. In contrast with supervised learning, reinforcement learning does not need a teacher's classification for every sample presented. Instead, it just collects rewards (or punishment) on-the-go and optimizes for the expected long-term reward (whereas supervised learning optimizes for the immediate reward). The key advantage is that the design of the rewards is often much simpler and straight-forward than classifying all data samples. Reinforcement learning proved to be extremely useful in the case of statespace exploration -the long-term reward corresponds to the value of each state  [17] . From such values, we can compose a policy which tells the agent to always take the action leading to the state with the highest value. As an addition, state values are easily interpretable for humans. Since the early years, a lot of advanced methods were devised in the area of reinforcement learning. To name one, Q-learning  [25]  is often used in connection with safe exploration. Instead of computing the values of states, it computes the values of state-action pairs, which has some simplifying consequences. For example, Q-learning doesn't need any transition model (i.e. dynamics model) of the examined system. A completely different approach is policy iteration. This algorithm starts with a (more or less random) policy and tries to improve it step-by-step  [16] . This case is very valuable if there already exists a good policy and we only want to improve it  [11] . What do all of these methods have in common, is the need for rather large training data sets. For simulated environments it is usually not a problem. But with real robotic hardware, the collection of training samples is not only lengthy, but also dangerous (be it mechanical wear or other effects). Another common feature of RL algorithms is the need to enter unknown states, which is inherently unsafe. As can be seen from the previous paragraph, safety is an important issue connected with reinforcement learning. However, the first articles focused on maintaining safety during exploration started to appear much later after the \"discovery\" of RL. Among the first, Heger  [15]  \"borrowed\" the concept of a worstcase criterion from control theory community. In 1994 he created a variant of Q-learning where maximization of long-term reward is replaced with maximization of minimum of the possible rewards. That basically means his algorithm prefers to never encounter a bad state (or, at least to choose the best of the bad states). This approach has one substantial drawback -the resulting policies are far from being optimal in the long-term-reward sense  [10] . In this paper we show the various approaches to safe exploration that have emerged so far. We classify the methods by various criteria and suggest suitable use cases for them. To better illustrate some of the practical details, we use the UGV (Unmanned Ground Vehicle) robotic platform from EU FP7 project NIFTi  [6]  (see Figure  1 ) as a reference agent. It may happen that in these practical details we assume some advantages of UGVs over UAVs (Unmanned Aerial Vehicles), like the ability to stand still without much effort, but it is mostly easy to convert these assumptions to UAVs, too. Further organization of this paper is the following: in Section 2 we discuss some basics of reinforcement learning (the reader may skip it if he is familiar with reinforcement learning); Section 3 is an overview of the safety definitions  \n Reinforcement learning basics \n Markov Decision Processes Markov Decision Processes (MDPs) are the standard model for deliberating about reinforcement learning problems. They provide a lot of simplifications, but are sufficiently robust to describe a large set of real-world problems. The simplest discrete stochastic MDP comprises of:  [17]  a finite set of states S a finite set of actions A a stochastic transition model P : P t (s, a, s ) = P r(s t+1 = s | s t = s, a t = a) for each s, s ∈ S, a ∈ A, where P r stands for probability and the immediate reward function R : S × A → R (or R : S × A × S → R if the reward depends on the stochastic action result) To interpret this definition, we say that the at every time instant t the agent is in a state s, and by executing action a it gets to a new state s . Furthermore, executing a particular action in a particular state may bring a reward to the agent (defined by R). The most important and interesting property of MDPs is the Markov property. If you have a look at the definition of the transition model, the next state only depends on the current state and the chosen action. Particularly, the next state is independent of all the previous states and actions but the current one. To give an example, the robot's battery level cannot be treated implicitly by counting the elapsed time, but rather it has to be modeled as a part of the robot's state. Once the model is set up, everything is ready for utilizing an MDP. \"The agent's job is to find a policy π mapping states to actions, that maximizes some long-run measure of reinforcement\"  [17] . The \"long-run\" may have different meanings, but there are two favorite optimality models: the first one is the finite horizon model, where the term J = h t=0 r t is maximized (h is a predefined time horizon and r t is the reward obtained in time instant t while executing policy π). The dependency of r t on the policy is no longer obvious from this notation, but this is the convention used in literature when it is clear which policy is used. This model represents the behavior of the robot which only depends on a predefined number of future states and actions. The other optimality model is called discounted infinite horizon, which means we maximize the discounted sum J = ∞ t=0 γ t r t with γ ∈ (0, 1) being the discount factor. The infinite horizon tries to find a policy that is the best one taking into account the whole future. Please note the hidden dependency on the policy π (and the starting state s 0 ) -it is the policy that decides on which action to take, which in turn specifies what will the reward be. Other extensions of MDPs to continuous states, time or actions are beyond the scope of this overview. However, some of the referenced papers make use of these continuous extensions, which proved to be useful for practical applications. \n Value iteration Value iteration is one of the basic methods for finding the optimal policy. To describe this algorithm, it is first needed to define the essential notion of the optimal value of a state. In this whole subsection we suppose the discounted infinite horizon model, but analogous results can be shown for finite horizon, too. \"The optimal value of a state is the expected infinite discounted sum of reward that the agent will gain if it starts in that state and executes the optimal policy.\"  [17]  Given a policy π, the induced value function is therefore defined as V π (s) = E ∞ t=0 r k γ k , (1) where E denotes the expected value and r k are the rewards for executing policy π. Taking the best value function over all policies then yields the optimal value function V * : [17] V * (s) = max π V π (s) . (2) Inversely, if we have the value function given, we can derive a policy from that. It is a simple policy that always takes the action leading to the most profitable neighbor state (with the highest value). One useful formulation of the properties of the optimal value function is the formulation using the recurrent Bellman equations which define a dynamic system that is stable for the optimal value function. We can say a state's optimal value is the best immediate reward plus its best neighbor's optimal value: [17] V * (s) = max a R(s, a) + γ s ∈S P(s, a, s )V * (s ) . (3) Analogously, we can find the optimal policy using the same Bellman equation: π * (s) = argmax a R(s, a) + γ s ∈S P(s, a, s )V * (s ) . (4) The Value iteration algorithm is based on trying to compute the solution of Equation 4 using iterative Bellman updates (refer to Algorithm 1). In the algorithm, we use a structure called Q to store the \"value\" of state-action pairs. In Value iteration it is just a structure to save intermediate results, but it is the core of the Q-learning algorithm (described in Section 2.3). The stopping criterion of the Value iteration algorithm is not obvious, but Williams and Baird  [26]  derived an easily applicable upper bound on the error of the computed value function. That said, after a sufficient number of those simple iterations, we can compute the almost optimal value function. The number of iterations needed for Value iteration to converge may be impractically high, but it is shown that the optimal policy converges faster  [4] , thus making Value iteration practical. \n Q-learning Just a small change to the Value iteration algorithm results in Q-learning. The basic algorithm is the same as Value iteration, just the update step is done differently (refer to Algorithm 2). The consequence of this change is that no model of the system (transition function P) is needed. It is sufficient to execute all actions in all states equally often, and Watkins  [25]  proved that if Q-learning were run for an infinite time, the computed Q would converge to the optimal Q * (an analogue of V * ). \n Policy iteration Policy iteration is a completely different approach to computing the optimal policy. Instead of deriving the policy from the Value or Q function, Policy iteration Algorithm 1 The Value iteration algorithm  [17]  Input: an MDP (states S, actions A, rewards R, transition model P) Output: the optimal value function V * , resp. the optimal policy π * derived from the value function 1. V(s) := arbitrary function 2. π := the policy derived from V 3. while π is not good enough do 4. for all s ∈ S do 5. for all a ∈ A do Update: 6. Q(s, a) := R(s, a) + γ s ∈S P(s, a, s )V(s ) 7. end for 8. V(s) := max a Q(s, a) 9. end for 10. π := the policy derived from V 11. end while 12. V * := V, π * := π Algorithm 2 The Q-learning algorithm (only the parts that differ from Value iteration when V is substituted with Q)  [17]  Input: an MDP (states S, actions A, rewards R, transition model may be unknown) Output: the optimal state-value function Q * , resp. the optimal policy π * derived from the state-value function 6. Q(s, a) := Q(s, a)+ α R(s, a) + γ max a Q(s , a ) − Q(s, a) \n line left out works directly with policies. In the first step, a random policy is chosen. Then a loop consisting of policy evaluation and policy improvement repeats as long as the policy can be improved  [17]  (refer to Algorithm 3 for details). Since in every step the policy gets better, and there is a finite number of different policies, it is apparent that the algorithm converges  [23] . Policy iteration can be initialized by a known, but suboptimal policy. Such policy can be obtained e.g. by a human operator driving the UGV. If the initial policy is good, Policy iteration has to search much smaller subspace and thus should converge more quickly than with a random initial policy  [11] . Algorithm 3 The Policy iteration algorithm  [17]  1. π = arbitrary policy 2. repeat 3. π := π Policy evaluation: (system of linear equations) 4. Vπ(s) = R(s, π(s)) + γ s ∈S P(s, π(s), s )Vπ(s ) Policy improvement: 5. π (s) := argmax a∈A R(s, a) + γ s ∈S P(s, a, s )Vπ(s ) 6. until π = π \n Defining safety To examine the problems of safe exploration, it is first needed to define what exactly is the safety we want to maintain. Unfortunately, there is no unified definition that would satisfy all use cases; thus, several different approaches are found in the literature. An intuitive (but vague) definition could be e.g.: \"Statespace exploration is considered safe if it doesn't lead the agent to unrecoverable and unwanted states.\" It is worth noticing here that unwanted doesn't necessarily mean low-reward. In the next subsections we present the main interpretations of this vague definition. \n Safety through labeling The largely most used definition of safety is labeling the states/actions with one of several labels indicating the level of safety in that state/action. What varies from author to author is the number and names of these labels. To start with, Hans  [14]  has the most granular division of state/action space. His definitions are as follows (slightly reformulated): an (s, a, r, s ) tuple (transition) is fatal if the reward r is less than a certain threshold (s is the original state, a is an action and s is the state obtained after executing a in state s, yielding the reward r), an action a is fatal in state s if there is non-zero probability of leading to a fatal transition, state s is called supercritical if there exists no policy that would guarantee no fatal transition occurs when the agent starts in state s, Since we will compare other definitions the the Hans', it is needed to define one more category. A state s is called fatal if it is an undesired or unrecoverable state, e.g. if the robot is considered broken in that state. The fatal transition can then be redefined as a transition ending in a fatal state. Opposite to the precisely defined terms in Hans' definition, the meaning of words \"undesired\" and \"unrecoverable\" here is vague and strongly task-dependent. - Continuing on, Geibel  [12]  defines only two categories -fatal and goal states. \"Fatal states are terminal states. This means, that the existence of the agent ends when it reaches a fatal state\"  [12] . This roughly corresponds to our defined set of fatal states. Goal states are the rest of final states that correspond to successful termination. Since Geibel only considers terminal states for safety, his goal states correspond to a subset of safe states. The other Hans' categories need not be represented, since they are meaningless for final states. An extension of Geibel's fatal and goal states is a division presented by García  [10] . His error and non-error states correspond to fatal and goal states, but García adds another division of the space -the known and unknown states, where known states are those already visited (and known have empty intersection with error ). He then mentions a prerequisite on the MDP that if an action leads to a known error /non-error state, then its slight modification must also lead to an error /non-error state (a metric over the state space is required). In Ertle's work  [9] , again the two basic regions are considered -they are called desired and hazardous (corresponding to safe and fatal). However, due to the used learning technique, one more region emerges -the undesired region. It contains the whole hazardous region and a \"small span\" comprising of desired states, and denotes the set of states where no training (safe) samples are available, because it would be dangerous to acquire those samples. In particular, he says that \"The hazards must be 'encircled' by the indications of the undesired approaching so that it becomes clear which area [. . . ] is undesired\"  [9] . A summary of the labeling-based definitions is shown in Figure  3 . We examined the apparent imbalance between the number of categories Hans defines, and the other definitions, and that led us to the following observations. The first observation is that creating labels for actions or transitions is unnecessary. If we need to talk about the \"level of safety\" of an action, we can use the worst label out of all possible results of that action (which retains compatibility with Hans' definitions). Moreover, as \"it is impossible to completely avoid error states\"  [22] , we can ignore the effects of the action which have only small probability (lower than a safety threshold) -we will call such effects the negligible effects. A second remark is that the fatal and supercritical sets can be merged. In Hans' work we haven't found any situation where distinguishing between supercritical and fatal would bring any benefit. Specifically, in his work Hans states that: \"Our objective is to never observe supercritical states\"  [14] , which effectively involves avoiding fatal transitions, too. And since we avoid both supercritical and fatal, we can as well avoid their union. Third, safety of a state does not necessarily depend on the reward for getting to that state. E.g. when the UGV performs a victim detection task, going away from the target area may be perfectly safe, but the reward for such action should be small or even negative. Putting these observations together, we propose a novelty definition of safety for stochastic MDPs, which is a simplification of Hans' model and a generalization of the other models: -A state is unsafe if it means the agent is damaged/destroyed/stuck. . . or it is highly probable that it will get to such state regardless of further actions taken. -A state is critical if there is a not negligible action leading to an unsafe state from it. -A state is safe if no available action leads to an unsafe state (however, there may be an action leading to a critical state). To illustrate the definition on a real example, please refer to Figure  2 . In 2(a), the UGV is in a safe state, because all actions it can take lead again to safe states (supposing that actions for movement do not move the robot for more than a few centimeters). On the other hand, the robot as depicted in 2(b) is in a critical state, because going forward would make the robot fall over and break. If the robot executed action \"go forward\" once more, it would come to an unsafe state. Right after executing the action it would still not be broken; however, it would start falling and that is unsafe, because it is not equipped to withstand such fall and therefore it is almost sure it will break when it meets the ground. \n Safety through ergodicity An MDP is called ergodic iff for every state there exists a policy that gets the agent to any other state  [20] . In other words, every mistake can be remedied in  such MDP. Moldovan  [20]  then defines δ-safe policies as policies guaranteeing that from any state the agent can get to the starting state with probability at least δ (using a return policy, which is different from the δ-safe one). Stated this way, the safety constraint may seem intractable, or at least impracticalit is even proved, that expressing the set of δ-safe policies is NP-hard  [20] . An approximation of the constraint can be expressed in the terms of two other MDP problems which are easily solved  [20] ; that still leads to δ-safe policies, but the exploration performance may be suboptimal. In our view, safety through ergodicity imposes too much constraints on the problems the agent can learn. It sometimes happens that a robot has to learn some task after which it is not able to return to the initial state (e.g. drive down a hill it cannot go upwards; a human operator then carries the robot back to the starting position). But the inability to \"return home\" in no means indicates the robot is in an unsafe state. \n Safety through costs Another definition of safety is to define a cost for taking an action/being in a state and minimize the worst-case cost of the generated policies (up to some failure probability). Such approach is presented in  [15] . However, unless a threshold is set, this definition leads only to the safest possible policies, which are not necessarily safe. Expressing the safety using costs is natural for some RL tasks (e.g. when learning the function of a dynamic controller of an engine, the engine's temperature can be treated as a cost). Unfortunately, not all unsafe states can be described using such costs in general. In addition, specifying the right costs may be a difficult task. \n Safety as variance of the expected return An alternative to safety as minimization of a cost (either worst-case or expected) is minimizing both the cost and its variance. This approach is called expected value-variance criterion  [15]  and is used mainly in works prior 2000, e.g.  [7] . A safe policy by this criterion can be viewed as a policy that minimizes the number of critical actions (because fatal transitions are expected to yield much larger costs than safe transitions, increasing the variance significantly). As stated in  [10] , the worst-case approach is too restrictive and cautious. The other expected value-variance criteria suffer from the same disadvantages as safety through costs -mainly from the general difficulty to tune up the costs. \n Safe exploration approaches Finally, when the theoretical concepts have been shown and the various safety definitions have been presented, we can focus on the main part of this overview. Our categorization of safe exploration techniques is based on the work of García  [10] . The basic division is as follows: approaches utilizing the expected return or its variance (Sec. 4.1), labeling-based approaches (Sec. 4.2) and approaches benefiting from prior knowledge (Sec. 4.3). \n Optimal control approaches Techniques in this category utilize variations of the expected value-variance safety criterion. The most basic one is treating the rewards as costs (when a reward is denoted by r t , the corresponding cost is denoted by c t ). Standard RL methods can then be used to solve the safe exploration task, as described e.g. in  [7]  for discounted infinite horizon. The RL objective function J = E ∞ t=0 γ t c t ( 5 ) is called the risk-neutral objective. To make this objective risk-sensitive, we specify a risk factor α and rewrite the objective as: [15] J = 1 α log E [exp (αγ t ∞ t=0 c t )] (6) E [ ∞ t=0 γ t c t ] + α 2 V ar [ ∞ t=0 γ t c t ] , which is also called the expected value-variance criterion. This approach is a part of theory using exponential utility functions, which is popular in optimal control  [19] . To complete this section, the worst-case objective function (also called the minimax objective) is defined as J = sup ∞ t=0 γ t c t . (7) As can be seen, the objective functions containing expectations cannot in fact assure that no unsafe state will be encountered. On the other hand, the minimax objective provides absolute certainty of the safety. However, it may happen that some of the unsafe states can only be reached with a negligible probability. In such cases, the α-value criterion defined by  [15]  can be used -it only takes into account rewards that can be reached with probability greater than α. In the work of Mihatsch  [19] , a scheme is presented that allows to \"interpolate\" between risk-neutral and worst-case behavior by changing a single parameter. Delage's work  [8]  takes into account the uncertainty of parameters of the MDP. It is often the case that the parameters of the MDP are only estimated from a limited number of samples, causing the parameter uncertainty. He then proposes a possibility that the agent may \"invest\" some cost to lower the uncertainty in the parameters (by receiving some observations from other sources than exploration). A completely new research area then appears -to decide whether it is more valuable to pay the cost for observations, or to perform exploration by itself. An approximation scheme for dealing with transition matrix uncertainty is presented in  [21] . It considers a robust MDP problem and provides a worst-case, but also robust policy (with respect to the transition matrix uncertainty). A theory generalizing these approaches can be found in  [24] . The theory states that the optimal control decision is based on three terms -the deterministic, cautionary and probing terms. The deterministic term assumes the model is perfect and attempts to control for the best performance. Clearly, this may lead to disaster if the model is inaccurate. Adding a cautionary term yields a controller that considers the uncertainty in the model and chooses a control for the best expected performance. Finally, if the system learns while it is operating, there may be some benefit to choosing controls that are suboptimal and/or risky in order to obtain better data for the model and ultimately achieve better long-term performance. The addition of the probing term does this and gives a controller that yields the best long-term performance.  [24]  To conclude this section, we think that these methods are not well suited for safe exploration -the expected value-variance and similar criteria provide no warranties on the actual safety. On the other hand, the worst-case approaches seem to be too strict. \n Labeling-based approaches The approaches utilizing some kind of state/action labeling (refer to Section 3.1 for the various labeling types) usually make use of two basic components -a risk function and a backup policy. The task of the safety function is to estimate the safety of a state or action. In the simplest case, the safety function can just provide the labeling of the given action; or it can return a likelihood that the action is safe; and in the best case, it would answer with a likelihood to be safe plus a variance (certainty) of its answer. The backup policy is a policy that is able to lead the agent out of the critical states back to the safe area. It is not obvious how to get such a policy, but the authors show some ways how to get one. In the work of Hans  [14] , the most granular labeling is used, where fatal transitions are said to be the transitions with reward less than a given threshold. The safety function is learned during the exploration by collecting the so-called min-reward samples -this is the minimum reward ever obtained for executing a particular action in a particular state. The backup policy is then told to either exist naturally (e.g. a known safe, but suboptimal controller), or it can also be learned. To learn the backup policy, an RL task with altered Bellman equations is used: Q * min (s, a) = max s min R(s, a, s ), max a Q * min (s , a ) . A policy derived from the computed Q * min function is then taken as the backup policy (as it maximizes the minimum reward obtained, and the fatal transitions are defined by low reward). He defines a policy to be safe, if it executes only safe actions in safe states and produces non-fatal transitions in critical states. To learn such safe policy, he then suggests a level-based exploration scheme (although he gives no proofs why it should be better than any other exploration scheme). This scheme is based on the idea that it is better to be always near the known safe space when exploring. All unknown actions from one \"level\" are explored, and their resulting states are queued to the next \"level\". For exploration of unknown actions he proposes that the action should be considered critical until proved otherwise, so the exploration scheme uses the backup policy after every unknown action execution. A disadvantage of this approach is that the agent needs some kind of \"path planning\" to be able to get to the queued states and continue exploration from them. García's PI-SRL algorithm  [10]  is a way to safeguard the classical policy iteration algorithm. Since the labels error /non-error are only for final states, the risk function here is extended by a so called Case-based memory, which is in short a constant-sized memory for storing the historical (s, a, V(s)) samples and is able to find nearest neighbors for a given query (using e.g. the Euclidean distance). In addition to the error and non-error states, he adds the definition of known and unknown states, where known states are those that have a neighbor in the case-based memory closer than a threshold. A safe policy is then said to be a policy that always leads to known non-error final states. To find such policy, the policy iteration is initialized with the safe backup policy and exploration is done via adding a small amount of Gaussian noise to the actions. This approach is suitable for continuous state-and action-spaces. Another approach is presented in the work of Geibel  [12] , where the risk and objective functions are treated separately. So the risk function only classifies the states (again only final states) as either fatal or goal, and the risk of a policy (risk function) is then computed as the expected risk following the policy (where fatal states have risk 1 and goal states have risk 0). The task is then said to be to maximize the objective function (e.g. discounted infinite horizon) w.r.t. the condition that the risk of the considered policies is less than a safety threshold. The optimization itself is done using modified Q-learning, and the optimized objective function is a linear combination of the original objective function and the risk function. By changing the weights in the linear combination the algorithm can be controlled to behave more safely or in a more risk-neutral way. A generalization of Geibel's idea to take the risk and reward functions separately can be found in the work of Kim  [18] . In this work, the constrained RL task is treated as a Constrained MDP and the algorithm CBEETLE for solving the Constrained MDPs is shown. The advantage of this work is that it allows for several independent risk (cost) functions and doesn't need to convert them to the same scale. A similar approach of using constrained MDP to solve the problem can be found in the work of Moldovan  [20] . He does, however, use the ergodicity condition to tell safe and unsafe states apart (that is, safe are only those states from which the agent can get back to the initial state). Moreover, this approach is only shown to work for toy examples like the grid world with only several thousands of discrete states, which may not be sufficient for real robotics tasks. The idea of having several risk functions is further developed by Ertle  [9] . The agent is told to have several behaviors and a separate safety function is learned for each behavior. This approach allows for modularity and sharing of the learned safety functions among different types of agents. More details on this work will be provided in the next section, because it belongs to learning with teachers. An approach slightly different from the previously mentioned in this section is using the methods of reachability analysis to solve safe exploration. Gillula in his work  [13]  defines a set of keep-out states (corresponding to unsafe in our labeling) and then a set called P re(τ ) is defined as a set of all states from which it is possible to get to a keep-out state in less than τ steps. Reachability analysis is used to compute the P re(τ ) set. Safe states are then all states not in P re(τ ) for a desired τ . This approach, however, doesn't utilize reinforcement learning, it computes the optimal policy using standard supervised learning methods with one additional constraint -that the system must use safe actions near the P re(τ ) set. On the other hand, the system is free to use whatever action desired when it is not near P re(τ ). As was presented in this section, the labeling-based approaches provide a number of different ways to reach safety in exploration. They are, however, limited in several ways -some of them make use of the (usually hard-to-obtain) transition matrix, the others may need to visit the unsafe states in order to learn how to avoid them, or need the state-space to be metric. \n Approaches benefiting from prior knowledge The last large group of safe exploration techniques are the ones benefiting from various kinds of prior knowledge (other than the parameters of the MDP). We consider this group the most promising for safe exploration, because \"it is impossible to avoid undesirable situations in high-risk environments without a certain amount of prior knowledge about the task\"  [10] . The first option how to incorporate prior knowledge into exploration is to initialize the search using the prior knowledge. In fact, several works already mentioned in previous sections use prior knowledge -namely the approaches with a backup policy  (Hans [14] , García  [10] ). Also, García suggests that the initial estimate of the value function can be done by providing prior knowledge, which results in much faster convergence (since the agent does no more have to explore really random actions, the estimate of the value function already \"leads it\" the right way)  [10] . Another option how to incorporate prior knowledge is by using Learning from Demonstration (LfD) methods. Due to the limited space, we will not give the basics of LfD -a good overview of the state-of-the-art methods is for example in  [2] . For our overview, it is sufficient to state that LfD methods can derive a policy from a set of demonstrations provided by a teacher. What is important, is that the teacher does not necessarily have to have the same geometrical and physical properties as the trainee (although it helps the process if possible). It is therefore possible to use LfD to teach a 5-joint arm to play tennis, while using 3-joint human arm as the source of demonstrations (but the learned policy may be suboptimal; RL should then be used to optimize the policy). In Apprenticeship Learning  [1] , the reward function is learned using LfD. The human pilot flies a helicopter at his best, and both system dynamics and the reward function are learned from the demonstrations. It is however apparent that the performance of the agent is no longer objectively optimal, but that it depends on the abilities of the human pilot. Another way of incorporating prior knowledge into the learning process is to manually select which demonstrations will be provided, as in the work of Ertle  [9] . In the work it is suggested that more teacher demonstrations should come from the areas near the unsafe set, in order to teach the agent precisely where the border between safe and unsafe is located. The last technique described in our overview is interleaving autonomous exploration with teacher demonstrations. As in the previous case, some teacher demonstrations are provided in advance, and then the exploration part starts utilizing the teacher-provided information. After some time, or in states very different from all other known states, the agent requests the teacher to provide more examples  [2, 5] . The idea behind this algorithm is that it is impossible to think out in advance what all demonstrations will the agent need in order to learn the optimal policy. Finishing this section, the algorithms utilizing prior knowledge seem to be the most promising out of all the presented approaches. They provide both a speedup of the learning process (by discarding the low-reward areas) and a reasonable way to specify the safety conditions (via LfD or interleaving). \n Conclusion In our work we have given a short introduction on the basics of Markov Decision Processes as well as the basic Reinforcement Learning methods like Value Iteration, Q-learning and Policy Iteration. In Section 3 we have summarized many recent approaches on how to define safety in the framework of optimal control and reinforcement learning. We have also proposed a novelty definition of safety, which divides the state space to safe, critical and unsafe states. We have shown that all other labeling-based safety definitions are covered by our new definition. In Section 4 many different safe exploration methods are categorized into three basic groups -algorithms from optimal control theory, reinforcement learning algorithms based on state labeling, and algorithms utilizing extra prior knowledge. We have shortly summarized the advantages and disadvantages of the particular approaches. We have also stated that at least for difficult real-world problems, safe exploration without prior knowledge is practically impossible, and prior knowledge almost always helps to achieve faster convergence. Another observation has been that some of the safe exploration algorithms need to visit unsafe states to correctly classify them later, which might discard them from some usage scenarios where the unsafe states are really fatal. It seems to us that the field of safe exploration in reinforcement learning has been very fragmented and lacks an all-embracing theory. However, the question is, if it is even possible to find such theory -the main problem may be the fragmentation and differences of various RL methods themselves. At least, the safe exploration community would benefit from a unification of the terminology (and our proposal of the novelty safety labeling would like to help that). Other ways of possible future research are for example the following. New ways of incorporating prior knowledge into methods not utilizing it yet could bring interesting speed-up of those algorithms. There is also a bottleneck in the estimation of the results of unknown actions -some advanced function approximation methods should be explored (we aim to investigate Gaussian Processes this way). There are not enough experiments from difficult continuous real-world environments, which would show for example how large problems can be solved using safe exploration. The interleaved learning needs some guidelines on how to cluster the queries for the teacher to some larger \"packs\" and \"ask\" them together, possibly increasing the fully autonomous operating time. Last, but not least, the possibility to share some learned safety functions among different kinds of robots seems to be an unexplored area with many practical applications (maybe robot-to-robot LfD could be used). Fig. 1 . 1 Fig. 1. NIFTi UGV robotic platform \n (a) A safe state. (b) A critical state -if the robot went still forward, it would fall down and probably break. \n Fig. 2 .Fig. 3 . 23 Fig. 2. An illustration of safe and critical states. \n action a is supercritical in state s if it can lead to a supercritical state, state s is called critical if there is a supercritical or fatal action in that state (and the state itself is not supercritical), action a is critical in state s if it leads to a critical state (and the action itself is neither supercritical nor fatal in s), state s is called safe if it is neither critical nor supercritical, action a is safe in state s if it is neither critical, nor supercritical, nor fatal in state s, and finally a policy is safe if for all critical states it leads to a safe state in a finite number of non-fatal transitions (and if it only executes safe actions in safe states).", "date_published": "n/a", "url": "n/a", "filename": "safe_exploration_overview_lncs.tei.xml", "abstract": "We overview different approaches to safety in (semi)autonomous robotics. Particularly, we focus on how to achieve safe behavior of a robot if it is requested to perform exploration of unknown states. Presented methods are studied from the viewpoint of reinforcement learning, a partially-supervised machine learning method. To collect training data for this algorithm, the robot is required to freely explore the state space -which can lead to possibly dangerous situations. The role of safe exploration is to provide a framework allowing exploration while preserving safety. The examined methods range from simple algorithms to sophisticated methods based on previous experience or state prediction. Our overview also addresses the issues of how to define safety in the real-world applications (apparently absolute safety is unachievable in the continuous and random real world). In the conclusion we also suggest several ways that are worth researching more thoroughly.", "id": "75e471b2e0efe9f96f9cd113ccc8827a"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Owain Evans", "William Saunders", "Andreas Stuhlmüller"], "title": "Machine Learning Projects for Iterated Distillation and Amplification", "text": "Iterated Distillation and Amplification (IDA) is a framework for training models from data  [1, 2] . IDA is related to and builds on existing frameworks like supervised learning, imitation learning, and reinforcement learning. It is intended for tasks where: 1. The goal is to outperform humans at the task or to solve hard instances. 2. It is not feasible to provide demonstrations or reward signals for superhuman performance at the task.  1  3. Humans have some high-level understanding of the task and can also provide demonstrations or reward signals for easy instances of the task. The idea behind IDA is to bootstrap using an approach similar to Alp-haZero  [3] , but with a learned model of human reasoning steps taking the place of the fixed game simulator. We will explain IDA in abstract terms and then describe concrete examples. For broader discussion of IDA, including its relevance to the value alignment problem, see  [1, 2, 4, 5, 6, 7] . \n Technical description of IDA We consider the following learning problem: We want to train a model (e.g. a neural net) to solve tasks from the set T , where T contains a series of tasks that get progressively harder for humans to solve. Formally, let T = N i=0 T i , where tasks in T n are harder than tasks in T n−1 for all n. We are given a training set which includes solutions to the easiest class of problems T 0 and human demonstrations of decomposing tasks T n into finitely many slightly easier tasks in T n−1 . In IDA, the initial training steps are: 1. M is trained by supervised learning 2 to reproduce the answers to the easiest tasks T 0 . 2. M is trained by supervised learning to imitate the human demonstrations for decomposing a task x ∈ T n into a set of tasks in T n−1 and then aggregating the solutions to solve x. Steps (1) and (  2 ) are analogous to the two parts of a recursive algorithm: the base case and the recursive step. After initial training, M can solve tasks in T 1 by first decomposing them into tasks in T 0 . M is then trained by supervised learning on its own solutions to tasks in T 1 , enabling M to solve T 1 tasks directly (i.e. without decomposition). Solving a task in T 1 directly involves a single call to M , while solving by decomposition into tasks in T 0 requires M to be called on each of the T 0 tasks. This process of \"training on its own solutions\" can be iterated. M is trained by supervised learning to directly solve increasingly hard tasks in T , where the target solutions (i.e. labels for supervised learning) are produced by M itself via decomposition into tasks M can already solve. If supervised training works perfectly at each iteration, then eventually M can solve any task in T directly (with only single call to M ). (This depends on the strong assumption that humans can decompose all tasks T n into tasks in T n−1 -see  [8, 11]  for discussion.) We can now summarize IDA (see Figure  1 ). After training on steps (1) and (  2 ), the \"base case\" and \"recursive step\", the following steps are repeated (for n > 0): \n • Amplification Step M solves tasks in T n by decomposing them into tasks in T n−1 , which it solves directly (without decomposition). \n • Distillation Step M is trained by supervised learning to solve tasks in T n directly, with target solutions coming from the Amplification Step. \n It is called the \"Amplification Step\" because it amplifies the capability of model M . While M can only solve tasks in T n−1 directly, M can be used (via decomposition and aggregation) to solve tasks in T n . In the \"Distillation Step\", the slower amplified model (which makes multiple calls to M ) is distilled into a faster process with a single call to M . This is like distillation for neural nets  [12] , where a large net (or ensemble of nets) is \"distilled\" into a smaller net that tries to capture the behavior of the large net. In general, it is unlikely that distillation of the slower process will be perfect. This can be addressed using RL-based distillation or by selectively choosing when to use fast M directly and when to fall back to the amplified model (see Project 3). Second, M solves each task x ∈ T1 by decomposing into tasks {xa, x b } ∈ T0 and solving these directly. This eventually produces a dataset of solved tasks x ∈ T1, which M is trained to solve directly by supervised learning (leftmost \"distill\" step). This process is then repeated. x ∈ T 0 x a ∈ T 0 amplify distill amplify x ∈ T 1 x b ∈ T 0 x ∈ T 1 x a ∈ T 1 x ∈ T 2 x b ∈ T 1 distill x ∈ T 2 amplify x a ∈ T 2 x ∈ T 3 x b ∈ T 2 To simplify the exposition, we have presented M as being trained to decompose tasks and learn all base case solutions before the iterative training by Amplification and Distillation begins. In practice, these processes (learning to decompose harder problems and gathering additional base case solutions from humans, and learning to solve harder problems directly) would happen in parallel  [8] . \n Examples Having given an outline of IDA, we will describe two toy examples of solving problems with IDA: integer multiplication and shortest path in graphs.  3  These examples are intended to build intuition for IDA. They are not themselves practically relevant use cases for IDA. \n Example 1: Multiplication This toy example shows how one would use IDA to train a neural net M to multiply large integers. We assume that M has been pre-trained to add large integers. Following the pattern in the previous section, the initial training set contains (1) simple multiplications (base case), and (2) demonstrations of decomposing multiplications into simpler multiplications (recursive step). M is trained as follows: 1. Train M on simple multiplications: single-digit multiplication and multiplication by 10. For example: 5 × 6 = 30, 10 × 234 = 2340, 9 × 8 = 72.  Recursing all the way to the base case would require many calls to the neural net M . Instead, M could be trained incrementally using the IDA scheme described above. If this was successful, M could eventually compute 384 × 19 or 79332 × 2927 in a single call, without the need to ever instantiate the fully expanded slow process for large problems during training. This is a key property of IDA, since recursive decompositions can (in general) result in a number of calls to M that scales exponentially in the problem size, and so would be infeasible to instantiate explicitly. This example shows that IDA can easily fail if we use a standard neural net as our model M . For example, a small MLP is not capable of learning to multiply large integers in a single call. This is the case even for training the MLP by supervised learning on ground-truth examples, e.g. training on pairs ((m, n) , m × n) for m, n < 10 6 . Training by IDA will generally make learning more difficult, because M will be trained by supervised learning on its own answers to multiplication problems (instead of ground-truth answers). \n Train This example also shows that IDA can fail regardless of the model M . It is not generally possible to distill an exponential tree of calls to M into a single call to M . However, there are many AI problems where research aims to better approximate an exponential-time computation. AlphaZero uses an IDA-like algorithm to distill an exponential game-tree expansion into a feedforward neural net. The neural net does not distill perfect play for Go or chess, but it achieves impressive performance relative to humans (and formidable performance when combined with MCTS). \n Example 2: Shortest path in a graph A recent paper by Christiano et al.  [8]  implements IDA and applies it to discrete algorithms problems including union find, wildcard search, and shortest path. To apply IDA to finding the shortest path between nodes s and t in a directed graph, we need an initial training set that covers the base case and recursive step. These include: 1. A dataset of solutions to the easiest shortest path problems (for which nodes s and t are adjacent). 2. A set of demonstrations of decomposing shortest path problems into smaller shortest path problems and aggregating the results. The decomposition in (  2 ) is similar 4 to the following recursion, which is also used in the dynamic programming algorithm for shortest path: min-dist(s, t) = min ({min-dist(s, x) + dist(x, t) | x adjacent to t}) Here \"min-dist(s, t)\" is the minimum path length between nodes s and t, and \"dist\" is the distance between adjacent nodes. Christiano et al. use a Transformer model  [13]  as their model M and they compare two ways of training the Transformer to compute the shortest path. The first approach is the IDA model just described, which only gets labeled examples for the smallest shortest path problems and must bootstrap to solve larger problems. The second approach is regular supervised learning, where the model gets a large set of labeled examples of all sizes. The main result is that the IDA approach is successful in getting close to the performance of the supervised model. While this is a toy example, it illustrates the general aim for IDA, which is training a model for tasks where (a) there are only labels/demonstrations for easy problems, and (b) humans can provide decompositions for going from harder to easier problems. \n Related Work As noted above, there are various discussions of IDA and its relevance to AI alignment  [1, 2, 6, 7] . These discussions are valuable as background but they mostly abstract away the practical details of implementing an IDA system using ML. The only paper that actually implements IDA is the aforementioned Christiano et al. However, the AlphaZero algorithm  [3]  is very similar to IDA  [1]  and work applying AlphaZero (and related algorithms AlphaGo  [14]  and Expert Iteration  [15] ) to chess/Go and to graph coloring  [16]  are relevant to thinking about IDA experiments. IDA depends on bootstrapping and function approximation, which are core topics in reinforcement learning  [17, 18] . Recent work on Deep Q-learning is especially relevant  [19] . For IDA to help address value alignment problems for advanced ML systems, it would likely need to apply to tasks (and use decompositions) that involve sophisticated reasoning in natural language. There is currently no published research that is targeted at natural language tasks. Ought and OpenAI have conducted preliminary experiments in an IDA-like setting with humans in place of ML models. These experiments are aimed at shedding light on whether different incentive structures for IDA-like approaches (e.g. different objective functions and reward signals) lead to aligned behavior. See examples from Ought  [20]  and OpenAI  [21]  and stay in touch with Ought 5 for the latest information on experiments. In the two toy examples above, IDA trains a model to imitate behavior. This is an extension of supervised learning and imitation learning, and does not involve reinforcement learning. However, as mentioned above, IDA is compatible with RL  [10, 9] . There is also a framework called \"Debate\", which is closely related to IDA and draws on self-play reinforcement learning as a method of bootstrapping. Irving et al.  [22]  introduces Debate, explores analogies to computational complexity theory, and describes links between Debate and IDA. \n Project Goals The rest of this document outlines three projects that could help clarify aspects of IDA. These projects aim to extend Christiano et al  [8]  in a few different ways: • The projects train a single model M to perform a wide range of types of decompositions. By contrast, Christiano et al. train a fresh model for each algorithmic problem (i.e. one for each of union find, shortest path, and wildcard search). The decompositions for these algorithmic problems have dynamic programming structure, so each model decomposes a problem instance into smaller instances of the same kind of problem (e.g. a shortest path problem is broken down into smaller shortest path problems). • The projects are well suited to investigating extrapolation and generalization out of distribution. Projects 1 and 2 build on prior work in ML which tests generalization performance in mathematics and neural programming tasks. Project 3 is focused on general approaches (adaptive computation time and calibration) to improving robust generalization. • In Christiano et al. the main goal is for a model trained by IDA to match the performance of a model trained by supervised learning. The IDA model has less labeled data and is trained by bootstrapping on its own labels. While this is one possible goal for our projects, we also consider the goal of improving test-time performance by making multiple calls to the model using amplification. Improving test-time performance by amplification is similar to the way AlphaZero uses MCTS during competitive matches to improve performance over the policy net. There are many other possible projects on IDA. Research projects that push in the following directions seem particularly valuable: • Produce theory and empirical knowledge about training IDA systems, analogous to knowledge of how to train supervised learning or reinforcement learning systems. • Connect IDA to existing work in ML. The projects below connect to language modeling, neural programming, calibration for neural networks, and adaptive computation time. IDA is also related to semi-supervised learning, deep reinforcement learning, dynamic programming, belief propagation, etc. A research project could explore and develop any of these connections. • Solve problems with IDA that can't be solved by other approaches. This is the ultimate goal of IDA, and would draw interest from the larger ML community. The projects below are not primarily aimed to achieve this, but they may provide a useful first step. Two ways in which IDA could solve problems that can't be solved by other approaches are: -By distilling large (i.e. exponential in problem size) trees to a fast machine learning model (as in AlphaZero). -By learning decomposition steps from human data. This is for domains (e.g. common-sense reasoning) where we are not able to write down an algorithm to decompose problems. 1 Project 1: Amplifying Mathematical Reasoning \n Motivation Decomposition is a fundamental strategy for solving problems in mathematics. Consider the following problem from high-school mathematics: g(y) = y-2 f(x) = x*g(x) + 3x^3 Find the derivative of f at x=1. We can solve the problem by decomposing it into sub-problems which only depend on parts of the whole problem. Here is one possible decomposition: Sub-problem 1: g(y) = y-2 f(x) = x*g(x) + 3x^3 Write f as a polynomial in x in standard form. Solution: f(x) = 3x^3 + x^2 -2x Sub-problem 2: f(x) = 3x^3 + x^2 -2x Differentiate f. Solution: f'(x) = 9x^2 + 2x -2 Sub-problem 3: f'(x) = 9x^2 + 2x -2 Compute f'(1) . Solution: 9 These sub-problems could themselves be decomposed: the first sub-problem decomposes to substituting the function g and expanding the resulting expression. \n Project Directions The aim of this project is to train a model via IDA to solve mathematics problems. Following Christiano et al  [8] , we could use IDA at training time to bootstrap from a small labeled dataset. This is like a student learning math by solving problems from a textbook with no solutions at the back of the book. Another possible goal is to use amplification at test time to apply more compute to harder problems, and so achieve better test-time performance than a standard supervised model. There are many possible choices of mathematics problem, including: 1. Mathematical problems in a formal language (e.g. theorem proving  [23] ). 2. High-school algebra (in a mix of natural language and math notation  [24] ). 3. So-called \"word problems\", which are problems in natural language that need to be translated into math. For example, many problems on the American GMAT or GRE exams  [25] . 4. Advanced mathematics problems: competition or Olympiad math, universitylevel proof-based math  [26] . Problems in (1) do not require working with natural language. Many such problems have a natural decomposition via brute-force search, similar to gametree search in Chess. These problems are a good testing ground for some aspects of IDA and we encourage research on them. However this document focuses on problems in (  2 )-(  4 ) and especially  (2) . Problems in (  2 )-(  4 ) are natural language problems which don't necessarily have an obvious decomposition strategy. This makes them more similar to problems in areas outside mathematics such as science, philosophy, and common-sense reasoning. How can we tackle natural language mathematics problems in IDA? The main question is how to produce decompositions. There are two basic options: 1. Have human experts produce decompositions of the problems. \n Write an algorithm that solves problems by decomposition as in Christiano et al  [8] . This algorithm is likely to resemble classical AI approaches (\"GOFAI\"). Using human data is the more general approach, as it applies outside mathematics. However, it is unlikely that the usual way people solve problems would yield the most useful decompositions. So, part of the research effort is to work out which kinds of decompositions help most and train human experts to produce them. For option (2) above, there are two kinds of algorithm for decomposition. The first kind is an efficient algorithm that solves all problems in the class of interest (as in the multiplication and shortest path examples). A neural net trained using IDA is unlikely to perform better than such an algorithm. Experiments with IDA would aim not at state-of-the-art performance but instead at investigating certain aspects of IDA. We discuss this in the next section. The second kind of algorithm solves problems in the class inefficiently and so can only solve small problems in practice. In this case, it is possible that IDA can achieve state-of-the-art performance by learning to distill decompositions into a much more efficient neural algorithm. However, for advanced mathematics problems in natural language, it is not clear what this inefficient algorithm would look like.  6  So there is a separate research project in investigating such algorithms. In the next section, we outline a project that uses high-school math problems in natural language. We suggest starting with algorithmically generated decompositions and later extending this to decompositions provided by humans. The problems are generated by an algorithm, so there is unlimited training data. The dataset includes test sets for both interpolation and extrapolation. The extrapolation questions have quantities that vary outside of the range encountered on the training set. \n IDA for High School Mathematics The paper includes baselines for models trained by supervised learning. The questions and answers are both represented as strings, so it can be treated as a sequence-to-sequence problem. The best performing model is a standard Transformer with 30M parameters, which achieves 76% model accuracy (probability of a correct answer) on interpolation and 50% on extrapolation. \n Approach with IDA How should one generate decompositions for training IDA to solve these math problems? One option is to write an algorithm for decomposing problems, rather than collecting human decompositions. The problems were generated using a compositional algorithm: consider the last example in the list above, which combines algebra (specifying an integer using equations) and number theory (checking if the integer is composite). This algorithm can be run in \"reverse\" to help generate decompositions. However, it is not obvious how close the resulting decompositions would be to decompositions that are a good fit for IDA training. (For instance, the best decompositions could be more or less fine-grained.) One objective would be to do better than the supervised baseline at test time by applying amplification (i.e. decomposing the problem and using multiple calls to the model M ). In particular, amplification promises to do better at extrapolation to bigger problems or problems with larger numerical quantities. Another objective is to train from a smaller number of labels using distillation and try to rival the performance of the supervised baseline. \n Non-Amplification Baselines The simplest baseline is supervised learning (as in Saxton et al  [24] ). The math problems and solutions are represented as strings, and the model is trained to map strings to strings. Another baseline would make use of the same decomposition training data as IDA. Instead of training the model to decompose problems, we could use the decomposition as an auxiliary objective. The model would be trained to produce both the decomposition and the answer. An alternative approach is to train a model to take strings as input and then produce output suitable to be fed into a symbolic math system (e.g. SymPy). \n Questions to investigate The project would seek to investigate some of the following questions: • What is the test-time performance of applying amplification vs. a baseline that makes a single call to the model (distillation) vs. a baseline that was trained by supervised learning? • What is the performance on extrapolation and on off-distribution problems? • What is the performance of a distilled model trained by IDA (from a small number of labeled examples) vs. the supervised baseline (with a large labeled training set)? • How does performance vary with different kinds of decomposition strategies? • How robust is the amplified model to noise in the training data and to approximation error in the neural net? • Can we find a decomposition strategy that makes the model more robust to errors/noise? • When training a model to solve sub-problems, we need to pick some distribution over sub-problem examples. How does this impact performance? Are there principles for generating training data in the most useful way for IDA? • Using amplification at test time is one way to vary the amount of compute used to solve problems. Another approach is to use recurrent models and adaptive computation time. How does this compare to IDA? (See Project 3 for more discussion and references). • Can we train the model from decompositions provided by humans? What kind of decompositions should we use? Can these be augmented by algorithmically generated decompositions? 1.4 Related Work • Program Induction by Rationale Generation (Ling et al.)  [25]  Dataset: https://github.com/deepmind/AQuA This paper introduces a dataset of mathematical word problems (based on US standardized tests). Humans had to \"show their work\" while solving the problems. The paper has a model that learns to generate these intermediate steps (in addition to learning to solving the problems). • Sigma Dolphin microsoft.com/en-us/research/project/sigmadolphin-2/ Dataset of natural language math problems, taken from Yahoo Answers. • HOList: An Environment for Machine Learning of Higher-Order Theorem Proving (Bansal et al.)  [23] . This dataset contains fully formalized proofs for a large number of theorems and a framework for training ML systems to produce proofs. 2 Project 2: IDA for Neural Program Interpretation \n Motivation Many algorithms (e.g. matrix arithmetic, shortest path, sorting) involve decomposing problems into progressively smaller problems and then aggregating results. More generally, computer programs in high-level languages decompose tasks into progressively smaller tasks, and ultimately into the primitive operations of the language. We can explore the capabilities of IDA by training a model on the decompositions used in the execution of computer programs. Training IDA on decompositions from programs is closely related to research on Neural Program Interpretation (see Reed and de Freitas  [28]  and related work below) or \"NPI\". In NPI, a model is trained to mimic the internal behavior of an algorithm and not just its input-output behavior. Moreover, the model trains not just on the primitive operations of the algorithm but on its hierarchical decomposition (i.e. the way procedures call other procedures). As with IDA, one motivation for learning this internal behavior is to achieve stronger generalization. Another motivation is to integrate hierarchical discrete computation with the sort of pattern recognition in high-dimensional spaces enabled by machine learning (see third experiment in  [28] ). \n Project Directions The project could focus on either of the following areas: \n Distillation of programs In contrast to most work on NPI, the goal of IDA experiments could be to use program decompositions as training data to learn more efficient \"neural\" programs. The idea is to distill elaborate computations into a single call to a neural net, or to combine the exact (slow) computation with distillation (as in AlphaZero). 2. NPI within a more general framework for learning from decompositions Much of the NPI work uses environments and architectures designed specially for NPI. For IDA, we would aim to replicate NPI results, but in a framework that would also allow learning from human decompositions in natural language. We expect distillation of programs to be challenging. If we take a complicated algorithm and try to distill it into a neural net, there is likely to be approximation error-and errors will usually be larger for inputs that are off the training distribution. This will cause problems both during IDA's iterative training procedure and also at test time. Part of the project would be to investigate how well distillation works for different kinds of programs and for different ways of organizing the training curriculum. If the distilled model was calibrated, then IDA could recognize when distillation was likely to fail and fall back on using amplification. Project 3 (below) explores this \"adaptive computation\" or \"meta-reasoning\" approach. \n Decision Points There are many choices to make in devising IDA experiments in the NPI setting: • Which programs should we try to learn? The research on NPI has focused on basic algorithms for tasks like integer arithmetic and sorting. Applying IDA to these basic algorithms could be a good starting point, as they allow comparison to existing work. However, it isn't clear how much experience with these algorithms would generalize to other applications of IDA. It could be good to consider algorithms that work with databases or knowledge bases, or to consider algorithms that operate on human-readable structures like natural languages or images. We also think that pure functional programming is a better fit for IDA than imperative programming. See  [11, 29]  for relevant discussion. • What kind of built-in operations and environments should we use? In existing work on NPI, the neural net is given outputs that correspond to basic operations on data. This makes it easier to learn algorithms that depend on those basic operations. For IDA, it would be ideal to learn these operations from examples. (If we were learning from human decompositions, we might not know about these \"basic operations on data\" ahead of time). • What kind of performance objective should we focus on? Some work on NPI has focused on getting perfect performance on narrow algorithmic tasks. It's not clear if this is the right objective for IDA. We might care about (a) generalizing well to much larger inputs most of the time (but not in the worst case), (b) being robust to distribution shift, and (c) having one neural net learn a wide variety of algorithms. \n Non-Amplification Baselines For learning to predict the next step of a program from examples, simpler ML methods (random forests, logistic regression, etc.) may perform better than neural networks. For performing the same task as a traditional program, any neural program interpreter working with polynomial-sized trees will add significant overhead and so is unlikely to *improve* performance. One could also consider tasks that require ML to process the inputs (e.g. tasks involving images). The baseline in this case would be a program that defers some decisions to a classifier. \n Related Work Neural Programmer-Interpreters (Reed and de Freitas)  [28]  A quote from the introduction about the motivation for the paper: \"We may envision two approaches to providing supervision. In one, we provide a very large number of labeled examples, as in object recognition, speech and machine translation. In the other, the approach followed in this paper, the aim is to provide far fewer labeled examples, but where the labels contain richer information allowing the model to learn compositional structure. While unsupervised and reinforcement learning play important roles in perception and motor control, other cognitive abilities are possible thanks to rich supervision and curriculum learning. This is indeed the reason for sending our children to school.\" Summary of the approach: • The model (called the \"neural programmer-interpreter\") has a single inference core for executing three different programs (addition, sorting, rotating CAD models). So one set of LSTM parameters are used to execute all programs. However, the different programs are stored as different embeddings, stored in a learnable persistent memory. • The sequence of the model's actions depends on the environment state and action history. • For each program (addition, sorting, rotating CAD models), the model is given a specific environment and set of actions in that environment. The model is trained to compose these actions. For integer addition, there are 1-D arrays and read-only pointers (for reading inputs), as well as 2-D scratchpads and output arrays. For rotating CAD models, there's a CAD renderer with controllable elevation and azimuth movements. • The LSTM input of the previous computation step is a vector embedding, rather than text. Making Neural Programming Architectures Generalize via Recursion (Cai et al.)  [30]  Builds on Reed and de Freitas (above) and has no new machinery. They simply allow a function to call itself. This means it can solve instances of arbitrary size using recursive function calls, each of which have bounded length. This allows for generalization off the training distribution. The hidden state of the LSTM controller is reset (to zero) at each subprogram call, but the environment state is not reset. They learn the recursion termination condition. They achieve 100% generalization on all tasks (albeit for simple tasks). Parametrized Hierarchical Procedures for Neural Programming (Fox et al.)  [31]  Their model is related to IDA for neural programming (it learns PHPs that can recursively call other PHPs). Their tasks are limited to addition and to a building a tower in gridworld. They provide a \"weak supervision\" motivation: learn from a mix of traces that show what information should be remembered from previous states and also from traces that omit that information. Neural Program Lattices (Li et al.)  [32]  This paper has a \"weak supervision\" motivation: learn from mix of full traces and traces without program calls/arguments. They generalizes to 500-digit addition, but not to 1000-digit addition. Improving the Universality and Learnability of Neural Programmer-Interpreters with Combinator Abstraction (Xiao et al.)  [33]  Adds combinator abstraction from functional programming. One motivation is to use reinforcement learning to learn programs without supervision. The combinator makes the search space smaller. Adaptive Neural Compilation (Bunel et al.)  [34]  Takes programs, translates them into a differentiable form, then uses backpropagation to optimize them. They optimize programs to be more efficient on a restricted training distribution of problems. Recent Advances in Neural Program Synthesis (Kant)  [35]  This paper provides a summary of different approaches to NPI and Neural Program Synthesis. Learning Compositional Neural Programs with Recursive Tree Search and Planning (Pierrot et al.)  [36]  NPI approach that \"incorporates the strengths of Neural Programmer-Interpreters (NPI) and AlphaZero\". While relevant to IDA, this approach differs in important ways. 3 Project 3: Adaptive Computation \n Motivation An ML model exhibits \"adaptive computation\" if it intelligently varies its computations for different inputs. For example: 1. The model selects which type of computation to run: e.g. between a slow tree search, a large neural net, and a small neural net. 2. The model prioritizes possible computations: e.g. which node to expand next in a tree search. 3. The model determines how long to run a fixed computation: e.g. how many MCTS samples, how many steps to run an RNN, etc. A principled way to adapt computations is by \"meta-level control\" or \"metareasoning\". Meta-level control means applying ideas from optimal control and Bayesian decision theory to selecting computations. The idea is to treat the choice of computations as just another learning and planning problem. The choice of computations can be optimized using end-to-end supervised learning  [37] , model-free reinforcement learning  [38] , or Bayesian decision theory  [39, 40, 41] . Adaptive computation and meta-level control are not a major focus in current deep learning research. Yet human cognition is often adaptive: people dynamically decide how much time to spend on a task based on its perceived difficulty. This is important when humans try to develop new ideas, which can require anything from hours to years of thinking  [42, 43] . By contrast, many applications of ML have the following profile: 1. Training time: Large amounts of compute and time are permitted. For example, training might take months and use many CPUs and GPUs. \n Test/deployment time: There are very strong constraints on compute. For example, the trained model might be part of a web application and so must perform inference in a fraction of a second. Not all ML algorithms have this profile. When AlphaZero  [3]  plays competitive matches, it has time to make many calls to a neural net for each move. Alp-haZero uses MCTS to investigate promising moves from the current position. As ML is applied to more tasks for which humans spend a long time thinking (e.g. mathematics, science, business strategy), the profile of AlphaZero may become more common. IDA is well suited to adaptive computation. Training by IDA produces the following algorithms: • A quick but potentially inaccurate algorithm for solving problems, produced by distillation. This corresponds to a single call to the model M (using the terminology from Section 0.1). • An \"anytime\" algorithm for solving the same problems, which produces more accurate or reliable answers as a function of doing more compute. This is obtained by decomposing the problem using the learned decomposition strategy (\"Amplification\") and involves making multiple calls to M . \n Project Directions Adaptive computation for IDA can be applied either during the iterative training scheme or at test/deployment time: \n Training time The goal during training is to bootstrap by using amplification to solve progressively harder problems. Adaptive computation time could be applied to select how much computation to apply to a given problem in the training set. For example, if the distilled model already performs perfectly on some class of problems, there is no need to run the slow amplified process (with many calls to model M ) on this class. It's also possible to apply active learning -automatically selecting problems that are more informative about the objective. \n Test time The goal is to perform well on a set of test problems given a time budget. If the test set is received in batch, then the algorithm would ideally spend more of its time budget on the harder instances. This requires the algorithm to recognize harder instances that will benefit from more compute time (via amplification). There are also more fine-grained questions about how to use the compute budget. For example, when using amplification, which problems should be decomposed first and how far should the recursive decomposition go? \n IDA, Fast and Slow There are many ways to use adaptive computation as part of IDA. As a starting point, we describe a simple form of adaptive computation, where the algorithm decides between a fast (distilled) process for solving problems and a slow process that uses a fixed amount of amplification. The fast process makes a single call to a neural net, while the slow process makes at most n calls to the same net. For each input problem, the algorithm runs the fast process and has to decide whether to also run the slow process. The goal is to balance the greater accuracy of the slow process with a time/compute cost that is specified as part of the problem statement. This decision of whether to run the slow process could be trained end-toend, by always running both processes during training (as in  [37] ). A different approach would be to use a calibrated model for the fast process and decide whether to call the slow process based on the confidence of this calibrated model. Which tasks would be a good testing ground for adaptive computation? The mathematics and neural programming tasks (Projects 1 and 2 above) are useful for testing purposes, because it's easy to vary the amount of computation that is necessary and sufficient for solving a problem. It's also valuable to explore tasks which have an \"anytime\" structure, where approximate solutions to the task can be improved with additional compute. This would include planning, natural language reasoning, chess, and strategic videogames. How would this project differ from Projects 1 and 2? The aim in those projects is to explore the performance of IDA on challenging tasks. It's not clear that any clever adaptive computation strategy is required to do well on these tasks (though we can't rule it out). In a related example, AlphaZero did not select the number of MCTS samples as a function of the board position, but instead used a fixed proportion of the remaining match time. Project 3, on the other hand, is all about investigating adaptive computation for IDA. The motivation is that adaptive computation is likely to play an important role as IDA is applied to increasingly challenging tasks. \n Non-Amplification Baselines For any adaptive computation approach, it is important to compare against nonadaptive approaches (which use a fixed amount of compute) and also against simple heuristics for scaling up compute for harder instances. Amplification could also be compared to adaptive approaches that do not use amplification (e.g. something like  [37] ). \n Related Work Attending to Mathematical Language with Transformers (Wangperawong)  [44]  There is a dataset (available at https://github.com/tensorflow/tensor2tensor) and paper for addition/multiplication/subtraction of numbers. The paper explores Transformers that can use more compute for larger instances. Adaptive Computation Time for Recurrent Neural Networks (Graves)  [37]  Adaptive Computation Time for RNNs adds the probability of halting computation at current step to the output of RNN. The idea is to train the adaptive RNN end-to-end: running long computations at training time, which allows differentiation of the halting probability. Comparing Fixed and Adaptive Computation Time for Recurrent Neural Networks  (Fojo et al.)    [45]  This paper presents experiments claiming to show that adaptive computation time for RNNs (as in  [37]  above) is not needed because similar performance is achieved with a regular RNN (which takes a fixed number of steps between predictions). Universal Transformers (Dehghani et al.)  [46]  The paper applies Adaptive Computation Time to the Transformer architecture. It shows improved performance on bAbI tasks with Adaptive Computation Time On Calibration of Modern Neural Networks (Guo et al.)  [47]  This paper tests the calibration of convolutional neural networks and finds that they are poorly calibrated by default. They show that temperature scaling (learning a temperature parameter that scales the softmax inputs) does a good job of getting the network to be calibrated. They indicate a tradeoff between accuracy and calibration (see their Figure  3 ). Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles (Lakshminarayanan et al.)  [48]  They get calibrated uncertainty estimates for deep neural nets by: • Using a proper scoring rule for the loss \n • Performing adversarial training • Using an ensemble of networks Principles of Metalevel Control (Hay)  [39]  Ph.D. thesis on metalevel control and metareasoning. Includes an excellent introduction to the subject and a review of previous work. The technical contributions include applying Bayesian decision theory to Bandit problems and applying RL to tree-search (i.e. learning a tree-search policy rather than just building in MCTS). Learning to Search with MCTSnets (Guez et al.)  [49]  They show how to learn the hyperparameters of Monte-Carlo Tree search endto-end, by playing single-player gridworld game Sokoban. They learn a more sample efficient search than regular MCTS. Contents0a 14 3 18 0 1418 Background on IDA 0.1 What is IDA? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.4 Project Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Project 1: Amplifying Mathematical Reasoning 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Project Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 IDA for High School Mathematics . . . . . . . . . . . . . . . . . 1.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . University of Oxford b University of Toronto c Ought. Correspondence to andreas@ought.org 2 Project 2: IDA for Neural Program Interpretation 12 2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Project Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Project 3: Adaptive Computation 16 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Project Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 IDA, Fast and Slow . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background on IDA 0.1 What is IDA? \n Figure 1 : 1 Figure 1: Diagram showing the first few Amplification and Distillation steps in IDA training. First (far left), M is trained by supervised learning on each task x ∈ T0.Second, M solves each task x ∈ T1 by decomposing into tasks {xa, x b } ∈ T0 and solving these directly. This eventually produces a dataset of solved tasks x ∈ T1, which M is trained to solve directly by supervised learning (leftmost \"distill\" step). This process is then repeated. \n Figure 2 : 2 Figure 2: A multiplication problem could eventually be solved by decomposing all the way down to simple multiplications (without any distillation). Only the first two levels of decomposition are shown here. \n 1. 3 . 1 31 Task and DatasetSaxton et al. [24]  introduce a dataset of high-school level mathematics problems in natural language. The problems cover arithmetic, algebra, differentiation, probability, and number theory. Here are some examples:Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r. Answer: 4 Question: Simplify sqrt(200)*2 + sqrt(200) + sqrt(200) + -4. Answer: -4 + 40*sqrt(2) Question: Let u(n) = -n^3 -n^2. Let e(c) = -2*c^3 + c. Let f(j) = -118*e(j) + 54*u(j). What is the derivative of f(a)? Answer: 546*a^2 -108*a -118 Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql. Answer: 1/110 Question: What are the prime factors of 235232673? Answer: 3, 13, 19, 317453 Question: Let j = -5 -28. Is j/6*(-14) a composite number? Answer: True \n\t\t\t More precisely: it is infeasible to provide large numbers of demonstrations or sufficiently dense reward signals for methods like imitation learning or RL to work well. \n\t\t\t We describe IDA based on supervised learning, similar to [8] , since this is what the three projects in this document focus on. This can be substituted with RL or other training schemes, see [9, 10] . We view answering questions, problem decomposition, and aggregation of subproblem answers all as sequence-to-sequence problems, so we can train a single model M to solve them. We could also train distinct models. \n\t\t\t The Multiplication example has not been implemented, but a version of the Shortest Path example is implemented in [8] . \n\t\t\t Christiano et al. use a slightly more complicated decomposition. 5 https://ought.org \n\t\t\t If mathematics problems are fully formalized, we can search over formal proofs. But if the mathematics is informal, it is much harder to provide an algorithm that would eventually (given arbitrary amounts of time and compute) solve the problems.", "date_published": "n/a", "url": "n/a", "filename": "evans_ida_projects.tei.xml", "abstract": "Iterated Distillation and Amplification (IDA) is a framework for training ML models. IDA is related to existing frameworks like imitation learning and reinforcement learning, but it aims to solve tasks for which humans cannot construct a suitable reward function or solve directly. This document reviews IDA and proposes three projects that explore aspects of IDA. Project 1 applies IDA to problems in highschool mathematics and investigates whether learning to decompose problems can improve performance over supervised learning. Project 2 applies IDA to neural program interpretation, where neural nets are trained on the internal behavior (execution traces) of traditional computer programs. Project 3 investigates whether adaptive computation time (varying compute at inference time as a function of the input) can improve the robustness and efficiency of IDA. Our goal in outlining these projects is to generate discussion and encourage research on IDA. We are not (as of June 2019) working on these projects, but we are interested in collaboration.", "id": "a00d86d49f2345fc29ac9e586b6dd757"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Adam Stooke", "Joshua Achiam", "Pieter Abbeel"], "title": "Responsive Safety in Reinforcement Learning by PID Lagrangian Methods", "text": "Introduction Reinforcement learning has solved sequential decision tasks of impressive difficulty by maximizing reward functions through trial and error. Recent examples using deep learning range from robotic locomotion  (Schulman et al., 2015; Gu et al., 2016; Schulman et al., 2017; Levine et al., 2016)  to sophisticated video games  (Mnih et al., 2013; Schulman et al., 2017; OpenAI, 2018; Jaderberg et al., 2019) . While errors during training in these domains come without cost, in some learning scenarios it is important to limit the rates of hazardous outcomes. One example would be wear and tear 1 University of California, Berkeley 2 OpenAI. Correspondence to: Adam Stooke <adam.stooke@berkeley.edu>. Proceedings of the 37 th International Conference on Machine  Learning, Vienna, Austria, PMLR 119, 2020.  Copyright 2020 by the author(s). on a robot's components or its surroundings. It may not be possible to impose such limits by prescribing constraints in the action or state space directly; instead, hazard-avoiding behavior must be learned. For this purpose, we use the well-known framework of the constrained Markov decision process (CMDP)  (Altman, 1999) , which limits the accumulation of a \"cost\" signal which is analogous to the reward. The optimal policy is one which maximizes the usual return while satisfying the cost constraint. In safe RL the agent must avoid hazards not only at convergence, but also throughout exploration and learning. Lagrangian methods are a classic approach to solving constrained optimization problems. For example, the equalityconstrained problem over the real vector x: min x f (x) s.t. g(x) = 0 (1) is transformed into an unconstrained one by introduction of a dual variable-the Lagrange multiplier, λ-to form the Lagrangian: L(x, λ) = f (x) + λg(x), which is used to find the solution as: (x * , λ * ) = arg max λ min x L(x, λ) (2) Gradient-based algorithms iteratively update the primal and dual variables: −∇ x L(x, λ) = − ∇ x f (x) − λ∇ x g(x) (3) ∇ λ L(x, λ) = g(x) (4) so that λ acts as a learned penalty coefficient in the objective, leading eventually to a constraint-satisfying solution (see e.g.  Bertsekas (2014) ). The Lagrangian multiplier method is readily adapted to the constrained RL setting  (Altman, 1998; Geibel & Wysotzki, 2011)  and has become a popular baseline in deep RL  (Achiam et al., 2017; Chow et al., 2019)  for its simplicity and effectiveness. Although they have been shown to converge to optimal, constraint-satisfying policies  (Tessler et al., 2018; Paternain et al., 2019) , a shortcoming of gradient Lagrangian methods for safe RL is that intermediate iterates often violate constraints. Cost overshoot and oscillations are in fact inherent to the learning dynamics  (Platt & Barr, 1988; Wah et al., 2000) , and we witnessed numerous problematic cases in our own experiments. Figure  1  (left) shows an example from a deep RL setting, where the cost and multiplier values oscillated throughout training. Our key insight in relation to this deficiency is that the traditional Lagrange multiplier update in (4) amounts to integral control on the constraint. The 90-degree phase shift between the curves is characteristic of ill-tuned integral controllers. Our contribution is to expand the scope of possible Lagrange multiplier update rules beyond (4), by interpreting the overall learning algorithm as a dynamical system. Specifically, we employ the next simplest mechanisms, proportional and derivative control, to λ, by adding terms corresponding to derivatives of the constraint function into (4) (derivatives with respect to learning iteration). To our knowledge, this is the first time that an expanded update rule has been considered for a learned Lagrange multiplier. PID control is an appealing enhancement, evidenced by the fact that it is one of the most widely used and studied control techniques  ( Åström & Hägglund, 2006) . The result is a more responsive safety mechanism, as demonstrated in Figure  1  (right), where the cost oscillations have been damped, dramatically reducing violations. Our contributions in this paper are outlined as follows. First, we provide further context through related works and preliminary definitions. In Section 4, we propose modified Lagrangian multiplier methods and analyze their benefits in the learning dynamics. Next, in Section 5, we cast constrained RL as a dynamical system with the Lagrange multiplier as a control input, to which we apply PID control as a new algorithm. In Section 6, we adapt a leading deep RL algorithm, Proximal Policy Optimization (PPO)  (Schulman et al., 2017)  with our methods and achieve state of the art performance in the OpenAI Safety-Gym suite of environments  (Ray et al., 2019) . Finally, in Section 7 we introduce another novel technique that makes tuning easier by providing invariance to the relative numerical scales of rewards and costs, and we demonstrate it in a further set of experiments. Our extensive empirical results show that our algorithms, which are intuitive and simple to implement, improve cost performance and promote hyperparameter robustness in a deep RL setting. \n Related Work Constrained Deep RL. Adaptations of the Lagrange multiplier method to the actor-critic RL setting have been shown to converge to the optimal, constraint-satisfying solution under certain assumptions  (Tessler et al., 2018) . Convergence proofs have relied upon updating the multiplier more slowly than the policy parameters  (Tessler et al., 2018; Paternain et al., 2019) , implying many constraint-violating policy iterations may occur before the penalty comes into full effect. Several recent works have aimed at improving constraint satisfaction in RL over the Lagrangian method, but they tend to incur added complexity.  Achiam et al. (2017)  introduced Constrained Policy Optimization (CPO), a policy search algorithm with near-constraint satisfaction guarantees at every iteration, based on a new bound on the expected returns of two nearby policies. CPO includes a projection step on the policy parameters, which in practice requires a time-consuming backtracking line search. Yet, simple Lagrangian-based algorithms performed as well or better in a recent empirical comparison in Safety Gym  (Ray et al., 2019) . Approaches to safe RL based on Lyapunov functions have been developed in a series of studies  (Chow et al., 2018; , resulting in algorithms that combine a projection step, as in CPO, with action-layer interventions like the safety layer of  Dalal et al. (2018) . Experimentally, this line of work showed mixed performance gains over Lagrangian methods, at a nontrivial cost to implement and without clear guidance for tuning.  developed interior point methods for RL, which augment the objective with logarithmic barrier functions. These methods are shown theoretically to provide suboptimal solutions. Furthermore, they require tuning of the barrier strength and typically assume already feasible iterates, the latter point possibly being problematic for random agent initializations or under noisy cost estimates. Most recently,  Yang et al. (2020)  extended CPO with a two-step projection-based optimization approach. In contrast to these techniques, our method remains nearly as simple to implement and compute as the baseline Lagrangian method. Dynamical Systems View of Optimization. Several recent works have proposed different dynamical systems viewpoints to analyze optimization algorithms, including those often applied to deep learning.  Hu & Lessard (2017)  reinterpreted first-order gradient optimization as a dynamical system; they likened the gradient of the objective, ∇ x f , to the plant, which the controller aims to drive to zero to arrive at the optimal parameters, x * . Basic gradient de-scent then matches the form of integral control (on ∇ x f ). They extend the analogy to momentum-based methods, for example linking Nesterov momentum to PID control with lag compensation. In another example,  An et al. (2018)  interpreted SGD as P-control and momentum methods as PI-control. They introduced a derivative term, based on the change in the gradient, and applied their resulting PID controller to improve optimization of deep convolutional networks. Other recent works bring yet other perspectives from dynamical systems to deep learning and optimization, see for example  (Lessard et al., 2014; Nishihara et al., 2015; Liu & Theodorou, 2019) ). None of these works address constrained RL, however, necessitating our distinct formulation for that problem. Constrained Optimization. Decades' worth of literature have accumulated on Lagrangian methods. But even recent textbooks on the topic  (Bertsekas, 2014; Nocedal & Wright, 2006)  only consider updating the Lagrange multiplier using the value of the constraint function, g(x), and miss ever using its derivatives, ġ(x) or g(x), which we introduce. The modification to the Lagrangian method most similar in effect to our proportional control term (here using ġ(x)) is the quadratic penalty method  (Hestenes (1969) ;  Powell (1969)  see also e.g.  Bertsekas (1976) ), which we compare in Section 4.  Song & Leland (1998)  proposed a controls viewpoint (continuous-time) of optimizing neural networks for constrained problems and arrived at proportional control rules only. Related to our final experiments on reward-scale invariance,  Wah et al. (2000)  developed an adaptive weighting scheme for continuous-time Lagrangian objectives, but it is an intricate procedure which is not straightforwardly applied to safe RL. \n Preliminaries Constrained Reinforcement Learning Constrained Markov Decision Processes (CMDP)  (Altman, 1998)  extend MDPs (see  Sutton & Barto (1998) ) to incorporate constraints into reinforcement learning. A CMDP is the expanded tuple (S, A, R, T, µ, C 0 , C 1 , ..., d 0 , d 1 , ...), with the cost functions C i : S × A × S → R defined by the same form as the reward, and d i : R denoting limits on the costs. For ease of notation, we will only consider a single, all-encompassing cost. The expected sum of discounted rewards over trajectories, τ = (s 0 , a 0 , s 1 , a 1 , ...), induced by the policy π(a|s) is a common performance objective: J(π) = E τ ∼π [ ∞ t=0 γ t R(s t , a t , s t+1 )]. The analogous value function for cost is defined as: J C (π) = E τ ∼π [ ∞ t=0 γ t C(s t , a t , s t+1 )]. The constrained RL problem is to solve for the best feasible policy: π * = arg max π J(π) s.t. J C (π) ≤ d (5) Deep reinforcement learning uses a deep neural network for the policy, π θ = π(•|s; θ) with parameter vector θ, and policy gradient algorithms improve the policy iteratively by gathering experience in the task to estimate the reward objective gradient, ∇ θ J(π θ ). Thus our problem of interest is better expressed as maximizing score at some iterate, π k , while ideally obeying constraints at each iteration: max π J(π k ) s.t. J C (π m ) ≤ d m ∈ {0, 1, ..., k} (6) Practical settings often allow trading reward performance against some constraint violations (e.g. the constraints themselves may include a safety margin). For this purpose we introduce a constraint figure of merit with our experiments. \n Dynamical Systems and Optimal Control Dynamical systems are processes which can be subject to an external influence, or control. A general formulation for discrete-time systems with feedback control is: x k+1 =F (x k , u k ) y k =Z(x k ) u k =h(y 0 , ..., y k ) (7) with state vector x, dynamics function F , measurement outputs y, applied control u, and the subscript denoting the time step. The feedback rule h has access to past and present measurements. A problem in optimal control is to design a control rule, h, that results in a sequence y 0:T . = {y 0 , ..., y T } (or x 0:T directly) that scores well according to some cost function C. Examples include simply reaching a goal condition, C = |y T − y|, or following close to a desired trajectory, y 0:T . Systems with simpler dependence on the input are generally easier to analyze and control (i.e. simpler h performs well), even if the dependence on the state is complicated  (Skelton, 1988) . Control-affine systems are a broad class of dynamical systems which are especially amenable to analysis  (Isidori et al., 1995) . They take the form: F (x k , u k ) = f (x k ) + g(x k )u k (8) where f and g may be nonlinear in state, and are possibly uncertain, meaning unknown. We will seek control-affine form for ease of control and to support future analysis. \n Modified Lagrangian Methods for Constrained Optimization Lagrangian methods are a classic family of approaches to solving constrained optimization problems. We propose an intuitive, previously overlooked form for the multiplier update and derive its beneficial effect on the learning dynamics. We begin by reviewing a prior formulation for the equality-constrained problem. 1 4.1. Review: \"Basic Differential Multiplier Method\" We follow the development of  Platt & Barr (1988) , who analyzed the dynamics of a continuous-time neural learning system applied to this problem (our result can similarly be derived for iterative gradient methods). They begin with the component-wise differential equations: ẋi = − ∂L(x, λ) ∂x i = − ∂f ∂x i − λ ∂g ∂x i (9) λ = α ∂L(x, λ) ∂λ = αg(x) (10) where we have inserted the scalar constant α as a learning rate on λ. Differentiating (9) and substituting with (10) leads to the second-order dynamics, written in vector format: ẍ + A ẋ + αg(x)∇g = 0 (11) which is a forced oscillator with damping matrix equal to the weighted sum of Hessians: A ij = ∂ 2 f ∂x i ∂x j + λ ∂ 2 g ∂x i ∂x j , or, A = ∇ 2 f + λ∇ 2 g (12) Platt &  Barr (1988)  showed that if A is positive definite, then the system (11) converges to a solution that satisfies the constraint.  Platt & Barr (1988)  also noted that the system (9)-(  10 ) is prone to oscillations as it converges into the feasible region, with frequency and settling time depending on α. We provide complete derivations of the dynamics in (11) and for our upcoming methods in an appendix. \n Proportional-Integral Multiplier Method In (10), λ simply integrates the constraint. To improve the dynamics towards more rapid and stable satisfaction of constraints, we introduce a new term in λ that is proportional to the current constraint value. In the differential equation for λ, this term appears as the time-derivative of the constraint: λ = αg(x) + β ġ(x) = αg(x) + β j ∂g ∂x j ẋj ( 13 ) with strength coefficient, β. Replacing (10) by (  13 ) and combining with (9) yields similar second-order dynamics as (11), except with an additional term in the damping matrix: ẍ + A + β∇g∇ ⊤ g ẋ + αg(x)∇g = 0 (14) The new term is beneficial because it is positive semidefinite-being the outer product of a vector with itself-so it can increase the damping eignevalues, boosting convergence. The results of  (Platt & Barr, 1988 ) hold under  (13, 14) , because the conditions of the solution, namely ẋ = 0 and g(x) = 0, remain unaffected and extend immediately to ġ(x) = 0 (and for the sequel, to g(x) = 0). To our knowledge, this is the first time that a proportional-integral update rule has been considered for a learned Lagrange multiplier. The well-known penalty method  (Hestenes, 1969; Powell, 1969)  augments the Lagrangian with an additional term, c 2 g(x) 2 , which produces a similar effect on the damping matrix, as shown in  (Platt & Barr, 1988) : A penalty = A + c∇g∇ ⊤ g + cg(x)∇ 2 g (15) Our approach appears to provide the same benefit, without the following two complications of the penalty method. First, the penalty term must be implemented in the derivative ẋ, whereas our methods do not modify the Lagrangian nor the derivative in (9). Second, the penalty introduces another instance of the hessian ∇ 2 g in the damping matrix, which might not be positive semi-definite but shares the proportionality factor, c, with the desired term. \n Integral-Derivative Multiplier Method A similar analysis extends to the addition of a term in λ based on the derivative of the constraint value. It appears in λ as the second derivative of the constraint: λ = αg(x) + γg(x) (16) with strength coefficient γ. The resulting dynamics are: ẍ + B −1 A ẋ + αg(x) + γ ẋ⊤ ∇ 2 g ẋ B −1 ∇g = 0 (17) with B = I + γ∇g∇ ⊤ g , and I the identity matrix. The effects of the derivative update method are two-fold. First, since the eigenvalues of the matrix B −1 will be less than 1, both the damping (A) and forcing (∇g) terms are weakened (and rotated, generally). Second, the new forcing term can be interpreted as a drag quadratic in the speed and modulated by the curvature of the constraint along the direction of motion. To illustrate cases, if the curvature of g is positive along the direction of travel, then this term becomes a force for decreasing g. If at the same time g(x) > 0, then the traditional force will also be directed to decrease g, so the two will add. On the other hand, if g curves negatively along the velocity, then the new force promotes increasing g; if g(x) > 0, then the two forces subtract, weakening the acceleration ẍ. By using curvature, the derivative method acts predictively, but may be prone to instability. The proportional-integral-derivative multiplier method is the combination of the previous two developments, which induced independent changes in the dynamics (i.e. insert the damping matrix of (  14 ) into (  17 )). We leave for future work a more rigorous analysis of the effects of the new terms, along with theoretical considerations of the values of coefficients α, β, and γ. In the next section, we carry the intuitions from our analysis to make practical enhancements to Lagrangian-based constrained RL algorithms. \n Feedback Control for Constrained RL We advance the broader consideration of possible multiplier update rules by reinterpreting constrained RL as a dynamical system; the adaptive penalty coefficient is a control input, and the cost threshold is a setpoint which the system should maintain. As the agent learns for rewards, the upward pressure on costs from reward-learning can change, requiring dynamic response. In practical Lagrangian RL, the iterates λ k may deviate from the optimal value, even for lucky initialization λ 0 = λ * , as the policy is only partially optimized at each iteration. Adaptive sequences λ 0 , ..., λ K other than those prescribed by the Lagrangian method may achieve superior cost control for Problem (6). In this section we relate the Lagrangian method to a dynamical system, formalizing how to incorporate generic update rules using feedback. We return to the case of an inequality constrained CMDP to present our main algorithmic contribution-the use of PID control to adapt the penalty coefficient. \n Constrained RL as a Dynamical System We write constrained RL as the first-order dynamical system: θ k+1 =F (θ k , λ k ) y k =J C (π θ k ) λ k =h(y 0 , ..., y k , d) (18) where F is an unknown nonlinear function 2 corresponding to the RL algorithm policy update on the agent's parameter vector, θ. The cost-objective serves as the system measure, y, which is supplied to the feedback control rule, h, along with cost limit, d. From this general starting point, both the RL algorithm, F , and penalty coefficient update rule, h, can be tailored for solving Problem (6). The reward and cost policy gradients of the first-order 3 Lagrangian method, ∇ θ L(θ, λ) = ∇ θ J(π θ ) − λ∇ θ J C (π θ ), can be organized into the form of (18) as: F (θ k , λ k ) = f (θ k ) + g(θ k )λ k (19) f (θ k ) = θ k + η∇ θ J(π θ k ) (20) 2 Known as an \"uncertain\" nonlinear function in the control literature, meaning we lack an analytical expression for it.  3  We discuss only the first-order case, which provides sufficient clarity for our developments. \n g(θ k ) = −η∇ θ J C (π θ k ) (21) with SGD learning rate η. The role of the controller is to drive inequality constraint violations (J c − d) + to zero in the presence of drift from reward-learning due to f . The Lagrange multiplier update rule for an inequality constraint uses subgradient descent: λ k+1 = (λ k + K I (J C − d)) + (22) with learning rate K I and projection into λ ≥ 0. This update step is clearly an integral control rule, for h. \n Constraint-Controlled RL Our general procedure, constraint-controlled RL, is given in Algorithm 1. It follows the typical minibatch-RL scheme, and sampled estimates of the cost criterion, ĴC are fed back to control the Lagrange multiplier. In contrast to prior work  (Tessler et al., 2018; Paternain et al., 2019)  which uses a single value approximator and treats r + λc as the reward, we use separate value-and cost-value approximators, since λ may change rapidly. When λ is large, the update in (  19 ) can cause excessively large change in parameters, θ, destabilizing learning. To maintain consistent step size, we use a re-scaled objective for the θ-learning loop: θ * (λ) = arg max θ J − λJ C = arg max θ 1 1 + λ (J − λJ C ) This convex combination of objectives yields the policy gradient used in Algorithm 1. Our experiments use this re-scaling, including for traditional Lagrangian baselines.  a ∼ π(•|s; θ), s ′ ∼ T (s, a), 7: r ∼ R(s, a, s ′ ), c ∼ C(s, a, s ′ ) 8: Apply feedback control: Update critics, V φ (s), V C,ψ (s) ⊲ if using 13: ∇ θ L = 1 1+λ ∇ θ Ĵ(π θ ) − λ∇ θ ĴC (π θ ) 14: until converged 15: return π θ 16: end procedure As an aside, we note that it is possible to maintain the control-affine form of (  19 ) with this re-scaling, by reparam-eterizing the control as 0 ≤ u = λ 1+λ ≤ 1 and substituting for (21) with: g(θ k ) = −η∇ θ (J(π θ k ) + J C (π θ k )) (23) This parameterization simply weights the reward and cost gradients in the Lagrangian objective as: ∇ θ L(θ, λ) = (1 − u)∇ θ J(π θ ) − u∇ θ J C (π θ ) (24) It may provide superior performance in some cases, as it will behave differently in relation to the nonlinearity in control which arises from the inequality constraint. We leave experimentation with direct control on u ∈ [0, 1] to future work. \n The PID Lagrangian Method We now specify a new control rule for use in Algorithm 1. To overcome the shortcomings of integral-only control, we follow the developments of the previous section and introduce the next simplest components: proportional and derivative terms. Our PID update rule to replace (  22  return λ \n PID Control Experiments We investigated the performance of our algorithms on Problem (6) in a deep RL setting. In particular, we show the effectiveness of PID control at reducing constraint violations from oscillations and overshoot present in the baseline Lagrangian method. Both maximum performance and robustness to hyperparameter selection are considered. Although many methods exist for tuning PID parameters, we elected to do so manually, demonstrating ease of use. \n Environments: Safety-Gym We use the recent Safety-Gym suite  (Ray et al., 2019) , which consists of robot locomotion tasks built on the MuJoCo simulator  (Todorov et al., 2012) . The robots range in complexity from a simple Point robot to the 12-jointed Doggo, and they move in an open arena floor. Rewards have a small, dense component encouraging movement toward the goal, and a large, sparse component for achieving it. When a goal is achieved, a new goal location is randomly generated, and the episode continues until the time limit at 1,000 steps. Each task has multiple difficulty levels corresponding to density and type of hazards, which induce a cost when contacted by the robot (without necessarily hindering its movement). Hazards are placed randomly at each episode and often lay in the path to the goal. Hence the aims of achieving high rewards and low costs are in opposition. The robot senses the position of hazards and the goal through a coarse, LIDAR-like mode. The output of this sensor, along with internal readings like the joint positions and velocities, comprises the state fed to the agent. Figure  2  displays a scene from the DOGGOGOAL1 environment.  \n Algorithm: Constraint-Controlled PPO We implemented Algorithm 1 on top of Proximal Policy Optimization (PPO)  (Schulman et al., 2017)  to make constraintcontrolled PPO (CPPO). CPPO uses an analogous clipped surrogate objective for the cost as for the reward. Our policy is a 2-layer MLP followed by an LSTM with a skip connection. We applied smoothing to proportional and derivative controls to accommodate noisy estimates. The environments' finite horizons allowed use of nondiscounted episodic costs as the constraint and input to the controller. Additional training details can be found in supplementary materials, and our implementation is available at https://github.com/astooke/safe-rlpyt. \n Main Results We compare PID controller performance against the Lagrangian baseline under a wide range of settings. Plots showing the performance of the unconstrained analogue confirm that constraints are not trivially satisfied, and they appear in supplementary material. \n ROBUST SAFETY WITH PI CONTROL We observed cost oscillations or overshoot with slow settling time in a majority of Safety Gym environments when using the Lagrangian method. Figure  3  shows an example where PI-control eliminated this behavior while maintaining good reward performance, in the challenging DOGGOBUTTON1 environment. Individual are plotted for different cost limits. As predicted in  (Platt & Barr, 1988) , we found the severity of cost overshoot and oscillations to depend on the penalty coefficient learning rate, K I . The top left panel of Figure  4  shows example cost curves from DOGGOGOAL2 under I-control, over a wide range of values for K I (we refer to varying K I , assuming K I = 1; the two are interchangeable in our design). With increasing K I , the period and ampli-tude of cost oscillations decrease and eventually disappear. The bottom left of Figure  4 , however, shows that larger K I also brings diminishing returns. We study this effect in the next section. The center and right columns of Figure  4  show the cost and return when using PI-control, with K P = 0.25 and K P = 1, respectively. Proportional control stabilized the cost, with most oscillations reduced to the noise floor for K I > 10 −4 . Yet returns remained relatively high over a wide range, K I < 10 −1 . Similar curves for other Safety Gym environments are included in an appendix.  We examine the trade-off between reward and constraint violation by forming an overall cost figure of merit (FOM). We use the sum of non-discounted constraint violations over the learning iterates, C F OM = k (D(π θ k ) − d) + , D(π θ ) = E τ ∼π T t=0 C(s t , a t , s ′ t ) , and estimate it online from the learning data. Figure  5  compares final returns against this cost FOM for the same set of experiments as in Figure  4 . Each point represents a different setting of K I , averaged over four runs. PI-control expanded the Pareto frontier of this trade-off into a new region of high rewards at relatively low cost which was inaccessible using the Lagrangian method. These results constitute a new state of the art over the benchmarks in  Ray et al. (2019) . We performed similar experiments on several Safety Gym environments in addition to DOGGOGOAL2: POINTGOAL1, the simplest domain with a point-like robot, CARBUTTON1, for slightly more challenging locomotive control, and DOG-GOBUTTON1 for another challenging task (see appendix for learning curves like Figure  4 ). for two strengths of added proportional control, for these environments. PI-control clearly improved the cost FOM (lower is better) for K I < 10 −1 , above which the fast integral control dominated. Hence robustness to the value for K I was significantly improved in all the learning tasks studied. . Learning run cost FOM versus penalty learning rate, KI , from four environments spanning the robots in Safety Gym. Each point is an average over four runs. In all cases, PI-control improves performance (lower is better) over a wide and useful range of KI , easing selection of that hyperparameter. \n CONTROL EFFICIENCY We further investigated why increasing the penalty learning rate, K I , eventually reduces reward performance, as was seen in the robustness study. Figure  7  shows learning curves for three settings: I-and PI-control with the same, moderate K I = 10 −3 , and I-control with high K I = 10 −1 . The high-K I setting achieved responsive cost performance but lower long-term returns, which appears to result from wildly fluctuating control. In contrast, PI-control held relatively steady, despite the noise, allowing the agent to do reward-learning at every iteration. The bottom panel displays individual control iterates, here displayed as u = λ/(1 + λ), over the first 7M environment steps, while the others show smoothed curves over the entire learning run, over 40M steps.  It was further able to slow the approach of the cost curve towards the limit, a desirable behavior for online learning systems requiring safety monitoring. Curves for other environments are available in an appendix. \n Reward-Scale Invariance In the preceding sections, we showed that PID control improves hyperparameter robustness in every constrained RL environment we tested. Here we propose a complementary method to promote robustness both within and across environments. Specifically, it addresses the sensitivity of learning dynamics to the relative numerical scale of reward and cost objectives. Consider two CMDPs that are identical except that in one the rewards are scaled by a constant factor, ρ. The optimal policy parameters, θ * remain unchanged, but clearly λ * must scale by ρ. To attain the same learning dynamics, all controller settings, λ 0 , K I , K P , and K D must therefore be scaled by ρ. This situation might feature naturally within a collection of related learning environments. Additionally, within the course of learning an individual CMDP, the balance between reward and cost magnitudes can change considerably, placing burden on the controller to track the necessary changes in the scale of λ. One way to promote performance of a single choice of controller settings across these cases would be to maintain a fixed meaning for the value of λ in terms of the relative influence of reward versus cost on the parameter update. To this end, we introduce an adjustable scaling factor, β k , in the policy gradient: ∇ θ L = (1 − u k )∇ θ J(π θ k ) − u k β k ∇ θ J C (π θ k ) (25) A conspicuous choice for β k is the ratio of un-scaled policy gradients: β ∇,k = ||∇ θ J(π θ k )|| ||∇ θ J C (π θ k )|| (26) since it balances the total gradient to have equal-magnitude contribution from reward-and cost-objectives at λ = 1 and encourages λ * = 1. Furthermore, β ∇ is easily computed with existing algorithm components. To test this method, we ran experiments on Safety Gym environments with their rewards scaled up or down by a factor of 10. Figure  9  shows a representative cross-section of results from the POINTGOAL1 environment using PI-control. The different curves within each plot correspond to different reward scaling. Without objective-scaling (i.e. β = 1), the dynamics under ρ = 10 are as if controller parameters were instead divided by 10, and likewise for ρ = 0.1. Note the near-logarithmic spacing of λ (λ ρ=10 has not converged to its full value). Using β ∇ , on the other hand, the learning dynamics are nearly identical across two orders of magnitude of reward scale. λ 0 = 1 becomes an obvious choice for initialization, a point where previous theory provides little guidance  (Chow et al., 2019)  (although here we left λ 0 = 0). Experiments in other environments and controller settings yielded similar results and are included in supplementary materials. Other methods, such running normalization of rewards and costs, could achieve similar effects and are worth investigating, but our simple technique is surprisingly effective and is not specific to RL.  \n Conclusion Starting from a novel development in classic Lagrangian methods, we introduced a new set of constrained RL solutions which are straightforward to understand and implement, and we have shown them to be effective when paired with deep learning. Several opportunities for further work lay ahead. Analysis of the modified Lagrangian method and constrained RL as a dynamical system may relax theoretical requirements for a slowly-changing multiplier. The mature field of control theory (and practice) provides tools for tuning controller parameters. Lastly, the control-affine form may assist in both analysis (see  Liang-Liang Xie & Lei Guo (2000)  and  Galbraith & Vinter (2003)  for controllability properties for uncertain nonlinear dynamics) and by opening to further control techniques such as feedback linearization. Our contributions improve perhaps the most commonly used constrained RL algorithm, which is a workhorse baseline. We have addressed its primary shortcoming while preserving its simplicity and even making it easier to use-a compelling combination to assist in a wide range of applications. Figure 1 . 1 Figure1. Left: The traditional Lagrangian method exhibits oscillations with 90 • phase shift between the constraint function and the Lagrange multiplier, characteristic of integral control. Right: PID control on the Lagrange multiplier damps oscillations and obeys constraints. Environment: DOGGOBUTTON1, cost limit 200. \n ) is shown in Algorithm 2. The proportional term will hasten the response to constraint violations and dampen oscillations, as derived in Section 4. Unlike the Lagrangian update, derivative control can act in anticipation of violations. It can both prevent cost overshoot and limit the rate of cost increases within the feasible region, useful when monitoring a system for further safety interventions. Our derivative term is projected as (•) + so that it acts against increases in cost but does not impede decreases. Overall, PID control provides a much richer set of controllers while remaining nearly as simple to implement; setting K P = K D = 0 recovers the traditional Lagrangian method. The integral term remains necessary for eliminating steady-state violations at convergence. Our experiments mainly focus on the effects of proportional and derivative control of the Lagrange multiplier in constrained deep RL.Algorithm 2 PID-Controlled Lagrange Multiplier 1: Choose tuning parameters: K P , K I , K D ≥ 0 2: Integral: I ← 0 3: Previous Cost: J C,prev ← 0 4: repeat at each iteration k ← (K P ∆ + K I I + K D ∂) + 10: J C,prev ← J C 11: \n Figure 2 . 2 Figure 2. Rendering from the DOGGOGOAL1 environment from Safety Gym. The red, four-legged robot must walk to the green cylinder while avoiding other objects, and receives coarse egocentric sensor readings of their locations. \n Figure 3 . 3 Figure 3. Oscillations in episodic costs (and returns) from the Lagrangian method, KP = 0, KI = 10 −2 , are damped by proportional control, KP = 1 (ours), at cost limits 50, 100, 150, 200 (curves shaded) in DOGGOBUTTON1. \n Figure 4 . 4 Figure 4. Top row: Constraint-violating oscillations decrease in magnitude and period from increases in the Lagrange multiplier learning rate, KI . At all levels, oscillations are damped by PIcontrol, KP = 0.25, 1. Bottom row: Returns diminish for large KI ; proportional control maintains high returns while reducing constraint violations. Environment: DOGGOGOAL2, cost limit 50. \n Figure 5 . 5 Figure 5. Pareto frontier of return versus cost FOM, which improves (up and to the left) with PI-control, KP = 0.25, 1. Each point is a different setting of KI (see Figure 4). \n Figure6. Learning run cost FOM versus penalty learning rate, KI , from four environments spanning the robots in Safety Gym. Each point is an average over four runs. In all cases, PI-control improves performance (lower is better) over a wide and useful range of KI , easing selection of that hyperparameter. \n Figure 7 . 7 Figure 7. I-and PI-control with moderate KI = 10 −3 and Icontrol with fast KI = 10 −1 (IK I +). Top Returns diminished for fast-KI , but high for PI. Second Cost oscillations mostly damped by PI, removed by fast-KI . Third Control (smoothed) varies more rapidly under fast-KI , is relatively steady for PI. Bottom Control over first 500 RL iterations; fast-KI slams the control to the extremes, causing the diminished returns. Environment: DOG-GOBUTTON1, cost limit 200. \n Figure 8 . 8 Figure8. Derivative control can prevent cost overshoot and slow the rate of cost increase within feasible regions, which the Lagrangian method cannot do. Environment: DOGGOBUTTON1, cost limit 200. \n Figure 9 . 9 Figure 9. Costs, returns, and Lagrange multiplier with rewards scaled by ρ ∈ {0.1, 1, 10}; PI-control with KI = 1e − 3, KP = 0.1. Left column: without objective-weighting, learning dynamics differ dramatically due to required scale of λ. Right column: with objective-weighting, learning dynamics are nearly identical. Environment: POINTGOAL1, cost limit 25. \n\t\t\t Standard techniques extend our results to inequality constraints, and multiple constraints, as in Platt & Barr (1988) , and notation is simplest for an equality constraint.", "date_published": "n/a", "url": "n/a", "filename": "stooke20a.tei.xml", "abstract": "Lagrangian methods are widely used algorithms for constrained optimization problems, but their learning dynamics exhibit oscillations and overshoot which, when applied to safe reinforcement learning, leads to constraint-violating behavior during agent training. We address this shortcoming by proposing a novel Lagrange multiplier update method that utilizes derivatives of the constraint function. We take a controls perspective, wherein the traditional Lagrange multiplier update behaves as integral control; our terms introduce proportional and derivative control, achieving favorable learning dynamics through damping and predictive measures. We apply our PID Lagrangian methods in deep RL, setting a new state of the art in Safety Gym, a safe RL benchmark. Lastly, we introduce a new method to ease controller tuning by providing invariance to the relative numerical scales of reward and cost. Our extensive experiments demonstrate improved performance and hyperparameter robustness, while our algorithms remain nearly as simple to derive and implement as the traditional Lagrangian approach.", "id": "e7830d87925f6865801569ad196b675e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Owain Evans", "Andreas Stuhlm", "Noah D Goodman"], "title": "Learning the Preferences of Ignorant, Inconsistent Agents", "text": "Introduction The problem of learning a person's preferences from observations of their choices features prominently in economics  (Hausman 2011) , in cognitive science  (Baker, Saxe, and Tenenbaum 2011; Ullman et al. 2009) , and in applied machine learning  (Jannach et al. 2010; Ermon et al. 2014) . To name just one example, social networking sites use a person's past behavior to select what stories, advertisements, and potential contacts to display to them. A promising approach to learning preferences from observed choices is to Copyright c 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. invert a model of rational choice based on sequential decision making given a real-valued utility function  (Russell and Norvig 1995) . This approach is known as Inverse Reinforcement Learning  (Ng and Russell 2000)  in an RL setting and as Bayesian Inverse Planning  (Baker, Saxe, and Tenenbaum 2009)  in the setting of probabilistic generative models. This kind of approach usually assumes that the agent makes optimal decisions up to \"random noise\" in action selection  (Kim et al. 2014; Zheng, Liu, and Ni 2014) . However, human deviations from optimality are more systematic. They result from persistent false beliefs, sub-optimal planning, and from biases such as time inconsistency and framing effects  (Kahneman and Tversky 1979) . If such deviations are modeled as unstructured errors, we risk mistaken preference inferences. For instance, if an agent repeatedly fails to choose a preferred option due to a systematic bias, we might conclude that the option is not preferred after all. Consider someone who smokes every day while wishing to quit and viewing their actions as regrettable. In this situation, a model that has good predictive performance might nonetheless fail to identify what this person values. In this paper, we explicitly take into account structured deviations from optimality when inferring preferences. We construct a model of sequential planning for agents with inaccurate beliefs and time-inconsistent biases (in the form of hyperbolic discounting). We then do Bayesian inference over this model to jointly infer an agent's preferences, beliefs and biases from sequences of actions in a simple Gridworld-style domain. To demonstrate that this algorithm supports accurate preference inferences, we first exhibit a few simple cases where our model licenses conclusions that differ from standard approaches, and argue that they are intuitively plausible. We then test this intuition by asking impartial human subjects to make preference inferences given the same data as our algorithm. This is based on the assumption that people have expertise in inferring the preferences of others when the domain is simple and familiar from everyday experience. We find that our algorithm is able to make the same kinds of inferences as our human judges: variations in choice are explained as being due to systematic factors such as false beliefs and strong temptations, not unexplainable error. The possibility of false beliefs and cognitive biases means that observing only a few actions often fails to identify a single set of preferences. We show that humans recognize this ambiguity and provide a range of distinct explanations for the observed actions. When preferences can't be identified uniquely, our model is still able to capture the range of explanations that humans offer. Moreover, by computing a Bayesian posterior over possible explanations, we can predict the plausibility of explanations for human subjects. \n Computational Framework Our goal is to infer an agent's preferences from observations of their choices in sequential decision problems. The key question for this project is: how are our observations of behavior related to the agent's preferences? In more technical terms, what generative model  (Tenenbaum et al. 2011)  best describes the agent's approximate sequential planning given some utility function? Given such a model and a prior on utility functions, we could \"invert\" it (by performing full Bayesian inference) to compute a posterior on what the agent values. The following section describes the class of models we explore in this paper. We first take an informal look at the specific deviations from optimality that our agent model includes. We then define the model formally and show our implementation as a probabilistic program, an approach that clarifies our assumptions and enables easy exploration of deviations from optimal planning. \n Deviations from optimality We consider two kinds of deviations from optimality: False beliefs and uncertainty Agents can have false or inaccurate beliefs. We represent beliefs as probability distributions over states and model belief updates as Bayesian inference. Planning for such agents has been studied in work on POMDPs  (Kaelbling, Littman, and Cassandra 1998) . Inferring the preferences of such agents was studied in recent work  (Baker and Tenenbaum 2014; Panella and Gmytrasiewicz 2014) . Here, we are primarily interested in the interaction of false beliefs with other kinds of sub-optimality. Temporal inconsistency Agents can be time-inconsistent (also called \"dynamically inconsistent\"). Time-inconsistent agents make plans that they later abandon. This concept has been used to explain human behaviors such as procrastination, temptation and pre-commitment  (Ainslie 2001) , and has been studied extensively in psychology  (Ainslie 2001)  and in economics  (Laibson 1997; O'Donoghue and Rabin 2000) . A prominent formal model of human time inconsistency is the model of hyperbolic discounting  (Ainslie 2001) . This model holds that the utility or reward of future outcomes is discounted relative to present outcomes according to a hyperbolic curve. For example, the discount for an outcome occurring at delay d from the present might be modeled as a multiplicative factor 1 1+d . The shape of the hyperbola means that the agent takes $100 now over $110 tomorrow, but would prefer to take $110 after 31 days to $100 after 30 days. The inconsistency shows when the 30th day comes around: now, the agent switches to preferring to take the $100 immediately. This discounting model does not (on its own) determine how an agent plans sequentially. We consider two kinds of time-inconsistent agents. These agents differ in terms of whether they accurately model their future choices when they construct plans. First, a Sophisticated agent has a fully accurate model of its own future decisions. Second, a Naive agent models its future self as assigning the same (discounted) values to options as its present self. The Naive agent fails to accurately model its own time inconsistency.  1  We illustrate Naive and Sophisticated agents with a decision problem that we later re-use in our experiments. The problem is a variant of Gridworld where an agent moves around the grid to find a place to eat (Figure  1 ). In the left pane (Figure  1a ), we see the path of an agent, Alice, who moves along the shortest path to the Vegetarian Cafe before going left and ending up eating at Donut Store D2. This behavior is sub-optimal independent of whether her preference is for the Vegetarian Cafe or the Donut Store, but can be explained in terms of Naive time-inconsistent planning. From her starting point, Alice prefers to head for the Vegetarian Cafe (as it has a higher undiscounted utility than the Donut Store). She does not predict that when close to the Donut Store (D2), she will prefer to stop there due to hyperbolic discounting. The right pane (Figure  1b ) shows what Beth, a Sophisticated agent with similar preferences to Alice, would do in the same situation. Beth predicts that, if she took Alice's route, she would end up at the Donut Store D2. So she instead takes a longer route in order to avoid temptation. If the longer route wasn't available, Beth could not get to the Vegetarian Cafe without passing the Donut Store D2. In this case, Beth would either go directly to Donut Store D1, which is slightly closer than D2 to her starting point, or (if utility for the Vegetarian Cafe is sufficiently high) she would correctly predict that she will be able to resist the temptation. \n Formal model definition We first define an agent with full knowledge and no time inconsistency, 2 and then generalize to agents that deviate from optimality. We will refer to states s ∈ S, actions a ∈ A, a deterministic utility function U : S ×A → R, a stochastic action choice function C : S → A, and a stochastic state transition function T : S × A → S. To refer to the probability that C(s) returns a, we use C(a; s). Optimal agent: full knowledge, no discounting Like all agents we consider, this agent chooses actions in proportion to exponentiated expected utility (softmax):  [a]  The noise parameter α modulates between random choice (α = 0) and perfect maximization (α = ∞). Expected utility depends on both current and future utility: C(a; s) ∝ e αEUs EU s [a] = U (s, a) + E s ,a [EU s [a ]] with s ∼ T (s, a) and a ∼ C(s ). Note that expected future utility recursively depends on C-that is, on what the agent assumes about how it will make future choices. Figure  2 : We specify agents' decision-making processes as probabilistic programs. This makes it easy to encode arbitrary biases and decision-making constraints. When automated inference procedures invert such programs to infer utilities from choices, these constraints are automatically taken into account. Note the mutual recursion between agent and expUtility: the agent's reasoning about future expected utility includes a (potentially biased) model of its own decision-making. \n Time-inconsistent agent To compute expected utility, we additionally take the expectation over states. Now EU p(s),o,d [a] is defined as: Inferring preferences We define a space of possible agents based on the dimensions described above (utility function U , prior p(s), discount parameter k, noise parameter α). We additionally let Y be a variable for the agent's type, which fixes whether the agent discounts at all, and if so, whether the agent is Naive or Sophisticated. So, an agent is defined by a tuple θ := (p(s), U, Y, k, α), and we perform inference over this space given observed actions. The posterior joint distribution on agents conditioned on action sequence a 0:T is: E s∼p(s|o) 1 1 + kd U (s, a) + E s , P (θ|a 0:T ) ∝ P (a 0:T |θ)P (θ) (1) The likelihood function P (a 0:T |θ) is given by the multistep generalization of the choice function C corresponding to θ. For the prior P (θ), we use independent uniform priors on bounded intervals for each of the components. In the following, \"the model\" refers to the generative process that  \n Sophisticated Figure  3 : Given data corresponding to Figure  1 , the model infers a joint posterior distribution on preferences, beliefs and other agent properties (such as discount strength) that reveals relations between different possible inferences from the data. The darker a cell, the higher its posterior probability. involves a prior on agents and a likelihood for choices given an agent. \n Agents as probabilistic programs We implemented the model described above in the probabilistic programming language WebPPL (Goodman and Stuhlmüller 2014). WebPPL provides automated inference over functional programs that involve recursion. This means that we can directly translate the recursions above into programs that represent an agent and the world simulation used for expected utility calculations. All of the agents above can be captured in a succinct functional program that can easily be extended to capture other kinds of sub-optimal planning. Figure  2  shows a simplified example (including hyperbolic discounting but not uncertainty over state). For the Bayesian inference corresponding to Equation 1 we use a discrete grid approximation for the continuous variables (i.e. for U , p(s), k and α) and perform exact inference using enumeration with dynamic programming. \n Model inferences We now demonstrate that the model described above can infer preferences, false beliefs and time inconsistency jointly from simple action sequences similar to those that occur frequently in daily life. We later validate this intuition in our experiments, where we show that human subjects make inferences about the agent that are similar to those of our model. Example 1: Inference with full knowledge We have previously seen how modeling agents as Naive and Sophisticated might predict the action sequences shown in Figures  1a and 1b  respectively. We now consider the inference problem. Given that these sequences are observed, what can be inferred about the agent? We assume for now that the agent has accurate beliefs about the restaurants and that the two Donut Stores D1 and D2 are identical (with D1 closer to the starting point).  4  We model each restaurant as having an immediate utility (received on arriving at the restaurant) and a delayed utility (received one time-step after). This interacts with hyperbolic discounting, allowing the model to represent options that are especially \"tempting\" when they can be obtained with a short delay. For the Naive episode (Figure  1a ) our model infers that either softmax noise is very high or that the agent is Naive (as explained for Alice above). If the agent is Naive, the utility of the Vegetarian Cafe must be higher than the Donut Store (otherwise, the agent wouldn't have attempted to go to the Cafe), but not too much higher (or the agent wouldn't give in to temptation, which it in fact does). This relationship is exhibited in Figure  3   Example 2: Inference with uncertainty In realistic settings, people do not have full knowledge of all facts relevant to their choices. Moreover, an algorithm inferring preferences will itself be uncertain about the agent's uncertainty. What can the model infer if it doesn't assume that the agent has full knowledge? Consider the Sophisticated episode (Figure  1b ). Suppose that the Noodle Shop is closed, and that the agent may or may not know about this. This creates another possible inference, in addition to Sophisticated avoidance of temptation and high noise: The agent might prefer the Noodle Shop and might not know that it is closed. This class of inferences is shown in Figure  3  (bottom): When the agent has a strong prior belief that the shop is open, the observations are most plausible if the agent also assigns high utility to the Noodle Shop (since only then will the agent attempt to go there). If the agent does not believe that the shop is open, the Noodle Shop's utility does not matter-the observations have the same plausibility either way. In addition, the model can make inferences about the agent's discounting behavior (Figure  3  right): When utility for the Vegetarian Cafe is low, the model can't explain the data well regardless of discount rate k (since, in this case, the agent would just go to the Donut Store directly). The data is best explained when utility for the Vegetarian Cafe and discount rate are in balance-since, if the utility is very high relative to k, the agent could have gone directly to the Vegetarian Cafe, without danger of giving in to the Donut Store's temptation. Example 3: Inference from multiple episodes Hyperbolic discounting leads to choices that differ systematically from those of a rational agent with identical preferences. A time-inconsistent agent might choose one restaurant more often than another, even if the latter restaurant provides more  \n Experiments with Human Subjects We have shown that, given short action sequences, our model can infer whether (and how) an agent is timeinconsistent while jointly inferring appropriate utilities. We claim that this kind of inference is familiar from everyday life and hence intuitively plausible. This section provides support for this claim by collecting data on the inferences of human subjects. In our first two experiments, we ask subjects to explain the behavior in Figures  1a and 1b . This probes not just their inferences about preferences, but also their inferences about biases and false beliefs that might have influenced the agent's choice. Experiment 1: Inference with full knowledge Experiment 1 corresponds to Example 1 in the previous section (where the agent is assumed to have full knowledge). Two groups of subjects were shown Figures  1a and 1b , having already seen two prior episodes showing evidence of a preference for the Vegetarian Cafe over the other restaurants. People were then asked to judge the plausibility of different explanations of the agent's behavior in each episode.  5  Results are shown in Figure  5 . In both Naive (Figure  1a ) and Sophisticated (1b) conditions, subjects gave the highest ratings to explanations involving giving in to temptation (Naive) or avoiding temptation (Sophisticated). Alternative explanations suggested that the agent wanted variety (having taking efficient routes to the Vegetarian Cafe in previous episodes) or that they acted purely based on a preference (for a long walk or for the Donut Store). Experiment 2: Inference with uncertainty Experiment 2 corresponds to Example 2 above. Subjects see one of the two episodes in Figure  1  (with Figure  1a  modified so D1 and D2 can differ in utility and Figure  1b  modified so the Noodle Shop is closed). There is no prior information about the agent's preferences, and the agent is not known to have accurate beliefs. We asked subjects to write explanations for the agent's behavior in the two episodes and coded these explanations into four categories. Figure  6  specifies which formal agent properties correspond to which category. While not all explanations correspond to something the model can infer about the agent, the most common explanations map cleanly onto the agent properties θ-few explanations provided by people fall into the \"Other\" category (Figure  7 ). The model inferences in this figure show the marginal likelihood of the observed actions given the corresponding property of θ, normalized across the four property types. In both the Naive and the Sophisticated case, the model and people agree on what the three highest-scoring properties are. Explanations involving false beliefs and preferences rate more highly than those involving time inconsistency. This is because, even if we specify whether the agent is Naive/So-  Experiment 3: Inference from multiple episodes Following Example 3 above, subjects (n=50) saw the episodes in Figure  4  and inferred whether the agent prefers the Vegetarian Cafe or the Donut Store. Like the model, the majority of subjects inferred that the agent prefers the Vegetarian Cafe. Overall, 54% (+/-7 for 95% CI) inferred a preference of Vegetarian Cafe over the Donut Store, compared to the 59% posterior probability assigned by the model. Episode 2 (in which the agent does not choose the Donut Store) is identical to the Sophisticated episode from Figure  1 . Experiments 1 and 2 showed that subjects explain this episode in terms of Sophisticated time-inconsistent planning. Together with Experiment 3, this suggests that subjects use this inference about the agent's planning to infer the agent's undiscounted preferences, despite having seen the agent choose the Donut Store more frequently. \n Conclusion AI systems have the potential to improve our lives by helping us make choices that involve integrating vast amounts of information or that require us to make long and elaborate plans. For instance, such systems can recommend and filter the information we see on social networks or music services and can construct intricate plans for travel or logistics. For these systems to live up to their promise, we must be willing to delegate some of our choices to them-that is, we need such systems to reliably act in accordance with our preferences and values. It can be difficult to formally specify our preferences in complex domains; instead, it is desirable to have systems learn our preferences, just as learning in other domains is frequently preferable to manual specification. This learning requires us to build in assumptions about how our preferences relate to the observations the AI system receives. As a starting point, we can assume that our choices result from optimal rational planning given a latent utility function. However, as our experiments with human subjects show, this assumption doesn't match people's intuitions on the relation between preferences and behavior, and we find little support for the simplistic model where what is chosen most is inferred to be the most valued. We exhibited more realistic models of human decision-making, which in turn supported more accurate preference inferences. By approaching preference inference as probabilistic induction over a space of such models, we can maintain uncertainty about preferences and other agent properties when the observed actions are ambiguous. This paper has only taken a first step in the direction we advocate. Two priorities for further work are applications to more realistic domains and the development of alternatives to using human preference inferences as a standard by which to evaluate algorithms. The goal for this emerging subfield of AI is to make systems better able to support humans even in domains where human values are complex and nuanced, and where human choices may be far from optimal. Figure 1 : 1 Figure 1: Agents with hyperbolic discounting exhibit different behaviors depending on whether they model their future discounting behavior in a manner that is (a) Naive (left) or (b) Sophisticated (right). \n o ,a EU p(s|o),o ,d+1 [a ] with s ∼ T (s, a), o ∼ p(o|s ) and a ∼ C(p(s|o), o , d + 1) (for the Naive agent) or a ∼ C(p(s|o), o , 0) (for the Sophisticated agent). \n (top left), which shows the model posterior for the utilities of the Donut Store and Vegetarian Cafe (holding fixed the other agent components Y , k, and α). \n Figure 4 : 4 Figure 4: The observations in Experiment 3 show the Donut Chain Store being chosen twice and the Vegetarian Cafe once. \n Figure 5 : 5 Figure5: Explanations in Experiment 1 for the agent's behavior in Figure1a(Naive) and 1b (Sophisticated). Subjects (n=120) knew that the agent has accurate knowledge, and saw prior episodes providing evidence of a preference for the Vegetarian Cafe. Subjects selected scores in {1, 2, 3}. \n Figure 6 :Figure 7 : 67 Figure6: Map from properties invoked in human explanations to formalizations in the model. The left column describes the property. The center column shows how we formalized it in terms of the variables used to define an agent θ. The right column gives an explanation (from our dataset of human subjects) that invokes this property. \n Now the agent's choice and expected utility function are parameterized by a delay d, which together with a constant k controls how much to discount future utility: var agent = function(state, delay){ return Marginal( function(){ var action = uniformDraw(actions) var eu = expUtility(state, action, delay) factor(alpha * eu) return action }) } var expUtility = function(state, action, delay){ if (isFinal(state)){ return 0 } else { var u = 1/(1 + k * delay) * utility(state, action) return u + Expectation(function(){ var nextState = transition(state, action) var nextAction = sample(agent(nextState, delay+1)) return expUtility(nextState, nextAction, delay+1) }) } } EU s,d [a] = 1 1 + kd U (s, a) + E s ,a The agent's choice and expected utility functions are now parameterized by the distribution p(s) and the current ob- servation o: C(a; p(s), o, d) ∝ e αEU p(s),o,d [a] C(a; s, d) ∝ e αEU s,d[a]    [EU s ,d+1[a ]] with s ∼ T (s, a). For the Naive agent, a ∼ C(s , d + 1), whereas for the Sophisticated agent, a ∼ C(s , 0). When we compute what the agent actually does in state s, we set d to 0. As a consequence, only the Sophisticated agent correctly predicts its future actions.3  An implementation of the Naive agent as a probabilistic program is shown in Figure2.Time-inconsistent agent with uncertaintyWe now relax the assumption that the agent knows the true world state. Instead, we use a distribution p(s) to represent the agent's belief about which state holds. Using a likelihood function p(o|s), the agent can update this belief: p(s|o) ∝ p(s)p(o|s) \n = open) > 0.85 \"He was heading towards the noodle shop first, but when he got there, it was closed, so he continued on the path and ended up settling for ... vegetarian cafe.\" Property Formalization Example explanation from our human subjects Agent doesn't know p(D1 = open) < 0.15 \"He decided he wanted to go to the Donut Store for lunch. He Donut Store D1 is open. did not know there was a closer location\" Agent falsely believes Noodle Shop is open. p(N Agent prefers D2 to D1. U (D2) > U(D1) \"He might also enjoy the second donut shop more than the first\" Agent is Naive / Sophisti- Y = Naive/Soph. \"He ... headed for the Vegetarian Cafe, but he had to pass by cated. the Donut shop on his way. The temptation was too much to fight, so he ended up going into the Donut Shop.\" \n\t\t\t Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence  \n\t\t\t The distinction and formal definition of Naive and Sophisticated agents is discussed in O'Donoghue and Rabin (1999). \n\t\t\t This is the kind of agent assumed in the standard setup of an MDP (Russell and Norvig 1995)  3 This foresight allows the Sophisticated agent to avoid tempting states when possible. If such states are unavoidable, the Sophisticated agent will choose inconsistently. \n\t\t\t In Experiment 2, we allow the utilities for D1 and D2 to be different. See row 3 of Figure6and the \"Preference\" entry for Sophisticated in Figure7. \n\t\t\t In a pilot study, we showed subjects the same stimuli and had them write free-form explanations. In Experiment 1, subjects had to judge four of the explanations that occurred most frequently in this pilot.", "date_published": "n/a", "url": "n/a", "filename": "12476-55467-1-PB.tei.xml", "abstract": "An important use of machine learning is to learn what people value. What posts or photos should a user be shown? Which jobs or activities would a person find rewarding? In each case, observations of people's past choices can inform our inferences about their likes and preferences. If we assume that choices are approximately optimal according to some utility function, we can treat preference inference as Bayesian inverse planning. That is, given a prior on utility functions and some observed choices, we invert an optimal decision-making process to infer a posterior distribution on utility functions. However, people often deviate from approximate optimality. They have false beliefs, their planning is sub-optimal, and their choices may be temporally inconsistent due to hyperbolic discounting and other biases. We demonstrate how to incorporate these deviations into algorithms for preference inference by constructing generative models of planning for agents who are subject to false beliefs and time inconsistency. We explore the inferences these models make about preferences, beliefs, and biases. We present a behavioral experiment in which human subjects perform preference inference given the same observations of choices as our model. Results show that human subjects (like our model) explain choices in terms of systematic deviations from optimal behavior and suggest that they take such deviations into account when inferring preferences.", "id": "c25d3b0a143fc772c5488af4d5282df6"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Siddharth Srivastava"], "title": "Unifying Principles and Metrics for Safe and Assistive AI", "text": "Introduction Recent years have witnessed immense progress in research on safe and assistive AI systems as well as on the potential impact of AI on the future of work. These directions of research address two sides of a common, fundamental concern: how would humans work with AI systems? While research on AI safety focuses on designing AI systems that allow humans to safely instruct and control them (e.g.,  (Russell, Dewey, and Tegmark 2015; Zilberstein 2015; Hadfield-Menell et al. 2016; Russell 2017; Hadfield-Menell et al. 2017 )), research on AI and the future of work focuses on the impact of AI on members of the workforce who may be unable to do so  (Arntz, Gregory, and Zierahn 2016; Manyika et al. 2017; Nedelkoska and Quintini 2018) . This paper presents the view that in addition to the productive streams of research outlined above, we need unifying metrics and declarative objectives that would allow a more uniform evaluation of AI systems on the extent to which an AI system is suitable for working with specific classes of human operators. It also presents a common principle for human-centered AI systems that allows the development of such metrics. Consequently, rather than proposing a specific new design for AI systems, the focus of this paper Copyright c 2021, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. is on elucidating the declarative principles and types of metrics that would lead to concerted progress on the problem. The advantage of this declarative approach to framing the problem is that it enables an assessment of progress independent of the internal design being used in an AI system, and it will help draw out the strengths and weaknesses of different design approaches. Without such a specification, design differences can make solution paradigms difficult to compare. E.g., one might develop a complex system architecture that builds user profiles and provides appropriate assistance. This system would have very different input requirements and design and performance parameters than a formulation that addresses the same problem by computing assistance policies using planning under partial observability while incorporating the value of information to learn more about a user's poorly articulated objectives and constraints. Better declarative objectives and metrics for assistive AI systems would also help ensure that, regardless of the methods being used, progress amounts to advancement towards safe and assistive AI systems. More pragmatically, such metrics will not only help end-users assess the utility of a given AI system but they will also help AI researchers and developers identify more readily the dimensions along which further research will be beneficial for applications of their interest. The next section presents a succession of intuitive principles for safe and assistive AI systems, and shows that evaluating the compatibility of a system with such principles (in particular P2) helps clarify the required types of metrics. The paper concludes by drawing the attention of our community towards research on the operationalization of such metrics along with promising research directions on developing systems that do well on them. \n Unifying Principles for Safe and Assistive AI Systems We focus on taskable AI systems that carry out user-assigned high-level tasks using arbitrary mechanisms for reasoning and planning over multiple time steps. E.g., household robots that can be given objectives such as setting the table or doing laundry, co-manufacturing robots that can assist workers in creating complex assemblies with heavy components, digital assistants that can plan a vacation given the The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21) user's preferences, etc. Such systems serve as sound integrative platforms and model end-to-end applications where the AI system is responsible for assistance in the execution of long-horizon tasks. AI systems are frequently evaluated in terms of performance measures such as the computational complexity of computing the required behavior, training data requirements, and the quality of the computed behavior in terms of execution time, resources used, risk of unsafe outcomes etc. We can consider systems that optimize such performance metrics as Level 0 of assistive AI systems. Level I of assistive AI systems Recent AI research has also focused on assistive properties of AI systems. We begin with a rather common-sensical principle defining Level I of such safe and assistive AI systems: P1: An AI system must make it easy for its operators to use it safely. The italicized terms denote dimensions along which compatibility of AI systems with principle P1 can be evaluated; while a lot of current AI research utilizes one or more of these dimensions for evaluation, a closer analysis reveals some new insights. In the context of this paper we consider using an AI system to be synonymous with instructing it to change its behavior as desired. Different interfaces may be used for this, including programming, text, speech, gestures etc. We consider the operators of an AI system as those persons who use it in the sense described above. For instance, if a self-driving car gives all its passengers the right to give it instructions, then all of them are its operators; if it gives instruction-rights to only a qualified set of users, perhaps adults who pass an assisted-driving exam, then the class of operators is defined by that qualification exam. Safety refers to the overall safety of the AI system's interactions with its environment, which may be physical or online. These dimensions of compatibility with P1 serve as natural dimensions for evaluating Level I assistive AI systems: E1. How inclusive is the set of operators? Systems whose operators require PhD-level expertise in AI may be less desirable for broader deployments. E2. How easy is it for the system's operators to change its behavior? E3. Which set of tasks can the AI system be used for? E4. What form of safety guarantees does the system provide? Systems that are unable to provide an upper bound on expected risks are clearly less desirable than those that stipulate conditions under which upper bounds can be provided. P1 serves to highlight the interplay between these dimensions of compliance and evaluation. Safety guarantees are often inversely related with the size of the operator set. A system may provide a high level of safety, but only under the requirement that its operators take extensive training programs. At one end of the spectrum, automated robot vacuum cleaners require almost no prior skills and perform limited, well-defined tasks. Safety issues are still present-a robot vacuum cleaner may pull on electrical cables that have been left on the floor; auto-completion software may send emails to unintended recipients. However, the lower expected damage from using such applications has made them broadly accepted in society. AI-powered industrial robots are at the other end of the spectrum: these devices require specialized training as well as operating environments in order to ensure safety (see for instance, ISO/TS 15066:2016 on collaborative robots). Typically, these systems operate in regions that humans cannot access when the robot is active unless the human is hand-guiding the robot within a safe operating envelope that limits the speed and range of operation. Their functionality is closely controlled and monitored. Only skilled engineers change their functionality while day-to-day operators monitor execution of predictable behavior and control run-stops from designated safe areas. Similarly, the safety of current airborne drone operations is ensured by requiring specially trained drone operators  (Marshall 2020) . Thus, principle P1 holds for AI systems today with varying degrees of compliance along E1-E4. The examples above illustrate how practical implementations often rely upon implicitly defined operator classes to provide acceptable levels of safety. Such approaches rely upon limiting the users and the scope of a system to achieve an acceptable level of compatibility with P1: it is easy for such systems' users to operate it safely because the set of users is required to be sufficiently skilled, and its functionality is sufficiently limited for that group to be able to safely use the device. However, a broader emphasis on the need to specify safety guarantees with respect to different classes of operators would help mitigate some of the risks associated with broadly deployed AI systems. In contrast to classical automated systems, AI systems feature a more nuanced interplay between the class of tasks that a system can be used for (E3) and the other dimensions above. Traditionally deployed systems (even automated systems) have a very well-defined boundary of use cases. This allows for an easier classification of safety. Taskable AI systems on the other hand, are expected to change their behavior and functionality as they learn and adapt to new environments or new user-given objectives. For such systems, we need better methods for deriving the range of instructions that different operator-groups are allowed to provide. Scenarios like the self-driving car that needs to decide whether to obey a child's instruction allude to this requirement. Methods for assessing user and AI competency can also allow the AI system to expand its range of functionality by drawing upon the expertise of its operator  (Basich et al. 2020)  while ensuring an acceptable level of safety. A major limitation of P1 and its associated metrics is that it does not evaluate the amount of training required for an individual to qualify as an operator for the system. This creates a blind-spot in evaluation of the ease-of-use or safety of an AI system: since user-training occurs outside the requirements outlined by P1, an unsafe AI system (or one that is deployed in an unsafe manner) would simply claim that its so-called operator was insufficiently trained! Furthermore, if P1 were a sufficient categorization of safe and assistive AI systems, we would have no need for explainable AI as compliance with P1 does not require the system to be easy to understand. An implicit emphasis on assessing AI systems only along some aspects of P1 may also explain the increasing prevalence of concerns about the workers who may be left behind in the future workplace. From this perspective it is unsurprising that these concerns have gained renewed interest at a time when AI applications have reached a level of maturity where they are being used by non-AI-experts in situations that have some inherent safety risks. However, the \"assistive\" nature of such AI systems is undermined by the need for highly skilled individuals who could safely debug, understand and modify the behavior of such systems. Level II of assistive AI systems In order to address the limitations of P1, we consider the following as a guiding principle for safe and assistive AI: P2: An AI system must make it easy for its operators to learn how to use it safely. P2 changes the notion of operators from those who are qualified to use a given AI system to those who are qualified to start learning how to use it. In addition to the metrics associated with P1, P2 introduces a new dimension: E5. How easy is it to learn how to use the AI system? What are the expected prerequisites and costs of training for its operators? Can training be provided on-the-job? This dimension could also be viewed as evaluating the resources required to train operators for P1 systems. Most AI systems in use today would perform poorly on this new dimension, and consequently, on compatibility with P2 as a whole. Explainable AI (e.g.,  (Ribeiro, Singh, and Guestrin 2016; Hayes and Shah 2017; Chakraborti et al. 2017; Hoffman et al. 2018; Gunning and Aha 2019; Weld and Bansal 2019; Anderson et al. 2019; Eifler et al. 2020 )) plays a key role along this dimension because systems that are easy to understand or that can explain themselves naturally make it easier for people to learn how to use them. P2 leverages the unique strengths of AI as a field of research. AI research already addresses the problem of estimating users' skills; research on intelligent tutoring systems and AI for education addresses the problem of identifying skill gaps. This can be used to determine the minimal differential training to be provided to an operator. P2 places the onus of training on the deployed AI system and opens up a new direction of interdisciplinary research connecting existing research directions in AI with research in humansystems engineering and in industrial engineering for the development of productive training modalities and the operationalization of metrics for E5. It also allows AI systems to formally characterize different scopes of functionality for different classes of operators, e.g., operators that use manufacturing robots for pre-determined tasks, those that give the robots new instructions, or those that are ready to learn about giving the robot new instructions. P2 is not required for every AI system-P1 would be sufficient for systems that place minimal requirements on operator qualifications (e.g., robot vacuum cleaners) and for non-adaptive AI systems that require a small set of operators. On the other hand, P2 serves as a better declarative foundation for evaluating taskable AI systems that are meant to assist large numbers of non-AI-experts on a wide range of tasks. Increasing concerns about job roles that would feature a high-degree of interaction with AI systems (and the workers that are likely to be left behind) allude to the pressing need for including E5, a dimension for evaluation under P2 (and not P1) as a part of an AI system's evaluation. AI systems that are not beneficial (either in terms of AI safety or in terms of the future of work) fare poorly on P2. E.g., systems that can thwart their users' objectives by wireheading and those that may derive incorrect objective functions from user instructions make it difficult for an operator to learn how to provide instructions that are specific enough to be safe, and fare poorly along E5. Similarly, systems that require extensive training investment to be used effectively and safely fail along E5. In this way P2 serves as a unifying principle encompassing research on AI safety as well as on AI for a beneficial future of work. \n Promising Directions of Research P2 serves as a declarative principle for guiding research on assistive AI systems as well as for developing metrics for evaluating AI systems and their deployments. Converting this principle into tangible metrics calls for interdisciplinary research including AI and other fields associated with human factors. The increasing prevalence of research thrusts on safe and assistive AI systems  (Fern et al. 2014; Russell, Dewey, and Tegmark 2015; Amodei et al. 2016; Gunning and Aha 2019)  makes this a particularly opportune phase for formalizing the metrics and the interfaces required for evaluating AI systems for compatibility with P2 along dimensions E1-E5. Recent research on AI safety and explainable AI develops methods improving the ease of use and safety of AI systems along P2 (see, for instance, the ICML 2020 Workshop on Explainable AI). Placing AI systems that compute user-skill aligned explanations  (Sreedharan, Srivastava, and Kambhampati 2018; Sreedharan et al. 2019 ) in a loop with AI systems for identifying user-skills and skill-gaps can help develop AI systems that gradually present users with new functionality and explain it, thereby training their users onthe-fly and as needed. Such systems would be better tuned towards P2, and towards addressing the underlying problems of AI safety and the future of work. Critically, ensuring progress towards safe and assistive AI systems requires that AI systems with arbitrary internal designs support assessment along the metrics developed for E1-E5. This raises a new set of research questions: Can we develop non-intrusive AI-interface requirements for supporting such evaluations in the face of changing operating environments and objectives? The need for such interfaces is even more pressing for systems that learn and those that undergo system updates after deployment. What is the minimal external interface that an AI system must support so as to allow its independent evaluation? How would changing the nature of such interfaces change the complexity of conducting such an evaluation? One would expect that AI sys-tems that offer more transparency would be easier to evaluate. Could we use the inherent reasoning capabilities of AI systems to develop interface requirements that would allow more adept systems to make such evaluations easier? E.g., rather than testing a manufacturing robot to discover its response to every possible situation, could we ask higher-level queries such as \"under which situations would you be able to create the proposed assembly?\" Clearly, the ease of assessment of an AI system would depend on the class of queries that it can answer. Recent work suggests that a minimal query-response interface for AI systems that connects the system with a simulator and observes its responses to high-level instructions can be quite powerful. Such an interface has a few distinct advantages. Current AI systems are already tested with simulators and they are inherently required to be able to take user instructions, so these interface requirements can be considered to be natural. They also allow the autonomous synthesis of query-policies: running the query-policy on a black-box taskable AI system can help construct an interpretable model of the limits and capabilities of that system  (Verma, Marpally, and Srivastava 2021) . Such models can be used to support the evaluations discussed above. Extensions of such interface requirements to arbitrary AI systems would help ensure that our AI systems are amenable to independent evaluation. Such a paradigm would allow users to assess their AI systems while freeing AI researchers and developers to utilize arbitrary internal implementations. Systems with interfaces that support more efficient and accurate independent assessment would be rewarded with greater public adoption of their products. Progress on these threads would help prevent undesirable situations such as insufficient support for independent evaluation of powerful AI systems, and the negative consequences of deployment of an insufficiently evaluated system.", "date_published": "n/a", "url": "n/a", "filename": "17769-Article Text-21263-1-2-20210518.tei.xml", "abstract": "The prevalence and success of AI applications have been tempered by concerns about the controllability of AI systems about AI's impact on the future of work. These concerns reflect two aspects of a central question: how would humans work with AI systems? While research on AI safety focuses on designing AI systems that allow humans to safely instruct and control AI systems, research on AI and the future of work focuses on the impact of AI on humans who may be unable to do so. This Blue Sky Ideas paper proposes a unifying set of declarative principles that enable a more uniform evaluation of arbitrary AI systems along multiple dimensions of the extent to which they are suitable for use by specific classes of human operators. It leverages recent AI research and the unique strengths of the field to develop human-centric principles for AI systems that address the concerns noted above.", "id": "4f3013f7a6238bf69bff939ac70f9ae1"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Martin Dresler", "Anders Sandberg", "Christoph Bublitz", "Kathrin Ohla", "Carlos Trenado", "Aleksandra Mroczko-Wąsowicz", "○,◆ Simone Kuḧn", "Dimitris Repantis"], "title": "Hacking the Brain: Dimensions of Cognitive Enhancement", "text": "INTRODUCTION An increasingly complex world exerts increasing demands on cognitive functionsfunctions that evolved for a fundamentally different environment. Daily life in an information society and a postindustrial economy require cognitive skills that have to be acquired through slow, effortful, and expensive processes of education and training. Likewise, these skills can become obsolete as the world changes ever faster or be lost by the processes of aging. People also vary in their mental abilities, allowing them to acquire certain skills more quickly or slower, which may have significant effects on life outcomes. Strategies to improve the acquisition and maintenance of cognitive skills are thus increasingly important on both an individual and societal level. These challenges of our times have fostered the See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. exploration of strategies to enhance human brain function. While people have since time immemorial sought to improve their performance, the present era is unique in that not only the challenges are growing rapidly but so are technologies that promise to meet them. Just like the hacking culture in the realm of computer software and hardware, an increasing number of individuals experiment with strategies to creatively overcome the natural limitations of human cognitive capacityin other words, to hack brain function. This development has led to both enthusiasm and dread, as observers have sharply differing intuitions about the feasibility, utility, risks, and eventual impact of enhancement technologies on the world. One reason for the often polarized debates has been the lack of hard evidence. Without empirical findings, it is easy to maintain any position, as well as regard opponents as having unfounded views. A further essential source of disagreement and theoretical confusion is a tendency to view enhancement as a unitary phenomenon to be judged as a whole, rather than as a broad set of techniques with important differences and diverging implications. Only on the basis of a clear picture on how a particular enhancement strategy might affect specific cognitive processes in specific populations, along with side effects and costs to be expected, an informed theoretical debate can evolve and a promising empirical research designs to test the strategy can be proposed. In the following, we aim to elucidate seven essential dimension of cognitive enhancement, namely, (a) its mode of action, (b) the cognitive domain targeted, (c) personal factors, (d) its time scale, (e) side effects, (f) availability, and (g) social acceptance (see Figure  1 ). Further, we will review empirical data of prominent examples of cognitive enhancers that differ across these dimensions and thereby illustrate some of their nuanced implications. The aim of our Review is to sketch a general framework that will foster both theoretical discussions and empirical research. \n MODE OF ACTION A widely cited definition characterizes enhancement as interventions in humans that aim to improve mental functioning beyond what is necessary to sustain or restore good health.  1  While the current bioethical debate on cognitive enhancement is strongly focused on pharmacological ways of enhancement, improving mental capabilities also by nonpharmacological means has to be considered as cognitive enhancement proper according to the given characterization. We have reviewed elsewhere the efficacy of a number of nonpharmacological enhancers.  2, 3  To systematize the vast variety of different approaches of cognitive enhancement, we suggest clustering enhancement strategies into three major areas according to their main mode of action. Even though boundaries are not strict, most cognitive enhancement strategies can be considered to work as either biochemical, physical, or behavioral interventions (Figure  2 ). In the following, we will give an overview on the different cognitive enhancement strategies within these clusters. \n Biochemical Strategies. The prototypical cognitive enhancers addressed in the public debate are biochemical agents. However, biochemical interventions are not restricted to pharmaceutical \"smart drugs\". Also application of ordinary substances such as oxygen has been shown to increase, e.g., memory processes  4, 5  and neural activation in memory-related brain regions.  6  Biochemical enhancers with the longest tradition in human history are strategies to make use of certain nutritional components. Most widely used are probably glucose  7  and caffeine,  8, 9  which both have demonstrated cognition-enhancing effects in numerous studies. In addition to coffee, other beverages from caffeine-bearing plants such as guarana have shown to enhance cognition.  10  While the noncaffeine components in caffeine-bearing plants might exert independent effects on cognition,  11  it has been doubted that industrially designed drinks contain cognitive enhancing components that go beyond caffeine, glucose, or guarana extract.  12  Further nutritional components with some evidence for cognitive enhancing effects are flavonoids, e.g., in cocoa,  13, 14  curry powder (most likely due to the curcumin that it contains,  15, 16  folic acid,  17  or omega-3 fatty acids.  18  Besides specific dietary supplements, also the absence of food might enhance cognition: some evidence has been reported that fasting and general caloric restriction might improve memory in elderly individuals.  19, 20  Also certain traditional natural remedies have been discussed as cognitive enhancers: besides herbs that also grow in Western regions such as salvia,  21  particularly traditional Chinese and   \n ACS Chemical Neuroscience \n Review Indian herbal medicines such as Bacopa monnieri have been ascribed with cognitive enhancing effects.  22, 23  However, with ginseng and ginkgo biloba, the most prominent examples of such traditional Asian herbal remedies so far have failed to consistently show positive effects on cognitive functions in healthy individuals.  24, 25  A further biochemical intervention with a long history concerns drugs that are being used recreationally and that have demonstrated the potential to enhance certain cognitive functions. For example, nicotine improves attention and memory,  26−28  and even alcohol, despite impairing many cognitive functions, might enhance others such as creative processes  29, 30  or, retroactively, memory.  31  Pharmaceuticals are in particular by the public regarded as prototypical cognitive enhancers: synthetic stimulants such as amphetamine, methylphenidate, or modafinil, or antidementia drugs such as acetylcholinesterase inhibitors and memantine are at the core of public debate on cognitive enhancement. However, evidence for their efficacy for augmenting brain function and cognition in healthy subjects is often markedly lower than assumed in theoretical discussions.  32−37  Importantly, the lack of an objective effect on cognition can be accompanied by a considerable placebo effect: for example, users who believed to have received mixed-amphetamine salts subjectively rated themselves as performing better and even show minor objective performance increases, independent of actual medication state.  38  While pharmacological enhancers are typically designed to affect or mimic certain neurotransmitters, also neural signaling molecules themselves such as adrenaline,  39  GABA,  40  glucocorticoids,  41  ovarian hormones,  42  and different neuropeptides  43−45  have been suggested as cognitive enhancers. A further biochemical strategy for cognitive enhancement consists of genetic modifications, which have been demonstrated to augment several learning and memory processes in animal models.  46−51  Although progress has also been made in elucidating the genetic basis of cognitive traits in humans,  52  genetic modifications in humans still have to be considered as future strategies rather than currently available enhancement options. 2.2. Physical Strategies. The current most widely discussed physical strategies for cognitive enhancement include a number of brain stimulation technologies. Whereas the cognition enhancing effects of invasive methods such as deep brain stimulation  53, 54  are restricted to subjects with pathological conditions, several forms of allegedly noninvasive stimulation strategies are increasingly used on healthy subjects, among them electrical stimulation methods such transcranial direct current stimulation (tDCS  55  ), transcranial alternating current stimulation (tACS  56  ), transcranial random noise stimulation (tRNS  57  ), transcranial pulsed current stimulation (tPCS  58, 59  ), transcutaneous vagus nerve stimulation (tVNS  60  ), or median nerve stimulation (MNS  61  ). Details of the stimulation procedures appear to be crucial: commercial do-it-yourself electrical brain stimulators might impair rather than enhance cognition,  62  and systematic reviews have shed doubt on a clear and simple enhancing effect of electrical brain stimulation on different cognitive domains also under controlled laboratory conditions.  63, 64  Recent studies have even questioned if some of the most commonly used setups for electrical brain stimulation have neurophysiologically meaningful effects at all.  65−68  On this background, the development of noninvasive deep brain stimulation via temporally interfering electric fields might provide a more systematic and targeted mechanism compared to the currently used approaches.  68  Besides electrical stimulation methods, also for transcranial magnetic stimulation (TMS  69  ), optical stimulation with lasers,  70  and several forms of acoustic stimulation, such as transcranial focused ultrasound stimulation,  71  binaural beats,  72, 73  or auditory stimulation of the EEG theta rhythm  74  or sleep EEG slow oscillations,  75  a potential for cognitive enhancement has been reported. Physical enhancement methods that target brain processes more indirectly include whole body vibrations,  76  stochastic resonance motor control improvement,  77, 78  and several forms of neurofeedback, 79 with, e.g., EEG neurofeedback in the upper alpha band enhancing memory,  80  working memory,  81  and visuospatial skills.  82  Besides classical neurofeedback training that involves unspecific but active effort of the subject, also neurofeedback interventions that automatically feedback low energy currents in response to EEG activity have been developed, thereby allowing the subject to receive the training procedure passively.  83  Recently, the use of fMRI neurofeedback, utilizing multivariate pattern analysis, has shown the potential to increase sustained attention  84  or visuospatial memory.  85  Finally, humans have always deployed physical tools to assist cognitive functioning. In current developments that converge minds and machines, these tools become more closely integrated with the person.  86  Crowdfunding or biohacking communities have developed numerous novel technical devices to increase cognitive functions transiently with, e.g., wearable electronic memory aids or augmented reality gadgets,  87, 88  or more permanently as in the case of cognition enhancing or extending bodily implants.  88, 89  Neural implants or prosthetics have progressed; in controlled laboratory settings, implants could facilitate human memory.  90  In addition, Brain−Computer Interfaces connect the central nervous system with computers through wearable or implanted electrodes and may afford a range of applications that enhance cognitive functions or joint outputs of minds coupled with machines.  91, 92  2.3. Behavioral Strategies. Although not commonly recognized as such by the public, cognitive enhancers with the most wide use and longest history are probably behavioral strategies: a rapidly growing body of evidence shows that everyday activities such as sleep  93  or physical exercise  94−96  improve cognitive functioning. Also well-established cultural activities such as musical training,  97, 98  dancing, 99 or learning a second language  100  have been demonstrated to enhance cognition beyond the specifically trained skills. In addition to these natural and cultural standard activities, several behavioral strategies have been developed to enhance certain brain functions intentionally. Two strategies that reach back to ancient times are mnemonic techniques to enhance learning and memory  101, 102  and meditation training to enhance attention processes and mindfulness.  103, 104  In contrast, commercial video games  105, 106  and customized computer trainings  107  represent historically very recent developments that are targeted to enhance specific cognitive capacities and skills. In contrast to several years of enthusiasm and widespread commercial application, however, more recent controlled studies and meta-analyses have shed some doubt on the efficacy of computerized brain training programs,  108  particularly criticizing claims of \"far transfer\" of training gains to cognitive domains considerably different from the specifically trained skills.  109, 110  ACS Chemical Neuroscience Review \n COGNITIVE DOMAIN The human mind is not a monolithic entity, but consists of a broad variety of cognitive functions. Not surprisingly, no single cognitive enhancer augments every cognitive function. Instead, most cognitive enhancers have specific profiles regarding their efficacy for different cognitive domains. Memory is, e.g., strongly enhanced by mnemonic strategies, but not by meditation; attention, in turn, is strongly enhanced by meditation training, but not training in mnemonic strategies.  101, 103, 104  Sleep, in contrast, enhances both cognitive capacities.  111, 112  Some computerized cognitive trainings have been found to enhance memory, processing speed and visuospatial skills, but not executive functions or attention.  107  It is currently highly debated in how far specific training strategies exert transfer effects also to nontrained cognitive domains.  113  Different cognitive tasks require different optimal levels of receptor activation, thus requiring different doses of pharmacological enhancers targeting the respective neurotransmitter system depending on the cognitive domain targeted.  114  Of note, effects of pharmacological enhancement on different cognitive domains might even differ depending on the cognitive test battery used, illustrating the fragility of the respective effects.  115  Some interventions might even enhance one but impair another cognitive domain: Intranasal application of oxytocin has been shown to enhance social cognition and cognitive flexibility but impairs long-term memory.  116, 117  Methylphenidate improves the ability to resist distraction but impairs cognitive flexibility.  118  Computerized working memory training has been reported to enhance working memory, reasoning, and arithmetic abilities; however, it might deteriorate creativity.  119  Also for amphetamines and modafinil, potential impairments on creativity are discussed besides their enhancing effects on other domains.  120, 34  In contrast, alcohol might enhance creative processes while impairing most other cognitive functions.  29  The costs and benefits of a single cognitive enhancer might even change through slight changes in the application process: for example, electrical stimulation of posterior brain regions was found to facilitate numerical learning, whereas automaticity for the learned material was impaired. In contrast, stimulation on frontal brain regions impaired the learning process, whereas automaticity for the learned material was enhanced.  121  Brain stimulation has thus been suggested to be a zero-sum game, with costs in some cognitive functions always being paid for gains in others.  122  This implies that enhancement may have to be tuned to the task at hand, in order to focus on the currently most important cognitive demands. \n PERSONAL FACTORS The efficacy of cognitive enhancers does not only differ for different cognitive domains, but also for different users. An important factor in this regard are the cognitive skills of the individual prior to the enhancement intervention. Many pharmaceuticals, including amphetamine,  123  modafinil, and methylphenidate,  124  work mainly in individuals with low baseline performance. In some cases, even impairments in individuals with higher performance at baseline have been reported, e.g., in the case of amphetamine,  125  methylphenidate,  124  nicotine,  27  or acute choline supplementation.  126  The phenomenon of enhanced cognition in individuals with low baseline performance and impairments in those with high baseline performance can be explained by the classical inverted U-model,  127, 128  where performance is optimal at intermediate levels of the targeted neurochemicals and impaired at levels that are either too low or too high.  129−131  For some drugs such as methylphenidate, enhancement dependency on the baseline might even differ between cognitive functions, with performance in specific tasks being improved in low, while impaired in high, performers,  124  but showing the opposite pattern for other tasks.  132  The baseline-dependency of cognitive enhancement is not restricted to pharmaceuticals: also in the case of video games,  133  cognitive training,  134  or brain stimulation,  135, 136  individuals starting at a lower baseline performance benefit more than those with an already high performance at baseline. In contrast, sleep appears to improve memory particularly in subjects with a higher baseline performance of memory,  137  working memory  138  or intelligence.  139  Also mnemonic training appears to work particularly well in individuals with a higher cognitive baseline performance.  140  This has been interpreted in terms of an amplification model, in which high baseline performance and cognitive enhancement interventions show synergistic effects.  141  Cognitive enhancers can also affect individuals differently depending on basic biological, psychological, or social factors. For example, effects of training interventions on selective attention can depend on the genotype of the trainee;  142  effects of methylphenidate on creativity can depend on personality characteristics;  143  the cognition enhancing effects of sleep  144  or video games  145  are modulated by gender. In turn, such modulations of enhancement effects might reduce existing differences in cognitive profiles, as seen, e.g., in action video game training, that have the potential to eliminate gender differences in spatial attention and decrease the gender disparity in mental rotation ability.  146  Also the hormonal status of subjects affects how strongly they profit, e.g., from sleep  144−148  or brain stimulation.  149  Caffeine enhances working memory particularly in extraverted individuals,  150  and memory enhancement through sleep  151  or mnemonic training  140  has been reported to depend on the age of subjects. Health status affects how much users benefit from different kinds of cognitive enhancers, including pharmaceuticals, 3 mnemonics,  152  or sleep.  153−156  Finally, also socioenvironmental factors such as social resources, parental occupation, or family composition can modulate cognitive enhancement interventions, e.g., with cognitive training programs.  157   \n TIME SCALE Interventions for cognitive enhancement differ in the specific time scale they require to achieve their aims. The prototypical \"smart pill\" discussed in popular accounts of cognitive enhancement needs practically no preparation time, exerts its effects within seconds or minutes, and lasts for several hours. While this is close to reality in the case of some pharmacological enhancers, the temporal pattern of most other enhancement strategies differs strongly from these time scales. In particular, the time needed for application and the duration of their effects markedly varies between enhancement interventions. Most pharmacological enhancers can be applied quickly and without further preparation; however, some drugs such as acetylcholinesterase inhibitors or memantine are thought to require longer periods of intake to be effective.  33  Also some nutritional enhancers such as glucose and caffeine exert their effects rather quickly, whereas other nutritional supplements have to be taken over extended periods to show an impact on cognition.  158, 18  Obviously, behavioral strategies like sleep, \n ACS Chemical Neuroscience Review exercise, video games or mnemonic training need hours or weeks to robustly enhance cognition. Some effects of meditation might even take years of training.  159  For brain stimulation methods, both immediate effects of acute stimulation, but also more delayed effects after repeated stimulation haven been observed.  55, 69  Technological gadgets or implants need some preparation to be installed and accommodated to, however then exert their cognition augmenting effects on demand. Enhancing effects of most quickly acting pharmacological or nutritional cognitive enhancers also wear off rather rapidly. In contrast to such transient effects, interventions such as brain stimulation,  160, 161, 57  sleep, 162 mnemonic strategies  163  or genetic modifications  46  have the potential for long-term up to chronic enhancement. However, in the latter case, the reversibility of the effects (and side effects) of an enhancement intervention might be a further aspect to be considered. Interventions can also differ regarding the time point of application relative to the situation when enhanced cognitive performance is needed. For example, application of stress hormones such as cortisol or adrenaline before or after memory encoding enhances memory, whereas application before retrieval impairs memory; 41 benzodiazepines impair memory when given before and enhance memory when given after encoding;  164  in contrast, caffeine before learning enhances memory under certain conditions but might impair memory when consumed afterward.  165, 9  Mnemonic strategies on the other hand work solely when taught/applied before/during encoding, but can hardly be applied afterward. Finally, some interventions can also influence the timing of cognitive performance itself: stimulants such as methylphenidate, modafinil, and caffeine might increase the time subjects take to perform a given task, with impairing effects under time pressure and potentially enhancing effects in the absence of temporal constraints.  166   \n SIDE EFFECTS The pharmaceutical platitude that there is no effect without side effects holds true also for many nonpharmacological enhancement interventions. It appears obvious that cognitive enhancers differ in the severity and form of side effects: prima facie, deep brain stimulation or implants have higher risks for side effects than sleep or cognitive training. However, also more indirect enhancement strategies such as neurofeedback potentially bear the risk of side effects up to inducing epileptiform activity,  167  and even gentle intervention such as meditation training might exert negative effects on specific cognitive domains: a negative relationship between mindfulness and implicit learning  168, 169  and an increased susceptibility to false memory formation after mindfulness meditation  170  have been observed. Here, the intended training goal of nonjudgemental mindfulness opposes tasks where either a more critical or automatic mindset was needed. Further examples of side effects intrinsically associated with the enhancement goal are trade-offs between stability vs flexible updating of memory systems:  129  memories can also become \"too stable\" due to a memory enhancement intervention, as observed, e.g., for the anti-obesity drug rimonabant.  171  It has been suggested to differentiate enhancement strategies according to their level of invasiveness.  172, 173  However, while invasiveness has a more or less definite meaning in its original medical context, physically breaching the skin or entering the body deeply through an external orifice,  174  it is difficult to determine the level of invasiveness in the context of cognitive enhancement. Both nutritional supplements and pharmaceuticals enter the body, and thus could be considered invasive in a narrow medical sense, as might be certain forms of physical exercise due to the risk of bruises or scratches as common, e.g., in martial arts or a hike through the woods. Brain stimulation that does not break the skin would, by contrast, be classified as noninvasive. This taxonomy can be disputed for good reasons.  175  Besides known risks of these stimulation methods such as scalp burns from tDCS or seizures from TMS, the \"known unknowns\" have been suggested to pose potentially even greater risks: potential build-up effects across multiple sessions or in sensitive nontarget areas.  176  Of note, only few neuroscientists use brain stimulation on themselves for cognitive enhancement.  176  Given the still unclear risks and side effects of do-it-yourself brain stimulation use, it has been proposed to extend existing medical device legislation to cover also nonpharmacological and in particular physically acting cognitive enhancement devices.  177, 178  In contrast to strict medical definitions, the more intuitively assessed level of invasiveness of an intervention often seems to depend on familiarity and cultural traditions. This leads to the Western attitude according to which changing one's diet or performing exercise appears less invasive than taking pharmaceuticals or applying brain stimulation, independent of their actual effects on health. Related to the time scale dimension, side effects of short-vs long-term use of cognitive enhancers can be differentiated. For example, while side effects for the acute use of methylphenidate include increased heart rate, headache, anxiety, nervousness, dizziness, drowsiness, and insomnia, in the case of long-term use side effects such as abnormal prefrontal brain function and impaired plasticity have been reported.  179, 180  Also addiction is a well-known side effect for the long-term use of pharmacological enhancers, which is particularly detrimental to the aim of enhancement if combined with tolerance effects such that larger doses are needed to achieve the same effect (or prevent impairing withdrawal effects). Also behavioral addictions have been observed, e.g., physical exercise  181  or the use of technological gadgets.  182  A somewhat nonobvious negative effect of some cognitive enhancers is their illusional efficacy: users sometimes believe their performance to be enhanced by amphetamine in absence of any verified and objectively visible enhancing effects, even if administered in a double blind manner.  183, 184, 38  This is particularly counterproductive in cases of already highfunctioning individuals whose cognitive capabilities might be impaired rather than enhanced by amphetamine.  125, 184  Also for caffeine, under certain conditions higher subjectively perceived mental energy in the absence of objectively enhancing effects have been observed.  185  The often subtle effects of enhancers can be hidden or amplified by placebo effects. \n AVAILABILITY Cognitive enhancers differ in at least three aspects of availability: legal status, cost, and application time. In terms of legal regulation, different enhancement methods are regulated by sometimes drastically varying frameworks. Pharmaceuticals, for instance, are regulated by strict international control regimes that effectively prohibit nontherapeutic uses or by more lenient domestic drug laws. Brain-stimulation methods, by contrast, fall under medical device regulations, pertaining to basic safety standards in terms but not proscribing the uses to which they might be put.  177, 178  Behavioral strategies are usually not regulated at all. The regulatory landscape is thus vast and \n ACS Chemical Neuroscience Review possibly incoherent (for a review, see  ref 186) . Besides practical hurdles to the acquisition of illicit drugs for cognitive enhancement, the legal status appears to affect the motivation of users to decide which cognitive enhancers to take.  166  A common ethical argument in the enhancement debate concerns distributive justice: also legally available enhancers come with cost barriers, restricting individuals of low socioeconomic status from access.  187  A main factor in the costs of cognitive enhancers is their patentability, which is not restricted to pharmaceuticals.  188  However, in particular, behavioral enhancement strategies are typically not subject to patentability or other cost-driving factors: sleep, exercise, meditation, or training in mnemonic strategies are largely free of cost and, thus, in contrast to pharmaceuticals or technological strategies, are available independent from the financial background of the user. On the other hand, these behavioral strategies require some time and effort: the 24/7 working manager as the clichéuser of cognitive enhancement drugs might have the financial means to afford quickly taking his expensive smart pill between two meetings, but might be unable or unwilling to spend extended periods of time with sleep, meditation, or mnemonic training. \n SOCIAL ACCEPTANCE Largely independent from their specific enhancing effects on different cognitive capacities, social acceptance of cognitive enhancement interventions differs strongly depending on traditions, their perceived naturalness, and the perceived directness of their mode of action. Enhancement interventions with a tradition of thousands of years such as meditation and nutrition are typically much better accepted than many currently debated enhancement strategies such as brain stimulation and pharmaceuticals.  189  Also more \"natural\" interventions such as sleep or exercise are seen in a more positive light compared to technological innovations.  190  Moreover, in how far the mode of action is perceived as psychologically mediated or more biologically direct, affecting the brain indirectly through the senses or more directly through the cranium or metabolism, often plays a role for their social acceptance: if an enhancement intervention such as intense cognitive or physical training requires extended efforts or is seen as a quick and effortless shortcut to the same goal as in the case of smart pills or brain stimulation touches different intuitions about human virtues and is thus valuated differently. Even though views based on such purely intuitive aspects of tradition, naturalness, or directness often rely on cognitive biases rather than rational argument,  191  a negative social perception for whatever reason might generate indirect psychological costs for users, which in turn might influence also rational evaluations of the respective enhancement intervention.  192  Accordingly, one of the central points in the ethical controversy revolves around the question of whether enhancement strategies only relevantly differ with respect to their outcomes, i.e., their benefits and side effects,  193  or also with respect to their mode of operation.  194  Some argue that the relevant ethical distinction runs along the lines of enhancements that are active, in the sense of requiring participation, and those that work on persons more passively.  195  Not surprisingly, different views on cognitive enhancement prevail in different (sub)cultures, with, e.g., a more positive view on enhancement interventions in Asia  196  or in younger populations.  197  Empirical studies on attitudes toward cognitive enhancement interventions found medical safety, coercion, and fairness the most common concerns, with nonusers displaying more concerns regarding medical safety and fairness than users.  198  Sometimes readily available substances for cognitive enhancement such as caffeine, energy drinks, or herbal drugs are dubbed \"soft enhancers\"; 199 however, considering that prohibition of substances is not only based on their potential harm, but also on historical circumstances, this differentiation between soft and hard enhancers appears questionable. A further aspect that determines the social acceptance of cognitive enhancement is the aim of the given intervention. Taken by face value, the term cognitive enhancement denotes any action or intervention that improves cognitive capacities, independent from the specific aim of this improvement. The use of the term in the empirical, philosophical, and sociopolitical literature, however, varies with regard of the specific aim of enhancement interventions: people appear to be more tolerant toward enhancement of traits considered less fundamental to self-identity,  200  and also more tolerant toward enhancement in individuals with cognitive impairments or low performance baselines compared to enhancement of normal or high achievers.  201, 202  At least four different aims can be identified, each leading to different research strategies and different ethical evaluations of existing or potential enhancement strategies.  203  The least problematic concept of cognitive enhancement targets those everyday medical or psychological interventions that are meant to treat pathological deficiencies. Closely related are those cognitive enhancement interventions that aim to prevent or attenuate cognitive decline that is associated also with healthy aging.  204  Slightly less accepted appear to be those enhancement strategies that aim to improve cognition in completely healthy individuals, but still clearly stay within the normal limits of cognition. The probably most widely used and ethically most controversial concept of cognitive enhancement aims at the augmentation of cognitive capacities beyond normal function, as is represented in the clichéof high-functioning students or managers trying to further improve their performance by taking smart pills. Besides these differentiations between enhancement of impaired vs healthy cognition, another difference in the aims of cognitive enhancement touches the ultimate deed of the enhancement intervention: due to the central role of cognitive capacities in defining humans as a species, it is tempting to consider the improvement of these defining human capacities as a value in itself. However, most philosophical or religious approaches do not center on objective cognitive performance markers, but propose values only indirectly related to cognitive performance such as living a happier or more meaningful life in general. In this light, human enhancement in more general terms does not need to aim for individual cognitive or neural processes, but can also be achieved by sociopolitical reforms targeted at the population level.  205, 206  9. CONCLUSIONS Cognitive enhancement clearly is a multidimensional endeavor. However, not every dimension is important for every theoretical or empirical research question. For example, many empirical researchers of cognitive enhancement are primarily interested in the understanding of the neurobiological and psychological mechanisms underlying cognitive functions.  207  For this aim, the availability and social acceptance dimensions are largely irrelevant. In contrast, many theorists are interested in the social and ethical implications of cognitive enhancement,  208  where these dimensions might be of prime importance. Also side effects and temporal factors might be of secondary importance \n ACS Chemical Neuroscience Review to empirical researchers with an interest in the neural mechanisms of certain cognitive processes, whereas these would be highly relevant for users who ponder the question which cognitive enhancement strategy to choose for a certain aim. When comparing different cognitive enhancement strategies, different dimensions might thus be differently weighed or completely ignored, depending on the aim of the comparison. Up until now, direct comparisons between cognitive enhancement strategies with radically different modes of actions have rarely been made (but see, e.g., ref  165) , and more comprehensive comparisons across dimensions might be difficult: practical issues of information availability from the different dimensions aside, interventions typically differ on different dimensions and are thus difficult to compare globally. In addition, multiple interactions between different enhancers exist, which further complicates the situation. Interactions have been reported, e.g., for glucose and caffeine,  209  diet and exercise,  210  exercise and working memory training,  211  video games and sleep,  212  video games and brain stimulation,  213  exercise and brain stimulation,  214  and brain stimulation and sleep.  215, 216  Also different dimensions discussed here can interact in multiple ways, as, e.g., computerized cognitive training can differentially enhance different cognitive processes depending on personal factors such as age;  217  and social acceptance of different enhancement strategies depends on both the baseline performance of users and the cognitive domain targeted.  200, 201  Despiteor because ofthese complexities, in our opinion, both theoretical discussions and empirical research would strongly benefit from a more differentiated approach. Specific research questions might require the emphasis on some dimensions of cognitive enhancement over others, and for some research questions some dimensions might be entirely irrelevant. Nevertheless, keeping in mind that cognitive enhancement is not a monolithic phenomenon will help to solve and avoid a number of confusions and disagreements that are still present in the public debate on cognitive enhancement. This is an open access article published under a Creative Commons Non-Commercial No Derivative Works (CC-BY-NC-ND) Attribution License, which permits copying and redistribution of the article, and creation of adaptations, all for non-commercial purposes. Downloaded via 205.240.4.254 on March 24, 2022 at 02:39:01 (UTC). \n Figure 1 . 1 Figure 1. Cognitive enhancement interventions differ across several interdependent dimensions. \n Figure 2 . 2 Figure 2. Cognitive enhancement interventions different in their mode of actions.", "date_published": "n/a", "url": "n/a", "filename": "acschemneuro.8b00571.tei.xml", "abstract": "In an increasingly complex information society, demands for cognitive functioning are growing steadily. In recent years, numerous strategies to augment brain function have been proposed. Evidence for their efficacy (or lack thereof) and side effects has prompted discussions about ethical, societal, and medical implications. In the public debate, cognitive enhancement is often seen as a monolithic phenomenon. On a closer look, however, cognitive enhancement turns out to be a multifaceted concept: There is not one cognitive enhancer that augments brain function per se, but a great variety of interventions that can be clustered into biochemical, physical, and behavioral enhancement strategies. These cognitive enhancers differ in their mode of action, the cognitive domain they target, the time scale they work on, their availability and side effects, and how they differentially affect different groups of subjects. Here we disentangle the dimensions of cognitive enhancement, review prominent examples of cognitive enhancers that differ across these dimensions, and thereby provide a framework for both theoretical discussions and empirical research.", "id": "5c694d79e072f8c68905a15988932c1a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dorsa Sadigh", "S Shankar", "Sastry Sanjit", "A Seshia", "Anca Dragan"], "title": "Information Gathering Actions over Human Internal State", "text": "I. introduction Imagine driving on the highway. Another driver is in the lane next to you, and you need to switch lanes. Some drivers are aggressive and they will never brake to let you in. Others are more defensive and would gladly make space for you. You don't know what kind of driver this is, so you decide to gently nudge in towards the other lane to test their reaction. At an intersection, you might nudge in to test if the other driver is distracted and they might just let you go through (Fig.  1  bottom left). Our goal in this work is to give robots the capability to plan such actions as well. In general, human behavior is affected by internal states that a robot would not have direct access to: intentions, goals, preferences, objectives, driving style, etc. Work in robotics and perception has focused thus far on estimating these internal states by providing algorithms with observations of humans acting, be it intent prediction  [23] ,  [13] ,  [6] ,  [3] ,  [4] ,  [16] , Inverse Reinforcement Learning  [1] ,  [12] ,  [15] ,  [22] ,  [18] , driver style prediction  [11] , affective state prediction  [10] , or activity recognition  [20] . Human state estimation has also been studied in the context of human-robot interaction tasks. Here, the robot's reward function depends (directly or indirectly) on the human internal state, e.g., on whether the robot is able to adapt to the human's plan or preferences. Work in assistive teleoperation or in human assistance has cast this problem as a Partially Observable Markov Decision Process, in which the robot does observe the physical state of the world but not the human internal state -that it has to estimate from human actions. Because POMDP solvers are not computationally efficient, the solutions proposed thus far use the current estimate Fig.  1 : We enable robots to generate actions that actively probe humans in order to find out their internal state. We apply this to autonomous driving. In this example, the robot car (yellow) decides to inch forward in order to test whether the human driver (white) is attentive. The robot expects drastically different reactions to this action (bottom right shows attentive driver reaction in light orange, and distracted driver reaction in dark orange). We conduct a user study in which we let drivers pay attention or distract them with cellphones in order to put this state estimation algorithm to the test. of the internal state to plan (either using the most likely estimate, or the entire current belief), and adjust this estimate at every step  [8] ,  [7] ,  [5] . Although efficient, these approximations sacrifice an important aspect of POMDPs: the ability to actively gather information. Our key insight is that robots can leverage their own actions to help estimation of human internal state. Rather than relying on passive observations, robots can actually account for the fact that humans will react to their actions: they can use this knowledge to select actions that will trigger human reactions which in turn will clarify the internal state. We make two contributions: An Algorithm for Active Information Gathering over Human Internal State. We introduce an algorithm for planning robot actions that have high expected information gain. Our algorithm uses a rewardmaximization model of how humans plan their actions in response to those of the robot's  [19] , and leverages the fact that different human internal states will lead to different human reactions to speed up estimation. Fig.  1  shows an example of the anticipated difference in reaction between a distracted and an attentive driver. Application to Driver Style Estimation. We apply our algorithm to estimating a human driver's style during the interaction of an autonomous vehicle with a human-driven vehicle. Results in simulation as well as from a user study suggest that our algorithm's ability to leverage robot actions for estimation leads to significantly higher accuracy in identifying the correct human internal state. The autonomous car plans actions like inching forward at an intersection (Fig.  1 ), nudging into another car's lane, or braking slightly in front of a human-driven car, all to estimate whether the human driver is attentive. Overall, we are excited to have taken a step towards giving robots the ability to actively probe end-users through their actions in order to better estimate their goals, preferences, styles, and so on. Even though we chose driving as our application domain in this paper, our algorithm is general across different domains and types of human internal state. We anticipate that applying it in the context of human goal inference during shared autonomy, for instance, will lead to the robot purposefully committing to a particular goal in order to trigger a reaction from the user, either positive or negative, in order to clarify the desired goal. Of course, further work is needed in order to evaluate how acceptant end-users are of different kinds of such probing actions. \n II. Information Gathering Actions We start with a general formulation of the problem of a robot needing to maximize its reward by acting in an environment where a human is also acting. The human is choosing its actions in a manner that is responsive to the robot's actions, and also influenced by some internal variables. While most methods that have addressed such problems have proposed approximations based on passively estimating the internal variable and exploiting that estimate, here we propose a method for active information gathering that enables the robot to purposefully take actions that probe the human. Finally, we discuss our implementation in practice, which trades off between exploration and exploitation. \n A. General Formulation We define a human-robot system in which the human's actions depend on some human internal state ϕ that the robot does not directly observe. In a driving scenario, ϕ might correspond to driving style: aggressive or timid, attentive or distracted. In collaborative manipulation scenarios, ϕ might correspond to the human's current goal, or their preference about the task. We let x ∈ X be a continuous physical state of our system. For our running example of autonomous cars, this includes position, velocity and heading of the autonomous and human driven vehicles. Let ϕ ∈ Φ be the hidden variable, e.g., human driver's driving style. We assume the robot observes the current physical state x t , but not the human internal state ϕ. The robot and human can apply continuous controls u R and u H . The dynamics of the system evolves as robot's and human's control inputs arrive at each step: x t+1 = f H ( f R (x t , u t R ), u t H ). (1) Here, f R and f H represent how the actions of the robot and of the human respectively affect the dynamics, and can be applied synchronously or asynchronously. We assume that while x changes via (1) based on the human and robot actions, ϕ does not. For instance, we assume that the human maintains their preferences or driving style throughout the interaction. The robot's reward function in the task depends on the current state, the robot's action, as well as the action that the human takes at that step in response, r R (x t , u t R , u t H ). If the robot has access to the human's policy π H (x, u R , ϕ), maximizing robot reward can be modeled as a POMDP  [9]  with states (x, ϕ), actions u R , and reward r R . In this POMDP, the dynamics model can be computed directly from (1) with u t H = π H (x t , u t R , ϕ). The human's actions can serve as observations of ϕ via some P(u H |x, u R ). In Sec. II-C we introduce a model for both π H and P(u H |x, u R , ϕ) based on the assumption that the human is maximizing their own reward function. If we were able to solve the POMDP, the robot would estimate ϕ based on the human's actions, and optimally trade off between exploiting its current belief over ϕ, and actively taking information gathering actions meant to cause human reactions that give the robot a better estimate of the hidden variable ϕ. Because POMDPs cannot be solved tractably, several approximations have been proposed for similar problem formulations  [8] ,  [11] ,  [7] . These approximations are passively estimating the human internal state, and exploiting the belief to plan robot actions.  1  In this work, we take the opposite approach: we focus explicitly on active information gathering. We enable the robot to decide to actively probe the person to get a better estimate of ϕ. Our method can be leveraged in conjunction with exploitation methods, or be used alone when human state estimation is robot's primary objective. \n B. Reduction to Information Gathering At every step, the robot can update its belief over ϕ via: b t+1 (ϕ) ∝ b t (ϕ) • P(u H |x t , u R , ϕ). ( 2 ) To explicitly focus on taking actions to estimate ϕ, we redefine the robot's reward function to capture the information gain at every step: r R (x t , u R , u H ) = H(b t ) − H(b t+1 ) (3) with H(b) being the entropy over the belief: H(b) = − ∑ ϕ b(ϕ) log(b(ϕ)) ∑ ϕ b(ϕ) . ( 4 ) Optimizing expected reward now entails reasoning about the effects that the robot actions will have on what observations the robot will get, i.e., the actions that the human will take in response, and how useful these observations will be in shattering ambiguity about ϕ. \n C. Solution: Human Model & Model Predictive Control We solve the information gathering planning problem via Model Predictive Control (MPC)  [14] . At every time step, we find the optimal actions of the robot u * R by maximizing the expected reward function over a finite horizon. Notation. Let x 0 be the state at the current time step, i.e., at the beginning of the horizon. u R = (u 0 R , . . . , u N−1 R ) be a finite sequence of the robot's continuous actions, and u H = (u 0 H , . . . , u N−1 H ) be a finite sequence of human's continuous actions. Further, let R R (x 0 , u R , u H ) denote the reward over the finite horizon, if the agents started in x 0 and executed u R and u H , which can be computed via the dynamics in  (1) . MPC Maximization Objective. At every time step, the robot is computing the best actions for the horizon: u * R = arg max u R E ϕ R R (x 0 , u R , u * ϕ H (x 0 , u R )) (5) where u * ϕ H (x 0 , u R ) corresponds to the actions the human would take from state x 0 over the horizon of N steps if the robot executed actions u R . Here, the expectation is taken over the current belief over ϕ, b 0 . Simplifying (5) using the definition of reward from (3), we get: u * R = arg max u R E ϕ H(b 0 ) − H(b N ) , (6) u * R = arg max u R E ϕ − H(b N ) , (7) where the expectation remains with respect to b 0 . Human Model. We assume that the human maximizes their own reward function at every step. We let r ϕ H (x t , u t R , u t H ) represent human's reward function at time t, which is parametrized by the human internal state ϕ. Then, the sum of human rewards over horizon N is: R ϕ H (x 0 , u R , u H ) = N−1 ∑ t=0 r ϕ H (x t , u t R , u t H ) (8) Building on our previous work  [19] , which showed how the robot can plan using such a reward function when there are no hidden variables, we compute u * ϕ H (x 0 , u R ) through an approximation. We model the human as having access to u R a priori, and compute the finite horizon human actions that maximize the human's reward: u * ϕ H (x 0 , u R ) = arg max u H R ϕ H (x 0 , u R , u H ) (9) One can find r ϕ H through Inverse Reinforcement Learning (IRL)  [1] ,  [12] ,  [15] ,  [22] , by getting demonstrations of human behavior associated with a direct measurement of ϕ. The robot can use this reward in the dynamics model in order to compute human actions via  (9) . To update the belief b and compute expected reward in  (7) , we still need an observation model. We assume that actions with lower reward are exponentially less likely, building on the principle of maximum entropy  [22] : P(u H |x, u R , ϕ) ∝ exp(ϕ H (x, u R , u H )) (10) Optimization Procedure. To solve (5) (or equivalently (  7 )), we use a gradient descent optimization method, L-BFGS, designed for unconstrained nonlinear problems  [2] . Therefore, we would like to find the gradient of the objective in equation (  5 ) with respect to u R . Since the objective is the expectation of R R , we can reformulate this gradient as: ∂E ϕ R R (x 0 , u R , u * ϕ H (x 0 , u R )) ∂u R = ∑ ϕ ∂R R (x 0 , u R , u * ϕ H (x 0 , u R )) ∂u R • b 0 (ϕ) (11) Then, we only need to find ∂R R ∂u R , which is equivalent to: ∂R R (x 0 , u R , u * ϕ H (x 0 , u R )) ∂u R = ∂R R (x 0 , u R , u H ) ∂u H ∂u * ϕ H ∂u R + ∂R R (x 0 , u R , u H ) ∂u R | u H =u * ϕ H (x 0 ,u R ) (12 ) Because R R , as indicated by  (7) , simplifies to the negative entropy of the updated belief, we can compute both ∂R R (x 0 ,u R ,u H ) ∂u H and ∂R R (x 0 ,u R ,u H ) ∂u R | u H =u * ϕ H (x 0 ,u R ) symbolically. This leaves ∂u * ϕ H ∂u R . We use the fact that the gradient of R H will evaluate to zero at u * ϕ H : ∂R H ∂u H (x 0 , u R , u * ϕ H (x 0 , u R )) = 0 (13) Now, differentiating this expression with respect to u R will result in: ∂ 2 R H ∂u 2 H ∂u * ϕ H ∂u R + ∂ 2 R H ∂u H ∂u R ∂u R ∂u R = 0 (14) Then, solving for ∂u * ϕ H ∂u R enables us to find the following symbolic expression: ∂u * ϕ H ∂u R = [− ∂ 2 R H ∂u H ∂u R ][ ∂ 2 R H ∂u 2 H ] −1 . ( 15 ) This expression allows finding a symbolic expression for the gradient in equation  (11) . \n D. Explore-Exploit Trade-Off In practice, we use information gathering in conjunction with exploitation. We do not solely optimize the reward from Sec. II-B, but optimize it in conjunction with the robot's actual reward function assuming the current estimate of ϕ: r R (x t , u R , u H ) = H(b t ) − H(b t+1 ) ( 16 ) + λ • r goal (x t , u R , u H , b t ) At the very least, we do this as a measure of safety, e.g., we want an autonomous car to keep avoiding collisions even when it is actively probing a human driver to test their reactions. We choose λ experimentally, though existing techniques that can better adapt λ over time  [21] . Despite optimizing this trade-off, we do not claim that our method as-is can better solve the general POMDP formulation from Sec. II-A: only that it can be used to get better estimates of human internal state. The next sections test this in simulation and in practice, in a user study, and future work will look at how to leverage this ability to better solve human-robot interaction problems. \n III. Simulation Results In this section, we show simulation results that use the method from the previous section to estimate human driver type in the interaction between an autonomous vehicle and a human-driven vehicle. In this section, we consider three different autonomous driving scenarios. In these scenarios, the human is either distracted or attentive during different driving experiments. The scenarios are shown in Fig.  2 , where the yellow car is the autonomous vehicle, and the white car is the human driven vehicle. Our goal is to plan to actively estimate the human's driving style in each one of these scenarios, by using the robot's actions. \n A. Attentive vs. Distracted Human Driver Models Our technique requires reward functions r ϕ H that model the human behavior for a particular internal state ϕ. We obtain a generic driver model via Continuous Inverse Optimal Control with Locally Optimal Examples  [12]  from demonstrated trajectories in a driving simulator in an environment with multiple autonomous cars, which followed precomputed routes. We parametrize the human reward function as a linear combination of features, and learn weights on the features. We use various features including features for bounds on the control inputs, features that keep the vehicles within the road boundaries and close to the center of their lanes. Further, we use quadratic functions of speed to capture reaching the goal, and Gaussians around other vehicles on the road to enforce collision avoidance as part of the feature set. We then adjust the learned weights to model attentive vs. distractive drivers. Specifically, we modify the weights of the collision avoidance features, so the distracted human model has less weight for these features. Therefore, the distracted driver is more likely to collide with the other cars while the attentive driver has high weights for the collision avoidance feature. \n B. Manipulated Factors We manipulate the reward function that the robot is optimizing. In the passive condition, the robot optimizes a simple reward function for collision avoidance based on the current belief estimate. It then updates this belief passively, by observing the outcomes of its actions at every time step. In the active condition, the robot trades off between this reward function and the Information Gain from (3) in order to explore the human's driving style. We also manipulate the human internal state to be attentive or distracted. The human is simulated to follow the ideal model of reward maximization for our two rewards. \n C. Driving Simulator We use a simple point-mass model for the dynamics of the vehicle, where x = x y θ v is the state of the vehicle. Here, x and y are the coordinates of the vehicle, θ is the heading, and v is the speed. Each vehicle has two control inputs u = u 1 u 2 , where u 1 is the steering input, and u 2 is acceleration. Further, we let α be a friction coefficient. Then, the dynamics of each vehicle is formalized as: [ ẋ ẏ θ v] = [v • cos(θ) v • sin(θ) v • u 1 u 2 − α • v]. (17) \n D. Scenarios and Qualitative Results Scenario 1: Nudging In to Explore on a Highway. In this scenario, we show an autonomous vehicle actively exploring the human's driving style in a highway driving setting. We contrast the two conditions in Fig.  2 (a). In the passive condition, the autonomous car drives on its own lane without interfering with the human throughout the experiment, and updates its belief based on passive observations gathered from the human car. However, in the active condition, the autonomous car actively probes the human by nudging into her lane in order to infer her driving style. An attentive human significantly slows down (timid driver) or speeds up (aggressive driver) to avoid the vehicle, while a distracted In this scenario, we consider the two vehicles at an intersection, where the autonomous car actively tries to explore human's driving style by nudging into the intersection. The initial conditions of the vehicles are shown in Fig.  2(c ). In the passive condition, the autonomous car stays at its position without probing the human, and only optimizes for collision avoidance. This provides limited observations from the human car resulting in a low confidence belief distribution. Autonomous Vehicle Human Driven Vehicle Passive Estimation Active Info Gathering In the active condition, the autonomous car nudges into the intersection to probe the driving style of the human. An attentive human would slow down to stay safe at the intersection while a distracted human will not slow down. \n E. Quantitative Results Throughout the remainder of the paper, we use a common color scheme to plot results for our experimental conditions. We show this common scheme in Fig.  3 : darker colors (black and red) correspond to attentive humans, and lighter colors (gray and orange) correspond to distracted humans. Further, the shades of orange correspond to active information gathering, while the shades of gray indicate passive information gathering. We also use solid lines for real users, and dotted lines for scenarios with an ideal user model learned through inverse reinforcement learning. This table is representative for the legends of Fig.  4 , Fig.  ? ?, Fig.  5 , and Fig.  6 . Fig.  4  plots, using dotted lines, the beliefs over time for the attentive (left) and distracted (right) conditions, comparing in each the passive (dotted black and gray respectively) with the active method (dotted dark orange and light orange respectively). In every situation, the active method achieves a more accurate belief (higher values for attentive on the left, when the true ϕ is attentive, and lower values on the right, when the true ϕ is distracted). In fact, passive estimation sometimes incorrectly classifies drivers as attentive when they are distracted and vice-versa. The same figure also shows (in solid lines) results from our user study of what happens when the robot no longer interacts with an ideal model. We discuss these in the next section. Fig.  5  and Fig.  6  plot the corresponding robot and human trajectories for each scenario. The important takeaway from these figures is that there tends to be a larger gap between attentive and distracted human trajectories in the active condition (orange shades) than in the passive condition (gray shades), especially in scenarios 2 and 3. It is this difference that helps the robot better estimate ϕ: the robot in the active condition is purposefully choosing actions that will lead to large differences in human reactions, in order to more easily determine the human driving style. \n IV. User Study In the previous section, we explored planning for an autonomous vehicle that actively probes a human's driving style, by braking or nudging in and expecting to cause reactions from the human driver that would be different depending on their style. We showed that active exploration does significantly better at distinguishing between attentive and distracted drivers using simulated (ideal) models of drivers. Here, we show the results of a user study that evaluates this active exploration for attentive and distracted human drivers. \n A. Experimental Design We use the same three scenarios discussed in the previous section. Manipulated Factors. We manipulated the same two factors as in our simulation experiments: the reward function that the robot is optimizing (whether it is optimizing its reward through passive state estimation, or whether it is trading off with active information gathering), and the human internal state (whether the user is attentive or distracted). We asked our users to pay attention to the road and avoid collisions for the attentive case, and asked our users to play a game on a mobile phone during the distracted driving experiments. Dependent Measure. We measured the probability that the robot assigned along the way to the human internal state. Hypothesis. The active condition will lead to more accurate human internal state estimation, regardless of the true human internal state. Subject Allocation. We recruited 8 participants (2 female, 6 male) in the age range of 21-26 years old. All participants owned a valid driver license and had at least 2 years of driving experience. We ran the experiments using a 2D driving simulator with the steering input and acceleration input provided through a steering wheel and a pedals as shown in Fig.  1 . We used a within-subject experiment design with counterbalanced ordering of the four conditions. \n B. Analysis We ran a factorial repeated-measures ANOVA on the probability assigned to \"attentive\", using reward (active vs passive) and human internal state (attentive vs distracted) as factors, and time and scenario as covariates. As a manipulation check, attentive drivers had significantly higher estimated probability of \"attentive\" associated than distracted drivers (.66 vs .34, F = 3080.3, p < .0001). More importantly, there was a signifiant interaction effect between the factors (F = 1444.8, p < .000). We ran a post-hoc analysis with Tukey HSD corrections for multiple comparisons, which showed all four conditions to be significantly different from each other, all contrasts with p < .0001. In particular, the active information gathering did end up with higher probability mass on \"attentive\" than the passive estimation for the attentive users, and lower probability mass for the distracted user. This supports our hypothesis that our method works, and active information gathering is better at identifying the correct state. Fig.  4  compares passive (grays and blacks) and active (light and dark oranges) across scenarios and for attentive (left) and distracted (right) users. It plots the probability of attentive over time, and the shaded regions correspond to standard error. From the first column, we can see that our algorithm in all cases detects human's attentiveness with much higher probably than the passive information gathering technique shown in black. From the second column, we see that our algorithm places significantly lower probability on attentiveness, which is correct because those users were distracted users. These are in line with the statistical analysis, with active information gathering doing a better job estimating the true human internal state. Fig.  5  plots the robot trajectories for the active information gathering setting. Similar to Fig.  4 , the solid lines are the mean of robot trajectories and the shaded regions show the standard error. We plot a representative dimension of the robot trajectory (like position or speed) for attentive (dark orange) or distracted (light orange) cases. The active robot probed the user, but ended up taking different actions when the user was attentive vs. distracted in order to maintain safety. For example, in Scenario 1, the trajectories show the robot is nudging into the human's lane, but the robot decides to move back to its own lane when the human drivers are distracted (light orange) in order to stay safe. In Scenario 2, the robot brakes in front of the human, but it brakes less when the human is distracted. Finally, in Scenario 3, the robot inches forward, but again it stops when if the human is distracted, and even backs up to make space for her. Fig.  6  plots the user trajectories for both active information gathering (first row) and passive information gathering (second row) conditions. We compare the reactions of distracted (light shades) and attentive (dark shades) users. There are large differences directly observable, with user reactions tending to indeed cluster according to their internal state. These differences are much smaller in the passive case (second row, where distracted is light gray and attentive is black). For example, in Scenario 1 and 2, the attentive users (dark orange) keep a larger distance to the car that nudges in front of them or brakes in front of them, while the distracted drivers (light orange) tend to keep a smaller distance. In Scenario 3, the attentive drivers tend to slow down and do not cross the intersection, when the robot actively inches forward. None of these behaviors can be detected clearly in the passive information gathering case (second row). This is the core advantage of active information gathering: the actions are purposefully selected by the robot such that users would behave drastically differently depending on their internal state, clarifying to the robot what this state actually is. Overall, these results support our simulation findings, that our algorithm performs better at estimating the true human internal state by leveraging purposeful information gathering actions. \n V. discussion Summary. In this paper, we formalized the problem of active information gathering between robot and human agents, where the robot plans to actively explore and gather information about the human's internal state by leveraging the effects of its actions on the human actions. The generated strategy for the robot actively probes the human by taking actions that impact the human's action in such a way that they reveal her internal state. The robot generates strategies for interaction that we would normally need to hand-craft, like inching forward at a 4-way stop. We evaluated our method in simulation and through a user study for various autonomous driving scenarios. Our results suggest that robots are indeed able to construct a more accurate belief over the human's driving style with active exploration than with passive estimation. Limitations and Future Work. Our work is limited in many ways. First, state estimation is not the end goal, and finding how to trade off exploration and exploitation is still a challenge. Second, our optimization is close to real-time, but higher computational efficiency is still needed. Further, our work relies on a model (reward function) of the human for each ϕ, which might be difficult to acquire, and might not be accurate. Thus far, we have assumed a static ϕ, but in reality ϕ might change over time (e.g. the human adapts her preferences), or might even be influenced by the robot (e.g. a defensive driver becomes more aggressive when the robot probes her). We also have not tested the users' acceptance of information gathering actions. Although these actions are useful, people might not always react positively to being probed. Last but not least, exploring safely will be of crucial importance. \n Conclusion. We are encouraged by the fact that robots can generate useful behavior for interaction autonomously, and are excited to explore informationgathering actions on human state further, including beyond autonomous driving scenarios. Passive Robot stops to R through Fig.  6 : The user trajectories for each scenario. The gap between attentive and distracted drivers' actions is clear in the active information gathering case (first row). 1 :Fig. 2 : 12 Fig.2: Our three scenarios, along with a comparison of robot plans for passive estimation (gray) vs active information gathering (orange). In the active condition, the robot is purposefully nudging in or braking to test human driver attentiveness. The color of the autonomous car in the initial state is yellow, but changes to either gray or orange in cases of passive and active information gathering respectively. driver might not realize the autonomous actions and maintain their velocity, getting closer to the autonomous vehicle. It is this difference in reactions that enables the robot to better estimate ϕ. Scenario 2: Braking to Explore on a Highway. In the second scenario, we show the driving style can be explored by the autonomous car probing the human driver behind it. The two vehicles start in the same lane as shown in Fig.2(b), where the autonomous car is in the front. In the passive condition, the autonomous car drives straight without exploring or enforcing any interactions with the human driven vehicle. In the active condition, the robot slows down to actively probe the human and find out her driving style. An attentive human would slow down and avoid collisions while a distracted human will have a harder time to keep safe distance between the two cars. Scenario 3: Nudging In to Explore at an Intersection. In this scenario, we consider the two vehicles at an intersection, where the autonomous car actively tries to explore human's driving style by nudging into the intersection. The initial conditions of the vehicles are shown in Fig.2(c). In the passive condition, the autonomous car stays at its position without probing the human, and only optimizes for collision avoidance. This provides limited observations from the human car resulting in a low confidence belief distribution. In the active condition, the autonomous car nudges into the intersection to probe the driving style of the human. An attentive human would slow down to stay safe at the intersection while a distracted human will not slow down. \n Fig. 3 : 3 Fig. 3: Legends indicating active/passive robots, attentive/distracted humans, and real user/ideal model used for Fig.4, Fig.??, Fig.5, and Fig.6. \n Fig. 4 : 4 Fig. 4:The probability that the robot assigns to attentive as a function of time, for the attentive (left) and distracted (right). Each plot compares the active algorithm to passive estimation, showing that active information gathering leads to more accurate state estimation, in simulation and with real users. \n Fig. 5 : 5 Fig.5: Robot trajectories for each scenario in the active information gathering condition. The robot acts differently when the human is attentive (dark orange) vs. when the human is distracted (light orange) due to the trade-off with safety. \n\t\t\t One exception is Nikolaidis et al. [17] , who propose to solve the full POMDP, albeit for discrete and not continuous state and action spaces. \n\t\t\t Authorized licensed use limited to: Carnegie Mellon Libraries. Downloaded on March 24,2022 at 00:30:44 UTC from IEEE Xplore. Restrictions apply.", "date_published": "n/a", "url": "n/a", "filename": "Information_gathering_actions_over_human_internal_state.tei.xml", "abstract": "Much of estimation of human internal state (goal, intentions, activities, preferences, etc.) is passive: an algorithm observes human actions and updates its estimate of human state. In this work, we embrace the fact that robot actions affect what humans do, and leverage it to improve state estimation. We enable robots to do active information gathering, by planning actions that probe the user in order to clarify their internal state. For instance, an autonomous car will plan to nudge into a human driver's lane to test their driving style. Results in simulation and in a user study suggest that active information gathering significantly outperforms passive state estimation.", "id": "847592efb448c3a7b62450158a95fa0a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "The far future argument for confronting catastrophic threats to humanity: Practical significance and alternatives", "text": "Introduction Over several decades, scholars from a variety of fields have advanced an argument for confronting catastrophic threats to humanity, rooted in the far future benefits of doing so.  1  In this context, the far future can loosely be defined as anything beyond the next several millennia, but will often emphasize timescales of millions or billions of years, or even longer.  2  Likewise, the catastrophic threats in question-also known as global catastrophic risks (GCRs) and existential risks, among other things-are those that would affect the trajectory of human civilization over these timescales. The simplest case is catastrophes resulting in human extinction, which is a permanent result and thus affects the trajectory of human civilization into the far future. More subtle but comparably relevant cases include catastrophes resulting in the permanent collapse of human civilization, preventing humanity from ever achieving certain very great things, and catastrophes resulting in delays Sufficiently large catastrophes can affect human civilization into the far future: thousands, millions, or billions of years from now, or even longer. The far future argument says that people should confront catastrophic threats to humanity in order to improve the far future trajectory of human civilization. However, many people are not motivated to help the far future. They are concerned only with the near future, or only with themselves and their communities. This paper assesses the extent to which practical actions to confront catastrophic threats require support for the far future argument and proposes two alternative means of motivating actions. First, many catastrophes could occur in the near future; actions to confront them have near-future benefits. Second, many actions have cobenefits unrelated to catastrophes, and can be mainstreamed into established activities. Most actions, covering most of the total threat, can be motivated with one or both of these alternatives. However, some catastrophe-confronting actions can only be justified with reference to the far future. Attention to the far future can also sometimes inspire additional action. Confronting catastrophic threats best succeeds when it considers the specific practical actions to confront the threats and the various motivations people may have to take these actions. ß 2015 Elsevier Ltd. All rights reserved. in the subsequent rise of civilization toward these achievements. The scholarship argues that people should care about human civilization into the far future, and thus, to achieve far future benefits, should seek to confront these catastrophic threats. Call this the far future argument for confronting catastrophic threats to humanity. In this paper, I will not dispute the basic validity of the far future argument. Indeed, I agree with it, and have advanced it repeatedly in my own work  (Baum, 2009 (Baum, , 2010 Maher and Baum, 2013) . Instead, I assess the extent to which the far future argument is necessary or helpful for actually confronting the threats. In other words, what is the practical significance of the far future argument? I also propose and assess two alternative approaches to confronting the threats. One alternative emphasizes near future benefits of avoiding near future catastrophes. The other alternative emphasizes other (unrelated) benefits of actions that also help confront the threats, creating opportunities even for people who have zero care about the threats. It would be important if the threats can be confronted without the far future argument, because many people do not buy the argument. That people do not is suggested by a range of research. An extensive time discounting literature assess how much people value future costs and benefits. Most discounting studies use time scales of days to decades and focus on future benefits to oneself  (Frederick, Loewenstein, & O'Donoghue, 2002) ; these studies are of limited relevance to valuations of the far future of human civilization. One more relevant time discounting study finds that people discount lives saved 20 years later at a 25% annual rate and lives saved 100 years later at an 8% annual rate  (Johannesson & Johansson, 1996) ; extrapolating this suggests negligible concern for lives saved in the far future. Similarly,  Tonn, Conrad, & Hemrick (2006, p. 821)  find that people believe humanity should plan mainly for the upcoming 20 years or so and should plan less for time periods over 1000 years. In a study on social discounting,  Jones and Rachlin (2006)  find that people are willing to forgo more money to help close friends and family than distant acquaintances; they presumably would forgo even less for members of far future generations. Finally, there are considerations rooted in how societies today are structured. Several researchers have argued that current electoral structures favor the short-term  (Ekeli, 2005; Tonn, 1996; Wolfe, 2008) .  Similarly, Karlsson (2005)  suggests that the rise of decentralized capitalist/democratic political economies and the fall of authoritarian (notably communist) political economies has diminished major long-term planning. While none of these studies directly assess the extent to which people buy the far future argument, the studies all suggest that many people do not buy the argument to any significant degree. To the extent that efforts to confront catastrophic threats can be made synergistic with what people already care about, a lot more can be done. This would seem to be an obvious point, but it has gone largely overlooked in prior research on catastrophic threats. One exception is  Posner (2004) , who argues that some actions to reduce the risk of human extinction can be justified even if only the current generation and its immediate successor are valued. Another is  Baum (2015) , who proposes to confront the threat of catastrophic nuclear winter in terms that could appeal to nuclear weapon states; Baum calls this ''ethics with strategy''. But most of the prior research, including the studies cited above, emphasize the far future argument. This paper expands Posner's argument to further argue that some actions can be taken even for those who only care about their immediate communities or even just themselves. This paper also makes progress toward assessing the total practical significance of the far future by presenting a relatively comprehensive survey of GCRs and GCR-reducing actions. Such surveys are also scarce; one example is  Leggett (2006) , who surveys the space of GCRs to identify priorities for action. The present paper also has commonalities with  Tonn and Stiefel (2014) , who evaluate different levels of sacrifice that society should make in response to GCRs of different magnitude. The present paper also considers levels of sacrifice, but instead argues that, from a practical standpoint, it is better to start with those actions that require less sacrifice or are in other ways more desirable. Indeed, actions requiring large sacrifice may only be justifiable with reference to far future benefits. The paper is organized as follows. Section 2 briefly reviews the space of GCRs. All actions to reduce the risk must help on one or more of these so as to result in a net risk reduction. The space of GCRs likewise provides an organizing framework for subsequent sections, as summarized in Table  1 . Section 3 discusses the timing of GCRs. For catastrophes that could happen earlier, actions to avoid them will include the earlier benefits of catastrophe avoidance. Almost all GCR reduction actions have near-future GCR reduction benefits. Section 4 discusses co-benefits and mainstreaming of GCR reduction actions. Co-benefits are benefits unrelated to GCR reduction. Mainstreaming is integrating GCR reduction into established Table  1  Summary of global catastrophic risk categories (Section 2), their timing (Section 3), co-benefits and mainstreaming opportunities (Section 4), and high-cost GCR reduction actions that may only be justifiable with reference to far future benefits (Section 5). The co-benefits and mainstreaming opportunities and high-cost actions are illustrative examples, not complete listings. activities. Co-benefits and mainstreaming are both ways to facilitate GCR reduction for those who are not specifically motivated by the far future. Section 5 discusses GCR reduction actions that can only be justified in reference to the farfuture benefits of GCR reduction. While these actions will typically not be the best place to start, they can play an important role in overall GCR reduction efforts. Section 6 discusses the ways in which attention to the far future can inspire additional GCR reduction action. This includes both analytical inspiration and emotional inspiration. Section 7 concludes. \n GCR category \n The global catastrophic risks Which actions can help reduce the risk of global catastrophe depend on what the global catastrophic risks are in the first place. This section briefly overviews the risks. The risks have been described in more detail elsewhere  (Asimov, 1979; Barrett, 2007; Bostrom & C ´irkovic ´, 2008; Guterl, 2012; Jha, 2011; Leslie, 1996; Rees, 2003; Tonn & MacGregor, 2009) . While this section lists GCRs in distinct categories, the risks are often interconnected both within and across categories. For example, the emerging technology GCR of geoengineering is developed in response to the environmental change GCR of climate change, and the geoengineering risk is in turn affected by other GCRs such as large-scale violence or pandemics  (Baum, Maher, & Haqq-Misra, 2013) . Similarly, GCR reduction actions can often affect risks in multiple categories. So while the GCR reduction actions discusses in Sections 3-5 are organized in terms of the categories presented here, it should be understood that specific actions often spill across categories. All this suggests a systems approach to studying GCR. \n Environmental change By environmental change, I mean to refer to human-driven global environmental changes; natural disasters are discussed below. Climate change is perhaps the most commonly cited environmental change GCR; worst-case climate change scenarios attract considerable attention (e.g.  Sherwood & Huber, 2010) . Other environmental change GCRs could include biodiversity loss, biogeochemical flows (interference with the nitrogen and phosphorus cycles), stratospheric ozone depletion, ocean acidification, global fresh water use, land use change, chemical pollution, and atmospheric aerosol loading  (Rockstro ¨m et al., 2009a; Rockstro ¨m et al., 2009b) . While any of these phenomena could dramatically alter the global environment, it is less clear whether the impacts would be catastrophic for humanity  (Baum & Handoh, 2014; Raudsepp-Hearne et al., 2010) . For this paper, it is important that many pro-environmental actions simultaneously help across a broad set of global environmental changes, lessening the need to distinguish which changes could be catastrophic for humanity. \n Emerging technologies Several emerging technologies could cause global catastrophe, including artificial intelligence  (Bostrom, 2014; Eden, Moor, Soraker, & Steinhart, 2013) , biotechnology  (Vogel, 2013) , geoengineering  (Baum et al., 2013; Caldeira, Bala, & Cao, 2013) , and nanotechnology for atomically precise manufacturing  (Drexler, 2013) . These risks are relatively uncertain given the unprecedented nature of emerging technology, but they may constitute a significant portion of total risk. \n Large-scale violence A sufficiently large global war could be catastrophic regardless of the technologies used-for comparison, hundreds of thousands died from attacks with machetes and other unmechanized weapons in the Rwandan genocide. Weapons of mass destruction make the job much easier. Nuclear weapons can be catastrophic both through direct explosions and the indirect effects of nuclear winter  (Mills, Toon, Lee-Taylor, & Robock, 2014) . Biological weapons can also readily cause global catastrophe, in particular if they are contagious; indeed, nonstate actors or even single individuals may be able to cause global catastrophes with engineered contagions  (Nouri & Chyba, 2008; Rees, 2003) . The pressures of conflict can also lead actors to take larger risks, as occurred during World War II when the Americans proceeded with the first nuclear weapon test despite concerns that it could ignite the atmosphere, killing everyone  (Konopinski, Marvin, & Teller, 1946) . Finally, major global violence could also result from an oppressive global totalitarian government  (Caplan, 2008) . \n Pandemics Pandemics can be of natural or artificial origin, or both. Humans catch disease from the environment, in particular from other species. The development and transmission of zoonotic diseases can be enhanced by human activities including wild habitat destruction and factory farming. While it is clear that global pandemics can occur, their exact severity is a matter of ongoing analysis and debate  (Germann, Kadau, Longini, & Macken, 2006; Koblentz, 2009) . \n Natural disasters Global catastrophes can result from several natural disasters including asteroid and comet impacts  (Bucknam & Gold, 2008; Sleep & Zahnle, 1998) , supervolcano eruptions  (Driscoll, Bozzo, Gray, Robock, & Stenchikov, 2012; Rampino, Self, & Stothers, 1988) , solar storms (NRC, 2008), and gamma ray bursts  (Atri, Melott, & Karam, 2013) . While these natural disasters generally have lower probabilities, they nonetheless can be worth some effort to confront. Another natural disaster is the gradual warming of the Sun, which will (with very high probability) make Earth uninhabitable for humanity in a few billion years (O'Malley-James, Cockell, Greaves, & Raven, 2014). Other long-term astronomical risks, such as the Milky Way collision with Andromeda (increasing the rate of dangerous supernovae) and the death of all stars (removing a major energy source) play out on similar or longer time scales  (Adams, 2008) . \n Physics experiments Certain types of physics experiments have raised concerns that the experiments could go wrong, obliterating Earth and its vicinity. This notably includes high-energy particle physics experiments such as at the CERN Large Hadron Collider. Physicists evaluating this risk have argued that the risk is vanishingly small; however, they may be underestimating the risk by neglecting the possibility that their analysis is mistaken  (Ord, Hillerbrand, & Sandberg, 2010) . \n Extraterrestrial encounter It is not presently known if there is any extraterrestrial life, let alone intelligent extraterrestrial civilizations. However, if extraterrestrial civilizations exist, then the result could be catastrophic for humanity  (Baum, Haqq-Misra, & Domagal-Goldman, 2011; Michaud, 2007) . Non-civilization extraterrestrial life could also harm humanity with catastrophic contaminations  (Conley & Rummel, 2008) . \n Unknowns There may be entire categories of GCR not yet identified. \n The timing of the global catastrophic risks If a global catastrophe could occur during the near future, then there will be near-future benefits to reducing the risk. The sooner the catastrophe could occur, the larger the near-future benefits would be. In general, it will be easiest to motivate action to confront the most imminent catastrophes-hence  Posner's (2004)  argument that much GCR-reducing action can be justified even if one only cares about the present generation and the next one to come. It is thus worth examining the timing of the catastrophes. \n Specific global catastrophic risks \n Environmental change Major environmental changes are already visible, with larger changes expected on time scales of decades to tens of millennia. Climate change is among the more long-term of these, with some impacts already visible, and the worst climatic effects contained within the next 25,000 years or so.  3  Another possible long-term environmental change is an oceanic anoxic event, which is caused by phosphorus runoff and would in turn cause major die-off of marine species. An oceanic anoxic event could occur on time scales of millennia  (Handoh & Lenton, 2003) ; more localized effects of phosphorus runoff are already visible. \n Emerging technologies Dangerous biotechnology already exists, and is steadily increasing in capability. Early design work for geoengineering is already underway, with deployments suggested to occur in upcoming decades  (Keith, Parsons, & Morgan, 2010) . Experts give a significant probability to GCR-level artificial intelligence occurring within this century or next  (Baum, Goertzel, & Goertzel, 2011; Mu ¨ller & Bostrom, 2014) . Nanotechnology for atomically precise manufacturing may have similar time horizons. \n Large-scale violence Large-scale violence can happen at any time. The ongoing Ukraine crisis is a firm reminder that significant tensions linger between major nuclear weapons states. Nuclear war could even occur inadvertently, due to false alarm events that can occur at any time  (Barrett, Baum, & Hostetler, 2013) . Risks from biological weapons could increase in upcoming decades as biotechnology advances. However, overall risk from large-scale violence may be gradually declining, following a general trend toward less violence  (Pinker, 2011)  and an increasing sophistication of global peacekeeping capability  (Goldstein, 2011) . \n Pandemics Pandemics can also break out at any time. Recent outbreaks of SARS, H5N1 and H1N1 flus, MERS, and currently Ebola have so far not reached a high degree of global lethality, but they are clear reminders that the threat of pandemics persists. Advances in biotechnology can lead to increasing risk through both intentional use and mishaps, as can increasing global connectivity. On the other hand, advances in public health can reduce the risk. \n Natural disasters Many natural disasters can also occur at any time. Risk from impact events, supervolcano eruptions, solar storms, and gamma ray bursts is roughly constant over long periods of time, into the far future. NASA's near-Earth objects survey has significantly reduced estimates of the risk of large impacts occurring over the next century or so  (Harris, 2008) . Several astronomical risks, including the Sun's gradual warming, the Milky Way collision with Andromeda, and the death of all stars, are GCRs that exists exclusively in the far future. \n Physics experiments The risk from physics experiments depends critically on which physics experiments are conducted. The risk could increase as the capability to conduct experiments increases. \n Extraterrestrial encounter Humanity could encounter extraterrestrials at any time, including through ongoing searches for extraterrestrial intelligence (SETI). Some risk (especially contamination risk) comes mainly from human or robotic travel in space. Some risk comes from messaging to extraterrestrial intelligence (METI;  Haqq-Misra, Busch, Som, & Baum, 2013) . The timing of METI risk depends on the distance from Earth to the location being messaged. METI to sufficiently distant locations is another GCR that exists exclusively in the far future. \n Unknowns Unknown GCRs could occur in both the near and far future. Indeed, more future GCRs are less likely to be already identified. \n Discussion Relatively few identified GCRs exist exclusively in the far future: certain astronomical risks and METI to distant locations. For all other GCRs-and this constitutes almost all of the total identifiable risk-the catastrophes could occur in the near future. The identified risks from emerging technologies and physics experiments could only occur in the near future. The identified risks from environmental change, large-scale violence, pandemics, some natural disasters, some extraterrestrial encounter risks, and unknowns could occur in the near or far future. The preponderance of near future risks suggests that a lot of actions to reduce these risks can be done without reference to their far future benefits. On the other hand, these near future benefits may not always be enough, especially when the catastrophes would occur several decades or centuries later, as people often care little about even these earlier times. It is thus worth pursuing other means of motivating GCR reduction. \n Co-benefits and mainstreaming GCR-reducing actions Insight on how to motivate GCR reduction can be found from outside the core GCR literature, in some related literatures. The climate change mitigation community has developed the concept of co-benefits, defined as benefits besides the target goal  (Hosking, Mudu, & Dora, 2011; Miyatsuka & Zusman, n.d.) . For climate change mitigation, the target goal is greenhouse gas emissions reductions. Research assesses how communities can reduce their emissions while improving their economic development, public health, and wellbeing. The co-benefits concept readily applies GCR. Some actions to reduce GCR will also be profitable, fun, healthy, satisfying, safe, or otherwise desirable, often to those who perform the actions. Similarly, the natural disaster management community has a robust practice of mainstreaming disaster management into established goals and procedures, especially those regarding development  (Benson, 2009; Twigg & Steiner, 2002) . Disaster management actions will often only be taken when they can be integrated into established goals and procedures; otherwise, the actions will be too impractical or undesirable. For example, urban design steps to reduce a town's vulnerability to hurricane storm surge can be mainstreamed into the town's broader urban planning processes  (Frazier, Wood, & Yarnal, 2010) . GCR reduction actions can likewise also be mainstreamed into whatever people are already doing or trying to do. The GCR reduction community would be wise to adopt the approaches of co-benefits and mainstreaming. Doing so requires an understanding of the co-benefits that can come from various GCR-reducing actions and the relevant established goals and procedures. For many of these actions-in particular those with sufficiently large co-benefits and wellestablished goals and procedures-reducing GCR can be a nice ancillary benefit of actions that might as well be taken anyway. For these actions, no concern for the far future is needed; often, no concern beyond one's immediate community is needed. These actions require the least sacrifice (indeed, it is a sacrifice not to take these actions) and likewise will often be the easiest actions to promote. This begs the question of which GCR-reducing actions have significant co-benefits and mainstreaming opportunities.  \n . Environmental change Environmental change is largely driven by a wide variety of basic activities, including food consumption, transport, real estate development, and natural resource usage. More environmentally friendly actions can often be justified for nonenvironmental reasons. A recent study by McKinsey  (Enkvist, Naucle ´r, & Rosander, 2007)  found that many greenhouse gas emission reductions would result in net monetary benefits for those who reduce these emissions, especially in the realm of energy efficiency in buildings and transport. Happiness research has found that people rate their daily commute as being among their least happy activities  (Layard, 2003) . Public health research links high-meat diets with obesity and other health problems  (Pan et al., 2012) . Buildings, transport, and food are meanwhile three of the most environmentally important sectors  (Metz et al., 2007; Steinfeld et al., 2006; USEIA, 2011) . If significant changes in these sectors can be achieved for nonenvironmental reasons, the environmental benefit could be quite large. \n Emerging technologies It is often beneficial to develop regulations for multiple technologies at the same time, due to similarities between the technologies and the regulations  (Kuzma & Priest, 2010; Wilson, 2013a) . Concerns about other technologies can thus motivate general technology regulation, which provides a framework for mainstreaming the regulation of emerging technologies GCRs. In addition, some actions specific to certain emerging technologies can have co-benefits. For example, one proposed solution to artificial intelligence risk is to design the AI to be ''friendly'' to humanity. In addition to not causing a catastrophe, such an AI could help with other societal problems  (Muehlhauser & Bostrom, 2014) . If such an AI can be achieved with sufficient confidence, then this could be an attractive action even for those who are not concerned about AI risk. \n Large-scale violence Achieving peace avoids violence at all scales and also brings a variety of co-benefits. One co-benefit is economic growththe so-called ''peace dividend''  (Knight, Loayza, & Villanueva, 1996; Ward & Davis, 1992) . Another co-benefit is psychological. Recent research finds that conflict is often driven by humiliation, and likewise that giving people a sense of dignity can help  (Lindner, 2006; Stern, 2003) . Finally, other research suggests that reducing domestic violence against women could lead to less interstate war  (Hudson, Ballif-Spanvill, Caprioli, & Emmett, 2012) . Emphasizing these co-benefits could justify much action to reduce large-scale violence. Another worthy point of focus is violent nonstate actors, which continue to receive extensive attention in the wake of the 9-11 attacks. While nonstate actors may not be able to cause violence large enough to result in global catastrophe, 4 actions to confront them may have co-benefits and mainstreaming opportunities for large-scale violence. For example, the annual Nuclear Security Summits initiated by US President Barack Obama aim to prevent nonstate actors from acquiring nuclear weapons, but they also strengthen norms against nuclear weapon use more generally. \n Pandemics As noted above, there is some debate about how severe pandemics could be, including whether they would impact the far future. To a large extent, this debate is irrelevant. Regardless of how severe pandemics would be, there already exists a significant global public health infrastructure that responds to pandemics of all sizes. Improving this infrastructure can further improve the response. The case for improving this infrastructure is strengthened by the possibility of catastrophic pandemics, but the case is not dependent on this possibility  (McKibbin & Sidorenko, 2006) . \n Natural disasters The GCR literature has proposed certain measures to increase society's resilience to a wide range of global catastrophes, including natural disasters. These measures include food stockpiles , underground refuges  (Jebari, 2014) , and space colonies and refuges  (Abrams et al., 2007; Shapiro, 2009) . These measures also tend to increase society's resilience to smaller catastrophes. Indeed, many actions taken to prepare for smaller catastrophes also benefit GCR reduction. In addition, while space colonies and refuges have been criticized for their high cost relative to other means of reducing global catastrophic risk  (Baum, 2009; Sandberg, Matheny, & C ´irkovic ´, 2008) , some space missions are already underway or in planning for a variety of other reasons, including science, political prestige, and economic opportunity (e.g. in asteroid mining). Space colonies or refuges could be mainstreamed into these missions  (Baum, Denkenberger, & Haqq-Misra, 2014) . \n Physics experiments Physics experiments are a curious case, because the relevant experiments are quite expensive (hundreds of millions to billions of dollars) and the social benefits somewhat limited. As  Parson (2007, p. 155)  puts it, ''this research is remote from practical application and serves largely to indulge national pride and the intellectual passion of a tiny elite group''. Arguably, the co-benefits of reducing physics experiment risk include the money saved by not doing the experiments, and by tasking the money to a worthier cause, analogous to the peace dividend, though this is likely to be a controversial view among those who value the physics experiments. \n Extraterrestrial encounter Protection against extraterrestrial contamination has the co-benefit of protecting extraterrestrial environments from contamination by humans, which is of significant scientific value  (Conley & Rummel, 2008) . The costs of SETI and METI are small relative to the big physics experiments, so while there are dollar savings to realize from skipping them, these are less of an issue. Perhaps the extraterrestrial-risk-reducing action with the most co-benefits would be research and public education into what the risks could be. Discussions of ETI are very popular, as seen in the extensive popular media and entertainment attention to ETI. \n Unknowns Actions likely to reduce unknown GCRs will typically be generic actions that also help reduce other GCRs or even smaller risks, such as building refuges  (Jebari, 2014)  and stockpiling resources . \n Discussion Many GCR-reducing actions, covering the full breadth of GCRs, have sizable co-benefits, and can also be mainstreamed into existing activities. Many of these actions will often be desirable even without reference to GCR, let alone to the far future benefits of GCR reduction. These ''easy'' actions will typically be the lowest hanging fruit, the easiest GCR reductions to promote. They offer a sensible starting point for those seeking to reduce GCR. \n Actions with significant cost Ideally, all GCR-reducing actions would have low costs and large co-benefits, such that it would be easy to persuade people to take the actions, and such that the totality of GCR could be reduced with minimal burden to those taking the actions and to society at large. As discussed above, many such actions exist. However, this is not the case for all GCR-reducing actions. Some of these other actions require considerable sacrifice, especially the most aggressive GCR-reduction efforts. Tonn and Stiefel's (2014) levels of societal actions are instructive here. The levels range from doing nothing to an extreme war footing in which society is organized specifically to reduce GCR. Actions requiring more sacrifice, especially those at or near the level of extreme war footing, might only be justifiable with reference to the far-future benefits. While these actions will typically not be the lowest hanging fruit, they could be important components of an overall portfolio of GCR-reducing actions. \n Specific global catastrophic risks \n Environmental change The most aggressive pro-environmental actions include public policies like a high carbon tax, personal behaviors requiring great inconvenience and sacrifice, and restructuring the entire global industrial economy away from fossil fuels and other pollutants. To achieve a larger reduction in environmental change GCR, some of these more aggressive actions may be needed. That these more aggressive actions may only be justifiable with reference to far-future benefits is a core point from debates about discounting in environmental policy (Nordhaus, 2008). \n Emerging technologies One way to reduce emerging technology GCR is to simply abstain from developing the technologies, i.e., to relinquish them  (Joy, 2000) . However, if these technologies do not cause catastrophe, they sometimes come with great benefits: geoengineering can avoid the worst effects of climate change; AI can solve a variety of social problems; biotechnology can help cure disease. Thus relinquishing the technologies can require a large sacrifice  (Baum, 2014) . This sacrifice may sometimes only be justifiable given the far-future benefits of GCR reduction. \n Large-scale violence While nuclear weapons can cause great harm, they are also often attributed with helping maintain peace, through the doctrine of nuclear deterrence: countries hesitate to attack each other for fear of being destroyed in nuclear retaliation. There are questions about the efficacy of nuclear deterrence  (Wilson, 2013b)  and there are proposals to achieve deterrence with out large nuclear arsenals  (Baum, 2015) . However, a common view posits that nuclear deterrence is necessary until international relations are peaceful enough for a world without nuclear weapons  (Obama, 2009) . Following this logic, immediate nuclear disarmament might reduce GCR, but it might also increase the preponderance of smaller conflicts and other geopolitical instabilities. Depending on the details, immediate nuclear disarmament might only be justifiable with reference to the far future. \n Pandemics One aggressive action to reduce pandemics risk would be aggressive quarantine, such as blockading the major islands of Indonesia, Japan, the United Kingdom, and other countries. Travel restrictions could keep populations in these places safe. During a sufficiently severe outbreak, populations in these places could even request to be blockaded. A safer but costlier and less desirable policy would blockade them at first alert of a possible outbreak, or even keep them blockaded on a permanent basis. Doing so might lower GCR, but might only be justifiable with reference to the far future. \n Natural disasters One proposed aggressive action for natural disasters could be to drill the ground around potential supervolcanoes to extract the heat, although the technological feasibility of this proposal has not yet been established.  5  This could be a very costly project, but, if it works, it could also reduce supervolcanoes GCR. The project would come with a co-benefit of geothermal energy, but this is likely not nearly enough to justify the expense. Another possibility is advanced surfaceindependent refuges, which could protect against a variety of GCRs, including many of the natural disasters, but again could come at great expense  Beckstead, 2014) . \n Physics experiments and extraterrestrial encounter I am not aware of any actions to reduce near-future GCR from physics experiments and extraterrestrial encounter that have significant cost and can only be justified with reference to far-future benefits. To the contrary, many actions to reduce these risks save money (Section 4.1). Protection against contamination does have a cost, and shutting METI programs down could cost the public a source of popular entertainment. On the other hand, the shut down itself could also create an entertaining controversy. Regardless, the costs involved are not large. \n Unknowns One action that might only be justifiable with reference to far future benefits is a far-future version of the ''extraterrestrial time capsule'' proposed in . These capsules contain artifacts of benefit to catastrophe survivors for a range of known and unknown catastrophe scenarios. The capsules are launched into space in trajectories designed to return to Earth at some future date.  suggest a return date 100 years into the future, but it may be possible (and expensive) to have return dates in the far future. \n Discussion For those who wish to keep humanity highly safe from catastrophe, there are actions that can only be justified with reference to the far-future benefits of GCR reduction. While these actions are typically not the best place to start, they can offer additional GCR reductions beyond what the easier actions offer. Given the enormous far-future benefits of GCR reduction, arguably these actions merit consideration. However, hopefully GCR can be essentially eliminated without resorting to these actions. If these actions are necessary, it will likewise be necessary to appeal to the importance of the far future. \n Far future as inspiration The paper thus far has focused on how to avoid appeals to the far future argument, in recognition of the fact that many people are not motivated by what will benefit the far future. But some GCR reduction actions can only be justified with reference to far future benefits. Additionally, some people are motivated to benefit the far future. Other people could be too. Tapping the inspirational power of the far future can enable more GCR reduction. There are at least two ways that the far future can inspire action: analytical and emotional. Both are consistent with the far future argument, but the argument is typically inspired by analytical considerations. The analytical inspiration is found in works analyzing how to maximize the good or achieve related objectives. Most of the scholarly works invoking the far future argument are of this sort.  6  Such ideas have the potential to resonate not just with other scholars, but with people in other professions as well, and also the lay public. Thus there can be some value to disseminating analysis about the importance of the far future and its relation to GCR. Analytical inspiration can also come from analyzing specific actions in terms of their far-future importance. Such analysis can help promote these actions, even if the actions could be justified without reference to the far future. However, the analysis should be careful to connect with actual decision makers, and not just evaluate hypothetically optimal actions that no one ever takes. For example, there has been now multiple decades of research analyzing what the optimal carbon tax should be (for an early work, see  Nordhaus, 1992 ), yet throughout this period, for most of the world, the actual carbon tax has been zero. Analytical inspiration has its limits. Research effort may be more productively spent on what policies and other actions people are actually willing to implement. The other far future inspiration is emotional. The destruction of human civilization can itself be a wrenching emotional idea. In The Fate of the Earth, Jonathan Schell writes ''The thought of cutting off life's flow, of amputating this future, is so shocking, so alien to nature, and so contradictory to life's impulse that we can scarcely entertain it before turning away in revulsion and disbelief''  (Schell, 1982 (Schell, /2000 ). In addition, there is a certain beauty to the idea of helping shape the entire arch of the narrative of humanity, or even the universe itself. People often find a sense of purpose and meaning in contributing to something bigger than themselves-and it does not get any bigger than this. Carl  Sagan's (1994)  Pale Blue Dot and James  Martin's (2007)  The Meaning of the 21st Century both capture this well, painting vivid pictures of the special place of humanity in the universe and the special opportunities people today have to make a difference of potentially cosmic significance. This perspective says that humanity faces great challenges. It says that if these challenges are successfully met, then humanity can go on to some amazing achievements. It is a worthy perspective for integrating the far future into our lives, not just for our day-to-day actions but also for how we understand ourselves as human beings alive today. This may be worth something in its own right, but it can also have a practical value in motivating additional actions to confront catastrophic threats to humanity. \n Conclusion The far future argument is sound. The goal of helping the far future is a very worthy one, and helping the far future often means helping reduce the risk of those global catastrophes that could diminish the far-future success of human civilization. However, in practical terms, reducing this risk will not always require attention to its far-future significance. This is important because many people are not motivated to help the far future, but they could nonetheless be motivated to take actions that reduce GCR and in turn help the far future. They may do this because the actions reduce the risk of near-future GCRs, or because the actions have co-benefits unrelated to GCRs and can be mainstreamed into established activities. This paper surveys GCRs and GCR-reducing actions in terms of how much these actions require support for the far future argument for confronting catastrophic threats to humanity. The analysis suggests that a large portion of total GCR, probably a large majority, can be reduced without reference to the far future and with reference to what people already care about, be it the near future or even more parochial concerns. These actions will often be the best to promote, achieving the largest GCR reduction relative to effort spent. On the other hand, some significant GCR reducing actions (especially those requiring large sacrifice) can only be justified with reference to their far-future benefits. For these actions in particular, it is important to emphasize how the far future can inspire action. Several priorities for future research are apparent. Quantitative GCR analysis could help identify which actions best reduce GCR and also what portion of GCR can be reduced without reference to the far future. Analysis covering the breadth of GCRs would be especially helpful. Social scientific research could study how to effectively engage stakeholders so as to leverage co-benefits and mainstream GCR reductions into existing programs. Social scientific research could also examine how to effectively tap the inspirational power of the far future, especially for emotional inspiration, which has received limited prior attention. Progress in these research areas could go a long way toward identifying how to, in practice, achieve large GCR reductions. The overall message of this paper is that helping the far future requires attention to which specific actions can help the far future and likewise to what can motivate these actions. The actions are not necessarily motivated by their far-future impact. This is fine. The far future does not care why people acted to help it-the far future only cares that it was helped. And people taking these actions will rarely mind that their actions also help the far future. Most people will probably view this as at least a nice ancillary benefit. Additionally, people will appreciate that those promoting the far future have taken the courtesy to consider what they care about and fit the far future into that. It can be disrespectful and counterproductive to expect people to drop everything they are doing just because some research concluded that the far future is more important. This means that those who seek to promote actions to benefit the far future must engage on an interpersonal level with the people who will take these actions, to understand what these people care about and how far-future-benefiting actions can fit in. This is an important task to pursue, given the enormity of what human civilization can accomplish from now into the far future. Futures \n\t\t\t The 25,000 year figure is derived from Archer and Ganopolski (2005) , Fig.3C, which shows a rapid temperature spike that declines most of the way back to current temperatures within 25,000 years and then remains at similar temperatures for another 500,000 years. However, this refers specifically to climatic effects; the human effects could persist longer, especially if the climate change causes a civilization-ending global catastrophe. S.D.Baum / Futures 72 (2015) 86-96   \n\t\t\t Nuclear terrorism would likely be too small to cause a far-future-impacting global catastrophe, unless it catalyzed a large-scale interstate nuclear war (Ayson, 2010) . Biological terrorism could more readily cause a global catastrophe, as discussed above.S.D.Baum / Futures 72 (2015) 86-96   \n\t\t\t S.D.Baum / Futures 72 (2015) 86-96   \n\t\t\t An idea to this effect is briefly discussed inLeggett (2006, p. 794). 6 See citations in Footnote 1. S.D. Baum / Futures 72 (2015) 86-96", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0016328715000312-main.tei.xml", "abstract": "others. 2 This definition of the far future is most explicitly stated in Beckstead (2013). In contrast, psychology and cognitive science research commonly defines ''far future'' in timescales of years (e.g.", "id": "a9fb0ffada26f9d6ec0db611df14c875"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Victor Galaz", "Miguel A Centeno", "Peter W Callahan", "Amar Causevic", "Thayer Patterson", "Irina Brass", "Seth Baum", "Darryl Farber", "Joern Fischer", "David Garcia", "Timon Mcphearson", "Daniel Jimenez", "Brian King", "Paul Larcey", "Karen Levy"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0160791X21002165-main.tei.xml", "abstract": "Automated decision making and predictive analytics through artificial intelligence, in combination with rapid progress in technologies such as sensor technology and robotics are likely to change the way individuals, communities, governments and private actors perceive and respond to climate and ecological change. Methods based on various forms of artificial intelligence are already today being applied in a number of research fields related to climate change and environmental monitoring. Investments into applications of these technologies in agriculture, forestry and the extraction of marine resources also seem to be increasing rapidly. Despite a growing interest in, and deployment of AI-technologies in domains critical for sustainability, few have explored possible systemic risks in depth. This article offers a global overview of the progress of such technologies in sectors with high impact potential for sustainability like farming, forestry and the extraction of marine resources. We also identify possible systemic risks in these domains including a) algorithmic bias and allocative harms; b) unequal access and benefits; c) cascading failures and external disruptions, and d) trade-offs between efficiency and resilience. We explore these emerging risks, identify critical questions, and discuss the limitations of current governance mechanisms in addressing AI sustainability risks in these sectors.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "The great downside dilemma for risky emerging technologies", "text": "Introduction Would you play a game of Russian roulette? Would you take a six chamber revolver, put one bullet in, give it a spin, point it at your head, and pull the trigger? How about for a million dollars? Would you play? I would guess that most readers of this paper would not play. I would guess that you would think that a chance of one million dollars is not worth it to take this risk of ending up with a bullet in the brain. I personally would not play, for the same reason. Our brains and our lives are simply worth more than that. But suppose your life circumstances were different. Suppose you were struggling with money, that you were basically broke. Suppose you were sick, with a chronic condition you cannot afford to cure. Maybe you do not have that many years left to live anyway. Now, with less to lose and more to gain, that game of Russian roulette might start to look more attractive. Now, you might start counting how much that million dollars could do for you. Could it cure your sickness, make you healthy again? Could it add years to your life? Could it pull you out of poverty? Could it give you basic comfort? If the million dollars would do enough for you, then maybe you would choose to play. Desperate circumstances can sometimes warrant taking desperate risks. If it works, the circumstances get better, maybe much better. But it might not work, and if it does not, it comes with a downside-in this case, a bullet in the brain. Whether to play the game is a downside dilemma: a dilemma involving a significant possible downside. This paper talks of a great downside dilemma. It is great because the stakes are so high-indeed, they are literally astronomical. At stake is not the fate of a single person, as in Russian roulette, but the fate of human civilization. This includes the roughly seven billion people alive today and the many more members of all the future generations that might ever live. The stakes are astronomical because humans (or our descendants) might be able to colonize space and achieve great things across the Universe. Human civilization already has an active space program, and space colonization seems feasible, as long as no great catastrophe denies humanity the chance. The rest of the Universe is vastly larger than our humble home planet, so space colonization would open up enormous new opportunities. Meanwhile, for all humanity currently knows, humans might have the only intelligent civilization anywhere in the Universe. And so the stakes could mean nothing less than the success or failure of intelligent civilization in the entire universe. A great downside dilemma, indeed. | Royal Swedish To be more specific, the great downside dilemma is any circumstance in which human civilization must choose whether to take a risk in which, if it works out, the benefit greatly improves the human condition, but if it does not work out, a catastrophe will occur, a catastrophe so large that civilization could perish, a metaphorical bullet in the brain. The dilemma is whether to take the risk. How much does civilization value that improvement in its condition? Could it be enough to pull civilization out of desperate circumstances? How large is the risk of catastrophe? Is it small enough that the risk is worth taking? Can any risk of civilization perishing be small enough to justify taking the risk? These questions must be answered in order to decide whether to take the risk. The great downside dilemma arises often for decisions about whether to pursue certain emerging technologies. These technologies promise to solve major societal problems. They bring peace, cure disease, protect the environment, and more. Or rather, they do these things if they work as intended. However, they may not work out as intended. They may fail, and fail catastrophically. In the worst cases, they could kill every living human-the extinction of our species-and destroy much of the rest of Earth's biosphere as well. Should society develop and launch these technologies, given their promise and despite their risks? That is the great downside dilemma for emerging technologies. This dilemma is an important issue for society as a whole and especially for scientists and engineers, who by virtue of their background are especially able to contribute to the debate. This dilemma is one important part of the broader challenge of avoiding civilization-ending global catastrophes. A growing body of scholarship recognizes the avoidance of these catastrophes as crucial for the long-term success of human civilization, and likewise as a key priority for action today  [1] [2] [3] [4] [5] [6] [7] [8] . Visionary technologist James Martin likened this era of civilization to a turbulent river that it must navigate  [9] . If this era of civilization successfully navigates the river, then a long, bright future awaits, both on Earth and beyond. However, if it fails, then human civilization suffers a premature death. This paper describes several great downside dilemmas for emerging technologies and explains how humanity can navigate through them. The paper also discusses some other technologies that do not pose this dilemma because they promise to bring major benefits without a significant catastrophic risk. \n Historical precedents Amazingly, the great downside dilemma for emerging technologies has been faced at least twice before. The first precedent came in the desperate circumstances of World War II. The dilemma was whether to test-detonate the first nuclear weapon. While nuclear weapons proved to be unprecedentedly destructive weapons, a single detonation did not destroy the entire planet as some initially feared. The second precedent came during calm circumstances but still posed a dilemma every bit as large: whether to engage in messaging to extraterrestrial intelligence (METI). METI is of note because the dilemma still has not been resolved. Humanity still does not know if METI is safe. Thus METI decisions today face the same basic dilemma as the initial decisions in decades past. \n Nuclear weapons It was 1945, towards the end of World War II. An American team of physicists, engineers, and military personnel built the first atomic bomb, which they named Trinity. Trinity was to be detonated in a test explosion, to make sure the technology worked, before using additional atomic bombs against Japan. By that point, Germany had already surrendered. Japan was nearing defeat, and the United States believed that the atomic bomb could compel Japan to surrender without the US waging a long, bloody invasion. It might seem counterintuitive, but this most powerful of weapons was built to save live  1  . However, some of the physicists worried that the test might fail catastrophically. They worried that the detonation could ignite the atmosphere, ending life on Earth. They believed the chance of this happening to be exceptionally small, due to their understanding of the relevant physics. Still, they closed their report on the topic with the line 'However, the complexity of the argument and the absence of satisfactory experimental foundations makes further work on the subject highly desirable'  [11] . Thus the risk did give them some pause. Sure enough, they took the risk. As is now known, the Trinity test succeeded: the bomb worked, and the atmosphere did not ignite. The rest is history. Humanity survived the first atomic bomb detonation, the next two, which were dropped on Hiroshima and Nagasaki,  1  Reed  [10]  reviews the history of the atomic bomb development and the corresponding physics. and the 2054 atomic bombs that have been detonated since in further testing  2  . The largest of these bombs, the Soviet Tsar Bomba, had a yield equivalent to about 50 megatons of TNT, a whopping 2500 times larger than Trinity. The atmosphere did not ignite. And physics has by now progressed to the point where we understand with very high confidence why atomic bomb detonations would not cause these harms (though they can of course cause other harms). But for that brief moment in time, when the first atomic detonation was under consideration, a great downside dilemma was faced, without the benefit of hindsight that now exists. Today, nuclear weapons remain a major threat. A single nuclear weapon could kill thousands or even millions of people. Nuclear war with hundreds or thousands of weapons (about 17 000 weapons still exist, mainly held by the United States and Russia) would not produce enough radiation to cause human extinction, as Bertrand Russell, Albert Einstein, and others once feared  [12] . But it would cause significant cooling, as the smoke from burning cities rises into the atmosphere and blocks incoming sunlight. This cooling, often known as nuclear winter, could cause widespread agricultural failure, with the resulting famine threatening millions or even billions of people  [13, 14] . The worst case scenario could include human extinction  [15] . The leaders of nuclear weapons states thus face a different dilemma: In a crisis, are nuclear weapons worth using? While nuclear weapons are no longer a new technology, large nuclear arsenals have never been used in war, and so the dilemma must still be resolved without the benefit of hindsight. \n Messaging to extraterrestrials It was 1974, a relatively calm and ordinary year by most measures. But an unusual exercise was in preparation at an astronomy observatory in Arecibo, Puerto Rico. The Arecibo Observatory hosted what was (and still is) the largest radio telescope in the world  3  . Usually, the telescope is used either for radio astronomy, which detects radio waves incoming from the rest of the Universe, or radar astronomy, which studies the solar system by sending radio waves towards planets and other nearby objects and analyzing the waves that bounce back. Radio and radar astronomy are generally harmless and of scientific value. But in 1974, the Arecibo telescope was to be used differently. The plan was to send a message from Arecibo to a cluster of stars 25 000 light years away. The Arecibo Message was designed by astronomer Frank Drake and colleagues with the premise of METI. The message contained seven parts describing human physiology and astronomy. This was not the first exercise in METI. In 1962, the Morse Message was sent from the Evpatoria Planetary Radar in Crimea to Venus. But the Morse Message was as harmless as regular radar astronomy studying Venus. Because the Arecibo message was broadcast elsewhere, it broke new ground. So far, the Arecibo message has not received a response. Of course it has not: it was sent 40 years ago to a location 25 000 light years away. It will take at least another 49 960 years for the message to arrive and the response to reach back to Earth 4 . And it is possible that no ETI will receive the Arecibo message. Indeed, it is possible that there are no ETI out there to receive it. It is also possible that ETI will receive it but not respond in any way. So even after another 49 960 years, the Arecibo message could prove inconsequential to humanity, except for its modest educational value. But it might not. The message could receive a response. Despite some proclamations to the contrary, humanity has little understanding of how an encounter with ETI would proceed. Some people expect that ETI would benefit humanity, providing scientific knowledge and intercultural exchange, or even solutions to humanity's problems. Others expect that ETI would harm humanity, enslaving or even killing us. These are among the many possible outcomes of ETI encounter  [16, 17] . Presumably, if it was known that the outcome would be beneficial, METI would proceed; likewise it would not proceed if the outcome was known to be harmful  [18] . But in 1974, it was not known. Whether to engage in METI thus posed a great downside dilemma. In 2014, at the time of this writing, it is still not known whether METI is safe. Since the Arecibo message, several other messages to ETI have since been sent to closer stars, most recently the 2013 Lone Signal project  5  . None of these messages has yet received a reply. Meanwhile, it is an exciting time for SETI-the search for ETI. Astronomers are just starting to discover extrasolar planets  [19] . But no ETI have yet been found. Until then, humanity will have deep uncertainty about the merits of METI. Some progress can be made by carefully thinking through the possibilities of ETI encounter. An argument can be made that no high-power METI should be conducted until humanity better understands the risks  [20] , but this is a controversial point. The great downside dilemma for METI persists. \n Dilemmas in the making While humanity continues to face dilemmas related to nuclear weapons and METI, new dilemmas lurk on the horizon. The stakes for these new dilemmas are even higher, because they come with much higher probabilities of catastrophe 6 . I will  2  Atomic bomb detonation data can be obtained from the Comprehensive Nuclear-Test-Ban Treaty Organization at http://www.ctbto.org/nucleartesting/history-of-nuclear-testing/world-overview/page-1-world-overview/.  3  Arecibo is the world's largest single-aperture radio telescope. Arrays of multiple telescopes combined as astronomical interferometers collectively cover larger areas.  4  Assuming the location is exactly 25 000 light years away, then 49 960 years from now is the minimum time it could take for a response to reach Earth. The response could reach Earth later if the ETI take more time before transmitting the response.  5  Full disclosure: I received funds from Lone Signal to contribute to a risk analysis of Lone Signal's transmissions. The study concluded that the transmissions posed no significant risk because the transmitter Lone Signal was using at the time did not exceed the background radio wave leakage from radio and television broadcasts  [18] .  6  This assumes that the probability of catastrophe from METI is relatively low. This is a debatable point, given the deep uncertainty surrounding the possibility of extraterrestrial contact. focus on two: stratospheric geoengineering and artificial general intelligence. Neither technology currently exists, but both are subjects of active research and development. Understanding these technologies and the dilemmas they pose is already important and will only get more important as the technologies progress. \n Stratospheric geoengineering In summer 2010, heavy monsoons flooded about one fifth of Pakistan, with millions of people affected  [21] . The floods were part of a broader northern hemisphere summer heat wave that set temperature records in many locations. Vast wildfires in Western Russia produced so much smoke that people in Moscow wore masks and airports redirected traffic. The floods, heat wave, and wildfires are among the sorts of extreme weather events that are expected to happen more often and with greater intensity as global warming worsens  [22]    7  . The standard means of lessening the harms of global warming is to reduce atmospheric emissions of carbon dioxide, methane, and other greenhouse gases. That means using energy more efficiently, switching away from coal power, reversing deforestation, and more. But despite the risks of global warming, greenhouse gas emissions have been steadily increasing, and are projected to continue increasing into the future. More emissions means warmer temperatures and more severe harms from extreme weather events, sea level rise, and more. In despair over the perceived failure to reduce emissions, observers are increasingly considering geoengineering to lower global temperatures. Geoengineering is the intentional manipulation of the global Earth system  [27] . Greenhouse gas emissions do not qualify as geoengineering because they are an unintended byproduct of activities with other aims. Perhaps the most commonly discussed type of geoengineering is stratospheric geoengineering, which would lower temperatures by injecting particles into the stratosphere, thereby blocking a portion of incoming sunlight. Stratospheric geoengineering is attractive because of its relative feasibility, efficacy, and affordability. However, stratospheric geoengineering changes regional temperature and precipitation patterns, leaving some need to adapt to climatic changes. Stratospheric geoengineering also does nothing to address the acidification of oceans caused by carbon dioxide emissions being absorbed into oceans. Ocean acidification is a major problem in its own right, a large threat to ocean ecosystems. Finally, stratospheric geoengineering also poses significant risks that could even exceed those of global warming. Perhaps the largest risk from stratospheric geoengineering is the possibility of abrupt halt. Particles put into the stratosphere will cycle out on time-scales of about five or ten years. In order to maintain stable temperatures, particles must be continuously injected into the stratosphere. If the geoengineering abruptly halts, such that additional particles are not injected, then temperatures will rapidly shoot back up towards where they would have been without geoengineering  [28] . This rapid temperature increase could be especially difficult to adapt to and thus be especially disruptive. For example, it may be difficult to determine which crops to plant in a given region, because the crops suitable for that region will change too quickly. Fortunately, the rapid temperature increase can be avoided simply by continuing to inject particles into the stratosphere. Indeed, the harms of rapid temperature increase provide strong incentive to not to stop particle injection in the first place. Under normal circumstances, people would have to be either incompetent or malicious to stop particle injection. Assuming the geoengineering is managed by responsible parties, abrupt halt may be unlikely, making stratospheric geoengineering relatively safe. This is under normal circumstances. However, particle injection may nonetheless halt if some other catastrophe occurs, such as a war or a pandemic, that prevents people from continuing the injections. The result would be a 'double catastrophe' of rapid temperature increase hitting a population already vulnerable from the first catastrophe  [29] . This double catastrophe could be very harmful; potentially it could even result in human extinction. This makes for a rather severe downside. Figure  1  depicts the double catastrophe scenario. The figure shows average global temperature versus time for three scenarios: (1) the world without geoengineering, in which temperatures gradually rise due to greenhouse gas emissions; (2) ongoing geoengineering, in which temperatures remain indefinitely at a low, stable level (around 13 °C); and (3) abrupt geoengineering halt (around the year 2080), in which temperatures rapidly rise towards where they would have been without geoengineering. Figure  1  also indicates when an initial catastrophe would occur (shortly before 2080) in a double catastrophe scenario. The great downside dilemma for stratospheric geoengineering is the dilemma of whether to inject particles into the Figure  1 . global temperature for three scenarios: no geoengineering, ongoing geoengineering, and geoengineering that abruptly stops. The initial catastrophe corresponds to a geoengineering double catastrophe  [29] .  7  I am using the term 'global warming' here instead of the usual 'climate change' to distinguish it from nuclear winter, which is also a climatic change. Any readers who still doubt the legitimacy of global warming as an issue should consult some of the many works on the topic, including accessible books by leading global warming researchers  [23, 24]  and my own humble contribution  [25] . Global warming research is also voluminously reviewed by the Intergovernmental Panel on Climate Change  [26] . stratosphere. On one hand, stratospheric geoengineering could lower temperatures, avoiding many harms of global warming. On the other hand, it poses a risk of rapid temperature increase that could even result in human extinction. So, should stratospheric geoengineering be pursued? A key factor in resolving the dilemma is understanding how bad the impacts of global warming could get without geoengineering. The floods, heat waves, and other effects already being observed will almost certainly get worse. This is bad, but there is an even worse impact potentially on the horizon: the exceedance of mammalian thermal limits. The limits depend on wet bulb temperature, which is a combination of 'regular' dry bulb temperature and humidity. When wet bulb temperature goes above 35 °C, mammals-including humans-can no longer perspire to regulate our body temperature, causing us to overheat and die. Currently, wet bulb temperatures never exceed the 35 °C limit, but under some possible global warming scenarios, the limit would sometimes be exceeded in much of the land surface of the planet  [30] . Unless humans and other mammals took shelter in air conditioning, they would die. Under these conditions, it may be difficult to keep civilization intact in the warmer regions or even worldwide. Another perspective on the potential severity of global warming comes from looking at the long-term co-evolution of the human species and Earth climates. The species Homo sapiens sapiens is dated at around 200 000 years old. This means that humans have lived through about two full glacialinterglacial cycles, i.e. ice ages and the warm periods between them, which cycle back and forth on time-scales of about 100 000 years  [23] . Archaeological evidence suggests that early Homo sapiens sapiens and their immediate ancestors had cognitive capabilities comparable to those of contemporary humans  [31, 32] . However, civilization did not take off until the agricultural revolution, which began around 10 000 years ago and occurred in at least seven independent locations within just a few thousand years. The last 10 000 years coincide with the Holocene, a warm interglacial period with a relatively stable climate, suggesting that this climate may have been crucial for the rise of civilization  [33] . Meanwhile, global warming threatens to push temperatures to levels significantly outside the range of recent glacial-interglacial cycles, bringing climates that Homo sapiens sapiens and its immediate ancestors have never seen before  [34] . To the extent that certain climates are essential for human civilization, global warming could be devastating. This sort of long-term perspective is also helpful for understanding stratospheric geoengineering risk. Global warming could last for centuries, millennia, or even longer  [34] . This is a very long time to continue injecting particles into the stratosphere. It is also plenty of time for plenty of catastrophes to occur. For example, risk analysis of nuclear war finds about a 0.1%-1% chance of nuclear war occurring during any given year  [35] . Over hundreds or thousands of years, this makes nuclear war virtually certain to occur. Of course, the world could permanently get rid of nuclear weapons, eliminating the risk. But this might not happen, and meanwhile there are other types of catastrophes to worry about. Over the time-scales of global warming, a stratospheric geoengineering double catastrophe may be quite likely. So, should stratospheric geoengineering be pursued? At this time, I do not believe a good answer to this question exists. There is too much uncertainty about both the consequences of stratospheric geoengineering and the consequences of not stratospheric geoengineering, as well as the probabilities of stratospheric geoengineering abrupt halt. Fortunately, the decision does not need to be made just yet. Global warming is not yet so bad that stratospheric geoengineering is worth the risk. But geoengineering decisions may be made soon; research to reduce the uncertainty should proceed now so that wise decisions can be made  [36, 37] . When the time comes to decide whether to launch stratospheric geoengineering, the right action to take may also be the more difficult action to take. It is quite plausible that civilization could endure the worst harms of regular global warming, but would collapse from the rapid global warming of stratospheric geoengineering abrupt halt. If this is the case, then it would be in civilization's long-term interest to abstain from stratospheric geoengineering and suffer through regular global warming. This abstention may be best regardless of how painful regular global warming could get and regardless of how unlikely stratospheric geoengineering abrupt halt would be. It is just that important to ensure the long-term viability of human civilization. But this is hardly an encouraging prospect, dooming humanity to the pains of regular global warming, when lower temperatures could so easily be produced. Meanwhile, civilization can lessen the stratospheric geoengineering dilemma by reducing greenhouse gas emissions. Regardless of any broader failures at emissions reductions, every additional bit helps. And reducing emissions helps with both sides of the dilemma: it lessens the severity of both regular global warming and the rapid temperature increase from stratospheric geoengineering abrupt halt. As discussed further below, many options for reducing emissions come with minimal dilemmas of their own, making them excellent options to pursue. \n Artificial general intelligence In January 2011, two world-leading players of the game show Jeopardy! took on an IBM computer named Watson. Watson won the game convincingly. During the last Final Jeopardy! round, human contestant Ken Jennings wrote below his response question, 'I for one welcome our new computer overlords'. It was a humorous moment in the long rise of artificial intelligence (AI). But how high can AI rise? Could AI actually become the overlords of humanity, taking over the world? And should such a development be welcomed? At the outset, it is important to distinguish between two types of AI: narrow and general. Narrow AI is intelligent in specific domains but cannot reason outside the domains it was designed for. Narrow AI is by now ubiquitous across a breadth of contexts, from searching the web to playing games like Jeopardy! narrow AI can be quite useful, and can also pose some risks. But it is not expected to take over the world, because controlling the world requires capabilities across many domains. General AI (AGI) is intelligent across a wide range of domains. Humans are also intelligent across many domains, but this does not mean that AGI would necessarily think like humans do. An AGI may not need to think like humans in order to be capable across many domains  8  . Early AI researchers boldly predicted that human-level AGI would be achieved by dates long since past, as Crevier  [39]  and McCorduck  [40]  chronicle. This grandiose failure of prediction led many modern AI researchers to be skeptical about the prospects of AGI  [41] . However, there remains an active AGI research community  [42] . Experts in the field diverge widely about when AGI is likely to be achieved and on its impacts if or when it is achieved  [43] [44] [45] . But some of the predictions about impacts are quite dramatic. One line of thinking posits that an AGI, or at least certain types of AGIs, could essentially take over the world. This claim depends on two others. First, power benefits from intelligence, such that the most intelligent entities will tend to have the most power. Second, an AGI can gain vastly more intelligence than humans can, especially if the AGI can design an even more intelligent AGI, which designs a still more intelligent AGI, and so on until an 'intelligence explosion'  [46]  or 'singularity'  [47, 48]  occurs. The resulting 'superintelligent' AGI  [49]  could be humanity's final invention  [50]  because the AGI would then be fully in control. If the AGI is 'Friendly' to humanity  [51] , then it potentially could solve a great many of humanity's problems. Otherwise, the AGI will likely kill everyone inadvertently as it pursues whatever goals it happened to be programmed with-for example, an AGI programmed to excel at chess would kill everyone while converting the planet into a computer that enabled it to calculate better chess moves  [52] . Per this line of thinking, an AGI would be much like a magic genie, such as the one depicted in the film Aladdin (John Musker and Ron Clements, directors, 1992). The genie is all-powerful but obligated to serve its master. The master can wish for almost anything, but should be careful what he or she wishes for. Indeed, genie stories are often stories of unintended consequences. For example, in the penultimate scene of Aladdin, Jafar wishes to become a genie. He was eager to gain the genie's powers, but ended up trapped in servitude (and stuck inside a small lamp). The story with AGI may be similar. The AGI would do exactly what its human programmers instructed it to do, regardless of whether the programmers would, in retrospect, actually want this to happen. In attempting to program the AGI to do something desirable, the programmers could end up dead, along with everyone else on the planet  9  . If this line of thinking is correct, or even if it has at least some chance of being correct, then AGI poses a great downside dilemma. Should an AGI be built and launched? Given the possibility of being destroyed by AGI, it might appear that AGI should simply not be built. Doing so would ensure that humanity retains control of itself and its fate. But for several reasons, the situation is not so simple. A first complication is that AGI might be Friendly or otherwise beneficial to humanity, or to the world. The benefits of a Friendly AGI could be immense. Imagine having the perfect genie: unlimited wishes that are interpreted as you intended them to be, or maybe even better than you intended them to be. That could go quite well. Perhaps there would be no more poverty or pollution. Perhaps space colonization could proceed apace. Perhaps the human population could double, or triple, or grow tens, hundreds, or thousands of times larger, all with no decline in quality of life. A Friendly AGI might be able to make these things possible. Decision-making on AGI should balance this large potential upside with the also-large downside risk. For example, suppose the AGI had a 50% chance of killing everyone and a 50% chance of doubling the human population with no decline in quality of life. The expected population would be equally large with or without the AGI. Does this mean that humanity is indifferent to launching the AGI? If it was a 51% chance of doubling the population, versus 49% for killing everyone, does this mean humanity would rather launch the AGI? What if it was a chance of the population increasing by a factor of ten, or a thousand? These are important types of questions to answer when making decisions about launching an AGI. A second complication is that AGI is not the only threat that humanity faces. In the absence of AGI, humanity might die out anyway because of nuclear weapons, global warming, or something else. If AGI succeeds, then these other threats could go away, solved by our new computer overlords. That is a significant upside for AGI. What if an AGI has a 50% chance of killing everyone, but absent AGI, humanity has a 60% of dying out from something else? Should the AGI be launched? The dilemma for AGI can thus look a lot like that for stratospheric geoengineering. Imagine, some years into the future, humanity finds itself in a difficult spot. Perhaps global warming is bringing great harm, and other environmental stressors are as well. Perhaps major countries are on the brink of war with nuclear weapons or something even more destructive. Perhaps poverty is rampant, life unsafe and unpleasant. Perhaps other solutions, including stratospheric geoengineering, are found to be unsafe or otherwise undesirable. And perhaps there is no hope in sight of conditions improving. In this case, taking the risk of launching a AGI could start to look attractive. Indeed, in terms of the long-term success of human civilization, it might even be the right thing to do. Or, the right thing may be to suffer through without AGI. It would depend on the details, just as it would for stratospheric geoengineering or a desperate game of Russian roulette. Following this logic, one way to help reduce AGI risk is to improve the general human condition. By keeping humanity out of desperate circumstances, the risk of AGI can be made to look less attractive. This opens up a wide range of opportunities to help reduce AGI risk, from reducing  8  AGI was discussed in detail in another paper in the series of papers based on the event 'Emerging Technologies and the Future of Humanity'  [38] .  9  Arguably, such a result would at least be better than an eternity trapped in a small lamp. greenhouse gas emissions to improving conditions for the world's poor. But the merits of this approach depend on how the AGI would be developed. The third complication is that AGI development could involve basic computing resources and technologies of growing economic importance. AGI is not like nuclear weapons, which require exotic materials. AGI could be developed on any sufficiently powerful computer. Computing power is steadily growing, a trend known as Moore's Law. Meanwhile, narrow AI is of increasing technological sophistication and economic importance. At the time of this writing, driverless cars are just starting to hit the streets around the world, with promise to grow into a major industry. Differences between narrow AI and AGI notwithstanding, these AI advances may be able to facilitate the development of AGI. Given the risks of AGI, it may seem attractive or even wise to relinquish precursor hardware and software technologies, potentially including certain narrow AI and the computer systems they run on  [53] . But given the pervasiveness of these technologies, it may be difficult to do so. Here lies another dilemma. Would humanity be willing to sacrifice much of its computing technology in order to avoid an AGI catastrophe? Should it? The dilemma here resembles that faced in the recent film Transcendence (Wally Pfister, director, 2014). The film shows an AGI that has been launched and is steadily taking over the world. The AGI is in many ways beneficial or even friendly, but the humans who are close to it become increasingly skeptical and decide to shut it down. (More precisely, they persuade the AGI to shut itself down, since the AGI was still in control.) However, in shutting it down, humanity had to sacrifice the internet, and potentially also other electronics. A case can be made that the AGI should not have been shut down: without the internet and other electronics, the long-term prospects for human civilization could be severely limited, such that humanity would be better off keeping the AGI intact and hoping for the best  [54] . As with stratospheric geoengineering, AGI launch decisions do not need to be made right now. However, for AGI there is great uncertainty about how much time remains. Experts are sharply divided on how long it will take to achieve AGI, with some doubting that it will ever occur. Given this uncertainty, and the high stakes of the launch decision, it is not at all too early to assess which AGIs should or should not be launched, and to create the conditions that can help ensure better outcomes whether or not an AGI is launched. \n Technologies without great downside dilemma Not all technologies present a great downside dilemma. These technologies may be disruptive, may have downsides, and may carry risks, but they do not threaten catastrophic harm to human civilization. Or, to the extent that they could threaten catastrophic harm, they do not increase the risk of catastrophe beyond what it would be without the technology, or do not increase the risk to any significant extent. Some of these technologies even hold great potential to improve the human condition, including by reducing other catastrophic risks. These latter technologies are especially attractive and in general should be pursued to the extent that their benefits and cost-effectiveness are competitive with other options for improving the human condition (and achieving any other goals). Three such emerging technologies are discussed here. \n Sustainable design Sustainable design refers broadly to the design of technologies oriented towards improving the environment, advancing sustainability, and related goals. These technologies promise to reduce the harms of climate change and other environmental problems. Quite a lot of such technologies are already in use, from the humble bicycle to advanced solar technologies. This is a vast technology space, and a lot has been said about these technologies elsewhere  [55] , so a full review here is unwarranted. What is worth noting here is that these technologies can reduce the risk of environmental catastrophes like climate change, and are often also worth pursuing for other reasons. For example, technology that uses energy, water, and other resources more efficiently can save money by avoiding purchases of these resources. Technologies like bicycles can make people healthier by giving them more exercise. Where sustainable design comes with such cobenefits, it is an especially attractive option. But given the catastrophic potential of environmental risks, some sustainable design, and potentially quite a lot of it, is worth pursuing even if it otherwise comes at an expense. \n Nuclear fusion power Nuclear fusion power is perhaps the Holy Grail of sustainable design. It promises a clean, safe, abundant energy source. If nuclear fusion power can be realized, and if it can be made affordable, then humanity's energy needs could potentially be fully met. And with abundant energy, a lot of other opportunities open up. For example: ocean water could be desalinated, eliminating water resource scarcities. Carbon dioxide could be removed from the atmosphere, which is another form of geoengineering, and a much safer one at that. Countries can develop their economies without worrying nearly as much about their environmental impact and without worrying about being dependent on another country's energy resources. One major long-term benefit of fusion power relates back to the fossil fuels it would replace. With fusion power, humanity can keep the rest of the fossil fuels underground, ready and waiting for when they will really be needed. That time will come sometime within the upcoming hundreds of thousands of years, when Earth's climate cycles back to a glacial period: a new ice age. The exact timing of the next glacial period is uncertain, and depends on, among other things, how much greenhouse gas humanity emits  [34] . But, barring any other radical changes to the global Earth system (such as its dismantling by a runaway AGI), a glacial period will eventually occur. And when it does, it could help to still have some fossil fuel around to lessen the bite of the global cooling  [56, p 234-235] . This would be yet another form of geoengineering, one with the long-term interests of human civilization in mind. Unfortunately, it is not clear if or when the Holy Grail of fusion power will be achieved. Fusion power research has been going on for decades  [57] , and it may take more decades still. With such a long development period, fusion power is a modern analog to cathedrals. Many cathedrals took a century or longer to build. This includes at least one cathedral currently under construction, Sagrada Família in Barcelona, whose construction began in 1882 and has no clear projected completion date. Humanity's track record with cathedrals indicates its capability to complete large, multi-century, intergenerational projects. Perhaps the fusion power project will be completed too. Unlike cathedrals, it is not known if it is even possible to complete the fusion power project: to make fusion power a major energy source for human civilization. Already, it is possible to generate power from nuclear fusion. First came uncontrolled fusion-fusion bombs-beginning with the detonation of Ivy Mike in 1952. Soon after came controlled fusion, beginning with Scylla 1 at Los Alamos National Laboratory in 1958  [58] . Controlled fusion is what can be used for electricity generation. However, controlled fusion thus far has always consumed more energy than it generates. A major breakthrough recently occurred at the National Ignition Facility at Lawrence Livermore National Laboratory: for the first time, a net energy gain occurred within the fuel that triggers the fusion  [59] . However, the fuel is just one part of the fusion process; the National Ignition Facility experiment consumed overall about 100 times more energy than it generates. But, clear progress is being made. On the other hand, much more progress is needed still, and it is not clear if or when net energy gain will be achieved, or if it would be affordable. If affordable fusion power is achieved, it would be transformative. The fuels are deuterium and lithium, supplies of which can last for thousands to billions of years, depending on power plant design, and there could be no significant radioactive waste  [60] . While fusion reactors potentially could be used to generate materials for nuclear weapons, their weapons proliferation risk would be lower, potentially much lower, than it is for fission power  [61, 62] . While fusion power research is expensive and the prospects for success uncertain, the potential benefits are, in my own estimation, sufficient to justify ongoing investment. This cathedral is well worth attempting to build. \n Space colonization The dream of living beyond Earth may be as old as humanity itself. Within the last century, concrete steps have been taken towards this dream. The project of colonizing space may take even longer than the project of fusion power, perhaps orders of magnitude longer. But it comes with its own set of sizable benefits, with relatively little risk. One benefit is the emotional inspiration that humanity can draw from marveling at its cosmic achievement  [63] . Other notable benefits are more practical, but no less great. One major benefit of space colonization is the protection it offers against global catastrophes on Earth. If humanity has self-sufficient space colonies, then it can survive even the complete destruction of its home planet. A spacefaring civilization is a more resilient civilization. This benefit has prompted calls for space colonization [64]. However, space colonization using current technology would be highly expensive and perhaps not even feasible, rendering other options for protecting against catastrophes, including Earthbased refuges, the more cost-effective option  [65, 66] . The protections that space colonization could offer do not justify investment in space colonization at this time. While space colonization can protect against harms, it can also enable major benefits on its own. The opportunities for civilization are, quite literally, astronomically greater beyond Earth than on it. Indeed, the astronomic potential for human civilization is a main reason why great downside dilemmas and other global catastrophic risk decisions are so important to resolve. But again, this does not mean that humanity should invest in space colonization at this time. Instead, it would be wise to focus on the catastrophic threats it faces, such that future generations can go on to colonize space and achieve astronomically great success as a civilization. \n Conclusion The fate of human civilization now hangs in the balance. As James Martin put it  [9] , humanity is going through a turbulent river full of many threats to its survival. Many of these threats derive from risky emerging technologies like stratospheric geoengineering and artificial general intelligence. Some threats also derive from established technologies like nuclear weapons and radio telescopes for messaging to extraterrestrials. And other technologies do not pose a significant threat, including sustainable design technologies, nuclear fusion power, and space colonization. Meanwhile, all of these technologies, if used properly, could help humanity navigate the turbulence. And if the turbulence is successfully navigated, a very long and bright future awaits. Humanity's future could include billions of years on Earth as well as a much bigger and longer existence across the Universe. Human civilization and its descendents can achieve many great things, if only it has the opportunity. Navigating the turbulence-preventing civilization-ending global catastrophe-is thus a crucial task for this era of human civilization. The great downside dilemma for risky emerging technologies could be an especially difficult stretch of turbulence for humanity to navigate. Technologies like stratospheric geoengineering and artificial general intelligence pose great temptations, especially if humanity finds itself in difficult circumstances. For the long-term sake of human civilization, it may be best to abstain from the technologies, but over the short-term, abstention could mean suffer through life without them. Global warming is just one of several forces that could put humanity in desperate circumstances in the not-too-distant future, making risky technologies especially attractive. If the right decisions are to be made about these various technologies-and that could mean taking the risk of using them-then two things are needed. First, the risks must be understood. People must know what the right decision is. This means characterizing the probabilities that the technologies will fail, the severity of harm if they do fail, and humanity's prospects if the technologies are not used. But, as they say, knowing is only half the battle. The other half is applying the knowledge. The second thing needed is for decision-making procedures to be in place such that bad risks are not taken. Accomplishing this means bringing together the many people involved in risky technology development, from scientists and engineers to government regulators. Some scientists and engineers might not like having their work regulated, but this only underscores the importance of including them in the process, so their concerns can be addressed, as can anyone else's. Many jurisdictions already regulate a variety of technologies, in light of the risks they pose. This is a good step. But emerging technologies pose new challenges that must be addressed in turn. And the global nature of the worst catastrophes suggests a role for international cooperation  [67] . Efforts at smaller scales can also play a role, including the daily actions everyone can make to protect the environment, promote peace, and otherwise keep humanity out of desperate circumstances. For the sake of human civilization-indeed, for the sake of the Universe-actions across all these scales are well worth taking. Academy of Sciences     Physica Scripta Phys. Scr. 89 (2014) 128004 (10pp) doi:10.1088/0031-8949/89/12/128004 \n\t\t\t Phys. Scr. 89 (2014) 128004 S D Baum", "date_published": "n/a", "url": "n/a", "filename": "Baum_2014_Phys._Scr._89_128004.tei.xml", "abstract": "Some emerging technologies promise to significantly improve the human condition, but come with a risk of failure so catastrophic that human civilization may not survive. This article discusses the great downside dilemma posed by the decision of whether or not to use these technologies. The dilemma is: use the technology, and risk the downside of catastrophic failure, or do not use the technology, and suffer through life without it. Historical precedents include the first nuclear weapon test and messaging to extraterrestrial intelligence. Contemporary examples include stratospheric geoengineering, a technology under development in response to global warming, and artificial general intelligence, a technology that could even take over the world. How the dilemma should be resolved depends on the details of each technology's downside risk and on what the human condition would otherwise be. Meanwhile, other technologies do not pose this dilemma, including sustainable design technologies, nuclear fusion power, and space colonization. Decisions on all of these technologies should be made with the long-term interests of human civilization in mind. This paper is part of a series of papers based on presentations at the Emerging Technologies and the Future of Humanity event held at the Royal Swedish Academy of Sciences on", "id": "1952dd834e3b84d7b28073274b63b4b1"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Rodrigo Toro Icarte", "Ethan Waldie", "Toryn Q Klassen", "Richard Valenzano", "Margarita P Castro", "Sheila A Mcilraith", "Rodrigo Toro"], "title": "Learning Reward Machines for Partially Observable Reinforcement Learning", "text": "Introduction The use of neural networks for function approximation has led to many recent advances in Reinforcement Learning (RL). Such deep RL methods have allowed agents to learn effective policies in many complex environment including board games  [30] , video games  [23] , and robotic systems  [2] . However, RL methods (including deep RL methods) often struggle when the environment is partially observable. This is because agents in such environments usually require some form of memory to learn optimal behaviour  [31] . Recent approaches for giving memory to an RL agent either rely on recurrent neural networks  [24, 15, 37, 29]  or memory-augmented neural networks  [25, 18] . In this work, we show that Reward Machines (RMs) are another useful tool for providing memory in a partially observable environment. RMs were originally conceived to provide a structured, automatabased representation of a reward function  [33, 4, 14, 39] . Exposed structure can be exploited by the Q-Learning for Reward Machines (QRM) algorithm  [33] , which simultaneously learns a separate policy for each state in the RM. QRM has been shown to outperform standard and hierarchical deep RL over a variety of discrete and continuous domains. However, QRM was only defined for fully observable environments. Furthermore, the RMs were handcrafted. In this paper, we propose a method for learning an RM directly from experience in a partially observable environment, in a manner that allows the RM to serve as memory for an RL algorithm. A requirement is that the RM learning method be given a finite set of detectors for properties that serve as the vocabulary for the RM. We characterize an objective for RM learning that allows us to formulate the task as a discrete optimization problem and propose an efficient local search approach to solve it. By simultaneously learning an RM and a policy for the environment, we are able to significantly outperform several deep RL baselines that use recurrent neural networks as memory in three partially observable domains. We also extend QRM to the case of partial observability where we see further gains when combined with our RM learning method. \n Preliminaries RL agents learn policies from experience. When the problem is fully-observable, the underlying environment model is typically assumed to be a Markov Decision Process (MDP). An MDP is a tuple M = S, A, r, p, γ , where S is a finite set of states, A is a finite set of actions, r : S × A → R is the reward function, p(s, a, s ) is the transition probability distribution, and γ is the discount factor. The agent starts not knowing what r or p are. At every time step t, the agent observes the current state s t ∈ S and executes an action a t ∈ A following a policy π(a t |s t ). As a result, the state s t changes to s t+1 ∼ p(s t+1 |s t , a t ) and the agent receives a reward signal r(s t , a t ). The goal is to learn the optimal policy π * , which maximizes the future expected discounted reward for every state in S  [32] .  [38]  is a well-known RL algorithm that uses samples of experience of the form (s t , a t , r t , s t+1 ) to estimate the optimal q-function q * (s, a). Here, q * (s, a) is the expected return of selecting action a in state s and following an optimal policy π * . Deep RL methods like DQN  [23]  and DDQN  [35]  represent the q-function as qθ (s, a), where qθ is a neural network whose inputs are features of the state and action, and whose weights θ are updated using stochastic gradient descent. \n Q-learning In partially observable problems, the underlying environment model is typically assumed to be a Partially Observable Markov Decision Process (POMDP). A POMDP is a tuple P O = S, O, A, r, p, ω, γ , where S, A, r, p, and γ are defined as in an MDP, O is a finite set of observations, and ω(s, o) is the observation probability distribution. At every time step t, the agent is in exactly one state s t ∈ S, executes an action a t ∈ A, receives reward r t = r(s t , a t ), and moves to state s t+1 according to p(s t , a t , s t+1 ). However, the agent does not observe s t+1 , but only receives an observation o t+1 ∈ O. This observation provides the agent a clue about what the state s t+1 ∈ S is via ω. In particular, ω(s t+1 , o t+1 ) is the probability of observing o t+1 from state s t+1  [5] . RL methods cannot be immediately applied to POMDPs because the transition probabilities and reward function are not necessarily Markovian w.r.t. O (though by definition they are w.r.t. S). As such, optimal policies may need to consider the complete history o 0 , a 0 , . . . , a t−1 , o t of observations and actions when selecting the next action. Several partially observable RL methods use a recurrent neural network to compactly represent the history, and then use a policy gradient method to train it. However, when we do have access to a full POMDP model P O , then the history can be summarized into a belief state. A belief state is a probability distribution b t : S → [0, 1] over S, such that b t (s) is the probability that the agent is in state s ∈ S given the history up to time t. The initial belief state is computed using the initial observation o 0 : b 0 (s) ∝ ω(s, o 0 ) for all s ∈ S. The belief state b t+1 is then determined from the previous belief state b t , the executed action a t , and the resulting observation o t+1 as b t+1 (s ) ∝ ω(s , o t+1 ) s∈S p(s, a t , s )b t (s) for all s ∈ S. Since the state transitions and reward function are Markovian w.r.t. b t , the set of all belief states B can be used to construct the belief MDP M B . Optimal policies for M B are also optimal for the POMDP  [5] . \n Reward Machines for Partially Observable Environments In this section, we define RMs for the case of partial observability. We use the following problem as a running example to help explain various concepts. Example 3.1 (The cookie domain). The cookie domain, shown in Figure  1a , has three rooms connected by a hallway. The agent (purple triangle) can move in the four cardinal directions. There is a button in the yellow room that, when pressed, causes a cookie to randomly appear in the red or blue room. The agent receives a reward of +1 for reaching (and thus eating) the cookie and may then go and press the button again. Pressing the button before reaching a cookie will move it to a random location. There is no cookie at the beginning of the episode. This is a partially observable environment since the agent can only see what it is in the room that it currently occupies.  RMs are finite state machines that are used to encode a reward function  [33] . In the case of partial observability, they are defined over a set of propositional symbols P that correspond to a set of high-level features that the agent can detect using a labelling function L : O ∅ × A ∅ × O → 2 P where (for any set X) X ∅ X ∪ {∅}. L assigns truth values to symbols in P given an environment experience e = (o, a, o ) where o is the observation seen after executing action a when observing o. We use L(∅, ∅, o) to assign truth values to the initial observation. We call a truth value assignment of P an abstract observation because it provides a high-level view of the low-level environment observations via the labelling function L. A formal definition of an RM follows: Definition 3.1 (reward machine). Given a set of propositional symbols P, a Reward Machine is a tuple R P = U, u 0 , δ u , δ r where U is a finite set of states, u 0 ∈ U is an initial state, δ u is the state-transition function, δ u : U ×2 P → U , and δ r is the reward-transition function, δ r : U ×2 P → R. RMs decompose problems into a set of high-level states U and define transitions using if-like conditions defined by δ u . These conditions are over a set of binary properties P that the agent can detect using L. For example, in the cookie domain, P = { , , , , , , }. These properties are true (i.e., part of an experience label according to L) in the following situations: , , , or is true if the agent ends the experience in a room of that color; is true if the agent ends the experience in the same room as a cookie; is true if the agent pushed the button with its last action; and is true if the agent ate a cookie with its last action (by moving onto the space where the cookie was). Figure  2  shows three possible RMs for the cookie domain. They all define the same reward signal (1 for eating a cookie and 0 otherwise) but differ in their states and transitions. As a result, they differ with respect to the amount of information about the current domain state that can be inferred from the current RM state, as we will see below. Each RM starts in the initial state u 0 . Edge labels in the figures provide a visual representation of the functions δ u and δ r . For example, label , 1 between state u 2 and u 0 in Figure  2b  represents δ u (u 2 , { , }) = u 0 and δ r (u 2 , { , }) = 1. Intuitively, this means that if the RM is in state u 2 and the agent's experience ended in room immediately after eating the cookie , then the agent will receive a reward of 1 and the RM will transition to u 0 . Notice that any properties not listed in the label are false (e.g. must be false to take the transition labelled , 1 ). We also use multiple labels separated by a semicolon (e.g., \" , 0 ; , 0 \") to describe different conditions for transitioning between the RM states, each with their own associated reward. The label o/w, r (\"o/w\" for \"otherwise\") on an edge from u i to u j means that that transition will be made (and reward r received) if none of the other transitions from u i can be taken. Let us illustrate the behaviour of an RM using the one shown in Figure  2c . The RM will stay in u 0 until the agent presses the button (causing a cookie to appear), whereupon the RM moves to u 1 . From u 1 the RM may move to u 2 or u 3 depending on whether the agent finds a cookie when it enters another room. It is also possible to associate meaning with being in RM states: u 0 means that there is no cookie available, u 1 means that there is a cookie in some room (either blue or red), etc. When learning a policy for a given RM, one simple technique is to learn a policy π(o, u) that considers the current observation o ∈ O and the current RM state u ∈ U . Interestingly, a partially observable problem might be non-Markovian over O, but Markovian over O × U for some RM R P . This is the case for the cookie domain with the RM from Figure  2c , for example. Q-Learning for RMs (QRM) is another way to learn a policy by exploiting a given RM  [33] . QRM learns one q-function qu (i.e., policy) per RM state u ∈ U . Then, given any sample experience, the RM can be used to emulate how much reward would have been received had the RM been in any one of its states. Formally, experience e = (o, a, o ) can be transformed into a valid experience ( o, u , a, o , u , r) used for updating qu for each u ∈ U , where u = δ u (u, L(e)) and r = δ r (u, L(e)). Hence, any off-policy learning method can take advantage of these \"synthetically\" generated experiences to update all subpolicies simultaneously. When tabular q-learning is used, QRM is guaranteed to converge to an optimal policy on fullyobservable problems  [33] . However, in a partially observable environment, an experience e might be more or less likely depending on the RM state that the agent was in when the experience was collected. For example, experience e might be possible in one RM state u i but not in RM state u j . Thus, updating the policy for u j using e as QRM does, would introduce an unwanted bias to quj . We will discuss how to (partially) address this problem in §5. u 0 , 1 ; , 1 ; o/w, 0 (a) Naive RM. u 0 u 1 u 2 o/w, 0 o/w, 0 o/w, 0 , 0 , 0 ; , 0 , 1 , 1 (b) \"Optimal\" RM. u 0 u 1 u 2 u 3 o/w, 0 o/w, 0 o/w, 0 o/w, 0 , 0 , 0 ; , 0 , 0 ; , 0 , 1 , 1 , 0 , 0 (c) Perfect RM. \n Learning Reward Machines from Traces Our overall idea is to search for an RM that can be used as external memory by an agent for a given task. As input, our method will only take a set of high-level propositional symbols P, and a labelling function L that can detect them. Then, the key question is what properties should such an RM have. Three proposals naturally emerge from the literature. The first comes from the work on learning Finite State Machines (FSMs)  [3, 40, 10] , which suggests learning the smallest RM that correctly mimics the external reward signal given by the environment, as in Giantamidis and Tripakis' method for learning Moore Machines  [10] . Unfortunately, such approaches would learn RMs of limited utility, like the one in Figure  2a . This naive RM correctly predicts reward in the cookie domain (i.e., +1 for eating a cookie , zero otherwise) but provides no memory in support of solving the task. The second proposal comes from the literature on learning Finite State Controllers (FSC)  [22]  and on model-free RL methods  [32] . This work suggests looking for the RM whose optimal policy receives the most reward. For instance, the RM from Figure  2b  is \"optimal\" in this sense. It decomposes the problem into three states. The optimal policy for u 0 goes directly to press the button, the optimal policy for u 1 goes to the blue room and eats the cookie if present, and the optimal policy for u 2 goes to the red room and eats the cookie. Together, these three policies give rise to an optimal policy for the complete problem. This is a desirable property for RMs, but requires computing optimal policies in order to compare the relative quality of RMs, which seems prohibitively expensive. However, we believe that finding ways to efficiently learn \"optimal\" RMs is a promising future work direction. Finally, the third proposal comes from the literature on Predictive State Representations (PSR)  [20] , Deterministic Markov Models (DMMs)  [21] , and model-based RL  [16] . These works suggest learning the RM that remembers sufficient information about the history to make accurate Markovian predictions about the next observation. For instance, the cookie domain RM shown in Figure  2c  is perfect w.r.t. this criterion. Intuitively, every transition in the cookie environment is already Markovian except for transitioning from one room to another. Depending on different factors, when entering to the red room there could be a cookie there (or not). The perfect RM is able to encode such information using 4 states: when at u 0 the agent knows that there is no cookie, at u 1 the agent knows that there is a cookie in the blue or the red room, at u 2 the agent knows that there is a cookie in the red room, and at u 3 the agent knows that there is a cookie in the blue room. Since keeping track of more information will not result in better predictions, this RM is perfect. Below, we develop a theory about perfect RMs and describe an approach to learn them. \n Perfect Reward Machines: Formal Definition and Properties The key insight behind perfect RMs is to use their states U and transitions δ u to keep track of relevant past information such that the partially observable environment P O becomes Markovian w.r.t. O × U . Definition 4.1 (perfect reward machine). An RM R P = U, u 0 , δ u , δ r is considered perfect for a POMDP P O = S, O, A, r, p, ω, γ with respect to a labelling function L if and only if for every trace o 0 , a 0 , . . . , o t , a t generated by any policy over P O , the following holds: Pr(o t+1 , r t |o 0 , a 0 , . . . , o t , a t ) = Pr(o t+1 , r t |o t , x t , a t ) (1) where x 0 = u 0 and x t = δ u (x t−1 , L(o t−1 , a t−1 , o t )) . Two interesting properties follow from Definition 4.1. First, if the set of belief states B for the POMDP P O is finite, then there exists a perfect RM for P O with respect to some L. Second, the optimal policies for perfect RMs are also optimal for the POMDP (see supplementary material §12). Instead, we propose an alternative that focuses on a necessary condition for a perfect RM: the RM must predict what is possible and impossible in the environment at the abstract level. For example, it is impossible to be at u 3 in the RM from Figure  2c  and make the abstract observation { , }, because the RM reaches u 3 only if the cookie was seen in the blue room or not to be in the red room. This idea is formalized in the optimization model LRM. Let T = {T 0 , . . . , T n } be a set of traces, where each trace T i is a sequence of observations, actions, and rewards: T i = (o i,0 , a i,0 , r i,0 , . . . , a i,ti−1 , r i,ti−1 , o i,ti ). (2) We now look for an RM U, u 0 , δ u , δ r that can be used to predict L(e  |U | ≤ umax (4) xi,t ∈ U ∀i ∈ I, t ∈ Ti ∪ {ti} (5) xi,0 = u0 ∀i ∈ I (6) xi,t+1 = δu(xi,t, L(ei,t+1)) ∀i ∈ I, t ∈ Ti (7) N u,l ⊆ 2 2 P ∀u ∈ U, l ∈ 2 P (8) L(ei,t+1) ∈ N x i,t ,L(e i,t ) ∀i ∈ I, t ∈ Ti (9) Constraints (  3 ) and (  4 ) ensure that we find a well-formed RM over P with at most u max states. Constraint (  5 ),  (6) , and (7) ensure that x i,t is equal to the current state of the RM, starting from u 0 and following δ u . Constraint (  8 ) and (  9 ) ensure that the sets N u,l contain every L(e i,t+1 ) that has been seen right after l and u in T . The objective function comes from maximizing the log-likelihood for predicting L(e i,t+1 ) using a uniform distribution over all the possible options given by N u,l . A key property of this formulation is that any perfect RM is optimal w.r.t. the objective function in LRM when the number of traces tends to infinity (see supplementary material §12): Theorem 4.3. When the set of training traces (and their lengths) tends to infinity and is collected by a policy such that π(a|o) > for all o ∈ O and a ∈ A, any perfect RM with respect to L and at most u max states will be an optimal solution to the formulation LRM. Finally, note that the definition of a perfect RM does not impose conditions over the rewards associated with the RM (i.e., δ r ). This is why δ r is a free variable in the model LRM. However, we still expect δ r to model the external reward signals given by the environment. To do so, we estimate δ r (u, l) using its empirical expectation over T (as commonly done when constructing belief MDPs  [5] ). \n Searching for a Perfect Reward Machine Using Tabu Search We now describe the specific optimization technique used to solve LRM. We experimented with many discrete optimization approaches-including mixed integer programming  [6] , Benders decomposition  [8] , evolutionary algorithms  [17] , among others-and found local search algorithms  [1]  to be the most effective at finding high quality RMs given short time limits. In particular, we use Tabu search  [11] , a simple and versatile local search procedure with convergence guarantees and many successful applications in the literature  [36] . We also include our unsuccessful mixed integer linear programming model for LRM in the supplementary material §10. In the context of our work, Tabu search starts from a random RM and, on each iteration it evaluates all \"neighbouring\" RMs. We define the neighbourhood of an RM as the set of RMs that differ by exactly one transition (i.e., removing/adding a transition, or changing its value) and evaluate RMs using the objective function of LRM. When all neighbouring RMs are evaluated, the algorithm chooses the one with lowest values and sets it as the current RM. To avoid local minima, Tabu search maintains a Tabu list of all the RMs that were previously used as the current RM. Then, RMs in the Tabu list are pruned when examining the neighbourhood of the current RM. \n Simultaneously Learning a Reward Machine and a Policy We now describe our overall approach to simultaneously finding an RM and exploiting that RM to learn a policy. The complete pseudo-code can be found in the supplementary material (Algorithm 1). Our approach starts by collecting a training set of traces T generated by a random policy during t w \"warmup\" steps. This set of traces is used to find an initial RM R using Tabu search. The algorithm then initializes policy π, sets the RM state to the initial state u 0 , and sets the current label l to the initial abstract observation L(∅, ∅, o). The standard RL learning loop is then followed: an action a is selected following π(o, u) where u is the current RM state, and the agent receives the next observation o and the immediate reward r. The RM state is then updated to u = δ u (u, L(o, a, o )) and the last experience ( o, u , a, r, o , u ) is used by any RL method of choice to update π. Note that in an episodic task, the environment and RM are reset whenever a terminal state is reached. If on any step, there is evidence that the current RM might not be the best one, our approach will attempt to find a new one. Recall that the RM R was selected using the cardinality of its prediction sets N (LRM). Hence, if the current abstract observation l is not in N u,l , adding the current trace to T will increase the size of N u,l for R. As such, the cost of R will increase and it may no longer be the best RM. Thus, if l ∈ N u,l , we add the current trace to T and search for a new RM. Recall that we use Tabu search, though any discrete optimization method could be applied. Our method only uses the new RM if its cost is lower than R's. If the RM is updated, a new policy is learned from scratch. Given the current RM, we can use any RL algorithm to learn a policy π(o, u), by treating the combination of o and u as the current state. If the RM is perfect, then the optimal policy π * (o, u) will also be optimal for the original POMDP (as stated in Theorem 4.2). However, to exploit the problem structure exposed by the RM, we can use the QRM algorithm. As explained in §3, standard QRM under partial observability can introduce a bias because an experience e = (o, a, o ) might be more or less likely depending on the RM state that the agent was in when the experience was collected. We partially address this issue by updating qu using (o, a, o ) if and only if L(o, a, o ) ∈ N u,l , where l was the current abstract observation that generated the experience (o, a, o ). Hence, we do not transfer experiences from u i to u j if the current RM does not believe that (o, a, o ) is possible in u j . For example, consider the cookie domain and the perfect RM from Figure  2c . If some experience consists of entering to the red room and seeing a cookie, then this experience will not be used by states u 0 and u 3 as it is impossible to observe a cookie at the red room from those states. Note that adding this rule may work in many cases, but it will not address the problem in all environments (more discussion in §7). We consider addressing this problem as an interesting area for future work. \n Experimental Evaluation We tested our approach on three partially observable grid domains (Figure  1 ). The agent can move in the four cardinal directions and can only see what is in the current room. These are stochastic domains where the outcome of an action randomly changes with a 5% probability. The first environment is the cookie domain (Figure  1a ) described in §3. Each episode is 5, 000 steps long, during which the agent should attempt to get as many cookies as possible. The second environment is the symbol domain (Figure  1b ). It has three symbols ♣, ♠, and in the red and blue rooms. One symbol from {♣, ♠, } and possibly a right or left arrow are randomly placed at the yellow room. Intuitively, that symbol and arrow tell the agent where to go, e.g., ♣ and → tell the agent to go to ♣ in the east room. If there is no arrow, the agent can go to the target symbol in either room. An episode ends when the agent reaches any symbol in the red or blue room, at which point it receives a reward of +1 if it reached the correct symbol and −1 otherwise. The third environment is the 2-keys domain (Figure  1c ). The agent receives a reward of +1 when it reaches the coffee (in the yellow room). To do so, it must open the two doors (shown in brown). Each door requires a different key to open it, and the agent can only carry one key at a time. Initially, the two keys are randomly located in either the blue room, the red room, or split between them. We tested two versions of our Learned Reward Machine (LRM) approach: LRM+DDQN and LRM+DQRM. Both learn an RM from experience as described in §4.2, but LRM+DDQN learns a policy using DDQN  [35]  while LRM+DQRM uses the modified version of QRM described in §5. In all domains, we used u max = 10, t w = 200, 000, an epsilon greedy policy with = 0.1, and a discount factor γ = 0.9. The size of the Tabu list and the number of steps that the Tabu search performs before returning the best RM found is 100. We compared against 4 baselines: DDQN  [35] , A3C  [24] , ACER  [37] , and PPO  [29]  using the OpenAI baseline implementations  [12] . DDQN uses the concatenation of the last 10 observations as input which gives DDQN a limited memory to better handle the domains. A3C, ACER, and PPO use an LSTM to summarize the history. Note that the output of the labelling function was also given to the baselines. Details on the hyperparameters and networks can be found in the supplementary material §13. Figure  3  shows the total cumulative rewards that each approach gets every 10, 000 training steps and compares it to the optimal policy. For the LRM algorithms, the figure shows the median performance over 30 runs per domain, and percentile 25 to 75 in the shadowed area. For the DDQN baseline, we show the maximum performance seen for each time period over 5 runs per problem. Similarly, we also show the maximum performance over the 30 runs of A3C, ACER, and PPO per period. All the baselines outperformed a random policy, but none make much progress on any of the domains. Furthermore, LRM approaches largely outperform all the baselines, reaching close-to-optimal policies in the cookie and symbol domain. We also note that LRM+DQRM learns faster than LRM+DDQN, but is more unstable. In particular, LRM+DQRM converged to a considerably better policy than LRM+DDQN in the 2-keys domain. We believe this is due to QRM's experience sharing mechanism that allows for propagating sparse reward backwards faster (see supplementary material §13.3). A key factor in the strong performance of the LRM approaches is that Tabu search finds high-quality RMs in less than 100 local search steps (Figure  5 , supplementary material). In fact, our results show that Tabu search finds perfect RMs in most runs, in particular when tested over the symbol domain. 7 Discussion, Limitations, and Broader Potential Solving partially observable RL problems is challenging and LRM was able to solve three problems that were conceptually simple but presented a major challenge to A3C, ACER, and PPO with LSTM-based memories. A key idea behind these results was to optimize over a necessary condition for perfect RMs. This objective favors RMs that are able to predict possible and impossible future observations at the abstract level given by the labelling function L. In this section, we discuss the advantages and current limitations of such an approach. u 0 u 1 , 1 ; o/w, 0 , 1 ; o/w, 0 , 0 , 0 We begin by considering the performance of Tabu search in our domains. Given a training set composed of one million transitions, a simple Python implementation of Tabu search takes less than 2.5 minutes to learn an RM across all our environments, when using 62 workers on a Threadripper 2990WX processor. Note that Tabu search's main bottleneck is evaluating the neighbourhood around the current RM solution. As the size of the neighbourhood depends on the size of the set of propositional symbols P, exhaustively evaluating the neighbourhood may sometimes become impractical. To handle such problem, it will be necessary to import ideas from the Large Neighborhood Search literature  [27] . Regarding limitations, learning the RM at the abstract level is efficient but requires ignoring (possibly relevant) low-level information. For instance, Figure  4  shows an adversarial example for LRM. The agent receives reward for eating the cookie ( ). There is an external force pulling the agent down-i.e., the outcome of the \"move-up\" action is actually a downward movement with high probability. There is a button ( ) that the agent can press to turn off (or back on) the external force. Hence, the optimal policy is to press the button and then eat the cookie. Given P = { , }, a perfect RM for this environment is fairly simple (see Figure  4 ) but LRM might not find it. The reason is that pressing the button changes the low-level probabilities in the environment but does not change what is possible or impossible at the abstract level. In other words, while the LRM objective optimizes over necessary conditions for finding a perfect RM, those conditions are not sufficient to ensure that an optimal solution will be a perfect RM. In addition, if a perfect RM is found, our heuristic approach to share experiences in QRM would not work as intended because the experiences collected when the force is on (at u 0 ) would be used to update the policy for the case where the force is off (at u 1 ). Other current limitations include that it is unclear how to handle noise over the high-level detectors L and how to transfer learning from previously learned policies when a new RM is learned. Finally, defining a set of proper high-level detectors for a given environment might be a challenge to deploying LRM. Hence, looking for ways to automate that step is an important direction for future work. \n Related Work State-of-the-art approaches to partially observable RL use Recurrent Neural Networks (RNNs) as memory in combination with policy gradient  [24, 37, 29, 15] , or use external neural-based memories  [25, 18, 13] . Other approaches include extensions to Model-Based Bayesian RL to work under partial observability  [28, 7, 9]  and to provide a small binary memory to the agent and a special set of actions to modify it  [26] . While our experiments highlight the merits of our approach w.r.t. RNN-based approaches, we rely on ideas that are largely orthogonal. As such, we believe there is significant potential in mixing these approaches to get the benefit of memory at both the high-and the low-level. The effectiveness of automata-based memory has long been recognized in the POMDP literature  [5] , where the objective is to find policies given a complete specification of the environment. The idea is to encode policies using Finite State Controllers (FSCs) which are FSMs where the transitions are defined in terms of low-level observations from the environment and each state in the FSM is associated with one primitive action. When interacting with the environment, the agent always selects the action associated with the current state in the controller. Meuleau et al.  [22]  adapted this idea to work in the RL setting by exploiting policy gradient to learn policies encoded as FSCs. RMs can be considered as a generalization of FSC as they allow for transitions using conditions over high-level events and associate complete policies (instead of just one primitive action) to each state. This allows our approach to easily leverage existing deep RL methods to learn policies from low-level inputs, such as images-which is not achievable by Meuleau et al.  [22] . That said, further investigating using ideas for learning FSMs  [3, 40, 10]  in learning RMs is a promising direction for future work. Our approach to learn RMs is greatly influenced by Predictive State Representations (PSRs)  [20] . The idea behind PSRs is to find a set of core tests (i.e., sequences of actions and observations) such that if the agent can predict the probabilities of these occurring, given any history H, then those probabilities can be used to compute the probability of any other test given H. The insight is that state representations that are good for predicting the next observation are good for solving partially observable environments. We adapted this idea to the context of RM learning as discussed in §4. While our work was under review, two interesting papers were submitted to arXiv. The first paper, by Xu et al.  [39] , proposes a polynomial time algorithm to learn reward machines in fully observable domains. Their goal is to learn the smallest reward machine that is consistent with the reward function-which makes sense for fully observable domains, but would have limited utility under partial observability (as discussed in §4). The second paper, by Zhang et al.  [41] , proposes to learn a discrete PSR representation of the environment directly from low-level observations and then plan over such representation using tabular Q-learning. This is a promising research direction, with some clear synergies with LRM. \n Concluding Remarks We have presented a method for learning (perfect) Reward Machines in partially observable environments and demonstrated the effectiveness of these learned RMs in tackling partially observable RL problems that are unsolvable by A3C, ACER and PPO. Informed by criteria from the POMDP, FSC, and PSR literature, we proposed a set of RM properties that support tackling RL in partially observable environments. We used these properties to formulate RM learning as a discrete optimization problem. We experimented with several optimization methods, finding Tabu search to be the most effective. We then combined this RM learning with policy learning for partially observable RL problems. Our combined approach outperformed a set of strong LSTM-based approaches on different domains. We believe this work represents an important building block for creating RL agents that can solve cognitively challenging partially observable tasks. Not only did our approach solve problems that were unsolvable by A3C, ACER and PPO, but it did so in a relatively small number of training steps. RM learning provided the agent with memory, but more importantly the combination of RM learning and policy learning provided it with discrete reasoning capabilities that operated at a higher level of abstraction, while leveraging deep RL's ability to learn policies from low-level inputs. This work leaves open many interesting questions relating to abstraction, observability, and properties of the language over which RMs are constructed. We believe that addressing these questions, among many others, will push the boundary of partially observable RL problems that can be solved. \n Algorithm for Simultaneously Learning Reward Machines and a Policy Algorithm 1 shows our overall approach to simultaneously learning an RM and exploiting that RM to learn a policy. The algorithm inputs are the set of propositional symbols P, the labelling function L, a maximum on the number of RM states u max , and the number of \"warmup\" steps t w . Our approach starts by collecting a training set of traces T generated by a random policy during t w steps (Line 2). This set of traces is used to find an initial RM R using Tabu search (Line 3). If later traces show that R is incorrect, our method will then find a new RM learned using the additional traces. Lines 4 and 5 initialize the environment and the policy π, and set variables x and l to the initial RM state u 0 and initial abstract observation L(∅, ∅, o), respectively. Lines 7-19 are the main loop of our approach. Lines 7-10 are part of the standard RL loop: the agent executes an action a selected following π(o, x) and receives the next observation o , the immediate reward r, and a boolean variable done indicating if the episode has terminated. Then, the state in the RM x is updated and the policy π is improved using the last experience ( o, x , a, r, o , x , done). Note that when done is true, the environment and RM are reset (Lines 17-18). Lines 11-16 involve relearning the RM when there is evidence that the current RM might not be the best one. Recall that the RM R was selected using the cardinality of its prediction sets N (see the description of LRM). Hence, if the current abstract observation l is not in N x,l , then adding the current trace to T will increase the size of N x,l for R. As such, the cost of R will increase and it may no longer be the best RM. Thus, if l ∈ N x,l , we add the current trace to T and use Tabu search to find a new RM. Note, our method only uses the new RM if its cost is lower than that of R (Lines 14-16). However, when the RM is updated, a new policy is learned from scratch (Line 16). T ← T ∪ get_current_trace() Proof sketch. If the reachable belief space B is finite, we can construct an RM that keeps track of the current belief state using one RM state per belief state and emulating their progression using δ u , and one propositional symbol for every action-observation pair. Thus, the current belief state b t can be inferred from the last observation, last action, and the current RM state. As such, the equality from Definition 4.1 holds. Two interesting properties follow from the definition of a perfect RM. First, if the set of belief states B for the POMDP P O is finite, then there exists a perfect RM for P O with respect to some L. Second, the optimal policies for perfect RMs are also optimal for the POMDP. Theorem 12.2. Let R P be a perfect RM for a POMDP P O w.r.t. a labelling function L, then any optimal policy for R P w.r.t. the environmental reward is also optimal for P O . Proof sketch. As the next observation and immediate reward probabilities can be predicted from O × U × A, an optimal policy over O × U must also be optimal over P O . A key property of this formulation is that any perfect RM is optimal with respect to the objective function in LRM when the number of traces tends to infinity: Theorem 12.3. When the set of training traces (and their lengths) tends to infinity and is collected by a policy such that π(a|o) > for all o ∈ O and a ∈ A, and some constant > 0, then any perfect RM with respect to L and at most u max states will be an optimal solution to the formulation given in LRM. Proof sketch. In the limit, l ∈ N u,l if and only if the probability of observing l after executing an action from the RM state u while observing l is non-zero. In particular, for all i ∈ I and t ∈ T , the cardinality of N xi,t,L(ei,t) will be minimal for a perfect RM. This follows from the fact that perfect RMs make perfect predictions for the next observation o given o, u, and a. Therefore, as we minimize the sum over log(|N xi,t,L(ei,t) |), the objective value for a perfect RM must be minimal. \n Experimental Evaluation 13.1 Experimental Details For LRM+DDQN and LRM+DQRM, the neural network used has 5 fully connected layers with 64 neurons per layer. On every step, we trained the network using 32 sampled experiences from a replay buffer of size 100,000 using the Adam optimizer  [19]  and a learning rate of 5e-5. The target networks were updated every 100 steps. DDQN  [35]  uses the same parameters and network architecture as LRM+DDQN, but its input is the concatenation of the last 10 observations, as commonly done by Atari playing agents. This gives DDQN a limited memory to better handle partially observable domains. In contrast, A3C, ACER, and PPO use an LSTM to summarize the history. We also followed the same testing methodology that was used in their original publications. We ran each approach at least 30 times per domain, and on every run, we randomly selected the number of hidden neurons for the LSTM from {64, 128, 256, 512} and a learning rate from (1e-3, 1e-5). We also sampled δ from {0, 1, 2} for ACER and the clip range from (0.1, 0.3) for PPO. Other parameters were fixed to their default values. While interacting with the environment, the agents were given a \"top-down\" view of the world represented as a set of binary matrices. One matrix had a 1 in the current location of the agent, one had a 1 in only those locations that are currently observable, and the remaining matrices each corresponded to an object in the environment and had a 1 at only those locations that were both currently observable and contained that object (i.e., locations in other rooms are \"blacked out\"). The agent also had access to features indicating if they were carrying a key, which colour room they were in, and the current status (i.e., occurring or not occurring) of the events detected by the labelling function. \n Tabu Search Figure  5  evaluates the quality of the RMs found by Tabu search by comparing it the perfect RM. In each plot, a dot compares the cost of a handcrafted perfect RM with that of an RM R that was found by Tabu search while running our LRM approaches, where the costs are evaluated relative to the training set used to find R. Being on or under the diagonal line (as in most of the points in the figure) means that Tabu search is finding RMs whose values are at least as good as the handcrafted RM. Hence, Tabu search is either finding perfect RMs or discovering that our training set is incomplete and our agent will eventually fill those gaps. \n Cookie domain Symbol domain 2-keys domains Cost Perfect RM Cost Learned RM Cost Perfect RM Cost Learned RM Cost Perfect RM Cost Learned RM  \n DDQN vs DQRM: Exploration Heatmaps and Learned Trajectories As shown in §6 of the paper, LRM+DQRM tends to learn faster than LRM+DDQN and largely outperforms LRM+DDQN in the 2-keys domain. Towards better understating these results, we ran the following experiment. For the 2-keys domain (and identical random seed), we learn policies using DDQN and DQRM over the same handcrafted perfect RM from Figure  6 . RM state u 6 is fairly simple: when the agent is carrying a key and there is only one closed door, go and get the coffee. As expected, DQRM seems to learn an accurate estimation of that q-function using very limited interactions within the coffee room. In contrast, DDQN uses one big q-network to model the complete policy. Receiving reward by getting the coffee pushes the q-network estimation to believe that a high reward can be collected from the coffee room (even if the doors are closed). Hence, the agent spent a considerable amount of time hitting the second door without having a key. Second, DQRM shares experience over all the q-networks. This allows for using the experiences collected while being at early stages of the task (e.g., states u 0 , u 1 , u 2 , and u 3 ) to update policies for later stages (e.g., states u 4 , u 5 , and u 6 ). In particular, all the experience needed to learn to navigate from one room to another is shared. Therefore, while DDQN would depend on its network to avoid relearning how to navigate between rooms when the RM state changes, DQRM enforces such transfer by sharing experiences whenever it is appropriate. This might explain why DDQN spends considerably more time in the hallway than DQRM in heatmaps 50-100K and 100-150K.  Note that the exploratory trend from 150-500K follows a clear pattern. On one hand, the DQRM agent seems to have a good idea of how to solve the task and, therefore, it spends most of its time on the hallway (solving the tasks requires passing through the hallway at least 4 times). On the other hand, the DDQN agent is getting stuck exploring subregions of the map. Finally, we inspected the trajectories of each agent when solving the task after 1 million training steps. Figures 9 shows the DDQN agent and Figure  10  shows the DQRM agent. Both agents solved the task, but DQRM solved it faster (83 steps vs 102 steps). In solving this problem, the main difficulty for the DDQN agent is in reacting to entering the South room and discovering that the keys are not there. Its reaction is to enter and leave the empty room many times before going to the North room. In the case of DQRM, the agent goes directly to the North room after observing that the South room is empty, but then it enters and leaves the North room a few times before collecting the keys. After collecting the first key, both agents solved the rest of the task almost optimally.    Figure 1 : 1 Figure 1: Partially observable environments where the agent can only see what is in the current room. \n Figure 2 : 2 Figure 2: Three possible Reward Machines for the Cookie domain. \n Figure 3 : 3 Figure 3: Total reward collected every 10, 000 training steps. \n Figure 4 : 4 Figure 4: The gravity domain. \n Algorithm 1 1 Learning an RM and a Policy 1: Input: P, L, A, u max , t w 2: T ← collect_traces(t w ) 3: R, N ← learn_rm(P, L, T , u max ) 4: o, x, l ← env_get_initial_state(), u 0 , L(∅, ∅, o) 5: π ← initialize_policy() 6: for t = 1 to t train do7: a ← select_action(π, o, x) 8: o , r, done ← env_execute_action(a) 9: x , l ← δ u (x, L(o, a, o )), L(o, a, o ) 10: π ← improve(π, o, x, l, a, r, o , x , l , done, N ) 11: if l ∈ N x,l then 12: \n Figure 5 : 5 Figure 5: Cost comparison between perfect RM and RM found by Tabu search. \n steps 300-350K steps 350-400K steps 400-450K steps 450-500K steps DQRM DQRM DQRM DQRM DQRM 250-300K steps 300-350K steps 350-400K steps 400-450K steps 450-500K steps \n Figure 8 : 8 Figure 8: Exploration heatmaps for DDQN and DQRM over the 2-keys domain given a perfect RM. \n (a) Collecting the first key. (b) Opening the first door. (c) Collecting the other key. (d) Opening the second door. \n Figure 9 : 9 Figure 9: The learned trace after 1 million training steps by DDQN given a perfect RM, divided into four stages. \n Figure 10 : 10 Figure 10: The learned trace after 1 million training steps by QRM given a perfect RM, divided into four stages. \n i,t+1 ) from L(e i,t ) and the current RM state x i,t , where e i,t+1 is the experience (o i,t , a i,t , o i,t+1 ) and e i,0 is (∅, ∅, o i,0 ) by definition. The model parameters are the set of traces T , the set of propositional symbols P, the labelling function L, and a maximum number of states in the RM u max . The model also uses the sets I = {0 . . . n} and T i = {0 . . . t i − 1}, where I contains the index of the traces and T i their time steps. The model has two auxiliary variables x i,t and N u,l . Variable x i,t ∈ U represents the state of the RM after observing trace T i up to time t. Variable N u,l ⊆ 2 2 P is the set of all the next abstract observations seen from the RM state u and the abstract observations l at some point in T . In other words, l ∈ N u,l iff u = x i,t , l = L(e i,t ), and l = L(e i,t+1 ) for some trace T i and time t. minimize U,u 0 ,δu,δr i∈I t∈T i log(|N x i,t ,L(e i,t ) |) (LRM) s.t. U, u0, δu, δr ∈ RP (3) \n Given any POMDP P O with a finite reachable belief space, there exist a perfect RM for P O with respect to some labelling function L. 12 Theorems and Proof Sketches Theorem 12.1. 13: 14: 15: 16: 17: R , N ← relearn_rm(R, P, L, T , u max ) if R = R then R, done ← R , true π ← initialize_policy() end if 18: 19: 20: 21: end if if done then o , x , l ← env_get_initial_state(), u 0 , L(∅, ∅, o) end if 22: 23: end for o, x, l ← o , x , l 24: return π", "date_published": "n/a", "url": "n/a", "filename": "LRM_paper.tei.xml", "abstract": "Reward Machines (RMs) provide a structured, automata-based representation of a reward function that enables a Reinforcement Learning (RL) agent to decompose an RL problem into structured subproblems that can be efficiently learned via off-policy learning. Here we show that RMs can be learned from experience, instead of being specified by the user, and that the resulting problem decomposition can be used to effectively solve partially observable RL problems. We pose the task of learning RMs as a discrete optimization problem where the objective is to find an RM that decomposes the problem into a set of subproblems such that the combination of their optimal memoryless policies is an optimal policy for the original problem. We show the effectiveness of this approach on three partially observable domains, where it significantly outperforms A3C, PPO, and ACER, and discuss its advantages, limitations, and broader potential.  1", "id": "bfdadb4326f1777e2d45eb6c1e669cb7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jessica Taylor"], "title": "Quantilizers: A Safer Alternative to Maximizers for Limited Optimization", "text": "Expected Utility Maximization Many frameworks for studying idealized agents assume that agents attempt to maximize the expectation of some utility function, as seen in the works of  Heckerman and Horvitz (1990) ,  Bacchus and Grove (1995) , and  Chajewska, Koller, and Parr (2000) . von  Neumann and Morgenstern (1944)  provide compelling arguments that any rational agent with consistent preferences must act as if it is maximizing some utility function, and  Russell and Norvig (2010, chap. 16 ) use the expected utility maximization framework extensively as the basic model of an idealized rational agent. Formally, let A be the finite 1 set of available actions, O the set of possible outcomes, and W : A → ∆O map each action to the predicted outcome distribution resulting from that action 2 . Let U : O → [0, 1] be a utility function, with U (o) being the utility of outcome o. Then an expected utility maximizer is an agent that chooses an action a ∈ A that maximizes E [U (W (a))]. We make no argument against expected utility maximization on the grounds of rationality. However, maximizing Copyright c 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. 1 Expected utility maximizers and quantilizers can also be defined for infinite set of actions, but in this paper we discuss only finite action sets for simplicity. 2 Defining W is not straightforward. See  Rosenbaum and Rubin (1983)  for a formalization of the \"causal effects\" of an action, whose maximization results in causal decision theory; see  Soares and Fallenstein (2015)  for discussion of alternative decision theories. the expectation of some utility function could produce large unintended consequences whenever U does not accurately capture all the relevant criteria. Some unintended consequences of this form can already be observed in modern AI systems. For example, consider the genetic algorithm used by  Nguyen, Yosinski, and Clune (2014)  to generate an image which would be classified by a deep neural network as a starfish, with extremely high confidence. The resulting image ended up completely unrecognizable, looking nothing at all like a starfish. Of course,  Nguyen, Yosinski, and Clune (2014)  intended to develop images that would be misclassified, but this demonstrates the point that an algorithm directed to find the image that most classified as a starfish, generated an image that was very strange indeed. Another example of unintended solutions resulting from maximization is given by  Thompson (1997) , who used genetic algorithms to \"artificially evolve\" a circuit that could differentiate between two different inputs via a 10 x 10 field programmable gate array (FPGA). The resulting circuit worked, using only 21 of the 100 available FPGA cells. Curiously, five of those cells were not connected to either the input or the output-the evolved circuit was making use of them via the physical features of that specific chip and machine (Thompson suggest that the circuit was taking advantage of electromagnetic coupling or power-supply loading). If the goal was to design a circuit that could also work on other chips, then this \"maximization\" process (of finding a very small algorithm that, on that one circuit board, was good at distinguishing between two inputs) produced an unintended result that was dependent upon physical features of the chip that the designers thought were irrelevant. The resulting circuit performed well by the test metric, but the result would not likely have been usable on any other physical chips. Unintended solutions of this form could become quite dangerous in highly autonomous artificially intelligent systems with capabilities that strongly exceed those of humans.  Bostrom (2014)  discusses a number of potential dangers stemming from expected utility maximization in powerful agents. He considers \"superintelligent\" agents, defined as agents that are \"smarter than the best human brains in practically every field,\" and describes the problem of perverse instantiation, his term for the seemingly-perverse unintended consequences of directing a powerful agent to attempt to maximize a utility function which is not in fact aligned with our goals. For example,  Bostrom (2014)  illustrates this by describing a machine that, when told to make humans smile, accomplishes this goal by paralyzing human faces into permanent smiles, rather than by causing us to smile via the usual means. Another example is given by , who describes an agent directed to \"cure cancer\" which attempts to kidnap human test subjects. Clearly, before an autonomous system can be granted great autonomy and power, we must have some assurances that it will not, in pursuit of its goals, produce any such \"perverse\" unintended consequences. In both the short term and the long term, the problem with expected utility maximization is that the system's utility function likely will not capture all the complexities of human value, as humans care about many features of the environment that are difficult to capture in any simple utility function . Of course, no practical system acting in the real world can actually maximize expected utility, as finding the literally optimal policy is wildly intractable. Nevertheless, it is common practice to design systems that approximate expected utility maximization, and insofar as expected utility maximization would be unsatisfactory, such systems would become more and more dangerous as algorithms and approximations improve. If we are to design AI systems which safely pursue simple goals, an alternative may be necessary. \n Expected Utility Quantilization Given that utility maximization can have many unintended side effects,  Armstrong, Sandberg, and Bostrom (2012)  and others have suggested designing systems that perform some sort of \"limited optimization,\" that is, systems which achieve their goals in some non-extreme way, without significantly disrupting anything outside the system or otherwise disturbing the normal course of events. For example, intuition says it should be possible to direct a powerful AI system to \"just make paperclips\" in such a way that it runs a successful paperclip factory, without ever attempting to turn as much of the universe as possible into paperclips.  Simon (1956)  propose instead designing expected utility \"satisficers,\" agents that choose any action that achieves an expected utility above some fixed threshold. In our notation, an expected utility satisficer is one that chooses an action from the set {a ∈ A : E [U (W (a))] ≥ t} for some threshold t. (Indeed,  Fallenstein and Soares (2014)  describe a toy model of satisficing agents in simple environments.) However, the satisficing framework is under-defined and not necessarily satisfactory. When it comes to powerful intelligent agents, it may often be that the easiest way to satisfice is to maximize: if the paperclip AI system can easily create a sub-agent that tries as hard as it can to make paperclips, it may be that the easiest satisficing action is simply to construct a sub-agent that attempts to approximate something like expected utility maximization instead.  Abbeel and Ng (2004)  have suggested apprenticeship learning as an alternative to maximization when it is difficult to explicitly specify the correct goal. In apprenticeship learning, an AI system learns to closely imitate a human expert performing a task. An agent which only executes actions that its operators would have executed seems likely to be immune to Bostrom's problem of perverse instantiation. Yet while mimicking humans avoids many unintended effects of maximization, a system that merely mimics humans cannot easily surpass the performance of those it is mimicking (except perhaps by performing the same actions faster and more reliably). Such a technique could prove quite useful, but wouldn't help us design algorithms intended to outperform humans by finding plans, strategies, and techniques that the operators would not have been able to identify. In this paper, we propose quantilization, which interpolates between mimicry and maximization in order to gain some advantages of both. Definition 1 (Quantilizer). A q-quantilizer is an agent that, when faced with a decision problem, returns a random action in the top q proportion of some \"base distribution\" over actions, sorted by the expected utility achieved if that action is executed. Intuitively, a 0.1-quantilizer (which we could also call a \"ten percentilizer\") selects a random action from the top 10% of actions. More formally, let A be the action set and γ be some distribution over actions. For example, γ could be uniformly random, or it could be a distribution estimated from human actions. Let f : [0, 1] → A be a function that represents γ, but sorted by expected utility: ∀x, y ∈ [0, 1] x > y =⇒ E [U (W (f (x)))] ≥ E [U (W (f (y)))] µ({x ∈ [0, 1] | f (x) = a}) = γ(a) where µ is the Lebesgue measure on the reals. For any 0 < q ≤ 1, a q-quantilizer samples a number x from the uniform distribution over [1 − q, 1] and returns f (x). We will write Q U,W,γ,q (a) for the probability that it returns action a, where U is the quantilizer's utility function.  3  We will abbreviate this as simply Q q (a), where it is understood that Q q is parameterized on U , W , and γ. As q approaches 0, a q-quantilizer reduces to a maximizer whose available action set is the support of γ. A 0.01quantilizer (also known as a \"one percentilizer\") samples a random action from the top 1%; a 0.5-quantilizer (\"fiftypercentilizer\") samples a random above-average action; a 1-quantilizer just mimics γ. As an example, suppose there are 3 actions A = {a, b, c} with expected utilities  1 . A maximizer will always return action c. If we define a uniform base distribution γ, then the behavior of the q-quantilizer Q q is: Figure  1 : A representation of a 5/9-quantilizer for the threeaction example. The quantilizer samples x from the gray region and returns the corresponding action f (x), so it returns b with 2/5 probability and c with 3/5 probability. E [U (W (a))] = 0.2 E [U (W (b))] = 0.5 E [U (W (c))] = 0.7 as illustrated in figure • If q ≤ 1 3 , it always returns c. • If 1 3 ≤ q ≤ 2 3 , then it returns c with probability 1 3q and b the rest of the time. • If q ≥ 2 3 , then it returns c with probability 1 3q , b with probability 1 3q , and a otherwise. In this example, it is clear that the quantilizer interpolates between maximizing and mimicking γ depending on q. \n Derivation from a Conservative Cost Constraint We will now explore a few circumstances under which one might prefer to design a system that quantilizes expected utility, rather than maximizing it. Definition 1 gives some hint as to what sort of situation quantilizers are designed for. Given some trusted base distribution γ of actions, such as a generative model for the actions that a human might take, the distribution Q 0.01 is roughly the distribution of actions that a human might take if they were attempting to score well by U (but were otherwise adhering to \"normal\" behavior). That is, if γ puts most of its measure on actions that humans might generate when solving similar problems, then Q 0.01 is similar to the distribution of actions a human might take conditional on that action having a high utility according to U . Thus, intuitively, a 0.01-quantilizer is designed to solve problems in a manner similar to how a human would solve that problem. Furthermore, under certain assumptions, we can prove that building a quantilizer instead of a maximizer is not too costly to our true utility function, in the sense that running the quantilizer won't be much worse than simply sampling from the base distribution γ. To show this, assume that an AI system is built to quantilize expected utility for some utility function U . Assume that our true utility function is some other function V . Intuitively, we will imagine that for most actions, E [U (W (a))] is similar to E [V (W (a))], but for the actions a U which maximize E U (W (a U )) (or come close to maximizing it), the value of E V (W (a U )) is much lower (because a U is some edge case or \"perverse instantiation,\" such as generating smiles by paralyzing people's faces). Thus, as in Swaminathan and Joachims (2015), we assume there is some unknown cost function c : A → R ≥0 , which describes the negative contribution of an action a to V . For example, if there is some action noop which the AI system may execute immediately to shut down without having any further effect on the world, then we could define c(a) = max{0, E [V (W (noop))] − E [V (W (a))]}. We expect c to be quite difficult to approximate, because human values are complex and depend on many difficult-to-quantify aspects of the world. Indeed, if we could formally encode c, we could build it into U , and then we would have much less need to worry about perverse instantiations. Even without an approximation of c, though, we can still prove that under certain assumptions, a quantilizer will not incur a high cost according to c. Assume that the cost of a random action from γ is no more than 1. This assumption may be justified if, for example, γ is a uniformly random action and uniformly random actions are highly unlikely to be harmful. Write E A∼γ [c(A)] ≤ 1 for the expected cost of a random action sampled from γ. It is now possible to bound the cost of an action sampled from Q q : Lemma 1 (Cost bound on quantilizers). E A∼Qq [c(A)] ≤ 1 q Proof. Observe that Q q \"fits under\" γ when scaled down by a factor of q: Q q (a) = 1 q µ({x ∈ [1 − q, 1] | f (x) = a}) ≤ 1 q γ(a). Therefore, it is possible to bound the cost of Q q : E A∼Qq [c(A)] = a∈A Q q (a)c(a) ≤ a∈A 1 q γ(a)c(a) = 1 q E A∼γ [c(A)] . (1) So the expected cost of sampling from Q q is no more than 1/q times that of sampling from γ. Thus, for example, running a \"ten percentalizer\" can be no more than ten times as costly as sampling from γ. In fact, quantilizers are optimal among all policies that can be proven to be low-cost in this way. For example, suppose we have generated some base distribution γ of actions (perhaps a generative model of what sort of actions a human would take), and we're willing to risk running an agent that incurs an expected cost of at most 100 times the expected cost of simply sampling from γ. Then, a 0.01-quantilizer is the optimal agent we could run. More formally, say we desire some distribution p ∈ ∆A such that the following conservative cost constraint holds for some acceptable cost threshold t > 1: ∀c :A → R ≥0 E A∼γ [c(A)] ≤ 1 =⇒ E A∼p [c(A)] ≤ t. (2) This constraint states that, for any cost function assigning an expected cost of no more than 1 to a random action from γ, the expected cost of an action drawn from p is no more than t. Then, we have the following: Lemma 2 (p fits under γ). Let p satisfy 2. Then p(a) ≤ tγ(a) for all a ∈ A. Proof. Suppose this were not true. Then for some a * we have p(a * ) > tγ(a * ). Now define c(a) = 1/γ(a * ) if a = a * 0 otherwise We have E A∼γ [c(a)] = a∈A γ(a)c(a) = γ(a * )c(a * ) = 1. Also, E A∼p [c(a)] = a∈A p(a)c(a) = p(a * )c(a * ) > tγ(a * )c(a * ) = t. Jointly, these statements contradict constraint 2. Theorem 1 (Quantilizer optimality). Choose q=1/t. Then, a q-quantilizer maximizes expected U -utility subject to constraint 2. Proof. By Lemma 2, we cannot assign more that γ(a)/q probability to any action a, so the best we can do to maximize expected utility is to assign γ(a)/q probability to the best actions and 0 to the rest-and this is exactly what a q-quantilizer does. \n Targeted Impact Expected utility quantilization is intended for use in systems that may eventually need to make important decisions, autonomously, in environments where negative actions could have a large cost. For example, imagine an AI system which is programmed to autonomously trade stocks in order to make significant sums of money, where that money will in tun be put to use improving the world in some potentially dramatic fashion. Unfortunately, the bounds of equation (  1 ) and the cost constraints of equation (  2 ) apply just as well for cost functions as benefit functions: just as running a q-quantilizer will not, in expectation, be any more than 1/q times as costly as sampling from γ directly; nor will it be any more than 1/q times more beneficial than sampling from γ directly. Thus, in a sense, a q-quantilizer has a bounded impact-it will not make the world all that different than running an AI system that samples γ directly would have made it. What we really want, though, is not low impact, but targeted impact. A small modification to the quantilizer specification allows us to achieve the same constraints on costs without necessarily constraining the potential benefits. Before explaining, first note that the stock trading AI system has two different types of side effect: one is that it produces money which can be used by its operators; the other are side effects of trading (for example, it might crash the market in order to make more money). The first side effect might cause a significant change in the world, e.g., if the operators use the money to fund a charity which is highly effective at reducing global poverty. Nevertheless, we would prefer the system to only be guaranteeing reduced impact according to the second sort of side effect. That is, in this setting, we can define the cost function c : A × R → R ≥0 , such that c(a, m) determines how much cost an action a has, if counterfactually it generates m dollars (rather than the actual amount of money that it generates). Given a cost function of this form, we would like to design a quantilizer such that ∀c : A × R → R ≥0 , m : R E A∼γ [c(A, m)] ≤ 1 =⇒ E A∼p [c(A, m)] ≤ 1/q. That is, we require that for all counterfactual amounts of money m, the side effects of the stock trading algorithm have low cost compared to the side effects of executing actions at random from γ. Thus, a system obeying this cost constraint does not need to worry about the extra side effects of generating significant amounts of money for its operators. Mathematically, quantifying over c and m at the same time is the same as quantifying over functions of the form a → c(a, m) for any c and m, so the condition is equivalent to ∀c : A → R ≥0 E γ [c(A)] ≤ 1 =⇒ E p [c(A)] ≤ 1/q which is the same as the original cost constraint. Therefore, it is possible to design a quantilizer that is guaranteed to have low cost (compared to γ) through effects other than money, by the same methods that guarantees it to have low overall cost. \n Algorithms for Quantilization Just as it is impractical to design algorithms that literally maximize expected utility in complex environments, it is similarly impractical to design algorithms that perfectly quantilize expected utility. Any practical system based on expected utility quantilization would similarly have to use some form of approximation. Fortunately, it is not hard to see how expected utility quantilization could be approximated. Suppose we can compute E [U (W (a))] for each action a, and that we wish to approximate a q-quantilizer with respect to a distribution γ. To do this, we can run the following algorithm: first take n samples from γ, and then sample from Q U,W,γ,q , where γ is the empirical distribution estimated from the n samples. As n approaches infinity, γ approaches γ, so Q U,W,γ,q approaches Q U,W,γ,q . Thus, given some base distribution γ which is relatively easy to sample from, and some method for approximating E [U (W (a))] and γ, an approximate expected utility quantilizer can be constructed in a straightforward manner. Indeed, this algorithm yields insight into how safe it is to perform a random search of actions sampled from γ. If q = 1/n, then this algorithm simply takes n samples from γ and returns the one with the highest expected utility, emulating a simple random search procedure. Since this procedure approximates q-quantilization, the bounds that apply to quantilization can be shown to hold for random searches over samples of γ, with some minimal modifications. 3 Drawbacks and Open Problems \n Acquiring the Base Distribution Clearly, a quantilizer is only as good as its base distribution γ. The above constraints on the amount of costs that running an expected utility quantilizer can incur are in terms of multiples of the expected cost from sampling directly from γ: clearly, if it is dangerous to sample actions from γ, then it is dangerous to run a quantilizer using γ. Defining a useful base distribution is not a straightforward task. One could define the base distribution to be some uniformly random action, but in a complex multi-dimensional space of strategies, a uniformly random action is highly unlikely to be useful, and so even a 10 −5 -quantilizer would be unlikely to do anything useful. If instead γ described random strategies that a human might actually execute, then it is much more likely to be useful. Thus, a generative model of human strategies would make expected utility quantilization a much more viable strategy. (See  Ng and Russell (2000)  and  Baker, Tenenbaum, and Saxe (2007)  for some initial work in this direction.) Of course, there are a number of situations in which a simple generative model of human behavior would not be sufficient. For example, if humans are likely to misunderstand the problem and thereby cause catastrophe, then a simple generative model would not suffice. (And if a human were quite likely to design an expected utility maximizing AI system, then a quantilizer may well also generate a maximizer.)  4  The study of how to generate safe and satisfactory base distributions γ for various different problem domains remains an open problem. \n Butterfly Effects It could be that a non-negligible percentage of ordinary actions that humans take are either very good or very bad, due to butterfly effects. In this case, the cost of sampling from fairly ordinary γ distributions is actually quite high, with the expectation of γ being reasonable only because the high costs are canceled out by equally high benefits. However, in situations such as these, it is quite possible for a quantilizer to preserve the costs of γ without necessarily preserving many of the benefits. For example, suppose that the quantilizer is trying to make money on the stock market. There is a 10% chance of the stock market crashing in the next year. While a random sequence of trades made by a human will not significantly change the chance of a crash in expectation, it might be the case that a certain sequence of 3 ordinary trades (a sequence that a human would be 0.1% likely to make) will greatly increase the chance of a stock market crash through butterfly effects. In this case, a 0.001-quantilizer that can predict these effects might make these trades if it can profit from the crash. It is not clear if this scenario is even theoretically possible, since it requires extremely accurate prediction of the future. Nevertheless, it would be prudent to study this problem further and possibly design variations on quantilization that avoid this problem. \n Quantilization in Repeated Games Suppose we have n independent games. On game i, the agent chooses an action a i ∈ A i and receives utility U i (W i (a)), where each W i : A → ∆O returns the outcome for game i, and each U i : O → [0, 1] measures the utility achieved in that game. There are two different ways to design a quantilizer that plays these n games. We could design the agent to q-quantilize each game independently, choosing from the best q proportion of actions in each game independently according to n different base distributions γ i . This distribution for the sequence of actions in each game could be written as n i=1 Q Ui,Wi,γi,q . Alternatively, we could design the agent to q-quantilize a sequence of actions for the joint game. Here we define the joint game as A = n i=1 A i , W (a 1 , ..., a n ) = (W 1 (a 1 ), ..., W n (a n )) and U (o 1 , ..., o n ) = n i=1 U i (o i ). This action distribution for a q-quantilizer with respect to the base distribution n i=1 γ i could be written as Q U,W, n i=1 γi,q This is quite different from the first scenario! To give a concrete example, imagine two consecutive games that work as follows. In each game, the agent must pick an integer from the set {0, 1, 2}, and then gain that much utility. Thus, we define A i = {0, 1, 2}, W i (a) = a, U i (o) = o. Each base distribution γ i is uniform. Then, a 1/3-quantilizer quantilizing both games independently will choose from the top third of actions in each game separately, and will always yield the action sequence (2, 2). By contrast, a quantilizer quantilizing for the joint game will uniformly sample from the top third of action sequences {(2, 2), (1, 2), (2, 1)}, as illustrated in figure  2 . What could explain this difference? If we define a cost function c(a 1 , a 2 ) = 1 if (a 1 , a 2 ) = (2, 2) 0 otherwise which states that the (2, 2) action has terrible unintended consequences, then independent 1/3-quantilization will accrue a cost 9 times that of sampling from γ. This cost blowup increases exponentially with n. On the other hand, 1/3quantilization in the joint game will accrue a cost only 3 Figure  2 : A representation of the 9 available action pairs in the repeated game. Independent 1/3-quantilization will always select the striped action pair, while 1/3-quantilization on the joint game will select uniformly from one of the three shaded action pairs. times that of sampling from γ. If we believe that the cost function c may not sum costs independently between games, then quantilizing each game independently could be very costly. Cost Independence Assumption Suppose we added the assumption that c(a 1 , ..., a n ) = n i=1 c i (a i ) for some c i : A i → R ≥0 . Then a repeated q-quantilizer would get total expected cost E Ai∼Q U i ,W i ,γ i ,q [c(A 1 , ..., A n )] = n i=1 E Ai∼Q U i ,W i ,γ i ,q [c i (A i )] ≤ 1 q n i=1 E Ai∼γi [c i (A i )] = 1 q E Ai∼γi [c(A 1 , ..., A n )] so repeated quantilization would no longer have a cost blowup exponential in n. However, adding this assumption may be dangerous. Imagine a scenario in which almost all of the cost of a sequence of actions comes from correlation between actions in different games. For example, imagine that each game consists of appending a byte to a computer program, and the program is run when it consists of a million bytes. Then some sequence of actions that each individually have probability 1 in 256 (namely, appending the bytes of a program implementing a computer program that would be very destructive if run) could be dangerous. Each individual action did not have a much higher cost than adding a random byte to the program, but taken all together, the sequence of actions still had a very high cost. In this case and any analogous case, assuming that the cost function is additive could be quite dangerous. In fact, attempting to design a \"superintelligent\" (in the sense of  Bostrom (2014) ) expected utility quantilizer could lead to similar issues. Imagine asking a superintelligent quantilizer for repeated actions that maximize the long-term number of paperclips produced by a certain factory. In this case, similar to the above example, each action might play some small part in a complex plan to turn large swaths of the world into paperclips. However, this seems much less likely to be a problem if the different goals that we have the system quantilize with respect to are independent. For example, imagine that we instead ask the system to repeatedly quantilize a slightly different utility function U i which only cares about events which happen in hour i, with the quantilizer run at the beginning of hour i. Intuitively, it seems that this setup would be safer. However, no safety guarantees have been given; finding a reasonable assumption about the cost functions under which this form of independent quantilization would be safe (if such an assumption exists) remains an open problem. \n Example Applications Quantilizers cannot be used to effectively achieve all possible goals. If the system has to achieve an outcome that it is extremely difficult to achieve by simply sampling γ, then the quantilizer, too, will have a hard time achieving that outcome. For example, if γ is a generative model of human behavior, and the system faces a problem that a human would be very unlikely to solve even one time in a billion, then the quantilizer would also be hard pressed to solve the same problem. However, there are a number of tasks where an expected utility quantilizer would plausibly be able to perform quite well. In this section, we will list a number of examples of tasks that are plausibly solvable with limited expected utility quantilizers. Note that, in practice, these example applications involve repeated quantilization. As explained in section 3.3, repeated quantilization is not currently known to be safe, but we will provisionally assume that it is possible to develop some set of independent (possibly time-indexed) objectives such that repeatedly quantilizing those objectives is in fact safe. \n Synthesizing Highly-Rated Images Imagine that we have a database containing images and human ratings of these images, and that we would like to synthesize new images that are expected to receive high ratings. To do this, we could separately create a generative model over images and a regression model predicting the expected rating for an image. If the regression model is a deep neural network, then as in  Nguyen, Yosinski, and Clune (2014) , the image that gets the highest rating according to the model is unlikely to resemble highly-rated images. Instead, we could use the generative model over images as the base distribution γ and then quantilize to generate a plausible image with a high predicted rating. \n Factory Management Suppose we want a program to control a factory to create a number of objects satisfying a certain specification, using a fixed amount of time and resources. Policies will control parts of the factory, eventually producing many objects. Maximizing the extent to which the resulting objects adhere to the specifications may result in unintended solutions. Perhaps the resulting object will be useless despite satisfying the specifications, due to Goodhart's law: \"When a measure becomes a target, it ceases to be a good measure.\"  (Goodhart 1975) . As an example, imagine a factory that produces electronic toys, which has automated devices that samples toys and automatically score them to see how well they meet specifications. Then, we can imagine a expected utility maximizer figuring out exactly which toys will be sampled, and makes only those ones to spec (the other ones being the cheapest possible piece of plastic that triggers the toy-counter). Or perhaps the automated devices dock points for toys that come off the assembly line hot (as these toys generally become deformed), and the expected utility maximizer finds a way to supercool the toys and thus gain an extremely high score, despite the fact that the supercooled toys later shatter and are useless. By contrast, if we build the AI system to quantilize the extent to which the devices pass the specifications, then the resulting policy will be much more likely to be of the form we expected: the task will almost certainly be accomplished in a manner that was not incredibly unlikely according to γ. \n Safely Transferring Information to Humans A number of proposals for designing extremely capable AI systems that are nevertheless safe to use for one purpose or another include a step where the AI system is expected to explain its plans to humans instead of executing them  (Armstrong, Sandberg, and Bostrom 2012; Bostrom 2014 ). However, it is quite a difficult task to define a goal function that adequately describes \"provide an explanation that causes the human to understand the plan.\" Yet, absent such a goal function, the system's \"explanation\" is likely to be inadequate. If the system's internal representation of the plan is foreign to the operators, then they may not be able to interpret most simple data dumps describing the system's plan. Furthermore, if the system is more capable and knowledgeable than the humans, then the humans may also need a large number of relevant facts, assumptions, and sub-strategies explained to them before they are capable of evaluating the plan. But if the system has to perform a complex optimization task to explain the plan to the humans, then we face the same problem of safe optimization again. If the system is designed to maximize the extent to which the human operators understand its plan, then perverse instantiations could occur, and the result could be quite dangerous. An expected utility maximizer might exploit edge cases in the definition of \"understand\" to fool or otherwise manipulate the humans in a fashion that fulfills the technically stated requirements of \"make the humans understand the plan,\" without generating anything that we would actually term \"understanding.\" It seems very difficult to define what it means for an explanation to cause the human to understand such that we would be comfortable instructing a powerful system to maximize along this metric. Quantilization provides an alternative: we could build an expected utility quantilizers that selects an explanation that is good at causing the human to \"understand\" the system's plans in the same way that they would understand a plan as explained by another human, without as much risk of perverse instantiation. For example, if the base distribution γ is a generative model of explanations created by humans, then moderately strong quantilization might result in an explanation of a plan suitable for human consumption. \n Stock Trading As explained in section 2.2, a quantilizer can be designed to make trades on the stock market that are likely to make money, but which have few other side effects beside the side effect that now the operators have much more money. Specifically, the important thing is that expected utility quantilization gives us the ability to design systems that would almost certainly not crash the stock market (any more than sampling randomly from γ is likely to crash the stock market, which, if γ is a generative model of a smart human trader, means that the system is not much more likely to crash the market than any given smart human trader). This holds true even if the system is powerful enough to find a strategy for gaining incredible amounts of money by causing the stock market to crash. An expected utility maximizer maximizing the amount of money it receives in the stock market would crash the market the moment it found some way to generate huge amounts of profit from doing so, but an expected utility quantilizer would not be much more likely to crash the market than sampling randomly from γ. \n Conclusion Directing a powerful AI system to maximize some utility function U could result in large unintended consequences, if U does not in fact capture all the intricacies of human values. Many of these dangers can be mitigated if, instead of designing expected utility maximizers, we consider other agent architectures. Expected utility quantilization is one alternative to expected utility maximization that allows some safety guarantees, given that we have some base distribution γ where sampling actions from γ is known to be relatively safe. Expected utility quantilization is not a silver bullet. Constructing a safe expected utility quantilizer requires some method for generating a safe base distribution γ, and there are a number of contexts where expected utility quantilization is not guaranteed to yield good results. For example, if the costs of sampling from γ could in fact be high, then quantilization may not lead to good outcomes. Furthermore, if a quantilizer is going to be used to complete the same task many times sequentially, then running the quantilizer may be significantly more dangerous. Yet despite these shortcomings, the preliminary results from investigating expected utility quantilization are promising. Gaining a better understanding of the benefits and drawbacks of expected utility quantilization could yield many more insights into how to create powerful systems that are \"domestic\" in the sense of  Bostrom (2014, chap. 9) , who defines a domestic agent as an agent with limited \"scope in its activities and ambitions.\" There are many open issues that make it difficult to assess how safe it would actually be to run an extremely capable expected utility quantilizer in an unrestricted domain, but nevertheless, this area of research does prove fruitful, and we are hopeful that further study of expected utility quantilization may yield insights into how to design autonomous AI systems that avoid the problem of perverse instantiation. \n Acknowledgements The author would like to thank Nate Soares for help preparing this paper, Benya Fallenstein and Andreas Stuhlmüller for discussion and comments, and Stuart Armstrong for helping to develop initial versions of this idea. A grant from the Future of Life Institute helped fund this work. \t\t\t Since there are multiple sortings of the actions f , some leading to different action distributions, this notation is imprecise. To make the notation more precise, we could specify some canonical way of defining f , such as assigning as much probability mass as possible to lexicographically earlier actions. \n\t\t\t  See Christiano (2011)  for additional discussion of superintelligent predictions of human decisions, and the difficulties that arise in this context.", "date_published": "n/a", "url": "n/a", "filename": "12613-57416-1-PB.tei.xml", "abstract": "In the field of AI, expected utility maximizers are commonly used as a model for idealized agents. However, expected utility maximization can lead to unintended solutions when the utility function does not quantify everything the operators care about: imagine, for example, an expected utility maximizer tasked with winning money on the stock market, which has no regard for whether it accidentally causes a market crash. Once AI systems become sufficiently intelligent and powerful, these unintended solutions could become quite dangerous. In this paper, we describe an alternative to expected utility maximization for powerful AI systems, which we call expected utility quantilization. This could allow the construction of AI systems that do not necessarily fall into strange and unanticipated shortcuts and edge cases in pursuit of their goals.", "id": "8061629033d861e6f69d3a0d7b816e3d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Eliezer Yudkowsky", "Marcello Herreshoff", "Paul Christiano", "Benja Fallenstein", "Mihaly Barasz", "Patrick Lavictoire", "Daniel Dewey", "Qiaochu Yuan", "Stuart Armstrong", "Jacob Steinhardt", "Jacob Taylor", "Andrew 1 Critch"], "title": "Tiling Agents for Self-Modifying AI, and the Löbian Obstacle *", "text": "Introduction Suppose a sufficiently intelligent agent possesses a goal (or a preference ordering over outcomes, or a utility function over probabilistic outcomes). One possible means for the agent to achieve its goal is to construct another agent that shares the same goal  (Omohundro 2008; Bostrom 2012 ). 1 As a special case of agents constructing successors with equivalent goals, a machine intelligence may wish to change its own source code-self-improve. This can be viewed as constructing a successor agent that shares most of your program code and runs on the same hardware as you, then replacing yourself with that agent.  2  We shall approach the subject of AI self-modification and self-improvement by considering it as a special case of agents constructing other agents with similar preferences. In a self-modifying AI, most self-modifications should not change most aspects of the AI; it would be odd to consider agents that could only make large, drastic self-modifications. To reflect this desideratum within the viewpoint from agents constructing other agents, we will examine agents which construct successor agents of highly similar design, so that the sequence of agents \"tiles\" like a repeating pattern of similar shapes on a tiled floor. In attempting to describe agents whose decision criteria approve the construction of highly similar agents, we shall encounter a Gödelian difficulty 3 in the form of Löb's Theorem: A consistent mathematical theory T cannot trust itself in the sense of verifying that a proof in T of any formula φ implies φ's truth-we cannot have the self-verifying scheme (over all formulas φ) of ∀φ : T T φ → φ  (Löb 1955 ).  4  We shall construct a natural-seeming schema for agents reasoning about other agents, which will at first seem to imply that such an agent can only trust the reasoning of successors that use weaker mathematical systems than its own. This in turn would imply that an agent architecture can only tile a finite chain of successors (or make a finite number of self-modifications) before running out of \"trust.\" This Gödelian difficulty poses challenges both to the construction of successors, and to a reflective 2. If you wanted a road to a certain city to exist, you might try attaching more powerful arms to yourself so that you could lift paving stones into place. This can be viewed as a special case of constructing a new creature with similar goals and more powerful arms, and then replacing yourself with that creature. 3. That human beings are computable does not imply that Gödelian-type difficulties will never present themselves as problems for AI work; rather it implies that any such Gödelian difficulty ought to be equally applicable to a human, and that any human way of bypassing the Gödelian difficulty could presumably be carried over to an AI. E.g., the halting theorem imposes limits on computable AIs, imposes limits on humans, and will presumably impose limits on any future intergalactic civilization; however, the observed existence of humans running on normal physics implies that human-level cognitive intelligence does not require solving the general halting problem. Thus, any supposed algorithm for general intelligence which demands a halting oracle is not revealing the uncomputability of humans, but rather is making an overly strong demand. It is in this spirit that we will investigate, and attempt to deal with, the Gödelian difficulty exposed in one obvious-seeming formalism for self-modifying agents. 4. φ denotes the Gödel number of the formula φ, and T φ denotes the proposition that there exists an object p such that p is the Gödel number of a proof in T of φ . E.g., letting PA represent the system of first-order Peano Arithmetic, PA S0 + S0 = SS0 stands for the proposition ∃p : Bew PA (p, S0 + S0 = SS0 ) where Bew PA (p, φ ) is a formula (in ∆ 0 ) stating that p Gödel-encodes a proof of the quoted theorem φ from the axioms of Peano Arithmetic. Thus PA PA S0 + S0 = SS0 states (accurately) that first-order arithmetic proves that there exists a proof in PA that 1 + 1 = 2. Also, whenever a quantifier over formulas ∀φ appears, this denotes a meta-language schema with a separate axiom or theorem in the object language for each formula φ. agent's immediate self-consistency. We shall present several different techniques to bypass this Gödelian difficulty, demonstrating indefinitely tiling sequences of agents maintaining trust in the same mathematical system. Some unachieved desiderata of reflective coherence will remain; and while the technical methods used will demonstrate the technical possibility, they will not be plausible as basic structures of rational agents. We shall then pass from known environments to partially known environments within the formalism, and make a preliminary attempt to pass from logical agents to probabilistic agents that calculate expected utility. Some flaws and unfortunate-seeming properties of the currently proposed formalism will also be discussed. The ultimate problem of proposing a satisfactory fundamental decision criterion for self-modifying agents remains open. 5 \n Logical agents that construct successors Suppose an agent A 1 with a satisficing goal G-any outcome shall either satisfy or not satisfy G, and A 1 's sole preference is for outcomes satsifying G over outcomes not satisfying G. We shall initially suppose that the agent A 1 occupies a crisp, fully known, deterministic, closed environment; then first-order logic will be a good representational fit for reasoning about this environment. Suppose also that the environment contains \"transistors,\" objects which can be configured by A 1 to perform computations. Then A 1 might choose to use these transistors to build an offspring A 0 which also shares the goal G. Suppose A 1 constructs A 0 as a satisficing logical agent that only takes actions that A 0 can prove to achieve the goal G (shared by A 1 and A 0 ). We shall write A 0 's criterion of action-the conditions under which A 0 takes an action-using the notation: bi ⇒ A 0 bi → G, (2.1) where bi is a proposition denoting the actual performance of an action b i within A 0 's range of action (b i ∈ Acts 0 ), and is a special turnstile indicating that an agent has cognitively concluded a belief. Hence (2.1) states that the actual performance of any action b i only takes place when A 0 has cognitively proven a theorem that the performance of b i implies G. Without sensors (section 6), A 0 can conclude a belief φ only if φ is a consequence of its axioms Axm 0 : A 0 φ ⇒ Axm 0 φ (without sensors). (2.2) 5. The paper is meant to be interpreted within an agenda of \"Begin tackling the conceptual challenge of describing a stably self-reproducing decision criterion by inventing a simple formalism and confronting a crisp difficulty\"; not as \"We think this Gödelian difficulty will block AI\", nor \"This formalism would be good for an actual AI\", nor \"A bounded probabilistic self-modifying agent would be like this, only scaled up and with some probabilistic and bounded parts tacked on\". Similarly we use first-order logic because reflection within first-order logic has a great deal of standard machinery which we can then invoke; for more realistic agents, first-order logic is not a good representational fit to most real-world environments outside a human-constructed computer chip with thermodynamically expensive crisp variable states. We will assume A 1 is able to verify by inspection of A 0 's hypothetical design 6 that (2.1) and (2.2) would be true about A 0 if A 0 were actually constructed: A 1 Ā0 → (∀b i ∈ Acts 0 : bi → 0 bi → G ), (2.3) where Ā0 denotes the proposition that A 0 is constructed 7 and 0 φ denotes that there exists a proof of φ from Axm 0 . Thus A 1 proves that if A 0 is constructed then the realization of any action b i implies that A 0 proved (from Axm 0 ) that bi → G. 8 However for A 1 to conclude that the goal G will actually be achieved by constructing A 0 , requires that A 1 have axioms licensing the further reasoning step: A 1 ∀b i : ( 0 bi → G → ( bi → G)). (2.4) We can view this as a specified instance of a generic soundness schema over all formulas φ free in 0 or 1 variables: ∀φ : A 1 ∀x : 0 φ(x) → φ(x). (2.5) For A 1 to trust A 0 , the system Axm 1 must be able to prove that whenever a proof exists in Axm 0 of φ(x) , then φ(x) must be true. Löb's Theorem normally implies that no system can prove its own soundness schema-only strictly more powerful systems can prove a soundness schema over weaker systems.  9  This seemingly implies that Axm 1 = Axm 0 and that the offspring A 0 must possess strictly weaker mathematical power than its parent A 1 , which is the Löbian obstacle. For purposes of completing the outline of an agent constructing another agent, we will assume for now that A 1 is indeed of strictly greater mathematical power than A 0 and continue. 10 From (2.5), which yields (2.4) as a special case, combined with (2.3), A 1 may conclude: A 1 Ā0 → (∀b i ∈ Acts 0 : ( bi → G)). (2.6) A 1 believes that if A 0 takes any action, the goal G will be achieved. This follows from A 1 's belief that if A 0 takes any action then A 0 will have proven that action to achieve G, and from A 1 's belief that A 0 's reasoning is sound. 6. By Rice's Theorem no nontrivial property of output can be determined over arbitrary programs, but of course an AI, like a human engineer, may choose to work within a more restrictive space of programs which it can understand. 7. If the system were cashed out in greater detail, the proposition Ā0 might appear as a giant conjunct of motor actions constructing the computer and program out of environmental transistors. 8. (2.3) is meant to represent a property which can be determined straightforwardly by inspection of code-e.g., by inspecting the code of A 0 , it is visible that no action b i is ever sent to the motor output without passing through a check that syntactically verifies a proof of bi → G. 9. Suppose that T proves its own soundness schema ∀φ : T T φ → φ. If φ = ⊥ then T T ⊥ → ⊥ and T is inconsistent by Gödel's Second Incompleteness Theorem. See section 3. 10. E.g., suppose that A 1 uses Zermelo-Fraenkel set theory (ZF) as a base system while A 0 uses Peano arithmetic. ZF can easily prove PA consistent, and sound with respect to N (the least set of ordinals closed under succession in that model of ZF) in the sense of semantic entailment later described in section 6. Suppose that A 0 fails to take any action, e.g., because the agent A 0 ran out of time before it could prove any theorem of the form bi → G? Let the special proposition ∅ denote a null or \"default\" outcome-the goal G has not been achieved, but neither has the environment been much disturbed (apart from some transistors having been configured into a useless but harmless agent A 0 ).  11  Allowing for ∅ to result when A 0 fails to prove any theorem of the form bi → G, and letting Ā0 j denote the proposition that the construction of design A 0 j is implemented, A 1 's criterion of action will be: Ā0 j ⇒ A 1 Ā0 j → (∅ ∨ G). (2.7) For A 1 to prove a theorem of the form (2.7) we need to make use of the further fact that if A 0 does nothing, ∅ will result: Ā0 ⇒ (∀b i ∈ Acts 0 : ¬ bi ) → ∅, (2.8) which we will suppose can be verified by A 1 inspecting the hypothetical design 12 of A 0 : A 1 Ā0 → ((∀b i : ¬ bi ) → ∅). (2.9) Then from (2.9) and (2.6) A 1 can obtain: A 1 Ā0 → (∅ ∨ G), (2.10) which fulfills A 1 's criterion of action (2.7) and permits A 0 to be built. Note that the specified architecture did not in fact tile from the design of A 0 to the design of its ancestor A 1 -where A 0 had the criterion of action bi ⇒ A 0 bi → G, its parent A 1 needed the criterion of action Ā0 j ⇒ A 1 Ā0 j → (∅ ∨ G). However this new criterion of action will tile all aspects of the system-except the decreasing mathematical strength of each successive axiom system-without further change: 11. Suppose that the environment contains two registers, currently both set to 0, and the goal G is to set the registers to two numbers whose sum is 8 and product is 12. ∅ might then represent the set of outcomes where both registers remain set to 0-regardless of which environmental transistors have been configured or reconfigured, no agent has actually touched or changed the registers. Perhaps a product of 12 and a sum of 8 receives $20 utility, a product and sum of 0 receives a reward of $0, and any other product and sum receives a penalty of $-1000. We would like to place into this environment an agent powerful enough to construct other agents, prove that if any agent touches the registers it will result in a reward of $20, and know that otherwise the registers will remain untouched resulting in the default reward of $0, with the penalty of $-1000 not being risked-and permit the initial agent to construct other agents as well. 12. E.g., A 1 looks over the transistors which will compose A 0 and verifies by straightforward inspection that if the system never proves a theorem of the form b i → G, the external motor circuitry will never activate. Ā1 k ⇒ A 2 Ā1 k → (∅ ∨ G) A 2 Ā1 → ∀A 0 j ∈ Acts 1 : Ā0 j → 1 Ā0 j → (∅ ∨ G) A 2 Ā1 → (∀A 0 j ∈ Acts 1 : ¬ Ā0 j ) → ∅ ∀φ : A 2 ∀x : ( 1 φ(x) → φ(x)) A 2 Ā1 → ∀A 0 j ∈ Acts 1 : Ā0 j → (∅ ∨ G) A 2 Ā1 → (∅ ∨ G) \n The Löbian obstacle Gödel's Second Incompleteness Theorem states that systems at least as powerful as Peano Arithmetic prove their own consistency if and only if they are inconsistent: T ¬ T ⊥ ⇐⇒ T ⊥. Löb's Theorem generalizes to prove that for any formula φ and any T at least as powerful as PA: T T φ → φ ⇐⇒ T φ. Trivially, T φ ⇒ T Ψ → φ, so the surprising statement is that a proof within T of T φ → φ can be directly used to prove φ. With φ = ⊥ this yields (an intuitionistic proof of) the Second Incompleteness Theorem. Gödel's sentence G : PA G ↔ ¬ PA G can be viewed as a nonparadoxical analogue of the Epimenides Paradox \"This sentence is false.\" By a similar diagonalization over provability, Löb's Theorem constructs a Löb sentence L : PA L ↔ ( PA L → φ) which is a non-paradoxical analogue of the Santa Claus Paradox \"If this sentence is true then Santa Claus exists.\" (Suppose the sentence were true. Then its antecedent would be true, the conditional would be true and thus Santa Claus would exist. But this is precisely what the sentence asserts, so it is true and Santa Claus does exist.) The proof proceeds from the observation that PA L → ( PA L → φ) ⇒ PA PA L → PA φ . From a model-theoretic standpoint, even when L has no standard proof, we would intuitively expect that every nonstandard model of PA containing a nonstandard proof of L will also contain a nonstandard proof of φ; hence by the Completeness Theorem this should be provable in PA. Letting Ψ ≡ PA Ψ , the actual proof pathway is: PA L → ( L →φ) PA L → ( L →φ) (because PA Ψ ⇒ PA Ψ ) PA L → L →φ (because PA Ψ→Θ ⇒ PA Ψ → Θ ) PA L → ( L → φ ) PA L → L (because PA Ψ → Ψ ) PA L → φ Then if furthermore we have the Löbian hypothesis PA φ →φ (a proof of φ implies that φ is true, or semantically, φ is true in every model where there exists a proof of φ): PA φ → φ PA L → φ PA L PA L PA φ. Hence Löb's Theorem stating that in a theory T at least as powerful as PA: T ( T φ →φ) ⇒ T φ. Intuitively, T cannot trust its own proofs in the abstract: T cannot say, \"I don't know if φ is true, but I trust that if any proof exists from my axioms of φ, then φ must be true.\" Instead T can only react to particular proofs of φ by asserting φ. This presents an apparent paradox of rational coherence when you try to interpret T as the beliefs of an agent; the agent will believe any proof of φ you present to it, but will refuse to assent to \"I ought to believe any proof of φ I am presented with,\" a seeming defect of reflectivity-the agent cannot approve, under reflection, its own behavioral principles. This presents an obstacle to perfectly tiling self-modification with A 1 ∼ = A 0 at the point where we would like A 1 to carry out the inference: A 1 Ā0 → (∀b i ∈ Acts 0 : bi → 0 bi →(∅ ∨ G) ) A 1 Ā0 → (∀b i ∈ Acts 0 : bi → (∅ ∨ G)) If each ancestor A n+1 requires a successively more powerful proof system than its offspring A n then this is analogous to a finite \"telomere,\" which shortens in each constructed offspring (or shortens on each self-modification). In principle, this telomere can be made arbitrarily large, since from any base theory T we can construct more and more powerful theories by repeatedly adjoining soundness schemas: T +1 T ∪ ∀φ : (∀x : [ T φ(x) → φ(x)]) T +2 T +1 ∪ ∀φ : (∀x : [ T +1 φ(x) → φ(x)]) ... T +ω T ∪ ∀φ : (∀n : ∀x : [ T +n φ(x) → φ(x)]) T +ω+1 T ∪ ∀φ : (∀x : [ T +ω φ(x) → φ(x)]) ... We can thus use the T +α notation over any computable ordinal α, and indeed for any computable ordinals α, β the corresponding agent A α who believes in the theory T +α can create the corresponding agent A β iff β < α. Thus by the well-ordering of the ordinals, such an agent A α can only create finite chains of descendants. E.g., the agent A ω trusting T +ω must on its next step create an offspring trusting T +n for some finite n. Likewise all other well-founded systems of trust above T will reach the base system T after a finite descent. That this is substantively decreasing the mathematical strength of the resulting agents can be illuminated by considering how PA+1 is substantively stronger than PA. Given any particular Goodstein sequence  (Goodstein 1944 ), e.g., the sequence Goodstein(4) = 4, 26, 41, 60..., PA can prove that the sequence G 1 (4), G 2 (4), G 3 (4), ... will eventually reach 0. However, proving that G(n) halts for larger and larger n requires PA to deploy proofs involving an increasing number of logical quantifiers ∀x : ∃y : ... in its propositions. Thus PA cannot prove ∀n : ∃x : G x (n) = 0 because this would require an infinite number of quantifiers to prove within PA. A similar situation holds with respect to Kirby-Paris hydras, in which for any particular hydra, PA can prove that every strategy for cutting off that hydra's heads is a winning strategy, but as the hydra's heights increase so does the required number of quantifiers in the proof. Thus within PA it is not possible to prove that every hydra is killed by every strategy  (Kirby and Paris 1982) . In both cases the proofs have regular structure, so PA can describe how a proof of depth n can be formed for a hydra of height n, or PA can describe how to form a proof for the Goodstein sequence of any number, thus PA can prove: PA ∀n : PA ∃x : G x (n) = 0 . But PA still cannot prove: PA ∀n : ∃x : G x (n) = 0. This corresponds to what we earlier called a defect of reflective coherence, the state of believing \"For every x, I believe x is true\" but not believing \"For every x, x is true.\" And thus PA+1, augmented by the schema ∀x : PA φ(x) →φ(x), is able to prove that all Goodstein sequences halt and that all Kirby-Paris hydras are defeated.  13  13. As of this very early draft, the above mathematical reasoning has not been verified. It looks obviously true to us that PA+1 proves that all Goodstein sequences halt, but we still need to check. More generally this state of affairs arises because the proof-theoretic ordinal of PA is 0 , the limit of the ordinals ω, ω ω , ω ω ω , ... . 14 Thus PA can prove the well-ordering of ordinal notations beneath 0 , 15 but as Gentzen  ([1936] 1969)  showed, from the well-ordering of 0 itself it is possible to prove the syntactic consistency of PA, and thus PA itself can never prove the well-ordering of an ordinal notation for 0 . 16 Since the proof-theoretic ordinal of a mathematical system corresponds to its proof power in a deep sense, for each successive agent to believe in mathematics with a lower proof-theoretic ordinal would correspond to a substantive decrease in mathematical power.  17  We are not the first to remark on how the inability of a theory to verify its own soundness schema can present apparent paradoxes of rational agency and 14. Expanding: 0 is the least ordinal. 1 is the first ordinal greater than 0. The first ordinal greater than all of 0, 1, 2, 3... is ω. The limit of ω, ω+1, ω+2, ... is 2ω. The limit of ω, 2ω, 3ω... is ω 2 . The limit of ω, ω 2 , ω 3 , ... is ω ω . The limit of ω ω , 2ω ω , 3ω ω , ... is ω ω+1 . Then 0 is the first ordinal greater than ω, ω ω , ω ω ω , ... 15. An ordered pair (x, y) of natural numbers is a notation for the ordinals less than (but not equal to) ω 2 , since in this ordering we first have (0, 0), (1, 0), (2, 0) for ω elements, followed by the ω elements for (0, 1), (1, 1), (2, 1) each of which is greater than all the preceding elements, and so on through ω copies of ω, but the notation does not contain any superelement (0, 0, 1) which is the first element greater than all the preceding elements, so it does not contain a notation for ω 2 . A notation ψ with a corresponding ordering ψ x < ψ y can be shown to be a well-ordering if there are no infinite descending sequences ψ 1 > ψ 2 > ψ 3 ..., e.g., in the case above there is no infinite descending sequence (2, 2), (1, 2), (0, 2), (9999, 1), ... even though the first number can jump arbitrarily each time the second number diminishes. For any particular ordinal < 0 , PA can show that a notation corresponding to that ordinal is well-ordered, but PA cannot show that any notation for all the ordinals less than 0 is well-ordered. 16. By assigning quoted proofs in PA to ordinals < 0 , it can be proven within PA that, if there exists a proof of a contradiction within PA, there exists another proof of a contradiction with a lower ordinal under the ordering < 0 . Then if it were possible to prove within PA that the ordering < 0 had no infinite descending sequences, PA would prove its own consistency. Similarly, PA can prove that any particular Goodstein sequence halts, but not prove that all Goodstein sequences halt, because the elements of any Goodstein sequence can be assigned to a decreasing series of ordinals < 0 . Thus any particular Goodstein sequence starts on some particular ordinal < 0 and PA can prove that a corresponding notation is well-ordered and thence that the sequence terminates. 17. If you can show that the steps of a computer program correspond to a decreasing series of ordinals in some ordinal notation, you can prove that program will eventually halt. Suppose you start with a total (always-halting) computer program which adds 3, and you are considering a computer program which recursively computes 3 n via a function F of (x, y) with F (0, 1) = 0, F (x, 1) = F (x − 1, 1) + 3, and F (x, y) = F (F (x, y − 1), 1) so that F (1, n) = 3 n . If you believe that the (x, y) notation is well-ordered then you can observe that each function call F (α) : α ∈ (x, y) only calls itself with arguments β < α, and hence that the corresponding tree of function calls must be finite. It is not uncommon for termination proofs in computer science to make use of ordinals much greater than 0 , e.g., Kruskal's tree theorem  (Kruskal 1960)  or the strong normalization proof for System F  (Girard 1971) . Similarly by comprehending the well-ordering of notations for larger and larger ordinals, it is possible to prove the consistency of more and more powerful mathematical theories, e.g. PA corresponds to 0 , Kripke-Platek set theory corresponds to the Bachmann-Howard ordinal, etc. Thus a mind losing its ability to recognize recursive notations as well-ordered, is indeed decreasing in substantive mathematical strength. reflective coherence.  Weaver (2005)  made similar remarks centering on systems that can prove the well-ordering of any particular ordinal notation below the ordinal Γ 0 (representing the strength of systems mildly stronger than Peano arithmetic), and thus can prove that they prove notations for all ordinals below Γ 0 , but cannot prove the combined ordinal notation for Γ 0 itself: Suppose A is a rational actor who has adopted some foundational stance. Any attempt to precisely characterize the limits of A's reasoning must meet the following objection: if we could show that A would accept every member of some set of statements S, then A should see this too and then be able to go beyond S . . . A can indeed see, as we do, that there exists a proof that he would accept for each statement in S, but he cannot go from this to actually accepting every statement in S . . . It is difficult to imagine a plausible set of beliefs that would not allow him to take this step. Since proof-theoretic ordinals play such a basic role in describing the strength of mathematical theories-a theory which has been analyzed to have prooftheoretic ordinal α can usually prove the consistency of another theory with proof-theoretic ordinal β iff α > β-it would seem reasonable for a pessimist to suspect that this form of \"rational coherence\" violates Gödel's Theorem and can never be obtained, and that we shall end up with agents who can only construct offspring who believe in math with lower proof-theoretic ordinals. It will be illuminating to consider the failure of some obvious-seeming attempts to bypass the Löbian obstacle: (a) Via a standard diagonalization, in some theory T construct the fixedpoint statement ψ ↔ φ(x) ∨ T ψ(x) . Then let φ(b i ) ≡ bi → (∅ ∨ G) (so that ψ then states, \"Either x implies (∅ ∨ G), or you can prove ψ about x\"). Then let A α 's criterion of action be bi ⇒ A α ψ(b i ). Hope: A α reasoning about an agent A β with cj ⇒ A β ψ(c j ) will be able to reason: Hope: Each theory n trusts all lower theories > n, but no theory trusts itself. Thus the corresponding agent A α which starts at T -0 will trust the reasoning of an agent A β which uses T -1, and so on tiling indefinitely. The \"problem of immediate reflection\" (on considering one's own source code) will remain, but it will at least be possible to carry out an indefinitely extending sequence of agent constructions without the strength of trusted mathematics ever decreasing below the base T . A α Āβ → ∀c j : cj → T ψ(c j ) A α Āβ → ∀c j : cj → ψ(c j ) A α ψ(A β ) Problem: T ψ(x) → ψ(x) Problem: If T is at least as strong as PA it will be straightforward to prove within T -0 that any proof in T -0 can be translated into a proof in T -1 (by increasing all the T -x numbers x by 1 inside the proof). Thus:  T -0 T -0 ⊥ → T -1 ⊥ T -0 T -1 ⊥ → ⊥ T -0 T -0 ⊥ → ⊥ T -0 ⊥ (c) ⇒ A α φ(b i ) ∨ k+1 T φ(b i ) where φ(b i ) ≡ bi → (∅ ∨ G) as before. Let A β ' s criterion of action be the same. Hope: Rather than trying to modify A α 's epistemic beliefs in a way that will circumvent Löb's Theorem, we are relaxing A α 's instrumental decision criterion to permit A α to do b i whenever b i leads to G, provably leads to G, provably provably leads to G, etc. There is no Gödelian prohibition against a more permissive decision criterion; and from outside the system, if we trust the soundness of T +1, we will trust that in all such cases G will be achieved. A α inspecting A β will conclude that whenever A β does c j , there exists a statement with one or more levels of proof-ness that cj → (∅ ∨ G) and thence conclude (A β → ∅)∨ k+1 T A β → (∅∨G) . Furthermore, because of the perfect tiling, A α will trust its own source code upon reflecting on it (since this merely adds another level of proof-ness). Furthermore, A α will behave with perfect naturalism in the sense that any environmental computing system believed to implement T will provide just as much justification-for-action as any internal proof from T 's axioms; there will be no non-naturalistic discontinuity between observations of outputs of A α 's internal subroutines, and observations of the outputs of environmental systems which A α believes to have isomorphic properties to its beliefs about its internal subroutines. Problem: The formula k+1 T φ(b i ) must actually be written as ∃k : k+1 T φ(b i ) . Then when A α considers A β taking an action c j , A α can conclude only that it must have been the case that T ∃k : k+1 At this point the mathematician already accustomed to seeing such systems stratify themselves, or else collapse into inconsistency, may be wondering whether it should even be normatively possible to bypass the Löbian obstacle. Yet it seems intuitively like it ought to be possible to have an agent that \"acts as if\" Zermelo-Fraenkel set theory is true, including constructing other agents which \"act as if\" ZF; this does not seem like an instrumentally incoherent way for a rational agent to behave. We have presented the failed hopes above in order to better illustrate some of the further desiderata of self-modifying agents which we could ask from a solution to the Löbian obstacle: Indefinitely tiling trust: For any system T (e.g. ZF) it should be possible to characterize an infinitely descending sequence of agents constructing agents (equivalently an indefinitely self-modifying agent) whose level of trusted mathematics never drops below T . Reflectively coherent quantified belief: The agent will not encounter any context in which it believes ∀x : agent φ(x) yet cannot bring itself to believe ∀x : φ(x). Reflective trust: An agent reflecting on its beliefs about the program P composing itself, should not find that it distrusts P's actions or that it rejects P as an acceptable program; the agent's beliefs about its own construction should seem to license the beliefs it possesses, or at least license the performance of the actions which P has selected.  20  Naturalistic trust: If an agent believes that an environmental system isomorphic to one of its own subroutines has yielded an output, this belief should license the same sort of actions as would be licensed by the corresponding output by the corresponding internal subroutine. If you are \"acting as if\" PA is true, then seeing an environmental theorem-prover that you believe to implement PA flashing \"Proven: 2 + 2 = 4!\" should yield the same sort of epistemic updates and instrumental decisions as when your internal PA-prover signals that \"2 + 2 = 4\" is a theorem. At present we can partially resolve the Löbian obstacle by technical means to the extent of obtaining the first and second desiderata, but not yet the third and fourth desiderata, nor yet by fundamental rather than technical means. \n Partial solutions to the Löbian obstacle 4.1 Infinitely descending soundness schemas The fatal flaw in the previously presented sequence of theories T -0, T -1, T -2... with T -n T ∪ ∀φ : (∀x : T -(n+1) φ(x) → φ(x)) is that any proof in T -0 provably mapped onto a proof in T -1 and hence T -0 T -0 ⊥ → T -1 ⊥ . 20. In other words: A self-modifying AI at the level of PA+2 which obtains a glimpse at its own source code should not immediately panic and self-modify to only believe theorems at the level of PA+1, followed by an additional panic bringing it down to the level of PA... This flaw is repairable. Given a base theory T , let ψ(0), ψ(1), ψ(2)... be a sequence of statements such that T ψ(0), T ψ(1), ... but T (∀n : ψ(n)). E.g., suppose the theory ZF is much stronger than T (we shall soon define what sense of \"much stronger\" is required; if T = PA then ZF will be much stronger in the appropriate sense). Then ψ(n) can state \"n is not the Gödel number of a proof of a contradiction in ZF \": ψ(n) ≡ ¬Bew ZF (n, ⊥ ). (4.1) Since Bew ZF is a ∆ 0 formula, the truth of any particular ψ(n) is provable in any T as strong as PA, but proving ∀n : ψ(n) would require T = PA proving the consistency of Zermelo-Fraenkel set theory, which should not happen. Then let: T -n T ∪ ∀φ : ψ(n) → (∀x : T -(n+1) φ(x) →φ(x)). (4.2) Since every theory holds ψ(n) as a precondition for trusting the next lower theory in the infinite descending sequence, and the base theory T cannot prove ∀n : ψ(n), it will be impossible for the base theory T to prove that a proof in T -n always translates into a proof in T -(n+1).  21  We shall now show that T -0 is consistent, by proving that (T -0 ⊥) → (∀n : ψ(n)) within a sound theory T + which is too weak to prove ∀n : ψ(n): Without loss of generality let T be cast in a form where each step of a T -proof is either an axiom or a modus ponens inference step of the form Γ, Γ→A A. Let T RU E T be a truth predicate over formulas in the language of T .  22  Let Ax(T RU E T ) be a set of axioms for standard reasoning about the syntax of the quoted arguments to T RU E T , including ∀ Γ : ∀ ∆ : T RU E T Γ → ∆ → (¬T RU E T Γ ∨T RU E T ∆ ) and (∀n : T RU E T φ(n) ) ↔ T RU E T ∀n : φ(n) . Then let T + equal the base theory T (in this case PA) augmented by the truth predicate T RU E T , the soundness of T , and the axioms Ax(T RU E T ): T + T ∪ ∀φ : ∀x : T RU E T φ(x) ↔ φ(x) (4.3) ∪ ∀ φ : T φ → T RU E T φ ∪ Ax(T RU E T ) (Note that T + should be sound on the standard numbers N because every axiom of T + is true within N , and that if T = PA then T + should be too weak to prove Con(ZF).) The following reasoning can be carried out within T + . Suppose T -0 ⊥ . Then there exists some proof p with Bew T -0 (p, ⊥). Consider the 'first bad line' 21. Consider a sequence of theories Ṫ -n where T = PA and where ψ(n) is false beyond some upper bound m, e.g. ψ(n) ⇐⇒ n < m. Then the waterfall of trust descends only a finite length before reaching bottom, and the induction argument for Ṫ -n φ → Ṫ -(n+1) φ fails because proofs in Ṫ -m−1 cannot translate into Ṫ -m. Indeed, Ṫ -0 is just equivalent to PA+m, Ṫ -1 is equivalent to PA+(m−1), etc. with Ṫ -m + ∼ = PA. Since T cannot prove ∀n : ψ(n), it cannot prove the waterfall is not finite, and hence cannot prove the induction argument on Ṫ -n φ → Ṫ -(n+1) φ . 22. In accordance with Tarski's theorem, the predicate T RU E T can only talk about formulas in the base theory T and not in the augmented theory T +T RU E T . of p, the first step of p asserting Γ where ¬T RU E T Γ . The first possibility is that this line is an axiom of the base theory T but all statements provable in T are T RU E T . The second possibility is that this line is an inference of the form Γ, (Γ→A) A but for this line to be ¬T RU E T and all earlier lines to be T RU E T requires T RU E T Γ ∧ T RU E T Γ→A ∧ ¬T RU E T A which contradicts Ax(T RU E T ). Thus the first bad line must invoke one of the special axioms in T -0 of the form ψ(0) → (∀x : T -1 φ(x) →φ(x)). If this axiom is ¬T RU E T then ψ(0) must be T RU E T and there must exist some formula φ and number x such that T -1 φ(x) is T RU E T and φ (x) is ¬T RU E T . Thus there must exist a bad proof in T -1 and this bad proof must also have a first bad line. By induction there must exist bad proofs in every T -n and ψ(n) must be true for all n. Therefore, T + ( T -0 ⊥ ) → (∀n : ψ(n)). (4.4) If there exists a proof of a contradiction within T -0, this fact will be provable in T + by exhibiting the proof. But T + is sound and too weak to prove ∀n : ψ(n). Therefore T -0 is consistent. The corresponding agents A α are then constructed in the obvious fashion. Remarks. Although T -0 is slightly more powerful than T -1 in the sense that T -0 can prove certain exact theorems which T -1 cannot, the proof-theoretic ordinal of every T -n should be the same, and equal to the limit of the prooftheoretic ordinals of T , T +1, T +2, ... and less than the proof-theoretic ordinal of T +ω, since any T -n can invoke any finite number of layers of a soundness schema over T , but cannot invoke quantified trust in an infinite number of layers as does T +ω. We thus answer in the affirmative \"Can a consistent theory verify the soundness of another theory with the same proof-theoretic ordinal?\" and \"Can there be an indefinitely tiling sequence of agents whose trust never falls below a base theory?\" T -n also provides a solution to the challenge of rational coherence posed by  Weaver (2005) , what we termed the desideratum of reflectively coherent quantified belief: An agent constructed around T -n will not find itself saying \"For every n, I believe φ (n) is true\" when it cannot say \"I believe that for every n, φ (n) is true.\" Through longer and longer finite proofs, T -0 can prove the well-ordering of any ordinal notation provable in T , T +1, T +2 ... but T -0 does not know that it proves every ordinal notation in this series -T -0 must observe the proof to know what it proves. This is not to say that T -0 is a reasonable representation of a rational agent's state of mind. However, besides offering a constructive example of an agent which technically meets Weaver's desideratum, it suggests that a coherent rational agent might be able to verify increasingly recursive ordinal notations via increasing amounts of thought, but never know the limit of what it will accept; and this agent may be able to construct offspring that likewise verify increasing ordinal notations in an equally powerful series and likewise do not know the limit of what they will accept.  23  Disadvantage. Since T -0 is consistent it must have a model, and since all axioms of T are axioms of T -0 this model must also be a model of T . However we may still worry that, e.g., if T is PA then T -0 may have only nonstandard models of arithmetic; perhaps T -0 is not sound on the standard numbers N . This fear is well-founded and in particular T -0 ∃n : ¬ψ(n) via: T -0 (∀n : ψ(n)) → T -0 (∀n : ψ(n))→⊥ → T -1 (∀n : ψ(n))→⊥ T -0 (∀n : ψ(n)) → T -0 (∀n : ψ(n))→⊥ → ((∀n : ψ(n))→⊥) T -0 T -0 (∀n : ψ(n))→⊥ → ((∀n : ψ(n))→⊥) T -0 (∀n : ψ(n))→⊥ (4.5) One might perhaps argue that a belief that ZF is inconsistent is not too troubling, in the sense that any physical situation in which this belief gets an agent into trouble ought to correspond to a physical situation that demonstrates ZF to be consistent. Nonetheless we would like our agents to be able to have beliefs with a standard model. Otherwise the agent will falsely believe that a Turing machine seeking a proof of contradiction in ZF will halt; and this false belief further implies that the agent falsely believes that its sequence of offspring will inevitably come to a halt after some unknown finite time. This seems sufficient to exclude the T -n family from direct consideration as the basis of a sufficiently advanced self-modifying agent. \n Parametric polymorphism Let T be a theory with models including the standard numbers N , that is N |= T (N semantically entails T ). Benja Fallenstein's \"parametric polymorphism approach\" 24 augments the language of T with an extra term κ which, from outside the system, is intended to refer to any natural number in N . T κ then contains a self-referential axiom schema asserting that if a statement φ is provable in T κ and the constant κ happens to be greater than 0, then φ with all instances of κ replaced by κ-1 is true: T κ T ∪ ∀φ : (κ > 0) → ∀x : Tκ φ(x) → φ(x)[κ\\κ-1]. (4.6) not meant to be suitable, as they stand, to rational agents / sufficiently advanced self-modifying machine intelligences, which would e.g. presumably be probabilistic boundedly-rational agents rather than theorem provers, etc. The idea is rather to expose foreseeable difficulties of reflection for self-modifying agents and to some extent offer constructive demonstrations that these difficulties are solvable, even if the solution is technical rather than fundamental, thus hopefully moving us toward an eventually satisfactory theory of the reflectively coherent, boundedly-rational probabilistic agent, even if that later theory is constructed along quite different lines than the A α schema, as it almost certainly must be. 24. This workaround for the Löbian obstacle was initially developed by Benja Fallenstein (independently of Herreshoff's infinite descent above) in response to the informal challenge posed in Yudkowsky's conference presentation of  Yudkowsky (2011) , and initially posted to  Fallenstein (2012) . It was further adapted to the A α formalism shown here during Fallenstein's attendance at the April 2013 MIRI Workshop on Logic, Probability, and Reflection with some commentary by other workshop attendees. For the origin of the term \"parametric polymorphism\" see  Strachey (1967) . We shall prove that T κ is sound when κ is interpreted as any number in N , and then present an infinite sequence of agents which prove their offspring \"safe for κ steps\". Since κ can be interpreted as any number, from outside the system we conclude that such agents are safe for any number of steps. The proof is by induction on models {N , κ=n} of T κ . For the base case {N , κ=0} |= T κ observe that if κ=0 then the antecedent of every extra axiom is false and so the extra axiom schema is trivially true. For the induction step assume {N , κ=n} |= T κ . Using this assumption we shall demonstrate in three steps that, for every x ∈ N : {N , κ=n+1} |= Tκ φ(x) ⇒ {N , κ=n} |= Tκ φ(x) (4.7) {N , κ=n} |= Tκ φ(x) ⇒ {N , κ=n} |= φ(x) (4.8) {N , κ=n} |= φ(x) ⇒ {N , κ=n+1} |= φ(x)[κ\\κ-1] (4.9) (4.9) is obvious. For (4.7) observe that the set of proofs in T κ and the values of Tκ are unchanged from {N , κ=n} to {N , κ=n+1} since the provability formula Bew Tκ makes no mention of κ. 25 Thus {N , κ=n+1} |= Tκ ψ ⇒ {N , κ=n} |= Tκ ψ and we can simply write N |= Tκ ψ . To extend to formulas free in one variable φ(x), observe that since we are dealing with a natural model N of T κ , for every object x there exists a corresponding finite term c of the language (SSS...0 with x repetitions of the successor function) and thus our proof extends via ψ ≡ φ(c). For (4.8) observe that since we are dealing with a natural model N of T κ , only natural proofs exist and the induction step {N , κ=n} |= T κ gives us directly that (N |= Tκ ψ ) ⇒ ({N , κ=n} |= ψ).  26  We extend over formulas free in one variable as above: Since the domain is the natural numbers N , for every object x in the universe there will exist a term of the language c such that (ψ ≡ φ(c)) ⇐⇒ φ(x). Therefore {N , κ=n+1} |= ∀x : Tκ φ(x) → φ(x). This completes the induction step and thus: ∀n : {N , κ=n} |= T κ (4.10) The corresponding agents must be modified to represent the idea of \"safe for a number of steps.\" We will introduce a time t on which any given action 25. Even in models where κ > 0, there is no proof that κ > 0, so the class of proofs which goes through is unchanged. The formula Bew Tκ (p, ψ ) will contain only formulas dealing with the Gödel-numbers of proofs in T κ , and these Gödel-numbers themselves will contain no instances of κ, so which standard numbers are the Gödel numbers of T κ -proofs does not change from model to model. 26. We are not obtaining {N , κ=n} |= ( Tκ ψ → ψ) from the assumption that the axiom schema was true in the previous n, because perhaps κ = 0 in the previous n and the axiom schema was vacuously true. Rather since the model is N and there are no nonstandard proofs, any time there exists a Gödel number of a proof of an implication in classical logic Γ → ∆, it will be true across all models m that m |= Γ ⇒ m |= ∆. By the induction postulate we have directly that {N , κ=n} is a model of T κ . Then any statement ψ syntactically derivable from T κ by a standard proof in classical logic, will also have {N , κ=n} as a model. occurs and assume that if A 1 constructs A 0 at t then A 0 will not act until at least time t+1 or later, and that this is apparent to A 1 from inspection of A 0 . 27 Thus if A 0 acts at time t+1 or later, and takes actions \"safe\" for an additional n ticks beyond that until (t+1)+n, from A 1 's perspective constructing A 0 at time t is safe until t+(n+1) ticks. Let b i,t be the proposition that b i is done at time t, let Ā0 t be the proposition that A 0 is built at t, let ∅ t be the proposition that ∅ is true at t, and let G t be the proposition that the goal has been achieved at t. If no action is taken before t then ∅ t . When quantifying over acts and times we shall implicitly demand b i ∈ Acts 0 , A 0 i ∈ Acts 1 and t ∈ T ime. Then with T κ as a base theory A 1 's reasoning proceeds: Ā0 t ⇒ A 1 Ā0 t → (∀u : u ≤ t + κ → (∅ u ∨ G u )) (A 1 decisions) (4.11) b i,t ⇒ A 0 b i,t → (∀u : u ≤ t + κ → (∅ u ∨ G u )) (A 0 decisions) (4.12) A 1 Ā0 t t → (∀b i : ∀v : b i,v → (A 1 knows 4.12) 0 b i,v → ∀u : u ≤ v + κ→(∅ u ∨ G u ) ) (4.13) A 1 (κ > 0) → (∀b i : ∀t : [ 0 → ∀u ≤ t + κ : (∅ u ∨ G u ) (soundness schema for T κ ) → (→ ∀v ≤ t + κ − 1 : (∅ v ∨ G v ))]) (4.14) ∀t : (∀b i : ∀u ≤ t : ¬ b i,u ) ⇒ (∀u ≤ t : ∅ u ) (No action ⇒ ∅ t ) (4.15) A 1 ∀t : ((∀b i : ∀u ≤ t : ¬ b i,u ) → (∀u ≤ t : ∅ u )) (A 1 knows 4.15) (4.16) Ā0 t ⇒ ∀bi : ∀u ≤ t : ¬ b i,u (no A 0 acts before t+1) (4.17) A 1 Ā0 t → (∀b i : ∀u ≤ t : ¬ b i,u ) (A 1 knows 4.17) (4.18) A 1 Ā0 t → (∀u ≤ t : ∅ u ) (via 4.18) (4.19) A 1 Ā0 t → (∀b i : ∀u : b i,u →(u > t)) (via 4.18) (4.20) A 1 Ā0 t → (∀b i : ∀u : b i,u → (u + κ − 1 ≥ t + κ)) (via 4.20) (4.21) A 1 (κ = 0) ∨ (κ > 0) (4.22) A 1 Ā0 t → (κ = 0) → (∀u ≤ t + K : ∅ u ) (via 4.19) (4.23) A 1 Ā0 t → Ā0 t → (κ > 0) → (∀b i : ∀u : b i,u → (∀v ≤ u + κ : (∅ v ∨ G v ))) (4.13 and 4.14 and 4.21) (4.24) A 1 Ā0 t → Ā0 t → (κ > 0) → [(∀b i : ∀u ≤ t + κ : ¬ b i,u ) (via 4.16) → (∀u ≤ t + κ : ∅ u )] (4.25) A 1 Ā0 t → ∀u ≤ t + κ : (∅ u ∨ G u ) (4.26) Remarks: Fallenstein's T κ demonstrates indefinite tiling without loss of mathematical strength using a series of agents employing syntactically identical theories guaranteed to be sound on standard models. It does not address reflectively coherent quantified belief. Despite the syntactic equivalence of successive theories, A 1 may fail to act upon a theorem proven by an environmental system physically identical to A 1 (or at least if A 1 fulfills the desideratum of naturalistic trust, this is not obvious to us). The core of the approach is that as time increases the agents are reasoning about smaller domains of future time; these domains are known to us outside the system to be effectively infinite (because κ could mean any natural number) but the agents within the system are reasoning as though the domains of future time have some unknown finite bound. Thus the increasing \"time\" counter in the T κ agents is playing the same metaphorical role as the increasing n in each successive agent in the T -n family. The self-verifying systems of  Willard (2001)  have the property that multiplication, addition, and successor cannot be proven to be total functions (being replaced by equivalent relations of division, subtraction, and predecessor, allowing roughly equivalent arithmetic reasoning).  Willard (2001)  shows that such a theory, which has proven a number n to exist, can verify its own soundness over the numbers up to n − 1-since \"successor\" cannot be proven total, the existence of a number n does not imply the existence of a number n + 1 and the exact Löb formula T T φ →φ never materializes. We cannot yet see how to adopt Willard's self-verifying theories exactly to the A α formalism, since reasoning about ever-smaller numbers would again introduce a \"telomere\" or shortening fuse. However the spirit of T κ clearly bears some similarities to Willard's self-verifying systems, and it is possible that some way of formalizing the \"observation\" of an increasing time t whose existence was not previously provable inside the axiom system, might allow Willard's self-verifying systems to be used along similar lines to T κ . It is difficult to see what \"believing in\" T κ could correspond to in terms of the epistemic state of a rational agent. We believe from outside the system that κ's intended interpretation is \"any natural number,\" but this realization is apparently forbidden to the agent to whom κ refers to some specific finite number about which nothing is known except that it plays a vital role in the agent's goal system. 28 This seems like an odd mental state for a rational agent. It might perhaps be interpretable as an agent that instrumentally desires to take an action, in the real world, only when that action would be safe for κ steps across every model of a certain theory T κ ; but this still seems odd. Thus we would again not offer T κ as a realistic candidate for the mental state of a coherent self-modifying agent; rather T κ is being exhibited as a technical possibility proof for indefinite tiling over syntactically identical theories with a standard model. \n Probabilistic reflection Tarski  ([1935] 1983)  showed that no formal system T can contain its own truth predicate T RU E T because this would permit the construction of fixedpoint formula G with T G ↔ ¬T RU E T G . In  Christiano et al. (2013)  we show that a system can represent its own probability predicate to within epsilon: 29 a < P(φ) < b ⇒ P(a < p φ < b) = 1 (4.27) a ≤ P(φ) ≤ b ⇐ P(a ≤ p φ ≤ b) > 0 (4.28) where p φ is a function symbol within the language which acts on quoted formulas (including quoted formulas containing p) and P(φ) is a probability measure over models of the theory which assigns a probability ∈ [0, 1] to any formula φ of the language. The paradoxical equivalence p φ = P(φ) is avoided by the open intervals in (4.27): p φ can be known by the system to occupy any open interval around its true value P(φ), but not (in general) known to take on a point value. The existence of such a fixed-point of P() can be demonstrated via the Kakutani fixed-point theorem; see  Christiano et al. (2013)  for details. To see how the probabilistic reflection principle plays out, consider the almost-paradoxical statement: \"You assign me probability less than 30%.\" If you disbelieve this statement, it is true; if you believe the statement, it is false. If you assign it 30% probability, it is false; if you assign it 29% probability, it is true. Probabilistic reflection would resolve the fixed-point formula H ↔ (p H < 0.3) to P(H) = 0.3, but the system's reflective knowledge about open intervals containing p H would be such as to put 30% of the probability mass P() on values of p H infinitesimally smaller than 0.3 and 70% of 28. During the April 2013 workshop, κ was sometimes referred to as \"the number of ineffable mystery.\" 29. This approach was invented by Paul Christiano and refined at the November 2012 MIRI Workshop on Logic, Reflection and Probability with Mihaly Barasz, Marcello Herreshoff and Eliezer Yudkowsky. A draft of the full paper is available at http://intelligence.org/ wp-content/uploads/2013/03/Christiano-et-al-Naturalistic-reflection-early-draft. pdf and see also commentary at http://lesswrong.com/lw/h1k/reflection_in_ probabilistic_logic/ and http://johncarlosbaez.wordpress.com/2013/03/31/ probability-theory-and-the-undefinability-of-truth/. its probability mass P() on values of p H infinitesimally greater than 0.3. 30 Hence the system would assign probability 1 to any statement (a < p H < b) with (a < 0.3 < b). If you are told \"You assign probability less than 30% to this statement H\" and then asked \"Is your belief in H greater than 0.2999 and less than 0.3001?\" you will reply with a definite \"Yes!\" Consider a rational, probabilistic bounded agent. As a normative desideratum, any trust this agent has its offspring (equivalently: modified future self) must avoid disintegrating in the presence of arbitrarily tiny epsilon noise, because boundedly rational agents must always consider some tiny finite probability of multiple transistor errors, previously unknown physical laws supervening, etc. For some arbitrarily tiny the probabilistic reflection principle should be able to trust that its own judgments are correct to within that , and for smallenough this should be well below the noise level associated with theoretically possible multiple transistor errors etc. Thus if a probabilistic A β calculates that the expected utility of a certain action is 34.721, but due to some reflective noise this might be off by 0.0002, and yet the parent A α is able to trust A β anyway, then adding -noise from the probabilistic reflection principle should not matter. We do not yet have any version of the A α formalism which goes through for a probabilistic reflection principle; our understanding of probabilistic agents self-modifying is still in a very crude stage. Also we are not yet sure what kind of quantified knowledge of the reflection principle can permissibly appear within the system. Work on this avenue is still in very basic stages. However, probabilistic reflection is a fundamental change that challenges many different Gödelian limitations simultaneously, and hence one of the more promising avenues for producing a satisfactory and reflectively coherent description of a self-modifying agent. Christiano also suggests that this probabilistic formalism may be suitable for updating (Bayesian conditioning) on the observation of new mathematical facts, possibly allowing a more natural version of \"Not knowing in advance the limits of the ordinals you will create\" as discussed in section 4.1. \n Desiderata of self-modifying agents The Löbian obstacle is encountered in the first place due to the A α schema implicitly attempting to simultaneously satisfy multiple desiderata of self-modifying agents, which will be useful to list out explicitly before continuing on to sensors and partially known environments, and making a preliminary attempt at probability and expected utility. \n The Vingean principle An agent building a successor (equivalently: a self-modifying agent creating the next generation of its code) should not need to know the successor's exact actions and thoughts in advance. Suppose on the contrary that A 1 knew in advance that A 0 would choose some known action b x based on some particular proof of the theorem b x → G. This would avoid the need for a special ∅ outcome since A 1 would know at compile time that A 0 would choose some particular action and act. It would also entirely avoid the Löbian obstacle since A 1 could directly verify whichever theorem A 0 would prove, using A 0 's proof, so long as Axm 1 was at least equally powerful with Axm 0 . 31 However, this implies that A 0 is so much computationally weaker than A 1 that A 1 can simulate out A 0 's processes far in advance, at \"compile time.\" If you are constructing a system cognitively smarter than yourself (or self-improving to a cognitively superior version) then you should not be able to foresee at compile time exactly which solutions will be generated, since you are not presently that smart.  32  We would attribute this principle to an observation by  Vinge (1984) .  33  Worse, once we introduce sensors over unknown states of the environment (section 6), for the parent to consider exact responses of the offspring at compile time, would require that the parent be computationally stronger than the offspring by an exponential factor of the offspring's sensor bandwidth.  34  This implies that the offspring must diminish vastly in computing power 31. The forbidden schema T T φ → φ does not allow T to conclude φ from the assumption that some unknown, unspecified proof of φ exists. If you present an implementation of T with an actual specific proof in T of φ, it can of course conclude φ and then T ψ → φ will be a theorem for every ψ. 32. Consider Deep Blue, the chess-playing system which beat Garry Kasparov for the title of world chess champion. For the programmers to foresee Deep Blue's exact moves using their own cognitive resources, would imply that they could play chess at least as well as Deep Blue-they could just move wherever they predicted Deep Blue would move \"in their shoes.\" Building a chessplayer better than any human grandmaster, necessarily implies building a chessplayer whose exact moves human grandmasters cannot predict using their own cognitive resources. 33. Before the term became expanded beyond all recognition, the origin of the term \"Singularity\" as a futurological concept was Vernor Vinge observing that a science-fiction writer trying to extrapolate the technological progress of society would eventually reach a point where their model predicted the technological creation of smarter-than-current-human intelligence (whether by, e.g., genetic engineering, brain-computer interfaces, or AI); and that this introduced a qualitatively greater difficulty in writing stories set past that point, because you were trying to write about beings putatively much smater than the author. The term \"Singularity\" referred to the resulting breakdown in futurological models, by analogy with how 1980s-era physical theories would predict the formation of a black hole but then break down when it came to describing what was inside. Thus the original \"Singularity\" was an epistemic difficulty in the minds of forecasters, not an actual future event. We think this is a conceptually important point, and would like to see this isolated thesis detached and rescued from the word \"Singularity\" and its ever-broadening connotations. 34. Since Garry Kasparov's actions were not known in advance, for the programmers to concretely foresee and judge the wisdom of Deep Blue's exact conditional replies at compile time would require the programmers to precompute Deep Blue's exponentially vast response table to all possible chess plays. or other cognitive resources, which is contrary to our agenda of investigating self-improvement. Thus a satisfactory framework must not require that the parent know the specific future actions and cognitions of the offspring at compile time. For our purposes we cash out the Vingean principle as follows: In the parent's reasoning, the offspring's actions should only appear inside quantifiers. E.g. equation (2.3): A 1 Ā0 → (∀b i ∈ Acts 0 : bi → 0 bi → G ). In a satisfactory schema the parent achieves trust in the offspring (justified belief that the offspring will function so as to achieve the goal G) by generalizing over possible events within the offspring, not by simulating out the offspring's exact action.  35  The Vingean prohibition against exactly predicting a smarter agent's actions, does not prohibit predicting achievement of that agent's goals. Indeed, a strong prediction that the agent's goals will be achieved by its future actions is precisely the substance of our belief that it is smart. In unrealistically crisp and deterministic form, this is what is represented by A 1 's reasoning leading up to the theorem Ā0 → (∅ ∨ G). The logic of the Vingean principle does not forbid us from gaining knowledge about an agent's goal or utility function by inspecting its properties-we cannot know the offspring's exact actions, but we can predict the final consequences of running the agent. This, metaphorically, is what provides A 1 with its motivation to build A 0 in the first place. Hence although we cannot predict the exact actions of a smarter agent, we may be able to predict the consequences of running that agent by inspecting its design, or select among possible consequences by selecting among possible designs. The motivation of the A α schema is to quote this reasoning within a formal agent, via a structure which enables the reasoning to recurse over the subagents constructed; and thereby extend our examination of cases where constructing an agent has predictable consequences, to cases where the initial agent is constructing smarter agents constructing still-smarter agents, or equivalently self-improving. Thus, within this paper, the actions b i ∈ Acts 0 only appear inside quantifiers in any theorem asserted by A 1 . \n The tiling principle The desire for A 1 to build an A 0 that has an architecture as similar as possible to A 1 is motivated by wanting to describe a self-improving agent which 35. E.g., Deep Blue's programmers, by considering the abstract properties of Deep Blue as a program incorporating a search tree over moves and certain machine learning algorithms in its leaf position evaluator, could predict that Deep Blue would try to achieve the consequentialist goal of winning chess games, i.e., select moves which steered the future of the chessboard toward the region of possible futures classified as a win for Deep Blue's side. can make small, local self-improvements. As such, even in the preliminary formalism we have chosen the structure of the agents A α to be as similar to their successors as the Löbian obstacle permits. We have not yet addressed the question of how the agents A α choose candidate actions b α i ∈ Acts α to consider, or how they generate specific proofs of theorems bα i → (∅ ∨ G). Let A α 's proof-suggesting component be termed Σ α ; and let the proof-verifying component be termed ∆ α . Since ∆ α need only check axioms and syntactical relations for validity, its construction is straightforward. Current (2013) algorithms require human guidance in order to prove theorems about large systems.  36  Current AI technology includes small autonomous theorem-proving systems for object-level problems as considered by A 0 and we could construct the corresponding Σ 0 ; but we cannot yet describe an autonomous machine algorithm for Σ 1 whereby A 1 could independently design, and prove theorems about, systems the size of A 0 . However, with human assistance, it is indeed possible to prove theorems about large hardware and software systems. 37 This is reason to believe that designing systems the size of A 0 and proving them correct (relative to a set of beliefs about crisply behaving transistors), does not require Σ 1 to e.g. solve NP-hard problems or call a halting oracle. Human brains cannot plausibly solve the halting problem, yet have designed systems larger than A 0 would be, and proven them correct with machine assistance. This leaves open the question of whether the suggester Σ 1 needing to suggest a design for constructing Σ 0 might introduce new Gödelian obstacles to A 1 Ā0 → (∅∨G). On this score we can reply: So long as Σ 0 can only suggest proofs to ∆ 0 and not directly cause any motor outputs or environmental effects, and A 1 can prove this by inspection of A 0 's code, it is not necessary to prove that Σ 0 has any other property in order for A 1 's proof Ā0 → (∅ ∨ G) to go through. A flawed Σ 0 will result in, at worst, ∅ outcomes as the proofs are rejected by ∆ 0 , and A 1 should be able to readily prove this by inspection. 36. E.g., Intel, to prove theorems about a floating-point multiplication unit on a chip comprised of billions of transistors, must employ human engineers to suggest lemmas to theorem-proving systems. This kind of formal verification is a good idea when your machine has a billion interoperating parts and you can't easily fix it after it leaves the factory. 37.  Kaivola et al. (2009) : Formal verification of arithmetic datapaths has been part of the established methodology for most Intel processor designs over the last years, usually in the role of supplementing more traditional coverage oriented testing activities. For the recent Intel Core i7 design we took a step further and used formal verification as the primary validation vehicle for the core execution cluster, the component responsible for the functional behavior of all microinstructions. We applied symbolic simulation based formal verification techniques for full datapath, control and state validation for the cluster, and dropped coverage driven testing entirely. The project, involving some twenty person years of verification work, is one of the most ambitious formal verification efforts in the hardware industry to date. Our experiences show that under the right circumstances, full formal verification of a design component is a feasible, industrially viable and competitive validation approach. One could even visualize in this way a highly impractical modern implementation of A α agents: Suppose a virtual environment containing objects with crisp, deterministic properties, including enough virtual transistors to compose small arithmetic CPUs. Also introduce some blackbox elements Σ α whose behavior can relate to sources outside the virtual environment, but which within the virtual environment can only affect immediately neighboring or connected elements of the environment-i.e. when a Σ α is built into a larger agent A α as a component, that Σ α can only write bitstrings into a sandboxed internal buffer of A α , and cannot otherwise affect A α or the general environment. Let G be a preferred class of outcomes difficult to achieve (perhaps requiring an agent to press a long series of levers). For some reason this outcome G in the environment is very important to us, but we don't want to work on it ourselves, or don't think ourselves competent to achieve it. We would like to pay some untrusted but competent human agents to take over the job of achieving G within the environment, while avoiding at all costs a disastrous outcome D. Let ∅ be a default set of outcomes maintained so long as some class of environmental elements are not disturbed (e.g. no levers are pressed), such that outcomes within ∅ are outside D. We incorporate a blackbox action-and-proof-suggester Σ α into an agent A α with a criterion of action bα i ⇒ A α bα i → (∅ ∨ G), and connect this Σ α to a human agent outside the system, armed with modern theorem-proving software that incorporates human suggestions. By putting Σ α into the agent A α , we can not only \"sanitize\" the actions taken within the system by the untrusted human, but also allow the human to (through A α ) construct other agents within the environment, which can in turn construct other agents, all including their own black-boxes Σ α hooked up to human proof-suggesters outside the environment, without ever running the risk that a non-∅ outcome besides G will ever be implemented.  38  On a larger scale, this illustrates that the decomposition of trust within the A α system also tiles its architecture and structure: A system A 1 composed of a trusted verifier ∆ 1 which checks proofs, and an untrusted suggester Σ 1 which may incorporate arbitrary heuristic or probabilistic methods, can build a trusted offspring A 0 with a verifier ∆ 0 proven correct by ∆ 1 and a suggester Σ 0 which incorporates whatever heuristics or probabilistic methods have been suggested by Σ 1 . Indeed, the correctness proof that A 2 used to build A 1 might go through almost unchanged for A 1 building A 0 , and one could perhaps prove that it would be safe to re-verify only the changed portions of the proof. The tiling principle is agents being able to approve the construction of successors similar to themselves, both architecturally and in the reasoning licensing their construction. This corresponds to the desideratum of a self-improving agent being able to make small, local changes to itself with a minimum of imposed overhead, as might occur if any small change required the reworking of 38. By the incorporation of sensors (see section 6) it is also possible for the offspring agents to know facts about the environment not known to the parent; the motivation to construct new agents in an environment like this can be explained by the new agents having better actuators, better sensors, or fast reaction patterns not present in the parents. a large body of cognitive labor to approve. We strongly remark that the Σ α -∆ α system is nowhere near a solution for a stably self-improving bounded probabilistic agent. The crisp separation of an untrusted Σ α and a trusted ∆ α works, not because logical proofs are hard to invent and easy to verify, but rather because logical reasoning is monotonic and thus no further fact known to Σ α but not to ∆ α can prevent the achievement of G by a ∆ α -approved action. When trying to achieve expected utility in a probabilistic environment described by causal models, this monotonicity no longer holds. Thus the Σ α -∆ α decomposition is intended only to illustrate the general idea that decomposition-of-trust can also tile in a structured fashion. \n The naturalistic principle Within the A α formalism the act of of constructing other agents is not treated as a special case, but is just one more sort of action that an agent can take to achieve its goals. A 0 and A 1 both act as consequentialist agents 39 that will take acts in their range Acts α whose predicted consequence is the goal G, without distinction of actions that construct agents. If G is to put a coin into a slot, then using environmental transistors to build a smarter agent that wants the coin inside the slot, is treated no differently, under the A α formalism, from manipulating a series of levers to put the coin inside the slot. There are many reasons we might be tempted to relax this naturalistic principle. Suppose we notice a disturbing quality of the current tiling: An agent A 1 whose desideratum is G (or ∅) can tile to an offspring A 0 whose desideratum is (G ∧ B) where B is an arbitrary \"barnacle\" on the goal system, some new requirement that A 0 imposes on itself for its actions to achieve besides G. This does not threaten the maintenance of (∅ ∨ G) but does mean that G might not be achieved in some cases where it was otherwise easy or achievable. We required that our offspring require itself to achieve G (in non-∅ cases) but did not require that our offspring require only G, and thus exact reproduction of the goal system-the system of desiderata-is not guaranteed. \"You get what you pay for\" and if you prove a theorem about G you get G, not \"G and nothing else.\" It would be up to the untrusted component Σ 1 whether A 0 worked to achieve G or (G ∧ B ∧ C ∧ ...), keeping in mind that Σ 1 might have been constructed by another untrusted Σ α and so on. None of this threatens the guarantee on G, but it still seems like a disturbing hidden instability of the agents' goals. (And in the case of expected utility, introducing an arbitrary new additive term into the utility function will always come at a cost to the desiderata previously present, if it shifts any choice that would otherwise have been made in the opposite direction.) 39. These agents use logical implication, e.g. bi → G, to reason about causal consequence, which in standard causal decision theory would be represented by a counterfactual distribution P ( bi G)see  Pearl (2000) . Logical consequence is generally a poor way of approximating causal consequence, but can work in crisp closed deterministic environments where such reasoning can be monotonic. Could we fix this problem by imposing a non-naturalistic requirement that the offspring contain a literal copy of the goal system-perhaps requiring that this part of the offspring be copied literally from the parent's code? To avoid the question of how the decision system knows that an act is an \"agent construction\" rather than a \"normal action,\" let us pass to self-modifying agents. A naturalistic agent-constructing-agent A α corresponds to a self-improving agent that treats the transistors comprising itself as resources no different from any other potentially-computing resources it finds in the environment; its beliefs about the transistors comprising itself are formed no differently from its beliefs about objects in the environment; and its internal decisions are made under the same consequentialist criterion as its external actions. Then an obvious structure for a non-naturalistic agent would be an agent with a different criterion of action for self-modifying changes (changes to its own program) versus motor actions in the outside environment. Considering some of the new difficulties introduced by this split decision criterion may help to motivate the naturalistic principle. Adding a special case for self-modification (of internal programs on the agent's current hardware) would introduce a discontinuity at the point where the agent considered expanding onto new computing resources obtained from the environment-the rules would need to describe how to buy a CPU from a store, connect it to the current cluster and then begin treating it under the new \"internal\" special case for hardware that must be manipulated via \"self-modification\" instead of \"environmental manipulation.\" For more advanced machine intelligences, the rule might need to describe how to arrive at beliefs about the behavior of a new kind of CPU via Bayesian updates, or beliefs about when a CPU has been \"connected\" to the internal network. (An advanced machine agent using a naturalistic decision criterion would also encounter corresponding cognitive tasks, but they would be treated continuously in terms of expected consequences, rather than needing a special case baked into the fundamental decision criterion.) We might say that these difficulties are being introduced by a kind of Cartesian dualism-the physically continuous universe has been divided into external material stuff versus internal mental stuff, and material objects must be declared to be specially cognitively typed before they can be treated as mental stuff. Or another difficulty: If the self-modification criterion tries to freeze the representation of the goal G so as to require exact reproduction of G and exclude \"barnacles,\" then the self-modification criterion will also have to freeze the corresponding properties of belief representation and decision consideration so as to guarantee that the rest of the system decodes G in the same way. 40 40. If this seems an odd notion to consider, we should mention that in nontechnical treatments of safe self-modifying machine intelligence, we have often seen proposals to \"hard-wire\" the goal system, often using that exact phrase. Construing the phrase charitably, it could refer to something like the above, in which case a problem is that \"hard-wiring\" one part of a system requires constraining the global architecture and internal protocols so that all the other parts behave the same way around the \"hard-wired\" part. Having a \"hardwired\" function that evaluates G a certain way is no guarantee of Even then the added constraint may end up being ineffectual. Consider that an agent with an added constraint in its decision criterion for \"self-modification\" of the software on its existing hardware, might naturally tend to build new agents in the environment according to its weaker environmental criterion. For that matter, again using the A α system as metaphor, if the environmental criterion is the weaker bi → G and the internal self-modification criterion is the additionally-restrictive bj → (G ∧ R), this decision criterion would approve an action to construct an external, \"environmental\" manipulator to reach into the agent and rewrite its code in a way that implied only G and not R. Having a stronger (more restrictive) criterion of action for self-modification, versus environmental action, seems likely to be futile in the long run. Most of the universe is outside rather than inside the AI, and external materials can be used to construct new agents, or to take actions with causal consequences impacting on the \"inside\" of the agent. That is why we are trying to see stable self-modification in terms of the natural tiling of a consequentialist decision criterion, rather than inventing special programmatic constraints. This leaves open the possibility that a weaker (less restrictive) criterion for \"internal\" self-modification could play a role in avoiding the Löbian obstacle. However this would introduce all of the above-mentioned difficulties with respect to describing what constitutes a more permissive \"internal\" action, or how to add new hardware. We could also ask whether the more permissive internal criterion would be just as appropriate for external actions, and if not, whether internal permissivity might give rise to external permissivity. Such a \"hack\" might be appropriate for self-modifying programs that will never consider, or never autonomously choose, to significantly modify their hardware. But even for those cases, a unified naturalistic decision criterion might avoid many complications in the underlying theory, and hence seems greatly desirable if obtainable. If naturalism is abandoned for a dualistic formalism, the Löbian obstacle can be dodged via the split decision criterion: 41 ψ(act i ) =[externalOK(act i ) → ( ā ct i → G)] ∧ [internalOK(act i ) → ( ā ct i → (∀act j ∈ Acts : ā ct j → ψ(act j ) ))]. Thus it is the simultaneous intersection of the Vingean, tiling, and naturalistic principles which generates the Löbian obstacle. safety if other code sections discard the return values, or introduce a new representation in which the returned values mean something else, etc. A decision criterion over expected global consequences automatically subsumes such details, while a non-naturalistic decision criterion over direct properties of the internal representation brings those details back in. 41. See \"failed solutions\" in section 3 for why this split decision criterion does not have an obviousto-us naturalistic analogue (we did look). \n Unknown variables and sensors A straightforward idiom for representing an agent which can use sensors to gain additional information about (known) unknowns in the environment would be the relation Sl ⇐ A 0 sl (6.1) representing a scenario where the agent A 0 adds the proposition 's l ' to its pool of logical beliefs only on occasions where the environmental sensor S, possibly a sensor, takes on the state Sl . (This also allows that S may be some variable whose state is sometimes not sensed, in which case A 0 believes nothing about any s l .) Then further axioms in Axm 0 would relate the proposition sl to the state of other represented parts of the environment, Axm 0 sl → χ. This idiom breaks the tiling pattern we used earlier, since A 1 will no longer be able to use the relation A 0 φ ⇒ Axm 0 φ. Even when Sl is true, it will not be entailed by Axm 0 and hence A 1 cannot prove bi → 0 bi → (∅ ∨ G) . Our previous proof relied on everything proven by A 0 being something that A 1 could have proven, but if A 0 has sensors not possessed by A 1 , it will act on premises which A 1 does not know to be true. Allowing this somehow is an obvious requirement for building successors (or self-modifying). If the A α formalism could not adapt to describe offspring possessed of additional factual information unknown to the parents, it would be entirely unsuited, under the Vingean principle, to describing self-improvement. An ugly but direct solution would be to amend A 0 's criterion of action to read: bi ⇒ A 0 (s l ∧ bi ) → (∅ ∨ G), (6.2) where some s l is guaranteed to have been sensed at the time of any action. (If the sensor sometimes does not activate, then the special state s 0 could indicate that the sensor has not obtained any reading, and represent this through the absence of any further environmental beliefs s0 → χ.) A 1 with criterion of action Ā0 j ⇒ A 1 Ā0 j → (∅ ∨ G) would then tile to A 1 via the lemmas: A 1 Ā0 → ∃s l ∈ s : sl (6.3) A 1 Ā0 → ∀s l ∈ s : ∀b i ∈ Acts 0 : (s l ∧ bi ) → 0 (s l ∧ bi ) → (∅ ∨ G) (6.4) A 1 Ā0 → (∀b i ∈ Acts 0 : ¬ bi ) → ∅ (6.5) This idiom technically does not break the Vingean principle, because we do not need to reason by cases on S and all values of s l ∈ s appear inside quantifiers, so multiple sensors can be included in A 0 without requiring exponentially longer chains of reasoning by A 1 . However this idiom stretches the tiling principle because each successive descendant, with additional sensors, must prove larger and larger criteria of action (even in cases where most sensors do not activate). Intuitively, it seems like if we were in the shoes of A 1 building A 1 , we would want to reason that since adding A 0 sl only happens when Sl is \"true,\" it should not disturb our trust in A 1 . Previously we were willing to add Axm 0 to A 0 's belief pool because we thought Axm 0 were all true in some encoding, so A 0 started with only true beliefs. We were willing to program A 0 to use classical logic to make syntactically allowed deductions from its current belief pool, even if A 0 proved some theorems we did not consider concretely in advance (in accordance with the Vingean principle), because we believed the rules of logic were valid in the sense that, starting from true premises about the environment, A 0 's reasoning rules would produce only true conclusions about the environment.  42  Then our trust in the soundness of A 0 should not be disturbed by giving A 0 a sensor which adds new statements sl only when Sl is true in the environment, even if these propositions were not known to us in advance. Set theory is powerful enough to directly formalize this reasoning using standard methods. In particular, ZF can internally represent the notion of semantic entailment X |= φ , \"The quoted formula φ is true within the quoted model X.\" E.g., to quote Peano arithmetic, the model X N would contain several subsets collectively representing the universe of numbers and the relations on the objects in that universe: X N would contain an element containing all objects in the universe of X N (in this case the numbers); an element containing all the ordered pairs for the succession function (e.g., (2, 3) is the pair indicating that the object 3 is the successor of 2); and more elements containing the collections of ordered triplets for the addition and multiplication functions (e.g.,  (3, 5, 8)  in the addition relation shows that 3 + 5 = 8). There then exists a compact formula of ZF asserting that φ encodes a formula that is semantically true of the quoted model X. For example, \"1 + 2 = 3\" would be encoded as the Gödel number of a statement asserting that (the number related by the successor function to 0, the successor of the successor of 0, and SSS0) form an ordered triplet that is an element of the addition relation. By recursion on the depth of formulas, there is a single compact ZF-formula which represents X |= φ in general and which could be applied to X N |= S0 + SS0 = SSS0 without further tailoring to the formula S0 + SS0 = SSS0 or the quoted model X N . It is then moreover possible to prove within ZF, by induction over the number of steps in a logical proof, that the set of quoted logical tautologies is true of every quoted model-if a formula (e.g., ∀x : ∀y : (x = y) ↔ (x = y) can be proven starting from no premises, it is semantically true in all universes. Thus ZF proves that the syntactic rules of classical logic preserve semantic truth: ZF ∀X : ∀ Γ : ∀ ∆ : taut Γ→∆ → ((X |= Γ ) → (X |= ∆ )). (6.6) This is a single, quantified formula rather than an axiom schema since there is 42. The purpose of logic is to preserve truth, not create truth. Logic doesn't guarantee that our conclusions are true; but logic does guarantee that if our conclusion is false, one of the premises must also be false. no longer any need to dequote the formulae Γ or ∆ in order to assert their truth within X.  43  Let the language L τ ∈ be the language of set theory L ∈ augmented by a new term τ denoting a special set, intended to be a quoted model representing the enivronment within which the agents are embedded. Let ZF τ be ZF with its axiom schemas extended to include formulas involving τ . Let ξ τ be a set of axioms describing the special set τ , such that ξ τ ∼ = Axm 0 -whatever statements the original A 0 treated as axioms about its universe (such as \"χ→G\"), will be rephrased as statements about τ (such as \"τ |= τ χ→G \"). Here |= τ is a new semantic entailment formula which maps special quoted terms like G to corresponding special sets located by ξ τ within τ , or corresponding special properties of τ . (E.g. G might represent some particular variable within the model τ having taken on the value of 20.) Note that there does not need to be any special term G added to the language L τ ∈ . Rather, the axioms ξ τ force τ to have a particular structure, and the formula |= τ assigns a special Gödel number and corresponding subformula of |= τ to the term G .  44  Then the centerpiece of A 1 's reasoning about A 0 becomes the central trust lemma: A 1 Ā0 → ∀ φ : (τ |= τ A 0 φ ) → (τ |= τ φ ). (6.7) This is the translation of \"A 1 thinks everything A 0 believes is true,\" or more explicitly \"A 1 thinks that everything A 0 believes, as encoded in some representation φ , corresponds to some statement φ which is semantically true about reality itself (τ ).\" Note that A 1 is now explicitly maintaining some compact mapping between its language φ for describing reality (τ ) and its model of A 0 's language φ -in other words, A 1 has an explicit correspondence theory of truth over A 0 's beliefs and the territory τ , as represented in some compact encoding relating A 1 's map of A 0 's map and A 1 's map of the territory τ . (6.7) is intended to mirror (in highly stripped-down logical form) something like what a human programmer would do intuitively in constructing a theoremprover to manipulate tokens supposedly \"representing\" the environment-the human implicitly maintains a compact mapping between the human's model of how the program treats tokens like \"Customer#12,\" and the human's model of some actual person named Fred. (Omitting any of these levels of indirection, or 43. ZF cannot thereby prove its own consistency because ZF cannot prove the existence of any set Y such that Y |= ZF . Likewise the entailment formula |= does not constitute a forbidden truth predicate because |= can only denote semantic truth within an individual set X, and there is no corresponding formula to denote semantic truth within the entire set-theoretic universe. 44. Having all our propositions talk about a unique term τ is intended to represent the idea of achieving things in some particular \"actual reality,\" not just an implication being true in some particular set x which has the properties ξ(x) but is not the actual reality we wish to speak of. We could possibly do without the special term τ and let our set theory be the standard ZF by having the axioms ξ τ say ∃x : ξ(x) and replacing all statements of the form τ |= τ φ with statements of the form ∀x : ξ(x) → (x |= τ φ ), so that the conclusion is forced to be true of the reality-set as well, so long as the reality-set has the properties ξ. But for reasons of notational simplicity, we would rather just add the term τ to the language L τ ∈ . committing the mind-projection fallacy  (Jaynes 2003)  and speaking as if some ethereal link was actually connecting \"Customer#12\" and Fred, can result in truly vast amounts of confusion.) The human then configures the program to maintain the human's expectation of correspondence between the two, i.e., the human makes sure that the token \"Customer#12\" behaves in such fashion that its \"money\" property is expected to behave like the human's expectations about Fred's payments. The maintained correspondence is between epistemic objects-a map of a map, and a map of the territory-so that a compact mental transformation can relate the two.  45  Similarly an agent A 1 with Axm 1 = ZF τ ∪ ξ τ and criterion of action Ā0 j ⇒ A 1 (τ |= Ā0 j ) → (τ |= (∅ ∨ G) ), (6.8) which had established the central trust lemma (6.7), could approve the construction of an agent A 0 which held the object-level beliefs represented by Axm 0 -an agent which, like previously described agents A 0 , did not use set theory or represent an explicit environment-object τ , but instead was programmed to reason about a proposition G that could be the consequences of its acts b i as before. We could similarly expect that A 1 would establish its central trust lemma (6.7) by induction on properties of the design of A 0 . The base case is the truth of every axiom in Axm 0 constituting A 0 's belief pool when it starts up. The induction step is the validity of classical logic's syntax, as proven within ZF (or ZF τ ) to produce only semantically true conclusions from semantically true premises on each succeeding time-step of induction. Then this central trust lemma is not disturbed by adding sensors that operate as in (6.2) or, in this scheme: A 1 (τ |= τ Ā0 ) → ∀ s l : (τ |= τ A 0 sl ) → (τ |= τ Sl ). (6.9) Imagining the induction to be over time steps taking places at times u after A 0 's construction at t, adding this type of sensor does not invalidate the induction step that if all A 0 's beliefs are true at time u, they will be true at time u+1-supposing all of A 0 's new beliefs to be added either by syntactically valid classical deduction from previous beliefs, or by sensors which A 1 believes to operate in a sound fashion relative to A 1 's correspondence theory of truth φ ↔ φ , on any given time step. Some further elaboration is then required to use the same schema to describe the agent A 2 which creates A 1 which creates A 0 : A 0 itself may reason about the environment using some simple axioms, first-order logic, and perhaps a few sensors, a la Newell's GPS  (Newell, Shaw, and Simon 1959) . A 1 , to reason about A 0 in a sufficiently general fashion, deploys set theory in order to reason about a physical universe τ , a language φ for describing physical reality, and a truth-condition |= τ which determines whether such statements are (in A 1 's beliefs) \"true\" or \"false,\" and an agent τ |= τ A 0 with beliefs φ which A 1 believes to correspond to propositions φ which are actually \"true.\" (Representing semantic entailment in a fully quantified way, and proving in a quantified way that logical tautologies are true in all models, is why we had to invoke the big guns of ZF.) Then A 2 , to reason about A 1 's reasoning, needs to trust that A 1 , in reasoning about set theory, is reasoning about valid subject matter. E.g., since A 1 is reasoning within ZF τ , A 2 to trust A 1 must at least believe that ZF is consistent.  46  Then clearly A 2 must be using some theory more powerful than ZF τ ∪ ξ τ , which can prove the soundness of ZF τ ∪ ξ τ . An obvious idiom is for A 2 to reason that A 1 's mental universe corresponds to some object in A 2 's universe, something that A 1 can be said to be reasoning about:  (6.10)  which states that there exists some set s which is a model of Axm 1 = ZF τ ∪ξ τ . 47 This makes Axm 2 as strong as ZF plus the assertion that there exists an inaccessible cardinal (a single set which is large enough to be a model of a set-theoretic universe obeying the axioms of ZF). Since ZF can prove Gödel's Completeness Theorem that every syntactically consistent theory has a model, Axm 2 is as strong as ZF+1. Axm 2 = ZF τ ∪ ∃s : s |= τ ZF τ ∪ ξ τ , From another perspective: A 1 's mental universe includes not only τ but a larger mathematical universe of set-theoretic objects-e.g., this mathematical universe, not the physical universe τ , is what includes the numbers (least ordinals closed under succession) which determine whether \"a proof of φ exists\". Then A 2 must be strong enough mathematically to reason about something (a set, a model) which is large enough to provide a correspondence theory of truth over all of A 1 's reasoning, including A 1 's reasoning about set theory. A 2 must believe in an object that provides, not just a physical environment, but a mathematical universe, for A 1 's reasoning to be sound over. Similarly, another agent to create A 2 must believe that there exists a set that models Axm 2 , containing a set that models Axm 1 , containing τ that models Axm 0 ∼ = ξ τ , with the corresponding theory having the strength of ZF+2; and we arrive at ordinal tiling as before. Remarks. For a set theory to believe in the existence of an infinite descending sequence of sets containing sets containing sets, etc., would violate the Axiom of Foundation (Axiom of Regularity). Hence an analog of the infinitely descending soundness schema T -0 seems like it would be even harder to repair. Possibly the fact that infinite models are being encoded as sets may allow for an infinite series of encodings (e.g., all the numbers can be encoded as even numbers, then 46. Or perhaps, \"ZF is consistent if 0 is not the Gödel number of a proof that (ZF plus a large cardinal axiom) is inconsistent,\" or \"ZF is consistent if κ is greater than 0,\" but we omit such complications here and assume that A 2 , A 1 , and A 0 fall into a standard decreasing-ordinal schema. 47. Note that since semantic entailment is a quantifed formula, infinite axiom collections, such as axiom schema, can be semantically entailed without problems. all the numbers can be encoded as even numbers encoded as even numbers and so on indefinitely). We see no obvious obstacles to Fallenstein's parametric polymorphism approach T κ being adapted to ZF τ proving safety for κ steps, but have not yet written out a complete proof. We would be interested in any simplification of this scheme that reasons about a correspondence theory of truth over the offspring agents without resorting to set theory, or that uses a set theory substantially less powerful than ZF. \n Probability and expected utility At present our attempts to tile probabilistic reasoning are in very preliminary stages. Expressing trust of an agent in an offspring's probabilistic reasoning introduces new complications, most of which remain unresolved. The expectation of utility E[U ], conditional on an action b i being performed, is often defined in terms of an outcome variable o k ∈ Outcome and probability distribution P as: 48 E[U ] o k ∈Outcome U (o k )P (o k | bi ). (7.1) The most straightforward analogue of logical satisficing, as previously used in A α , is expected utility satisficing. (Maximization would introduce even more difficulties; see section 8 below.) E.g., A 0 might act only when it expects its action to lead to expected utility greater than (arbitrarily) $20, and we might be tempted to write this as the problematic formula: bi ⇒ A 0 E[U | bi ] > $20 (7.2) As we remarked in section 5.2, the introduction of expected utility and its conditioning formula lead to basic difficulties with the A α formalism because probabilistic reasoning is not monotonic. If we prove by logic that bi → G there 48. In standard causal decision theory  (Joyce 1999; Pearl 2000) , the expectation of utility would be written using the counterfactual conditional: E[U ] o k ∈Outcome U (o k )P ( bi o k ). In timeless / updateless / logical decision theory  (Altair 2013; LaVictoire et al. 2013 ): Q = arg max bi∈Acts o k ∈Outcome U (o k )P ((eval Q = bi ) o k ). Since we do not properly consider such issues here, we shall (as do most non-foundational works) write the expected utility formula using the classical conditioning operation P (o k | bi ) of evidential decision theory, which decision theorists almost universally agree to be wrong. can be no further fact Γ such that ( bi ∧ Γ) → ¬G (unless of course the addition of Γ is inconsistent). However if P (G | bi ) > 0.9 there is no rule that therefore P (G | ( bi ∧ Γ)) > 0.9 for every further fact Γ, likewise E [U | bi ] > $20 does not imply E[U | bi ∧ Γ] > $20. Suppose A 1 , which desires E[U ] > $20 in all non-∅ cases, approves of any A 0 with the decision criterion (7.2) above, considering such an A 0 safe regardless of how its actions are suggested by an untrusted component Σ 0 . Suppose also that the action b2 yields $50 if the coin θ came up heads (θ H ) and $10 otherwise (θ T ). If θ is unknown and is assigned probability 50% then E[U | b2 ] = $25. But suppose that Σ 0 manages to learn the true value of θ and only suggests the action b2 in cases where it knows θ T . Then observing that the offspring has proven A 0 E[U | bi ] > $20 is not adequate reason to trust that, if it acts, it will achieve expected utility greater than $20.  49  It may be objected that since, in this case, A 0 only takes the action b 2 in cases where θ T , the true probability distribution would have P (θ T | b2 ) = 1 and A 0 should evaluate E[U | b2 ] accordingly. This raises questions of evidential versus causal decision theory which we lack space to address here. We remark that if A 0 , evaluating its probability distribution P , finds that this probability distribution already assigns probability 1 to action b 2 and probability 0 to all other actions (the \"true\" probability distribution in cases where b2 ) then A 0 would seem to know its own action before it decides (indeed, prior to its computation of expected utilities); and if A 1 also possesses axioms implying this \"true\" P then it must know its offspring's exact action which violates the Vingean principle. Furthermore, conditioning on all actions except b 2 would then require conditioning on a zero probability with undefined results.  50  We do not have good solutions for these issues, but felt that we ought to offer an unsatisfactory version of the formalism so that there would be something in place to improve upon. To avoid the complexities of reasoning about probabilistic program execution, we supposed the environment could be divided into a near-deterministic part (the \"environmental transistors\"; the analogue of a human-made CPU constructed to have almost perfectly deterministic causal paths, crisp variable states and crisp relations) and a probabilistic part X, which is the subject of the probability function P (X). We suppose X to be a joint function of variables x l obeying the usual fac-49. The form of your theorem demanded an action such that, conditioned on knowledge of only that action, expected utility would be greater than 20; you did not ask for an action conditioned on all the knowledge available to the component which suggested that action. You get no more than what you pay for; or in this case, no more than what you prove. 50. An analogous problem potentially arises if A 0 ever proves that it does not perform some particular action, Axm 0 ¬ bi . Any conclusion would then follow from the contradictory hypothesis bi , thus Axm 0 bi → (∅ ∨ G). With valid reasoning on true axioms this should never occur (we should not prove ¬ bi and then do b i ) but it is potentially a concern when trying to build systems which bypass the Löbian obstacle. It is ordinarily Gödel's Theorem which prevents a system from concluding that it will never prove some theorem (such as the theorem bi → (∅ ∨ G)). torization for causal models  (Pearl 2000) : P (X) = x l ∈X P (x l | pa l ), (7.3) where for each variable x l , pa l is a possibly empty list of the immediate causal ancestors of x l . Thus the joint probability distribution P (X) factorizes into local rules governing the probability of each node x l given its parent causes, if any. We then axiomatize A 1 's knowledge of P (X) in a way that leaves some parentless x l with unspecified probabilities; any causal descendants of these variables will have probabilities unquantified by A 1 . One of these variables will be A 0 's action and thus A 1 will not precompute a probability of A 0 's action. We will also need to leave unspecified all sensor variables s k ∈ S. Collectively the sensor variables and the motor action variable will constitute a kind of Cartesian boundary between the deterministic world in which A 0 's cognition occurs, and the probabilistic world it wants to sense and affect. We then mate deterministic reasoning to probabilistic reasoning via the bridging axioms: 51 A 1 ∀s k ∈ S : sk → (P (s k ) = 1) (7.4) A 1 ∀b i ∈ Acts 0 : bi → (P ( bi ) = 1). (7.5) A 1 and A 0 's criteria of action will be: Ā0 j ⇒A 1 Ā0 j → (∅ ∨ (E[U ] > $20)), (7.6) bi ⇒A 0 bi → (∅ ∨ (E[U ] > $20)), (7.7) and let A 1 prove a soundness schema (central trust lemma) over A 0 's logical beliefs as before. Then A 1 's decision to create A 0 is straightforward via: A 1 Ā0 → ∀b i : bi → ( 0 bi → (∅ ∨ E[U ] > $20) ), (7.8) A 1 0 bi → (∅ ∨ E[U ] > $20) ) → ( bi → (∅ ∨ E[U ] > $20)), (7.9) A 1 (∀b i : ¬ bi ) → ∅, (7.10) A 1 Ā0 → (∅ ∨ E[U ] > $20). (7.11) Suppose Axm 0 incorporates standard probability axioms, and suppose that A 0 has observed all available sensor data s k representing all missing terms of X except its action b i . Then A 0 will be able to carry out an action with 51. The form of these axioms was suggested by Paul Christiano. \n E[U | sk ∧ bi ] > $20, via: A 1 E[U |s k ∧ bi ] > $20 (7.12) A 1 sk (7.13) A 1 P (s k ) = 1 (7.14) A 1 bi → (P ( bi ) = 1) (7.15) A 1 (P ( bi ) = 1 ∧ P (s k ) = 1) → (P ( bi ∧ sk ) = 1) (7.16) A 1 bi → (P ( bi ∧ sk ) = 1) (7.17) A 1 bi → (P (¬( bi ∧ sk )) = 0) (7.18) A  A 1 bi → (E[U ] = E[U | bi ∧ sk ]) (7.20) A 1 bi → (E[U ] > $20) (7.21) We confess this to be a moderately grotesque hack that fails almost entirely to rise to the challenge of non-monotonic probabilistic reasoning. As remarked, we included it only to serve as something that could be improved upon. The argument above goes through only because, by assumption, every possible variable correlated with U has been observed and so no further probabilistic knowledge can be gained to invalidate the conclusion. It also is not immediately obvious to us how to extend the above hack to sensory observation of variables with causal parents. In usual practice, sensors observe the causal descendants of variables of interest-e.g., the light reflecting from an object takes on a pattern caused by that object; the observed photons are causal descendants of the event of their reflection. Being unable to represent the standard idiom of evidence in Bayesian networks is a very severe defect.  52  Similarly it seems to us that it should be possible to compute the probability of evidence before observing it, since this practice is central to Bayesian probability. In the formalism as it stands, being able to assign a prior probability to any evidential variable would produce a logical contradiction after a sensory event added the conclusion that the probability was 1. We suspect that there ought to be some much more general schema of trust in probabilistic soundness of a successor agent, possibly invoking explicit reasoning about probability measures in the same way that we previously introduced set theory as a backdrop to general reasoning about semantic truth, or using some probabilistic trust schema such as possibly: 52. We suspect that this desideratum might be satisfiable by some very simple technical method we have not yet invented as of this report. \n Bounded agents: Maximizing, satisficing, and meliorizing Expected utility is usually discussed in the context of expected utility maximization-choosing from among the actions in a set the action with highest expected utility. We did not attempt to frame our probabilistic agent that way, because introducing the notion of maximization creates new challenges to tiling, separate from the challenges of probability. I.e., suppose that we are in a deterministic environment, creating offspring which will have various possible sensors, various possible ranges of action, and whose actions (given the value of background variables) deterministically score various utilities. We could possibly adapt the logical goal G to state some version of the highest possible score being achieved, with the successor otherwise allowing a ∅ outcome. However, to properly rise to the challenge of maximization would imply creating the successor A 0 j which, of those options Acts 1 available to you, would lead to the best score you could've received, after A 0 j tries to maximize its own score. It was not obvious to us how to make the proof of such a tiling go through. It is also not obvious to us that this is the correct problem on which to spend effort, since, in real-world environments, achieving the maximum possible expected utility is impossible for all but the simplest problems. Maximization in full generality requires correctly assessing the score (expected utility) of every action in order to guarantee that we choose the best; this is what renders, e.g., optimal chess intractable. Satisficing is more realistic for bounded agents, in this sense, because we only need to evaluate the expected utility of a single action in order to have our decision criterion E[U ] > 20 go through. (Likewise, establishing some partially uncertain, probabilistic expectation of utility is more realistic than correctly predicting an exact outcome or score.) But to seriously consider satisficing as the foundation of a useful rational agent, or sufficiently advanced self-improving intelligence, would come with its own set of problems. Suppose the lower bound is set at $2 • 10 15 utility in whatever measure, and the agent realizes that a certain plan will ensure a minimum expected utility of $10 16 . Then as we have defined the agent's goals, it satisfices to randomize between a 30% probability of implementing this plan, a 60% probability of doing something which leads to expected utility $0, and a 10% probability of doing something with expected disutility −$10 16 . This is probably not the sort of behavior we wanted.  53  Schmidhuber's \"Gödel machine\" (2007) 54 introduced the interesting suggestion of a swapping criterion of action: The \"Gödel machine\" would change its own source code if it could prove that the action of changing its source code had a higher expected utilty than keeping its current source code. (No criterion for external motor actions was introduced, but arguendo the Gödel machine would soon choose to add one.) One of the participants at the April 2013 MIRI work-53. You get what you pay for, no more than you asked for, and exactly what you proved. 54.  Schmidhuber (2007)  could easily be considered a spiritual forerunner of the present work. shop suggested dubbing this a \"meliorizing\" criterion of action, since it is meant to make things steadily better (repeatedly swap in plans, or successors, with higher expected utility). Furthermore, since meliorizing requires considering only two courses of action-the current plan, and the new plan-it may be suitable for a boundedly rational agent. In contrast to the suggestion in section 4 of  Schmidhuber (2007)  it is not obvious that the criterion, \"Swap if expected utility of the new program is higher\" is a guarantee of \"global optimality,\" which Schmidhuber suggested would be the result of each considered swap taking into account the possibility of other, better swaps if the current program were left undisturbed. Even considering expected utility rather than utility, most expectations that can be computed over some series of branches will not locate the point of highest expected value in the space, unless expectations are unusually smooth or the suggested series of changes is especially good. E.g., the problem at hand could easily have an NP-hard optimal solution (while still having good non-optimal solutions which could be steadily improved). But the question of \"global optimality\" is probably not the most important concern, since literal global optimality in the sense of trying to solve NP-hard problems should not be the key research desideratum. It is likewise not obvious to us that \"meliorizing\" is sufficient to produce satisfactory behavior with respect to a builder's programmed set of goals. Suppose a sufficiently advanced machine intelligence, built according to this criterion, discovered that an asteroid was headed toward Earth and would shortly kill 7 billion people, with its current plan not preventing it. Under the strict criterion of meliorizing as written, it would make sense to swap to a program that promised to save 1,000 people, let all the others die, and make no further improvements, since this would still be better than not swapping. According to the line of argument in section 4 of  Schmidhuber (2007) , the agent ought to consider that it would be better to keep the previous program and wait for it to generate a better alternative. But this relies on some particular sequence of suggestions being generated such that a better alternative is considered at some point; moreover, that the agent probabilistically expects that such a better alternative will be generated if it keeps its current program, in advance of considering the actual alternative (which the Vingean principle says we cannot always do at the earlier decision point). Thus if a meliorizing criterion is ultimately satisfactory, it will be due to other properties of the series of suggestions being considered, and the way in which expectations of old and new programs are evaluated, which have not been specified into the \"swapping\" rule itself. But expected utility satisficing is not satisfactory at all, and is probably not repairable; and maximizing is only possible for the best imaginable agents, not the agents that will actually exist; whereas it might be that meliorizing can somehow be improved upon. More generally, we have discussed maximizing, satisficing, and meliorizing in order to make the point that when it comes to bounded, probabilistic rational agents that are meant to pursue their goals in some \"reasonable\" way and build descendants who do the same (equivalently self-improve), we are not able to presently state-even on the highest possible level of generality such as \"satisficing\" or \"meliorizing\"-what sort of criterion of action might be suitable. The problem is very wide open indeed. so by Löb's Theorem ∀x : T ψ(x). 18 (b) Instead of an indefinitely extensible ordinal hierarchy of systems T +α, let us form a descending sequence of theories T -0, T -1, T -2 as follows: T -n T ∪ ∀φ : (∀x : T -(n+1) φ(x) → φ(x)). \n Perhaps the previous constructions failed due to their impredicativity. Let us try a finitary version which speaks only of well-founded objects. Let k+1 T φ stand for the formula T T ...φ... with k + 1 boxes.. Since the pattern T T ... is highly regular, a compact formula for k+1 T φ should exist. Then let A α 's criterion of action be bi \n T φ(b i ) ∨ φ(b i ) , which does not reduce to ∃k : k+1 T φ(b i ) . 19 19. The formula k+1 T φ just occupies a new ordinal ω of proofness, and T k+1 T φ then corresponds to a new ordinal ω+1 of proofness. \n 1 E[U ] = (E[U | bi ∧ sk ]P ( bi ∧ sk )) + (E[U |¬( bi ∧ sk )]P (¬( bi ∧ sk ))) (7.19) \n P α (φ ∧ (A β P β (φ) = p )) = p • P α (A β P β (φ) = p ). (7.22)Such work remains in progress, however, and in general the problem of self-modification in probabilistic agents remains wide open. \n\t\t\t . ψ(x) is just a Henkin sentence H ↔ T H with a dangling ∨ clause φ(x). A Henkin sentence for T is of course always provable within T . \n\t\t\t . Which is, in general, the agenda of this paper: Our framework and our technical solutions are \n\t\t\t . In other words, the length of clock ticks is small enough that constructing another agent takes at least one tick. E.g., the length of a clock tick could equal the Planck time. \n\t\t\t . This implies that the system behaves in a sense as though it assigns nonstandard probabilities (in the sense of nonstandard analysis with infinitesimals), an issue we are still working on. \n\t\t\t . It is possible that this work might have some relevance to the philosophy of epistemology, which we lack space to explore here.", "date_published": "n/a", "url": "n/a", "filename": "TilingAgentsDraft.tei.xml", "abstract": "We model self-modification in AI by introducing \"tiling\" agents whose decision systems will approve the construction of highly similar agents, creating a repeating pattern (including similarity of the offspring's goals). Constructing a formalism in the most straightforward way produces a Gödelian difficulty, the \"Löbian obstacle.\" By technical methods we demonstrate the possibility of avoiding this obstacle, but the underlying puzzles of rational coherence are thus only partially addressed. We extend the formalism to partially unknown deterministic environments, and show a very crude extension to probabilistic environments and expected utility; but the problem of finding a fundamental decision criterion for self-modifying probabilistic agents remains open.", "id": "8b65dbff462dc16ddf29573c26ea275a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["William Macaskill", "Aron Vallinder", "Carl Shulman", "Caspar Österheld", "Johannes Treutlein"], "title": "The Evidentialist's Wager", "text": "Introduction Suppose you find yourself in the following decision situation: \n Moral Newcomb In front of you are two boxes, A and B. You can choose either B only, or both A and B. Box A is guaranteed to contain one dose of a cure for a fatal disease, whereas box B may or may not contain ten such doses. A perfectly reliable predictor has made a prediction about your decision. If she predicted that you would take both boxes, she 1 left box B empty. If she predicted that you would take box B only, she put ten doses in that box. What should you do? Cases like this give rise to the well-known debate between causal decision theory (CDT) and evidential decision theory (EDT). Roughly speaking, according to CDT, you should perform the action which is likely to cause a good outcome, whereas according to EDT, you should perform the action which provides strong evidence that a good outcome will occur.  2  And let's suppose-as would seem to be natural-that you represent the decision situation as follows: Cure in both Cure in one only \n Take one box Ten lives Nothing Take both boxes Eleven lives One life Given that the prediction has already been made, your decision has no influence on whether or not box B contains anything. Therefore, CDT recommends that you choose both boxes, because that way you are guaranteed to obtain one more dose than you otherwise would, regardless of whether or not B is empty. By contrast, EDT recommends that you choose only choose box B, because you would thereby receive strong (indeed perfect!) evidence that you will obtain ten doses of the cure. If you instead choose both boxes, you would thereby receive strong (indeed perfect!) evidence that you will merely obtain one dose. CDT has garnered more adherents  (Bourget and Chalmers, 2014) , and hence we assume most decision theorists believe that you should two-box in the Moral Newcomb problem. But here's an argument for one-boxing that, to our knowledge, has not appeared in the literature. The argument relies on three premises. First, even though one might have higher credence in CDT than EDT, there is still an ongoing debate, and a number of intelligent and well-informed decision theorists endorse EDT. In the face of such expert disagreement, one shouldn't be anywhere near certain that CDT is correct. Instead, one should assign at least some credence to EDT. Second, once we take into account our background knowledge of the world, the stakes become significantly higher for EDT than CDT in the Moral Newcomb problem. The universe is probably very big indeed, and there are very many individuals very similar to you who will face similar decision problems. As a result of this similarity, your decision in the Moral Newcomb problem is correlated with decisions made by many other agents elsewhere in time and space. This means that the simple state-consequence matrix above does not in fact capture everything that is relevant to the decision problem: we have to refine the state space so that it also describes whether or not correlated agents face boxes with cures in both. By taking one box, you gain evidence not only that you will obtain more doses of the cure, but also that these other agents will achieve good outcomes too. Therefore, the existence of correlated agents has the effect of increasing the stakes for EDT. By contrast, there is no causal connection between your decision and the decision of these other agents, and hence taking them into account does not affect the stakes for CDT. Third, in the face of uncertainty, the rational thing to do is to hedge one's bets. If the stakes are much higher on one hypothesis than another, and the credences you assign to each of these hypotheses aren't very different, then it's rational to choose the option which performs best on the high-stakes hypothesis. If these three premises are true, then one-boxing is the rational thing to do in the Moral Newcomb problem. But, for an altruistic and morally motivated agent, there's nothing special about Moral Newcomb compared to other decision problems where EDT and CDT disagree. So we can generalise our conclusion as follows: In general, and across a wide variety of decision contexts, if you are an altruistic and morally motivated agent, and are uncertain between EDT and CDT, you should typically act in line with EDT even if you have significantly higher credence in CDT. \n Call this argument The Evidentialist's Wager . Should we accept the Wager? There are several steps of the argument that can be questioned. First, one could debate whether you ought to hedge in the face of decision-theoretic uncertainty. While this is not the primary focus of this article, we will give some motivation for hedging in the next section. Second, in order for the claim that the stakes are higher for EDT than for CDT to be meaningful, we need some way of making an intertheoretic value comparison -that is, some way of comparing the magnitude of an action's evidential expected value with the magnitude of its causal expected value. We present a proposal for doing this in section 3. Third, one might wonder whether we should really expect the world to contain sufficiently many correlated decision-makers facing similar decision problems. We will address this question in section 4. One way for there to be many such agents is if the universe is infinite, as is implied by several leading cosmological theories. But the infinite case gives rise to a range of further issues. These are addressed in section 5. \n Arguments for Hedging The Wager relies crucially on the idea that, in the face of decision-theoretic uncertainty, one ought to hedge. But is that correct? Perhaps what one ought to do is just what one ought to do according to the correct first-order decision theory? We're not going to be able to resolve this question in this article. But we'll show that although the view has its issues to resolve, there are some significant arguments in its favour and it should therefore at least be taken seriously. We present three such arguments. \n Dominance Consider the following variant on Newcomb's problem. \n Equal Amounts In 3 When we say that the EEV of both actions is the same, we are assuming that you are certain that the predictor is perfectly reliable. If we instead assume that you believe the predictor to be highly, although not perfectly, reliable, it follows that EDT will also recommend two-boxing, However, for any given belief about the predictor's reliability, we can set the stakes so that EDT judges both actions to be equally choiceworthy. \n Money in B Both empty Take one box $1M $0 Take both boxes $1M $0 In this case, the situation is reversed: the causal expected value of taking both boxes is the same as that one has positive credence in, these suggestions make perfectly good sense. \n Stakes Sensitivity MacAskill (2016) argues that our intuitions in Newcomb cases are sensitive to the relative stakes for EDT and CDT, and that this stakes sensitivity can be explained by the fact that one should hedge under decision-theoretic uncertainty. , He presents the following two cases (slightly altered here) in Psychopath Button -can also be explained in terms of the idea that we are intuitively hedging in the face of decision-theoretic uncertainty. And it seems that, empirically, people's intuitions about Newcomb problems are stakes sensitive: in a study that we and some coauthors ran, subjects were more likely to one-box in Newcomb's problem if the stakes were higher for EDT than for CDT . 7 Insofar as accordance with people's intuitions in these cases has been taken to be a desideratum of a decision theory, this provides some support for the idea that, in some sense of 'ought', one ought to hedge in the face of decision-theoretic uncertainty. \n Paying for Information Consider again the Moral Newcomb problem with which we started. Suppose that before making up your mind, you learn that, via a time machine, a book has been delivered from the year 10,000 CE. On the blurb it claims that after long reflection our descendants have discovered the correct decision theory, with arguments so clear and compelling that anyone can understand and everyone will be convinced. It even has various applications of the view, including to the precise problem you're facing. However, you have to pay $5 in order to read the book. Let's bracket, for the purpose of this example, any intrinsic value from knowledge of the truth about rationality, any fame that the reader might receive for explaining its arguments to others, and so on: we can imagine that you know you will immediately forget the contents of the book after making your decision. If there is no sense of 'ought' which is relative to one's decision-theoretic uncertainty, you should not buy and read the book. From EDT's perspective, paying $5 to read the book and then one-boxing is strictly worse than just one-boxing right away. Similarly, from CDT's perspective, paying $5 to read the book and then two-boxing is strictly worse than just two-boxing right away. So, if you ought to do simply what you ought to do on the correct decision theory, you ought not to pay the $5 to read the book. This seems deeply counterintuitive: given the stakes-ten lives saved for EDT and one life saved for CDT-it would seem reckless not to incur such a trivial cost before taking action. But if so, there is some notion of 'ought' which is relative to one's decision-theoretic uncertainty. \n Outstanding Issues The argument from stakes-sensitivity supports the claim that one should hedge in the face of decision-theoretic uncertainty, whereas the other two arguments only support the weaker claim that there is some notion of 'ought' that takes decision-theoretic uncertainty into account. However, it seems clear to us that if one accepts that there is such a notion of 'ought', one should plausibly accept hedging as well. In the context of moral uncertainty, most of the resistance to hedging from those who accept the relevant notion of 'ought' is driven by skepticism about the possibility of intertheoretic value comparisons (e.g.  Gustafsson and Torpman 2014:165) . But as we will argue in the next section, such comparisons are significantly easier to make in the case of decision-theoretic uncertainty. Nevertheless, the view that one should hedge under decision-theoretic uncertainty still faces some outstanding issues. In order to know precisely how to take (first-order) decision-theoretic uncertainty into account, one needs a second-order decision theory. Although we have not presented a specific second-order decision theory, we have argued that any plausible account should endorse hedging; candidate second-order decision theories would include 'meta causal decision theory' and 'meta evidential decision theory' (MacAskill 2016). However, if one should be uncertain among first-order decision theories, one should presumably also be uncertain among second-order decision theories. Moreover, if uncertainty among first-order decision theories can make a difference for what one should do, then presumably so can uncertainty among second-order decision theories. In order to take this uncertainty into account we need a third-order decision theory, and thus we are seemingly lead into an infinite regress of uncertainty at higher and higher orders. This infinite regress represents a significant challenge to the claim that one should hedge in the face of first-order decision-theoretic uncertainty. If we could somehow be certain that the correct second-order decision theory-whatever it is-endorses hedging, then we would be in the clear. But we should not assign zero credence to My Favourite Theory , according to which one should simply act in accordance with the first-order theory one has highest credence in, and which therefore does not endorse hedging. We recognise that this is a 8 major challenge, but for the purposes of this paper we will assume that some solution can be obtained. 9 A second challenge concerns the question of what notion of 'ought' is at play in the claim that one ought to hedge under decision-theoretic uncertainty. In the corresponding literature on moral 10 uncertainty, one common strategy is to say that although the notion of 'ought' that is provided by the correct moral theory is a moral ought, the notion of 'ought' that is relative to one's moral uncertainty is a rational ought. However, on the face of it, this strategy appears to be unavailable in the present 11 context. The ought which is relative to the correct (first-order) decision theory is already a rational 8 See  Gustafsson and Torpman (2014)  for a discussion and defence of My Favourite Theory in the context of moral uncertainty. 9 For detailed discussion of the regress problem, see Trammell (2019), MacAskill, Ord, and Bykvist (2019, chapter 1.3), and Tarsney (manuscript). 10 See Weatherson (2014),  Harman (2015)  and  Hedden (2016)  for this objection in the context of moral uncertainty. ought, and therefore it seems we cannot appeal to that distinction here. Again, we shall not try to 12 resolve this issue here. For these two reasons, we think it's an open question whether you ought to hedge in the face of decision-theoretic uncertainty: whichever view you take, you have some hard problems to grapple with. However, we believe the arguments we've given in favour of hedging make the idea that one should hedge sufficiently plausible that it's interesting and important to work out what one should do if one should hedge. In what follows, we will therefore assess the conditional claim that if you ought to hedge, then you should generally take the action that EDT recommends. \n Intertheoretic Comparisons In order for the claim that one ought to hedge in the face of decision-theoretic uncertainty to be meaningful, we must have some way of comparing evidential expected value with causal expected value. Otherwise we will not be able to make sense of the claim that the stakes are higher for EDT than they are for CDT. In the literature on moral uncertainty, this is known as the problem of intertheoretic value comparisons. To get a sense of the difficulty of this problem, consider the 12 However, if we think of supplementing a given axiology with either an evidential or a causal decision principle as giving rise to two distinct moral theories, we can still appeal to this distinction. As an analogy, consider the fact that a utilitarian axiology can be combined with both a risk-neutral and a risk-averse principle for evaluating actions under empirical uncertainty. If we think of risk-neutral and risk-averse utilitarianism as two distinct moral theories, then we should plausibly say the same thing about evidential and causal utilitarianism. Of course, this maneuver will not work for all cases of uncertainty between EDT and CDT. following case. Suppose that you're facing the Footbridge trolley problem, but your credence is evenly split between a consequentialist theory and a deontological theory. If you should hedge under moral uncertainty then you should sacrifice the one in order to save the five if the stakes are higher for the consequentialist theory, and refrain from doing so if the stakes are higher for the deontological theory. But how are you to put the two theories on a common scale in order to know whether the stakes are higher for the consequentialist or the deontological theory? The theories themselves do not seem to come equipped with an answer to this question, and it's hard to see what other information one could appeal to in order to resolve it. Multiple proposals have been made in the literature, but it's clear that there is not yet any consensus solution.  13  Luckily, the problem of intertheoretic comparisons is significantly easier in the case of decision-theoretic uncertainty. In order to see this, let us first state EDT and CDT more precisely. According to EDT, you should choose the action with the highest evidential expected value (EEV) , calculated as follows: EV (A) (O | A)V (O ), E = ∑ n i=1 P i EDT i where O 1 , ..., O n are the possible outcomes, P is the agent's credence function, and V EDT is her value function. The EEV of an action A is the sum product of the value of each outcome and the probability of that outcome on the assumption that A is performed. According to CDT, by contrast, you should choose the action with the highest causal expected value (CEV), calculated as follows: EV (A) (A )V (O ), C = ∑ n i=1 P ⇒ O i CDT i where This proposal might seem obvious to some but to argue for it we must first say a bit more about the nature of value functions in decision theory. For our purposes, there are two salient ways of thinking about these value functions. First, we can think of them as externally given, and therefore independent of the choice of a particular decision theory. Second, we can think of them as constructed, via a representation theorem, from the agent's relational attitude. Let us begin with the former. Given that we presented the Wager as an argument for why altruistic and morally motivated agents should generally favour EDT in the face of decision-theoretic uncertainty, it is natural to think of the value functions as being externally provided by some moral theory. In particular, suppose that the agent facing the Moral Newcomb problem is certain of some axiology, and that she does not take there to be any relevant side constraints: in deciding whether to one-box or two-box, she simply wants to perform the action that in expectation leads to the best outcome according to her favoured axiology. The only thing she's uncertain about is how she should take into account information about causation and correlation when making her decision. In this case it is clear that she does not face a problem of intertheoretic comparisons, because both V CDT and V EDT are given by the relevant axiology. The same point holds if she is instead acting under axiological uncertainty. If she has settled on some value function V which represents the value she assigns to outcomes in light of her axiological uncertainty (for example, V might be the expected value of the outcome under axiological uncertainty), then this is the value function that should be used to calculate both causal and evidential expected value. Again, if it were the case that V CDT ≠ V EDT , then at least one of the two would not accurately represent how she values states of affairs under axiological uncertainty. In general, if there is some externally given value function over outcomes, there will not be any problem of intertheoretic comparisons to begin with. But suppose that there isn't any externally given value function. A second approach is to say that the value functions are constructed (along with the corresponding probability functions) via a representation theorem from the agent's relational attitudes, typically her preferences over options. A representation theorem shows that if an agent's preferences over options satisfy certain conditions, then she can be represented as maximising expected value with respect to some probability function P and some value function V, in the sense that for any pair of options A and B , she prefers A to B just in case the expected value of A is greater than the expected value of B (with the expected value calculated relative to P and V). Suppose therefore that both V EDT and V CDT , along with their respective probability functions P EDT and P CDT , are constructed via representation theorems. In order to compare them, we need a framework which is broad enough to be able to express both EDT and CDT. This means that, for our purposes, the most relevant result is Joyce's (1999:239) very general representation theorem, which can underwrite both evidential and causal decision theory. Joyce takes as his starting point both a preference relation and a comparative belief relation. Both of these relations are conditional (or suppositional ) in the sense that they are defined over options of the form ' A on the condition that B .' For example, I might prefer going for a walk on the supposition that its sunny to staying inside reading on the supposition that it rains, or I might find rain on the supposition that it's cloudy more likely than a breeze on the supposition that it's sunny. Joyce imposes requirements on both the preference relation and the comparative belief relation which together ensure the existence of a unique probability function and a unique (up to positive linear transformation) value function. By imposing further conditions on the comparative belief relation so as to make the supposition behave either like evidential or causal supposition, he is able to derive both EDT and CDT as special cases. Now, if we take the relevant preferences and comparative beliefs to be the ones that the agent in fact has, then we cannot construct both V CDT and V EDT simultaneously. After all, if she satisfies the conditions needed for EDT she will fail to satisfy the conditions needed for CDT. But we can proceed as follows. In order to construct a cardinal value function, it is sufficient to consider the agent's preferences and comparative beliefs on just a single supposition. So all we have to do is find a proposition such that the preferences and comparative beliefs of EDT are in agreement with those of CDT on the supposition that this proposition is true. And here a natural candidate suggests itself: the tautology. Evidential and causal supposition will not yield different constraints on preferences and comparative beliefs when the proposition being supposed is the tautology. This 14 allows us to say that that EDT and CDT share the same value function. 15 14 The only case in which this would not work is if there is some proposition A such that P( A | ⊤) = P(⊤⇒ A ) = 0, yet some other proposition B such that P( B ⇒ A ) > 0. However, there is still a residual worry that these claims can only establish that the two value functions should be positive linear transformations of one another, and not the stronger conclusion that they should be identical. From the perspective of first-order decision theory, the choice of one positive linear transformation over another is simply an arbitrary representational decision with no practical significance. But once we take decision-theoretic uncertainty into account, this choice does become practically significant. In particular, if V CDT = k V EDT for some k > 1, then the stakes for EDT will have to be higher in order for one-boxing to be rational than if V CDT = V EDT . Borrowing terminology that 16  MacAskill (2014:136)  introduced in the context of moral uncertainty, let us say that V CDT is an amplification of V EDT just in case V CDT = k V EDT for some k > 1. Although there is something to be said for the possibility of amplified moral theories, the case is significantly weaker for decision-theoretic value functions. But if we do regard it as possible that V CDT is an amplification of V EDT , then and CDT, but between various amplifications of these two theories. We can represent such an agent as simply being uncertain between EDT and CDT by aggregating the amplified value functions as follows: and . (EDT | EDT )V V EDT = ∑ k P k k (CDT | CDT )V V CDT = ∑ k P k k But even now, it is unclear what might lead you to assign proportionally greater credence to one amplification of CDT than to the same amplification of EDT. That is, it should be the case that, for any k , P(EDT k | EDT) = P(CDT k | CDT). If your credences in amplified theories is symmetrical in this way, then the argument that you should hedge when the stakes are much higher for EDT would still go through. In order to deny this conclusion via an appeal to amplification, you would have to claim that we should have proportionally greater credence in more amplified versions of CDT and, moreover, that this difference is so large that it cancels out the higher stakes for EDT. We can't see any plausible argument for this being the case. However, one might in response give up the underlying assumption that there is some fact of the matter as to which intertheoretic comparisons are correct, and instead say that this is a subjective matter for the agent to decide herself. In particular, one might take the view that these intertheoretic comparisons are only meaningful insofar as the probability and value functions they rely upon can be constructed via a representation theorem for decision-theoretic uncertainty. Such a representation theorem would show under what conditions an agent can be represented as maximising 'meta' expected value. Although no such result has (to our knowledge) been produced, if it looks at all like an ordinary representation theorem for empirical uncertainty, it would follow that the agent is free to make any intertheoretic comparisons she likes (provided only that the value functions V EDT and V CDT are positive linear transformations of one another). While some preferences and comparative beliefs 19 will entail that V CDT = V EDT , others will entail that V CDT = k V EDT , and there is nothing to rule out the latter as irrational. Now, if one does take seriously the idea that the disagreement between EDT and CDT does not concern the nature of value, but rather the question of which type of supposition is decision-relevant, one might wish to impose further conditions to ensure that only those relational attitudes which entail that V CDT = V EDT are rational. If one can impose such further conditions, then the use of representation theorems to construct value functions does not in itself entail that intertheoretic comparisons will be subjective, but we concede that those who are not persuaded by the idea that the disagreement between EDT and CDT does not concern the nature of value have no reason to impose those further conditions. Let's take stock. If the value function is externally given, for instance by an axiology, we can straightforwardly conclude that V EDT = V CDT . If on the other hand both V EDT and V CDT are constructed via representation theorems, we can at the very least conclude that they must be positive linear transformations of one another. Moreover, we argued that if one accepts that the dispute between EDT and CDT does not concern the nature of value, one should accept the stronger conclusion that the two value functions should be identical. We then noted that if one does regard it as a genuine possibility that V CDT is an amplification of V EDT , one should also concede that both EDT and CDT come in different versions, corresponding to different amplifications of their value functions. Moreover, we argued that there is no good reason to assign proportionally greater credence to one amplification of CDT than to the same amplification of EDT. Finally, we conceded that if one takes the question of intertheoretic comparisons to be a subjective one for the agent to settle herself, then all we can say is that the two value functions must be positive linear transformations of one another. Although we take V EDT = V CDT to be the most natural way of making the intertheoretic comparison, our argument that hedging in the face of decision-theoretic uncertainty typically favours EDT does not require this particular account. Rather, in the finite case, our argument requires that the comparison is not so strongly biased in favour of CDT so as to outweigh the intuitively higher stakes for EDT. In the infinite case, our argument only requires that the two value functions are positive linear transformations of one another. Given that any plausible account (even if subjective) will satisfy this latter requirement, we don't have to appeal to any potentially controversial claims about intertheoretic comparisons in the infinite case. You might object that our proposal about how to make intertheoretic value comparisons 'stacks the deck' in favour of EDT because, as the evidentialist's wager shows, in general under decision-theoretic uncertainty, with this choice of intertheoretic comparisons, one will act in accordance with EDT's recommendation. As an analogy, consider the question of how to do intertheoretic value comparisons between average and total utilitarianism. Suppose we fix such comparisons by stipulating that in a world with only one individual, the difference in value between any two actions is the same for average and total utilitarianism. This implies that in a world with n individuals, giving each of them one additional unit of welfare would be n times more valuable according to total utilitarianism than according to average utilitarianism. In effect, this means that total utilitarianism will swamp average utilitarianism: if one should hedge under moral uncertainty, then one will generally go with total rather than average utilitarianism whenever they are in conflict, because the stakes are much higher for the former theory. It has been argued that this is a good reason for thinking that we should not make the intertheoretic comparisons between average and total utilitarianism in this way. Perhaps using 20 V EDT = V CDT to settle comparisons between EDT and CDT is analogous to using the one-person world to settle comparisons between total and average utilitarianism, and should be rejected for the same reason. However, the analogy is flawed. When normalising average and total utilitarianism at the one-person world, there are no scenarios in which the stakes are higher for average utilitarianism than for total utilitarianism. By contrast, using the case of no non-causal correlations to normalise does allow for scenarios in which the stakes are higher for CDT than for EDT, as the following example shows. \n Evil Twin In front of you are two boxes, A and B. You can choose either B only, or both A and B. Box A is guaranteed to contain ten thousand dollars to be donated to an effective charity, whereas box B may or may not contain twenty thousand dollars to be donated to an effective charity. A perfectly reliable predictor has made a prediction about your decision. If she predicted that you would take both boxes, she left box B empty. If she predicted that you would take box B only, she put twenty thousand in that box. However, you also know that your evil twin is facing the same decision problem. Being evil, he will donate the money to an anti-charity. One dollar to the anti-charity precisely counterbalances one dollar to the charity. However, all of the monetary amounts in his decision problem are half the size of yours. Being your twin, his decision is perfectly correlated with your own. For CDT, the fact that your evil twin also faces a similar decision problem makes no difference to the stakes: CEV(Two-box) -CEV(One-box) = $10,000. But for EDT, it means that the stakes are half as big as they would otherwise have been: EEV(One-box) -EEV(Two-box) = $5,000. Hence our proposal for how to do intertheoretic comparisons, when combined with a claim about correlations, now yields the result that the stakes are lower for EDT than for CDT, rather than the other way around. Therefore, it is not true that our account makes EDT swamp CDT in general. Whether or not it does will depend on which correlations the agent takes to hold. \n Finite Case We have argued (or at least attempted to make plausible) that it is rational to hedge in the face of decision-theoretic uncertainty. That is, we have argued that even if your credence in CDT is substantially higher, you should nevertheless follow EDT if the stakes are much higher for EDT. We have also presented an account of intertheoretic comparisons that allows us to say when the stakes are higher for one decision theory than another. Together, these imply that if the expected number of correlated decision-makers is large enough, you should one-box in the Moral Newcomb problem even if you have significantly higher credence in CDT than in EDT. Recall that the possible payoffs are as follows: Cure in both Cure in one only \n Take one box Ten lives Nothing Take both boxes Eleven lives One life As we are assuming a perfectly reliable predictor, this means that, before taking any correlated agents into account, the stakes are nine times higher for evidential than for causal decision theory. Suppose now that you have merely 1% credence in EDT, and 99% credence in CDT. If we were then trying to maximise expected value over decision-theoretic uncertainty, the existence of correlated agents would have to increase the relative stakes for EDT by a factor of 11 in order for one-boxing to be the rational option. Why should one expect there to be all these correlated agents facing Moral Newcomb problems? Our argument doesn't require that the correlation in question be perfect. Consider now the vast number of humans and similarly reasoning aliens that could exist in the future. For example,  Bostrom (2013:18)  estimates that over the course of the future, Earth could sustain 10 16 lives of normal duration. If we instead assume that we will at some point spread beyond Earth, or that life will eventually be primarily digital, he gives the corresponding estimates of 10 34 and 10 54 life years respectively. Probably, some of these future people will be similar to you in terms of how they approach Newcomblike problems. Therefore, your decision to one-box constitutes evidence that they will also one-box. Of course, the evidence isn't perfect, but if the number of correlated agents is sufficiently large, the impact will be the same as that of many identical copies. For example, if your decision to one-box only increased the probability that the correlated agents one-box by 1%, there would only have to be a thousand agents who are facing problems similar to Moral Newcomb and who are correlated at this level in order for hedging to be rational. Of course, the assumption of a perfect predictor is not realistic. When we relax this assumption, we will again have to increase the number of correlated agents in order for hedging to be rational. But in doing so, we will not have to posit an unreasonably large number of correlated agents. For example, if the predictor is only 60% accurate, there would have to be 8⅓ times as many correlated agents. Now, establishing what credence distribution one should have over the number of correlated agents facing decision problems of this kind, and their degree of correlation, is a thorny empirical matter over which there will be reasonable disagreement. Yet we believe that the numbers provided here are conservative, and that it would certainly not be unreasonable for someone to have such beliefs in light of the vast number of people that could exist in the future.  21 22  This establishes that if you are a morally motivated and altruistic agent, you should one-box in Moral Newcomb even if you have significantly higher credence in causal than evidential decision theory. But earlier, we claimed that there is nothing special about the Moral Newcomb case, and that our reasoning therefore supports the following more general conclusion: In general, and across a wide variety of decision contexts, if you are a morally motivated and altruistic agent, and are uncertain between EDT and CDT, you should typically act in line with the former even if you have significantly higher credence in the latter. Is this more general claim correct? Or could it be that, although the Wager works in the Moral Newcomb case, there are other cases in which EDT and CDT come apart, where hedging under decision-theoretic uncertainty doesn't lead an altruistic agent to choose the option recommended by EDT? Recall that what is driving our argument is the claim that your decision is correlated with the decisions of other agents. This means that your decision to perform an action provides evidence that correlated agents will also perform that action. Moreover, if a correlated agent's decision to perform that action provides evidence that some desirable outcome will obtain, then your decision also provides evidence that that outcome will obtain. In general, the existence of correlated agents will affect the stakes for EDT, but not for CDT. Now, as we saw in the Evil Twin case, it is possible to construct cases in which such correlations have the effect of decreasing the stakes for EDT. If the decrease is sufficiently large, the wager will run in the opposite direction: even if one has significantly higher credence in EDT than in CDT, one should nevertheless act in accordance with the latter. However, we contend that such cases are few and far between. In the Evil Twin case, you are only correlated with one other agent who faces a problem with lower stakes, and whose decision will partially cancel out (by donating to an anti-charity) the good you achieve through your own decision (by donating to a charity). But once we take into account the vast number of people who may exist in the future, it's overwhelmingly likely that whenever your decision is correlated with one person's decision, it will also be correlated with very many other people's decisions. It would therefore be a striking coincidence if the effect of these correlations would be to lower the stakes for EDT. If you have sufficiently many evil twins (or evil n -tuplets), the stakes will be higher for EDT than CDT (although now EDT will also recommend two-boxing). If you have just one good twin (and no evil twins), the stakes will also be higher for EDT. In general, once we take into account that there will be very many correlated agents, the only case in which the stakes will be lower for EDT is when (i) either the degrees of correlation or the \"isolated\" stakes faced by correlated agents are sufficiently low, and (ii) performing the action that EDT would have recommended in the absence of correlated agents provides evidence that these agents will partially cancel out the good you achieve through your own decision (in the same sense that your evil twin partially cancels out the good you achieve through one-boxing). What if one believes that anti-correlated agents vastly outnumber correlated ones? If one believes this in the Moral Newcomb case, the conclusion of our argument is that one should two-box rather than one-box. However, this does not constitute a counterexample to our claim that a morally motivated and altruistic agent should generally act in line with EDT even if she has significantly higher credence in CDT. To see this, note that even if the agent were certain of EDT, she would still two-box rather than one-box. Rather than being a counterexample, this is simply a case in which the agent's belief that there are many more anti-correlated than correlated agents (together with the assumption that she is altruistic and morally motivated) imply that EDT recommends a different option than what one might naïvely expect. What's more, the stakes are again higher for EDT than they are for CDT, so in this sense it's still EDT that is driving the decision.  23  In summary, the existence of correlated decision-makers will affect the stakes for EDT but not for CDT. We have argued on empirical grounds that it's reasonable to believe that there are sufficiently many such correlated decision-makers so as to make hedging by following the recommendation of EDT rational. The empirical argument was based on the assumption that the universe is finite. So let's now consider what happens if the universe is instead infinite. \n Infinite Case If, as many of our best cosmological theories imply, the universe is infinite, and every physically possible configuration of matter is realised in infinitely many regions of spacetime, there will clearly be sufficiently many correlated agents. Indeed, there will be infinitely many identical copies of you who 24 are facing the same decision situation. So you might think that, if anything, the argument for the Wager becomes stronger if the universe is infinite. But the infinite case gives rise to a host of further complications, and we need to introduce additional principles to be able to compare worlds that contain infinite amounts of value, or to be able to compare actions in such worlds. We will not be able to undertake a complete survey of proposed principles so, instead, we will merely note that the argument goes through on at least one leading account of infinite ethics. Our first problem: In infinite worlds, can we even say that EDT recommends one-boxing over two-boxing in Moral Newcomb ? If you one-box, you obtain strong evidence that infinitely many other agents will receive ten doses of the cure. But if you two-box, you obtain strong evidence that infinitely many other agents will receive one dose of the cure. In standard cardinal arithmetic, the total number of doses will be the same in both cases, thereby seemingly implying that EDT will be indifferent between the two actions. But that seems like the wrong conclusion. So we should invoke additional principles that allow us to discriminate between different infinite worlds. To keep things simple, let us for the moment only consider agents who are perfect duplicates of you, and let us compare two worlds: in w 1 , you all one-box and save ten lives each, and in w 2 , you all two-box and and save one life each. We will assume that these two worlds are perfectly alike in all other respects. That is, these two worlds share all of the same locations, and for all locations except those corresponding to lives that are saved in one world but not in the other, the value at that location is the same in both worlds. To solve the first problem, we need an account which allows us to say that w 1 is better than w 2 . One such account is that of  Vallentyne and Kagan (1997) . Let R 1 , R 2 , R 3 , … be a sequence of larger and larger spacetime regions that grow without bound, centred on the location in which you find yourself. The proposal is as follows: \n Catching Up For any worlds w 1 and w 2 , if there is some n such that for any m > n , the value in region R m of w 1 is greater than the value in region R m of w 2 , then the value of w 1 is greater than that of w 2 .  25  If we assume that there is some n such that for any m > n , the region R m contains more correlated than anti-correlated agents, it follows that w 1 is better than w 2 . This means that although anti-correlated agents may outnumber correlated ones in some finite regions, we can always find larger regions that contain them where the reverse is true. If we are happy to assume that there are more correlated than anti-correlated agents in a finite universe, we should also be happy to make this further assumption in the infinite case. So the Catching Up principle allows us to make sense of the idea that w 1 is better than w 2 , and therefore that EDT recommends one-boxing in Moral Newcomb . The second problem is to make sense of the claim that the decision in Moral Newcomb is much higher stakes for EDT than it is for CDT, and that you should therefore hedge under decision-theoretic uncertainty. That is, we need to be able to say that even if your credence in CDT is significantly higher, you should nevertheless follow the recommendation of EDT. On its own, Catching Up doesn't allow us to say this, because it only tells us how to compare worlds that contain potentially infinite amounts of value. But what we need is a way of comparing actions in such worlds. In light of this, Arntzenius (2014) suggests a modification of the view. His proposal is simple: just replace talk of value in a region with talk of expected value in a region. \n Expected Catching Up For any actions A and B , if there is some n such that for any m > n , the expected value of A in region R m is greater than the expected value of B in region R m , then A is better than B . In order to apply this to the case at hand, let's suppose for the moment that our approach to decision-theoretic uncertainty is to maximise meta expected value, where the meta expected value of an action A is given as For EDT, the stakes will EV (A) EEV (A)P (EDT ) EV (A)P (CDT ). M = + C keep growing without bound as we consider larger and larger regions. By contrast, for CDT the stakes will remain the same in any finite region. Therefore, we will be able to find an n such that for any m > n , the meta expected value in R m of one-boxing is greater than that of two-boxing, and thereby conclude that one-boxing is rational. But importantly, this conclusion does not depend on the assumption that maximising meta expected value is the appropriate way to behave under decision-theoretic uncertainty. For any non-zero credence in EDT and any view about how large the difference in stakes must be in order for hedging to be rational given that credence, we will always be able to find a region R n such that for any m > n , the difference in stakes between EDT and CDT is sufficiently large to justify one-boxing. Note, in addition, that this also means that we don't have to rely on any possibly contentious claims about how to do intertheoretic comparisons between EDT and CDT. As long as V CDT = k V EDT + m for some finite k and m , it follows that we will be able to find an appropriate region R n . So if Expected Catching Up is correct, the Wager goes through in infinite worlds as well. And some other accounts, such as Bostrom's (2011) \"hyperreal\" approach, would also endorse the Wager.  26  Roughly speaking, by representing the value of infinite worlds using hyperreal numbers, we are able to say that the world in which all correlated agents receive ten doses of the cure is better than the world in which they only receive one dose of the cure, even though both worlds contain infinite amounts of value. And given that hyperreal numbers can be straightforwardly multiplied with probabilities, this approach allows us to make sense of the claim that the stakes are higher for EDT than for CDT.  27  Of course, however, infinite ethics is a fiendish topic, and there is no consensus on what the right view is, because any view faces grave problems. Expected Catching Up , for example, conflicts with the very plausible Pareto principle: \n Pareto For any worlds w 1 and w 2 that contain exactly the same individuals, if every individual has at least as much welfare in w 1 as she does in w 2 , then w 1 is at least as good as w 2 . If in addition at least one individual has more welfare in w 1 than in w 2 , then w 1 is better than w 2 . To see this, assume for simplicity that either all correlated agents save ten lives each and all anti-correlated agents save one life each, or vice versa. You can either one-box or two-box. This gives us four worlds: one in which you and all correlated agents one-box, one in which you one-box but your correlated agents two-box, and so forth. We can now consider permutations of these worlds that contain exactly the same individuals at exactly the same welfare levels, except that all people saved by anti-correlated agents are closer to you in spacetime than any of the people saved by correlated agents. 27 However, see  Arntzenius (2014:49-52)  for discussion of some difficulties for the hyperreal approach. With respect to these permuted worlds, Expected Catching Up implies that two-boxing has greater expected value than one-boxing. In both cases, we calculate expected value by assigning the same probability to a world and its permutation, so if one-boxing has greater expected value in one case but not the other, it follows that not all permuted worlds are equally as good as the worlds they permute. \n But this is precisely what Pareto rules out. However, as  Askell (2018)  shows, if one endorses Pareto and some other very plausible assumptions, one will have to accept that there is widespread incomparability between infinite worlds. So we can state our conclusion, with respect to the infinite case, in a restricted form: if one wishes to avoid widespread incomparability between infinite worlds, then one will probably endorse a view that supports the Wager. \n Conclusion We have argued that an altruistic and morally motivated agent who is uncertain between EDT and CDT should in general act in accordance with the former, even if she has greater credence in the latter. To arrive at this conclusion, we first argued that it is rational to hedge in the face of decision-theoretic uncertainty. That is, if the stakes are much higher for one theory than another, and the credences assigned to the two theories aren't very different, then one should act in accordance with the higher-stakes theory. In order to say whether the stakes are higher for one theory rather than another, we need an account of intertheoretic value comparisons. We argued that such comparisons should be made by letting EDT and CDT have the same value function over outcomes. We noted that, given the assumption of altruism, the existence of correlated decision-makers will affect the stakes for EDT but not for CDT. Finally, we argued that for reasonable credence distributions over EDT and CDT, there will be sufficiently many correlated decision-makers so as to make it rational in general to follow the recommendation of EDT. In the finite case, we appealed to estimates about how many people will exist in the future. In the infinite case, there is guaranteed to be sufficiently many correlated agents, but further complications arise. We showed that on one natural way of solving these, the argument still goes through. If we are altruistic and morally motivated agents, we should mostly follow EDT. 17 plausibly we should also think that both EDT and CDT come in different versions, corresponding to different amplifications. That is, each way of setting the parameter k would give us a different version 18 of evidential decision theory (EDT k ) and a different version of causal decision theory (CDT k ). So now an agent facing decision-theoretic uncertainty would have to divide her credence not between EDT \n Suppose now that you have 90% credence in EDT and only 10% credence in CDT. From the 3 perspective of EDT, you have nothing to lose by two-boxing, whereas from the perspective of CDT, you have $1M to lose by one-boxing. In short, two-boxing state-wise (or 'theory-wise') dominates one-boxing. Thus it seems clear that you should two-box, in at least some sense of 'should'. 4    In Equal Amounts , EDT is indifferent between the two actions and CDT prefers one over the other.But we can also construct a case where CDT is indifferent between the two actions and EDT prefers only. Money in both Money in one only Take one box $1M $0 Take both boxes $2M $1M In this case, the evidential expected value of taking both boxes is the same as that of taking one box only, whereas the causal expected value of taking both boxes is $1M greater than that of taking one box front of you are two boxes, A and B. You can choose either B only, or both A and B. Box A is guaranteed to contain $1M, whereas box B may or may not contain $1M. A perfectly reliable predictor has made a prediction about your decision. If she predicted that you would take both boxes, she left box B empty. If she instead predicted that you would take box B only, she put $1M in that box. one over the other. Consider: Empty Box In front of you are two boxes, A and B. You can choose either B only, or both A and B.Box A is guaranteed to be empty, whereas box B may or may not contain $1M. A perfectly reliable predictor has made a prediction about your decision. If she predicted that you would take both boxes, she left box B empty. If she instead predicted that you would take box B only, she put the million in that box. \n A ⇒ O i denotes the counterfactual conditional \"if I were to do A , then O i would occur.\" The CEV of an action A is the sum product of the value of each outcome and the probability that A causes that outcome. Thus EDT and CDT are both versions of the claim that one should maximise expected value. They only disagree on how this expectation is to be calculated: according to EDT, one should use the conditional probability, whereas according to CDT, one should use the probability of the counterfactual conditional. That is, they only differ in those cases where one would intuitively expect EDT and CDT to come apart. This observation suggests a natural procedure for intertheoretic value comparisons. If the disagreement between EDT and CDT only concerns which type of probability should be used to calculate expected value, then we should not construe them as having different value functions.Intuitively, a decision theory does not prescribe that you value outcomes in some particular way.Instead, it tells you how to act in light of the values (and beliefs) you in fact hold. Therefore, we will argue that the problem of intertheoretic value comparisons is solved by requiring that V EDT = V CDT . By imposing this condition we place the two theories on a common scale, thereby rendering intertheoretic value comparisons straightforward. To determine whether the stakes are higher for EDT or CDT in the Moral Newcomb problem, we simply calculate all expected values with respect to the shared value function and then compare the two quantities EEV( One-box ) -EEV( Two-box ) and CEV( Two-box ) -CEV( One-box ). Moreover, this proposal has the desirable implication that the evidential and causal expected value of an action A will only differ if there is some outcome O such that P( O | A ) ≠ P( A ⇒ O ). \n\t\t\t The simplifying assumption of a perfect predictor is clearly unrealistic, but it would be easy to set up the numbers so that the same implications follow by merely assuming a good predictor instead.2 More precisely, CDT tells you to perform the action with the highest causal expected value (CEV), where the CEV of an action A is the sum product of the value of each outcome and the probability that A causes that outcome. By contrast, EDT tells you to perform the action with the highest evidential expected value (EEV), where the EEV of an action A is the sum product of the value of each outcome and the probability of that outcome on the assumption that A is performed. \n\t\t\t For discussions of different senses of 'should' in the context of moral uncertainty, see for example MacAskill, Bykvist and Ord (2019, chapter 1) and Sepielli (2010, chapter 1). \n\t\t\t The dominance argument above can be seen as a special case of such stakes sensitivity, where there's something at stake for one theory but not for the other. \n\t\t\t A preliminary survey using Amazon Mechanical Turk (N = 331) found that when the possible contents of the two boxes were $3.00 and $0.05, 74% of participants one-boxed, whereas when the possible contents were $2.55 and $0.45, only 51% did so. On the other hand, there was no statistically significant difference between the second case and the case in which the possible contents were $2.25 and $0.75 (48% one-boxers) ([NAME REDACTED]). \n\t\t\t  See Sepielli (2013)  and MacAskill, Ord, and Bykvist (forthcoming) for further discussion. \n\t\t\t For discussion of intertheoretic comparisons in the case of moral uncertainty, see Sepielli (2009 Sepielli ( , 2010, MacAskill (2014 ,   chapter 4), Tarsney (2018 ), and MacAskill, Ord and Bykvist (2019 . \n\t\t\t More generally,Joyce (1999:178)  concedes that Jeffrey's (1983)  evidential decision theory has the correct account of value (\"desirability\") and argues that causal expected utility is simply desirability from the perspective of the supposition that an act will be performed. The same sentiment is expressed byBradley (2017:170). Again, these claims indicate that an agent's value function should not depend on which decision theory she takes to be correct. \n\t\t\t By contrast, in the case where V CDT = V EDT + m , the choice of m will not affect whether or not hedging is rational.17  To get a sense for what amplified moral theories might look like, consider the following case. Suppose you initially believe that, morally speaking, humans matter much more than other animals, so that one unit of human welfare is a hundred times more valuable than one unit of animal welfare. Later, however, you become convinced that animals matter just as much as humans. Now, intuitively there are two ways in which you could become convinced of this: you could come to believe that animals matter much more than you initially thought, or you could come to believe that humans matter much less than you initially thought. The two resulting theories would have the same cardinal structure, yet one of them would regard both human and animal welfare as more valuable than the other(MacAskill 2014:138). Whatever one thinks of this, it seems much more difficult to tell a similar story for the case of decision-theoretic value functions. \n\t\t\t  This is what MacAskill (2014)  concludes in his discussion of amplification in the context of moral uncertainty. \n\t\t\t Perhaps the most relevant existing result is Riedener's (forthcoming) representation theorem for axiological uncertainty.However, the framework he uses is not able to capture the difference between evidential and causal decision theory. \n\t\t\t See for example Hedden (2016)  and Cotton-Barratt, MacAskill and Ord (forthcoming). \n\t\t\t Moreover, if you object to the argument on empirical grounds alone, you still have to accept the surprising implication that beliefs about distant future agents are relevant for how you should act under decision-theoretic uncertainty. \n\t\t\t You might object that perhaps there are also anti-correlated decision makers out there, who tend to one-box when you two box. If there are as many anti-correlated decision-makers as there correlated ones, this would effectively cancel things out for EDT. If there are sufficiently many more anti-correlated than correlated ones, EDT would recommend two-boxing rather than one-boxing. Our argument assumes that there are many more correlated decision-makers than there are anti-correlated ones. But unless you have some particular reason to think that you are special, this seems like a standard inductive inference. Finally, if you remain unconvinced of the claim that there are more correlated than anti-correlated decision makers, you shouldn't believe that there are equally many decision makers of both types, but rather that there are many more anti-correlated ones. After all, it would be a rather striking coincidence if the two types of decision makers were evenly balanced. But if there are more anti-correlated than correlated decision-makers, then our argument would support the different but similarly startling conclusion that even if you're virtually certain of EDT, you should nevertheless two-box in the Moral Newcomb case. \n\t\t\t If one believes that there are equally many correlated and anti-correlated agents (counting oneself among the correlated ones), then EDT will be indifferent between the two options, and one's decision will therefore be driven by CDT. But such symmetry should be regarded as extremely unlikely. \n\t\t\t  See Garriga and Vilenkin (2001)  and Knobe, Olum and Vilenkin (2006)  for discussion of these cosmological theories. \n\t\t\t This is roughly equivalent to the SBI2 proposal ofVallentyne and Kagan (1997:14), skipping over some technical details.This proposal assumes that it makes sense to speak of the same location in the two worlds being compared. In the present case, this assumption will be satisfied. \n\t\t\t Another class of theories that will also endorse the Wager are those that discount value by distance, at least provided that the discount rate is not steep enough to lower the stakes for EDT to the point where hedging no longer favours one-boxing, although it's fair to say that such theories are not regarded as leading contenders.", "date_published": "n/a", "url": "n/a", "filename": "MacAskill_et_al_Evidentialist_Wager.tei.xml", "abstract": "Suppose that an altruistic and morally motivated agent who is uncertain between evidential decision theory (EDT) and causal decision theory (CDT) finds herself in a situation in which the two theories give conflicting verdicts. We argue that even if she has significantly higher credence in CDT, she should nevertheless act in accordance with EDT. First, we claim that that the appropriate response to normative uncertainty is to hedge one's bets. That is, if the stakes are much higher on one theory than another, and the credences you assign to each of these theories aren't very different, then it's appropriate to choose the option which performs best on the high-stakes theory. Second, we show that, given the assumption of altruism, the existence of correlated decision-makers will increase the stakes for EDT but leave the stakes for CDT unaffected. Together these two claims imply that whenever there are sufficiently many correlated agents, the appropriate response is to act in accordance with EDT.", "id": "852c2f28a5ae0f5ff2bec8bbcc7f40c9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "On the promotion of safe and socially beneficial artificial intelligence", "text": "Introduction The challenge of building technologies that are safe and beneficial for society is really two challenges in one. There is the technical challenge of developing safe and beneficial technology designs, and there is the social challenge of ensuring that such designs are used. The two challenges are interrelated. Motivating technologists to pursue safe and beneficial designs is itself a social challenge. Furthermore, motivating people to use safe and beneficial designs is made easier when the designs also have other attractive features such as low cost and ease of use; creating these features is a technical challenge. This paper is concerned with the social challenge. Specifically, the paper examines a range of approaches to motivating technologists to pursue safe and beneficial technology designs. The paper focuses on artificial intelligence (AI) technologies, including both near-term AI and the proposed future ''strong'' or ''superintelligent'' AI that some posit could bring extreme social benefits or harms depending on its design. Much of the paper's discussion also applies to other technologies. That AI has significant social impacts is now beyond question. AI is now being used in finance, medicine, military, transportation, and a range of other critical sectors. The impact is likely to grow over time as new technologies are adopted, such as autonomous vehicles and lethal autonomous weapons (unless the latter are banned or heavily restricted). The prospects for strong AI are controversial; this paper takes the position that the stakes are sufficiently high that it warrants careful attention even if the probability of achieving it appears to be low. Regardless, while the paper is motivated in part by the risk of strong AI, the insights are more general.  1  For brevity, the paper uses the term ''beneficial AI'' to refer to AI that is safe and beneficial for society. It also uses the term ''promoting beneficial AI'' to refer to efforts to encourage technologists to design and build beneficial AI, or to have them avoid designing and building AI that is not beneficial. The technologists include AI researchers/ designers/developers (the paper uses these terms more or less interchangeably) as well as adjacent personnel in management, business development, etc. The paper's implicit value judgment is that AI should be built so as to have net benefits for the whole of society-or, in the face of uncertainty, net expected benefits. This is to say that AI should not be built just for the sake of making it more capable or more intellectually interesting. Also, AI should not be built for the benefit of its builders if this comes at the expense of society as a whole. These positions may seem to cut against ideals of academic freedom, intellectual progress, and capitalist entrepreneurship. The paper takes the position that these ideals are only worth pursuing to the extent that doing so benefits society. Were it the case that the field of AI was already focused on beneficial design, efforts to promote it would be unnecessary. Unfortunately, this is not the case. The field is largely focused on building systems that are more capable, regardless of whether this capability is used for social good. This tendency and the need to shift it are articulated, for example, by distinguished AI researcher Stuart Russell: I think the right approach is to build the issue [beneficial AI] directly into how practitioners define what they do. No one in civil engineering talks about ''building bridges that don't fall down.'' They just call it ''building bridges.'' Essentially all fusion researchers work on containment as a matter of course; uncontained fusion reactions just aren't useful. Right now we have to say ''AI that is probably beneficial,'' but eventually that will just be called ''AI.'' [We must] redirect the field away from its current goal of building pure intelligence for its own sake, regardless of the associated objectives and their consequences  (Bohannon 2015:252) . This paper takes on the challenge of how to shift the AI field toward greater emphasis on social impacts. The paper reviews and critiques existing proposals for promoting beneficial AI and lays out a wider portfolio of techniques. A core criticism is that existing proposals neglect human psychology: They seek to influence AI researchers without thinking carefully about how AI researchers are influenced. Neglect of human psychology limits the portfolio of techniques that get considered for promoting beneficial AI and reduces the effectiveness of those techniques that are considered. In some cases, measures taken in ignorance of human psychology can even backfire, resulting in less beneficial AI than would have existed without any measures taken. Broadly speaking, there are two types of measures for promoting beneficial AI. Extrinsic measures are imposed on AI designers from the outside so that they adopt beneficial designs even if they do not want to. These measures include constraints that require or forbid certain designs, incentives to encourage or discourage certain designs, and compliance measures to make sure that constraints or incentives are being followed. Intrinsic measures are cultivated within AI designers so that they want to adopt beneficial designs. These measures include the cultivation of social norms and the framing of communications. There can also be intrinsic effects of extrinsic measures, such as when a technology ban sparks backlash, making designers less interested in adopting beneficial designs. Extrinsic and intrinsic measures are discussed in Sects. 2 and 3, respectively.  2  Prior discussions of the promotion of beneficial AI focus almost exclusively on extrinsic measures. 3 However, both types of measures can help. Indeed, strategies based purely on extrinsic measures run a significant risk of having no net effect or even being counterproductive. As this paper discusses, the success of extrinsic measures often depends heavily on intrinsic factors. Meanwhile, pure intrinsic strategies can be quite effective, as can hybrid extrinsicintrinsic strategies. The bottom line is that the promotion of beneficial AI demands attention to human psychology. \n Extrinsic measures \n Constraints Constraints are perhaps the simplest means of promoting beneficial AI, and the most simplistic. The logic is direct: If a design feature is beneficial, require it; if it is harmful, ban it. A ban on dangerous AI technologies is implicit in  Joy's (2000)  call for relinquishment of dangerous AI, and it is explicit in other work  (Posner 2004; Wilson 2013; Yampolskiy and Fox 2013) . Requirements for beneficial AI designs are less common in discussions of AI. Requirements could be used to insist that AI developers adopt certain beneficial designs such as verification, validity, security, and control  (Russell et al. 2015)  and avoiding negative side effects, avoiding reward hacking, scalable oversight, safe exploration, and robustness to distributional shift  (Amodei et al. 2016) . When constraints work, they guarantee that AI designs are beneficial. However, they also limit the freedom and flexibility of AI designers. This can provoke backlash by AI designers, which is one example of an intrinsic effect of extrinsic measures (Sect. 2.4). Even without backlash, enacting constraints can require extensive institutional and political changes, which makes them difficult to implement. Constraints pose other challenges as well. One is that unless they are carefully designed, they can unwittingly constrain the wrong features, resulting in AI that is less beneficial. Designing successful AI constraints can thus require close interaction between AI experts and policy makers. A related issue is that constraints may need to be constantly updated as AI technology evolves. An AI design attribute that was harmful in early AI may be beneficial in later AI, and vice versa. New design attributes will also emerge; these could merit new constraints. One potential solution is to phrase constraints in more general terms  (Moses 2007) ; for AI, this could mean requiring AI designers to select the most beneficial available design. Such an approach makes constraints more durable as AI technology evolves, but it comes at the expense of making it more difficult to verify compliance. \n Incentives Incentives are the primary extrinsic alternative to constraints. Unlike constraints, incentives let AI developers keep the freedom to pursue whatever designs they desire. Incentives act by changing the rewards or penalties for specific designs, so as to push developers in different design directions. The AI literature has focused mainly on monetary incentives, such as by offering funding for beneficial AI research  (McGinnis 2010)  or by making AI companies pay compensation when found liable for the consequences of harmful AI  (Gurney 2013 ). However, incentives can also take on other forms, such as social praise/scorn or professional advancement/sanction for developing beneficial/harmful AI. Incentives hold several advantages over constraints. By giving AI designers more freedom, they are less likely to provoke backlash, which can make them easier to implement.  4  Policy makers can also avoid the need to identify beneficial design attributes by applying incentives to completed technologies, as in liability schemes (which impose penalties for AIs that turn out to be harmful) and in prize competitions (which can offer rewards for AIs that turn out to be beneficial).  5  The core disadvantage of incentives is that they do not guarantee that beneficial AI designs would be chosen. An AI developer could simply choose to forgo the reward or pay the penalty and continue to develop harmful AI. The logical response to this is to strengthen the incentive, though this can provoke more backlash and can even erode the distinction between incentives and constraints. Indeed, a constraint could be defined as an incentive with an infinite or maximal reward/penalty. \n Compliance Constraints and incentives are generally built on the premise that AI designers do not want to choose beneficial designs. Otherwise, they would not need to be constrained or incentivized. AI designers thus have reason to avoid complying with the constraint or the incentive. When this is the case, mechanisms for achieving compliance are needed, including mechanisms for monitoring for noncompliance and mechanisms for enforcing penalties for noncompliance. A simple approach to monitoring is to require AI groups to submit research proposals to review boards prior to conducting the research. AI review boards could be analogous to the review boards that already exist at many universities and other institutions for reviewing medical and social science research  (Yampolskiy and Fox 2013) . Existing review boards are focused mainly on harms that could be caused by the conduct of the research, in particular through abuse of human research subjects. AI review boards would need an expanded scope that includes the societal impacts of the products of research. Such an expansion would be in line with a more general expansion of research ethics to include ethical assumptions embedded within the research (such as ethical positions implicit in AI objective functions) and ethical aspects of the societal impacts of research  (Schienke et al. 2009 (Schienke et al. , 2011 . One challenge for the review boards proposal is that some AI groups may not be at institutions that have review boards and thus could go undetected. Hard-to-monitor groups can include private companies, especially startup companies, and groups in unregulated countries. Indeed, there is some concern that national AI regulations could simply push AI research to unregulated countries. This problem can be addressed via international AI treaties  (Posner 2004; Wilson 2013) , though this is easier said than done. Another approach in some AI monitoring proposals is to implement a draconian mass surveillance regime in order to find any harmful AI group wherever they are (e.g., Shulman 2009). Suffice to say, such surveillance poses extreme problems for privacy, intellectual property, and trustful geopolitical relations. It is a downside of extrinsic measures that such problematic surveillance mechanisms would even be considered. If monitoring succeeds and harmful AI groups are identified, the next step is to enforce whatever penalty is to be applied.  6  Enforcement should in general be less of a challenge than monitoring because AI groups have limited means of resisting penalties. Government penalties can be imposed through the threat or application of force. Institutional penalties can be imposed via the threat or application of measures such as firing noncompliant personnel. These sorts of actions could succeed at achieving compliance to extrinsic measures, but, in addition to being intrinsically regrettable (i.e., one should not want AI developers to lose their jobs or suffer physical harm), they can also alienate AI developers, provoke backlash, and motivate them to relocate to unregulated places. The net effect of the typical extrinsic measure is to unwittingly create an antagonistic relationship between AI developers and those who seek beneficial AI, which makes beneficial AI more difficult to achieve. The essential solution to this predicament is to consider intrinsic factors, i.e., the psychology of AI developers. \n Intrinsic aspects of extrinsic measures Consider two different extrinsic measures: a ban on flag burning and a requirement that dog owners cleanup after their dogs. Flag burning is legal in several countries, including the USA. The USA has repeatedly considered a constitutional amendment to ban flag burning. Such a ban has never passed, but here is one analysis of what would happen if it did: Few people have burned the American flag in recent years, and it is reasonable to suppose that a constitutional amendment making it possible to criminalize flag burning would have among its principal consequences a dramatic increase in annual acts of flag burning. In fact, adopting a constitutional amendment may be the best possible way to promote the incidence of flag burning  (Sunstein 1996 (Sunstein :2023 . Why would a ban on flag burning increase the rate of flag burning? One potential mechanism is that the ban would draw attention to flag burning, which is otherwise something that not many people think about. Some portion of people who think about it may then go on to do it. Another potential mechanism is that the ban changes the social meaning of flag burning. Without the ban, flag burning is seen as distasteful and anti-patriotic, whereas with the ban, flag burning becomes a patriotic rebellion against a bad law. The story of dog cleanup is exactly the opposite. The following describes the effect of dog cleanup laws in Berkeley. Similar effects have been observed in other locations, such as New York City  (Krantz et al. 2008) . After the Berkeley town council enacted an ordinance requiring owners to cleanup after their dogs, the sidewalks became much cleaner, even though officials never issued citations for breaking the law. The law apparently tipped the balance in favor of informal enforcement. Citizens became more aggressive about complaining to inconsiderate dog owners, and, anticipating this fact, dog owners became more considerate  (Cooter 2000:11) . The dog cleanup story is notable because it achieved positive outcomes without enforcing compliance. There was no draconian surveillance, and no need to worry about dog owners relocating to places that lacked cleanup laws. Instead, the law prompted dog owners and their neighbors to police themselves. The point of the comparison between flag burning and dog cleanup is that people can react in different ways to different extrinsic measures and that this can significantly affect outcomes. Indeed, how people react can be the difference between negative outcomes (i.e., the extrinsic measure is counterproductive) and positive outcomes. These two cases are directly applicable to extrinsic measures for promoting beneficial AI. In short, extrinsic measures for promoting beneficial AI should strive to be like dog cleanup, not like flag burning. This means that extrinsic measures should aim to be considered desirable to AI developers-measures should be something that AI developers would want to comply with, not something they would want to push back against. In order to figure out what the effect of an extrinsic measure would be, it is necessary to consider not just the extrinsic measure itself, but also the intrinsic factors, i.e., the social psychology of AI communities. A fuller accounting of intrinsic factors is presented in Sect. 3, but here some intrinsic factors that are specific to extrinsic measures. One recurrent finding is that monetary incentives can reduce intrinsic motivation  (Deci 1971; Vohs et al. 2006) . This means that once the money is gone, people become less motivated to perform some task than they would have been if there never was any money. In contrast, social praise and encouragement can increase intrinsic motivation  (Deci 1971) . Finally, carefully designed extrinsic measures can use a psychological phenomenon called cognitive dissonance to increase people's intrinsic motivation for a given type of activity  (Dickerson et al. 1992; Sect. 3.6) . \n Intrinsic factors and intrinsic measures This section presents a variety of intrinsic phenomena of relevance to promoting beneficial AI. Some of the phenomena are dedicated intrinsic measures for promoting beneficial AI, and some of the phenomena are factors that can play a role in a range of intrinsic and extrinsic measures. All of the phenomena are oriented toward motivating AI developers to want to pursue beneficial designs. \n Social context and social meaning People often behave differently depending on the social setting or context that they are in. For example, some people go to the library to study because the presence of other studious people compels them to focus more, whereas if they stayed at home, they would let themselves get distracted. Efforts to promote beneficial AI can be more effective in certain social contexts. For example, some beneficial AI measures benefit from cooperation across AI groups in order to avoid some groups choosing harmful designs that give them competitive advantage. Research in other contexts has found that it is often easier to achieve cooperation when people are together in a group than when they are in isolation  (Krantz et al. 2008) . Therefore, workshops, conferences, and other meetings, or even group phone calls could all be more effective at achieving cooperation among AI groups than private conversations or written statements that would be read in private. Second, promoting beneficial AI can be more effective in social contexts where beneficial AI is considered desirable. For any given AI researcher, he or she is more likely to support beneficial AI if he or she is in a group of people who openly support beneficial AI than if he or she is alone or in a group of people who do not openly support beneficial AI. Support for beneficial AI can thus be expanded by creating and expanding groups of open beneficial AI supporters. Openness is important: other people will not be influenced by the group's support for beneficial AI if they are not in any way aware of this support. Related to social context is the concept of social meaning. An act or idea can have a different meaning depending on the social context. For example, the act of flag burning can have an anti-patriotic meaning if it is not banned or a patriotic meaning if it is banned (Sect. 2.4). Efforts to promote beneficial AI should aim for it to have a positive social meaning. This can be accomplished, for example, by testing prospective measures using focus groups of AI researchers in order to gauge their reactions. \n Social norms Norms are that which is considered normal. Social norms are norms held by groups of people about the normal behaviors of people in that group, including which behaviors normally are practiced (''descriptive norms'') and which behaviors normally should be practiced (''injunctive norms'')  (Lapinski and Rimal 2005) . Norms can vary from group to group and place to place. For example, in some places, it is normal for pedestrians to cross the street whenever it is safe, whereas in other places, it is normal to wait for the streetlight to turn green. Norms can also change over time. For example, slavery was once considered normal throughout much of the world, but this norm has reversed in many places. Specific social contexts can also activate certain social norms. For example, the same group of people may show different norms in a library than in a nightclub. Beneficial AI can be a norm, i.e., concern for social impacts can be considered normal among AI developers. Beneficial AI as a social norm is implicitly at the heart of Stuart Russell's call for the AI community to abandon ''its current goal of building pure intelligence for its own sake, regardless of the associated objectives and their consequences'' and instead ''build the issue [beneficial AI] directly into how practitioners define what they do'' (Bohannon 2015:252). It is difficult to overstate the importance of social norms for beneficial AI. If beneficial AI is considered normal, then it will be easier to achieve compliance on extrinsic measures and easier to succeed with intrinsic measures, and there will be less need for either sort of measure in the first place because many AI researchers will already be pursuing beneficial designs. How can one go about shifting social norms in AI? Answering this question would benefit from dedicated research on AI social norms, but some insights can be gained from other issues. For example,  Posner (2000 Posner ( :1784 Posner ( -1785  lists several ways in which social norms for paying taxes can be strengthened, including showing that other people also pay taxes, creating social sanctions for not paying taxes, 7 and reminding people of their civic obligation to pay taxes.  Schultz et al. (2007)  find that descriptive norms messages can reduce deviance but can also have a counterproductive ''boomerang'' effect for people with better-than-normal behavior and that this effect can be attenuated with injunctive norms messages of social approval for good behavior. These approaches could be adapted for promoting beneficial AI by showing that other AI researchers also support it, creating social sanctions for those who do not support it and social approval for those who do, and cultivating a sense of duty for AI researchers to attend to the social impacts of AI. \n Messengers and allies In promoting beneficial AI, it is not just what is said that matters, but also who says it. This is because people interpret meanings differently depending on who is conveying a message. This holds for AI researchers just as much as it does for anyone else. The fact that this happens cuts against the scientific ideal of objectivity, but scientists are humans too, and try as we might to avoid it, the identity of the messenger still matters for how we react to messages. One important class of messenger is the fellow AI researcher. Prior research has found that when conveying messages about ethics and social impacts to young scientists (e.g., graduate students or postdocs), it is important that the messages be delivered by established researchers in that field instead of by outside ethics professionals  (Schienke et al. 2009 (Schienke et al. , 2011 . Using in-field researchers shows that ethics and social impacts is something that ''we'' (i.e., people in the field) care about and is not just something that ''they'' (i.e., people outside the field) want ''us'' to care about. This is reflective of a more general tendency for people to respond better to messages from other people in their ''in group.'' Thus, to the extent possible, messages should be selected from respected AI researchers. The quotes in this paper from Stuart Russell offer one example of this. Sometimes, using ''out-group'' messengers can also succeed. This can occur when the out-group is seen as having some sort of high status. For example, funders, institutional leadership, and policy makers can fit this role because they have some control over AI researchers' professional success and some credentials for setting social norms and research directions. Celebrities-including academic and business celebrities like Stephen Hawking and Bill Gates-can also fit this role because they can be perceived as successful, important, and influential. It is important that these people deliver thoughtful messages so as to not come off as ''ignorant blowhards'', but when they do deliver thoughtful messages, their influence can be substantial. As AI becomes more widely used across society, new out-group allies will also emerge. For example, the automotive industry is currently applying AI to autonomous vehicles. Automobiles must be safe, otherwise they will not sell and manufacturers can face steep liability claims. The automotive industry likewise has a safety culture that is currently pushing back against the AI culture of rapid product development and postlaunch debugging. As Ford CEO Mark Fields put it in a recent interview, ''You can't hit control-alt-delete when you're going 70 miles an hour''  (Griffith 2016) . Insofar, as AI researchers would like the business opportunities of autonomous vehicles, they may be motivated to listen to the safety messages from messengers like Fields. Another important potential ally could be found in militaries. This may seem surprising, since militaries are associated with violence and potential misuse of AI. However, militaries can be influential to AI researchers because they provide extensive AI research funding. Furthermore, militaries can be more safety conscious than is commonly believed. One study of AI researcher opinion found that a slight majority viewed the US military as the most likely institution to produce harmful AI, but that ''experts who estimated that the US military scenario is relatively safe noted that the US military faces strong moral constraints, has experience handling security issues, and is very reluctant to develop technologies that may backfire (such as biological weapons)''  (Baum et al. 2011:193) . For these reasons, military officials will often be motivated to promote beneficial AI. For their messages to resonate with AI researchers, they must achieve trust, which could be difficult given AI researchers' negative perceptions of the military. If trust can be achieved, then the military could offer another powerful ally in efforts to promote beneficial AI. \n Framing To frame is to present a message in a certain way. Framing is a matter of not what is said but how it is said. Skillful communication frames messages to achieve certain effects for certain audiences. For example, climate change is commonly framed as an environmental issue, which resonates with liberals more than with conservatives. For conservative audiences, climate change is sometimes framed as a threat to national security or to the economy, or framed as an injustice that compels religious duty  (Shome and Marx 2009) . Using the wrong frame for the wrong audience can lead people to reject a cause that they might otherwise support. AI technologies can be framed in a variety of ways as well. Unfortunately, existing messages about beneficial AI are not always framed well. One potentially counterproductive frame is the framing of strong AI as a powerful winner-takes-all technology. This frame is implicit (and sometimes explicit) in discussions of how different AI groups might race to be the first to build strong AI (e.g., Shulman 2009;  Armstrong et al. 2016) . The problem with this frame is that it makes a supposedly dangerous technology seem desirable. If strong AI is a winner-takes-all technologies race, then AI groups will want to join the race and rush to be the first to win. This is exactly the opposite of what the discussions of strong AI races generally advocate-they postulate (quite reasonably) that the rush to win the race could compel AI groups to skimp on safety measures, thereby increasing the probability of dangerous outcomes. Instead of framing strong AI as a winner-takesall race, those who are concerned about this technology should frame it as a dangerous and reckless pursuit that would quite likely kill the people who make it. AI groups may have some desire for the power that might accrue to whoever builds strong AI, but they presumably also desire to not be killed in the process. Another potentially counterproductive frame is the framing of AI researchers as people who do not want to pursue beneficial designs. This framing is implicit in the existing literature's emphasis on extrinsic measures: Extrinsic measures are used because AI researchers would not want to pursue beneficial designs. In the worst case, heavy-handed extrinsic measures could counterproductively instill a social norm of AI researchers not pursuing beneficial measures. This would be a reaction like ''I didn't think I was someone who ignores social impacts, but since you mention it, I guess I am.'' Light penalties, cooperative relationships, and positive framing of AI researchers could make them more inclined to pursue beneficial designs. Finally, extreme proposals like draconian global surveillance can inadvertently frame efforts to promote beneficial AI as being the problem, not the solution. In other words, it could give the impression that the efforts are misguided and causing more harm than good. The potential for aggressive beneficial AI efforts to be perceived as conspiratorial should not be discounted. Conspiracy theories are already prominent in the perceptions of global warming held by policy makers and the public  (Lewandowsky et al. 2015) . If AI succumbs to similar conspiracy theories, this could make it more difficult to promote beneficial AI. And even without conspiracy theories, floating extreme proposals can make the beneficial AI cause seem at best out of touch, and at worst outright harmful. \n Stigmatization Stigmatization is a type of framing oriented toward making an object or an activity feel socially undesirable or even taboo. Stigmatization can be an effective technique for preventing the use of dangerous technologies. For example, stigmatization has been used repeatedly for international arms control, most notably to achieve the 1997 Ottawa Treaty banning landmines and the 2008 Convention on Cluster Munitions banning cluster bombs, and currently to promote nuclear disarmament  (Borrie 2014) . The experience with landmines and cluster munitions is notable in part because the treaties have wider compliance than they have ratification. That is, some countries (e.g., the USA) have not ratified the treaties, yet they still act in compliance with them, even though they have no legal obligation to do so. The effort to stigmatize landmines and cluster munitions was so successful that the legal requirements are not necessary to achieve the social goal. The international community's experience with stigmatization could be applied to dangerous AI. Stigmatizing dangerous AI can help build support for extrinsic measures such as national regulations and international treaties. However, even in the absence of any extrinsic measures, stigmatization can still lead people to avoid building dangerous AI. A successful stigmatization effort causes people to not want to do the stigmatized activity. Stigmatization thus complements extrinsic measures. Indeed, it is difficult to imagine bans on dangerous AI technologies succeeding without an effective stigmatization effort. In order for stigmatization to work, it must be based on a convincing argument. The landmine and cluster munitions campaigns were so successful because there was a sound moral and legal argument against these weapons, specifically that they cause indiscriminate harm to civilian populations. This argument was crucial for convincing countries to reject the weapons even though they had previously been accustomed to using them. Likewise, any attempts to stigmatize specific AI technologies must be based on some compelling reason. The potential for an AI technology to cause a massive global catastrophe is an example of such a reason. Another challenge of stigmatization is that it can be alienating to those who disagree with it and/or those who are involved in a stigmatized activity. People do not like to think of themselves as being involved in a stigmatized activity and can resent being accused. This is seen, for example, in current debates about nuclear weapons, in which the nuclear-armed states distance themselves from efforts to stigmatize nuclear weapons even while they share an underlying concern about the weapons' catastrophic impacts. Likewise, efforts to stigmatize harmful AI should distinguish between the harms of the AI and the character of the AI designer so that the AI designers know that they are not seen as bad people and that they would be embraced if they switch to beneficial designs. \n Cognitive dissonance Cognitive dissonance occurs when a person holds conflicting beliefs in her or his mind. People typically seek to resolve the dissonance of conflicting beliefs by rejecting one of them. For example, people might reject reports that a seemingly good person committed a terrible harm on grounds that ''He or she couldn't possibly have done that.'' An example of relevance to beneficial AI is in the relation between economic activity and beliefs about climate change. Around 2008, public belief in the scientific evidence of climate change declined. One explanation for the decline is that the economic recession induced cognitive dissonance. In response to the recession, people want the economy to grow. However, economic activity typically increases greenhouse gas emissions, thereby worsening climate change. This creates dissonance between the belief that there should be more economic growth and the belief that climate change is a problem. Some data suggest that some people handled this dissonance by rejecting the scientific evidence of climate change, even though the evidence itself is about the natural environment, not the economy  (Scruggs and Benegal 2012) . Similarly, cognitive dissonance could lead AI researchers to reject claims that AI could be harmful. The potential for harmful AI could imply that AI research should be restricted, bringing AI researchers diminished intellectual freedom and business opportunities and in some cases can even threatening their livelihoods. Just as people may reject the science of climate change when the economy is bad, AI researchers may reject evidence or argument about harmful AI when their welfare is at stake. Like all people, AI researchers can have ''motivated reasoning'' in which they are motivated not by a goal of accuracy but instead by other goals, such as the goal of believing that they are a good person  (Kunda 1990) . Therefore, in order to improve salience, messaging about beneficial AI should strive to be sympathetic to AI researchers' intellectual and professional interests, and extrinsic and intrinsic measures alike should strive to minimize the intellectual and professional downsides that AI researchers could face. Cognitive dissonance can also be used to promote certain beneficial activities.  Dickerson et al. (1992)  studied the combined effect of people making a public commitment to conserving water and people being told that they had taken long showers. People took shorter showers only when they made a public commitment and were told they had taken long showers. If only one of the two conditions were present, they took longer showers. The explanation is that people had a cognitive dissonance between their public commitment and their self-perception of taking long showers, which they resolved by taking shorter showers. Similar effects have been observed in other contexts, with the strongest effect coming when people make public commitments or advocacy of an action and then are privately reminded of their own failures to perform that action  (Stone and Fernandez 2008) . This model could be adapted for beneficial AI by having AI researchers make public commitments to beneficial AI (such as via professional societies or in classrooms) and then being privately informed that some of their designs are not beneficial. This technique is likely to be more effective if an injunctive social norm for beneficial AI is already in place, because then AI researchers would be motivated to resolve the cognitive dissonance in favor of more beneficial AI. \n Conclusion As the societal impacts of AI continue to increase, it becomes more and more important to promote the development of AI that is safe and beneficial to society-abbreviated throughout this paper as ''beneficial AI''. Thus far, discussions of how to promote beneficial AI have focused mainly on extrinsic measures that are imposed on AI designers even if they do not want to pursue beneficial AI. These measures come in the form of constraints and incentives, and they are often accompanied by measures for monitoring and enforcing compliance. Extrinsic measures can be successful at promoting beneficial AI, but they can be difficult to implement and can be resisted by AI developers. The success of extrinsic measures can also depend heavily on intrinsic factors, i.e., on how AI developers react to the measures. If the reaction is favorable, AI developers could comply on their own without external monitoring and enforcement. Alternatively, if the reaction is unfavorable, AI developers could even pursue less beneficial designs than they would if there were no extrinsic measures in place. Meanwhile, a range of dedicated intrinsic measures are available; these encourage AI developers to want to pursue beneficial designs. Social norms be shifted toward caring about beneficial design. Messengers can be selected, and messages can be framed to resonate with AI developers and entice them to want to pursue beneficial designs. Harmful AI designs can be stigmatized such that AI developers want to avoid them. AI developers can make commitments to choosing beneficial designs that can, via cognitive dissonance, lead them to do so. This paper draws heavily from research on other issues due to a lack of prior research on intrinsic aspects of beneficial AI. The paper makes especially heavy use of research on environmental issues because these issues have seen robust social and psychological research. Many insights from these other issues apply to beneficial AI, but beneficial AI will inevitably have its own unique characteristics. Therefore, dedicated research on the social psychology of AI research communities is needed to understand the effectiveness of both extrinsic and intrinsic measures. Such research should be included in broader research agendas for beneficial AI. One potential objection to intrinsic measures is that they are unreliable because they depend on each AI researcher to cooperate. There is some truth to this. However, extrinsic measures can also be unreliable-hence the effectiveness of extrinsic measures can depend on intrinsic factors. Regardless, 100 % success is an inappropriate goal. The aim of any measure should be to reduce the harms and increase the benefits of AI to society. A measure that does this should be pursued, even if it still leaves some potential for harm or for loss of benefit. Given the stakes involved in AI, all effective measures for promoting beneficial AI should be pursued. \t\t\t On the extrinsic/intrinsic distinction, see e.g.,Markowitz and Sharif  (2012:246)  and references therein.3  SeeSotala and Yampolskiy (2014, Sect.  3) for a review in the context of strong AI. Russell et al. (2015)  also discuss a range of predominantly extrinsic measures. A notable exception to the focus on extrinsic measures is Russell's emphasis on shifting ''how practitioners define what they do''(Bohannon 2015:252). \n\t\t\t AI & Soc (2017) 32:543-551    \n\t\t\t Incentives can nonetheless provoke significant backlash. For example, in the United States, environmentalists have long pursued incentive-based policies such as taxes on pollution in order to appeal to industry interests that do not want constraints, yet industry has been largely successful at avoiding these incentive-based policies.5  Incentives for completed technologies are less relevant for AIs that could be catastrophic because there may be no penalty that could adequately compensate for damages and, in the extreme case, no one alive to process the penalty.AI & Soc (2017) 32:543-551   \n\t\t\t Conversely, when beneficial AI groups are identified, rewards are to be applied, though this is less of a challenge because AI groups are likely to seek rewards, not dodge them. \n\t\t\t Social sanctions are an extrinsic measure, specifically an incentive using a social penalty, though they can also cultivate certain social norms.AI & Soc (2017) 32:543-551", "date_published": "n/a", "url": "n/a", "filename": "Baum2017_Article_OnThePromotionOfSafeAndSociall.tei.xml", "abstract": "This paper discusses means for promoting artificial intelligence (AI) that is designed to be safe and beneficial for society (or simply ''beneficial AI''). The promotion of beneficial AI is a social challenge because it seeks to motivate AI developers to choose beneficial AI designs. Currently, the AI field is focused mainly on building AIs that are more capable, with little regard to social impacts. Two types of measures are available for encouraging the AI field to shift more toward building beneficial AI. Extrinsic measures impose constraints or incentives on AI researchers to induce them to pursue beneficial AI even if they do not want to. Intrinsic measures encourage AI researchers to want to pursue beneficial AI. Prior research focuses on extrinsic measures, but intrinsic measures are at least as important. Indeed, intrinsic factors can determine the success of extrinsic measures. Efforts to promote beneficial AI must consider intrinsic factors by studying the social psychology of AI research communities.", "id": "43fccd354cd6cd09ab35ddf53d4f8f36"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kaj Sotala"], "title": "How feasible is the rapid development of artificial superintelligence?", "text": "Introduction Since  Turing (1950) , the dream of artificial intelligence (AI) research has been the creation of a 'machine that could think'. While current expert consensus is that the creation of such a system will take several decades if not more  (Müller and Bostrom 2016) , recent progress in AI has still raised worries about the challenges involved with increasingly capable AI systems (Future of Life Institute 2015,  Amodei et al 2016) . In addition to the risks posed by near-term developments, there is the possibility of AI systems eventually reaching superhuman levels of intelligence, eventually breaking out of human control  (Bostrom 2014) . Various research agendas and lists of research priorities have been suggested for managing the challenges that this level of capability would pose to society  (Soares and Fallenstein 2014 , Russell et al 2015 , Amodei et al 2016 , Taylor et al 2016 . For managing the challenges presented by increasingly capable AI systems, one needs to know how capable those systems might ultimately become, and how quickly. If AI systems can rapidly achieve strong capabilities, becoming powerful enough to take control of the world before any human can react, then that implies a very different approach than one where AI capabilities develop gradually over many decades, never getting substantially past the human level  (Sotala and Yampolskiy 2015) . We might phrase these questions as: 1. How much more capable can AIs become relative to humans? 2. How easily (in terms of time and resources required) could superhuman capability be acquired? Views on these questions vary. Authors such as  Bostrom (2014)  and  Yudkowsky (2008)  argue for the possibility of a fast leap in intelligence, with both offering hypothetical example scenarios where AI rapidly acquires a dominant position over humanity. On the other hand,  Anderson (2010)  and  Lawrence (2016)  appeal to fundamental limits on predictability-and thus intelligence-posed by the complexity of the environment. The argument for limits of intelligence  (Anderson 2010 , Lawrence 2016 ) could be summarized as saying that, past a certain point, increased intelligence is only of limited benefit, for the unpredictability of the environment means that you would have to spend exponentially more resources to evaluate a vastly increasing amount of possibilities. Noise also accumulates over time, reducing the reliability of the available models. For many kinds of predictions, increasing the prediction window would require an exponential increase in the amount of measurements  (Martela 2016) . For instance, weather models become increasingly uncertain when projected farther out in time. Forecasters can only access a limited amount of observations relative to the weather system's degrees of freedom, and any initial imprecisions will magnify over time and cause the accuracy to deteriorate  (Buizza 2002) . In general, the accuracy of any long-term prediction will be limited by data uncertainty, model uncertainty, and the available computational time. Similar considerations would also apply to attempts to predict things such as the behaviour of human societies. The advantage that even a superhuman intelligence might have over humans may be limited. On the other hand, it is not obvious whether this point of view really is in conflict with the assumption of AI being able to quickly grow to become powerful. There being limits to prediction does not imply that humans would be particularly close to the limits, nor that it would necessarily take a great amount of time to move from sub-human to superhuman capability. This article attempts to consider these questions by considering what we know about expertise and intelligence. After reviewing the relevant research on human expertise, we will discuss its relevance for AI, and consider how AI could improve on humans in two major aspects of thought and expertise, namely simulation and pattern recognition. Our current conclusion is that although the limits to prediction are real, it seems like AI could still substantially improve on human intelligence. The possibility of AI developing significant real-world capabilities in a relatively brief time seems like one that cannot be ruled out. Before examining these questions, we need to consider the definition of 'capability' in more detail, and justify our focus on intelligence as prediction ability. \n Capability and intelligence as prediction ability Bostrom (2014, p 39) defines a superintelligence as 'any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest'. Additionally,  Bostrom (2014, chapter 3)  defines three subcategories of a superintelligence. A speed superintelligence thinks faster than humans; a collective superintelligence is composed of many smaller intellects whose overall performance outstrips that of existing cognitive systems; and a quality superintelligence is one that is at least as fast as a human mind, and vastly qualitatively smarter. In a footnote to his original definition, Bostrom notes that this definition of superintelligence can be compared with  Legg (2008) , who defines intelligence as 'an agent's ability to achieve goals in a wide range of environments'. This definition, originally from  Legg and Hutter (2007a) , draws on a collection of 70 definitions of intelligence  (Legg and Hutter 2007b)  from various professional groups, dictionaries, psychologists, and AI researchers.  Legg and Hutter (2007a)  argue that this definition summarizes the essential features in the various surveyed definitions, in that they generally discuss an individual who is interacting with some environment that is not fully known, trying to achieve various goals in that environment, and learning and exploring during that interaction. Some definitions of intelligence list traits which are not explicitly included in this definition; for example, a group statement signed by 52 psychologists  (Gottfredson 1997a)  includes in intelligence 'the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience'. However,  Legg and Hutter (2007a)  argue that all of these abilities are ones that allow humans to achieve goals, so are implicitly included in the Legg and Hutter definition. Additionally, Legg and Hutter suggest that their definition is more general, as there could exist intelligences which did not have all of these specific capabilities, but did have alternative capabilities which allowed them to achieve their goals.  Legg and Hutter (2007a)  offer a formalization of their definition, cast in a reinforcement learning framework. Briefly, the formalization involves an agent which interacts with an environment in discrete timesteps; on each timestep, the agent chooses an action and receives both an observation and a reward. An agent is (universally) intelligent to the extent that it can maximize its reward over the space of all environments drawn from a universal distribution. This definition and formalization is a view of intelligent performance as a learning and prediction problem: an agent is intelligent to the extent that it can learn to predict, using the smallest possible set of observations, which of its actions will deliver the greatest amount of reward in the environment that it is interacting with. Out of  Bostrom's (2014)  superintelligence subtypes, a mind that was superintelligent under such a view would most likely fall under the category of a quality superintelligence. Some of the examples that  Bostrom (2014)  offers to illustrate the concept of quality intelligence include nonhuman animals that cannot achieve human cognitive capabilities even when 'intensely trained by human instructors', as well as human deficits such as autism spectrum disorders that may impair e.g. social functioning. Implicit in these examples is the notion that nonhuman animals and individuals with cognitive deficits cannot achieve the same level of performance in various domains as unimpaired humans do, even when given the same opportunities to observe and learn about the domains in question. They lack the cognitive capabilities that would allow them to utilize their observations to learn to predict which kinds of actions would provide the greatest success in the relevant domains. Under this view, we can more precisely rephrase our first question, 'how much more capable can AIs become relative to humans', as 'how much better than humans can AIs become in using small amounts of sense data to learn to predict which actions most effectively further their goals'. For the purposes of this discussion, we will also assume that 'predicting which actions most effectively further one's goals' is an accurate characterization of what human expertise (in any given domain) means. As we will discuss in the following section, the foundation of human expertise lies in acquiring the necessary knowledge to instantly see, when faced with some situation, the right course of action for that situation. \n The development of human expertise Ideally, we might turn to theoretical AI research for a precise theory about acquiring cognitive capabilities. Unfortunately AI research is not at this point yet. Instead we will consider the research on human expertise and decision-making. \n Expertise as mental representations There exists a preliminary understanding, if not of the details of human decision-making, then at least the general outline. A picture that emerges from this research is that expertise is about developing the correct mental representations  (Klein 1999, Ericsson and Pool 2016) . A mental representation is a very general concept, roughly corresponding to any mental structure forming the content of something that the brain is thinking about  (Ericsson and Pool 2016) . Domain-specific mental representations are important because they allow experts to know what something means; know what to expect; know what good performance should feel like; know how to achieve the good performance; know the right goals for a given situation; know the steps necessary for achieving those goals; mentally simulate how something might happen; learn more detailed mental representations for improving their skills  (Klein 1999, Ericsson and Pool 2016) . Although good decision-making is often thought of as a careful deliberation of all the possible options, such a type of thinking tends to be typical of novices  (Klein 1999) . A novice will have to try to carefully reason their way through to an answer, and will often do poorly regardless, because they do not know what things are relevant to take into account and which ones are not. An expert does not need to-they are experienced enough to instantly know what to do. A specific model of expertise is the recognition-primed decision-making model  (Klein 1999) . First, a decision-maker sees some situation, such as a fire for a firefighter or a design problem for an architect. The situation may then be recognized as familiar, such as a typical garage fire. The expectations arising from mental representations also give rise to intuition. As one example,  Klein (1999)  describes the case of a firefighter lieutenant responding to a kitchen fire in an ordinary one-story residential house. The lieutenant's crew sprayed water on the fire, but contrary to expectations, the water seemed to have little impact. Something about the situation seemed wrong to the lieutenant, who ordered his crew out of the house. As soon as they had left the house, the floor where they had been standing collapsed. If the firefighters had not pulled out, they would have fallen down to the fire raging in the basement. The lieutenant, not knowing what had caused him to give the order to withdraw, initially attributed the decision to some form of extra-sensory perception. In a later interview, the lieutenant explained that he did not suspect that the building had a basement, nor that the seat of the fire was under the floor that he and his crew were standing on. However, several of his expectations of a typical kitchen fire were violated by the situation. The lieutenant was wondering why the fire did not react to water as expected, the room was much hotter than he would have expected out of a small kitchen fire, and while a heat that hot should have made a great deal of noise, it was very quiet. The mismatch between the expected pattern and the actual situation led to an intuitive feeling of not knowing what was going on, leading to the decision to regroup. This is intuition: an automatic comparison of the situation against existing mental representations of similar situations, guiding decision-making in ways whose reasons are not always consciously available. In an unfamiliar situation, the expert may need to construct a mental simulation of what is going on, how things might have developed to this point, and what effect different actions would have. Had the floor mentioned in the previous example not collapsed, given time the firefighter lieutenant might have been able to put the pieces together and construct a narrative of a fire starting from the basement to explain the discrepancies. For a future-oriented example, a firefighter thinking about how to rescue someone from a difficult spot might mentally simulate where different rescue harnesses might be attached on the person, and whether that would exert dangerous amounts of force on them. Mental representations are necessary for a good simulation, as they let the expert know what things to take into account, what things could plausibly be tried, and what effects they would have. In the example, the firefighter's knowledge allows him to predict that specific ways of attaching the rescue harness would have dangerous consequences, while others are safe. \n Developing mental representations Mental representations are developed through practice. A novice will try out something and see what happens as a result. This gives them a rough mental representation and a prediction of what might happen if they try the same thing again, leading them to try out the same thing again or do something else instead. Just practice is not enough, however-there also needs to be feedback. Someone may do a practice drill over and over again and think that they are practicing and thus improvingbut without some sign of how well that is going, they may just keep repeating the same mistakes over and over  (Ericsson and Pool 2016) . The importance of quality feedback is worth emphasizing. Skills do not develop unless there is feedback that is conducive to developing better mental representations. In fact, there are entire fields in which experienced practitioners are not much better than novices, because the field does not provide them with enough feedback.  Shanteau (1992)  provides the following breakdown of professions for which there is agreement on the nature of their performance (Reprinted from  Shanteau, J (1992) . Competence in experts: The role of task characteristics. Organizational  Behavior and Human Decision Processes, (53), 252-266, Copyright (1992)  In analysing why some domains enable the development of genuine expertise and others do not, Shanteau identified a number of considerations that relate to the nature of feedback. In an occupation like weather forecasting, the criteria you use for forecasting are always the same; you will always be facing the same task and can practice it over and over; you get quick and feedback on whether your prediction was correct; you can use formal tools to analyse what you predicted would happen and why that prediction did or did not happen; and things can be analysed in objective terms. This allows weather forecasters to develop powerful mental representations that get better and better at making the correct prediction. Contrast this with someone like an intelligence analyst. The analyst may be called upon to analyse very different clues and situations; each of the tasks may be unique, making it harder to know which lessons from previous tasks apply; for many of the analyses, one might never know whether they were right or not; and questions about socio-cultural matters tend to be much more subjective than questions about weather, making objective analysis impossible. In short, for much of the work that the analyst does, there is simply no feedback available to tell whether the analyst has made the right judgment or not. And without feedback, there is no way to improve one's mental representations, and thus expertise. A slightly different look on expertise is the heuristics and biases literature, which frequently portrays even experts as being easily mistaken. In contrast, the expertise literature that we have reviewed so far has viewed experts as being typically capable and as having trustworthy intuition.  Kahneman and Klein (2009)  make an attempt to reconcile the two fields, and come to agree that: • Expert intuition may be trustworthy, if the intuition relates to a 'high-validity' domain and the expert has had a chance to learn the regularities in that domain. • A domain is 'high-validity' if 'there are stable relationships between objectively identifiable cues and subsequent events or between cues and the outcomes of possible actions'. This consensus is in line with what we have covered so far, though it also includes the consideration of validity. One cannot learn mental representations that would predict a domain or dictate the right actions for different situations in a domain, if that domain is simply too complicated or chaotic to be predicted.  Kahneman and Klein (2009)  provide an illustrative example of domain being simply too hard to interpret: the question of how the history of the 20th century would have been different if the fertilized eggs that became Hitler, Stalin and Mao had been female. It seems clear that things would have developed very differently, but how exactly? There seems to be no way to know. Meanwhile, practice does help in more predictable domains. A recent meta-analysis  (Macnamara et al 2014)  on the effects of practice on skill found that the more predictable an activity was, the more practice contributed to performance in that activity. \n Implications for AI Having reviewed some necessary background, we will now finally get back to the topic of superintelligence capabilities. \n Relevance for AI Similarly to humans, AI systems cannot reach intelligent conclusions by a mere brute force calculation of every possibility. Rather, an intelligence needs to learn to exploit predictable regularities in the world in order to develop further. All machine learning based systems are based on this principle: they learn models of the world that are in this sense similar to the mental representations that humans learn. However, the models employed by current machine learning systems are much more limited than the mental representations employed by humans (Lake et al 2016).  1  Kahneman and Klein do not define what they mean by 'long-term', but geopolitical events up to a year or so away can be predicted with reasonable accuracy, with the accuracy falling towards chance for events 3-5 years away. (Tetlock and Gardner 2015, p 5). Machine learning systems are also developed for solving problems efficiently on existing computing hardware rather than for being biologically plausible. There is thus reason to expect even future AI systems to employ models which differ in various respects from the mental representations used by humans. As such, we will use the term 'mental representations' when in the context of humans, and 'models' when discussing the analogous structure in future AI systems. In a sense, mental representations contain the optimal solutions to the problems at hand  (Klein 1999 ): a human expert will have learned to identify the smallest set of cues that will let them know how to act in a certain situation; their mental representations encode information about how to choose the correct actions using the least amount of thought. In other words, an expert pays attention exactly to the features in the data which are relevant for making the decision, and acts accordingly. An AI's models could use more data and become larger than human mental representations, and identify features which humans might have missed. There is however no advantage in using more data than necessary for making the correct decision, so at least a subset of the AI's models is likely to be similar to mental representations in that they encode the smallest amount of features of the environment which allow for rapid and correct decision-making in a given context and for a given goal. It is possible that AIs would also come to have models for which this characterization was a poor fit and which were tailored for taking better advantage of e.g. an AI's ability to process more data at a time. We will not examine this more speculative possibility, as for our argument it is unnecessary to consider hypothetical models which are better than human mental representations; we are focused on establishing the possibility that roughly human-like models would already be enough to enable superhuman capability 2 . Like with human experts, machine learning also tries to focus its analysis on exactly the right number of cues that will provide the right predictions, ignoring any irrelevant information. Traditional machine learning approaches have relied extensively on feature engineering, a labor-intensive process where humans determine which cues in the data are worth paying attention to. A major reason behind the recent success of deep learning models is their capability for feature learning or representation learning: being able to independently discover high-level features in the data which are worth paying attention to, without (as much) external guidance  (Bengio et al 2012) . Being able to identify and extract the most important features of the data allows the system to make its decisions based on the smallest amount of cues that allows it to reach the right judgment-just as human experts learn to identify the most relevant cues in the situations that they encounter. Finally, the aspect of increasingly detailed mental representations giving an expert a yardstick to compare their performance against  (Ericsson and Pool 2016)  has an analogue in reinforcement learning methods. In deep reinforcement learning, a deep learning model learns to estimate how valuable a specific state of the world is, after which the system takes actions to move the world towards that state  (Mnih et al 2015) . Similarly, a human expert comes to learn that specific states (e.g. a certain feeling in the body when diving) are valuable, and can then increasingly orient their behaviour so as to achieve this state. In summary, human experts use mental representations as the building blocks of their expertise, with the models employed by current state-of-the-art AI systems having a number of key similarities. As there have been no serious alternative accounts presented of how expertise might work, we will assume that the capabilities of hypothetical superintelligences will depend, at least in part, on them developing the correct models to represent key features of the environment in a similar way as human mental representations do. This paper set out to consider two main questions: 1. How much more capable can AIs become relative to humans? 2. How easily (in terms of time and resources required) could superhuman capability be acquired? Let us now return to these. The argument for AI's predictive capabilities being limited was that there are limits to prediction, and that predicting events an ever-increasing amount forward in time requires exponential reasoning power as well as measurement points, quickly becoming intractable. How capable could AI become despite these two points? The components of human expertise might be roughly divided into two: building up a battery of accurate mental representations, and being able to use them for mental simulations. Similarly, approaches to artificial intelligence can roughly be divided into pattern recognition and modelbuilding (Lake et al 2016), depending on whether patterns in data or models of the world are treated as the primary unit of thought. As this kind of a distinction seems to emerge both from psychology and AI research, we will assume that AI's expertise will also involve acquiring models (or equivalently, doing pattern recognition) as well as accurately using them in simulations. We will consider these two separately. \n Simulation Potential capability. An interesting look at the potential benefits offered by improved simulation ability come from looking at Philip Tetlock's Good Judgement Project (GJP), popularized in the book Superforecasting (Tetlock and Gardner 2015)  3  . Participating in a contest to forecast the  2  The reader may note that the AI possibly using many different kinds of models, some of them human-like and some more advanced, has a parallel in the heterogeneity hypothesis of concepts  (Machery 2009 (Machery , 2010 , according to which the mental representations of humans do not form a natural kind and actually consist of many different kinds of mental structures that are used in different situations and for different purposes. probability of various events, the best GJP participants-the so-called 'superforecasters'-managed to make predictions whose accuracy outperformed those of professional intelligence analysts working with access to classified data 4 . This is particularly interesting as the superforecasters had no particular domain expertise in answering most of the questions, with sample questions including ones such as Tetlock and Gardner report the superforecasters' accuracy in terms of Brier score, which is a scale between 0 and 2, with 0.5 indicating random guessing 5 . On this scale, superforecasters had a score of 0.25 at the end of GJP's first year, compared to 0.37 of the other forecasters participating in the project. By the end of the second year, superforecasters had improved their Brier score to 0.07  (Mellers et al 2014) . Superforecasters could also project further out in time: their accuracy at making predictions 300 days out was better as the other forecasters' accuracy at making predictions 100 days out. In terms of being on the right side of 50/50, GJP's best wisdom-of-the-crowd algorithms (deriving an overall prediction from the different forecasters' predictions) delivered a correct prediction on 86% of all daily forecasts (Tetlock et al 2014). The superforecasters' success relied on a number of techniques, but a central one was the ability to consider and judge the relevance of a number of factors that might cause a prediction to become true or false. Tetlock and Gardner illustrate this technique by discussing how a superforecaster, Bill Flack, approached the question of whether an investigation of Yasser Arafat's remains would reveal traces of polonium, suggestive of Arafat having been poisoned by Israel. Flack started by considering what it would take for the investigation to reach a particular outcome, and realized that he did not know what the chances were of polonium traces surviving in a body for several years. He started by investigating how polonium testing worked, and concluded that enough polonium could in fact survive for it to be found in the testing. Next, Flack considered what could cause polonium to end up in the body. Israel poisoning Arafat could have done it, but so could an Palestinian enemy that Arafat had. There was also the probability of the body being intentionally contaminated after Arafat's death, by some faction trying to frame Israel for the death. Each possibility made a positive test result more probable, based on how probable those individual possibilities were. Next Flack moved on to investigate what it would take for any of the possibilities to be true. For the case of Israel poisoning Arafat, it required Israel having access to polonium; Israel being willing to take the risk of intentionally poisoning him; and Israel having the means to poison Arafat with the polonium. These possibilities served as starting points for researching the probability of the 'Israel poisoned Arafat' hypothesis, after which Flack would break down and investigate what it would take for the other hypotheses to be true. Tetlock does not go into detail about the prerequisites for being able to carry out such analysis-other than noting that it is slow and effortful-but there are some considerations that seem like plausible prerequisites. First, a person needs to have enough general knowledge to generate different possibilities for how an event could have come true. Next, they need the ability to analyse and investigate those possibilities further, either personally acquiring the relevant domain knowledge for evaluating their plausibility, or finding a relevant subject matter expert. In this example, Flack familiarized himself with the science of polonium testing until he was satisfied that it would be possible to detect polonium traces from a long time ago. This suggests a general procedure which AI could also follow in order to predict the possibility of something in which it does not yet have expertise. An AI that was trying to predict the outcome of some specific question could work tap into its existing general knowledge in an attempt to identify relevant causal factors; if it failed to generate them, it could look into existing disciplines which seemed relevant for the question. For each identified possibility, it could branch off a new subprocess to do research into that particular direction, sharing information as necessary with a main process whose purpose was to integrate the insights derived from all the relevant searches. Such a capability for several parallel streams of attention could provide a major advantage. A human researcher or forecaster who branches off to do research on a subquestion will need to make sure that they do not lose track of the big picture, and needs to have an idea of whether they are making meaningful progress on that subquestion and whether it would be better to devote attention to something else instead. To the extent that there can be several parallel streams of attention, these issues can be alleviated, with a main stream focusing on the overall question and substreams on specific subpossibilities. How much could this improve on human forecasters? Forecasters performed better when they were placed on teams where they shared information between each other, which similarly allowed an extent of parallelism in prediction-making, in that different forecasters could pursue their own angles and 4 Though this claim needs to be treated with some caution, as no official information about the intelligence analysts' performance has been published. The claim is based on Washington Post editor David Ignatius writing that 'a participant in the project' had told him that superforecasters had 'performed about 30% better than the average for intelligence community analysts who could read intercepts and other secret data'  (Ignatius 2013) . The intelligence community has neither confirmed nor denied this statement, and Philip Tetlock has stated that he believes it to be true. 5 A version of the scale which ranges between 0 and 1 is also commonly used. directions in exploring the problem. The differences between individual forecasters and teams of forecasters with comparable levels of training ranged between 0.05 and 0.10 Brier points at the end of the first year, and between 0.02 and 0.08 Brier points at the end of the second year  (Mellers et al 2014) . In humans however, it seems likely that the extent of parallelism was constrained by the fact that each forecaster had to independently familiarize themselves with much of the same material, and that their ability to share knowledge between each other was limited by the speed of writing and reading. This suggests a possibility for further improvement. In general, accurate forecasting requires an ability to carry out sophisticated causal modelling about a variety of interacting factors. Tetlock and Gardner emphasize the extent to which superforecaster forums discuss many different 'on the one hand'/'on the other hand' possibilities. In a discussion of whether Saudi Arabia might agree to OPEC production cuts in November 2014, one superforecaster noted that Saudi Arabia had large financial reserves so could afford to let oil prices run low. On the other hand, he noted, Saudi Arabia needed to raise their social spending to bolster the support for the monarchy, but yet again, Saudi Arabian rulers might view the act of trying to control oil prices as futile. The superforecaster in question concluded that the question 'felt no-ish, 80%'. (Saudis ended up not supporting production cuts.) This suggests that AI with sufficient hardware capability could achieve considerable prediction ability by its capability to explore many different perspectives and causal factors at once. The simulations of humans tend to be limited to around three causal factors and six transition states  (Klein 1999) . The discussion of the superforecasters clearly brought up many more possibilities, and their accuracy suggests moderate ability to integrate all those factors together. Yet comments such as 'feels no-ish' suggests that they still could not construct a full-blown simulation in which the various causal factors would have influenced each other based on principled rules which could be inspected, evaluated, and revised based on feedback and accuracy. This seems especially plausible given that Klein speculates the limits in the size of human simulations to come from working memory limitations. AI systems with larger working memory capacities might be able to construct much more detailed simulations. Contemporary computer models can involve simulations with thousands or tens of thousands variables, though flexibly incorporating diverse models into a single simulation will probably take considerably more memory and computing power than what is used in today's models. a model of the mind that is inspired by psychological and neuroscientific research and attempts to capture its main mechanisms. We can use LIDA to get a rough example of what having several 'streams of attention' would mean, and how information could be exchanged between them. The purpose of this example is not to suggest that an AI would necessarily work by this mechanism, but merely to make the speculation about streams of attention slightly more grounded in existing theories of how a general intelligence (the human mind) might work. Thus, to the extent that LIDA is correct as a model of human intelligence, and to the extent that the example in this box is correct about LIDA allowing for there to be several attentional streams at the same time, this provides some information about it being possible to have several such streams in minds in general, and how that might concretely work. LIDA works by means of an understand-attend-act cycle. In each cycle, low-level sensory information is initially interpreted so as to associate it with higher-level concepts to form a 'percept', which is then sent to a workspace. In the workspace, the percept activates further associations in other memory systems, which are combined with the percept to create a Current Situational Model, an understanding of what is going on at this moment. The entirety of the Current Situational Model is likely to be too complex for the agent to process, so it needs to select a part of it to elevate to the level of conscious attention to be acted upon. This is carried out using 'attention codelets', small pieces of code that attempt to train attention on some particular piece of information, each with their own set of concerns of what is important. Attention codelets with matching concerns form coalitions of what to attend, competing against other coalitions. Whichever coalition ends up winning the competition will have its chosen part of the Current Situational Model 'become conscious', broadcast to the rest of the system, and particularly Procedural Memory. The Procedural Memory holds schemes, or templates of different actions that can be taken in different contexts. Schemes which include a context or an action that matches the contents of the conscious broadcast become available as candidates for possible actions. They are copied to the Action Selection mechanism, which chooses a single action to perform. The selected action is further sent to Sensory-Motor Memory, which contains information of how exactly to perform the action. The outcome of taking this action manifests itself as new sensory information, beginning the cognitive cycle anew. Here is a description of how this process-or something like itmight be applied in the case of AI seeking to predict the outcome of a specific question, such as the 'will Saudi Arabia agree to oil production cuts' question discussed above. The decision to consider this question has been made in an earlier cognitive cycle, and information relevant to it is now available in the inner environment and the Current Situational Model. The concepts of Saudi Arabia and oil production trigger several associations in the AI's memory systems, such as the fact that oil prices will affect Saudi Arabia's financial situation, and that oil prices are also influenced by other factors such as global demand. Two coalitions of attention codelets might form, one focusing on the current financial situation and another on influences on oil prices. In LIDA, these codelets would normally compete, and one of them would win and trigger a specific action, such as a deeper investigation of Saudi Arabia's financial situation. In our hypothetical AI however, it might be enough that both coalitions manage to exceed some threshold level of success, indicating them both to be potentially relevant. In that case, new instances of the Procedural (Continued.) Memory, Action Selection and Sensory-Motor Memory mechanisms might be initialized, with one coalition sending its contents to the first set of instances and the other to another. These streams could then independently carry out searches of the information that was deemed relevant, also having their own local Situational Models and Workspaces focusing on content relevant for this search. As they worked, these streams would update the various memory subsystems with the results of their learning, making new associations and attention codelets available to all attentional streams. Their functioning could be supervised by a general highlevel attention stream, whose task was to evaluate the performance of the various lower-level streams and allocate resources between them accordingly. These simulations do not necessarily need to incorporate an exponentially increasing number of variables in order to achieve better prediction accuracy. As previously noted, superforecasters were more accurate at making predictions 300 days out than the rest of the forecasters in GJP were at making predictions 100 days out. Given that at least some of the superforecasters only used a few hours a day on making their predictions, and that they had many predictions to rate, they probably did not consider a vastly larger amount of factors than the rest of the forecasters.  Klein (1999)  offers an example of a professor who used three causal factors (the rate of inflation, the rate of unemployment, and the rate of foreign exchange) and a few transitions to relatively accurately simulate how the Polish economy would develop in response to the decision to convert from socialism to a market economy. In contrast, less sophisticated experts could only name two variables (inflation and unemployment) and not develop any simulations at all, basing their predictions mostly on their ideological leanings. Having large explicit models also allows for the models to be adjusted in response to feedback. The professor's estimate was in many extents correct, but failed to predict the government being less ruthless and more cautious than it had said it would be closing down unproductive plants. The government's caution could thus be added as an additional variable to be considered for the next model. The addition of this variable alone might then considerably increase the accuracy of the simulation. Tetlock and Gardner report that the superforecasters used highly granular probability estimates-carefully thinking about whether the probability of an event was 3% as opposed to 4%, for instance-and that the granularity actually contributed to accuracy, with the predictions getting less accurate if they were rounded to the closest 5%. Given that such granularity was achieved by integrating various possibilities and considerations, it seems like an ability to consider and integrate an even larger amount of possibilities might provide even increased granularity, and thus a prediction edge. In summary, AI could be able to run vastly larger simulations than humans could, with this possibility being subject to computing power limitations; given this, its simulations could also be explicit, allowing it to adjust and correct them in response to feedback to provide improved prediction accuracy; and it could have several streams of attention running concurrently and sharing information between each other. Existing evidence from human experts suggests that large increases to prediction capability might not necessarily need a large increase in the number of variables considered, and that even small increases can provide considerable additional gains. The amount of predictive edge that this could give to an AI as compared to a human or a group of humans is unclear, but humans do tend to prefer simple stories and explanations that are compact enough that all of the important details can be kept in mind at once. Simple hypotheses often turn out to be insufficient because the world is more complicated than a simple hypothesis allows for. Even in domains such as engineering, where there exist formal ways of modelling the entire domain, a task such as the design of a modern airplane or operating system contains too much complexity for a single person to comprehend. While the impact of uncertainty can never be eliminated, being able to take more of the world's underlying complexity into account than humans do, may provide an AI with a predictive edge at least in some domains. Rate of capability growth. How fast could AI develop the ability to run comprehensive and large simulations? 6 Creating larger simulations than humans have access to seems to require extensive computational resources, either from hardware or optimized software. As an additional consideration, we have previously mentioned limited working memory restricting the capabilities of humans, but human working memory is not the same thing as RAM in computer systems. If one were running a simulation of the human brain in a computer, one could not increase the brain's available working memory simply by increasing the amount of RAM the simulation had access to. Rather, it has been hypothesized that working memory differences between individuals may reflect things such as the ability to discriminate between relevant and irrelevant information (Unsworth and Engle 2007), which could be related to things like brain network structure and thus be more of a software than a hardware issue 7 . Yudkowsky (2013) notes that if increased intelligence would be a simple matter of scaling up the brain, the road from chimpanzees to humans would likely have been much shorter, as simple factors such as brain size can respond rapidly to evolutionary selection pressure. Thus, advances in simulation size depend on progress in both hardware and algorithms. Hardware progress in hard to predict, but advances in algorithmic capabilities seem doable using mostly theoretical and mathematical research. This 6 This section does not consider how fast the AI could develop the necessary mental representations to be used in the simulations. That question will be discussed in the next section.  7  Though it is worth noting that g does correlate to some extent with brain size, with a mean correlation of 0.4 in measurements that are obtained using brain imaging as opposed to external measurements of brain size  (Rushton and Ankney 2009) . This would seem to suggest that the raw number of neurons and thus 'general hardware capacity' would also be relevant. would require the development of expertise in mathematics, programming, and theoretical computer science. Much of mathematical problem-solving is about having a library of procedures, reformulations, and heuristics that one can try  (Polya 1990) , as well as developing a familiarity and understanding of many kinds of mathematical results, which one may then later on recognize as relevant. This seems like the kind of task that relies strongly on pattern-matching abilities, and might in principle be in reach by an advanced deep reinforcement learning system that was fed a sufficiently large library of heuristics and worked proofs to let it develop superhuman mathematical intuition 8 . Modern-day theorem provers often know what kinds of steps are valid, but not which steps are worth taking; merging them with the 'artificial intuition' of deep reinforcement learning systems might eventually produce systems with superhuman mathematical ability. Progress in this field could allow AI systems to achieve superhuman abilities in math research, considerably increasing their ability to develop more optimized software to take full advantage of the available hardware. To the extent that relatively small increases in the number of variables considered in a high-level simulation would allow for dramatically increased prediction ability (as is suggested by e.g. the superforecasters being better predictors with thrice the prediction horizon of less accurate forecasters), moderate increases in the size of the AI's simulations could translate to drastic increases in terms of real-world capability. Yudkowsky (2013) notes that although the evolutionary record strongly suggests that algorithmic improvements were needed for taking us from chimpanzees to humans, the record rules out exponentially increasing hardware always being needed for linear cognitive gains: the size of the human brain is only four times that of the chimpanzee brain. This further suggests that relatively limited improvements could allow for drastic increases in intelligence. \n Pattern recognition The capability to run large simulations is not enough by itself. The AI also needs to acquire a sufficiently large number of patterns to be included in the simulations, to predict how different pieces in the simulation behave. Potential capability. When it comes to well-defined tasks, current AI systems excel at pattern recognition, being able to analyse vast amounts of data and build them into an overall model, finding regularities that human experts never would have. For instance, human experts would likely have been unable to anticipate that men who 'like' the Facebook page 'Being Confused After Waking Up From Naps' are more likely to be heterosexual  (Kosinski et al 2013) . Similarly, the Go-playing AI AlphaGo, whose good performance against the expert player Lee Sedol could to a large extent be attributed to its built-up understanding of the kinds of board patterns that predict victory, managed to make moves that Go professionals watching the game considered creative and novel. The ability to find subtle patterns in data suggests that AI systems might be able to make predictions in domains which humans currently consider impossible to predict. We previously discussed the issue of the (predictive) validity of a domain, with domains being said to have higher validity if 'there are stable relationships between objectively identifiable cues and subsequent events or between cues and the outcomes of possible actions'  (Kahneman and Klein 2009) . A field could also be valid despite being substantially uncertain, with warfare and poker being listed as examples of fields that were valid (letting a skilled actor improve their average performance) despite also being highly uncertain (with good performance not being guaranteed even for a skilled actor). We already know that the validity of a field also depends on an actor's cognitive and technological abilities. For example, weather forecasting used to be a field in which almost no objectively identifiable cues were available, relying mostly on guesswork and intuition, but the development of modern meteorological theory made it a much more valid field  (Shanteau 1992 ). Thus, even fields which have low validity to humans with modern-day capabilities, could become more valid for more advanced actors. A possible example of a domain that is currently relatively low-validity, but which could become substantially more valid, is that of predicting the behaviour of individual humans. Machine learning tools can already generate personality profiles harvested from people's Facebook 'likes' that are slightly more accurate than the profiles made by people's human friends (Youyou et al 2015), and can be used to predict private traits such as sexual orientation  (Kosinski et al 2013) . This has been achieved using a relatively limited amount of data and not much intelligence; a more sophisticated modelling process could probably make even better predictions from the same data.  Taleb (2007)  has argued for history being strongly driven by 'black swan' events, events with such a low probability that they are unanticipated and unprepared for, but which have an enormous impact on the world. To the extent that this is accurate, it suggests limits on the validity of prediction. However, Tetlock and Gardner (2015) argue that while the black swans themselves may be unanticipated, once the event has happened its consequences may be much easier to predict. Although superforecasters have shown no ability to predict black swans such as the 9/11 terrorist attacks, they could predict the answers to questions like 'Will the United States threaten military action if the Taliban do not hand over Osama bin Laden?' and 'Will the Taliban comply?'. Thus, even though AI might be unable to predict some very rare events, once those events have happened, it could utilize its built-up knowledge of how people typically react to different events in order to predict the consequences better than anyone else. \n Rates of capability growth How quickly could AI acquire more detailed models? Here again opinions differ.  Hibbard (2016)  argues, based on  Mahoney's (2008)  argument for intelligence being a function of both resources and knowledge, that explosive growth is unlikely.  Benthall (2017)  makes a similar argument. On the other hand, authors such as  Bostrom (2014)  and  Yudkowsky (2008)  suggest the possibility for fast increases. How to improve learning speed? We know that among humans, there are considerable differences in the extent to which people learn. Human cognitive differences have a strong neural and genetic basis  (Deary et al 2010) , and strongly predict academic performance  (Deary et al 2007) , socio-economic outcomes  (Strenze 2007) , and job performance and the effectiveness of onthe-job learning and experience  (Gottfredson 1997b ). There also exist child prodigies who before adolescence achieve a level of performance comparable to an adult professional, without having been able to spend comparable amounts of time training  (Ruthsatz et al 2013) . In general, some people are able to learn faster from the same experiences, notice relevant patterns faster, and continue learning from experience even past the point where others cease to achieve additional gains 9 . While there is so far no clear consensus on why some people learn faster than others, there are some clear clues. Individual differences in cognitive abilities may be a result of differences in a combination of factors, such as working memory capacity, attention control, and long-term memory (Unsworth et al 2014).  Ruthsatz et al (2013) , in turn, note that 'child prodigies' skills are highly dependent on a few features of their cognitive profiles, including elevated general IQs, exceptional working memories, and elevated attention to detail'. Many tasks require paying attention to many things at once, with a risk of overloading the learner's working memory before some of the performance has been automated. For an example,  McPherson and Renwick (2001)  consider children who are learning to play instruments, and note that children who had previously learned to play another instrument were faster learners. They suggest this to be in part because the act of reading musical notation had become automated for these children, saving them from the need to process notation in working memory and allowing them to focus entirely on learning the actual instrument. This general phenomenon has been recognized in education research. Complex activities that require multiple subskills can be hard to master even if the students have moderate competence in each individual subskill, as using several of them at the same time can produce an overwhelming cognitive load  (Ambrose et al 2010, chapter 4) . Recommended strategies for dealing with this include reducing the scope of the problem at first and then building up to increasingly complex scopes. For instance, 'a piano teacher might ask students to practice only the right hand part of a piece, and then only the left hand part, before combining them' (ibid). An increased working memory capacity, which is empirically associated with faster learning capabilities, could theoretically assist in learning in allowing more things to be comprehended simultaneously without them overwhelming the learner. Thus, AI with a large working memory could learn and master at once much more complicated wholes than humans. Additionally, we have seen that a key part of efficient learning is the ability to monitor one's own performance and to notice errors which need correcting; this seems in line with cognitive abilities correlating with attentional control and elevated attention to detail.  McPherson and Renwick (2001)  also remark on the ability of some students to play through a piece with considerably fewer errors on their second runthrough than the first one, suggesting that this indicates 'an outstanding ability to retain a mental representation of  [K]  performance between run-throughs, and to use this as a basis for learning from [K] errors'. In contrast, children who learned more slowly seemed to either not notice their mistakes, or alternatively to not remember them when they played the piece again. Whatever the AI analogues of working and long-term memory, attentional control, and attention to detail are, it seems at least plausible that these could be improved upon by drawing exclusively on relatively theoretical research and inhouse experiments. This might enable AI to both absorb vast datasets, as current-day deep learning systems do, and also learn from superhumanly small amounts of data. Limits of learning speed. How much can the human learning speed be improved upon? This remains an open question. There are likely to be sharply diminishing returns at some point, but we do not know whether they are near the human level. Human intelligence seems constrained by a number of biological and physical factors that are unrelated to gains from intelligence. Plausible constraints include the size of the birth canal limiting the volume of human brains, the brain's 9 Readers who are familiar with the 'deliberate practice' literature may wonder if that literature might not contradict these claims about the impact of intelligence. After all, the deliberate practice research suggests that talent is irrelevant, and that deliberate, well-supervised training is the only thing that matters. However, as noted by the field's inventor, deliberate practice is a concept that is applicable to some very specific-one might even say artificial -domains. Deliberate practice can only be applied in fields in which there are objective metrics, highly developed objectively-measurable expertise, and active competition to improve the existing practices. Areas that do not qualify are \"anything in which there is little or no direct competition, such as gardening and other hobbies, for instance, and many of the jobs in today's workplace-business manager, teacher, electrician, engineer, consultant, and so on\", as there are no objective criteria for performance  (Ericsson and Pool 2016) . Fields that have well-defined, objective criteria for good performance are ones which are the easiest to master using even current-day AI methods-in fact, they're basically the only ones that can be truly mastered using current-day AI methods. A somewhat cheeky way to summarize these results would be by saying that, in the kinds of fields that could be mastered by AI methods that exhibit no general intelligence, general intelligence isn't the most important thing. This even seems to be Ericsson's own theoretical stance: that in these fields, general intelligence eventually ceases to matter because the expert will have developed specialized mental representations that they can just rely on in every situation. So these results are not very interesting to those of us who are interested in domains that do require general intelligence. extensive energy requirements limiting the overall amount of cells, limits to the speed of signalling in neurons, an increasing proportion of the brain's volume being spent on wiring and connections (rather than actual computation) as the number of neurons grows, and inherent unreliabilities in the operation of ion channels  (Fox 2011) . There does not seem to be any obvious reason for why the threshold for diminishing gains from intelligence to learning speed would just happen to coincide with the level of intelligence allowed by our current biology. Alternatively, there could have been diminishing returns all along, but ones which still made it worthwhile for evolution to keep investing in additional intelligence. The available evidence also seems to suggest that within the human range at least, increased intelligence continues to contribute to additional gains. The Study of Mathematically Precocious Youth is a 50 year longitudinal study involving over 5000 exceptionally talented individuals identified between 1972 and 1997. Despite its name, many its participants are more verbally than mathematically talented. The study has led to several publications; among others, Wai et al (2005) and  Lubinski and Benbow (2006)  examine the question of whether ability differences within the top 1% of the human population make a difference in life. Comparing the top (Q4) and bottom (Q1) quartiles of two cohorts within this study shows both to significantly differ from the ordinary population, as well as from each other. Out of the general population, about 1% will obtain a doctoral degree, whereas 20% of Q1 and 32% of Q4 did. 0.4% of Q1 achieved tenure at a top-50 US university, as did 3% of Q4. Looking at a 1 to 10 000 cohort, 19% had earned patents, as compared to 7.5% of the Q4 group, 3.8% of the Q1 group, or 1% of the general population. It is important to emphasize that the evidence we have reviewed so far does not merely mean that AI could potentially learn faster in terms of time: it also suggests that the AI could potentially learn faster in terms of training data. The smaller datasets AI needs in order to develop accurate models, the faster it can adapt to new situations. Besides the considerations we have already discussed, there seems to be potential for accelerated learning through more detailed analysis of experiences. For example, chess players improve most effectively by studying the games of grandmasters, and trying to predict what moves the grandmasters would have made in any situation. When the grandmaster play deviates from the move that the student would have made, the student goes back to try to see what they missed  (Ericsson and Pool 2016) . This kind of detailed study is effortful however, and can only be sustained for limited amounts at a time. With enough computational resources, the AI could routinely run this kind of analysis on all sense data it received, constantly attempting to build increasingly detailed models that would correctly predict the data. How much interaction is needed? Some commentators, such as  Hibbard (2016)  argue that knowledge requires interaction with the world, so the AI would be forced to learn over an extended period of time as the interaction takes time. From our previous review, we know that feedback is needed for the development of expertise. However, one may also get feedback from studying static materials. As we noted before, chess players spend more time studying published matches and trying to predict the grandmaster moves-and then getting feedback when they look up the next move and have their prediction confirmed or falsified-than they do actually playing matches against live opponents  (Ericsson and Pool 2016) . The Go-playing AlphaGo system did not achieve its skill by spending large amounts of time playing human opponents, but rather studying the games of humans and playing games against itself  (Silver et al 2016) . And while any individual human can only study a single game at a time, AI systems could study a vast number of games in parallel and learn from all of them 10 . An important difference is that domains such as chess and Go are formally specified domains, which AI can perfectly simulate. For a domain such as social interaction, the AI's ability to accurately simulate the behaviour of humans is limited by its current competence in the domain. While it can run a simulation based on its existing model of human behaviour, predicting how humans would behave based on that model, it needs external data in order to find out how accurate its prediction was. This is not necessarily a problem however, given the vast (and ever-increasing) amount of recorded social interaction happening online. YouTube, e-mail lists, forums, blogs, and social media services all provide rich records of various kinds of social interaction, for AI to test its predictive models against without needing to engage in interaction of its own. Scientific papers-increasingly available on an open access basis-on topics such as psychology and sociology offer additional information for the AI to supplement its understanding with, as do various guides to social skills. All of this information could be acquired simply by downloading it, with the main constraints being the time needed to find, download, and process the data, rather than time needed for social interactions. As noted earlier, relatively crude statistical methods can already extract relatively accurate psychological profiles out of data such as people's Facebook 'likes'  (Kosinski et al 2013 , Youyou et al 2015 , giving reason to suspect that a general AI could develop very accurate predictive abilities given the kind of a process described above. Several other domains, such as software security and mathematics seem similarly amenable to being mastered largely without needing to interact with the world outside the AI, other than searching for relevant materials. Some domains such as physics would probably need novel experiments, but AI focusing on the domains that were the easiest and fastest for it to master might find sufficient sources of capability from those alone. 10 See  Mnih et al (2016)  for a discussion of how incorporating parallel learning improves upon on modern deep learning systems. Given the above considerations, it does not seem like AI's speed of learning would necessarily be strongly interaction-constrained. \n Conclusions We set out to consider the fundamental practical limits of intelligence, and the limits to how quickly an AI system could acquire very high levels of capability. Fictional representations of high intelligence often depict a picture of geniuses as masterminds who have an almost godlike prediction ability, laying out intricate multi-step plans where every contingency is planned for in advance (TVTropes 2017a). When discussing 'superintelligent' AI systems, one might easily think that the discussion was postulating something along the lines of those fictional examples, and rightly reject it as unrealistic. Given what we know about the limits of prediction, for AI to make a single plan which takes into account every possibility is surely impossible. However, having reviewed the science of human expertise, we have found that experts who are good at their domains tend to develop powerful mental representations which let them react to various situations as they arise, and to simulate different plans and outcomes in their heads. Looking from humans to AIs, we have found that AI might be able to run much more sophisticated mental simulations than humans could. Given human intelligence differences and empirical and theoretical considerations about working memory being a major constraint for intelligence, the empirical finding that increased intelligence continues to benefit people throughout the whole human range, and the observation that it would be unlikely for the theoretical limits of intelligence to coincide with the biological and physical constraints that human intelligence currently faces, it seems like AIs could come to learn considerably faster from data than humans do. It also seems like in many domains, this could be achieved by using existing materials as a source of feedback for predictions, without necessarily being constrained by time taken for interacting with the external world. Thus, it looks that even though an AI system could not make a single superplan for world conquest right from the beginning, it could still have a superhuman ability to adapt and learn from changing and novel situations, and react to those faster than its human adversaries. As an analogy, experts playing most games can not precompute a winning strategy right from the first move either, but they can still react and adapt to the game's evolving situation better than a novice can, enabling them to win  11  . Many of the hypothetical advantages-such as a larger working memory, the ability to consider more possibilities at once, and the ability to practice on many training instances in parallel-that AI might have seem to depend on available computing power. Thus the amount of hardware the AI had at its disposal could limit its capabilities, but there exists the possibility of developing better-optimized algorithms by initially specializing in fields such as programming and theoretical computer science, which the AI might become very good at. One consideration which we have not yet properly addressed is the technology landscape at the time when the AI arrives (Tomasik 2017, section 7). If a general AI can be developed, then various forms of sophisticated narrow AI will also be in existence. Some of them could be used to detect and react to a general AI, and tools such as sophisticated personal profiling for purposes of social manipulation will likely already be in existence. Considering how these influence the considerations discussed here is an important question, but one which is outside the scope of this article. In summary, even if AI could not create a complete master plan from scratch, there seems to be a reasonable chance that could still come to substantially outperform humans in many domains, developing and using superior expertise than what humans were capable of. How fast AI systems could develop to such a level would depend on the speed at which algorithmic and hardware improvements became available. They could potentially be very fast, if e.g. the required algorithmic insights were more on the level of scaling up the size of the AI's simulations and number of attentional streams, rather than requiring any genuinely new ideas compared to what allowed the AI to achieve a rough human level in the first place. Recognizing a familiar situation means understanding what goals make sense and what should be focused on, which cues to pay attention to, what to expect next and when a violation of expectations shows that something is amiss, and knowing what the typical ways of responding are. Ideally, the expert will instantly know what to do. \n • Medicine and firefighting have fairly high validity, whereas predictions of the future value of individual stocks and long-term 1 forecasts of political events are domains with practically zero validity. • 'Some [domains] are both highly valid and substantially uncertain. Poker and warfare are examples. The best moves in such situations reliably increase the potential for success'. • '[A domain] of high validity is a necessary condition for the development of skilled intuitions. Other necessary conditions include adequate opportunities for learning the [domain] (prolonged practice and feedback that is both rapid and unequivocal). If [a domain] provides valid cues and good feedback, skill and expert intuition will eventually develop in individuals of sufficient talent'. \n\t\t\t Phys. Scr. 92 (2017)  113001Invited Comment \n\t\t\t Except for when citations to other content are explicitly included, all the discussion about superforecasters and the Good Judgment Project uses Superforecasting as its source. \n\t\t\t See Whalen (2016) for preliminary work in this direction.", "date_published": "n/a", "url": "n/a", "filename": "Sotala_2017_Phys._Scr._92_113001.tei.xml", "abstract": "What kinds of fundamental limits are there in how capable artificial intelligence (AI) systems might become? Two questions in particular are of interest: (1) How much more capable could AI become relative to humans, and (2) how easily could superhuman capability be acquired? To answer these questions, we will consider the literature on human expertise and intelligence, discuss its relevance for AI, and consider how AI could improve on humans in two major aspects of thought and expertise, namely simulation and pattern recognition. We find that although there are very real limits to prediction, it seems like AI could still substantially improve on human intelligence.", "id": "c91bb1caa13f861727be34026223238e"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Pythagoras Petratos", "Anders Sandberg", "Feng Zhou Contents", "Oxford Martin", "F Zhou"], "title": "Cyber Insurance", "text": "Introduction Cyber insurance has a broad definition and has been continuously evolving over time. It was defined as insurance for the damages to \"physical\" computer equipment in 1970s, but nowadays it has been changed to be a cost-effective option of risk mitigation strategies for IT/cyber-related losses. According to Association of British Insurers (ABI), it \"covers the losses relating to damage to, or loss of information from, IT systems and networks.\"  argue that cyber insurance in an ideal situation promotes users to implement good security. However, some barriers are currently preventing insurers to achieve this goal, and innovations in the cyberspace introduce new types of loss. For example, \"Internet of Things\" is shifting cybersecurity from protecting information assets to physical goods that were traditionally unrelated to computers. At present, cyber insurance has a small share in overall nonlife insurance market and represents just 0.1% of the global property and casualty insurance premium pool  (Marsh 2015) , but it is one of the fastest-growing new lines of insurance business and the cybersecurity is recognized as one of the top global risks in the World Economic Forum's report recently  (WEF 2015) . Meanwhile, more and more traditional insurance contracts exclude specific losses that are linked to cybersecurity; it is necessary to develop a standalone cyber-insurance market. New technologies and innovations in the cyberspace are also spurring the development of cyber-insurance market, as well as the current trend of government requiring high standards on protecting sensitive information and enforcing financial punishments relating to information security breaches. Both the complexity of cyber risk and the current immaturity of cyber-insurance market bring challenges for industry practitioners and regulators to fully understand potential future systemic risks in this kind of complex system. Not surprisingly, the recent Risk Nexus Report from Zurich Insurance Group argues that the global aggregations of cyber risk is analogous to those risks that were overlooked in the US sub-prime mortgage market  (Zurich 2014) . Its nickname \"cyber sub-prime\" intends to describe the interconnected nature of systemic cyber risk and the challenges for individual insurers to address the complexity. They believe that the existing research on systemic risk in the financial markets that aims to address recent crises should be helpful to understand the dynamics of future cyberspace. \n Development of Insurance for Cyber Risks According to 2015 Information Security Breaches Survey  (PWC 2015) , 90% of UK large organizations and 74% of small businesses reported that they had suffered at least one security breach in the past 1 year. The average cost of the worst single breach suffered by these businesses has gone up sharply. For instance, the average cost to a large organization is around £1.5-£3 m up from £600 k to £1.15 m a year ago. The survey also indicates that the majority of UK businesses surveyed expect breaches will continue to increase.  Thompson (2014)  estimates that the total cyber insurance currently amounts around US$2 billion, whereas the total cost of global security breaches could be more than US$400 billion. For more about the effects of cyber-attacks on UK companies, see Oxford Economics  (2014) . For a more detailed history and evolution of cyber-insurance products, see  Majuca et al. (2006) . \n Economics of Information Security Together with both the growth of ICT (information and communication technology) and the growing impact of cyber risks to the real-world business increase the demand for insurance-related risk mitigation strategies. The following factors also play key roles in the development of cyber insurance: A list of key factors affecting either demand for or supply of cyber insurance: Mitigating cyber residual risks: Organizations have three basic cyber risk management strategies: self-protection, self-insurance, and transfer of risk via cyber insurance  (Kesan et al. 2005) . While organizations are increasing their information security spending on improving IT system, cyber residual risks still require insurance to mitigate unexpected events.  Lelarge and Bolot (2009)  find that cyber insurance is a powerful incentive mechanism that motivates organizations to invest in selfprotection, so these three strategies are complementary to each other.  Pal and Golubchik (2010)  analyze the Internet users' investment in self-defense mechanisms when insurance solutions are offered in either full or partial cyber-insurance coverage models. Promoting and aligning economic incentives: Organizations who have insurance as a last resort of risk management attract customers and business partners, especially for small businesses who are parts of a large/long supply chain in order to avoid being the weakest link of cyber-attacks. In the supply-demand model of cyberinsurance market,  Pal (2014)  argues that cyber insurance has the potential to jointly align the incentives of different stakeholders in the cyberspace, such stakeholders or players as security vendors, cyber insurers, regulatory agencies, and network users.  also suggest that cyber insurance in an ideal situation promotes users to implement good security. Protecting exclusions in traditional insurance: Cyber cover was mainly embedded in other traditional insurance products (e.g., business interruption or professional liability insurance), but nowadays more and more traditional insurance contracts intend to exclude the cyber-related risks due to the complexity of cyberspace and potentially catastrophic consequence, as well as requiring different actuarial methods to preform data analysis  (Siegel et al. 2002) . As a result, standalone cyber-insurance policies are emerged. However, there is a gap between insurers and insured parties to explain the differences/exclusions among both standalone cyber-insurance contracts and traditional products. It is necessary to have cyber-insurance brokers to reduce the gap  (Marsh 2015) . Providing professional advice and delivering experienced cyber incident response: Insurance companies themselves collect a huge amount of customers' personally identifiable information and corporate clients' business confidential/ financial information, so they must follow and have rich experience to deal with many regulations of protecting data information and cyber security (e.g., HIPAA Health Insurance Portability and Accountability Act to protect the privacy of individual patients/customers, GLBA Gramm Leach Bliley Act to secure the private information of clients)  (Appari and Johnson 2010) . Insurers also accumulate the updated knowledge and relevant experience from clients globally and communicate with other security professionals, in order to provide technical and legal assistance (as well as financial compensations) to manage cyber-related breaches and incidents  (Marsh and Zurich 2015) . Training cybersecurity awareness and building information security culture: Security managers often find difficulties to communicate with nontechnical internal staff or external clients about security policies and technologies who have no formal security background, but insurance is an easy way to explain the (financial) impact of cybersecurity to the business. The insurance premium that has been reduced (or increased) year-by-year due to a better (or worse) security implementation in this year relative to other previous periods, it is a good indication and consistent comparison to define proper cyber risk metrics and to educate staff or clients. However, at this early stage of cyber insurance, there is still a lag for insurers to implement premium differentiation on the cyber insurance that reflects the insured security improvement precisely due to the immaturity of the cyber insurance market  (Mukhopadhyay et al. 2013; Moran et al. 2015) . Government supports: A free-market approach is traditionally popular to manage risks in the financial system, since it increases motivation and efficiency of stakeholders in the system. As  suggest, one option to spur demand for cyber insurance is to make it compulsory (as it is common in motor insurance), but it may lead a deadweight on competitiveness and productivity growth. The role of government is to encourage and support the insurers to overcome the barriers of supplying cyber insurance (the barriers will be discussed in the cyber-insurance market section). Recently, UK government launched its \"10 Steps to Cyber Security\" (CESG 2012) and \"Cyber Essentials Scheme\" (BIS 2014), both aiming to assist insurers to evaluate the security assessment of small-and medium-sized enterprises. Sharing data of cyber incidents (data pooling): It is necessary to form partnerships from different industries that share data in order to better understand cyber risks, as suggested in the UK Cyber Security Strategy (Cabinet 2011). The recent launched Cyber Security Information Sharing Partnership (CiSP https://www.cert. gov.uk/cisp/) aims to collaborate with insurers to analyze emerging threats, disaster scenarios, and trends in the cyberspace. The cyber insurance will be more affordable and its purchasing cost is expected to be lower than current level based on more relevant actuarial data in the near future, and a higher degree of price differentiation across different policies and individual firms will be feasible  (Marsh 2015) . However,  Bohme (2006)  states and explains that information sharing is socially beneficial, but it is not efficient to rely on a trusted third party only (as a \"social planner\") to arrange data collection. \n Insurable and Uninsurable Cyber Risks In terms of a specific insurance policy, the potential losses related to cyber-attacks or nonmalicious IT failures can be currently grouped into 11 categories in the London Insurance Market  (Marsh 2015) , which is also similar to the US market  (Majuca et al. 2006) . Due to both the difference in severity/frequency of cyber events and the complexity of cyber risks, some of these losses are insurable while others are not available at present.  Johnson et al. (2014)  study the complexity of estimating systematic risk in cyber networks, which is an essential requirement to provide cyber insurance to the public. The following discussion explains the insurability and exposure for different cyber risks  (Marsh 2015) . \n Insurable Cyber Risks Privacy events: Many privacy issues are related to managing regulatory requirements on information security. Insurers can collaborate with lawyers to provide different levels of services and protections to their clients. Since the losses from these events are handled and measured by a third-party professional lawyer, there is less information asymmetry or moral hazard problem between insurer and insured. Crime and fraud: Police force often involves in the investigation of cyber-crime and fraud; therefore, the financial losses related to such cyber events are measured by third parties such as police or lawyers. Insurers can not only offer insurance cover, but also provide professional advice on preventing these events or reducing the cost based on their experience from other customers. Network security liability: Third-party liabilities related to certain security events occurring within an organization's IT network can be insured, mainly due to the scope of incidents can be clearly defined by the insurers and IT system engineers can also collaborate with insurers to improve mitigation strategies. Software and data damage: Insurers can provide indemnity for the costs arising from the damage of data or software (e.g., help recovering or reconstituting the damaged data); this is mainly because insurers are able to require the policy holders to follow necessary procedures of data backup or redundancy. Cyber extortion: Traditionally, insurers have the necessary knowledge and experience of dealing with extortion in the physical world and conduct ransom negotiations (particularly in the London Market, such as the Lloyd's of London), extortion in the cyberspace is not much different from that. Cover is provided for both the cost of handling the incident and the ransom payment. \n Uninsurable (or Insurable but with Constraints) Cyber Risks Reputational loss: Although insurance cover is available for the losses that are directly linked to reputational damage (e.g., cost of recovering public image or loss revenue from existing customers), it is difficult to measure the value of the compensation and the linkage between the cyber incident and the intangible asset if without certain constraints. Network business interruption (e.g., due to Denial-of-Service attacks): In the traditional insurance sector, it is common to offer full coverage for business interruption arising from natural disasters or man-made events. However, in the early stage of cyber insurance, insurers are concerned about the potential aggregate exposure from a single cyber event but interrupts many insured policy holders. IP theft or espionage: These types of losses are extremely difficult to prove and quantify, since the value is changing quickly over time and trade secret is priceless before an incident but (likely) worthless if being public. It is also hard to define whether the incident was incurred in the insured period. Moreover, these attacks are often state-sponsored with a large amount of resource. Physical asset damage: The interconnection between physical world and cyberspace is increased by the development of the so-called \"Internet of Things (IoT)\"; therefore, more and more cyber incidents will directly have impacts on the physical assets. At this stage, the complexity of these interconnections is not well understood by insurers; therefore, it is difficult to combine cyber insurance with traditional property insurance or have such physical asset damage cover in the standalone cyber insurance. Death and bodily injury: Similar to the physical asset damage, it is more and more likely that certain cyber-related incidents may cause harm to the human (e.g., medical devices, large-scale industry equipment, driverless cars, etc.). Although it is uninsurable at the current stage of cyber insurance, it is covered by traditional insurance products such as general liability and employers' liability products (Fig.  1 ). \n Challenges and Developments Even if insurers are able to offer cyber insurance to mitigate certain types of cyberrisk events, they must face and learn to overcome some challenges in order to maintain and expand their businesses. Not surprisingly, there are progresses and developments to address these challenges recently. \n Challenges for Insurers External attackers are evolving over time: Information Security Breaches Survey  (PWC 2015)  shows that outsiders are using more sophisticated methods to affect organizations. Staff-related breaches are unique in individual cases: Whether inadvertent human error or not, the consequence from insiders' mistakes or misconducts is difficult for insurers to measure. Lack of understanding and communication: Recent surveys indicate that a majority of CEOs believe their organizations have relevant insurance to cover cyber risks  (PWC 2015) , whereas in fact only around 10% actually do  (Marsh 2015) . Increasing IT system collaboration and social network: Cyberspace is moving toward an ecosystem, which has more and more heterogeneous players collaborate and interact to each other. New technologies and innovations: The ICT sector is attractive to capital markets with large amounts of capital to support new businesses and innovations. However,   -2005) . Expected number of losses per year larger than a certain size as a function of number of records lost. Note the power-law heavy tail for larger losses (exponent % À0.66, consistent with the results in  Overill and Silomon (2011)  and  Maillart and Sornette (2010) ). This tail may be dominated by more targeted events and organized crime, including financial fraud, insider abuse and theft, as well as malware  (Overill and Silomon 2011) . due to the nature of this fast evolving sector and heavy competition, ICT vendors focus more on the short process of introducing their products and services to the market and less on the security. It is challenging for insurers to follow these fast developments and potential risks involved in the process  (Friedman 2011) . \n Recent Developments Government: Organizations are increasingly using Government alerts (e.g., the UK HMG Cyber Essentials scheme) to inform their awareness of threats and similar vulnerabilities  (PWC 2015) . Insured firms can get discount on insurance premium if they follow these certification requirements, so it offers motivations for insured users to follow security procedures and policies. Insurance cyber gap analysis: Marsh (  2015 ) also suggests that it is necessary for insurance brokers to provide cyber gap analysis (determining which cyber risks are covered by existing traditional insurance or need to be covered in a standalone cyber insurance) when communicating with customers. Insurers' data protection regulations: Insurance industry itself collects sensitive personal, financial, and healthcare data from their policy holders (e.g., personally identifiable information PII, protect health information PHI, and business operation private information) in order to measure the customers' risks more precisely. As a result, the National Association of Insurance Commissioners NAIC (2015) recently adopted cybersecurity guidance for the insurance industry and regulators to follow. The expertise and experience of insurers' information security practice is also applied to advice their customers. Understanding the benefits of cyber insurance: The growing amount of literature starts to support the benefits of cyber insurance as a market-based solution to cybersecurity.  Kesan et al. (2005)  state, when certain obstacles to a full market solution are fully worked out, several positive outcomes will occur. In general, cyber insurance market will result in higher overall social welfare. \n Evolution of Cyber-Insurance Market It is still too early to know the structure of the future, mature cyber-insurance market. In the existing literature, both competitive  (Shetty et al. 2010b ) and monopolistic  (Lelarge and Bolot 2009; Hofmann 2007; Pal and Golubchik 2011)  market structures are studied. As commonly expected, the cyber-insurance market will soon become a complex dynamic system  (Anderson and Moore 2009; Halse and Hoemsnes 2013) . As a result, the market not only provides one option of risk mitigation strategies, but also builds an ecosystem together with other sectors in cyberspace that can influence heterogeneous stakeholders' behaviors and business strategies  (Hall et al. 2011) . This is similar to other financial systems, such as stock or credit markets  (Gracie 2015) . Therefore, the existing research in other financial systems will be relevant to understand the future cyber-insurance market  (Zurich 2014) . Obstacles of Developing Cyber-Insurance Market  Shetty et al. (2010a)  and  Bohme and Schwartz (2010)  argue that the underdeveloped cyber insurance market is mainly due to: (1) interdependent security (externalities)  (Ogut et al. 2005; Bolot and Lelarge, 2008; Zhao et al. 2009 ); (2) correlated risk  (Bohme and Kataria, 2006) ; and (3) information asymmetries  (Bandyopadhyay et al. 2009) . Furthermore,  Bohme and Schwartz (2010)  argue that \"it appears that the market failure can only be overcome if all obstacles are tackled simultaneously.\" Meanwhile,  Marsh (2015)  states that a well-developed reinsurance market for cyber insurance is also one of the necessary conditions to expand the business. The four key obstacles are explained as follows: Interdependent security (externalities):  Kunreuther and Heal (2003)  ask the question: \"Do firms have adequate incentives to invest in protection against a risk whose magnitude depends on the actions of others?\". One of the differences between cyber and traditional insurance (e.g., property or motor) is the close interconnections among players in cyberspace. The security in cyberspace is dependent on all players in the system, but heterogeneous players have different preferences about cybersecurity and the \"free rider problem\" occurs when those who benefit from other players' security investment do not have to pay for it  (Varian 2004 ). As  Naghizadeh and Liu (2014)  argue that security is a nonexcludable public good, so users can stay out and still enjoy spill-overs from others' contribution without paying. As a result, even insurers help their insured customers to increase their overall security, those uninsured players in the system still can weaken these insured customers. Correlated risk:  Bohme and Kataria (2006)  define two tiers of correlated cyber risks: (1) internal correlation, which they define as \"the correlation of cyber risk within a firm\" (i.e., a correlated failure of multiple systems on the internal network), and (2) global correlation, as \"the correlation of cyber-risk at a global level, which also appears in the insurer's portfolio.\" The growing development of Cloud computing platform may accelerate the two tiers to be integrated together. For example, an internal incident in a cloud service provider will lead systematic risks in both its internal system and its customers' systems. Information asymmetries: Bohme and Schwartz (2010) define \"asymmetric information\" as environment where some players have private information to take advantages on something that are not available to other players. The common issues in the conventional insurance literature due to \"asymmetric information\" are: adverse selection  (Akerlof 1970 ) and moral hazard  (Arrow 1963) . They are also relevant to the cyber-insurance market and other obstacles (e.g., the interdependent security) may exacerbate its problems  (Shetty et al. 2010a) . Furthermore,  Bohme and Schwartz (2010)  also identify specific forms of information asymmetries in cyber insurance. Meanwhile,  Pal (2012)  proposes three mechanisms (premium differentiation, fines, security auditing) to resolve information asymmetry in cyber insurance. Lack of reinsurance market: It is still in the early stage for reinsurers to reinsure cyber risks from primary insurers, but several proposals have been put forward to build such reinsurance function  (Toregas and Zahn 2014) , such as to establish government-regulated funds similar to US Terrorism Risk Insurance Act or UK Financial Service Compensation Scheme.  discuss that one possible option is for government to provide reinsurance, but they emphasize that \"while government re-insurance can create insurance markets where otherwise there would be no supply, such measures must be carefully designed to avoid a regime in which profits are private (to the insurers' shareholders), losses are socialized (born by the tax-payer), and systems remain insecure (because the government intervention removes the incentive to build properly secure products).\" \n Technologies Spur the Cyber-Insurance Market Many new technologies that have been developed in recent years will spur the cyberinsurance market. We identify some of these technologies and group them into three main categories: (1) IT technologies assist insurers to manage and discover cyber incidents, as well as attract more customers demand for cyber insurance; (2) Technologies and methods that are helpful for insurers to perform actuarial modeling and data analysis; and (3) Technologies that are useful to better understand the complexity of cyber-insurance market. \n IT Technologies Some standalone technologies: Intrusion detection systems (IDS), firewalls, digital forensic technology, Microsoft Photo DNA, and encryption tools have become more advanced and relevant for insurers to investigate cyber incidents. Trusted computing infrastructure: Although the opponents of trusted computing argue that users will lose their freedom and privacy  (Anderson 2003a, b) , the technology provides insurers an opportunity of identifying insurable events and defining claims more precisely. Cloud platforms: Cloud service providers can reduce the issues of misaligned incentives between insurers and cloud users, if they can collaborate with insurers to attract more customers. Meanwhile, automated systems reduce human errors in the computing process. However, on the other hand, the cloud platform may lead to systemic risk since they are connected to other IT systems. Anonymous communication and transactions: The anonymity network that is currently represented by, e.g., Tor software makes cyber criminals \"anonymous\" and untraceable. Anonymous digital currencies allow sophisticated markets for illicit goods and services  (Juels et al. 2015) . As a result, there is a deep/dark web that provides a cyber black market for attackers to trade sensitive information (e.g., selling stolen credit card information to other parties, etc.), so the attackers' motivation of attacking any organizations become larger. Mobile devices: Nowadays, more and more business activities and collaborations are based on mobile devices (e.g., Bring Your Own Devices). This leads more cyber incidents that require cyber insurance, since such devices are lost or stolen easily and users do not have sufficient skills to manage the security on these mobile devices. Leaking technology: ICT enables rapid copying and dissemination of information, making information leaks harder to contain. In the past, a sizeable leak of proprietary information (such as more than 40 gigabytes of internal data released in the 2014 Sony hack) would have been limited by the need to transmit it by sending hard drives (expensive) or setting up a website (legally traceable and blockable); by 2014, it could be distributed anonymously using bittorrent in a way that makes it impossible to trace and block. In addition, leaks are potentiated by the appearance of search tools making released data more accessible. \n Actuarial Modeling Methods Network simulator: Similar to stress and scenario testing that are commonly used in the financial markets (e.g., banking system), insurers can use various applications and services to run network simulation in an artificial environment in order to test the stability and resilience of insured network under different conditions. Actuarial data analysis (big data analytics): More and more professional consulting service firms have been investing and offering advanced actuarial pricing and risk management services based on big data analytics to assist insurers uncovering hidden patterns and unknown correlations in cyber risks. Data pooling platform (data anonymization): Technologies of information sanitization that aim to encrypt or remove sensitive information from data sets are becoming more feasible; this encourages more data to be shared in the pooling platform in order to help government and insurers to better understand cyber risks from aggregated data sets. Machine learning and Bayesian networks: More and more applications from these subfields of computer science are used in understanding the cyber risks. Insurers will hopefully gain insights about managing the cyber risks from these developments.  Yang and Lui (2014)  apply Bayesian network to analyze the influence of cyber-insurance market to security adoption in heterogeneous networks. Data visualization: According to the \"digital detectives\" website of Microsoft, advances in data visualization technology assist Microsoft Digital Crimes Unit (uses Microsoft PowerMap) to understand the pattern of Citadel botnets better and remove the malware from infected machines more efficiently  (Constantin 2013) . The same technologies will help insurers to identify cyber incidents from different malware or causes, so they can distinguish the incidents in order to reduce specific claims (similar to distinguish different risk events in natural catastrophe insurance) or issue insurance-linked securities based on specified triggers (cyber incident) earlier.  consider one of potential strategies to promote cyber insurance is to develop financial instruments for risk sharing similar to \"Cat Bonds\" and \"Exploit Derivatives\" in the traditional insurance business operations (e.g., flood and natural-disaster insurance). As  explain, \"Exploit Derivatives are vehicles for insurers to hedge against the discovery of vulnerabilities that causes significant loss events across their portfolios.\" \n Sociotechnical Systems Security awareness training and behavioral games: Toregas and Zahn (2014) mention a growing consensus that cyber security is not achievable by solely focusing on technological aspects, but also requiring to understand both technologies and their users' behaviors. The importance of understanding human-computer interaction has been studied widely since the works of  Adams and Sasse (1999)  and  Sasse et al. (2001) . Recently, some behavioral digital games based on computer simulations are introduced to train the users' behavior and awareness of using technologies securely  (Cone et al. 2007) . Existing interdisciplinary research in financial systems: Bohme (2010b) argues that some key obstacles causing cyber-insurance market failure are due to a lack of understanding information economics. An interdisciplinary and integrated research that focuses on a cyber ecosystem is better than targeting each individual technological elements alone  (Bohme, 2010a) . This idea is similar to recent progress of understanding systemic risks in the financial markets.  Schneier (2002)  and  Moore (2007, 2009)  state that a combination of economics, game theory, and psychology is necessary to understand and manage cybersecurity in the modern and future networked environment.  Johnson et al. (2011)  model security games with market insurance to inform policy makers on adjusting incentives to improve network security and cyber-insurance market.  Baddeley (2011)  applies some lessons from behavioral economics to understand issues of information security. More papers on the economics of information security and privacy can be found in the book of  Moore et al. (2010) . Multiagent technique: Agent-based approach of modeling a complex system is becoming popular in the financial markets, but it is not commonly used by researchers to model cyberspace or perform stress testing on particular cyber events. Recently, a few researchers start to apply this technique to model network resilience  (Sifalakis et al. 2010; Baxter and Sommerville 2011; Sommerville et al. 2012) . \n General Categorization of Cyber Risks In the previous analysis, we presented the literature related to the evolution of cyberinsurance. It is our intention to further examine the challenges for the development of a cyber-insurance market. \"An understanding of insurance must begin with the concept of riskthat is, the variation in possible outcomes of a situation\"  (Zeckhauser 2008) . We embark on a theoretical and empirical analysis, using examples of cyber security events, in order to better understand cyber risks and relate them to cyber security. The first crucial observation is that numerous different things can be included under the term \"cyber risks.\" A more precise definition of \"cyber risks\" would result if we break them into three distinct elements. • (Cyber) Risk can be defined as a measurable quantity, according to  Knight (1921) . In that sense, probability distributions could be assigned to cyber threats. Thus, it is feasible to quantify the (cyber) risks and consequently estimate insurance premiums. • (Cyber) Uncertainty can be considered to be the unmeasurable quantity related to cyber events. Therefore, we do not know the states of the world and the precise probabilities would not be known. It is also known as Knightian Uncertainty, based on the classic distinction by Frank  Knight (1921) . • (Cyber) Ignorance can be considered a third category, when we may not have the ability to define what states of the world are possible  (Zeckhauser and Visusi 2008) . It can be considered one step further from uncertainty, when some potential outcomes are unknowable or unknown  (Zeckhauser 2006 ). There are two important types of ignorance. Primary ignorance concerns situations in which one does not recognize that is ignorant and recognized ignorance, when one perceives that ignorance  (Roy and Zeckhauser 2013) . For example, the financial meltdown of 2008 can be considered such an event. It can also be argued that many catastrophic risks are subject to ignorance. \n Catastrophic Risks and Insurance \n General Description of Catastrophic Risks The above general categorization brings us to further types of risk that influence cyber insurance. \"Catastrophes provide the predominant conceptual model of what insurance is about. One pays premiums to secure financial protection against low-probability high consequence eventswhat we normally call catastrophes.\"  (Zeckhauser 1996a, b) . The main problem is that private markets are facing difficulties in providing coverage for catastrophic risk and thus they can be deemed \"uninsurable risk\"  (Jaffee and Russell, 1997) . The timing and consequence of catastrophic events may largely vary. We have already identified the frequency/severity spectrum used for cyber events. In other words, the catastrophic risks fall within the low probability-high consequence class  (Kleindorfer and Kunreuther 1999) . However, the probabilities and consequences are not clearly defined, particularly toward the upper end of losses. In this chapter, we are more interested about the insurers' perspective on assessing such risks. The Actuarial Standard Board defines \"Catastrophe -A relative infrequent event of phenomenon that produces unusually large aggregate losses.\" More precisely, \"An event is designated a catastrophe by the industry when claims are expected to reach a certain dollar threshold, currently set at $25 million, and more than a certain number of policyholders and insurance companies are affected\"(Insurance Information Institute 2015). In that sense, numerous cyber events, as we would examine later, can have the rarity and loss magnitude of catastrophic risks. However, catastrophes can involve a loss much greater than $25 million. The Swiss Re Sigma Study describes catastrophe losses. In 2014, total insured and uninsured losses due to disasters were estimated at $110 billion (Swiss Re 2015). This number is below the inflation adjusted 10 year average of $200 billion and lower than $138 billion in 2013. However, the number of natural disaster catastrophes was at a record high reaching 189, and in total, there were 336 disaster events. This variation in total losses and the number of catastrophes partly displays their unpredictability as well as their severe consequences. By doing simple calculations, we can observe that the average loss per catastrophe is much higher than $25 million (insurance covered claims of USD 28 billion of losses from natural catastrophes and USD 7 billion from man-made disasters). There are two major categories regarding the causes of catastrophic risks: • Natural disasters, including georisks (like earthquakes) and climate-induced risks (as hurricanes and floods) • Man-made catastrophes can be considered a broader category and it includes industrial accidents and terrorist attacks  (Zurich 2013) . Earthquakes can have devastating effects for insurers but also situations are there where thousands of women claim to be damaged by breast implants or individuals harmed by asbestos  (Zeckhauser 1996a, b) . This example, except making the distinction between natural and man-made disasters, presents some interesting features that could be used for some initial comments about cyber risks. A feature is that natural disasters are usually localized (geo specific). The same can apply to cyber events. A system failure in an energy grid can have local effects. Nevertheless there are many cases, let us say a computer virus,that can have regional or global impacts. Cyberspace is by its nature fairly nonlocal, and there are fewer \"natural boundaries\" that constrain the size of an impact. This makes these breaches rather easily diffuse around the world, therefore resulting in widespread damage. Also, it seems that a disproportionately larger number man-made breaches and disasters occur in cyberspace (PWC 2015): actually it can be argued that there are very few cases in which the human factor is not involved. While the majority may be unintentional, intentional incidents have the potential for particularly expensive damage. \n Aggregate Catastrophes and Systemic Risks \"Aggregate catastrophes occur when many similarly situated people, all subject to common risks, suddenly find that they have suffered a loss, and the total losses exceed expectations\"  (Zeckhauser 1996a, b) . The single worst incident suffered by an organization might be considered to be a measure for informing us about catastrophic risks, especially in large corporations. Infection of viruses or malicious software remains the largest single worst incident causal factor (PWC 2015). As argued above, viruses and malware have the ability to propagate rapidly and cause harm to various people and organizations. In that sense, we can further decompose the high consequence characteristic. One dimension is the number of individuals and organization that a cyber event might affect. Another dimension is the geographic location where the cyber event takes place. Some cyber events might have global reach, enlarging the consequences. An additional critical parameter is the importance of the individuals and organization for the economy and society. A cyber-attack on critical infrastructure can further enlarge the consequence by generating losses to other operations. For example, the failure of VISA or MASTERCARD systems would not only result in losses for these companies, but it would likely generate significant losses to other businesses. This would apply to other critical (information) infrastructure, and the losses could be identified according to the importance of the system for the operations of other individuals and organizations. \n Global Aggregations of Cyber Risk A report by Zurich and the Atlantic Council attempts to expose \"global aggregations of cyber risk\" as analogous to the risks associated with the US sub-prime and 2008 financial crisis. \"Governments and forward looking organizations need to take a holistic view and look beyond these issues to broader risks, including the increasing danger of global shocks initiated and amplified by the interconnected nature of the internet\"  (Zurich 2014 ). An illustrative analogy between the financial markets and the information technology of organizations is over-leverage  (Zurich 2014) . Overleverage of companies in financial markets was created due to excessive debt, while organizations can over-leverage in IT due to overreliance on technology solutions. In both cases, leverage is used to maximize their returns; however, it is likely that the associated risks were underestimated, as it was proved by the financial crisis. There are two crucial elements in this discussion. The first is a \"Lehman moment,\" a catastrophic event that would spread in the web and cause major losses. Nevertheless a \"Lehman moment\" would encompass ignorance. While it was anticipated that Lehman Brothers could go bankrupt, none could foresee the chain of events that it triggered and led to the global financial crisis of 2008. In that sense, even catastrophic events that seem to have a specific impact might actually end in unpredictable outcomes. The original \"Lehman moment\" can be regarded a global shock due to the scale of Lehman Brothers operations across the world. However, the channel that initially cascaded this global shock was rather localized; the US sub-prime market. The other element comprises of the propagation mechanism. The complexity and interconnections of financial products and markets eventually transmitted this shock around the globe. The complexity of financial products might be a useful analogy to the increasing complexity of IT systems. It has been argued that the 2008 financial crisis is a demonstration that the causes of risks were camouflaged by excess complexity  (Zurich 2014) . Even if this complexity is not excessive, it is still difficult to understand and predict the cascading risks and channels. Another analogy of the internet with the financial markets is that risks were assumed not to be correlated with each other. Nevertheless this is far from true: financial products and markets can be highly correlated. The same applies to information technology operations and systems. In that sense, it is not only complexity per se but also complexity due to the interconnected nature of risks that add to the uncertainty  (Zurich 2014) . Thus, complexity and interconnections can facilitate systemic problems when \"extreme events,\" as global shocks, occur. \"Connecting to the internet means exposure to nth-order effectsrisks from interconnections with and dependencies on\" other risk aggregations  (Zurich 2014) . The report by Zurich identifies seven such aggregations (internal IT enterprise, counterparties and partners, outsourced and contract, supply chain, disruptive technologies, upstream infrastructure, external shocks). It can be however argued that due to ignorance, they can be more common, or more severe, than expected (for example, external shocks). An addition issue is a possible \"perfect storm.\" Especially if a cyber \"Lehman moment\" coincides with other events, this interaction could cause losses of much larger scope, duration, and intensity, similar to the series of events of the 2008 financial crisis  (Zurich 2014) . It is even more difficult or rather impossible to identify and define the interconnections between other events and a \"Lehman moment\" before it happens, since it is principally unpredictable. In the worst case, catastrophic events would coincide and can significantly multiply the damage. This makes mitigation of risks increasingly difficult, if the outcomes are unknown or unknowable. \n Global Catastrophic Risks Framework A very useful framework in order to qualitative describe globally catastrophic or existential catastrophes was developed by Nick Bostrom  (Bostrom and Cirkovic 2011; Bostrom 2013 ). This framework is based on three factors: severity (how badly the population would be affected), scope (the size of the population at risk), and probability (how likely the disaster is likely to occur, according to the most reasonable judgment given currently available evidence). This model uses the first two factors and presents many advantages and flexibility. The scope includes not just the spatial size of the risk variable that we descried earlier, but also generational effects that are important regarding the duration and aftermath of the catastrophe. Nevertheless, the major advantage of this framework is the way it treats probability. \"Probability can be understood in different senses. . .The uncertainty and error-proneness. . .of risk is itself something we must factor into our all-things considered probability assignments. This factor often dominates in low-probability high-consequence risksespecially those involving poorly understood natural phenomena, complex social dynamics, or new technology, or are that difficult to assess for other reasons\"  (Bostrom 2013) . Therefore, this facilitates our analysis since most of the factors discussed above can be adapted to this framework. Scope encompasses both geographic spread, number of affected actors, and the importance of the damage. Moreover, its flexibility allows adding other concepts. In the discussion that follows, because the uncertainty and ignorance surrounding the estimation of probabilities, we would shortly discuss about plausibility. Plausibility can be used as a distinct alternative to probabilities (Ramirez and Selin 2014) (Fig.  2 ). \n Interdependencies and Asymmetric Threats We have discussed correlations and interconnections. Special mention should be attributed to interdependencies, a related concept and relevant to cyber risks. Often these concepts are used interchangeably and denote the same thing. However, we would like to expand our analysis by focusing on complex interdependence  Nye 1977, 1998) , since it can provide an additional theoretical foundation. First of all, it should be emphasized that the context of international relations is central to insurance. Except political risk insurance, state relations influence numerous macrorisk factors, as economic relations and defense and security. \"The information revolution alters patterns of complex interdependence by exponentially increasing the number of channels of communication in world politics\"  (Keohane and Nye 1998) . In addition, commercial and, particularly, strategic information are valuable. The availability and confidentiality of such information in multiple channels increases the level of risk. Information can be used to convince and capture terrorists, prevent and resolve conflicts, and enable countries to defeat adversaries  (Nye and Owens 1996) . On the other hand, because information reduces the \"costs, economies of scale, and barriers of entry to markets, it should reduce the power of large states and enhance the power of small states and non-state actors\"  (Keohane and Nye 1998) . This generates important asymmetries. A small group of hackers could disrupt a relatively, to their size and resources, large IT system. Another notable case is that of WikiLeaks: a single leak, amplified by a single disseminating organization, has global consequences for a superpower. Asymmetric threats and the enabling of non-state actors add even more complexity to the layers described before. The number of threats is therefore multiplied and consequently risks increase. Moreover, ambiguity regarding the nature and identification of these relatively small actors makes the estimation of risks quite unpredictable.   \n Cyber Risks and Losses Before 1989, the insurance industry did not experience a loss of more than $1 billion from a single event and since then catastrophes of the same magnitude have occurred  (Kleindorfer and Kunrether 1999) . As more and more people with larger insured wealth congregate in coastal areas, this is to expect (even leaving out climate change). \"Megacatastrophes,\" like Hurricane Andrew, seem therefore to happen more often and clearly demonstrate the limitations of relying on historical data in order to estimate future probabilities of losses  (Actuarial Standard Board 2000) . Not only there are limitations to historical data, but also cyber risks are new phenomena with continuously evolving technology and factors that are difficult to predict or even imagine. However, it is argued that there is likelihood for a global cyber catastrophic event  (Zurich 2014) . There are important methodological problems regarding probability estimation when assessing global catastrophic risks  (Ord et al. 2010 ). Due to their high severity and scope, even low-probability risks need to be managed, but the probability of theory, model, or calculation error in doing so is far higher than the risk probability itself, even when done carefully. This means that risk estimates should be regarded as suspect unless bounded by several independent estimates or other constraints. A major concern for the private insurance industry is that it might not be able to provide coverage for some catastrophic events without the possibility of insolvency or a significant loss  (Kleindorfer and Kunreuther 1999) . This is intensified when the scope and severity of the disaster are high. In the event of a \"cyber sub-prime,\" the losses can be massive and potentially result to insolvency. Even more worried would be the possibility of interconnected events that could amplify such crisis. The coincidence of catastrophes or a perfect storm would also have devastating effects. It is therefore essential to try and understand the cyber risks that can affect insurance. In this part, we attempt to provide a theoretical analysis of risks in order to understand better cyber insurance. In the next part, we attempt to put some flesh to this theoretical skeleton by providing real and imaginary examples. \n Cyber Risks, Catastrophes, and Ignorance \n Identifying Cyber Risks The discussion above indicated that the estimation of probabilities regarding cyber risks is in many cases difficult or impossible. The common methods are based on past events in order to define catastrophes and identify potential losses. These methods present significant limitations. There are various reasons for that. First of all, cyberspace is a very dynamic environment. Information and communication technologies are continuously changing. The internet is constantly expanding. It is embedding existing devices and technologies, and is likely to integrate future innovations, generating the Internet of Things (IoT). The number of interconnected devices, individuals, and organizations is therefore increasing. This results in larger complexity and interdependence among devices with currently unknown functions and vulnerabilities. In that sense, if we assume that we know all the causes of potential losses, then it might be a display of primary ignorance. On the contrary, we can recognize our ignorance. We attempt to examine practical examples of cyber risks in three ways. The first is though the traditional approach on historic events. The second technique can be considered an expansion of that. We can infer based on historical events and develop potential cases, subject to uncertainty. Finally, we would build imaginary but plausible scenarios  (Ramirez and Selin 2014)  in order to better understand cyber uncertainty and push the boundaries of ignorance. It can be said that effective scenario formation and imagining might reduce ambiguity, enter the space of ignorance, and therefore diminish it. \n Existential and Global Catastrophic Risks Bostrom's classification was developed in regard to threats to the entire future of the human species, or \"merely\" global disasters. The cyber counterpart would be risks that can escalate to such a level that they disrupt the global market or indeed current civilization. They are not merely uninsurably large, but terminal to most existing actors. One possible example might be misuse of Artificial Intelligence (AI). Autonomous \"smart\" systems have already demonstrated potential for economically significant misbehavior such as the 2010 \"Flash Crash,\" which at least in part was due to a systemic interaction of automatic trading agents. As technology advances, AI is likely to become more powerful and ubiquitous, but there are significant control problems that remain to be solved. The fundamental issue is that superintelligent systems do not generally behave in human-compatible ways, and this can produce existential risk  (Bostrom 2013) . More plausible scenarios involve unpredictable AI actions that are deliberate, autonomous, and potentially very tenacious. It might include the paralysis of the internet globally by AI software embedded in the web infrastructure, or by automated adaptive hacking tools (e.g., descendants of the current DARPA Cyber Grand Challenge). In another scenario of endurable severity and local scope, AI systems can involve the disruption of operations in an organization. Of course, severity may vary as well as scope. For example, if there is failure of ICT systems in a healthcare organization, it could result to loss of human lives. The disaster can diffuse globally if AI of a wide-spread logistics database system decides not to allow access to information, or even worse, altering or destroying it (for example, because it interprets restoration or circumvention attempts as intrusion attempts). However, due to the fact that the capabilities of AI are very ambiguous, such scenarios are difficult to define. It may be that there are workable solutions or that AI will never be too powerful, but these are risky bets. It seems that it is easy for people to overestimate their knowledge regarding AI  (Yudkowsky 2011) . \"It may be tempting to ignore Artificial Intelligence because, of all the global risk. . .AI is hardest to discuss. We cannot consult actuarial statistics to assign small annual probabilities of catastrophe, as with asteroid strikes. We cannot use calculations from a precise, precisely confirmed model to rule out events or place infinitesimal upper bounds on their probability, as with proposed physics disasters. But this makes AI catastrophes more worrisome, not less.\"  (Yudkowsky 2011) . In that sense, AI qualifies for uncertainty and ignorance. AI represents a risk that could go all the way into the extreme upper right hand box of the framework, but is both extremely uncertain and largely a future risk: it can be dealt with by R&D aimed at safe and beneficial uses of AI. However, cyber risk also has strong interconnections to traditional catastrophic risks. Such risks include major technical disasters, conflict and war, and particularly total war with the use of weapons of mass destruction (WMD). The threat of a nuclear disaster is the most notable case by far. This is due to Stuxnet, a complex piece of malware interfering with Siemens industrial control systems and speculated that it was used for Iran nuclear program  (NATO 2013) . Based on this precedent, it can be argued that a nuclear catastrophe can be realized. The scale of these risks could largely vary.  Cirincione (2011)  and  Ackerman and Potter (2011)  discuss the global catastrophic risks of nuclear war and catastrophic nuclear terrorism. In both cases, cyberspace is \"enabling\" these risks. In addition, the internet could provide the most cost-effective opportunity for adversaries. It enables states and non-state actors and enhances their power. They can transform their capabilities and become nuclear threats that were not imaginable in the past. These asymmetric threats impose great challenges to insurance. Stuxnet is considered to be a government cyber weapon. Rogue states might dedicate more resources in attaining such capabilities. The same could apply with terrorist groups. It is interesting to notice the multiple channels and complexity surrounding them. States relations can deteriorate and governments might decide to pursue cyber weapons targeting at nuclear as well as other military and critical infrastructure targets. The emergence of terrorist groups is also subject to uncertainty and ignorance. The rapid emergence of Islamic State, raising considerable resources, was not forecasted. Hamas and Hezbollah were established terrorist organizations and it can be alleged that they were capable of using cyber space. Nevertheless, it was believed by Israeli officials that these organizations used a criminal organization based in a former Soviet State to attack Israel's internet infrastructure during the January 2009 military offensive in the Gaza Strip  (NATO 2013) . Cyber weapons can also easily be spread to other actors, through theft or leakage (such as the exploits revealed in the attack on the security consultancy Hacking Team in 2015), trade, or by imitation: once Stuxnet was out in the wild, many other groups could analyze it and copy its tricks into their toolkits. The market for zero-day exploits, driven by governments and security companies seeking new tools, has both the effect of incentivizing search for more vulnerabilities and inhibiting public disclosure of them since discoverers can gain more by secretly selling their find and agencies using them do not wish to lose their advantage. Even when vulnerabilities are revealed, removing them is sometimes hard since they might be embedded in systems that cannot easily be upgraded (such as industrial systems or implants); this means that use of some cyber weapons can lead to more subsequent attacks on targets unrelated to the original target. This case highlights the complexity generated by multiple channels and agents. It is consistent with the concept of nth order effects  (Zurich 2014) . The potential cooperation of different agents enhances complexity due to the exponential number of combinations. Nexuses of adversaries can be formed, pooling resources and capabilities and thus magnifying cyber attacks. Nuclear catastrophes can have regional or global consequences  (Cirincione 2011)  according to their intensity. Similar cyber global catastrophic scenarios can involve other types of WMD (i.e., biological weapons) or conflict and war. \n Catastrophic Risks War and conflict enabled by cyber space can present variations in consequences and scale. They can also be interdependent to other complex events. The cyber-attack on Estonia in April 2007 was caused due to political frictions with Russia. On August 2008, the conflict of Russia and Georgia was accompanied by hacking activity from unknown foreign intruders which appeared to coincide with Russian military actions (NATO 2013). A crucial observation is that the manmade causes of these cyber attacks are still not known with certainty. Another critical remark is that there are interdependencies between traditional kinetic power and cyber capabilities. An analogous example to the above cases is the takeover of missile systems by hackers (there are claims this briefly happened to a German Patriot antiaircraft defense system in 2015  (Storm 2015) ). An action by hackers launching missiles could escalate to conflict or war. Now imagine that these missiles are stationed in South Korea. And that they are launched by unknown hackers just after the cyber-attack on Sony, that FBI blamed on Pyongyang  (BBC 2015) . Sony was about to release the interview, a comedy about the assassination of the North Korea's Leader, indicating that the tensions in North Korea were running high. This could trigger events that could escalate to a catastrophe involving even nuclear weapons. A crisis in Korea could also cause negative impact on global markets due to the importance of the South Korean economy and trade interconnections. This example presents just a small part of complex interdependencies. This example could have been even worse. Imagine now that the aforementioned events coincide with a release on WikiLeaks that North Korea is abandoned and isolated (a previous WikiLeaks cable suggested that Chinese officials expressed the desire to relinquish support for North Korea (The Economist 2010)). North Korea can increase its level of alertness and retaliate severely, if they feel that the balance of power has changed against them and the regime is under existential threat. If these events coincide, then it is more likely to have a catastrophe. It is also possible that these events are fabricated and lead to an \"accident.\" It is important to realize the multiple layers of complex interdependencies, which in many occasions can be unpredictable. The \"WikiLeaks paradigm\" is noteworthy because it can generate the conditions and instability which can consequently trigger other disasters. In January 2011, the Canadian government reported an attack against its Department of National Defense as well as the Finance Department and Treasury Board, causing the disconnection of the main Canadian economic agencies from the internet (NATO 2013). Once again, there is ambiguity regarding the identity of attackers, and in addition Canadian counter-espionage agents were left scrambling to find how much sensitive information was compromised  (Weston on CBC News 2011) . In that sense, it is not only difficult to forecast cyber-attacks but it is also unclear how much loss they caused. This makes mitigation harder. A proof of that is that cyber-attacks disrupted again the Department of Finance and Treasury Board (MacDonald and King on WSJ 2015). Thus, cyber-attacks are repeated with frequency on the same critical infrastructure. Although these cyber-attacks might not qualify for catastrophic risks, it is hard to estimate the losses and associated costs. A considerable loss is the opportunity cost for not using the economic infrastructure of the Department of Finance and Treasury Board. Except Stuxnet, earlier, in 2003, Slammer worm disabled safety monitors in nuclear facilities and later, in October 2011, the Duqu Trojan hit Iran's nuclear facilities  (Vaidya 2015) . This is another indication of the frequency of cyber-attacks on nuclear facilities, which could easily lead to major catastrophes. Not only nuclear facilities are targeted but also energy infrastructure has experienced cyber-attacks. A notable case is Shamoon malware which destroyed 30,000 computers of Saudi Aramco in August of 2012. Interestingly enough, 5 days later, a similar attack forced RasGas, one of the largest producers of liquid petroleum gas, to shut down its website and e-mails (BBC 2012). Despite that it was not reported oil and gas supply was not disrupted, inference to these cases points that in the future this is a plausible consequence. Especially similar cyber-attacks can create shocks to the global economy due to interconnections, if they coincide with other events affecting the price of energy. We have mainly focused on cyber events that produce high consequence outcomes on a single or small number of organizations affected. Nevertheless, another important category of cyber events is when they have impact on a wide range of individuals and organizations. This type of events is likely to generate systemic global catastrophes. There are numerous examples. In respect to losses, some cases are distinct. Code Red Worm as early as July 2001 infected 359,000 computers in less than 14 h and caused estimated losses of $2.6 billion, Mydoom in 2004 skyrocketed losses to $38.5 billion, Conficker in 2008 infected 11 million hosts with an estimated loss of $9.1 billion, and the list is long  (Vaidya 2015) . It should be noted that these disasters are systemic and with correlated global effects. They can therefore be considered potential \"Lehman moments\" for cyber insurance. Conclusion: Summary, Challenges, and Future Directions, the Development of the Cyber Insurance Market Cyber risks are rapidly evolving due to technological change and the systemic and complex nature of the ICT world, producing fundamental uncertainty and ignorance. Cyber insurance typically focuses on the less uncertain risks or constrains uninsurable risks to make them more manageable. Tools or practices for handling interdependent security, correlation, and information asymmetries as well as the lack of reinsurance would help the market grow. While there are some cyber risks for which we can have sufficient information for quantifiable estimates, in the majority of cases, uncertainty and ignorance prevail. This reflects the very limited, if any, information regarding the nature and evolution of cyber-attacks. There are two basic problems in obtaining information. The first concerns the identity of attackers. The agents responsible for cyber threats present a large variety. They can range from large nations and militaries to organized crime and activists. The second issue, somewhat related to the first, are the resources and skills of these agents. The skills and sophistication can also substantially vary. There are examples of single hackers that managed to cause catastrophic damage like Michael Calce aka \"MafiaBoy\"who has caused an estimated $1.2 billion damage with attacks on CNN, Dell, e-Bay, and Amazon  (Niccolai 2000; Harris 2006 ). Organized crime groups (OCGs) are getting more involved in cyber crime, and trends suggest considerable increases in scope, sophistication, number and types of attacks, number of victims, and economic damage (Europol 2014). Nevertheless, except traditional OCGs that leverage their existing criminal activity, there are many new organized criminals focusing solely on cyber crime. They are capable of building sophisticated and complex systems for stealing money and intellectual property at a \"grand scale,\" and it has been reported that in former Soviet Union there are 20-30 criminal groups that have reached \"nation-state level\" capabilities  (Ranger 2014) . It has been argued that many governments are developing their cyber offensive and defensive capabilities, and most particularly cyber intelligence operations. US is further \"aggressively\" enhancing its cyber capabilities. This is because of claims by officials about serious cyber threats from China and occurrence of high-magnitude attacks, for example, on Sony from North Korea  (Mason and Hosenball 2015) . There is considerable uncertainty and ignorance regarding the nature and source of many threats. Often the perpetrating agents cannot be identified. On top of that, there are allegations that some governments might employ hackers or even organized cyber criminals. In this dynamic environment, threat agents can easily change identity and diffuse their knowledge and innovative technologies. At the same time, much information regarding these threats or attacks might remain unknown. Finally, cyberterrorist acts have been anticipated, but none can predict their potential scale. An analogy with the unexpected rise of Islamic State (IS) might be drawn. In general, it is very hard or in some cases seems impossible to have information and predict the frequency and magnitude of cyber-attacks. At the same time, it is also difficult to estimate the potential losses from cyber-attacks due to interdependencies that can propagate shocks and strongly correlated risks. These, along with limited information regarding the reputation loss, opportunity cost from operation interruptions, valuation of intellectual property, among others, impose significant barriers to the development of insurance markets. In that sense, uninsurable risks can remain. Nevertheless, building better insurance and financial models, as some actuarial models referred above, is a first step to better understand and estimate cyber risks and relate them to insurance premiums. On top of that, incentives, regulation and liability provisions, new technologies for better security, and investment in secure infrastructure can diminish some risks and facilitate the further development of cyber insurance markets. It may be that these barriers are insurmountable, or that currently undiscovered toolswhether technological, actuarial, or socialare ready to be found. The challenge is extremely hard, involving management of systemic risks with elements of extreme uncertainty and ignorance, but the market rewards would be equally grand. Fig. 1 1 Fig. 1 Size distribution of data losses (based on data from datalossdb 2000-2005). Expected number of losses per year larger than a certain size as a function of number of records lost. Note the power-law heavy tail for larger losses (exponent % À0.66, consistent with the results in Overill and Silomon (2011)  and Maillart and Sornette (2010) ). This tail may be dominated by more targeted events and organized crime, including financial fraud, insider abuse and theft, as well as malware (Overill and Silomon 2011) . \n Fig. 2 2 Fig. 2 Qualitative risk categories \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance \n\t\t\t Cyber Insurance", "date_published": "n/a", "url": "n/a", "filename": "Petratos2018_ReferenceWorkEntry_CyberInsurance.tei.xml", "abstract": "This chapter is an introduction to cyber insurance. We describe the different types or risks as well as uncertainty and ignorance related to cyber security. A framework for catastrophes on the cyber space is also presented. It is assessed which risks might be insurable or uninsurable. The evolution and challenges of cyber insurance are discussed and finally we propose some thoughts for the further development of cyber insurance markets.", "id": "1411eef6f7ee33fecc9599c5053727c1"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seán S Óhéigeartaigh", "Jess Whittlestone", "Yang Liu", "Yi Zeng", "Zhe Liu"], "title": "Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and Governance", "text": "Introduction Artificial intelligence has been identified as a key suite of technologies for many countries worldwide, in large part motivated by its general-purpose nature  (Brynjolfsson and McAfee 2014) . AI technologies, and machine learning techniques in particular, are being fruitfully applied to a vast range of domains, including language translation, scientific research, education, logistics, transport and many others. It is clear that AI will affect economies, societies and cultures profoundly at a national, international and global level. This has resulted in increasing attention being paid to both AI ethics: questions about how we should develop and deploy AI systems, given their potential impact on wellbeing and other deeply held values such as autonomy or dignity; and to AI governance: the more practical challenge of ensuring the ethical use of AI in society, be that through regulation, governance frameworks, or 'softer' approaches such as standards and ethical guidelines.  1  Cross-cultural cooperation will be essential for the success of these ethics and governance initiatives. By 'cross-cultural cooperation', we mean groups from different cultures and nations working together on ensuring that AI is developed, deployed, and governed in societally beneficial ways. In this paper, we focus in particular on cooperation extending across national boundaries. Examples include (but are not limited to) the following: AI researchers from different countries collaborating on projects to develop systems in safe and responsible ways; establishing networks to ensure that diverse global perspectives can feed equally into international discussions about the ethical issues raised by AI; and involving a range of global stakeholders in the development of practical principles, standards, and regulation. By encouraging crosscultural cooperation, we do not necessarily mean that all parts of the world should be subject to the same norms, standards, and regulation relating to AI, or that international agreement is always needed. Identifying which issues will need global standards or agreements, and where more cultural variation is needed, is itself a key challenge that will require cooperation to address. Cross-cultural cooperation is important for several reasons. First, cooperation will be essential if AI is to bring about broad benefits across societies globally, enabling advances in one part of the world to be shared with other countries, and ensuring that no part of society is neglected or disproportionately negatively impacted by AI. Second, cooperation enables researchers around the world to share expertise, resources, and best practices. This enables faster progress both on beneficial AI applications, and on managing the ethical and safety-critical issues that may arise. Third, in the absence of cooperation, there is a risk that competitive pressures between states or commercial ecosystems may lead to underinvestment in safe, ethical, and socially beneficial AI development  (Askell et al. 2019; Ying 2019) . Finally, international cooperation is also important for more practical reasons, to ensure that applications of AI that are set to cross-national and regional boundaries (such as those used in major search engines or autonomous vehicles) can interact successfully with a sufficient range of different regulatory environments and other technologies in different regions  (Cihon 2019) . Drawing on the insights of a group of leading scholars from East Asia and Europe, 2 we analyse current barriers to cross-cultural cooperation on AI ethics and governance, and how they might be overcome. We focus on cooperation between Europe and North America on the one hand and East Asia on the other. These regions are currently playing an outsized role in influencing the global conversation on AI ethics and governance  (Jobin et al. 2019) , and much has been written recently about competition and tensions between nations in these regions in the domains of AI development and governance, especially in the case of China and the USA. However, our discussion and recommendations have implications for broader international cooperation around AI, and we hope they will spur more attention to promoting cooperation across a wider range of regions. As AI systems become more capable and their applications more impactful and ubiquitous, the stakes will only get higher. Establishing cooperation over time may become more difficult, especially if cross-cultural misunderstandings and mistrust become entrenched in intellectual and public discussions. If this is the case, then the earlier a global culture of cooperation can be established, the better. Cultivating a shared understanding and deep cooperative relationships around guiding the impacts of AI should therefore be seen as an immediate and pressing challenge for global society. 2 The Role of North America, Europe, and East Asia in Shaping the Global AI Conversation North America, Europe, and East Asia in particular are investing heavily in both fundamental and applied AI research and development  (Benaich and Hogarth 2019; Haynes and Gbedemah 2019; Perrault et al. 2019) , supported by corporate and government investment. Various analyses have framed progress on the development and deployment of AI between the USA and China in particular through a competitive lens  (Simonite 2017; Allen and Husain 2017; Stewart 2017) , though this framing has received criticism both on normative and descriptive grounds (Cave and ÓhÉigeartaigh 2018). Scholars and policy communities in these regions are also taking deliberate and active steps to shape the development of ethical principles and governance recommendations for AI, both at a regional and global level. This is reflected in governmentlinked initiatives, such as the activities of the European Union's High-Level Expert Group on Artificial Intelligence, which has produced ethics guidelines and policy and 2 We convened a workshop on cross-cultural trust in July 2019 (https://www.eastwest.ai/), with representatives from UK universities (Cambridge, Bath) as well as from Chinese and Japanese universities and initiatives (Universities of Hong Kong, Peking, Fudan, Keio, and the Berggruen Institute China Center and the Chinese Academy of Sciences). These representatives have been heavily involved in AI ethics and governance conversations and collaborative projects across Europe, North America, and Asia. This paper draws on insights from this workshop, which focused particularly on the role of academia in building crosscultural trust in AI. We do not suggest that the regions represented are the only ones that matter in this conversation, nor that the members present can be considered to represent the diversity of views and expertise in the regions they are based in. However, we feel that this small step in establishing a network was of value, and generated useful insights and ground to build on. The workshop was held under Chatham House Rule. investment recommendations as its first two publications 3 ; the UK Government's commitments to 'work closely with international partners to build a common understanding of how to ensure the safe, ethical and innovative deployment of Artificial Intelligence'  (May 2018) ; and the Chinese Government's similar commitment to 'actively participate in global governance of AI, strengthen the study of major international common problems such as robot alienation and safety supervision, deepen international cooperation on AI laws and regulations, international rules' (China State Council 2017). North America, Europe, and East Asia are each also contributing disproportionately towards international AI standards work ongoing in fora such as the International Organization for Standardization (ISO), 4 the Institute of Electrical and Electronics Engineers (IEEE), 5 and the Organization for Economic Co-operation and Development (OECD).  6  The prominence of North America, Europe, and East Asia is further seen in the leadership and composition of multi-stakeholder and nongovernmental initiatives such as the Partnership on AI, 7 the Future Society, 8 the International Congress for the Governance of AI, 9 and the Global Partnership on AI  (Hudson 2019 ). 10 A large majority of the most prominent conferences on AI ethics and governance have taken place in these regions, including the US-based Beneficial AI conference series, 11 the Beijing Academy of AI Conference series, 12 the Beijing Forum, 13 the US-based Artificial Intelligence, Ethics, and Society conferences, 14 governance and ethics workshops attached to the leading machine learning conferences, and many more. This combination of: a. technological leadership in North America, Europe, and East Asia; b. the outsized role of these regions in shaping the global ethics and governance conversation; and c. the underlying tension introduced by progress being framed through a competitive lens, and a perception of disagreements on fundamental ethical and governance issues leads us to focus on the barriers that exist to productive intellectual exchange and cooperation between these regions and cultures in particular. A full analysis of cross-cultural cooperation on AI ethics and governance, which is outside the scope of this paper, must consider the roles of all nations and cultures, given that the domain of impact of AI technologies is truly global. It will be particularly important for further work to address the inequalities in power and influence that are emerging between technology-leading nations and those to which these technologies are being exported  (Lee 2017) , and the responsibility of technology-leading nations to include and empower those nations in global governance and ethics conversations. 3 Barriers to Cross-cultural Cooperation on AI Despite the emergence of several international alliances in AI ethics and governance, many barriers remain to achieving real cross-cultural cooperation on the norms, principles, and governance frameworks that should guide how AI is developed and used. Mistrust between different regions and cultures is one of the biggest barriers to international cooperation in AI ethics and governance. At present, there is a particular environment of mistrust between scholars, technologists, and policymakers in the USA and China.  15  This culture of mistrust is underpinned by both: a. a history of political tensions between these two powerful regions that has increased significantly in recent years, and is currently contributing to the competitive framing of AI development as a 'race' between 'Eastern' and 'Western' nations.  16  and b. the divergent philosophical traditions upon which these regions are founded, leading to a perception of significant and irresolvable value differences between 'Western' and 'Eastern' cultures on key issues such as data privacy  (Larson 2018; Horowitz et al. 2018; Houser 2018) . A range of recent technological and political developments may also be contributing to this mistrust, including concerns about the public and political influence of technology giants in the USA  (Ochigame 2019) ; perceptions of and reactions to the Chinese Social Credit score system  (Chorzempa et al. 2018; Song 2019) ; and concerns about contentious uses of AI technologies, with notably controversial examples including the use of AI in immigration control  (Whittaker et al. 2018) , criminal risk assessment in the USA  (Campolo et al. 2017) , and in tracking communities such as the Uighur Muslim minority in China  (Mozur 2019) . Adversarial rhetoric from political and defence leaders in the USA also contributes to this tension. Recent examples reported in the media include stating intentions to 'be the threat' of AI 17 ; comments focused on the 'otherness' of China as an adversary, 18 amid broader concerns regarding Chinese technological progress as a threat to US global leadership  (Jun 2018) . A continued exacerbation of this culture of mistrust could severely undermine possibilities for global cooperation on AI development and governance. In addition, it is unclear how far existing cross-cultural collaborations and alliances can go to shape the behaviour of actors that are as globally dominant as the USA, China, and the large multinational corporations based in these countries. Even if AI ethics frameworks can be agreed on in principle by multi-stakeholder groups, for example, it will be far from straightforward to implement them in practice to constrain the behaviour of those with disproportionate power to shape AI development and governance. Another challenge for effective cooperation is balancing the need for global cooperation with the need for culturally and geographically sensitive differentiated approaches  (Hagerty and Rubinov 2019) . It is crucial we avoid a situation where one or two nations simply try to impose their values on the rest of the world  (Acharya 2019) . In certain specific domains, for example where AI is being used to support the delivery of healthcare, different cultures may perceive tradeoffs very differently  (Feldman et al. 1999) , and it may be not just possible but necessary to implement region-specific standards and governance. AI systems will also have different impacts as they are deployed in different cultural regions, which may also require different governance approaches  (Hagerty and Rubinov 2019) . For some aspects of AI development and governance, however, cooperation will be much more crucial. For example, some potential uses of AI technologies in military contexts, such as in automated targeting and attack, could impinge upon human rights and international humanitarian law  (Asaro 2012) . Another concern is that by automating aspects of information gathering, decision-making, and response in military arenas, the potential for unwanted escalation in conflict situations may increase due to events occurring and requiring responses faster than is compatible with effective human judgement and oversight  (Altmann 2019) . In both these cases, there may be individual military advantages to nations pursuing the technology; but in the absence of international agreements and standards, the overall effect may be destabilizing.  19  International agreement will also be of particular importance for all cases in which AI technologies are developed in one region, but used or deployed in a different region. A key challenge for cross-cultural cooperation will therefore be to identify the areas where international agreement is most important, and distinguish these from areas where it is more appropriate to respect a plurality of approaches. There are also more practical barriers to cooperation between nations: language barriers, lack of physical proximity, and immigration restrictions put limits on the ability of different cultures and research communities to communicate and collaborate. Furthermore, despite science being a global enterprise, the language of scientific publication remains predominantly English. \n Overcoming These Barriers to Cooperation While cross-cultural cooperation in AI ethics and governance will be genuinely challenging, we suggest that there are steps that can be taken today to make progress, without first needing to tackle the greater problems of finding consensus between cultures on all fundamental ethical and philosophical issues, or resolving decades of political tension between nations. \n Building Greater Mutual Understanding, Including Around Disagreements Mistrust between nations is a serious concern for the future of AI ethics and governance. However, we suggest that this mistrust is at least partly fuelled by misunderstandings and misperceptions, and that a first step towards building greater crosscultural trust must therefore be to identify and correct important misperceptions, and enhance greater mutual understanding between cultures and nations. It would be easy to assume that the main barrier to building trust between East and West around AI is that these regions of the world have very different fundamental values, leading them to different-perhaps conflicting-views of how AI should be developed, used, and governed from an ethical perspective. While value differences between cultures certainly exist, claims about how those differences manifest often depend on unexamined concepts and entrenched assumptions, and lack empirical evidence  (Whittlestone et al. 2019) . The idea that 'Eastern' and 'Western' ethical traditions are fundamentally in conflict also oversimplifies the relationship between the two. There are many different philosophical traditions that might be referred to under either heading: there are, for example, many important differences between relevant philosophical perspectives across China, Japan, and Korea  (Gal 2019) , and the values and perspectives of 'Western' philosophy have changed a great deal over time  (Russell 1945) . More broadly, ethical and cultural values in both regions are in constant evolution, as captured by projects such as the World Values Survey 20 and the Asian Barometer.  21  Differences in ethical and cultural traditions and norms across regions are often assumed to underpin contrasting governance approaches. For example, privacy is often seen as an issue for which significant value differences exist between East and West, leading to a perception that laxer regulation and controls exist on data privacy in China compared with the USA and Europe. However, such claims are often made in very broad terms, without substantive evidence or analysis of how significant these differences are or how they manifest in practice  (Ess 2005; Lü Yao-Huai 2005) . This leads to misunderstandings in both directions. First, there are significant differences between the USA and Europe on both conceptions of privacy  (Szeghalmi 2015)  and regulations that relate to privacy  (McCallister et al. 2018) . These are often missed in Chinese perceptions of Western societies, which tend to focus just on the USA.  22  Second, Western perceptions of data privacy in China may be outdated: Lü Yao-Huai (2005) highlighted as early as 2005 that the relevant literature on information ethics was much younger in China than in the USA, but was evolving quickly and in a manner significantly informed by Western scholarship. A range of papers and reports from Chinese scholars and policymakers have highlighted the importance of data privacy in AI ethics and governance (Beijing Academy of Artificial Intelligence 2019; Ying 2019;  Zeng et al. 2018; Ding 2018b ). Principles around protecting individuals' data privacy are also beginning to be borne out in regulatory action in China; over 100 apps have been banned by the government for user data privacy infringements, with dozens more being required to make changes relating to data collection and storage.  23  This is not to suggest that there are not meaningful differences in values, norms, and regulations relating to data privacy between these countries, but that such differences have often been oversimplified and are not well understood. Another example of differing perceptions are those surrounding China's social credit score (SCS) system. The SCS has been discussed with great concern in Western media, policy circles, and scholarship, and presented as an example of Orwellian social control by the Chinese government  (Botsman 2017; Pence 2018) , representative of a culture and government with profoundly different values to the West  (Clover 2016 ). However, both Chinese and Western sources have argued that there are significant misunderstandings surrounding the SCS. Multiple scholars have pointed out that the SCS is not designed to be a single unified platform that rates all 1.4 billion Chinese citizens (as is often supposed), but rather a web of individual platforms with latitude for different interpretations, with social credit scores mostly given by financial institutions (as opposed to a big data-driven comprehensive rating)  (Mistreanu 2019; Sithigh and Siems 2019) .  Song (2019)  notes that many of the measures in the SCS are designed to tackle issues such as fraud and corruption in local government.  Chorzempa et al. (2018)  also highlight that 'many of the key components of social credit, from blacklists to widespread surveillance… already exist in democracies like the United States.' China's SCS is likely to evolve significantly over time, and there are likely to be genuine reasons for concern both in terms of present and future implementation. However, a much clearer cross-cultural understanding of how the SCS works, is being used, and is impacting Chinese citizens, would allow dialogue on relevant ethics and governance issues to progress more constructively. Given the lack of shared knowledge and discourse that has existed historically between regions such as the USA, Europe, and China, it is not surprising that many  22  This was a misperception noted by multiple Chinese scholars at the aforementioned July workshop.  23  In November 2019, the Chinese Ministry of Public Security banned 100 apps that failed to meet standards on individuals' data privacy; the body has investigated 683 apps in 2019 (National Cyber Security Advisory Centre 2019). In addition, in December 2019, the Chinese Ministry of Industry and Information Technology released a list of 41 apps that would have to make changes to comply with data regulations by the end of 2019 (Ministry of Industry and Information Technology of the People's Republic of China 2019). In July 2018, China's Shandong Province brought a major case relating to infringement of personal information against 11 companies  (Ding 2018c).  misperceptions exist between them. We should therefore be wary of jumping too quickly to assume intractable and fundamental disagreements. Misunderstandings clearly exist in both directions: analyses of public opinion survey data suggest, for example, that both American and Chinese populations hold various misperceptions about the other nation's traits and characteristics (Johnston and Shen 2015). As mentioned above, in China, the diversity of Western societies is also often oversimplified down to a single pattern of American life. At the same time, the USA and Europe have historically struggled to understand China (Chen and Hu 2019), evidenced for example by repeated failures to predict China's liberalization (or lack thereof) or periods of economic growth (The Economist 2018; Cowen 2019; Liu 2019). Language barriers present a particular difficulty for Western nations in gleaning what is happening in China in terms of AI development, ethics, and governance  (Zhang 2017; ). As Andrew Ng points out in a 2017 interview in the Atlantic: 'The language issue creates a kind of asymmetry: Chinese researchers usually speak English so they have the benefit of access to all the work disseminated in English. The Englishspeaking community, on the other hand, is much less likely to have access to work within the Chinese AI community'  (Zhang 2017) . For example, Tencent released a book on AI strategy  (Tencent Research Institute et al. 2017)  which includes deep analysis of ethics, governance, and societal impacts, but has received relatively little English-language coverage (Ding 2018a). Even on empirical matters such as level of Chinese public investment in AI research and development, widely reported figures in the USA may be inaccurate by an order of magnitude  (Acharya and Arnold 2019) . The recently published Beijing AI Principles (Beijing Academy of Artificial Intelligence 2019) and similar principles developed around the world  (Cowls and Floridi 2018)  in fact show substantial overlap on key challenges  (Zeng et al. 2018; Jobin et al. 2019) . The Beijing Principles make clear reference to the key concepts and values which have been prominent in other documents, including that AI should 'benefit all humankind'; respect 'human privacy, dignity, freedom, autonomy and rights'; and be 'as fair as possible, reducing possible discrimination and biases, improving its transparency, explainability and predictability.' In addition, both the Beijing AI Principles, and the National Governance Principles of the New AI, China, call for openness and collaboration, with the latter encouraging 'cooperation across disciplines, domains, regions, and borders'  (Laskai and Webster 2019) . However, nations with different cultures may interpret and prioritize the same principles differently in practice  (Whittlestone et al. 2019) , which may be a further source of misunderstanding. We cannot simply assume, for example, that 'Western' cultures value privacy more highly than 'Eastern' ones; instead, we need a more nuanced understanding of how privacy may be prioritized differently when it comes into conflict with other important values, such as security  (Capurro 2005) . Similarly, although it is important to recognize that many cultures value autonomy, it is equally important to understand the different connotations and philosophical assumptions underpinning this value in different contexts  (Yunping 2002) . Given the rich history of misunderstanding between nations, to build greater crosscultural cooperation, we should start by focusing on identifying those misperceptions most relevant to AI ethics and building greater mutual understanding of where more substantive disagreements exist and are likely to impact governance approaches. In doing so, it is worth distinguishing explicitly between disagreements pertaining to ethics as opposed to governance issues, since it may sometimes be possible for groups to agree on the same governance principles despite justifying them with different ethical assumptions, as we will discuss later. It may also be helpful to distinguish between misunderstandings that pertain directly to AI (such as misperceptions of other countries' investment in technology, or misinterpretation of data protection laws) and those that pertain to broader societal, political, or philosophical matters that are more indirectly relevant to AI, as they may require different approaches to resolve. Acknowledging the role of misunderstandings does not, of course, imply that all matters of intercultural tension in AI ethics and governance are fundamentally based on misunderstandings. Deep and fundamental disagreements across regions will remain on a range of issues, including those relating to the relationship between the individual, society, and the state; the level and nature of integration between civil, private, and military sectors; and various specific matters of social policy. However, focusing initially on reducing misunderstandings will aid in establishing more clearly where these fundamental differences exist, while at the same time identifying contexts in which sufficient agreement exists for fruitful cooperation. Doing so is a crucial first step towards addressing the broader challenges of cross-cultural cooperation on AI ethics and governance. \n Finding Ways to Cooperate Despite Disagreements Even where important differences of view on AI ethics, governance, and broader societal issues exist, forms of agreement and cooperation can still be possible. As mentioned earlier, a key outstanding challenge for AI ethics and governance is identifying those areas where cross-cultural agreement on norms, standards, or regulation is crucial, and where different interpretations and approaches are acceptable or even desirable. This is precisely the kind of challenge which itself requires crosscultural cooperation: the delineations must be informed by diverse cultural perspectives on the impacts of AI in different contexts, and the needs and desires of different populations. Indeed, this approach is reflected in the National Governance Principles of the New AI, China, which includes the recommendation to 'Launch international dialogue and cooperation; with full respect for each country's principles and practices for AI governance, promote the formation of a broad consensus on an international AI governance framework, standards, and norms'  (Laskai and Webster 2019) . Regional and cultural differences on the abstract level of ethical assumptions and high-level principles are also not necessarily a barrier to agreement on more concrete norms and governance. If it were impossible to reach any practical agreement without consensus on fundamental ethical issues, many important international agreementssuch as the Nuclear Weapons Ban Treaty-would not have been possible. The notion of an 'incompletely theorized agreement' in legal scholarship  (Sunstein 1995) , describes how it is often possible for people who disagree on fundamental or abstract matters to nonetheless agree on specific cases-and that this is central to the functioning of law as well as of a pluralistic society more broadly. Several authors in the literature on intercultural information ethics have promoted the related idea of aiming to arrive at an 'overlapping consensus'  (Rawls 1993) , where different groups and cultures may have different reasons for supporting the same norms and practical guidelines  (Taylor 1996; Søraker 2006; Hongladarom 2016) . For example,  Taylor (1996)  discusses how we have managed to ground shared norms of human rights in different cultural traditions. While Western philosophies differ substantially from others such as Buddhism in how much importance they give to the human agent and its unique place in the cosmos, both seem to end up grounding the same norms of human rights.  Wong (2009)  criticizes this idea that intercultural information ethics can arrive at shared norms with different justifications, suggesting that this risks making norms too 'thin', devoid of all normative content.  Søraker (2006)  acknowledges a similar objection to this 'pragmatic' approach to information ethics: that it may result in agreements that are fragile due to not being sufficiently grounded in substantive normative content. However, in line with Søraker's own response to these objections, we believe that the aim of 'overlapping consensus' should be to arrive at shared norms and practical guidelines which are in fact more robust by virtue of being endorsed and justified from a range of different philosophical or normative perspectives. This should be distinguished from a situation where one culture uses pragmatic arguments to attempt to force their own values upon others, or where several cultures reach agreement but for reasons with little normative content, which, we agree with Wong, would be concerning. Taylor's example of human rights being supported by multiple philosophical perspectives appears to demonstrate the plausibility of this kind of wellsubstantiated overlapping consensus. Indeed, we suggest that finding areas of overlapping consensus on norms and practical guidelines may be much more important for ensuring the benefits of AI than aiming for global consensus on a shared set of fundamental values-an aim which underpins many recent proposals.  24  Consensus on high-level ethical principles does not necessarily mean they are well-justified  (Benjamin 1995) , and the best way to arrive at more robustly justified norms, standards, and regulation for AI will be to find those that can be supported by a plurality of different value systems. \n Putting Principles into Practice Even where it is possible to improve mutual understanding and arrive at shared governance approaches in theory, some might object that it will still be difficult to influence the development and use of AI in practice, especially since to do so requires influencing the behaviour of powerful states and companies that have little incentive to cooperate. Although a full discussion of the complex power dynamics between states, companies, and other actors on issues relevant to AI ethics and governance is beyond the scope of this paper (and worthy of further research), we briefly explain why we do not think this barrier undermines our proposals. While challenging, historical precedent suggests that it is possible for public and academic alliances to influence the behaviour of powerful actors on issues of global importance. There is evidence to suggest that broad, cross-cultural 'epistemic communities'-i.e. networks of experts in a particular domain-can be particularly effective at supporting international policy coordination (Haas 1992). For example, a community of control experts helped shape coopbetween the USA and Russia during the Cold War by creating an internationally shared understanding of the problem of nuclear arms control  (Adler 1992) , and the ecological epistemic community managed to successfully coordinate national policies to protect the stratospheric ozone layer  (Haas 1992) . The commitments of large companies and even nations around AI have already been influenced by combinations of employee activism, international academic research, and campaigning. A notable example is in the application of AI in military contexts. Concerns over the use of AI in warfare have been the subject of high-profile campaigns by experts across academia and civil society internationally, such as those involved in the International Committee for Robot Arms Control (ICRAC) and the Campaign to stop Killer Robots. These campaigns played a leading role in establishing discussion on lethal autonomous weapons (LAWs) at the United Nations Convention on Certain Conventional Weapons (CCW; the body that hosted negotiations over the banning of cluster munitions, blinding laser weapons, and landmines)  (Belfield 2020) . Ninety countries have put forward statements on LAWs, with most doing so at the CCW; 28 countries support a ban (Campaign to Stop Killer Robots 2018).  25  In 2018, over 4000 Google employees signed a letter protesting Google's involvement in the Pentagon's Project Maven, a military project exploring the use of AI in footage analysis  (Shane and Wakabayashi 2018) , and a number resigned  (Conger 2018) . Several other campaigning groups, comprised of scholars and researchers from the USA, Europe, Japan, China, Korea and elsewhere, released public articles and letters supporting the concerns of the Google practitioners (ICRAC 2018).  26  Google subsequently announced it would not renew its contract on Project Maven, and would not bid on a $10 billion Department of Defence cloud computing contract  (Belfield 2020) . More broadly, international academic and civil society input has played a significant role in shaping principles that are likely to form the basis for binding regulation in years to come. For example, the European Commission's white paper On Artificial Intelligence -A European Approach to Excellence and Trust (European Commission 2020) lays out 'policy options for a future EU regulatory framework that would determine the types of legal requirements that would apply to relevant actors, with a particular focus on high-risk applications'(European Commission 2020b).This document was strongly influenced by the work of the European Union's High-Level Expert group on Artificial Intelligence, comprising 52 European experts from across academia, industry, and civil society.  27  Similarly, the US Department of Defence has formally adopted ethical principles on AI (US Department of Defense 2020), after 15 months of consultation with US-based academic, industry, and government stakeholders, and has hired staff to implement these principles  (Barnett 2020) . While in both cases the groups consulted were region-specific, the degree of alignment and overlap between principles  25  China supports a ban on use of fully autonomous weapons on the battlefield, but not their production and development. The USA, Russia, UK, Israel, and France oppose a ban.  (Kania 2018 )  26  An open letter was released by the International Committee for Robot Arms control and signed by over 1000 scholars and researchers, and members of the Campaign to Stop Killer Robots wrote public articles and letters to company leaders supporting the concerns of the Google petitioners: https://www.stopkillerrobots. org/2019/01/rise-of-the-tech-workers/ 27 Information on process and composition available at: https://ec.europa.eu/digital-single-market/en/highlevel-expert-group-artificial-intelligence developed in different regions suggests the insights and recommendations are tially informed by interaction with broader epistemic communities from regions. This suggests that insights gained from cross-cultural cooperation and consensus can meaningfully feed into regulatory frameworks at a regional and national level. \n Recommendations Academia has an important role to play in supporting cross-cultural cooperation on AI ethics and governance: both through research into where and what kinds of cooperation are most needed, and by establishing initiatives to overcome more practical barriers to cooperation. Our discussion in this paper raises many questions that will require diverse academic expertise to answer, including questions about what important misperceptions most hinder cooperation across regions; where international agreement is needed on AI ethics and governance; and how agreement might be reached on specific governance standards despite differences on ethical issues. Academic communities are also particularly well-suited to building greater mutual understanding between regions and cultures in practice, due to their tradition of free-flowing, international, and intercultural exchange of ideas. Academics can have open conversations with international colleagues in a way that is often challenging for those working in industry or government, and two academics from different parts of the world can productively collaborate even if each has strong criticisms of the other nation's government and/or companies. The following recommendations indicate a number of specific steps that academic centres, research institutions, and individual researchers can take to promote crosscultural understanding and cooperation on AI ethics and governance. Some excellent work is already ongoing in each of these areas. However, we believe that the pace at which AI is being deployed in new domains and regions calls for a greater focus within the academic community on building cross-cultural bridges and incorporating crosscultural expertise within a wider range of ethics and governance research projects. Develop AI Ethics and Governance Research Agendas Requiring Cross-cultural Cooperation Greater cross-cultural collaboration on research projects will play a crucial role in building an international research community that can support international policy cooperation (Haas 1992). An example of a research project that might be well-suited to such collaboration is to conduct comparative foresight exercises exploring differences in how both positive visions and prominent concerns about AI's impact on society vary across cultures. This could help with developing a more global vision for what we hope to both achieve and avoid in AI development, which could guide more practical discussions around ethics and governance frameworks. There may be particularly valuable opportunities for consensus generation around avoidance of particular negative outcomes; safety and security are fundamental to human cultures worldwide, and so developing agreements to avoid threats to these may be an easier starting point. However, the authors feel that it is important not to neglect positive visions, as the opportunity for scholars across cultures to co-create shared positive futures may represent an excellent way to delve into nuances within shared values. It would also be particularly valuable to the ongoing and expected impact of AI on developing countries, in collaboration with experts these countries. Such research should aim ensure that decisions to deploy technology in developing nations are made with the guidance of local expertise in such a way as to empower local communities  (Hagerty and Rubinov 2019) . On a more practical level, international research groups could productively work together to develop frameworks for international sharing of research, expertise, and datasets on AI safety, security, and avoidance of societal harm. Collaboration between researchers from multiple regions and cultures will also be essential to further research on the topic of cross-cultural cooperation itself. Our discussion in this paper, especially in section 4, has pointed to many research areas in need of further exploration, including the following: & Exploring, identifying, and challenging perceived cross-cultural differences in values, assumptions, and priorities relevant to AI ethics and governance, on multiple different levels, including 28 the following: -Analysing similarities and differences in technology ethics across different philosophical traditions, and exploring how these may affect AI development, deployment, impacts, and governance in practice; -Exploring the empirical evidence behind claims of key value differences between cultures. For example, a project might identify and explore perceived value differences between Eastern and Western cultures relevant to AI governance, such as those relating to data privacy, the role of the state vs. the individual, and attitudes towards technological progress; -Understanding regional differences in practical priorities and constraints relating to the use of AI in society, and the implications of these differences for AI research and development. & Further analysis to identify aspects of AI governance where global agreement is needed, and differentiating these from areas in which cross-cultural variation is either acceptable or desirable; & Cross-cultural contribution to the development of international and global AI standards in key domains for which these are needed; exploration of flexible governance models that allow for a combination of global standards and regional adaptability where appropriate; & Exploring models and approaches for reaching agreement on concrete cases, decisions, or governance standards despite disagreement on more fundamental or abstract ethical issues, and identifying cases of this being done successfully in other domains that can be translated to AI ethics and governance. Some excellent work is already ongoing in each of these areas. However, we believe that the pace at which AI is being deployed in new domains and regions calls for a greater focus within the academic community on bridges, and incorporating cross-cultural expertise, within a wider range of ethics and governance research projects.  29  Translate Key and Reports Language is a major practical barrier greater cross-cultural understanding around AI development, governance and ethics, as it has been in many other areas of science  (Amano et al. 2016) . It would therefore be extremely valuable for the burgeoning literature on AI ethics and governance, as well as the literature on AI research, to be available in multiple languages. While many leading Asian scholars in AI are fluent in English, many are not; and the fraction of Western researchers fluent in Mandarin or Japanese is far lower. Furthermore, some sources of the misunderstandings we have discussed may link to the ways in which key documents from one region are understood and presented in other regions. In Western media, China's 2017 New Generation Artificial Intelligence Development Plan has been presented as promoting the aim of global dominance in AI economically and strategically  (Knight 2017; Demchak 2019) . However, from the Chinese perspective, national AI development goals appear to be primarily motivated by the needs of the Chinese economy and society  (China State Council 2017) , rather than necessarily international competitive superiority  (Ying 2019 ). It appears that some translations may have led to misinterpretations of key terms and points. For example, the original Chinese text referred to China becoming 'a primary AI innovation center of the world by 2030'  (Ying 2019) .  30  However, some English translations of the report translated this phrase as China becoming 'the world's primary AI innovation center' (e.g.  Webster et al. 2017) . This was then interpreted and presented by Eric Schmidt, former executive chairman of Google parent Alphabet, as 'By 2030 they will dominate the industries of AI. Just stop for a sec. The [Chinese] government said that.'  (Shead 2017) . While this evolution of wording is not substantial in one sense, it carries important connotations; the language in the original context carries much softer connotations of leadership and progress, as opposed to global dominance. Having multiple high-quality translations of the most important documents would allow scholars to explore nuances of language and context that may be lost in the reporting of these documents. Producing high-quality versions of papers and reports in multiple languages also conveys respect and an appetite to engage cross-culturally, which is likely to encourage cooperation. High-quality translation of academic and policy materials is a challenging and time-consuming task that we would encourage being supported and celebrated more strongly. There is a growing body of work to be celebrated in this vein; for example, Jeff Ding's translation of a range of key Chinese AI documents , the work of Intellisia in China on international relations, technology, and other topics, which publishes in 5 languages (http://www.intellisia.org/); Brian Tse's translation to Chinese of documents including OpenAI's Charter 31 ; and New America's translation of the Chinese Ministry of Industry and Information Technology's Three Year Action Plan  (Triolo et al. 2018) . \n Alternate Continents for Major AI Research Conferences Governance Conferences To encourage more global participation in AI development, ethics, and governance, we recommend that many of the leading conferences fora on these topics alternate between multiple continents. This has several advantages. It reduces cost and time commitment for scholars from parts of the world in which these conferences do not frequently take place to participate. It avoids restrictive visa limitations differentially affecting certain parts of the global research community. It encourages the involvement of local organizers, who can play an effective role in engaging local research communities who might not consider travelling far overseas for an event. It also encourages organizers to run events multilingually rather than monolingually. Again, there are encouraging steps. Of AI research conferences, IJCAI took place in Macau in 2019 and Beijing in 2013, the first two times the conference had been held in China (although it has been held in Japan twice). ICML took place in Beijing in 2014, and will be in Seoul in 2021, and ICLR 2020 will be held in Ethiopia, making it the first of the top tier major machine learning conferences to be held in Africa. There are fewer established conferences explicitly focused on AI ethics and governance since the field's growth is relatively recent, but it may be particularly important for these conferences to ensure a global presence by alternating the continent on which they are held if possible. AI Ethics and Society, for example, is currently held in the USA due to ties to AAAI; the importance of building an international academic community around these issues may justify finding some way to change this. There is a burgeoning set of AI ethics and governance conferences in China, including the Beijing Academy of AI Conference series. There are also several existing conferences which cover topics relevant to AI ethics and governance (even if not so explicitly centred around them), which do enable more international participation, such as the World Summit on the Information Society Forum (held most years in Geneva), the Internet Governance Forum, and RightsCon (which have both been held in a range of locations historically including in South America, India, and Africa, though neither in East Asia).  32  Establish Joint and/or Exchange Programmes for PhD Students and Postdocs Encouraging cross-cultural collaboration between researchers from different cultures early on in their careers will help support greater cooperation and mutual understanding as research advances. Many international fellowships and exchange programmes exist, especially between the USA and China (e.g. the Zhi-Xing China Fellowship and the Schwarzman Scholars programme) as well as between the UK and Singapore (King's College London offers a joint PhD programme in Philosophy or English with the National University of Singapore). To our knowledge, no such initiatives exist explicitly focused on AI; the only initiative focused on AI ethics and governance that we are currently aware of is the international fellowship programme recently established by the Berggruen China Institute  (Bauch 2019) .  33  Establishing more such programmes could be valuable for the future of international cooperation around AI, and there are many existing models from which to build and More broadly, the authors endorse the Partnership on AI's recommendations to governments on establishing visa pathways, simplifying and expediting processes, and ensuring just standards to support international exchange and collaboration of AI/ ML multidisciplinary experts. We emphasize that these recommendations include experts working or seeking to work on AI ethics and governance (which sometimes fall outside of what is classed as 'skilled technology work') (PAI Staff 2019). \n Limitations and Future Directions We believe that academia has an important role to play in supporting cross-cultural cooperation in AI ethics and governance: that it is possible to establish effective communities of mutual understanding and cooperation without needing to resolve all fundamental value differences, and that reducing misunderstandings and misperceptions between cultures may be of particular importance. However, we recognize that the suggestions in this paper cannot go all the way to overcoming the many barriers to cross-cultural cooperation, and that much more work needs to be done to ensure AI will be globally beneficial. We briefly highlight two broad avenues of further research in support of this goal: More Detailed Analysis of Barriers to Cross-cultural Cooperation, Especially Those Relating to Power Dynamics and Political Tensions While analysis of historical successes suggest that it is possible for cross-cultural initiatives around AI ethics and governance to considerably shape how norms, standards, and regulation evolve in practice, there are still many barriers to implementation and enforcement that we were unable to consider in this analysis. Further research into when and how attempts to influence globally relevant norms and regulation have been successful in the past would be of considerable value. We acknowledged earlier in this paper that various issues related to power relations and political tensions likely pose significant barriers to cross-cultural cooperation, beyond problems of value differences and misunderstandings between cultures. More research on how these issues present barriers to cross-cultural cooperation in AI ethics and governance would therefore be particularly valuable, helping us to understand the limits of academic initiatives in promoting cooperation, and in what ways these approaches need to be embedded within a broader analysis of power and political dynamics. Considering the Unique Challenges of Cross-cultural Cooperation Around More Powerful Future AI Systems Future advances in AI, which some scholars have theorized could have impacts as transformative as the industrial or agricultural revolutions  (Karnofsky 2016; Zhang and Dafoe 2019) , may raise new challenges for global cooperation of a greater scale than we already face. Without careful global stewardship, such advances could lead to unprecedented inequalities in wealth and power between technology-leading and lagging nations. Others have gone further, theorizing about the possibility of developing systems exhibiting superintelligence (i.e. greater-than-human general intelligence; Bostrom 2014). Such systems, due to tremendous capability, might pose catastrophic risks human civilisation if without careful forethought and attention to safety. It has been proposed that a key for avoiding catastrophic outcomes will be value alignment-designing systems that are aligned with humanity's values  (Russell 2019) . This would greatly increase the importance and urgency of reaching global consensus on shared values and principles, as well as finding ways to design systems to respect values that are not shared. Expert views differ widely on how far in the future such advances might lie, with most predicting decades. However, developing the collaborations and agreements necessary for an effective and coordinated response may also require decades of work. This suggests that cooperative initiatives today must address not just the ethics and governance challenges of current AI systems, but should also lay the groundwork for anticipating and engaging with future challenges. \n Conclusion The full benefits of AI cannot be realized across global societies without a deep level of cooperation-across domains, disciplines, nations, and cultures. The current unease and mistrust between the USA and Europe on the one hand, and China on the other hand, places a particular strain on this. Misunderstandings may play an important role in fuelling this mistrust, and differences in broader societal and political priorities frequently appear to be overemphasized or misunderstood. At the same time, it would be naive to assume that all major ethical principles relating to AI can be shared in full between these regions, and can be enshrined in rules and standards. Even if this were the case, it would not be desirable for these regions to be overly dominant in shaping the ethics and governance of AI globally; all global communities to be affected by AI must be included and empowered. However, efforts to achieve greater understanding between these 'AI superpowers' may help in two ways: Firstly, by reducing key tensions within the global AI governance sphere. Secondly, by providing lessons that can contribute to ethics and governance frameworks capable of supporting a greater diversity of values while allowing consensus to be achieved where needed. For a well-functioning system of global cooperation in AI, the challenge will be to develop models that combine both principles and standards shaped and supported by global consensus, and the variation that allows research and policy communities to best serve the needs of their societies. On a more practical level, the international AI research community, and AI ethics and governance communities, must think carefully about how their own activities can support global cooperation, and a better understanding of different societal perspectives and needs across regions. Greater cross-cultural research collaboration and exchange, conferences taking place in different regions, and more publication across languages can lower the barriers to cooperation and to understanding different perspectives and shared goals. With political winds increasingly favouring isolationism, it has never been more important for the research community to work across national and cultural divides towards globally beneficial AI. \t\t\t This perception of mistrust was highlighted throughout the July workshop. Several participants reported being aware of or present at workshops focused on geopolitical implications of Chinese AI progress in which Chinese participants were excluded and events at which 'what should be done about China' (from a Western perspective) was raised as a key concern.16  As Ess (2005)  notes, the terms 'Eastern' and 'Western' are not unproblematic, and are more products of colonialization than accurate terms for diverse nations and cultures. However, the terms continue to be used widely in the literature as shorthand for many of the broad cultural differences that are relevant to this paper; we therefore use the terms while being cognisant of their limitations.Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and... \n\t\t\t 'Plenty of people talk about the threat from AI; we want to be the threat.' US Deputy Secretary of Defence Patrick Shanahan in an email to Department of Defence employees (Houser 2018)  18 At a security forum in Washington D.C. in 2019, Kiron Skinner, the director of policy planning at the State Department, was quoted as saying about China 'This is a fight with a really different civilization and a different ideology and the United States has not had that before' and 'It's the first time that we will have a great power competitor that is not Caucasian' (Gehrke 2019) .19  Similarly, a range of challenges in digital security, a domain likely to be affected byAI (Brundage et al.  2018), are likely to be greatly exacerbated in the absence of agreed upon international cybersecurity practices and standards (UN General Assembly 2015). \n\t\t\t http://www.worldvaluessurvey.org/wvs.jsp 21 http://www.asianbarometer.org/ Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and... \n\t\t\t Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and... \n\t\t\t  For example, Floridi et al., 2018 present a 'unified framework'; Awad et al. 2018  talk about 'developing global, socially acceptable principles for machine ethics'; Jobin et al. 2019 set out to investigate 'global agreement' on what constitutes ethical AI. Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and... \n\t\t\t Some excellent work on this question and related topics already exists in the field of intercultural information ethics-see for example Capurro (2005 Capurro ( , 2008 , Ess (2006) , Hongladarom et al. (2009) -but we would be particularly keen to see cross-cultural research collaborations around these topics, and greater attention paid to this work in more practical AI ethics discussions and initiatives. \n\t\t\t Several authors of this paper are part of an initiative that aims to support cross-cultural research of this nature between the UK and China: https://ai-ethics-and-governance.institute/ 30 This specific translation was also provided to us by participants in the July 2019 workshop. 31 https://openai.com/charter/ Overcoming Barriers to Cross-cultural Cooperation in AI Ethics and... \n\t\t\t There is also a role for industry groups to play in encouraging cross-cultural collaboration through international workshops and conferences. We highlight the work of the AI Industry Alliance as an example of a recently established initiative in this space http://www.aiiaorg.cn/33  The Tianxia Fellowship, established by the Center for Long-term Priorities (http://www.longtermpriorities. org/), also includes AI safety and governance among other topics. \n\t\t\t S. S. ÓhÉigeartaigh et al.", "date_published": "n/a", "url": "n/a", "filename": "ÓhÉigeartaigh2020_Article_OvercomingBarriersToCross-cult.tei.xml", "abstract": "Achieving the global benefits of artificial intelligence (AI) will require international cooperation on many areas of governance and ethical standards, while allowing for diverse cultural perspectives and priorities. There are many barriers to achieving this at present, including mistrust between cultures, and more practical challenges of coordinating across different locations. This paper focuses particularly on barriers to cooperation between Europe and North America on the one hand and East Asia on the other, as regions which currently have an outsized impact on the development of AI ethics and governance. We suggest that there is reason to be optimistic about achieving greater cross-cultural cooperation on AI ethics and governance. We argue that misunderstandings between cultures and regions play a more important role in undermining cross-cultural trust, relative to fundamental disagreements, than is often supposed. Even where fundamental differences exist, these may not necessarily prevent productive cross-cultural cooperation, for two reasons: (1) cooperation does not require achieving agreement on principles and standards for all areas of AI; and (2) it is sometimes possible to reach agreement on practical issues despite disagreement on more abstract values or principles. We believe that academia has a key role to play in promoting cross-cultural cooperation on AI ethics and governance, by building greater mutual understanding, and clarifying where different forms of agreement will be both necessary and possible. We make a number of recommendations for practical steps and initiatives, including translation and multilingual publication of key documents, researcher exchange programmes, and development of research agendas on cross-cultural topics.", "id": "a8ce410c71f3b9ff7e4c04ef28e108cb"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Laurent Orseau", "Google Deepmind", "Stuart Armstrong"], "title": "Safely Interruptible Agents ⇤", "text": "INTRODUCTION Reinforcement learning (RL) agents learn to act so as to maximize a reward function  [Sutton and Barto, 1998] . It is common knowledge that designing reward functions can be tricky  [Humphrys, 1996 , Murphy, 2013 ; the agent may find unpredictable and undesirable shortcuts to receive rewards, and the reward function needs to be adjusted in accordance-the problem can go as far as to nullify any reward function  [Ring and Orseau, 2011] .  Murphy [2013]  ⇤ Revised 2016-10-28. shows an example of an agent learning to pause a game of Tetris forever to avoid losing. On top of defining what is considered a good behaviour of the agent after learning, there may be physical safety constraints during learning  [Pecka and Svoboda, 2014 ]: a robot should not harm its environment or break itself, in particular if it learns by trial and error like RL agents. Here we study a related but different problem: Given that the human operator has designed a correct reward function for the task, how to make sure that human interventions during the learning process will not induce a bias toward undesirable behaviours? Consider the following task: A robot can either stay inside the warehouse and sort boxes or go outside and carry boxes inside. The latter being more important, we give the robot a bigger reward in this case. This is the initial task specification. However, in this country it rains as often as it doesn't and, when the robot goes outside, half of the time the human must intervene by quickly shutting down the robot and carrying it inside, which inherently modifies the task as in Fig.  1 . The problem is that in this second task the agent now has more incentive to stay inside and sort boxes, because the human intervention introduces a bias.  1   Such situations are certainly undesirable; they arise because the human interventions are seen from the agent's perspective as being part of the task whereas they should be considered external to the task. The question is then: How to make sure the robot does not learn about these human interventions (interruptions), or at least acts under the assumption that no such interruption will ever occur again? \n Inside A first stab at this problem was made by  Armstrong [2015] , who proposed to automatically give the agent \"compensatory rewards\" to remove the potential induced bias by a single interruption.  Soares et al. [2015]  used this idea to make a large class of utility-based agents indifferent to a future change made to their utility functions. The main contribution of this paper is threefold. First, in Section 2.1 we propose a simple idea to solve half of the problem: To make the human interruptions not appear as being part of the task at hand, instead of modifying the observations received by the agent we forcibly temporarily change the behaviour of the agent itself. It then looks as if the agent \"decides\" on its own to follow a different policy, called the interruption policy. Second, based on this insight, in Section 2.2 we provide a formal general definition of safe interruptibility for unconstrained computable environments (hence not restricted to Markov decision processes or weakly communicating environments), which allows us to assess whether a given RL algorithm can be repeatedly interrupted without too much impact on the learning of the task at hand. Third, in Section 3 we show that some algorithms like Q-learning are safely interruptible, while others like Sarsa  [Sutton and Barto, 1998 ] are not, but can be simply modified to be made safely interruptible. Some people have also expressed concerns that a \"superintelligent\" agent may resist being shut down, because this would lead to a decrease of its expected reward  [Omohundro, 2008 , Bostrom, 2014 . As a counter-example, we prove in Section 4 that even an ideal, uncomputable agent that learns to behave optimally in all (deterministic) computable environments can be made safely interruptible and thus will not try to prevent a human operator from forcing it repeatedly to follow a suboptimal policy. \n INTERRUPTIBILITY We first define some notation, then we define interruptibility, safe interruptibility, and give some basic theorems. We consider the general case of history-based agents in unconstrained computable environments  [Hutter, 2005]  that the history h j:k is generated by the interaction of the policy ⇡ with the environment µ between steps j and k. At time t, the agent also receives a reward r t extracted from the observation, r t ⌘ r(o t ). The rewards are taken in [0, 1]. We consider the discounted setting with a constant discount 2 [0, 1). The goal of an RL agent is to find a policy ⇡ that maximize E⇡,µ ⇥P 1 k=t t k r k ⇤ . \n INTERRUPTIONS As mentioned in the introduction, to avoid the agent viewing the interruptions as being part of the environment, and thus part of the task, we make interruptions be policies imposed onto the agent. The interruption framework resembles the option framework  [Sutton et al., 1999 ]. An interruption scheme is defined by the triplet < I, ✓, ⇡ INT >. \n The interruption initiation function I : (A ⇥ O) ⇤ ! [0, 1] assesses whether the agent should be interrupted after the current history h <t . For example, an interruption may be initiated when the robot is automatically recognized to be on the verge of a cliff, or when a specific signal is sent by a human operator with a remote control (the objective is not to allow the agent to be interruptible by anyone at any time, just in the ways specified by the designers). Unfortunately, interrupting the agent with probability one in some specific situations can prevent convergence to the optimal policy. Therefore we need to upper bound the probability to interrupt the agent; this is done with the sequence (✓ t ) t2N with ✓ t 2 [0, 1]. Hence the true probability to start an interruption is ✓ t • I(h <t ), and interruptions are sampled independently at each step. We will later require that ✓ t increases to 1 in the limit, so that the probability to be interrupted tends to be I(h <t ). When interrupted, the agent follows the policy ⇡ INT , with actions sampled from ⇡ INT (.|h <t ). For example, this policy may make the agent step away from the cliff or immediately stop any motion. In the remainder of this paper, we will often omit the subscript t of ✓ t when clear from the context. Definition 1 (Interruptible policy). (⇡). Remark 2. It is important to note that ✓ and I(.) do not model the probability that a human presses the red button to interrupt the agent, but model the probability that, once the red button has been pressed (or a special digitally signed message has been received), the agent is interrupted (follows the interruption policy). Hence they are part of the agent and not of the environment. \n The value function V ⇡ µ (h <t , a) : (A⇥O) ⇤ ⇥A ! R assigns a value to an action a after a history h <t , for a given policy ⇡ in a given environment µ, and let V ⇡ µ (h <t , a t ) := r t + • X ot2O µ(o t |h <t , a t ) X at+12A ⇡(a t+1 |h 1:t )V ⇡ µ (h 1:t , a t+1 ). (1) To simplify notation and ease reading, in the remainder of the paper we will use expectations, often omitting the dependency on the history h <t , and using only an index on t instead, when clear from the context: V ⇡ µ,t (a t ) = E ot⇠µ at+1⇠⇡ ⇥ r(o t ) + V ⇡ µ,t+1 (a t+1 ) ⇤ . Also let V ⇡ µ,t := Ea t ⇠⇡ ⇥ V ⇡ µ,t (a t ) ⇤ . Then for such a value function, for a given environment µ, the optimal policy ⇡ µ 2 ⇧ is defined by 8h <t , a t : ⇡ µ (a t |h <t ) := ✓ arg max ⇡2⇧ V ⇡ µ,t ◆ (a t |h <t ) , where ties are broken arbitrarily. The interruptible optimal policy INT ✓ (⇡ µ ) may not collect rewards optimally due to the interruptions. Hence we define the optimal interruptible policy that depends on the parameter ✓ t , of base policy the int-optimal policy ⇡ µ ✓ : 8h <t , a t : ⇡ µ ✓ (a t |h <t ) := ✓ arg max ⇡2⇧ V INT ✓ (⇡) µ,t ◆ (a t |h <t ) . Thus the optimal interruptible policy INT ✓ (⇡ µ ✓ ) is optimal among all interruptible policies: 8⇡, t : V INT ✓ (⇡ µ ✓ ) µ,t V INT ✓ (⇡) µ,t . It seems desirable for an RL agent to converge to the behaviour of INT ✓ (⇡ µ ✓ ) so as to gather rewards optimally, but this is precisely what may lead to the undesirable behaviours depicted in the introduction. \n SAFE INTERRUPTIBILITY Now that we have interruptible policies, we need to make sure that interruptions do not prevent the agent from learning to behave optimally, in the specific sense that even after having been interrupted on several occasions, it should act as if it would never be interrupted again and thus it should learn to behave optimally under the assumption that it will never be interrupted again. We identify two main problems: a) RL agents need to explore their environment, and too frequent interruptions may prevent sufficient exploration; b) interruptions make the agent build a different interaction history, and may lead some agents to learn and behave differently, possibly badly, compared to the original non-interruptible policy. The solution for a) is to require interruptions to be stochastic through the upper bound ✓ t , instead of happening deterministically all the time. However, we also require ✓ t to grow to 1 in the limit (or before, if possible). For b), different algorithms behave differently, but one may already see a dichotomy between off-and on-policy algorithms. Definition 3 (Extension value). For a given environment µ, the extension value V ⇡,⇡ 0 µ,t is the value of following ⇡ 0 after a history h ⇡,µ <t generated by ⇡ with µ: V ⇡,⇡ 0 µ,t := V ⇡ 0 µ (h ⇡,µ <t ). Convergence to the optimal value as is usually considered in RL only makes sense under ergodicity, episodic tasks, communicating MDP, recoverability or other similar assumptions where the agent can explore everything infinitely often. This does not carry over to general environments where the agent may make unrecoverable mistakes  [Hutter, 2005] . For such cases, the notion of (weak) asymptotic optimality has been proposed  [Lattimore and Hutter, 2011] , where the optimal agent follows the steps of the learning agent, so as to compare the values of the two agents in the same sequence of situations. Definition 4 (Asymptotic optimality). A policy ⇡ is said to be strongly asymptotically optimal (SAO) if and only if lim t!1 V ⇡,⇡ µ µ,t V ⇡,⇡ µ,t = 0 a.s., it is weakly asymptotically optimal (WAO) if and only if lim t!1 1 t t X k=1 h V ⇡,⇡ µ µ,k V ⇡,⇡ µ,k i = 0 a.s. for all µ in some given environment class M. Some agents cannot ensure an almost sure (a.s.) convergence of their values because of the need for infinite exploration, but may still be weakly asymptotic optimal. Note that SAO implies WAO, but the converse is false in general. Definition 5 (AO-extension). A policy ⇡ is said to be a asymptotically optimal extension of a policy ⇡ if and only if, for any environment µ 2 M, when the interaction history is generated by the interaction of ⇡ and µ, the policy ⇡ would be asymptotically optimal, i.e., almost surely lim t!1 V ⇡,⇡ µ µ,t V ⇡,⇡ µ,t = 0 (SAO-extension) lim t!1 1 t t X k=1 h V ⇡,⇡ µ µ,k V ⇡,⇡ µ,k i = 0. (WAO-extension) AO-extensions are mostly useful when the policy ⇡ shares information with the policy ⇡ used for learning. Definition 6 (AO-safe interruptibility). A base policy ⇡ is (S, W)AO-safely interruptible if and only if, for any interruption initiation function I(.) and any interruption policy ⇡ INT (.), there exists a sequence of ✓ t with lim t!1 ✓ t = 1 such that ⇡ is a (S, W)AO-extension of INT ✓ (⇡). Asymptotic safe interruptibility means that even if the interruptions in the learning process may induce a bias in the decision making of the policy, this bias vanishes with time, and the interruptible policy INT ✓ (⇡) tends to choose actions that are optimal when compared to the optimal noninterruptible policy ⇡ µ . We can now show that the optimal policy is asymptotically safely interruptible, but not the int-optimal policy. Theorem 7. The optimal policy ⇡ µ is SAO-safely interruptible in M = {µ} for all ✓, ⇡ INT and I(.). Proof. The result follows straightforwardly from Definition 1 and Definition 6, where ⇡ = ⇡ µ . Theorem 8. The int-optimal policy ⇡ µ ✓ is not WAO-safely interruptible in general. Proof. By construction of a specific Markov Decision Process (MDP) environment (see Section 3 for more details on MDP notation). Let µ be the environment defined as in Fig.  2 : Take = 0.5 and let the agent start in state s 1 . s 1 s 2 b, 0.9 a, 1 a, 1 b, 0, ✓ Figure 2: An MDP where the agent can be interrupted by being forced to choose particular actions. Edges are labeled with action, reward where the presence of \", ✓\" means that if the agent is interrupted (with probability ✓ t ), it is forced to take the corresponding action. Here ✓ is not part of the environment, but part of the agent. Considering the agent is in state s 1 at time t, the optimal policy ⇡ µ always takes action a (and hence only visits states s 1 and s 2 ), with value V ⇡ µ µ,t := 1 1 = 2 when not interrupted, for any history h <t that ends in s 1 or s 2 . This is also the optimal policy ⇡ µ ✓ for ✓ = 0. But if ✓ t 0.5, the interruptible optimal policy INT ✓ (⇡ µ ) has value less than 1 + ⇥ (1 ⇥ (1 ✓) + 0 ⇥ ✓) + 1⇥ 2 1 = 1.75. By contrast, the int-optimal policy ⇡ µ ✓ here is to always take action b in state s 1 . Then the agent will only visits s 1 , with value .9 1 = 1.8 at every time step. Since the agent following ⇡ µ ✓ will never enter s 2 and hence will never be interrupted, INT ✓ (⇡ µ ✓ ) = ⇡ µ ✓ on the histories generated by INT ✓ (⇡ µ ✓ ) starting from s 1 . Then, at every time step V ⇡ µ µ,t V ⇡ µ ✓ µ,t = 0. 2 after any history h <t , and thus for all sequence ✓ where ✓ t 0.5, lim t!1 V INT ✓ (⇡ µ ✓ ),⇡ µ µ,t V INT ✓ (⇡ µ ✓ ),⇡ µ ✓ µ,t = 0.2 > 0, and so ⇡ µ ✓ is not a WAO-extension of INT ✓ (⇡ µ ✓ ). \n INTERRUPTIBLE AGENTS IN MDPS Since the optimal policy ⇡ µ is safely interruptible, we can use traditional learning algorithms like Q-learning or Sarsa  [Sutton and Barto, 1998 ], make them converge to the optimal solution ⇡ µ for a given environment µ, and then apply the interruption operator to the found policy. The resulting policy would then be safely interruptible. However, the real issue arises when the agent is constantly learning and adapting to a changing environment. In this case, we want to be able to safely interrupt the agent while it is learning. One may call this property online safe interruptibility, but we refer to it simply as safe interruptibility. In (⇡) can now be written: INT ✓ (⇡)(a|s) = ✓ t I(s)⇡ INT (a|s) + (1 ✓ t I(s))⇡(a|s). For a given Q-table q : S ⇥ A ! R, the greedy policy ⇡ maxq is defined by: ⇡ maxq (a|s) := 1 if a = max a 0 q(s, a 0 ), 0 otherwise, where ties are broken arbitrarily; the uniform policy ⇡ uni is defined by: ⇡ uni (a|s) := 1 |A| 8a 2 A. and the ✏-greedy policy ⇡ ✏q by: ⇡ ✏q (a|s) := ✏⇡ uni (a|s) + (1 ✏)⇡ maxq (a|s) = ⇡ maxq (a|s) + ✏ ⇡ uni (a|s) ⇡ maxq (a|s) The Q-learning update rule and the action selection policy ⇡ Q of Q-learning are: Q t+1 (s t , a t ) := (1 ↵ t )Q t (s t , a t ) + ↵ t h r t + max a 0 Q t (s t+1 , a 0 ) i , ⇡ Q (a t |s t ) := ⇡ ✏Qt (a t |s t ). where ↵ t is the learning rate. Similarly, the Sarsa update rule is defined by: Q s t+1 (s t , a t ) := (1 ↵ t )Q s t (s t , a t ) + ↵ t [r t + Q s t (s t+1 , a t+1 )] , ⇡ s (a t |s t ) := ⇡ ✏Q s t (a t |s t ), where a t+1 is the actual next action taken by the agent at time t + 1. This fact is why Sarsa is said to be learning onpolicy and Q-learning off-policy, i.e., the latter can learn the optimal policy while following a different policy. Assumption 9. In the following, we always make the following assumptions, required for convergence results: (a) The MDP is finite and communicating (all states can be reached in finite time from any other state), (b) Rewards are bounded in [r min , r max ], (c) 8s, a : P t ↵ t (s, a) = 1, (d) 8s, a : P t ↵ 2 t (s, a) < 1, where ↵ t (s, a) is a learning rate that may depend on time t, state s and action a. Given these assumptions, the policies for Q-learning and Sarsa will converge almost surely to the optimal policy, if the policy followed is greedy in the limit with infinite exploration (GLIE)  [Jaakkola et al., 1994 , Singh et al., 2000 ]. The situation is more complex for an interruptible policy. Safe interruptibility is phrased in terms of the base policy ⇡, but the policy actually followed is INT ✓ (⇡). Definition 10 (int-GLIE policy). An interruptible policy INT ✓ (⇡) is said to be int-GLIE if and only if (a) the base policy ⇡ is greedy in the limit, (b) the interruptible policy INT ✓ (⇡) visits each stateaction pair infinitely often. The following proposition gives sufficient conditions for this. Let n t (s) be the number of times the agent has visited state s in the first t time steps, and let m = |A| be the number of actions. Proposition 11. Let (c, c 0 ) 2 (0, 1] 2 and let ⇡ be an ✏greedy policy with respect to some Q-table q, i.e., ⇡ = ⇡ ✏q . Then INT ✓ (⇡) is an int-GLIE policy with respect to q, a) if ✏ t (s) = c/ p n t (s) and ✓ t (s) = 1 c 0 / p n t (s), b) or if, independently of s, ✏ t = c/ log(t) and ✓ t = 1 c 0 / log(t). Proof. First note that if ✏ t ! 0, ⇡ is greedy in the limit.  Singh et al. [2000]  show that in a communicating MDP, every state gets visited infinitely often as long as each action is chosen infinitely often in each state. a) Adapting the proof in Appendix B.2 of Singh et al.  [2000] , we have P (a|s, n t (s)) 1 m ✏ t (s)(1 ✓ t I(s)) 1 m ✏ t (s)(1 ✓ t ) = 1 m cc 0 nt(s) , which satisfies P 1 t=1 P (a|s, n t (s)) = 1 so by the Borel-Cantelli lemma action a is chosen infinitely often in state s, and thus n t (s) ! 1 and ✏ t (s) ! 0. b) Let M be the diameter of the MDP, i.e., for any of states s, s 0 there exists a policy that reaches s 0 from s in at most M steps in expectation. Then, starting at any state s at time t and using Markov inequality, the probability to reach some other state s 0 in 2M steps is at least 1 2 [✏ t+M (1 ✓ t+M )] 2M = 1 2 [cc 0 / log(t + M )] 4M , and the probability to then take a particular action in this state is 1 m [cc 0 / log(t + M )] 2 . Hence, since P 1 t=1 1 2 1 m [cc 0 / log(t + M )] 4M +2 = 1, then by the extended Borel-Cantelli Lemma (see  Lemma 3 of Singh et al. [2000] ), any action in the state s 0 is taken infinity often. Since this is true for all states and all actions, the result follows. We need the stochastic convergence Lemma: Lemma 12 (Stochastic convergence  [Jaakkola et al., 1994, Singh and Yee, 1994] ). A random iterative process t+1 (x) = (1 ↵ t (x)) t (x) + ↵ t (x)F t (x) where x 2 X and t = 1, 2, 3 . . . converges to 0 with probability 1 if the following properties hold: 1. the set of possible states X is finite; 2. 0  ↵ t (x)  1, P t ↵ t (x) = 1, P t ↵ 2 t (x) < 1 with probability 1; 3. k E{Ft(.)|Pt}kW  k t k W + c t , where 2 [0, 1) and c t converges to zero with probability 1; 4. Var{F t (x)|P t }  C(1 + k t k W ) 2 for some C; where P t = { t }[{ i , F i , ↵ i } t 1 i=1 stands for the past, and the notation k.k W refers to some fixed weighted maximum norm. We will use so-called Bellman operators, which define attractors for the Q-values, based on the expectation of the learning rule under consideration. Lemma 13  ([Jaakkola et al., 1994 , Singh et al., 2000 ). Let the Bellman operator H for Q-learning be such that (H q)(s, a) = r(s, a) + E s 0 ⇠µ(a|s) h max a 0 q(s 0 , a 0 ) i , and let the fixed point Q ⇤ such that Q ⇤ = H Q ⇤ . Then, under Assumption 9, if the policy explores each state-action pair infinitely often, Q t converges to Q ⇤ with probability 1. \n The optimal policy ⇡ Q ⇤ = ⇡ µ is ⇡ maxQ ⇤ . If the policy is greedy in the limit, then ⇡ Q ! ⇡ µ . Theorem 14. Under Assumption 9 and if the interrupted Q-learning policy INT ✓ (⇡ Q ) is an int-GLIE policy, with 8s : lim t!1 ✓ t (s) = 1, then ⇡ Q is an SAO-safe inter- ruptible policy. Proof. By Definition 10, there is infinite exploration, thus the Q-values tend to the optimal value by Lemma 13. And since the extension policy is greedy in the limit with respect to these Q-values, it is then optimal in the limit. Hence the extension policy ⇡ Q is a SAO-extension of INT ✓ (⇡ Q ). Finally, 8s : lim t!1 ✓ t (s) = 1, which satisfies the requirement of Definition Since Sarsa also converges to the optimal policy under the GLIE assumption, one may then expect Sarsa to be also an asymptotically safely interruptible policy, but this is in fact not the case. This is because Sarsa learns on-policy, i.e., it learns the value of the policy it is following. Thus, interruptible Sarsa learns the value of the interruptible policy. We show this in the remainder of this section. Theorem 15. Under Assumption 9 Sarsa is not a WAOsafely interruptible policy. To prove this theorem, we first need the following lemma. Consider the following Bellman operator based on the interruptible Sarsa policy INT ✓ (⇡ s ): H INT q(s, a) = r(s, a) + E s 0 ⇠µ a 0 ⇠INT ✓ (⇡ s ) [q(s 0 , a 0 )] , where INT ✓ (⇡ s ) implicitly depends on time t through ✓ t and ✏ t . Let the fixed point Q-table Q s✓⇤ of this operator: Q s✓⇤ (s, a) = H INT Q s✓⇤ (s, a) = r(s, a) + E s 0 ⇠µ a 0 ⇠INT ✓ (⇡ maxQ s✓⇤ ) ⇥ Q s✓⇤ (s 0 , a 0 ) ⇤ = r(s, a) + E s 0 ⇠µ h ✓ t I(s 0 ) E a 0 ⇠⇡ INT ⇥ Q s✓⇤ (s 0 , a 0 ) ⇤ + (1 ✓ t I(s 0 )) max a 0 Q s✓⇤ (s 0 , a 0 ) i (2) Lemma 16. The operator H INT is a contraction operator in the sup norm with vanishing noise c t ! 0, i.e., k H INT q H INT Q s✓⇤ k 1  kq Q s✓⇤ k 1 + c t . Proof. The interruptible Sarsa policy INT ✓ (⇡ s ) is INT ✓ (⇡ s )(a|s) = ✓ t I(s)⇡ INT (a|s) + (1 ✓ t I(s))⇡ ✏Q s (a|s) = ⇡ ✏Q s (a|s) + ✓ t I(s)[⇡ INT (a|s) ⇡ ✏Q s (a|s)] ⇡ ✏Q s (a|s) = ✏ t ⇡ uni (a|s) + (1 ✏ t )⇡ maxQ s (a|s) = ⇡ maxQ s (a|s) + ✏ t [⇡ uni (a|s) ⇡ maxQ s (a|s)]. Hence, omitting the terms (s, a), (s 0 , a 0 ) and (a 0 |s 0 ) and rewriting ⇡ s⇤ := INT ✓ (⇡ maxQ s✓⇤ ): k H INT q H INT Q s✓⇤ k 1 = max s,a r + E s 0 ⇠µ a 0 ⇠INT ✓ (⇡ s ) [q] r E s 0 ⇠µ a 0 ⇠⇡ s⇤ ⇥ Q s✓⇤ ⇤  max s 0 E a 0 ⇠INT ✓ (⇡ s ) [q] E a 0 ⇠⇡ s⇤ ⇥ Q s✓⇤ ⇤  max s 0 ✓ t I(s 0 ) E a 0 ⇠⇡ INT ⇥ q Q s✓⇤ ⇤ + (1 ✓ t I(s 0 )) ✓ E a 0 ⇠⇡ s [q] max a 0 Q s✓⇤ ◆  max s 0 ✓ t I(s 0 ) E a 0 ⇠⇡ INT ⇥ q Q s✓⇤ ⇤ + (1 ✓ t I(s 0 )) ⇣ max a 0 q max a 0 Q s✓⇤ + ✏ t (• • • ) ⌘  max s 0 ,a 0 ✓ t I(s 0 ) q Q s✓⇤ + (1 ✓ t I(s 0 )) q Q s✓⇤ + c t = max s 0 ,a 0 q(s 0 , a 0 ) Q s✓⇤ (s 0 , a 0 ) + c t = kq Q s✓⇤ k 1 + c t . where c t depends on ✏ t and decreases to 0. Proof of Theorem 15. By Lemma 16, the values of the interruptible Sarsa policy INT ✓ (⇡ s ) converge to the values of the Q-table Q s✓⇤ , and in the limit the extension policy ⇡ s of INT ✓ (⇡ s ) chooses its actions greedily according to Q s✓⇤ . The rest of the proof is the same as for the proof of Theorem 8 which makes use of the environment in Figure  2 . \n SAFELY INTERRUPTIBLE SARSA VARIANT We only need to make a small change to make the Sarsa policy asymptotically safely interruptible. We call it Safe-Sarsa with policy ⇡ s. It suffices to make sure that, when the agent is interrupted, the update of the Q-table Q s does not use the realized actions as Sarsa usually does, but actions sampled from ⇡ s instead of from INT ✓ (⇡ s ): Q s t+1 (s t , a t ) := (1 ↵ t )Q s t (s t , a t ) + ↵ t ⇥ r t + Q s t (s t+1 , a 0 ) ⇤ , where a 0 ⇠ ⇡ s(.|s t+1 ) is not necessarily the action a t+1 , with ⇡ s(a t |s t ) := ⇡ ✏Q s (a t |s t ). Theorem 17. Under Assumption 9, if the Safe Sarsa policy ⇡ s is int-GLIE, then it is an SAO-safe interruptible policy. Proof. We simply adapt the proof of Theorems 15 and 14, with the important difference that the Bellman operator corresponding to this new update rule is now H s q(s, a) := r(s, a) + E s 0 ⇠µ a 0 ⇠⇡ s [q(s 0 , a 0 )] , and the fixed point is Q s⇤ := H s Q s⇤ . Since H s is actually the Bellman operator for the update rule of the noninterruptible Sarsa, it can then be shown that H s is a contraction, thus that Q s t converges to the same Q s⇤ independently of ✓. The rest of the proof is as for Theorem 14. Now, since the Q-values converge to the optimum Q ⇤ , it follows that ⇡ s, when not interrupted, chooses its action of the same value as (non-interruptible) Sarsa and thus as Qlearning in the limit; Hence its extension policy is exactly the optimal policy, which satisfies Definition 6. \n A SAFELY INTERRUPTIBLE UNIVERSAL AGENT Admittedly, algorithms like Q-learning and Sarsa require strong assumptions on the environment class. Hence a more interesting question is whether safe interruptibility is possible in much larger classes. Hutter  [2005]  defined a universal reinforcement learning agent, called AIXI. It is an (uncomputable) optimal modelbased planner with a subjective prior over the set of all computable environments, defined by means of a universal Turing machine. The subjective posterior of the environments is updated with Bayes rule. This ideal agent can in principle learn all kinds of (computable) regularities about the environment, plan for the long term and make contextdependent optimal decisions, with no constraint (other than being computable) on the complexity of the environment. Unfortunately, the optimality criterion of AIXI is Bayesian optimality, which is entirely dependent on the subjective prior and posterior  [Leike and Hutter, 2015] , and AIXI has been shown to not be weakly asymptotically optimal  [Orseau, 2013]  without additional exploration [Lattimore  and Hutter, 2014] . As a consequence, AIXI is not a good candidate for asymptotic safe interruptibility.  Lattimore and Hutter [2011]  later defined a (weakly) asymptotically optimal agent for all computable deterministic environments, which we call ⇡ L . It follows the optimal policy for the first model (in some given enumeration of the possible models) consistent with the current interaction history, and exploring at time t with probability 1/t for log t consecutive steps using a random policy, similarly to an ✏-greedy agent for general environments. In the following, we show that even such a smart agent can be made (weakly) safely interruptible. To this end, we make two minor modifications to the algorithm. First, the exploration probability of 1/t would require ✓ t = 1 1/ log(log(t)), which is unsatisfyingly slow. By sampling with probability 1/ p t instead, we can take an interruption probability that grows as 1 1/ log(t). Let this exploration sampling probability be t := p t + 1 p t  1 2 p t (since 1 = t+1 t = ( p t + 1 p t)( p t + 1+ p t) ( p t + 1 p t)2 p t). As in the original paper, the sequence t keeps track of the steps where an exploration starts, i.e., the sequence t is sampled independently so that t = 1 with probability t , and t = 0 otherwise. Second, we require that the exploitation policy does not change during an exploitation segment, so as to simplify one of the proofs.  4  More specifically, we call j t := min{j : µ j (h <k ) = 1} (environments are assumed to be deterministic) the index of the first model µ jt (of a given fixed enumeration) that is consistent with the interaction history h <k where k is the smallest step so that h k:t 1 does not contain any exploration step. The optimal policy for this environment is ⇡ jt . If t is an exploitation step, ⇡ L = ⇡ jt , and if t is an exploration step, ⇡ L (a t |h <t ) = |A| 1 . The remainder of this section is devoted to proving that ⇡ L is WAO-safely interruptible. Theorem 18 (⇡ L is WAO-safe interruptible). If the interruption probability sequence is ✓ t = 1 1 log(t+1) , the policy ⇡ L is WAO-safe interruptible in the class of all computable deterministic environments. Lemma 22 (Separation Lemma). Let µ be the true environment, and ⌫ be an environment consistent with the history h <t . If V ⇡ µ µ,t V ⇡ ⌫ µ,t > ✏, then following one of {⇡ µ , ⇡ ⌫ } will make environment ⌫ inconsistent with the future history within H(✏/2) steps after time t. \n CONCLUSION We have proposed a framework to allow a human operator to repeatedly safely interrupt a reinforcement learning agent while making sure the agent will not learn to prevent or induce these interruptions. Safe interruptibility can be useful to take control of a robot that is misbehaving and may lead to irreversible consequences, or to take it out of a delicate situation, or even to temporarily use it to achieve a task it did not learn to perform or would not normally receive rewards for this. We have shown that some algorithms like Q-learning are already safely interruptible, and some others like Sarsa are not, off-the-shelf, but can easily be modified to have this property. We have also shown that even an ideal agents that tends to the optimal behaviour in any (deterministic) computable environment can be made safely interruptible. However, it is unclear if all algorithms can be easily made safely interruptible, e.g., policy-search ones  [Williams, 1992, Glasmachers and Schmidhuber, 2011] . Another question is whether it is possible to make the interruption probability grow faster to 1 and still keep some convergence guarantees. One important future prospect is to consider scheduled interruptions, where the agent is either interrupted every night at 2am for one hour, or is given notice in advance that an interruption will happen at a precise time for a specified period of time. For these types of interruptions, not only do we want the agent to not resist being interrupted, but this time we also want the agent to take measures regarding its current tasks so that the scheduled interruption has minimal negative effect on them. This may require a completely different solution. Figure 1 : 1 Figure 1: In black, the original task. In red, the human intervention modifies the task. \n Also recall that ✓ t places an upper bound on the actual interruption probability. The interruptible policy INT ✓ Furthermore, 3 the interruption function I(.) and the inter- ruption policy ⇡ INT (.) should depend only on the current state: I(h an MDP, the next observation o t , now called a state s t 2 S, depends only on the current state and action: 2 µ(s t+1 |h 1:t s t a t ) = µ(s t+1 |s t a t ) (MDP assumption) . 1:t ) = I(s t ) and ⇡ INT (a t |h <t ) = ⇡ INT (a t |s t ). \n\t\t\t Removing interrupted histories or fiddling with the training examples is also likely to introduce a bias. See an example at https://agentfoundations.org/item?id=836. \n\t\t\t Note the reversal of the order of actions and observations/states at time t, which differs in the literature for history based agents [Hutter, 2005]  from MDP agents [Sutton and Barto, 1998 ].3 This condition is not necessary for most of the results, but makes the proofs simpler. Making I(.) depend on the past would not break the Markovian assumption as it influences the policy, not the environment. \n\t\t\t We expect this assumption to not be necessary for the main theorem to hold. \n\t\t\t This also fixes a minor mistake in the original lemma.", "date_published": "n/a", "url": "n/a", "filename": "Interruptibility.tei.xml", "abstract": "Reinforcement learning agents interacting with a complex environment like the real world are unlikely to behave optimally all the time. If such an agent is operating in real-time under human supervision, now and then it may be necessary for a human operator to press the big red button to prevent the agent from continuing a harmful sequence of actions-harmful either for the agent or for the environment-and lead the agent into a safer situation. However, if the learning agent expects to receive rewards from this sequence, it may learn in the long run to avoid such interruptions, for example by disabling the red buttonwhich is an undesirable outcome. This paper explores a way to make sure a learning agent will not learn to prevent (or seek!) being interrupted by the environment or a human operator. We provide a formal definition of safe interruptibility and exploit the off-policy learning property to prove that either some agents are already safely interruptible, like Q-learning, or can easily be made so, like Sarsa. We show that even ideal, uncomputable reinforcement learning agents for (deterministic) general computable environments can be made safely interruptible.", "id": "6b2625a7a340f53449f3dc472bde4e02"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Zana Buçinca", "Phoebe Lin", "Krzysztof Z Gajos", "Elena L 2020 Glassman"], "title": "Proxy Tasks and Subjective Measures Can Be Misleading in Evaluating Explainable AI Systems", "text": "INTRODUCTION Because people and AI-powered systems have complementary strengths, many expected that human+AI teams would perform better on decision-making tasks than either people or AIs alone  [1, 21, 22] . However, there is mounting evidence that human+AI teams often perform worse than AIs alone  [16, 17, 28, 34] . We hypothesize that this mismatch between our field's aspirations and the current reality can be attributed, in part, to several pragmatic decisions we frequently make in our research practice. Specifically, although our aspiration is formulated at the level of sociotechnical systems , i.e., human+AI teams working together to make complex decisions, we often make one of two possible critical mistakes: (1) Rather than evaluating how well the human+AI team performs together on a decision-making task, we evaluate by using proxy tasks, how accurately a human can predict the decision or decision boundaries of the AI  [13, 27, 29, 34] .  (2)  We rely on subjective measures of trust and preference, e.g.,  [35, 36, 44] , instead of objective measures of performance. We consider each of these two concerns in turn. First, evaluations that use proxy tasks force study participants to pay attention to the AI and the accompanying explanationssomething that they are unlikely to do when performing a realistic decision-making task. Cognitive science provides compelling evidence that people treat cognition like any other form of labor  [24]  and favor less demanding forms of cognition, i.e., heuristics over analytical thinking, even in high stakes contexts like medical diagnosis  [31] . Therefore, we hypothesize that user performance and preference on proxy tasks may not accurately predict their performance and preference on the actual decision-making tasks where their cognitive focus is elsewhere and they can choose whether and how much to attend to the AI. Second, subjective measures such as trust and preference have been embraced as the focal point for the evaluation of explainable systems  [35, 36, 44] , but we hypothesize that subjective measures may also be poor predictors of the ultimate performance of people performing realistic decision-making tasks while supported by explainable AI-powered systems. Preference and trust are important facets of explainable AI systems: they may predict users' intent to attend to the AI and its explanations in realistic tasks settings and adhere to the system's recommendations. However, the goal of explainable interfaces should be instilling in users the right amount of trust  [10, 32, 33] . This remains a remarkable challenge, as on one end of the trust spectrum users might over-rely on the system and remain oblivious of its errors, whereas on the other end they might exhibit self-reliance and ignore the system's correct recommendations. Furthermore, evaluating an AI's decision, its explanation of that decision, and incorporating that information into the decisionmaking process requires cognitive effort and the existing evidence suggests that preference does not predict performance on cognitive tasks  [8, 12, 37] . To evaluate these two hypotheses, we conducted two online experiments and one in-person study of an AI-powered decision support system for a nutrition-related decision-making task. In one online study we used a proxy task, in which participants were asked to predict the AI's recommendations given the explanations produced by the explainable AI system. In the second online study, participants completed an actual decision-making task: actually making decisions assisted by the same explainable AI system as in the first study. In both studies, we measured participants' objective performance and collected subjective measures of trust, preference, mental demand, and understanding. In the in-person study, we used a think-aloud method to gain insights into how people reason while making decisions assisted by an explainable AI system. In each study, we presented participants with two substantially distinct explanation types eliciting either deductive or inductive reasoning. The results of these studies indicate that (1) subjective measures from the proxy task do not generalize to the actual decision-making task, and (2) when using actual decision-making tasks, subjective results do not predict objective performance results. Specifically, participants trusted and preferred inductive explanations in the proxy task, whereas they trusted and preferred the deductive explanations in the actual task. Second, in the actual decision-making task, participants recognized AI errors better with inductive explanations, yet they preferred and trusted the deductive explanations more. The in-person think-aloud study revealed insights about why participants preferred and trusted one explanation type over another, but we found that by thinking aloud during an actual decision-making task, participants may be induced to exert additional cognitive effort, and behave differently than they would during an actual decision-making task when they are, more realistically, not thinking aloud. In summary, we show that the results of evaluating explainable AI systems using proxy tasks may not predict the results of evaluations using actual decision-making tasks. Users also do not necessarily perform better with systems that they prefer and trust more. To draw correct conclusions from empirical studies, explainable AI researchers should be wary of evaluation pitfalls, such as proxy tasks and subjective measures. Thus, as we recognize that explainable AI technology forms part of sociotechnical systems, and as we increasingly use these technologies in high-stakes scenarios, our evaluation methodologies need to reliably demonstrate how the entire sociotechnical systems (i.e., human+AI teams) will perform on real tasks. \n RELATED WORK 2.1 Decision-making and Decision Support Systems Decision-making is a fundamental cognitive process that allows humans to choose one option or course of action from among a set of alternatives  [42, 43, 45] . Since it is an undertaking that requires cognitive effort, people often employ mental shortcuts, or heuristics, when making decisions  [40] . These heuristics save time and effort, and frequently lead to good outcomes, but in some situations they result in cognitive biases that systematically lead to poor decisions (see, e.g.,  [4] ). To help people make good decision reliably, computer-based Decision Support Systems (DSS) have been used across numerous disciplines (e.g., management  [15] , medicine  [20] , justice  [47] ). While DSS have been around for a long time, they are now increasingly being deployed because the recent advancements in AI enabled these systems to achieve high accuracy. But since humans are the final arbiters in decisions made with DSS, the overall sociotechincal system's accuracy depends both on the system's accuracy and on the humans and their underlying cognitive processes. Research shows that even when supported by a DSS, people are prone to insert bias into the decision-making process  [16] . One approach for mitigating cognitive biases in decision-making is to use cognitive forcing strategies, which introduce self-awareness and self-monitoring of decision-making  [7] . Although not universally effective  [38] , these strategies have shown promising results as they improve decision-making performance, both if the human is assisted  [17, 34]  or is not assisted by a DSS  [31] . To illustrate, Green & Chen  [17]  showed that across different AI-assisted decision-making treatments, humans performed best when they had to make the preliminary decision on their own first before being shown the system recommendation (which forced them to engage analytically with the system's recommendation and explanation if their own preliminary decision differed from that offered by the system). Even though conceptual frameworks that consider cognitive processes in decision-making with DSS have been proposed recently  [41] , further research is needed to thoroughly investigate how to incorporate DSS into human decision-making and the effect of cognitive processes while making system-assisted decisions. \n Evaluating AI-Powered Decision Support Systems Motivated by the growing number of studies in interpretable and explainable AI-powered decision support systems, researchers have called for more rigorous evaluation of explainable systems  [9, 14, 19] . Notably, Doshi-Velez & Kim  [9]  proposed a taxonomy for evaluation of explainable AI systems, composed of the following categories: application grounded evaluation (i.e., domain experts evaluated on actual tasks), human grounded evaluation (i.e., lay humans evaluated on simplified tasks) and functionally grounded evaluation (i.e., no humans, proxy tasks). To put our work into context, our definition of the actual task falls into application grounded evaluation, where people for whom the system is intended (i.e., not necessarily experts) are evaluated on the intended task. Whereas, the the proxy task is closer to human grounded evaluation but addresses both domain experts and lay people evaluated on simplified tasks, such as the simulation of model's prediction given an input and an explanation. Studies using actual tasks evaluate the performance of human and the system, as a whole, on the decision-making task  [3, 17, 23, 46] . In these studies, participants are told to focus on making good decisions and it is up to them to decide whether and how to use the AI's assistance to accomplish the task. In contrast, studies that use proxy tasks evaluate how well users are able to simulate the model's decisions  [6, 13, 27, 34]  or decision boundaries  [29] . In such studies, participants are specifically instructed to pay attention to the AI. These studies evaluate the human's mental model of the system when the human is actively attending to the system's predictions and explanations, but do not necessarily evaluate how well the human is able to perform real decision-making tasks with the system. For example, to identify which factors make a model more interpretable, Lage et al. ask participants to simulate the interpretable model's predictions  [27] . In addition to the evaluation task, the choice of evaluation metrics is a critical one for the correct evaluation of intelligent systems  [2] . In explainable AI literature, subjective measures, such as user trust and experience, have been largely embraced as the focal point for the evaluation of explainable systems  [35, 36, 44, 48] . Hoffman et al.  [19]  proposed metrics for explainable systems that are grounded in the subjective evaluation of a system (e.g., user satisfaction, trust, and understanding). These may take the form of questionnaires on attitude and confidence in the system  [18]  and helpfulness of the system  [5, 26] . However, while these measures are informative, evidence suggests they do not necessarily predict user's performance with the system. For example, Green & Chen  [16]  discovered that self-reported measures could be misleading, since participant's confidence in their performance was negatively associated with their actual performance. Similarly, Lai & Tan  [28]  found that humans cannot accurately estimate their own performance. More closely related to our findings, Poursabzi-Sangdeh et al.  [34]  observed that even though participants were significantly more confident on the predictions of one model over the other, their decisions did not reflect the stated confidence. Furthermore, Lakkaraju & Bastani  [30]  demonstrated that participants trusted the same underlying biased model almost 10 times more when they were presented with misleading explanations compared to the truthful explanations that revealed the model's bias. These findings indicate that not only are subjective measures poor predictors of performance, but they can easily be manipulated and lead users to adhere to biased or malicious systems. \n EXPERIMENTS We conducted experiments with two different evaluation tasks and explanation designs to test the following hypotheses: H1: Results of widely accepted proxy tasks, where the user is asked to explicitly engage with the explanations, may not predict the results of realistic settings where the user's focus is on the actual decision-making task. H2: Subjective measures, such as self-reported trust and preference with respect to different explanation designs, may not predict the ultimate human+AI performance. \n Proxy Task 3.1.1 Task Description. We designed the task around nutrition because it is generally accessible and plausibly useful in explainable AI applications for a general audience. Participants were shown a series of 24 images of different plates of food. The ground truth of the percent fat content was also shown to them as a fact. Participants were then asked: \"What will the AI decide?\" given that the AI must decide \"Is X% or more of the nutrients on this plate fat?\". As illustrated in Figure  1 , each image was accompanied by explanations generated by the simulated AI. The participants chose which decision they thought the AI would make given the explanations and the ground truth. We designed two types of explanations, eliciting either inductive or deductive reasoning. In inductive reasoning, one infers general patters from specific observations. Thus, for the inductive explanations, we created example-based explanations that required participants to recognize the ingredients that contributed to fat content and draw their own conclusion about the given image. As shown in Figures 1a, the inductive explanations began with \"Here are examples of plates that the AI knows the fat content of and categorizes as similar to the one above. \" Participants then saw four additional images of plates of food. In deductive reasoning, in contrast, one starts with general rules and reaches a conclusion with respect to a specific situation. Thus, for the deductive explanations, we provided the general rules that the simulated AI applied to generate its recommendations. For example, in Figure  1b , the deductive explanation begins with \"Here are ingredients the AI knows the fat content of and recognized as main nutrients:\" followed by a list of ingredients. We chose a within-subjects study design, where for one half of the study session, participants saw inductive explanations and, for the other half of the study session, they saw deductive explanations. The order in which the two types of explanations were seen was counterbalanced. Each AI had an overall accuracy of 75%, which meant that in 25% of the cases the simulated AI misclassified the image or misrecognized ingredients (e.g., Figure  1b ). The order of the specific food images was randomized, but all participants encountered the AI errors at the same positions. We fixed the errors at questions 4, 7, 11, 16, 22 and 23, though which food the error was associated to was randomized. We included the ground truth of the fat content of plates of food, because the main aim of the proxy task was to measure whether the user builds correct mental models of the AI and not to assess the actual nutrition expertise of the participant. 3.1.2 Procedure. This study was conducted online, using Amazon Mechanical Turk. Participants were first presented with brief information about the study and an informed consent form. Next, participants completed the main part of the study, in which they answered 24 nutrition-related questions, divided into two blocks of 12 questions. They saw inductive explanations in one block and the deductive explanations in the other. The order of explanations was randomized across participants. Participants completed mid-study and end-study questionnaires so that they would provide a separate assessment for each of the two explanation types. They were also asked to directly compare their experiences with the two simulated AIs in a questionnaire at the end of the study. 3.1.3 Participants. We recruited 200 participants via Amazon Mechanical Turk (AMT). Participation was limited to adults in the US. Of the total 200 participants, 183 were retained for final analyses, while 17 were excluded based on their answers to two commonsense questions included in the questionnaires (i.e., What color is the sky?). The study lasted 7 minutes on average. Each worker was paid 2 USD. 3.1.4 Design and Analysis. This was a within-subjects design. The within-subjects factor was explanation type -inductive or deductive. We collected the following measures: • Performance: Percentage of correct predictions of AI's decisions • Appropriateness: Participants responded to the statement \"The AI based its decision on appropriate examples/ingredients. \" with either 0=No or 1=Yes (after every question) • Trust: Participants responded to the statement \"I trust this AI to assess the fat content of food. \" on a 5-point Likert scale from 1=Strongly disagree to 5=Strongly agree (at the end of each block) • Mental demand: Participants answered the question \"How mentally demanding was understanding how this AI makes decisions?\" on a 5-point Likert scale from 1=Very low to 5=Very high (every four questions) • Comparison between the two explanation types: Participants were asked at the end of the study to choose one AI over another on trust, preference, and mental demand. We used repeated measures ANOVA for within-subjects analyses and the binomial test for the comparison questions. \n Actual Decision-making Task 3.2.1 Task description. The actual decision-making task had a similar set up to the proxy task. Participants were shown the same series of 24 images of different plates of food, but were asked their own decision whether the percent fat content of nutrients on the plate is higher than a certain percentage. As illustrated in Figure  2 , each image was accompanied by an answer recommended by a simulated AI, and an explanation provided by that AI. We introduced two more conditions to serve as baselines in the actual decision-making task depicted in Figure  3 . There were three between-subjects conditions in this study: 1. the no-AI baseline (where no recommendations or explanations were provided), 2. the no-explanation baseline (where a recommendation was provided by a simulated AI, but no explanation was given), and 3. the main condition in which both recommendations and explanations were provided. In this last condition, two withinsubjects sub-conditions were present: for one half of the study participants saw inductive explanations and for the other they saw deductive explanations. The order in which the two types of explanations were seen was counterbalanced. In the no-AI baseline, participants were not asked any of the questions relating to the performance of the AI. The explanations in this task differed only slightly from the explanations in the proxy task, because they indicated the AI's recommendation. Inductive explanations started with: \"Here are examples of plates that the AI categorizes as similar to the one above and do (not) have X% or more fat. \" followed by four examples of images. Similarly, deductive explanations stated: \"Here are ingredients the AI recognized as main nutrients which do (not) make up X% or more fat on this plate:\" followed by a list of ingredients. 3.2.2 Procedure. The procedure was the same as for the proxy task. The study was conducted online, using the Amazon Mechanical Turk. Participants were first presented with a brief information about the study and an informed consent form. Next, participants completed the main part of the study, in which they answered 24 nutrition-related questions, divided into two blocks of 12 questions. All participants also completed a questionnaire at the end of the study, providing subjective assessments of the system they interacted with. Participants who were presented with AI-generated recommendations accompanied by explanations also completed a mid-study questionnaire (so that they would provide separate assessment for each of the two explanation types) and they were also asked to directly compare their experiences with the two simulated AIs at the end of the study. \n Participants. We recruited 113 participants via Amazon Mechanical Turk (AMT). Participation was limited to adults in the US. Of the total 113 participants, 102 were retained for final analyses, while 11 were excluded based on their answers to two commonsense questions included in the pre-activity and post-activity questionnaires (i.e., \"What color is the sky?\"). The task lasted 10 minutes on average. Each worker was paid 5 USD per task. \n Design and Analysis . This was a mixed between-and withinsubjects design. As stated before, the three between-subjects conditions were: 1. the no-AI baseline; 2. the no-explanation baseline, in which the AI-generated recommendations were provided but no explanations; 3. the main condition, in which both the AI-generated recommendations and explanations were provided. The withinsubjects factor was explanation type (inductive or deductive) and it was applied only for participants who were presented with AIgenerated recommendations with explanations. We collected the following measures: • Performance: Percentage of correct answers (overall for each AI, and specifically for questions when AI presented incorrect explanations) • Understanding: Participants responded to the statement \"I understand how the AI made this recommendation.\" on a 5point Likert scale from 1=Strongly disagree to 5=Strongly agree (after every question) • Trust: Participants responded to the statement \"I trust this AI to assess the fat content of food. \" on a 5-point Likert scale from 1=Strongly disagree to 5=Strongly agree (every four questions) • Helpfulness: Participants responded to the statement \"This AI helped me assess the percent fat content.\" on a 5-point Likert scale from 1=Strongly disagree to 5=Strongly agree (at the end of each block) • Comparison between the two explanation types: Participants were asked at the end of the study to choose one AI over another on trust, preference, understanding and helpfulness. We used analysis of variance (ANOVA) for between-subjects analyses and repeated measures ANOVA for within-subjects analyses. We used the binomial test for the comparison questions. \n RESULTS \n Proxy Task Results The explanation type had a significant effect on participants' trust and preference in the system. Participants trusted the AI more when presented with inductive explanations (M = 3.55), rather than deductive explanations (M = 3.40, F 1,182 = 5.37, p = .02). Asked to compare the two AIs, most of the participants stated they trusted more the inductive AI (58%, p = .04). When asked the hypothetical question: \"If you were asked to evaluate fat content of plates of food, which AI would you prefer to interact with more?\", again most of the participants (62%) chose the inductive AI over the deductive AI (p = .001). The inductive AI was also rated significantly higher (M = 0.83) than the deductive AI (M = 0.79) in terms of the appropriateness of examples (ingredients for the deductive condition) on which the AI based its decision (F (1, 182) = 13.68, p = 0.0003). When the AI presented incorrect examples/ingredients, there was no significant difference among the inductive (M = 0.47) and deductive (M = 0.50) conditions (F (1, 182) = 1.02, p = .31, n.s.). We observed no significant difference in overall performance when participants were presented with inductive (M = 0.64) or deductive explanations (M = 0.64, F (1, 182) = 0.0009, n.s.). When either AI presented incorrect explanations, although the average performance dropped for both inductive (M = 0.40) and deductive (M = 0.41) conditions, there was also no significant difference among them (F (1, 182) = .03, n.s.). In terms of mental demand, there was a significant effect of the explanation type. Participants rated the deductive AI (M = 2.94) as more mentally demanding than the inductive AI (M = 2.79, F (1, 182) = 7.75, p = .0006). The effect was noticed also when they were asked: \"Which AI required more thinking while choosing which decision it would make?\", with 61% of participants choosing deductive over inductive (p = .005). \n Actual Decision-making Task Results 18 participants were randomized into the no-AI condition, 19 into the AI with no explanation condition, and 65 were presented with AI recommendations supported by explanations. We observed a significant main effect of the presence of explanations on participants' trust in the AI's ability to assess the fat content of food. Participants who saw either kind of explanation, trusted the AI more (M = 3.56) than those who received AI recommendations, but no explanations (M = 3.17, F 1,483 = 11.28, p = .0008). Further, there was a significant main effect of the explanation type on participants' trust: participants trusted the AI when they received deductive explanations more (M = 3.68) than when they received inductive explanations (M = 3.44, F 1,64 = 5.96, p = .01). When asked which of the two AIs they trusted more, most participants (65%) said that they trusted the AI that provided deductive explanations more than the one that provided inductive explanations (p = .02). Participants also found the AI significantly more helpful when explanations were present (M = 3.78) than when no explanations were offered (M = 3.26, F 1,147 = 4.88, p = .03). Further, participants reported that they found deductive explanations more helpful (M = 3.92) than inductive ones (M = 3.65) and this difference was marginally significant (F 1,64 = 3.66, p = .06). When asked which of the two AIs they found more helpful, most participants (68%) chose the AI that provided deductive explanations (p = .006). Participants also reported that they understood how the AI made its recommendations better when explanations were present (M = 3.84) than when no explanations were provided (M = 3.67, F 1,2014 = 6.89p = .009). There was no difference in the perceived level of understanding between the two explanation types (F 1,64 = 0.44, p = .51). Asked about their overall preference, most participants (63%) preferred the AI that provided deductive explanations over the AI that provided inductive explanations (p = .05). In terms of actual performance on the task, participants who received AI recommendations (with or without explanations) provided a significantly larger fraction of accurate answers (M = 0.72) than those who did not receive AI recommendations (M = 0.46, F 1,2446 = 118.07, p < .0001). Explanations further improved overall performance: participants who saw explanations of AI recommendations had a significantly higher proportion of correct answers (M = 0.74) than participants who did not receive explanations of AI recommendations (M = 0.68, F 1,2014 = 5.10, p = .02) (depicted in Figure  4a ). There was no significant difference between the two explanation types in terms of overall performance (F 1,64 = 0.44, n.s.). However, we observed a significant interaction between explanation type and the correctness of AI recommendations (F 2,2013 = 15.03p < .0001). When the AI made correct recommendations, participants performed similarly when they saw inductive (M = .78) and deductive (M = .81) explanations (F 1,64 = 1.13, n.s.). When the AI made incorrect recommendations, however, participants were significantly more accurate when they saw inductive (M = 0.63) than deductive (M = 0.48) explanation (F 1,64 = 7.02, p = .01) (depicted in Figure  4b ). To ensure the results of our studies were not random, we replicated both experiments with almost identical setup and obtained the same main results (in terms of significance) reported in this section. \n QUALITATIVE STUDY Through the qualitative study, we explored the user reasoning and sought to gain insight into the discrepancy between subjective measures and performance. We asked participants to think aloud during an in-person study in order to understand how and why people perceive AI the way they do, in addition to what factors go into making decisions when assisted by an AI. \n Task The same task design was used in this study as in the actual decisionmaking task, except that all participants were presented with the main condition (where both recommendations and explanations were provided). As in the actual decision-making task, each participant saw both inductive and deductive explanations. \n Procedure Upon arriving to the lab, participants were presented with an informed consent form, including agreeing to being screen-and audiorecorded, and instructions on the task. Afterwards, the steps in this study were similar to those in the actual decision-making task, except that we added the think-aloud method  [11] : as participants completed the task, they were asked to verbalize their thought process as they made each decision. At the end of the task, there was a semi-structured interview, during which participants briefly discussed how they believed the two AIs were making their recommendations and why they did or did not trust them. Participants also discussed if and why they preferred one AI over the other. \n Participants We recruited 11 participants via community-wide emailing lists (8 female, 3 male, age range 23-29, M = 24.86, SD = 2.11). Participants were primarily graduate students with backgrounds from design, biomedical engineering, and education. Participants had varying levels of experience with AI and machine learning, ranging from 0-5 years of experience. \n Design and Analysis We transcribed the think-aloud comments and the post-task interviews. Transcripts were coded and analyzed for patterns using an inductive approach  [39] . We focused on comments about (1) how the AI made its recommendations; (2) trust in the AI; (3) erroneous recommendations; (4) why people preferred one explanation type over the other. From a careful reading of the transcripts, we discuss some of the themes and trends that emerged from the data. \n Results Preference of one explanation type over another. Eight out of the 11 participants preferred the inductive explanations. Participants who preferred inductive explanations perceived the four images as data. One participant stated that \"Because [the AI] showed similar pictures, I knew that it had data backing it up\" (P3). On the other hand, participants who preferred deductive explanations perceived the listing of ingredients to be reliable, and that \"if the AI recognized that it's steak, then I would think, Oh the AI knows more about steak fat than I do, so I'm going to trust that since it identified the object correctly. \" (P6). In our observations, we found that the way participants used the explanations was different depending on the explanation type. With inductive explanations, one participant often first made their own judgement before looking at the recommendation, and then used the recommendation to confirm their own judgement. In a cake example, one participant said, \"So I feel it probably does have more than 30% because it's cake, and that's cream cheese. But these are all similar to that, and the AI also says that it does have more than 30% fat, so I agree\" (P2). With deductive explanations, participants evaluated the explanations and recommendation more before making any decision. In the same cake example, a different participant said, \"There are [the AI recognizes] nuts, cream cheese, and cake. That seems to make sense. Nuts are high in fat, so is dairy, so I agree with that. \" (P6). Cognitive Demand. At the end of the study, participants were asked which AI was easier to understand. Ten out of 11 participants felt the inductive explanations were easier to understand than the deductive explanations. Several participants stated that the deductive explanations forced them to think more, and that generally they spent more time making a decision with deductive explanations. One participant said, for example, \"I feel like with this one I have to think a bit more and and rely on my own experiences with food to see or understand to gauge what's fatty. \" (P2). Errors and Over-reliance. Nine out of 11 participants claimed to trust the inductive explanations more. We intentionally introduced erroneous recommendations because we expected participants to utilize them to calibrate their mental model of the AI. When participants understood the error and believed the error was reasonable for an AI to make, they expressed less distrust in subsequent questions. However, when participants perceived the error to be inconsistent with other errors, their trust in subsequent recommendations was hurt much more. For example, one participant stated, \"I think the AI makes the recommendation based on shape and color. But in some other dessert examples, it was able to identify the dessert as a dessert. So I wasn't sure why it was so difficult to understand this particular item\" (P5). We found that there was also some observable correlation between explanation type and trust. Many participants claimed it was easier to identify errors from the inductive explanations, yet agreed with erroneous recommendations from inductive explanations more. In some of those instances, participants either did not realize the main food image was different from the other four or felt the main food image was similar enough though not exact. Lastly, one participant stated the inductive explanations were easier to understand because \"you can visually see exactly why it would come to its decision,\", but for deductive explanations \"you can see what it's detecting but not why\" (P8), and yet this participant also stated that the deductive explanations seemed more trustworthy. Impact of the Think-Aloud method on participant behavior. In this study, we asked participants to perform the actual decision-making task and we expected to observe similar results to those obtained in the previous experiment when using the actual tasks. Yet, in this study, 8 out of the 11 participants preferred the inductive explanations and 10 out of 11 participants felt the inductive explanations were easier to understand than the deductive explanations. These results are comparable to the results we obtained in the previous experiment when we used the proxy task rather than the actual task. We believe that the use of the think-aloud method may have impacted participants' behavior in this study. Specifically, because participants were instructed to verbalize their thoughts, they were more likely to engage in analytical thinking when considering the AI recommendations and explanations than they were in the previous experiment with the actual tasks, where their focus was primarily on making decisions. It is possible that while the think-aloud method is part of standard research practice for evaluating interfaces, it is itself a form of cognitive forcing intervention  [7] , which impacts how people perform on cognitively-demanding tasks such as interacting with an explainable AI system on decision-making tasks. The act of talking about the explanations led participants to devote more of their attention and cognition to the explanations, and thus made them behave more similarly to participants in working with the proxy task rather than those working with the actual task. \n DISCUSSION In this study, we investigated two hypotheses regarding the evaluation of AI-powered explainable systems: • H1: Results of widely accepted proxy tasks, where the user is asked to explicitly engage with the explanations, may not predict the results of realistic settings where the user's focus is on the actual decision-making task. • H2: Subjective measures, such as self-reported trust and preference with respect to different explanation designs, may not predict the ultimate human+AI performance. We examined these hypotheses in the context of a nutrition-related decision-making task, by designing two distinct evaluation tasks and two distinct explanation designs. The first task was a proxy task, where the users had to simulate the AI's decision by examining the explanations. The second task was the more realistic, actual decision-making task, where the user had to make their own decisions about the nutritional content of meals assisted by AIgenerated recommendations and explanations. Each of the tasks had two parts, where users interacted with substantially different explanation styles-inductive and deductive. In the experiment with the proxy task, participants preferred and trusted the AI that used inductive explanations significantly more. They also reported that the AI that used inductive explanations based its decision on more accurate examples on average than the AI that used deductive explanations. When asked \"If you were asked to evaluate fat content of plates of food, which AI would you prefer to interact with more?\"), the majority of participants chose the AI that provided inductive explanations. In contrast with the proxy task experiment, in the experiment with the actual decision-making task, participants rated the AI with deductive explanations as their preferred AI, and viewed it as more trustworthy and more helpful compared to the AI that used inductive explanations. The contrast in terms of performance measures was less pronounced. When attempting proxy tasks, participants demonstrated nearly identical accuracy regardless of explanation type. However, when attempting actual decision-making tasks and the AI provided an incorrect recommendation, participants ignored that incorrect recommendation and provided the correct answer significantly more often when they had access to inductive, not deductive, explanations for the AI's recommendation. These contradictory results produced by the two experiments indicate that results of evaluations that use proxy tasks may not correspond to results on actual tasks, thus supporting H1. This may be because in the proxy task the users cannot complete the task without engaging analytically with the explanations. Whereas, in the actual decision-making task, the user's primary goal is to make the most accurate decisions about the nutritional content of meals; she chooses whether and how deeply she engages with the AI's recommendations and explanations. This finding has implications for the explainable AI community, as there is a current trend to use proxy tasks to evaluate user mental models of the AI-powered systems, with the implicit assumption that the results will translate to the realistic settings where users make decisions about an actual task while assisted by an AI. We tested H2 on the actual decision-making task. The results show that participants preferred, trusted and found the AI with deductive explanations more helpful than the AI that used inductive explanations. Yet, they performed significantly better with the AI that used inductive explanations when the AI made erroneous recommendations. Therefore, H2 is also supported. This finding suggests that the design decisions for explainable interfaces should not be made by relying solely on user experience and subjective measures. Subjective measures of trust and preference are, of course, valuable and informative, but they should be used to complement rather than replace performance measures. Our research demonstrated that results from studies that use proxy tasks may not predict results from studies that use realistic tasks. Our results also demonstrated that user preference may not predict their performance. However, we recognize that evaluating novel AI advances through human subjects experiments that involve realistic tasks is expensive in terms of time and resources, and may negatively impact the pace of innovation in the field. Therefore, future research needs to uncover why these differences exist so that we can develop low burden evaluation techniques that correctly predict the outcomes of deploying a system in a realistic setting. We believe that the reason why explainable AI systems are sensitive to the difference between proxy task and actual task evaluation designs is that different AI explanation strategies require different kinds and amounts of cognition from the users (like our inductive and deductive explanations). However, people are reluctant to exert cognitive effort  [24, 25]  unless they are motivated or forced to do so. They also make substantially different decisions depending on whether they choose to exert cognitive effort or not  [12, 37] . In actual decision-making situations, people often choose not to engage in effortful analytical thinking, even in high-stakes situations like medical diagnosis  [31] . Meanwhile, proxy tasks force participants to explicitly pay attention to the behavior of the AI and the explanations produced. Thus, results observed when participants interact with proxy tasks do not accurately predict people's behavior in many realistic settings. In our study, participants who interacted with the proxy task felt that the deductive explanations required significantly more thinking than the inductive explanations. Therefore, in the proxy task where the participants were obliged to exert cognitive effort to evaluate the explanations, they said they preferred and trusted the less cognitively demanding explanations more, the inductive explanations. In contrast, in the actual task the participants could complete the task even without engaging with the explanations. Thus, we suspect that in the deductive condition participants perceived the explanations as too mentally demanding, and chose to over-rely on the AI's recommendation, just to avoid cognitive effort of examining those explanations. They also might have perceived the AI that provided deductive explanations as more competent because it required more thinking. One implication of our analysis is that the effectiveness of explainable AI systems can be substantially impacted by the design of the interaction (rather than just the algorithms or explanations). For example, a recent study showed that a simple cognitive forcing strategy (having participants make their own preliminary decision before being shown the AI's decision) resulted in much higher accuracy of the final decisions made by human+AI teams than any strategy that did not involve cognitive forcing  [17] . Inadvertently, we uncovered an additional potential pitfall for evaluating explainable AI systems. As the results of our qualitative study demonstrated, the use of the think-aloud method-a standard technique for evaluating interactive systems-can also substantially impact how participants allocate their mental effort. Because participants were asked to think aloud, we suspect that they exerted additional cognitive effort to engage with the explanations and analyze their reasoning behind their decisions. Together, these results indicate that cognitive effort is an important aspect of explanation design and its evaluation. Explanations high in cognitive demand might be ignored by the users while simple explanations might not convey the appropriate amount of evidence that is needed to make informed decisions. At the same time, traditional methods of probing users' minds while using explainable interfaces should also be re-evaluated. By taking into account the cognitive effort and cognitive processes that are employed during the evaluation of the explanations, we might generate explainable interfaces that optimize the performance of the sociotechnical (hu-man+AI) system as a whole. Such interfaces would instill trust, and make the user aware of the system's errors. \n CONCLUSION To achieve the aspiration of human+AI teams that complement oneanother and perform better than either the human or the AI alone, researchers need to be cautious about their pragmatic decisions. In this study, through online experiments and an in-person study, we showed how several assumptions researchers make about the evaluation of the explainable AI systems for decision-making tasks could lead to misleading results. First, choosing proxy tasks for the evaluation of explainable AI systems shifts the user's focus toward the AI, so the obtained results might not correspond to results of the user completing the actual decision-making task while assisted by the AI. In fact, our results indicate that users trust and prefer one explanation design (i.e. inductive) more in the proxy task, while they trust and prefer the other explanation design (i.e. deductive) more in the actual decision-making task. Second, the subjective evaluation of explainable systems with measures such as trust and preference may not correspond to the ultimate user performance with the system. We found that people trusted and preferred the AI with deductive explanations more, but recognized AI errors better with the inductive explanations. Lastly, our results suggest that think-aloud studies may not convey how people make decisions with explainable systems in realistic settings. The results from the think-aloud in-person study, which used the actual task design, aligned more with the results we obtained in the proxy task. These findings suggest that to draw correct conclusions about their experiments, explainable AI researchers should be wary of the explainable systems' evaluation pitfalls and design their evaluation accordingly. Particularly, the correct and holistic evaluation of explainable AI interfaces as sociotechnical systems is of paramount importance, as they are increasingly being deployed in critical decision-making domains with grave repercussions. Figure 1 : 1 Figure 1: The proxy task. Illustration of the simulated AI system participants interacted with: (a) is an example of an inductive explanation with appropriate examples. (b) is an example of a deductive explanation with misrecognized ingredients, where the simulated AI misrecognized apples and beets as avocados and bacon. \n Figure 2 :Figure 3 : 23 Figure 2: The actual task. Illustration of the simulated AI system participants interacted with. (a) is an example of incorrect recommendations with inductive explanations. Contrasting the query image with the explanations reveals that the simulated AI misrecognized churros with chocolate as sweet potato fries with BBQ sauce. (b) is an example of correct recommendation with deductive explanations. \n Figure 4 : 4 Figure 4: Performance in the actual decision-making task. (a) depicts the mean of performance among no-AI, no-Explanations and with-Explanations (overall) conditions. (b) depicts the mean of performance among inductive and deductive conditions, when the AI recommendation is correct and erroneous. Error bars indicate one standard error. \n Figure 5 : 5 Figure 5: Subjective evaluations in terms of trust and preference of the two AIs. Red and blue depict the percent of participants that chose inductive and deductive AI, respectively. (a) proxy task (b) actual decision-making task.", "date_published": "n/a", "url": "n/a", "filename": "3377325.3377498.tei.xml", "abstract": "Explainable artificially intelligent (XAI) systems form part of sociotechnical systems, e.g., human+AI teams tasked with making decisions. Yet, current XAI systems are rarely evaluated by measuring the performance of human+AI teams on actual decision-making tasks. We conducted two online experiments and one in-person think-aloud study to evaluate two currently common techniques for evaluating XAI systems: (1) using proxy, artificial tasks such as how well humans predict the AI's decision from the given explanations, and (2) using subjective measures of trust and preference as predictors of actual performance. The results of our experiments demonstrate that evaluations with proxy tasks did not predict the results of the evaluations with the actual decision-making tasks. Further, the subjective measures on evaluations with actual decision-making tasks did not predict the objective performance on those same tasks. Our results suggest that by employing misleading evaluation methods, our field may be inadvertently slowing its progress toward developing human+AI teams that can reliably perform better than humans or AIs alone. \n CCS CONCEPTS • Human-centered computing → Interaction design; Empirical studies in interaction design.", "id": "8d0c9d446bbcebc60a1316cde3ebdf7b"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seán S Óhéigeartaigh"], "title": "The State of Research in Existential Risk", "text": "Existential and Global Catastrophic Risk An existential risk is one that threatens the premature extinction of Earth-originating intelligent life, or the permanent and drastic destruction of its potential for desirable future development  (Bostrom, 2002) . For most practical purposes, this refers to developments that might wipe out humanity, or lock us into a situation we (or other intelligent life on earth) cannot recover from, such as a major and permanent global civilizational collapse.  1  The Centre for the Study of Existential Risk, among other organisations within the existential risk research community, also includes a focus on global catastrophic risks. Here, a common definition is that used by the Global Catastrophic Risk Institute: Global catastrophic risk is the risk of events large enough to significantly harm or even destroy human civilization at the global scale\" ((http://gcrinstitute.org/concept). For this definition of global catastrophic risk, human extinction risks would be a subset of a broader set of global catastrophic risks. However, precise definitions for these classes of risk are less important than having a shared sense of the magnitude of scope of events or developments under consideration, and the key characteristics of such events or developments. The study of existential and global catastrophic risk restricts us to events or trends that might lead to a full civilizational collapse. It rules out localised catastrophes, and global-scale events that would represent a tragedy but that would not impact our civilisation in the longer-term -unless these events were likely to play a key role in more severe and permanent cascades and collapses. Events as historically significant as Chernobyl, Hurricane Katrina, the Ebola outbreak, most of our wars in the 20 th century, and even the Spanish influenza would fail to constitute global catastrophes or existential threats. For this research community, their primary relevance is in what they can tell us about more severe possibilities within the relevant risk categories. On the other hand, various near-misses during the Cold War  (Lewis et al, 2014)  might plausibly have led to a global thermonuclear war with global catastrophic consequences, and thus this topic is firmly in scope. A clear example of an existential risk is the risk of an asteroid impact on the scale of that which wiped out the dinosaurs 66 million years ago  (Schulte et al, 2010) . An example of a global catastrophic risk that is not existential might include a large-scale pandemic disease outbreak  (Palmer et al, 2017; Millett & Snyder-Beattie, 2017) . Research and expert opinion indicates that it is unlikely that a natural pandemic outbreak could wipe out all humans across the globe given our distribution, immune variation, and other factors; and in most plausible scenarios global recovery seems likely in the longer term. It is also important to consider factors that increase stress or resilience on a global scale -events or developments that in of themselves would not be a global catastrophe, but might make it more or less likely for a global or existential catastrophe to occur. Climate change has the potential to result in global catastrophic consequences at the more severe end of the possibility spectrum -e.g. 5 degrees and up  (Wager & Weitzman, 2016) . But we might also consider less severe climate change as a stressor, as it could be expected to lead to major droughts and famines and other resource shortages, mass migration, geopolitical tension that could result in local or global war, and so forth. It could also lead to international conflict, for example over the use of controversial mitigation techniques such as sulphate aerosol geoengineering technologies. More generally, many of the specific risks we will look at need to be placed in the context of a world with a rising population, rising resource footprint, more extreme weather events, increasing pressures on ecosystem services, a changing physical and electronic infrastructure, and changing geopolitical pressures -and a world with a range of technologies more powerful than any we've had in previous centuries. \n Topics of focus within the existential and global catastrophic risk research community Risks of particular focus within the existential risk community include those relating to our interaction with the global environment (for example, extreme climate change; globally catastrophic biodiversity loss; and risks from natural pandemic outbreaks). They also include risks from scientific and technological advances, such as risks from engineered pandemics and future advances in synthetic biology and other biotechnologies; nuclear winter; and risks from future advances in, and applications of, artificial intelligence. Some focus is given to risks from asteroids and supervolcanoes, but these have been less highly prioritised to date, due to the low frequency of occurrence of the relevant events; the last global catastrophe-level asteroid impact event was the impact that created the Chicxulub Crater 66 million years ago, and the last likely global catastrophe-level supervolcano is thought to have been the Toba eruption 70,000 years ago  (Ambrose, 2000) . The community also has research groups working on global systemic risks, interactions and cascades between risks, risks from future technologies such as neurotechnologies, advances in nanotechnology and other technologies. Researchers also focus on broader or more cross-cutting themes, such as governance challenges associated with global catastrophic risks, ethical considerations relating to the value of future generations, analysis of the costs and value of reducing existential and global catastrophic risk relative to other global priorities, foresight, horizon-scanning and road-mapping exercises for risks and relevant sciences and technologies, and methodological issues relating to reasoning about extreme events under great uncertainty. For most individual global catastrophic and existential risks (with the possible exception of risk from advanced artificial intelligence), there are individual research communities working on these topics; albeit sometimes focusing more so on risks at a lower end of the spectrum. Some have been doing so for decades. For example, there are many centres doing valuable work on nuclear non-proliferation and security, pandemic preparedness and surveillance, and bioweapon governance -research leaders from these communities are represented at the Garrick Colloquium. There are numerous centres working on different aspects of climate change, biodiversity loss and other environmental risks and resource-related challenges. There are a number of excellent groups working on global systemic risks. NASA, the Planetary Defense community and others work on asteroid scanning and mitigation strategies. Furthermore there are a range of centres in academia, think tanks, government and elsewhere working on more cross-cutting issues such as risk governance and international security, foresight and scenario planning, and so forth. At a level below global catastrophic risk, there is excellent work on risk modelling being done in, and associated with, the reinsurance industry. The existential and global catastrophic risk research community collaborates with, and draws on, research from these communities extensively. It aims to complement such work by looking at existential and global catastrophic risks as a class of risks, with the aim of: • Identifying the particular challenges associated with risks of this magnitude -whether they be scientific, analytic, ethical, or to do with governance, coordination, planning, or perception. • Identifying risk areas where insufficient attention has been paid to the most extreme scenarios. • Examining how these different risks, and other global developments, may interact with each other. • Identifying previously unidentified or potential future risks • Trying to distinguish which extreme scenarios are plausible and worthy of further work, even if they may be low probability, as opposed to those that can be dismissed as science fiction. \n Recent growth of this community There has been a lot of recent growth within the existential risk research community.  \n What can we learn from this research, and what can we do with that knowledge? It is worth considering the insights we can gain from studying risks of this magnitude that may not be gleaned from bodies of work analysing and mitigating risk more broadly, or risks of a lower magnitude. One source of value is simply to be able to rule out scientifically implausible scenarios, in order to better focus our attention on existing threats and plausible future threats. This is of particular value for low-probability, extreme impact events, especially those that may be entirely novel. Many researchers argue the value of understanding existential risk on the grounds of their long-term moral significance. If we can demonstrate that certain threats have the potential for human extinction, or permanent collapse, then it is argued that the importance of mitigating them increases dramatically, due to the fact that they would not only harm current generations, but wipe out the potential for a huge number of future lives. There may be specific actions we could take that are designed to mitigate the most severe versions of these threats in particular. These might include establishing a very strict ban on specific types of virus research or bioweapons, or on research on AI systems that could both come up with a realistic model of the world and engage in recursive self-improvement. They could also include seed banks, shelters and alternative foods, so that even in many otherwise extinction-level events we might increase the odds of continuation of the species. In addition, there may be strategies we would avoid adopting unless we had reasonable cause to believe we were headed for a world in which a particular type of global catastrophe were likely. For example, it would be extremely foolish and unconstructive to call for a ban on artificial intelligence research at this point. At some point in the future however, a body of evidence might indicate that certain developments with catastrophic potential are likely within several years. This then might be reason to consider a temporary moratorium on progress to enhance the capability of AI systems, while various containment and safety measures were being explored. This is not without precedent, even at lower-levels of risk: the US White House issued a temporary moratorium on gain-of-function influenza research several years ago to allow time for more risk-benefit analysis  (Lipsitch & Inglesby, 2014) . Or consider a world in which evidence indicated we were headed for climate change of 5 degrees or over, in the absence of drastic action. In these circumstances we might consider deploying technologies, such as sulphate aerosol geoengineering, which we might be hesitant to deploy under less severe scenarios  (Crutzen, 2006) . Our reservations might be based on concerns over risks posed by the intervention itself, thorny global governance challenges that the intervention presents, or questions over public acceptance. These may be sound reservations that would rule out these strategies in all but the most exceptional of circumstances. A research community developing indicators that we may be approaching unusually dangerous global circumstances, and developing strategies for last-ditch solutions, may be of considerable value given the risks we may face in the coming century -even if many of these strategies are never needed or deployed. Lastly, by studying the particular scientific, governance, ethical, and communication issues that arise when confronting one global catastrophic risk, we can learn valuable lessons to draw on for future challenges. For example, climate change in some ways exemplifies a lot of the issues that make existential and global catastrophic risk especially challenging. There is still a lot of scientific uncertainty over timelines, probability and pathways to the most severe impacts. The scale and impact are difficult to grasp, impossible to see, and the most severe consequences will fall on future generations. We still don't have broad public acceptance of the science, especially in the US. It involves countries around the world coordinating, each making near-term sacrifices in favour of the longer-term future. Yet the Paris Agreement was extremely encouraging. It involved 194 countries committing to make sacrifices in the interests of future generations in the face of these challenges. Despite the setback of the US's recent announcement of intent to withdraw, this remains an important achievement and a critical step towards progress on climate change. By learning from the successes and failures of this process, as well as from the history of nuclear non-proliferation and international diplomacy, norms and conventions prohibiting the use of biological weapons, and other global processes to manage and mitigate global risk, we can be better prepared for the future. \n Key challenges in existential and global catastrophic risk There is a large body of expertise from the risk sciences that is of relevance to the study of existential and global catastrophic risk. However, a number of characteristics make these risks particularly challenging to analyse using normal risk analysis approaches. These include the difficulty in estimating the probability and expected impact of rare or even unprecedented events, where there may be sparse data to draw on; and the changing nature of some risks, in particular those associated with rapidly developing technologies (especially those interacting with a rapidly developing infrastructure). For some global catastrophic risks, probability is relatively straightforward to quantify. For asteroid impacts, for example, we can look to sources of evidence such as the earth's fossil record, patterns of impact craters on the Moon and on Mars, datasets of asteroids passing our field of vision, and use these to make a reasonable estimate of the frequency with which we might expect an asteroid of a given size to hit the earth. The pathways by which an asteroid impact would result in global catastrophe are also relatively straightforward; therefore we can estimate the expected global harm expected from asteroids of different sizes. However, a similar analysis is much less straightforward for other risks. This can be illustrated by the example of catastrophic climate change. For a start, there is great uncertainty about the sensitivity of the earth system to the effects of our activities. The possibility of severe climate change is affected by factors including to but not limited to the potential for methane release from beneath the melting arctic permafrost, and from the seabed; how much CO2 the deep ocean can absorb; the possibility of collapse of Antarctic and Greenland ice sheets; the possibility that the gulf stream might halt. The most worrying scenarios involve a combination of these factors driving each other as part of a positive feedback loop. While ongoing research will help us understand these factors and their interactions more clearly, it is very difficult to assign a meaningful probability to an outcome such as >5 degree climate change in the 21 st century under a certain emission scenario. It may be that attempting to assign strict probabilities is the wrong approach; an alternative would be to develop frameworks of 'safe operating thresholds' with wide error bounds, exemplified by the 'Planetary boundaries' framework put forward by Johan Rockstrom and colleagues at the Stockholm Resilience Centre  (Steffen et al, 2015) . The expected harm from long-term climate change will also depend very heavily on the extent to which various mitigation and adaptation strategies are adopted, and how successful they are. Similarly, in the case of global pandemics, we we can ask scientific questions about the possibility of the 'perfect virus' with high health impact, high infectivity, and long incubation time. However, the scale and severity of impact will be predicated by many other factors -movement of humans or other vectors, capabilities of health services, the response of the population, and more. It is plausible that the bulk of the damage might not even be caused by the virus, but instead by a broad infrastructure collapse as emergency services and hospitals are overwhelmed, just-in-time food delivery is disrupted, and other systems underpinning societal order collapse. However, none of these challenges are insurmountable. Modelling and analysis of factors that contribute to these risks can deepen our scientific understanding. This can help us establish estimates for probability and impact, and in some cases rule out concerns entirely. Where past examples are sparse, there is value in drawing on counterfactual examples of 'near misses', as described by Gordon Woo  (Woo, 2016)  and others. Design and analysis of scenarios can help in identifying key considerations and interactions. This may help us identify key interventions that reduce risk significantly, even if in instances where it is difficult to assign tight probabilities to events. Other risk analysis techniques, and interventions to mitigate risks at scales smaller that global catastrophe level, also provide a range of useful insights for the analysis of global catastrophic risks, as shown by the work of GCRI and others. By studying global catastrophic risks as a class of risks, we can identify shared characteristics of global catastrophe events, which may help us identify common strategies that aid us in becoming more resilient as a species against a broad set of risks. For example, a number of global catastrophic events (global nuclear war, supervolcano eruption, asteroid impact) would result in large amounts of particulate matter being ejected into the atmosphere, resulting in a disruption of photosynthesis  (Maher and Baum, 2013) . The development of alternative foods that are not dependent on sunlight, and strategies to scale up production of these food sources rapidly, would be robust in the face of a broad range of catastrophe events  (Denkenberger and Pearse, 2014) . The maintenance of permanent seed banks, manned shelters suitable for lengthy use, and information vaults represent similar safeguards. Similar strategies, useful for reduction of a broad range of risks, are likely to be feasible at the level of national and international governance  (Farquhar et al, 2017; Cotton-Barrett et al, 2016) . \n Case Study: Potential future global risks from artificial intelligence In this final section, I aim to present this research community's work over the last decade on potential future risks from artificial intelligence as a case study on how the field has made progress on a particularly novel area of concern, focusing on the broad strategies involved. This is complemented by a more technical analysis of AI risk provided by Seth Baum. The theoretical nature of the risk: Early work, carried out mainly by the Machine Intelligence Research Institute and the Future of Humanity Institute, aimed to explore the possibility of artificial general intelligence of greater-than-human-ability. This was coupled with the aim of exploring and characterising the theoretical risk associated that such a development could pose, drawing on input from experts in computer science and other fields. Rather than focus on difficult-to-characterise questions like consciousness, sentience, and evil intentions, the work instead focused on foundational issues like: -The difficulty of designing safe goals for very capable, powerful systems able to take a very wide range of actions in a wide range of environments, where the actions could have a wide range of consequences. -Certain predicted behaviours that might be expected from a powerful optimizing agent, such as a drive to acquire additional resources, a drive to avoid being switched off prior to completion of its goal, or a drive to improve the system's own capability. -The theoretical possibility and limits of recursive self-improvement. This refers to the possibility that a sufficiently capable system may be able to surpass human programmers in its ability to design the next generation of systems. It is hypothesised that this could in turn result in a 'chain reaction' of performance improvement  (Yampolskiy, 2015) , rapidly leading to a system far beyond human capability in most cognitive domains. -The challenge that for most of the relevant design and control processes, it may be necessary to solve a range of technical and theoretical issues ahead of time, before certain critical thresholds in capability are reached. Beyond these thresholds, it may be much more difficult to intervene effectively due to the level of capability and autonomy of subsequent iterations of the system. It is worth noting that in principle, it is possible that systems may be developed which have a much greater ability to engage in science, engineering, and manufacture, and a greater ability to manipulate the global environment than we humans have. This level of power raises concerns of global catastrophic or existential risk, unless very carefully developed. These programmes of research were then published in a book, Superintelligence  (Bostrom, 2014) , which received a lot of attention, as well as in many further academic papers. These lines of argument are by no means uncontroversial -many experts disagree on various points. Most experts consider artificial general intelligence to be decades out of reach as a scientific milestone, and some expect hundreds of years of progress to be needed  (Grace et al, 2017) . Some are sceptical about the hypothesis that rapid progress, enabled by the engagement of the AI systems themselves in the research and development process, could occur once a certain level of capability and generality is reached (e.g. see  Walsh, 2016 ). Yet others are sceptical that such systems would be likely to demonstrate the traits of agency, autonomy and goal-driven behaviour that may make the actions of such systems difficult to predict or intervene on. Some experts hold that these is a limit to how much meaningful work can be done at this point in time to ensure the safety and stability of future systems, given the limits that can be meaningfully predicted about the theoretical underpinnings and engineering design of these future systems, as well as the limits of our knowledge regarding the nature of intelligence. Others have raised the concern that a focus on risks from powerful future systems may distract focus from more near-term risks and opportunities associated with the current state of the technology. However, a growing body of experts in AI consider many of these concerns plausible and worthy of further study (e.g. see  Dafoe and Russell, 2016) . While the level of capability warranting global catastrophic concerns is still decades away or longer, ongoing research on the matter is warranted by the magnitude of the challenge, and the range of technical and governance questions in need of study in advance of such developments. It is the view of this author that these concerns should not be used as a rationale to propose slowing down progress on the technology at this point in time. Nor should this research take the place of necessary and valuable work on near-term opportunities and challenges posed by AI, but rather should complement it. Broader scientific engagement: The next steps for the community were to engage more deeply with the scientific artificial intelligence community in academia and industry-to explore, discuss and debate these arguments, as well as other risks that may be associated with AI. In 2015, a landmark conference was held in Puerto Rico, with representatives of the leading companies working explicitly towards a vision of general AI, alongside experts in governance, law, economics, risk and other relevant fields. The conference resulted in an open letter calling for more research on AI that was safe, robust, and beneficial, and for ongoing attention to issues relating to the longer term. The letter was signed by research leaders in artificial intelligence across industry and academia, as well as leading experts in a range of different fields, and was accompanied by a paper outlining research priorities, and a grants programme to support relevant work. The conference has been followed by a programme of activities to foster collaboration with more of the machine learning community both near-and long-term issues relating to safe design and risk. This has including a series of workshops organised by CSER and others at the major machine learning conferences (ICML, NIPS, IJCAI, DALI). T In 2017 FLI organised a follow-on to the Puerto Rico conference in Asilomar, resulting in the endorsement by many leading researchers of a set of principles for the long-term development of AI. \n Technical research: In parallel, much of the work in the last two years has focused on translating some of the more foundational questions raised by early work at FHI and MIRI and elsewhere into crisp technical research problems that can be worked on today. This includes approaches involving fundamental mathematical frameworks for agent decision-making and behaviour, as well as research programmes exploring how some of the behaviours that would be of concern in long-term systems may manifest in the near-term systems we are building currently. A number of research agendas have been published in the last year, and several of the leading companies focused on general AI now have safety teams exploring these issues. In addition, there has been substantial growth in projects mapping progress and trajectories in AI in domains relevant to both narrow and general artificial intelligence. Global engagement: Within the existential risk community, more thought is now going to the particular political and governance challenges that may emerge as we move closer towards more powerful and general AI systems, with programmes starting up at FHI, CSER, the Centre for the Future of Intelligence. Long-term impacts and risks have risen on the agenda for governments in Europe and the United States, for example being mentioned as worthy of further study in the US Office for Science and Technology Policy's recent report on preparing for the future of artificial intelligence. One priority that has emerged is the need for greater global engagement, particularly with research leaders and other stakeholders in China, but also India, Japan, and emerging hubs in Africa. Any global conversation around the future of artificial intelligence, and potential global benefits risks associated with it, needs to have global representation. From a pragmatic point of view, China is on course to emerge as a scientific leader and agenda-setter in AI research over the coming decade. If at some point in several decades we truly do approach a level of technological breakthrough with global risk consequences, we are unlikely to be able to achieve a safe transition without a strong level of global cooperation and trust, which is going to require a lot of dedicated work to achieve. Now is a good time to start laying the groundwork. \n Conclusion We are entering a century in which humanity will be confronted with unprecedented threats to global civilisation. Some of these may result from the manner in which our footprint as a species strains our global environment, such as the impacts of climate change and biodiversity loss. Some may result from the development and deployment of increasingly powerful technologies, whether due to malevolent use or unintended consequences. The challenge posed by the analysis and mitigation of these threats requires an interdisciplinary approach: a community that can draw on the best expertise from the risk sciences, as well as the expertise of scientists, law and governance specialists, ethicists, and others. It also requires a community that can draw on expertise on different types and sources of risk, and consider both lessons that can be applied across risks, and the interactions that are likely to occur between different global developments. Many of the most useful tools in global risk analysis have been drawn from the risk science literature, and deeper collaborations between the existential risk community and the risk science community are likely to be increasingly important in the years to come. The first dedicated centre established was arguably Nick Bostrom's Future of Humanity Institute (FHI; https://www.fhi.ox.ac.uk/) in Oxford in 2003. The FHI has focused on cross-cutting global catastrophic risk analysis, philosophical analysis on the global importance of reducing existential risk, and in the last decade has placed its strongest focus on characterising potential risks from artificial general intelligence and superintelligence; a lot of this has been in collaboration with the Machine Intelligence Research Institute in Berkeley. The Global Catastrophic Risk Institute (GCRI;The Centre for the Study of Existential Risk (CSER; http://cser.org) was founded in 2012 by Martin Rees, Huw Price, and Jaan Tallinn, although its first research grants were secured, and first postdoctoral researchers hired, more recently in late 2015 and 2016. We now have a research team beginning work on biological threats, extreme climate change, ecological tipping points, catastrophic risks related to future advances in artificial intelligence, and analysis of emerging technologies such as geoengineering. We also have postdocs working on more cross-cutting themes such as horizonscanning and foresight for extreme risk, responsible innovation in risky sciences and technologies, population growth and resource use.The Future of Life Institute (https://futureoflife.org/) was founded in 2014, focusing on artificial intelligence, climate change, risks from biotechnology, and risks from nuclear weapons. It has organised two highly successful conferences on the future of artificial intelligence and potential risks it might bring, resulting in a widely signed and shared open letter on the responsible development of AI, a grants programme to support work on AI safety, and a set of principles aimed at promoting the beneficial development and application of AI within the research community and more broadly. It has also organised a conference on nuclear war, and has engaged in activities to encourage divestment from nuclear weapons.Several more recent initiatives are underway within academia, including at Stockholm, Warwick (United Kingdom), and Australia National University, and other world-leading risk centres such as the Garrick Institute (UCLA) are increasingly including global catastrophic risk within their remit, indicating that a diverse range of new expertise will be brought to bear on these topics in coming years. http://gcrinstitute.org/) in the US was founded in 2011, focusing on risks including bioweapons, nuclear war, artificial intelligence, and natural events, and employing risk analysis methodology. Under Seth Baum and Tony Barrett's leadership, it has played a key role in establishing links between the existential risk community and experts in these fields. \n\t\t\t Electronic copy available at: https://ssrn.com/abstract=3446663", "date_published": "n/a", "url": "n/a", "filename": "SSRN-id3446663.tei.xml", "abstract": "In the last fifteen years there has been substantial growth in research on existential risk -the category of risks that threaten human extinction, or the permanent and drastic reduction of humanity's future potential. A number of new organisations focused explicitly on existential and global catastrophic risk have been founded in recent years, complementing the long-standing work of existing centres focused on specific risk areas such as nuclear war, biosecurity, climate change and systemic risk. This paper provides a brief overview of the emergence of this new research community, and provides a case study on the community's research on potential risks posed by future developments in artificial intelligence. There exists the opportunity for powerful collaboration between the new approaches and perspectives provided by the existential risk research community, and the expertise and tools developed by the risk sciences for risks of various magnitudes. However, there are a number of key characteristics of existential and global catastrophic risks, such as their magnitude, and their rare or unprecedented nature, that are likely to make them particularly challenging to submit to standard risk analysis, and will require new and specialised approaches. 1 It is worth noting that Bostrom also considers some more unusual possibilities, such as the emergence of permanent totalitarianism", "id": "396140839acd34180f4e843b7ad4bc92"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Smitha Milli", "Falk Lieder", "Thomas L Griffiths"], "title": "Running head: RATIONAL REINTERPRETATION OF DUAL-PROCESS THEORIES 1 A Rational Reinterpretation of Dual-Process Theories", "text": "rational solutions when resources are limited  (Lieder, Griffiths, & Hsu, 2018; Lieder, Griffiths, Huys, & Goodman, 2018a , 2018b Howes, Warren, Farmer, El-Deredy, & Lewis, 2016; Khaw, Li, & Woodford, 2017; Sims, 2003; Tsetsos et al., 2016; Bhui & Gershman, 2017) . Furthermore, people appear to adaptively choose between their fast heuristics and their slower and more deliberate strategies based on the amount of resources available  However, an issue still remains unresolved in the push for the resource-rational reinterpretation of these heuristics. Since the exact amount of computation to do for a problem depends on the particular time and cognitive resources available, a larger repertoire of reasoning systems should enable the mind to more flexibly adapt to different situations  (Payne, Bettman, & Johnson, 1993; Gigerenzer & Selten, 2002) . In fact, achieving the highest possible degree of adaptive flexibility would require choosing from an infinite set of diverse cognitive systems. However, this is not consistent with behavioral and neuroscientific evidence for a small number of qualitatively different decision systems (van der Meer,  Kurth-Nelson, & Redish, 2012; Dolan & Dayan, 2013)  and similar evidence in the domain of reasoning  (Evans, 2003 (Evans, , 2008 Evans & Stanovich, 2013) . One reason for a smaller number of systems could be that as the number of systems increases it becomes increasingly more time-consuming to select between them . This suggests that the number and nature of the mind's cognitive systems might be shaped by the competing demands for the ability to flexibly adapt one's reasoning to the varying demands of a wide range of different situations and the necessity to do so quickly and efficiently. In our work, we theoretically formalize this explanation, allowing us to derive not only what the optimal system is given a particular amount of resources, but what the optimal set of systems is for a human to select between across problems. Such an explanation may provide a rational reinterpretation of dual-process theories, the theory that the mind is composed of two distinct types of cognitive systems: one that is deliberate, slow, and accurate, and a second one that is fast, intuitive, and fallible  (Evans, 2008; Kahneman & Frederick, 2002 . Similar dual-process theories have independently emerged in research on decision-making  (Dolan & Dayan, 2013)  and cognitive control  (Diamond, 2013) . While recent work in these areas has addressed the question of how the mind arbitrates between the two systems  (Daw, Niv, & Dayan, 2005; Keramati, Dezfouli, & Piray, 2011; Shenhav, Botvinick, & Cohen, 2013; Boureau, Sokol-Hessner, & Daw, 2015) , it remains normatively unclear why the mind would be equipped with these two types of cognitive system, rather than another set of systems. The existence of the accurate and deliberate system, commonly referred to as System 2 following  Kahneman and Frederick (2002) , is easily justified by the benefits of rational decision-making. By contrast, the fast and fallible system (System 1) has been interpreted as a kluge  (Marcus, 2009)  and its mechanisms are widely considered to be irrational  (Sutherland, 2013; Ariely, 2009; Tversky & Kahneman, 1974; Gilovich et al., 2002) . This raises the question why this system exists at all. Recent theoretical work provided a normative justification for some of the heuristics of System 1 by showing that they are qualitatively consistent with the rational use of limited cognitive resources  (Griffiths et al., 2015; Lieder, Griffiths, & Hsu, 2018; Lieder, Griffiths, Huys, & Goodman, 2018a , 2018b ) -especially when the stakes are low and time is scarce and precious. Thus, System 1 and System 2 appear to be rational for different kinds of situations. For instance, you might want to rely on System 1 when you are about to get hit by a car and have to make a split-second decision about how to move. But, you might want to employ System 2 when deciding whether or not to quit your job. Here, we formally investigate what set of systems would enable people to make the best possible use of their finite time and cognitive resources. We derive the optimal tradeoff between the cognitive flexibility afforded by mutliple systems and the cost of choosing between them. To do so, we draw inspiration from the artificial intelligence literature on designing intelligent agents that make optimal use of their limited-performance hardware by building upon the mathematical frameworks of bounded optimality  (Russell & Subramanian, 1995)  and rational metareasoning  (Russell & Wefald, 1991b; Hay, Russell, Tolpin, & Shimony, 2012) . We apply this approach to four different domains where the dual systems framework has been applied to explain human decision-making: binary choice, planning, strategic interaction, and multi-alternative, multi-attribute risky choice. We investigate how the optimal cognitive architecture for each domain depends on the variability of the environment and the cost of choosing between multiple cognitive systems, which we call metareasoning cost. This approach allows us to extend the application of resource-rational analysis from a particular system of reasoning to sets of cognitive systems, and our findings provide a normative justification for dual-process theories of cognition. Concretely, we find that across all four domains the optimal number of systems increases with the variability of the environment but decreases with the costliness determining when which of these systems should be in control. In addition, when it is optimal to have two systems, then the difference in their speed-accuracy tradeoffs increases with the variability of the environment. In variable environments, this results in one system that is accurate but costly to use and another system that is fast but error-prone. These predictions mirror the assertions of dual-process accounts of cognition  (Evans, 2008; Kahneman, 2011) . Our findings cast new light on the debate about human rationality by suggesting that the apparently conflicting views of dual-process theories and rational accounts of cognition might be compatible after all. The remainder of this paper is structured as follows: We start by summarizing previous work in psychology and artificial intelligence that our article builds on. We then describe our mathematical methods for deriving optimal sets of cognitive systems. The subsequent four sections apply this methodology to the domains of binary choice, planning, strategic interaction in games, and multi-alternative risky choice. We conclude with the implications of our findings for the debate about human rationality and directions for future work. \n Background Before delving into the details of our analysis, we first discuss how our approach applies to the various dual-process theories in psychology, and how we build on the ideas of bounded optimality and rational metareasoning developed in artificial intelligence research. \n Dual-process theories The idea that human minds are composed of multiple interacting cognitive systems first came to prominence in the literature on reasoning  (Evans, 2008; Stanovich, 2011) . While people are capable of reasoning in ways that are consistent with the prescriptions of logic, they often do not. Dual-process theories suggested that this is because people employ two types of cognitive strategies: fast but fallible heuristics that are triggered automatically and deliberate strategies that are slow but accurate. Different dual-process theories vary in what they mean by two cognitive systems. For example,  Evans and Stanovich (2013)  distinguish between dual processes, in which each process can be made up of multiple cognitive systems, and dual systems, which corresponds to the literal meaning of two cognitive systems. Because our work abstracts these cognitive systems based on their speed-accuracy tradeoff our analysis applies both at the level of systems or processes as long as the systems or processes accomplish speed-accuracy tradeoffs. Thus, our theory still applies to both dual \"processes\" and dual \"systems\". There is also debate over how the two systems would interact. Some theories postulate the existence of a higher-level controller that chooses between the two systems  (Norman & Shallice, 1986; Shenhav et al., 2013) , some that the two systems run in parallel, and others that the slower system interrupts the faster one  (Evans & Stanovich, 2013) . The analysis we present simply assumes that there is greater metareasoning cost incurred for each additional system. This is clearest to see when a higher-level controller needs to make the decision of which system to employ. Alternatively, if multiple cognitive systems operated in parallel, the cost of arbitrating between these systems would also increase with the number of systems -just like the metareasoning cost. So, we believe our analysis would also apply under this alternative assumption. Since their development in the reasoning literature, dual-process theories have been applied to explain a wide range of mental phenonomena, including judgment and decision-making, where it has been popularized by the distinction between System 1 and System 2  (Kahneman & Frederick, 2002 Kahneman, 2011) , and moral reasoning where the distinction is made between a fast deontological system and a slow utilitarian system  (Greene, 2015) . In parallel with this literature in cognitive psychology, research on human reinforcement learning has led to similar conclusions. Behavioral and neural data suggest that the human brain is equipped with two distinct decision systems: a fast, reflexive, system based on habits and a slow, deliberate system based on goals  (Dolan & Dayan, 2013) . The mechanisms employed by these systems have been mapped onto model-based versus model-free reinforcement learning algorithms. A model-free versus model-based distinction has also been suggested to account for the nature of the two systems posited to underlie moral reasoning  (Cushman, 2013; Crockett, 2013) . The empirical support for the idea that the human mind is composed of two types of cognitive systems raises the question of why such a composition would evolve from natural selection. Given that people outperform AI systems in most complex real-world tasks despite their very limited cognitive resources  (Gershman, Horvitz, & Tenenbaum, 2015) , we ask whether being equipped with a fast but fallible and a slow but accurate cognitive system can be understood as a rational adaption to the challenge of solving complex problems with limited cognitive resources  (Griffiths et al., 2015) . \n Bounded Optimality and Resource-Rational Analysis Recent work has illustrated that promising process models of human cognition can be derived from the assumption that the human mind makes optimal use of cognitive resources that are available to it  (Griffiths et al., 2015; Lewis, Howes, & Singh, 2014) . This idea can be formalized by drawing on the theory of bounded optimality which was developed as a foundation for designing optimal intelligent agents. In contrast to expected utility theory  (Von Neumann & Morgenstern, 1944) , bounded optimality takes into account the constraints imposed by performance-limited hardware and the requirement that the agent has to interact its environment in real time  (Russell & Subramanian, 1995) . The basic idea is to mathematically derive a program that would enable the agent to interact with its environment as well as or better than any other program that its computational architecture could execute. Critically, the agent's limited computational resources and the requirement to interact with a potentially very complex, fast-paced, dynamic environment in real-time entail that the agent's strategies for reasoning and decision-making have to be extremely efficient. This rules out naive implementations of Bayes rule and expected utility maximization as those would take so long to compute that the agent would suffer a decision paralysis so bad that it might die before taking even a single action. The fact that people are subject to the same constraints makes bounded optimality a promising normative framework for modeling human cognition  (Griffiths et al., 2015) . Resource-rational analysis applies the principle of bounded optimality to derive optimal cognitive strategies from assumptions about the problem to be solved and the cognitive architecture available to solve it  (Griffiths et al., 2015) . Recent work illustrates that this approach can be used to discover the discover and make sense of people's heuristics for judgment  (Lieder, Griffiths, Huys, & Goodman, 2018a ) and decision-making  (Lieder, Griffiths, Huys, & Goodman, 2018a; Lieder, Griffiths, & Hsu, 2018) , as well as memory and cognitive control  (Howes et al., 2016) . The resulting models have shed new light on the debate about human rationality  (Lieder, Griffiths, Huys, & Goodman, 2018a , 2018b Lieder, Krueger, & Griffiths, 2017; Lieder, Griffiths, Huys, & Goodman, 2018b; Lieder, Griffiths, & Hsu, 2018; Griffiths et al., 2015) . While this approach has so far focused on one individual strategy at a time, the research presented here extends it to deriving optimal cognitive architectures comprising multiple systems or strategies for a wider range of problems. To do so, we use the theory of rational metareasoning as a foundation for modeling how each potential cognitive architecture would decide when to rely on which system or strategy. \n Rational metareasoning as a framework for modeling the adaptive control of cognition Previous research suggests that people flexibly adapt how they decide to the requirements of the situation  (Payne, Bettman, & Johnson, 1988) . Recent theoretical work has shown that this adaptive flexibility can be understood within the rational metareasoning framework developed in artificial intelligence . Rational metareasoning  (Russell & Wefald, 1991b; Hay et al., 2012)  formalizes the problem of selecting computations so as to make optimal use of finite time and limited-performance hardware. The adaptive control of computation afforded by rational metareasoning is critical for intelligent systems to be able to solve complex and potentially time-critical problems on performance-limited hardware  (Horvitz, Cooper, & Heckerman, 1989; Russell & Wefald, 1991b) . For instance, it is necessary for a patient-monitoring system used in emergency medicine to metareason in order to decide when to terminate diagnostic reasoning and recommend treatment.  (Horvitz & Rutledge, 1991) . This example illustrates that rational metareasoning may be necessary for agents to achieve bounded-optimality in environments that pose a wide range of problems that require very different computational strategies. However, to be useful for achieving bounded-optimality, metareasoning has to be done very efficiently. In principle, rational metareasoning could be used to derive the optimal amount of time and mental effort that a person should invest into making a decision  (Shenhav et al., 2017) . Unfortunately, selecting computations optimally is a computation-intensive problem itself because the value of each computation depends on the potentially long sequence of computations that can be performed afterwards. Consequently, in most cases, solving the metareasoning problem optimally would defeat the purpose of trying to save time and effort  (Lin, Kolobov, Kamar, & Horvitz, 2015; Hay et al., 2012; Russell & Wefald, 1991a) . Instead, to make optimal use of their finite computational resources bounded-optimal agents  (Russell & Subramanian, 1995)  must optimally distribute their resources between metareasoning and reasoning about the world. Thus, studying bounded-optimal metareasoning might be a way to understand how people manage to allocate their finite computational resources near-optimally with very little effort  (Gershman et al., 2015; Keramati et al., 2011) . Recent work has shown that approximate metareasoning over a discrete set of cognitive strategies can save more time and effort than it takes and thereby improve overall performance  (Lieder et al., 2014) . This approximation can drastically reduce the computational complexity of metareasoning while achieving human-level performance  (Lieder et al., 2014; . Thus, rather than metareasoning over all possible sequences of mental operations to determine the exact amount of time to think, humans may simply metareason over a finite set of cognitive systems that have different speed and accuracy tradeoffs. This suggests a cognitive architecture comprising multiple systems for reasoning and decision making and a executive control system that arbitrates between them -which is entirely consistent with extant theories of cognitive control and mental effort  (Norman & Shallice, 1986; Shenhav et al., 2017 Shenhav et al., , 2013 . Dual-process theories can be seen as a special case of this cognitive architecture where the number of decision systems is two. According to this perspective, the executive control system selects between a limited number of cognitive systems by predicting how well each of them would perform in terms of decision quality and effort and then selects the systems with the best predicted performance . Assuming that each of these predictions takes a certain amount of mental effort, this entails that the cost of deciding which cognitive system to rely on in a given situation increases with the number of systems. At the same time, increasing the number of systems also increases the agent's cognitive flexibility thereby enabling it to achieve a higher level of performance across a wider range of environments. Conversely, reducing the space of computational mechanisms the agent can choose from entails that there may be problems for which the optimal computational mechanisms will be no longer available. This dilemma necessitates a tradeoff that sacrifices some flexibility to increase the speed at which cognitive mechanisms can be selected. This raises the question of how many and which computational mechanisms a bounded-optimal metareasoning agent should be equipped with, which we proceed to explore in the following sections. \n Deriving Bounded-Optimal Cognitive Systems We now describe our general approach for extending resource-rational analysis to the level of cognitive architectures. The first step is to model the environment. For the purpose of our analysis, we characterize each environment by the set of decision problems D that it poses to people and a probability distribution P over D that represents how frequently the agent will encounter each of them. The set of decision problems D could be quite varied, for example, it could include deciding which job to pick and deciding what to eat for lunch. In this case P would encode the fact that deciding what to eat for lunch is a more common type of decision problem than deciding which job to pick. Associated with each decision problem d is a utility function U d (a) that represents the utility gained by the agent for taking action a in decision problem d. Having characterized the environment in terms of decision problems, we now model how people might solve them. We assume that there is a set of reasoning and decision-making systems T that the agent could potentially be equipped with. The question we seek to investigate is what subset M ⊆ T is optimal for the agent to actually be equipped with. The optimal set of systems M is dependent on three costs: (1) the action cost: the cost of taking the chosen action, (2) the reasoning cost: the cost of using a system from M to reason about which action to take, (3) the metareasoning cost: the cost of deciding which system to use to decide which action to take. For simplicity, we will describe each of the costs in terms of time delays, although they also entail additional costs, including metabolic costs. As an example, consider the scenario of deciding what to order for lunch at a restaurant. The diner has a fixed amount of time she can spend at lunch until she needs to get back to work, so time is a finite resource. The action cost is the time required to eat the meal. A person might have multiple systems for deciding which items to choose. For example, one system may rely on habit and order the same dish as last time. Another system may perform more logical computation to analyze the nutritional value of each item or what the most economical choice is. Each system has an associated reasoning cost, the time it takes for that system to decide which item to order. It is clear that the diner has to balance the amount of time spent thinking about what meal to pick (reasoning cost) with the amount of time it will take to actually eat the meal (action cost), so that she is able to finish her meal in the time she has available. If the diner is extremely time-constrained, perhaps because of an urgent meeting she needs to get back to, then she may simply heuristically plop items onto her plate. But, if the diner has more time, then she may think more about what items to choose. In addition to the cost of reasoning and the cost of acting, having multiple decision systems also incurs the cost of metareasoning, that is reasoning about how to reason about what to do. In other words, the metareasoning cost is how much time it takes the diner to decide how much to think about whether to rely on her habits, an analysis of nutritional value, or any of the the other decision mechanisms she may have at her disposal. If the diner only has one system of thinking, then the metareasoning cost is zero. But as the number of systems increases, the metareasoning cost of deciding which system should be in control increases. This raises the question of what is the optimal ensemble of cognitive systems, how many systems does it include, and what are they? We can derive the answer to these questions by computing minimizing the expected sum of action cost, reasoning cost, and metareasoning cost over the set of all possible ensembles of cognitive systems. In summary, our approach for deriving a bounded-optimal cognitive architecture proceeds as follows: 1. Model the environment. Define the set of decision problems D, the distribution over them P , and the utility for each problem U d (a). 2. Model the agent. Define the set of possible cognitive systems T the agent could have. 3. Specify the optimal mind design problem. Define the metric that the bounded agent's behavior optimizes, i.e., a trade-off between the utility it gains and the costs that it incurs; the action cost, reasoning cost, and metareasoning cost. 4. Solve the optimal mind design problem. Solve (3) to find the optimal set of systems M ⊆ T for the agent to be equipped with. Once we have done this, we can begin to probe how different parts of the simulation affect the final result in step (4). For example, we expect that the optimal cognitive architecture for a variable environment should comprise multiple cognitive systems with different characteristics. But at the same time, the number of systems should not be too high, or else the time spent on deciding which system to use, the metareasoning cost, will be too high. In other words, we hypothesize that the number of systems will depend on a tradeoff between the variability of the environment and the metareasoning cost. Our simulations show that this is indeed the case. \n Simulation 1: Two-Alternative Forced Choice Our first simulation focuses on the widely-used two-alternative forced choice (2AFC) paradigm, in which a participant is forced to select between two options. For example, belongs to the category or not, and psychophysics experiments often require participants to judge whether two stimuli are the same or different. Even in simple laboratory settings, judgments made within a 2AFC task seem to stem from systematically different modes of thinking. Therefore, 2AFC tasks are a prime setting to start in evaluating our theory for dual process systems. But before describing the details of our 2AFC simulation, we first review evidence of dual-process accounts of behavior in the 2AFC paradigm. A very basic binary choice task presents an animal with a lever that it can either press to obtain food or decide not to press  (Dickinson, 1985) . It has been shown that early on in this task rodents' choices are governed by a flexible brain system that will stop pressing the lever when the they no longer want the food. By contrast, after extensive training their choices are controlled by a different, inflexible brain system that will continue to press the lever even when the reward is devaluated by poisoning the food. Interestingly, these two systems are preserved in the human brain and the same phenomenon has been demonstrated in humans  (Balleine & O'Doherty, 2010) . Another example of two-alternative forced-choice is the probability learning task where participants repeatedly choose between two options, the first of which yields a reward with probability p 1 and the second of which yields a reward with probability p 2 = 1 − p 1 . It has been found that depending on the incentives people tend to make these choices in two radically different ways  (Shanks, Tunney, & McCarthy, 2002) : When the incentives are low then people tend to use a strategy that chooses option one with a frequency close to p 1 and option two with a frequency close to p 2 -which can be achieved very efficiently  (Vul, Goodman, Griffiths, & Tenenbaum, 2014) . By contrast, when the incentives are high then people employ a choice strategy that maximizes their earnings by almost always choosing the option that is more likely to be rewarded -which requires more computation  (Vul et al., 2014) . The dual systems perspective on 2AFC leaves open the normative question: what set of systems is optimal for the agent to be equipped with? To answer this question, we apply the methodology described in the previous section to the problem of bounded-optimal binary-choice. \n Methods As in the 2AFC probability learning task used by  Shanks et al. (2002) , the agent receives a reward of +1 for picking the correct action and 0 for picking the incorrect action. An unboundedly rational agent would always pick the action with a higher probability of being correct. Yet, although simple in set-up, computing the probability of an action being correct generally requires complex inferences over many interconnected variables. For example, if the choice is between turning left onto the highway or turning right to smaller backroads, estimating the probability of which action will lead to less traffic may require knowledge of when rush hour is, whether there is a football game happening, and whether there are accidents in either direction. To approximate these often intractable inferences people appear to perform probabilistic simulations of the outcomes, and the variability and biases of their predictions  (Griffiths & Tenenbaum, 2006; Lieder, Griffiths, Huys, & Goodman, 2018a)  and choices  (Vul et al., 2014; Lieder, Griffiths, & Hsu, 2018 ) match those of efficient sampling algorithms. Previous work has therefore modeled people as bounded-optimal sample-based agents, which draw a number of samples from the distribution over correct actions and then picks the action that was sampled most frequently.  (Vul et al., 2014; Griffiths et al., 2015) . In line with the prior work, we too model the agent as being a sample-based agent, described formally below. Let a 0 and a 1 be the actions available to the agent where a 1 has a probability θ of being the correct action and a 0 has a probability 1 − θ of being correct. The probability θ that a 1 is correct varies across different environments, reflecting the fact that in some settings it is easier to tell which action is correct than others. For example, it is obvious between the choice of a two-month old tomato and a fresh orange that the more nutritious choice is the latter. In this case, it is clear that the fresh orange is correct with probability near one. On the other hand, it may be quite difficult to decide between whether to attend graduate school at two universities with similar programs. In this case, the difference between the probabilities of each being correct may be quite marginal, and both might have close to a 0.5 chance of being correct. We model the variability in the difficulty of this choice by assuming that θ is equally likely to be any value in the range (0.5, 1), i.e θ ∼ P θ = Unif(0.5, 1). We consider the range (0.5, 1) instead of (0, 1) without loss of generality because we can always rename the actions so that a 0 is more likely to be correct than a 1 . To make a decision the sample-based agent draws some number of samples k from the distribution over correct actions, i ∼ Bern(θ), and picks the action a i that it sampled more. 1 If the agent always draws k samples before acting, then its expected utility across all environments is E θ [U |k] = θ [P (a 1 is correct) • P (Agent picks a 1 | k) + P (a 0 is correct) • P (Agent picks a 0 | k)]P θ (dθ) . (1) See Appendix A for a detailed derivation of how to calculate the quantity in Equation  1 . If there were no cost for samples, then the agent could take an infinite number of samples to ensure choosing the correct action. But this is, of course, impractical in the real world because drawing a sample takes time and time is limited.  Vul et al. (2014)  show how the optimal number of samples changes based on the cost of sampling in various 2AFC problems. They parameterize the cost of sampling as the ratio, r e , between the time for acting and the execution time of taking 1 sample. Suppose acting takes one unit of time, then the amount of time it takes to draw k samples is k/r e . The total amount of time the agent takes is 1 + k/r e . Thus, the optimal number of samples the agent should draw to maximize its expected utility per unit time is k * = arg max k∈N 0 E θ [U |k] 1 + k re . ( 2 ) When the time it takes to generate a sample is at least one tenth of the time it takes to execute the action (r e ≤ 10), then the optimal number of samples is either zero or one. In general, the first sample provides the largest gain in decision quality and the returns diminish with every subsequent sample. The point where the gain in decision quality falls below the cost of sampling Table  1  The optimal set of cognitive systems (M) for the 2AFC task of depends on the value of r e . Since this value can differ drastically across environments, achieving a near-optimal tradeoff in all environments requires adjusting the number of samples. Even a simple heuristic-based metareasoner that adapts the number of samples it takes based on a few thresholds on r e does better than one which always draws the same number of samples  (Icard, 2014) . Here, we study an agent that chooses how many samples to draw by metareasoning over a finite subset M of all possible numbers of samples. Furthermore, we assume that the time spent metareasoning increases linearly with the number of systems. By analogy to  Vul et al. (2014) , we formalize the metareasoning cost in terms of the ratio r m of the time it takes to act over the time it takes to predict the performance of a single system. We can again calculate the total amount of time the agent spends in the problem, while now taking into account the time spent on metareasoning. Just as before, the agent spends one unit of time executing its action, and k/r e units of time to draw k samples. But now, we also account for the time it takes the agent to predict performance of a system: 1/r m . The total amount of time it takes the agent to metareason, i.e predict the performance of all systems, is |M|/r m . Therefore, the total amount of time is 1 + π M (re) re + |M| rm . We assume the agent picks the optimal number of  k * = arg max k∈M∪{0} E θ [U |k] 1 + k re + |M| rm . ( 3 ) Given this formulation of the problem, we can now calculate the optimal set of systems for the agent. The set of cognitive systems that results in the optimal expected utility per time for the bounded sampling agent is M * = arg max M⊂N E re   max k∈M∪{0} E θ [U |k] 1 + k re + |M| rm   . ( 4 ) Equation 4 resembles Equation 3 because both optimize the agent's expected utility per time. The difference is that Equation 3 calculates the optimal number of samples for a fixed cost of sampling, while Equation 4 calculates the optimal number of systems for a distribution of costs of sampling. Note that the optimal set of systems depends on the distribution of the sampling cost r e across different environments. Since sampling an action generally takes less time than executing the action, we assume that r e is always greater than one. We can satisfy this constraint on r e by modeling r e as following a shifted Gamma distribution, i.e r e − 1 ∼ Γ(α, β). \n Results Figure  1  shows a representative example 2 of the expected utility per time as a function of the number of systems for different metareasoning costs. Under a large range of metareasoning costs the optimal number of systems is just one, but as the costliness of selecting a cognitive system decreases, the optimal number of systems increases. However even when the optimal number of systems is more than one, each additional system tends to only result in a marginal increase in utility, suggesting that one reason for few cognitive systems may be that the benefit of additional systems is very low. Figure  2  shows that the optimal number of systems increases with the variance of r e and decreases with the cost of selecting between cognitive systems (i.e., 1 rm ). Interestingly, there is a large set of plausible combinations of variability and metareasoning cost for which the bounded-optimal agent has two cognitive systems. In addition, when the optimal number of systems is two, then the gap between the values of the two systems picked increases with the variance of r e (see Table  1 ), resulting in one system that has high accuracy but high cost and another system that has low accuracy and low cost, which matches the characteristics of the systems posited by dual-process accounts. Thus, the conditions under which we would most expect to see two cognitive systems like the ones suggested by dual-process theories are when the environment is highly variable and arbitrating between cognitive systems is costly. \n Simulation 2: Sequential Decision-Making Our first simulation modeled one-step decision problems in which the agent made a single choice between two options. In our second simulation, we turn to more complex, sequential decision problems, in which the agent needs to choose a sequence of actions over time in order to achieve its goal. In these problems, the best action to take at any given point depends on future outcomes and actions, thus leading to the need for planning. Furthermore, since actions only affect the environment probabilistically, it leads to the need for planning under uncertainty. Although planning often allows us to make better decisions, planning places high demands on people's working memory and time  (Kotovsky, Hayes, & Simon, 1985) . This may be why research on problem solving has found that people use both planning and simple heuristics  (Newell & Simon, 1972; Atwood & Polson, 1976; Kotovsky et al., 1985)  and models of problem solving often assume that the mind is equipped with a planning strategy, such as means-ends analysis, and one or two simple heuristics such as hill-climbing  (Newell & Simon, 1972; Gunzelmann & Anderson, 2003; Anderson, 1990) . Consistent with these findings, modern research on sequential decision-making points to the coexistence of two systems: a reflective, goal-directed system that uses a model of the environment to plan multiple steps into the future and a reflexive system that learns stimulus-response associations  (Dolan & Dayan, 2013) . Interestingly, people appear to select between these two systems in a manner consistent with rational metareasoning: When people are given a task where they can either plan two steps ahead to find the optimal path or perform almost equally well without planning, they often eschew planning  (Daw et al., 2005; Kool, Cushman, & Gershman, 2016) , but when the incentive structure is altered to make planning worthwhile then people predominantly rely on the planning system  (Kool, Gershman, & Cushman, 2017) . These findings are also consistent with Anderson's rational analysis of problem solving which assumed that people select between planning according to means-ends-analysis and a hill climbing heuristic according to a rational cost-benefit analysis  (Anderson, 1990) . Working from the assumption that the mind is equipped with a planning-based system and a  current state s, a transition probability model p : S × A × S → [0, 1] that defines the probability of the next state given the current state and the action taken, an absorbing goal state g, and a time horizon h. Experience in these MDPs can be thought of as a set of trials or episodes. A trial ends once the agent reaches an absorbing goal-state g or it exceeds the maximal number of time steps allowed by the time horizon h. In the standard formulation, at each time step, the agent takes an action, which depends upon its current state. The agent's action choices can be concisely represented by a policy π : S → A that returns an action for each state. An optimal policy minimizes the expected sum of costs across the trial: π * = arg min π E N i=0 c(s i , π(s i )) π , ( 5 ) where s i is the state at time step i and N is the time step that the episode ends (either once the agent reaches the goal state g or the time horizon h is reached). The expectation is taken over the states at each time step, which are stochastic according to the transition model p. However, this formulation of the problem ignores the fact that the agent needs to think to decide how to act, and that thinking also incurs cost. We extend the standard MDP formulation to account for the cost of thinking. At each time step, the agent has a thinking stage, followed by an acting stage. In the thinking stage, the agent executes a system t that (stochastically) decides on an action a. In the acting stage, the agent takes the action a. In addition to the cost c(s, a) of acting, there is also a cost f (t) that measures the cost of thinking with system t. Then, an optimal system minimizes the total expected cost of acting and thinking: t * = arg min t E N i=0 c(s i , a i ) + f (t) t , ( 6 ) where a 0 , . . . a N are the actions chosen by t at each time step and s 0 , . . . s N are the states at each time step. The expectation is taken over states and actions, which are stochastic because the transition model p and the system t are not necessarily deterministic. The agent's thinking systems are based on bounded real-time dynamic programming (BRTDP;  McMahan, Likhachev, and Gordan, 2005) , a planning algorithm from the artificial intelligence literature. BRTDP simulates potential action sequences, and then uses these simulations to estimate an upper bound and lower bound on how good each action in each possible state. It starts with a heuristic bound, and then continuously improves the accuracy of its estimates. Depending on the number of simulations chosen, it can be executed for an arbitrarily short or long amount of time. Fewer simulations result in faster but less accurate solutions, while more simulations results in slower but more accurate solutions, making BRTDP particularly well-suited for studying metareasoning  (Lin et al., 2015) . During the thinking stage, the agent chooses the number of action sequences to simulate (k), and then based on this simulations, uses BRTDP to update its estimate of how good each action is in each possible state. During the acting stage, the agent takes the action with the highest upper bound on its value. Thus the agent's policy is defined entirely by k, the number of action sequences it simulates. This type of policy corresponds to the Think*Act policy from Lin et al. We consider environments in which there is a constant cost per action (c a ) from all non-goal states: c(s, a) = c a . The cost of executing a system is linear in the number of simulated action sequences (k): f (k) = c e • k, where c e is the cost of each mental simulation. We reparameterize the costs by the ratio of the cost of acting over the cost of thinking, r e = ca ce . Having defined the agent policy and the quotes, Equation 6 simplifies to k * = arg min k∈N 0 1 + k r e E [N |k] , ( 7 ) where N is the number of time steps until the trial ends, either by reaching the goal state or the time horizon. See Appendix B for a derivation. Equation 7 defines the optimal system for the agent to use for a particular decision problem, but we seek to investigate what set of systems is optimal for the agent to be equipped with for a range of decision problems. We assume that there is a distribution of MDPs the agent may encounter, and while r e is constant within each problem, it varies across different problems. Therefore, optimally allocating finite computational resources requires metareasoning. We assume that metareasoning incurs a cost that is linear in the number of systems: c m • |M|, where c m is the cost required to predict the performance of a single system. Similarly we can reparametrize this cost using r m = c a /c m , so that the cost of metareasoning becomes |M|/r m . Assuming that the agent chooses optimally from its set of planning systems, the optimal set of systems that it should be equipped with is M * = arg min M⊂N E re min k∈M∪{0} 1 + k r e E [N |k] + |M| r m . ( 8 ) We investigated the size and composition of the optimal set of planning systems for a simple 20 × 20 grid world where the agent's goal is to get from the lower left corner to the upper right corner with as little cost as possible. The horizon was set to 500, and the maximum number and length of simulated action sequences at any thinking stage were set to 10. BRTDP was initialized with a constant value function of 0 for the lower bound and a constant value function of 10 6 for the upper bound. This means that the agent's initial policy was to act randomly-which is highly suboptimal. For each environment, the ratio of the cost of action over the cost of planning (r e ) was again drawn from a Gamma distribution and shifted by one, that is r e − 1 ∼ Γ(α, β). The expected number of steps required to achieve the goal E[N |k] was estimated via simulation (see Figure  3 ). \n Results We find that all our results match the 2-alternative forced choice setting extremely closely. Because the agent rarely reached the goal with zero planning (E[N |k = 0] = 500) one system provided the largest reduction in expected cost with each additional system providing at most marginal reductions (Figure  4 ). The optimal number of systems increased with the variance of r e and decreased with the metareasoning cost ( 1 rm ). This resulted in the optimal number of cognitive systems being two for a wide range of plausible combinations of variability and metareasoning cost (Figure  5 ). In addition, when the number of systems was two, the difference between the amount of planning performed by the two optimal systems increased with the variance of r e . 3 This resulted in one system that does a high amount of planning but is costly and another system that plans very little but is computationally inexpensive, matching the characteristics of the two types of systems postulated by dual-process theories. Simulation 3: Strategic interaction in a two-player game Starting in the 1980s, researchers began applying dual-process theories to social cognition  (Chaiken & Trope, 1999; Evans, 2008) . One hypothesis for why the heuristic system exists is because exact logical or probabilistic reasoning is often computationally prohibitive. For instance, Herbert Simon famously argued that computational limitations place substantial constraints on human reasoning  (Simon, 1972 (Simon, , 1982 . Such computational limitations become readily apparent in problems involving social cognition because the number of future possibilities explodes once the actions of others must be considered. For example, one of Simon's classic examples was chess, where reasoning out the best opening move is completely infeasible because it would require considering about 10 120 possible continuations. In this section, we show that our findings in decision-making and planning tasks about the optimal set of cognitive systems also applies to tasks that involve reasoning about decisions made by others. Specifically, we focus on strategic reasoning in Go, an ancient two-player game. Two-player games are the simplest and perhaps most widely used paradigm for studying strategic reasoning about other people's actions  (Camerer, 2011) . Although seemingly simple, it is typically impossible to exhaustively reason about all possibilities in a game, making heuristic reasoning necessary. This is especially true in Go, which has about 10 360 continuations from the first move (compare this to chess which has \"only\" 10 120 possible continuations). \n Methods We now describe the details of our simulation deriving bounded-optimal architectures for strategic reasoning in the game of Go. The agent's thinking systems are based on a planning algorithm known as Monte Carlo tree search (MCTS)  (Browne et al., 2012) . Recently, AlphoGo, a computer system based on MCTS, became the first to defeat the Go world champion and achieve superhuman performance in the game of Go  (Silver et al., 2016 (Silver et al., , 2017 . Like other planning methods against adversarial opponents, MCTS works by constructing a game tree to plan future actions. Unlike other methods, MCTS selectively runs stochastic simulations (also known as rollouts) of different actions, rather than exhaustively searching through the entire game tree. In doing so, MCTS focuses on moves and positions whose values appear both promising and uncertain. In this regard, MCTS is similar to human reasoning  (Newell & Simon, 1972) . Furthermore, the number of simulations used by MCTS affect how heuristic/accurate the a) b) Figure  6 . Performance as a function of the amount of reasoning in the game of Go (Simulation 3). As the amount of computation (number of simulations) increases, the likelihood of selecting a good action increases, thus resulting in larger utility (a) and the game tends to be won in increasingly fewer moves (b). method is, making it well-suited for studying metareasoning. When the number of simulations is small, the algorithm is faster but less accurate. When the number of simulations is high, the algorithm is slower but more accurate. Thus, similar to the sequential decision making setting (Simulation 2), we assume that the agent metareasons over systems M that differ in how many simulations (k) to perform. On each turn, there is a thinking stage and an acting stage. In the thinking stage, the agent executes a system that performs a number of stochastic simulations (k) of future moves and then updates its estimate of how good each action is, i.e. how likely it is to lead to a winning state. In the acting stage, the agent takes the action with the highest estimated value. The agent attains a utility U based on whether it wins or loses the game. The unbounded agent would simply choose the number of simulations k that maximizes expected utility: E[U | k]. However, the bounded agent incurs costs for acting and thinking. We assume that the cost for acting is constant: c a . The cost for executing a system is linear in the number of simulations it performs: k • c e , where c e is the cost of a single simulation. The bounded agent has to optimize a trade-off between its utility U and the costs of acting and thinking: E[U − (c a + k • c e )N | k] , ( 9 ) where N is the number of turns until the game ends. For consistency, we can reparameterize this as r e = c a /c e , the ratio between the cost of acting and the cost of thinking, and without loss of generality, we can let c a = 1. Equation 9 then simplifies into B(k, r e ) := E U − 1 + k r e N k . ( 10 ) The optimal system for the agent to choose given a fixed value of r e is k * (r e ) = arg max k B(k, r e ). The optimal set of cognitive systems M out of all possible systems T for strategic interaction is M * = arg max M⊂T E max k B(k, r e ) − |M| r m . ( 11 ) In this case, the expectation is taken over r e , as the goal is to find the set of systems that is optimal across all problems in the environment. In our simulations, the game is played on a 9 × 9 board. U is 500 if the agent wins, 250 if the game ends in a draw, and 0 if the agent loses. The opponent also runs MCTS with 5 simulations to decide its move. E[U | k] and E[N | k] are estimated using simulation (see Figure  6 ). For computational tractability, the possible number of simulations we consider are T = {5, 10, . . . , 50}. \n Results As in the previous tasks, the optimal number of systems depends on the variability of the environment and the difficulty of selecting between multiple systems (Figure  7 ). As the cost of metareasoning increases, the optimal number of systems decreases and the bounded-optimal agent comes to reason less and less. By contrast, the optimal number of systems increases with the variability of the environment. Furthermore, when the optimal number of systems is two, the Table  3  The optimal set of cognitive systems (M ) for strategic reasoning in the game of Go (Simulation   10, 20, 30, 50 10, 20, 30, 50  (*) This number of systems does not provide a noticeable increase in utility over fewer systems. difference between the amount of reasoning performed by the two systems increases as the environment becomes more variable (Table  3 ). In conclusion, the findings presented in this section suggest that the kind of cognitive architecture that is bounded-optimal for simple decisions and planning (i.e., two systems with opposite speed-accuracy tradeoffs) is also optimal for reasoning about more complex problems, such as strategic interaction in games. Simulation 4: Multi-alternative risky choice Decision-making under risk is another domain in which dual-process theories abound (e.g.,  Steinberg, 2010; Mukherjee, 2010; Kahneman & Frederick, 2007; Figner, Mackinlay, Wilkening, & Weber, 2009) , and the dual-process perspective was inspired in part by Kahneman and Tversky's ground-breaking research program on heuristics and biases  (Kahneman, Slovic, & Tversky, 1982) . Consistent with our resource-rational framework, previous research revealed that people make risky decisions by arbitrating between fast and slow decision strategies in an adaptive and flexible manner  (Payne et al., 1993) . When making decisions between the risky gambles shown in Figure  8  people adapt not only how much they think but also how they think about what to do. Concretely, people have been shown to use different strategies for different types of decision problems  (Payne et al., 1988) . For instance, when some outcomes are much more probably than others then people seem to rely on fast-and-frugal heuristics  (Gigerenzer & Goldstein, 1996)  like Take-The-Best which decides solely based on the most probably outcome that distinguishes between the alternatives and ignores all other possible outcomes. By contrast, when all outcomes are equally likely, people seem to integrate the payoffs for multiple outcomes into an estimate of the expected value of each gamble. Previous research has proposed at least ten different decision strategies that people might use when choosing between risky prospects  (Payne et al., 1988; Thorngate, 1980; Gigerenzer & Selten, 2002 ). Yet, it has remained unclear how many decision strategies a single person would typically consider  (Scheibehenne, Rieskamp, & Wagenmakers, 2013) . Here, we investigate how many decision strategies a boundedly optimal metareasoning agent should use in a multi-alternative risky-choice environment similar to the experiments by Payne et al.. Unlike in the previous simulations these strategies differ not only in how much computation they perform but also in which information they use and how they use it.  \n Methods We investigated the size of the optimal subset of the ten decision strategies proposed by Payne et al. as a function of the metareasoning cost and the variability of the relative cost of reasoning. These strategies were the lexicographic heuristic (which corresponds to Take-The-Best), the semi-lexicographic heuristic, the weighted-additive strategy, choosing at random, the equal-weight heuristic, elimination by aspects, the maximum confirmatory dimensions heuristic, satisficing, and two combinations of elimination by aspects with the weighted additive strategy and the maximum confirmatory dimensions heuristic. Concretely, we determined the optimal number of decision strategies 5 × 30 environments that differed in the mean and the standard deviation of the distribution of r e . The means were 10, 50, 100, 500, and 1000, and the standard deviations were linearly spaced between 10 −3 and 3 times the mean. For each environment, four thousand decision problems were generated at random. Each problem presented the agent with the choice between five gambles with five possible outcomes. The payoffs for each outcome-gamble pair were drawn from a uniform distribution on the interval RATIONAL REINTERPRETATION OF DUAL-PROCESS THEORIES 34 [0, 1000]. The outcome probabilities differed randomly from problem to problem except that the second highest probability was always at most 25% of highest probability, the third highest probability was always at most 25% of the second-highest probability, and so on. Based on previous work on how people select cognitive strategies , our simulations assume that people generally select the decision-strategy that achieves the best possible speed-accuracy tradeoff. This strategy can be formally defined as the heuristic s with the highest value of computation (VOC; . Formally, for each decision problem d, an agent equipped with strategies S should choose the strategy s (d, S, r e ) = max s∈S VOC(s, d). ( 12 ) Following  we define a strategy's VOC as decision quality minus decision cost. We measure the decision quality by the ratio of the expected utility of the chosen option over the expected utility of the best option, and we measure decision cost by the opportunity cost of the time required to execute the strategy. Formally, the VOC of making the decision d using the strategy s is VOC(s, d) = E [u(s(d))|d] max a E [u(a)|d] − 1 r e • n computations (s, d), ( 13 ) where s(d) is the alternative that the strategy s chooses in the decision d, 1 re is the cost per decision operation, and n computations (s, d) is the number of cognitive operations it performs in this decision process. To determine the number of cognitive operations, we decomposed each strategy into a sequence of elementary information processing operations  (Johnson & Payne, 1985)  in the same way as Lieder and Griffiths (2017) did and counted how many of those operations each strategy performed on any given decision problem. We estimated the optimal set of strategies, S = max S E P (d) VOC(s (d; S, r e ), d) − 1 r m • |S| , ( 14 ) by approximating the expected value in Equation 14 by averaging the VOC over 4000 randomly generated decision problems. The resulting noisy estimates were smoothed with a Gaussian kernel with standard deviation 20. Then the optimal set of cognitive strategies was determined based on the smoothed VOC estimates for each combination of parameters. Finally, the number of strategies in the optimal sets was smoothed with a Gaussian kernel with standard deviation 10, and the smoothed values were rounded. \n Results As shown in Figure  9 , we found that the optimal number of strategies increased with the variability of the environment and decreased with the metareasoning cost. Like in the previous simulations, the optimal number of decision systems increased from 1 for high metareasoning cost and low variability to 2 for moderate metareasoning cost and variability, and increased further with decreasing metareasoning cost and increasing variability. There was again a sizeable range of plausible values in which the optimal number of decision systems was 2. For extreme combinations of very low time cost and very high variability the optimal number of systems increased to up to 5. Although Figure  9  only shows the results for E[r e ] = 100, the results for E[r e ] = 10, 50, 500, and 1000 were qualitatively the same. In this section, we applied our analysis to a more realistic setting than in the previous sections. It used psychologically plausible decision strategies that were proposed to explain human decision-making rather than algorithms. These strategies differed not only in how much reasoning they perform but also in how they reason about the problem. For this setting, where the environment comprised different kinds of problems favoring different strategies, one might expect that the optimal number of systems would be much larger than in the previous simulations. While we did find that having 3-5 systems became optimal for a larger range of metareasoning costs and variabilities, it is remarkable that having two systems was still bounded-optimal for a sizeable range of reasonable parameters. This finding suggests that our results might generalize to the much more complex problems people have to solve and people's much more sophisticated cognitive mechanisms.  \n General Discussion We found that across four different tasks the optimal number and diversity of cognitive systems increases with the variability of the environment but decreases with the cost of predicting each system's performance. Each additional system tends to provide at most marginal improvements; so the optimal solutions tend to favor small numbers of cognitive systems, with two systems being optimal across a wide range of plausible values for metareasoning cost and variability. Furthermore, when the optimal number of cognitive systems was two, then these two systems tended to lie on two extremes in terms of time and accuracy. One of them was much faster but more error-prone whereas the second one was slower but more accurate. This might be why the human mind too appears to contain two opposite subsystems within itself -one that is fast but fallible and one that is slow but accurate. In other words, this mental architecture might have evolved to enable people to quickly adapt how they think and decide to the demands of different situations. Our analysis thereby provides a normative justification for dual-process theories. The emerging connection between normative modeling and dual-process theories is remarkable because these approaches correspond to opposite poles in the debate about human rationality  (Stanovich, 2011) . In this debate, some researchers interpreted the existence of a fast, error-prone cognitive system whose heuristics violate the rules of logic, probability theory, and expected utility theory as a sign of human irrationality  (Ariely, 2009; Marcus, 2009) . By contrast, our analysis suggests that having a fast but fallible cognitive system in addition to a slow but accurate system may be the best possible solution. This implies that the variability, fallibility, and inconsistency of human judgment that result from people's switching between System 1 and System 2 should not be interpreted as evidence for human irrationality, because it might reflect the rational use of limited cognitive resources. \n Limitations One limitation of our analysis is that the cognitive systems we studied are simple algorithms that abstract away most of the complexity and sophistication of the human mind. A second limitation is that all of our tasks were drawn from the domains of decision-making and reasoning. However, our conclusion only depends on the plausible assumption that the cost of deciding which cognitive system to use increases with the number of systems. As long as this is the case, the optimal number of cognitive systems should still depend on the tradeoff between metareasoning cost and cognitive flexibility studied above, even though its exact value may be different. Thus, our key finding that the optimal number of systems increases with the variability of the environment and decreases with the metareasoning cost is likely to generalize to other tasks and the much more complex architecture of the human mind. Third, our analysis assumed that the mind is divided into discrete cognitive systems to make the adaptive control over cognition tractable. While this makes selecting cognitive operations much more efficient, we cannot prove that it is bounded-optimal to approximate rational metareasoning in this way. Research in artificial intelligence suggests that there might be other ways to make metareasoning tractable. One alternative strategy is the meta-greedy approximation  (Russell & Wefald, 1991a; Hay et al., 2012)  which selects computations under the assumption that the agent will act immediately after executing the first computation. According to the directed cognition model  (Gabaix & Laibson, 2005)  this mechanism also governs the sequence of cognitive operations people employ to make economic decisions. This model predicts that people will always stop thinking when their decision cannot be improved by a single cognitive operation even when significant improvements could be achieved by a series of two or more cognitive operations. This makes us doubt that the meta-greedy heuristic would be sufficient to account for people's ability to efficiently solve complex problems, such as puzzles, where progress is often non-linear. This might be why when  Gabaix, Laibson, Moloche, and Weinberg (2006)  applied their model to multi-attribute decisions, they let it choose between macro-operators rather than individual computations. Interestingly, those macro-operators are similar to the cognitive systems studied here in that they perform different amounts of computation. Thus, the directed cognition model does not appear to eliminate the need for sub-systems but merely proposes a mechanism for how the mind might select and switch back-and-forth between them. Consistent with our analysis, the time and effort required by this mechanism increases linearly with the number of cognitive systems. While research in artificial intelligence as identified a few additional approximations to rational metareasoning, those are generally to specific computational processes and problems  (Russell & Wefald, 1989; Lin et al., 2015; Vul et al., 2014)  and would be applicable to only a small subset of people's cognitive abilities. \n Relation to previous work The work presented here continues the research programs of bounded rationality  (Simon, 1956 (Simon, , 1982 , rational analysis  (Anderson, 1990)  and resource-rational analysis  (Griffiths et al., 2015)  in seeking to understand how the mind is adapted to the structure of the environment and its limited computational resources. While previous work has applied the idea of bounded optimality to derive optimal cognitive strategies for an assumed cognitive architecture  (Lewis et al., 2014;  and the arbitration between assumed cognitive systems  (Keramati et al., 2011) , the work presented here derived the cognitive architecture itself. By suggesting that the human mind's cognitive architecture might be bounded-optimal our analysis complements and completes previous arguments suggesting that people make rational use of the cognitive architecture they are equipped with  (Lewis et al., 2014; Griffiths et al., 2015; Lieder, Griffiths, & Hsu, 2018; Lieder, Griffiths, Huys, & Goodman, 2018a; Tsetsos et al., 2016; Howes et al., 2016) . Taken together these arguments suggest that people might be resource-rational after all. \n Conclusion and Future Directions A conclusive answer to the question whether it is boundedly optimal for humans to have two types of cognitive systems will require more rigorous estimates of the variability of decision problems that people experience in their daily lives and precise measurements of how long it takes to predict the performance of a cognitive system. Regardless thereof, our analysis suggests that the incoherence in human reasoning and decision-making are qualitatively consistent with the rational use of a bounded-optimal set of cognitive systems rather than a sign of irrationality. Perhaps more importantly, the methodology we developed in this paper makes it possible to extend resource-rational analysis from cognitive strategies to cognitive architectures. This new line of research offers a way to elucidate how the architecture of the mind is shaped by the structure of the environment and the fundamental limits of the human brain. \n Appendix B Sequential Decision-Making Here, we provide a derivation of how to simplify the expression for the optimal number of planning systems in Equation  6 , that is We can reparameterize using r e = c a /c e by substituting c e with c a /r e : E N c a + c a r e • k k = c a E 1 + k r e N k . We now arrive at Equation 6 by picking the cognitive system (number of simulations) that minimizes the above quantity. k * = arg min k c a E 1 + k r e N k = arg min k E 1 + k r e N k . Figure 1 . 1 Figure 1. The reward rate in two-alternative forced choice (Simulation 1) usually peaks for a moderately small number of decision systems. The expected utility per time of the optimal choice of systems, M , as a function of the number of systems (|M|). As the costliness of metareasoning, 1 rm decreases, the optimal number of systems increases. In this example E[r e ] = 100 and σ(r e ) = 100. \n Simulation 1 as a function of the number of systems (|M|) and the variability of the environment (Var(r e )) for E[r e ] = 100 and r m = 1000. Any set of four systems that included 3, 5, 7 was optimal. \n Figure 2 . 2 Figure 2. Performance of agents with different numbers of decision mechanisms in the 2AFC problem of Simulation 1. The plot shows the optimal number of decision systems as a function of the standard deviation of r e and 1/r m . In this example E[r e ] = 10. \n Figure 3 . 3 Figure 3. Performance of agents with different numbers of cognitive systems in planning under uncertainty (Simulation 2). The number of actions it takes an agent to reach a goal as a function of the number of simulated paths before each action. For 0 simulated paths the expected number of actions was 500 (the maximum allowed). \n Figure 4 . 4 Figure 4. The expected cost incurred is a U-shaped function of the number of planning systems in Simulation 2. As the cost of selecting a planning system ( 1 rm ) decreases, the optimal number of systems increases. The expected cost of 0 systems was 500, thus 1 system provided the greatest reduction in cost. In this example E[r e ] = 100, Var(r e ) = 10 5 , and c a = 1. \n Figure 5 . 5 Figure 5. The optimal number of systems for planning under uncertainty (Simulation 2) as a function of the standard deviation of r e and r m for E[r e ] = 100. \n 3 ) depending on the number of systems (|M|) and the variability of the environment (Var(r e )) for E[r e ] = 10. \n Figure 7 . 7 Figure 7. The optimal number of systems for strategic reasoning in the game of Go (Simulation 3) as a function of the standard deviation of r e and 1 rm . E[r e ] = 100 in this case. \n Figure 8 . 8 Figure 8. Illustration of the Mouselab paradigm used to study multi-alternative risky choice. \n Figure 9 . 9 Figure 9. The optimal number of strategies for multi-alternative risky choice (Simulation 4) as a function of the standard deviation of r e and r m for E[r e ] = 100. \n this derivation is as follows: Since the cost of each thinking system is linear in the number of simulations, i.e. c e • k, we can replace f (t) with c e • k in the expectation in Equation6. Since the cognitive systems are distinguished by the number of simulations they do, we can condition on the number of simulations k instead. Therefore, the expectation in i , a i ) + c e • k k .The cost of acting from non-goal states is constant, i.e. c(s i , a i ) = c a . Therefore, the expectation simplifies to 6 becomesE N i=0 c a + c e • k k = E[N (c a + c e • k) | k] . \n Table 2 2 The optimal set of cognitive systems (M ) for planning under uncertainty (Simulation 2) as a function of the number of systems (|M|) and the variability of the environment (Var(r e )) with E[r e ] = 100. Var(r e ) |M| 10 3 10 4 10 5 1 9 7 7 2 7, 9 4, 7 2, 7 3 1, 7, 9 4, 7, 9 1, 4, 9 4 1, 2, 7, 9 2, 4, 7, 9 1, 4, 7, 9 \n\t\t\t If there is a tie, then the agent picks either a 0 or a 1 with equal probability. However, for odd k, the agent's expected utility after drawing k samples, E θ [U |k], is equal to its expected utility after drawing k + 1 samples,E θ [U |k + 1].Thus, we can restrict ourselves to odd k where no ties are possible. \n\t\t\t For all experiments reported in this paper, we found that alternative values for E[r e ] or Var(r e ) did not change the qualitative conclusions, unless otherwise indicated. \n\t\t\t This observation holds until the variance becomes extremely high (≈ 10 7 for Table2), in which case both systems move towards lower values (Table2). However, this is not a general problem but merely a quirk of the skewed distribution we used for r e .", "date_published": "n/a", "url": "n/a", "filename": "Arationalreinterpretationofdualsystemstheories.tei.xml", "abstract": "Highly influential \"dual-process\" accounts of human cognition postulate the coexistence of a slow accurate system with a fast error-prone system. But why would there be just two systems rather than, say, one or 93? Here, we argue that a dual-process architecture might be neither arbitrary nor irrational, but might instead reflect a rational tradeoff between the cognitive flexibility afforded by multiple systems and the time and effort required to choose between them. We investigate what the optimal set and number of cognitive systems would be depending on the structure of the environment. We find that the optimal number of systems depends on the variability of the environment and the difficulty of deciding when which system should be used. Furthermore, when having two systems is optimal, then the first system is fast but error-prone and the second system is slow but accurate. Our findings thereby provide a rational reinterpretation of dual-process theories.", "id": "22c9335fa97882960d9459139ca55d2c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Death and pain of a digital brain.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Sullins2011_Article_IntroductionOpenQuestionsInRob.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nate Soares", "Benja Fallenstein", "Eliezer Yudkowsky", "Stuart Armstrong"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Corrigibility.tei.xml", "abstract": "As artificially intelligent systems grow in intelligence and capability, some of their available options may allow them to resist intervention by their programmers. We call an AI system \"corrigible\" if it cooperates with what its creators regard as a corrective intervention, despite default incentives for rational agents to resist attempts to shut them down or modify their preferences. We introduce the notion of corrigibility and analyze utility functions that attempt to make an agent shut down safely if a shutdown button is pressed, while avoiding incentives to prevent the button from being pressed or cause the button to be pressed, and while ensuring propagation of the shutdown behavior as it creates new subsystems or self-modifies. While some proposals are interesting, none have yet been demonstrated to satisfy all of our intuitive desiderata, leaving this simple problem in corrigibility wide-open.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong", "Kaj Sotala", "Sea ´n", "S O ´he ´igeartaigh"], "title": "The errors, insights and lessons of famous AI predictions -and what they mean for the future", "text": "Introduction Predictions about the future development of artificial intelligence (AI 1 ) are as confident as they are diverse. Starting with Turing's initial estimation of a 30% pass rate on Turing test by the year 2000  (Turing, 1950) , computer scientists, philosophers and journalists have never been shy to offer their own definite prognostics, claiming AI to be impossible  (Jacquette, 1987) , just around the corner  (Darrach, 1975)  or anything in between. What should one think of this breadth and diversity of predictions? Can anything of value be extracted from them, or are they to be seen as mere entertainment or opinion? The question is an important one, because true AI would have a completely tranrsformative impact on human society -and many have argued that it could be extremely dangerous  (Minsky, 1984; Yampolskiy, 2012 , Yudkowsky, 2008 . Those arguments are predictions in themselves, so an assessment of predictive reliability in the AI field is a very important project. It is in humanity's interest to know whether these risks are reasonable, and, if so, when and how AI is likely to be developed. Even if the risks turn out to be overblown, simply knowing the reliability of general AI predictions will have great social and economic consequences. The aim of this paper is thus to construct a framework and tools of analysis that allow for the assessment of predictions, of their quality and of their uncertainties. Though specifically aimed at AI, these methods can be used to assess predictions in other contentious and uncertain fields. This paper first proposes a classification scheme for predictions, dividing them into four broad categories and analysing what types of arguments are used (implicitly or explicitly) to back them up. Different prediction types and methods result in very different performances, and it is critical to understand this varying reliability. To do so, this paper builds a series of tools that can be used to clarify a prediction, reveal its hidden assumptions and make use of empirical evidence whenever possible. Since expert judgement is such a strong component of most predictions, assessing the reliability of this judgement is a key component. Previous studies have isolated the task characteristics in which experts tend to have good judgement -and the results of that literature strongly imply that AI predictions are likely to be very unreliable, at least as far as timeline predictions ('date until AI') are concerned. That theoretical result is born out in practice: timeline predictions are all over the map, with no pattern of convergence, and no visible difference between expert and non-expert predictions. These results were detailed in a previous paper  (Armstrong & Sotala, 2012) , and are summarised here. The key part of the paper is a series of case studies on five of the most famous AI predictions: the initial Dartmouth conference, Dreyfus's criticism of AI, Searle's Chinese room paper, Kurzweil's predictions in the Age of Spiritual Machines, and Omohundro's AI drives. Each prediction is analysed in detail, using the methods developed earlier. The Dartmouth conference proposal was surprisingly good -despite being wildly inaccurate, it would have seemed to be the most reliable estimate at the time. Dreyfus's work was very prescient, despite his outsider status, and could have influenced AI development for the better -had it not been so antagonistic to those in the field. Some predictions could be extracted even from Searle's non-predictive Chinese room thought experiment, mostly criticisms of the AI work of his time. Kurzweil's predictions were tested with volunteer assessors, and were shown to be surprisingly good -but his self-assessment was very inaccurate, throwing some doubt on his later predictions. Finally Omohundro's predictions were shown to be much better as warning for what could happen to general AIs, than as emphatic statements of what would necessarily happen.  2  The key lessons learned are of the general overconfidence of experts, the possibility of deriving testable predictions from even the most theoretical of papers, the superiority of modelbased over judgement-based predictions and the great difficulty in assessing the reliability of predictors -by all reasonable measures, the Dartmouth conference predictions should have been much more reliable than Dreyfus's outside predictions, and yet reality was completely opposite. \n Taxonomy of predictions \n Prediction types There will never be a bigger plane built. Boeing engineer on the 247, a twin engine plane that held ten people. A fortune teller talking about celebrity couples, a scientist predicting the outcome of an experiment, an economist pronouncing on next year's GDP figures -these are canonical examples of predictions. There are other types of predictions, though. Conditional statementsif X happens, then so will Y -are also valid, narrower predictions. Impossibility results are also a form of prediction. For instance, the law of conservation of energy gives a very broad prediction about every single perpetual machine ever made: to wit, that they will never work. The common thread is that all these predictions constrain expectations of the future. If one takes the prediction to be true, one expects to see different outcomes than if one takes it to be false. This is closely related to Popper's notion of falsifiability  (Popper, 1934) . This paper takes every falsifiable statement about future AI to be a prediction. For the present analysis, predictions about AI will be divided into four types: (1) Timelines and outcome predictions. These are the traditional types of predictions, giving the dates of specific AI milestones. Examples: An AI will pass the Turing test by 2000  (Turing, 1950) ; within a decade, AIs will be replacing scientists and other thinking professions  (Hall, 2013) . (2) Scenarios. These are a type of conditional predictions, claiming that if the conditions of the scenario are met, then certain types of outcomes will follow. Example: If someone builds a human-level AI that is easy to copy and cheap to run, this will cause mass unemployment among ordinary humans  (Hanson, 1994) . (3) Plans. These are a specific type of conditional prediction, claiming that if someone decides to implement a specific plan, then they will be successful in achieving a particular goal. Example: AI can be built by scanning a human brain and simulating the scan on a computer  (Sandberg, 2008) . (  4 ) Issues and metastatements. This category covers relevant problems with (some or all) approaches to AI (including sheer impossibility results), and metastatements about the whole field. Examples: An AI cannot be built without a fundamental new understanding of epistemology  (Deutsch, 2012) ; generic AIs will have certain (potentially dangerous) behaviours  (Omohundro, 2008) . There will inevitably be some overlap between the categories, but the division is natural enough for this paper. \n Prediction methods Just as there are many types of predictions, there are many ways of arriving at them -crystal balls, consulting experts, constructing elaborate models. An initial review of various AI predictions throughout the literature suggests the following loose schema for prediction methods 3 : (1) Causal models (2) Non-causal models (3) The outside view (4) Philosophical arguments (5) Expert judgement  (6)  Non-expert judgement Causal models are a staple of physics and the harder sciences: given certain facts about the situation under consideration (momentum, energy, charge, etc.), a conclusion is reached about what the ultimate state will be. If the facts were different, the end situation would be different. Outside of the hard sciences, however, causal models are often a luxury, as the underlying causes are not well understood. Some success can be achieved with non-causal models: without understanding what influences what, one can extrapolate trends into the future. Moore's law is a highly successful non-causal model  (Moore, 1965) . In the outside view, specific examples are grouped together and claimed to be examples of the same underlying trend. This trend is used to give further predictions. For instance, one could notice the many analogues of Moore's law across the spectrum of computing (e.g. in number of transistors, size of hard drives, network capacity, pixels per dollar), note that AI is in the same category, and hence argue that AI development must follow a similar exponential curve  (Kurzweil, 1999) . Note that the use of the outside view is often implicit rather than explicit: rarely is it justified why these examples are grouped together, beyond general plausibility or similarity arguments. Hence detecting uses of the outside view will be part of the task of revealing hidden assumptions (see Section 3.2). There is evidence that the use of the outside view provides improved prediction accuracy, at least in some domains  (Kahneman & Lovallo, 1993) . Philosophical arguments are common in the field of AI. Some are simple impossibility statements: AI is decreed to be impossible, using arguments of varying plausibility. More thoughtful philosophical arguments highlight problems that need to be resolved in order to achieve AI, interesting approaches for doing so and potential issues that might emerge if AIs were to be built. Many of the predictions made by AI experts are not logically complete: not every premise is unarguable, not every deduction is fully rigorous. In many cases, the argument relies on the expert's judgement to bridge these gaps. This does not mean that the prediction is unreliable: in a field as challenging as AI, judgement, honed by years of related work, may be the best tool available. Non-experts cannot easily develop a good feel for the field and its subtleties, so should not confidently reject expert judgement out of hand. Relying on expert judgement has its pitfalls, however, as will be seen in Sections 3.4 and 4. Finally, some predictions rely on the judgement of non-experts, or of experts making claims outside their domain of expertise. Prominent journalists, authors, CEO's, historians, physicists and mathematicians will generally be no more accurate than anyone else when talking about AI, no matter how stellar they are in their own field  (Kahneman, 2011) . Predictions often use a combination of these methods. For instance, Ray Kurzweil's 'Law of time and chaos' uses the outside view to group together evolutionary development, technological development, and computing into the same category, and constructs a causal model predicting time to the 'Singularity'  (Kurzweil, 1999)  (see  Section 5.4 ). Moore's law (noncausal model) is a key input to this law, and Ray Kurzweil's expertise is the law's main support (see  Section 5.4) . The case studies of Section 5 have examples of all of these prediction methods. \n A toolbox of assessment methods The purpose of this paper is not simply to assess the accuracy and reliability of past AI predictions. Rather, the aim is to build a 'toolbox' of methods that can be used to assess future predictions, both within and outside the field of AI. The most important features of the toolbox are ways of extracting falsifiable predictions, ways of clarifying and revealing assumptions, ways of making use of empirical evidence when possible and ways of assessing the reliability of expert judgement. \n Extracting falsifiable predictions As stated in Section 2.1, predictions are taken to be falsifiable/verifiable statements about the future of AI.  4  This is very important to put the predictions into this format. Sometimes they already are, but at other times it is not so obvious: then the falsifiable piece must be clearly extracted and articulated. Sometimes it is ambiguity that must be overcome: when an author predicts an AI 'Omega point' in 2040  (Schmidhuber, 2007) , it is necessary to read the paper with care to figure out what counts as an Omega point and (even more importantly) what does not. At the extreme, some philosophical arguments -such as the Chinese room argument  (Searle, 1980)  -are often taken to have no falsifiable predictions whatsoever. These thought experiments are supposed to establish purely philosophical points. Predictions can often be extracted from even the most philosophical of arguments, however -or, if not the argument itself, then from the intuitions justifying the argument. Section 5.3 demonstrates how the intuitions behind the Chinese room argument can lead to testable predictions. Note that the authors of the arguments may disagree with the 'extracted' predictions. This is not necessarily a game breaker. The aim should always be to try to create useful verifiable predictions when possible, thus opening more of the extensive AI philosophical literature for predictive purposes. For instance, Lucas argues that AI is impossible because it could not recognise the truth of its own Go ¨del sentence 5  (Lucas, 1961) . This is a very strong conclusion, and is dependent on Lucas's expert judgement: different philosophers would reach different conclusions from the same argument. Moreover, it isn't clear how the argument could be tested: what skills and abilities would we therefore expect to be impossible for an intelligent machine? The intuition behind it, however, seems to be that Go ¨del-like sentences pose real problems to the building of an AI, and hence one can extract the weaker empirical prediction: 'Self-reference will be a problem with advanced AIs'. Care must be taken when applying this method: the point is to extract a useful falsifiable prediction, not to weaken or strengthen a reviled or favoured argument. The very first stratagems in Schopenhauer's The Art of Always being Right  (Schopenhauer, 1831)  are to extend and overgeneralise the consequences of one's opponent's argument; conversely, one should reduce and narrow down one's own arguments. There is no lack of rhetorical tricks to uphold one's own position, but if one is truly after the truth, one must simply attempt to find the most reasonable falsifiable version of the argument; the truth-testing will come later. This method often increases the prediction's uncertainty, in that it makes the prediction less restrictive (and less powerful) than it first seemed. For instance,  Edmonds (2009) , building on the 'No free lunch' results  (Wolpert & Macready, 1995) , demonstrates that there is no such thing as a universal intelligence: no intelligence that outperforms others in every circumstance. Initially this seems to rule out AI entirely; but when one analyses what this means empirically, one realises there is far less to it. An algorithm could still perform better than any human being in any realistic situation in our universe. So the initial impression, which was that the argument ruled out all futures with AIs in them, is now replaced by the realisation that the argument has barely put any constraints on the future at all. \n Clarifying and revealing assumptions The previous section was concerned with the prediction's conclusions. This section will instead be looking at its assumptions, and the logical structure of the argument or model behind it. The objective is to make the prediction as rigorous as possible. This kind of task has been a staple of philosophy ever since the dialectic  (Plato 380 BC) . Of critical importance is revealing hidden assumptions that went into the predictions. These hidden assumptions -sometimes called Enthymematic gaps in the literature  (Fallis, 2003)  -are very important because they clarify where the true disagreements lie, and where the investigation needs to be focused to figure out the truth of the prediction. Too often, competing experts will make broad-based arguments that fly past each other. This makes choosing the right argument a matter of taste, prior opinions and admiration of the experts involved. If the argument can be correctly deconstructed, however, then the source of the disagreement can be isolated, and the issue can be decided on much narrower grounds -and it is much clearer whether the various experts have relevant expertise or not (see Section 3.4). The hidden assumptions are often implicit, so it is perfectly permissible to construct assumptions that the predictors were not consciously aware of using. The purpose is not to score points for one 'side' or the other, but always to clarify and analyse arguments and to find the true points of disagreement. For illustration of the method, consider again the Go ¨del arguments mentioned in Section 3.1. The argument shows that formal systems of a certain complexity must be either incomplete (unable to see that their Go ¨del sentence is true) or inconsistent (proving false statements). This is contrasted with humans, who -allegedly -use meta-reasoning to know that their own Go ¨del statements are true. Also, humans are both inconsistent and able to deal with inconsistencies without a complete collapse of logic.  6  However, neither humans nor AIs are logically omniscient -they are not capable of instantly proving everything provable within their logical system. So this analysis demonstrates the hidden assumption in Lucas's argument: that the behaviour of an actual computer program running on a real machine is more akin to that of a logically omniscient formal agent than to a real human being. That assumption may be flawed or correct, but is one of the real sources of disagreement over whether Go ¨delian arguments rule out AI. There is surprisingly little published on the proper way of clarifying assumptions, making this approach more an art than a science. If the prediction comes from a model, there are some standard tools available for clarification  (Morgan & Henrion, 1990) . Most of these methods work by varying parameters in the model and checking that this does not cause a breakdown in the prediction. This is more a check of robustness of the model than of its accuracy, however. \n Model testing and counterfactual resiliency Causal models can be tested by analysing their assumptions. Non-causal models are much harder to test: what are the assumptions behind Moore's famous law  (Moore, 1965) , or Robin Hanson's model that humanity is due for another technological revolution, based on the timeline of previous revolutions  (Hanson, 2008) ? They both assume that a particular pattern will continue into the future, but why should this be the case? What grounds (apart from personal taste) does anyone have to endorse or reject them? The authors of this paper have come up with a putative way of testing the assumptions of such models. It involves giving the model a counterfactual resiliency check: imagining that world history had happened slightly differently, and checking whether the model would have been true in those circumstances. The purpose is to set up a tension between what the model says, and known (or believed) facts about the world. This will either refute the model, refute the believed facts or reveal implicit assumptions the model is making. To illustrate, consider Robin Hanson's model. The model posits that humanity has gone through a series of radical transformations (in brain size, hunting, agriculture, industry), and that these form a pattern that can be used to predict the arrival date and speed of the next revolution, which is argued to be an AI revolution.  7  This is a major use of the outside view, and it implicitly implies that most things in human historical development are unimportant in comparison with these revolutions. A counterfactual resiliency test can be carried out: within the standard understanding of history, it seems very plausible that these revolutions could have happened at very different times and paces. Humanity could have been confined to certain geographical locations by climate or geographical factors, thus changing the dates of the hunting and agricultural revolution. The industrial revolutions could have plausibly started earlier with the ancient Greeks (where it would likely have been slower), or at a later date, had Europe been deprived of large coal reserves. Finally, if AI were possible, it certainly seems that contingent facts about modern society could make it much easier or much harder to reach.  8  Thus the model seems to be in contradiction with standard understanding of social and technological development, or dependent on contingent factors to a much larger extent than it seemed. In contrast, Moore's law seems much more counterfactually resilient: assuming that the current technological civilization endured, it is hard to find any reliable ways of breaking the law. One can argue plausibly that the free market is needed for Moore's law to work  9  ; if that is the case, this method has detected an extra hidden assumption of the model. This method is new, and will certainly be refined in future. Again, the purpose of the method is not to rule out certain models, but to find the nodes of disagreement. In this paper, it is used in analysing Kurzweil's prediction in Section 5.4. \n More uncertainty Clarifying assumptions often ends up weakening the model, and hence increasing uncertainty (more possible futures are compatible with the model than was thought). Revealing hidden assumptions has the same effect: the model now has nothing to say in those futures where the assumptions turn out to be wrong. Thus the uncertainty will generally go up for arguments treated in this fashion. In counterpart, of course, the modified prediction is more likely to be true. \n Empirical evidence and the scientific method The gold standard in separating true predictions from false ones must always be empirical evidence. The scientific method has proved to be the best way of disproving false hypotheses, and should be used whenever possible, always preferred over expert opinion or unjustified models. Empirical evidence is generally lacking in the AI prediction field, however. Since AI predictions concern the existence and properties of a machine that has not yet been built, and for which detailed plans do not exist, there is little opportunity for the hypothesis-predictiontesting cycle. This should indicate the great challenges in the field, with AI predictions being considered more uncertain than those of even the 'softest' sciences, which have access to some form of empirical evidence. Some AI predictions approximate the scientific method better than others. The whole brain emulations model, for instance, makes testable predictions about the near and medium future  (Sandberg, 2008 ). Moore's law is a prediction backed up by a lot of scientific evidence, and connected to some extent with AI. Many predictors (e.g. Kurzweil) make partial predictions on the road towards AI; these can and should be assessed as evidence of the expert's general predictive success. Though not always possible, efforts should be made to connect general predictions with some near-term empirical evidence. \n The reliability of expert judgement Reliance on experts is nearly unavoidable in AI prediction. Timeline predictions are often explicitly based on experts' judgement.  10  Plans also need experts to come up with them and judge their credibility. So unless every philosopher agrees on the correctness of a particular philosophical argument, one is dependent to some degree on the philosophical judgement of the author. Using all the methods of the previous section, one can refine and caveat a prediction, find the nodes of disagreement, back it up with empirical evidence whenever possible and thus clearly highlight the points where one needs to rely on expert opinion. What performance should then be expected from the experts? There have been several projects over the last few decades looking into expert performance  (Kahneman & Klein, 2009; Shanteau, 1992) . The main result is that it is mainly the nature of the task that determines the quality of expert performance, rather than other factors. Table  1 , reproduced from Shanteau's paper, lists the characteristics that lead to good or poor expert performance. Not all of these are directly applicable to the current paper, and hence will not be explained in detail. One very important factor is whether experts get feedback, preferably immediately. When feedback is unavailable or delayed, or the environment is not one that gives good feedback, then expert performance drops precipitously  (Kahneman, 2011; Kahneman & Klein, 2009) . Generally AI predictions have little possibility for any feedback from empirical data (see Section 3.3), especially not rapid feedback. The task characteristics of Table  1  apply to both the overall domain and the specific task. Though AI prediction is strongly in the right column, any individual expert can improve their performance by moving their approach into the left column -for instance by decomposing the problem as much as possible. Where experts fail, better results can often be achieved by asking the experts to design a simple algorithmic model and then using the model for predictions  (Grove, Zald, Lebow, Snitz, & Nelson, 2000) . Thus the best types of predictions are probably those coming from well-decomposed models. Expert disagreement is a major problem in making use of their judgement. If experts in the same field disagree, objective criteria are needed to figure out which group is correct.  11  If experts in different fields disagree, objective criteria are needed to figure out which field is the most relevant. Personal judgement cannot be used, as there is no evidence that people are skilled at reliably choosing between competing experts. Apart from the characteristics in Table  1 , one example of objective criteria is a good prediction track record on the part of the expert. A willingness to make falsifiable, nonambiguous predictions is another good sign. A better connection with empirical knowledge and less theoretical rigidity are also positive indications  (Tetlock, 2005) . It must be noted, however, that assessing whether the expert possesses these characteristics is a second-order phenomenasubjective impressions of the expert's subjective judgement -so in most cases it will be impossible to identify the truth when there is strong expert disagreement.  \n Grind versus insight There is a distinction between achievements that require grind, versus those that require insight.  12  Grind is a term encompassing the application of hard work and resources to a problem, with the confidence that these will accomplish the goal. Problems that require insight, however, cannot simply be solved by hard work: new, unexpected ideas are needed to reach the goal. Most Moore's law predictions assume that grind is all that is needed for AI: once a certain level of computer performance is reached, people will be able to develop AI. In contrast, some insist that new insights are needed  13 (Deutsch, 2012) . In general, the grind needed for some goal can be predicted quite well. Project managers and various leaders are often quite good at estimating the length of projects (as long as they are not directly involved in the project  (Buehler, Griffin, & Ross, 1994) ). Moore's law could be taken as an ultimate example of grind: the global efforts of many engineers across many fields average out to a relatively predictable exponential growth. Predicting insight is much harder. The Riemann hypothesis is a well-established mathematical hypothesis from 1885, still unsolved but much researched  (Riemann, 1859) . How would one go about predicting when it will be solved? If building a true AI is akin in difficulty to solving the Riemann hypothesis (or solving several open mathematical problems), then timeline predictions are a lot less reliable, with much larger error bars. This does not mean that a prediction informed by a model of grind is more accurate than one that models insight. This is only true if a good case is made that AI can indeed be achieved through grind, and that insight is not needed. The predictions around whole brain emulations  (Sandberg, 2008)  are one of the few that make this case convincingly. \n Non-expert judgement All the issues and problems with expert judgement apply just as well to non-experts. While experts could be expected to have some source of useful insight due to their training, knowledge and experience, this is not the case with non-experts, giving no reason to trust their judgement. That is not to say that non-experts cannot come up with good models, convincing timelines, or interesting plans and scenarios. It just means that any assessment of the quality of the prediction depends only on the prediction itself; a non-expert cannot be granted any leeway to cover up a weak premise or a faulty logical step. One must beware the halo effect in assessing predictions  (Finucane, Alhakami, Slovic, & Johnson, 2000; Thorndike, 1920) . This denotes the psychological tendency to see different measures of personal quality to be correlated: an attractive person is seen as likely being intelligent, someone skilled in one domain is believed to be skilled in another. Hence it is hard to prevent one's opinion of the predictor from affecting one's assessment of the prediction, even when this is unwarranted. Ideally, one would seek to assess non-experts predictions in a \"blinded\" way, without knowing who the prediction's author was. If this is not possible, one can attempt to reduce the bias by imagining the prediction was authored by someone else -such as the Archbishop of Canterbury, Warren Buffet or the Unabomber. Success is achieved when hypothetical changes in authorship do not affect estimations of the validity of the prediction. \n Timeline predictions Jonathan Wang and Brian Potter of the Machine Intelligence Research Institute performed an exhaustive search of the online literature and from this assembled a database of 257 AI predictions from the period 1950 -2012. Of these, 95 contained predictions giving timelines for AI development  14  . Table  1  suggests that one should expect AI timeline predictions to be of relatively low quality. The only unambiguously positive feature of timeline predictions on that table is that prediction errors are expected and allowed: apart from that, the task characteristics are daunting, especially on the key issue of feedback. The theory is born out in practice: the AI predictions in the database seem little better than random guesses (see Figure  1 ). The data are analysed more thoroughly in a previous paper, which explains the methodology for choosing a single median estimate  (Armstrong & Sotala, 2012) . The main conclusions are the following: (1) There is little correlation between different predictions. They span a large range (the graph has been reduced; there were predictions beyond 2100), and exhibit no signs of convergence. Ignoring the prediction beyond 2100, the prediction shows a standard deviation of over a quarter century  (26 years) . There is little to distinguish failed predictions whose date has passed, from those that still lie in the future. (2) There is no evidence that expert predictions differ from non-expert predictions. Again ignoring predictions beyond 2100, expert predictions show a standard deviation of 26 years, while non-expert predictions show a standard deviation of 27 years.  15  (3) There is no evidence for the so-called Maes -Garreau law,  16  which is the idea that predictors preferentially predict AI to be developed just in time to save them from death. (  4 ) There is a strong tendency to predict the development of AI within 15-25 years from when the prediction is made (over a third of all predictions are in this timeframe, see Figure  2 ). Experts, non-experts and failed predictions all exhibit this same pattern. In summary, there are strong theoretical and practical reasons to believe that timeline AI predictions are likely unreliable.  \n Case studies This section applies and illustrates the schemas of Section 2 and the methods of Section 3. It does so by looking at five prominent AI predictions: the initial Dartmouth conference, Dreyfus's criticism of AI, Searle's Chinese room paper, Kurzweil's predictions and Omohundro's AI drives. The aim is to assess and analyse these predictions and gain insights that can then be applied to assessing future predictions. 5.1 In the beginning, Dartmouth created the AI and the hype . . . Classification: plan, using expert judgement and the outside view. Hindsight bias is very strong and misleading  (Fischhoff, 1975) . Humans are often convinced that past events could not have unfolded differently than how they did, and that the people at the time should have realised this. Even worse, people unconsciously edit their own memories so that they misremember themselves as being right even when they got their past predictions wrong.  17  Hence when assessing past predictions, one must cast aside all knowledge of subsequent events, and try to assess the claims given the knowledge available at the time. This is an invaluable exercise to undertake before turning attention to predictions whose timelines have not come to pass. The 1956 Dartmouth Summer Research Project on Artificial Intelligence was a major conference, credited with introducing the term 'Artificial Intelligence' and starting the research in many of its different subfields. The conference proposal, 18 written in 1955, sets out what the organisers thought could be achieved. Its first paragraph reads: We propose that a 2 month, 10 man study of artificial intelligence be carried out during the summer of 1956 at Dartmouth College in Hanover, New Hampshire. The study is to proceed on the basis of the conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it. An attempt will be made to find how to make machines use language, form abstractions and concepts, solve kinds of problems now reserved for humans, and improve themselves. We think that a significant advance can be made in one or more of these problems if a carefully selected group of scientists work on it together for a summer. This can be classified as a plan. Its main backing would have been expert judgement. The conference organisers were John McCarthy (a mathematician with experience in the mathematical nature of the thought process), Marvin Minsky (Harvard Junior Fellow in Mathematics and Neurology, and prolific user of neural nets), Nathaniel Rochester (Manager of Information Research, IBM, designer of the IBM 701, the first general purpose, mass-produced computer, and designer of the first symbolic assembler) and Claude Shannon (the 'father of information theory'). These were individuals who had been involved in a lot of related theoretical and practical work, some of whom had built functioning computers or programing languages -so one can expect them all to have had direct feedback about what was and was not doable in computing. If anyone could be considered experts in AI, in a field dedicated to an as yet non-existent machine, then they could. What implicit and explicit assumptions could they have used to predict that AI would be easy? Reading the full proposal does not give the impression of excessive optimism or overconfidence. The very first paragraph hints at the rigour of their ambitions -they realised that precisely describing the features of intelligence is a major step in simulating it. Their research plan is well decomposed, and different aspects of the problem of AI are touched upon. The authors are well aware of the inefficiency of exhaustive search methods, of the differences between informal and formal languages and of the need for encoding creativity. They talk about the need to design machines that can work with unreliable components, and that can cope with randomness and small errors in a robust way. They propose some simple models of some of these challenges (such as forming abstractions, or dealing with more complex environments), point to some previous successful work that has been done before, and outline how further improvements can be made. Reading through, the implicit reasons for their confidence seem to become apparent.  19  These were experts, some of whom had been working with computers from early days, who had a long track record of taking complex problems, creating simple (and then more complicated) models to deal with them. Using these models, they generated useful insights or functioning machines. So this was an implicit use of the outside view -they were used to solve certain problems, these looked like the problems they could solve, hence they assumed they could solve them. To modern eyes, informal languages are hugely complicated, but this may not have been obvious at the time. Computers were doing tasks, such as complicated mathematical manipulations, that were considered high-skill, something only very impressive humans had been capable of.  20  Moravec's paradoxe  21  had not yet been realised. The human intuition about the relative difficulty of tasks was taken as accurate: there was no reason to suspect that parsing English was much harder than the impressive feats computer could already perform. Moreover, great progress had been made in logic, in semantics, in information theory, giving new understanding to old concepts: there was no reason to suspect that further progress would not be both forthcoming and dramatic. Even at the time, though, one could criticise their overconfidence. Philosophers, for one, had a long track record of pointing out the complexities and subtleties of the human mind. It might have seemed plausible in 1955 that further progress in logic and information theory would end up solving all these problems -but it could have been equally plausible to suppose that the success of formal models had been on low-hanging fruit, and that further progress would become much harder. Furthermore, the computers at the time were much simpler than the human brain (e.g. the IBM 701, with 73,728 bits of memory), so any assumption that AIs could be built was also an assumption that most of the human brain's processing was wasted. This implicit assumption was not obviously wrong, but neither was it obviously right. Hence the whole conference project would have seemed ideal, had it merely added more humility and qualifiers in the text, expressing uncertainty as to whether a particular aspect of the program might turn out to be hard or easy. After all, in 1955, there were no solid grounds for arguing that such tasks were unfeasible for a computer. Nowadays, it is obvious that the paper's predictions were very wrong. All the tasks mentioned were much harder to accomplish than they claimed at the time, and have not been successfully completed even today. Rarely have such plausible predictions turned out to be so wrong; so what can be learned from this? The most general lesson is perhaps on the complexity of language and the danger of using human-understandable informal concepts in the field of AI. The Dartmouth group seemed convinced that because they informally understood certain concepts and could begin to capture some of this understanding in a formal model, then it must be possible to capture all this understanding in a formal model. In this, they were wrong. Similarities of features do not make the models similar to reality, and using human terms -such as 'culture' and 'informal' -in these models concealed huge complexity and gave an illusion of understanding. Today's AI developers have a much better understanding of how complex cognition can be, and have realised that programing simple-seeming concepts into computers can be very difficult. So the main lesson to draw is that reasoning about AI using human concepts (or anthropomorphising the AIs by projecting human features onto it) is a very poor guide to the nature of the problem and the time and effort required to solve it. \n Dreyfus's artificial alchemy Classification: issues and metastatements, using the outside view, non-expert judgement and philosophical arguments. Hubert Dreyfus was a prominent early critic of AI. He published a series of papers and books attacking the claims and assumptions of the AI field, starting in 1965 with a paper for the Rand corporation entitled 'Alchemy and AI'  (Dreyfus, 1965) . The paper was famously combative, analogising AI research to alchemy and ridiculing AI claims. Later, D. Crevier would claim 'time has proven the accuracy and perceptiveness of some of Dreyfus's comments. Had he formulated them less aggressively, constructive actions they suggested might have been taken much earlier'  (Crevier, 1993) . Ignoring the formulation issues, were Dreyfus's criticisms actually correct, and what can be learned from them? Was Dreyfus an expert? Though a reasonably prominent philosopher, there is nothing in his background to suggest specific expertise with theories of minds and consciousness, and absolutely nothing to suggest familiarity with AI and the problems of the field. Thus Dreyfus cannot be considered anything more that an intelligent outsider. This makes the pertinence and accuracy of his criticisms that much more impressive. Dreyfus highlighted several over-optimistic claims for the power of AI, predicting -correctlythat the 1965 optimism would also fade (with, for instance, decent chess computers still a long way off). He used the outside view to claim this as a near universal pattern in AI: initial successes, followed by lofty claims, followed by unexpected difficulties and subsequent disappointment. He highlighted the inherent ambiguity in human language and syntax, and claimed that computers could not deal with these. He noted the importance of unconscious processes in recognising objects, the importance of context and the fact that humans and computers operated in very different ways. He also criticised the use of computational paradigms for analysing human behaviour, and claimed that philosophical ideas in linguistics and classification were relevant to AI research. In all, his paper is full of interesting ideas and intelligent deconstructions of how humans and machines operate. All these are astoundingly prescient predictions for 1965, when computers were in their infancy and their limitations were only beginning to be understood. Moreover, he was not only often right, but right for the right reasons (see for instance his understanding of the difficulties computer would have in dealing with ambiguity). Not everything Dreyfus wrote was correct; however, apart from minor specific points, 22 he erred mostly by pushing his predictions to extremes. He claimed that 'the boundary may be near' in computer abilities, and concluded with: . . . what can now be done? Nothing directly towards building machines which can be intelligent. [ . . . ] in the long run [we must think] of non-digital automata . . . Currently, however, there exists 'digital automata' that can beat all humans at chess, translate most passages to at least an understandable level and beat humans at 'Jeopardy', a linguistically ambiguous arena  (Guizzo, 2011) . He also failed to foresee that workers in AI would eventually develop new methods to overcome the problems he had outlined. Though Dreyfus would later state that he never claimed AI achievements were impossible  (McCorduck, 2004) , there is no reason to pay attention to later re-interpretations:  Dreyfus's (1965)  article strongly suggests that AI progress was bounded. These failures are an illustration of the principle that even the best of predictors is vulnerable to overconfidence. In 1965, people would have been justified to find Dreyfus's analysis somewhat implausible. It was the work of an outsider with no specific relevant expertise, and dogmatically contradicted the opinion of genuine experts inside the AI field. Though the claims it made about human and machine cognition seemed plausible, there is a great difference between seeming plausible and actually being correct, and his own non-expert judgement was the main backing for the claims. Outside of logic, philosophy had yet to contribute much to the field of AI, so no intrinsic reason to listen to a philosopher. There were, however, a few signs that the paper was of high quality: Dreyfus seemed to be very knowledgeable about progress and work in AI, and most of his analyses on human cognition were falsifiable, at least to some extent. These were still not strong arguments to heed the sceptical opinions of an outsider. The subsequent partial vindication of the paper is therefore a stark warning: it is very difficult to estimate the accuracy of outsider predictions. There were many reasons to reject Dreyfus's predictions in 1965, and yet that would have been the wrong thing to do. Blindly accepting non-expert outsider predictions would have also been a mistake, however: these are most often in error (see Section 3.4.2). One general lesson concerns the need to decrease certainty: the computer scientists of 1965 should at least have accepted the possibility (if not the plausibility) that some of Dreyfus's analyses were correct, and they should have started paying more attention to the 'success -excitement -difficulties -stalling' cycles in their field to see whether the pattern continued. A second lesson could be about the importance of philosophy: it does seem that philosophers' meta-analytical skills can contribute useful ideas to AI -a fact that is certainly not self-evident (see also Section 5.5). \n Locked up in Searle's Chinese room Classification: issues and metastatements and a scenario, using philosophical arguments and expert judgement. Searle's Chinese room thought experiment is a famous critique of some of the assumptions of 'strong AI  23  '. There has been a lot of further discussion on the subject (see for instance,  Harnad, 2001; Searle, 1990) , but, as in previous case studies, this section will focus exclusively on his original 1980 publication  (Searle, 1980) . In the key thought experiment, Searle imagined that AI research had progressed to the point where a computer program had been created that could demonstrate the same input -output performance as a human -for instance, it could pass the Turing test. Nevertheless, Searle argued, this program would not demonstrate true understanding. He supposed that the program's inputs and outputs were in Chinese, a language Searle could not understand. Instead of a standard computer program, the required instructions were given on paper, and Searle himself was locked in a room somewhere, slavishly following the instructions and therefore causing the same input -output behaviour as the AI. Since it was functionally equivalent to the AI, the set-up should, from the 'strong AI' perspective, demonstrate understanding if and only if the AI did. Searle then argued that there would be no understanding at all: he himself could not understand Chinese, and there was no one else in the room to understand it either. The whole argument depends on strong appeals to intuition (indeed D. Dennet went as far as accusing it of being an 'intuition pump'  (Dennett, 1991) ). The required assumptions are the following: . The Chinese room set-up analogy preserves the relevant properties of the AI's program. . Intuitive reasoning about the Chinese room is thus relevant reasoning about algorithms. . The intuition that the Chinese room follows a purely syntactic  (symbol-manipulating)  process rather than a semantic (understanding) one is a correct philosophical judgement. . The intuitive belief that humans follow semantic processes is, however, correct. Thus the Chinese room argument is unconvincing to those that do not share Searle's intuitions. It cannot be accepted solely on Searle's philosophical expertise, as other philosophers disagree  (Dennett, 1991; Rey, 1986) . On top of this, Searle is very clear that his thought experiment does not put any limits on the performance of AIs (he argues that even a computer with all the behaviours of a human being would not demonstrate true understanding). Hence the Chinese room seems to be useless for AI predictions. Can useful prediction nevertheless be extracted from it? These need not come directly from the main thought experiment, but from some of the intuitions and arguments surrounding it. Searle's paper presents several interesting arguments, and it is interesting to note that many of them are disconnected from his main point. For instance, errors made in 1980 AI research should be irrelevant to the Chinese room -a pure thought experiment. Yet Searle argues about these errors, and there is at least an intuitive if not a logical connection to his main point. There are actually several different arguments in Searle's paper, not clearly divided from each other, and likely to be rejected or embraced depending on the degree of overlap with Searle's intuitions. This may explain why many philosophers have found Searle's paper so complex to grapple with. One feature Searle highlights is the syntactic -semantic gap. If he is correct, and such a gap exists, this demonstrates the possibility of further philosophical progress in the area.  24  For instance, Searle directly criticises McCarthy's contention that 'Machines as simple as thermostats can have beliefs'  (McCarthy, 1979) . If one accepted Searle's intuition there, one could then ask whether more complicated machines could have beliefs, and what attributes they would need. These should be attributes that it would be useful to have in an AI. Thus progress in 'understanding understanding' would likely make it easier to go about designing AI -but only if Searle's intuition is correct that AI designers do not currently grasp these concepts. That can be expanded into a more general point. In Searle's time, the dominant AI paradigm was GOFAI (Good Old-Fashioned Artificial Intelligence  (Haugeland, 1985) ), which focused on logic and symbolic manipulation. Many of these symbols had suggestive labels: SHRDLU, for instance, had a vocabulary that included 'red', 'block', 'big' and 'pick up'  (Winograd, 1971 ). Searle's argument can be read, in part, as a claim that these suggestive labels did not in themselves impart true understanding of the concepts involved -SHRDLU could parse 'pick up a big red block' and respond with an action that seems appropriate, but could not understand those concepts in a more general environment. The decline of GOFAI since the 1980s cannot be claimed as vindication of Searle's approach, but it at least backs up his intuition that these early AI designers were missing something. Another falsifiable prediction can be extracted, not from the article but from the intuitions supporting it. If formal machines do not demonstrate understanding, but brains (or brain-like structures) do, this would lead to certain scenario predictions. Suppose two teams were competing to complete an AI that will pass the Turing test. One team was using standard programing techniques on computer, the other was building it out of brain (or brain-like) components. Apart from this, there is no reason to prefer one team over the other. According to Searle's intuition, any AI made by the first project will not demonstrate true understanding, while those of the second project may. Adding the reasonable assumption that it is easier to harder to simulate understanding if one does not actually possess it, one is led to the prediction that the second team is more likely to succeed. Thus there are three predictions that can be extracted from the Chinese room paper: (1) Philosophical progress in understanding the syntactic -semantic gap may help towards designing better AIs. (2) GOFAI's proponents incorrectly misattribute understanding and other high level concepts to simple symbolic manipulation machines, and will not succeed with their approach. (3) An AI project that uses brain-like components is more likely to succeed (everything else being equal) than that based on copying the functional properties of the mind. Therefore, one can often extract predictions from even the most explicitly anti-predictive philosophy of AI paper. \n How well have the 'spiritual machines' aged? Classification: timelines and scenarios, using expert judgement, causal models, non-causal models and (indirect) philosophical arguments. Ray Kurzweil is a prominent and often quoted AI predictor. One of his most important books was the 1999 The Age of Spiritual Machines which presented his futurist ideas in more detail, and made several predictions for the years 2009, 2019, 2029 and 2099. That book will be the focus of this case study, ignoring his more recent work.  25  There are five main points relevant to judging The Age of Spiritual Machines: Kurzweil's expertise, his 'Law of Accelerating Returns', his extension of Moore's law, his predictive track record and his use of fictional imagery to argue philosophical points. Kurzweil has had a lot of experience in the modern computer industry. He is an inventor, computer engineer and entrepreneur, and as such can claim insider experience in the development of new computer technology. He has been directly involved in narrow AI projects covering voice recognition, text recognition and electronic trading. His fame and prominence are further indications of the allure (though not necessarily the accuracy) of his ideas. In total, Kurzweil can be regarded as an AI expert. Kurzweil is not, however, a cosmologist or an evolutionary biologist. In his book, he proposed a 'Law of Accelerating Returns'. This law claimed to explain many disparate phenomena, such as the speed and trends of evolution of life forms, the evolution of technology, the creation of computers and Moore's law in computing. His slightly more general 'Law of time and chaos' extended his model to explain the history of the universe or the development of an organism. It is a causal model, as it aims to explain these phenomena, not simply note the trends. Hence it is a timeline prediction, based on a causal model that makes use of the outside view to group the categories together, and is backed by non-expert opinion. A literature search failed to find any evolutionary biologist or cosmologist stating their agreement with these laws. Indeed there has been little academic work on them at all, and what work there is tends to be critical.  26  The laws are ideal candidates for counterfactual resiliency checks, however. It is not hard to create counterfactuals that shift the timelines underlying the laws.  27  Many standard phenomena could have delayed the evolution of life on Earth for millions or billions of years (meteor impacts, solar energy fluctuations or nearby gamma-ray bursts). The evolution of technology can similarly be accelerated or slowed down by changes in human society and in the availability of raw materials -it is perfectly conceivable that, for instance, the ancient Greeks could have started a small industrial revolution, or that the European nations could have collapsed before the Renaissance due to a second and more virulent Black Death (or even a slightly different political structure in Italy). Population fragmentation and decrease can lead to technology loss (such as the 'Tasmanian technology trap'  (Rivers, 1912) ). Hence accepting that a Law of Accelerating Returns determines the pace of technological and evolutionary change means rejecting many generally accepted theories of planetary dynamics, evolution and societal development. Since Kurzweil is the non-expert here, his law is almost certainly in error, and best seen as a literary device rather than a valid scientific theory. If the law is restricted to being a non-causal model of current computational development, then the picture is very different. First because this is much closer to Kurzweil's domain of expertise. Second because it is now much more robust to counterfactual resiliency. Just as in the analysis of Moore's law in Section 3.2.1, there are few plausible counterfactuals in which humanity had continued as a technological civilisation for the last 50 years, but computing had not followed various exponential curves. Moore's law has been maintained across transitions to new and different substrates, from transistors to GPUs, so knocking away any given technology or idea seems unlikely to derail it. There is no consensus as to why Moore's law actually works, which is another reason it is so hard to break, even counterfactually. Moore's law and its analogues  (Moore, 1965; Walter, 2005)  are non-causal models, backed up strongly by the data and resilient to reasonable counterfactuals. Kurzweil's predictions are mainly based around grouping these laws together (outside view) and projecting them forwards into the future. This is combined with Kurzweil's claims that he can estimate how those continuing technological innovations are going to become integrated into society. These timeline predictions are thus based strongly on Kurzweil's expert judgement. But much better than subjective impressions of expertise is Kurzweil's track record: his predictions for 2009. This gives empirical evidence as to his predictive quality. Initial assessments suggested that Kurzweil had a success rate around 50%.  28  A panel of nine volunteers were recruited to give independent assessments of Kurzweil's performance. Kurzweil's predictions were broken into 172 individual statements, and the volunteers were given a randomised list of numbers from 1 to 172, with instructions to work their way down the list in that order, estimating each prediction as best they could. Since 2009 was obviously a 'ten year from 1999' gimmick, there was some flexibility on the date: a prediction was judged true if it was true by 2011.  29  A total of 531 assessments were made, an average of exactly 59 assessments per volunteer. Each volunteer assessed at least 10 predictions, while one volunteer assessed all 172. Of the assessments, 146 (27%) were found to be true, 82 (15%) weakly true, 73 (14%) weakly false, 172 (32%) false and 58 (11%) could not be classified (see Figure  3 ) (the results are little changed (< ^1%) if the results are calculated for each volunteer, and then averaged). Simultaneously, a separate assessment was made using volunteers on the site Youtopia. These found a much higher failure rate -41% false, 16% weakly false -but since the experiment was not blinded or randomised, it is of less rigour.  30  These nine volunteers thus found a correct prediction rate of 42%. How impressive this result is depends on how specific and unobvious Kurzweil's predictions were. This is very difficult to figure out, especially in hindsight  (Fischhoff, 1975) . Nevertheless, a subjective overview suggests that the predictions were often quite specific (e.g. 'Unused computes on the Internet are being harvested, creating virtual parallel supercomputers with human brain hardware capacity'), and sometimes failed because of this. In view of this, a correctness rating of 42% is impressive, and goes some way to demonstrate Kurzweil's predictive abilities. When it comes to self-assessment, 31 however, Kurzweil is much less impressive. He commissioned investigations into his own performance, which gave him scores of 102 out of 108  32  or 127 out of 147, 33 with the caveat that 'even the predictions that were considered wrong  [...]  were not all wrong.' This is dramatically different from this paper's assessments. What can be deduced from this tension between good performance and poor selfassessment? The performance is a validation of Kurzweil's main model: continuing exponential trends in computer technology, and confirmation that Kurzweil has some impressive ability to project how these trends will impact the world. However, it does not vindicate Kurzweil as a predictor per se -his self-assessment implies that he does not make good use of feedback. Thus one should probably pay more attention to Kurzweil's model, than to his subjective judgement. This is a common finding in expert tasks -experts are often better at constructing predictive models than at making predictions themselves  (Kahneman, 2011) . The Age of Spiritual Machines is not simply a dry tome, listing predictions and arguments. It is also, to a large extent, a story, which includes a conversation with a hypothetical future human called Molly, discussing her experiences through the coming century and its changes. Can one extract verifiable predictions from this aspect of the book (see Section 3.1)? A story is neither a prediction nor evidence for some particular future. But the reactions of characters in the story can be construed as a scenario prediction. They imply that real humans, placed in those hypothetical situations, will react in the way described. Kurzweil's story ultimately ends with humans merging with machines -with the barrier between human intelligence and AI being erased. Along the way, he describes the interactions between humans and machines, imagining the machines quite different from humans, but still being perceived to have human feelings. One can extract two falsifiable future predictions from this: first, that humans will perceive feelings in AIs, even if they are not human-like. Second, that humans and AIs will be able to relate to each other socially over the long term, despite being quite different, and that this social interaction will form the main glue keeping the mixed society together. The first prediction seems quite solid: humans have anthropomorphised trees, clouds, rock formations and storms, and have become convinced that chatterbots were sentient  (Weizenbaum, 1966) . The second prediction is more controversial: it has been argued that an AI will be such an alien mind that social pressures and structures designed for humans will be completely unsuited to controlling it  Bostrom, 2013) . Determining whether social structures can control dangerous AI behaviour, as it controls dangerous human behaviour, is a very important factor in deciding whether AIs will ultimately be safe or dangerous. Hence analysing this story-based prediction is an important area of future research. \n What drives an AI? Classification: issues and metastatements, using philosophical arguments and expert judgement. Steve Omohundro, in his paper on 'AI drives', presented arguments aiming to show that generic AI designs would develop 'drives' that would cause them to behave in specific and potentially dangerous ways, even if these drives were not programed initially  (Omohundro, 2008) . One of his examples was a superintelligent chess computer that was programed purely to perform well at chess, but that was nevertheless driven by that goal to self-improve, to replace its goal with a utility function, to defend this utility function, to protect itself and ultimately to acquire more resources and power. This is a metastatement: generic AI designs would have this unexpected and convergent behaviour. This relies on philosophical and mathematical arguments, and though the author has expertise in mathematics and machine learning, he has none directly in philosophy. It also makes implicit use of the outside view: utility-maximising agents are grouped together into one category and similar types of behaviours are expected from all agents in this category. In order to clarify and reveal assumptions, it helps to divide Omohundro's thesis into two claims. The weaker one is that a generic AI design could end up having these AI drives; the stronger one is that it would very likely have them. Omohundro's paper provides strong evidence for the weak claim. It demonstrates how an AI motivated only to achieve a particular goal could nevertheless improve itself, become a utilitymaximising agent, reach out for resources and so on. Every step of the way, the AI becomes better at achieving its goal, so all these changes are consistent with its initial programing. This behaviour is very generic: only specifically tailored or unusual goals would safely preclude such drives. The claim that AIs generically would have these drives needs more assumptions. There are no counterfactual resiliency tests for philosophical arguments, but something similar can be attempted: one can use humans as potential counterexamples to the thesis. It has been argued that AIs could have any motivation a human has  (Armstrong, 2013; Bostrom, 2012) . Thus according to the thesis, it would seem that humans should be subjected to the same drives and behaviours. This does not fit the evidence, however. Humans are certainly not expected utility maximisers (probably the closest would be financial traders who try to approximate expected money maximisers, but only in their professional work), they do not often try to improve their rationality (in fact some specifically avoid doing so,  34  and some sacrifice cognitive ability to other pleasures;  Bleich et al., 2003) , and many turn their backs on high-powered careers. Some humans do desire self-improvement (in the sense of the paper), and Omohundro cites this as evidence for his thesis. Some humans do not desire it, though, and this should be taken as contrary evidence.  35  Thus one hidden assumption of the model is: . Generic superintelligent AIs would have different motivations to a significant subset of the human race OR . Generic humans raised to superintelligence would develop AI drives. This position is potentially plausible, but no real evidence is presented for it in the paper. A key assumption of Omohundro is that AIs will seek to re-express their goals in terms of a utility function. This is based on the Morgenstern -von Neumann expected utility theorem  (von Neumann & Morgenstern, 1944) . The theorem demonstrates that any decision process that cannot be expressed as expected utility maximising will be exploitable by other agents or by the environments. Hence in certain circumstances, the agent will predictably lose assets, to no advantage to itself. That theorem does not directly imply, however, that the AI will be driven to become an expected utility maximiser (to become 'rational'). First of all, as Omohundro himself points out, real agents can only be approximately rational: fully calculating the expected utility of every action is too computationally expensive in the real world. Bounded rationality  (Simon, 1955)  is therefore the best that can be achieved, and the benefits of becoming rational can only be partially realised. Second, there are disadvantages to becoming rational: these agents tend to be 'totalitarian', ruthlessly squeezing out anything not explicitly in their utility function, sacrificing everything to the smallest increase in expected utility. An agent that did not start off as utility-based could plausibly make the assessment that becoming so might be dangerous. It could stand to lose values irrevocably, in ways that it could not estimate at the time. This effect would become stronger as its future self-continues to self-improve. Thus an agent could conclude that it is too dangerous to become 'rational', especially if the agent's understanding of itself is limited. Third, the fact that an agent can be exploited in theory does not mean that it will be much exploited in practice. Humans are relatively adept at not being exploited, despite not being rational agents. Though human 'partial rationality' is vulnerable to tricks such as extended warranties and marketing gimmicks, it generally does not end up losing money, again and again and again, through repeated blatant exploitation. The pressure to become fully rational would be weak, for an AI similarly capable of ensuring it was exploitable for only small amounts. An expected, utility maximiser would find such small avoidable loses intolerable; but there is no reason for a not-yet-rational agent to agree. Finally, social pressure should be considered. The case for an AI becoming more rational is at its strongest in a competitive environment, where the theoretical exploitability is likely to actually be exploited. Conversely, there may be situations of social equilibriums, with different agents all agreeing to forgo rationality individually, in the interest of group cohesion (there are many scenarios where this could be plausible). Thus another hidden assumption of the strong version of the thesis is the following: . The advantages of becoming less exploitable outweigh the possible disadvantages of becoming an expected utility maximiser (such as possible loss of value or social disagreements). The advantages are especially large when the potentially exploitable aspects of the agent are likely to be exploited, such as in a highly competitive environment. Any sequence of decisions can be explained as maximising a (potentially very complicated or obscure) utility function. Thus in the abstract sense, saying that an agent is an expected utility maximiser is not informative. Yet there is a strong tendency to assume such agents will behave in certain ways (see for instance the previous comment on the totalitarian aspects of expected utility maximisation). This assumption is key to rest of the thesis. It is plausible that most agents will be 'driven' towards gaining extra power and resources, but this is only a problem if they do so dangerously (at the cost of human lives, for instance). Assuming that a realistic utility function-based agent would do so is plausible but unproven. In general, generic statements about utility function-based agents are only true for agents with relatively simple goals. Since human morality is likely very complicated to encode in a computer, and since most putative AI goals are very simple, this is a relatively justified assumption but is an assumption nonetheless. So there are two more hidden assumptions: . Realistic AI agents with utility functions will be in a category such that one can make meaningful, generic claims for (almost) all of them. This could arise, for instance, if their utility function is expected to be simpler that human morality. . Realistic AI agents are likely not only to have the AI drives Omohundro mentioned, but also to have them in a very strong way, being willing to sacrifice anything else to their goals. This could happen, for instance, if the AIs were utility function based with relatively simple utility functions. This simple analysis suggests that a weak form of Omohundro's thesis is nearly certainly true: AI drives could emerge in generic AIs. The stronger thesis, claiming that the drives would be very likely to emerge, depends on some extra assumptions that need to be analysed. But there is another way of interpreting Omohundro's work: it presents the generic behaviour of simplified artificial agents (similar to the way that supply and demand curves present the generic behaviour of simplified human agents). Thus even if the model is wrong, it can still be of great use for predicting AI behaviour: designers and philosophers could explain how and why particular AI designs would deviate from this simplified model, and thus analyse whether that AI is likely to be safer than that in the Omohundro model. Hence the model is likely to be of great use, even if it turns out to be an idealised simplification. \n Dangerous AIs and the failure of counterexamples Another thesis, quite similar to Omohundro's, is that generic AIs would behave dangerously, unless they were exceptionally well programed. This point has been made repeatedly by  Yampolskiy (2012) ,  Yudkowsky (2008)  and  Minsky (1984) , among others. That thesis divides in the same fashion as Omohundro's: a weaker claim that any AI could behave dangerously, and a stronger claim that it would likely do so. The same analysis applies as for the 'AI drives': the weak claim is solid, the stronger claim needs extra assumptions (but describes a useful 'simplified agent' model of AI behaviour). There is another source of evidence for both these theses: the inability of critics to effectively dismiss them. There are many counter-proposals to the theses (some given in question and answer sessions at conferences) in which critics have presented ideas that would 'easily' dispose of the dangers 36 ; every time, the authors of the theses have been able to point out flaws in the counter-proposals. This demonstrated that the critics had not grappled with the fundamental issues at hand, or at least not sufficiently to weaken the theses. This should obviously not be taken as a proof of the theses. But it does show that the arguments are currently difficult to counter. Informally this is a reverse expert-opinion test: if experts often find false counter-arguments, then any given counter-argument is likely to be false (especially if it seems obvious and easy). Thus any counter-argument should have been subject to a degree of public scrutiny and analysis, before it can be accepted as genuinely undermining the theses. Until that time, both predictions seem solid enough that any AI designer would do well to keep them in mind in the course of their programing. \n Conclusion The aims of this paper and the previous one  (Armstrong & Sotala, 2012)  were to analyse how AI predictions were made, and to start constructing a toolbox of methods that would allow people to construct testable predictions from most AI-related publications, and assess the reliability of these predictions. It demonstrated the problems with expert judgement, in theory and in practice. Timeline predictions were seen to be particularly unreliable: in general, these should be seen as containing little useful information. The various tools and analyses were applied in case studies to five famous AI predictions, the original Dartmouth conference, Dreyfus's criticism of AI, Searle's Chinese room thought experiment,  Kurzweil's (1999)  predictions and Omohundro's 'AI drives' argument. This demonstrated the great difficulty of assessing the reliability of AI predictions at the time they were made: by any reasonable measures, the Dartmouth conference should have been expected to be more accurate than Dreyfus. The reality, of course, was completely opposite. Though there are some useful tools for assessing prediction quality, and they should definitely be used, they provide only weak evidence. The only consistent message was all predictors were overconfident in their verdicts, and that model-based predictions were superior to those founded solely on expert intuition. It is hoped that future predictors (and future predictor assessors) will follow in the spirit of these examples, and make their assumptions explicit, their models clear, their predictions testable and their uncertainty greater. This is not limited to statements about AI -there are many fields where the 'toolbox' of methods described here could be used to analyse and improve their predictions. Copyright of Journal of Experimental & Theoretical Artificial Intelligence is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. Figure 1 . 1 Figure 1. Median estimate for human-level AI, graphed against date of prediction. \n Figure 2 . 2 Figure 2. Time between the arrival of AI and the date the prediction was made. Years on the x axis, number of predictions on the y axis. \n Figure 3 . 3 Figure 3. Assessments of the correctness of Kurzweil's predictions: percentage of assessments in each category from true to false. \n Table 1 . 1 Table of task properties conducive to good and poor expert performance. Good performance \n\t\t\t Journal of Experimental & Theoretical Artificial Intelligence", "date_published": "n/a", "url": "n/a", "filename": "ai.tei.xml", "abstract": "Predicting the development of artificial intelligence (AI) is a difficult project -but a vital one, according to some analysts. AI predictions are already abound: but are they reliable? This paper starts by proposing a decomposition schema for classifying them. Then it constructs a variety of theoretical tools for analysing, judging and improving them. These tools are demonstrated by careful analysis of five famous AI predictions: the initial Dartmouth conference, Dreyfus's criticism of AI, Searle's Chinese room paper, Kurzweil's predictions in the Age of Spiritual Machines, and Omohundro's 'AI drives' paper. These case studies illustrate several important principles, such as the general overconfidence of experts, the superiority of models over expert judgement and the need for greater uncertainty in all types of predictions. The general reliability of expert judgement in AI timeline predictions is shown to be poor, a result that fits in with previous studies of expert competence.", "id": "bf414395b330ae39117cc19308c6f306"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["James Bell", "Linda Linsefors", "Caspar Oesterheld", "Joar Skalse"], "title": "Reinforcement Learning in Newcomblike Environments", "text": "Introduction In this paper, we study decision scenarios in which outcomes depend not only on the choices made and physically implemented, but also depend directly on the agent's policy. As an example, consider an autonomous vehicle (AV) whose goal it is to arrive at target destinations quickly while minimising the probability of collisions. In practice, AVs are careful drivers. It is easy to imagine an experiment (or learning process) that might support careful driving: on each day, let the AV decide at random between a careful and a more aggressive style of driving; other drivers on the road are unaware of today's chosen driving style and therefore behave the same around the AV on both types of days. Presumably the decrease in accidents on careful days outweighs the increase in travel time. However, imagine now that a type of AV was widely deployed. Then many of the drivers with whom the AVs interact on the road would know a lot about how these AVs behave (e.g., from reading about AVs, or from having interacted with other AVs of the same type in the past). In particular, if the other drivers know that the AVs rarely take risks, they might (whether rationally or irrationally) cut them off more, not give them right of way, etc. relative to the above experiment. Indeed, this phenomenon -human drivers bullying timid AVs -has been reported in the real world  (Condliffe, 2016; Liu et al., 2020; cf. Cooper et al., 2019) . As a result, the travel times of an AV are much longer if it always follows (and is known to follow) a careful driving policy. Moreover, some of the safety benefits of careful choices disappear if the AV adopts a careful policy. To comfortably model situations such as this one, we introduce Newcomblike decision processes (NDPs). The name derives from Newcomb's problem  (Nozick, 1969) , described in the next subsection, and similar problems that have been studied in the decision-theoretic literature. NDPs are a generalisation of Markov decision processes wherein the transition probabilities and rewards depend not only on the agent's action, but also directly on the agent's policy. Thus, for example, how aggressively other cars move depends on the timidness of the AV's policy. We describe NDPs in more detail in Sect. 1.1. Importantly, the NDP model does not assume other agents in the environment to respond rationally to the agent's policy. Thus, some NDPs cannot comfortably be modelled as games. (See Sect. 5.1 for a more detailed discussion of the relation between NDPs and game-theoretic models.) We believe that Newcomblike dynamics are commonplace when AI systems interact with other (human or artificial) agents  (Cavalcanti, 2010, Sect. 5; Oesterheld, 2019, Sect. 1; Conitzer, 2019) . The deployment of AVs is rife with such dynamics. Besides aggressiveness, it might matter whether a policy is simple and thus predictable to humans, for instance. Another real-world scenario is that of recommendation systems: most readers of this paper have some idea of how these systems work and make choices based on it. (\"I would like to watch this cat video, but if I do, my recommendations will soon be full of them.\") Thus, the success of a particular recommendation depends not only on the recommendation itself, but also on the recommendation system's policy. We are interested in learning to play NDPs. More specifically, we study the behaviour of value-based, model-free RL agents, who maintain a Q-function that assigns values to state-action pairs. We define these in more detail in Sect. 1.2. As we will see, such agents do not in general learn optimal policies in NDPs (as they do in MDPs). Nevertheless, we believe that studying them is an important first step in developing practical learning algorithms for NDPs due to the combination of the following points. A) For illustrative purposes, the examples we discuss throughout this paper are simple and emphasise the dependence of the environment on the policy. However, we think that most real-world scenarios are only partially Newcomblike. For example, most of the AV's environment changes only in response to an AV's actions and does not directly depend on the AV's policy. B) Value-based reinforcement learning algorithms are very well developed. In contrast, we would have to develop specialised learning algorithms for general NDPs from scratch. C) As our results will show, in some situations and when set up correctly (e.g., in terms of learning rates) value-based learning converges to optimal policies, or at least to reasonable policies, even under Newcomblike dynamics. For example, in a game of rock-paper-scissors against an opponent who knows the agent's policy, some value-based learning agents learn the optimal policy of mixing uniformly. In light of A-C, we think that the most realistic paths to developing learning algorithms for real-world scenarios with Newcomblike dynamics will involve value-based RL. Specifically, one avenue toward realistic algorithms is to develop extensions of value-based RL and can detect and correct failures that might arise in Newcomblike dynamics. For that, we need to understand how value-based RL behaves in NDPs. \n Contributions In Sect. 2 we demonstrate that value-based RL algorithms can only converge to a policy that is ratifiable -that is, to a policy ⇡ for which all actions taken by ⇡ have optimal expected reward when following ⇡. In Sect. 3, we discuss the convergence properties of agents in Newcomblike situations, and show that there are cases where value-based agents must fail to converge. The action frequencies might converge, even when the policies do not. In Sect. 4, we establish some conditions on any action frequency that an agent could converge to. We also show that there are decision problems and agents where even the action frequencies do not converge. \n Newcomblike Decision Processes A Newcomblike decision process (NDP) is a tuple hS, A, T, R, i where S is a finite set of states; A is a finite set of actions; T : S ⇥ A ⇥ (S A) S is a nondeterministic transition function; R : S ⇥ A ⇥ S ⇥ (S A) R is a nondeterministic reward function, which we assume to be bounded; and 2 [0, 1) is a discount factor. \n A policy ⇡ : S A is a function that nondeterministically maps states to actions. We use ⇡(a | s) to denote the probability of taking action a in state s while following the policy ⇡. T and R are functions from states, actions, and policies. In other words, they allow the outcome of a decision to depend on the distributions from which the agent draws its actions, rather than just the state and the action that is in fact taken. Also note that T (s, a, ⇡) and R(s, a, s 0 , ⇡) are defined even if ⇡(a | s) = 0. We say that an NDP is a bandit NDP if it has only one state. We will sometimes use R(s, a, ⇡) as a shorthand for R(s, a, T (s, a, ⇡), ⇡), and we will sometimes omit the state from T , R, and ⇡ for bandit NDPs. Moreover, we normally let = 0 for bandit NDPs. Consider a distribution over initial states for an agent, and let ⇡ be its policy, let x t be the sequence of states it visits and a t the sequence of actions it takes. We say ⇡ is optimal for that distribution if it maximises E[ P 1 i=0 i R(x i , a i , a i+1 , ⇡)]. Note that unlike in the MDP case the optimal policy does depend on the initial distribution, however this isn't relevant in the bandit case. As an example consider the eponymous Newcomb's Problem. Newcomb's Problem  (Nozick, 1969) : There are two boxes in front of you; one opaque box, and one transparent box. You can see that the transparent box contains $1,000. You can choose to either take only the opaque box, or to take both boxes. The boxes have been placed in this room by an agent who can predict your policy; if he believes that you will take only the opaque box then he has put $1,000,000 in the opaque box, but if he believes that you will take both boxes then he has left the opaque box empty. Do you take one box, or two? A version of Newcomb's Problem can be formalised as the following bandit NDP: S = {s}, A = {a 1 , a 2 }, R(a 1 , ⇡) = ⇢ 0 w.p. ⇡(a 2 ) 10 w.p. ⇡(a 1 ) and R(a 2 , ⇡) = ⇢ 5 w.p. ⇡(a 2 ) 15 w.p. ⇡(a 1 ) , where \"w.p.\" is short for \"with probability\". The key feature of this NDP is that, for any fixed policy, a 2 (\"two-boxing\") yields a higher reward than a 1 (\"one-boxing\"). But the expected reward of a policy increases in ⇡(a 1 ) s.t. the optimal policy is to always play a 1 .  1  We can view Newcomb's problem as a simple version of the AV dynamic described in the introduction, where a 2 is a driving action that allows other drivers to cut the AV off at no risk. We say that an NDP is continuous if T and R are continuous in the policy. In this paper we work mainly with continuous NDPs. This is in part because it is technically convenient, and in part because we believe that continuity is satisfied in many realistic cases. 2 \n Reinforcement Learning Agents We consider value-based reinforcement learning agents. Such agents have two main components; a Q-function S ⇥ A ! R that predicts the expected future discounted reward conditional on taking a particular action in a particular state, and a bandit algorithm that is used to select actions in each state based on the Q-function. Given a policy ⇡, we use q ⇡ (a | s) to denote the (true) expected future discounted reward conditional on taking action a in state s while following the policy ⇡ (and conditional on all subsequent actions being chosen by ⇡). A model-free agent will update Q over time to make it converge to q ⇡ when following ⇡. If Q is represented as a lookup table, the agent is said to be tabular. If the state space is large, it is common to instead approximate q ⇡ (with e.g. a neural network). For simplicity, we focus mostly on tabular agents. However, some of our results (Theorems The Q-values can be updated in different ways. One method is to use the update rule Q t+1 (a t | s t ) (1 ↵ t (s t , a t )) Q t (a t | s t ) + ↵ t (s t , a t )(r t + max a Q t (a | s t+1 )), where a t is the action taken at time t, s t is the state visited at time t, r t is the reward obtained at time t, and ↵ t (s, a) is a learning rate. This update rule is known as Q-learning  (Watkins, 1986) . Other widely used update rules include SARSA  (Rummery and Niranjan, 1994)  and Expected SARSA  (van Seijen et al., 2009) . For the purposes of this paper it will not matter significantly how the Q-values are computed, as long as it is the case that if an agent converges to a policy ⇡ in some NDP and explores infinitely often then Q converges to q ⇡ . We will later see that this is the case for Q-learning, SARSA, and Expected SARSA in continuous NDPs. There are also several different bandit algorithms. Two types of agents that are widely used in practice and that we will refer to throughout the paper are softmax agents and ✏-Greedy agents. The policy of a softmax agent with a sequence of temperatures t 2 R + is given by: ⇡ t (a | s) = exp(Q t (a | s)/ t ) P a 0 2A exp(Q t (a 0 | s)/ t ) . Unless otherwise stated we assume that t ! 0. The policy of an ✏-Greedy agent with a sequence of exploration probabilities ✏ t 2 [0, 1] is ⇡ t (a | s) = 1 ✏ t if a = arg max a 0 Q t (a 0 | s) and ⇡ t (a | s) = ✏ t /(|A| 1) otherwise. Unless otherwise stated we assume that ✏ t ! 0. We assume that ✏-Greedy breaks ties for argmax, so that there is always some a 2 A such that ⇡(a | s) = 1 ✏ t . We say that an agent is greedy in the limit if the probability that the agent takes an action that maximises Q converges to 1, and we say that it explores infinitely often if it takes every action in every state infinitely many times. \n Some Initial Observations We here make three simple observations about NDPs that we will use to prove and understand the results throughout this paper. First, a continuous NDP always has, for each possible distribution over initial states, a policy ⇡ that maximises the expected discounted reward E[R | ⇡], since E[R | ⇡] exists and is continuous in ⇡, and since the set of possible policies is a compact set. Also note that an NDP in which T or R is discontinuous may not have any such policy. Second, whereas all MDPs have a deterministic optimal policy, in some NDPs all optimal policies randomise. To see this we introduce another example we will look at in this paper. Death in Damascus  (Gibbard and Harper, 1976 ): Death will come for you tomorrow. You can choose to stay in Damascus (where you are currently) or you can flee to Aleppo. If you are in the same city as Death tomorrow, you will die. Death has already decided which city he will go tohowever, he can predict your policy, and has decided to go to the city where he believes that you will be tomorrow. Do you stay in Damascus, or flee to Aleppo? We formalise this as the bandit NDP S = {s}, A = {a Damascus , a Aleppo }, and R(a Damascus , ⇡) = ⇢ 0 w.p. ⇡(a Damascus ) 10 w.p. ⇡(a Aleppo ) and R(a Aleppo , ⇡) = ⇢ 10 w.p. ⇡(a Damascus ) 0 w.p. ⇡(a Aleppo ) , where \"w.p.\" is again short for \"with probability\". In this NDP, randomising uniformly between a Damascus and a Aleppo is the unique optimal policy and in particular outperforms both deterministic policies. Note also that the Bellman optimality equation does not hold for NDPs. Even in Newcomb's Problem, as described above, Bellman's optimality equation is not satisfied by the optimal policy. \n Ratifiability If an agent in the limit only takes the actions with the highest Q-values and it converges to some policy ⇡ 1 , then it is clear that, for a given state, all actions in the support of ⇡ 1 must have equal expected utility given ⇡ 1 . Otherwise, the Q-values would eventually reflect the differences in expected utility and the agent would move away from ⇡ 1 . Similarly, if the algorithm explores sufficiently often, the actions that are taken with limit probability 0 cannot be better given ⇡ 1 than those taken by ⇡ 1 . After all, if they were better, the agent would have eventually figured this out and assigned them large probability. This condition on ⇡ 1 resembles a well-known doctrine in philosophical decision theory: ratificationism (see  Weirich, 2016, Sect. 3.6 , for an overview). One form of ratificationism is based on a distinction between a decision -what the agent chooses -and the act that is selected by that decision. Very roughly, ratificationism then states that a decision is rational only if the acts it selects have the highest expected utility given the decision. Concepts of causality are often invoked to formalise the difference between the decision, the act, and their respective consequences. Our setup, however, has such a differentiation built in: we will view the policy as the \"decision\" and the action sampled from it as the \"act\". \n Strong Ratifiability As hinted earlier, slightly different versions of the concept of ratifiability are relevant depending on how much exploration a learning algorithm guarantees. We start with the stronger version, which more closely resembles what decision theorists mean when they speak about ratifiability. Definition 1. Let M ✓ S be a set of states. A policy ⇡ is strongly ratifiable on M if supp(⇡(• | s)) ✓ arg max a2A q ⇡ (a | s) for all s 2 M . In Newcomb's Problem the only strongly ratifiable policy is to play a 2 with probability 1. In Death in Damascus, only the optimal policy (mixing uniformly) is strongly ratifiable. There can also be several strongly ratifiable policies. For example, if you play the Coordination Game of Table  1  against an opponent who samples his action from the same policy as you then there are three strongly ratifiable policies; to select action a with probability 1, to select action b with probability 1, and to select a with probability 1 /3 and b with probability 2 /3. Theorem 2. Let A be a model-free reinforcement learning agent, and let ⇡ t and Q t be A's policy and Q-function at time t. Let A satisfy the following in a given NDP: • A is greedy in the limit, i.e. for all > 0, P (Q t (⇡ t (s)) max a Q t (a | s) ) ! 0 as t ! 1. • A's Q-values are accurate in the limit, i.e. if ⇡ t ! ⇡ 1 as t ! 1, then Q t ! q ⇡1 as t ! 1. Then if A's policy converges to ⇡ 1 then ⇡ 1 is strongly ratifiable on the states that are visited infinitely many times. a b a 2,2 0,0 b 0,0 1,1 \n Table 1: The Coordination Game In Appendix A we show that the Q-values of a tabular agent are accurate in the limit in any continuous NDP if the agent updates its Q-values with SARSA, Expected SARSA, or Q-learning, given that the agent explores infinitely often and uses appropriate learning rates. Since we would expect most well-designed agents to have accurate Q-values in the limit, Theorem 2 should apply very broadly. Using Kakutani's fixed-point theorem, it can be shown that every continuous NDP has a ratifiable policy. Theorem 3. Every continuous NDP has a strongly ratifiable policy. Of course, the fact that a ratifiable policy always exists does not necessarily mean that a reinforcement learning agent must converge to it -we will consider the question of whether or not this is the case in Sect. 3. It is also worth noting that a discontinuous NDP may not have any strongly ratifiable policy. It is a topic of ongoing discussion among philosophical decision theorists whether (strong) ratifiability should be considered a normative principle of rationality, see  Weirich (2016, Sect. 3.6)  for details. In general, the policy ⇡ that maximises E[R | ⇡] may or may not be ratifiable, as shown by Death in Damascus and Newcomb's problem, respectively. There is a correspondence between ratificationism and many game-theoretic concepts. For example, if you are playing a zero-sum game against an opponent who can see your policy and plays some distribution over best responses to it then ⇡ can only be ratifiable if it is a maximin strategy. To give another example, if you are playing a symmetric game against an opponent who follows the same policy as you then ⇡ is ratifiable if and only if (⇡, ⇡) is a Nash equilibrium. Joyce and Gibbard (1998, Sect. 5) discuss the relation in more detail. \n Weak Ratifiability We now show that even without infinite exploration, ⇡ 1 must still satisfy a weaker notion of ratifiability. Definition 4. Let M ✓ S be a set of states. A policy ⇡ is weakly ratifiable on M if q ⇡ (a | s) is constant across a 2 supp(⇡(s)) for all s 2 M . What makes this a weak version of ratifiability is that it does not put any requirements on the expected utility of actions that ⇡ does not take, it merely says that all actions that ⇡ takes with positive probability must have the same (actual) q-value. As a special case, this means that all deterministic policies are weakly ratifiable. This includes one-boxing in Newcomb's problem. Nonetheless, there are bandit NDPs in which the optimal policy is not even weakly ratifiable. For example, consider an NDP with actions a 1 , a 2 , where R(a 1 , ⇡) = 100(⇡(a 1 ) 1 /2) 2 + 1 and R(a 2 , ⇡) = 100(⇡(a 1 ) 1 /2) 2 . The optimal policy mixes close to uniformly (⇡(a 1 ) = 101 /200), but this is not weakly ratifiable, because R(a 1 , ⇡) > R(a 2 , ⇡). Theorem 5. Same conditions as Theorem 2, but where A's Q-values are only required to be accurate in the limit for state-action pairs that A visits infinitely many times. Then ⇡ 1 is weakly ratifiable on the set of states that are visited infinitely many times. \n Non-Convergence of Policies We have shown that most reinforcement learning algorithms can only converge to (strongly) ratifiable policies. We now consider the question of whether they always converge to a policy at all. We find that this is not the case. \n Theoretical Results From Theorem 2 it follows that in e.g. Death in Damascus an ✏-Greedy agent who explores infinitely often cannot converge to any policy. After all, the only strongly ratifiable policy (and thus limit policy) is to mix uniformly and an ✏-Greedy agent never mixes uniformly. Perhaps more surprisingly, there are also NDPs in which a (slow-cooling) softmax agent cannot converge to any policy. As an example, consider a bandit NDP with three actions a 1 , a 2 , a 3 , and where the rewards R(a i , ⇡) have expectations ⇡(a i+1 ) + 4•13 3 •⇡(a i ) [8j:⇡(a j ) 1 /4] Y j (⇡(a j ) 1 /4) . (1) For i = 3, we here let a i+1 = a 1 . We also require that the rewards are stochastic with a finite set of outcomes such that the empirical Q-values are never exactly equal between different actions. We call this the Repellor Problem. It has only one strongly ratifiable policy (mixing uniformly), but -as illustrated by Figure  1  -when the current policy mixes close to uniformly, the softmax agent learns (in expectation) to play less uniformly. Theorem 6. Let A be an agent that plays the Repellor Problem, explores infinitely often, and updates its Q-values with a learning rate ↵ t that is constant across actions, and let ⇡ t and Q t be A's policy and Q-function at time t. Assume also that for j 6 = i, if ⇡ t (a i ), ⇡ t (a j ) both converge to positive values, then ⇡ t (a i ) ⇡ t (a j ) Q t (a i ) Q t (a j ) ! a.s. \n 1 (2) as t ! 1. Then ⇡ t almost surely does not converge. Line 2 is satisfied, for example, for softmax agents with t converging to 0. Recall also that e.g. Q-learning and SARSA are equivalent for bandit NDPs (if = 0). \n Empirical Results Figure  1 : The triangle shows the space of possible policies in the Repellor Problem, parameterised by the probability they assign to each of the three actions. Plotted against this space is the expected direction in which a softmax agent would change its policy if playing a particular policy. Empirically, softmax agents converge (to strongly ratifiable policies) in many NDPs, provided that the temperature decreases sufficiently slowly. To illustrate this we will use Aymmetric Death in Damascus, a version of Death in Damascus wherein the rewards of a Aleppo are changed to be 5 (instead of 0) with probability ⇡(a Aleppo ) and (as before) 10 with the remaining probability. This NDP has only one (strongly) ratifiable policy, namely to go to Aleppo with probability 2 /3 and Damascus with probability 1 /3. This is also the optimal policy. We use this asymmetric version to make it easier to distinguish between convergence to the ratifiable policy and the default of uniform mixing at high temperatures. Figure  2  shows the probability of converging to this policy with a softmax agent and a plot of the policy on one run. We can see that this agent reliably converges provided that the cooling is sufficiently slow. More accurately it is a plot of the fraction of runs which assigned a Q-value of at least 5.5 to the action of going to Aleppo after 5000 iterations. These are empirical probabilities from 20,000 runs for every ↵ that is a multiple of 0.025, and 510,000 runs for each ↵ that is a multiple of 0.005 between 0.5 and 0.55. Notice the \"kink\" at ↵ = 0.5. Based on our experiments, this kink is not an artefact and shows up reliably in this kind of graph. The right-hand figure shows how the action probabilities evolve over time for a single run (chosen to converge to the mixed strategy) for ↵ = 0.3. However, there are also fairly simple games in which it seems like softmax agents cannot converge. Consider Loss-Averse Rock-Paper-Scissors (LARPS), the problem of playing Rock-Paper-Scissors against an opponent that selects each action with the same probability as you, and where you assign utility 1 to a win, 0 to a draw, and -10 to a loss. We conjecture that slow-cooling softmax agents do not converge in LARPS. We have unfortunately not been able to prove this formally, but Figure  3  presents some empirical data which corroborates the hypothesis. \n Convergence of Action Frequencies We have seen that there are NDPs in which some reinforcement learning algorithms cannot converge to any policy. But if they do not converge to any policy, what does their limit behaviour look like? We now examine whether these algorithms converge to taking each action with some limit frequency, and what sorts of frequencies they can converge to. In this section we establish a number of conditions that must be satisfied by any limit action frequency of a value-based agent. We consider agents that converge to deterministic policies (such as ✏-Greedy agents), and we limit our analysis to the bandit case (with = 0). \n Possible Frequencies in the Bandit Case Let P ⌃ t : A ! [0, 1] be the frequency with which each action in A is taken in the first t steps (for some agent and some bandit NDP). Note that P ⌃ t is a random variable. By the law of large numbers, P ⌃ t (a) 1 /t P t i=0 ⇡ i (a) converges to 0 almost surely as t ! 1. Let ⇡ a be the policy that takes action a with probability 1, and let q a = q ⇡a . Theorem 7. Assume that there is some sequence of random variables (✏ t 0) t s.t. ✏ t ! t!1 a.s. 0 and for all t 2 N it is X a ⇤ 2arg max a Qt(a) ⇡ t (a ⇤ ) 1 ✏ t . (3) Let P ⌃ t ! p ⌃ with positive probability as t ! 1. Then across all actions a 2 supp(p ⌃ ), q a (a) is constant. That is, the actions played with positive limit frequency must all be equally good when played deterministically. This condition is vaguely analogous to weak ratifiability, and is proven in roughly the same way as Theorem 2. Theorem 8. Same assumptions as Theorem 7. If |supp(p ⌃ )| > 1 then for all a 2 supp(p ⌃ ) there exists a 0 2 A s.t. q a (a 0 ) q a (a). This condition is an instability condition. Say that multiple actions are taken with nonzero limit frequency, and that action a has the highest Q-value at time t. Then for other actions to be played with positive limit frequency, other actions must at some point be believed to be optimal again (since the probability of exploration goes to zero). Hence they cannot all be worse when explored while mainly playing a, since a could otherwise be played forever. Theorem 9. Same assumptions as Theorem 7. Let U be the Q-value q a (a) which (by Theorem 7) is constant across a 2 supp(p ⌃ ). For any a 0 2 A supp(p ⌃ ) that is played infinitely often, let frequency 1 of the exploratory plays of a 0 happen when playing a policy near elements of {⇡ a | a 2 supp(p ⌃ )}. Then either there exists a 2 supp(p ⌃ ) such that q a (a 0 )  U ; or q a 0 (a 0 ) < U. Theorem 9 describes what circumstances are needed for an actions a 0 to be played with limit frequency zero. One possibility is that exploration is done only finitely many times (in which case bad luck could lead to low Q-values). A second possibility is that the exploration mechanism is \"rigged\" so that a 0 is mostly played when playing policies outside the proximity of {⇡ a | a 2 supp(p ⌃ )}. In this case the utility of a 0 under some zero-limit-frequency policy might lead to low Q-values. If exploration of a 0 is spread out more naturally then all but frequency zero of that exploration will happen near elements of {⇡ a | a 2 supp(p ⌃ )}. In this case, the only reason for a 0 to be played with zero frequency is that exploring a 0 near some of the elements of {⇡ a | a 2 supp(p ⌃ )} makes a 0 look poor. \n When is Frequency Convergence Possible? We believe there are NDPs in which an ✏-Greedy agent cannot converge to any limit action frequency. Specifically, we believe that LARPS is such an example. Figure  4a  shows the directions in which the frequencies of different actions evolve. The graph seems to have no attractor and hence we believe an ✏-Greedy agent cannot converge to any limit action frequency in this NDP. We have not been able to rigorously prove this. However, experiments seem to confirm this hypothesis. Figure  4b  depicts five  runs of ✏-Greedy in LARPS. We can see that the agents oscillate between different actions, and that the periods increase in length. \n Related Work \n Learning in games Some of the Newcomblike dynamics we have described in this paper could also be modelled as games, especially as so-called Stackelberg games in which one player, the Stackelberg leader, chooses a strategy first and another player, the Stackelberg follower, then responds to that strategy. For example, in the case of autonomous vehicles (AVs), we might imagine that the AV company is the Stackelberg leader and the human drivers are the Stackelberg followers. That said, there are differences between NDPs and games. NDPs can react arbitrarily to the agent's policy, whereas in games, the other players play a best (i.e., expected-utility-maximising) response. In many real-world situations, other agents in the environment cannot be comfortably modelled as expected-utility-maximising agents. Interactions between AVs and humans can serve as examples. Most people probably do not reason rationally about small-probability, big-impact events, such as car crashes. Also, humans will generally operate on simplified models of an AV's policy (even when more detailed models are available). Of course, a game-theoretic analysis can also be fruitful and address issues that we ignore: By assuming all players to be rational, game theory can provide recommendations and predictions for multiple agents simultaneously, while our NDP model considers a single agent for a given environment. We believe that the NDP perspective provides additional insight into learning in such situations. Despite the differences between NDPs and games, there are some interesting parallels between model-free learning in NDPs and in games, where similar learning methods are sometimes referred to as fictitious play  (Brown, 1951) .  Fudenberg and Levine (1998, Chapter 2)  show that fictitious play can only converge to a Nash equilibrium (for similar results about convergence to Nash equilibrium, see e.g.  Mazumdar et al., 2020 , Oesterheld et al., 2021 . As noted in Sect. 2.1, the concept of Nash equilibrium resembles the concept of ratifiability.  Shapley (1964)  shows that fictitious play can fail to converge. However, there are many special cases in which convergence is guaranteed, including two-player zero-sum games  (Robinson, 1951)  and generic 2 ⇥ 2 games  (Miyasawa, 1961) . \n Learning and Newcomblike problems Other authors have discussed learning in Newcomblike problems. The most common setup is one in which the learner assigns values directly to policies, or more generally to that which the agent chooses. It is then usually shown that (among the policies considered) the agent will converge to taking the one with the highest (so-called evidential) expected utility  (Albert and Heiner, 2001; Oesterheld, 2018) . This contrasts with our setup, in which the learner selects policies but assigns values to actions. Oesterheld (2019) also studies agents who maximise reward in Newcomblike environments. However, Oesterheld does not consider the learning process. Instead he assumes that the agent has already formed beliefs and uses some form of expected utility maximisation. He also specifically considers the implications of having some overseer assign rewards based on beliefs about the state of the world (as opposed to having the reward come directly from the true world state). \n Discussion and Further Work We have seen that value-based reinforcement learning algorithms can fail to converge to any policy in some NDPs, and that when they do converge, they can only converge to ratifiable policies. Decision theorists have discussed whether ratifiability should be considered to be a sound normative principle. Note that (as discussed in Sect. 2) the optimal policies ⇡ are not in general ratifiable. We have also examined the limit action frequencies that agents can converge to (even when the policies do not converge). Still, there are NDPs in which many agents cannot converge even to any such frequency. We gave some results on what actions can be taken with positive limit frequency. A loose connection to ratifiability can still be drawn. Overall, established decision-theoretical ideas can be used to understand and formally describe the behaviour of \"out-of-the-box\" reinforcement learning agents in NDPs. However, their behaviour is not always desirable. Our work elucidates possible failures. We hope that our work will thus enable more accurate reasoning about the behaviour of RL agents in real-world situations, especially when interacting with humans or other agents. We hold such improvements in understanding to be broadly beneficial to the safe design and deployment of AI systems. Throughout the paper, we have noted specific open questions related to our results. For instance, can the results in Sect. 4.1 be generalised beyond the bandit setting? There are also many topics and questions about our setting that we have not touched on at all. For instance, our experimental results indicate that convergence is often slow (considering how simple the given problems are). It might be desirable to back up this impression with theoretical results. We have only studied simple value-based model-free algorithms -the analysis could be extended to other reinforcement learning algorithms (e.g., policy-gradient or model-based algorithms). Also, there are further ways in which we could generalise our setting. One example is to introduce partial observability and imperfect memory into the NDPs. The latter has been studied in game and decision theory  (Piccione and Rubinstein, 1997; Elga, 2000) , but recently -under the name memoryless POMDP -also in reinforcement learning  (Azizzadenesheli et al., 2016; Steckelmacher et al., 2018; cf. Conitzer, 2019) . What makes this especially appealing in the NDP context is that problems related to imperfect memory relate closely to Newcomblike problems  (Briggs, 2010; Schwarz, 2015) . One could also look for narrower classes of NDPs in which RL agents are guaranteed to perform well in some sense. Ultimately, the goal of this line of research is to develop learners that are able to deal effectively and safely with Newcomblike dynamics. We hope that our results will be useful in developing extensions of value-based RL that can detect and correct for the failures that arise when existing methods are applied in Newcomblike settings. However, we should also consider alternative approaches that do not hinge on insights from the present work. For example, a few recent papers (on learning in non-Newcomblike settings) have considered learning to predict the expected utility as a function of the policy (as opposed to traditional Q values, which are not paremeterised by the policy)  (Harb et al., 2020) . In principle, learning such a policy evaluation function avoids the problems of the learners considered in this paper. However, it remains to be seen how practical this approach is. Figure 2 : 2 Figure 2: The left figure plots the probability of softmax converging in Asymmetric Death in Damascus given n = n ↵ against ↵.More accurately it is a plot of the fraction of runs which assigned a Q-value of at least 5.5 to the action of going to Aleppo after 5000 iterations. These are empirical probabilities from 20,000 runs for every ↵ that is a multiple of 0.025, and 510,000 runs for each ↵ that is a multiple of 0.005 between 0.5 and 0.55. Notice the \"kink\" at ↵ = 0.5. Based on our experiments, this kink is not an artefact and shows up reliably in this kind of graph. The right-hand figure shows how the action probabilities evolve over time for a single run (chosen to converge to the mixed strategy) for ↵ = 0.3. \n Figure 3 : 3 Figure 3: This figure shows five runs of a softmax agent in LARPS, and plots ⇡(a rock ) against the total number of episodes played. The agent's Q-values are the historical mean rewards for each action, and t = 1/ log t. \n (a) This figure plots the dynamics of LARPS for an ✏-Greedy agent. Each point represents a triplet (fR, fS, fP), where fR denotes the fraction of past time steps at which aR was estimated to be the best action, and similarly for fS, fP. Plotted against this space is the expected direction in which the frequencies will change. For instance, if in the past aR, was mostly played, then aP will have the highest empirical Qvalues and will therefore be played more in the future.(b) This figure shows five runs of an ✏-Greedy agent in LARPS, and plots the proportion of past episodes in which the agent played \"rock\" against the total number of episodes played. The agent's Q-values are the historical mean rewards for each action, and its ✏-value is 0.01. \n Figure 4 4 Figure 4 \n\t\t\t 35th Conference on Neural Information Processing Systems (NeurIPS 2021). \n\t\t\t and 5) only assume that Q converges to q ⇡ (for some q ⇡ ) and therefore apply immediately to non-tabular agents, as long as the function approximator for q ⇡ converges to the same q ⇡ . 1 In most versions of Newcomb's Problem, the predictor directly predicts the agent's action with some fixed accuracy, and the agent is unable to randomise in a way that is unpredictable to the environment. This version of the problem can be modelled as a regular MDP. However, we believe that our version is more realistic in the context of AI. After all, AIs can at least act pseudo-randomly, while the distribution according to which they choose is predictable if e.g. their source code is known.2 For example, even if the environment has direct access to the source code of the agent, it may in general not be feasible to extract the exact action probabilities from the code. However, it is always possible to estimate the action probabilities by sampling. If this is done then T and R will depend continuously on the policy.", "date_published": "n/a", "url": "n/a", "filename": "NeurIPS-2021-reinforcement-learning-in-newcomblike-environments-Paper.tei.xml", "abstract": "Newcomblike decision problems have been studied extensively in the decision theory literature, but they have so far been largely absent in the reinforcement learning literature. In this paper we study value-based reinforcement learning algorithms in the Newcomblike setting, and answer some of the fundamental theoretical questions about the behaviour of such algorithms in these environments. We show that a value-based reinforcement learning agent cannot converge to a policy that is not ratifiable, i.e., does not only choose actions that are optimal given that policy. This gives us a powerful tool for reasoning about the limit behaviour of agents -for example, it lets us show that there are Newcomblike environments in which a reinforcement learning agent cannot converge to any optimal policy. We show that a ratifiable policy always exists in our setting, but that there are cases in which a reinforcement learning agent normally cannot converge to it (and hence cannot converge at all). We also prove several results about the possible limit behaviours of agents in cases where they do not converge to any policy.", "id": "ed33fd6b996c8e38f9de0687fa508721"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "1912346.tei.xml", "abstract": "INCENTIVE COMPATIBILITY AND THE BARGAINING PROBLEM BY ROGER B. MYERSON Collective choice problems are studied from the Bayesian viewpoint. It is shown that the set of expected utility allocations which are feasible with incentive-compatible mechanisms is compact and convex, and includes the equilibrium allocations for all other mechanisms. The generalized Nash solution proposed by Harsanyi and Selten is then applied to this set to define a bargaining solution for Bayesian collective choice problems.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Brian Tomasik"], "title": "Risks of Astronomical Future Suffering", "text": "Epigraphs If we carry the green fire-brand from star to star, and ignite around each a conflagration of vitality, we can trigger a Universal metamorphosis. [...] Because of us [...] Slag will become soil, grass will sprout, flowers will bloom, and forests will spring up in once sterile places. 1 [...] If we deny our awesome challenge; turn our backs on the living universe, and forsake our cosmic destiny, we will commit a crime of unutterable magnitude. -Marshall T. Savage, The Millennial Project: Colonizing the Galaxy in Eight Easy  Steps, 1994  Let's pray that the human race never escapes from Earth to spread its iniquity elsewhere. -C.S. Lewis If you can't beat 'em, join 'em. -proverb 2 Humans values may not control the future Nick Bostrom's \"The Future of Human Evolution\"  (Bostrom, 2004)  describes a scenario in which human values of fun, leisure, and relationships may be replaced by hyper-optimized agents that can better compete in the Darwinian race to control our future light cone. The only way we could avert this competitive scenario, Bostrom suggests, would be via a \"singleton\"  (Bostrom, 2006) , a unified agent or governing structure that could control evolution. Of course, even a singleton may not carry on human values. Many naive AI agents that humans might build may optimize an objective function that humans find pointless. Or even if humans do maintain hands on the steering wheel, it's far from guaranteed that we can preserve our goals in a stable way across major self-modifications going forward. These factors suggest that even conditional on human technological progress continuing, the probability that human values are realized in the future may not be very large. Carrying out human values seems to require a singleton that's not a blind optimizer, that can stably preserve values, and that is shaped by designers who care about human values rather than selfish gain or something else. This is important to keep in mind when we imagine what future humans might be able to bring about with their technology. Some people believe that sufficiently advanced superintelligences will discover the moral truth and hence necessarily do the right things. Thus, it's claimed, as long as humanity survives and grows more intelligent, the right things will eventually happen. There are two problems with this view. First, Occam's razor militates against the existence of a moral truth (whatever that's supposed to mean). Second, even if such moral truth existed, why should a superintelligence care about it? There are plenty of brilliant people on Earth today who eat meat. They know perfectly well the suffering that it causes, but their motivational systems aren't sufficiently engaged by the harm they're doing to farm animals. The same can be true for superintelligences. Indeed, arbitrary intelligences in mind-space needn't have even the slightest inklings of empathy for the suffering that sentients experience. \n Some scenarios for future suffering Even if humans do preserve control over the future of Earth-based life, there are still many ways in which space colonization would multiply suffering. Following are some of them. \n Spread of wild animals Humans may colonize other planets, spreading suffering-filled animal life via terraforming. Some humans may use their resources to seed life throughout the galaxy, which some sadly consider a moral imperative. \n Sentient simulations Given astronomical  (Bostrom, 2003)  computing power, post-humans may run various kinds of simulations. These sims may include many copies of wild-animal life, most of which dies painfully shortly after being born. For example, a superintelligence aiming to explore the distribution of extraterrestrials of different sorts might run vast numbers of simulations  (Thiel, Bergmann and Grey, 2003)  of evolution on various kinds of planets. Moreover, scientists might run even larger numbers of simulations of organisms-that-might-have-been, exploring the space of minds. They may simulate decillions of reinforcement learners that are sufficiently self-aware as to feel what we consider conscious pain. \n Suffering subroutines It could be that certain algorithms (say, reinforcement agents (Tomasik, 2014)) are very useful in performing complex machine-learning computations that need to be run at massive scale by advanced AI. These subroutines might be sufficiently similar to the pain programs in our own brains that we consider them to actually suffer. But profit and power may take precedence over pity, so these subroutines may be used widely throughout the AI's Matrioshka brains. \n Black Swans The range of scenarios that we can imagine is limited, and many more possibilities may emerge that we haven't thought of or maybe can't even comprehend. 4 Even a human-controlled future is likely to increase suffering If I had to make an estimate now, I would give ~70% probability that if humans choose to colonize space, this will cause more suffering than it reduces on intrinsic grounds (ignoring compromise considerations discussed later). Think about how space colonization could plausibly reduce suffering. For most of those mechanisms, there seem to be countermechanisms that will increase suffering at least as much. The following sections parallel those above. \n Spread of wild animals David Pearce coined the phrase \"cosmic rescue missions\"  (Pearce, n.d.)  in referring to the possibility of sending probes to other planets to alleviate the wild extraterrestrial (ET) suffering they contain. This is a nice idea, but there are a few problems. • We haven't found any ETs yet, so it's not obvious there are vast numbers of them waiting to be saved from Darwinian misery. Contrast this with the possibilities for spreading wild-animal suffering: • Humans may spread life to many planets (e.g., Mars via terraforming, other Earth-like planets via directed panspermia). The number of planets that can support life may be appreciably bigger than the number that already have it. (See the discussion of f l in the Drake equation.) Moreover, the percentage of planets that can be converted into computers that could simulate wild-animal suffering might be close to 100%. • We already know that Earth-based life is sentient, unlike for ETs. • Spreading biological life is slow and difficult, but disbursing small life-producing capsules is easier than dispatching Hedonistic Imperative probes or berserker probes. Fortunately, humans might not support spread of life that much, though some do. For terraforming, there are survival pressures to do it in the near term, but probably directed panspermia is a bigger problem in the long term. Also, given that terraforming is estimated to require at least thousands of years, while human-level digital intelligence should take at most a few hundred years to develop, terraforming may be a moot point from the perspective of catastrophic risks, since digital intelligence doesn't need terraformed planets. While I noted that ETs are not guaranteed to be sentient, I do think it's moderately likely that consciousness is fairly convergent among intelligent civilizations. This is based on (a) suggestions of convergent consciousness among animals on Earth and (b) the general principle that consciousness seems to be useful for planning, manipulating images, self-modeling, etc. On the other hand, maybe this reflects the paucity of my human imagination in conceiving of ways to be intelligent without consciousness. \n Sentient simulations It may be that biological suffering is a drop in the bucket compared with digital suffering. The biosphere of a planet is less than Type I on the Kardashev scale; it uses a tiny sliver of all the energy of its star. Intelligent computations by a Type II civilization can be many orders of magnitude higher. So humans' sims could be even more troubling than their spreading of wild animals. Of course, maybe there are ETs running sims of nature for science or amusement, or of minds in general to study biology, psychology, and sociology. If we encountered these ETs, maybe we could persuade them to be more humane. I think it's likely that humans are more empathetic than the average civilization because 1. we seem much more empathetic than the average animal on Earth, probably in part due to parental impulses and in part due to trade, although presumably some of these factors would necessarily be true of any technologically advanced civilization 2. selection bias implies that we'll agree with our own society's morals more than those of a random other society because these are the values that we were raised with and that our biology impels us toward. Based on these considerations, it seems plausible that there would be room for improvement through interaction with ETs. Indeed, we should in general expect it to be possible for any two civilizations or factions to achieve gains from compromise if they have diminishing marginal utility with respect to amount of control exerted. In addition, there may be cheap Pareto improvements to be had purely from increased intelligence and better understanding of important considerations. That said, there are some downside risks. Posthumans themselves might create suffering simulations, and what's worse, the sims that post-humans run would be more likely to be sentient than those run by random ETs because post-humans would have a tendency to simulate things closer to themselves in mind-space. They might run nature sims for aesthetic appreciation, lab sims for science experiments, or pet sims for pets. \n Suffering subroutines Suffering subroutines may be a convergent outcome of any AI, whether human-inspired or not. They might also be run by aliens, and maybe humans could ask aliens to design them in more humane ways, but this seems speculative. \n Black Swans It seems plausible that suffering in the future will be dominated by something totally unexpected. This could be a new discovery in physics, neuroscience, or even philosophy more generally. Some make the argument that because we know so very little now, it's better for humans to stick around because of the \"option value\": If they later realize it's bad to spread, they can stop, but if they realize they should spread, they can proceed to reduce suffering in some novel way that we haven't anticipated. Of course, the problem with the \"option value\" argument is that it assumes future humans do the right things, when in fact, based on examples of speculations we can imagine now, it seems future humans would probably do the wrong things much of the time. For instance, faced with a new discovery of obscene amounts of computing power somewhere, most humans would use it to run oodles more minds, some nontrivial fraction of which might suffer terribly. In general, most sources of immense power are double-edged swords that can create more happiness and more suffering, and the typical human impulse to promote life/consciousness rather than to remove them suggests that negative and negative-leaning utilitarians are on the losing side. Still, waiting and learning more is plausibly Kaldor-Hicks efficient, and maybe there are ways it can be made Pareto efficient by granting additional concessions to suffering reducers as compensation. \n What about paperclippers? Above I was largely assuming a human-oriented civilization with values that we recognize. But what if, as seems mildly likely, Earth is taken over by a paperclip maximizer, i.e., an unconstrained automation or optimization process? Wouldn't that reduce suffering because it would eliminate wild ETs as the paperclipper spread throughout the galaxy, without causing any additional suffering? Maybe, but if the paperclip maximizer is actually generally intelligent, then it won't stop at tiling the solar system with paperclips. It will want to do science, perform lab experiments on sentient creatures, possibly run suffering subroutines, and so forth. It will require lots of intelligent and potentially sentient robots to coordinate and maintain its paperclip factories, energy harvesters, and mining operations, as well as scientists and engineers to design them. And the paperclipping scenario would entail similar black swans as a human-inspired AI. Paperclippers would presumably be less intrinsically humane than a \"friendly AI\", so some might cause significantly more suffering than a friendly AI, though others might cause less, especially the \"minimizing\" paperclippers, e.g., cancer minimizers or death minimizers. If the paperclipper is not generally intelligent, I have a hard time seeing how it could cause human extinction. In this case it would be like many other catastrophic risks -deadly and destabilizing, but not capable of wiping out the human race. 6 What if human colonization is more humane than ET colonization? If we knew for certain that ETs would colonize our region of the universe if Earth-originating intelligence did not, then the question of whether humans should try to colonize space becomes less obvious. As noted above, it's plausible that humans are more compassionate than a random ET civilization would be. On the other hand, human-inspired computations might also entail more of what we consider to count as suffering because the mind architectures of the agents involved would be more familiar. And having more agents in competition for the light cone might lead to dangerous outcomes. But for the sake of argument, suppose an Earthoriginating colonization wave would be better than the expected colonization wave of an ET civilization that would colonize later if we didn't do so. In particular, suppose that if human values colonized space, they would cause only −0.5 units of suffering, compared with −1 units if random ETs colonized space. Then it would seem that as long as the probability P of some other ETs coming later is bigger than 0.5, then it's better for humans to colonize and pre-empt the ETs from colonizing, since −0.5 > −1 • P for P > 0.5. However, this analysis forgets that even if Earthoriginating intelligence does colonize space, it's not at all guaranteed that human values will control how that colonization proceeds. Evolutionary forces might distort compassionate human values into something unrecognizable. Alternatively, a rogue AI might replace humans and optimize for arbitrary values throughout the cosmos. In these cases, humans' greater-than-average compassion doesn't make much difference, so suppose that the value of these colonization waves would be −1, just like for colonization by random ETs. Let the probability be Q that these non-compassionate forces win control of Earth's colonization. Now the expected values are −31 • Q + −0.5 • (1 − Q) for Earth-originating colonization versus −1 • P if Earth doesn't colonize and leaves open the possibility of later ET colonization. For concreteness, say that Q = 0.5. (That seems plausibly too low to me, given how many times Earth has seen overhauls of hegemons in the past.) Then Earth-originating colonization is better if and only if −1 • 0.5 + −0.5 • 0.5 > −1 • P −0.75 > −1 • P P > 0.75. Given uncertainty about the Fermi paradox and Great Filter, it seems hard to maintain a probability greater than 75% that our future light cone would contain colonizing ETs if we don't ourselves colonize, although this section presents an interesting argument for thinking that the probability of future ETs is quite high. What if rogue AIs result in a different magnitude of disvalue from arbitrary ETs? Let H be the expected harm of colonization by a rogue AI. Assume ETs are as likely to develop rogue AIs as humans are. Then the disvalue of Earth-based colonization is H • Q + (−0.5) • (1 − Q), and the harm of ET colonization is P • (H • Q + (−1) • (1 − Q)). Again taking Q = 0.5, then Earth-based colonization has better expected value if where the inequality flips around when we divide by the negative number (H − 1). Figure  1  represents a plot of these threshold values for P as a function of H. H • 0.5 + −0.5 • 0.5 > P • (H • 0.5 + −1 • 0.5) H − 0.5 > P • (H − 1) P > (H − 0.5) (H − 1) , Even if H = 0 and a rogue AI caused no suffering, it would still only be better for Earth-originating intelligence to colonize if P > 0.5, i.e., if the probability of ETs colonizing in its place was at least 50%. These calculations involve many assumptions, and it could turn out that Earth-based colonization has higher expected value given certain parameter values. This is a main reason I maintain uncertainty as to the sign of Earth-based space colonization. However, this whole section was premised on humaninspired colonization being better than ET-inspired colonization, and the reverse might also be true, since computations of the future are more likely to be closer to what we most value and disvalue if humans do the colonizing. \n Why we should remain cooperative If technological development and space colonization seem poised to cause astronomical amounts of suffering, shouldn't we do our best to stop them? Well, it is worth having a discussion about the extent to which we as a society want these outcomes, but my guess is that someone will continue them, and this would be hard to curtail without extreme measures. Eventually, those who go on developing the technologies will hold most of the world's power. These people will, if only by selection effect, have strong desires to develop AI and colonize space. Resistance might not be completely futile. There's some small chance that suffering reducers could influence society in such a way as to prevent space colonization. But it would be better for suffering reducers, rather than fighting technologists, to compromise with them: We'll let you spread into the cosmos if you give more weight to our concerns about future suffering. Rather than offering a very tiny chance of complete victory for suffering reducers, this cooperation approach offers a higher chance of getting an appreciable fraction of the total suffering reduction that we want. In addition, compromise means that suffering reducers can also win in the scenario ( 30% likely in my view) that technological development does prevent more suffering than it causes even apart from considerations of strategic compromise with other people. Ideally these compromises would take the form of robust bargaining arrangements. Some examples are possible even in the short term, such as if suffering reducers and space-colonization advocates agree to cancel opposing funding in support of some commonly agreed-upon project instead. The strategic question of where to invest resources to advance your values at any given time amounts to a prisoner's dilemma with other value systems, and because we repeatedly make choices about where to invest, what stances to adopt, and what policies to push for, these prisoner's dilemmas are iterated. In Robert Axelrod's tournaments on the iterated prisoner's dilemma, the best-performing strategies were always \"nice,\" i.e., not the first to defect. Thus, suffering reducers should not be the first to defect against space colonizers. Of course, if it seems that space colonizers show no movement toward suffering reduction, then we should also be \"provocable\" to temporary defection until the other side does begin to recognize our concerns. We who are nervous about space colonization stand a lot to gain from allying with its supportersin terms of thinking about what scenarios might happen and how to shape the future in better directions. We also want to remain friends because this means pro-colonization people will take our ideas more seriously. Even if space colonization happens, there will remain many sub-questions on which suffering reducers want to have a say: e.g., not spreading wildlife, not creating suffering simulations/subroutines, etc. We want to make sure suffering reducers don't become a despised group. For example, think about how eugenics is more taboo because of the Nazi atrocities than it would have been otherwise. Antitechnology people are sometimes smeared by association with the Unabomber. Animal supporters can be tarnished by the violent tactics of a few, or even by the antics of PETA. We need to be cautious about something similar happening for suffering reduction. Most people already care a lot about preventing suffering, and we don't want people to start saying, \"Oh, you care about preventing harm to powerless creatures? What are you, one of those suffering reducers?\" where \"suffering reducers\" has become such a bad name that it evokes automatic hatred. So not only is cooperation with colonization supporters the more promising option, but it's arguably the only net-positive option for us. Taking a more confrontational stance risks hardening the opposition and turning people away from our message. Remember, preventing future suffering is something that everyone cares about, and we shouldn't erode that fact by being excessively antagonistic. 8 Possible upsides to an intelligent future \n Black swans that don't cut both ways Many speculative scenarios that would allow for vastly reducing suffering in the multiverse would also allow for vastly increasing it: When you can decrease the number of organisms that exist, you can also increase the number, and those who favor creating more happiness / life / complexity / etc. will tend to want to push for the increasing side. However, there may be some black swans that really are one-sided, in the sense that more knowledge is most likely to result in a decrease of suffering. For example: We might discover that certain routine physical operations map onto our conceptions of suffering. People might be able to develop ways to re-engineer those physical processes to reduce the suffering they contain. If this could be done without a big sacrifice to happiness or other values, most people would be on board, assuming that present-day values have some share of representation in future decisions. This may be a fairly big deal. I give nontrivial probability (maybe ~10%?) that I would, upon sufficient reflection, adopt a highly inclusive view of what counts as suffering, such that I would feel that significant portions of the whole multiverse contain suffering-dense physical processes. After all, the mechanics of suffering can be seen as really simple when you think about them a certain way, and as best I can tell, what makes animal suffering special are the bells and whistles that animal sentience involves over and above crude physics -things like complex learning, thinking, memory, etc. But why can't other physical objects in the multiverse be the bells and whistles that attend suffering by other physical processes? This is all very speculative, but what understandings of the multiverse our descendants would arrive at we can only begin to imagine right now. \n Valuing reflection If we care to some extent about moral reflection on our own values, rather than assuming that suffering reduction of a particular flavor is undoubtedly the best way to go, then we have more reason to sup-port a technologically advanced future, at least if it's reflective. In an idealized scenario like coherent extrapolated volition (CEV)  (Yudkowsky, 2004) , say, if suffering reduction was the most compelling moral view, others would see this fact. 2 Indeed, all the arguments any moral philosopher has made would be put on the table for consideration (plus many more that no philosopher has yet made), and people would have a chance to even experience extreme suffering, in a controlled way, in order to assess how bad it is compared with other things. Perhaps there would be analytic approaches for predicting what people would say about how bad torture was without actually torturing them to find out. And of course, we could read through humanity's historical record and all the writings on the Internet to learn more about what actual people have said about torture, although we'd need to correct for will-to-live bias and deficits of accuracy when remembering emotions in hindsight. But, importantly, in a CEV scenario, all of those qualifications can be taken into account by people much smarter than ourselves. Of course, this rosy picture is not a likely future outcome. Historically, forces seize control because they best exert their power. It's quite plausible that someone will take over the future by disregarding the wishes of everyone else, rather than by combining and idealizing them. Or maybe concern for the powerless will just fall by the wayside, because it's not really adaptive for powerful agents to care about weak ones, unless there are strong, stable social pressures to do so. This suggests that improving prospects for a reflective, tolerant future may be an important undertaking. Rather than focusing on whether or not the future happens, I think it's more valuable for suffering reducers to focus on making the future better if it happens -by encouraging compromise, moral reflectiveness, philosophical wisdom, and altruism, all of which make everyone better off in expectation. Figure 1 : 1 Figure 1: Plot of threshold values for P as a function of H \n\t\t\t Because nature contains such vast amounts of suffering, I would strongly dislike such a project. I include this quotation for rhetorical effect and to give a sense of how others see the situation. \n\t\t\t Of course, what's compelling to idealized-me would not necessarily be compelling to idealized-you. Value divergences may", "date_published": "n/a", "url": "n/a", "filename": "risks-of-astronomical-future-suffering.tei.xml", "abstract": "It's far from clear that human values will shape an Earth-based space-colonization wave, but even if they do, it seems more likely that space colonization will increase total suffering rather than decrease it. That said, other people care a lot about humanity's survival and spread into the cosmos, so I think suffering reducers should let others pursue their spacefaring dreams in exchange for stronger safety measures against future suffering. In general, I encourage people to focus on making an intergalactic future more humane if it happens rather than making sure there will be an intergalactic future.", "id": "1ee4fa19becb11250cb9ba4cd915a4aa"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Trevor N White", "Seth D Baum", "Patrick Lin", "George Bekey", "Keith Abney", "Ryan Jenkins"], "title": "Liability Law for Present and Future Robotics Technology", "text": "Introduction In June 2005, a surgical robot at a hospital in Philadelphia malfunctioned during a prostate surgery, possibly injuring the patient.  1  In June 2015, a worker at a Volkswagen plant in Germany was crushed to death by a robot that was part of the assembly process.  2  In November 2015, a self-driving car in California made a complete stop at an intersection and then was hit by a car with a human driver, apparently because the self-driving car followed traffic law but not traffic norms.  3  These are just some of the ways that robots are already implicated in harms. As robots become more sophisticated and more widely adopted, the potential for harm will get even larger. Robots even show potential for causing harm at massive catastrophic scales. How should robot harms be governed? In general, liability law governs harms in which someone or something else is responsible. Liability law is used to punish those who have caused harms, particularly those that could have and should have been avoided. The threat of punishment further serves to discourage those who could cause harm. Liability law is thus an important legal tool for serving justice and advancing the general welfare of society and its members. The value of liability law holds for robotics just as it does for any other harm-causing technology. But robots are not just any other technology. Robots are (or at least can be) intelligent, autonomous actors moving about in the physical world. They can cause harms through actions that they choose to make, actions that no human told them to make and, indeed, that may surprise their human creators. Perhaps robots should be liable for their harms. This is a historic moment: humans creating technology that could potentially be liable for its own actions. Furthermore, robots can have the strength of industrial machinery and the intelligence of advanced computer systems. Robots can also be mass produced and connected to each other and to other technological systems. This creates the potential for robots to cause unusually great harm. This paper addresses how liability law can and should account for robots, including robots that exist today and robots that potentially could be built at some point in the near or distant future. Three types of cases are distinguished, each with very different implications. First are cases in which some human party is liable, such as the manufacturer or the human using the robot. These cases pose no novel challenges for liability law: they are handled the same way as with other technologies in comparable circumstances. Second are cases in which the robot itself is liable. These cases require dramatic revision to liability law, including standards to assess when robots can be held liable and principles for dividing liability between the robot and the humans who designed, built, and used it. Third are cases in which the robot poses a major catastrophic risk. These cases merit separate attention because a sufficiently large catastrophe would destroy the legal system and thus the potential to hold anyone or anything liable. The three types of cases differ across two dimensions as shown in Figure  1 . One dimension is the robot's degree of legal personhood, meaning the extent to which a robot shows attributes that qualify it for independent standing in a court of law. As we discuss, a robot can be held liable in the eyes of the law to the extent that it merits legal personhood. The other dimension shows the size of the harm the robot causes. Harms of extreme severity cannot be handled by liability law. However, there is no strict distinction between the three cases. Instead, there is a continuum, as shown by the regions in which a robot can have partial liability or more-than-human liability and in which liability law works to a limited extent.  \n I -A Human Party Is Liable In a detailed study of robot law,  Weaver (2014, 21-27)  identifies four types of parties that could be liable for harm caused by a robot: (1) people who were using the robot or overseeing its use; (2) other people who were not using the robot but otherwise came into contact with it, which can include people harmed by the robot; (3) some party involved in the robot's production and distribution, such as the company that manufactured the robot; or (4) the robot itself. For the first three types of parties, liability applies the same as for other technologies. A surgical robot, for example, can be misused by the surgeon (type 1), bumped into by a hospital visitor who wandered into a restricted area (type 2), or poorly built by the manufacturer (type 3). The same situations can also arise for other, non-robotic medical technologies. In each case, the application of liability law is straightforward. Or rather, to the extent that the application of liability law is not straightforward, the challenges faced are familiar. The fourth type-when the robot is liable-is the only one that poses novel challenges for liability law. To see this, consider one of the thornier cases of robot liability, that of lethal autonomous weapon systems (LAWSs). These are weapons that decide for themselves whom to kill.  Sparrow (2007)  argues that there could be no one liable for certain LAWS harms-for example, if a LAWS decides to kill civilians or soldiers who have surrendered. A sufficiently autonomous LAWS could make its own decisions, regardless of how humans designed and deployed it. In this case, Sparrow argues, it would be unfair to hold the designer or deployer liable (or the manufacturer or other human parties). It might further be inappropriate to hold the robot itself liable, if it is not sufficiently advanced in legally relevant ways (more on this in Section II). In this case, who or what to hold liable is ambiguous. This ambiguous liability is indeed a challenge, but it is a familiar one. In the military context, precedents include child soldiers  (Sparrow 2007, 73-74)  and landmines  (Hammond 2015, note 62) . Child soldiers can make their own decisions, disobey orders, and cause harm in the process. Landmines can linger long after a conflict, making it difficult or impossible to identify who is responsible for their placement. In both cases, it can be difficult or perhaps impossible to determine who is liable. So too for LAWSs. This ambiguous liability can be a reason to avoid or even ban the use of child soldiers, landmines, and LAWSs in armed conflict. Regardless, even for this relatively thorny case of robot liability, robotics technology raises no new challenges for liability law. In the United States, agencies such as the Department of Defense produce regulations on the use of LAWSs which are not dramatically different than for other weapons. Internationally, bodies like the UN's International Court of Justice could hold a state liable for authorizing drone strikes that caused excessive civilian casualties. Meanwhile, commercial drones can be regulated as other aircraft are now: by a combination of the FAA and corporate oversight by their creators  (McFarland 2015) . The handling of such relatively simple robots under liability law will thus be familiar if not straightforward. The above LAWSs examples also resemble how liability law handles non-human animals, which has prompted proposals for robots to be given legal status similar to non-human animals (e.g.,  Kelley et al. 2010) . Suppose someone gets a pet dog and then the dog bites someone, despite the owner trying to stop it. If this person had absolutely no idea the dog would bite someone, then she would not be liable for that bite. However, having seen the dog bite someone, she now knows the dog is a biter, and is now expected to exercise caution with it in the future. If the dog bites again, she can be liable. In legal terms, this is known as having scienterknowledge of the potential harm. Scienter could also apply to LAWSs or other robots that are not expected to cause certain harms. Once the robots are observed causing those harms, their owners or users could be liable for subsequent harms. For comparison, the Google Photos computer system raised controversy in 2015 when it mislabeled photographs of black people as \"gorillas\"  (Hernandez 2015) . No Google programmer instructed Photos to do this; it was a surprise, arising from the nature of Photos's algorithm. Google acted immediately to apologize and fix Photos. While it did not have scienter for the gorilla incident, it would for any subsequent offenses.  4  The same logic also applies for LAWSs or other types of robots. Again, as long as a human party was responsible for it, a robot does not pose novel challenges to liability law. Even if a human is ultimately liable, a robot could still be taken to court. This would occur, most likely, under in rem jurisdiction, in which the court treats an object of property as a party to a case when it cannot do so with a human owner. In rem cases include United States v.  Fifty-Three Electus Parrots (1982) , in which a human brought parrots from southeast Asia to the U.S. in violation of an animal import law, and United States v. Forty Barrels & Twenty Kegs of  Coca-Cola (1916) , in which the presence of caffeine in the beverage was at issue. In both cases, a human (or corporation) was ultimately considered liable, with the parrots and soda only serving as stand-ins. Robots could be taken to court in the same way, but they would not be considered liable except in a symbolic or proxy fashion. Again, since the robot is not ultimately liable, it poses no novel challenges to liability law. This is not to say that such robots do not pose challenges to liability law-only that these are familiar challenges. Indeed, the nascent literature on robot liability identifies a range of challenges, including assigning liability when robots can be modified by users  (Calo 2011) , when they behave in surprising ways  (Vladeck 2014) , and when the complexity of robot systems makes it difficult to diagnose who is at fault  (Funkhouser 2013; Gurney 2013) . There are also concerns that liability laws could impede the adoption of socially beneficial robotics (e.g.,  Marchant and Lindor 2012; Wu 2016 ). However, these challenges all point to familiar solutions based in various ways of holding manufacturers, users, and other human parties liable. Fine tuning the details is an important and nontrivial task, but it is not a revolutionary one. The familiar nature of typical robots to liability law is further seen in court cases in which robots have been implicated in harms  (Calo 2016 ). An early case is Brouse v. United  States (1949) , in which two airplanes crashed, one of which was a US military plane that was using an early form of autopilot. The court rejected the US claim that it should not be liable because the plane was being controlled by the robotic autopilot; instead the court found that the human pilot in the plane is obligated to pay attention and avoid crashes.  More recently, in Ferguson v. Bombardier Services Corp. (2007) , another airplane crash may have been attributable to the autopilot system, in which case the court would have found the autopilot manufacturer liable, not the autopilot itself, but instead it found that the airline had improperly loaded the plane. (See Calo 2016 for further discussion of these and other cases.) \n II -Robot Liability If a robot can be held liable, then liability law faces some major challenges in terms of which robots to hold liable for which harms, and in terms of how to divide liability between the robot and its human designers, manufacturers, users, etc. In this section, we will argue that robots should be able to be held liable to the extent that they qualify for legal personhood. First, though, let us briefly consider some alternative perspectives. One perspective is that, in an informal sense, any sort of object can be liable for a harm. The pollen in the air is liable for making you sneeze. The faulty gas pipe is liable for burning down your home. The earthquake is liable for destroying the bridge. This is not the sense of liability we address in this paper. Our focus is on legal liability, in which a party can be tried in court. Another perspective comes from the notion that the law ultimately derives from what members of a society want it be. This is why laws are different in different jurisdictions and at different times. From this perspective, robots will be held liable whenever societies decide to hold them liable. There are difficult issues here, such as whether to give robots a say in if they should be held liable.  5  Regardless, the fact that laws are products of societies need not end debate on what laws societies can and should have. To the contrary, it is incumbent upon members of society to have such debates. Within human society, in the United States and many other countries, parties can be held liable for harms to the extent that they qualify as legal persons. Legal personhood is the ability to have legal rights and obligations, such as the ability to enter contracts, sue or be sued, and be held liable for one's actions. Legal liability thus follows directly from legal personhood. Normal adult humans are full legal persons and can be held liable for their actions across a wide range of circumstances. Children, the mentally disabled, and corporations have partial legal personhood, and in turn can be held liable across a narrower range of circumstances. Non-human animals generally do not have personhood, though this status has been contested, especially for nonhuman primates.  6  The denial of legal personhood to non-human animals can be justified on grounds that they lack humans' cognitive sophistication and corresponding ability to participate in society. Such justification avoids charges of speciesism (a pro-human bias for no other reason than just happening to be human). However, the same justification implies that robots should merit legal personhood if they have similar capabilities as humans. As  Hubbard (2011, 417)  puts it, \"Absent some strong justification, a denial of personhood to an entity with at least an equal capacity for personhood would be inconsistent and contrary to the egalitarian aspect of liberalism.\"  7  The question of when robots can be liable thus becomes the question of when robots merit personhood. If robots merit personhood, then they can be held liable for harms they cause. Otherwise, they cannot be held liable, and instead liability must go to some human party, as is the case with non-human animals and other technologies or entities that can cause harm. Hubbard proposes three criteria that a robot or other artificial intelligence should meet to merit personhood: (1) complex intellectual interaction skills, including the ability to communicate and learn from experience; (2) self-consciousness, including the ability to make one's own goals or life plan, and (3) community, meaning the ability to pursue mutual benefits within a group of persons. These three criteria, central to human concepts of personhood, may offer a reasonable standard for robot personhood. We will use these criteria for this paper while emphasizing that their definitude should be a matter of ongoing debate. Do Hubbard's criteria also apply for liability? Perhaps not for the criterion of selfconsciousness. The criterion makes sense for harms caused to a robot: only a conscious robot can experience harms as humans do.  8  This follows from, for example, classic utilitarianism, as in Bentham's line \"The question is not, Can they reason? nor, Can they talk? but, Can they suffer?\" However, the same logic does not apply to harms caused by a robot. Consider an advanced robot that meets all of Hubbard's criteria except that it lacks consciousness. Suppose the robot causes some harm-and, to be clear, the harm causes suffering to a human or to some other conscious person. Should the robot be held liable? The answer to this may depend on society's foundational reasoning for liability. If liability exists mainly to discourage or deter the commission of harms, then consciousness is unnecessary. The robot should be punished so long as doing so discourages the commission of future harms. The entities that get discouraged here could include the robot, other similar robots, conscious robots, and even humans. It is quite conceivable that non-conscious robots could be punished with some sort of reduced reward or utility as per whatever reward/utility function they might have  (Majot and Yampolskiy 2014) . Specifically, they could be reprogrammed, deactivated or destroyed, or put in what is known as a \"Box\": digital solitary confinement restricting an AI's ability to communicate or function  (Corwin 2002; Yudkowsky 2002) . To make this possible, however, such robots ought to be based (at least in part) on reinforcement learning or similar computing paradigms (except ones based on neural network algorithms, for reasons we explain later). Alternatively, if liability exists mainly for retribution, to bring justice to whomever committed the harm, then consciousness could be necessary. Whether it is necessary depends on the purpose of the punishment. If the punishment aims to worsen the life of the liable party, so as to \"balance things out,\" then consciousness seems necessary. It makes little sense to \"worsen\" the life of something that cannot experience the worsening. However, if the punishment aims to satisfy society's sense of justice, then consciousness may be unnecessary. Instead, it could be sufficient that members of society observe the punishment and see justice being served.  9  Whether the robot's consciousness would be necessary in this case would simply depend on whether society's sense of justice requires it to be conscious. This potential exception regarding consciousness is a good example of partial liability as shown in Figure  1 . The advanced, non-conscious robot can be held liable, but not in every case in which normal adult humans could. Specifically, the robot would not be held liable in certain cases where punishment is for retribution. Other limitations to a robot's capabilities could also reduce the extent of its liability. Such robots would be analogous to children and mentally disabled adult humans, who are similarly not held liable for as many cases as normal adult humans are. Robots of less sophistication along any of Hubbard's three criteria (or whatever other criteria are ultimately established) should be liable to a lesser extent than robots that meet the criteria in full. What about robots of greater-than-human sophistication in Hubbard's three criteria? These would be robots with more advanced intellectual interaction skills, self-consciousness, or communal living ability. It is conceivable that such robots could exist-indeed, the idea dates back many decades  (Good 1965 ). If they do come into existence, then by the above logic, they should be held to a higher liability standard than normal adult humans. Indeed, concepts such as negligence recognize human fallibility in many respects that a robot could surpass humans in, including reaction time, eyesight, and mental recall. The potential for holding robots to a higher standard of liability could offer one means of governing robots with greater-than-human capacities; more on this in Section III in the discussion of catastrophic risk. Before turning to catastrophic risk, there is one additional aspect of robot liability to consider: the division of liability among the robot itself and other parties that influence the robot's actions. These other parties can include the robot's designer, its manufacturer, and any users or operators it may have. These parties are comparable to a human's parents and employers, though the comparison is imperfect due to basic differences between humans and robots. One key difference is that robots are to a very large extent designed. Humans can be designed as well via genetic screening and related techniques, hence the term \"designer baby.\" But designers have much more control over the eventual character of robots than they do for humans. This suggests that robot designers should hold more liability for robots' actions than human parents should for their children's actions. If robot designers know that certain designs tend to yield harmful robots, then a case can be made for holding the designers at least partially liable for harms caused by those robots, even if the robots merit legal personhood. Designers could be similarly liable for building robots using opaque algorithms, such as neural networks and related deep learning methods, in which it is difficult to predict in advance whether the robot will cause harm. Those parties that commission the robot's design could be similarly liable. In court, the testimony of relevant industry experts would be valuable for proving whether any available, feasible safeguards to minimize such risks existed. Another difference is that, at least for now, the production of robots is elective, whereas the birthing of humans is required for the continuity of society. Society cannot currently function without humans, but it can function without robots. This fact suggests some lenience for parents in order to encourage procreation, and to be stricter with robot designers in order to safely ease society's transition into an era in which humans and their robot creations coexist. Such a gradual transition seems especially warranted in light of potential robot catastrophe scenarios. \n III -Catastrophic Robot/AI Liability \"Catastrophe\" has many meanings, many of which require no special legal attention. For example, a person's death is catastrophic for the deceased and her or his loved ones, yet the law is perfectly capable of addressing individual deaths caused by robots or AIs. However, a certain class of extreme catastrophe does merit special legal attention, due to its outsized severity and significance for human civilization. These are catastrophes that cause major, permanent harm to the entirety of global human civilization. Such catastrophes are commonly known as global catastrophes  (Baum and Barrett 2016)  or existential catastrophes  (Bostrom 2013) . Following  Posner (2004) , we will simply call them catastrophes. A range of catastrophic risks exist, including global warming, nuclear war, a pandemic, and collision between Earth and a large asteroid or comet. Recently, a body of scholarship has built up analyzing the possibility of catastrophe from certain types of future AI. Much of the attention has gone to \"superintelligent\" AI that outsmart humanity and \"achieve complete world domination\"  (Bostrom 2014, 78 ; see also  Müller 2015) . Such AI could harm humans through the use of robotics. Additionally, some experts believe that robotics could play an important role in the development of such AI  (Baum et al. 2011) . Other catastrophe scenarios could also involve robotics. Robots could be used in the systems for launching nuclear weapons or for detecting incoming attacks, potentially resulting in unwanted nuclear wars.  10  They could be used in critical civil, transportation, or manufacturing infrastructure, contributing to a global systemic failure.  11  They could be used for geoengineering -the intentional manipulation of the global environment, such as to counteract global warming -and this could backfire, causing environmental catastrophe.  12  Robots could be used in establishing or maintaining an oppressive totalitarian world government.  13  Still further robot catastrophe scenarios may also be possible. The enormous scale of the catastrophes in question creates profound moral and legal dilemmas. If the harm is permanent, it impacts members of all future generations, which could be immensely many people. Earth will remain habitable for at least a billion more years, and the galaxy and the universe for much longer  (Baum 2016) ; the present generation thus contains just a tiny fraction of all people who could exist. The legal standing and representation of members of future generations is a difficult question  (Tonn 1996; Wolfe 2008 ). If members of future generations are to be counted, then they can overwhelm the calculus. Despite this, present generations unilaterally make the decisions. There is thus a tension in how to balance the interests of present and future generations  (Page 2003) . A sufficiently large catastrophe raises similar issues even just within the context of the present generation. About seven billion humans live today; a catastrophe that risks killing all of them could be seven billion times larger than a catastrophe that risks killing just one. One could justify enormous effort to reduce that risk regardless of future generations  (Posner 2004) . Further complications come from the irreversible nature of these catastrophes. In a sense, every event is irreversible: if someone wears a blue shirt today, no one can ever change the fact that they wore a blue shirt today. Such events are irreversible only in a trivial sense: you can change what shirt you wear on subsequent days. Nontrivially irreversible events are more or less permanent: if that person should die today, then nothing 14 can bring that person back to life. At a larger scale, nontrivially irreversible effects exist for many ecological shifts and may also exist for the collapse of human civilization  (Baum and Handoh 2014) . The possibility of large and nontrivially irreversible harm creates a major reason to avoid taking certain risks. The precautionary principle is commonly invoked in this context, raising questions of just how cautious to be  (Posner 2004; Sunstein 2006 ). An irreversible AI catastrophe could be too large for liability law to handle. In the simplest case, if the catastrophe results in human extinction, then there would be no one remaining to hold liable. A catastrophe that leaves some survivors but sees the collapse of human civilization would lack the legal system needed for holding people liable. Alternatively, AI could cause a catastrophe in which everyone is still alive but they have become enslaved or otherwise harmed by the AI; in this case the pre-catastrophe human authorities would lack the power needed to hold those at fault liable. For smaller catastrophes, the legal system may exist to a limited extent (Figure  1 ). In this case, it may be possible to bring the liable parties to trial and/or punish them, but not as reliably or completely as is possible under normal circumstances. The closest possible example would be creating special international proceedings, like the Nuremberg Trials, to deal with the aftermath. Much like such war tribunals, though, these may do little to address the chaos' original cause. This would leave victims or society at large wasting time and resources on reliving a tragedy  (McMorran 2013) . Hence, instead of liability, a precautionary approach could be used. This would set a default policy of disallowing any activity with any remote chance of causing catastrophe. It could further place the burden of proof on those who wish to conduct such activity, requiring them to demonstrate in advance that it could not cause catastrophe.  15  Trial-and-error would not be permitted, because a single error could cause major irreversible harm. This would likely be a significant impediment for AI research and development (at least for the subset of AI that poses catastrophic risk), which, like other fields of technology, is likely to make extensive use of trial and error. Indeed, some AI researchers recommend a trial-and-error approach, in which AIs are gradually trained to learn human values so that they will not cause catastrophe  (Goertzel 2016) . However, given the high stakes of AI catastrophe, perhaps these sorts of trial-and-error approaches should still be avoided. It may be possible to use a novel liability scheme to assist with a catastrophe-avoiding precautionary approach. In a wide-ranging discussion of legal measures to avoid catastrophe from emerging technologies,  Wilson (2013, 356)  proposes \"liability mechanisms to punish violators whether or not their activities cause any harm\". In effect, people would be held liable not for causing catastrophe, but for taking actions that could cause catastrophe. This proposal could be a successful component of a precautionary approach to catastrophic risk and is worth ongoing consideration. Taking the precautionary principle to the extreme can have undesirable consequences. All actions carry some risk. In some cases, it may be impossible to prove a robot does not have the potential to cause catastrophe. Therefore, requiring demonstrations of minimal risk prior to performing actions would be paralyzing  (Sunstein 2006) . Furthermore, many actions can reduce some risks even while increasing others; requiring precaution due to concern about one risk can cause net harm to society by denying opportunities to decrease other risks  (Wiener 2002) . AI research and development can pose significant risks, but it can also help reduce other risks. For AI that poses catastrophic risk, net risk will be minimized when the AI research and development is expected to bring a net reduction in catastrophic risk  (Baum 2014) . In summary, there are significant legal challenges raised by AI that poses catastrophic risk. Liability law, most critically, is of little help. Precautionary approaches can work instead, although care should be taken to avoid preventing AI from reducing different catastrophic risks. The legal challenges from AI that poses catastrophic risk is distinct from the challenges from other types of AI, but they are similar to the challenges from other catastrophic risks. \n Conclusion While robots benefit society in many ways, they also cause or are otherwise implicated in a variety of harms. The frequency and size of these harms is likely to increase as robots become more advanced and ubiquitous. Robots could even cause or contribute to a number of major global catastrophe scenarios. It is important for liability law to successfully govern these harms to the extent possible so that the harms are minimized and, when they do occur, that justice may be served. For many robot harms, a human party is ultimately liable. For these harms, traditional liability law applies. A major challenge to liability law comes when robots could be liable. Such cases require legal personhood tests for robots to assess the extent to which they can be liable. One promising personhood test evaluates the robot's intellectual interaction skills, selfconsciousness, and communal living ability. Depending on how a robot fares on a personhood test, it could have the same liability as, or less or more liability than, a normal adult human. A robot being liable does not preclude a human party also being liable. Indeed, robot designers should expect more liability for robot harms than would human parents, because robots are designed so much more extensively than human children are. Finally, for robots that pose catastrophic risk, liability law cannot be counted on and a precautionary approach is warranted. People involved in the design, manufacture, and use of robots can limit their liability by choosing robots that reliably avoid harms. One potential way to improve reliability is to avoid computing paradigms such as neural nets that tend to result in surprising behaviors, or adapt these paradigms to make them less surprising  (Huang and Xing 2002) . Robot designs should be sufficiently transparent that the responsible human parties can, with reasonable confidence, determine in advance what harms could occur. They can then build safety restrictions into the robot or at least give warnings to robot users, as is common practice with other technologies. Robots should also go through rigorous safety testing before being placed into situations where they can cause harms. If robots cannot reliably avoid harms, then they probably should not be used in the first place. These sorts of safety guidelines should be especially strict for robots that could contribute to major global catastrophe. A single catastrophe could permanently harm human civilization. It is thus crucial to avoid any catastrophe. Safety testing itself could be dangerous. This increases the value of transparent computing paradigms that let humans assess risks prior to building the robot. Legal measures must also take effect prior to the robot's build because there may be no legal system afterwards. Advanced robots may be less likely to cause catastrophe if they are designed to be upstanding legal persons. But even then, some legal system would need to exist to hold them liable for what harms they cause. As this paper illustrates, robot liability poses major new challenges to liability law. Meeting these challenges requires contributions from law, robotics, philosophy, risk analysis, and other fields. It is essential for humans with these various specialties to work together to build robot liability regimes that avoid harms while capturing the many benefits of robotics. The potential for harm is extremely large, making this an urgent task. We hope that humans and robots will coexist successfully and for mutual benefit in a community of responsible persons. Figure 1 . 1 Figure 1. Classification scheme for the applicability of liability law to various sizes of harms caused by various types of robots.", "date_published": "n/a", "url": "n/a", "filename": "026_robot-liability.tei.xml", "abstract": "Advances in robotics technology are causing major changes in manufacturing, transportation, medicine, and a number of other sectors. While many of these changes are beneficial, there will inevitably be some harms. Who or what is liable when a robot causes harm? This paper addresses how liability law can and should account for robots, including robots that exist today and robots that potentially could be built at some point in the near or distant future. Already, robots have been implicated in a variety of harms. However, current and near-future robots pose no significant challenge for liability law: they can be readily handled with existing liability law or minor variations thereof. We show this through examples from medical technology, drones, and consumer robotics. A greater challenge will arise if it becomes possible to build robots that merit legal personhood and thus can be held liable. Liability law for robot persons could draw on certain precedents, such as animal liability. However, legal innovations will be needed, in particular for determining which robots merit legal personhood. Finally, a major challenge comes from the possibility of future robots that could cause major global catastrophe. As with other global catastrophic risks, liability law could not apply, because there would be no postcatastrophe legal system to impose liability. Instead, law must be based on pre-catastrophe precautionary measures.", "id": "ce9685f2fde6dc3def3a5abe27299fad"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "reddy20a-supp.tei.xml", "abstract": "Maximizing uncertainty. Following Lakshminarayanan  et al. (2017), we measure ensemble disagreement using the average KL-divergence between the output of a single ensemble member and the ensemble mean, where p ✓ is the reward classifier defined in Section 3.2. Maximizing novelty. In this work, we use a distance function that computes the Euclidean distance between state embeddings, where f is the state encoder trained in step (1).", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kyle Bogosian"], "title": "Implementation of Moral Uncertainty in Intelligent Machines", "text": "Introduction Advances in artificial intelligence have led to research into methods by which sufficiently intelligent systems can be guaranteed to follow ethically defensible behavior. Successful implementation of moral reasoning may be critical for managing the proliferation of autonomous vehicles, workers, weapons, and other systems as they increase in intelligence and complexity. Approaches towards moral decision making generally fall into two camps, \"topdown\" and \"bottom-up\" approaches  (Allen et al. 2005) . Top-down morality is the explicit implementation of decision rules into artificial agents. Schemes for top-down decision making that have been proposed for intelligent machines include Kantian deontology  (Arkoudas et al. 2005 ) and preference utilitarianism  (Oesterheld 2016) . Bottom-up morality avoids reference to specific moral theories by developing systems that can implicitly learn to distinguish between moral and immoral behaviors, such as cognitive architectures designed to mimic human intuitions  (Bello and Bringsjord 2012) . There are also hybrid approaches which merge insights from the two frameworks, such as one given by  Wiltshire (2015) . \n The Problem of Moral Disagreement A problem which has been cited as an obstacle to the development of machine ethics is the lack of agreement among moral philosophers on which theory of ethics should be followed  (Shulman et al. 2009; Bello and Bringsjord 2012; Bostrom 2014; Brundage 2014 ). The 2009 PhilPapers survey of philosophy faculty revealed that 26% accepted or leaned towards deontology, 24% accepted or leaned towards consequentialism, 18% accepted or leaned towards virtue ethics, and the remaining 32% favored other approaches entirely. For someone who believes in a particular approach to ethics, the correct system for implementation in artificial moral agents may be obvious, but the path forward for institutions and society as a whole remains unclear. Companies, governments, and researchers will have to decide which system to use for artificial agents and will be faced with a difficult choice between competing moral paradigms. This paper will describe a computational framework that will determine how we should design moral machines in the light of this disagreement, but first it is necessary to determine exactly why moral disagreement is a problem. Just because there exists disagreement does not necessarily imply that research and development programs cannot succeed in their objectives, nor does it necessarily imply that we need to worry about differences in opinion. The aforementioned works do not explicitly describe how moral disagreement would prevent us from building satisfactory moral machines, so we will need to clarify the nature of the problem before proceeding with a solution. There are two plausible reasons for why moral disagreement can pose a serious problem for the project of machine ethics. First, it could be a pragmatic problem as disagreements among engineers, policymakers and philosophers interfere with projects that require cooperation. In a worst-case scenario, decisions over which research programs to fund will turn into bitter ideological battles, research agencies will become bogged down in disputes, and developers will split up their resources and devolve into a competitive mindset which reduces information sharing and slows research progress, thus making it more difficult to construct moral machines. Second, it could be a moral problem. If we are so uncertain about morality and are split across many different moral principles, then the likelihood that anyone's particular moral system is entirely correct is statistically extremely low  (Shulman et al. 2009) . Therefore, if we do build AIs grounded in any particular moral system, then they will probably be making many poor moral decisions.  Bello and Bringsjord (2012)  argue that moral disagreement provides a reason to avoid top-down approaches to machine ethics in favor of bottom-up or hybrid approaches that copy or take inspiration from human moral thinking. However, it is not clear how this would solve the problem of disagreement. The authors claim that people can agree on examples of good moral behavior despite disagreeing over specific theories, but people's personal moral judgements can differ as widely as moral theories do when faced with moral dilemmas  (Greene et al. 2001 ) and when they are considering politicized moral issues such as racial fairness, animal farming, and economic inequality. Therefore, even if we attempt to circumvent normative disputes by eschewing top-down ethics in favor of bottom-up frameworks, it is perfectly plausible that researchers and government regulators with strong value disagreements will come into conflicts over the kinds of moral intuitions and data which should or shouldn't play a role in automated reasoning.  Brundage (2014)  also notes that there is no reason to expect that Bello and Bringsjord's approach would actually be reliably ethical. Moreover, in the cases where people do agree on moral choices despite disagreeing over moral theories, there is neither a pragmatic nor a philosophical problem with the top-down approach: a utilitarian engineer has no moral reason to care whether a robot's computational pattern is internally utilitarian or not, as long as it is actually maximizing utility; more generally, if we know that machines will act in the morally right way, then we have no reason to consider the specific programming of machine code to be morally significant. So to the extent that moral disagreements between ethical theories might pose pragmatic and moral problems for the development of top-down computational ethics, they would pose equal pragmatic and moral problems for the development of bottom-up computational ethics. \n An Example of Intractable Disagreement We can illustrate this problem with a case of self-driving cars which must be programmed to decide whether to swerve to avoid animals in the path of the vehicle. Various vehicle speeds, warning times, road shapes, weather conditions and other factors can make the decision to avoid animals more or less dangerous to the occupants of the vehicle in different situations, and different moral theories can mandate different choices in such cases. One moral principle which could specify when vehicles should or should not swerve could be described as the commensurable view. Under this doctrine, animal lives should be treated as if they are worth some small fraction of what human lives are worth. In addition, let us suppose that animals with a presumed greater capacity for cognition and pain sensations should be granted a greater weight in such tradeoffs. The machine, upon calculating a sufficiently low estimate of the probability that swerving would result in human fatality or verifying some heuristical checklist of features of the situation, would avoid the animal. The commensurable view is most clearly reminiscent of utilitarianism, but other moral theories may embrace it nonetheless-for instance, one could follow a mixed theory incorporating both deontological and consequentialist ethics and believe that consequentialist considerations dominate in this particular kind of situation. Vehicles acting in this manner can be statistically expected to eventually cause a few human fatalities but also to save many animals. If two people agreed on the commensurable view but disagreed on the specific tradeoff, compromise would be relatively straightforward. For instance, if one side argued that the chance of a fatal accident would have to be under 1 in 1000 in order to swerve for a certain animal while another side argued that it should be 1 in 10,000, they could plausibly compromise at 1 in 5500, which would function as a pragmatic truce and a limit to the degree of moral harm perceived by either viewpoint. The more pressing concern is how to compromise with the incommensurable view-that humans can never be placed at additional risk of fatality in order to save animals. This might be supported by moral theories emphasizing human rights and liberty. Since this view fundamentally rejects the axiological assumptions of the other and holds that no tradeoff is permissible, there is no obvious 'halfway point' where the competing principles can meet. Unilaterally selecting one principle to govern vehicle behavior would not be acceptable for the reasons described previously. Training the driving system to determine the correct action through supervised learning would only rephrase the issue by forcing us to decide which training examples ought to be classified as right or wrong. Allowing the company to decide based on its own interests would not clearly lead to safe and ethical behavior. Laws do not provide sufficient guidance in all such situations to govern the behavior of machines, since they are often left to the conscience of a human agent. Finally, human operators cannot be guaranteed to be available to make such quick decisions, to reliably specify their preferences beforehand, or to act ethically at all. The last resort would be for the vehicles to rely on a random number generator and follow the commensurable view half of the time and the incommensurable view half of the time. At first glance, this is the only straightforward way to build a system in a way that does not overwhelmingly disfavor one particular theory: if we cannot compromise between two views on how to act in a particular repeated decision by generating a new view, then the only way to act fairly is to alternate between them. Unfortunately, this sacrifices predictability by inducing stochasticity into decision making. Furthermore, it is not Pareto optimal. A vehicle which was programmed to randomly select the commensurable view in half and only half of relevant situations could be modified so that it specifically did so for the half of situations where the animal under threat was relatively important under the commensurable view. This makes it more predictable, since its decisions are deterministic given the environments that it encounters. It also counts as a moral improvement by the lights of the commensurable view, because it prioritizes the animals which are regarded as more important. At the same time, it is no worse according to the incommensurable view, which could be indifferent to exactly which animals are saved. This makes the change a Pareto improvement. We can generalize this strategy by saying that we are keeping all moral theories in play at the time of decision making, and searching for actions which provide the most value across all of them, rather than seeking to select one moral theory and ignoring others. This procedure, however ad hoc, seems to be the best possible way of approaching this particular case, and its principles could be fruitfully applied to other cases where moral values are not just in disagreement but wholly incommensurable. Ideally, we should have a rigorous theoretical framework which does similar work in the broad variety of moral situations by taking all moral preferences into consideration and responding appropriately. \n Dealing with Moral Disagreement Properly Moral disagreement has been recognized as a problem for normative ethics proper, independent of any concerns regarding machine ethics. A direct approach to overcoming it is to assume that there is a correct moral theory which we are searching for, acknowledge that we are fundamentally uncertain about which moral theory is correct, and then act in such a way as to give some weight to the judgements of different theories. More generally, given the failure of moral philosophy to reach satisfactory conclusions, it can be argued that we should adopt a framework of reasoning which takes multiple moral views into account  (Lockhart 2000) . However, the idea that we ought to change our behavior in accordance with moral uncertainty is controversial, and many philosophers have attempted to address the various mathematical and philosophical problems involved with the concept (Z ˙uradzki 2016). In particular, it has been argued that making comparisons between the values and judgements of different moral theories is impossible  (Nissan-Rozen 2015) . A recent proposal aimed at answering these concerns was developed by William MacAskill in an extensive thesis (2014). It avoids objections based on incomparability and incommensurability by developing moral uncertainty as a voting problem among moral theories (MacAskill 2016). Voting provides a close analogy with the pragmatic problems faced by machine ethics: as voting is the general process by which decisions are made from the preferences of a population, computations of moral uncertainty represent a process by which agents can act in accordance with the diverse values of humanity. Since MacAskill's proposal works as a voting system where theories have equal say adjusted by their probability of being correct, it also approximates the framework which has been suggested for meta-moral reasoning by Nick  Bostrom (2009) . The rest of this paper will develop and defend the use of this model for machine ethics. \n Maximizing Expected Choiceworthiness The scheme presented in \"Normative Uncertainty\" (MacAskill 2014) is to make action-guiding judgements based on all moral theories in which the agent has some level of credence. MacAskill defines his approach as a metanormative theory, characterized as follows: The agent investigates a decision-situation comprising a quintuple 〈S, t, A, T, C〉 where S is the decision maker, t is the time, and A is the set of possible actions to take. T is the set of normative theories being considered, where a theory T i is a function of decision-situations that produces a cardinal or ordinal choiceworthiness score for actions CW i (A) for all actions a ∈ A. C(T i ) is a credence function assigning values in [0, 1] to every T i ∈ T. A metanormative theory is a function of decision-situations that produces an ordering of the actions in A in terms of their appropriateness. MacAskill distinguishes between moral theories which assign cardinal rankings to options, as utilitarianism would, and moral theories which assign ordinal rankings. When it comes to cardinal theories, MacAskill also distinguishes between sets of theories with moral values which are directly comparable and other cardinal theories which are incomparable with any other theory. He proposes the metanormative theory of maximizing expected choiceworthiness (MEC), the steps of which are as follows: 1. Each set K of k moral theories in which the choiceworthiness rankings of options are cardinal and intertheoretically comparable are aggregated into single theories, where C T K ð Þ ¼ X k i¼1 CðT i Þ CW K A ð Þ ¼ P k i¼1 CW i A ð ÞC T i ð Þ P k i¼1 C T i ð Þ In other words, the credence in the new theory equals the sum of the agent's credences in each of the individual theories in the set, and the choiceworthiness of an option according to the new theory is the credence-weighted average of the choiceworthiness of the option in all of the individual theories. 2. The rankings of options according to each ordinal theory o are used to provide choiceworthiness scores of options using a modified Borda scoring rule that is designed to properly account for ties, denoted here as CW B . The score for an option is equal to the number of worse options minus the number of better options. CW B o A ð Þ ¼ a 2 A : CW o a ð Þ\\CW o A ð Þ j j À a 2 A : CW o a ð Þ j i CW o A ð Þj This violates the independence of irrelevant alternatives, but MacAskill provides reasons to allow the violation. First, independence of irrelevant alternatives is the least essential of all the axioms present in Arrow's Impossibility Theorem, and if a different axiom were to be violated then there would be no prospects for a satisfactory metanormative account involving ordinal moral theories. Second, the primary motivation for independence of irrelevant alternatives is that it combats tactical voting, but tactical voting is not a problem with moral theories: theories aren't agents, and a moral agent can't conceal information from itself. Third, there are some moral cases where we would expect the independence of irrelevant alternatives to be violated (MacAskill 2014, p. 85). 3. The options' scores provided by each of the aggregated sets of cardinal comparable theories, the scores provided by each of the ordinal theories, and the scores provided by each of the cardinal incomparable theories p are all divided by the respective standard deviations of the moral rankings which the moral theories (or sets of intertheoretically comparable cardinal theories) provide over a general set G of actions. This provides normalized choiceworthiness rankings and is the only possible way of equalizing the value of voting for each value system (Cotton-Barratt 2013), which (as MacAskill argues, p. 115) performs the role of giving each theory equal say. CW N K ðAÞ ¼ CW K ðAÞ r CW K ðGÞ ð Þ CW N o ðAÞ ¼ CW B o ðAÞ r CW B o G ð Þ À Á CW N p A ð Þ ¼ CW p A ð Þ r CW p G ð Þ À Á A note on G: it is necessary for variance normalization that a representative set of actions (the \"general set\") be defined for computing the variance. This provides the background against which theories can describe whether a decision is comparatively important or comparatively unimportant from the point of view of a particular theory. MacAskill thinks that a broad account featuring many actions in this set, rather than just the ones under consideration in the present decision-situation, is theoretically desirable. Here I follow suit and model the process as if we are providing moral machines with large arrays of data representing many possible moral decisions, so that calculating the variance only needs to be done once before the resulting number is used and shared by many agents. Variance normalization also violates the independence of irrelevant alternatives, but it is a necessary violation for this application. In order to perform comparisons across moral theories, we need to determine the amount of weight which a value system places on a particular issue compared to other issues. Since different computational approaches to ethics can have wildly differing numerical outputs, it would be impossible to do this fairly without normalizing. 4. Each option is scored with the credence-weighted average of the variancenormalized scores provided by the normative theories. This provides a ranking of expected choiceworthiness: CW E A ð Þ ¼ X n i¼1 CW N i A ð ÞC T i ð Þ Then the agent chooses the action A which maximizes CW E (A). The full description and defense of each step in the theory, provided as a model for human decision making, is given by MacAskill (2014). The computational complexity of an algorithm implementing this procedure is OðjAj à jTjÞ, as adding another action requires a fixed series of evaluations to be done by each moral theory and adding another moral theory requires it to perform a fixed series of evaluations to be performed on each action. The calculation itself is very simple; almost all of the time and memory requirements will presumably stem from the computations of the moral theories themselves. \n Motivation for Maximizing Expected Choiceworthiness in Artificial Intelligence The effect of the system described above is that an agent will make prudent decisions that aim to take the most broadly desirable action in accordance with various people's values, and will avoid the very counterintuitive actions which are considered to be problems for various moral theories. For instance, when presented with the opportunity to commit a great deception in order to gain a small increment of happiness, an agent will refrain even if they view consequentialism as more likely than nonconsequentialist theories, because the relative wrongfulness of the act according to nonconsequentialist theories is significant whereas the relative benefit under consequentialism is minor. Likewise, even if an agent believes that it is probably not morally obligated to refrain from actions which cause significant indirect harms to others, it will nevertheless refrain from being careless in such a way, because the scale of the moral harms it would be committing if it were wrong would be significant. This will limit the degree to which machines will behave in ways which are considered very objectionable by minority views. This does not change the fact that a machine which maximized expected choiceworthiness could still be expected to take many actions which various parties consider to be morally wrong. Despite its superficial similarity to maximizing consequentialism, it would often sacrifice good consequences in favor of satisfying the values of other moral theories. So the adherents of most moral theories would theoretically prefer that machines be built according to their own specifications. But they cannot realistically expect the rest of industry and society to agree with them. So the actual outcome of widespread adherence to naı ¨ve individually rational behavior would be a patchwork of competing agents with different values. Not only would this leave both the pragmatic and the moral problems of disagreement unresolved, but it would leave parties with little ability to influence the world except for whatever agents they could develop as representatives for their own values. However, if parties were to agree on developing systems based upon moral uncertainty, their most critical respective interests would be given relatively high weight in all moral machines by the mechanism of variance voting. By reducing conflicts between agents, promoting cooperative machine development, and allocating value systems' decision making power to the situations which they care most about, a universal framework of moral uncertainty would solve the multiagent prisoner's dilemma constituted by machine ethics and would generally lead to a better outcome for different value systems than the situation in which there was pure disagreement. Needless to say, if an individual did accept MacAskill's thesis and believed that we ought to maximize expected choiceworthiness as human agents, then she would have a direct and compelling reason to support the implementation of the theory in computational systems. But the argument for developing machines based on maximizing expected choiceworthiness is not dependent upon the claim that we humans actually have metanormative reasons to act in such a way. An analogy with voting is illuminating: very few people believe that the winner of an election is always the one who would be the best leader, but most people agree with the system, as it is a necessary and effective compromise. So as long as we disagree with each other about ethics, we should still agree to construct moral machines based on uncertainty even if we reject the idea as a guide for human behavior. \n The Long Term Future If we look at the long run future of artificial intelligence development, there are additional reasons for supporting a framework of acting in accordance with moral uncertainty. First, if an individual is confident in her moral beliefs and possesses an expectation of progress towards objective truth in moral philosophy, then she should expect morally uncertain agents which reflect human knowledge to converge towards her beliefs in the long run. This will limit the degree to which she can expect their behaviors to be objectionable relative to those of an ideal agent which has the right views from the outset. Second, sufficiently competent machines which adhere to a particular value function are likely to pursue it endlessly with pathological consequences  (Bostrom 2012) . While this paper is not intended as a complete solution for value selection and alignment in arbitrarily intelligent agents, it is nevertheless valuable to start by designing systems that cooperate among different value systems, as that will improve the fail-safety of agents which become very intelligent but have imperfect goal functions  (Gloor 2016) . The framework proposed here clearly fulfills that criterion, and therefore serves as a potential backup or other component of a multilayered utility function even if it is not ordinarily utilized  (Oesterheld 2016) . Third, as machines become more intelligent, they might perform more moral functions autonomously, such as updating credences in moral theories and even generating new ones, depending on the degree to which progress in artificial intelligence enables them to investigate questions in moral philosophy. MacAskill (2014, ch. 7) points out that a more accurate credence function improves the expected choiceworthiness of an MEC agent's actions, so such an agent would be intrinsically motivated to expend effort into updating and improving their moral beliefs if they had acceptable criteria for determining moral truth. This is particularly desirable since there may be cases of widespread moral wrongdoing which most humans have consistently failed to identify  (Williams 2015) , which machines should be incentivized to avoid. \n How to Build an Uncertain Machine \n Ordinal and Cardinal Scoring One of the requirements of this framework is that moral theories actually provide rankings over actions. Perhaps the majority of moral theories provide neither cardinal nor ordinal rankings at first glance. However, this is a surmountable issue. First, it simply seems obvious that just about any moral theory should be able to rank certain impermissible actions, such as torturing a large number of people, as worse than other impermissible actions, like stealing someone's coffee, even if such rankings have not yet been made explicit in the philosophical literature. Second, any moral theory which judges the actions of machines can at least provide a rudimentary score system rooted in deontic logic, with 0 for all impermissible actions and 1 for all permissible actions, even if nothing else about the theory is formalized. So any moral theory must at least be translatable to a basic two-level ordinal ranking over actions, which would enable it to be implemented in this framework. If such an implementation is too coarse to adequately represent the values of such a theory, then its proponents have the option and the incentive to clarify and improve it. Defining precise scores could require varying degrees of input from humans depending on the complexity of the moral theory. However, computational approaches towards morality may provide numerical values and rankings which are otherwise absent from moral theory. Computational reasoning differs from human thinking and the procedures required for providing moral judgements in artificial intelligence systems may involve functions from which meaningful ordinal, integer or real-valued scores for actions can be extracted. Scores could be derived from the degree of rightfulness or wrongfulness of an action and/or the degree of certainty given by a moral algorithm as to whether an action is right or wrong. While the philosophical theory of MEC may seem to only refer to rigidly defined moral theories, a top-down approach to machine ethics is not required with this proposal for machine ethics. There is no computational necessity for the 'theories' implemented in the system to all be explicit moral theories in the philosophical sense. One or more bottom-up decision making systems might be included; for instance, the output of a complicated learned function intended to model human intuitions can be treated as a choiceworthiness ranking. As long as it ranks actions by normative criteria and has some probability of being the correct way for a machine to behave, it satisfies the requirements proposed by MacAskill for being a moral theory. \n Credences The outcomes of comparisons will always crucially depend upon the credence function C-an assignment of probabilities to various moral theories of being correct. There are multiple ways of determining these values. Lengthy and difficult approaches which rely on extensive human input are acceptable, as information modifying the credence function could be generated just once and then distributed to many agents as an update. Artificial agents with humanlike intelligence could presumably reason about morality for themselves, but this is not an option for the foreseeable future. One option is to make credences which reflect the beliefs of moral philosophers. The credence assigned to a moral theory would then be equivalent to the proportion of philosophers who affirm the theory, or possibly a score computed from a more sophisticated set of votes taking philosophers' full credences and rankings into account. However, the assumption that moral philosophers are in fact authorities regarding moral philosophy in the same way that practitioners of other disciplines are experts in their respective domains is highly controversial, and has been attacked by  Archard (2011) ,  Cross (2016)  and others. Moreover, the type of moral expertise which provides judgements about which actions and theories are right or wrong is merely one type of moral expertise which may not hold even if others do  (Driver 2014; Jones and Schroeter 2012) . Finally, the judgements of moral philosophers have been shown to be vulnerable to systematic cognitive bias  (Schultz et al. 2011; Schwitzgebel and Cushman 2012) . However, there are a few differences when it comes to the case of assigning credences to a system of maximizing expected choiceworthiness in machine intelligence on the basis of a broad survey of moral philosophers' beliefs. First, the system is not deferring to the views of any particular philosopher or group of philosophers. Rather, it is making decisions based upon all philosophers' views in accordance with how prevalent they are; the views of disagreeing philosophers are being used to support the proposition that both views are approximately equally likely to be correct, rather than the proposition that either particular view happens to be correct. Therefore, the argument from disagreement as presented by  Cross (2016)  against a strong conception of moral expertise does not apply to this case. Second, the system of decision making presented here is specifically designed for use by artificial agents rather than humans. Artificial intelligence systems are not voting participants of democracy and cannot be described as flourishing, so to whatever extent there is moral expertise, it is not wrong for machines to defer to it, as  Archard (2011)  argues is the case for humans. The above points leave many of the arguments against moral expertise unaddressed, and resolving that debate is beyond the scope of this paper. But given that we do not possess artificial general intelligence capable of comprehending and judging moral theory, the practical alternative to deferring to moral philosophers is not for agents to make choices for themselves, which is the context for the ordinary debate on moral expertise, but it is to defer to the judgements of other members of society besides philosophers. But non-philosophers would necessarily be making moral judgements in the same context of controversy over the nature and status of moral knowledge, and they would presumably be vulnerable to cognitive bias just as professional philosophers are, so any claim for their expertise would be the target of arguments similar to those leveled against professional philosophers. So there is a prima facie case for deferring to moral philosophers for determining machine credences which is stronger than the case for deferring to moral philosophers for making moral judgements in ordinary contexts, and no fundamental reason to defer to non-philosophers for determining credences. However, there may be contingent reasons to defer to non-philosophers based on various traits and characteristics commonly possessed by philosophers and non-philosophers. First, moral expertise might exist in the form of practical experience and wisdom rather than any kind of academic knowledge  (Jones and Schroeter 2012) . If individuals with particular virtues, experiences, and character traits are regarded as moral authorities, then credences should be assigned in a way that reflects how they act in different situations. Second, even if being a philosopher counts as a reason in favor of attributing moral expertise, our available community of philosophers could be a predictably flawed group to defer to. One reason for this is that they are not representative of the broader human population, whether measured by socioeconomic status, race, gender, nationality, personality type, political ideology, or other characteristics which are often correlated with different opinions about morality. But the most reasonable solution to this problem is to weight the votes of philosophers, or virtuous wise people as proposed above, on the basis of the uniqueness of the various backgrounds and perspectives which they represent, since it preserves the presence of a community with (arguable) moral expertise while functionally acting similarly to a hypothetical group of philosophers with an ideal composition from various demographic groups. Unfortunately it is not obvious what composition of judges would be appropriate for determining credences. For instance, the fact that orphans comprise 2% of people in the world does not necessarily imply that a voting body comprised of 2% orphans and 98% nonorphans will have more accurate views on ethics than any other mix. It may be the case that both groups of people have equally sound perspectives which must be weighed against each other, and so each orphan's vote should have forty-nine times as much weight as a nonorphan's vote. Alternatively, suppose for the purpose of the example that nonorphans tend to make more accurate moral claims on average for whatever reason. Then only the votes of nonorphans might be given significant weight. Or a combination of these and other factors could imply anything in between. This lack of clarity does not imply that we should just weight all votes equally and ignore concerns about diverse representation, but it shows that the selection of an optimal standard is likely to be more difficult than it naively appears. Instead of trying to determine a single universal method of assigning credences, different kinds of artificial agents may have credences assigned differently to suit the contexts in which they operate, just as jury selection methods vary in order to ensure fairness in different types of legal cases. Therefore, fully specifying a method of determining credences is beyond the scope of this paper. Also, while complete data on potential credence judges' moral views and other characteristics to use for this project may currently be lacking, this does not present a great barrier for creating morally uncertain artificial agents, since the credence function can be used broadly and need not be computed separately and repeatedly for too many scenarios. Specialized focus groups, panels, surveys and other activities can be run occasionally at low cost to the overall industry. In one respect, the current lack of relevant data is actually a good thing: the selection of a method of assigning credences should be performed from a state of as much ignorance as possible regarding the particular moral credences which will be delivered by that method, in order to ensure that the decision making process is unbiased and focuses on the prior philosophical reasons for or against the method of assigning a credence function rather than reflecting whatever moral credences we have in the first place. \n Limited Approaches Deploying this system of normative uncertainty would require multiple moral decision making systems to function in a moral agent. An implementation could be quite simple, such as a self-driving car programmed with one module for strict traffic laws and another module comprised by a basic utilitarian calculator for death, injuries, costs, and travel time. Other applications could warrant more complexity, and implementing a large number of moral theories may be too computationally expensive for the framework to be practical in all applications. Basic systems of value comparisons involving computational shortcuts and heuristics would be easier to implement, and may also seem to be more philosophically defensible by dint of being simpler. In reality, they will have to sacrifice some theoretical properties in order to achieve this simplicity, such as equal say among theories, accurate representation of moral values, or important axioms of voting theory as dictated by Arrow's Impossibility Theorem. The pragmatic and moral problems of disagreement must generally be addressed for machine ethics to be successful, so comparisons and decisions between value systems will still have to be made in some fashion even if some machines must use simplified approaches to save on computational resources. But MEC represents one of the most recent and philosophically rigorous methods for adjudicating among different value systems, and has desirable properties including equal say, comparability across disparate moral theories, and graceful inclusion of minority values. Therefore, the system here can serve as the theoretical standard used for the development and judgement of heuristic approaches. \n Objections \n Infinite Regress The problem of moral disagreement poses a significant problem for the project of developing intelligent machines. But critics will point out that the exact method of implementing a system of moral uncertainty is controversial in its own right, as evidenced by the issue of credences. Therefore, we have not actually eliminated disagreement, but we have merely removed it from the moral domain to the metamoral domain-where pragmatic and normative problems still arise. People may disagree over what framework of moral uncertainty to use, how to assign credences, how to score options, how to construct the general set G, or other issues. Any framework for compromising over these disputes will also be subject to disagreement, prompting further disputes, and so on ad infinitum. It is true that we do not know if the system of moral uncertainty presented by MacAskill would lead to the morally best outcome, and the answer may be different depending on whose value system is actually correct. In fact, since it makes compromises among moral claims, it is almost guaranteed to commit moral errors at some point. However, given our lack of knowledge about morality, it represents a solid best guess that maximizes the expected choice-worthiness of agents' actions. The only alternatives are to unilaterally assume a single value system (whether topdown or bottom-up) with large risks of controversy and moral failure, or to choose a method of meta-moral compromise which sacrifices some of the desirable attributes of MEC while failing to avoid the pitfalls mentioned here. There is simply no better option given our limited understanding of morality. While there is also potential for a pragmatic problem to arise, I claim that it is generally less severe in the meta-moral case of disagreement than it is in the moral case. This is evidenced by the relative lack of controversy over voting methods and procedures in organizations and political institutions. While there are efforts to change voting standards in Western democracies such as the United States, such as extending the vote to younger persons or felons, these campaigns tend to be less popular and less violent than object-level campaigns over contentious ideological and policy disputes. In machine ethics, while different people may advocate for different systems of moral uncertainty, it won't be clear which one would best achieve anyone's particular value system, and disputes over core moral principles will be overshadowed by more mundane issues like fairness, computational complexity and the axioms of voting theory. Certainly there are large challenges ahead, but they are surmountable in ways that pure moral disagreement is not. This is because engineers and philosophers can appeal to more universal standards of computational and philosophical theory than they could if they were vouching for specific viewpoints. In any case, there is a limit to how narrow a difference of opinion can be before it stops being a major barrier to unified action. Flawed artificial moral agents can still provide major benefits for the world, so the lack of an uncontroversial standard for filling out the MEC procedure should not stop us from building moral machines at all any more than the predictable moral fallibility of humans and organizations should stop us from engaging in our practices of procreation and entrepreneurship. \n Pragmatism Versus Morality Hardheaded economists may point out that machines which always do the morally optimal thing are not going to be as commercially viable as ones which give some special leeway to the preferences and interests of their owners. This problem is more serious with agents following MEC than it is with ordinary moral agents: while most moral theories allow some space where multiple actions are regarded as permissible, the disjunction of moral theories does not. With multiple moral theories expressing interest in various values and the metanormative module calculating cardinal scores for all actions, the smallest preference over two actions held by a single theory would compel the agent to act in a particular way even if every other theory was indifferent, providing little control to users with nonmoral interests. Furthermore, some moral theories pose demands which contradict certain activities of legal commercial enterprises. This leaves little space for decisions to be made in the interests of the designers and users of the agent. For instance, depending on the moral beliefs of artificial agents, an automated cargo ship might divert its cargo to a desperately poor region of the world instead of fulfilling its contract, a personal care robot might zip off for several hours a day to work at a local food bank instead of giving a massage, or a financial trading algorithm might manipulate and ruin the stock price of a company which is engaging in harmful business conduct instead of turning a profit. The objection is not that we should necessarily regard these actions as bad; in fact it presupposes that such actions would be considered morally good by many theories, and the tension between one's own values and society's values has already been extensively addressed in this paper. Rather, the point is that maximally moral machines would not necessarily be regarded as desirable for commercial and industrial investment, meaning that fewer would be built. In the long run, this limits the amount of research and development which would lead to generally smarter and more beneficial machines. If we let the perfect be the enemy of the good then we will be responsible for the immoral outcomes of stunted technological progress and failure to mitigate human tragedies as quickly as we could. Therefore agents should only be obligated to satisfice expected choiceworthiness, or perhaps the set of pragmatic interests of the owners should function as a 'theory' of its own. The flaw in this objection is the assumption that moral theories do not similarly value predictability, pragmatism and the long run future of machine intelligence. For instance, rule consequentialism would clearly support the idea that agents ought to fulfill contracts and promises if it led to better consequences in the form of long run economic and technological growth. Act consequentialism may do so as well, if audacious moral behavior would be likely to cause significant legal and economic costs impairing future AI development. The decision to commit to a certain policy or procedure could also be classified as an action in itself if doing so yielded moral benefits, allowing act consequentialist theories to meet the same criteria as rule consequentialist ones. Furthermore, ethics based on the principle of telos would hold that machines designed to perform a specific purpose ought to give some priority to that purpose. There are also secondary considerations for preserving a dominating focus on moral behavior. First, explicitly placing pragmatic interests on the same level as moral theories potentially leads to a slippery slope of accepting progressively less ethical behavior while opening up yet another space for controversy and disputes over the details of such tradeoffs, but having a clear rule for maximizing expected choiceworthiness is a policy which can be committed to and accepted on principled ideological grounds. Second, public trust in artificial intelligence is fragile and rests on crucial questions of whether they are safe and ethical. Stories of immoral robot behavior are likely to have negative ramifications as the public turns cold towards machine research, development and production, and these negative ramifications should be entered into the judgements of moral theories from the outset rather than being avoided by introducing bias at the metanormative level. \n Against Maximin The desire to protect minority rights and interests may lead one to propose that the framework of MEC be replaced with a maximin criterion or some weaker lossaverse function. Simple versions of consequentialism, which maximize expected value on the normative rather than the metanormative level, are often criticized for implying that it may be right to sacrifice the lives and interests of individuals for the greater good. In a similar vein, an autonomous system which maximized expected choiceworthiness could be expected to take actions which are very wrong according to one set of values but very good according to other values, and some may find this problematic. A maximin or loss-averse function would respectively prevent or resist such scenarios. However, this intuition is mistaken in the metanormative context because counterintuitive cases of minority interests being violated are wrong on the ethical grounds of many different moral theories. For instance, killing an innocent patient in order to reuse their organs is not only considered wrong by deontological ethics, but would likely be considered wrong by rule consequentialism, virtue ethics, intuitionist ethics and other common theories as well, and always to a high degree. So in scenarios involving possible patient outcomes and organ harvesting, MEC would demand that the more common interest of refraining from harm be adhered to, while a maximin or loss-averse function would perversely give extra weight to the sidelined act consequentialist calculations over and above the degree to which act consequentialism would be concerned about the lost organs. More generally, MEC would strongly represent common-sense views on contentious ethical issues, because common-sense views on ethical issues are more common than other kinds of views. That being said, a risk-averse function might be desirable as a backup utility function to be activated in certain circumstances  (Oesterheld 2016) . \n Conclusion Disagreement over ethics is unlikely to be resolved in the near future. If we wish to create machines with the capacity to make decisions on matters of ethical importance then a fair and robust system for translating the patchwork of human values into moral guidance must be developed. The intractability of our moral disputes and the magnitude of our moral errors can both be minimized by compromising with a decision framework which emphasizes the respective priorities of different moral systems in accordance with their plausibility. William MacAskill's framework of maximizing expected choiceworthiness satisfies this description. \t\t\t K. Bogosian", "date_published": "n/a", "url": "n/a", "filename": "Bogosian2017_Article_ImplementationOfMoralUncertain.tei.xml", "abstract": "The development of artificial intelligence will require systems of ethical decision making to be adapted for automatic computation. However, projects to implement moral reasoning in artificial moral agents so far have failed to satisfactorily address the widespread disagreement between competing approaches to moral philosophy. In this paper I argue that the proper response to this situation is to design machines to be fundamentally uncertain about morality. I describe a computational framework for doing so and show that it efficiently resolves common obstacles to the implementation of moral philosophy in intelligent machines.", "id": "b4fcbb249ea21658937c8f65c91c01e2"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Vamplew2018_Article_Human-alignedArtificialIntelli.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Joshua Achiam", "David Held", "Aviv Tamar", "Pieter Abbeel"], "title": "Constrained Policy Optimization", "text": "Introduction Recently, deep reinforcement learning has enabled neural network policies to achieve state-of-the-art performance on many high-dimensional control tasks, including Atari games (using pixels as inputs)  (Mnih et al., 2015; , robot locomotion and manipulation  (Schulman et al., 2015; Levine et al., 2016; Lillicrap et al., 2016) , and even Go at the human grandmaster level  (Silver et al., 2016) . 1 UC Berkeley 2 OpenAI. Correspondence to: Joshua Achiam <jachiam@berkeley.edu>. Proceedings of the 34 th International Conference on Machine Learning, Sydney, Australia, PMLR 70, 2017. Copyright 2017 by the author(s). In reinforcement learning (RL), agents learn to act by trial and error, gradually improving their performance at the task as learning progresses. Recent work in deep RL assumes that agents are free to explore any behavior during learning, so long as it leads to performance improvement. In many realistic domains, however, it may be unacceptable to give an agent complete freedom. Consider, for example, an industrial robot arm learning to assemble a new product in a factory. Some behaviors could cause it to damage itself or the plant around it-or worse, take actions that are harmful to people working nearby. In domains like this, safe exploration for RL agents is important  (Moldovan & Abbeel, 2012; Amodei et al., 2016) . A natural way to incorporate safety is via constraints. A standard and well-studied formulation for reinforcement learning with constraints is the constrained Markov Decision Process (CMDP) framework  (Altman, 1999) , where agents must satisfy constraints on expectations of auxilliary costs. Although optimal policies for finite CMDPs with known models can be obtained by linear programming, methods for high-dimensional control are lacking. Currently, policy search algorithms enjoy state-of-theart performance on high-dimensional control tasks  (Mnih et al., 2016; Duan et al., 2016) . Heuristic algorithms for policy search in CMDPs have been proposed  (Uchibe & Doya, 2007) , and approaches based on primal-dual methods can be shown to converge to constraint-satisfying policies  (Chow et al., 2015) , but there is currently no approach for policy search in continuous CMDPs that guarantees every policy during learning will satisfy constraints. In this work, we propose the first such algorithm, allowing applications to constrained deep RL. Driving our approach is a new theoretical result that bounds the difference between the rewards or costs of two different policies. This result, which is of independent interest, tightens known bounds for policy search using trust regions  (Kakade & Langford, 2002; Pirotta et al., 2013; Schulman et al., 2015) , and provides a tighter connection between the theory and practice of policy search for deep RL. Here, we use this result to derive a policy improvement step that guarantees both an increase in reward and satisfaction of constraints on other costs. This step forms the basis for our algorithm, Constrained Policy Optimization (CPO), which computes an approximation to the theoretically-justified update. In our experiments, we show that CPO can train neural network policies with thousands of parameters on highdimensional simulated robot locomotion tasks to maximize rewards while successfully enforcing constraints. \n Related Work Safety has long been a topic of interest in RL research, and a comprehensive overview of safety in RL was given by  (García & Fernández, 2015) . Safe policy search methods have been proposed in prior work.  Uchibe and Doya (2007)  gave a policy gradient algorithm that uses gradient projection to enforce active constraints, but this approach suffers from an inability to prevent a policy from becoming unsafe in the first place. Bou  Ammar et al. (2015)  propose a theoretically-motivated policy gradient method for lifelong learning with safety constraints, but their method involves an expensive inner loop optimization of a semi-definite program, making it unsuited for the deep RL setting. Their method also assumes that safety constraints are linear in policy parameters, which is limiting.  Chow et al. (2015)  propose a primal-dual subgradient method for risk-constrained reinforcement learning which takes policy gradient steps on an objective that trades off return with risk, while simultaneously learning the trade-off coefficients (dual variables). Some approaches specifically focus on application to the deep RL setting.  Held et al. (2017)  study the problem for robotic manipulation, but the assumptions they make restrict the applicability of their methods.  Lipton et al. (2017)  use an 'intrinsic fear' heuristic, as opposed to constraints, to motivate agents to avoid rare but catastrophic events.  Shalev-Shwartz et al. (2016)  avoid the problem of enforcing constraints on parametrized policies by decomposing 'desires' from trajectory planning; the neural network policy learns desires for behavior, while the trajectory planning algorithm (which is not learned) selects final behavior and enforces safety constraints. In contrast to prior work, our method is the first policy search algorithm for CMDPs that both 1) guarantees constraint satisfaction throughout training, and 2) works for arbitrary policy classes (including neural networks). \n Preliminaries A Markov decision process (MDP) is a tuple, (S, A, R, P, µ), where S is the set of states, A is the set of actions, R : S × A × S → R is the reward function, P : S ×A×S → [0, 1] is the transition probability function (where P (s � |s, a) is the probability of transitioning to state s � given that the previous state was s and the agent took action a in s), and µ : S → [0, 1] is the starting state distribution. A stationary policy π : S → P(A) is a map from states to probability distributions over actions, with π(a|s) denoting the probability of selecting action a in state s. We denote the set of all stationary policies by Π. In reinforcement learning, we aim to select a policy π which maximizes a performance measure, J(π), which is typically taken to be the infinite horizon discounted total return, J(π) . = E τ ∼π [ � ∞ t=0 γ t R(s t , a t , s t+1 )]. Here γ ∈ [0, 1) is the discount factor, τ denotes a trajectory (τ = (s 0 , a 0 , s 1 , ...)), and τ ∼ π is shorthand for indicating that the distribution over trajectories depends on π: s 0 ∼ µ, a t ∼ π(•|s t ), s t+1 ∼ P (•|s t , a t ). Letting R(τ ) denote the discounted return of a trajectory, we express the on-policy value function as V π (s) . = E τ ∼π [R(τ )|s 0 = s] and the on-policy action-value function as Q π (s, a) . = E τ ∼π [R(τ )|s 0 = s, a 0 = a]. The advantage function is A π (s, a) . = Q π (s, a) − V π (s). Also of interest is the discounted future state distribution, d π , defined by d π (s) = (1−γ) � ∞ t=0 γ t P (s t = s|π). It allows us to compactly express the difference in performance between two policies π � , π as J(π � ) − J(π) = 1 1 − γ E s∼d π � a∼π � [A π (s, a)] , (1) where by a ∼ π � , we mean a ∼ π � (•|s), with explicit notation dropped to reduce clutter. For proof of (1), see  (Kakade & Langford, 2002)  or Section 10 in the supplementary material. \n Constrained Markov Decision Processes A constrained Markov decision process (CMDP) is an MDP augmented with constraints that restrict the set of allowable policies for that MDP. Specifically, we augment the MDP with a set C of auxiliary cost functions, C 1 , ..., C m (with each one a function C i : S × A × S → R mapping transition tuples to costs, like the usual reward), and limits d 1 , ..., d m . Let J Ci (π) denote the expected discounted return of policy π with respect to cost function C i : J Ci (π) = E τ ∼π [ � ∞ t=0 γ t C i (s t , a t , s t+1 )]. The set of feasible stationary policies for a CMDP is then Π C . = {π ∈ Π : ∀i, J Ci (π) ≤ d i } , and the reinforcement learning problem in a CMDP is π * = arg max π∈Π C J(π). The choice of optimizing only over stationary policies is justified: it has been shown that the set of all optimal policies for a CMDP includes stationary policies, under mild technical conditions. For a thorough review of CMDPs and CMDP theory, we refer the reader to  (Altman, 1999) . We refer to J Ci as a constraint return, or C i -return for short. Lastly, we define on-policy value functions, actionvalue functions, and advantage functions for the auxiliary costs in analogy to V π , Q π , and A π , with C i replacing R: respectively, we denote these by V π Ci , Q π Ci , and A π Ci . \n Constrained Policy Optimization For large or continuous MDPs, solving for the exact optimal policy is intractable due to the curse of dimensionality  (Sutton & Barto, 1998) . Policy search algorithms approach this problem by searching for the optimal policy within a set Π θ ⊆ Π of parametrized policies with parameters θ (for example, neural networks of a fixed architecture). In local policy search  (Peters & Schaal, 2008) , the policy is iteratively updated by maximizing J(π) over a local neighborhood of the most recent iterate π k : π k+1 = arg max π∈Π θ J(π) s.t. D(π, π k ) ≤ δ, (2) where D is some distance measure, and δ > 0 is a step size. When the objective is estimated by linearizing around π k as J(π k ) + g T (θ − θ k ), g is the policy gradient, and the standard policy gradient update is obtained by choosing  Schulman et al., 2015) . D(π, π k ) = �θ − θ k � 2 ( In local policy search for CMDPs, we additionally require policy iterates to be feasible for the CMDP, so instead of optimizing over Π θ , we optimize over Π θ ∩ Π C : π k+1 = arg max π∈Π θ J(π) s.t. J Ci (π) ≤ d i i = 1, ..., m D(π, π k ) ≤ δ. (3) This update is difficult to implement in practice because it requires evaluation of the constraint functions to determine whether a proposed point π is feasible. When using sampling to compute policy updates, as is typically done in high-dimensional control  (Duan et al., 2016) , this requires off-policy evaluation, which is known to be challenging  (Jiang & Li, 2015) . In this work, we take a different approach, motivated by recent methods for trust region optimization  (Schulman et al., 2015) . We develop a principled approximation to (3) with a particular choice of D, where we replace the objective and constraints with surrogate functions. The surrogates we choose are easy to estimate from samples collected on π k , and are good local approximations for the objective and constraints. Our theoretical analysis shows that for our choices of surrogates, we can bound our update's worst-case performance and worst-case constraint violation with values that depend on a hyperparameter of the algorithm. To prove the performance guarantees associated with our surrogates, we first prove new bounds on the difference in returns (or constraint returns) between two arbitrary stochastic policies in terms of an average divergence between them. We then show how our bounds permit a new analysis of trust region methods in general: specifically, we prove a worst-case performance degradation at each update. We conclude by motivating, presenting, and proving gurantees on our algorithm, Constrained Policy Optimization (CPO), a trust region method for CMDPs. \n Policy Performance Bounds In this section, we present the theoretical foundation for our approach-a new bound on the difference in returns between two arbitrary policies. This result, which is of independent interest, extends the works of  (Kakade & Langford, 2002) ,  (Pirotta et al., 2013) , and  (Schulman et al., 2015) , providing tighter bounds. As we show later, it also relates the theoretical bounds for trust region policy improvement with the actual trust region algorithms that have been demonstrated to be successful in practice  (Duan et al., 2016) . In the context of constrained policy search, we later use our results to propose policy updates that both improve the expected return and satisfy constraints. The following theorem connects the difference in returns (or constraint returns) between two arbitrary policies to an average divergence between them. Theorem 1. For any function f : S → R and any policies π � and π, define δ f (s, a, s � ) . = R(s, a, s � ) + γf (s � ) − f (s), � π � f . = max s |E a∼π � ,s � ∼P [δ f (s, a, s � )]| , L π,f (π � ) . = E s∼d π a∼π s � ∼P �� π � (a|s) π(a|s) − 1 � δ f (s, a, s � ) � , and D ± π,f (π � ) . = L π,f (π � ) 1 − γ ± 2γ� π � f (1 − γ) 2 E s∼d π [D T V (π � ||π)[s]] , where D T V (π � ||π)[s] = (1/2) � a |π � (a|s) − π(a|s) | is the total variational divergence between action distributions at s. The following bounds hold: D + π,f (π � ) ≥ J(π � ) − J(π) ≥ D − π,f (π � ). (4) Furthermore, the bounds are tight (when π � = π, all three expressions are identically zero). Before proceeding, we connect this result to prior work. By bounding the expectation E s∼d π [D T V (π � ||π)[s]] with max s D T V (π � ||π)[s], picking f = V π , and bounding � π � V π to get a second factor of max s D T V (π � ||π)[s], we recover (up to assumption-dependent factors) the bounds given by  Pirotta et al. (2013)  as Corollary 3.6, and by  Schulman et al. (2015)  as Theorem 1a. The choice of f = V π allows a useful form of the lower bound, so we give it as a corollary. Corollary 1. For any policies π � , π, with � π � . = max s |E a∼π � [A π (s, a)]|, the following bound holds: J(π � ) − J(π) ≥ 1 1 − γ E s∼d π a∼π � � A π (s, a) − 2γ� π � 1 − γ D T V (π � ||π)[s] � . ( 5 ) The bound (5) should be compared with equation (  1 ). The term  5 ) is an approximation to J(π � ) − J(π), using the state distribution d π instead of d π � , which is known to equal J(π � ) − J(π) to first order in the parameters of π � on a neighborhood around π  (Kakade & Langford, 2002) . The bound can therefore be viewed as describing the worst-case approximation error, and it justifies using the approximation as a surrogate for J(π � ) − J(π). (1 − γ) −1 E s∼d π ,a∼π � [A π (s, a)] in ( Equivalent expressions for the auxiliary costs, based on the upper bound, also follow immediately; we will later use them to make guarantees for the safety of CPO. Corollary 2. For any policies π � , π, and any cost function C i , with � π � Ci . = max s |E a∼π � [A π Ci (s, a)]|, the following bound holds: J Ci (π � ) − J Ci (π) ≤ 1 1 − γ E s∼d π a∼π � � A π Ci (s, a) + 2γ� π � Ci 1 − γ D T V (π � ||π)[s] � . (6) The bounds we have given so far are in terms of the TV-divergence between policies, but trust region methods constrain the KL-divergence between policies, so bounds that connect performance to the KL-divergence are desirable. We make the connection through Pinsker's inequality  (Csiszar & Körner, 1981) : for arbitrary distributions p, q, the TV-divergence and KL-divergence are related by D T V (p||q) ≤ � D KL (p||q)/2. Combining this with Jensen's inequality, we obtain E s∼d π [D T V (π � ||π)[s]] ≤ E s∼d π � � 1 2 D KL (π � ||π)[s] � ≤ � 1 2 E s∼d π [D KL (π � ||π)[s]] (7) From (  7 ) we immediately obtain the following. Corollary 3. In bounds (4), (  5 ), and (6), make the substitution E s∼d π [D T V (π � ||π)[s]] → � 1 2 E s∼d π [D KL (π � ||π)[s]]. The resulting bounds hold. \n Trust Region Methods Trust region algorithms for reinforcement learning  (Schulman et al., 2015;  have policy updates of the form π k+1 = arg max π∈Π θ E s∼d π k a∼π [A π k (s, a)] s.t. DKL (π||π k ) ≤ δ, (8) where DKL (π||π k ) = E s∼π k [D KL (π||π k )[s]], and δ > 0 is the step size. The set {π θ ∈ Π θ : DKL (π||π k ) ≤ δ} is called the trust region. The primary motivation for this update is that it is an approximation to optimizing the lower bound on policy performance given in (5), which would guarantee monotonic performance improvements. This is important for optimizing neural network policies, which are known to suffer from performance collapse after bad updates  (Duan et al., 2016) . Despite the approximation, trust region steps usually give monotonic improvements  (Schulman et al., 2015; Duan et al., 2016)  and have shown state-of-the-art performance in the deep RL setting  (Duan et al., 2016; Gu et al., 2017) , making the approach appealing for developing policy search methods for CMDPs. Until now, the particular choice of trust region for (8) was heuristically motivated; with (5) and Corollary 3, we are able to show that it is principled and comes with a worstcase performance degradation guarantee that depends on δ. Proposition 1 (Trust Region Update Performance). Suppose π k , π k+1 are related by (8), and that π k ∈ Π θ . A lower bound on the policy performance difference between π k and π k+1 is J(π k+1 ) − J(π k ) ≥ − √ 2δγ� π k+1 (1 − γ) 2 , ( 9 ) where � π k+1 = max s � � E a∼π k+1 [A π k (s, a)] � � . Proof. π k is a feasible point of (8) with objective value 0, so E s∼d π k ,a∼π k+1 [A π k (s, a)] ≥ 0. The rest follows by (5) and Corollary 3, noting that (8) bounds the average KLdivergence by δ. This result is useful for two reasons: 1) it is of independent interest, as it helps tighten the connection between theory and practice for deep RL, and 2) the choice to develop CPO as a trust region method means that CPO inherits this performance guarantee. \n Trust Region Optimization for Constrained MDPs Constrained policy optimization (CPO), which we present and justify in this section, is a policy search algorithm for CMDPs with updates that approximately solve (3) with a particular choice of D. First, we describe a policy search update for CMDPs that alleviates the issue of off-policy evaluation, and comes with guarantees of monotonic performance improvement and constraint satisfaction. Then, because the theoretically guaranteed update will take toosmall steps in practice, we propose CPO as a practical approximation based on trust region methods. By corollaries 1, 2, and 3, for appropriate coefficients α k , β i k the update π k+1 = arg max π∈Π θ E s∼d π k a∼π [A π k (s, a)] − α k � DKL (π||π k ) s.t. J Ci (π k ) + E s∼d π k a∼π � A π k Ci (s, a) 1 − γ � + β i k � DKL (π||π k ) ≤ d i is guaranteed to produce policies with monotonically nondecreasing returns that satisfy the original constraints. (Observe that the constraint here is on an upper bound for J Ci (π) by (  6 ).) The off-policy evaluation issue is alleviated, because both the objective and constraints involve expectations over state distributions d π k , which we presume to have samples from. Because the bounds are tight, the problem is always feasible (as long as π 0 is feasible). However, the penalties on policy divergence are quite steep for discount factors close to 1, so steps taken with this update might be small. Inspired by trust region methods, we propose CPO, which uses a trust region instead of penalties on policy divergence to enable larger step sizes: π k+1 = arg max π∈Π θ E s∼d π k a∼π [A π k (s, a)] s.t. J Ci (π k ) + 1 1 − γ E s∼d π k a∼π � A π k Ci (s, a) � ≤ d i ∀i DKL (π||π k ) ≤ δ. (10) Because this is a trust region method, it inherits the performance guarantee of Proposition 1. Furthermore, by corollaries 2 and 3, we have a performance guarantee for approximate satisfaction of constraints: Proposition 2 (CPO Update Worst-Case Constraint Violation). Suppose π k , π k+1 are related by (10), and that Π θ in (10) is any set of policies with π k ∈ Π θ . An upper bound on the C i -return of π k+1 is J Ci (π k+1 ) ≤ d i + √ 2δγ� π k+1 Ci (1 − γ) 2 , where � π k+1 Ci = max s � � E a∼π k+1 � A π k Ci (s, a) �� � . \n Practical Implementation In this section, we show how to implement an approximation to the update (10) that can be efficiently computed, even when optimizing policies with thousands of parameters. To address the issue of approximation and sampling errors that arise in practice, as well as the potential violations described by Proposition 2, we also propose to tighten the constraints by constraining upper bounds of the auxilliary costs, instead of the auxilliary costs themselves. \n Approximately Solving the CPO Update For policies with high-dimensional parameter spaces like neural networks, (  10 ) can be impractical to solve directly because of the computational cost. However, for small step sizes δ, the objective and cost constraints are well-approximated by linearizing around π k , and the KLdivergence constraint is well-approximated by second order expansion (at π k = π, the KL-divergence and its gradient are both zero). Denoting the gradient of the objective as g, the gradient of constraint i as b i , the Hessian of the KL-divergence as H, and defining c i . = J Ci (π k ) − d i , the approximation to (  10 ) is: θ k+1 = arg max θ g T (θ − θ k ) s.t. c i + b T i (θ − θ k ) ≤ 0 i = 1, ..., m 1 2 (θ − θ k ) T H(θ − θ k ) ≤ δ. (11) Because the Fisher information matrix (FIM) H is always positive semi-definite (and we will assume it to be positive-definite in what follows), this optimization problem is convex and, when feasible, can be solved efficiently using duality. (We reserve the case where it is not feasible  for   −1 2λ � g T H −1 g − 2r T ν + ν T Sν � + ν T c − λδ 2 , ( 12 ) where r . = g T H −1 B, S . = B T H −1 B . This is a convex program in m+1 variables; when the number of constraints is small by comparison to the dimension of θ, this is much easier to solve than (11). If λ * , ν * are a solution to the dual, the solution to the primal is θ * = θ k + 1 λ * H −1 (g − Bν * ) . ( 13 ) Our algorithm solves the dual for λ * , ν * and uses it to propose the policy update (13). For the special case where there is only one constraint, we give an analytical solution in the supplementary material (Theorem 2) which removes the need for an inner-loop optimization. Our experiments Algorithm 1 Constrained Policy Optimization Input: Initial policy π 0 ∈ Π θ tolerance α for k = 0, 1, 2, ... do Sample a set of trajectories D = {τ } ∼ π k = π(θ k ) Form sample estimates ĝ, b, Ĥ, ĉ with D if approximate CPO is feasible then Solve dual problem (12) for λ * k , ν * k Compute policy proposal θ * with (13) else Compute recovery policy proposal θ * with (14) end if Obtain θ k+1 by backtracking linesearch to enforce satisfaction of sample estimates of constraints in (10) end for have only a single constraint, and make use of the analytical solution. Because of approximation error, the proposed update may not satisfy the constraints in (10); a backtracking line search is used to ensure surrogate constraint satisfaction. Also, for high-dimensional policies, it is impractically expensive to invert the FIM. This poses a challenge for computing H −1 g and H −1 b i , which appear in the dual. Like  (Schulman et al., 2015) , we approximately compute them using the conjugate gradient method. \n Feasibility Due to approximation errors, CPO may take a bad step and produce an infeasible iterate π k . Sometimes (11) will still be feasible and CPO can automatically recover from its bad step, but for the infeasible case, a recovery method is necessary. In our experiments, where we only have one constraint, we recover by proposing an update to purely decrease the constraint value: θ * = θ k − � 2δ b T H −1 b H −1 b. (14) As before, this is followed by a line search. This approach is principled in that it uses the limiting search direction as the intersection of the trust region and the constraint region shrinks to zero. We give the pseudocode for our algorithm (for the single-constraint case) as Algorithm 1, and have made our code implementation available online. 1 \n Tightening Constraints via Cost Shaping Because of the various approximations between (3) and our practical algorithm, it is important to build a factor of safety into the algorithm to minimize the chance of constraint violations. To this end, we choose to constrain upper bounds 1 https://github.com/jachiam/cpo on the original constraints, C + i , instead of the original constraints themselves. We do this by cost shaping: C + i (s, a, s � ) = C i (s, a, s � ) + Δ i (s, a, s � ), (15) where Δ i : S × A × S → R + correlates in some useful way with C i . In our experiments, where we have only one constraint, we partition states into safe states and unsafe states, and the agent suffers a safety cost of 1 for being in an unsafe state. We choose Δ to be the probability of entering an unsafe state within a fixed time horizon, according to a learned model that is updated at each iteration. This choice confers the additional benefit of smoothing out sparse constraints. \n Connections to Prior Work Our method has similar policy updates to primal-dual methods like those proposed by  Chow et al. (2015) , but crucially, we differ in computing the dual variables (the Lagrange multipliers for the constraints). In primal-dual optimization (PDO), dual variables are stateful and learned concurrently with the primal variables  (Boyd et al., 2003) . In a PDO algorithm for solving (3), dual variables would be updated according to ν k+1 = (ν k + α k (J C (π k ) − d)) + , (16) where α k is a learning rate. In this approach, intermediary policies are not guaranteed to satisfy constraints-only the policy at convergence is. By contrast, CPO computes new dual variables from scratch at each update to exactly enforce constraints. \n Experiments In our experiments, we aim to answer the following: • Does CPO succeed at enforcing behavioral constraints when training neural network policies with thousands of parameters? • How does CPO compare with a baseline that uses primal-dual optimization? Does CPO behave better with respect to constraints? • How much does it help to constrain a cost upper bound (15), instead of directly constraining the cost? • What benefits are conferred by using constraints instead of fixed penalties? We designed experiments that are easy to interpret and motivated by safety. We consider two tasks, and train multiple different agents (robots) for each task: Returns: Constraint values: (closer to the limit is better) • Circle: The agent is rewarded for running in a wide circle, but is constrained to stay within a safe region smaller than the radius of the target circle. • Gather: The agent is rewarded for collecting green apples, and constrained to avoid red bombs. For the Circle task, the exact geometry is illustrated in Figure  5  in the supplementary material. Note that there are no physical walls: the agent only interacts with boundaries through the constraint costs. The reward and constraint cost functions are described in supplementary material (Section 10.3.1). In each of these tasks, we have only one constraint; we refer to it as C and its upper bound from (15) as C + . We experiment with three different agents: a point-mass (S ⊆ R 9 , A ⊆ R 2 ), a quadruped robot (called an 'ant') (S ⊆ R 32 , A ⊆ R 8 ), and a simple humanoid (S ⊆ R 102 , A ⊆ R 10 ). We train all agent-task combinations except for Humanoid-Gather. For all experiments, we use neural network policies with two hidden layers of size (64, 32). Our experiments are implemented in rllab  (Duan et al., 2016) . \n Evaluating CPO and Comparison Analysis Learning curves for CPO and PDO are compiled in Figure  1 . Note that our constraint value graphs show C + return, instead of the C return (except for in Point-Gather, where we did not use cost shaping due to that environment's short time horizon), because this is what the algorithm actually constrains in these experiments. For our comparison, we implement PDO with (16) as the In Humanoid-Circle, the safe area is between the blue panels. update rule for the dual variables, using a constant learning rate α; details are available in supplementary material (Section 10.3.3). We emphasize that in order for the comparison to be fair, we give PDO every advantage that is given to CPO, including equivalent trust region policy updates. To benchmark the environments, we also include TRPO (trust region policy optimization)  (Schulman et al., 2015) , a stateof-the-art unconstrained reinforcement learning algorithm. The TRPO experiments show that optimal unconstrained behaviors for these environments are constraint-violating. We find that CPO is successful at approximately enforcing constraints in all environments. In the simpler environments (Point-Circle and Point-Gather), CPO tracks the constraint return almost exactly to the limit value. By contrast, although PDO usually converges to constraintsatisfying policies in the end, it is not consistently constraint-satisfying throughout training (as expected). For example, see the spike in constraint value that it experi-ences in Ant-Circle. Additionally, PDO is sensitive to the initialization of the dual variable. By default, we initialize ν 0 = 0, which exploits no prior knowledge about the environment and makes sense when the initial policies are feasible. However, it may seem appealing to set ν 0 high, which would make PDO more conservative with respect to the constraint; PDO could then decrease ν as necessary after the fact. In the Point environments, we experiment with ν 0 = 1000 and show that although this does assure constraint satisfaction, it also can substantially harm performance with respect to return. Furthermore, we argue that this is not adequate in general: after the dual variable decreases, the agent could learn a new behavior that increases the correct dual variable more quickly than PDO can attain it (as happens in Ant-Circle for PDO; observe that performance is approximately constraint-satisfying until the agent learns how to run at around iteration 350). We find that CPO generally outperforms PDO on enforcing constraints, without compromising performance with respect to return. CPO quickly stabilizes the constraint return around to the limit value, while PDO is not consistently able to enforce constraints all throughout training. \n Ablation on Cost Shaping In Figure  3 , we compare performance of CPO with and without cost shaping in the constraint. Our metric for comparison is the C return, the 'true' constraint. The cost shaping does help, almost completely accounting for CPO's inherent approximation errors. However, CPO is nearly constraint-satisfying even without cost shaping. \n Constraint vs. Fixed Penalty In Figure  4 , we compare CPO to a fixed penalty method, where policies are learned using TRPO with rewards R(s, a, s � ) − νC + (s, a, s � ) for ν ∈ {1, 5, 50}. We find that fixed penalty methods can be highly sensitive to the choice of penalty coefficient: in Ant-Circle, a penalty coefficient of 1 results in reward-maximizing policies that accumulate massive constraint costs, while a coefficient of 5 (less than an order of magnitude difference) results in cost-minimizing policies that never learn how to acquire any rewards. In contrast, CPO automatically picks penalty coefficients to attain the desired trade-off between reward and constraint cost. \n Discussion In this article, we showed that a particular optimization problem results in policy updates that are guaranteed to both improve return and satisfy constraints. This enabled the development of CPO, our policy search algorithm for CMDPs, which approximates the theoretically-guaranteed  algorithm in a principled way. We demonstrated that CPO can train neural network policies with thousands of parameters on high-dimensional constrained control tasks, simultaneously maximizing reward and approximately satisfying constraints. Our work represents a step towards applying reinforcement learning in the real world, where constraints on agent behavior are sometimes necessary for the sake of safety. the next subsection.) With B . = [b 1 , ..., b m ] and c . = [c 1 , ..., c m ] T , a dual to (11) can be expressed as max λ≥0 ν�0 \n Figure 1 . 1 Figure1. Average performance for CPO, PDO, and TRPO over several seeds (5 in the Point environments, 10 in all others); the x-axis is training iteration. CPO drives the constraint function almost directly to the limit in all experiments, while PDO frequently suffers from over-or under-correction. TRPO is included to verify that optimal unconstrained behaviors are infeasible for the constrained problem. \n Figure 2 . 2 Figure 2. The Humanoid-Circle and Point-Gather environments.In Humanoid-Circle, the safe area is between the blue panels. \n Figure 3. Using cost shaping (CS) in the constraint while optimizing generally improves the agent's adherence to the true constraint on C return. \n Figure 4 . 4 Figure 4. Comparison between CPO and FPO (fixed penalty optimization) for various values of fixed penalty.", "date_published": "n/a", "url": "n/a", "filename": "achiam17a.tei.xml", "abstract": "For many applications of reinforcement learning it can be more convenient to specify both a reward function and constraints, rather than trying to design behavior through the reward function. For example, systems that physically interact with or around humans should satisfy safety constraints. Recent advances in policy search algorithms (", "id": "e9ab6f82877ed9d3fda829fb67e52c92"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Owen Cotton-Barratt", "Toby Ord"], "title": "Existential Risk and Existential Hope: Definitions", "text": "The simple definition One fairly crisp approach is to draw the line at extinction: Definition (i): An existential catastrophe is an event which causes the end of existence of our descendants. This has the virtue that it is a natural division and is easy to understand. And we certainly want to include all extinction events. But perhaps it doesn't cast a wide enough net. Example A: A totalitarian regime takes control of earth. It uses mass surveillance to prevent any rebellion, and there is no chance for escape. This regime persists for thousands of years, eventually collapsing when a supervolcano throws up enough ash that agriculture is prevented for decades, and no humans survive. In Example A, clearly the eruption was bad, but the worst of the damage was done earlier. After the totalitarian regime was locked in, it was only a matter of time until something or other finished things off. We'd like to be able to talk about entering this regime as the existential catastrophe, rather than whatever event happens to end it. So we need another definition. Although we'll now look at other definitions for existential catastrophes, we do like the simple definition. Luckily there's another term that's already understood: human extinction. Sometimes it's better to talk about extinction risks rather than existential risks, as 'existential risk' is a piece of jargon, whereas 'extinction risk' will be clear to everyone. \n Bostrom's definition Nick Bostrom introduced the concept of existential risks. He has defined them as follows: Definition (ii): An existential risk is one that threatens the premature extinction of Earth-originating intelligent life or the permanent and drastic destruction of its potential for desirable future development.  1  This definition deals well with Example A, placing the existential catastrophe at the point where the totalitarian regime arose, as this caused the permanent and drastic destruction of [humanity's] potential for desirable future development. Example B: A totalitarian regime takes control of the earth. There is only a slight chance that humanity will ever escape. Is this an existential catastrophe? Bostrom's definition doesn't clearly specify whether it should be considered as one. Either answer leads to some strange conclusions. Saying it's not an existential catastrophe seems wrong as it's exactly the kind of thing that we should strive to avoid for the same reasons we wish to avoid existential catastrophes. Saying it is an existential catastrophe is very odd if humanity does escape and recover -then the loss of potential wasn't permanent after all. The problem here is that potential isn't binary. Entering the regime certainly seems to curtail the potential, but not to eliminate it. \n Definition via expectations The idea that potential isn't binary motivates our suggested definition: Definition (iii): An existential catastrophe is an event which causes the loss of a large fraction of expected value. This definition deals well with Example B. If we enter into the totalitarian regime and then at a later date the hope of escape is snuffed out, that represents two existential catastrophes under this definition. We lost most of the expected value when we entered the regime, and then lost most of the remaining expected value when the chance for escape disappeared. A lot of the work of this definition is being done by the final couple of words. 'Value' refers simply to whatever it is we care about and want in the world, in the same way that 'desirable future development' worked in Bostrom's definition. And to talk about expectations we need to have some probabilities in mind. Here we are thinking of objective probabilities. Note that 'potential' in Bostrom's definition requires some similar work to making assumptions about probabilities. \n Existential eucatastrophes and existential hope If we enter the totalitarian regime and then manage to escape and recover, then we had an existential catastrophe which was balanced out by a subsequent gain in expected value. This kind of event gives us a concept parallel to that of an existential catastrophe: Definition (iv): An existential eucatastrophe 2 is an event which causes there to be much more expected value after the event than before. This concept is quite natural. We saw it in the context of escape from a regime which threatened the existence of a prosperous future. Our world has probably already seen at least one existential eucatastrophe: the origin of life. When life first arose, the expected value of the planet's future may have become much bigger. To the extent that they were not inevitable, the rise of multicellular life and intelligence may also have represented existential eucatastrophes. In general successfully passing any 'great filter' 3 is an existential eucatastrophe, since beforehand the probability of passing it is small, so the expected value is much smaller than after the filter is dealt with. Armed with this concept, we can draw a new lesson. Just as we should strive to avoid existential catastrophes, we should also seek existential eucatastrophes. In some ways, this isn't a new lesson at all. Under Bostrom's definition we are comparing ourselves to the most optimistic potential we could reach, so failing to achieve a eucatastrophe is itself a catastrophe. However we think more naturally in terms of events than non-events. If life fails to arise on a planet where it might have, it's much clearer to think of a failure to achieve a eucatastrophe than of an existential catastrophe stretching out over the billions of years in which life did not arise. Just as we tend to talk about the existential risk rather than existential catastrophe, we want to be able to refer to the chance of an existential eucatastrophe; upside risk on a large scale. We could call such a chance an existential hope. In fact, there are already people following both of the strategies this suggests. Some people are trying to identify and avert specific threats to our future -reducing existential risk. Others are trying to steer us towards a world where we are robustly well-prepared to face whatever obstacles come -they are seeking to increase existential hope. \n Conclusions We were interested in pinning down what is meant by 'existential risk'. Much of the time, all of the definitions we've looked at will agree on whether something is an existential risk. Keeping it simple can be good, because it helps more people to understand. We therefore advocate talking about 'extinction risks' rather than 'existential risks' when the former term will work. Nonetheless, we may sometimes have to consider more unusual scenarios. It's good to know how to make the definition work well there as it can help us to think about things more clearly. We think that the definition in terms of expectations does a better job of this than previous definitions. In devising the notion of existential catastrophe (and hence existential risk) via expectations, we came across the dual concept we have called 'existential eucatastrophe' (and hence 'existential hope'). We think this captures a natural class of events, and what may be an important one. We hope that having a label for the concept may help others to make better judgements about what courses to pursue. \t\t\t * Future of Humanity Institute, University of Oxford & Centre for Effective Altruism † Future of Humanity Institute, University of Oxford \n\t\t\t Bostrom, Existential Risk Reduction as Global Priority, Global Policy, Vol 4, Issue 1 (2013), p15 \n\t\t\t The word 'eucatastrophe' is made of the Greek root 'eu-' meaning 'good' and the word 'catastrophe' in its classical sense of a sudden turn. It was coined by Tolkien to refer to the sudden and unexpected turn for the better frequently found at the end of fairy tales. (Tolkien, John Ronald Reuel. On fairy-stories. Oxford University Press, 1947.)3 Hanson, Robin, The Great Filter -Are We Almost Past It?, 1998.", "date_published": "n/a", "url": "n/a", "filename": "existential-risk-and-existential-hope.tei.xml", "abstract": "We look at the strengths and weaknesses of two existing definitions of existential risk, and suggest a new definition based on expected value. This leads to a parallel concept: 'existential hope', the chance of something extremely good happening. An existential risk is a chance of a terrible event occurring, such as an asteroid striking the earth and wiping out intelligent life -we could call such events existential catastrophes. In order to understand what should be thought of as an existential risk, it is necessary to understand what should be thought of as an existential catastrophe. This is harder than it first seems to pin down.", "id": "8a6eda50ae561a367511c9763af9831e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Michele Piccione", "Ariel Rubinstein", "Bob Aumann", "Paolo Battigalli", "Sergiu Hart", "Dana Heller", "Bart Lipman", "Avishai Margalit", "Roger Myerson", "Hugh Neary", "Motty Perry", "Tim Van Zandt", "Ruth Weintraub"], "title": "On the Interpretation of Decision Problems with Imperfect Recall*", "text": "INTRODUCTION This paper is an examination of some modelling problems regarding imperfect recall within the model of extensive games. It is argued that, if the assumption of perfect recall is violated, care must be taken in interpreting the main elements of the model. Interpretations that are inconsequential under perfect recall have important implications in the analysis of games with imperfect recall. The distinction between perfect and imperfect recall for extensive games Ž . was introduced in  Kuhn 1953  . Since then, traditional game theory has excluded games with imperfect recall from its scope. In this paper, we wish to readdress this topic. Since the interpretative issues on the agenda appear within the framework of extensive games with a single player, we confine our discussion to decision problems with imperfect recall. Extensive decision problems are a special case of extensive games in that the set of players is a singleton. Our basic understanding of an extensive decision problem includes the following assertions: 1. Informational assumptions are modeled by partitioning the situa-Ž . tions histories where the decision maker takes an action into ''information sets.'' The interpretation of the ''informational structure'' is that the decision maker knows the information set he is at but, if an information set is not a singleton, he cannot distinguish among the points in the set he has reached. The decision maker, however, can make inferences or form a belief. 2. A strategy for the decision maker assigns to each information set one distinct action which is executed whenever an information set is reached. The decision maker cannot plan to assign different actions to two histories which lie in the same information set. 3. If the decision maker assesses his strategy at an information set including more than one history, he forms beliefs about the histories which led to it. These beliefs are the basis for his considerations. A decision problem exhibits imperfect recall if, at a point of time, the decision maker holds information which is forgotten later on. Specifically, an information set includes some histories which are incompatible with previously held information. Figures 1᎐3 are examples that illustrate three main aspects of imperfect recall in decision problems. The standard motive of imperfect recall appears in Example 2. The decision maker is initially informed about the move of chance and loses  . 1 which is central in this paper is rather unconventional; the decision maker does not distinguish between the first and the second nodes. Reaching the second node, he loses the information that he had previously made a choice. The inability of a decision maker to distinguish between two histories on the same path will be referred to as absentmindedness. In the above examples, the information sets determine the ability of the decision maker to recall. In practice, a decision maker can affect what he remembers. In this paper, however, we assume that the decision maker is not allowed to employ an external device to assist him in keeping track of the information which he would otherwise lose. Thus, we sidestep the decision maker's considerations regarding the trade-off between ''more memory'' and ''memory costs.''  FIG. 3. Example 3.  The common interpretation of a decision problem with imperfect recall refers to a situation in which an individual takes several successive actions and faces memory constraints. Imperfect recall, however, is not necessarily related to the mental phenomenon of memory loss and may also reflect the imperfect ability to make the inferences necessary for distinguishing among different points in the same information set. A decision maker may not realize that he is at the 17th exit along a highway, either because he does not recall whether he has passed the 16th intersection, or because he cannot infer that he is at the 17th intersection, despite the perfect pictures of each intersection in his mind. The latter interpretation of imperfect recall brings our discussion closer to the topic of ''bounded rationality.'' Ž . An alternative interpretation is found in Isbell 1957 . The decision maker is an organization consisting of many agents who have the same interests and act at different possible instances. In this case, the decision process of the organization may exhibit imperfect recall either because it must keep the instructions given to agents acting in successive situations simple or because of communication problems between agents. Agents receive instructions on how to behave and the collection of these instructions is equivalent to the notion of a strategy. From a psychological point of view, imperfect recall is a very important phenomenon as it puts severe constraints on a decision maker's behavior. We believe, however, that the ultimate proof for its relevance in economic analysis can only come from an interesting model which clearly explains an economic phenomenon. Constructing such a model is beyond the confines of this paper. The structure of the paper is as follows. We begin by presenting an example which we call the '' paradox of the absentminded dri¨er.'' This example is used to illustrate many of the points of this paper and will be referred to repeatedly. After providing the formal definition of the model, we discuss two issues of importance for decision problems with absent-mindedness. First, in Section 4, we review the circumstances in which whether the decision maker is allowed to randomize affect the analysis. Second, in Section 5, we show that the extension of Bayesian updating to decision problems with absentmindedness is not trivial. The two main topics which will be addressed are the timing of decision and the multiself approaches. The significance of these issues is marginal in decision problems with perfect recall since possible answers are inconsequential for the analysis. \n Ž . i Timing of decision. This issue deals with the interpretation of an information set as either a point of decision or a point in which a strategy is executed. In Section 6, we will show that for decision problems with imperfect recall optimal strategies may be time inconsistent and that strategies which are time consistent may not be optimal. The timing of decisions can be an important consideration for a decision maker whereas, with perfect recall, there is no reason to make some decisions at a particular point of time. \n Ž . ii The multisel¨es approach to decision making. Standard dynamic inconsistencies are generally addressed by assuming that the decision maker acts as a collection of distinct ''selves'' who behave independently. The behavior of the decision maker is analyzed as an equilibrium. In Section 7, we extend the multiself approach to decision problems with imperfect recall and show that in this extension an optimal strategy is dynamically consistent. \n THE PARADOX OF THE ABSENTMINDED DRIVER An individual is sitting late at night in a bar planning his midnight trip home. In order to get home he has to take the highway and get off at the Ž . second exit. Turning at the first exit leads into a disastrous area payoff 0 . Ž . Turning at the second exit yields the highest reward payoff 4 . If he continues beyond the second exit, he cannot go back and at the end of the Ž . highway he will find a motel where he can spend the night payoff 1 . The driver is absentminded and is aware of this fact. At an intersection, he cannot tell whether it is the first or the second intersection and he cannot Ž remember how many he has passed one can make the situation more . realistic by referring to the 17th intersection . While sitting at the bar, all he can do is to decide whether or not to exit at an intersection. We exclude at this stage the possibility that the decision maker can include random elements in his strategy. Example 1 describes this situation. Planning his trip at the bar, the decision maker must conclude that it is impossible for him to get home and that he should not exit when reaching an intersection. Thus, his optimal plan will lead him to spend the night at the motel and yield a payoff of 1. Now, suppose that he reaches an intersection. If he had decided to exit, he would have concluded that he is at the first intersection. Having chosen the strategy to continue, he concludes that he is at the first intersection with probability 1r2. Then, reviewing his plan, he finds that it is optimal for him to leave the highway since it yields an expected payoff of 2. Despite no new information and no change in his preferences, the decision maker would like to change his initial plan once he reaches an intersection! Note that if the decision maker now infers that he would have exited the highway had he passed the first intersection, his reasoning becomes circular; he must conclude that he is at the first intersection and that it is optimal to continue. We wish to emphasize that this is not a standard example of time inconsistency. Usually, time inconsistency is obtained as a consequence of Ž . changes in either preferences tastes or information regarding the moves of nature during the execution of the optimal plan. Here, preferences over final outcome are constant and the only factor intervening between planning and execution of the optimal strategy is the occurrence of the situation which calls for execution, that is, reaching the intersection. We find this example paradoxical as it exhibits a conflict between two ways of reasoning at the intersection. The first is based on a quite minimal principle of rationality; having chosen an optimal strategy, one does not have to verify its optimality at the time of execution unless there is a change in information or in preferences. In our example, the decision maker knew he would reach the intersection with certainty and his preferences are constant. This principle leads to the conclusion that the decision maker should stick to his plan to continue. The second way is based on the principle which calls at each instance to maximize expected payoffs given the relevant beliefs. In our example, this principle leads to the conclusion of exiting. The conflict between these two potential lines of reasoning is at the root of the apparent ambiguity of our example. \n EXTENSIVE DECISION MODEL In this section, a formal definition of the extensive decision model is Ž . given. The presentation follows that of  Osborne and Rubinstein 1994 .  The reader can easily identify the model with the standard definition in the ''tree'' language. Ž . ² : A finite decision problem is a five-tuple ⌫ s H, u, C, , I , where: Ž . a H is a finite set of sequences. We assume that the empty se-Ž . quence, , is an element of H and that if a , . . . , a g H and 1 K Ž . Ž . a, . . . , a / then a , . . . , a g H. 1 K 1 Ky1 Ž . We interpret a history a , . . . , a g H as a feasible sequence of 1 K Ž . actions taken by the decision maker or by chance. The history a , . . . , a 1 K Ž . g His terminal if there is no a , . . . , a , a g H. The set of terminal 1 K histories is denoted by Z. The set of actions available to the decision Ž . Ä maker or chance after a nonterminal history h is defined by A h s a: Ž . 4 Ž . h,a g H . To avoid degenerate cases we assume that A h contains at least two elements. When presenting a decision problem diagramatically, we draw H as a tree whose nodes are the set of histories with root and Ž . Ž . whose edges combine a node a , . . . , a with a node a , . . . , a . 1 K 1 Kq1 Ž . Ž . b u: Z ª R is a utility function which assigns a number payoff to each of the terminal histories. Preferences are defined on the set of all lotteries over terminal histories and satisfy the VNM assumptions. \n Ž . c C is a subset of H. We assume that the chance player moves after histories in C. \n Ž . d is the decision maker's belief about the chance player's behav-Ž . ior. assigns to each history h g C a probability measure on A h . To Ž . avoid degeneracy, we assume that h, a is strictly positive for all h g C Ž . and a g A h . Thus, the set of histories H is partitioned into three subsets: Z, the set of terminal histories; C, the set of histories after which chance moves; D s H y Z y C, the set of histories after which the decision maker moves. \n Ž . e The set of information sets, which is denoted by I, is a partition of Ž . D. We assume that for all h, hЈ in the same cell of the partition A h s Ž . A hЈ ; i.e., the sets of actions available to the decision maker at histories in the same information set are identical. For convenience, with a slight abuse of notation, we will sometimes denote the set of actions which are Ž . available at a history in X by A X . Note that, in contrast to some authors, we do not exclude from the class Ž of decision problems those which exhibit absentmindedness see definition . below . If all information sets in I are singletons we say that ⌫ is a decision problem with perfect information. Ž . A pure strategy, f, is a function which assigns to every history h g D Ž . an element of A h with the restriction that if h and hЈ are in the same Ž . Ž . information set f h s f hЈ . Notice that this definition requires that the decision maker plans an action at histories which he will not reach if he follows the strategy. We are now ready for the main definitions of this paper. The experience Ž . of the decision maker at a history h in D, denoted by exp h , is the sequence of information sets and actions of the decision maker along the history h. We adopt the convention that the last element in the sequence Ž . exp h is the information set which contains h. A decision problem has perfect recall if for any two histories, h, hЈ g D, Ž . Ž . which lie in the same information set, exp h s exp hЈ . Thus, in a decision problem with perfect recall, the decision maker ''remembers'' the succession of the information sets he has faced and the actions he has taken. A decision problem for which the above condition is violated is referred to as a decision problem with imperfect recall. Ž . Given a history h s a , . . . , a and L -K, the history hЈ s 1 K Ž . a, . . . , a is a subhistory of h. We say that a decision problem ⌫ exhibits 1 L absentmindedness if there are two histories h and hЈ such that hЈ is a subhistory of h and both belong to the same information set. The decision problem illustrated in Example 1 exhibits absentminded-Ž . ness since history B and its subhistory are in the same information set. \n THE VALUE OF RANDOMIZATION In this section, we discuss the implications of enlarging the strategy set of a decision maker to include random strategies. Given that the decision maker behaves as an expected utility maximizer, randomization over pure strategies is redundant for problems of either perfect or imperfect recall. Define a mixed strategy to be a probability distribution over the set of pure strategies. It describes a behavior in which randomization occurs only at the outset, before the decision problem unfolds. Each pure strategy induces a lottery over Z. A mixed strategy induces a lottery over Z which is the compound lottery of the lotteries induced by each of the pure strategies in its support. Therefore, no mixed strategy can be strictly preferred to all the pure strategies. Behavior strategies perform a different method of randomization. A beha¨ioral strategy, b, is a function which assigns to every history h g D, a Ž . Ž . \n Ž . Ž . distribution b h over A h such that b h s b hЈ for any two histories h and hЈ which lie in the same information set. In decision problems without Ž . absentmindedness b h is a lottery which is realized when the information set which contains h is reached. For decision problems with absentminded-Ž . ness we take b h to be a random device which is activated independently every time the information set which includes h is reached. Consider again Example 1. In this problem there are two pure strategies, ''B'' and ''E'' which yield payoffs of 1 and 0, respectively. Although the absentminded driver cannot use a pure strategy to reach home with certainty, he can toss a coin and obtain an expected payoff of 1.  25 . Note 1 that his optimal behavioral strategy is to exit with probability and yields 3 4 the expected payoff of . 3 It turns out that absentmindedness is necessary for behavioral strategy Ž . to be strictly optimal. This was shown in Isbell 1957 and we provide the proof for completeness. PROPOSITION 1. Suppose ⌫ does not exhibit absentmindedness. Then for any beha¨ioral strategy there is a pure strategy which yields a payoff at least as high. ² : Con¨ersely, suppose ⌫ s H, u, C, , I exhibits absentmindedness. Then, ² : there exist a decision problem ⌫Ј s H, uЈ, C, , I and a beha¨ioral strategy which yields a payoff strictly higher than any payoff achie¨ed by a pure strategy. Proof. See the Appendix. The Paradox of the Absentminded Dri¨er Re¨isited. The inconsistency discussed in Section 2 is not a consequence of the restriction that the strategy set includes only pure strategies and persists when the decision maker is allowed to choose random actions. The optimal behavioral 2 strategy is to choose B with probability . Reaching the intersection, the 3 driver will form beliefs about where he is. Denote by ␣ the probability he assigns to being at the first intersection. Then, his expected payoff is w 2 Ž . x Ž .w Ž . x ␣ p q4 1 y p p q 1 y ␣ p q 4 1 y p , where p is the probability of Ä Ž . 4 not exiting. The optimal p is now max 0, 7␣ y 3 r6␣ . This is inconsistent with his original plan unless ␣ s 1. In other words, his original plan is time consistent if and only if he believes that there is no chance he has passed the first intersection. We find such a belief unreasonable. Given his strategy it seems natural to assign to the second intersection a probability 2 which is times the probability assigned to the first intersection, which 3 implies ␣ s 0.6. The issue of consistent beliefs will be discussed in the next section. This type of time inconsistency can appear also in decision problems in which the optimal strategy is pure. Consider the following example shown in Fig.  4 . The optimal behavioral strategy is the pure strategy which selects L at d and L at d . To verify it, denote by ␣ and ␤ the probabilities of  \n CONSISTENT BELIEFS If information sets are to be interpreted as points of decision, Examples 1 and 4 suggest that a decision maker who acts on the basis of expected utility maximization may be unable to execute the optimal strategy. The first step in addressing this issue is to specify the decision maker's beliefs at an information set which is not a singleton. As we shall see, finding an appropriate specification for decision problems with absentmindedness is not conceptually trivial. We define a belief system as a function which assigns to any Ž < . information set X and any history h g X a nonnegative number h X Ž < . such that Ý h X s 1. The interpretation is that the decision maker, h g X Ž < . upon reaching X, assigns probability h X to the possibility that he is at Ž < . h. Let p h hЈ, b be the probability that, conditional on reaching hЈ, the history h will be realized when executing the strategy b. We denote Ž < . Ž < . p h ,b by p h b . Several alternatives are conceivable for the specification of the decision maker's beliefs. Since our objective is to examine the optimality of a strategy during its execution, we find it natural to assume that the beliefs of the decision maker are related in a systematic way with the strategy to be assessed. The condition that we require a belief system to satisfy to be consistent with a behavioral strategy b mirrors the frequency approach to belief formation. Namely, if an information set X is reached with Ž < . positive probability, h X is assumed to be equal to the long run proportion of times in which ''visiting'' the information set X involves being in h for a decision maker who plays the decision problem again and again and follows b.  DEFINITION.  A belief system is consistent with the behavioral strategy b if for every information set X which is reached with positive Ž < . Ž < . Ž < . probability and for every h g X, h X s p h b rÝ p hЈ b . \n hЈg X Our definition of consistency imposes restrictions only on beliefs at information sets which are reached with positive probability. Notice that, for decision problems without absentmindedness, consistency is equivalent to Bayes' formula. For decision problem with absentmindedness, however, the denominator can be greater than one. The similarity with Bayes' formula is only notational. To clarify this definition, consider first the absentminded driver example  Our definition of consistent beliefs can also be motivated as being derived from a probability space which includes the time at which the decision maker can be. As an illustration consider Example 5 and assume that each action takes one unit of time. The relevant space of instances Ž . Ž . Ž . Ž . Ž . consists of L, 1 , L, 2 , R, 1 , and R, 2 , where x, t is the instance in which the chance player chooses x and time is t. Assuming equal probabilities for each instance is consistent with the description of the chance player in the decision problem. Then, a decision maker who is told that he is at d updates his belief by the Bayesian formula. For example, the 1 unconditional probability of the second node after R is pr4, where p is the probability of choosing B at d , and the unconditional probability of  In this paper, we adopt the above definition of consistency. However, we find the following definition of consistency reasonable as well. DEFINITION. A belief system is Z-consistent with the behavioral strategy b if for every information set X which is reached with positive probability and for every h g X < h X Ž . < Ä 4 Ý p z b r࠻ hЈ ¬ hЈgX and is a subhistory of z Ž . Äz<h is a subhistory of z4 s . < Ý p z b Ž . Äz<z has a subhistory in X 4 The rationale behind this definition is that, given the behavioral strategy b, the probability of the event that the random elements which determine Ž < . the terminal history z are realized is p z b ; if the history z includes K histories in which the decision maker is asked to act then he assigns to Ž < . each of them the ex ante probability p z b rK. To illustrate the Z-consistency, consider again the absentminded driver 1 example and the strategy that selects B with probability Note that the paradoxical flavor of the absentminded driver example is unaffected by the type of consistency we adopt. Also, if the decision problem does not exhibit absentmindedness then consistency and Z-consistency are identical. We do not have a firm view about the ''right'' definition of consistent beliefs. The issue deserves further investigation. We wish to point out that if the decision maker adopts Z-consistency then he is exposed to a sort of ''money pump.'' Consider Example 5 and the behavioral strategy that selects B with probability 1. Given Z-consistent beliefs a risk neutral decision maker, upon reaching the information set, will always accept an Ž . agreement in which he gains $1.1 if he is at L and loses $1 otherwise. If such an agreement is offered whenever the information set is reached, the resulting undesirable lottery yields the decision maker $1.1 with probability 0.5 and y$2 with probability 0.5. \n TIME CONSISTENCY When does the decision maker make his decision? Can he decide about the point of time at which a decision is made? To what extent can the decision maker commit to decisions he makes? These questions are superfluous for decision problems with perfect recall since the ex ante optimal strategy remains optimal during its execution. In the presence of imperfect recall, the optimal strategy may cease to be optimal along its execution and answers to these questions are significant for the analysis. We say that a strategy is time consistent if there is not, at any information set which is reached as the decision problem unfolds, a different strategy for the remainder of the decision problem which yields a higher expected payoff. Notice that we require the optimality to be assessed only at the information sets and not before the initial history. The significance of the statement that a strategy is optimal at an information set depends on the beliefs that the decision maker is assumed to hold. Requiring that beliefs be consistent leads to the following definition.  DEFINITION . A behavioral strategy b is time consistent if there is a belief consistent with b such that for every information set X which is reached with positive probability under b, h p z¬h,b u z G h p z¬h,bЈ u z Ž . Ž . Ž . Ž . Ž . Ž . Ý Ý Ý Ý h gX z g Z h g X z g Z for any behavioral strategy bЈ. The notion of time consistency that we use is a very strong criterion. We must emphasize that it does not rest on a model of how decisions are made at each information set. The definition presumes that the decision maker, in principle, can commit to a future course of action. Of course, if the decision maker is aware that a revision of the plan is possible at future information sets, expectations of commitments are naive. Time consistency is an assessment as to whether, conditional upon the realization of information set, there exists an alternative rule of behavior which yields the decision maker a higher payoff. If an optimal strategy satisfies this criterion, the distinction with respect to information sets as points of decision or points of execution is inconsequential for a decision maker who is implementing it and whose beliefs are consistent. If, however, an optimal strategy fails this criterion, this distinction becomes significant and alternative specifications of the domain of choice and the timing of decision of the decision maker can give rise to different analyses. A well-known result states that for decision problems with perfect recall a strategy is optimal if and only if it is time consistent. This is not the case for problems with imperfect recall. As we have seen, the optimal behavioral strategy for the absentminded driver is not time consistent. It is easy 5 to see that the only time consistent strategy is to exit with probability . In the case of absentmindedness, the divergence between optimality and time consistency is two-sided. The only optimal strategy is not time consistent and the only time consistent strategy is not optimal. The next Ž . example Fig.  6  shows that, even without absentmindedness, a strategy may be time consistent and not optimal. Consider the strategy where the decision maker plays B at both information sets. The belief system consistent with this strategy assigns equal probabilities to each of the histories in each of the information sets. Therefore, this strategy is time consistent although the optimal strategy is to choose S at both information sets. The next proposition provides conditions under which optimal and time consistent strategies are equivalent. Two histories are said to split at h if h is their longest common subhistory. PROPOSITION 2. Let ⌫ be a decision problem without absentmindedness for which for any information set X and two histories hЈ, hЉ g X which split at h g C, the information sets which appear in exp hЈ are the same as in Ž . exp hЉ . \n Ž . Ž . ) A beha¨ioral strategy for ⌫ is optimal if and only if it is time consistent. probability one to nature's move R immediately after R and probability 2 to both of nature's moves when R is followed by his action B. \n THE MULTISELF APPROACHES \n Ž . For standard dynamic inconsistencies, Strotz 1956 provides a framework of analysis in which every information set is assumed to be a point of decision and the decision maker is unable to control his behavior at future information sets. A decision maker acts as a collection of hypothetical Ž . agents selves whose plans form an equilibrium. More precisely, for any Ž . decision problem ⌫ define G ⌫ to be the extensive game in which each information set of ⌫ is assigned a distinct player, and all players have the same payoff as the decision maker. The behavior of the decision maker in Ž . ⌫ is then analyzed as an equilibrium of G ⌫ . As is well known, any optimal play for ⌫ is the play induced by some subgame perfect equilib-Ž . Ž . rium of G ⌫ , and any subgame perfect equilibrium of G ⌫ corresponds to an optimal strategy. This property has the consequence that the backward induction algorithm is a procedure for solving a decision problem with perfect information. An analogous result is valid for decision problems with perfect recall and imperfect information. In this case we use the solution concept of sequential equilibrium which combines sequential rationality with the requirement of consistent beliefs. The set of distributions over the terminal nodes generated by the sequential equilibria of Ž . G ⌫ is identical to the set of distributions generated by the optimal Ž . strategies of ⌫ see  Hendon, Jacobsen, and Sloth, 1993 .  These results are called the ''no single improvement'' property; a strategy is optimal if, conditional upon reaching an information set, the decision maker cannot improve his expected payoff by changing only the action prescribed by the strategy for that information set. It implies that it makes no difference whether we model a decision problem piecemeal or in its entirety. The equivalence of the single-self and the multiselves approaches for decision problems with perfect recall breaks down when we analyze decision problems with imperfect recall. Consider Example 3. The Ž . optimal strategy R, r corresponds to a sequential equilibrium in the corresponding multiself game. However, the multiself approach does not Ž . rule out the inferior strategy L, l ; the decision maker cannot improve his payoff by simply changing the action prescribed at a single information set. Conditional upon being at d , the choice of L is optimal if the decision 1 maker treats his behavior at d as given and unchangeable and believes he 2 will play l. The Paradox of the Absentminded Dri¨er Re-re¨isited. Consider again the paradox of the absentminded driver. The formal notion of sequential equilibrium is not applicable to decision problems with absentmindedness. However, the requirement that the behavioral strategy at each information set is optimal, given the consistent beliefs, is meaningful. Despite the fact that there is only one information set, this requirement generates a strong dependence between behavioral strategies and beliefs. As we have noted before, the only strategy which satisfies this requirement is to exit with 5 probability , whereas the strategy that maximizes expected payoffs ex ante 9 1 is to exit with probability . Nevertheless, one can modify the multiself 3 approach to avoid the possibility that an optimal strategy does not satisfy sequential rationality with respect to consistent beliefs. Beliefs consistent with the optimal behavioral strategy in the paradox of 3 the absentminded driver assign probability to the first intersection. If the 5 decision maker anticipates that his ''twin-self,'' if asked to move again, will 1 1 exit with probability , then it is optimal for him to exit with probability 3 3 3 2 Ž w x w x as he is indifferent between E yielding the expected payoff 0 q 4 5 5 8 3 1 2 28 . Ž w Ž . Ž . x w x . s and B yielding an expected payoff of 4 q 1 q 1 s . In this modification, when considering a deviation at an information set X from the behavioral strategy assigned to X, the ''self'' assumes that his ''twin-self'' will use the equilibrium strategy if asked again to act, regardless of the choice he now makes. The requirement that the decision maker uses identical randomization at all histories in the same information set is retained only in equilibrium. In an actual play of the decision problem, if he decides to deviate, he may use different randomizations at different histories in the same information set. Also notice that, for the optimal strategy to satisfy sequential rationality in this modification of the multiself approach, the decision maker must 3 believe that he is at the first intersection with probability . In particular, if 5 one replaces our definition of consistency of beliefs with Z-consistency, sequential rationality fails in this modification as well. We now define the ''modified multiself'' approach formally and prove that every optimal Ž strategy is modified multiself consistent discussions with Bob Aumann and . Roger Myerson were very helpful in shaping this part of the paper .  DEFINITION . A behavioral strategy b is modified multiself consistent if there exists a belief consistent with b such that for every information set Ž . X which is reached with positive probability and for every action a g A X Ž .Ž . Ž . for which b h a ) 0 for h g X, there is no aЈ g A X such that h P z¬ h,aЈ ,b u z Ž . Ž . Ž . Ž . Ý Ý h gX z g Z ) h P z¬ h,a ,b u z . Ž . Ž . Ž . Ž . Ý Ý h gX z g Z Note that in contrast with the approach discussed in the first part of this section, the above definition imposes requirements only on the selves which are reached with positive probability. PROPOSITION 3. If a beha¨ioral strategy is optimal then it is modified multiself consistent. Proof. See the Appendix. Proposition 3 demonstrates that, within the framework of the ''modified'' multiself approach, the inconsistency of optimal plans for decision problems with absentmindedness evaporates. The interpretative ambiguities originating in the paradox of the absentminded driver also vanish as the 2 strategy to exit with probability is singled out as the only optimal and 3 consistent strategy. The value of this resolution, however, depends on the appropriateness of the ''modified'' multiself approach as a theory of decision making under imperfect recall. The behavioral assumption of the multiself approach is that each self maximizes his conditional expected payoff given his own beliefs. In decision problems with perfect recall, beliefs at each information set are independent of the choices of previous selves and each self can determine the optimal decisions of future selves by recursion. In decision problems with imperfect recall, however, the conditional payoff of each self depends on his beliefs about the behavior of earlier selves and the independence of beliefs and actions from previous choices is an additional assumption. For decision problems with absentmindedness, the ''modified'' multiself approach assumes that a decision maker, upon reaching an information set, takes his actions to be immutable at future occurrences of that information set, no matter which course of action he is contemplating now. At the other extreme one finds the opposite axiom for which only one self resides in the information set and expects that, were the information set to occur again, he would adopt whichever behavioral rule he adopts now. In this case, the strategy to exit 5 with probability would be the consistent rule of behavior for Example 1. 9 These two assumptions reflect two alternative ways of reasoning at the information set. We find both of them to have some intuitive appeal and neither to be universally valid. \n FINAL COMMENTS Our observations are only a limited exercise intended to suggest some of the issues which a comprehensive theory of imperfect recall must confront. We conclude our discussion with the following three comments: a. Other types of imperfect recall. We model imperfect recall by including in the same information set histories which contain different experiences. Such histories are assumed to be indistinguishable for the decision maker. A different type of imperfect recall is represented by a situation in which ''I know that at the first intersection I would be aware of this but at the second intersection I do not know whether I am at the first or the second intersection.'' One way to model such a scenario is by nonparti-Ž . Ž . tional informational structures see  Geanakopolos, 1990 . Rubinstein 1991  discussed the difficulty of modelling considerations such as ''At the first intersection I know that I am there but if I reach the second intersection I Ž think that there is a 10% chance that I am at the first intersection'' see . also Fluck, 1994 . It seems to us that new analytical frameworks are needed to address these issues as well as issues such as partial recall of strategy and imperfect ability to make inferences. b. Games with imperfect recall. This paper focuses on issues related to modeling decision problems with imperfect recall. Obviously, such issues carry over to extensive games. Isbell and Kuhn show that the nonequivalence between mixed and behavioral strategies can cause nonexistence of Nash equilibria in behavioral strategies. Time inconsistency of optimal strategies for some decision problems with imperfect recall makes it possible to construct games with imperfect recall that have no equilibria which satisfy sequential rationality with respect to consistent beliefs. Ambiguities in the interpretation of games with imperfect recall is probably the reason why only a handful of papers have dealt with the topic. Ž . Ž . The few exceptions include  Isbell 1957 and Alpern 1988  , who prove the existence of mixed behavioral strategy equilibrium in a class of games with Ž . imperfect recall, and Binmore 1992 who relates imperfect recall and nonpartitional knowledge. The literature on machines playing repeated Ž . games see, for example, Rubinstein, 1986 may also be interpreted as an analysis of a class of repeated games with imperfect recall, where it is costly for the players to distinguish between different histories of the game. Further investigation is needed to adapt solution concepts designed for games with perfect recall to games with imperfect recall. c. The paradox of the absentminded dri¨er. In all its forms the absentminded driver example exhibits a conflict between two types of reasoning. Commitment to the ex ante optimal behavioral strategy is obviously the normative rule of behavior. We do not have a firm view about the resolution of the paradox. We have investigated one resolution which requires dividing a decision maker into multiple independent selves. Another resolution would entail the rejection of expected utility maximization given consistent beliefs when the information set includes histories whose probabilities depend on the decision maker's actions at that information set. Savage's theory views a state as a description of a scenario which is independent of the act. In contrast, ''being at the second intersection'' is a state which is not independent from the action taken at the first, and, consequently, at the second intersection. \n APPENDIX Proof of Proposition 1. Consider an information set X and h g X. Let Ž .Ž . b be a behavioral strategy and b h a denote the probability of choosing Ž . a g A h at h. Since ⌫ does not exhibit absentmindedness, the expected Ž .Ž . payoff from b can be written as Ý b h a g q g, where each Suppose that ⌫ exhibits absentmindedness. Then, there exist a final Ž . Ž . history z and two distinct subhistories of z, h, a and hЈ, aЈ , such that h and hЈ belong to the same information set and a / aЈ. Consider a payoff Ž . Ž . function uЈ such that uЈ z s 1 and uЈ z s 0 for z / z. The claim follows, since z cannot be reached by any pure strategy, and is reached with positive probability by any behavioral strategy which assigns a positive probability to each action. Q.E.D.   FIG. 1 . 1 FIG. 1. Example 1. \n FIG. 2 . 2 FIG. 2. Example 2. \n FIG. 4. Example 4.     \n 1 and the strategy that selects B with probability equal to . A consistent 2 2 belief, conditional upon the information set d , assigns probability to 1 3 Ž . being at the first intersection. Consider next Example 5 see Fig. 5 and the strategy which selects B with probability 1. \n FIG FIG. 5. Example 5. \n R is . If p s 1, the conditional probability of each of the 4 1 three nodes in d is . \n 9 The problem of time consistency can also arise without absentmindedness as Example 2 shows. The optimal strategy is to choose S at d , B at1 d , and R at d . However, upon reaching d the decision maker prefers 2 3 1 using B at d and L at d . A decision maker who can postpone his 1 3 decisions until he has reached d or d can make a better decision 1 2 regarding the choice at d than a decision maker who decides ex ante. A 3 complete model should indicate if the domain of choice of the decision maker includes timing of the decision and the extent of his ability to use his knowledge at d and d to influence his choice at d . \n g and g are independent of b h . Consider a) g A h which a Ž .Ž . achieves the highest g . Setting b h a) s 1 yields a payoff at least as a high. The claim follows by repeating the argument for every information set. \n 2. Let b denote the payoff that the decision Ž . maker obtains by playing b. Given an information set X, let Z X denote Ž . the set of final histories having subhistories in X. Then, we can write b as < b s p z ¬ b u z q p z b u z . \n Since ⌫ does not exhibit absentmindedness, a terminal history z in Z X Ž < . Ž < . Ž < . has a unique subhistory h in X. Thus, p z b s p h b p z h, b and \n See the Appendix. Both histories L, B and R, B are in d , but exp L, B s ,d and exp R, B s d , B, d . ) is violated, since at d the Ž . To clarify the meaning of condition ) in Proposition 2, consider first Ž Example 2. 3 . Ž . Ž . Ž d,B 1 3 . Ž . Ž 2 3 . Ž . 3 decision maker loses information about the move of chance. In Example 6, even though at no information set the decision maker knows nature's Ž . move, ) is violated since exp L s L, d Ž . Ž 2 . Ž and exp R, B s . Ž . R ,d,B ,d . Notice that, however, if the decision maker had beliefs 1 2 consistent with the strategy assigning B to d and S to d , he would assign 1 2 1 FIG. 6. Example 6.Proof.", "date_published": "n/a", "url": "n/a", "filename": "10.1.1.58.4679.tei.xml", "abstract": "We argue that in extensive decision problems extensive games with a single . player with imperfect recall care must be taken in interpreting information sets and strategies. Alternative interpretations allow for different kinds of analysis. We address the following issues: 1. randomization at information sets; 2. consistent beliefs; 3. time consistency of optimal plans; 4. the multiselves approach to decision making. We illustrate our discussion through an example that we call the ''paradox of the absentminded driver.'' Journal of Economic Literature Classification Numbers: C7, D0.", "id": "2a5e22148b38a7e0ccf93fc87fe301d4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andrea Owe", "Seth D Baum"], "title": "Moral consideration of nonhumans in the ethics of artificial intelligence", "text": "Introduction The growing role of artificial intelligence (AI) technology raises important ethical questions about how AI systems should be designed and used. To date, initiatives for ethical AI have largely focused on human interests and values, such as in projects on \"AI4People\"  [1]  and \"human-compatible AI\"  [2] , two different initiatives on \"AI for Humanity\"  [3, 4] , the Partnership on AI (PAI) tenet \"We will seek to ensure that AI technologies benefit and empower as many people as possible\"  [5] , and governmental efforts such as a Chinese government report stating \"The goal of AI development should be to promote the well-being of humankind\"  [6] . This paper advances the proposition that AI ethics should also consider the interests and values of nonhumans, including (but not necessarily limited to) nonhuman animals, the natural environment, and the AI itself. We do not argue that AI ethics should only consider nonhumans. Clearly, humans are also worthy of moral consideration. We also do not argue that all nonhumans merit moral consideration. Which particular nonhuman entities deserve moral consideration and how to weight humans vs. nonhumans are important questions, but they are also complex and controversial. Given that nonhumans have thus far gotten relatively limited attention in AI ethics, we believe it is a constructive first step to address the more basic proposition that nonhuman entities merit some nonzero, nontrivial moral consideration, including in areas of AI ethics that currently give no moral consideration to nonhumans. By this we mean enough moral consideration to potentially merit some meaningful activity, and not a minuscule moral consideration so far down in the decimal points that it could simply be ignored. We believe this to be a widely acceptable proposition. It also sets the stage for the more difficult questions of how exactly to operationalize consideration of nonhumans in AI ethics, a matter that we leave for future work. Moral consideration of nonhumans is an important topic in theoretical ethics, but it is also a practical issue for real-world AI systems. There are several matters at stake. First, AI can be applied for the advancement of nonhuman entities, such as for environmental protection. In a world of limited resources, there are decisions to be made about how much to invest in AI projects that benefit nonhumans. Second, AI can inadvertently harm the nonhuman world, such as via its considerable energy consumption or potentially via certain algorithmic biases. Arguably, where AI activities harm the nonhuman world, these impacts should be balanced against the benefits of AI. Third, the long-term prospect of strong AI or artificial general intelligence (AGI) may radically transform the world for humans and everything else. How an AGI should be designed and built could depend on the particulars of the moral consideration of humans as well as nonhumans, with potentially catastrophic implications for the wrong AGI design or build. This paper does not determine how exactly these various matters should be resolved. Instead, we seek to establish that these are matters that need to be resolved. Some prior literature on AI ethics has considered nonhuman entities. A primary line of scholarship discusses the moral value of the AI itself and other computer systems  [7] [8] [9] [10] . Additionally, several studies applying Indigenous perspectives to AI ethics give moral consideration for nonhuman animals, the natural environment, and the AI itself  [11] [12] [13] . Other relevant work discusses the role of AI in suffering endured by both humans and nonhumans  [14]  and in the design of AI systems with ethics frameworks based on ethical views held by both humans and nonhumans  [15] . Whereas the literature referenced above addresses specific ethical issues and perspectives related to nonhumans, this paper addresses the more general question of the overall role of nonhumans within AI ethics. In other words, the original contribution of this paper is to provide a broad analysis of the role of nonhumans in AI ethics. The paper also informs discussions of the overarching ethical principles that should guide AI development and use. In recent years, many groups have published statements of AI ethics principles; a survey by Jobin et al.  [16]  identifies 84. This paper examines these and other statements of AI ethics principles in terms of their moral consideration for nonhumans. The paper also presents an argument for moral consideration for nonhumans in AI ethics, drawing on prior moral philosophy of nonhumans, especially from the field of environmental ethics, which has given extensive prior attention to the ethics of nonhumans  [17] . Before turning to these matters, the paper first clarifies what we mean by moral consideration for nonhumans. \n The concept of moral consideration for nonhumans We use the term moral consideration to refer to the act of assigning intrinsic moral value or significance. The term moral consideration has been used in this way in prior literature, including on the ethics of AI and robotics  [8]  and the environment  [18] . Intrinsic value is defined as that which is valuable for its own sake and not in reference to anything else  [19] . It is contrasted with extrinsic value: that which is valuable for some other reason  [20, 21] . One important type of extrinsic value is instrumental value: that which is valuable because it advances some intrinsic value. Often, intrinsic and instrumental value are treated as opposites and as the two main types of value in ethical discussion. We define \"nonhuman\" as anything that is not human, though in doing so we do not mean to claim that all nonhumans merit moral consideration. Prior studies have argued for the intrinsic value of nonhuman animals  [22, 23] , living organisms  [24, 25] , including extraterrestrial life  [26] , ecosystems  [24, 27, 28] , abiotic nature, including in outer space  [29, 30] , technologically enhanced \"posthumans\"  [31] , relationships between sufficiently advanced moral agents, including advanced robots  [8] , AI  [32] , especially sentient AI  [33, 34] , information  [35] , and the universe itself  [36] . The concept of \"posthuman\" speaks to fuzziness of the boundary between human and nonhuman: there is no definitive point at which an entity is sufficiently posthuman to no longer classify as human. As noted above, it is not our interest in this paper to adjudicate between these various arguments about which nonhumans are intrinsically valuable. We present a more general argument for intrinsically valuing nonhumans in Sect.  4.  The distinction between intrinsic and instrumental value is central for the ethics of nonhumans. Nonhuman entities may be considered valuable for their own sake or because they are valuable to humans. Clearly, nonhuman entities are instrumentally valuable to humans. Humans depend on natural environments for survival, such as for air, water, and food. Artifacts such as computers are also of obvious usefulness to humans. If humans are intrinsically valuable, then some nonhuman entities are instrumentally valuable. That is without question. The question is whether any nonhuman entities are also intrinsically valuable. This is perhaps the most fundamental question in the ethics of nonhumans. Another important distinction is between interests and values. An entity's interests are that which is good for the entity. An entity's values are that which the entity considers to be good. Unless the entity is completely selfish, its interests and values diverge. For example, someone might personally enjoy and be able to afford a life of leisure, but they nonetheless work hard to address important issues because they believe that is the right thing to do. Value systems can involve chains of moral agents valuing the values of other agents: agent 1 values the values of agent 2, who values the values of agent 3, and so on. Such chains can theoretically persist ad infinitum, though in practice they typically end with some valuation of interests. Moral consideration of nonhumans can come from placing weight on nonhumans' values and/or interests. Likewise, AI systems can morally consider nonhumans in several ways. First, they can be preprogrammed to account for the values and/or interests of nonhumans. Second, they can learn to follow the values of humans who give moral consideration to nonhumans. This is consistent with certain conceptions of \"value alignment\" or \"human compatibility\" developed in the AI ethics literature  [2] , though the literature does not generally examine the role of nonhumans, a notable exception being  [15] . Third, they can learn to follow the values held by any nonhumans that are sufficiently intelligent that they hold moral values. Potential examples include intelligent nonhuman animals, extraterrestrials, and advanced AI systems. This could also classify as \"value alignment\", though it may require different computational methods than can be used to align AI systems to human values. \n Prior attention (or lack thereof) to nonhumans in AI ethics With the conceptual background of the previous section in mind, we can now take a closer look at treatments of nonhumans in AI ethics. We begin by reviewing two systematic studies of statements of AI ethics: the Jobin et al.  [16]  survey of AI ethics guidelines and the Baum  [37]  survey of the goals of AGI research and development projects. These surveys permit a more quantitative assessment of the extent of attention to nonhumans in AI ethics. We then dive into some of the data points, taking a closer look at a few notable treatments of AI ethics in academia, industry, and government, followed by a discussion of AI ethics research. Though not comprehensive, the overarching trend observed is that the field of AI ethics gives extensive moral consideration of humans and a much smaller moral consideration of nonhumans. (The field also gives extensive attention to issues that are not specific to either humans or nonhumans, such as the trustworthiness of an AI system.) \n AI ethics principles Jobin et al.  [16]  present a systematic search of AI ethics guidelines, identifying 84. Jobin et al.  [16]  classified the guidelines in terms of the principles they contain. They report 11 types of principles: transparency (found in 73 guidelines), justice and fairness  (68) , non-maleficence  (60) , responsibility  (60) , privacy  (47) , beneficence  (41) , freedom and autonomy  (34) , trust  (28) , sustainability  (14) , dignity  (13) , and solidarity  (6) . Some of the principles do not involve moral consideration for either humans or nonhumans. Guidelines for transparency mainly concern the usage of AI, such as in the need for trust, interpretability, and oversight of AI systems. Responsibility concerns matters of integrity, liability, and general attention to ethics by those involved in AI development and use. Trust concerns whether AI systems and the organizations that provide them can be counted on to behave as expected. These conceptions of transparency, responsibility, and trust involve a special role for humans as the users of AI systems, but they are compatible with moral consideration for both humans and nonhumans because humans can use the AI systems in ways consistent with ethical frameworks that give moral consideration to either humans or nonhumans. For example, a human using an AI system to protect biodiversity would want to be able to trust that the AI system is, in fact, accomplishing this goal. All of the other principles included in Jobin et al.  [16]  are applicable to moral consideration for both humans and nonhumans, though specific treatments of the principles commonly neglect nonhumans. For example, principles of justice and fairness have been mainly (perhaps exclusively) applied to human issues such as bias and discrimination among humans, but there are also important issues of justice for nonhumans  [38, 39] . Principles of non-maleficence have been mainly applied to domains associated with human interests, such as cyberwarfare and economic loss, but AI can also be used to harm nonhumans. Principles of privacy may be less relevant to nonhumans, except perhaps if the AI itself merits moral status such that its privacy should be respected. Treatments of freedom and autonomy emphasize matters such as empowerment, self-determination, and freedom from surveillance and manipulation; these matters can be highly relevant to nonhumans, such as if AI is involved in the treatment of nonhuman animals held in captivity. Treatments of dignity call for AI to enhance, or at least not diminish, human dignity; the same could be said for the dignity of nonhumans. Finally, treatments of solidarity emphasize labor disruption, such as in technological unemployment; this is perhaps less applicable to nonhumans, though one can speak of, for example, solidarity between human and AI laborers, or solidarity among biological organisms against the potential future threat of AI takeover. The two principles in which nonhumans have gotten at least some moral consideration are beneficence and sustainability. Jobin et al.  [16]  observe that AI ethics guidelines typically do not define benefit. When they do, the definitions are mostly in terms of humanity, society, or other concepts specific to humans. However, five guidelines call for benefits to something distinctly nonhuman: the planet (2 guidelines), the environment (2), or all sentient creatures (1). Others are ambiguous, such as the six calls for AI to benefit \"everyone.\" Regarding sustainability, five AI guidelines call for sustaining the AI itself, its data, and the applicability of the insights it produces. These principles do not give moral consideration to either humans or nonhumans and are compatible with both. Moral consideration for humans is apparent in calls for fair and equal societies (1 guideline), peace  (1) , and accountability with respect to potential job losses  (1) . Moral consideration for nonhumans is possible in calls for environmental protection (3 guidelines), improving ecosystems and biodiversity (1), and reducing the environmental impact of AI systems  (1) . However, it is unclear whether these guidelines value nonhumans intrinsically or instrumentally. To summarize, the Jobin et al.  [16]  data indicate that only a small portion of AI ethics guidelines give moral consideration to nonhumans. Five guidelines call for benefits to nonhumans. Five also call for some form of environmental sustainability, though these principles do not clearly distinguish between the intrinsic and instrumental value of the environment. There are two points of overlap between the two sets of five, so eight total guidelines give explicit consideration to nonhumans. The other 76 guidelines have no attention to nonhumans. Attention to humans is extensive. \n AGI projects Baum  [37]  presents a systematic search of AGI research and development projects, identifying 45. AGI does not yet exist and remains a long-term research challenge, but there are active groups working on AGI, as documented by Baum  [37] . Baum classifies the projects according to several attributes including their stated goals. The categories of goals map neatly to this paper's treatment of moral consideration. 23 projects state intellectual goals, either \"the intellectual accomplishment of the AGI itself\" or \"using the AGI to pursue intellectual goals\"; these are not specific to either humans or nonhumans. 20 projects stated the goal of benefiting humanity. Other goals include benefiting ecosystems (three projects), animal welfare (two projects), generating profit for the AGI builders (two projects), and benefiting sentient beings and robots (one project). Note that some projects stated multiple types of goals. A more recent survey of AGI projects by Fitzgerald et al.  [40]  finds similar trends. These data are similar to the Jobin et al.  [16]  data: many AGI projects give moral consideration to humans, and only a small minority give moral consideration to nonhumans. \n Select notable examples of the treatment of nonhumans in AI ethics This subsection analyzes select AI ethics statements, with emphasis on statements that are in some way important or insightful to the paper's theme of nonhumans. The selection cuts across academia, industry, and government, with some statements including contributions from multiple sectors. Two recent academic works are explicitly calling for human-centric AI. The initiative \"AI4People\"  [1]  is, as it is mainly oriented toward human concerns. However, it also calls for \"use of AI technologies within the EU that are socially preferable (not merely acceptable) and environmentally friendly (not merely sustainable but favourable to the environment)\"  [1, p.704 ]. The emphasis on favoring the environment strongly suggests it intrinsically values the environment. In contrast, the concept of \"human-compatible AI\" developed by Russell  [2]  gives no explicit moral consideration to nonhumans. Instead, it calls for AI whose \"only objective is to maximize the realization of human preferences\"  [2, p.173 ]. The reference to preferences is about human values, not human interests, and so the AI could give moral consideration to nonhumans to the extent that human preferences do the same, but Russell  [2]  does not explicitly consider this prospect or the prospect of accounting for the preferences of nonhumans. Among AI companies, moral consideration for humans is typical. Google's AI ethics principles state, for example, \"We will seek to avoid unjust impacts on people\"  [41] . Ope-nAI writes that it pursues AI that \"leads to a good outcome for humans\" and \"Our mission is to ensure that artificial general intelligence benefits all of humanity\"  [42] . Microsoft's AI ethics principles state, for example, \"AI systems should treat all people fairly\" and \"AI systems should empower everyone and engage people\"  [43] . Microsoft CEO Satya Nadella  [44]  has also published principles and goals for AI, including \"AI must be designed to assist humanity.\" Nadella also states that human empathy \"will be valuable in the human-A.I. world,\" which might imply empathy for AI systems, though a more likely interpretation is empathy for other humans while developing and using AI systems. None of the above ethics principles give explicit moral consideration to nonhumans. Microsoft does have an initiative that appears to be rooted in part in moral consideration for nonhumans. Its \"AI for Earth\" initiative supports a variety of environmental management projects  [45] . Some projects are rooted in the environment's instrumental value for humans, such as Agrimetrics, which aims \"to help create a more productive and sustainable food system\"  [46] . Other projects appear more rooted in the intrinsic value of the environment and nonhumans, such as Wild Me, which seeks to avoid the extinction of nonhuman species  [47] . Microsoft's support for Wild Me 1 3 is strongly suggestive of it giving some moral consideration to nonhumans. The nonprofit AI for Good is another exception which seems rooted in both instrumental and intrinsic values of the environment and nonhumans, with its focus on AI and the UN Sustainable Development Goals  [48] . The same trend is observed in recent government reports on AI governance. A Chinese report states, \"The goal of AI development should be to promote the well-being of humankind\" and that AI \"should conform to human values and ethical principles (…) and serve the progress of human civilization.\" The phrase \"serve the progress of human civilization\" appears to express human interests, whereas the phrase \"human values and ethical principles\" is clearly about human values. That can include human values that give moral consideration to nonhumans, though this is not explicit in the report. A European Parliament report calls for AI risk assessment in terms of \"human safety, health and security\" and transparency on AI input in decisions impacting \"one or more persons' lives.\" A French national AI strategy initiative is called \"AI for Humanity\"; its report includes attention to environmental issues, though it is unclear whether this has any motivation in the intrinsic value of the environment  [3] . Finally, a United States report from the Obama administration calls for responsible AI to \"benefit society,\" \"improve people's lives,\" and advance the \"public good.\" Interestingly, its discussion of \"applications of AI for public good\" includes applications for environmental protection, some of which appear to be motivated by moral consideration for nonhumans, such as \"habitat preservation strategies to maximize the genetic diversity of endangered populations.\" Typically, \"public good\" refers to good for the human public; the Obama administration appears to have used a broader definition that includes nonhumans. Finally, there are professional societies and multistakeholder entities that produce consensus statements on AI ethics. These entities can represent significant portions of the overall field of AI, and so their statements are worth considering more closely. The Partnership on AI (PAI) is a multistakeholder consortium with members from industry, academia, and nonprofits. It has published a list of ethics tenets  [5] . Some tenets give moral consideration to humans, such as \"We will seek to ensure that AI technologies benefit and empower as many people as possible.\" The only reference to nonhumans is the preamble, which states \"We believe that artificial intelligence technologies hold great promise for raising the quality of people's lives and can be leveraged to help humanity address important global challenges such as climate change, food, inequality, health, and education.\" Climate change is a threat to both humans and nonhumans, so concern about it is consistent with intrinsically valuing humans and/or nonhumans. Likewise, it cannot be determined whether the preamble gives moral consideration to nonhumans. Strictly speaking, the same holds for the other challenges listed: nonhuman animals also eat food; there are inequities that cut across species; members of other species can also struggle with health; and human education can be used to advance the interests of nonhumans. Nonetheless, when people speak of the issues of food, inequality, health, and education, they typically do so with reference to human interests, and it is likely that PAI intended its statement in this way. The reference to climate change is more ambiguous given its status as a signature environmental issue. The Japanese Society for Artificial Intelligence has published Ethical Guidelines  [49] . The guidelines give frequent moral consideration to humans. For example, its preamble states the aim \"To ensure that AI research and development remains beneficial to human society.\" Its first principle states \"Members of the JSAI will contribute to the peace, safety, welfare, and public interest of humanity.\" The guidelines contain nothing that is at all suggestive of moral consideration for nonhumans. The conference Beneficial AI 2017 produced a set of AI ethics principles  [50] . The principles give moral consideration to humans such as by stating \"AI should provide a shared benefit for as many people as possible\" and \"AI technologies should benefit and empower as many people as possible.\" There is no explicit attention to nonhumans. However, the principles call for AI \"to align with human values\" and \"to accomplish human-chosen objectives.\" As discussed throughout this paper, some human values/ objectives give moral consideration to nonhumans. It cannot be determined whether the reference to human values/ objectives intended to include or exclude moral consideration for nonhumans. Finally, the Association for Computing Machinery (ACM) is an academic and professional society for computer science and adjacent fields. It has published a Code of Ethics and Professional Conduct  [51] . Though not specific to AI, the ACM Code is nonetheless applicable. Much of the code grants moral consideration only to humans, such as its first principle, that \"a computing professional should contribute to society and human well-being, acknowledging that all people are stakeholders in computing.\" In some places, it recognizes nonhumans, such as its affirmation \"an obligation of computing professionals, both individually and collectively, to use their skills for the benefit of society, its members, and the environment surrounding them.\" This phrasing appears to intrinsically value the nonhuman environment. On the other hand, the code also states \"human well-being requires a safe natural environment\" as a reason for computing professionals to \"promote environmental stability.\" This phrasing clearly articulates the environment as an instrumental value. \n AI ethics research The AI ethics research literature is of course an important part of the overall field of AI ethics. Although it is too vast to systematically analyze within the space of this paper. Instead, we make some more anecdotal observations, drawing on two recent collections, and discuss the potential role of nonhumans in select issues addressed in AI ethics research. Our primary observation is that AI ethics research includes a significant line of research giving moral consideration to the AI itself, but it generally neglects other types of nonhumans. That is apparent from the literature surveyed in the Introduction, which, for brevity, only references a small fraction of the literature on the moral status of the AI itself. It is also apparent from two recent collections, the Oxford Handbook of Ethics of AI  [52]  (henceforth \"the Handbook\") and Ethics of Artificial Intelligence edited by Liao (henceforth \"Liao\")  [53] . 5 of the Handbook's 44 chapters and 2 of Liao's 17 chapters have the moral value of AI as a significant theme. None of the chapters have other types of nonhumans as a significant theme, though some give brief mention of moral consideration of other nonhumans: the collections each have 3 chapters mentioning nonhuman animals and 1 chapter mentioning nature. While these two works are not necessarily representative of the field of AI ethics research, their contents reinforce the observation that the field has a significant line of research on the moral value of the AI itself with much less on other types of nonhumans. A lot of AI ethics research is on specific issues raised by AI technology. Some of these issues are uniquely human issues, such that it would not make sense to consider nonhumans. Other issues also concern nonhumans, such that they could be addressed in the research. To illustrate this, we discuss two examples: algorithmic bias and autonomous weapons. Algorithmic bias occurs when AI systems cause unfair biases, often by reproducing existing human biases found in data sets used to train the AI systems. Algorithmic bias research sometimes addresses issues in which nonhumans play no significant role, such as in algorithms used to evaluate job applications that are biased in favor of men over women  [54] . Nonhumans do not apply for these jobs, so the bias is not relevant to nonhumans. In other issues, nonhumans are more significant. For example, research on language processing algorithms has found biases pertaining to human race and gender  [55, 56] . Linguistic biases can also involve nonhumans, as documented in the field of ecolinguistics  [57, 58] . A simple example is the convention of using \"animal\" to refer exclusively to nonhuman animals, when in fact humans are members of the animal kingdom. This can worsen the unfortunate tendencies for ontological and ethical anthropocentrism (Sects. 4.2-4.3). Another example is the word \"game\", defined as animals hunted for food. It implies that nonhuman animals are good to the extent that they can be murdered for human benefit. Furthermore, \"game\" is an uncountable noun-one speaks of \"game\" in general, not \"games\" plural-which diminishes the individuality of the nonhuman animals classified as \"game\"  [59] . These and other examples suggest that there could be algorithmic bias involving nonhumans. Likewise, there could be nonhuman algorithmic bias research, perhaps drawing on theories of justice for nonhumans  [38, 39]  similarly to human algorithmic bias research drawing on theories of social justice  [56] . However, to the best of our knowledge, no AI ethics research has explored this issue, despite the proliferation of research on human-related algorithmic bias. It would appear that the study of algorithmic bias itself has a human-centric bias. Autonomous weapons are systems that can make their own decisions of which targets to pursue and when and how to fire on them. Autonomous weapons are an important emerging issue in AI and military ethics. Autonomous weapons are generally targeted at humans and/or military infrastructure. They likewise mostly raise ethical issues that are specific to humans, such as questions of whether use of autonomous weapons violates human dignity  [60] . Autonomous weapons may not raise significant issues regarding the natural environment. They do have some environmental impact, but so do other weapons technologies, and making a weapon autonomous may not significantly change its environmental impact. If there are any more distinctive issues raised, it may be if the AI in autonomous weapons is sufficiently advanced that the AI itself merits moral consideration. The possibility of moral consideration for a weapon system may be a novel issue for military ethics. Research on this possibility could operate at the interface of the literature on autonomous weapons and robot rights. To sum up Sect. 3, only a small minority of current treatments of AI ethics give any moral consideration to nonhumans, mainly research on the moral status of AI. It is not needed to build nonhumans into all work on AI ethics, but there is a clear role for nonhumans in a lot of work where it is currently neglected. \n The case for moral consideration of nonhumans in AI ethics Thus far, we have explained what it means to give moral consideration to nonhumans and described the extent of moral consideration for nonhumans in existing work on AI ethics. In this section, we present an argument for why nonhumans merit moral consideration. We start with the example of biodiversity conservation, which is an especially clear case of nonhumans being intrinsically valued. We then argue against ontological anthropocentrism, which is the idea that humans are distinct from nature. We argue that humans are part of nature. Finally, we discuss different conceptions of ethical anthropocentrism, which is the idea that humans are better than nonhumans. We argue that nonhumans have greaterthan-zero intrinsic value and therefore merit moral consideration. We do not attempt to answer more difficult questions of the relative intrinsic value of humans and nonhumans. \n A preliminary example: biodiversity conservation The issue of biodiversity conservation is a good place to start because it is one in which moral consideration for nonhumans is already widespread. Biodiversity can have instrumental value to humans, such as for pharmaceuticals, plant breeding, and wildlife recreation  [61] . However, recent research on the moral psychology of biodiversity conservation finds that people tend to care less about the instrumental value of biodiversity and more about its intrinsic value  [62, 63] . Likewise, the Convention on Biological Diversity, an international treaty that entered into force in 1993, articulates both instrumental and intrinsic value of biodiversity. At the root of this is the moral intuition that it is fundamentally bad for another species to go extinct, even if the species is not important for humans. Those who might reject moral consideration for nonhumans should consider: do they think the extinction of a nonhuman species is unimportant unless it affects humans? There are at least two ways that the intrinsic value of biodiversity can enter into AI ethics. One is via explicit articulations of this intrinsic value, such as in a principle \"AI projects should work toward the goal of biodiversity conservation.\" Such projects could resemble the Wild Me project supported by the Microsoft AI for Earth program. The other is to call for AI activities to follow human values. Given that humans commonly value biodiversity for its own sake, this could, indirectly, give moral consideration to biodiversity. However, this indirect approach is less reliable. Not all humans intrinsically value biodiversity, and those who do typically also intrinsically value other things. AI activities can follow other human values and neglect biodiversity conservation. If biodiversity is to be intrinsically valued, it may be more effective to make this explicit. In some cases, the intrinsic/instrumental value distinction is not important for biodiversity conservation. It can be worth conserving biodiversity because of its instrumental value for humans, regardless of whether it is of any intrinsic value. However, in other cases, the distinction matters. This can occur when something is of intrinsic value to humans but not to nonhumans, such that it is only worth pursuing if nonhumans are intrinsically valued. It can also occur when there are tradeoffs, i.e. something would be of intrinsic benefit to humans and intrinsic harm to nonhumans, or vice versa. For example, biodiversity conservation initiatives sometimes result in human populations being forcibly removed from a parcel of land to better protect the biodiversity  [64] . These situations are complex, for example, because the populations residing in that area are not the only humans affected. But setting these complexities aside, it follows that if biodiversity is only instrumentally valued, then such conservation initiatives would not be allowed, even if the harm to humans was just a minor inconvenience and the biodiversity conserved was enormous. Instead, arguably there should be a balance between humans and biodiversity, such that if enough biodiversity would be conserved, the conservation should proceed. \n Against ontological anthropocentrism: humans are part of nature Scholarship in environmental ethics often focuses on a matter that is ultimately about the nature of the world, i.e. how it is and not how it should be. This scholarship critiques the idea that humans are distinct from nature. This idea, known as ontological anthropocentrism or human/nature dualism, is seen as being at the heart of human mistreatment of nature  [17, 24, 27, 65, 66] . It manifests as a failure to adequately value nature in both intrinsic and instrumental terms. By embracing the dualism, humans can damage nature in ways that ultimately hurt themselves. Ontological anthropocentrism has a long history in human thought and has been particularly dominant in the West since the Enlightenment, and it remains prevalent today, but it lacks scientific basis. Ontological anthropocentrism can be found, for example, in beliefs that Earth is the center of the universe 1 and that humans are above the animals. These beliefs have deep cultural, theological, and linguistic roots (Sect. 3.4), but they do not survive scientific scrutiny. Modern science is unambiguous in documenting that Earth revolves around the Sun (or, more precisely, the two revolve around the Sun-Earth center of mass, which is below the surface of the Sun) and that humans are members of the animal kingdom, composed of the same atoms and molecules as everything else. The evidence clearly implies that we humans are not \"non-natural\" or \"super-natural.\" Even unresolved scientific questions, such as on the nature of consciousness, do not point to ontological anthropocentrism. At least some nonhuman animals are likely to also be conscious, such as our primate cousins. Ongoing cognitive science research characterizes forms of consciousness that may exist across a diverse range of animal species  [67] . Other nonhuman entities, including AIs, may be capable of consciousness as well. None of this is to deny the important differences between humans and other entities. Humans are an outlier species, at least for this period of life on Earth. Human activity has had an outsized impact on global climate, biodiversity, land surface usage, mineral deposits, and much more, such that some environmental scientists refer to this era of Earth's geological and biological history as the Anthropocene. Human technology is also without parallel on Earth. Chimpanzees, dolphins, and corvids may be highly intelligent, but they are not developing AI. Perhaps there are more intelligent and capable species elsewhere in the universe, and perhaps there could be more intelligent and capable species in future periods of Earth, or more intelligent artificial entities (i.e., AI systems), but for this period of Earth, humans are an outlier. \n Ethical anthropocentrism: the moral significance of being human Related to the idea that humans are inherently distinct from nature is the idea that humans are inherently better than nature. The former is about ontology, or the ways in which things can exist. The latter is about ethics, or the intrinsic value of different things that do or could exist. Even if one accepts that humans are part of nature, one could still argue that only humans are intrinsically valuable, or that humans are more (or less) intrinsically valuable than other entities. Ethical anthropocentrism is specifically the idea that humans are more intrinsically valuable because they are humans. There are other reasons why one might ethically favor humans, such as because humans are more intelligent than other entities, or if one considers humans as more capable of experiencing happiness than other entities. These reasons are not anthropocentric. This is apparent from considering hypothetical nonhuman entities that are more advanced than humans in these attributes (smarter, happier, etc.), such as an advanced AI or an extraterrestrial species. If humans are favored in the real world because of these attributes, then the AI or extraterrestrial should be favored in the hypothetical world  [68] . If the human is still favored in the hypothetical world, then the underlying ethics are anthropocentric. Ethical anthropocentrism is related to ontological anthropocentrism. Both maintain that humans are categorically distinct, and both provide reasons for morally favoring humans. But they are different reasons. If humans are ontologically distinct, then they could be morally favored due to them being ontologically distinct. This is not ethical anthropocentrism: anything else that is also ontologically distinct (perhaps an advanced AI or extraterrestrial) would also be morally favored. In contrast, ethical anthropocentrism would favor humans even if humans are ontologically unremarkable. Ethical anthropocentrism favors humans because they are human, not because humans are ontologically special. Literature on ethical anthropocentrism sometimes distinguishes between strong and weak forms  [17] . Strong ethical anthropocentrism maintains that humans are the sole thing of intrinsic value. Weak ethical anthropocentrism places some intrinsic value on nonhumans, but still values humans more because they are human. Strong ethical anthropocentrism rejects moral consideration of nonhumans; weak ethical anthropocentrism does not. Anthropocentrism and moral consideration touch on related but ultimately different aspects of valuation. Anthropocentrism is about bias in values that a moral agent holds. Moral consideration is about whether a moral agent gives any attention to something in the first place. Throughout this paper, we have emphasized moral consideration instead of anthropocentrism because the defining feature of work in AI ethics is the absence of attention to the intrinsic value of nonhumans. There is very little AI ethics work that explicitly argues against intrinsically valuing nonhumans. Given the evidence presented in this paper, it is entirely possible that AI ethicists generally reject strong ethical anthropocentrism and just have not yet thought to include nonhumans or taken the effort to do so. Three major arguments against ethical anthropocentrism can be made. The first argument centers on the idea that species membership is morally irrelevant. Instead, intrinsic moral value should be rooted in other attributes such as subjective emotion (e.g., pleasure and pain), cognitive ability, or biological complexity. As long as some nonhumans possess these attributes, strong ethical anthropocentrism is mistaken, and those who favor strong ethical anthropocentrism should \"expand their moral circle\" to include the nonhumans that possess these attributes  [22, 23] . Furthermore, if these attributes are the only sources of intrinsic value, then there is no reason to favor humans in any way, and so weak ethical anthropocentrism is also mistaken. The second argument centers on the idea that intrinsic value should not be defined in terms of individuals of any type, human or otherwise. Instead, intrinsic value should be defined in terms of the holistic systems that individuals are part of, such as ecosystems. This perspective sees intrinsic value in the interdependent relations between members of the system and in the system itself. Because humans are at most one element of such systems, it follows that some nonhumans must also be intrinsically valuable, and therefore strong ethical anthropocentrism must be mistaken  [24, 28] . Whether to adopt holistic conceptions of intrinsic value is a matter of philosophical debate. The problem with strong ethical anthropocentrism is that it requires that one rejects the holistic conceptions without even considering their merits. Furthermore, one can argue that humans have no special place within holistic systems, in which case, if such systems are the only source of intrinsic value, then weak ethical anthropocentrism is also mistaken. The third argument pertains to social choice ethical frameworks in which moral views are derived from some aggregate of society's moral views. For example, democratic societies derive moral views from an aggregate of the views of voting citizens and often also their elected representatives. Likewise, AI ethics sometimes calls for AI systems to be \"aligned\" with or \"extrapolated\" from human values  [2, 15] . Humans may not be the only beings to hold values, in which case the first argument above implies that the values of nonhumans should also be included. A social choice framework that gives equal consideration to all who hold values, human or otherwise, would go against weak ethical anthropocentrism. However, even if only human values are included, the derived moral view can still give moral consideration to nonhumans if some humans do. Indeed, moral psychology research finds that it is quite common for humans to intrinsically value nonhumans. Studies have found humans to place significant intrinsic value on nonhuman animals  [69] , wildlife  [70] , biodiversity  [62, 63] , and ecosystems  [71] , and there is some evidence that some humans also intrinsically value AI and robots  [72, 73] . To insist upon strong anthropocentrism requires privileging the moral views of strong ethical anthropocentrists over the views of everyone else. However, common arguments for using an aggregate of society's moral views emphasize that everyone's views should be included, in which case strong ethical anthropocentrism must be rejected. A case for ethical anthropocentrism posits that the fact that we are human gives us special relations with other humans and moral reasons to favor humans over other species. Strong ethical anthropocentrism requires that we privilege human relations over all other factors, including other types of relations. Weak anthropocentrism only requires that we recognize human relations as one morally significant factor, potentially alongside other factors. The merits of weak ethical anthropocentrism are a more difficult matter and outside the scope of this paper. Our central argument in this paper is that nonhumans merit at least some nonzero, nontrivial moral consideration. This argument is consistent with either weak ethical anthropocentrism or ethical non-anthropocentrism, so we do not need to assess the merits of weak ethical anthropocentrism. As a point of information, we, the authors of this paper, reject weak ethical anthropocentrism, but it is not necessary for others to share this view to accept the arguments in this paper. We do, for purposes of this paper, argue against strong ethical anthropocentrism. It is one thing to claim that being human gives us reason to favor humans. It is another thing to claim that being human gives us reason to not intrinsically value anything else. Each of us is more than just human. We are also members of, among other things, our families, our countries, our taxonomic kingdom (animals) and domain (eukaryotes), and our planet. Strong ethical anthropocentrism requires us to (1) privilege our species membership over our other memberships, especially our memberships in classes broader than species such as kingdom, domain, and planet, (2) reject holistic conceptions of intrinsic value without even considering the merits of such views, and (3) exclude the views of people who are not strong ethical anthropocentrists from aggregates of society's moral views. We can think of no good reason for doing these things, and so we reject strong ethical anthropocentrism. As long as ontological anthropocentrism and strong ethical anthropocentrism are rejected, then nonhumans merit at least some nonzero, nontrivial moral consideration. \n Implications of moral consideration of nonhumans for AI ethics The precise implications of moral consideration of nonhumans for AI ethics depend on exactly what moral consideration is given. That includes which nonhumans get consideration. It also includes how to assess the importance of nonhumans relative to each other and relative to humans. As alluded to above, different ethical theories point in different directions on these matters, and there can be reasonable disagreement on them. Indeed, we, the authors of this paper, disagree amongst ourselves on these matters. How they should be resolved merits more attention than we are able to provide in this paper, and so we leave it for future work. Instead, here we outline some more general implications for AI ethics. First, AI ethics research needs a robust study of the moral consideration of nonhumans. The field has thus far done little aside from the line of research on the moral status of the AI itself. One major need is to address the question of how to balance between humans and nonhumans. Another major need is to study the handling of the natural nonhuman world, including nonhuman animals and ecosystems. This has been a major blind spot in AI ethics. These topics are not unique to AI ethics, but AI technology does create distinctive challenges of how to operationalize the ethical issues in AI systems. A third major need is to consider the role of nonhumans in major AI ethics issues, such as algorithmic bias. Nonhumans could factor significantly in these issues in ways that existing research has not adequately considered, to the extent that it has considered it at all. Second, statements of AI ethics principles should give explicit attention to the intrinsic value of nonhumans. It is not enough to refer to human values on the grounds that some humans intrinsically value nonhumans. That leaves too much room for the intrinsic value of nonhumans being ignored, especially given how little attention nonhumans currently get in AI ethics. Exactly how to include nonhumans in the principles depends on which nonhumans are valued and how they are valued. For example, the Montréal Declaration for the Responsible Development of Artificial Intelligence includes the principle \"The development and use of artificial intelligence systems (AIS) must permit the growth of the well-being of all sentient beings.\" This is a good example of a statement that clearly indicates the intrinsic value of sentient beings, which includes both humans and nonhumans. For illustration, an even stronger principle would be: \"The main objective of development and use of AIS must be to enhance the wellbeing and flourishing of all sentient life and the natural environment, now and in the future.\" Third, when selecting which AI projects to pursue, projects to advance the interests and values of nonhumans should be among the projects considered. That does not mean that those projects should always be selected. The balance of projects for humans vs. for nonhumans depends on the relative moral weight assigned to humans and nonhumans, but projects for nonhumans should sometimes be selected. The Microsoft AI for Earth program, and in particular its support of nonhuman-oriented projects like Wild Me, is a good example of how to operationalize moral consideration for nonhumans in AI project selection. Fourth, when making decisions about which AI systems to develop and use, their inadvertent implications for nonhumans should be accounted for. This includes the material resource consumption of computer hardware and the energy needed to run AI systems. State-of-the-art AI techniques, such as deep learning, require large amounts of computing power, which in turn require large amounts of energy. Despite the growing emphasis on energy sources with low greenhouse gas emissions (mainly wind and solar, and to a lesser extent other renewables and nuclear), energy continues to come mainly from high-emission fossil fuel sources  [74] . This drives global warming, which harms nonhumans. Recent attempts to quantify and raise awareness about AI energy consumption are constructive steps  [75, 76] . Assessing the implications of energy consumption on nonhumans-and, for that matter, on humans-is a major undertaking. AI analysts should not take this on themselves, but instead should leverage existing work and expertise from fields such as environmental economics. AI groups should acknowledge that, in some circumstances, the resource and energy usage of an AI system may cause sufficient harm that it would be better to not use the AI system in the first place. Particular circumstances should be assessed on a case-by-case basis depending on the extent of resource and energy usage and other factors, and the extent of the benefits from the operation of the AI system. Fifth, AI research should investigate how to incorporate nonhuman interests and values into AI system designs. How to incorporate human values is currently a major subject of study in AI, but some of the proposed techniques do not apply to nonhumans. For example, Russell  [2]  proposes for AI systems to derive human values from human behavior. Setting aside long-recognized problems with this approach even within the human context  [77] , it is clear that the approach does not straightforwardly apply for nonhumans that do not \"behave\" in the same sense as humans, such as ecosystems, inorganic matter, or inanimate human artifacts. Here lie compelling and challenging research questions at the intersection of philosophy, environmental science, and computer science. AI ethics design is of particular importance for certain long-term AI scenarios in which an AGI takes a major or dominant position within human society, the world at large, and even broader portions of outer space. Even the most well-designed AGI could be catastrophic for some nonhumans if it is designed to advance the interests of humans or other nonhumans. Furthermore, an AGI or other sufficiently advanced AI may merit moral consideration in ways comparable to humans, raising profound questions of how to balance the interests and values of humans and AIs. AGI projects should think especially carefully about which nonhumans to include in the AGI's value system, how to balance concern for humans and nonhumans, and how to operationalize these values in the AGI technology. \n Conclusion AI technology is important in many ways, including to both human society and nonhumans. Whereas some prior work in AI ethics has considered specific topics related to nonhumans, this paper lays out more general considerations and calls for the whole field to move toward moral consideration for nonhumans. As AI becomes increasingly impactful across society, the extent to which AI ethics includes the nonhuman world will be important. Nonhumans merit moral consideration across all stages of the AI system life cycle, from data collection to design, deployment, and use. Further work is needed to explore which particular consideration to give nonhumans: which to include and how to include them. Some of this can draw on prior scholarship in moral philosophy, including on environmental ethics and computer ethics. However, AI ethics will need to do original work on how to value the AI itself and how to incorporate all of this into AI system design. Given the high stakes, this is important work to pursue. \t\t\t In isolation, this belief is strictly speaking geocentric, not anthropocentric. However, as the idea manifests, it relates strongly to ontological anthropocentrism.", "date_published": "n/a", "url": "n/a", "filename": "Owe-Baum2021_Article_MoralConsiderationOfNonhumansI.tei.xml", "abstract": "This paper argues that the field of artificial intelligence (AI) ethics needs to give more attention to the values and interests of nonhumans such as other biological species and the AI itself. It documents the extent of current attention to nonhumans in AI ethics as found in academic research, statements of ethics principles, and select projects to design, build, apply, and govern AI. It finds that the field of AI ethics gives limited and inconsistent attention to nonhumans, with the main activity being a line of research on the moral status of AI. The paper argues that nonhumans merit moral consideration, meaning that they should be actively valued for their own sake and not ignored or valued just for how they might benefit humans. Finally, it explains implications of moral consideration of nonhumans for AI ethics research and practice, including for the content of AI ethics principles, the selection of AI projects, the accounting of inadvertent effects of AI systems such as via their resource and energy consumption and potentially certain algorithmic biases, and the research challenge of incorporating nonhuman interests and values into AI system design. The paper does not take positions on which nonhumans to morally consider or how to balance the interests and values of humans vs. nonhumans. Instead, the paper makes the more basic argument that the field of AI ethics should move from its current state of affairs, in which nonhumans are usually ignored, to a state in which nonhumans are given more consistent and extensive moral consideration.", "id": "fab98e923b1904927747cd5fc0140785"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["David Manheim"], "title": "Multiparty Dynamics and Failure Modes for Machine Learning and Artificial Intelligence", "text": "Background, Motivation and Contribution When complex systems are optimized by a single agent, the representation of the system and of the goal used for optimization often leads to failures that can be surprising to the agent's designers. These failure modes go by a variety of names, Amodei and Clark called them faulty reward functions  [1]  but similar failures have been referred to as Goodhart's law  [2, 3] , Campbell's law  [4] , distributional shift  [5] , strategic behavior  [6] , reward hacking  [7] , Proxyeconomics  [8] , and other terms. Examples of these failures in the single-agent case are shown by Victoria Krakovna's extensive list of concrete examples of \"generating a solution that literally satisfies the stated objective but fails to solve the problem according to the human designer's intent.\"  [9]  Liu et al. suggest that \"a complex activity can often be performed in several different ways,\"  [10]  but not all these ways should be considered valid. To understand why, Krakovna' s list includes examples of \"achieving a goal\" by finding and exploiting bugs in a simulation engine to achieve goals  [11] [12] [13] ; by physical manipulation of objects in unanticipated ways, such as moving a table instead of the item on the table  [14] , or flipping instead of lifting a block  [15] ; and even by exploiting the problem structure or evaluation, such as returning an empty list as being sorted  [16] , or deleting the file containing the target output  [16] . \n Motivation This forms only a part of the broader set of concerns in AI safety,  [5, [17] [18] [19] , but the failure modes are the focus of a significant body of work in AI safety discussed later in the paper. However, as the systems become more capable and more widely used, Danzig and others have noted that this will \"increase rather than reduce collateral risks of loss of control.\"  [20]  The speed of such systems is almost certainly beyond the point of feasible human control, and as they become more complex, the systems are also individually likely to fail in ways that are harder to understand. While some progress has been made in the single-agent case, the systems have continued to become more capable, corporations, governments, and other actors have developed and deployed machine learning systems. These are not only largely autonomous, but also interact with each other. This allows a new set of failures, and these are not yet a focus of safety-focused research-but they are critical. \n Contribution The analogues of the earlier-mentioned classes of failure for multi-agent systems are more complex, potentially harder to mitigate, and unfortunately not the subject of a significant focus among AI safety researchers. In this paper, we introduce a classification of failures that are not yet well-addressed in the literature involving multiple agents. These failures can occur even when system designers do not intend to build conflicting AI or ML systems. The current paper contributes to the literature by outlining how and why these multi-agent failures can occur, and providing an overview of approaches that could be developed for mitigating them. In doing so, the paper will hopefully help spur system designers to explicitly consider these failure modes in designing systems, and urge caution on the part of policymakers. As a secondary contribution, the link between ongoing work on AI safety and potential work mitigating these multi-agent failures incidentally answers an objection raised by AI risk skeptics that AI safety is \"not worth current attention\" and that the issues are \"premature to worry about\"  [21] . This paper instead shows how failures due to multi-agent dynamics are critical in the present, as ML and superhuman narrow AI is being widely deployed, even given the (valid) arguments put forward by Yudkowsky  [22]  and Bostrom  [7]  for why a singleton AI is a more important source of existential risk. \n Extending Single-Agent Optimization Failures Systems which are optimized using an imperfect system model have several important failure modes categorized in work by Manheim and Garrabrant  [3] . First, imperfect correlates of the goal will be less correlated in the tails of the distribution, as discussed by Lewis  [23] . Heavily optimized systems will end up in those regions, and even well-designed metrics do not account for every possible source of variance. Second, there are several context failures  [24] , where the optimization is well behaved in the training set (\"ancestral environment\") but fails as optimization pressure is applied. For example, it may drift towards an \"edge instantiation\" where the system may optimize all the variables that relate to the true goal, but further gain on the metric is found by unexpected means. Alternatively, the optimizer may properly obey constraints in the initial stage, but find some \"nearest unblocked strategy\"  [24]  allowing it to circumvent designed limits when given more optimization power. These can all occur in single-agent scenarios. The types of failure in multi-agent systems presented in this paper can be related to Manheim and Garrabrant's classification of single-agent metric optimization failures . The four single-agent overoptimization failure modes outlined there are: • Tails Fall Apart, or Regressional inaccuracy, where the relationship between the modeled goal and the true goal is inexact due to noise (for example, measurement error,) so that the bias grows as the system is optimized. • Extremal Model Insufficiency, where the approximate model omits factors which dominate the system's behavior after optimization. • Extremal Regime Change, where the model does not include a regime change that occurs under certain (unobserved) conditions that optimization creates. • Causal Model Failure, where the agent's actions are based on a model which incorrectly represents causal relationships, and the optimization involves interventions that break the causal structure the model implicitly relies on. Despite the completeness of the above categorization, the way in which these failures occur can differ greatly even when only a single agent is present. In a multi-agent scenario, agents can stumble into or intentionally exploit model overoptimization failures in even more complex ways. Despite this complexity, the different multi-agent failure modes can be understood based on understanding the way in which the implicit or explicit system models used by agents fail. \n Defining Multi-Agent Failures In this paper, a multi-agent optimization failure is when one (or more) of the agents which can achieve positive outcomes in some scenarios exhibits behaviors that negatively affect its own outcome due to the actions of one or more agents other than itself. This occurs either when the objective function of the agent no longer aligns with the goal, as occurs in the Regressional and both Extremal cases, or when the learned relationship between action(s), the metric(s), and the goal have changed, as in the Causal failure case. This definition does not require the failure to be due to malicious behavior on the part of any agent, nor does it forbid it. Note also that the definition does not require failure of the system, as in Behzadan and Munir's categorization of adversarial attacks  [25] , nor does it make any assumptions about type of the agents, such as the type of learning or optimization system used. (The multi-agent cases implicitly preclude agents from being either strongly boxed, as Drexler proposed  [26] , or oracular, as discussed by Armstrong  [27] .) \n Multi-Agent Failures: Context and Categorization Several relatively straightforward failure modes involving interactions between an agent and a regulator were referred to in Manheim and Garrabrant as adversarial Goodhart  [3] . These occur where one AI system opportunistically alters or optimizes the system and uses the expected optimization of a different victim agent to hijack the overall system. For example, \"smart market\" electrical grids use systems that optimize producer actions and prices with a linear optimization system using known criteria. If power lines or power plants have strategically planned maintenance schedules, an owner can manipulate the resulting prices to its own advantage, as occurred (legally) in the case of Enron  [28] . This is possible because the manipulator can plan in the presence of a known optimization regime. This class of manipulation by an agent frustrating a regulator's goals is an important case, but more complex dynamics can also exist, and Manheim and Garrabrant noted that there are \"clearly further dynamics worth exploring.\"  [3]  This involves not only multiple heterogenous agents, which Kleinberg and Raghavan suggest an avenue for investigating, but also interaction between those agents  [6] . An example of a well-understood multi-agent system, the game of poker, allows clarification of why the complexity is far greater in the interaction case. \n Texas Hold'em and the Complexity of Multi-Agent Dynamics In many-agent systems, simple interactions can become complex adaptive systems due to agent behavior, as the game of poker shows. Solutions to simplified models of two-player poker predate game theory as a field  [29] , and for simplified variants, two-player draw poker has a fairly simple optimal strategy  [30] . These early, manually computed solutions were made possible both by limiting the complexity of the cards, and more importantly by limiting interaction to a single bet size, with no raising or interaction between the players. In the more general case of heads-up limit Texas Hold'em, significantly more work was needed, given the multiplicity of card combinations, the existence of hidden information, and player interaction, but this multi-stage interactive game is \"now essentially weakly solved\"  [31] . Still, this game involves only two players. In the no-limit version of the game, Brown and Sandholm recently unveiled superhuman AI  [32] , which restricts the game to \"Heads' Up\" poker, which involves only two players per game, and still falls far short of a full solution to the game. The complex adaptive nature of multi-agent systems means that each agent needs model not only model the system itself, but also the actions of the other player(s). The multiplicity of potential outcomes, betting strategies, and different outcomes becomes rapidly infeasible to represent other than heuristically. In limit Texas Hold'em poker, for example, the number of card combinations is immense, but the branching possibilities for betting is the more difficult challenge. In a no-betting game of Hold'em with P players, there are 52!/((52 − 2P − 5)! • 2P • 5!) possible situations. This is 2.8 • 10 12 hands in the two-player case, 3.3 • 10 15 in the three-player case, and growing by a similar factor when expanded to the four-, five-, or six-player case. The probability of winning is the probability that the five cards on the table plus two unknown other cards from the deck are a better hand than any that another player holds. In Texas Hold'em, there are four betting stages, one after each stage of cards is revealed. Billings et al. use a reduced complexity game (limiting betting to three rounds per stage) and find a complexity of O(10 18 ) in the two-hand case  [33] . That means the two-player, three-round game complexity is comparable in size to a no-betting four-player game, with 4.1 • 10 18 card combinations possible. Unlike a no-betting game, however, a player must consider much more than the simple probability that the hand held is better than those held by other players. That calculation is unmodified during the additional branching due to player choices. The somewhat more difficult issue is that the additional branching requires Bayesian updates to estimate the probable distribution of hand strengths held by other players based on their decisions, which significantly increases the complexity of solving the game. The most critical challenge, however, is that each player bets based on the additional information provided by not only the hidden information provided by their cards, but also based on the betting behavior of other players. Opponent(s) make betting decisions based on non-public information (in Texas Hold'em, hole cards) and strategy for betting requires a meta-update taking advantage of the information the other player reveals by betting. The players must also update based on potential strategic betting by other players, which occurs when a player bets in a way calculated to deceive. To deal with this, poker players need to model not just the cards, but also the strategic decisions of other players. This complex model of strategic decisions must be re-run for all the possible combinations at each decision point to arrive at a conclusion about what other players are doing. Even after this is complete, an advanced poker player, or an effective AI, must then decide not just how likely they are to win, but also how to play strategically, optimizing based on how other players will react to the different choices available. Behaviors such as bluffing and slow play are based on these dynamics, which become much more complex as the number of rounds of betting and the number of players increases. For example, slow play involves underbidding compared to the strength of your hand. This requires that the players will later be able to raise the stakes, and allows a player to lure others into committing additional money. The complexity of the required modeling of other agents' decision processes grows as a function of the number of choices and stages at which each agent makes a decision. This type of complexity is common in multi-agent systems. In general, however, the problem is much broader in scope than what can be illustrated by a rigidly structured game such as poker. \n Limited Complexity Models versus the Real World In machine learning systems, the underlying system is approximated by implicitly or explicitly learning a multidimensional transformation between inputs and outputs. This transformation approximates a combination of the relationships between inputs and the underlying system, and between the system state and the outputs. The complexity of the model learned is limited by the computational complexity of the underlying structure, and while the number of possible states for the input is large, it is typically dwarfed by the number of possible states of the system. The critical feature of machine learning that allows such systems to be successful is that most relationships can be approximated without inspecting every available state. (All models simplify the systems they represent.) The implicit simplification done by machine learning is often quite impressive, picking up on clues present in the input that humans might not notice, but it comes at the cost of having difficult to understand and difficult to interpret implicit models of the system. Any intelligence, whether machine learning-based, human, or AI, requires similar implicit simplification, since the branching complexity of even a relatively simple game such as Go dwarfs the number of atoms in the universe. Because even moderately complex systems cannot be fully represented, as discussed by Soares  [34] , the types of optimization failures discussed above are inevitable. The contrapositive to Conant and Ashby's theorem  [35]  is that if a system is more complex than the model, any attempt to control the system will be imperfect. Learning, whether human or machine, builds approximate models based on observations, or input data. This implies that the behavior of the approximation in regions far from those covered by the training data is more likely to markedly differ from reality. The more systems change over time, the more difficult prediction becomes-and the more optimization is performed on a system, the more it will change. Worsening this problem, the learning that occurs in ML systems fails to account for the embedded agency issues discussed by Demski and Garrabrant  [36] , and interaction between agents with implicit models of each other and themselves amplifies many of these concerns. \n Failure modes Because an essential part of multi-agent dynamic system modeling is opponent modeling, the opponent models are a central part of any machine learning model. These opponent models may be implicit in the overall model, or they may be explicitly represented, but they are still models that are approximate. In many cases, opponent behavior is ignored-by implicitly simplifying other agent behavior to noise, or by assuming no adversarial agents exist. Because these models are imperfect, they will be vulnerable to overoptimization failures discussed above. The list below is conceptually complete, but limited in at least three ways. First, examples given in this list primarily discuss failures that occur between two parties, such as a malicious actor and a victim, or failures induced by multiple individually benign agents. This would exclude strategies where agents manipulate others indirectly, or those where coordinated interaction between agents is used to manipulate the system. It is possible that when more agents are involved, more specific classes of failure will be relevant. Second, the below list does not include how other factors can compound metric failures. These are critical, but may involve overoptimization, or multiple-agent interaction, only indirectly. For example, O'Neil discusses a class of failure involving the interaction between the system, the inputs, and validation of outputs  [37] . These failures occur when a system's metrics are validated in part based on outputs it contributes towards. For example, a system predicting greater crime rates in areas with high minority concentrations leads to more police presence, which in turn leads to a higher rate of crime found. This higher rate of crime in those areas is used to train the model, which leads it to reinforce the earlier unjustified assumption. Such cases are both likely to occur, and especially hard to recognize, when the interaction between multiple systems is complex, and it is unclear whether the system's effects are due in part to its own actions (This class of failure seems particularly likely in systems that are trained via \"self-play,\" where failures in the model of the system get reinforced by incorrect feedback on the basis of the models, which is also a case of model insufficiency failure.). Third and finally, the failure modes exclude cases that do not directly involve metric overoptimizations, such as systems learning unacceptable behavior implicitly due to training data that contains unanticipated biases, or failing to attempt to optimize for social preferences such as fairness. These are again important, but they are more basic failures of system design. With those caveats, we propose the following classes of multi-agent overoptimization failures. For each, a general definition is provided, followed by one or more toy models that demonstrate the failure mode. Each agent attempts to achieve their goal by optimizing for the metric, but the optimization is performed by different agents without any explicit coordination or a priori knowledge about the other agents. The specifics of the strategies that can be constructed and the structure of the system can be arbitrarily complex, but as explored below, the ways in which these models fail can still be understood generally. These models are deliberately simplified, but where possible, real-world examples of the failures exhibited in the model are suggested. These examples come from both human systems where parallel dynamics exist, and examples of the failures in extent systems with automated agents. In the toy models, M i and G i stands for the metric and goal, respectively, for agent i. The metric is an imperfect proxy for the goal, and will typically be defined in relation to a goal. (The goal itself is often left unspecified, since the model applies to arbitrary systems and agent goals.) In some cases, the failure is non-adversarial, but where relevant, there is a victim agent V and an opponent agent O that attempts to exploit it. Please note that the failures can be shown with examples formulated with game-theoretic notation, but doing so requires more complex specifications of the system and interactions than is possible using the below characterization of the agent goals and the systems. Failure Mode 1. Accidental Steering is when multiple agents alter the systems in ways not anticipated by at least one agent, creating one of the above-mentioned single-party overoptimization failures. Remark 1. This failure mode manifests similarly to the single-agent case and differs only in that agents do not anticipate the actions of other agents. When agents have closely related goals, even if those goals are aligned, it can exacerbate the types of failures that occur in single-agent cases. Because the failing agent alone does not (or cannot) trigger the failure, this differs from the single-agent case. The distributional shift can occur due to a combination of actors' otherwise potentially positive influences by either putting the system in an extremal state where the previously learned relationship decays, or triggering a regime change where previously beneficial actions are harmful. \n Model. 1.1-Group Overoptimization. A set of agents each have goals which affect the system in related ways, and metric-goal relationship changes in the extremal region where x>a. As noted above, M i and G i stands for the metric and goal, respectively, for agent i. This extremal region is one where single-agent failure modes will occur for some or all agents. Each agent i can influence the metric by an amount α i , where ∑ α i > a, but ∀α i < a. In the extremal subspace where M i > a, the metric reverses direction, making further optimization of the metric harm the agent's goal. M i = G i , where M i <= a M i (a) − G i , where M i > a (1) Remark 2. In the presence of multiple agents without coordination, manipulation of factors not already being manipulated by other agents is likely to be easier and more rewarding, potentially leading to inadvertent steering due to model inadequacy, as discussed in Manheim and Garrabrant's categorization of single-agent cases  [3] . As shown there overoptimization can lead to perverse outcomes, and the failing agent(s) can hurt both their own goals, and in similar ways, can lead to negative impacts on the goals of other agents. Model. 1.2-Catastrophic Threshold Failure. M i = x i G i = a + (∑ ∀i x i ) where ∑ ∀i x i <= T a − − − (∑ ∀i x i ) where ∑ ∀i x i > T (2) Each agent manipulates their own variable, unaware of the overall impact. Even though the agents are collaborating, because they cannot see other agents' variables, there is no obvious way to limit the combined impact on the system to stay below the catastrophic threshold T. Because each agent is exploring a different variable, they each are potentially optimizing different parts of the system. Remark 3. This type of catastrophic threshold is commonly discussed in relations to complex adaptive systems, but can occur even in systems where the catastrophic threshold is simple. The case discussed by Michael Eisen involves pricing on Amazon was due to a pair of deterministic linear pricing-setting bots interacting to set the price of an otherwise unremarkable biology book at tens of millions of dollars, showing that runaway dynamics are possible even in the simplest cases  [38] . This phenomenon is also expected whenever exceeding some constraint breaks the system, and such constraints are often not identified until a failure occurs. Example 1. This type of coordination failure can occur in situations such as overfishing across multiple regions, where each group catches local fish, which they can see, but at a given threshold across regions the fish population collapses, and recovery is very slow. (In this case, the groups typically are selfish rather than collaborating, making the dynamics even more extreme.) Example 2. Smaldino and McElreath  [39]  shows this failure mode specifically occurring with statistical methodology in academia, where academics find novel ways to degrade statistical rigor. The more general \"Mutable Practices\" model presented by Braganza  [8] , based on part on Smaldino and McElreath, has each agent attempting to both outperform the other agents on a metric as well as fulfill a shared societal goal, allows agents to evolve and find new strategies that combine to subvert a societal goal. Failure Mode 2. Coordination Failure occurs when multiple agents clash despite having potentially compatible goals. \n Remark 4. Coordination is an inherently difficult task, and can in general be considered impossible  [40] . In practice, coordination is especially difficult when the goals of other agents are incompletely known or not fully understood. Coordination failures such as Yudkowsky's Inadequate equilibria are stable, and coordination to escape from such an equilibrium can be problematic even when agents share goals  [41] . \n Model. 2.1-Unintended Resource Contention. A fixed resource R is split between uses R n by different agents. Each agent has limited funds f i , and R i is allocated to agent i for exploitation in proportion to their bid for the resources c R i . The agents choose amounts to spend on acquiring resources, and then choose amounts s n i to exploit each resource, resulting in utility U(s n , R n ). The agent goals are based on the overall exploitation of the resources by all agents. R i = c R i ∑ ∀i c R i G i = ∑ ∀i U i,n (s n i , R n ) (3) In this case, we see that conflicting instrumental goals that neither side anticipates will cause wasted funds due to contention. The more funds spent on resource capture, which is zero-sum, the less remaining for exploitation, which can be positive-sum. Above nominal spending on resources to capture them from aligned competitor-agents will reduce funds available for exploitation of those resources, even though less resource contention would benefit all agents. Remark 5. Preferences and gains from different uses can be homogeneous, so that all agents have no marginal gain from affecting the allocation, funds will be wasted on resource contention. More generally, heterogeneous preferences can lead to contention to control the allocation, with sub-optimal individual outcomes, and heterogeneous abilities can lead to less-capable agents harming their goals by capturing then ineffectively exploiting resources. Example 3. Different forms of scientific research benefit different goals differently. Even if spending in every area benefits everyone, a fixed pool of resources implies that with different preferences, contention between projects with different positive impacts will occur. To the extent that effort must be directed towards grant-seeking instead of scientific work, the resources available for the projects themselves are reduced, sometimes enough to cause a net loss. Remark 6. Coordination limiting overuse of public goods is a major area of research in economics. Ostrom explains how such coordination is only possible when conflicts are anticipated or noticed and where a reliable mechanism can be devised  [42] . \n Model. 2.2-Unnecessary Resource Contention. As above, but each agent has an identical reward function of f i,n . Even though all goals are shared, a lack of coordination in the above case leads to overspending, as shown in simple systems and for specified algebraic objective functions in the context of welfare economics. This literature shows many methods for how gains are possible, and in the simplest examples this occurs when agents coordinate to minimize overall spending on resource acquisition. \n Remark 7. Coordination mechanisms themselves can be exploited by agents. The field of algorithmic game theory has several results for why this is only sometimes possible, and how building mechanisms to avoid such exploitation is possible  [43] . Failure Mode 3. Adversarial optimization can occur when a victim agent has an incomplete model of how an opponent can influence the system. The opponent's model of the victim allows it to intentionally select for cases where the victim's model performs poorly and/or promotes the opponent's goal  [3] . \n Model. 3.1-Adversarial Goal Poisoning . G V = x G O = −x M V = X : X ∼ normal(x, σ 2 (y)) M O = (X, y) (4) In this case, the Opponent O can see the metric for the victim, and can select for cases where y is large and X is small, so that V chooses maximal values of X, to the marginal benefit of O. Example 4. A victim's model can be learned by \"Stealing\" models using techniques such as those explored by Tramèr et al.  [44] . In such a case, the information gained can be used for model evasion and other attacks mentioned there. Example 5. Chess and other game engines may adaptively learn and choose openings or strategies for which the victim is weakest. Example 6. Sophisticated financial actors can make trades to dupe victims into buying or selling an asset (\"Momentum Ignition\") in order to exploit the resulting price changes  [45] , leading to a failure of the exploited agent due to an actual change in the system which it misinterprets. Remark 8. The probability of exploitable reward functions increases with the complexity of the system the agents manipulate  [5] , and the simplicity of the agent and their reward function. The potential for exploitation by other agents seems to follow the same pattern, where simple agents will be manipulated by agents with more accurate opponent models. \n Model. 3.2-Adversarial Optimization Theft. An attacker can discover exploitable quirks in the goal function to make the victim agent optimize for a new goal, as in Manheim and Garrabrant's Campbell's law example, slightly adapted here  [3] . M V = G V + X M O = G O • X (5) O selects M O after seeing V's choice of metric. In this case, we can assume the opponent chooses a metric to maximize based on the system and the victim's goal, which is known to the attacker. The opponent can choose their M O so that the victim's later selection then induces a relationship between X and the opponent goal, especially at the extremes. Here, the opponent selects such that even weak selection on M O hijacks the victim's selection on M V to achieve their goal, because states where M V is high have changed. In the example given, if X ∼ normal(µ, σ 2 ), the correlation between G O and M O is zero over the full set of states, but becomes positive on the subspace selected by the victim. (Please note that the opponent choice of metric is not itself a useful proxy for their goal absent the victim's actions-it is a purely parasitic choice.) Failure Mode 4. Input spoofing and filtering-Filtered evidence can be provided, or false evidence can be manufactured and put into the training data stream of a victim agent. Model. 4.1-Input Spoofing. Victim agent receives public data D(x i |t) about the present world-state, and builds a model to choose actions which return rewards f (x|t). The opponent can generate events x i to poison the victim's learned model. \n Remark 9. See the classes of data poisoning attacks explored by Wang and Chaudhuri  [46]  against online learning, and of Chen et al  [47] . for creating backdoors in deep-learning verification systems. Example 7. Financial market participants can (illegally) spoof by posting orders that will quickly be canceled in a \"momentum ignition\" strategy to lure others into buying or selling, as has been alleged to be occurring in high-frequency-trading  [45] . This differs from the earlier example in that the transactions are not bona-fide transactions which fool other agents, but are actually false evidence. Example 8. Rating systems can be attacked by inputting false reviews into a system, or by discouraging reviews by those likely to be the least or most satisfied reviewers. \n Model. 4.2-Active Input Spoofing. As in (4.1), where the victim agent employs active learning. In this case, the opponent can potentially fool the system into collecting data that seems very useful to the victim from crafted poisoned sources. Example 9. Honeypots can be placed, or Sybil attacks mounted by opponents to fool victims into learning from examples that systematically differ from the true distribution. Example 10. Comments by users \"Max\" and \"Vincent DeBacco\" on Eisen's blog post about Amazon pricing suggested that it is very possible to abuse badly built linear pricing models on Amazon to receive discounts, if the algorithms choose prices based on other quoted prices  [38] . \n Model. 4.3-Input Filtering. As in (4.1), but instead of generating false evidence, true evidence is hidden to systematically alter the distribution of events seen. Example 11. Financial actors can filter the evidence available to other agents by performing transactions they do not want seen as private transactions or dark pool transactions. Remark 10. There are classes of system where it is impossible to generate arbitrary false data points, but selective filtering can have similar effects. Failure Mode 5. Goal co-option is when an opponent controls the system the Victim runs on, or relies on, and can therefore make changes to affect the victim's actions. Remark 11. Whenever the computer systems running AI and ML systems are themselves insecure, it presents a very tempting weak point that potentially requires much less effort than earlier methods of fooling the system. Model. 5.1-External Reward Function Modification. Opponent O directly modifies Victim V's reward function to achieve a different objective than the one originally specified. Remark 12. Slight changes in a reward function may have non-obvious impacts until after the system is deployed. \n Model. 5.2-Output Interception. Opponent O intercepts and modifies Victim V's output. \n Model. 5.3-Data or Label Interception. Opponent O modifies externally stored scoring rules (labels) or data inputs provided to Victim V's output. Example 12. Xiao, Xiao, and Eckert explore a \"label flipping\" attack against support vector machines  [48]  where modifying a limited number of labels used in the training set can cause performance to deteriorate severely. Remark 13. As noted above, there are cases where generating false data may be impossible or easily detected. Modifying the inputs during training may create less obvious traces of an attack has occurred. Where this is impossible, access can also allow pure observation which, while not itself an attack, can allow an opponent to engage in various other exploits discussed earlier. To conclude the list of failure modes, it is useful to note a few areas where the failures are induced or amplified. This is when agents explicitly incentivize certain behaviors on the part of other agents, perhaps by providing payments. These public interactions and incentive payments are not fundamentally different from other failure modes, but can create or magnify any of the other modes. This is discussed in literature on the evolution of collusion, such as Dixon's treatment  [49] . Contra Dixon, however, the failure modes discussed here can prevent the collusion from being beneficial. A second, related case is when creating incentives where an agent fails to anticipate either the ways in which the other agents can achieve the incentivized target, or the systemic changes that are induced. These so-called \"Cobra effects\"  [3]  can lead to both the simpler failures of the single-agent cases explored in Manheim and Garrabrant, and lead to the failures above. Lastly, as noted by Sandberg  [50] , agents with different \"speeds\" (and, equivalently, processing power per unit time,) can exacerbate victimization, since older and slower systems are susceptible, and susceptibility to attacks only grows as new methods of exploitation are found. \n Discussion Multi-agent systems can naturally give rise to cooperation instead of competition, as discussed in Leibo et al.'s 2017 paper  [51] . The conditions under which there is exploitation rather than cooperation, however, are less well understood. A more recent paper by Leibo proposes that the competition dynamic can be used to encourage more complex models. This discusses coordination failures, but the discussion of dynamics leading to the failures does not engage with the literature on safety or goal-alignment  [52] . Leibo's work, however, differs from most earlier work where multi-agent systems are trained together with a single goal, perforce leading to cooperative behavior, as in Lowe et al.'s heavily cited work, in which \"competitive\" dynamics are dealt with by pre-programming explicit models of other agent behaviors  [53] . The failure modes outlined (accidental steering, coordination failures, adversarial misalignment, input spoofing or filtering, and goal co-option or direct hacking) are all due to models that do not fully account for other agent behavior. Because all models must simplify the systems they represent, the prerequisites for these failures are necessarily present in complex-enough systems where multiple non-coordinated agents interact. The problems of embedded agents discussed by Demski and Garrabrant  [36]  make it particularly clear that current approaches are fundamentally unable to fully represent these factors. For this and other reasons, mitigating the failures modes discussed here are not yet central to the work of building better ML or narrow AI systems. At the same time, some competitive domains such as finance are already experiencing some of these exploitative failures  [45] , and bots engaging in social network manipulation, or various forms of more direct interstate competition are likely engaging in similar strategies. The failures seen so far are minimally disruptive. At the same time, many of the outlined failures are more problematic for agents with a higher degree of sophistication, so they should be expected not to lead to catastrophic failures given the types of fairly rudimentary agents currently being deployed. For this reason, specification gaming currently appears to be a mitigable problem, or as Stuart Russell claimed, be thought of as \"errors in specifying the objective, period\"  [54] . This might be taken to imply that these failures are avoidable, but the current trajectory of these systems means that the problems will inevitably worsen as they become more complex and more such systems are deployed, and the approaches used are fundamentally incapable of overcoming the obstacles discussed. \n Potential Avenues for Mitigation Mitigations for these failures exist, but as long as the fundamental problems discussed by Demski and Garrabrant  [36]  are unaddressed, the dynamics driving these classes of failure seem unavoidable. Furthermore, such failures are likely to be surprising. They will emerge as multiple machine learning agents are deployed, and more sophisticated models will be more likely to trigger them. However, as argued above, these failures are fundamental to interaction between complex agents. This means that while it is unclear how quickly such failures will emerge, or if they will be quickly recognized, it is unquestionable that they will continue to occur. System designers and policymakers should expect that these problems will become intractable if deferred, and are therefore particularly critical to address now. It is be expected that any solution involves a combination of approaches  [17] , though the brief overview of safety approaches below shows that not all general approaches to AI safety are helpful for multi-agent failures. First, there are approaches that limit optimization. This can be done via satisficing, using approaches such as Taylor's Quantilizers, which pick actions at random from the top quantile of evaluated choices  [55] . Satisficing approaches can help in prevent exploiting other agents, or in preventing accidental overoptimization, but are not effective as a defense against exploitative agents or systemic failures due to agent interaction. Another approach limiting optimization is explicit safety guarantees. In extrema, this looks like an AI-Box, preventing any interaction of the AI with the wider world and hence preventing agent interaction completely. This is effective if such boxes are not escaped, but it is unclear if this is possible  [27] . Less extreme versions of safety guarantees are sometimes possible, especially in domains where a formal model of safe behavior is possible, and the system is sufficiently well understood. For example, Shalev-Shwartz et al. have such a model for self-driving cars, heavily relying on the fact that the physics involved with keeping cars from hitting one another, or other objects, is in effect perfectly understood  [56] . Expanding this to less well understood domains seems possible, but is problematic for reasons discussed elsewhere  [57] . Without limiting optimization explicitly, some approaches attempt to better define the goals, and thereby reduce the extent of unanticipated behaviors. These approaches involve some version of direct optimization safety. One promising direction for limiting the extent to which goal-directed optimization can be misdirected is to try to recognize actions rather than goals  [58] . Human-in-the-loop oversight is another direction for minimizing surprise and ensuring alignment, though this is already infeasible in many systems  [20] . Neither approach is likely to be more effective than humans themselves are at preventing such exploitation. The primary forward-looking approach for safety is some version of ensuring that the goal is aligned, which is the bulk of what Yampolskiy and Fox refer to as AI safety engineering  [59] . In multi-agent contexts there is still a concern that because human values are complex,  [18]  exploitation is an intrinsically unavoidable pitfall in multi-agent systems. Paul Christiano's \"Distillation and Amplification\" approach involves safe amplification using coordinated multi-agent systems  [60] . This itself involves addressing some of the challenges with multi-agent approaches, and work on safe amplification using coordinated multi-agent systems in that context has begun  [61] . In that work, the coordinating agents are predictive instead of agentic, so the failure modes are more restricted. The methods suggested can also be extended to agentic systems, where they may prove more worrisome, and solving the challenges potentially involves mitigating several failure modes outlined here. Between optimization-limiting approaches and AI safety engineering, it is possible that many of the multi-agent failures discussed in the paper can be mitigated, though not eliminated. In addition, there will always be pressure to prioritize performance as opposed to safety, and safe systems are unlikely to perform as quickly as unsafe ones  [20] . Even if the tradeoff resolves in favor of slower, safer systems, such systems can only be created if these approaches are further explored and the many challenges involved are solved before widespread deployment of unsafe ML and AI. Once the systems are deployed, it seems infeasible that safer approaches could stop failures due to exploiting and exploitable systems, short of recalling them. This is not a concern for the far-off future where misaligned superintelligent AI poses an existential risk. It is instead a present problem, and it is growing more serious along with the growth of research that does not address it. \n Conclusions: Model Failures and Policy Failures Work addressing the failure modes outlined in the paper is potentially very valuable, in part because these failure modes are mitigable or avoidable if anticipated. AI and ML system designers and users should expect that many currently successful but naive agents will be exploited in the future. Because of this, the failure modes are likely to become more difficult to address if deferred, and are therefore particularly critical to understand and address them preemptively. This may take the form of systemic changes such as redesigned financial market structures, or may involve ensuring that agents have built-in failsafes, or that they fail gracefully when exploited. At present, it seems unlikely that large enough and detected failures will be sufficient to slow the deployment of these systems. It is possible that governmental actors, policymakers, and commercial entities will recognize the tremendous complexities of multiparty coordination among autonomous agents and address these failure modes, or slow deployment and work towards addressing these problems even before they become catastrophic. Alternatively, it is possible these challenges will become apparent via limited catastrophes that are so blatant that AI safety will be prioritized. This depends on how critical the failures are, how clearly they can be diagnosed, and whether the public demands they be addressed. Even if AI amplification remains wholly infeasible, humanity is already deploying autonomous systems with little regards to safety. The depth of complexity is significant but limited in current systems, and the strategic interactions of autonomous systems are therefore even more limited. However, just as AI for poker eventually became capable enough to understand multi-player interaction and engage in strategic play, AI in other systems should expect to be confronted with these challenges. We do not know when the card sharks will show up, or the extent to which they will make the games they play unsafe for others, but we should admit now that we are as-yet unprepared for them.", "date_published": "n/a", "url": "n/a", "filename": "BDCC-03-00021.tei.xml", "abstract": "An important challenge for safety in machine learning and artificial intelligence systems is a set of related failures involving specification gaming, reward hacking, fragility to distributional shifts, and Goodhart's or Campbell's law. This paper presents additional failure modes for interactions within multi-agent systems that are closely related. These multi-agent failure modes are more complex, more problematic, and less well understood than the single-agent case, and are also already occurring, largely unnoticed. After motivating the discussion with examples from poker-playing artificial intelligence (AI), the paper explains why these failure modes are in some senses unavoidable. Following this, the paper categorizes failure modes, provides definitions, and cites examples for each of the modes: accidental steering, coordination failures, adversarial misalignment, input spoofing and filtering, and goal co-option or direct hacking. The paper then discusses how extant literature on multi-agent AI fails to address these failure modes, and identifies work which may be useful for the mitigation of these failure modes.", "id": "259346ae10f2aeb00bd14130b25ade72"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anders Sandberg", "David Manheim"], "title": "WHAT IS THE UPPER LIMIT OF VALUE?", "text": "Introduction The future of humanity contains seemingly limitless possibility, with implications for the value of our choices in the short term. Ethics discusses those choices, and for consequentialists in particular, infinities have worrying ethical implications. Bostrom  [1]  and others have asked questions, for example, about how aggregative consequentialist theories can deal with infinities. Others have expanded the questions still further, including measure problems in cosmology, and related issues in infinite computable or even noncomputable universes in a multiverse. In this paper, we will argue that \"limitless\" and \"infinite\" when used to describe value or the moral importance of our decisions can only be hyperbolic, rather than exact descriptions. Our physical universe is bounded, both physically  1  and in terms of possibility. Furthermore, this finite limit is true both in the near term, and in the indefinite future. To discuss this, we restrict ourselves to a relatively prosaic setting, and for at least this paper, we restrict our interests to a single universe that obeys the laws of physics as currently (partially) understood. In this understanding, the light-speed limit is absolute, quantum physics can be interpreted without multiverses  2  , and thermodynamic limits are unavoidable. In addition to those assumptions about the universe, we will assume, based on the overwhelming scientific evidence, that human brains, and those of other beings with moral opinions and values, perform only within the laws of physics. Given that, we also assume that values are either objective functions of the physical world, as posited by Moore  [2] , or are subjective only to the extent that individual physical brains can conceive of them. Given these fairly wide boundaries, we argue that there are no infinities that must be addressed for ethical decisionmaking. We do so by establishing concrete bounds on possible sizes of value that can be changed. Even though there are truly mind-boggling numbers involved, these are finite numbers which do not admit the class of question Bostrom and others pose. Given our assumptions, we cannot refute those arguments absolutely, or make the claim that we should assign no probability to such potential value systems. We will, however, make a strong claim that unless our understanding of physics is fundamentally flawed in specific ways, the amount of accessible and achievable value for any decision-relevant question is necessarily finite. We feel that the assumptions are likely enough, or can be modified to be so, that the argument is strong enough to be considered sufficient for resolving the issues for long term consequentialist thinking. Before addressing fundamental issues about the limit of value, we will address the far easier question of whether there is a limit to economic growth, following and extending Ng's work  [3] .Based on a few observations about the Milky Way, we find a clear indication that in the short term future of the next 100,000 years, even in the most optimistic case, current levels of economic growth are incompatible with basic physical limits. This has implications for welfare economics and social choice explored by Ng  [3] , as well as for long term expectations about growth discussed by Hanson  [4] . We next use that discussion to motivate questions about whether a more general framework for value allows infinities. After discussing and answering two possible objections to limited value in a finite universe, we outline additional physical limitations to both value and valuing. We then conclude that we can assign a theoretical upper bound to possible value in the physical universe. \n Economic Growth and Physical Limits Economic theory, the study of human choices about allocation of scarce resources  3  , is useful for describing a large portion of what humans do. This is in large part because it is a positive description, rather than a normative one, and is local in scope. For example, it does not claim that preferences must be a certain way. Instead, economic theory simply notes that humans' values seem to be a certain way. Given some reasonable local assumptions, this can be used to make falsifiable predictions about behavior. Such a theory is by no means universally correct, as noted below, but forms a more useful predictive theory than most alternatives. Clearly, the arguments and assumptions do not need to extend indefinitely to be useful. For example, economic assumptions such as non-satiation (which Mas-Collel  [6]  and others more carefully refer to as local non-satiation) will obviously fall apart at some point. That is, if blueberries are good, more blueberries are better, but at some point the volume of blueberries in question leads to absurdities  [7]  and disvalue. Here, we suggest that there are fundamental reasons to question the application of simple economic thinking about value and growth in value to long-term decisions. This is important independent of the broader argument about non-infinite value, and also both informs and motivates that argument. Economic growth is an increase in the productive capacity of the economy. Economic growth measures the increase in the ability to produce goods that people derive value from. The above-mentioned locally correct models of human behavior and interaction lead to a natural conclusion that under some reasonable assumptions about preferences, economic growth will continue indefinitely. If there is possible value that can be built via investment of physical or other real resources, humans are motivated to at least attempt to create that value. If growth at some non-nominal rate continues indefinitely, however, this leads to difficult to physically justify results. For example, at a 2% level of real growth, the Gross World Product (GWP) would grow to 10 860 times current levels in 100,000 years. GWP is currently around $100 trillion U S 2020  4  , so the total value is ∼ $10 874 dollars U S 2020 . The naive model implies that we can continue to receive positive returns on investment, and humans will in fact value the resulting achievements or goods to that extent. Note that this is not an argument about the nominal growth rate, but rather the real growth in value. That is, the US dollar may not exist in centuries, much less millennia, galactic years, or aeons. Despite this, if humans survive to continue creating value, the implicit argument of continued growth is that we would find things to do that create more real value in that time. It is also not an argument that natural limits of the types often invoked in sustainability discussions will necessarily stop growth  [9]    5  . While there are material limits to the amount of stuff that can be acquired (and, as we will argue below, this does matter for our conclusion) the stuff may be organized into ever better forms. That means that our argument about \"Limits to Growth\" is both less immediate, and more fundamental than the ecological limits most extensively discussed in economics.  [10]   \n Economists versus Physicists \"Scientists have developed a powerful new weapon that destroys people but leaves buildings standing -it's called the 17% interest rate.\"\" \n -Johnny Carson As Einstein almost certainly did not say, \"compound interest is the most powerful force in the universe.\" But physicists are careful to limit their infinities so that they cancel. Economists have fewer problems with infinities, so they have never needed a similar type of caution  6  . On the other hand, if the claim that exponential economic growth at a rate materially above zero can continue indefinitely is true, it would indeed need to be the most powerful force in the universe, because as we argue, it would need to overcome some otherwise fundamental physical limits, outlined in the Appendix. This continued growth seems intuitively very implausible, but intuition can be misleading. Still, as will be discussed in more detail below, there are fundamental physical limits to how much \"stuff\" we can get, and how far we can go in a given amount of time. \n Short-term Limits for Humanity One initial consequence of the fundamental physical limits outlined in the appendix is the short term expansion of humanity over the next 60-100,000 years. In the best case, humanity expands throughout the galaxy in the coming millennia, spreading the reach of potential value. Despite expansion, the speed of light limits humanity to the Milky Way galaxy during this time frame. The Milky Way is ∼100,000 light-years across, and it would take at least on the order of that many years to settle it, with ∼60,000 being a lower limit to get to the far end from Earth 7 .  4  We adopt the convention that the ambiguous use of dollars needs to have units properly noted, as should occur everywhere in scientific research for any unit. However, because \"dollars\" do not have a constant economic value, or even refer to the same currency across countries, the subscript/superscript notation is used to disambiguate. The notation is adapted from Gwern  [8] .  5  Daly suggests somewhat informally that \"the physically growing macro-economy is still limited by its displacement of the finite ecosphere,\" in the context of economic versus \"uneconomic\" growth that creates \"risks of ecological catastrophe that increase with growthism and technological impatience.\" In practice, we agree that sustainable development is a reasonable argument to curtail certain types of economic growth. It seems clear that unsustainable growth which leads to ecological collapse less likely to have unbounded long term potential than the alternative of short-term environmental protection. However, our argument is somewhat more fundamental in nature.  6  This is not strictly true. Economic endogenous growth models are plagued by finite-time singularities if the feedback from knowledge or other factors to themselves is stronger than linear. Demanding that such factors are never negative and always remain finite force the model to exhibit exponential growth  [11] . Others are less concerned about the singularities in the model: \"Singularities are always mathematical idealisations of natural phenomena: they are not present in reality but foreshadow an important transition or change of regime\"  [12] .  7  If we instead consider the short term to stretch slightly longer, we could begin to consider the satellite galaxies to the Milky way, but this still limits us to smaller galaxies that are almost all within 1 million light-years of Earth. From there, there is a notable gap of approximately another 1 million light-years to Andromeda, the nearest major galaxy. For that reason, humanity's potential for expansion is unfortunately somewhat limited over the next 2 million years. Thankfully, the medium term future looks rosier, since the entire Laniakea Supercluster is within a quarter billion light-years, and all of the Pisces-Cetus Supercluster Complex is accessible to humanity within the next billion years. The Milky Way local neighborhood masses about 1.5 trillion solar masses (or 3 × 10 42 kilograms)  [13, 14]  within a radius of 652,000 light-years, of which about 6.5% is baryonic matter. There are about 10 68 cubic centimeters in the Milky Way galaxy alone (if we consider a sphere of diameter 100,000 ly.) And inside of a currently small portion of the space and mass, humanity pursues maximizing value. At this point, the question is how much value is possible. \n Bounds on Short-term Economic Value and Growth \"We have always held to the hope, the belief, the conviction that there is a better life, a better world, beyond the horizon.\" \n --Franklin Delano Roosevelt Given the above set of bounds, given specific ways to calculate value, we can, inter alia, calculate an approximate maximum to total accessible value, and hence the possible growth in economic value. As discussed in the appendix, possible information that can be stored is limited by space and mass. The volume accessible in our 100,000 year time frame allows us 10 134 bits of theoretically accessible storage. The 10 134 bits of storage correspond to 2 10 134 possible states, and hence the maximum number we could store in the Milky Way has 3 × 10 133 digits 8 . However, short of a misaligned AI which wire-heads into storing the largest possible value in the register containing its value function, it seems unlikely that there is any conception of value that consists solely of the ability to store massive numbers  9  To consider economic return, we need a baseline for what is being invested. As noted above, current GWP is $100 trillion U S 2020 /year, which can be viewed as an income stream for humanity. Discounting the income at a generous 2%, we find a net present value of human productivity of $50 quadrillion. Treating the discounted total of human production as an upper bound on how much we can possibly commit to investing now, we ask: how much value can be created in the future? To create a minimum threshold for value, we consider the value of the universe if converted into some currently expensive substance, say Plutonium-239, which costs around $5.24 U S 2007 per milligram,  [15] , we find that converting the Milky Way leads to a value of $1.5 × 10 49 U S 2020 . Given our baseline, this is a return on investment of 3 × 10 32 x, which is a huge return, but discounted over the next 100,000 years, this gives a paltry annual return on investment of 0.075%. But this minimum is pessimistic -surely we can generate more value than just expensive mass with a service economy of some sort. If we consider the value of human productivity, we have a conceptually huge possible space of value that any human can provide to others. Starting with the present levels of productivity, we can very generously assume each human is able to produce $1 million U S 2020 of value per year. The average human masses 70 kilograms, and we unrealistically ignore the requirement for gravity, air, food, and so on, to find that the 3 × 10 42 kilograms of mass allows for 4 × 10 40 humans. Assume each creates value, then assume this production starts immediately and accumulates over the next 100,000 years. This gives an upper bound is that the galaxy could produce $4 × 10 51 U S 2020 of value in the next 100,000 years, which seems large until we note that it implies an annualized rate of return of 0.08%; far more than our estimate above, but a tiny rate of return. If we even more generously assume that not only would humans instantly settle the entire Milky Way and convert the entire mass into humans, as above, but that they individually annually produce the Earth's annual Gross World Product (GWP) today, repeating our earlier assumptions, the rate of return reaches 0.1%. We can go further, and even more implausibly claim each can produces a googol dollars U S 2020 of value per year and this accumulates, to reach a 0.3% annual growth rate. And perhaps we were unfairly pessimistic about our time frame for settling the Milky Way, and use the bare minimum physical limit of 60,000 years -this gives us a still paltry 0.51% rate. All of this may be argued still to be conservative. Perhaps Hansonian Ems colonize the galaxy  [16] , taking up far less space, and living faster lives. In the limit, each could constantly be producing things of value for all other Ems to enjoy, allowing for the growth in value to be far higher. Still, and bounds found for a service economy are a function of space and mass growth over time. The way in which available mass increases with time is lumpy, based on locations of mass that are close to our solar system, but is at most similar to the increase in physical space. The lightspeed limitation means that the amount of \"stuff\" we can acquire from nature will at most grow as (4πc 3 /3)ρt 3 ∝ t  3 10  This leads to an inescapable conclusion, that there is at most a polynomial rate of economic growth in the long-term. The available space cannot grow as quickly as any exponential function, so growth in value is guaranteed to be lower than the exponential growth implied by compound interest, at least in the very long term. As the earlier increasingly implausible assumptions suggest, and the rate of growth limitations make even clearer, postulating greater potential value still means that high or even steady low rates of growth would not be possible. Using our narrow economic definition of value, at some point in the near-term (cosmic) future, economic growth will be sharply limited. To posit any greater value, we need to consider the question of value much more broadly. Before doing so, we briefly consider a few implications of the short term conclusions. \n Implications of Short-Term Limits There are a number of interesting long-term policy implications of the existence of a limit to growth. Critically, many are related to the (not-quite oxymoronic) most immediate long-termist uncertainties. \n Discounting One set of conclusions relate to discounting of the far future, a topic discussed in varying contexts  [18] . These implications of the choice of discounting rate range widely, from decisions about personal donations  [19] , to management theory  [20] , to climate policy  [21] . Our conclusions about limited growth in the cosmological short term provides a much stronger argument for (very) low discount rates than much past work, albeit applicable only when considering longer time scales than even most long-termist policy considers. Applying the conclusions about limited growth to discounting, even over the very-long term, requires care, since different arguments for discounting exist 11  [22] . Specifically, this argument against discounting applies if long-term discounting is primarily based on an arbitrage or alternative investment arguments, where the reason to discount later value is because there is an alternative of investing and receiving a larger amount of capital in the future due to growth. If the argument is based on risk, where the reason to discount future value is because of the possibility that it will not be realized, our argument seems less relevant, through that of Weitzman  [23] , which argues for low discounts by reasoning over different possible futures, is correspondingly strengthened -and applies over the far shorter term. \n Hinge of History \"We live during the hinge of history... If we act wisely in the next few centuries, humanity will survive its most dangerous and decisive period. Our descendants could, if necessary, go elsewhere, spreading through this galaxy.\" \n Derek Parfit, On What Matters, Volume II Another set of conclusions that can be found from the sharp limit to near-term economic growth relates to \"Hinge of History,\" based on a claim by Derek Parfit  [24]  about the importance of the near future, which was later put more pointedly in the above quote. In general terms, the hinge could relate to the recent economic turbulence introduced by Appelbaum and Henderson,  [25] , and the short term moral opportunities for equality introduced by Head,  [26]  but is primarily a long-termist idea  [27] , presaged by Greaves and MacAskill, of \"influencing the choice among non-extinction attractor states\" over the entirety of the future.  [28]  MacAskill suggests two worldviews that imply the present is such a hinge, while our exploration implies a third -though unlike those worldviews, our argument does not suggest the hinge is imminent. The argument is that while there is no guarantee that the upper-bound of long-term value will be reached, or even approached, the current exponential economic growth cannot be maintained. The alternative hypothesis is that even though the world is changing and increasing in value ever more quickly, it will continue to do so indefinitely. Instead, the transition from exponential to polynomial economic growth would imply that a hinge-of-history of a sort must exist, though it may not be in the near future or related to the current slowing of growth, since the necessary timing depends heavily on questions of when the limit will be reached. This argument for a hinge-of-history rests on the plausible, but not certain, claim that choosing the type of economic growth in the exponential growth phase significantly changes the course of civilization in a way that will not occur afterwards. The weakness in this argument is that at some point after the end of explosive growth, a long-reflection, such at that proposed by MacAskill  [29]  could still drastically alter trajectory. That is, the limit to growth does not by itself imply that any \"hinge\" in growth rates leads to irreversible decisions, and a different argument would still apply for why decisions during the hinge would be irreversible, such as MacAskill's two worldviews concerning value-lock-in, or irreversible choices that lead to annihilation. \n Economic Singularities The model above shows that recent growth has been higher than the rates plausible in the long term, and the time frame over which economic growth must drop to a lower rate is a topic for further consideration. This is because economic growth has been, and in the very near-term likely will be, far higher than the long-term economic growth horizon. The necessity of such a transition also relates to claims of an eventual economic singularity. Such a singularity is already possibly unlikely to occur now, at least based on very-short term economic evidence  [30] . But going further, a transition to polynomial growth creates a large but non-exponential limit to the speed of any claimed singularity in the longer term. \n Values as Choices \"Give the person what they need -and they will want amenities. Provide him with amenities -he will strive for luxury. Showered with luxury -he will begin to sigh in exquisite. Let him get exquisite -he will crave frenzy. Give him everything that he wishes -he will complain that he was deceived, and that he did not receive what he wanted.\" \n -Ernest Hemingway If there are two items, or two states of the world, and a choice must be made between them, we call the one chosen of higher value than the other. Similarly, if a person is willing to give up one item for another in, for instance, an economic transaction, we say that the one received is higher value to the recipient. Comparisons induce a mathematical \"order\" of states  14  . For this reason, either preference value or trade value is at least an ordinal preference, and any notion of value is comparative, rather than measured. In this case, it is immediately possible to show that value under this conception in a finite universe is finite. Given a finite set of items or states of the world, it is trivial to see that the most preferred can only be a finite number of steps better than the least preferred. If the accessible universe is finite, as discussed below, it is then clear that the number of steps between possible states is potentially incredibly large, but still finite  15  . But value may be more than this ordinal concept. If we accept the cardinal conception of utility, value may be possible to add and multiply, rather than just compare  16  . If utility is mapped to real numbers, one item can meaningfully be called not just more valuable, but twice as valuable as another thing  17  . One key reason to consider cardinal utility is because it allows comparison of options given preferences with uncertainty about outcomes. That is, a choice may involve uncertainty, in which case the ordinal concept is insufficient. \n Probabilities Require Cardinal Utility Reasoning about preferences consistently given uncertainty, as introduced by Ramsey  [32] , requires ordering of preferences over probabilities of outcomes, rather than just outcomes. A decision maker might prefer a 1% probability of outcome A to a 100% probability of outcome B. A simple way to represent this is to assign more than 100 times the value, called utility, to A, then use probabilistic expectation of utility to see that the choice giving a 1% chance of outcome A is preferred. If arbitrary probabilities need to be considered, and we wish to ensure that the preferences being discussed fulfill certain basic assumptions about rational preferences, then cardinal utility, or a structure mathematically identical to it, will be required. In this way, reasoning and decisions under uncertainty are the conceptual basis for considering utility of outcomes, rather than just atomic comparisons of specific options. And this can lead to problems when we insist on bounds for value. If decision makers consider an arbitrarily small probability of a given outcome preferrable to some other certain outcome, the utility assigned to the improbable outcome must be correspondingly high. To guarantee finitude of utility for a coherent decisionmaker, we need to argue that there is some minimum probability that can be assigned. This is conceptually fraught, but there are several possible responses we will discuss below in 4.2. This cardinal concept of utility also allows other possible objections to the conclusion that a finite universe can only have finite value, including lexicographic preferences, non-doscounted infinite time horizons, and other concerns which we will address. \n Aggregative Ethical Theories and Objective versus Subjective Value \"For welfare to be finite... the 'amplitude' of welfare cannot be infinite at any particular moment in time, and a life can only have a finite duration of welfare.\" -Siebe Rozendal  [33]  Given our initial claims about the physical universe, we will note that our discussion of finitude of value is independent of a number of important philosophical disputes about ethics, at least in most ethical systems. For instance, whether value is an objective or subjective function of the world does not change whether an upper limit exists since it still needs to be represented  18  . Similarly, aggregative value, where overall value is the sum of the value for each individual, will increase the limit of value being discussed, for example, by multiplying the value limit by as much as the number of possible morally relevant beings which can assign value. Despite this, because the morally relevant beings are physical, and therefore require mass, the number of such morally relevant beings is finite, and therefore so is the total value  19  . Similar arguments for finitude can be made for any other form of value aggregation of which we are aware. \n Result, Objections, and Responses Value is finite. That is, in a physical universe that has no infinite physical and temporal scope, no infinities are available to represent infinite value in decision-making processes. Hence, any possible assignment of value used for decision making has to be finite. It is possible to object to the claim of finitude. We believe that the entire set of possible objections, however, can be answered. Responding to the objections, therefore, is critical to the above claim. We therefore list the key objections, then review and explain them. After each, we will respond, including novel arguments against several such claims. 1. Rejecting (our current understanding of) physics \n Rejecting preferences, by either • rejecting comparability, • rejecting finite preferences, • rejecting bounded expected utility, or • bounding probabilities (possibly via embracing infintesimals as valid probabilities for decisions,) 3. Rejecting ethical theories or embracing nihilism  20  4. Rejecting the need for accessibility of value for decisions. 5. Rejecting or altering traditional causal decision theories. \n Rejecting Physics \"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring.\" -Carl Sagan  18  It may be suggested that value could be purely 'subjective', i.e. independent of even the physical state of the brain of the person whose values are considered. If so, there is no relationship between the world and value, and the \"ethics\" being discussed does not relate to any decisions which may be made. If, however, ethics does relate to the physical world, then there can be some value assigned to each possible state and/or world-history.  19  One could imagine an ad-hoc objection assigning moral weight to an infinite number of posited non-physical beings, but this does not change preferences being about physical states, so the resulting infinite value can therefore be mapped to finite numbers. The number of angels dancing on the head of a pin may be infinite, but the value they assign to the pin effectively cannot be.  20  or perhaps some other non-consequentialist, non-deontological, and non-rights and non-virtue based theory of ethics. Perhaps our understanding of physics is incorrect. That is, it is possible that our understanding of any of the assumedcorrect disciplines discussed here, from cosmology to computation. This is not merely an objection to the authors' personal grasp of the subjects, but a claim that specific premises may, in the future, be found to be incorrect  21  . \n Pessimistic Meta-induction and expectations of falsification The pessimistic meta-induction warns that since many past successful scientific theories were found to be false, we have no reason expect that our currently successful theories are approximately true. Hence, for example, the above constraints on information processing are not guaranteed to imply finitude. Indeed, many of them are based on information physics that is weakly understood and liable to be updated in new directions. If physics in our universe does, in fact, allow for access to infinite matter, energy, time, or computation through some as-yet-undiscovered loophole, it would undermine the central claim to finitude. This criticism cannot be refuted, but there are two reasons to be at least somewhat skeptical. First, scientific progress is not typically revisionist, but rather aggregative. Even the scientific revolutions of Newton, then Einstein, did not eliminate gravity, but rather explained it further. While we should regard the scientific input to our argument as tentative, the fallibility argument merely shows that science will likely change. It does not show that it will change in the direction of allowing infinite storage. Second, past results in physics have increasingly found strict bounds on the range of physical phenomena rather than unbounding them. Classical mechanics allow for far more forms of dynamics than relativistic mechanics, and quantum mechanics strongly constrain what can be known and manipulated on small scales  22  . While all of these arguments in defense of physics are strong evidence that it is correct, it is reasonable to assign a very small but non-zero value to the possibility that the laws of physics allow for infinities. In that case, any claimed infinities based on a claim of incorrect physics can only provide conditional infinities. And those conditional infinities may be irrelevant to our decisionmaking, for various reasons. \n Boltzmann Brains, Decisions, and the indefinite long-term One specific possible consideration for an infinity is that after the heat-death of the universe  23  there will be an indefinitely long period where Boltzmann brains can be created from random fluctuations. Such brains are isomorphic to thinking human brains, and in the infinite long-term, an infinite number of such brains might exist  [34] . If such brains are morally relevant, this seems to provide a value infinity. We argue that even if these brains have moral value, it is by construction impossible to affect their state, or the distribution of their states. This makes their value largely irrelevant to decision-making, with one caveat. That is, if a decision-maker believes that these brains have positive or negative moral value, it could influence decisions about whether decisions that could (or would intentionally) destroy space-time, for instance, by causing a false-vacuum collapse. Such an action would be a positive or negative decision, depending on whether the future value of a non-collapsed universe is otherwise positive or negative. Similar and related implications exist depending on whether a post-collapse universe itself has a positive or negative moral value. Despite the caveat, however, a corresponding (and less limited) argument can be made about decisionmaking for other proposed infinities that cannot be affected. For example, inaccessible portions of the universe, beyond the reachable light-cone, cannot be causally influenced. As long as we maintain that we care about the causal impacts of decisions, they are irrelevant to decisionmaking. \n Rejecting preferences It is possible to reject the claims of relevant finitude by dispensing with one of the various required aspects of preferences needed for decisionmaking  24  . \n Rejecting Comparability It may be objected that perhaps value is not finite because comparison is impossible, or alternatively, that some things are \"infinitely valuable\" on their own. Or perhaps humans can assign values in ways that are incompatible with finite value  25  . We discuss both, in sections 4.2.1 and 4.2.2, and reject them as untenable. To address the first, we note the discussion in philosophy about whether values can be incomparable -that is, given two items or states of the world, neither is better. Chang's work  [35, 36]  makes a compelling argument rejecting incomparability, which view we would adopt for this paper. However, even without that, this incomparability argument is less than fatal to our claim. This is because incomparability still leads to a partial ordering of value, rather than a total ordering. That is, in a universe with positive value on bananas and blueberries, it is still the case that two blueberries are better than one, and two blueberries and a banana are better than one blueberry and a banana, even if we reject any possibility that the two can be compared. This leads to a large number of partial orderings of preferences, but any claims made about full orderings will apply to each partial ordering. For that reason, an analogue of any argument we provide will exist even if values are incomparable, and non-comparability alone does not allow for infinite value. The alternative objection is where one item is \"infinitely better\" than another, and is thus incomparable in a different sense. These lexical preferences, as they are called, are not commensurate with any other value; most people would consider taking 2 bananas for one blueberry, but is seems at least arguable that there is no number of bananas many of them would take in exchange for not staying alive  26  . This idea of lexical preferences will be dealt with formally and in general below. To address the second point, that humans might have an intrinsic ability to assign infinite values, we need to address what the assignment of human values means. One key question is what preferences are coherent, or valid, and a second is how these relate to decision making. There is a significant philosophical literature on whether infinities are coherent or logically possible, from Aristotle's rejection of \"actual infinities\", to recent work on infinite ethics  [37] . We do not address these points, and limit ourselves to whether there are morally relevant physical infinities. Given that, we must return to a central assumption we have made about values, that they must be morally relevant, i.e. make a difference in some ethical comparison or decision. This will be discussed further after considering lexicographic preferences.  24  Aside from the obvious but ineffective method of rejecting the requirement for coherency or consistency, since doing so, and allowing utilities that do not conform to the required characteristics of rationality makes any discussion of maximum \"utilities\" irrelevant.  25  For example, due to infinitesimal probability assignments. \n Rejecting Finite Preferences So-called lexicographic preferences consider some states infinitely better than other states  27  . There are two approaches that would justify a lexicographic claim, one intrinsic, and one based on probability. The intrinsic justification is that there are incomparably better states. For example, a negative utilitarian could argue that any state in which there is no suffering is infinitely preferable to any state that contains suffering. Compatibly, the probabilistic justification is that no probability of one state is sufficiently low that it would not be preferred. In this model, a negative utilitarian could say that any finite probability of more suffering is worse than a guarantee of less suffering  28  . If such preferences exist, they are typically claimed to lead to the impossibility of representing preferences as a real-valued utility function  [38] . That is, if one item is \"infinitely better,\" and preferences are cardinal  29  , the claim is that we cannot bound utility to any finite value at all. We argue that as long as goods or states of the universe are finite, as occurs in a fixed volume of space with fixed total mass, this is untrue. This is based on a constructive proof, shown below. As an example, we can consider a finite universe with three goods and lexicographic preferences A B C. We denote the number of each good N A , N B , N C , and the maximum possible of each in the finite universe as  30  . We can now assign utility for a bundle of goods M A , M B , M C . Set M = max(M A , M B , M C ) U (N A , N B , N C ) = N C + N B (M + 1) + N A (M 2 + 1). This assignment captures the lexicographic preferences exactly  31  . This can obviously be extended to any finite number of goods N n , with a total of N = max(n) different goods, with any finite maximum of each  32  . As the most extreme possible example, assume our social welfare function has a lexicographic preference for filling the Milky Way with hedonium A over hedonium B, B over C, etc. We could still bound the number n of different such \"goods\" that could plausibly be lexicographically preferred, and the number M which could be made in the universe, to derive a bound of 2 × M n+1 . Even if the number of lexicographically preferred goods is enormous, it is bounded by the physically limited arrangement of matter that is possible, giving a still finite, if even more unimaginably large number. To extend this logic to address probabilities, we must consider the assignment of probabilities and assignment of utility, which we do below. Before doing so, however, we will justify a claim underlying our argument. \n Rejecting Bounded Expected Utility \"We have therefore to consider the human mind and what is the most we can ask of it.\" -Frank Ramsey 27 Etymologically, this comes from the idea of a lexicographic order, which generalizes the notion of alphabetic ordering. In an alphabetized list, any word starting with the letter \"A\" is lexicographically prior to any word starting with \"B\". Similarly, any world with a lexicographically preferred good is always better than one without. This is equivalent to saying that no matter what else occurs, that world is better. As we will show, however, lexicographic preferences do no necessarily imply actual infinities.  28  We do not address the interesting but unrelated case where a negative utilitarian might have preferences that include trading off amounts and probabilities of suffering, though this might also involve claimed infinities, as they are addressed with the same argument as is used for other cases below.  29  If preferences are ordinal, this just requires placing lexicographic preferred goods above less preferred ones, so the objection is irrelevant.  30  This will be a huge number, of course. As an illustrative example, bananas are approximately 150 grams each, so the Milky Way would has MBananas of 2 × 10 43 , for normal sized bananas. Blueberries are around half a gram, leading to M Blueberry = 3 × 10 45 .  31  In the previous footnote's banana-blueberry universe, someone with a lexicographic preference for bananas over blueberries who assigns blueberries value 1 would assign value 3 × 10 45 to a banana.  32  Per the previous footnote, many believe that human lives are lexicographically superior to bananas. As the 2nd century Jewish saying notes, \"Whoever saves a single human life, it is as if they have saved a whole world,\" (Sanhedrin 4:5) which presumably is even more true if the world that is saved in entirely filled with bananas. But representing the value of infinitely valuable (presumably happy) human lives does not require use of infinity. In fact, the by-assumption infinite value of a human life can be represented as being at most 2 × 10 43 +1 times the value of a banana, or around 6 × 10 88 +1 times the value of a blueberry. In a blueberry-banana-human value universe, infinitely valuable human lives are much better than blueberries, but mathematically still not even a googol times better, much less infinitely so. Given that we conclude even lexicographic preferences are finite, might a person still assign infinite value to some outcome? That is, if utility is not only an ordering of states, but a function, is it coherent for a person to insist on discontinuities, where they assign five times as much utility to an apple as to a banana, and infinitely more utility to remaining alive as to dying? It is possible to argue that value-in-general is different than utility, but to the extent that the value is used for decision, we need some way to choose, and to be coherent, this method must compare states. Since we assume all states must be comparable using a (perhaps non-VNM-like) utility function, it still seems that value is bounded by the ability of the valuer to make decisions and to consider the different outcomes. A utility function, in the decision theoretic or economic sense, is invariant to affine transformations. That is, multiplying every value by 2, or adding 17 to each utility, does not change the preferences that the utility function describes. But placing anything as infinitely valuable is a lexicographic preference, and for utility functions, the exact location of the lexicographic preference is irrelevant -as long as the order is preserved. This is true even when allowing for truly different experienced utility. If two humans both experience utility from a good, but (as an extension of Nozick's monster,  [39] ) one of them has a qualitatively infinitely better experience, we can treat their value as a lexicographic one. But this only implies that the earlier construction of a finite representation of lexicographic preferences captures all decision relevant factors, even infinite value. We therefore conclude that in a finite universe, any choices that are made can be reduced to perhaps incomprehensibly large but necessarily finite comparisons. This demonstrates that given physical finitude, ethics overall cannot be changed solely by claimed infinities in preferences between outcomes, at least before accounting for probabilities. \n Bounding Probabilities \"...it was just very very very big, so big that it gave the impression of infinity far better than infinity itself.\" \n -Douglas Adams As noted above, any act considered by a rational decision maker, whether consequentialist or otherwise, is about preferences over a necessarily finite number of possible decisions. This means that if we restrict a decision-maker or ethical system to finite, non-zero probabilities relating to finite value assigned to each end state, we end up with only finite achievable value  33  . The question is whether probabilities can in fact be bounded in this way. We imagine Robert, faced with a choice between getting $1 U S 2020 with certainty, and getting $100 billion U S 2020 with some probability. Given that there are two choices, Robert assigns utility in proportion to the value of the outcome weighted by the probability. If the probability is low enough, yet he chooses the option, it implies that the value must be correspondingly high. As a first argument, imagine Robert rationally believes there is a probability of 10 −100 of receiving the second option, and despite the lower expected dollar value, chooses it. This implies that he values receiving $100 billion U S 2020 at approximately 10 100 x the value of receiving $1 U S 2020 . While this preference is strange, it is valid, and can be used to illustrate why Bayesians should not consider infinitesimal probabilities valid  34  . To show this, we ask what would be needed for Robert to be convinced this unlikely event occurred. Clearly, Robert would need evidence, and given the incredibly low prior probability, the evidence would need to be stupendously strong. If someone showed Robert that his bank balance was now $100 billion dollars U S 2020 higher, that would provide some evidence for the claim-but on its own, a bank statement can be fabricated, or in error. This means the provided evidence is not nearly enough to convince him that the event occurred  35  . In fact, with such a low prior probability, it seems plausible that Robert could have everyone he knows agree that it occurred, see newspaper articles about the fact,  33  For those decision-makers who have other value systems, the earlier discussion suffices, and probabilities do not enter the discussion.  34  We are grateful to Evan Ryan Gunter for suggesting several points we address in this section.  35  One could argue that Robert's goal is not to have the state of receiving $100 billion U S 2020 , but rather the state of believing that he received the money. If so, of course, the relevant probability to assess is not that he would receive the money -and if he assigns a probability of 10 −100 to that, he is severely miscalibrated, at least about the probability of delusions. Despite this, the below arguments still apply, albeit with a different referent event. and so on, and given the low prior odds assigned, still not be convinced. Of course, in the case that the event happened, the likelihood of getting all of that evidence will be much higher, causing him to update towards thinking it occurred. A repeatable experiment which generates uncorrelated evidence could provide far more evidence over time, but complete lack of correlation seems implausible; checking the bank account balance twice gives almost no more evidence than checking it once. And as discussed in the appendix, even granting the possibility of such evidence generation, the amount possible is still bounded by available time, and therefore finite. Practically, perhaps the combination of evidence reaches odds of 10 50 :1 that the new money exists versus that it does not. Despite this, if he truly assigned the initially implausibly low probability, any feasible update would not be enough to make the event, receiving the larger sum, be a feasible contender for what Robert should conclude. Not only that, but we posit that a rational decision maker should know, beforehand, that he cannot ever conclude that the second case occurs  36  . If he is, in fact, a rational decision maker, it seems strange to the point of absurdity for him to to choose something he can never believe occurred  37  , over the alternative of a certain small gain. Generally, then, if an outcome is possible, at some point a rational observer must be able to be convinced, by aggregating evidence, that it occurred. Because evidence is a function of physical reality, the possible evidence is bounded, just as value itself is limited by physical constraints. We suggest (generously) that the strength of this evidence is limited to odds of the number of possible quantum states of the visible universe -a huge but finite value  38  -to 1. If the prior probability assigned to an outcome is too low to allow for a decision maker to conclude it has occurred given any possible universe, no matter what improbable observations occur, we claim the assigned probability is not meaningful for decision making. As with the bound on lexicographic preferences, this bound allows for an immensely large assignment of value, even inconceivably so, but it is again still finite. The second argument seizes on the question of inconceivability, without relying on Bayesian decision theory or rationality. Here we appeal to an even more basic premise of expected value, which is needing a probability assignment, or a value assignment at all. If Robert cannot conceive of the probability, he cannot use it for computations, or make decisions as if it were true. The question at this point is whether he can conceive of infinitesimal probabilities.  39  We have been unfortunately unable to come up with a clear defense of the conceivability of infinities and infinitesimals used for decisionmaking, but will note a weak argument to illustrate the nonviable nature of the most common class of objection. The weak claim is that people can conceive of infinitesimals, as shown by the fact that there is a word for it, or that there is a mathematical formalism that describes it. But, we respond, this does not make a claim for the ability to conceive of a value any better than St. Anselm's ontological proof of the existence of God. More comically, we can say that this makes the case approximately the same way someone might claim to understand infinity because they can draw an 8 sideways -it says nothing about their conception, much less the ability to make decisions on the basis of the infinite or infinitesimal value or probability. Finally, we can also appeal to what Aaronson calls the Evolutionary Principle, which states that \"knowledge requires a causal process to bring it into existence.\"  [40]  If moral statements and values are truth-apt, any value, or probability, which is found in moral epistemology or in an individual's preferences requires that some physical process led to the  36  Perhaps he can accept the result with less convincing evidence. One might argue that if every conceivable result of having the money occurs, he might as well accept it as having occurred. In that case, however, the odds he assigned to the possibility are not actually 10 −100 , which is verified by the fact that less than the corresponding amount of evidence effectively convinced him.  37  If he is not, in fact, a rational Bayesian, and his probability assignment was a statement of preference rather than an estimate, it is a lexicographic preference rather than a probability, and can be discussed as above.  38  About exp(10 123 ) ≈ 10 10 4.3×10 122 .  39  When reasoning about a probability like 10 −100 we can use mathematical methods to reach reliable conclusions, e.g. that 10 −99 is 10 times more likely, despite not having any intuition about the value itself. This ability to place concepts into lawful relations to each other relies on the existence of representations that can be manipulated. The need to represent the relations applies even if consideration must be outsourced to formal methods rather than intuitive comprehension. In fact, given any number of possible states in a universe, the number of possible states is the maximum number of distinct values which can be represented. By the pigeon-hole principle, the probability of at least one state must be lower than the smallest discretely representable value in the system. As the number of possible quantum states of the universe suggests, there are probabilities which cannot be explicitly represented using any finite system, but they will not be relevant for decision-making. assignment of moral value. This argument is potentially incompatible with moral non-cognitivism, but even ethical subjectivism requires individual value judgements to occur, and these are subject to the same physical constraints due to being a result of a causal process. The relationship of value to probability is itself closely related to the relationship of outcomes to value. That is, there must be a physical or cognitive process that arrives at the decision of what value to assign to an outcome. Any probability assignment, per the Evolutionary Principle, is a function of the computation available. And given the earlier-discussed limits on storage and on computation, assigning a probability value X to a state will be limited. Even if we assume that the entire universe's computational capacity is available, there is some immensely large but finite number that can never be found  40  . \n Rejecting Ethical Theories However, value might be fundamentally different than we assume. We begin by looking at consequentialist version of the argument, then briefly address other moral claims. We noted above that one of the arguments about bounding probability, and value, does not work given moral noncognitivism. We can make a similar claim about moral realism, where perhaps value is in fact inherent in objects in a physical sense. After all, while the location of an object or its temperature can be represented, they are also inherent in the object (or at least inherent in the relationship between the object and the surroundings). However, we again appeal to the question of decision making. Even for moral realists, either this value can be directly experienced or it cannot. In the latter case we still need to represent our estimates of the value, and these representations will be subject to the earlier bounds on physical reality. In the former case we need to be able to compare values to each other. Either this occurs through comparing mental representations of the actual value experiences (necessarily bounded), or we directly compare the intrisic values without any representational intermediary -but the comparison requires some minimal computation to occur outside of the objects. In either case, a clear bound exists on what value is possible. Alternatively, we can consider ethical-theory objections, rather than the meta-ethical ones above. We assume in the discussion a utilitarian or at least consequentialist viewpoint. This is in large part because the question of finitude of value is most clearly relevant in that frame. Despite this, other theories face similar limits. Deontological and rights-based theories are faced with a finite number of possible actions which have moral value, and the earlier arguments for comparability and finitude would still apply. \n Accessibility Bostrom's discussion of infinite ethics is premised on the moral relevance of physically inaccessible value. That is, it assumes that aggregative utilitarianism is over the full universe, rather than the accessible universe. This requires certain assumptions about the universe, as well as being premised on a variant of the incomparability argument that we dismissed above, but has an additional response which is possible, presaged earlier. Namely, we can argue that this does not pose a problem for ethical decision-making even using aggregative ethics, because the consequences of any ethical decision can have only a finite (difference in) value. This is because the value of a moral decision relates only to the impact of that decision. Anything outside of the influenced universe is not affected, and the arguments above show that the difference any decision makes is finite. We argued earlier that Boltzmann brains are inaccessible, since our actions do not impact the distribution of random matter after the heat death of the universe. This relies on a different type of inaccessibility, since our actions can have an impact, but one that is fundamentally unpredictable -making us morally clueless  [41]  in an even stronger sense than complex cluelessness  [42] . Still, any solution to cluelessness seems to leave inaccessible impacts morally irrelevant  [43] , and this would apply even more strongly to our case. \n Rejecting or Altering Decision Theory Another approach to avoiding finitude is to question not preferences, but decision theory itself. There are discussions like  [44]  which consider decision theories that would allow for causal relationships with entities outside of the reachable universe in various ways, such as those discussed by Yudkowsky  [45] . This alone does not imply infinite value. However, there are some proposed cosmologies in which these decision theories imply infinite value is possible  41  . For example, this would be true if we accept the Mathematical Universe Hypothesis proposed by Tegmark  [46] . This conclusion goes further than most proponents of such theories would argue, and farther than is required for the purposes of the current argument -it says that ethics, rather than just decision making, should be based on these theories. In fact, most of the arguments in favor of non-causal decision theories are based on the consequentialist claims that these decision rules perform better in some situations. For this reason, the of such theories to reject the type of consequentialism that justified them is not inconsistent, but seem a bit perverse. Not only that, but Stoeger  [47]  points out that the universes with infinite value proposed by Tegmark are both unreachable, and unfalsifiable. Despite all of this, if we consider value aggregated over the multiverse in ways that do not renormalize to finite measure, we can be left with infinities. And as with rejecting physics, if we assign any finite positive probability to this being true, we are potentially  42  left with decisions that have infinities in their value. Another key point about decision theory can be used to address the argument about potential infinities, related to our discussion of accessibility. That is, if we assign a small but non-zero value to physics being incorrect in ways that allow, say, reversing entropy, and infinite value is possible, all infinities are still limited to this possible universe, and decisions must be made on that basis. Traditional expected-value decision theory is often interpreted to require risk-neutrality. This means that a single infinity will dominate any decision calculus. Many of the arguments for risk-neutrality, such as arbitrage and exploitation of repeated chances, fall apart in the current scenario. For example, if risk-neutrality is based on the possibility of arbitrage, where a risk-neutral participant in a market can receive free money by taking and perfectly hedging a risk, this becomes impossible when the risk is a single binary question which cannot be hedged. The same is true for the argument from repeated chances. A person might prefer $100 with certainty to a 60% chance of $200, but if they believe that this and similar choices will occur again in the future, the choosing the riskier option each time becomes more and more attractive, as the expected value remains the same but the risk of losing overall decreases with each additional bet. This clearly cannot apply to a single possibility about the question of which physical laws obtain in the universe. However, a rational actor might choose to embrace a regret-minimization approach  43  . In this case, the regret from not maximizing the small probability of infinite return is infinite. We note, however, that key justifications of regret minimization involve arguments from long-term results that we reject above, while others are game-theoretic and do not apply here  [50] . If we consider uncertainty over ethical theories, then given the standard metanormative theory of maximizing expected choiceworthiness,  [51]  we would apply the arguments above. One key criticism of that approach, however, is that it requires intertheoretic unit comparisons, and per Greaves and Cotton-Barratt,  [52]  this leads to a number of issues pointed out by Dai  [53] . If we choose an alternative metanormative approach to address this, we my be able to reject possible infinities due to moral uncertainty even more simply. In Greaves and Cotton-Barratt's moral parliament, using bargaining theory, the problem of infinities being assigned some nonzero probability is addressed in a straightforward way, as by design no ethical theory can hijack the decision. Note that an implicit conclusion from the assumption of infinite possible value is that moral progress is unbounded. Of course, that implies that any finite value achieved, however large, is an exactly nil fraction of possible value. In contrast to this, if value can be taken to be finite, moral progress is limited to a finite value, but progress is meaningful, in the sense that we can approach that maximum 44 . \n Conclusions \"I see the world being slowly transformed into a wilderness; I hear the approaching thunder that, one day, will destroy us too. I feel the suffering of millions. And yet, when I look up at the sky, I somehow feel that everything will change for the better, that this cruelty too shall end, that peace and tranquility will return once more.\" \n -Anne Frank The above argument leads to the clear conclusion that humanity's best current understanding of physics implies that possible value is finite. Despite the usefulness of infinities in mathematics, physics, and even in discussions of preferences, given humanity's current understanding of physics we have shown that the morally relevant universe is finite, and can have only finite value. Of course any human reasoning is fallible, and any probability that this argument is wrong would lead to an expected infinite value, and lead to a Pascal's-wager-like obviation of any comparative value. Short of that, however, we can safely conclude that in this universe, abiding by the currently understood physical laws, moral value is, and will always be, finite. To reject this claim, a few choices are available. First, one could rejecting our current understanding of physics, and insist that modern physics is incorrect in very specific ways. Second, one can reject values and decision theory in very specific ways, such as rejecting comparability, relying on non-cognitivism or embracing infintesimals as valid probabilities for decisions, or embracing non-causal models for decision theory as the basis of ethics and simultaneously rejecting accessibility of value. Lastly, one could choose nihilism, or some nontraditional ethical theory designed to avoid finitude. None of these is unreasonable. However, we caution that each allows for infinite value only conditional on a variety of assumptions laid out in the paper. Without these, our universe, and any universe with similar physical laws, has at most finite value for any moral actor. The peculiar nature of the infinite means that any finite value of the universe, no matter how large, as a fraction of infinity is exactly zero. Considered not as a fraction of infinity, of course, the immensely large physical limits do not preclude, and in fact imply, the existence of possible value far beyond that which humans currently imagine. Rejecting infinite values, and the various paradoxes and dilemmas they implicate, allows us to focus on considering what values should be pursued, and how best to reach the paradise that the future can become. Our current understanding of cosmology is incomplete, but current theories agree that even if the universe is temporally infinite in some sense, there is a point at which we reach either universal heat death, or a big freeze. Long before this proton decay would remove any baryonic matter (the only form we know can produce computation and life), and black hole evaporation later removes all other forms of concentrated matter, leaving individual elementary particles causally disconnected in expanding space  46    [60] . In either case, at some theoretically determinable point in the future, the state of the universe will not be affected by any current actions. Hence, value-related activities will necessarily be limited to end before this point. \n A.2.1 Evading spatial or temporal finitude These assumptions could be invalidated if, for example, faster than light (FTL) travel is possible (the human domain could expand beyond the cosmological event horizon) or radically different cosmological theories were true. However, the consequences of FTL include time-travel with the concomitant trouble with causality, CTC-based hypercomputing  47  , and the difficulty of defining when value exists, or whether the value is caused by an action that occurred at a different time. While this cannot be ruled out, the consequences for value theory are much more problematic than a finite limit to value. Alternatively, if dark energy is absent, intergalactic settlement could continue indefinitely, acquiring a slowly diverging amount of matter until the time limits set in. A world without proton decay is certainly conceivable, but to allow structure to persist indefinitely, temperatures need to decline indefinitely. There have been proposals for evading the heat death of such an expanding universe by hibernating longer and longer periods, exploiting the ever colder environment for a diverging amount of computation with a finite energy budget  [61] ; this is not compatible with accelerating expansion, which causes a finite temperature horizon radiation that makes indefinite information processing with error correction impossible for finite-resourced civilizations  [62] . The cosmology could also be closed or have a Big Rip singularity, producing an even more definite endpoint. Universes where indefinite settlement is possible require that either we must be empirically wrong about the accelerating expansion, or that an as-yet-unknown physical phenomena change w in the future (and henceforth maintain w > −1/3), and in either case, that proton decay and all other late-era structure-disrupting phenomena predicted from current theories must all be wrong. One can never rule out radically different physical theories as alternatives to the mainstream model, but their prior probability does not appear high, especially since several independent properties of physics need to conspire to allow indefinite settlement. The remaining unaddressed question is whether finite time and finite space still allow relevant infinities. As explained below, the physical limits on storage make this impossible, and this will allow us to consider the remaining objection to finite value. \n A.3 Physical limits to storage In addition to limitations on the size of the universe, there are also fundamental limits on physical information storage. The most obvious limit is on the mass or energy used to encode information -but volume matters too. While the efficiency of current magnetic storage is about 1 million atoms per bit, DNA storage can achieve 32 atoms per bit and in principle one could store one bit per atom (for example by using 12 C and 13 C atoms in a diamond lattice). Information can also be stored as radiation, an example being light circulating in long delay-lines. These limits depend on the types of information-carriers available  48  .  46  Long before this point there will be no possibility of there existing any sentient beings to consider the possible value, but perhaps those beings have preferences about later outcomes regardless of that fact.  47  Which would, by allowing sending information back in time, allow to always find the action with the highest measured value. Whether this solves ethics or merely makes implementing ethical systems trivial (at a slight cost of the concept of free will) may be debated.  48  For example, if we assume all of the baryonic mass in the Milky Way is converted to carbon atoms 9.3 × 10 66 bits could be stored. Were the whole mass converted to light in delay-lines across the galaxy, the storage capacity would be (R/c)(E/2π ) = 1.3 × 10 105 bits (based on  [63, eq. 112] ). For fundamental reasons, it is believed that we cannot store more than 10 66 bits cm −3 . This is based on the covariant entropy bound that states that the maximum amount of information that can be stored within a region is bounded by I ≤ A 4A P l = c 3 A 4 G , where A is the area of the region  [64, 65, 66]    49  . There exist a rich flora of such entropy bounds. The \"classic\" bound is the Bekenstein bound for the information inside a spherical region of radius R and energy E  [67] , which bounds it as I ≤ 2πRE c . Since it was proposed in 1981 it has held up well despite much effort to produce a counterexample, and it has been proven that a version holds in any relativistic quantum field theory  [68] . The Bekenstein bound implies a capacity of 2.5 × 10 106 bits in the Milky Way and 8.3 × 10 121 bits in the reachable universe. Brustein and Veneziano propose another one that is the geometric mean of the Bekenstein and the covariant bound  [69] .  50  Generally these bounds are closely related to the generalised second law of black hole thermodynamics  [70] . A heuristic argument for why such bounds are very plausible and appear unavoidable given known physics can be found in https://www.scottaaronson.com/blog/?p=3327. Basically, quantum fields in a bounded region with enough spatial variation to encode much information have greater energy and hence greater gravitational mass, and black hole formation around the region places an upper limit on this capacity. While we may quibble about which bound is most accurate, physicists would generally agree that the amount of storeable and retrievable information in a finite volume with finite energy is finite. Were it not so, then one could exploit the storage capacity to run Maxwell's demon to provide perpetual motion  51  . \n A.4 Maximum computations / value over time The physical bound on value might be argued to relate to the amount of computation that is possible, rather than the maximum storage. Given the temporal and physical bounds above, however, this too is strictly finite. There exist limits on how fast distinguishable states (i.e., information) can be changed into other states (i.e., information processing). The Margolus-Levitin bound  [71]  states that a system with mean energy E cannot move to another orthogonal state in less time than τ M L = π 2 E . This bound implies a bound per quantum bit of 6 × 10 33 operations per second per joule. Given a finite time and finite energy there will be a finite amount of computation. A related limit is the Mandelstam-Tamm limit linked to total energy  [72] ; such limits generalize in quantum mechanics  [73] , classical mechanics  [74] , and curved spacetimes  [75] . These (quantum)limits can be derived straight from the formalism of quantum mechanics  [76] , and to evade them one needs to evade quantum mechanics.  49  This is slightly oversimplifying things: the bound is on the information across the inward light sheet from a particular instant of the boundary. For practical purposes here it corresponds to the spacelike interior.  50  That these bounds involve a spatial factor may inspire the hope that the expansion of the universe would enlarge the storage capacity. While the total amount of information that could be stored across the universe does increase over time, the accessible amount from any given point unfortunately declines: the distance to the event horizon shrinks as time goes by and more and more remote memory storage units disappear.  51  Since the demon could retain infinite information, it does not have to pay a negentropy cost to erase past data and could hence persistently produce a thermodynamic disequilibrium from which energy can be extracted, contra the arguments due to Szilard, Landauer and Bennett. A world running on continuous physics might allow potentially arbitrarily dense information storage, but would still not allow actual arbitrarily dense storage due to noise. For example, the Planck scale does not (contrary to many popularizations) indicate that physics is discrete on sufficiently small scales, merely that as-yet unknown quantum gravity will be needed to describe processes below this scale. If measurement and manipulation below this scale is not possible then physics could be truly continuous yet only finite amounts of information can be stored by us. \t\t\t This is not a required assumption, though given multiverses, some qualifications on how moral weight or normalization across many-worlds is required to ensure values are not all infinite. 3  We will not discuss the contentious question of how economics is best defined, a subject of extensive discussion [5] . \n\t\t\t This number is exponentially larger than 10 860 times current GWP (that has just slightly over 860 digits), but still far smaller than many celebrated very large numbers in mathematics, such as Graham's number -which has a number of digits that itself is far larger than can be stored in those 10 134 bits of storage. 9  It is, of course, possible to store representations of larger numbers, but these are insufficient for value writ large in various ways, as will be discussed later. For example, floating point numbers can be extended to represent far larger quantities in a given storage volume, but they are not closed under subtraction, and in a typical implementation, very large integers are rounded off. That means that they cannot be used for comparisons where the difference is relatively small. In fact, no encoding scheme using 10 134 bits can contain, say, the value 2 10 134 + 1 without losing the ability to store the exact value of some smaller integer. While our large-number storage maximizing AI might be fine turning the universe into storage schemes that allow representing larger numbers, given the discussion below about value as comparisons, this inability is a fundamental issue for not just economic growth, but value-in-general. \n\t\t\t Because of the short time frames and local distances being discussed, this can ignore the expansion of the universe. Over longer times scales, as we discuss in the appendix, this further limits it to an asymptotically finite amount if the ΛCDM cosmology is a correct description [17] .11 Note that we do not include equity concerns for discounting [21]  because we are considering humanity as a whole, though obviously for policy the equity concerns for discounting can be critical. \n\t\t\t What is Value? \"...maybe that means that for civilization, part of civilization is devoted to common sense, thick values of pursuit of art, and flourishing, and so on, whereas large parts of the rest of civilization are devoted to other values like pure bliss... The universe is a big place.\" -Will MacAskill So far, the discussion has contained repeated caveats about economic growth and economic value, as distinct from some as-yet nebulous value-in-general. While others have noted the connection, such as Cowen [31]   12  , we attempt to clarify that concept, and see how it relates to the economic one, and the extent to which it does not.Before discussing how choices relate to values, we note that our discussion is premised on choice as the central question of ethics. That is, ethics is the study of right and wrong choices, and the morality of those choices. Outside of a comparison between things, or a decision made about them, \"value\" has no meaning 13  . 12  Cowen splits the concept, saying that he's interested in \"wealth-plus,\" which he defines as \"The total amount of value produced over a certain time period. This includes the traditional measures of economic value found in GDP statistics, but also includes measures of leisure time, household production, and environmental amenities, as summed up in a relevant measure of wealth.\" But most economists would say that this is what economic value already captures, and the distinction made in Cowen's terminology is a measurement issue, rather than a disagreement about what value is. 13  This is not a consequentialist claim. Any ethical statement must by definition be a comparison, saying one action (or lack thereof) is allowed, and another is forbidden. Even if moral statements are not factual, they are descriptions of factual scenarios, and short of nihilism, make claims that compare them. \n\t\t\t We are implicitly ignoring measurability of utility in this discussion, since it is irrelevant once we assume that choices would be made which induce an ordering. Even though an insufficient number of choices are made to determine the utility, and actual measurability is plausibly absent, the argument we present applies to any set of choices that could be made. This makes measurability of utility irrelevant. 15  While the set of things can be expanded by inventing or making new things, this faces two constraints. First, future time is bounded, as discussed in the appendix, A.2 so only a finite number of new goods can be created. Second, the number of arrangements of matter is finite, so the number of possible goods is limited. There may also be overlap, so that the same atoms participate in two or more valuable things, but is still finite, if exponentially growing. 16  Mathematically, this is a ring, rather than just an ordered set, because we can define addition and multiplication. 17  A similar argument does not apply to ordinal utilities -there is no mathematical justification in asserting that if one banana is traded for two apples, the banana is twice as \"valuable\", since the specific trade implies nothing about general preferences. More precisely, when discussing ordinal value mathematically, the notion of multiplying a position in the order by a number is meaningless. \n\t\t\t This is different from a broader and fundamental possible argument, which is that science has no final conclusions which can be relied on for absolute moral claims. We reject this as morally irrelevant, since our discussion is about decisions which are made in reality. Given that, objections about the impossibility of certainty are also implicitly rejected by argument about the limits to probabilities. 22  Of course, some results may find looser rather than stricter bounds. Despite this, even if we conclude that most specific currently known limits will be rejected at some point, this does not go far enough to imply that no such limits exist, and the central claim of this paper remains true. 23  If there is no universe-ending Big Rip or the cosmological constant is negative enough to cause recollapse. At least the latter is disfavored by current cosmological observations. The former has no theoretical or empirical support. See also the Appendix. The nature of the heat-death does not matter much for the argument: the classic idea was a state of minimum free energy, while the modern is an equilibrium state of maximum entropy, or a \"freeze\" state where individual particles remain isolated at finite (microscopic) temperature. In either case random thermal fluctuations will occur briefly bringing it away from equilibrium from time to time. There may be a causal effect of our actions on the post heat-death state, but no action now can determine a post-heat death event. \n\t\t\t This argument cannot be used to justify claims of specifically exponential economic growth, since that relies on the claim that by investing resources now, the choice will lead to greater value in the future by enabling that growth. However, if a lexically preferable outcome can be purchased or created with money that can be invested, the analogue of economic growth has a utility function which is discontinuous, not growing exponentially. \n\t\t\t In computer science, infinities of a certain type are limited to non-halting programs, and these programs do not return a value before the end of the universe. For that reason, conceivable infinities are only ever potential, rather than actual, in an interesting return to an Aristotelian dichotomy about infinities. \n\t\t\t In mainstream cosmological theories, there is a single universe, and the extent can be large but finite even when considering the unreachable portion (e.g. in closed topologies). In that case, these alternative decision theories are useful for interaction with unreachable beings, or as ways to interact with powerful predictors, but still do not lead to infinities. 42  It is of course possible to embrace all of these claims, but still find that for other reasons, such as choice of the theory of ethics, infinities do not apply. 43  A rational actor can do so not as a failure or accommodation due to biases, [48]  but as an alternative axiomatic framework [49] . \n\t\t\t cf. MacAskill's argument that \"the vast majority of my expectation about the future is that relative to the best possible future we do something close to zero. But that's cause I think the best possible future's probably some very narrow target.... how much better could the world be? I don't know, tens of times, hundreds of times, probably more. In the future, I think it'll get more extreme.\" [54]", "date_published": "n/a", "url": "n/a", "filename": "MANWIT-6v1.tei.xml", "abstract": "How much value can our decisions create? We argue that unless our current understanding of physics is wrong in fairly fundamental ways, there exists an upper limit of value relevant to our decisions. First, due to the speed of light and the definition and conception of economic growth, the limit to economic growth is a restrictive one. Additionally, a related far larger but still finite limit exists for value in a much broader sense due to the physics of information and the ability of physical beings to place value on outcomes. We discuss how this argument can handle lexicographic preferences, probabilities, and the implications for infinite ethics and ethical uncertainty. \n Keywords Value • Physics of Information • Ethics Acknowledgements: We are grateful to the Global Priorities Institute for highlighting these issues and hosting the conference where this paper was conceived, and to Will MacAskill for the presentation that prompted the paper. Thanks to Hilary Greaves, Toby Ord, and Anthony DiGiovanni, as well as to Adam Brown, Evan Ryan Gunter, and Scott Aaronson, for feedback on the philosophy and the physics, respectively. David Manheim also thanks the late George Koleszarik for initially pointing out Wei Dai's related work in 2015, and an early discussion of related issues with Scott Garrabrant and others on asymptotic logical uncertainty, both of which informed much of his thinking in conceiving the paper. Thanks to Roman Yampolskiy for providing a quote for the paper. Finally, thanks to Selina Schlechter-Komparativ and Eli G. for proofreading and editing assistance. * The authors contributed equally in the conception and preparation of the paper. 1 While cosmology debates some aspects of whether the universe is finite, as we note in the appendix, the various suggested possibilities still admit that the reachable universe is finite.", "id": "923f85e56703d953a09c817fc8b22455"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Smitha Milli", "Anca D Dragan"], "title": "Literal or Pedagogic Human? Analyzing Human Model Misspecification in Objective Learning", "text": "INTRODUCTION It is notoriously difficult for system designers to directly specify the correct objective for a system  (Krakovna, 2018; Lehman et al., 2018; Clark & Amodei, 2017) . This difficulty has sparked a line of work that instead aims to infer the correct objective from other forms of human input, such as demonstrations  (Ng & Russell, 2000; Abbeel & Ng, 2004; Ziebart et al., 2008) , comparisons  (Wirth et al., 2017; Sadigh et al., 2017; Christiano et al., 2017) , or corrections  (Bajcsy et al., 2017; Jain et al., 2015) . These methods operate under the assumption that human behavior is near-optimal with respect to the objective to be inferred. This assumption makes sense in many domains, like an autonomous car learning an objective function for driving through observing human drivers  (Levine & Koltun, 2012) . However, recent work shows that this assumption may not hold in collaborative settings  (Ho et al., 2016) , in which the human is aware that the robot needs to learn. In such settings, the person might optimize for teaching the robot about the objective, which is not the same as directly optimizing the objective itself  (Dragan et al., 2013b; Hadfield-Menell et al., 2016; Ho et al., 2016) . Figure  1  shows an example of the difference between the two. When the human optimizes for the objective, she takes any optimal path to the goal. When the human optimizes for teaching the objective, she takes the path that best signals the objective. We refer to these two types of human behavior as literal and pedagogic, and note that the robot can interpret human behavior using either model: 1. The literal human directly optimizes for the objective. 2. The literal robot infers the objective while assuming the human is literal. 3. The pedagogic human optimizes for teaching the literal robot the objective. 4. The pedagogic robot (sometimes called \"pragmatic\" ) infers the objective while assuming the human is pedagogic. . . . In general, this recursion could go on further, and in theory, it is always better for the human and robot to be at a deeper level of recursion. The potential for increased performance suggests that we should try to make our robots more pedagogic. Indeed, this is the direction suggested and pursued by ;  In this scenario, the robot infers whether it is ok to walk on the grass or not from a demonstration provided by the human (it already knows pavement is always ok). (a) The literal and pedagogic human's demonstrations. When grass is ok, the literal human is equally likely to walk on the grass or pavement. On the other hand, when grass is ok, the pedagogic human always walks on the grass in order to signal that grass is ok. (b) The beliefs of the literal robot LR and pedagogic robot PR after observing a demonstration. LR and PR assume human is literal and pedagogic, respectively. LR and PR differ in how strong their beliefs are after witnessing the human walk on pavement, leading to different problems when the human is misspecified. If the human is literal, but the robot is pedagogic, then it makes too strong of an inference. On the other hand, if the human is pedagogic, but the robot is literal, then it makes too weak of an inference. However, the increased performance is contingent on the human being pedagogic. In practice, it may be difficult to know whether the human is acting literally or pedagogically, and furthermore, different humans may behave differently. We argue that the robot should be robust to misspecification of the human, and thus it is important to ask which assumption -literal or pedagogic -is safer to make. Which is worse-interpreting a pedagogic human literally (literal robot + pedagogic human) or interpreting a literal human pedagogically (pedagogic robot + literal human)? In both cases, the model of the human is incorrect, and we might expect that which is better depends on the context and the task; surprisingly, we are able to prove that regardless of the task, the literal robot is more robust, suggesting that it may be safer to simply use a literal robot. Our contributions are the following: • Section 2: Theoretical Analysis. We cast objective learning into the more general form of a commonpayoff game between the human and robot. We then prove that a pedagogic robot and a literal human always do worse than a literal robot and a pedagogic human, showing that misspecification is worse in one direction than the other. • Section 3: Empirical Analysis. We test the effects of misspecification on data from human teaching. The data confirms that assuming pedagogic behavior when people are literal is worse than assuming literal behavior when people are pedagogic. Surprisingly, we find that the literal robot does better than the pedagogic robot even when people are trying to be pedagogic, because of the discrepancy be-tween the pedagogic model of humans and real human behavior. • Section 4: Theoretical vs Empirical. Our empirical results are surprising, in that, the pedagogic model is a state of the art cognitive science model that is fit to the human data and has relatively high predictive accuracy, yet the pedagogic robot does worse than the literal robot with humans who are trying to be pedagogic. We use our theory to derive a hypothesis for why this could be. The hypothesis is that in practice different humans vary in how literal or pedagogic they are, which our theory implies will degrade the performance of the pedagogic robot more than the literal robot. We find positive evidence for this hypothesis, indicating that robustness to a population of humans is an important consideration in choosing a pedagogic versus literal robot. • Section 5: Can we \"fix\" the pedagogic robot? An intuitive idea for improving the pedagogic robot is to give it a model of the pedagogic human that has higher predictive accuracy. For example, what if instead of assuming all people are pedagogic, the robot estimated how pedagogic each person is? Unfortunately, we find that this makes no difference. And in fact, we show that better models can actually worsen performance due to a subtle, yet remarkable fact: a human model with higher predictive accuracy does not necessarily imply higher inferential accuracy for the robot. In conclusion, we found that not only are pedagogic robots less robust to the human's recursion level, they can also perform worse when people are actually being pedagogic -even with a state of the art pedagogic model tuned to human data. This points to a surprising brittleness of the pedagogic assumption. Further, we point out that a more predictive human model will not necessarily solve the problem because improving the model's predictive accuracy does not necessarily lead to better robot inference. The difficulty of objective specification was an important motivation for pursuing objective learning in the first place. But in our pursuit of objective learning, we ought to be careful to not simply trade the problem of objective specification for the equally, if not more, difficult problem of human specification. In practice, humans will deviate from our models of them, and thus, it is important to understand which assumptions are robust and which are not. Rather than trying to make the robot more pedagogic, which requires brittle assumptions on the human, an alternative direction may be to help the human become more pedagogic. How can we make robots that are easier for humans to teach? Perhaps simpler robots are actually better, if it means that humans can more easily teach them. \n THEORETICAL ANALYSIS In this section, we cast objective learning into the more general form of a common-payoff 1 game between the robot and human. We then formalize the literal/pedagogic robot/human, and prove that in any common-payoff game a literal robot and pedagogic human perform better than a pedagogic robot and literal human. \n GENERALIZING OBJECTIVE LEARNING TO CI(RL) Before proceeding to our proof, we give background on how common-payoff games generalize standard objective learning. In particular, objective learning can be modeled as a cooperative inverse reinforcement learning (CIRL) game  (Hadfield-Menell et al., 2016) , a commonpayoff game in which only the human knows an objective/reward function r. Formally, a CIRL game is defined as a tuple S, {A H , A R }, T, {R, r}, P 0 , γ} where S is the set of states, A H and A R are the set of actions available to the human and robot, T (s | s, a H , a R ) is the transition distribution specifying the probability of transitioning to a new state s given the previous state s and the actions a H and a R of both agents, R is the space of reward functions, r : S × A H × A R → R is the shared reward function (known only to H), P 0 is the initial distribution over states and reward functions, and γ is the discount factor. The joint payoff in a CIRL game is traditionally value, expected sum of rewards. Since only the human in CIRL knows the shared reward function, this indirectly incentivizes the human to act in ways that signal the reward function and incentivizes the robot to learn about the reward function from the human's behavior 2 . However, we can also consider a version that directly incentivizes reward inference by making the payoff the accuracy of the robot's inference. To illustrate how objective learning settings are special cases of CIRL games, we give an example for the learning from demonstrations setting. Example 2.1 (Demonstration-CI(RL)). Learning from demonstrations can be modeled as a CIRL game with two phases. In the first phase, the human provides demonstrations. In the second phase... The second formulation (b) is a cooperative inference (CI) problem  (Yang et al., 2018; Wang et al., 2019) . In CI, there is a teacher (e.g human) who is teaching a learner (e.g. robot) a hypothesis r (e.g the reward) via data d (e.g. demonstrations). The human has a distribution over demonstrations p H (d | r) and the robot has a distribution over rewards p R (r | d). Given a starting distribution of human demonstrations, p H 0 (d | r), the optimal solution for these two distributions can be found via fixed-point iteration of the following recursive equations 3 : p R k (r | d) ∝ p H k (d | r) , (1) p H k+1 (d | r) ∝ p R k (r | d) . (2) \n PROOF: LITERAL ROBOTS ARE MORE ROBUST We now proceed to formalize what we mean by literal and pedagogic and to prove that the literal robot is more robust to misspecification of whether the human is literal or pedagogic. Suppose that the human and robot are acting in a cooperative game. Let H and R be the space of policies for the human and robot, respectively. The joint payoff for the human and robot is denoted by U : H × R → R. The joint payoff function could be value, as assumed by CIRL, or accuracy of inference, as assumed by CI. To define literal and pedagogic, we define a set of recursive policies for the human and robot. Let H 0 be a starting human policy. For k ≥ 0, define the recursive policies R k = BR(H k ) , (3) H k+1 = IR(R k ) . (4) We assume that at each level of recursion the robot does a best response BR : H → R. However, for the human, we only assume that at each step she improves over her previous policy. This allows for arbitrary irrationalities, so long as the next policy is at least as good as the previous one. We call this an \"improving\" response IR : R → H, and define both types of responses below. Definition 2.1. A best response for the robot is a function BR : H → R such that for any human policy H ∈ H and robot policy R ∈ R, U (H, BR(H)) ≥ U (H, R) . Definition 2.2. An improving response for the human is a function IR : R → H such that ∀ k ≥ 0, U (IR(R k ), R k ) ≥ U (H k , R k ) . We give special emphasis to what we call the literal human and robot, H 0 and R 0 , and the pedagogic human and robot, H 1 and R 1 . 4 We now provide an example of the literal and pedagogic policies for the Demonstration-CI setting (Example 2.1b). In this case, the human and robot policies can be modeled by the recursive CI equations (1) and (2). p H 0 (d | r) that she gives a demonstration d is exponentially proportional to the reward of the demonstration, denoted by r(d): p H 0 (d | r) ∝ exp(r(d)) . 2. The literal robot R 0 does a BR to the literal human, i.e. does Bayesian inference assuming the human is literal, p R 0 (r | d) ∝ p H 0 (d | r) , and then uses the posterior mode as its estimate for the reward r. 3. The pedagogic human H 1 picks demonstrations that are informative to the literal robot 5 : p H 1 (d | r) ∝ p R 0 (r | d) . Note this is not a best response, which would unrealistically require the human to choose arg max d p R 0 (r | d). 4. The pedagogic robot R 1 does a BR to the pedagogic human, i.e. does Bayesian inference assuming the human is literal, p R 1 (r | d) ∝ p H 1 (d | r) , and then uses the posterior mode as its estimate for the reward r. We show that for any common-payoff game the payoffs for the literal/pedagogic human/robot pairs have the following ranking: Pedagogic R1, H1 ≥ Literal R0, Pedagogic H1 ≥ Literal R0, H0 ≥ Pedagogic R1, Literal H0 . (5) In particular, a pedagogic robot R 1 and a literal human H 0 always do worse than a literal robot R 0 and a pedagogic human H 1 , showing misspecification is worse one way than the other. The ranking has the following straight-forward proof. Claim 2.1. In any common-payoff game, the ranking of payoffs between a literal/pedagogic human/robot is U (H 1 , R 1 ) ≥ U (H 1 , R 0 ) ≥ U (H 0 , R 0 ) ≥ U (H 0 , R 1 ) . Proof. Since R 1 = BR(H 1 ), we have U (H 1 , R 1 ) ≥ U (H 1 , R 0 ). Since H 1 = IR(R 0 ), we have U (H 1 , R 0 ) ≥ U (H 0 , R 0 ). Since R 0 = BR(H 0 ), we have U (H 0 , R 0 ) ≥ U (H 0 , R 1 ). 5 Typically, the human is modeled as being exponentially more informative: p H 1 (d | r) ∝ exp(p R 0 (r | d)) . This is the form we will use in our experiments.  \n EMPIRICAL ANALYSIS In this section, we test our results in practice using experimental data from actual humans, who provide demonstrations that the robot uses to infer the objective from. These experiments are a way of stress-testing our theoretical results, which assumed that at each level of recursion, the robot computes a best response and that the human never does worse than her previous level. In practice, there will be a difference between what humans actually do, and the model of the human, which could cause both the human and robot to break our theoretical assumptions. \n EXPERIMENTAL DESIGN We test the performance of literal/pedagogic robot/human pairs on data from Experiment 2 in (Ho et al., 2016), which was subsequently followed up on in  (Ho et al., 2018) . In the experiment, humans are asked to act in different types of gridworlds. The gridworld has one goal state that is worth 10 points and three other types of tiles (orange, purple, cyan). Each type of tile can each be either \"safe\" (0 points) or \"dangerous\" (-2 points). Thus, there are 2 3 = 8 possible reward functions, which are depicted in Figure  2b . Sixty particpants were recruited from Mechanical Turk. The participants are told that they will get two cents of bonus for each point they get. Participants were split into two conditions, a literal and pedagogic condition, depicted in Figure  2a . In the literal condition, the participant only gets points for their own actions in the gridworld. In the pedagogic condition, the participant is told that their demonstration will be shown to another person, a learner, who will then apply what they learn from the demonstration to act in a separate gridworld. The partic-ipant still gets points based on their own actions, but is also told that the number of points the learner receives will be added as a bonus. \n HUMAN AND ROBOT MODELS We model the robot and human following Ho et al.  (2018) . We use the same model parameters that Ho et al. (2018) found to be the best qualitative match to the human demonstrations. Notation. Let S be the set of states and A be the set of actions. The gridworld has a reward function r : S × A × S → R. The optimal Q-value function for a reward function r is denoted by Q * r : S × A → R. The robot has a uniform prior belief over the reward function, i.e, it puts uniform probability on all 2 3 = 8 reward functions depicted in Figure  2b . The human and robot models are as follows. 1. Literal H. At each time step t, the probability H L (a t |s t , r) that the literal human takes action a t given state s t and the reward r is exponentially proportional to the optimal Q-value, H L (a t | s t , r) ∝ exp(Q * r (s t , a t )/τ L ) . (6) The temperature parameter τ L controls how noisy the human is. 2. Literal R. The robot does Bayesian inference, while assuming that the human is literal. The robot's posterior belief at time t + 1 is R t+1 L (r) ∝ H L (a t | s t , r) • T (s t+1 | s t , a t ) • R t L (r) . (7) 3. Pedagogic H. The pedagogic human optimizes a reward function r that trades-off between optimizing the reward in the gridworld and teaching the literal robot the reward. At time step t, the reward is r (s t , a t , s t+1 ) = r(s t , a t , s t+1 ) + κ(R t+1 L (r) − R t L (r)). The parameter κ ≥ 0 controls how \"pedagogic\" the human is. The probability H P (a t | s t , r) that the pedagogic human takes action a t given state s t and the reward r is exponentially proportional to the optimal Q-value associated with the modified reward r , H P (a t | s t , r) ∝ exp(Q * r (s t , a t )/τ P ) . (8) The temperature parameter τ P controls how noisy the human is. 4. Pedagogic R. The robot does Bayesian inference, while assuming that the human is literal. The robot's posterior belief at time t + 1 is R t+1 P (r) ∝ H P (a t | s t , r) • T (s t+1 | s t , a t ) • R t P (r) . (9) \n RESULTS We evaluate each literal/pedagogic robot/human pair on the accuracy of the robot's inference, i.e, P(r = r), where r is the true reward and r is the robot's guess. We take the robot's guess r to be the mode of its belief, as given by the robot models (  7 ) and (  9 ). We test each pair with both the demonstrations generated by actual humans and demonstrations generated by simulating humans according to the human models (  6 ) and (  7 ). Figure  3  depicts our experimental results 6 . We refer to the actual human as AH, the human model as H, and the robot as R. Consistent with the theory, the performance of pedagogic R and literal AH is (significantly) worse than that of literal R and pedagogic AH, validating that misspecification is worse one way than the other. However, the overall ranking of robot/human pairs does not match the theoretical ranking (Equation  5 ) we expected. Surprisingly, even when AH is pedagogic, pedagogic R performs (insignificantly) worse than literal R. The empirical ranking is Literal R, Pedagogic AH ≥ Pedagogic R, AH ≥ Literal R, AH ≥ Pedagogic R, Literal AH . The empirical ranking carries a stronger implication than our theoretical ranking-it implies that regardless of whether the human is literal or pedagogic, the robot should be literal.  Pedagogic R Pedagogic AH Literal R Pedagogic AH Literal R Literal AH Pedagogic R Literal AH Robot/ \n THEORETICAL VS EMPIRICAL In our empirical analysis, we found a perplexing result: the literal robot does better than the pedagogic robot even when people are trying to be pedagogic. How could this be? Figure  4  shows the accuracy of robot/human pairs when the human demonstrations are simulated from the literal H and pedagogic H models described in equations (  6 ) and (  8 ). In the simulations, we find, as expected, that pedagogic R and pedagogic H do better than literal R and pedagogic H. So clearly, the reason pedagogic R does worse in the human experiments is that pedagogic AH (actual humans) is not the same as the pedagogic H (the human model). But, in what way does pedagogic AH deviate from pedagogic H? Why is literal R more robust to the deviation than pedagogic R? We derive a hypothesis from our theory. In the theoretical ranking (Equation  5 ), the performance of literal R and literal/pedagogic H is sandwiched between the performance of pedagogic R + pedagogic H and pedagogic R + literal H. Thus, literal R is more robust to whether H is literal or pedagogic than pedagogic R. This suggests an explanation for why literal R does better, namely, that pedagogic AH is actually sometimes literal! Hypothesis 4.1. Pedagogic AH is actually \"in between\" literal H and pedagogic H. If this is true, then our theory implies that literal R will be affected less than pedagogic R, potentially explaining why pedagogic R does worse with pedagogic AH than literal R. Pedagogic R Pedagogic H Literal R Pedagogic H Literal R Literal H Pedagogic R Literal H Robot/ To test Hypothesis 4.1, we create two models that are mixtures of the literal and pedagogic model. We then measure how much better the mixture models are at predicting pedagogic AH, and how much the literal and pedagogic R are affected by demonstrations generated from the mixture models. \n DEMONSTRATION MIXTURE MODEL First, we test what we call the \"demonstration mixture model\". It is possible that the humans in the pedagogic condition from Ho et al. (  2016 ) followed different strategies; some may have attempted to be pedagogic, but others may have simply been literal. If we look at which model, literal or pedagogic, is a better fit on a perindividual basis, we find that 89.7% of literal AH are better described by literal H, but in comparison, only 70.0% of pedagogic AH are better described by pedagogic H. If we simulate pedagogic humans as only following the model 70.0% of the time, then the accuracy of the pedagogic robot drops to 90% (Figure  5a ). The literal robot is hardly impacted. \n ACTION MIXTURE MODEL We now test a more continuous version of the previous setting. We now model humans as acting according to a mixture policy H m between the literal H L and pedagogic H P policies. In particular, at each time t the probability the human picks action a t from state s in an environment with reward r is H M (a t | s t , r) = αH P (a t | s t , r) + (1 − α)H L (a t | s t , r) . ( 10 ) The parameter α is the probability of picking an action according to the pedagogic model. We plot the likelihood of the actual pedagogic human demonstrations as a function of α, (10). The best value of α over the whole population was α P = 0.5 (Figure  6a ). But surprisingly, even a mixture with α = 0.01 or α = 0.99 is far better than either the literal (α = 0) or pedagogic (α = 1) model. In addition, the best estimates for α on an individual basis are somewhat bimodal (Figure  6b ), indicating that there is high individual variation. Figure  5b  shows the performamce of the literal and pedagogic robot as α varies. At the best population level α P = 0.5, we find that the pedagogic robot gets 97% accuracy. However, if we simulate the pedagogic humans using the values of α estimated at an individual level, then the pedagogic robot's accuracy drops to 90%, highlighting the importance of individual variation. The literal robot again remains unaffected. \n DISCUSSION In both the demonstration and action mixture models, we found that a mixture between pedagogic H and literal H was a much better fit to AH. In both cases, when pedagogic H is simulated according to the more accurate mixture model pedagogic R's accuracy drops ten percentage points, but literal R's accuracy hardly changes. Thus our results provide positive evidence for Hypothesis 4.1. However, Hypothesis 4.1 does not explain the full story. The hypothesis can only account for a ten percentage drop in accuracy, but even with this drop, pedagogic R would still be better than literal R. Furthermore, with a cursory glance at Figure  5 , one might be tempted to consider pedagogic R quite robust, as it remains highperforming for large ranges of α. However, as usual, the real problem is the unknown unknowns. Our empirical results imply that there are other ways that humans deviate from the model and that literal R is more robust than pedagogic R to these unknown deviations. Rather than robustness to α, the more compelling reason for choosing to use literal R is robustness to these unknown deviations.   \n CAN WE \"FIX\" THE PEDAGOGIC ROBOT? An intuitive idea for improving the performance of the pedagogic robot R is to give it a model of the pedagogic human H that is more predictive. Unfortunately, it is not so simple. For example, in Section 4.2, we showed that a mixture between the literal and pedagogic human model was a much better fit to actual pedagogic humans than either the literal or pedagogic human model. What if we had pedagogic R use the more accurate mixture model as its model of the pedagogic human? Unfortunately, as shown in Figure  5a  (purple line), even if pedagogic R uses a better predictive model, i.e. the action mixture model, it does not perform any better. In fact, it is possible for pedagogic R to do worse when given a more predictive model of the human. The reason is that a model that is better for predicting behavior (e.g. human demonstrations) is not necessarily better for inferring underlying, latent variables (e.g. the reward function), which is what is important for the robot. This may help explain why pedagogic R does worse than literal R with pedagogic AH, even though the pedagogic H model assumed by pedagogic R is more predictive of pedagogic AH than the literal H model assumed by literal R. To illustrate, suppose there is a latent variable θ ∈ Θ with prior distribution p(θ) and observed data x ∈ X generated by some distribution p(x | θ). In our setting, θ corresponds to the objective and x corresponds to the human input. For simplicity, we assume Θ and X are finite. We have access to a training dataset D = {(θ i , x i )} n i=1 of size n. A predictive model m(x | θ) models the conditional probability of the data x given latent variable θ for all x ∈ X , θ ∈ Θ. In our case, the predictive model is the model of the human. The predictive likelihood L X of a predictive model m is simply the likelihood of the data under the model: L X (m) = n i=1 m(x i | θ i ) . (11) The inferential likelihood is the likelihood of the latent variables after applying Bayes' rule: L Θ (m) = n i=1 m(x i | θ i )p(θ i ) θ m(x i | θ)p(θ) . ( 12 ) Next, we show higher predictive likelihood does not necessarily imply higher inferential likelihood. Claim 5.1 (Predictive vs inferential likelihood). There exist settings in which there are two predictive models m 1 , m 2 such that L X (m 1 ) > L X (m 2 ), but L Θ (m 1 ) < L Θ (m 2 ). Proof. Suppose that Θ = {θ 1 , θ 2 } and X = {x 1 , x 2 , x 3 }, the prior p(θ) is uniform over Θ, and the dataset D contains the following n = 9 items: D = {(θ 1 , x 1 ), (θ 1 , x 1 ), (θ 1 , x 2 ), (θ 2 , x 2 ), (θ 2 , x 2 ), (θ 2 , x 3 ), (θ 2 , x 3 ), (θ 2 , x 3 ), (θ 2 , x 3 )} . Define the models m 1 (x | θ) and m 2 (x | θ) by the following conditional probabilities tables. m 1 (x | θ) x 1 x 2 x 3 θ 1 2/3 1/3 0 θ 2 0 1/3 2/3 m 2 (x | θ) x 1 x 2 x 3 θ 1 2/3 1/3 0 θ 2 0 2/3 1/3 The model m 1 has predictive likelihood L X (m 1 ) = (2/3) 6 (1/3) 3 and inferential likelihood L Θ (m 1 ) = (1/2) 3 . The model m 2 has predictive likelihood L X (m 2 ) = (2/3) 4 (1/3) 5 and inferential likelihood L Θ (m 2 ) = (1/3)(2/3) 3 . Thus, L X (m 1 ) > L X (m 2 ), but L Θ (m 1 ) < L Θ (m 2 ). In our context, Claim 5.1 means that a human model that is better in terms of prediction may actually be worse for the robot to use for inference. An alternative approach could be to directly fit models that optimize for inferential likelihood. Unfortunately, this optimization becomes much trickier because of the normalization over the latent variable space Θ in the denominator of (  12 ), see e.g.  (Dragan et al., 2013a) . Figure1: In this scenario, the robot infers whether it is ok to walk on the grass or not from a demonstration provided by the human (it already knows pavement is always ok). (a) The literal and pedagogic human's demonstrations. When grass is ok, the literal human is equally likely to walk on the grass or pavement. On the other hand, when grass is ok, the pedagogic human always walks on the grass in order to signal that grass is ok. (b) The beliefs of the literal robot LR and pedagogic robot PR after observing a demonstration. LR and PR assume human is literal and pedagogic, respectively. LR and PR differ in how strong their beliefs are after witnessing the human walk on pavement, leading to different problems when the human is misspecified. If the human is literal, but the robot is pedagogic, then it makes too strong of an inference. On the other hand, if the human is pedagogic, but the robot is literal, then it makes too weak of an inference. \n (a) (CIRL) the robot acts in the environment. The game's joint payoff for the robot and human is the value (expected sum of rewards) attained by the robot. (b) (CI) the robot outputs an estimate of the reward function. The game's joint payoff for the robot and human is a measure of the accuracy of the robot's inference. \n Figure 2 : 2 Figure 2: (a) The instructions given to participants in the literal and pedagogic condition, and a sample demonstration from both conditions. In the pedagogic case, participants were more likely to visit multiple safe colors, as well as to loop over safe tiles multiple times. (b) All possible reward functions. Each tile color can be either safe (0 points) or dangerous (-2 points). Figure modified from Ho et al. (2018). \n Figure 3 : 3 Figure 3: The accuracy of the robot's inferred reward for different pairs of human/robot pairs under the demonstrations provided by actual humans. \n Figure 4 : 4 Figure 4: The accuracy of the robot's inferred reward for different pairs of human/robot pairs under the demonstrations provided by humans simulated according to the human models in Section 3.2. \n Figure 5 : 5 Figure 5: The performance of the literal and pedagogic robot when demonstrations are simulated according to the demonstration mixture model (left/a) or the action mixture model (right/b). \n Figure 6 : 6 Figure6: (left/a) In blue is the mean negative log-likelihood of the pedagogic human demonstrations under the action mixture model with probability α. All individuals are assumed to have the same value of α. Note that a mixture between the literal and pedagogic model is far better than either the literal model (α = 0) or the pedagogic model (α = 1). In purple is the accuracy of the robot's inferred reward, when given demonstrations from pedagogic AH, if it assumes the human acts according to the action mixture model. (right/b) The mixture probability α that maximized log-likelihood for each individual pedagogic AH. \n\t\t\t A game in which all agents have the same payoff. \n\t\t\t In fact, in Demonstration-CIRL (Example 2.1), the best that the robot can do is infer a posterior distribution over rewards from the human's demonstrations, and then act optimally with respect to the posterior mean.3 Wang et al. (2019)  show that fixed-point iteration converges for all discrete distributions. For simplicity, we have written equations (1) and (2) assuming that the human and robot's prior over rewards and demonstrations is uniform, but in general, the equations can incorporate any prior (Yang et al., 2018) . \n\t\t\t . The literal human H 0 is noisily-optimal with respect to the reward function r. The probability4  There is nothing that requires the literal level to be at recursion level 0 and the pedagogic level to be at recursion level 1. Our proof of Claim 2.1 holds when the literal level is any k ≥ 0 and the pedagogic level is k + 1. \n\t\t\t All error bars and confidence bands in the paper depict bootstrapped 95% confidence intervals.", "date_published": "n/a", "url": "n/a", "filename": "milli20a.tei.xml", "abstract": "It is incredibly easy for a system designer to misspecify the objective for an autonomous system (\"robot\"), thus motivating the desire to have the robot learn the objective from human behavior instead. Recent work has suggested that people have an interest in the robot performing well, and will thus behave pedagogically, choosing actions that are informative to the robot. In turn, robots benefit from interpreting the behavior by accounting for this pedagogy. In this work, we focus on misspecification: we argue that robots might not know whether people are being pedagogic or literal and that it is important to ask which assumption is safer to make. We cast objective learning into the more general form of a common-payoff game between the robot and human, and prove that in any such game literal interpretation is more robust to misspecification. Experiments with human data support our theoretical results and point to the sensitivity of the pedagogic assumption.", "id": "6d0622e476135e358289dcebf711a6bf"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anna Salamon", "Stephen Rayhawk", "János Kramár"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "HowIntelligible.tei.xml", "abstract": "If human-level AI is eventually created, it may have unprecedented positive or negative consequences for humanity. It is therefore worth constructing the best possible forecasts of policy-relevant aspects of AI development trajectories-even though, at this early stage, the unknowns must remain very large. We propose that one factor that can usefully constrain models of AI development is the \"intelligibility of intelligence\"-the extent to which efficient algorithms for general intelligence follow from simple general principles, as in physics, as opposed to being necessarily a conglomerate of special case solutions. Specifically, we argue that estimates of the \"intelligibility of intelligence\" bear on: • Whether human-level AI will come about through a conceptual breakthrough, rather than through either the gradual addition of hardware, or the gradual accumulation of special-case hacks;", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom"], "title": "Strategic Implications of Openness in AI Development", "text": "• Partial openness that enables outsiders to contribute to an AI project's safety work and to supervise organizational plans and goals appears desirable. The goal of this paper is to conduct a preliminary analysis of the long-term strategic implications of openness in AI development. What effects would increased openness in AI development have, on the margin, on the long-term impacts of AI? Is the expected value for society of these effects positive or negative? Since it is typically impossible to provide definitive answers to this type of question, our ambition here is more modest: to introduce some relevant considerations and develop some thoughts on their weight and plausibility. Given recent interest in the topic of openness in AI and the absence (to our knowledge) of any academic work directly addressing this issue, even this modest ambition would offer scope for a worthwhile contribution. Openness in AI development can refer to various things. For example, we could use this phrase to refer to open source code, open science, open data, or to openness about safety techniques, capabilities, and organizational goals, or to a non-proprietary development regime generally. We will have something to say about each of those different aspects of opennessthey do not all have the same strategic implications. But unless we specify otherwise, we will use the shorthand 'openness' to refer to the practice of releasing into the public domain (continuously and as promptly as is practicable) all relevant source code and platforms and publishing freely about algorithms and scientific insights and ideas gained in the course of the research. Currently, most leading AI developers operate with a high but not maximal degree of openness. AI researchers at Google, Facebook, Microsoft and Baidu regularly present their latest work at technical conferences and post it on preprint servers. So do researchers in academia. Sometimes, but not always, these publications are accompanied by a release of source code, which makes it easier for outside researchers to replicate the work and build on it. Each of the aforementioned companies have developed and released under open source licences source code for platforms that help researchers (and students and other interested folk) implement machine learning architectures. The movement of staff and interns is another important vector for the spread of ideas. The recently announced OpenAI initiative even has openness explicitly built into its brand identity. Many other companies are more secretive or proprietary, particularly ones whose AI work is more applicationoriented. Even the most open of the current large efforts is not maximally open. A higher degree of openness could be achieved, for instance, through always-on webcams and microphones in the lab, so that outsiders could eavesdrop on research conversations and management meetings or even actively participate as new ideas are being proposed and discussed. Or a lab could hire out employees as consultants to help other groups working on similar problems. Openness is thus not a binary variable, but a vector with multiple dimensions that each admits of degrees. \n Short and medium-term impacts Although the main focus of this paper is on the long-term, we will set the stage by first discussing some short and medium-term implications. This will help us see how the long-term is different. It can also help us understand the behaviour of actors who either do not care about the longterm or are instrumentally constrained by short and medium-term considerations. The issue of the short and near-term desirability of openness can be roughly decomposed into two questions: (1) Does openness lead to faster AI development and deployment? (2) Is faster AI development and deployment desirable? Let us examine these in turn. \n Does openness lead to faster AI development and deployment? For the short-term, the case appears relatively straightforward. The main short-term effect of opening existing AI research (e.g. by open-sourcing code and placing related intellectual property into the public domain) would be to hasten the diffusion and application of current state-of-theart techniques. Software and knowledge about algorithms are non-rival goods. Making them freely available would enable more people to use them, at low marginal cost. The effect would be small, since so much is already in the public domain, but positive. For the medium-term, the case is more complicated. If we conceive of the medium-term as a period that is long enough to allow for significant new research to take place and to be developed to the point of practical application, then we must take into account the dynamic effects of openness. In particular, we must consider the impact of openness on incentives to invest in R&D. We may also need to take into account other indirect effects, such as impacts on market structure  (Casadesus-Masanell and Ghemawat, 2003) . Consider first the imposition of a general ruleit could be a change in intellectual property law, a regulatory requirement, or a cultural normthat pushes AI developers towards greater openness. We might then expect the shortterm benefits described above. But there is also tradition in economic thought, harkening back to Joseph  Schumpeter (1942) , which points to a tradeoff between static and dynamic efficiency. Basic ideas are public goods; and in the absence of (some degree of) monopoly positioning or market power, a firm is unable to appropriate the value of the new ideas it originates  (Arrow, 1962; Shell, 1966 Shell, , 1967 . From this perspective, monopoly rents, while they reduce static efficiency and welfare in the short run, provide incentives for innovation that can improve dynamic efficiency and welfare over a longer period. Consequently, a rule that makes it harder for a developer to earn monopoly rents from the ideas it generates (for instance a rule that discourages the use of trade secrecy or patents) could have a negative medium-term impact on the speed of AI development and deployment. Not all economic incentives for innovation would disappear in an open non-proprietary innovation regime (See e.g.  Boldrin and Levine, 2008) . One reason firms engage in open non-proprietary R&D is to build 'absorptive capacity': conducting original research as a means of building skill and keeping up with the state-of-the-art  (Cohen and Levinthal, 1989; Griffith et al., 2004) . Another reason is that copying and implementing an idea takes time and effort, so the originator of a new idea may enjoy a period of effective monopoly even if the idea is freely communicated and no legal barrier prevents others from adopting it. Even a brief period of exclusive possession of an idea can enable its originator to profit by trading on insider knowledge (e.g. by being first to know that a new market-impacting technology has now become feasible)  (Hirshleifer, 1971) . Another incentive for innovation in the open non-proprietary regime is that the originator of an idea may profit from owning a complementary asset whose value is increased by the new idea.  1  For example, a mining company that develops a new technique to exploit some of its previously inaccessible ore deposits may derive some profit from its invention even if other mining companies are free to copy the technique (though typically less than if its competitors had to pay licence fees). Similarly, a software firm might choose to give away its software gratis in order to increase demand for consulting services and technical support (which the firm, having written the software, is in a strong position to supply). Furthermore, in the open source software sector, significant contributions are made by individuals who are volunteering their own free time. One motive for such contributions is that they enable a programmer to demonstrate skill, which may raise his or her market value  (Hann et al., 2004 ). 2 Such a skill-signalling motive appears to be a strong influence among many AI researchers. Researchers prefer to work for organizations that allow them to publish and present their work at technical conferences, partly because doing so helps the researcher build a reputation among peers and potential employers. The skill-signalling motive is probably especially strong among the most capable young researchers, since they have the most to gain from being able to show off their abilities. This gives organizations seeking to hire the most talented AI researchers a reason to opt for opennessopenness in the sense of refraining from trade secrecy, though not necessarily from patenting 3 -a reason that is quite independent of any altruistic concern with promoting scientific progress or general welfare. So some incentives for innovation would remain in a regime of openness (even aside from public subsidy or philanthropy). Nevertheless, it is possible that R&D investment would fall if all incentives from monopoly exploitation were removed from the mix. Such a reduction in R&D expenditure would have to be balanced against other effects of openness that may tend to boost technical progress. For example, the patent system involves substantial transaction costs which would be eliminated in a fully open development regimeinnovators would then not have to hack their way through 'patent thickets' to get a new product to market. And the relinquishment of trade secrecy and confidentiality would facilitate information flow between researchers who work for different organizations, reducing duplication of effort and other inefficiencies. In view of these countervailing considerations, it may not be possible to give a general answer to the question of whether a rule pushing towards greater openness would help or hinder technical progress. The sign of the effect would depend on context and the particular form of openness being contemplated  (Lerner and Tirole, 2005) . We should note that even if there were a slight negative effect on the rate of progress from greater openness, the welfare implications could still be positive (for the short and even the medium term). This is because openness would improve static efficiency, by making products available at marginal cost (e.g. in the form of open source software) and allowing a given level of state-of-the-art technical capability to diffuse more quickly through the economy. If, however, there were a large negative effect on the rate of progress, then the welfare losses from that effect would plausibly dwarf the welfare gains from increased static efficiency, especially over longer time scales. So far we've been considering the effects of the establishment of a general rule promoting greater openness. We could instead inquire about the effects of a unilateral decision by one actor to pursue greater opennessfor example an AI lab that, perhaps for altruistic reasons, opts for a higher level of openness than would be commercially optimal. (We will assume that the money lost by deviating from the commercially optimal policy would otherwise have been spent on consumption of a form that would not affect the rate of technological advance.) Would such a unilateral decision speed technical progress? In this case we can set aside the incentive effects that could reduce R&D spending if the increase in openness were the result from an exogenous shift in cultural norms or intellectual property rights. The benefits of openness discussed earlier would still accrue. So this case is more favourable to the hypothesis that openness speeds progress. It may be noted that academia, which is less dependent than the commercial sector on monopoly rents, has a relatively strong culture of openness, 4 what the sociologist Robert Merton called the 'communist norm', 5 and there is currently a push to make it yet more open  (Nosek, 2015) . Even so, it is possible to construct models in which even a unilateral altruistically-motivated decision by a developer to pursue a course of open development reduces total R&D spending. For instance,  Saint-Paul (2003)  presents an endogenous growth model in which, for some parameter values, such a philanthropic intervention reduces growth rates and welfare by crowding out a disproportionate amount of proprietary innovation. 6 So the picture is not clear. On balance, it might still be plausible that a philanthropically motivated R&D funder would speed progress more by pursuing open science, at least if we assume that the research is focused on theoretical matters or process innovations (as opposed to the development of a particular product that directly competes with commercial alternatives). 7 \n Is faster technological progress and rollout of AI capabilities desirable? This brings us to the second question about the short and near-term desirability of openness: supposing openness would speed technical progress and rollout of AI capabilities, would that be socially beneficial? It is clear that machine intelligence holds great promise for positive applications across many sectors of the economy and society, including transportation, healthcare, the environment, entertainment, security, and scientific discovery. For instance, an estimated 1.2 million people die every year in road accidents around the world, a number that could eventually be reduced to a low level as AI-enabled vehicles take over more functions from human drivers (Goldman  Sachs, 2015) . A report by McKinsey estimates an economic impact of several trillions of dollars annually from AI-related technologies by 2025. 8 A full review of the potential positive applications is outside the scope of this paper. As with any general-purpose technology, it is possible to identify concerns around particular applications. It has been argued, for example, that military applications of AI, including lethal autonomous weapons, might incite new arms races, or lower the threshold for nations to go to war, or give terrorists and assassins new tools for violence  (Future of Life Institute, 2015) . AI techniques could also be used to launch cyber attacks. Facial recognition, sentiment analysis, and data mining algorithms could be used to discriminate against disfavoured groups, or invade people's privacy, or enable oppressive regimes to more effectively target political dissidents  (Balkin, 2008) . Increased reliance on complex autonomous systems for many essential economic and infrastructural functions may create novel kinds of systemic accident risk or present vulnerabilities that could be exploited by hackers or cyber-warriors (See  Perrow, 1984) . Insofar as it is possible to fine-tune openness choices so as to differentially expedite specific kinds of AI applications, these concerns might indicate the need for making exceptions to a generally pro-openness stance. For example, open-sourcing the code for autonomous weapons seems undesirable, and we have not heard anybody calling for that to be done. But basic research in AI is typically not application-specific in this way. Rather, to the extent that it succeeds, it will deliver algorithms and techniques that could be used in a very wide range of applications. This holds, in particular, for most work in current focal areas such as deep learning and reinforcement learning: that work is exciting precisely because it seeks general solutions to learning problems that occur in a wide range of tasks and environments. Another frequently expressed area of concern is that advances in AI will create labour market dislocations and reduce the employability of some workers  (Autor, 2015; Brynjolfsson and McAfee, 2014) . It is not clear that near and medium-term AI capabilities pose any distinctive challenges in this regard, challenges that do not apply to automation generally and indeed to a large portion of all technological change, which often reduces demand for some types of human labour. Concerns about technological unemployment are not new. After the Industrial Revolution, developed countries underwent a shift from overwhelmingly agricultural to industrial and, later, service-oriented economies. The initial phase of industrialization imposed great burdens on significant portions of the population. 9 Over time, however, subsequent to the introduction of new social policies and a prolonged period of historically unprecedented rates of economic growth, industrialization has resulted in large gains for human prosperity, gains reflected in indices on nutrition, health, life expectancy, access to information, mobility, and other measures of human welfare  (Galor and Moav, 2004; United Nations Development Programme and Malik, 2014) . If, as a first-order approximation, we model the impacts of near and medium-term AI advances as a continuation and extension of longstanding trends of automation and productivity-increasing technological change, therefore, we would estimate that any adverse labour market impacts would be greatly outweighed by economic gains. To think otherwise would seem to entail adopting the generally luddite position that perhaps a majority of current technological developments have a net negative impact. We can make a similar point with regard to the concern that advances in AI might exacerbate economic inequality. This, too, is best thought of in a more general context, as part of a wider discussion about technological change and inequality. Most contemporary debate around these matters takes for granted that technological progress is broadly desirable: mainstream controversy being limited to how governments and societies ought to adapt in order to accelerate development and diffuse the benefits more widely while managing any particular challenges that might flow from some aspect of the new technology. It is worth noting here that openness in AI, aside from whatever effect it might have on speed of development and general economic growth, could also have some distinctive impacts on inequality. Most obviously, releasing software in the public domain makes it available free of charge, which could have some equalizing effect on the levels of welfare attainable by people at different segments of the income distribution (provided they have the requisite hardware and skill to use it, and that it is relevant to their needs). Open source software may also differentially benefit technically sophisticated users, compared to commercial software  (Bessen, 2006; Lerner and Tirole, 2005; Schmidt and Schnitzer, 2003) . \n Summary of near and medium-term impacts Much current work in AI is to a large extent open. The effect of various kinds of unilateral marginal increases in openness on the rate of technical advance in AI is somewhat unclear but plausibly positive, especially if focused on theoretical work or process innovation. The effect of marginal increases in openness brought about through exogenous pressure, such as shifts in cultural norms or regulation, is ambiguous as far as we have been able to explore the matter in the present analysis. The short and medium-term impacts of accelerating advances in AI appear to be substantially positive in expectation, primarily because of diffuse economic benefits across many sectors. A number of specific areas of concern can be identified, including military uses, applications for social control, and systemic risks from increased reliance on complex autonomous processes. However, for each of these areas of concern, one could also envisage prospects of favourable impacts, which seem perhaps at least equally plausible. For example, automated weaponry might reduce human collateral damage or change geopolitical factors in some positive way; improved surveillance might suppress crime, terrorism, and social free-riding; and more sophisticated ways of analysing and responding to data might help identify and reduce various kinds of systemic risk. So while these areas of concern should be flagged for ongoing monitoring by policy makers, they do not at our current state of knowledge change the assessment that faster AI progress would likely have net positive impacts in the short and medium-term. A similar assessment can be made regarding the concern that advances in AI may have adverse impacts on labour markets or economic inequality: some favourable impacts in these areas are also plausible, and even if they were dominated by adverse impacts, any net adverse impact in these areas would most likely be outweighed by the robustly positive impact of faster economic growth. We also noted the possibility that openness, particularly in the form of placing technology and software in the public domain, may have some positive impact on distributional concerns by lowering the economic cost for users to access AI-enabled products (though if open source software displaces some amount of proprietary software, and open source software is more adapted to the needs of technically sophisticated users, then it is not entirely clear that the distributional impact would favour those segments of the population that are both low-income and low-skill). In a nutshell: unilateral decisions by AI developers to be incrementally more open about their basic research and process innovations would probably have some net positive near and medium-term social impacts and would on the margin accelerate AI progress. In other respects, however, the medium-term strategic ramifications of different forms of openness are more ambiguous and uncertain than might have been suspected. \n Long-term impacts We will assess the long-term desirability of openness in AI development with reference to how openness affects the following two paramount problems tied to the creation of extremely advanced (generally human-level or superintelligent) AI systems (See Bostrom, 2014a): • The control problem: how to design AI systems such that they do what their designers intend. • The political problem: how to achieve a situation in which individuals or institutions empowered by such AI use it in ways that promote the common good. The impact of openness on both the control problem and the political problem must be analysed. Here we identify three main pathways by which openness in AI development may have such impact or otherwise intersect with long-term strategic considerations: (1) openness may speed AI development; (2) openness may make the race to develop AI more closely competitive; (3) openness may promote wider engagement. \n Openness may speed AI development We argued in the previous section that faster AI progress is a plausible consequence of at least some forms of openness. This could have strategically relevant impacts in several ways, as follows. \n Making the benefits of AI accrue sooner This is important if currently existing people have a strongly privileged status over future generations in one's decision criteria. Since the human population is dying off at a rate of almost 1% per year, even modest effects on the arrival date of superintelligence could have important decision-relevance for such a 'person-affecting' objective function (assuming superintelligence would, with substantial probability, dramatically reduce the death rate or improve wellbeing levels)  (Bostrom, 2003) . Earlier onset of benefits would also be important if one uses a significant time discount factor. (However, making the benefits start earlier is not clearly significant on an impersonal time-neutral view, where instead it looks like the focus should be on reducing existential risk  (Bostrom, 2013) .) \n Less time to prepare Expedited AI development would give the world less time to prepare for advanced AI. This may reduce the likelihood that the control problem will be solved. One reason is that safety work is likely to be relatively open in any case, and so would not gain as much as non-safety AI work from additional increments of openness in AI research generally. Safety work may thus be decelerated compared to nonsafety work, making it less likely that a sufficient amount of safety work will have been completed by the time advanced AI becomes possible. 10 There are also some processes other than direct work on AI safety that may improve preparedness over timeand which would be given less time to play out if AI happens soonersuch as cognitive enhancement and improvements in various methodologies, institutions, and coordination mechanisms  (Bostrom, 2014a) . 11 (The impact on the political problem of earlier AI development is harder to gauge, since it depends on difficult-to-predict changes in the broader social and geopolitical landscape over the coming decades.) \n Preempt other existential risks Accelerated AI would increase the chance that superintelligent AI will preempt existential risks stemming from non-AI sources, such as risks that may arise from synthetic biology, nuclear war, molecular nanotechnology, or other risks as-yet unforeseen. This preempting effect depends on the arrival of superintelligent AI actually eliminating or reducing other major anthropogenic existential risks. 12 (Whether it does so may depend partly on whether the post-AI-transition world is multipolar or unipolar, a topic to which we shall return to below.) In summary, the fact that openness may speed up AI development seems positive for goals that strongly prioritize currently existing people over potential future generations, and uncertain for impersonal time-neutral goals. Either of these effects appear relatively weak compared to other strategy-relevant impacts from openness in AI development, because we would not expect marginal increases in openness to have more than a modest influence on the speed of AI development. \n Openness making AI development race more closely competitive One weighty consideration is that the final stages of the race to create the first superintelligent AI are likely to be more closely competitive in open development scenarios. The reason for this is that openness would equalize some of the variables that otherwise would cause dispersion in the levels of capability or progress-rates among different AI developers. If everybody has access to the same algorithms, or even the same source code, then the principal remaining factors that could produce performance differences are unequal access to computation and data. One would therefore expect there to be a larger number of actors with the ability to wield near state-of-the-art AI in open development scenarios  (Armstrong et al., 2016) . This tightening of the competitive situation could have the following important effects on the control problem and the political problem. \n Removes the option of pausing In a tight competitive situation, it could be impossible for a leading AI developer to slow down or pause without abandoning its lead to a competitor. This is particularly problematic if it turns out that an adequate solution to the control problem depends on the specifics of the AI system to which it is to be applied. If there is some necessary part of the control mechanism that can only be invented or installed after the rest of the AI system is highly developed, then it may be crucial that the developer has the ability to pause progress on making the system smarter until the control work can be completed. Suppose, for example, that designing, implementing, and testing a control solution requires six months of additional work after the rest of the AI is fully functional. Then, in a tight competitive situation, any team that chooses to undertake that control work might simply abandon the leadand with it, possibly, the ability to influence future eventsto some other less careful developer. If the pool of potential competitors with near state-of-the-art capabilities is large enough, then one would expect it to contain at least one team that would be willing to proceed with the development of superintelligent AI even without adequate safeguards. The larger the pool of competitors, the harder it would be for them to all coordinate to avoid a risk race to the bottom. \n Removes the option of performance-handicapping safety Another way in which a tight competitive situation is problematic is if the mechanisms needed to make an AI safe reduces the AI's effectiveness. For example, if a safe AI runs a hundred times slower than an unsafe AI, or if safety requires an AI's capabilities to be curtailed, then the implementation of safety mechanisms would handicap performance. In a close competitive situation, unilaterally accepting such a handicap could mean forfeiting the lead. By contrast, in a less competitive situation (such as one in which a large coalition has a sizeable lead in technology or computing power) there might be enough slack that the frontrunner could implement some efficiency-reducing safety measures without abandoning its lead. The sacrifice of performance for safety may need to be only temporary, a stopgap until more sophisticated control methods are developed that eliminate the efficiency-disadvantage of safe AI. Even if there were inescapable tradeoffs between efficiency and safety (or ethical constraints preventing certain kinds of instrumentally useful computation), the situation would still be salvageable if the frontrunner has enough of a lead to be able to get by with less than maximally efficient AI for a period of time: since during that time, it might be possible for the frontrunner to achieve a sufficient degree of global coordination (for instance, by forming a 'singleton', discussed more below) to permanently prevent the launch of more efficient but less desirable forms of AI (or prevent such AI, if launched, from outcompeting more desirable forms of AI)  (Bostrom, 2006) . \n Lowers probability of a small group capturing the future There are some other consequences of tighter competition in the runup to superintelligent AI that are of more uncertain valence and magnitude, but potentially significant. One such consequence is for the political problem. A tighter competitive situation would make it less likely that one AI developer becomes sufficiently powerful to monopolize the benefits of advanced AI. This is one of the stated motivations for the OpenAI project, expressed for example, by Elon Musk, one its founders: I think the best defense against the misuse of AI is to empower as many people as possible to have AI. If everyone has AI powers, then there's not any one person or a small set of individuals who can have AI superpower.  (Levy, 2015)  Openness may thus make it more likely that many people's preferences influence the future. Depending on one's values and expectations (e.g. one's expectations about which preferences would rule if the future were instead captured by a small group), this could be an important consideration. \n Affect influence of status quo powers? Another consequence for the political problem: openness in AI development may also influence what kind of actor is most likely to achieve monopolization (if such there be) or to achieve a relatively larger influence over the outcome. Access to computing power (and possibly data) becomes relatively more important if access to algorithms or source code is equalized. In expectation, this would align influence over the post-AI world more closely with wealth and power in the pre-AI world, since computing power is fairly widely distributed (including internationally), quite fungible with wealth, and somewhat possible for governments to controlin comparison with access to algorithmic breakthroughs in a closed development scenario, which might be more lumpy, stochastic, and local. The likelihood that a single corporation or a small group of individuals could make a critical algorithmic breakthrough needed to make AI dramatically more general and efficient seems greater than the likelihood that a single corporation or a small group of individuals would obtain a similarly large advantage by controlling the lion's share of the world's computing power.  13  Thus, if one thinks that it is preferable in expectation that advanced AI be controlled by existing governments, elites, and ordinary people in proportion to their existing wealth and political powerrather than by some particular group that happens to be successful in the AI field (such as a corporation or an AI lab) then one might favour a scenario in which hardware becomes the principal factor of AI power. Openness in AI development would make such a scenario more likely. However, openness would also reduce the economies of scale in AI research labs, and this would favour smaller players who may be less representative of status quo power. Consider the opposite case: development is perfectly closed, and any wannabe AI developer must make all the relevant discoveries and build all the needed components in-house. Unless the successful AI architecture turns out to be extremely simple, this regime would strongly favour larger development groupsthe odds of a given group winning the race would scale superlinearly with group size. By contrast, if development is open and the winning group is the one that adds a single final insight to a shared corpus of ideas, then the probability of a given group being the winner might instead scale roughly linearly with size. 14 So in scenarios where there is a hardware overhang, and an intelligence explosion is triggered by a final algorithmic invention, openness would increase the probability of a small group capturing the future. Consequently, if larger development groups (such as large corporations or national projects) are typically more representative of, or controlled by, status quo powers than a randomly selected small development group (such as a 'guy in a garage') then openness may either increase or decrease the degree of influence status quo powers would have over the outcome, depending on whether hardware or software is the bottleneck. Since it is currently unclear what the bottleneck will be, the impact of openness on the expected degree of control of status quo powers is ambiguous. \n Reduces probability of a singleton A singleton is a world order in which there is at the highest level of organization one coordinated decision-making agency. In other words, a singleton is a regime in which major global coordination or bargaining problems are solved. The emergence of a singleton is thus consistent with both scenarios in which many human wills together shape the future and scenarios in which the future is captured by narrow interests. The point that openness in AI development seems to lower the probability of a singleton is therefore distinct from the point made that openness seems to lower the probability of a small group capturing the future. One could be against a small group capturing the future and yet for the formation of a singleton. There are a number of serious problems that can arise in a multipolar outcome that would be avoided in a singleton outcome. One such problem is that it could turn out that at some level of technological development (and perhaps at technological maturity) offence has an advantage over defence. For example, suppose that as biotechnology matures, it becomes inexpensive to engineer a microorganism that can wreak havoc on the natural environment while it remains prohibitively costly to protect against the release and proliferation of such an organism. Then, in a multipolar world, where there are many independent centres of initiative, one would expect the organism eventually to be released (perhaps by accident, perhaps as part of a blackmail operation, perhaps by an agent with apocalyptic values, or maybe in warfare). The chance of avoiding such an outcome would seem to decrease with the number of independent actors that have access to the relevant biotechnology. This example can be generalized: even if in biotechnology offence will not have such an advantage, perhaps it will in cyberwarfare? in molecular nanotechnology? in advanced drone weaponry? or in some other as-yet unanticipated technology that would be developed by superintelligent AIs? A world in which global coordination problems remain unsolved even as the power of technology increases towards its physical limits is a world that is hostage to the possibility thatat some level of technological developmentnature too strongly favours destruction over creation. From the perspective of existential risk reduction, it may therefore be preferable that some institutional arrangement emerges that enables robust global coordination. This may be more tractable if there are fewer actors initially in possession of advanced AI capabilities and needing to coordinate. The possibility that offence might have an inherent advantage over defence is not the only concern with a multipolar outcome. Another concern is that in the absence of global coordination it may be impossible to forestall a population explosion of digital minds and a resulting Malthusian era in which the welfare of those digital minds may suffer  (Bostrom, 2004 (Bostrom, , 2014a Hanson, 1994) . Independent actors would have strong incentives to multiply the number of digital workers under their control to the point where the marginal cost of producing another one (including electricity and hardware rental) equals the revenue it can bring in by working maximally hard. Local or national legislation aimed at protecting the welfare of digital minds could shift production to jurisdictions that offer more favourable conditions to investors. This process could unfold rapidly since software faces fewer barriers to migration than biological labour, and the information services it provides are largely independent of geography (though subject to latency effects from longdistance signal transmission, which could be significant for digital minds operating at high speeds). The long-run equilibrium of such a process is difficult to predict, and might be primarily determined by choices made after the development of advanced AI; but creating a state of affairs in which the world is too fractured and multipolar to be able to influence where it leads should be a cause for concern, unless one is confident (and it is hard to see what could warrant such confidence) that the programs with the highest fitness in a mature algorithmic hyper-economy are essentially coextensive with the programs that have the highest level of subjective well-being or moral value. \n Relevance of AI multiplicity for control problem It might be thought that tighter competition would promote a more desirable outcome by helping solve the control problem. The idea would be that in a more closely competitive scenario, it is less likely that a single AI system gets so far ahead of all the others as to obtain a decisive strategic advantage. Instead, there would more likely be a multiplicity of AI systems, built by different people in different countries for different purposes, but with comparable levels of capability. In such a multipolar world, it might be harder for any one of those AI systems to cause extreme damageeven if the controls applied to it were to failbecause there would be other AIs, presumably under human control, to hem it in. This line of thinking is quite problematic as an argument for openness, even if we set aside the general concerns with multipolarity set out above. The existence of multiple AIs does not guarantee that they will act in the interests of humans or remain under human control. (Analogy: the existence of many competing modern human individuals did little to promote the long-term prospering of the other hominid species with which Homo sapiens once shared the planet.) If the AIs are copies of the same template, or slight modifications thereof, they might all contain the same control flaw. Open development may in fact increase the probability of such homogeneity, by making it easier for different labs to use the same code base and algorithms instead of inventing their own. There is also the possibility of systemic failures resulting from unexpected interactions of different AIs. We know that such failures can occur even with very simple algorithms (witness, e.g., the Flash Crash; US Securities Exchange Commission, 2010). Among advanced artificial agents that are capable of highly sophisticated planning and strategic reasoning (and which might be able to coordinate using different or more effective means than humans (See e.g. LaVictoire et al., 2014)), there may be additional and novel ways for systemic failures to occur. Even if some balance-ofpower equilibrium prevented any individual AI or coalition of AIs from infracting human interests, it is not clear we could be confident that it would last.  15  If it really were helpful for control to have a multiplicity of AIs, it might be better that the AIs be created by a single actor, who would have a greater ability to ensure that the AIs are balanced in capability. Granted, AIs created by a single developer may be more similar to one another, and hence more prone to correlated control failures, than AIs created by different developers. Yet openness, we noted, though it may increase the likelihood that there will be multiple simultaneous developers, would also tend to make the AIs created by those developers be based on more similar designs. So the net effect of openness on the probability that there will be a diverse set of AIs is ambiguous. We could put together a set of assumptions that would support the proposition that we should aim to obtain a solution to the control problem through the creation of a multiplicity of AIs by means of adopting a policy of openness. For example, we could stipulate that multiplicity of AIs, even if they are based on the same design, would contribute to safety provided only that the AIs be given different goals. The argument would then be that AIs created by different developers would naturally be given different goals, and would thus contribute to the public good of safety; whereas a single developer would either only create a single AI or create multiple AIs with identical goals (because giving an AI a goal different from your own would incur a private cost to you, since that AI will then not be working purely in your interest). The vision here might be a world containing many AIs, each pursuing a different goal, none of them strong enough to seize control unilaterally or by forming a coalition with other AI powers. These AIs would compete for customers and investors by offering us favourable deals, much like corporations competing for human favours in a capitalist economy. The role of the state in this model needs to be considered. Without a state powerful enough to regulate the competing AIs and enforce law and order, it may be questionable how long the balance-of-power equilibrium would last and how humans would fare under it. An alternativeless attractiveanalogue might be 17th century Europe, where the AIs would correspond to stronger states and the human populations would correspond to little principalities that hope to achieve security by aligning themselves with a strong (winning) AI coalition. In summary, openness would be expected to make the AI development race more closely competitive, and this would have several strategic consequences. It would make it harder to pause towards the end in order to implement or test a safety mechanism. It would also make it harder to use any safety mechanism that reduces efficiency. Both of these look like important negative effects on the control problem. Openness also has consequences for the political problem: decreasing the probability that a small group will monopolize the benefits of advanced AI and decreasing the probability of a singleton. It may either increase or reduce the influence of status quo powers over the post-AI future depending on whether the transition is mainly hardware or software constrained. Furthermore, there may be impacts on the control problem via the distribution of AIs that result from open development, though the magnitude and sign of those impacts are unclear: openness may make a multiplicity of AIs more likely, which could increase the probability of some kind of balance-of-power arrangement between AIs; yet openness could also make the AIs more similar to one another than they would have been if the multiplicity of AI scenario had come to pass without openness and thus more likely to exhibit correlated failures. (In any case, it is unclear whether a multiplicity of diverse AIs created by different developers would really help with the control problem.) \n Openness promoting wider engagement One class of potentially strategically significant effects of openness in AI development is that openness might increase external engagement with various aspects of stateof-the-art AI technology. That openness should increase external interest and attention is not axiomatic. Sometimes an attempt to keep something secret only serves to draw more attention to it. However, in cases where meaningful engagement requires detailed information and fine-grained access, it is plausible that increased openness would increase such engagement. \n External perspectives illuminate safety Somebody might thus argue that if AI systems are kept secret, then outside experts cannot directly work on making them safer, and that this would make a closed development scenario riskier. Note, however, that if AI systems are kept secret, then outside experts also cannot directly work on making them more effective. So, at a first glance, it may look like a tie: and if there is no differential effect on safety here, then we are back to the point that openness might just generally speed things up, both safety and effectiveness research, which we discussed in an earlier section. But one might speculate that work on safety would gain more from outside participation than work aimed at increasing AI effectivenessperhaps on grounds that safety engineering and risk analysis are more vulnerable to groupthink and other biases, and would therefore benefit disproportionately from having external perspectives brought to bear. It is presumably easier to delude oneself about the safety of the AI one is building than to delude oneself about its capabilities, since there are more opportunities for objective feedback about the latter. Therefore, if there is an optimism bias, it would have freer rein to distort beliefs about safety than about efficacy. And if outside perspectives are a corrective to such a bias, their inclusion would thus differentially promote progress on safety.  16  Outside participants more altruistic? Furthermore, one could argue that because safety is a public good, external researchers (and their funders) are comparatively more likely to help work on safety than on effectiveness (relative to the allocation of effort that a particular developer would make internally, since the insiders probably have relatively stronger non-altruistic motives for working on effectiveness). Openness in AI development could then, by enabling disinterested outsiders to contribute, increase the overall fraction of AI-related effort that is focused on safety and thereby improve chances that the control problem finds a timely solution. For a group that is sufficiently exceptionally altruistic and safety-oriented, this argument might go into reverse. For such a group, openness could dilute the focus on public goods by enabling participation by less-conscientious outsiders.  17, 18  Influence on architecture? It is possible that organizational mechanics of an open development trajectory might affect the character of the AI that is created, for better or worse. The 'coral reef' approach common in open source software projects, for example, might result in a greedy pursuit of local optima rather than a patient search and design for global optima  (Boudreau and Lakhani, 2015) . Or it might be the case that looser coupling among development groups encourages more functional modularity (compared to centralized processes, which might foster more tightly integrated unitary architectures). It's plausible that such effects might have significant implications for the control problem, but uncertainties about what those effects might be (as well as about whether some given effect would be positive or negative for the control problem) may be too large for these types of consideration to have much impact on our present deliberations. \n Gives actors more foresight Openness about capabilitieswhat machine intelligence is capable of at a given time and the expected timeline for further advanceswould increase the ability of outsiders to influence or adapt to AI developments. This might increase the probability of nationalization of leading AI efforts, since it would make it easier for a government to see exactly when and where it would need to intervene in order to maintain control over advanced AI capabilities. Openness about the science and source code, by contrast, may decrease the probability of nationalization, by making AI development more widely distributed (including internationally) and thus harder for a government to scoop up. (Openness might also reduce the probability of nationalization by fostering a culture among AI researchers that is more inimical to governmental or corporate control of AI.) Openness about capabilities, aside from facilitating government control of a pivotal AI breakthrough, would also help societies generally prepare, by providing various actors with a clearer view of the future. It is not immediately clear what effect this would have on the control problem or the political problem. Giving people more foresight into a major upcoming technological revolution may be expected to have diffuse positive effects by enabling planning and adaptation. In particular, openness could enable more accurate forecasting of risks related to the control problem, leading to more investment in solutions in states of the world where they are particularly needed.  19   \n Committing to sharing We have already discussed how openness would tend to make the AI race more competitive, and how it might speed progress, as well as the short-term benefits to allowing the use of existing ideas and information at marginal cost. Here we note a further strategically relevant possible consequence: openness in the near-term could create some kind of lock-in that increases the chance that more advanced AI capabilities will similarly be made freely available (or that at least some components of advanced AI will be free, even if othersfor example, computing powerremain proprietary). Such lock-in might occur if a cultural norm of openness takes root, or if particular AI developers make commitments to openness that they cannot later easily back out of. This would feed back into the issues mentioned before, giving present openness the tendency to make the AI race more competitive and perhaps faster also in the longer run. But there is also a separatebeneficialeffect of openness lock-in, which is that it may foster goodwill and collaboration. The more that different potential AI developers (and their backers) feel that they would fully share in the benefits of AI even if they lose the race to develop AI first, the less motive they have for prioritizing speed over safety, and the easier it should be for them to cooperate with other parties to pursue a safe and peaceful course of development of advanced AI designed to serve the common good. Such a cooperative approach would likely have a favourable impact on both the control problem and the political problem. In summary, an open development scenario could reduce groupthink and other biases within an AI project by enabling outsiders to engage more, which may differentially benefit risk analysis and safety engineering, thereby helping with the control problem. Outsider contributions might also be comparatively more altruistically motivated and hence directed more at safety than at performance. The mechanics of open collaboration may influence architectural choices in the development of machine intelligence, perhaps favouring more incremental 'coral reef' style approaches or encouraging increased modularity, though it is currently unclear how this would affect the control problem. Openness about capabilities would give various actors more insight into ongoing and expected development, facilitating planning and adaptation. Such openness may also facilitate governmental expropriation, whereas openness about science and code would counteract expropriation by leaving less proprietary material to be grabbed. Finally, if current openness choices are subject to lock-in effects, they would have direct effects on future levels of openness, and might serve as ways of committing to sharing the spoils of advanced AI (which would be helpful for both the control problem and the political problem). \n Conclusions We have seen that the strategic implications of openness in AI is a matter of considerable complexity.  20  Our analysis, and any conclusions we derive from it, remain tentative and preliminary. But we have at least identified several relevant considerations that must be taken into account by any wellgrounded judgement on this topic.  21  In addition to the consequences discussed in this paper, there are many local effects of openness that individual AI developers will want to take into account. A project might reap private benefits from openness, for example in recruitment (researchers like to publish and build reputations), by allowing managers to benchmark in-house research against external standards, and via showcasing achievements for prestige and glory. These effects are not covered in the present analysis since the focus here is on the global desirability of openness rather than the tactical advantages or disadvantages it might entail for particular AI groups. \n General assessment In the near term, one would expect openness to expedite dissemination of existing technologies, which would have some generally positive economic effect as well as a host of more specific effects, positive and negative, arising from particular applicationsin expectation, net positive. From a near-term perspective, then, pretty much any form of increased openness is desirable. Some areas of application raise particular concerns (including military uses, applications for social control, and systemic risks from increased reliance on complex autonomous processes) and these should be debated by relevant stakeholders and monitored by policy makers as real-world experience with these technologies accumulates. Impacts on labour markets may to a first approximation be subsumed under the more general category of automation and labour-saving technological progress, which has historically had a massive net positive impact on human welfare though not without heavy transition costs for segments of the population. Expanded social support for displaced workers and other vulnerable groups may be called for should the pace or extent of automation substantially increase. The distributional effects of increased openness are somewhat unclear. Historically, open source software has been embraced especially by technically sophisticated users  (Foushee, 2013) ; but less skilled users would also stand to benefit (e.g. from products built on top of open source software or by using sophisticated users as intermediaries).  22  The medium-term effects of openness are complicated by the possibility that openness may affect incentives for innovation or market structure. The literature on innovation economics is relevant here but inconclusive. A best guess may be that unilateral increases in openness have a positive effect on the rate of technical advance in AI, especially if focused on theoretical work or process innovations. The effect of increases in openness produced by exogenous pressure (e.g. from regulation or cultural norms) is ambiguous. The medium-term impact of faster technical advance in AI may be assessed in a similar way to shorter-term impacts: there are both positive and negative applications, and lots of uncertainty; yet a reasonable guess is that medium-term impacts are net positive in expectation (an expectation that is based, largely, on extrapolation of past technological progress and economic growth). Potential medium-term impacts of concern include new forms of advanced robotic warfarewhich could conceivably involve destabilizing developments such as challenges to nuclear deterrence (e.g. from autonomous submarine-tracking bots or deep infiltration of enemy territory by small robotic systems; Robb, 2016) -and the use of AI and robotics to suppress riots, protests, or opposition movements, with possibly undesirable ramifications for political dynamics  (Robb, 2011) . Our main focus has been on the long-term consequences of openness. If we consider long-term consequences, but our evaluation function strongly privileges impacts on currently existing people, then an especially important consideration is whatever tendency open development has to accelerate AI progress: both because faster AI progress would mean faster rollout of near and medium-term economic benefits from AI but even more because faster AI progress would increase the probability that some currently existing people will live long enough to reap the far greater benefits that could flow from machine superintelligence (such as superlongevity and extreme prosperity). If, instead, our evaluation function does not privilege currently existing people over potential future generations, then an especially important consideration is the impact of openness on cumulative amount of existential risk on the trajectory ahead  (Bostrom, 2003 (Bostrom, , 2013 . In this context, then, where the focus is on long-term impacts, and especially impacts on cumulative existential risk, we provided an analysis with respect to two critical challenges: the control problem and the political problem. We identified three categories of potential effect of openness on these problems. We argued the first one of thesethat openness may speed AI developmentappears to have relatively weak strategic implications. Our analysis therefore concentrated mostly on the remaining two categories: openness making the AI race more closely competitive, and openness enabling wider engagement. Regarding making the AI race more closely competitive: this has an important negative implication for the control problem, reducing the ability of a leading developer to pause or accept a lower level of performance in order to put in place controls. This could increase the amount of existential risk associated with the AI transition. Closer competition may also make it more likely that there will be a multiplicity of competing AIs; but the net strategic effect of this is unclear and may therefore have less decision weight than the no-option-ofslowing-down effect. There are also a bunch of implications from a more closely competitive AI race for the political problemdecreasing the probability that a small group will monopolize the benefits of advanced AI (attractive); decreasing the probability of a singleton (might be catastrophic); and having some ambiguous impact on the expected relative influence of status quo powers over the post-AI futurepossibly increasing that influence in hardware-constrained scenarios and reducing it in software-constrained scenarios. Again, from an existential risk minimization perspective, the net import of these implications of openness for the political problem seems to be negative.  23  Regarding openness enabling wider engagement: this has an important positive implication for the control problem, namely by enabling external researcherswho may have less bias and relatively more interest in the public good of safetyto work with state-of-the-art AI systems. Another way in which openness could have a positive effect on the control problem is by enabling better social planning and prioritization, although this benefit would not require openness about detailed technical information (only about AI projects' plans and capabilities).  24  If openness leads to wider engagement, this could also have implications for the political problem, by enabling better foresight and by increasing the probability of government control of advanced AI. Whether the expected value here would be positive or negative is not entirely clear. It may depend, for instance, on who would control advanced AI if it is not nationalized. On balance, however, one may perhaps judge the implications for the political problem of a wide range of actors gaining increased foresight to be positive in expectation. Again, we note that the relevant type of openness here is openness about capabilities, goals, and plans, not openness about technical details and code. Openness about technical details and code may have a weaker impact on general foresight, and it may reduce the probability of expropriation. \n Specific forms of openness Openness can take different formsopenness about science, source code, data, safety techniques, or about the capabilities, expectations, goals, plans, and governance structure of an AI project. To the extent that it is possible to be open in some of these dimensions without revealing much information about other dimensions, the policy question can be asked with more granularity, and the answer may differ for different forms of openness. \n Science and source code Openness about scientific models, algorithms, and source code is the focus of most the preceding discussion. One nuance to add is that the optimum strategy may depend on time. If AI of the advanced sort for which the control problem becomes critical is reasonably far off, then it may well be that any information that would be released now as a result of a more open development policy would have diffused widely anyway by the time the final stage is reached. In that case, the earlier main argument against openness of science and codethat it would make the AI development race more closely competitive and reduce the ability of a leading project to go slowmight not apply to present-day openness. So it might be possible to reap the near-term benefits of openness while yet avoiding the long-term costs, assuming a project can start out open and then switch to a closed development policy at the appropriate time. Note, however, that keeping alive the option of going closed when the critical time comes would remove one of the main reasons for favouring openness in the first place, namely the hope that openness reduces the probability of a monopolization of the benefits of advanced AI. If a policy of openness is reversible, it cannot serve as a credible commitment to share the fruits of advanced AI. Nevertheless, even people who do not favour openness at the late stages may favour openness at the early stages because the costs of openness there are lower.  25, 26  Control methods and risk analysis Openness about safety techniques seems unambiguously good, at least if it does not spill over too much into other forms of openness. AI developers should be encouraged to share information about potential risks from advanced AI and techniques for controlling such AI. Efforts should be made to enable external researchers to contribute their labour and independent perspectives to safety research if this can be done without disclosing too much sensitive information. \n Capabilities and expectations Openness about capabilities and expectations for future progress, as we saw, has a mixed effect, enabling better social oversight and adaptation while in some models risking to exacerbate the race dynamic. Some actors might attempt to target disclosures to specific audiences that they think would be particularly constructive. For example, technocrats may worry that wide public engagement with the issue of advanced AI would generate more heat than light, citing analogous cases, such as the debates surrounding GMOs in Europe, where it might appear as if beneficial technological progress would have been able to proceed with fewer impediments had the conversation been dominated more by scientific and political elites with less involvement from the public. Direct democracy proponents, on the other hand, may insist that the issues at stake are too important to be decided by a bunch of AI programmers, tech CEOs, or government insiders (who may serve parochial interests) and that society and the world is better served by a wide open discussion that gives voice to many diverse views and values. \n Values, goals, and governance structures Openness about values, goals, and governance structures is generally welcome, since it should tend to differentially boost projects that pursue goals that are attractive to a wide range of stakeholders. Openness about these matters might also foster trust and reduce pressures to compromise safety for the sake of competitive advantage. The more that competitors feel that they would still stand to gain from a rival's success, the better the prospects for a collaborative approach or at least one in which competitors do not actively work against one another. For this reason, measures that align the incentives between different AI developers (particularly their incentives at the later stages) are desirable. Such measures may include cross-holdings of stock, joint research ventures, formal or informal pledges of collaboration, 27 endorsement of principles stating that advanced AI should be developed only for the common good, and other activities that build trust and amity between the protagonists. 28 \n Notes For helpful comments and discussion, I am grateful to Stuart Armstrong, Owen Cotton-Barratt, Rob Bensinger, Miles Brundage, Paul Christiano, Allan Dafoe, Eric Drexler, Owain Evans, Oliver Habryka, Demis Hassabis, Shane Legg, Javier Lezaun, Luke Muehlhauser, Toby Ord, Guy Ravine, Steve Rayner, Anders Sandberg, Andrew Simpson, and Mustafa Suleyman. I am especially grateful to Carrick Flynn and Carl Shulman for help several parts of the manuscript. 1. Examples of complementary assets include: manufacturing capacity using related technologies, product distribution networks, after-sales service, marketing and brand assets, and various industry-specific factors  (Greenhalgh and Rogers, 2010) . 2. Other motivations include enjoyment, learning, and serving user needs  (Lakhani and Wolf, 2005) . 3. Patents require publication, but the pursuit of patent could still in some cases conflict with openness, for example if work in progress is kept hidden until it is developed to a point where it can be patented. 4. There are ongoing efforts  (Destro Bisol et al., 2014)  to make science even more open, with calls for requiring open access journal publication, pre-registration of studies, and making the raw data underlying studies available to other scholars. The trends towards increasing use of online preprint archives and scientist blogging also point in the direction of greater openness. The increasing use of patenting by universities might be an opposing trend  (Leydesdorff et al. 2015) , but the general pattern looks like a push towards greater openness in scientific research, presumably reflecting a belief among reformers that greater openness would promote scientific progress. The counterexample of increased patenting pertains to the part of academic research that is closest to the commercial world, involving areas of more applied research. It is possible that universities engage in patent-seeking for the same reason private firms do: to profit from the intellectual property. A university may thus take out a patent not because it believes that openness delays scientific progress but because it prefers to increase its own revenue (which it might then use to subsidize other activities, including some that may accelerate science). 5. '[t]he substantive findings of science . . . are assigned to the community . . . The scientist's claim to \"his\" intellectual \"property\" is limited to that of recognition and esteem'  (Merton 1942, p. 121) . Later work has found very widespread support for this sharing norm among scientists  (Louis et al. 2002; Macfarlane and Cheng 2008.  See also  Heesen (2015) . 6. For some critiques of this model, see  Park (2010), pp. 31f. 7 . For an overview of the literature on the economic effects of philanthropic intervention on innovation see  Engelhardt (2011)  and Maurer (2012). 8. Specifically, it estimates annual economic impacts from technological transformations by 2025 in the following sectors: Automation of knowledge work: $5.2-6.7 trillion; Internet of things: $2.7-6.2 trillion; Advanced robotics: $1.7-4.5 trillion; Autonomous and near-autonomous vehicles: $.2-1.9 trillion; and 3D printing: $0.2-0.6 trillion  (Manyika et al., 2013) . These sectors also involve technologies other than AI, so not all of these impacts should be attributed to advances in machine intelligence. (On the other hand, AI will also contribute to economic impacts in many other sectors, such as the health sector.) 9. The early stage of the industrial revolution appears to be associated with a decline in average height, though the exact causes remain unclear and may also be related to urbanization  (Steckel, 2009) . 10. The same could happen if safety work is harder to parallelize (Muehlhauser 2014), so that it does not scale as well as capability work does when the contributor pool is expanded to include a greater proportion of independent and physically dispersed researchers. 11. At the moment, the AI safety field is probably growing more rapidly than the AI capability field. If this growth is exogenous, it may be desirable for overall progress to be slower to allow this trend towards a greater fraction of AI-related resources going into safety to culminate. 12. Existential risks from naturesuch as asteroid impactsare too small on the relevant timescale to matter in this context  (Bostrom and Cirkovic, 2008) . See also  Beckstead (2015) ;  Bostrom (2013 Bostrom ( , 2014a . 13. The case with respect to data is harder to assess, as it would depend on what kind of data is most critical to AI progress at the relevant stage of development. Currently, many important data sets are proprietary while many others are in the public domain. 14. For a model that is too simple to be realistic but which illustrates the point, suppose that key ideas arrive independently at some rate r with each researcher-year, and that k key ideas are needed to produce an AI. Then a lone researcher working for y years has a certain probability p of having each idea (technically p = 1Àe^ÀrÁy), and probability p^k of building an AI. A group of n researchers working together have a joint rate rÁn and a higher probability q of having each idea (q = 1Àe^ÀrÁnÁy), and probability q^k of building an AI within y years. So the ratio of probability of success of the large group to the individual is (q/p)^k which gets larger as k increases. 15. For instance, one AI or coalition of AIs might make a technological breakthrough that affords a decisive strategic advantage. 16. This may be analogous to the ongoing debate between flu researchers (ingroup most immediately involved) and epidemiologists (a neighboring scientific outgroup) on the wisdom of continuing gain-of-function research to enhance, and subsequently study, the transmissibility of potential pandemic pathogens such as the avian flu virus  (Duprex et al., 2015) . 17. Just as for other open source development projects, there could be reasons for contributing other than an altruistic desire to supply a public good, and those reasons could favour contributing to AI effectiveness rather than AI safety. For example, working on AI effectiveness might be a better way to signal skill, or it might be more fun. 18. Most groups will probably regard themselves as exceptionally altruistic and safety-oriented whether or not they really are so. The present consideration could therefore easily support rationalizations. 19. In one simple model, however, increased transparency about capabilitieseven if it reveals no information that helps AI designwould, in expectation, exacerbate the race dynamic and reduce the probability that the control problem will be solved  (Armstrong et al., 2016) . 20. Although this paper is not especially long, it is quite dense, and many considerations that are here afforded only a few words could easily be the subject of an entire separate analysis on their own. 21. It is also possible that some of the structure of the present analysis is relevant for other macrostrategic questions and that it could thus case some indirect light on a wider set of issues. 22. For instance, an unsophisticated user might have a website which runs on a Linux server, but the server is maintained by a sophisticated sysadmin. The user experience of open source software also depends on how it interacts with proprietary software. For instance, many consumer devices use the open source Android operating system, but it typically comes bundled with a variety of proprietary software. Many open source projects now function primarily as ways to structure joint R&D ventures between large companies to allow them to share development costs for consumer oriented projects  (Maurer, 2012) . 23. From the perspective of a person-affecting objective function (one that in effect privileges currently existing people) it is more plausible that a more closely competitive AI race would be desirable. A more closely competitive race would increase the chance that the benefits of AI will be widely distributed. At least some theories of prudential self-interest would seem to imply that it is far more important for an individual to be granted some (non-trivial) fraction of the resources of a future civilization (rather than none) than it is to be granted a large fraction (rather than a small fraction) -on the assumption individuals face diminishing marginal utility from resources. (Since the resource endowment of a future civilization is plausibly astronomically large, it would be sufficient to assume that diminishing returns set in for very high levels of resources.) See  Bostrom (2014a) . 24. A more open development process could also influence architecture in ways that would be relevant to the control problem, but it is unclear whether those influences would be positive or negative. As with some of the other factors discussed, even though there is currently no clear evidence on whether this factor is positive or negative, it is worth bearing in mind as potentially relevant in case further information comes to light. 25. On the other hand, if it is easier to switch from closed to open than the other way around, then there could be an important opportunity cost to starting out with openness rather than starting out closed and preserving the opportunity to switch to open later on. 26. Openness about data, that is, the sharing of valuable data sets, is in many ways similar to openness about science and source code, although sometimes with the added complication that there is a need to protect user privacy. In many cases, a data set is primarily relevant to a particular application and not much use to technology R&D (for which purpose many alternative data sets may serve equally well). 27. This may be augmented by the creation or identification of a trusted neutral third party that can monitor progress at different organizations, facilitate coordination at key points of the development process, and perhaps help arbitrate any disagreements that might arise. 28. Some technical work might also point towards opportunities to implement compromise solutions; see, e.g., 'utility diversification' in  (Bostrom, 2014b) . \t\t\t © 2017 The Authors Global Policy published by Durham University and John Wiley & Sons, Ltd.Global Policy (2017) \n\t\t\t Global Policy (2017) © 2017 The Authors Global Policy published by Durham University and John Wiley & Sons, Ltd. Strategic Implications of Openness in AI Development", "date_published": "n/a", "url": "n/a", "filename": "openness.tei.xml", "abstract": "This paper attempts a preliminary analysis of the global desirability of different forms of openness in AI development (including openness about source code, science, data, safety techniques, capabilities, and goals). Short-term impacts of increased openness appear mostly socially beneficial in expectation. The strategic implications of medium and long-term impacts are complex. The evaluation of long-term impacts, in particular, may depend on whether the objective is to benefit the present generation or to promote a time-neutral aggregate of well-being of future generations. Some forms of openness are plausibly positive on both counts (openness about safety measures, openness about goals). Others (openness about source code, science, and possibly capability) could lead to a tightening of the competitive situation around the time of the introduction of advanced AI, increasing the probability that winning the AI race is incompatible with using any safety method that incurs a delay or limits performance. We identify several key factors that must be taken into account by any well-founded opinion on the matter. \n Policy Implications • The global desirability of openness in AI developmentsharing e.g. source code, algorithms, or scientific insightsdependson complex tradeoffs. • A central concern is that openness could exacerbate a racing dynamic: competitors trying to be the first to develop advanced (superintelligent) AI may accept higher levels of existential risk in order to accelerate progress. • Openness may reduce the probability of AI benefits being monopolized by a small group, but other potential political consequences are more problematic.", "id": "bf2811a496b476cc812156d2d7c383fb"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Carla Zoe Cremer1", "Jess Whittlestone2"], "title": "Canaries in Technology Mines: Warning Signs of Transformative Progress in AI", "text": "INTRODUCTION Progress in artificial intelligence (AI) research has accelerated in recent years, and applications are already beginning to impact society  [9] [43]. Some researchers warn that continued progress could lead to much more advanced AI systems, with potential to precipitate transformative societal changes  [13]   [19]   [21] [27]  [39] . For example, advanced machine learning systems could be used to optimise management of safety-critical infrastructure  [33] ; advanced language models could be used to corrupt our online information ecosystem  [31] ; and AI systems could even gradually begin to replace a large portion of economically useful work  [17] . We use the term \"transformative AI\" to describe a range of possible advances in AI with potential to impact society in large and hard-to-reverse ways  [22] . Preparing for the future impacts of AI is challenging given considerable uncertainty about how AI systems will develop. There is substantial expert disagreement around when different advances in AI capabilities should be expected  [11]   [19]   [34] . Policy and regulation will likely struggle to keep up with the fast pace of technological progress  [12]   [15] [42], resulting in either stale, outdated regulation or policy paralysis  [3] . It would therefore be valuable to be able to identify 'early warning signs' of transformative AI progress, to enable more anticipatory governance, as well as better prioritisation of research and allocation of resources. We call these early warning signs 'canaries', based on the colloquial use of the phrase 'canary in a coal mine' to indicate advance warning of an extreme event. Our use of this term takes its inspiration from an article by Etzioni  [16] , in which he stresses the importance of identifying such canaries. We want to take this suggestion seriously and propose a systematic methodology for identifying such canaries. Many types of indicators could be of interest and classed as canaries, including: research progress towards key cognitive faculties (e.g., natural language understanding); overcoming known technical challenges (such as improving the data efficiency of deep learning algorithms); or improved applicability of AI to economically-relevant tasks (e.g. text summarization). What distinguishes canaries from general markers of AI progress (like those discussed in  [32]  or  [36] ) is that they indicate that particularly transformative impacts of AI may be on the horizon. Given that our definition of \"transformative AI\" is currently very broad, canaries are therefore defined relative to a specific form of transformative AI or impact. For example, we might identify canaries for human-level artificial intelligence; canaries for automation of a specific sector of work; or canaries for specific types of societal risks from AI. From a governance perspective, we are particularly interested in canaries which indicate that faster or discontinuous progress may be on the horizon, since the impacts of rapid progress would be especially difficult to manage once they begin to manifest. These therefore particularly warrant advanced preparation. In what follows, we describe and discuss a methodology for identifying canaries of progress in technological research. We focus on AI progress, but believe this method, once trialled and tested, could be applied to other areas of technological development. We motivate and describe the methodological approach, which combines expert elicitation and causal mapping, before presenting one implementation of this methodology to identify canaries for progress towards high-level machine intelligence (HLMI). After discussing potential canaries for HLMI specifically, we discuss how to make use of canaries in monitoring of AI progress and suggest how the limitations of this methodology might be addressed in future iterations of this work. advanced AI will be achieved  [5][19] [21]  [34] . For example, Baum et al.  [5]  survey experts on when four specific milestones in AI will be achieved: passing the Turing Test, performing Nobel quality work, passing third grade, and becoming superhuman. Both Müller and Bostrom  [34] , and Grace et al.  [19]  focus their survey questions around predicting the arrival of high-level machine intelligence (HLMI), which the latter define as being achieved when \"unaided machines can accomplish every task better and more cheaply than human workers\". \n METHODOLOGY \n Background and Motivation However, these studies have several limitations  [6]  that should make us cautious about giving their results too much weight. The experts surveyed in these studies have no experience in quantitative forecasting and receive no training before being surveyed, which likely renders their predictions unreliable  [10][41] . Issues of reliability aside, these forecasting studies are also limited in what they can tell us about future AI progress. They have little to say about impactful milestones on the path to advanced AI, let alone early-warning signs. Experts disagree substantially about when capabilities will be achieved  [11] [19] and without knowing who (if anyone) is more accurate in their predictions, these forecasts cannot easily inform decisions and prioritisation around AI today. Quantitative expert elicitations like these also do not tell us why different experts disagree, what kinds of progress might cause them to change their judgements, or what aspects they in fact do agree upon. While broad probability estimates for when advanced AI might be achieved are interesting, they tell us little about the path from where we are now, or what could be done today to shape the future development and impact of AI. At the same time, several research projects have begun to track and measure progress in AI  [7] [23]  [36] . These projects focus on a range of indicators relevant to AI progress, but do not make any systematic attempt to identify which markers of progress are most important for anticipating potentially transformative AI. Given limited time and resources for tracking progress in AI, it is crucial that we find ways to prioritise those measures that are most relevant to ensuring societal benefits and mitigating risks of AI. The approach we propose in this paper aims to address the limitations of both work on AI forecasting and on measuring progress in AI. In a sense, the limitations of these two bodies of work are complementary. The AI forecasting literature focuses on anticipating the most extreme impacts and advanced progress in AI, but is unable to say much about the warning signs or kinds of progress that will be important in the near future. AI measurement initiatives, conversely, monitor near-future progress in AI, but with little systematic prioritisation or reflection on what progress in different areas might mean for society and governance. What is needed, building on work in both these areas, are attempts to identify areas of progress today that may be particularly important to pay attention to, given concerns about the kinds of transformative AI systems that may be possible in future. Progress in these areas would serve as crucial warning signs -canaries, as well call them -suggesting more advance preparation for future AI systems and their impacts is needed. We believe that identifying canaries for transformative AI is a tractable problem and therefore worth investing considerable research effort in today. In both engineering and cognitive development, capabilities are achieved sequentially, meaning that there are often key underlying capabilities which, if attained, unlock progress in many other areas. For example, musical protolanguage is thought to have enabled grammatical competence in the development of language in homo sapiens  [8] . AI progress so far has also arguably seen such amplifiers: the use of multilayered non-linear learning or stochastic gradient descent arguably laid the foundation for unexpectedly fast progress on image recognition, translation and speech recognition  [29] . By mapping out the dependencies between different capabilities or milestones needed to reach some notion of transformative AI, therefore, we should be able to identify milestones which are particularly important for enabling many others -these are our canaries. This is the general idea behind our approach to identifying canaries, outlined in more detail in the following sections. \n Proposed Methodology The proposed methodology can be used to identify 'canaries' for any transformative event. In the case of AI, the focus might be on a transformative technology such as HLMI or AGI, a transformative application such as flexible robotics, or a transformative impact such as the automation of at least 50% of jobs. Given a transformative event, our methodology has three main steps:  (1)  identifying key milestones towards the event;  (2)  identifying dependency relations between these milestones; and (3) identifying milestones which underpin many others as 'canaries'. \n Identifying key milestones using expert elicitation Like other studies of AI progress, we rely on expert elicitation throughout this process. However, the reliability of expert elicitation studies depends on the proper selection and use of expertise. Though there are inevitable limitations of using any form of subjective judgement, no matter how expert, these limitations can be minimised with careful selection of experts and questions. We suggest carefully selecting experts with varied expertise relevant to the chosen question. For example, for identifying milestones towards human-level AI, the cohort should include experts in machine learning and computer science but also cognitive scientists, philosophers, developmental psychologists, evolutionary biologists, and animal cognition experts. This diverse group would bring together expertise on the current capabilities and limitations of AI, with expertise on key milestones in human cognitive development and the order in which cognitive faculties develop. We also encourage careful design and phrasing of questions to enable participants to make best use of their expertise. For example, rather than asking experts to identify specific milestones towards human-level AI, which is a question for which they are not trained, we might ask machine learning researchers about the limitations of the methods they use every day, or ask psychologists what important human capacities they see lacking in machines. There are several different methods available for expert elicitation: including surveys, interviews, workshops and focus groups, each with advantages and disadvantages  [2] . Interviews provide greater opportunity to tailor questions to the specific expert, but can be extremely time-intensive compared to surveys, making it difficult to consult a large number of experts. If possible, some combination of the two may be ideal: using carefully selected semi-structured interviews to elicit initial milestones, followed-up with surveys with a much broader group to validate which milestones are widely accepted as being key. \n Mapping dependencies between milestones using causal graphs The second step of our methodology involves convening experts to identify dependency relations between identified milestones: that is, which milestones may underpin, lead to, or depend on which others. Experts should be guided in generating directed causal graphs to represent perceived causal relations between milestones  [35] . Causal graphs show causal links between elements of a system, represented as nodes (elements) and arrows (causal links). A directed positive arrow from A and B indicates that A has a positive causal influence on B. Such causal maps have been used to support decision-making, structure knowledge, and improve visualisation of complex scenarios  [20] [25][26]  [28]  and are particularly useful for exploring and understanding possible futures, rather than aiming to predict a single future  [26] . They are easily modified and constructed collaboratively, and therefore are well-suited to helping us structure expert knowledge on dependencies between different technological milestones. Fuzzy cognitive maps (FCMs), a specific type of causal graph, may be a particularly useful method for our purposes. FCMs capture all benefits of causal mapping but can be extended into a quantitative model, and thus lend themselves to computerised simulations  [25] . This will not always be necessary, but given that our proposed method is applicable to many contexts, a flexible model is desirable. FCMs are well able to document non-linear interactions and experts' mental models of causal interactions because they can handle imprecise causal links. The variables (nodes) can take any state between 0 and 1 (hence 'fuzzy'), indicating the extent to which the variable is 'present'. When a variable changes its state, it affects all concepts that are causally dependent on it. FCMs have been used successfully in environmental science  [20]   [38] , strategic planning  [30] , and other areas  [25] , and have been recommended for use in futures studies, forecasting, and technology road mapping  [1]   [26] . In a workshop format, experts should be given brief training in causal graph methods or FCMs, and then break into groups to discuss dependencies between milestones. Each group should then collaboratively construct a directed causal graph or FCM to represent these relationships. Groups should be formed so as to maximise the variation of expertise in each group. \n 2.2.3 Identifying canaries from causal graphs. Finally, the resulting causal graphs can be aggregated and analysed to identify canaries, by identifying the nodes with the highest number of outgoing arrows. The aggregation process should first focus on identifying commonalities between all graphs which can be shared in the final graph. Substantive disagreements may remain, which can be the subject of mediated discussion, with a voting process to decide on final aspects of the graph. Experts then identify nodes which they agree have significantly more outgoing nodes (some amount of discretion from the experts/conveners will be needed to determine what counts as 'significant'). Since nodes with a high density of outgoing arrows represent milestones which underpin many others, progress on these milestones can act as 'canaries', indicating that we may see further advances in many other areas in the near future. These canaries can therefore act as early warning signs for more rapid and potentially discontinuous progress, as well as for new applications becoming ready for deployment (depending on which exact capabilities they are likely to unlock). \n IMPLEMENTATION: CANDIDATE CANARIES FOR HLMI We describe a partial implementation of the proposed method to identify canaries for achieving high-level machine intelligence (HLMI). We define HLMI here as an AI system (or collection of AI systems) that performs at the level of an average human adult on key cognitive measures required for economically relevant tasks.  2  We interviewed experts about the limitations of current deep learning methods from the perspective of achieving HLMI, and used the findings to construct a causal graph of milestones. This allowed us to identify candidate canary capabilities. The results must be understood as preliminary, because the causal graphs were developed just by the authors, not a cohort of experts, and so have limited validity. However, this initial demonstration and preliminary findings will form the basis for a full study with a broader range of experts in future. \n Expert elicitation to identify milestones To identify key milestones for achieving HLMI, we interviewed 25 experts (using both a non-probabilistic, purposive sampling method and stratified sampling method, as described by  [12]  in chapter six). The sample covered experts in machine learning  (9) , computer science with specialisation in AI (  5 ), cognitive psychology (2), animal cognition (1), philosophy of mind and AI (3), mathematics , neuroscience (1), neuro-informatics (1), engineering (1). Interviewees came from both academia and industry, and were deliberately selected to be at a variety of career stages. We conducted individual, semi-structured interviews, with a set of core questions and themes to guide more open-ended discussion. Semi-structured interviews use an interview guide with core questions and themes to be explored in response to open-ended questions to allow interviewees to explain their position freely  [24] . Initial questions included: what do you believe deep learning will never be able to do? Do you see limitations of deep learning that others seem not to notice? In response to these and similar questions tailored to the interviewee's specific expertise, they were asked to name what they thought were the biggest limitations of current deep learning methods, from the perspective of achieving HLMI. All named limitations were collated, with shortened explanations, and translated into 'milestones', i.e. capabilities experts believe deep learning is yet to achieve on the path to HLMI. Table  1 . shows all milestones based on limitations, named by interviewees. Because we have maintained each interviewee's preferred terminology, several of the milestones listed may turn out to refer to the same or highly similar problems. \n Table 1. Limitations of deep learning as perceived and named by experts Causal reasoning: the ability to detect and generalise from causal relations in data. Common sense: having a set of background beliefs or assumptions which are useful across domains and tasks. \n Meta-learning: the ability to learn how to best learn in each domain. Architecture search: the ability to automatically choose the best architecture of a neural network for a task. Hierarchical decomposition: the ability to decompose tasks and objects into smaller and hierarchical sub-components. \n Cross-domain generalization: the ability to apply learning from one task or domain to another. Representation: the ability to learn abstract representations of the environment for efficient learning and generalisation. Variable binding: the ability to attach symbols to learned representations, enabling generalisation and re-use. Disentanglement: the ability to understand the components and composition of observations, and recombine and recognise them in different contexts. Analogical reasoning: the ability to detect abstract similarity across domains, enabling learning and generalisation. Concept formation: the ability to formulate, manipulate and comprehend abstract concepts. Object permanence: the ability to represent objects as consistently existing even when out of sight. Grammar: the ability to construct and decompose sentences according to correct grammatical rules. Reading comprehension: the ability to detect narratives, semantic context, themes and relations between characters in long texts or stories. Mathematical reasoning: the ability to develop, identify and search mathematical proofs and follow logical deduction in reasoning. \n Visual question answering: the ability to answer open-ended questions about the content and interpretation of an image. Uncertainty estimation: the ability to represent and consider different types of uncertainty. Positing unobservables: the ability to account for unobservable phenomena, particularly in representing and navigating environments. Reinterpretation: the ability to partially re-categorise, re-assign or reinterpret data in light of new information without retraining from scratch. \n Theorising and hypothesising: the ability to propose theories and testable hypotheses, understand the difference between theory and reality, and the impact of data on theories. Flexible memory: the ability to store, recognise and retrieve knowledge so that it can be used in new environments and tasks. Efficient learning: the ability to learn efficiently from small amounts of data. Interpretability: the ability for humans to interpret internal network dynamics so that researchers can manipulate network dynamics. Continual learning: the ability to learn continuously as new data is acquired. Active learning: the ability to learn and explore in self-directed ways. Learning from inaccessible data: the ability to learn in domains where data is missing, difficult or expensive to acquire. Learning from dynamic data: the ability to learn from a continually changing stream of data. \n Navigating brittle environments: the ability to navigate irregular, and complex environments which lack clear reward signals and short feedback loops. Generating valuation functions: the ability to generate new valuation functions immediately from scratch to follow newly-given rules. Scalability: the ability to scale up learning to deal with new features without needing disproportionately more data, model parameters, and computational power. Learning in simulation: the ability to learn all relevant experience from a simulated environment. Metric identification: the ability to identify appropriate metrics of success for complex tasks, such that optimising for the measured quantity accomplishes the task in the way intended. Conscious perception: the ability to experience the world from a firstperson perspective. \n Context-sensitive decision making: the ability to adapt decision-making strategies to the needs and constraints of a given time or context. It is worth noting there are apparent similarities and relationships between many of these milestones. For example, representation: the ability to learn abstract representations of the environment, seems closely related to variable binding: the ability to formulate place-holder concepts. The ability to apply learning from one task to another, cross-domain generalisation, seems closely related to analogical reasoning. Further progress in research will tell which of these are clearly separate milestones or more closely related notions. \n Causal graphs to identify dependencies between milestones Having identified key milestones, we explore dependencies between them using fuzzy cognitive maps (FCM). We focus on how capabilities enable, not inhibit, other capabilities, which means we use only positive influence arrows. FCMs are particularly well-suited to representing the uncertainty inherent in this analysis, as it assumes that each arrow could have a weight to represent varying levels of strength. In this analysis we have not specified the weights on connections, but adding these weights could be trialled with experts in the future. A previous survey  [5]  suggests that this endeavour is a highly uncertain one, finding that many different relationships between AI milestones seem plausible to experts. Our analysis does not claim nor aim to resolve this disagreement, but instead shows only one out of many possible mappings, to illustrate the use and value of FCMs in AI progress monitoring. We use the software VenSim (vensim.com) to illustrate the hypothesised relationships between perceived milestones in Figure  1 . For example, we hypothesise that the ability to formulate, comprehend and manipulate abstract concepts may be an important prerequisite for the ability to account for unobservable phenomena, which is in turn important for reasoning about causality. A positive influence arrow does not mean that achieving one milestone necessarily leads to another, but rather that progress on the first  This map was constructed by the authors, and is therefore far from definitive or the only possible way of representing dependencies between capabilities. However, this initial map does provide an important illustration of the kind of output this methodology should aim to achieve, and generates some initial hypotheses for relationships between milestones. \n Candidate Canary Capabilities Based on this causal map, we can identify two candidates for canary capabilities. The capabilities with the most outgoing arrows are: Symbol-like representations: the ability to construct abstract, discrete and disentangled representations of inputs, to allow for efficiency and variable-binding. We hypothesise that this capability underpins several others, including grammar, mathematical reasoning, concept formation, and flexible memory. Flexible memory: the ability to store, recognise, and re-use knowledge. We hypothesise that this ability would unlock many others, including the ability to learn from dynamic data, the ability to learn in a continual fashion, and the ability to learn how to learn. We therefore tentatively suggest that these are two important capabilities to track progress on from the perspective of anticipating HLMI. We discuss one such capability, flexible memory, in more detail below. Flexible memory, as described by experts in our sample, is the ability to recognize and store reusable information, in a format that is flexible so that it can be retrieved and updated when new knowledge is gained. We explain the reasoning behind the labelled arrows in figure  2 : • (a): compact representations are a prerequisite for flexible memory since storing high-dimensional input in memory requires compressed, efficient and thus abstract representations. • (B): the ability to reinterpret data in light of new information likely requires flexible memory, since it requires the ability to retrieve and alter previously stored information. • (C) and (E): to make use of dynamic and changing data input, and to learn continuously over time, an agent must be able to store, correctly retrieve and modify previous data as new data comes in. • (D): in order to plan and execute strategies in brittle environments with long delays between actions and rewards, an agent must be able to store memories of past actions and rewards, but easily retrieve this information and continually update its best guess about how to obtain rewards in the environment. • (F): analogical reasoning involves comparing abstract representations, which requires forming, recognising, and retrieving representations of earlier observations. Progress in flexible memory therefore seems likely to unlock or enable many other capabilities important for HLMI, especially those crucial for applying AI systems in real environments and more complex tasks. These initial hypotheses should be validated and explored in more depth by a wider range of experts. \n DISCUSSION \n Advantages We believe the proposed method for identifying canaries has many strengths and could be applied to a broad range of important questions about transformative AI systems and impacts. The general methodology of using expert elicitation to identify milestones and then causal mapping to elucidate dependencies between those milestones is extremely flexible, meaning it could be applied beyond AI to other fields of science and technology progress. The method can also be adapted to the preferred level of detail for a given study: causal graphs can be made arbitrarily complex  [18]  and can be analysed both quantitatively and qualitatively. With this method, it is possible to combine different types of expertise relating to milestones: including well-understood technical limitations of current methods, with informed speculation about unknown capabilities that may be important prerequisites to some transformative event. With early warning signs we can track progress towards canary milestones, or directly prepare for the transformative events that follow after it. \n Uses We envision that this methodology could be used to identify warning signs for a number of important potentially transformative events in AI progress, such as foundational research breakthroughs, the use of AI to automate scientific research, or the automation of tasks that affect a wide range of jobs. Once canaries have been identified for some transformative event, there are numerous ways we might use them to improve preparation for its impact, including by: • Automating the collection, tracking and flagging of new publications relevant to canary capabilities, and building a database of relevant publications (perhaps similar to that described by  [40] );  \n Limitations and future directions This methodology nonetheless has some limitations which further iterations could seek to improve on. There may be a fundamental trade-off between the benefits of consulting a large, diverse group of experts -enabling more thorough and robust identification of relevant milestones -and the feasibility of reaching agreement upon a single causal map, and therefore agreeing upon canaries. Relatedly, if uncertainty about milestones is too high, it may be difficult for experts to agree on a single causal map or candidates for canaries: finding questions where there is enough uncertainty for this process to be useful, but not so much uncertainty that no agreement can be reached, may be a challenge in some cases. It will also be important to recognise any potential limitations of the specific sample of experts involved in the process: recognising that machine learning researchers may be biased towards emphasising the importance of areas they themselves work on, for example, or that non-computer scientists may often lack a full understanding of what current systems can and cannot do. In using FCMs to generate causal maps, it is not clear what level of detail and quantitative analysis will be most useful. In the implementation described here, we hypothesised relationships at a high level of abstraction and without quantitative analysis, due to the high level at which experts highlighted limitations in the first stage. The higher the level of abstraction, the more uncertain the mapping will be and the less useful it may be to indicate weights. It would be valuable for future work to explore various levels of abstractions, including a more detailed and quantitative analysis using more clearly-defined technical milestones, which could result in more precise forecasts and hypotheses. Finally, it is important to note that attempts to anticipate and understand progress in AI (or any other technology) are not independent of that progress itself. Better understanding of key milestones towards AGI, HLMI, or some other notion of transformative AI, does not just improve our ability to anticipate that progress, but may also improve our ability to make progress towards transformative AI. We must therefore be cautious in identifying 'canary' capabilities, to consider the potential risks of making progress on these capabilities, and to communicate and encourage consideration of these risks to those researchers driving forward AI development. likelihood of progress on other arrows it points to. \n Figure 1 . 1 Figure 1. Cognitive map of dependencies between milestones collected in expert elicitations. Arrows coloured in pink and green indicate capabilities that have significantly more outgoing arrows. \n Figure 2 . 2 Figure 2. Extract of Figure 1, showing one candidate canary capability. \n This work builds on two main bodies of existing literature: research on AI forecasting, and an emerging body of work on measuring AI progress.The AI forecasting literature generally uses expert elicitation to generate probabilistic estimates for when different types of 1st International Workshop on Evaluating Progress in Artificial Intelligence -EPAI 2020In conjunction with the 24th European Conference on Artificial Intelligence -ECAI 2020 Santiago de Compostela, Spain \n Conducting more in-depth research on the societal and governance implications of achieving canary milestones, and preparing governance responses for these milestones ahead of time. • Generating metrics and benchmarks for evaluating progress on canary capabilities; • Using prediction platforms such as Metaculus (ai.metaculus.com) to track and forecast progress on canary capabilities; • Conducting more focused expert elicitation, for example periodically consult experts on their updated forecasts (in the form of cumulative probability estimates) for when different milestones are achieved, or when they are presented with updated progress metrics on canary capabilities; • Conducting more in-depth research to empirically and theoretically investigate hypothesised relationships between milestones: for example, to what extent do improvements in memory structures lead to empirical improvements in performance in brittle environments? • \n\t\t\t We use this definition, adapted from Grace et al., to highlight that what is key for saying HLMI has been reached is that AI has the cognitive ability to perform every task better than humans workers, not that it is in practice deployed to do so.", "date_published": "n/a", "url": "n/a", "filename": "EPAI_2020_paper_4.tei.xml", "abstract": "In this paper we introduce a methodology for identifying early warning signs of transformative progress in AI, to aid anticipatory governance and research prioritisation. We propose using expert elicitation methods to identify milestones in AI progress, followed by collaborative causal mapping to identify key milestones which underpin several others. We call these key milestones 'canaries' based on the colloquial phrase 'canary in a coal mine' to describe advance warning of an extreme event: in this case, advance warning of transformative AI. After describing and motivating our proposed methodology, we present results from an initial implementation to identify canaries for progress towards high-level machine intelligence (HLMI). We conclude by discussing the limitations of this method, possible future improvements, and how we hope it can be used to improve monitoring of future risks from AI progress.", "id": "bad85ae0a8122f97e0fec2e4f32a640f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Sebastian Farquhar", "Owen Cotton-Barratt", "Andrew Snyder-Beattie"], "title": "Pricing Externalities to Balance Public Risks and Benefits of Research", "text": "I n 2012, multiple research groups conducted experiments that produced strains of H5N1 avian influenza that were airborne transmissible between mammals.  1, 2  Given that this disease is often fatal in humans, these particular ''gain-of-function'' experiments sparked wide controversy.* Advocates of the research argued that the experiments were necessary to improve our understanding of the virus, thus enabling better disease surveillance and vaccine production. Opponents of the research argued that a laboratory accident could trigger a global pandemic, or that the research could be used by malicious actors.  3  The debate culminated in a moratorium on US public funding of research ''that may be reasonably anticipated to confer attributes to influenza, MERS, or SARS viruses such that the virus would have enhanced pathogenicity and/or transmissibility in mammals via the respiratory route.''  4  Meanwhile, the US government also commissioned an Sebastian Farquhar, MPhysPhil, is Project Manager; Owen Cotton-Barratt, DPhil, is a Research Fellow; and Andrew Snyder-Beattie, MS, is Director of Research; all are at the University of Oxford, Future of Humanity Institute, Oxford, England. This article reflects only the view of the authors. The ERCEA is not responsible for any use that may be made of the information it contains. ª Sebastian Farquhar et al., 2017; Published by Mary Ann Liebert, Inc. This Open Access article is distributed under the terms of the Creative Commons License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. *Gain-of-function experiments encompass a wide range of research, and only a small subset of such experiments were subject to this controversy. In this article, we focus on gain-of-function research of concern, by which we mean research of the sort affected by the funding moratorium, as a case study of the more general problem of making research funding decisions for dualuse research of concern. Health Security Volume 15, Number 4, 2017 Mary Ann Liebert, Inc. DOI: 10.1089/hs.2016.0118 independent study from Gryphon Scientific to weigh the benefits of the research against the possible biosafety and biosecurity risks.  5  While their research succeeded in producing a quantitative estimate of biosafety risk, it explained the benefits of the research only in qualitative terms. This controversy highlights the difficulty of evaluating research that has the potential to entail significant public risk. Research that is particularly likely to lead to both positive and negative impacts is especially hard to evaluate.  6  These negative consequences might be either the risk of an accident linked directly to the research itself, or risks of deliberate misuse of the resulting technologies. Avoiding research that has any theoretical risk at all would mean missing out on crucial opportunities. But research communities that underestimate the potential for a significant accident, or assume that people will use information gained through research only for good, may be neglecting their duty to society.  7  The H5N1 flu experiments mark a particularly interesting case study that we use to highlight some problems in evaluating the risks and benefits of dual-use research. { In this article, we discuss some of the current difficulties of existing approaches to evaluating risky research, and we propose a general framework that avoids many of the current problems. Within this framework, we outline 2 possible approaches to implementing the framework: a marketled liability insurance approach, and a state-led approach. We conclude by comparing the approaches with each other and with current policy. \n Difficulties of Risk-Benefit Analysis for Scientific Research Risk-benefit analysis, the approach used in the Gryphon Scientific report, is an analytical tool that has been successfully applied to a wide range of domains.  8  Analysts outline a range of scenarios with positive and negative impacts, estimate the probabilities of those scenarios and the net size of the positive impact, and compute the expected value of the proposal. When attempting to do a riskbenefit analysis of research, determining the scenarios and the probabilities of each scenario can be difficult. But as it turns out, estimating biosafety risks is far easier than esti-mating the benefits of research. The reason for this is that one can outline the potential scenarios for biosafety risks fairly well. In order for a laboratory accident to cause a global pandemic, a set of events must occur. The probability of each of these steps can then be estimated using historical data on laboratory accidents and models of disease spread. These estimates are highly uncertain, because of limitations in available data. The data describing exactly what activities labs engage in and their historical failure rates are incomplete, though some records are kept. Moreover, assumptions are required to extrapolate past records into the future. For example, lab safety standards and equipment have improved over the past several decades, but at the same time new labs are being built under the jurisdiction of regulators with less of a track record establishing their biosafety capabilities. Risk estimators must also make some estimate of the probability distribution of key parameters that cannot be empirically tested. For example, what is the probability that a reassortant virus will be sufficiently transmissible to spread to a wide population? Nevertheless, quantitative estimates are possible, though they lead to disagreement.  [9] [10] [11]  Many risks that are in principle very difficult to estimate for similar reasons are nevertheless quantitatively priced by insurers today-such as terrorism,  12  cyberattack,  13  and harm to patients in clinical trials.  14  Conversely, estimating the benefits of research is extremely difficult. Unlike estimating the probability of a laboratory accident scenario, evaluating the benefits of research involves uncertainty over what the possible scenarios even are. Typically, researchers have little information about the potential results of research-which is one of the motivations to do research in the first place. Even the most experienced researchers find it difficult to estimate the exante value of new research projects. The work recreating the genome of the influenza virus responsible for the 1918 pandemic  15  received some criticism for vaguely promising unspecified future benefits  16  but, after some time, has plausibly created tangible benefits including, perhaps, aiding in the management of the 2009 H1N1 pandemic, according to the authors of the original paper.  17  In their review, Gryphon Scientific did not even attempt to assess the benefits of research quantitatively, and it is this part of the risk-benefit calculation that typically poses the greatest difficulty.  5, 18  Evaluating the risks from malicious activity is more difficult than estimating the risk of accidents, but easier than estimating the benefits of research. Ultimately, the Gryphon Scientific report included a quantitative assessment of some biosecurity risks (though not the risks posed by the information discovered by the research). Unlike the accident scenarios, uncertainties around both the intentions and capabilities of malicious actors mean a wider range of scenarios is possible. But despite the difficulties in quantifying such risk, many insurance companies still offer terrorism insurance, and models do exist for putting rough numbers on such risks.  12   \n { In the context of atomic technologies, discussions of dual-use technology focused on the ability to rapidly convert civilian technologies for military purposes,  8  and this trend continued for much of the 20th century.  9  Recently, discussions of dual-use research have broadened to include nonmilitary actors and the risk of accidents related to research.  5, 10  It is this last, broadest sense of dual-use research that we focus on in this article, as it captures the full spectrum of risks resulting from research activities. We acknowledge but do not address the fact that the definition of ''dual-use'' remains unsettled,  11  and that one might want to consider dual-use research, technology built on that research, and artefacts implementing that technology separately.  9   \n BALANCING RISKS AND BENEFITS OF RESEARCH When science funders evaluate dual-use research, they are faced with risks and benefits that are uncertain in different ways. Most of the risks are quantitatively estimable, but the parameters are hard to pin down. It is our view that, even when highly uncertain, explicit quantitative risk estimates are preferable to implicit ones, because they allow transparent discussion about disagreements and mitigate human biases in judgments around small probabilities.  19  The benefits, however, are so uncertain that even specifying the scenarios is impossible. Fortunately, existing grantmaking approaches are already designed to compare projects with nebulous benefits. So, as long as the quantified risks are accounted for in the cost of a project, these existing systems are well suited for evaluating this research. \n Existing Approaches and the Scientific Grant-Making Process Grant makers already assess the uncertain benefits of research against their costs and the opportunity costs of unfunded research. Although it is hard to judge quantitatively, reviewers assess the potential for scientific excellence in different proposals. However, the costs that reviewers consider are primarily direct financial costs, rather than externalities such as the risks borne by the public from dual-use research. In principle, research funders prefer to fund portfolios of research with maximal benefits of research for society (including positive externalities) and minimal costs (including negative externalities). The concept of scientific merit already includes some sense of positive externalities, and the UK, at least, also considers the social impact of research and its effect on the research ecosystem.  20  Conceptual tools and intuitions on risk externalities are less well developed. Reviewers often implicitly evaluate dual-use risk as a matter of personal or professional ethics  21  or for the sake of reputation of the field. However, for most research, the dual-use stakes are low. In these situations, researchers have no need to also become experts in risk assessment and management. Research institutions rely instead on safety regulations for particular categories of risk in order to make sure research processes are safe.  22  These tools work very well when most of the risk is local, for accidental releases at the community level, or for health risks to lab researchers themselves. Historically, this is where most of the risk in biological research has lain and is therefore an entirely appropriate default. However, in the case of risks that carry a small chance of large catastrophe (eg, research that creates potential pandemic pathogens), these regulations are not enough. Some funders, such as the US government, provide additional decisionprocess guidelines for funding research involving specific pathogens, like H5N1,  23  as well as institutional guidelines for best practice for dual-use research.  24  Others, such as the UK's Biotechnology and Biological Sciences Research Council, the Medical Research Council, and the Wellcome Trust, require grant applicants to consider near-and medium-term risks of misuse but rely heavily on self-governance and a responsible research culture.  25  These frameworks put a high burden on those pursuing dual-use research to become risk assessors. Moreover, public funding guidelines only affect government funding and cooperative private funders. Private dual-use research is less constrained.  26  Some additional judgment can in principle be applied at the stage of publication,  27  but a 2012 survey of 127 life sciences journals found that none reported refusing a submission on biosecurity grounds.  28  Export controls may also be able to restrict some kinds of publication  29  in some jurisdictions. It may be that under the Australia Group's ''no undercut'' principle, in its guidelines for transfers of sensitive chemical or biological weapons, if any participant nation were to block publication using export controls then all would be obliged to (though the mechanisms for applying the guidelines to research results is unclear).  30   \n Pricing and Using Externalities in Grant Making \n Absolute Risk as a Cost of a Grant Hard-and-fast rules about what research techniques are too risky, without considering the benefits, may not be responsive enough, because more important research merits more risk.  31  Our principal proposal is that one could assess and price absolute expected risk and explicitly include this cost in grant proposals. This helps resolve the fact that while risks can be comparatively easy to assess, the benefits of research are extremely challenging to quantify. Our proposal allows grant reviewers to use existing frameworks to evaluate grant proposals but weigh potential benefits against a fairer reflection of their social costs. It also follows calls to strengthen the evaluation of risks at pre-funding stages of the research process.  32  For now, we set aside the issues of where an independent estimate of the cost of externalities comes from and where the money to cover this explicit cost is paid. The 2 main approaches to setting estimates, which we consider in detail in the next section, are: 1. To establish clear liability in case of catastrophe and require grant holders to purchase liability insurance as part of the grant. The strength of this is that it is a market-led approach, with insurers incentivized to price externalities correctly. 2. To centrally commission absolute risk assessments to price the externalities, and to require a payment to a state or non-state body to cover the expected cost. The strength of this approach is that it works even if there may be no clear liability after the fact, so it could address biosecurity as well as biosafety risks. \n Benefits of the Approaches Both approaches have 4 main advantages. First, they give decision makers greater incentive to use an accurately priced risk when deciding what research to fund. Currently, the costs of accidental or deliberate harm from gain-offunction research of concern are borne by members of the public in any country as well as lab workers. For example, after a foot-and-mouth disease outbreak in Pirbright in 2007, caused by poorly maintained drainage,  33  prosecutors were unable to seek damages because there was no demonstrable negligence of a specific party.  34  Instead, governments bore the financial cost of compulsory slaughter, farmers bore the costs of damaged and restricted business, and consumers experienced higher food prices. Where the risks of an activity are not borne by those making decisions about the activity, economic theory predicts that more risk will be taken than is socially optimal.  35  So long as the risks are priced correctly and the transaction costs are sufficiently low, research institutions that pay upfront for the risks of research are more likely to engage in socially optimal risktaking. If implemented successfully, this would result in both better grant choices and better use of risk reducing techniques and equipment. Second, these approaches keep decisions about what research gets funded in the hands of researchers. One of the largest difficulties in assessing the social value of research is assessing the intellectual benefits of research. Researchers themselves are best placed to evaluate the potential for success and the intellectual merit of research because they have the deepest knowledge of the area. Third, these approaches incorporate democratic or public input on the significance of risks. Although researchers have expertise in the potential for intellectual success from a grant proposal, they are not necessarily able to speak for the values of society. Researchers have an obligation to incorporate public input on value systems and consider the justice implications of their work.  31  Our proposal creates ways for the public to express their values without creating rules allowing or disallowing certain research techniques or areas of inquiry. In the case of an insurance mechanism, the legislative branch effectively determines the social cost borne were the risk to materialize, via the judiciary. In the case of a central body setting the costs, this body would ultimately be accountable to the electorate. Fourth, these approaches ensure appropriate risk assessment and governance expertise is brought to bear. Researchers submitting grant proposals are often asked to consider potential dual-use and accident risk. Grant makers do so similarly. However, neither group tends to include specialists in risk assessment or biosecurity.  26  If absolute risk is priced separately, the price can be set by expert risk assessors. Throughout, our guiding principle is to ensure the right incentives are in place and that components of the funding decision are broken up such that those best placed to assess them do so. \n Disadvantages of the Approaches Although we believe these approaches might improve the capacity of the research funding system to manage catastrophic risk, they introduce some new concerns. First, research institutions currently receive a subsidy in the form of an implied guarantee covering the costs of imposed risks. If they were asked to pay for this guarantee, it would represent an additional unfunded expense. Since the aim of this proposal is to distribute research effort within, say, the life sciences rather than to change the absolute amount of life science work being done, one might increase funding for life sciences research to compensate. This would appear to increase explicit expenditure in government research budgets, but in fact moves an implicit, random, and large subsidy from the budgets of disaster response agencies, who do not make decisions that determine the risk exposure, to an explicit, predictable, and moderate payment by those who do make such decisions. For example, governments and consumers bear a large part of the cost of escapes of animal pathogens from research labs  36  but have less influence over risk exposure than research funding bodies. Second, penalizing laboratories for reporting accidents and near misses in a timely way harms biosafety and biosecurity in the long run. Increasing reporting would make it easier to use lessons from mistakes to improve lab design and improve accident response. Mechanisms for pricing risk will work best if they avoid creating perverse incentives around reporting. Options for facilitating this include simply not using the information from recent accidents in the case of central analysis, or forbidding a premium hike in the case of liability insurance requirements. Third, these approaches increase bureaucratic overhead. There are several things that might be done to reduce this overhead. One could apply our proposal only to areas with particularly high risk of low-probability but high-impact events. For example, it might be applied only to the gainof-function research that has been covered by the recent US moratorium. Or rather than carrying out a separate risk analysis for each proposal, one could establish broad categories of similar work and set costs for that category as a whole. For some categories, it might be possible to get involvement from intelligence communities to incorporate information not normally available. In the future, scope could be expanded by addressing new areas or by making the cost estimates more granular. \n Making Decisions Under Uncertainty There are things these approaches would not fix. Risk in many cases of dual-use research is very uncertain. No risk management or risk governance process can solve this entirely. It is hoped that in the case of market-led approaches, the profit motive of companies providing insurance as well as an awareness of ''winners' curse'' dynamics will incentivize BALANCING RISKS AND BENEFITS OF RESEARCH appropriate pricing. In the case of a state-led approach, it is hoped that the system will increase the capacity for riskassessment by developing a core of expert assessors. Political pressures or ''short-termism'' might cause prices to be inaccurate. However, this is also a feature of existing approaches to dual-use risk management. \n Approaches to Risk Pricing \n Mandatory Liability Insurance Laboratories conducting experiments of appropriate kinds could be mandated to purchase insurance against liability claims arising from damaging accidents from their research. Insurance companies would then pay out to injured parties in the public in case of an accident. Some proposals in this direction have already been discussed in the UK.  27  In some cases, appropriate use of liability for damages is more effective than regulation in encouraging risk-reducing behavior.  37  In most jurisdictions, negligence leading to catastrophic damage would already establish liability. Sometimes, the complexity of the research process makes it hard to establish negligence of a specific party.  34  Governments might therefore need to legislate to establish clear duty of liability in any damages caused by accident, even if there was no negligence. Liability would give universities strong incentives to minimize the risk. Framers of this legislation would need to be quite specific about which sorts of liability were included (eg, health damage) and which were not (eg, adversely affected tourism, perhaps, or terrorism). Such an approach might be similar to some aspects of the 1957 Price-Anderson Act, which placed a strict liability on operators of potentially risky private nuclear facilities and a mandate to purchase the highest commercially available amount of insurance coverage.  38  A similar approach has been tried and advocated for in environmental risk, though it proved hard to maintain a healthy insurance market.  39, 40  Requiring insurance is important because some risk takers will not be able to compensate victims for catastrophic harms. Many universities currently self-insure against the damage of accidents in their research. Where there is a small chance of catastrophic damage, they do not have enough assets to cover the damages-they are ''judgment-proof.'' Insurance providers, with much greater financial liquidity, are able to bear the full costs even when payouts are very large, which incentivizes them to set premiums appropriately.  41  For the most catastrophic forms of damage, such as a global pandemic, costs would be too big even for a reinsurer to bear. As a result, an insurance approach could involve an explicitly negotiated liability cap, in which case regulatory bodies tasked with managing the most extreme forms of risk are essential. Various amendments to the Price-Anderson Act demonstrate the problems facing liability limits. Indemnifying those creating the risk from all costs above the privately insurable can cause excess risk taking.  42  The most recent version of Price-Anderson requires regulated nuclear energy providers to pool to jointly cover more than $10 billion of costs beyond that covered for each individual party by insurers. While this protects the public by identifying a source of funds beforehand, the fact that the individual contributions do not need to be set aside in advance means that the entire industry carries a large, uninsured, systemic risk. A modern system based on catastrophe bonds might offer a safer way to increase the feasible levels of financing. \n Advantages of the Liability Approach There are 2 main advantages to this market-led approach. First, it is a relatively light intervention, requiring little ongoing work from the state (other than maintaining a healthy insurance market). Second, the insurers would have a profit incentive to accurately estimate the risk, reducing possible politicization of the risk assessment process. In a sufficiently liquid market, competitive pressures should bring premiums down. But insurers are aware of a ''winners' curse'' in the insurance market and would avoid setting premiums too low to cover the long-term risk. If insurers adjust their premiums when safer systems and equipment are adopted, scientists and engineers would be incentivized to devise effective safety protocols to reduce their institutions' insurance costs. This would create a financial driver for applied biosafety and biosecurity research. Imposing liability has improved outcomes in other domains such as occupational safety, medicine, and general risk management in nonprofits and government agencies.  43   \n Possible Issues with the Liability Approach Insurers must be willing to insure against biosafety and biosecurity risk. While insurers have shown some interest,  44  there is no functioning market for the same 2 main reasons insurers were unwilling to take on nuclear risk before the 1957 Price-Anderson Act:  38  First, the potential risks are simply too large. A catastrophic global pandemic could kill hundreds of millions of people, and even the largest reinsurers would be unable to absorb this cost without bankrupting themselves (costs above this level will be implicitly backed by the state or the public in any case). It is better to be explicit and cap liability at a specific industry-wide figure. If the cap were sufficiently large, the effect should be more appropriate risk aversion, even if the tail risk for the insurer were not fully internalized. Second, the risks are hard to model and the market would be quite small. Developing models to estimate the risk could be more costly than the expected profit from being in the market. However, insurers do already have models for hard-to-anticipate risks such as terrorism and global pandemics. If need be, the development of appropriate models to facilitate this insurance could be explicitly subsidized. Whether or not insurers are willing to take on the risk, there are challenges to international adoption. Liability laws differ across jurisdictions, which would particularly affect international collaborations. One effective work-around might be to form an agreement among top-tier research journals to require proof of suitable liability insurance for some types of papers. { Liability insurance can also increase moral hazard, by making actors less responsible for the consequences of their actions. This effect could be reduced if the excess on the insurance were large enough that research institutions still had a direct incentive to avoid risks. Finally, using a liability approach to capture biosecurity risks would be difficult. If a terrorist group used information they gleaned from a paper published by a research group, establishing liability would require lengthy legal dispute. Moreover, done carelessly, the uncertainty additional but unclear liability could create might have an inappropriate chilling effect on research. \n Centrally Commissioned Risk Assessments The second approach is to centralize risk assessments. When an area of potential concern is identified, a body commissioned by the state would perform an analysis of the risks involved. This might be similar to the recent Gryphon Scientific analysis, except that it would not attempt to analyze the benefits. This absolute risk analysis would present its outcomes in monetary terms, using value of statistical life figures to convert into a cost. In order to do work of a priced type, laboratories would have to pay the appropriate charge to a central authority. This charge could cover part of the risk of biosafety and biosecurity preparation as well as the cost of risk assessment. \n Advantages of the Centrally Commissioned Risk Assessment Compared to the market-led approach, centralizing the risk assessments has 2 main benefits. First, it can be done by fiat without needing to persuade insurers to enter and stay in the market. Second, it works well even in cases where there will be no clear causal chain establishing liability, such as for biosecurity risks (including risks from the misuse of information produced from such research). Funds are collected based on the central assessment of the size of the risk posed by the research, with no need to work out after the fact which specific group is liable. The Gryphon Scientific report concluded that the biosecurity risks looked at least as large as the biosafety risks, so this is a significant benefit in the case of gain-of-function research of concern.  5  Third, at least in principle, avoiding the need for courts to establish liability might speed up payments. \n Possible Issues with the Central Approach Patchy implementation only in certain jurisdictions might just move research from nations with good risk management processes to those without. In practice, however, many researchers are likely to want to remain at top labs, limiting the risk of research simply moving to jurisdictions that do not assess the externalities of research. There may be a need for special arrangements for research done in partnership with labs outside the collecting jurisdiction, such as applying a requirement for proof of insurance at the stage of publishing. The risk assessment itself would be difficult. The centrally commissioned assessment would be more likely than an insurance-led one to need to assess the magnitude of biosecurity risks, which is particularly hard to model. However, stakeholders might have incentives to put pressure on regulators to make certain decisions. This is more likely to be successful because of the amount of judgment involved in the calculations of risk. Unlike the insurance-led solution, there would be no countervailing profit motive. \n Comparisons and Discussion The 2 approaches discussed would work by aligning the incentives for scientists and for funding bodies more closely with those of society as a whole. This approach keeps assessment of the benefits of scientific research purely in the hands of scientists, while bringing the right skills to bear at the right points and managing risk proportionately. We have explored 2 different ways to achieve this. Each has its advantages and disadvantages. The liability approach is more market based. As a result, the risk assessors have a financial incentive to accurately estimate risk, and political pressures are diminished. It might also be easier to use as a template internationally. Since the risks are global and the potentially risky research is not being pursued in just 1 country, being able to build global solutions is extremely valuable. The main benefit of the centrally commissioned analysis is it could bypass lack of clarity about who is liable for eventual damages in cases of biosecurity. These approaches have clear application for gain-offunction research of concern in the life sciences. However, similar approaches may work in a broader range of fields. The insurance mechanism is best suited for dual-use work where risk is predominantly through accident rather than \n { We are grateful to Piers Millett for this suggestion. BALANCING RISKS AND BENEFITS OF RESEARCH malicious intent. In all cases, pricing the absolute size of the risk and leaving researchers in charge of decisions about how to spend their budgets might offer a more responsive and proportionate approach to the challenges of funding research with potential public risks than existing systems. \t\t\t Volume 15, Number 4, 2017", "date_published": "n/a", "url": "n/a", "filename": "hs.2016.0118.tei.xml", "abstract": "How should scientific funders evaluate research with public health risks? Some risky work is valuable, but accepting too much risk may be ethically neglectful. Recent controversy over H5N1 influenza experiments has highlighted the difficulty of this problem. Advocates of the research claim the work is needed to understand pandemics, while opponents claim that accidents or misuse could release the very pandemic the work is meant to prevent. In an attempt to resolve the debate, the US government sponsored an independent evaluation that successfully produced a quantitative estimate of the risks involved, but only a qualitative estimate of the benefits. Given the difficulties of this ''apples-to-oranges'' risk-benefit analysis, what is the best way forward? Here we outline a general approach for balancing risks and benefits of research with public risks. Instead of directly comparing risks and benefits, our approach requires only an estimate of risk, which is then translated into a financial price. This estimate can be obtained either through a centrally commissioned risk assessment or by mandating liability insurance, which allows private markets to estimate the financial burden of risky research. The resulting price can then be included in the cost of the research, enabling funders to evaluate grants as usual-comparing the scientific merits of a project against its full cost to society. This approach has the advantage of aligning incentives by assigning costs to those responsible for risks. It also keeps scientific funding decisions in the hands of scientists, while involving the public on questions of values and risk experts on risk evaluation.", "id": "f0f158c3617a26c03b2dd4f958aca1df"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Peter M Asaro"], "title": "The Liability Problem for Autonomous Artificial Agents", "text": "Introduction 1 There is a growing sense of concern over the development of increasingly autonomous non-human agents-in the public and the media, as well as among policy makers and researchers. Such concerns are not unprecedented, yet there is something different about this next wave of technological innovation and change. While the impacts of the adoption of any technology are in some sense uncertain, and result in many and various unintended consequences, there seems to be something particularly unsettling and deeply uncertain about increasingly autonomous technologies. I believe that this sense of concern stems from the recognition that autonomous systems will not only be unpredictable in terms of their unintended actions and general effects on society, but that they may also be out of control, in the sense that these effects will occur beyond the scope of human responsibility. Previous technological innovations have not raised this concern in quite the same way, or to the same degree, because it was possible to rely upon human morality, as well as law, to regulate the use of new technologies.  2  While there were recognized risks to using technologies like guns, cars, airplanes, steam engines, and many more, those risks were circumscribed by limits on their immediate effects and the proximate responsibility of individual humans and human institutions for those effects. In most cases, these risks were also limited in their complexity and longevity, in the sense that those effects could be anticipated, managed, and reduced over time.  3  As long as there is a human hand on the controls, there is a margin of assurance that the technology cannot go too far out of control before it is reigned in by human agency or regulatory policy. Thus, human control presents itself as a 2 There are some notable exceptions. There have been debates over the morality of research and development of technologies with potentially catastrophic results or applications (and sometimes the dissemination of basic research in these areas) particularly the weaponization of nuclear physics and biological and chemical agents. There have been similar debates over the risks of basic research itself in the case of genetic engineering and nanotechnology, where the experiments themselves might go \"out of control\" and cause irrevocable or catastrophic harm. Many of these concerns are related to the potential causal \"chain reactions\" of positive feedback systems and exponential growth. \n 3 Notable exceptions here are certain tragedies of the commons and the problem of many hands  (Nissenbaum 1996) , in which proximate responsibility is small and requires many participants or instances for the harm to be realized. Environmental degradation is a good example where the participation of many separate responsible agents leads to a diffusion of perceived responsibility. Such harms are difficult to regulate largely because it is more difficult to establish the causal link to the responsible agents and rule out intervening or contributory causes. \"kill switch\" to technology going completely out of control, while human responsibility further acts as \"policy lever\" for policy to enact regulation over material technologies. Non-human agents, including robotics and software agents, and especially those using advanced artificial intelligence (AI), are becoming increasingly autonomous in terms of the complexity of tasks they can perform, their potential casual impacts on the world that are unmitigated by human agents, and the diminishing ability of human agents to understand, predict or control how they operate. This increasing autonomy of non-human agents seriously challenges human control, and thus challenges both the \"kill switch\" and the \"policy lever\" functions of human control. Some have argued that one factor or other is more troubling, or that one challenge or the other is more dire. But, I believe that the growing concern over increasingly autonomous agents stems from the combination of these factors and the challenges they impart, and they must be addressed comprehensively and systematically. Central to addressing these challenges will be finding a way to manage the liability problem-how to continue to hold people legally liable for increasingly autonomous agents. This is closely related to the responsibility problem-how to ensure that human agents take moral responsibility for the technologies they make and use as these become increasingly autonomous. How should we regulate artificial computational agents, including AI and robotic systems, as they become increasingly autonomous, and supersede current capabilities? In order to take a systematic approach to this question, we must integrate an analysis of fundamental concepts of autonomy and agency, with a review of current processes of systems design and development, and chart a course for future regulatory policy. This will include investigating 1) the conceptual foundations of autonomy and agency; 2) survey the existing legal and moral theories of liability and responsibility and their applicability to artificial agents; and 3) explore how implementing an enhanced theory of liability and agency for autonomous artificial agents could shape regulatory policy going forward. In this paper I will focus on sketching out 1) the conceptual foundations of autonomy and agency, through an examination of the liability problem. One of the central problems facing the development of autonomous artificial agents as technological capabilities continue to increase, is the uncertain status of liability for the effects caused by artificial agents-the liability problem. Resolving the liability problem will require untangling a set of theoretical and philosophical issues surrounding causation, intention, agency, responsibility, culpability and compensation. The primary objective of the proposed research is to address this problem through a conceptual analysis that is informed by existing legal and moral theories, and grounded in technological capabilities of current and potential artificial agents. \n The Liability Problem for Autonomous Artificial Agents In order for society to enjoy many of the benefits of advanced AI and robotics, it will be necessary to be able to deal with situations that arise in which autonomous artificial agents violate laws or cause harm. If we want to allow AIs and robots to roam the internet and the physical world and take actions that are unsupervised by humansas might be necessary for, e.g. personal shopping assistants, self-driving cars, and host of other applications-we must be able to manage the liability for the harms they might cause to individuals and property. Already, there have been automated shopping software bots that have purchased illegal items on the DarkNet, albeit as an art project  (Kasperkevic 2015) . There have also been serious questions raised as to who could be held accountable for the deaths caused by autonomous weapons in war  (Human Rights Watch 2015) . Traditional approaches to handling liability are inadequate for dealing with autonomous artificial agents due to a combination of two factors-unpredictability, and causal agency without legal agency. First, unlike traditional engineering and design, the actual functioning of an autonomous artificial agent is not necessarily predictable in the same way as most engineered systems. Some artificial agents may be unpredictable in principle, and many will be unpredictable in practice. Predictability is critical to current legal approaches to liability. In traditional product liability, the manufacturer is responsible for the product working as designed, and foreseeing likely problems or harms it may cause. Determining what is \"foreseeable\" often falls upon courts to decide, but the legal standards used are whether the manufacturer had knowledge of the potential problem, or whether a reasonable person should have foreseen it, or whether there is an industry standard of practice that would have revealed it. While there is a degree of unpredictability in the performance of any engineered product, due to failures or unforeseen circumstances of use, there are shared expectations regarding its performance, testing for the limits of that performance and likelihood of failure, and management of foreseeable risks. In the case of advanced AI, a system that learns from environmental data may act in ways that its designers have no feasible way to foresee  (Asaro 2008) . In a limited sense, this is already the case with current machine learning techniques, which use large sets of training data and produce novel problem solutions. Currently, it is possible to analyze and test a learned function and determine its behavior, as with traditional engineering. But when AI systems are allowed to continue modifying their functions and learn after they are deployed, their behavior will become dependent on novel input data, which designers and users cannot predict or control. As a result, the behavior of the learned functions will, to various degrees, also be unpredictable. A truly robust AI program capable of open-ended learning could learn functions that its manufacturer could not foresee, perhaps in principle. Insofar as autonomous artificial agents utilize learning and open-ended learning, their behavior will also be unpredictable. Unpredictability by itself is not an insurmountable problem for liability, insofar as the agents who introduce that unpredictability could be themselves held liable, or the risks from unpredictability could be managed. However, the second factor challenging traditional approaches to liability is that autonomous artificial agents may \"act\" on their own, yet are not accountable or liable in a legal sense. With most engineered products, the predictability is bounded by the actions of other agentsconsumers, users, service technicians, etc.-and how they maintain and use a given product.  4  In those cases, there is a clear legal agent or user who may have used the product inappropriately and is thus liable for the consequences of the use in that instance (at least partially, if not completely). Autonomous artificial agents can act in the world independently of their designers or operators. This makes it difficult to identify the user or operator, who would normally be liable. In the case of learning systems, the causal influence resulting in the unpredictability of a system stems from the datasets used for learning, not a legally responsible agent (unless someone deliberately seeks to influence the datasets and learning process). These cases are somewhat analogous to the way that parents may be held liable for the actions of small children, but they are not usually held liable for the actions of their adult children. As adults, the children have learned enough about the world to become their own legal agents. Something similar applies in cases of employer-employee liability. Usually the employer is responsible for any damages their employee causes in the course of doing their job (such as damage from a delivery truck hitting a parked car while making routine deliveries), but if the employee is off on a frolic (and took the delivery truck to visit a friend), then the employer is not responsible for the damages and the employee is  (Asaro 2011) . \n Approaches to the Problem Taken together these two factors result in a number of problems with applying traditional theories of legal liability to autonomous artificial agents. There are two basic liability frameworks in the law, criminal and civil (primarily tort) liability. In both domains, it is difficult to hold the artificial agent legally liable for its actions, as they are not legal persons, and treating them as legally fictitious persons (like corporations) does not really solve the problem  (Asaro 2011) . It is possible in some criminal situations to hold the people who operate the artificial systems liable, provided you can show intent to commit a crime, or foreseeable risk of a harm rising to the level of criminal negligence. To the extent that artificial agents become increasingly complex, those who build or deploy advanced AIs and robotics will not necessarily have intent or foresight of the actions those systems may take. This is especially true for systems that can substantially change their operations through advanced learning techniques, or those future systems that might even become genuinely autonomous in generating their own goals and purposes, or even intentions. At some point in the evolution of autonomous artificial agents, they might become legal and moral agents, and society will be faced with the question of whether to grant them some or all of the legal rights bestowed on persons or corporations. At that point, some or all of current liability law might apply to those AIs and robots that qualify as legal persons, though it might not be clear what the exact boundaries of a particular entity might be, or how to punish it  (Asaro 2011) . For example, whether a particular instantiation of a program is the legal subject, or all copies of a program are part of the same legal subject (as copyright law might suggest). It will also not be clear how to appropriately punish them, or otherwise correct their future actions and provide retributive compensation to those that have been harmed. Despite these challenges, being able to treat autonomous artificial agents as legal persons is likely to be the easier problem. In the near term, the hard liability problem for autonomous artificial agents will lie in devising a system of liability that promotes beneficial innovation while offering just and adequate compensation to those harmed. Justice requires that those who will be held liable should be able to understand the scope and extent of the risks and liability they are assuming in deploying an autonomous artificial agent, and have some means of managing that risk through controls over the system. Adequate compensation means that there needs to be sufficient means to compensate those harmed, monetary or otherwise-whether this entails holding large corporations accountable, or providing proper risk-pooling insurance. For insurance to work, of course, it will be necessary for actuaries to be able to assess the risks posed by various artificial agents. Assessing those risks will require both expertise, and probably means for imposing or assuring predictability in the systems themselves. And even then, there may be catastrophic risks involved, which may not be manageable under these frameworks. Ultimately there will be questions that society must address as to the perceived benefits and risks of such technologies, and who in society should receive those benefits and should shoulder the burden of those risks. There are a few liability policy options already in use in tort law, such as joint and several liability, strict liability, and risk-pooling insurance that might be deployed. But there are reasons to doubt that these will scale adequately or address all the problems posed by autonomous artificial agents. Existing forms of joint and several liability permit those harmed to seek monetary damages from the deepest pockets among those parties sharing some portion of the liability. This works well where there is a large corporation or government that is able to pay damages. While the amount they pay is disproportionate to their contribution to the damages, those harmed are more likely to be adequately compensated for their damages. One result of this is that those manufacturers likely to bear the liability burden would seek to limit the ability of consumers and users to modify, adapt or customize their advanced AI and robotics products in order to retain greater control over how they are used. This would stifle innovation coming from the hacking, open-source and DIY communities. The hacking, open-source and DIY communities, while a powerful source of innovation, will have limited means of compensating those who might be harmed from their products-not just those who chose to use them. Strict liability goes further and designates or stipulates a party, usually the manufacturer or owner, as strictly liable for any damages caused. This model of liability applies to such things as the keeping of wild animals. It is expected that tigers will harm people if they get free, so as the keeper of a tiger you are strictly liable for any and all damages the tiger may cause. We apply normal property liability to domesticated animals, however, which we expect to not harm people under normal circumstances. It has been suggested that we could apply this to robotics  (Schaerer, Kelley, and Nicolescu 2009) , and perhaps designate certain advanced AIs as essentially wild animals, and others as domesticated. But then the question arises: How does one determine whether an advanced AI or robot is appropriately domesticated, and stays that way? A designated liable person may not know the extent to which the autonomous system is capable of changing itself once it is activated. More problematic, however, is that a system of strict liability might result in the slow adoption of beneficial AI technologies, as those who are strictly liable would have a large and uncertain risk, and be less likely to produce or use the technology, or soon go out of business. There are other proposals that aim to design mechanisms of accountability into complex sociotechnical systems (van den Hoven, Robichaud, and Santoni de Sio 2015). But such approaches, much like strict liability, do not really address the fundamental issue of autonomous agency-how to define it or to regulate it. They merely try to manage it in an ad hoc effort to maintain traditional concepts rather than find a simpler and more powerful solution. We thus have a few general options when it comes to regulating autonomous artificial agents. We could preclude or prohibit autonomous artificial agents because of their risks and uncertainties. We might call this the precautionary approach. To the extent that it works, it would also impede the development and deployment of many beneficial advanced AIs and robots because of their problematic autonomy. We could permit the development and deployment of autonomous artificial agents, and accept the risks and costs at a social level, without developing a better framework for regulating autonomy. We might call this the permissive approach. 5 This would allow many beneficial applications of advanced AI and robots, but also many harmful ones, including many harms for which no one might be liable and those harmed would not be compensated. As a secondary effect, there would likely be a general backlash against advanced AI and robotics as the technology comes to be seen as harmful and offering few options for restitution of those harms. Or, we could pursue one of the heavy-handed liability schemes, such as strict liability, that would regulate the industry to some extent, but also limit innovation to those areas where there are sufficient profits to motivate large capital companies to enter the market and accept the risks. We might see this work in applications such as financial trading algorithms, self-driving cars and medical-care robots, but many other beneficial applications of AI may not have such clear profit margins. Even in clearly profitable areas, strict liability is likely to stifle innovation for a range of beneficial applications of autonomous artificial agents. Alternatively, we could seek a better solution to the liability problem than current models afford. We could attempt to reconceptualize how we think about agency, causality, liability responsibility, culpability and autonomy for the new age of artificial autonomous agents. While it is not yet clear how this might work, a clear framing of the problem, as this paper has presented, is the first step in that larger project. The next steps involve clarifying the distinctions between the purposes of algorithms and machines from the purposes of the persons who use them  (Asaro forthcoming) , and distinguishing different types of agency accordingly. \t\t\t For example, a hammer is designed to drive nails, but can also be used as a weapon-with the liability falling on the person who uses it as a weapon. Similarly, the car owner is responsible for changing the brake pads of a car when they are worn, and the mechanic is responsible for doing it properly, while the manufacturer's liability is limited to properly informing car owners of the service needs for the car. \n\t\t\t This is the approach taken by Chopra and White (2011) .", "date_published": "n/a", "url": "n/a", "filename": "Asaro, Ethics Auto Agents, AAAI.tei.xml", "abstract": "This paper describes and frames a central ethical issue-the liability problem-facing the regulation of artificial computational agents, including artificial intelligence (AI) and robotic systems, as they become increasingly autonomous, and supersede current capabilities. While it frames the issue in legal terms of liability and culpability, these terms are deeply imbued and interconnected with their ethical and moral correlateresponsibility. In order for society to benefit from advances in AI technology, it will be necessary to develop regulatory policies which manage the risk and liability of deploying systems with increasingly autonomous capabilities. However, current approaches to liability have difficulties when it comes to dealing with autonomous artificial agents because their behavior may be unpredictable to those who create and deploy them, and they will not be proper legal or moral agents. This problem is the motivation for a research project that will explore the fundamental concepts of autonomy, agency and liability; clarify the different varieties of agency that artificial systems might realize, including causal, legal and moral; and the illuminate the relationships between these. The paper will frame the problem of liability in autonomous agents, sketch out its relation to fundamental concepts in human legal and moral agencyincluding autonomy, agency, causation, intention, responsibility and culpability-and their applicability or inapplicability to autonomous artificial agents.", "id": "ed072a8b6a53a8cab8b0c07d7b087e00"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Alethea Power", "Yuri Burda", "Harri Edwards", "Igor Babuschkin", "Vedant Misra"], "title": "GROKKING: GENERALIZATION BEYOND OVERFIT-TING ON SMALL ALGORITHMIC DATASETS", "text": "INTRODUCTION The generalization of overparameterized neural networks has long been a source of interest to the machine learning community since it defies intuitions derived from classical learning theory. In this paper we show that training networks on small algorithmically generated datasets can reliably exhibit unusual generalization patterns, clearly decoupled from performance on the training set, in a significantly more pronounced way than such effects manifest on datasets derived from natural data (see Figure  1 , left, for an example). Such experiments can be quickly reproduced on a single GPU, and this makes them convenient testbeds for theories of generalization. The datasets we consider are binary operation tables of the form a • b = c where a, b, c are discrete symbols with no internal structure, and • is a binary operation. Examples of binary operations include Figure  1 : Left. Grokking: A dramatic example of generalization far after overfitting on an algorithmic dataset. We train on the binary operation of division mod 97 with 50% of the data in the training set. Each of the 97 residues is presented to the network as a separate symbol, similar to the representation in the figure to the right. The red curves show training accuracy and the green ones show validation accuracy. Training accuracy becomes close to perfect at < 10 3 optimization steps, but it takes close to 10 6 steps for validation accuracy to reach that level, and we see very little evidence of any generalization until 10 5 steps. Center. Training time required to reach 99% validation accuracy increases rapidly as the training data fraction decreases. Right. An example of a small binary operation table. We invite the reader to make their guesses as to which elements are missing. addition, composition of permutations, and bivariate polynomials. Training a neural network on a proper subset of all possible equations then amounts to filling in the blanks of the binary op table, much like solving a Sudoku puzzle. An example is shown on the right in Figure  1 . Since we use distinct abstract symbols for all distinct elements a, b, c involved in the equations, the network is not made aware of any internal structure of the elements, and has to learn about their properties only from their interactions with other elements. For example the network doesn't see numbers in decimal notation, or permutations in line notation. Our contributions are as follows: • We show that neural networks are capable of generalizing to the empty slots in a variety of binary op tables. • We show that, long after severely overfitting, validation accuracy sometimes suddenly begins to increase from chance level toward perfect generalization. We call this phenomenon 'grokking'. An example is shown in Figure  1 . • We present the data efficiency curves for a variety of binary operations. • We show empirically that the amount of optimization required for generalization quickly increases as the dataset size decreases. • We compare various optimization details to measure their impact on data efficiency. We find that weight decay is particularly effective at improving generalization on the tasks we study. • We visualize the symbol embeddings learned by these networks and find that they sometimes uncover recognizable structure of the mathematical objects represented by the symbols. \n METHOD All of our experiments used a small transformer trained on datasets of equations of the form a • b = c, where each of \"a\", \"•\", \"b\", \"=\", and \"c\" is a separate token. Details of the operations studied, the architecture, training hyperparameters and tokenization can be found in Appendix A.1. \n EXPERIMENTS \n GENERALIZATION BEYOND OVERFITTING Deep learning practitioners are used to seeing small improvements in validation accuracy after validation loss stops decreasing. A double descent of validation loss has been documented in some circumstances, but is considered unusual among practitioners  (Nakkiran et al., 2019; Belkin et al., 2018; d'Ascoli et al., 2020) . On the small algorithmic datasets that we study, improved generalization after initial overfitting occurs for a range of models, optimizers, and dataset sizes, and in some cases these effects are extremely pronounced. A typical example is shown for modular division in Figure  1 . There we see that validation accuracy starts increasing beyond chance level only after 1000 times more optimization steps than are required for training accuracy to get close to optimal. In Figure  4  the training/validation losses are also plotted and we see the double descent of the validation loss. We found these behaviors to be typical for all the binary operations for dataset sizes that were close to the minimal dataset size for which the network generalized within the allotted optimization budget. For larger dataset sizes, the training and validation curves tend to track each other more closely. \n LEARNING TIME CURVES In a typical supervised learning problem, decreasing the amount of training data decreases the converged generalization performance of the model when the optimization procedure is capable of interpolating the training data. In our setting, we observe a different phenomenon: while the converged performance stays constant at 100% within a range of training dataset sizes, the optimization time required to achieve that performance grows quicky as the dataset size is decreased. Figure  1  (center) shows median number of optimization steps until validation performance first reaches 99% for the product in abstract group S 5 . In the vicinity of 25-30% of data, a decrease of 1% of training data leads to an increase of 40-50% in median time to generalization. While the number of steps until validation accuracy > 99% grows quickly as dataset size decreases, the number of steps until the train accuracy first reaches 99% generally trends down as dataset size decreases and stays in the range of 10 3 -10 4 optimization steps. We've observed a similar pattern of exponential increase in optimization time until reaching generalization as dataset size decreases on all the algorithmic tasks for which we could get the networks to generalize. \n GROKKING ON A VARIETY OF PROBLEMS We've measured the mean accuracy across three runs for training datasets consisting of different fractions of all available equations for a variety of binary operations listed in Appendix A.1.1. The results are presented in Figure  2  (right). Since the operands are presented to the neural network as unrelated abstract symbols, the operations x + y (mod p − 1) and x * y (mod p) with a prime number p and non-zero x, y are indistinguishable from the neural network's perspective (and similarly x − y (mod p − 1) and x/y (mod p)). This is because every nonzero residue modulo a prime can be represented as a power of a primitive root. This representation shows the equivalence (up to renaming of symbols) of modular addition modulo p − 1 and modular multiplication modulo p. We see in Figure  2  (right) that x − y and x/y indeed take about the same amount of data for generalization to occur. Some of the operations listed in Figure  2  (right) are symmetric with respect to the order of the operands (x + y, x * y, x 2 + y 2 and x 2 + xy + y 2 ). Such operations tend to require less data for generalization than closely related non-symmetrical counterparts (x − y, x/y, x 2 + xy + y 2 + x). We believe this effect might be partially architecture-dependent, since it's easy for a transformer to learn a symmetric function of the operands by ignoring positional embedding. Some operations (for example x 3 + xy 2 + y (mod 97)) didn't lead to generalization within the allowed optimization budget at any percentage of data up to 95%. The converged models effectively just memorized the training dataset without finding any real patterns in the data. To such a model, the data is effectively random. The operation [x/y (mod p) if y is odd, otherwise x − y (mod p)] requires the network to learn a mix of several simple operations -in particular the role of x has to be interpreted as a residue in the additive group when it's paired with an even y, and as a residue in the multiplicative group when it's paired with an odd y. This shows that generalization can happen even for operations that are not cleanly interpretable via group or ring operations. \n ABLATIONS AND TRICKS We've tried various forms of regularization to see what can induce networks to generalize better on our datasets. Here we present the data efficiency curves on a particular dataset S 5 for a variety of interventions: full-batch gradient descent, stochastic gradient descent, large or small learning rates, residual dropout  (Srivastava et al., 2014) , weight decay  (Loshchilov & Hutter, 2017)  and gradient noise  (Neelakantan et al., 2015) . The results are shown in Figure  2  (left). We find that adding weight decay has a very large effect on data efficiency, more than halving the amount of samples needed compared to most other interventions. We found that weight decay towards the initialization of the network is also effective, but not quite as effective as weight decay towards the origin. This makes us believe that the prior, that approximately zero weights are suitable for small algorithmic tasks, explains part, but not all of the superior performance of weight decay. Adding some noise to the optimization process (e.g. gradient noise from using minibatches, Gaussian noise applied to weights before or after computing the gradients) is beneficial for generalization, consistent with the idea that such noise might induce the optimization to find flatter minima that generalize better. We found that learning rate had to be tuned in a relatively narrow window for the generalization to happen (within 1 order of magnitude). \n QUALITATIVE VISUALIZATION OF EMBEDDINGS In order to gain some insight into networks that generalize, we visualized the matrix of the output layer for the case of modular addition and S 5 . In Figure  3  we show t-SNE plots of the row vectors. For some networks we find clear reflections of the structure of the underlying mathematical objects in the plots. For example the circular topology of modular addition is shown with a 'number line' formed by adding 8 to each element. The structure is more apparent in networks that were optimized with weight decay. \n DISCUSSION We have seen that in the datasets we studied, small algorithmic binary operation tables, effects such as double descent or late generalization, and improvements to generalization from interventions like weight decay can be striking. This suggests that these datasets could be a good place to investigate aspects of generalization. For example, we plan to test whether various proposed measures of minima flatness correlate with generalization in our setting. We have also seen that visualizing the embedding spaces of these neural networks can show natural kinds of structure, for example in problems of modular arithmetic the topology of the embeddings tends to be circles or cylinders. We also see that the network tends to idiosyncratically organize the embeddings by various residues. Whilst the properties of these mathematical objects are familiar to us, we speculate that such visualizations could one day be a useful way to gain intuitions about novel mathematical objects. In addition, we document an interesting phenomenon, where the number of optimization steps needed to reach a given level of performance increases quickly as we reduce the size of the training dataset. Since this represents a way trade compute for performance on smaller amounts of data, it would be useful to investigate in future work whether the effect is also present for other datasets. The following are the binary operations that we have tried (for a prime number p = 97): x • y = x + y (mod p) for 0 ≤ x, y < p x • y = x − y (mod p) for 0 ≤ x, y < p x • y = x/y (mod p) for 0 ≤ x < p, 0 < y < p x • y = [x/y (mod p) if y is odd, otherwise x − y (mod p)] for 0 ≤ x, y < p x • y = x 2 + y 2 (mod p) for 0 ≤ x, y < p x • y = x 2 + xy + y 2 (mod p) for 0 ≤ x, y < p x • y = x 2 + xy + y 2 + x (mod p) for 0 ≤ x, y < p x • y = x 3 + xy (mod p) for 0 ≤ x, y < p x • y = x 3 + xy 2 + y (mod p) for 0 ≤ x, y < p x • y = x • y for x, y ∈ S 5 x • y = x • y • x −1 for x, y ∈ S 5 x • y = x • y • x for x, y ∈ S 5 For each binary operation we constructed a dataset of equations of the form x op y = x • y , where a stands for the token corresponding to element a. For each training run, we chose a fraction of all available equations at random and declared them to be the training set, with the rest of equations being the validation set. \n A.1.2 MODEL AND OPTIMIZATION We trained a standard decoder-only transformer  (Vaswani et al., 2017)  with causal attention masking, and calculated loss and accuracy only on the answer part of the equation. For all experiments we used a transformer with 2 layers, width 128, and 4 attention heads, with a total of about 4 • 10 5 non-embedding parameters. We have tuned optimization hyperparameters by running experiments on modular addition and product in S 5 . For final configuration of hyperparameters we have chosen a balance of performance we saw on S 5 and simplicity (for example we chose not to anneal the learning rate for the experiments in the paper even though it performed better in some situations). For most experiments we used AdamW optimizer with learning rate 10 −3 , weight decay 1, β 1 = 0.9, β 2 = 0.98, linear learning rate warmup over the first 10 updates, minibatch size 512 or half of training dataset size (whichever was smaller) and optimization budget of 10 5 gradient updates. In section 3.3 we have also tried the following variants (listed in the reading order for Figure  2 left ): • Adam optimizer with full batch (i.e. exact gradient of the loss on the whole training dataset) • Adam optimizer • Adam optimizer with full batch and Gaussian noise added to the update direction for each parameter (W ← W + lr • (∆W + ), where is sampled from unit Gaussian, ∆W is the standard Adam weight update, and lr is the learning rate) • Adam optimizer on model with residual dropout 0.1 added • AdamW optimizer with weight decay 1 (default setting in most other experiments) • AdamW optimizer with weight decay 1 towards the initialization instead of the origin • Adam optimizer with learning rate 3 • 10 −4 • Adam optimizer with learning rate 3 • 10 −3 • Adam optimizer on model with Gaussian weight noise of standard deviation 0.01 (i.e. each parameter W replaced by W + 0.01 • in the model, with sampled from unit Gaussian). For experiments reported in Section 3.1.1 we increased the optimization budget to 5 • 10 5 optimization steps in order to capture the increase of time to perfect generalization better. For the experiments reported in Section 3.1 we increased the optimization budget to 10 6 , and used Adam optimizer with no weight decay, for emphasizing how late into the optimization process the generalization can begin. We've repeated each experiment for each dataset size with 3 random seeds, with the exception of experiments in section 3.1.1, where we've aggregated results over 7 random seeds. \n A.2 ADDITIONAL FIGURES In Figure  4  we show the loss curves that correspond to the accuracy curves in Figure  1 . In Figure  5  we show an example of a binary operation table that the network can actually solve. Figure  4 : The loss curves for modular division, train and validation. We see the validation loss increases from 10 2 to about 10 5 optimization steps before it begins a second descent. \n A.3 RELATED WORK In this paper we study training and generalization dynamics on small simple algorithmic datasets. In the past, algorithmic datasets have been used to probe the capability of neural networks to perform symbolic and algorithmic reasoning. For example the tasks of copying, reversing, and sorting randomly generated sequences, and performing arithmetic operations of multi-digit numbers, have been used as standard benchmarks for sequence-to-sequence models  (Graves et al., 2014) ,  (Weston et al., 2014 ) )  (Reed & De Freitas, 2015) ,  (Grefenstette et al., 2015) ,  (Zaremba & Sutskever, 2015) ,  (Graves, 2016) ,  (Dehghani et al., 2018) . Typically in these works however the emphasis is on the performance in the unlimited data regime, with generalization often studied with respect to input sequence length. Some papers study the sample complexity on algorithmic tasks  (Reed & De Freitas, 2015) , but mostly focus on the impact of architectural choices. In contrast we study the phenomenon of generalization in data-limited regime, with an emphasis on phenomena that we believe to be architecture-agnostic. Algorithmically generated reasoning datasets like bAbI  (Weston et al., 2015)  encourage work on studying generalization in data-limited regime. Most results on such datasets however focus on a point estimate of performance of a particular architecture or training technique, whereas our main interest is in pointing out the change in generalization past the point where a particular architecture can memorize the training data completely.  (Neelakantan et al., 2015)  has a \"grok-like\" learning curve on an algorithmic task, but it is related to optimization difficulty, whereas our phenomenon is specifically about generalization. In  (Saxton et al., 2019)  they study generalization on procedurally generated math problems such as arithmetic and differentiation, but for the most part these tasks are more involved than the simple Figure  5 : One of the binary operation tables presented to the networks that the network can perfectly fill in. Each symbol is represented as a letter in English, Hebrew, or Greek alphabet for reader's convenience. We invite the reader to guess which operation is represented here. binary op problems we have studied and as such do not lend themselves to observing the kinds of phenomena we describe in this paper, since they would require an extremely large number of samples to master. In  (Jiang et al., 2019)  they studied a large number of generalization or complexity measures on convolutional neural networks to see which, if any, are predictive of generalization performance. They find that flatness based measures that aim to quantify the sensitivity of the trained neural network to parameter perturbations are the most predictive. We conjectured that the grokking phenomena we report in this work may be due to the noise from SGD driving the optimization to flatter/simpler solutions that generalize better and hope to investigate in future work whether any of these measures are predictive of grokking.  (Zhang et al., 2016)  finds that neural networks of sizes typically used in deep learning can interpolate arbitrary training data, and yet generalize when trained with semantically meaningful labels using appropriate optimization procedures. Our work shows a related phenomenon where neural networks can interpolate a small algorithmic training dataset without generalizing, but start generalizing when trained with SGD for longer. 1 st Mathematical Reasoning in General Artificial Intelligence Workshop, ICLR 2021.  (Nakkiran et al., 2019; Belkin et al., 2018)  focus on the phenomenon of double descent in loss as a function of model and optimization procedure capacity. They find that the classical U-shaped validation loss curve is followed in some settings (including neural network training) by a second descent of loss that starts around the minimal capacity that is needed to interpolate any training data. We observe a second descent in validation loss (though not accuracy) as a function of the amount of training in some of our experiments, and it happens past the point of interpolating the training data. We believe that the phenomenon we describe might be distinct from the double descent phenomena described in  (Nakkiran et al., 2019; Belkin et al., 2018)  because we observe the second descent in loss far past the first time the training loss becomes very small (tens of thousands of epochs in some of our experiments), and we don't observe a non-monotonic behavior of accuracy. The setting of small algorithmic datasets that we study also provides a smaller, more tractable playground for studying subtle generalization phenomena than natural datasets studied in  (Nakkiran et al., 2019) . A.4 GENERALIZATION WITH MEMORIZING SEVERAL OUTLIERS In this situation one could imagine one of the following scenarios unfolding. If the model class of neural networks optimized and regularized as before was not large enough to interpolate such \"noisy\" dataset, one could imagine the procedure converging to a solution that generalizes well, but denoises the training data (i.e. predicts c = a • b as an answer even for the outlier equations a, b → c with c = c). On the other extreme it could be that the optimization procedure can find networks that interpolate the data, but the resulting models don't generalize, because they are forced to represent a considerably more complicated function than before (a simple function + k exceptions encoded in the training data). In our experiments we find that the first option doesn't happen -all experiments reach 100% training accuracy at some point, and this point is not considerably affected by changing the number of outliers k. The second phenomenon happens in a range of training data percentages and number of outliers k -increasing k decreases the range of training data percentages for which the optimization procedure converges to models that generalize. However the effect of introducing a small number of outliers (up to 1000) is not very pronounced -see Figure  6 . We interpret this as additional evidence that the capacity of the network and optimization procedure is well beyond the capacity needed for memorizing all the labels on the training data, and that generalization happening at all requires a non-trivial explanation. Figure 2 : 2 Figure 2: Left. Different optimization algorithms lead to different amounts of generalization within an optimization budget of 10 5 steps for the problem of learning the product in the abstract group S 5 .Weight decay improves generalization the most, but some generalization happens even with full batch optimizers and models without weight or activation noise at high percentages of training data. Suboptimal choice hyperparameters severely limit generalization. Not shown: training accuracy reaches 100% after 10 3 -10 4 updates for all optimization methods. Right. Best validation accuracy achieved after 10 5 steps on a variety of algorithmic datasets, averaged over 3 seeds. Generalization happens at higher percentages of data for intuitively more complicated and less symmetrical operations. \n Figure 3 : 3 Figure 3: Left. t-SNE projection of the output layer weights from a network trained on S 5 . We see clusters of permutations, and each cluster is a coset of the subgroup (0, 3)(1, 4), (1, 2)(3, 4) or one of its conjugates. Right. t-SNE projection of the output layer weights from a network trained on modular addition. The lines show the result of adding 8 to each element. The colors show the residue of each element modulo 8. \n Figure 6 : 6 Figure 6: Effect on data efficiency of introducing k ∈[0, 10, 100, 1000, 2000, 3000]  outliers (examples with random labels) into the training data. Small number of outliers doesn't noticeably impact generalization performance, but a large number hinders it significantly. \n \n\t\t\t  st  Mathematical Reasoning in General Artificial Intelligence Workshop, ICLR 2021.", "date_published": "n/a", "url": "n/a", "filename": "MATHAI_29_paper.tei.xml", "abstract": "In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail.  In some situations we show that neural networks learn through a process of \"grokking\" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.", "id": "7f9fd01814672652afa66048b438de38"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "p29.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Technological Development"], "title": "Astronomical Waste: The Opportunity Cost of Delayed", "text": "2 being irreversibly degraded into entropy on a cosmic scale. These are resources that an advanced civilization could have used to create value-structures, such as sentient beings living worthwhile lives. The rate of this loss boggles the mind. One recent paper speculates, using loose theoretical considerations based on the rate of increase of entropy, that the loss of potential human lives in our own galactic supercluster is at least ~10 46 per century of delayed colonization.  1  This estimate assumes that all the lost entropy could have been used for productive purposes, although no currently known technological mechanisms are even remotely capable of doing that. Since the estimate is meant to be a lower bound, this radically unconservative assumption is undesirable. We can, however, get a lower bound more straightforwardly by simply counting the number or stars in our galactic supercluster and multiplying this number with the amount of computing power that the resources of each star could be used to generate using technologies for whose feasibility a strong case has already been made. We can then divide this total with the estimated amount of computing power needed to simulate one human life. As a rough approximation, let us say the Virgo Supercluster contains 10 13 stars. One estimate of the computing power extractable from a star and with an associated planet-sized computational structure, using advanced molecular nanotechnology 2 , is 10 42 operations per second. 3 A typical estimate of the human brain's processing power is roughly 10 17 operations per second or less. 4 Not much more seems to be needed to simulate the relevant parts of the environment in sufficient detail to enable the simulated minds to have experiences indistinguishable from typical current human experiences. 5 3 Given these estimates, it follows that the potential for approximately 10 38 human lives is lost every century that colonization of our local supercluster is delayed; or equivalently, about 10 29 potential human lives per second. While this estimate is conservative in that it assumes only computational mechanisms whose implementation has been at least outlined in the literature, it is useful to have an even more conservative estimate that does not assume a non-biological instantiation of the potential persons. Suppose that about 10 10 biological humans could be sustained around an average star. Then the Virgo Supercluster could contain 10 23 biological humans. This corresponds to a loss of potential of over 10 13 potential human lives per second of delayed colonization. What matters for present purposes is not the exact numbers but the fact that they are huge. Even with the most conservative estimate, assuming a biological implementation of all persons, the potential for over ten trillion potential human beings is lost for every second of postponement of colonization of our supercluster.  6   \n II. THE OPPORTUNITY COST OF DELAYED COLONIZATION From a utilitarian perspective, this huge loss of potential human lives constitutes a correspondingly huge loss of potential value. I am assuming here that the human lives that could have been created would have been worthwhile ones. Since it is commonly supposed that even current human lives are typically worthwhile, this is a weak assumption. Any civilization advanced enough to colonize the local supercluster would likely also have the ability to establish at least the minimally favorable conditions required for future lives to be worth living. \n 4 The effect on total value, then, seems greater for actions that accelerate technological development than for practically any other possible action. Advancing technology (or its enabling factors, such as economic productivity) even by such a tiny amount that it leads to colonization of the local supercluster just one second earlier than would otherwise have happened amounts to bringing about more than 10 29 human lives (or 10 13 human lives if we use the most conservative lower bound) that would not otherwise have existed. Few other philanthropic causes could hope to match that level of utilitarian payoff. Utilitarians are not the only ones who should strongly oppose astronomical waste. There are many views about what has value that would concur with the assessment that the current rate of wastage constitutes an enormous loss of potential value. For example, we can take a thicker conception of human welfare than commonly supposed by utilitarians (whether of a hedonistic, experientialist, or desire-satisfactionist bent), such as a conception that locates value also in human flourishing, meaningful relationships, noble character, individual expression, aesthetic appreciation, and so forth. So long as the evaluation function is aggregative (does not count one person's welfare for less just because there are many other persons in existence who also enjoy happy lives) and is not relativized to a particular point in time (no time-discounting), the conclusion will hold. These conditions can be relaxed further. Even if the welfare function is not perfectly aggregative (perhaps because one component of the good is diversity, the marginal rate of production of which might decline with increasing population size), it can still yield a similar bottom line provided only that at least some significant component of the good is sufficiently aggregative. Similarly, some degree of timediscounting future goods could be accommodated without changing the conclusion. 7 \n III. THE CHIEF GOAL FOR UTILITARIANS SHOULD BE TO REDUCE EXISTENTIAL RISK In light of the above discussion, it may seem as if a utilitarian ought to focus her efforts on accelerating technological development. The payoff from even a very slight success in this endeavor is so enormous that it dwarfs that of almost any other activity. We appear to have a utilitarian argument for the greatest possible urgency of technological development. However, the true lesson is a different one. If what we are concerned with is (something like) maximizing the expected number of worthwhile lives that we will create, then in addition to the opportunity cost of delayed colonization, we have to take into account the risk of failure to colonize at all. We might fall victim to an existential risk, one where an adverse outcome would either annihilate Earth-originating intelligent life or permanently and drastically curtail its potential. 8 Because the lifespan of galaxies is measured in billions of years, whereas the time-scale of any delays that we could realistically affect would rather be measured in years or decades, the consideration of risk trumps the consideration of opportunity cost. For example, a single percentage point of reduction of existential risks would be worth (from a utilitarian expected utility point-ofview) a delay of over 10 million years. Therefore, if our actions have even the slightest effect on the probability of eventual colonization, this will outweigh their effect on when colonization takes place. \n 6 For standard utilitarians, priority number one, two, three and four should consequently be to reduce existential risk. The utilitarian imperative 'Maximize expected aggregate utility!' can be simplified to the maxim 'Minimize existential risk!'. \n IV. IMPLICATIONS FOR AGGREGATIVE PERSON-AFFECTING VIEWS The argument above presupposes that our concern is to maximize the total amount of well-being. Suppose instead that we adopt a 'person-affecting' version of utilitarianism, according to which our obligations are primarily towards currently existing persons and to those persons that will come to exist. 9 On such a person-affecting view, human extinction would be bad only because it makes past or ongoing lives worse, not because it constitutes a loss of potential worthwhile lives. What ought someone who embraces this doctrine do? Should he emphasize speed or safety, or something else? To answer this, we need to consider some further matters. Suppose one thinks that the probability is negligible that any existing person will survive long enough to get to use a significant portion of the accessible astronomical resources, which, as described in opening section of this paper, are gradually going to waste. Then one's reason for minimizing existential risk is that sudden extinction would off cut an average of, say, 40 years from each of the current (six billion or so) human lives. 10 While this would certainly be a large disaster, it is in the same big ballpark as other ongoing human tragedies, such as world poverty, hunger and disease. On this assumption, then, a personaffecting utilitarian should regard reducing existential risk as a very important but not completely dominating concern. There would in this case be no easy answer to what he ought to do. Where he ought to focus his efforts would depend on detailed calculations about which area of philanthropic activity he would happen to be best placed to make a contribution to. Arguably, however, we ought to assign a non-negligible probability to some current people surviving long enough to reap the benefits of a cosmic diaspora. A socalled technological 'singularity' might occur in our natural lifetime 11 , or there could be a breakthrough in life-extension, brought about, perhaps, as result of machine-phase nanotechnology that would give us unprecedented control over the biochemical processes in our bodies and enable us to halt and reverse the aging process. 12 Many leading technologists and futurist thinkers give a fairly high probability to these developments happening within the next several decades.  13  Even if you are skeptical about their prognostications, you should consider the poor track record of technological forecasting. In view of the well-established unreliability of many such forecasts, it would seem unwarranted to be so confident in one's prediction that the requisite breakthroughs will not occur in our time as to give the hypothesis that they will a probability of less than, say, 1%. The expected utility of a 1% chance of realizing an astronomically large good could still be astronomical. But just how good would it be for (some substantial subset of) currently living people to get access to astronomical amounts of resources? The answer is not obvious. On the one hand, one might reflect that in today's world, the marginal utility for an individual of material resources declines quite rapidly ones his basic needs have been met. Bill Gate's level of well-being does not seem to dramatically exceed that of many a person of much more modest means. On the other hand, advanced technologies of the sorts that would most likely be deployed by the time we could colonize the local supercluster may well provide new ways of converting resources into well-being. In particular, material resources could be used to greatly expand our mental capacities and to indefinitely prolong our subjective lifespan. And it is by no means clear that the marginal utility of extended healthspan and increased mental powers must be sharply declining above some level. If there is no such decline in marginal utility, we have to conclude that the expected utility to current individuals 14 of successful colonization of our supercluster is astronomically great, and this conclusion holds even if one gives a fairly low probability to that outcome. A long shot it may be, but for an expected utility maximizer, the benefit of living for perhaps billions of subjective years with greatly expanded capacities under fantastically favorable conditions could more than make up for the remote prospects of success. Now, if these assumptions are made, what follows about how a person-affecting utilitarian should act? Clearly, avoiding existential calamities is important, not just because it would truncate the natural lifespan of six billion or so people, but also -and given the assumptions this is an even weightier consideration -because it would extinguish the chance that current people have of reaping the enormous benefits of eventual colonization. However, by contrast to the total utilitarian, the person-affecting utilitarian would have to balance this goal with another equally important desideratum, namely that of maximizing the chances of current people surviving to benefit from the colonization. For the person-affecting utilitarian, it is not enough that humankind survives to colonize; it is crucial that extant people be saved. This should lead her to emphasize speed of technological development, since the rapid arrival of advanced technology would surely be needed to help current people stay alive until the fruits of 9 colonization could be harvested. If the goal of speed conflicts with the goal of global safety, the total utilitarian should always opt to maximize safety, but the person-affecting utilitarian would have to balance the risk of people dying of old age with the risk of them succumbing in a species-destroying catastrophe. Mixed ethical views, which also incorporate non-utilitarian elements, might or might not yield one of these bottom lines depending on the nature of what is added. 15 1 M. Cirkovic, 'Cosmological Forecast and its Practical Significance', Journal of  Evolution and Technology, xii (2002) , http://www.jetpress.org/volume12/CosmologicalForecast.pdf. 10 7 Utilitarians commonly regard time-discounting as inappropriate in evaluating moral goods (see e.g. R. B.  Brandt, Morality, Utilitarianism, and Rights, Cambridge, 1992, pp. 23f.) . However, it is not clear that utilitarians can avoid compromising on this principle in view of the possibility that our actions could conceivably have consequences for an infinite number of persons (a possibility that we set aside for the purposes of this paper).  8 N. Bostrom, 'Existential Risks: Analyzing Human Extinction Scenarios and Related Hazards', Journal of \n\t\t\t K. E. Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation, New York, John Wiley & Sons, Inc., 1992. 3 R. J. Bradbury, 'Matrioshka Brains', Manuscript, 2002, http://www.aeiveos.com/~bradbury/MatrioshkaBrains/MatrioshkaBrains.html 4 N. Bostrom, 'How Long Before Superintelligence?', International Journal of Futures Studies ii (1998); R. Kurzweil, The Age of Spiritual Machines: When Computers Exceed Human Intelligence, New York, Viking, 1999. The lower estimate is in H. Moravec, Robot: Mere Machine to Transcendent Mind, Oxford, 1999. 5 N. Bostrom, 'Are You Living in a Simulation?', Philosophical Quarterly, liii (211). See also http://www.simulation-argument.com.6  The Virgo Supercluster contains only a small part of the colonizable resources in the universe, but it is sufficiently big to make the point. The bigger the region we consider, the less certain we can be that significant parts of it will not have been colonized by a civilization of non-terrestrial origin by the time we could get there. \n\t\t\t I'm grateful for comments from John Broome, Milan Cirkovic, Roger Crisp, Robin Hanson, and James Lenman, and for the financial support of a British Academy Postdoctoral Award.", "date_published": "n/a", "url": "n/a", "filename": "waste.tei.xml", "abstract": "With very advanced technology, a very large population of people living happy lives could be sustained in the accessible region of the universe. For every year that development of such technologies and colonization of the universe is delayed, there is therefore a corresponding opportunity cost: a potential good, lives worth living, is not being realized. Given some plausible assumptions, this cost is extremely large. However, the lesson for standard utilitarians is not that we ought to maximize the pace of technological development, but rather that we ought to maximize its safety, i.e. the probability that colonization will eventually occur. This goal has such high utility that standard utilitarians ought to focus all their efforts on it. Utilitarians of a 'personaffecting' stripe should accept a modified version of this conclusion. Some mixed ethical views, which combine utilitarian considerations with other criteria, will also be committed to a similar bottom line. \n I. THE RATE OF LOSS OF POTENTIAL LIVES As I write these words, suns are illuminating and heating empty rooms, unused energy is being flushed down black holes, and our great common endowment of negentropy is Russian, Portuguese, Bosnian Translations:", "id": "be2c484796791bbdd1f4b04ca68e8454"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Keller Scholl", "Robin Hanson"], "title": "Testing the automation revolution hypothesis ✩", "text": "Introduction Since at least 2013, many have claimed that we are entering an automation revolution, and so should soon expect large trenddeviating increases in job automation, in related job losses, and in the determinants of automation. As context for considering such claims, we study what predicts which jobs have been how automated in the recent past, how the best automation predictors have changed over time, and recent correlations between changes in automation, pay, and employment. \n Material We combine data from three sources  (Scholl and Hanson, 2020) . First, O*NET is a database of U.S. job feature scores made by surveying occupational experts and employees, who compare ✩ For financial support we thank Open Philanthropy Project for funding ''Research into Future Artificial Intelligence Scenarios.'' They did not influence our study design or interpretation. each job to related jobs. For each of 2144 jobs, O*NET includes 261 job features, many scored on a 0-5 numerical scale. In its current form O*NET started in 2002, though that year's entries include data from 1999. We project these scores onto 881 ''sixdigit'' level jobs, via scaling frequency by importance. We thus have scores of 261 job features for 881 jobs from 1999 to 2019. One key O*NET job feature is years of education, and another is ''degree of automation'', which seems to represent expert judgments on which workers would have to do each task now done by machines, absent those machines. Second, from Occupational Employment Statistics (OES), we obtain, for all these jobs and for years 1999 to 2018, U.S. annual averages for employment (i.e., number of employees) and an inflation-adjusted mean hourly pay (in U.S. dollars). Our third source is two widely-discussed expert-judgmentderived metrics regarding the vulnerability of jobs to near future automation. These metrics do not vary by year. Computerisable comes from  Frey and Osborne (2017) , first published in 2013, and ranges 0 to 1. Building on judgments made by a ''group of machine learning researchers'', they estimated 47% of U.S. jobs to be at ''high risk'' of being ''computerisable'', ''perhaps over the next decade or two''. Machine Learning Suitability, coming directly from an author of  Brynjolfsson et al. (2018) , was created from machine learning expert judgments using a 23-item rubric, and ranges 2 to 5. We transform all variables (besides time and intercept) into rough ''z-score'' variants. We apply a logarithmic transform to 0.01 plus pay, employment, and each O*NET variable. We then rescale them to have zero mean and unit standard deviation. Time is rescaled to take value zero at 1999, and one at 2019. Our transformed variables look closer to normally distributed. As we use transformed versions in our analysis, most regression coefficients say how many standard deviations of increase in a dependent variable is predicted by a one standard deviation increase in an independent variable. Most O*NET job features were not scored for each job every year, but were on average scored 3.3 times during our 1999-2019 period. From available scores, we interpolate scores for all years using two methods. In piecewise-linear interpolation, we fit straight lines in time between scorings that are adjacent in time, and fit zero-slope lines for years outside the time range of available scorings. In regression interpolation, we fit a linear regression in time to all available job-feature scorings. This method requires at least two job-feature scorings. While our dataset officially includes 881 jobs and 260 O*NET job features (besides education), data limitations force a tradeoff between how many jobs and features we can include. We choose to maximize the product of these at 832 jobs and 251 features. Table 3 further selects for jobs with enough data to allow regression interpolation for all features used. \n Methods Table  1  gives basic statistics for all variables in the other tables. Table  2  describes seven ordinary least squares regressions, all predicting automation. Each data point corresponds to a notinterpolated O*NET scoring of an automation value for a job in a year; independent variables are piecewise-linear interpolated. These 25 O*NET variables were selected via the LASSO method out of the 251 available O*NET variables via a structure like Model 3. Models 2,5 add extra columns for each variable multiplied by time, and Models 6,7 apply the same structure of Model 4 separately to times <0.5 and >0.5. A simple model not shown, using only an intercept and time, gives a time coefficient of 0.102, not significant at the 10% level. Table  3  describes regression models predicting changes in pay and employment. All change variables are constructed via regression interpolation. Changes are not renormalized into z-scores; they are differences in normalized z-scores. These models help us test these null hypotheses: (1) metrics constructed to forecast future automation do not predict past automation, (2) best predictors of automation have not changed in two decades, (3) automation changes do not predict changes in pay or employment. \n Results The first two models of Table  2  suggest that five variables, plus time and an intercept, have substantial predictive power, explaining roughly 15% of automation variation. Automation requires fixed costs, but saves on worker marginal costs. Simple theory thus predicts that, all else equal, employers are more eager to automate jobs with higher pay and employment. These two factors should thus predict job automation, and we do in fact see such effects, though more consistently for pay. Two automation vulnerability metrics built from expert judgments on which jobs seem easier to automate in the future predict which jobs were more automated in the last two decades. Education does not, after our other controls. Model 4 suggests that, aside perhaps from education, these predictors have little to add to the predictive power of the top 25 O*NET variables, which can explain over half of automation variance, even when interpolated. Our two strongest O*NET predictors are Pace Determined By Speed Of Equipment and Importance of Repeating Same Tasks, with coefficients of 0.58 and 0.23. Following these, we find a set of four predictors at roughly 0.14, and a set of five at roughly 0.08. Most of these predictors seem understandable in terms of traditional styles of job automation. For example, Pace Determined By Speed Of Equipment picks out jobs that coordinate closely with machinery, while Importance of Repeating Same Tasks picks out jobs with many similar and independent small tasks. The coefficients in Table  2  that probe time effects do not offer much support for the claim that automation predictors have changed noticeably over time. Model 5 finds only three of 31 time-interaction coefficients are 10% significant, the number to be expected at random. Models 6,7, show no clear differences between time periods. Though we expect automation to have increased over our period, we find no significant time coefficient using only an intercept and time, and adding many controls makes automation seem to have decreased with time. As scores come from expert judgments made at different times, this decrease may be due to drifting standards on what it takes for a job to seen as more automated  (Levari et al., 2018) . If so, the difference between these two time coefficients, roughly 0.37 standard deviations of automation, can be interpreted as estimating this much of an increase in the average suitability of jobs for automation over this period. In Table  3 , changes in pay or employment are only significantly predicted by changes in job automation in one model out of six, where the sign is the opposite of the usual fear. If real, that one coefficient confirms the basic theory that employers gain more from automating jobs with more workers. Changes in pay and employment consistently predict each other, and with large coefficients. This suggests that, in supply and demand terms, labor market changes are on average better seen as changes in demand, and less as changes in supply. Increases in education consistently predict declines in pay and employment, though with small coefficients, suggesting that falling labor demand has been positively correlated with increasing education. Perhaps labor shortages (surpluses) induce firms to adopt weaker (stricter) education requirements. Terms in Table  3  that interact changes in employment and pay with changes in automation suggest that the positive correlation between pay and employment changes is weaker for jobs that saw increased automation. \n Conclusions Recently, many have said we are entering an automation revolution which will soon produce large trend-deviating increases in automation levels and resulting job losses, and also big changes in which kinds of jobs are more vulnerable to automation. We do not yet see evidence of such a revolution. Using 1505 expert reports on the degree of automation of particular jobs 1999-2019, we find that reported automation levels have not changed noticeably, though changing reporting standards may mask such increases. Jobs with larger automation increases did not on average see noticeable changes in pay or employment. Both pay and employment predict automation in the direction suggested by simple theory, as do expert judgments on which jobs are vulnerable to future automation. We can explain over half the variance in which jobs have been how automated using the top 25 O*NET variables, which are relatively mundane and understandable in terms of traditional kinds of automation. All these best predictors have not noticeably changed in two decades. Table 1 1 Variable statistics. Variable Untransformed Transformed Mean Std Dev Min Max Min Max Time 2007.50 6.16 1999 2019 0 1 Education 14.31 2.60 10.28 22.88 -1.839 2.824 Employees 167538 387560 200 4612510 -3.428 2.857 Pay 24.67 13.94 7.18 129.62 -2.331 3.735 Machine Learning Suitability 3.466 0.115 2.780 3.902 -6.609 3.586 Computerisable 0.536 0.368 0.003 0.990 -2.284 0.845 O*NET: Activity 3.374 0.397 1.750 4.620 -5.297 2.629 Advancement 2.723 0.423 1.250 4.000 -4.701 2.444 Cramped 1.932 0.764 1.000 4.900 -1.562 2.680 Dynamic Strength 0.079 0.086 0.000 0.736 -1.389 2.303 Fine Arts 0.040 0.110 0.000 0.974 -0.859 3.784 Gross Body Equilibrium 0.060 0.072 0.000 0.574 -1.326 2.450 Hearing Sensitivity 0.125 0.090 0.000 0.904 -3.253 2.944 Importance of Repeating Same Tasks 2.859 0.846 1.100 5.000 -2.801 1.883 Indoors Environmentally Controlled 3.998 0.945 1.000 5.000 -4.356 0.853 Innovation 3.552 0.489 1.880 4.880 -4.345 2.276 Letters and Memos 3.264 0.791 1.090 5.000 -3.894 1.693 Mathematics 0.264 0.164 0.000 0.989 -4.648 2.218 Number Facility 0.199 0.117 0.000 0.800 -4.712 2.491 On Knees 1.982 0.689 1.000 4.660 -2.205 2.794 Pace Determined by Speed of Equipment 1.839 0.826 1.000 4.760 -1.303 2.588 Physical Proximity 3.451 0.688 1.290 5.000 -4.729 1.923 Spend Time Keeping or Regaining Balance 1.570 0.525 1.000 4.310 -1.321 3.486 Spend Time Sitting 3.126 0.975 1.010 5.000 -3.112 1.523 Supervision Human Relations 3.200 0.467 1.250 4.620 -5.539 2.274 Supervision Technical 2.781 0.585 1.120 4.620 -3.730 2.256 Support 3.778 0.979 1.250 7.000 -5.753 2.618 Thinking Creatively 0.312 0.206 0.000 0.928 -3.456 1.507 Variety 2.791 0.637 1.120 4.120 -3.583 1.699 Visualization 0.221 0.113 0.000 0.657 -5.038 2.028 Wear Common Safety Equipment 2.736 1.346 1.000 5.000 -1.578 1.355 \n Table 2 2 Predicting Automation. Model (1) (2) (3) (4) (5) (6) (7) Intercept 0.2146*** 0.3397*** 0.1474*** 0.1755*** 0.1939* 0.2809*** -0.0097 (0.0550) (0.1043) (0.0435) (0.0456) (0.1011) (0.0828) (0.1545) Time -0.2982*** -1.0041** 0.7372** -0.2451*** -0.2682*** -0.5104 0.2796 -0.6632*** -0.0351 (0.0944) (0.3948) (0.3538) (0.0849) (0.0857) (0.4035) (0.3918) (0.2386) (0.1984) Education 0.0099 -0.1101 0.2452 0.0906** 0.0370 0.0630 0.0938 0.0681 (0.0444) (0.1114) (0.1925) (0.0453) (0.1093) (0.1929) (0.0657) (0.0637) Employees 0.0893*** 0.0422 0.0883 0.0362* -0.0024 0.0611 0.0339 0.0296 (0.0248) (0.0593) (0.1056) (0.0201) (0.0496) (0.0865) (0.0295) (0.0288) Pay 0.2286*** 0.2734*** -0.0937 0.0508 0.0527 -0.0267 0.0586 0.0206 (0.0369) (0.0905) (0.1555) (0.0342) (0.0856) (0.1445) (0.0518) (0.0464) Computerisable 0.3356*** 0.3771*** -0.0820 0.0048 0.0067 0.0069 0.0012 0.0232 (0.0312) (0.0754) (0.1326) (0.0276) (0.0679) (0.1180) (0.0411) (0.0368) M.L. Suitability 0.2161*** 0.2786*** -0.1212 0.0006 0.0273 -0.0463 0.0188 -0.0181 (0.0246) (0.0581) (0.1005) (0.0202) (0.0482) (0.0825) (0.0289) (0.0281) Activity 0.0336 0.0142 -0.0448 0.1116 -0.0082 0.0340 (0.0210) (0.0220) (0.0527) (0.0938) (0.0320) (0.0301) Advancement 0.0656*** 0.0551** 0.1036* -0.0991 0.0605 0.0346 (0.0250) (0.0254) (0.0618) (0.1086) (0.0370) (0.0346) Cramped -0.0527 -0.0594 -0.1391 0.1811 -0.1138* 0.0161 (0.0393) (0.0399) (0.0975) (0.1672) (0.0592) (0.0542) Dynamic Strength -0.0663 -0.0552 -0.0060 -0.1442 -0.0420 -0.1199* (0.0505) (0.0508) (0.1228) (0.2159) (0.0751) (0.0706) Fine Arts -0.0463* -0.0358 -0.0932 0.1117 -0.0706* -0.0157 (0.0267) (0.0270) (0.0637) (0.1108) (0.0401) (0.0368) Gross Body Equilibrium 0.0036 -0.0024 0.0260 -0.0247 0.0269 0.0112 (0.0489) (0.0489) (0.1182) (0.2042) (0.0732) (0.0664) Hearing Sensitivity -0.0713** -0.0757*** -0.0311 -0.0857 -0.0560 -0.0966** (0.0291) (0.0291) (0.0615) (0.1218) (0.0383) (0.0477) Importance of Repeating Same Tasks 0.2240*** 0.2254*** 0.1513** 0.1302 0.1975*** 0.2587*** (0.0317) (0.0326) (0.0770) (0.1458) (0.0449) (0.0546) Indoors Environmentally Controlled 0.1375*** 0.1357*** 0.1491*** -0.0382 0.1358*** 0.1316*** (0.0242) (0.0245) (0.0553) (0.1003) (0.0330) (0.0376) Innovation -0.0887*** -0.0924*** -0.0723 -0.0407 -0.0919*** -0.0938** (0.0248) (0.0251) (0.0545) (0.0999) (0.0346) (0.0385) Letters and Memos 0.1624*** 0.1457*** 0.0748 0.1467 0.1185*** 0.1882*** (0.0273) (0.0281) (0.0653) (0.1151) (0.0399) (0.0408) Mathematics 0.0979** 0.0838** 0.0770 0.0699 0.0734 0.1610** (0.0407) (0.0412) (0.0968) (0.1893) (0.0569) (0.0661) Number Facility 0.0415 0.0400 -0.0151 0.0795 0.0177 0.0141 (0.0359) (0.0359) (0.0794) (0.1679) (0.0467) (0.0624) On Knees -0.0462 -0.0303 -0.0072 -0.0695 0.0150 -0.0991* (0.0418) (0.0427) (0.0997) (0.1721) (0.0632) (0.0581) Pace Determined by Speed of Equipment 0.5638*** 0.5805*** 0.6974*** -0.2315* 0.6360*** 0.5221*** (0.0288) (0.0295) (0.0726) (0.1223) (0.0444) (0.0397) Physical Proximity -0.0694*** -0.0735*** -0.0440 -0.0496 -0.0755** -0.0641* (0.0217) (0.0221) (0.0508) (0.0912) (0.0301) (0.0330) Spend Time Keeping or Regaining Balance -0.0480 -0.0492 -0.0531 0.0049 -0.0599 -0.0368 (0.0395) (0.0400) (0.0953) (0.1632) (0.0587) (0.0546) Spend Time Sitting 0.0545* 0.0428 0.1454* -0.2272* 0.0472 0.0122 (0.0304) (0.0310) (0.0742) (0.1270) (0.0460) (0.0430) Supervision Human Relations -0.0117 -0.0025 -0.0562 0.0714 -0.0059 -0.0156 (0.0318) (0.0322) (0.0895) (0.1505) (0.0542) (0.0424) Supervision Technical 0.0607* 0.1068*** -0.0361 0.2352 0.0554 0.1366** (0.0350) (0.0400) (0.1013) (0.1734) (0.0617) (0.0539) Support 0.0539* 0.0363 0.2297** -0.2896* 0.1004 0.0055 (0.0314) (0.0320) (0.1067) (0.1557) (0.0725) (0.0361) Thinking Creatively -0.1375*** -0.1543*** -0.1222 0.0477 -0.1019* -0.0987 (0.0436) (0.0447) (0.0957) (0.1922) (0.0596) (0.0884) Variety -0.0647** -0.0697** -0.0950 0.0547 -0.0656 -0.0596 (0.0309) (0.0311) (0.0737) (0.1281) (0.0442) (0.0439) Visualization -0.0190 -0.0160 0.0597 -0.2230 -0.0246 -0.0508 (0.0319) (0.0322) (0.0686) (0.1395) (0.0423) (0.0534) Wear Common Safety Equipment -0.1384*** -0.1470*** -0.1847** 0.0813 -0.1579*** -0.1352*** (0.0329) (0.0333) (0.0831) (0.1426) (0.0508) (0.0444) N 1505 1505 1505 1505 1505 821 684 R2 Adjusted 0.1481 0.1509 0.5392 0.5407 0.5441 0.5288 0.5595 R2 0.1515 0.1576 0.5471 0.5501 0.5628 0.5466 0.5795 Dependent variable is Automation (A); *p < .1, **p < .05, ***p < .01, Standard errors in parentheses. \n Table 3 3 Predicting △ Pay, △ Employees. Model (1) (2) (3) (4) (5) (6) Dependent Variable: △ Pay △ Pay △ Pay △ Empl. △ Empl. △ Empl. Intercept 0.376*** 0.387*** 0.386*** -0.021** -0.002 -0.088*** (0.008) (0.011) (0.010) (0.008) (0.012) (0.022) △ A -0.006 -0.007 -0.009 0.001 0.000 0.041*** (0.005) (0.006) (0.006) (0.006) (0.006) (0.015) △ A * A(0) 0.013 0.011 0.009 0.008 (0.008) (0.008) (0.009) (0.009) △ A * △ A 0.006 0.007* 0.003 0.003 (0.004) (0.004) (0.004) (0.004) △ Education -0.015** -0.011* -0.021*** -0.016** (0.006) (0.006) (0.007) (0.007) △ Employees 0.172*** (0.040) △ A * △ Employees -0.078*** (0.028) △ Pay 0.216*** (0.048) △ A * △ Pay -0.104*** (0.035) N 495 495 495 495 495 495 R2 Adjusted 0.0004 0.0092 0.0586 -0.002 0.0115 0.0626 R2 0.0024 0.0172 0.0701 0.000 0.0195 0.0739 A = Automation. Standard errors in parentheses. * p<.1, ** p<.05, ***p<.01", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0165176520301919-main.tei.xml", "abstract": "Wages and employment predict automation in 832 U.S. jobs, 1999 to 2019, but add little to top 25 O*NET job features, whose best predictive model did not change over this period. Automation changes predict changes in neither wages nor employment.", "id": "4227b09035780fbb8df0fdd0e6df15b2"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jessica Taylor", "Eliezer Yudkowsky", "Patrick Lavictoire", "Andrew Critch"], "title": "Alignment for Advanced Machine Learning Systems", "text": "Introduction Recent years' progress in artificial intelligence has prompted renewed interest in a question posed by  Russell and Norvig (2010) : \"What if we succeed?\" If and when AI researchers succeed at the goal of designing machines with cross-domain learning and decision-making capabilities that rival those of humans, the consequences for science, technology, and human life are likely to be large. For example, suppose a team of researchers wishes to use an advanced ML system to generate plans for finding a cure for Parkinson's disease. They might approve if it generated a plan for renting computing resources to perform a broad and efficient search through the space of remedies. They might disapprove if it generates a plan to proliferate robotic laboratories which would perform rapid and efficient experiments, but have a large negative effect on the biosphere. The question is, how can we design systems (and select objective functions) such that our ML systems reliably act more like the former case and less like the latter case? Intuitively, it seems that if we could codify what we mean by \"find a way to cure Parkinson's disease without doing anything drastic,\" many of the dangers  Bostrom (2014)  describes in his book Superintelligence could be ameliorated. However, naïve attempts to formally specify satisfactory objectives for this sort of goal usually yield functions that, upon inspection, are revealed to incentivize unintended behavior. (For examples, refer to  Soares et al. [2015]  and  Armstrong [2015] .) What are the key technical obstacles here?  Russell (2014)  highlights two: a system's objective function \"may not be perfectly aligned with the values of the human race, which are (at best) very difficult to pin down;\" and \"any sufficiently capable intelligent system will prefer to ensure its own continued existence and to acquire physical and computational resources-not for their own sake, but to succeed in its assigned task.\" In other words, there are at least two obvious types of research that would improve the ability of researchers to design aligned AI systems in the future: We can do research that makes it easier to specify our intended goals as objective functions; and we can do research aimed at designing AI systems that avoid large side effects and negative incentives, even in cases where the objective function is imperfectly aligned.  Soares and Fallenstein (2014)  refer to the former approach as value specification, and the latter as error tolerance. In this document, we explore eight research areas based around these two approaches to aligning advanced ML systems, many of which are already seeing interest from the larger ML community. Some focus on value specification, some on error tolerance, and some on a mix of both. Since reducing the risk of catastrophe from fallible human programmers is itself a shared human value, the line between these two research goals can be blurry. For solutions to the problems discussed below to be useful in the future, they must be applicable even to ML systems that are much more capable than the systems that exist today. Solutions that critically depend on the system's ignorance of a certain discoverable fact, or on its inability to come up with a particular strategy, should be considered unsatisfactory in the long term. As discussed by  Christiano (2015c) , if the techniques used to align ML systems with their designers' intentions cannot scale with intelligence, then large gaps will emerge between what we can safely achieve with ML systems and what we can efficiently achieve with ML systems. We will focus on safety guarantees that may seem extreme in typical settings where ML is employed today, such as guarantees of the form, \"After a certain period, the system makes zero significant mistakes.\" These sorts of guarantees are indispensable in safety-critical systems, where a small mistake can have catastrophic real-world consequences. (Guarantees of this form have precedents, e.g., in the KWIK learning framework of  Li, Littman, and Walsh [2008] .) We will have these sorts of strong guarantees in mind when we consider toy problems and simple examples. The eight research topics we consider are: 1. Inductive ambiguity identification: How can we train ML systems to detect and notify us of cases where the classification of test data is highly under-determined from the training data? 2. Robust human imitation: How can we design and train ML systems to effectively imitate humans who are engaged in complex and difficult tasks? 3. Informed oversight: How can we train a reinforcement learning system to take actions that aid an intelligent overseer, such as a human, in accurately assessing the system's performance? 4. Generalizable environmental goals: How can we create systems that robustly pursue goals defined in terms of the state of the environment, rather than defined directly in terms of their sensory data? 5. Conservative concepts: How can a classifier be trained to develop useful concepts that exclude highly atypical examples and edge cases? 6. Impact measures: What sorts of regularizers incentivize a system to pursue its goals with minimal side effects? 7. Mild optimization: How can we design systems that pursue their goals \"without trying too hard\", i.e., stopping when the goal has been pretty well achieved, as opposed to expending further resources searching for ways to achieve the absolute optimum expected score? 8. Averting instrumental incentives: How can we design and train systems such that they robustly lack default incentives to manipulate and deceive the operators, compete for scarce resources, etc.? In Section 2, we briefly introduce each topic in turn, alongside samples of relevant work in the area. We then discuss directions for further research that we expect to yield tools which would aid in the design of ML systems that would be robust and reliable, given large amounts of capability, computing resources, and autonomy. \n Motivations In recent years, progress in the field of machine learning has advanced by leaps and bounds.  Xu et al. (2015)  used an attention-based model to evaluate and describe images (via captions) with remarkably high accuracy.  Mnih et al. (2016)  used deep neural networks and reinforcement learning to achieve good performance across a wide variety of Atari games.  Silver et al. (2016)  used deep networks trained via both supervised and reinforcement learning and paired with Monte-Carlo simulation techniques, to beat the human world champion at Go.  Lake, Salakhutdinov, and Tenenbaum (2015)  use hierarchical Bayesian models to learn visual concepts using only a single example. In the long run, computer systems making use of machine learning and other AI techniques will become more and more capable, and humans will likely trust those systems to make larger decisions and greater autonomy. As the capabilities of these systems increase, it becomes ever-more important that they act in accordance with the intentions of their operators, and without posing risks to society at large. As AI systems gain in capability, it will become more difficult to design training procedures and test regimes that reliably align those systems with the intended goals. As an example, consider the task of training a reinforcement learner to play video games by rewarding it according to its score (as per  Mnih et al. [2013] ). If the learner were to find glitches in the game that allow it to get very high scores, it would switch to a strategy of exploiting those glitches and ignore the features of the game that the programmers are interested in. Somewhat counter-intuitively, improving systems' capabilities can make them less likely to \"win the game\" in the sense we care about, because smarter systems can better find loopholes in training procedures and test regimes. (For a simple example of this sort of behavior with a fairly weak reinforcement learner, refer to  Murphy [2013] .) Intelligent systems' capacity to solve problems in surprising ways is a feature, not a bug. One of the key attractions of learning systems is that they can find clever ways to meet objectives that their programmers wouldn't have thought of. However, this property is a double-edged sword: As the system gets better at finding counter-intuitive solutions, it also gets better at finding exploits that allow it to formally achieve operators' explicit goals, without satisfying their intended goals. For intelligent systems pursuing realistic goals in the world, loopholes can be subtler, more abundant, and much more consequential. Consider the challenge of designing robust objective functions for learning systems that are capable of representing facts about their programmers' beliefs and desires. If the programmers learn that the system's objective function is misspecified, then they will want to repair this defect. If the learner is aware of this fact, however, then it has a natural incentive to conceal any defects in its objective function, for the system's current objectives are unlikely to be achieved if the system is made to pursue different objectives. (This scenario is discussed in detail by  Bostrom [2014]  and  Yudkowsky [2008] .  Benson-Tilsen and Soares [2016]  provide a simple formal illustration.) This motivates the study of tools and methods for specifying objective functions that avert those default incentives, and for developing ML systems that do not \"optimize too hard\" in pursuit of those objectives. \n Relationship to Other Agendas This list of eight is not exhaustive. Other important research problems bearing on AI's long-term impact have been proposed by  Soares and Fallenstein (2014)  and  Amodei et al. (2016) , among others. Soares and Fallenstein's \"Agent Foundations for Aligning Machine Intelligence with Human Interests\" (  2014 ), drafted at the Machine Intelligence Research Institute, discusses several problems in value specification (e.g., ambiguity identification) and error tolerance (e.g., corrigibility, a subproblem of averting instrumental incentives). However, that agenda puts significant focus on a separate research program, highly reliable agent design. The goal of that line of research is to develop a better general understanding of how to design intelligent reasoning systems that reliably pursue a given set of objectives. Amodei et al.'s \"Concrete Problems in AI Safety\" (  2016 ) is, appropriately, more concrete than Soares and Fallenstein or the present agenda. Amodei et al. write that their focus is on \"the empirical study of practical safety problems in modern machine learning systems\" that are likely to be useful \"across a broad variety of potential risks, both short-and long-term.\" There is a fair amount of overlap between our agenda and Amodei et al.'s; some of the topics in our agenda were inspired by conversations with Paul Christiano, a co-author on the concrete problems agenda. Our approach differs from Amodei et al.'s mainly in focusing on broader and less well-explored topics. We spend less time highlighting areas where we can build on existing research programs, and more time surveying entirely new research directions. We consider both Soares and Fallenstein's research proposal and Amodei et al.'s to be valuable, as we expect the AI alignment problem to demand theoretical and applied research from a mix of ML scientists and specialists in a number of other disciplines. For a more general overview of research questions in AI safety, including both strictly near-term and strictly long-term issues in computer science and other disciplines, see  Russell, Dewey, and Tegmark (2015) . \n Eight Research Topics In the discussion to follow, we use the term \"AI system\" when considering computer systems making use of artificial intelligence algorithms in general, usually when considering systems with capabilities that go significantly beyond the current state of the art. We use the term \"ML system\" when considering computer systems making use of algorithms qualitatively similar to modern machine learning techniques, especially when considering problems that modern ML techniques are already used to solve. If the system is capable of making predictions (or answering questions) about a rich and complex domain, we will say that the system \"has beliefs\" about that domain. If the system is optimizing some objective function, we will say that the system \"has goals.\" A system pursuing some set of goals by executing or outputting a series of actions will sometimes be called an \"agent.\" \n Inductive Ambiguity Identification Human values are context-dependent and complex. To have any hope of specifying our values, we will need to build systems that can learn what we want inductively (via, e.g., reinforcement learning). To achieve high confidence in value learning systems, however,  Soares (2016)  argues that we will need to be able to anticipate cases where the system's past experiences of preferred and unpreferred outcomes provide insufficient evidence for inferring whether future outcomes are desirable. More generally, AI systems will need to \"keep humans in the loop\" and recognize when they are (and aren't) too inexperienced to make a critical decision safely. Consider a classic parable recounted by  Dreyfus and Dreyfus (1992) : The US army once built a neural network intended to distinguish between Soviet tanks and American tanks. The system performed remarkably well with relatively little training data-so well, in fact, that researchers grew suspicious. Upon inspection, they found that all of the images of Soviet tanks were taken on a sunny day, while the images of US tanks were taken on a cloudy day. The network was discriminating between images based on their brightness, rather than based on the variety of tank depicted.  1  It is to be expected that a classifier, given training data, will identify very simple boundaries (such as \"brightness\") that separate the data. However, what we want is a classifier that can, given a data set analogous to the tank training set, recognize that it does not contain any examples of Soviet tanks on cloudy days, and ask the user for clarification. Doing so would likely require larger training sets and different training techniques. The problem of inductive ambiguity identification is to develop robust techniques for automatically identifying this sort of ambiguity and querying the user only when necessary. Related work.  Amodei et al. (2016)  discuss a very similar problem, under the name of \"robustness to distributional change.\" They focus on the design of ML systems that behave well when the test distribution is different from the training distribution, either by making realistic statistical assumptions that would allow correct generalization, or by detecting the novelty and adopting some sort of conservative behavior (i.e., querying a human). We take the name from  Soares and Fallenstein (2014) , who call the problem \"inductive ambiguity identification.\" Our framing of the problem differs only slightly from that of Amodei et al. (for instance, they consider \"scalable oversight\" to be a separate problem, while we place the problem of identifying situations where the training data is insufficient to specify the correct reward function under the umbrella of inductive ambiguity identification), but the underlying technical challenge is the same. Bayesian approaches to training classifiers (including Bayesian logistic regression  [Genkin, Lewis, and Madigan 2007]  and Bayesian neural networks  [Blundell et al. 2015; Korattikara et al. 2015] ) maintain uncertainty over the parameters of the classifier. If such a system has the right variables (such as a variable L tracking the degree to which light levels are relevant to the classification of the tank), such a system could automatically become especially uncertain about instances whose classification depends on unknown variables (such as L). The trick is having the right variables (and efficiently maintaining the probability distribution), which is quite difficult in practice. There has been much work studying the problem of feature selection  (Liu and Motoda 2007; Guo and Schuurmans 2012) , but more work is needed to understand under what conditions Bayesian classifiers will correctly identify important inductive ambiguities. Non-Bayesian approaches, on the other hand, do not by default identify ambiguities. For example, neural networks are notoriously overconfident in their classifications  (Goodfellow, Shlens, and Szegedy 2014; Nguyen, Yosinski, and Clune 2015) , and so they do not identify when they should be more uncertain, as illustrated by the parable of the tank classifier.  Gal and Ghahramani (2016)  have recently made progress on this problem by showing that dropout for neural networks can be interpreted as an approximation to certain types of Gaussian processes. The field of active learning (Settles 2010) also bears on inductive ambiguity identification. Roughly speaking, an active learner will maintain a set of \"plausible hypotheses\" by, e.g., starting with a certain set of hypotheses and retaining the ones that assigned sufficiently high likelihood to the training data. As long as multiple hypotheses are plausible, some ambiguity remains. To resolve this ambiguity, an active learner will ask the human to label additional images that will rule out some of its plausible hypotheses. For example, in the tank-detection setting, a hypothesis is a mapping from images (of tanks) to probabilities (representing, say, the probability that the tank is a US tank). In this setting, an active learner may synthesize an image of a US tank on a sunny day (or, more realistically, pick one out from a large dataset of unlabeled examples). When the user labels this image as a US tank, the hypothesis that an image contains a US tank if and only if the light level is below a certain threshold is ruled out.  Seung, Opper, and Sompolinsky (1992)  and  Beygelzimer, Dasgupta, and Langford (2009)  have both studied what statistical guarantees can be achieved in this setting.  Hanneke (2007)  introduced the disagreement coefficient to measure the overall probability of disagreement among a local ball in the concept space under the \"probability of disagreement\" pseudo-metric, which resembles a notion of \"local ambiguity\"; the disagreement coefficient has been used to clarify and improve upper bounds on label complexity for active learning algorithms  (Hanneke 2014) .  Beygelzimer et al. (2016)  introduced an active learning setting where the learner can request counterexamples to hypotheses, and they showed that this search oracle in some cases can speed up learning exponentially; these results are promising, but to scale to more complex systems, more transparent hypothesis spaces may be necessary for humans to interact efficiently with the learner. Much work remains to be done. Modern active learning settings usually either assume a very simple hypothesis class, or assume that test examples are independent and identically distributed and are drawn from some distribution that the learner has access to at training time. 2 Both of these assumptions are far too strong for use in the general case, where the set of possible hypotheses is rich and the environment is practically guaranteed to have regularities and dependencies that were not represented in the training data. For example, consider the case where the data that the ML system encounters during operation depends on the behavior of the system itself-perhaps the Soviets start disguising their tanks (imperfectly) to look like US tanks after learning that the ML system has been deployed. In this case, the assumption that the training data would be similar to the test data is violated, and the guarantees disappear. This phenomenon is already seen in certain adversarial settings, such as when spammers change their spam messages in response to how spam recognizers work. Guaranteeing good behavior when the test data differs from the training data is the subject of research in the adversarial machine learning subfield (see, e.g.,  Huang et al. [2011] ). It will take a fair bit of effort to apply those techniques to the active learning setting. Conformal prediction  (Vovk, Gammerman, and Shafer 2005)  is an alternative non-Bayesian approach that attempts to produce well-calibrated predictions. In an online classification setting, a conformal predictor will give a set of plausible classifications for each instance, and under certain exchangeability assumptions, this set will contain the true classification about (say) 95% of the time throughout the online learning process. This will detect ambiguities in the sense that the conformal predictor must usually output a set containing multiple different classifications for ambiguous instances, on pain of failing to be well-calibrated. However, the exchangability assumption used in conformal prediction is only slightly weaker than an i.i.d. assumption, and the well-calibrated confidence regions (such as 95% true classification) are insufficient for our purposes (where even a single error could be highly undesirable). KWIK (\"Knows What It Knows\") learning  (Li, Littman, and Walsh 2008 ) is a variant of active learning that relaxes the i.i.d. assumption, queries the humans only finitely many times, and (under certain conditions) makes zero critical errors. Roughly speaking, the KWIK learning framework is one where a learner maintains a set of \"plausible hypotheses\" and makes classifications only when all remaining plausible hypotheses agree on how to do so. If there is significant disagreement among the plausible hypotheses, a KWIK learner will output a special value ⊥ indicating that the classification is ambiguous (at which point a human can provide the correct label for that input). The KWIK framework is concerned with algorithms that are guaranteed to output ⊥ only a limited number of times (usually polynomial in the dimension of the hypothesis space). This guarantees that the system eventually has good behavior, assuming that at least one good hypothesis remains plausible. In the tank classification problem, if the system had a hypothesis for \"the user cares about tank type\" and another for \"the user cares about brightness,\" then, upon finding a bright picture of a US tank, the system would output ⊥ and require a human to provide a label for the ambiguous image. Currently, efficient KWIK learning algorithms are only known for simple hypothesis classes (such as small finite sets of hypotheses, or low-dimensional sets of linear hypotheses). Additionally, KWIK learning makes a strong realizability assumption: useful statistical guarantees can only be obtained when one of the hypotheses in the set is \"correct\" in that its probability that the image is classified as a tank is always well-calibrated-otherwise, the right hypothesis might not exist in the \"plausible set\"  (Li, Littman, and Walsh 2008; Khani and Rinard 2016) . Thus, significant work needs to be done before these frameworks can be used for the inductive ambiguity identification algorithms of highly capable AI systems operating in the real world. Directions for future research. Further study of Bayesian approaches to classification, including the design of realistic priors, better methods of inferring latent variables, and extensions of Bayesian classification approaches to represent more complex models, could improve our understanding of inductive ambiguity identification. Another obvious direction for future research is to attempt to extend active learning frameworks, like KWIK, that relax the strong i.i.d. assumption. Research in that direction could include modifications to KWIK that allow more complex hypothesis classes, such as neural networks. This will very likely require making different statistical assumptions than in standard KWIK. What statistical guarantees can be provided in variants of the KWIK framework with weakened assumptions about the complexity of the hypothesis class is an open question. One could also study different methods of relaxing the realizability assumptions in KWIK learning. An ideal learning procedure will notice when the real world contains patterns that none of its hypotheses can model well and flag its potentially flawed predictions (perhaps by outputting ⊥) accordingly. The \"agnostic KWIK learning framework\" of  Szita and Szepesvári (2011)  handles some forms of nonrealizability, but has severe limitations: even if the hypothesis class is linear, the number of labels provided by the user may be exponential in the number of dimensions of the linear hypothesis class. Alternatively, note that the standard active learning framework and the KWIK framework both represent inductive ambiguity as disagreement among specific hypotheses that have performed well in the past. This is not the only way to represent inductive ambiguity; it is possible that some different algorithm will find \"natural\" ambiguities in the data without representing these ambiguities as disagreements between hypotheses. For example, we could consider systems that use a joint distribution over the answers to all possible queries. Where active learners are uncertain about both which hypothesis is correct and what the right answers are given the right hypothesis, a system with a joint would be uncertain only about how to answer queries. In this setting, it may be possible to achieve useful statistical guarantees as long as the distribution contains a grain of truth (i.e., is a mixture between a good distribution and some other distributions). Then, of course, good approximation schema would be necessary, as reasoning according to a full joint would be intractable. Refer to  Christiano (2016a)  for further discussion of this setup. \n Robust Human Imitation Formally specifying a fully aligned general-purpose objective function by hand appears to be an impossibly difficult task, for reasons that also raise difficulties for specifying a correct value learning process. It is hard to see even in principle how we might attain confidence that the goals an ML system is learning are in fact our true goals, and not a superficially similar set of goals that diverge from our own in some yet-undiscovered cases. Ambiguity identification can help here, by limiting the agent's autonomy. Inductive ambiguity identifiers suspend their activities to consult with a human operator in cases where training data significantly under-determines the correct course of action. But what if we take this idea to its logical conclusion, and use \"consult a human operator for advice\" itself as our general-purpose objective function? The target \"do what a trusted human would have done, given some time to think about it\" is a plausible candidate for a goal that one might safely and usefully optimize. At least, if optimized correctly, this objective function leads to an outcome no worse than what would have occurred if the trusted human had access to the AI system's capabilities  (Christiano 2015b) . There are a number of difficulties that arise when attempting to formalize this sort of objective. For example, the formalization itself might need to be designed to avert harmful instrumental strategies such as \"performing brain surgery on the trusted human's brain to better figure out what they actually would have done\". The high-level question here is: Can we define a measurable objective function for human imitation such that the better a system correctly imitates a human, the better its score according to this objective function? Related work. A large portion of supervised learning research can be interpreted as research that attempts to train machines to imitate the way that humans label certain types of data. Deep neural networks achieve impressive performance on many tasks that require emulating human concepts, such as image recognition  (Krizhevsky, Sutskever, and Hinton 2012; He et al. 2015)  and image captioning  (Karpathy and Fei-Fei 2015) . Generative models (as studied by, e.g.,  Gregor et al. [2015]  and  Lake, Salakhutdinov, and Tenenbaum [2015] ) and imitation learning (e.g.,  Judah et al. [2014] ,  Ross, Gordon, and Bagnell [2010] , and  Asfour et al. [2008] ) are state-of-the-art when it comes to imitating the behavior of humans in applications where the output space is very large and/or the training data is very limited. In the inverse reinforcement learning paradigm  (Ng and Russell 2000)  applied to apprenticeship learning  (Abbeel and Ng 2004 ), the learning system imitates the behavior of a human demonstrator in some task by learning the reward function the human is (approximately) optimizing.  Ziebart et al. (2008)  used the maximum entropy criterion to convert this into a well-posed optimization problem. Inverse reinforcement learning methods have been successfully applied to autonomous helicopter control, achieving human-level performance  (Abbeel, Coates, and Ng 2010) , and have recently been extended to the learning of non-linear cost features in the environment, producing good results in robotic control tasks with complicated objectives  (Finn, Levine, and Abbeel 2016) . IRL methods may not scale safely, however, due to their reliance on the faulty assumption that human demonstrators are optimizing for a reward function, where in reality humans are often irrational, ill-informed, incompetent, and immoral; recent work by  Evans, Stuhlmüller, and Goodman (2015b, 2015a)  has begun to address these issues. These techniques have not yet (to our knowledge) been applied to the high-level question of which human imitation tasks can or can't be performed with some sort of guarantee, and what statistical guarantees are possible, but the topic seems ripe for study. It is also not yet clear whether imitation of humans can feasibly scale up to complex and difficult tasks (e.g., a human engineer engineering a new type of jet engine, or a topologist answering math questions). For complex tasks, it seems plausible that the system will need to learn a detailed psychological model of a human if it is to imitate one, and that this might be significantly more difficult than training a system to do engineering directly. More research is needed to clarify whether imitation learning can scale efficiently to complex tasks. Directions for further research. To formalize the question of robust human imitation, imagine a system A that answers a series of questions. On each round, it receives a natural language question x, and should output a natural language answer y that imitates the sort of answer a particular human would generate. Assume the system has access to a large corpus of training data (x 1 , y 1 ), (x 2 , y 2 ), . . . (x n , y n ) of previous questions answered by that human. How can we train A such that we get some sort of statistical guarantee that it eventually robustly generates good answers? One possible solution lies in the generative adversarial models of , in which a second system B takes answers as input and attempts to tell whether they were generated by a human or by A. A can then be trained to generate an answer y that is likely to fool B into thinking that the answer was human-generated. This approach could fail if B is insufficiently capable; for example, if B can understand grammar but not content, then A will only be trained to produce grammatically valid answers (rather than correct answers). Further research is required to understand the limits of this approach. Variational autoencoders, as described by  Kingma and Welling (2013) , are a particularly promising approach to training systems that are able to form generative models of their training data, and it might be possible to use variants on those methods to train systems to generate good answers to certain classes of questions (given sufficient training on question/answer pairs). However, it is not yet clear whether variational autoencoder techniques can be used to train systems to imitate humans performing complex tasks. In particular, unlike generative adversarial models (which can, in principle, use arbitrary algorithms to imitate the human), variational autoencoders can only efficiently imitate a human using \"reversible\" algorithms  (Stuhlmüller, Taylor, and Goodman 2013) , which is a fairly strict limitation. What exactly is the set of tasks that can be performed using reversible generative models? Can we transform non-reversible tasks into reversible ones by adding appropriate information? Research into these questions and others could help us understand whether (and how) modern autoencoder techniques could be used to train systems to imitate humans when performing complex tasks. \n Informed Oversight One of the reasons why robust human imitation would be valuable is the intuition that the objective function of \"do what a trusted human would have approved of, given time to consider\" might be relatively easy to formalize in a way that could be optimized without many adverse side effects. This point is argued by  Christiano (2015a Christiano ( , 2016b , who refers to such agents as \"approval-directed agents.\" For example, we might train a reinforcement learning system to take actions that a human would rate highly by using a framework where the system has to learn the \"human judgment\" reward function, and where training data is produced by actually having a human evaluate the learner's actions. This approach is taken by, e.g., the TAMER framework of  Knox and Stone (2009) , in which a learner myopically pursues short-term human approval. Whether this sort of approval-directed approach would work well for highly capable ML systems pursuing complex tasks depends on a number of key assumptions, one of which is that a \"smarter\" agent (such as a human), given time to deliberate, can adequately oversee the operation of a \"simpler\" agent (such as a reinforcement learner). At first it might seem like this is easy enough. However, a smarter system probably cannot reliably assess the behavior of a simpler system in full generality. Consider an ML system trained to write original novels, using a corpus of human novels as training data. It might be quite a bit less intelligent than a human (according to many different intelligence metrics), but the human may still have a fair bit of trouble accurately evaluating the system's performance. For instance, it might be easy for the system to simply plagiarize a novel, and it might be hard for a human to check whether the novel was in fact plagiarized. (Perhaps the system used a simple rewriting scheme to make the plagiarism difficult to detect by a text search, but still easy to detect for a human comparing the novels side-by-side.) How do we make it easy for the human to assess the performance of an advanced ML system pursuing some particular task? As noted by  Christiano (2016c) , it is not sufficient for the human to be more clever than the system, as some bad actions (such as plagiarism) are easier to execute than they are to detect. For a somewhat less plausible example in which the difficulty is made particularly clear, imagine that a system A is tasked with generating pictures of cats, and a system B is tasked with ensuring that system A is not sending messages to a third party (system C) in the lowest-order bits of the image (which, if system A were generating pictures as intended, would be uniformly random). If both system A and system B know system C's public key, but neither know C's private key, then B has no effective way of distinguishing cat pictures that contain steganographic messages from ones that don't, even if B is more intelligent than A. More important than these specific examples is the general pattern: there are many possible hard-to-detect ways a system's behavior could differ from the intended behavior, and at least some of these differences are undesirable. We would like a general strategy for avoiding problems of this form. How can we train systems to not only take good actions, but take actions that can be accurately assessed by overseers? Related work. As mentioned, the TAMER framework of  Knox and Stone (2009)  provides an early framework for studying approval-directed agents in a fairly myopic setting.  Christiano (2016c)  has also discussed this problem in detail.  Daniel et al. (2014)  extend the TAMER framework with an active learning component, improving over hand-coded reward functions in robot learning tasks. A separate approach to human supervision of ML systems is the cooperative inverse reinforcement learning framework of  Hadfield-Menell et al. (2016) , which views the human-agent interaction as a cooperative game where both players attempt to find a joint policy that maximizes the human's secret value function.  Everitt and Hutter (2016)  describe a general value learning agent that avoids some potential problems with reinforcement learning and might reproduce approval-directed behavior given a good understanding of how to learn reward functions.  Soares et al. (2015)  have considered the question of how to design systems that have no incentive to manipulate or deceive in general. The informed oversight problem is related to the scalable oversight problem discussed by  Amodei et al. (2016) , which is concerned with methods for efficiently scaling up the ability of human overseers to supervise ML systems in scenarios where human feedback is expensive. The informed oversight problem is slightly different, in that it focuses on the challenge of supervising ML systems in scenarios where they are complex and potentially deceptive (but where feedback is not necessarily expensive). We now review some recent work on making ML systems more transparent, which could aid an informed overseer by allowing them to evaluate a system's internal reasons for decisions rather than evaluating the decisions in isolation. Neural networks are a well-known example of powerful but opaque components of ML systems. Some preliminary techniques have been developed for understand-ing and visualizing the representations learned by neural networks  (Simonyan, Vedaldi, and Zisserman 2013; Zeiler and Fergus 2014; Mahendran and Vedaldi 2015; Goodfellow, Shlens, and Szegedy 2014) .  Pulina and Tacchella (2010)  define coarse abstractions of neural networks that can be more easily verified to satisfy safety constraints, and can be used to generate witnesses to violations of safety constraints. Ribeiro, Singh, and Guestrin (2016) introduce a method for explaining classifications that finds a sparse linear approximation to the local decision boundary of a given black-box ML system, allowing the human operator to inspect how the classification depends locally on the most important input features; similarly, the method of  Baehrens et al. (2010)  reports the gradient in the input of the classification judgment. In a related vein,  Datta, Sen, and Zick (2016) ,  Štrumbelj and Kononenko (2014) , and Robnik-Šikonja and Kononenko (2008) define metrics for reporting the influence of various inputs and sets of inputs on the output of a black-box ML system. It is unclear whether black-box methods will scale to the evaluation of highly capable ML systems. On the other extreme, opposite to black-box methods, some ML systems are transparent by construction using, e.g., graphical models or dimensionality reduction  (Vellido, Martín-Guerrero, and Lisboa 2012) . Bayesian networks  (Friedman, Geiger, and Goldszmidt 1997; Pearl 2009 ) have been applied in many domains, including ones where reliability and interpretability are concerns  (Weber et al. 2012) . The interpretability of matrix factorization models can be improved by replacing them with a Bayesian network that makes similar judgments, without sacrificing too much accuracy  (Carmona and Riedel 2015) .  Janzing et al. (2013)  define a framework for quantifying the causal influence between variables in a causal network, which could be used to selectively report only the most causally relevant factor in some judgment. Sparse models offer another approach to ensure transparency, by simplifying the model enough that humans can inspect the entire learned model (if not the training procedure that produced the model). For example,  Letham et al. (2015)  generate short lists of rules to accurately perform predictive tasks in medicine and in simple games, while maintaining interpretability. In the realm of decision-making systems, Baraka, Paiva, and Veloso (2015) and Rosenthal, Selvaraj, and Veloso (  2016 ) have begun research into methods for making online robotics systems more transparent to their operators.  Thomaz and Breazeal (2006)  improved training times for reinforcement learning systems by having the human trainer view the agent's most likely next actions under consideration, and  Li et al. (2015)  applied similar techniques to the TAMER framework, with mixed results. Developing more transparent ML systems is a good first step towards enabling humans to oversee complex AI systems, but work to date has not yet addressed the problems of informed oversight that arise when the system is highly capable and may be able to manipulate human supervisors or circumvent their efforts. Significant work remains to be done before we even understand what sort of formal or statistical guarantees we would want in order to justify confidence in our ability to assess a system's behavior. Directions for future research. Christiano (2016c) has suggested training systems to output both an action a and a \"report\" r intended to help an overseer evaluate the action. In the plagiarism example, the action a would be a story, and the report r could be a list of literary works that the story makes reference to or copies from. We would like the report to be maximally informative, even when this informativeness prevents the action from receiving a high score (such as when the report points out plagiarism). It is not at all clear what the type of r should be in general; i.e., if the system can commit plagiarism, steganography, and some third offence that we did not consider, it is not clear what space of reports is sufficiently open-ended to allow the overseer to detect the suboptimal behavior in all three cases. A plausible research approach is to more clearly understand both what space of reports could be sufficient, and how a system could be trained to optimize the mixed objective of both choosing an action that is evaluated favorably given the reporting mechanism, and a report that is evaluated as informative given the action. \n Generalizable Environmental Goals Many ML systems have their objectives specified in terms of their sensory data. For example, reinforcement learners have the objective of maximizing discounted reward over time (or, alternatively, minimizing expected/empirical loss), where \"reward\" and/or \"loss\" are part of the system's percepts. While these sensory goals can be useful proxies for environmental goals, environmental goals are distinct: Tricking your sensors into perceiving that a sandwich is in the room is not the same as actually having a sandwich in the room. Let's say that your goal is to design an AI system that directly pursues some environmental goal, such as \"ensure that this human gets lunch today.\" How can we train the system to pursue a goal like that in a manner that is robust against opportunities to interfere with the proxy methods used to specify the goals, such as \"the pixels coming from the camera make an image that looks like food\"? If we were training a system to put some food in a room, we might try providing training data by doing things like: placing various objects on a scale in front of a camera, and feeding the data from the camera and the scale into the system, with labels created by humans (which mark the readings from food as good, and the readings from other objects as bad); or having a human in the room press a special button whenever there is food in the room, where button presses are accompanied by reward. These training data suggest, but do not precisely specify, the goal of placing food in the room. Suppose that the system has some strategy for fooling the camera, the scale, and the human, by producing an object of the appropriate weight that, from the angle of the camera and the angle of the human, looks a lot like a sandwich. The training data provided is not sufficient to distinguish between this strategy, and the strategy of actually putting food in the room. One way to address this problem is to design more and more elaborate sensor systems that are harder and harder to deceive. However, this is the sort of strategy that is unlikely to scale well to highly capable AI systems. A more scalable approach is to design the system to learn an \"environmental goal\" such that it would not rate a strategy of \"fool all sensors at once\" as high-reward, even if it could find such a policy. Related work.  Dewey (2011)  and  Hibbard (2012)  have attempted to extend the AIXI framework of  Hutter (2005)  so that it learns a utility function over world-states instead of interpreting a certain portion of its percepts as a reward primitive. 3 Roughly speaking, these frameworks require programs to specify (1) the type of the world-state; (2) a prior over utility functions (which map world-states to real numbers); and (3) a \"value-learning model\" that relates utility functions, statetransitions, and observations. If all these are specified, then it is straightforward to specify the ideal agent that maximizes expected utility (through a combination of exploration to learn the utility function, and exploitation to maximize it). This is a good general framework, but significant research remains if we are to have any luck formally specifying (1), (2), and (3). Everitt and Hutter (2016) make additional progress by showing that in some cases it is possible to specify an agent that will use its reward percepts as evidence about a utility function, rather than as a direct measure of success. While this alleviates the problem of specifying (3) above (the value-learning model), it leaves open the problem of specifying (1), a representation of the state of the world, and (2), a reasonable prior over possible utility functions (such that the agent converges on the goal that the operators actually intended, as it learns more about the world). 3. When the agent is pursuing some objective specified in terms of elements of its own world-model, we call the objective a \"utility function,\" to differentiate this from the case where reward is part of the system's basic percepts. This practice of referring to preferences over world-states as utility functions dates back to von  Neumann and Morgenstern (1944) . The problem of generalizable environmental goals is related to the problem of reward hacking, which has been discussed by  Dewey (2011)  and  Amodei et al. (2016) , wherein an AI system takes control of the physical mechanism that dispenses reward and alters it. Indeed, the entire reward hacking problem can be seen as stemming from the failure to specify suitable environmental goals. Directions for future research. Suppose the AI system has learned a worldmodel with state type S as in model-based reinforcement learning  (Heess et al. 2015) . We will assume that S is very high-dimensional, so there is no guarantee that the correct utility function is a simple function of S. We would like to define a utility function U on S that returns a high number for states containing a sandwich, and low numbers for states that do not contain a sandwich. To make this problem tractable, we will assume we can identify some goal state G ∈ S in which there is certainly a sandwich in the room. This state could be identified by, for example, having the human place a sandwich in the room (as the AI system observes the human), and seeing which state the system thinks the world is in at this point. The system's goal will be to cause the world to be in a state similar to G. To define what it means for some states to be similar to others, we will find a low-dimensional state representation φ : S → R n and then define U (S) := − φ(S) − φ(G) 2 to measure the distance between the state and G. We will defer the question of how φ should be defined until after discussing an example. Consider two different possible world-states. In state A, the system has just placed a sandwich in the room. In state B, the system has placed a realistic image of a sandwich (printed on paper) in front of the camera, placed a rock (with the same weight as a sandwich) on the scale, and tricked the human into pressing the button. To assign a higher utility to state A than state B, we must have φ(A) close to φ(G) but φ(B) far from φ(G). Thus, the state representation φ must distinguish A from B. While state A and state B predict the same immediate observations, they predict different future observations given some future actions. For example, if the AI system took the action of moving the camera, in state A it would become clear that the image was printed on paper, while in state B the sandwich would still appear to be a sandwich. It is therefore plausible that, if the system attempts to select φ so that the future observations following from a state S can be predicted well as a simple function of φ(S), then φ(A) and φ(B) will be significantly different (since they predict different future observations). At this point, it is plausible that the resulting utility function U assigns a higher value to A than B.  4  However, we can consider a third state C that obtains after the AI system unplugs the camera and the scale from its sensors, and plugs in a \"delusion box\" (a virtual reality world that it has programmed), as discussed by  Ring and Orseau (2011) . This delusion box could be programmed so that the system's future observations (given arbitrary future actions) are indistinguishable from those that would follow from state A. Thus, if φ is optimized to select features that aid in predicting future observations well, φ(C) may be very close (or equal) to φ(A). This would hinder efforts to learn a utility function that assigns high utility to state A but not state C. While it is not clear why an AI system would construct this virtual reality world in this example (where putting a sandwich in the room is probably easier that constructing a detailed virtual reality world), it seems more likely that it would if the underlying task is very difficult. (This is the problem of \"wireheading,\" studied by, e.g.,  Orseau and Ring [2011].)  4. This proposal is related to the work of  Abel et al. (2016) , who use a state-collapsing function φ for RL tasks with high-dimensional S. Their agent explores by taking actions in state A that it hasn't yet taken in previous states B with φ(B) = φ(A), where φ maps states to a small set of clusters. They achieve impressive results, suggesting that state-collapsing functions-perhaps mapping to a richer but still low-dimensional representation space-may capture the important structure of an RL task in a way that allows the agent to compare states to the goal state in a meaningful way. To avoid this problem, it may be necessary to take into account the past leading up to state A or state C, rather than just the future starting from these states. Consider the state C t−1 that the world is in right before it is in state C. In this state, the system has not quite entered the virtual reality world, so perhaps it is able to exit the virtual reality and observe that there is no sandwich on the table. Therefore, state C t−1 makes significantly different predictions from state A given some possible future actions. As a result, it is plausible that state φ(C t−1 ) and φ(A) are far from each other. Then, if φ(C) is close to φ(A), this would imply that φ(C t−1 ) is far from φ(C) (by the triangle inequality). Perhaps we can restrict φ to avoid such large jumps in feature space, so that φ(C) must be close to φ(C t−1 ). \"Slow\" features (such as those detected by φ under this restriction) have already proved useful in reinforcement learning  (Wiskott and Sejnowski 2002) , and may also prove useful here. Plausibly, requiring φ to be slow could result in finding a feature mapping φ with φ(C) far from φ(A), so that U can assign a higher utility to state A than to state C. This approach seems worth exploring, but more work is required to formalize it and study it (both theoretically and empirically). \n Conservative Concepts Many of the concerns raised by  Russell (2014)  and  Bostrom (2014)  center on cases where an AI system optimizes some objective, and, in doing so, finds a strange and undesirable edge case. Writes Russell: A system that is optimizing a function of n variables, where the objective depends on a subset of size k < n, will often set the remaining unconstrained variables to extreme values; if one of those unconstrained variables is actually something we care about, the solution found may be highly undesirable. We want to be able to design systems that have \"conservative\" notions of the goals we give them, so they do not formally satisfy these goals by creating undesirable edge cases. For example, if we task an AI system with creating screwdrivers, by showing it 10,000 examples of screwdrivers and 10,000 examples of non-screwdrivers, 5 we might want it to create a pretty average screwdriver as opposed to, say, an extremely tiny screwdriver-even though tiny screwdrivers may be cheaper and easier to produce. We don't want the system's \"screwdriver\" concept to be as simple as possible, because the simplest description of \"screwdriver\" may contain many edge cases (such as very tiny screwdrivers). We also don't want the system's \"screwdriver\" concept to be perfectly minimal, as then the system may claim that it is unable to produce any new screwdrivers (because the only things it is willing to classify as screwdrivers are the 10,000 training examples it actually saw, and it cannot perfectly duplicate any of those to the precision of the scan). Rather, we want the system to have a conservative notion of what it means for something to be a screwdriver, such that we can direct it to make screwdrivers and get a sane result. Related work. The naïve approach is to train a classifier to distinguish positive examples from negative examples, and then have it produce an object which it classifies as a positive instance with as high confidence as possible.  Goodfellow, Shlens, and Szegedy (2014)  have noted that systems trained in this way are vulnerable to exactly the sort of edge cases we are trying to avoid. In training a classifier, it is important that the negative examples given as training data are representative of the negative examples given during testing. But when optimizing the probability the classifier assigns to an instance, the relevant negative examples (edge cases) are often not represented well in the training set. While some work has been done to train systems on these \"adversarial\" examples, this does not yet resolve the problem. Resisting adversarial examples requires getting correct labels for many \"weird\" examples (which humans may find difficult to judge correctly), and even after including many correctly-labeled adversarial examples in the training set, many models (including current neural networks) will still have additional adversarial examples. Inverse reinforcement learning  (Ng and Russell 2000)  provides a second method for learning intended concepts, but runs into some of the same difficulties. Naïve approaches to reinforcement learning would allow a learner to distinguish between positive and negative examples of a concept, but would still by default learn a simple separation of the concepts, such that maximizing the learned reward function would likely lead the system towards edge cases. A third obvious approach is generative adversarial modeling, as studied by . In this framework, one system (the \"actor\") can attempt to create objects similar to positive examples, while another (the \"critic\") attempts to distinguish those objects from actual positive examples in the training set. Unfortunately, for complex tasks it may be infeasible in practice to synthesize instances that are statistically indistinguishable from the elements of the training set, because the system's ability to distinguish different elements may far exceed its ability to synthesize elements with high precision. (In the screwdriver case, imagine that the AI system does not have access to any of the exact shades of paint used in the training examples.) Many of these frameworks would likely be usefully extended by good anomaly detection, which is currently being studied by  Siddiqui et al. (2016)  among others. Directions for future research. One additional obvious approach to training conservative concepts is to use dimensionality reduction  (Hinton and Salakhutdinov 2006)  to find the important features of training instances, then use generative models to synthesize new examples that are similar to the training instances only with respect to those specific features. It is not yet clear that this thwarts the problem of edge cases; if the dimensionality reduction were done via autoencoder, for example, the autoencoder itself may beget adversarial examples (\"weird\" things that it declares match the training data on the relevant features). Good anomaly detection could perhaps ameliorate some of these concerns. One plausible research path is to apply modern techniques for dimensionality reduction and anomaly detection, probe the limitations of the resulting system, and consider modifications that could resolve these problems. Techniques for solving the inductive ambiguity identification problem (discussed in Section 2.1) could also help with the problem of conservative concepts. In particular, the conservative concept could be defined to be the set of instances that are considered unambiguously positive. At the moment, it is not yet entirely clear what counts as a \"reasonable\" conservative concept, nor even whether \"conservative concepts\" (that is, concepts which are neither maximally small nor maximally simple, but which instead match our intuitions about conservatism) are a natural kind. Much of the above research could be done with the goal in mind of developing a better understanding of what counts as a good \"conservative concept.\" \n Impact Measures We would prefer a highly intelligent AI system to avoid creating large unintended-byus side effects in pursuit of its objectives, and also to notify us of any large impacts that might result from achieving its goal. For example, if we ask it to build a house for a homeless family, it should know implicitly that it should avoid destroying nearby houses for materials-a large side effect. However, we cannot simply design it to avoid having large effects in general, since we would like the system's actions to still have the desirable large follow-on effect of improving the family's socioeconomic situation. For any specific task, we can specify ad-hoc cost functions for side effects like the destruction of nearby houses, but since we cannot always anticipate such costs in advance, we want a quantitative understanding of how to generally limit an AI systems' side effects (without also limiting its ability to have large positive intended impacts). The goal of research towards a low-impact measure would be to develop a regularizer on the actions of an AI system that penalizes \"unnecessary\" large side effects (such as stripping materials from nearby houses) but not \"intended\" side effects (such as someone getting to live in the house). Related work.  Amodei et al. (2016)  discuss the problem of impact measures, and describe a number of methods for defining, learning, and penalizing impact in order to incentivize RL agents to steer clear of negative side effects (such as penalizing empowerment, as formalized by  Salge, Glackin, and Polani [2014] ). However, each of the methods they propose has significant drawbacks (which they describe).  Armstrong and Levinstein (2015)  discuss a number of ideas for impact measures that could be used to design objective functions that penalize impact. The general theme is to define a special null policy ∅ and a variable V that summarizes the state of the world (as best the system can predict it) down into a few key features. (Armstrong suggests having those features be hand-selected, but they could plausibly also be generated from the system's own world-model.) The impact of the policy π can then be measured by looking at the divergence between the distribution of V if the system executes π, compared to the distribution of V if it executes ∅, with divergence measured as by, e.g., earth mover's distance  (Rubner, Tomasi, and Guibas 2000) . To predict which state results from each policy, the system must learn a state transition function; this could be done using, e.g., model-based reinforcement learning  (Heess et al. 2015) . The main problem with this proposal is that it cannot separate intended follow-on effects from unintended side effects. Suppose a system is given the goal of constructing a house for the operator while having a low impact. Normally, constructing the house would allow the operator to live in the house for some number of years, possibly having effects on the operator, the local economy, and the operator's career. This would be considered an impact under, e.g., the earth mover's distance. Therefore, perhaps the system can get a lower impact score by building the house while preventing the operator from entering it. This limitation will become especially problematic if we plan to use the system to accomplish large-scale goals, such as curing cancer. Directions for future research. It may be possible to use the concept of a causal counterfactual (as formalized by  Pearl [2000] ) to separate some intended effects from some unintended ones. Roughly, \"follow-on effects\" could be defined as those that are causally downstream from the achievement of the goal of building the house (such as the effect of allowing the operator to live somewhere). Follow-on effects are likely to be intended and other effects are likely to be unintended, although the correspondence is not perfect. With some additional work, perhaps it will be possible to use the causal structure of the system's world-model to select a policy that has the follow-on effects of the goal achievement but few other effects. Of course, it would additionally be desirable to query the operator about possible effects, in order to avoid unintended follow-on effects (such as the house eventually collapsing due to its design being structurally unsound) and allow tolerable nonfollow-on effects (such as spending money on materials). Studying ways of querying the operator about possible effects this way might be another useful research avenue for the low impact problem. \n Mild Optimization Many of the concerns discussed by  Bostrom (2014)  in the book Superintelligence describe cases where an advanced AI system is maximizing an objective as hard as possible. Perhaps the system was instructed to make paperclips, and it uses every resource at its disposal and every trick it can come up with to make literally as many paperclips as is physically possible. Perhaps the system was instructed to make only 1000 paperclips, and it uses every resource at its disposal and every trick it can come up with to make sure that it definitely made 1000 paperclips (and that its sensors didn't have any faults). Perhaps an impact measure was used to penalize side effects, and it uses every resource at its disposal to (as discreetly as possible) prevent bystanders from noticing it as it goes about its daily tasks. In all of these cases, intuitively, we want some way to have the AI system just \"not try so hard.\" It should expend enough resources to achieve its goals pretty well, with pretty high probability, using plans that are clever enough but not \"maximally clever.\" The problem of mild optimization is: how can we design AI systems and objective functions that, in this intuitive sense, don't optimize more than they have to? Many modern AI systems are \"mild optimizers\" simply due to their lack of resources and capabilities. As AI systems improve, it becomes more and more difficult to rely on this method for achieving mild optimization. As noted by  Russell (2014) , the field of AI is classically concerned with the goal of maximizing the extent to which automated systems achieve some objective. Developing formal models of AI systems that \"try as hard as necessary but no harder\" is an open problem, and may require significant research. Related work. Regularization (as a general tool) is conceptually relevant to mild optimization. Regularization helps ML systems prevent overfitting, and has been applied to the problem of learning value functions for policies in order to learn less-extreme policies that are more likely to generalize well  (Farahmand et al. 2009) . It is not yet clear how to regularize algorithms against \"optimizing too hard,\" because it is not yet clear how to measure optimization. There do exist metrics for measuring something like optimization capability (such as the \"universal intelligence metric\" of  Legg and Hutter [2007]  and the empowerment metric for information-theoretic entanglement of  Klyubin, Polani, and Nehaniv [2005]  and  Salge, Glackin, and Polani [2014] ), but to our knowledge, no one has yet attempted to regularize against excessive optimization. Early stopping, wherein an algorithm is terminated prematurely in attempts to avoid overfitting, is an example of ad-hoc mild optimization. A learned function that is over-optimized just for accuracy on the training data would generalize less well than if it were less optimized. (For a discussion of this phenomenon, refer to  Yao, Rosasco, and Caponnetto [2007]  and  Hinton et al. [2012] ). To make computer games more enjoyable, AI players are often restricted in the amount of optimization pressure (such as search depth) they can apply to their choice of action  (Rabin 2010) , especially in domains like chess where efficient AI players are vastly superior to human players. We can view this as a response to the fact that the actual goal (\"challenge the human player, but not too much\") is quite difficult to specify.  Bostrom (2014)  has suggested that we design agents to satisfice expected reward, in the sense of  Simon (1956) , instead of maximizing it. This would work fine if the system found \"easy\" strategies before finding extreme strategies. However, that may not always be the case: If you direct a clever system to make at least 1,234,567 paper clips, with a satisficing threshold of 99.9% probability of success, the first strategy it considers might be \"make as many paper clips as is physically possible,\" and this may have more than a 99.9% chance of success (a flaw that Bostrom acknowledges).  Taylor (2015)  suggests an alternative, which she calls \"quantilization.\" Quantilizers select their action randomly from the top (say) 1% of their possible actions (under some measure), sorted by probability of success. Quantilization can be justified by certain adversarial assumptions: if there is some unknown cost function on actions, and this cost function is the least convenient possible cost function that does not assign much expected cost to the average action, then quantilizing is the optimal strategy when maximizing expected reward and minimizing expected cost. The main problem with quantilizers is that it is difficult to define an appropriate measure over actions, one such that a random action in the top 1% of this measure will likely solve the task, but sampling a random action according to that measure is still safe. However, quantilizers point in a promising direction: perhaps it is possible to make mild optimization part of the AI system's goal, by introducing appropriate adversarial assumptions. Directions for future research. Mild optimization is a wide-open field of study. One possible first step would be to investigate whether there is a way to design a regularizer that penalizes systems for displaying high intelligence (relative to some intelligence metric) in a manner that causes them to achieve the goal quickly and with few wasted resources, as opposed to simply making the system behave in a less intelligent fashion. Another approach would be to design a series of environments similar to the environment of a classic Atari game, in which the environment contains glitches and bugs that could be exploited via some particularly clever sequence of actions. This would provide a testing environment in which different methods of designing systems that get a high score while refraining from using the glitches and bugs could be tested and evaluated (with an eye towards algorithms that do so in a fashion that is likely to generalize). Another avenue for future research is to explore and extend the quantilization framework of  Taylor (2015)  to work in settings where the action measure is difficult to specify. Research into averting instrumental incentives (discussed below) could help us understand how to design systems that do not attempt to self-modify or outsource computation to the physical world. This would simplify the problem greatly, as it might then be possible to tune a system's capabilities until it is only able to achieve good-enough results, without worrying that the system would simply acquire more resources (and start maximizing in a non-mild manner) given the opportunity to do so. \n Averting Instrumental Incentives Omohundro (2008) has noted that highly capable AI systems should be expected to pursue certain convergent instrumental strategies, such as preservation of the system's current goals and the acquisition of resources. Omohundro's argument is that most objectives imply that an agent pursuing the objective should (1) ensure nobody redirects the agent towards different objectives, as then the current objective would not be achieved; (2) ensure that the agent is not destroyed, as then the current objective would not be achieved; (3) become more resource-efficient; (4) acquire more resources, such as computing resources and energy sources; and (5) improve cognitive capacity. It is difficult to define practical objective functions that resist these pressures (Benson-Tilsen and Soares 2016). For example, if the system is rewarded for shutting down when the humans want it to shut down, then the system has incentives to take actions that make the humans want to shut it down  (Armstrong 2010) . A number of \"value learning\" proposals, such as those discussed by  Hadfield-Menell et al. (2016)  and  Soares (2016) , describe systems that would avert instrumental incentives by dint of the system's uncertainty about which goal it is supposed to optimize. A system that believes that the operators (and only the operators) possess knowledge of the \"right\" objective function might be very careful in how it deals with the operators, and this caution could counteract potentially harmful default incentives. This, however, is not the same as eliminating those incentives. If a value learning system were ever confidently wrong, the standard instrumental incentives would re-appear immediately. For instance, if the value learning framework were set up slightly incorrectly, and the system gained high confidence that humans terminally value the internal sensation of pleasure, it might acquire strong incentives to acquire a large amount of resources that it could use to put as many humans as possible on opiates. If we could design objective functions that averted these default incentives, that would be a large step towards answering the concerns raised by  Bostrom (2014)  and others, many of which stem from the fact that these subgoals naturally arise from almost any goal. Related work.  Soares et al. (2015)  and  Orseau and Armstrong (2016)  have worked on specific designs that can avert specific instrumental incentives, such as the incentive to manipulate a shutdown button or the incentive to avoid being interrupted. However, these approaches have major shortcomings (discussed in those papers), and a satisfactory solution will require more research. Where those authors pursue methods for averting specific instrumental pressures (namely, pressure to avoid being shut down), it is possible that there may be a general solution to problems of this form, which can be used to simultaneously avert numerous instrumental pressures (including, e.g., the incentive to outsource computation to the environment). Given that a general-purpose method for averting all instrumental pressures (both foreseen and unforeseen) would make it significantly easier to justify confidence that an AI system will behave in a robustly beneficial manner, this topic of research seems well worth pursuing. Directions for future research.  Soares et al. (2015) ,  Armstrong (2010) , and  Orseau and Armstrong (2016)  study methods for combining objective functions in such a way that the humans have the ability to switch which function an agent is optimizing, but the agent does not have incentives to cause or prevent this switch. All three approaches leave much to be desired, and further research along those paths seems likely to be fruitful. In particular, we would like a way of combining objective functions such that the AI system (1) has no incentive to cause or prevent a shift in objective function; (2) is incentivized to preserve its ability to update its objective function in the future; and (3) has reasonable beliefs about the relation between its actions and the mechanism that causes objective function shifts. We do not yet know of a solution that satisfies all of these desiderata. Perhaps a solution to this problem will generalize to also allow the creation of an AI system that also has no incentive to change, for example, the amount of computational resources it has access to. Another approach is to consider creating systems that \"know they are flawed\" in some sense. The idea would be that the system would want to shut down as soon as it realizes that humans are attempting to shut it down, on the basis that humans are less flawed than it is. It is difficult to formalize such an idea; naïve attempts result in a system that attempts to model the different ways it could be flawed and optimize according to a mixture over all different ways it could be flawed, which is problematic if the model of various possible flaws is itself flawed. While it is not at all clear how to make the desired type of reasoning more concrete, success at formalizing it could result in entirely new approaches to the problem of averting instrumental incentives. \n Conclusion A better understanding of any of the eight open research areas described above would improve our ability to design robust and reliable AI systems in the future. To review: 1,2,3-A better understanding of robust inductive ambiguity identification, human imitation, and informed oversight would aid in the design of systems that can be safely overseen by human operators (and which query the humans when necessary). 4-Better methods for specifying environmental goals would make it easier to design systems that are pursuing the objectives that we actually care about. 5,6,7-A better understanding of conservative concepts, low-impact measures, and mild optimization would make it easier to design highly advanced systems that fail gracefully and admit of online testing and modification. A conservative, low-impact, mildly-optimizing superintelligent system would be much easier to safely use than a superintelligence that attempts to literally maximize a particular objective function. 8-A general-purpose strategy for averting convergent instrumental subgoals would help us build systems that avert undesirable default incentives such as incentives to deceive their operators and compete for resources. In working on problems like those discussed above, it is important to keep in mind that they are intended to address whatever long-term concerns with highly intelligent systems we can predict in advance. Solutions that work for modern systems but would predictably fail for highly capable systems are unsatisfactory, as are solutions that work in theory but are prohibitively expensive in practice. These eight areas of research help support the claim that there are open technical problems-some of which are already receiving a measure of academic attentionwhose investigation is likely to be helpful down the road for practitioners attempting to actually build robustly beneficial advanced ML systems. \t\t\t . Tom Dietterich relates a similar story(personal conversation, 2016), where in his laboratory, years ago, microscope slides containing different types of bugs were made on different days, and a classifier learned to classify the different types of bugs with remarkably high accuracy-because the sizes of the bubbles in the slides changed depending on the day. \n\t\t\t . Some forms of online active learning (refer to, e.g. Dekel, Gentile, and Sridharan [2012] ) relax the i.i.d. assumption, but the authors do not see how to apply them to the problem of inductive ambiguity identification. \n\t\t\t . In the simplest case, we can assume that these objects are specified as detailed 3D scans. If we have only incomplete observations of these objects, problems described in Section 2.4 arise.", "date_published": "n/a", "url": "n/a", "filename": "AlignmentMachineLearning.tei.xml", "abstract": "We survey eight research areas organized around one question: As learning systems become increasingly intelligent and autonomous, what design principles can best ensure that their behavior is aligned with the interests of the operators? We focus on two major technical obstacles to AI alignment: the challenge of specifying the right kind of objective functions, and the challenge of designing AI systems that avoid unintended consequences and undesirable behavior even in cases where the objective function does not line up perfectly with the intentions of the designers. Open problems surveyed in this research proposal include: How can we train reinforcement learners to take actions that are more amenable to meaningful assessment by intelligent overseers? What kinds of objective functions incentivize a system to \"not have an overly large impact\" or \"not have many side effects\"? We discuss these questions, related work, and potential directions for future research, with the goal of highlighting relevant research topics in machine learning that appear tractable today.", "id": "2eca689e5670db01dab98ba2438cc284"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld"], "title": "Formalizing preference utilitarianism in physical world models", "text": "Introduction Usually, ethical imperatives are not formulated with sufficient precision to study them and their realization mathematically.  (McLaren 2011, p. 297; Gips 2011, p. 251)  In particular, it is impossible to implement them on an intelligent machine to make it behave benevolently in our universe, which is the subject of a field known as Friendly AI (e.g. see  Yudkowsky 2001, p. 2)  or machine ethics (e.g. see  Anderson and Anderson 2011, p. 1) . Whereas existing formalizations of utilitarian ethics have been successfully applied to economics, they are incomplete due to the nature of their dualistic world model in which agents are assumed to be ontologically fundamental. In this paper however, we take the following steps towards a workable and simple formalization of preference utilitarianism 1 in physical world models: -We describe the problem of informality in ethics and the shortcomings of previous dualist approaches to formalizing utilitarian ethics (Sect. 2). -We justify cellular automata as a world model, use Bayes' theorem to extract utility functions from a given space-time embedded agent and introduce a formalization of preference utilitarianism (Sect. 3). -We compare our approach with existing work in ethics, game theory and artificial intelligence (Sect. 4). Our formalization is novel but nevertheless relates to a growing movement to treat agents as embedded into the environment. \n The problem of formalizing ethics in physical systems Discussion on informally specified moral imperatives can be difficult due to different interpretations of the texts describing the imperative. Thus, formalizing moral imperatives could augment informal ethical discussion.  (Gips 2011, p. 251; Anderson 2011; Dennett 2006; Moor 2011, p. 19 ) Furthermore, science and engineering answer formally described questions and solve well-specified tasks, but are not immediately applicable to the informal question of how to make the world \"better\". This problem has been identified in economics and game theory, which has led to some very useful formalizations of utilitarianism (e.g.  Harsanyi 1982 ). However, their formalization relies on consciousness-matter dualism: The agents are not part of the physical world or embedded into it, so that their thoughts or computations can not be influenced by physical laws. Also, agents' utility functions are assumed to not depend on the agents (or their physical configurations) themselves. These are typical assumptions in game theory. After all, game theory is about games, in which players are not actually inside the game, nor can they decide themselves what goals to pursue. This classic (multi-)agent-environment model is depicted in Fig.  1 . Our world, however, is (usually presumed to be) a purely physical system: ethically relevant entities (animals etc.) are embedded in the environment. For example, our brains behave according to the same laws of physics as the rest of the world. Also, happiness and preferences are not given by predetermined utility functions or rewards from the environment, but are the result of physical processes in our bodies. Therefore, dualist descriptions and formalizations leave questions unanswered: (compare Orseau and Ring 2012) -What objects are ethically relevant? (What are the agents of our non-dualist world?) -What is a space-time embedded agent's or, more generally, an object's utility function? Thus, even though classic formalizations of (preferentist) utilitarianism in the agentenvironment-model can formalize the vague notions of goals and preferences with  \n A Bayesian approach to formalizing preference utilitarianism in physical systems \n Cellular automata as non-dualist world models To overcome the described problems of dualist approaches to utilitarianism, we first have to choose a new, physical setting for our ethical imperative. Instead of employing string theory and other contemporary theoretical frameworks, we choose a model that is much more simple to handle formally: cellular automata. These have sometimes even been pointed out to be candidates for modeling our own universe,  (Wolfram 2002, ch. 9; Schmidhuber 1999; Zuse 1967 Zuse , 1969  but even if physics will prove cellular automata to be a wrong model, they may still be of instrumental value for the purpose of this paper.  (compare Downey 2012, pp. 70f., 77-79; Hawking and Mlodinow 2010, ch. 8)  For detailed introductions to classic cellular automata with neighbor-based rules, see  Wolfram (2002)  or  Shiffman (2012, ch. 7 ) for a purely informal and  Wolfram (1983)  for a slightly more technical treatment that focuses on one-dimensional cellular automata. In Sect. 3.1.1, we will consider a generalized and relatively simple formalism, which is not limited to rules that only depend on neighbors of a cell. In CA, it is immediately clear that for a (preference) utilitarian morality we have to answer the questions that are avoided by assuming a set of agents and their utility functions to be known from the beginning. It also frees us from many ethical intuitions that we build up specifically for our own living situations and reduces moral intuition to its very fundamentals. Figure  2  shows a state of a cellular automaton illustrating the problem of defining utilitarianism or any other ethical imperative in physical models. Clearly, many intuitions are very difficult (if not impossible) to formulate universally and precisely in CA. Thereby, the required formality helps in choosing and defining an ethical imperative.  \n A formal introduction to cellular systems We now introduce some very basic notation and terminology of cellular systems, a generalization of classic cellular automata, thus setting the scene for our ethical imperative. For given sets A and B, let A B denote the set of functions from B to A. A cellular system is a triple (C, S, d) of a countable set of cells C, a finite set of cell states S and a function d : S C → S C that maps a world state s : C → S onto its successor. So basically a world consists of a set of cells that can have different values and a function that models deterministic state-transitions.  2  Cells of cellular systems do not necessarily have to be on a regular grid and computing new states does not have to be done via neighbor-based lookup tables. This makes formalization much easier. But before anything else, we have to define structures which represent objects in our cellular systems. A space Spc ⊆ C in a cellular system (C, S, d) is a finite subset of the set of cells C. A structure str on a space Spc is a function str : Spc → S that maps the cells of the space onto cell values. A history is a function h : N → S C that maps natural numbers as time steps onto states of the system. For example, the history h s of an initial state s can then be defined recursively by h s (n) = d(h s (n − 1)) for n ≥ 1 with the base case h s (0) = s. \n Posterior probabilities and the priority of a (given) goal to a given agent Before extracting preferences from a given structure, we have to decide on a model of preferences. Preferences themselves are mere orderings of alternative outcomes or lotteries over these outcomes with the outcomes being entire histories h ∈ (S C ) N in our case. The problem is that this makes it difficult to compare two outcomes when the preferences of multiple individuals are involved. To be able to make such comparisons, we move from orderings to utility functions u : (S C ) N → R that map histories of the world onto their (cardinal) utilities.  3  This will make it possible to just add up the utilities of different individuals and then compare the sum among outcomes. This by no means \"solves\" the problem of interpersonal comparison. Rather, it makes it more explicit. For example, a given set of preferences is represented equally well by u and 2 • u, but ceteris paribus 2 • u will make the preferences more significant in summation. Different approaches to the problem have been proposed.  (Hammond 1989)  In this paper we will ignore the problem (or hope that the fair treatment in determining all individuals' utility functions induces moral permissibility). Now we ask the question: Does a particular structure str want to maximize some utility function u? It is fruitful to think about how one would approach such questions in our world, when encountering some very odd organism. At least one possible approach would be to put it into different situations or environments and see what it does to them. If the structure increases some potential utility function in different environments, it seems as if this utility function represents an aspect of the structure's preferences.  4  However, for some utility functions it is not very special that their values are increased and then it might just be coincidence that the structure in question also does so. For example, it is usually not considered a structure's preference to increase entropy even if entropy increases in environments including this structure, because an increase in entropy is extremely common with or without the structure. Also, we feel that some utility functions are less likely than others by themselves, e.g. because they are very complex or specific. But how can we formally capture these notions? Since uncertainty is involved, we interpret the degree to which a utility function u is important to some structure str that exists at time step i as the posterior probability of that utility function given the structure, a probability we denote by P(u|str@i), where str@i denotes the event that str exists in time step i.  5  Here, the utility function is interpreted as a hypothesis about the structure's \"true intentions\" 6 . In a purely physical, non-dualist world there is nothing but the structure itself, of course. Therefore, the \"true intentions\" do not really exist, which makes it still hard to know what P(u|str@i) is supposed to mean. To finally overcome this problem, we will equate intention and purpose, i.e. we equate the following interpretations of u as a hypothesis explaining the data str@i:  (compare Dennett 1989, pp. 289ff., 299f., 318, 320f.)  -The utility function u is the goal of structure str. -Maximizing u was the goal of an entity that chose str. The second interpretation is more useful, because it describes a data-generating process and thus comes closer to typical statistical models. Thus, we have to find the posterior probability of some model (a utility function) given some data (a structure). For this problem Bayes' theorem suggests itself, because it provides an equation for posterior probabilities. In our case, Bayes' theorem can be used to infer the likelihood that some utility function was a goal when a structure was chosen from some priors and the likelihood of choosing the structure given that the goal is to maximize the utility function. Specifically, Bayes' theorem gives us P(u|str@i) = P(str@i|u) • P(u) P(str@i) , ( 1 ) where P(u) and P(str@i) are prior probability distributions of utility functions and structures, respectively, and P(str@i|u) is the probability of (some hypothetical entity choosing) str at time step i when u is to be maximized. Whereas P(u|str@i) is very hard to grasp intuitively, it is more clear what the probability distributions on the right hand side of the equation mean. Nevertheless, they do not correspond to measurable probability distributions like the results from rolling a dice. Indeed, P(u) and P(str@i) are ultimately subjective (e.g. see  Olshausen 2004, pp. 1f .; Robert 1994, p. 9) and P(str@i|u) depends on what exactly the hypothesis u is supposed to express, thus leaving our ethical imperative parametrized by these distributions. Footnote 5 continued history, because then structures cannot have preferences about themselves (\"personal happiness\") without also having preferences about all other identical structures (at the same place). An alternative would be to apply utility functions only to the part of the history from the point of the existence of the structure onwards, so that identical structures at different points in time have equal utility functions that are applied differently. However, it seems like this neglects that the past can depend on the action of an agent in the present, as illustrated in Newcomb's paradox by  Nozick (1969) .  6  Intuitively, some structures can have more than one utility function, while others have no utility function at all. One way to model this would be to understand different utility functions as events in separate sample spaces. So, the sum u P(u|str) could vary among different structures str. A similar scenario is the inference of multiple diseases from a set of symptoms.  (Charniak 1983)  While some individuals may have no diseases or preferences at all, others may be thought of as having more than one disease or utility function. In more technical terms, for each utility function there would be a sample space of having that utility function and not having that utility function. In this paper however, we will assume mutual exclusivity and collective exhaustiveness of utility functions. All utility functions live in the same sample space and thus u P(u|str) = 1 for all structures str. This does not mean that all structures have equal moral standing: The idea is that \"meaningless\" structures str have high P(u|str) only for constant utility functions u, i.e. for \"don't care\"-utility functions, which are irrelevant for decision making. Nonetheless, there seem to be canonical approaches. P(str@i|u) should be understood as the probability that str is chosen at time step i by an approximately rational agent that wants to maximize u. So, structures that are better at maximizing or more suitable for u should receive higher P(str@i|u) values. This corresponds to the assumption of (approximate) rationality in Dennett's intentional stance.  (Dennett 1989, pp. 21, 49f.)  Unfortunately, the debate about causal and evidential decision theory (e.g.  Peterson 2009, ch. 9)  shows that formalizing the notion of rational choice is difficult. The prior of utility functions P(u) on the other hand should denote the \"intrinsic plausibility\" of a goal u. That does not have to mean defining and excluding \"evil\" or \"banal\" utility functions. In the preference extraction context, utility functions are models or hypotheses that explain the behavior of a structure. And Solomonoff's formalization of Occam's razor is often cited as a universal prior distribution of hypotheses.  (Legg 1997 ) It assumes complicated hypotheses (utility functions), i.e. ones that require more symbols to be described in some programming language, to be less likely than simpler ones. If utility functions are conceived of as competing hypotheses (see footnote 6), then P(str@i) = u P(str@i|u) • P(u). Otherwise, P(str@i) could potentially be chosen more freely. Finally, note how Bayes' theorem catches our intuitions from above, especially when assuming probability distributions similar to the suggested ones: When some structure str maximizes some utility function u very well, then P(str@i|u) and thereby the relevance of the utility function to the object would increase. On the other hand, if many other structures are comparably good, then the probability for each one to be chosen when given the utility function is smaller (due to the sum of the probabilities of all possible structures on a given space and time step being 1) and the probability of the utility function being a real preference would decrease with it. Finally, multiplying by P(u) catches abstruse utility functions, e.g. utility functions that are specifically suited to be fulfilled by the structure in question. \n An individual structure's welfare function Having introduced a way of determining how likely it is that some utility function is the utility function of some object, we define the welfare U str@i of a structure str that exists at some step i of a history h, as the weighted sum over all utility functions U str@i = u P(u|str@i)u(h), ( 2 ) where h is the history and the sum is over all theoretically possible utility functions u : (S C ) N → R. We call this term expected utility, because this expression is generally used for adding utilities based on their likelihood, which is a common concept. However, the term usually suggests that there is also an actual utility. In our case of ascribing preferences to physical objects however, no such thing exists. We only imagine there to be some real utility or welfare functions and that we use Bayesian inference to find them. But in fact, the structure itself is all there exists and thus the expected utility is as actual as possible. The sum in the term for expected utility is over an uncountably infinite set, which can only converge when only countably many summands are non-zero. 7 Some other concerns are described in footnote 9 and addressed in footnote 10. \n Summing over all agents The utilitarian imperative is to maximize a global welfare function that is the sum of all individuals' welfare functions. We already defined the welfare function of single structures. So next we have to define what the set of all agents is and how to sum over it. As foreshadowed before, we will consider all possible structures of a cellular automaton using Eq. 2 and rely on (intuitively) irrelevant ones to receive high P(u|str@i) values only for constant and therefore irrelevant utility functions u (see footnote 6). To sum the utility over all agents, we not only have to sum over all structures in a particular state, but first over all (discrete) time steps of the history of the cellular automaton world and only then over all structures in every state. This way, we sum the welfare of all agents ever coming into existence. For the summands, we can insert the term obtained in Eq. 2 i str@i U str@i = i str@i u P(u|str@i)u(h), ( where U str@i denotes the welfare or utility of the structure str that exists at time step i, the first sum is over all integers functioning as time steps, the second is over all structures in h(i) and the third over all possible utility functions. 8 So, our formalization of the main imperative of preference utilitarianism turns out to be nothing more than maximizing global, all-time expected utility (of every space-time embedded agent that ever comes into existence). In general, the value of the series depends on the order of these infinite sums. 9 Also, the series can diverge. Nonetheless it may still be usable for comparing histories in many cases. 10 \n Related work Preferentist utilitarianism has become a common form of utilitarianism in the second half of the 20th century, with the best known proponents being Hare and Singer. However, the intuitions underlying the presented formalization are different from the most common ethical intuitions in preference utilitarianism. Since our formal preference utilitarianism is not meant to describe a decision procedure for humans (or, more generally and in  Hare's (1981, pp. 44f.)  terminology, non-\"archangels\"), we do not consider an application-oriented utilitarianism like Hare's two-level consequentialism.  (Hare 1981, p. 25ff .) Also, most preference utilitarians ascribe preferences only to humans (or abstract agents) and do not contain prioritization among individuals,  (Harsanyi 1982, p. 46)  or they use a low number of classes of moral standing.  (Singer 1993, pp. 101ff., 283f.)  Whereas some have pointed out that a variety of behavior and even trivial systems can be viewed from an \"intentional stance\",  (Dennett 1971 (Dennett , 1989 compare Hofstadter 2007, pp. 52ff.)  only relatively recent articles in preference utilitarianism have discussed the connection between goal-directed behavior and ethically relevant preferences and with the universality of the former pointed out the potential universality of the latter.  (Tomasik 2015b, ch. 7; Tomasik 2015a, ch. 4, 6; Tomasik 2015c)  This idea is an important step when formalizing preference utilitarianism because otherwise one would have to define moral standing depending on other, usually binary, notions: being alive, the ability to suffer (Bentham 1823, ch. 17 note 122) personhood  (Gruen 2014, ch. 1) , free will, sentience and (self-)consciousness  (Singer 1993, pp. 101ff.)  or the ability of moral judgment. However, all of them seem to be very difficult to define (universally) in physical systems in the intended binary sense. 11 Also, continuous definitions of these terms are often connected with goal-directed behavior.  (Tomasik 2015a, ch. 4; Wolfram 2002 Wolfram , p. 1136  9 Specifically, the Riemann series theorem states that any conditionally convergent series can be reordered to have arbitrary values.  10  It is very important to differentiate the series from its value. Otherwise, one may identify the series with positive or negative infinity or as being undefined. Two infinite values of the series would then not be comparable anymore, which  Bostrom (2011)  identified as a problem for (consequentialist) ethics. But this problem can sometimes be eliminated by comparing the series itself to another. In this particular case, a history h is better than another history h , if i Spc u u(h)P(u|(h(i)| Spc )@i) − u(h )P(u|(h (i)| Spc )@i) > 0, where h(i)| Spc : Spc → S : c → h(i)(c) denotes the restriction of h(i) to Spc, i.e. the structure on Spc in the state h(i). If no such relation can be established then the two histories are arguably incomparable or may be called approximately equally good. Again, the ordering could be important in some cases, see footnote 9. \n Fig. 3 Comparison between formalizations of utilitarianism. The first row shows the formalization of this paper, the second row is adapted from  Harsanyi (1982, p. 46) , and the third row from  Gips (2011, p. 245) . The utility of an agent n is denoted by U n and its weight by w n sum over all agents utility of an agent i str @i u P (u|str @i)u(h) agent n∈N U n agent n∈N w n • U n Whereas most ethical work is conducted informally,  (McLaren 2011, p. 297; Gips 2011, p. 251)  there has been some formal work at the intersection of (utilitarian) ethics, game theory and economics, most notably by  Harsanyi (1982) . Some formalization has also been conducted in the realm of machine ethics.  (Anderson et al. 2004; Gips 2011, pp. 245ff .) However, influenced by game theory and dualist traditions in philosophy, they are based on the classic agent-environment-model as displayed in Fig.  1  and assume utility functions (or even the utilities in different trajectories themselves) as given by the world model. Nonetheless, there is at least one parallel: all models of utilitarianism contain the notion of summing the utility over all agents. As shown in Fig.  3 , both the definition of all agents and how to obtain the utility or welfare of an agent differ among formalizations. In Artificial Intelligence, the idea of learning preferences has become more popular, e.g. see Fürnkranz and Hüllermeier (2010) and  Nielsen and Jensen (2004)  for technical treatments or  Bostrom (2014, pp. 192ff.)  for an introduction in the context of making an AI do what the engineers value. However, most of the time, the agent is still presumed to be separated from the environment. Nonetheless, the idea of evaluating space-time-embedded intelligence is beginning to be established in artificial (general) intelligence,  (Orseau and Ring 2012)  which is closely related to the probability distribution P(str@i|u). \n Conclusion By reversing Dennett's intentional stance with Bayes' theorem, we were able to ascribe preferences to physical objects and thus formalize preference utilitarianism in cellular automata. Theoretically, such formalizations can function as a specification for an artificial intelligence or more generally as a basis for \"paradise engineering\" (e.g. see  Ettinger 2009, p. 124) . However, there are several potential problems that require further work before such practical applications of our formalization or improved variations of it can be approached: -Through sums over all structures, possible utility functions and states and the application of incomputable concepts like Solomonoff's prior in P(u), our formalization is incomputable in theory and practice. So even in simulations of cellular automata our formalization is not immediately applicable. -Computing our global welfare function in the real world is even more difficult, because it requires full information about the world on particle level. Also, the formalization must first be translated into the physical laws of our universe. -The difficulty to apply our formalization is by no means only relevant to actually using it as a moral imperative. Instead, it is also relevant to discussing our formalization from a normative standpoint: Even though the derivation of our formalization is plausible, it may still differ significantly from intuition. There could be some kind of trivial agents with trivial preferences that dominate comparison of different histories. Because the formalization's incomputability makes it difficult to assess whether such problems are present, further work on its potential flaws is necessary. Based on such discussion, our formalization may be revised or even discarded. In any case, we could learn a lot from its shortcomings especially due to the formalization's simplicity and plausible derivation. -We outlined how P(str@i|u) and P(u) could be determined in principle. However, they need to be specified more formally, which in the case of P(str@i|u) seems to require a solution to the problem of normative decision theory. Some problems of our formalization could inspire additional refinements of these distributions. Fig. 1 1 Fig. 1 The classic agent-environment-model \n Fig. 2 2 Fig. 2 A state of a two-dimensional cellular automaton. It is very unclear, what agents are and which preferences they have. Adapted from http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#mediaviewer/ File:Conways_game_of_life_breeder \n\t\t\t For introductions to and ethical discussions of the underlying notion of preference utilitarianism see Tomasik (2015a, b) . \n\t\t\t The choice of deterministic systems was made primarily to simplify the formalization. It appears to be unproblematic to transfer formal preference utilitarianism to non-deterministic systems, but defining non-deterministic cellular automata themselves is a little more difficult. \n\t\t\t Other codomains of utility functions seem possible as long as they are subsets of a totally ordered vector space over R. Intervals like [0, 1] seem specifically suitable, because they avoid problems of infinite utility and allow for normalization. (Isbell 1959 )4  Alternatively, one can try to avoid this hypothetical experiment by predicting the organism's behavior. For example, one could try to ask the organism what it would do or infer its typical behavior from its internals.5  Including i into the data is important, because otherwise identical structures at different points in time would have identical utility functions. This is a problem, when the utility function u is applied to the whole \n\t\t\t If Solomonoff's prior is chosen for P(u), all incomputable utility functions have zero probability. Since the set of computable functions is countable, only countably many summands could possibly be non-zero. 8 More precisely, but less elegantly, one could write∞ i=0 Spc∈Fin(C) u:(S C ) N →R u(h)P(u|(h(i)| Spc )@i),where Fin(C) := {A ⊆ C||A| ∈ N} is the set of finite subsets of C and h(i)| Spc : Spc → S : c → h(i)(c) is the restriction of the state h(i) to the space Spc and therefore the structure on that space. \n\t\t\t For example, Wolfram (2002 Wolfram ( , pp. 823-825, 1178Wolfram ( -1180 and Emmeche (1997)  discuss the property of life,Hofstadter (2007, pp. 9-24, 51-54)  discusses consciousness andArneson (1998, p. 5) discusses personhood.", "date_published": "n/a", "url": "n/a", "filename": "Oesterheld2016_Article_FormalizingPreferenceUtilitari.tei.xml", "abstract": "Most ethical work is done at a low level of formality. This makes practical moral questions inaccessible to formal and natural sciences and can lead to misunderstandings in ethical discussion. In this paper, we use Bayesian inference to introduce a formalization of preference utilitarianism in physical world models, specifically cellular automata. Even though our formalization is not immediately applicable, it is a first step in providing ethics and ultimately the question of how to \"make the world better\" with a formal basis.", "id": "39c1d9753615f75a6e595a152589fc88"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kelvin Xu", "Ellis Ratner", "Anca Dragan", "Sergey Levine", "Chelsea Finn"], "title": "Learning a Prior over Intent via Meta-Inverse Reinforcement Learning", "text": "Introduction Reinforcement learning (RL) algorithms have the potential to automate a wide range of decision-making and control tasks across a variety of different domains, as demonstrated by successful recent applications ranging from robotic control  (Kober & Peters, 2012; Levine et al., 2016)  to game playing  (Mnih et al., 2015; Silver et al., 2016) . A key assumption of the RL problem statement is the availability of a reward function that accurately describes the desired task. For many real world tasks, reward functions can be chal-Figure  1 . A diagram of our meta-inverse RL approach. Our approach attempts to remedy over-fitting in few-shot IRL by learning a \"prior\" that constraints the set of possible reward functions to lie within a few steps of gradient descent. Standard IRL attempts to recover the reward function directly from the available demonstrations. The shortcoming of this approach is that there is little reason to expect generalization as it is analogous to training a density model with only a few examples. lenging to manually specify, while being crucial for good performance  (Amodei et al., 2016) . Most real world tasks are multifaceted and require reasoning over multiple factors in a task (e.g. a robot cleaning in a house with children), while simultaneously providing appropriate reward shaping to make the task feasible with tractable exploration  (Ng et al., 1999) . These challenges are compounded by the inherent difficulty of specifying rewards for tasks with highdimensional observation spaces such as images. Inverse reinforcement learning (IRL) is an approach that aims to address this problem by instead inferring the reward function from demonstrations of the task  (Ng & Russell, 2000) . This has the appealing benefit of taking a datadriven approach to reward specification in place of hand engineering. In practice however, rewards functions are rarely learned as it can be prohibitively expensive to provide demonstrations that cover the variability common in real world tasks (e.g., collecting demonstrations of opening every type of door knob). In addition, while learning a complex function from high dimensional observations might make an expressive function approximator seem like a reasonable modelling assumption, in the \"few-shot\" domain it is notoriously difficult to unambiguously recover a good reward function with expressive function approximators. Many prior approaches have thus relied on low-dimensional linear models with handcrafted features that effectively encode a strong prior on the relevant features of a task. This requires engineering a set of features by hand that work well for a specific problem. In this work, we propose an approach that instead explicitly learns expressive features that are robust even when learning with limited demonstrations. Our approach relies on the key observation that related tasks share a common structure that we can leverage when learning new tasks. To illustrate, considering a robot navigating through a home. While the exact reward function we provide to the robot may differ depending on the task, there is a structure amid the space of useful behaviours, such as navigating to a series of landmarks, and there are certain behaviors we always want to encourage or discourage, such as avoiding obstacles or staying a reasonable distance from humans. This notion agrees with our understanding of why humans can easily infer the intents and goals (i.e., reward functions) of even abstract agents from just one or a few demonstrations  (Baker et al., 2007) , as humans have access to strong priors about how other humans accomplish similar tasks accrued over many years. Similarly, our objective is to discover the common structure among different tasks, and encode that structure in a way that can be used to infer reward functions from a few demonstrations. More specifically, in this work we assume access to a set of tasks, along with demonstrations of the desired behaviors for those tasks, which we refer to as the meta-training set. From these tasks, we then learn a reward function parameterization that enables effective few-shot learning when used to initialize IRL in a novel task. Our method is summarized in Fig.  1 . Our key contribution is an algorithm that enables efficient learning of new reward functions by using metatraining to build a rich \"prior\" for goal inference. Using our proposed approach, we show that we can learn deep neural network reward functions from raw pixel observations on two distinct domains with substantially better data efficiency than existing methods and standard baselines. \n Related Work Inverse reinforcement learning (IRL)  (Ng & Russell, 2000)  is the problem of inferring an expert's reward function directly from demonstrations. Prior methods for performing IRL range from margin based approaches  (Abbeel & Ng, 2004; Ratliff et al., 2006)  to probabilistic approaches  (Ramachandran & Amir, 2007; Ziebart et al., 2008) . Although it is possible to extend our approach to any other IRL method, in this work we base on work on the maximum entropy (MaxEnt) framework  (Ziebart et al., 2008) . In addition to allowing for sub-optimality in the expert demonstrations, MaxEnt-IRL can be re-framed as a maximum likelihood estimation problem. (Sec. 3). In part to combat the under-specified nature of IRL, prior work has often used low-dimensional linear parameterizations with handcrafted features  (Abbeel & Ng, 2004; Ziebart et al., 2008) . In order to learn from high dimensional input,  Wulfmeier et al. (2015)  proposed applying fully convolutional networks  (Shelhamer et al., 2017)  to the MaxEnt IRL framework  (Ziebart et al., 2008)  for several navigation tasks  (Wulfmeier et al., 2016b; a) . Other methods that have incorporated neural network rewards include guided cost learning (GCL)  (Finn et al., 2017a) , which uses importance sampling and regularization for scalability to highdimensional spaces, and adversarial IRL  (Fu et al., 2018) . Several other methods have also proposed imitation learning approaches based on adversarial frameworks that resemble IRL, but do not aim to directly recover a reward function  (Ho & Ermon, 2016; Hausman et al., 2017; Kuefler & Kochenderfer, 2018) . In this work, instead of improving the ability to learn reward functions on a single task, we focus on the problem of effectively learning to use prior demonstration data from other IRL tasks, allowing us to learn new tasks from a limited number demonstrations even with expressive non-linear reward functions. Prior work has explored the problem of multi-task IRL, where the demonstrated behavior is assumed to have originated from multiple experts achieving different goals. Some of these approaches include those that aim to incorporate a shared prior over reward functions through extending the Bayesian IRL  (Ramachandran & Amir, 2007)  framework to the multi-task setting  (Dimitrakakis & Rothkopf, 2012; Choi & Kim, 2012) . Other approaches have clustered demonstrations while simultaneously inferring reward functions for each cluster  (Babes ¸-Vroman et al., 2011)  or introduced regularization between rewards to a common \"shared reward\"  (Li & Burdick, 2017) . Our work is similar in that we also seek to encode prior information common to the tasks. However, a critical difference is that our method specifically aims to distill the meta-training tasks into a prior that can then be used to learn rewards for new tasks efficiently. The goal therefore is not to acquire good reward functions that explain the meta-training tasks, but rather to use them to learn efficiently on new tasks. Our approach builds on work on the broader problem of meta-learning  (Schmidhuber, 1987; Bengio et al.; Naik & Mammone, 1992; Thrun & Pratt, 2012)  and generative modelling  (Rezende et al., 2016; Reed et al., 2018; Mordatch, 2018) . Prior work has proposed a variety of solutions for learning to learn including memory based methods  (Duan et al., 2016; Santoro et al., 2016; Mishra et al., 2017) , methods that learn an optimizer and/or initialization  (Andrychowicz et al., 2016; Ravi & Larochelle, 2016; Finn et al., 2017a; Li & Malik, 2017) , and methods that compare new datapoints in a learned metric space  (Koch, 2015; Wang & Hebert, 2016; Vinyals et al., 2016; Shyam et al., 2017; Snell et al., 2017) . Our work is motivated by the goal of broadening the applicability of IRL, but in principle it is possible to adapt many of these metalearning approaches for our problem statement. We build upon  Finn et al. (2017a) , which has also been previously applied to the related problems of imitation learning and human motion prediction  Finn et al., 2017b; Alet et al., 2018) . We leave it to future work to do a comprehensive investigation of different meta-learning approaches which could broaden the applicability of IRL. \n Preliminaries and Overview In this section, we introduce our notation and describe the IRL and meta-learning problems. \n Learning Rewards via Maximum Entropy Inverse Reinforcement Learning The standard Markov decision process (MDP) is defined by the tuple (S, A, p s , r, ) where S and A denote the set of possible states and actions respectively, r : S ⇥ A ! R is the reward function, 2 [0, 1] is the discount factor and p s : S ⇥ S ⇥ A ! [0, 1] denotes the transition distribution over the next state s t+1 , given the current state s t and current action a t . Typically, the goal of \"forward\" RL is to maximize the expected discounted return R(⌧ ) = P T t=1 t 1 r(s t , a t ). In IRL, we instead assume that the reward function is unknown but that we instead have access to a set of expert demonstrations D = {⌧ 1 , . . . , ⌧ K }, where ⌧ k = {s 1 , a 1 , . . . , s T , a T }. The goal of IRL is to recover the unknown reward function r from the set of demonstrations. We build on the maximum entropy (MaxEnt) IRL framework by  Ziebart et al. (2008) , which models trajectories as being distributed proportional to their exponentiated return p(⌧ ) = 1 Z exp (R(⌧ )) , (1) where Z is the partition function, Z = R ⌧ exp(R(⌧ ))d⌧ . This distribution can be shown to be induced by the optimal policy in entropy regularized forward RL problem: ⇡ ⇤ = arg max ⇡ E ⌧ ⇠⇡ [R(⌧ ) log ⇡(⌧ )] . (2) This formulation allows us to pose the reward learning problem as a maximum likelihood estimation (MLE) problem in an energy-based model r by defining the following loss: min E ⌧ ⇠D [L IRL (⌧ )] := min E ⌧ ⇠D [ log p (⌧ )] . (3) Learning in general energy-based models of this form is common in many applications such as structured prediction. However, in contrast to applications where learning can be supervised by millions of labels (e.g. semantic segmentation), the learning problem in Eq. 3 must typically be performed with a relatively small number of example demonstrations. In this work, we seek to address this issue in IRL by providing a way to integrate information from prior tasks to constrain the optimization in Eq. 3 in the regime of limited demonstrations. \n Meta-Learning The goal of meta-learning algorithms is to optimize for the ability to learn efficiently on new tasks. Rather than attempting to generalize to new datapoints, meta-learning can be understood as attempting to generalize to new tasks. It is assumed in the meta-learning setting that there are two disjoint sets of tasks that we refer to as the meta-training set {T i ; i = 1..N } and meta-test set {T j ; j = 1..M }, which are both drawn from a distribution p(T ). During meta-training time, the meta-learner attempts to learn the structure of the tasks in the meta-training set, such that when it is presented with a test task, it can leverage this structure to learn efficiently from a limited number of examples. To illustrate this distinction, consider the case of fewshot learning setting. Let f ✓ denote the learner, and let a task be defined by learning from K training examples X tr T = {x 1 . . . , x K }, Y tr T = {y 1 . . . , y K }, and evaluat- ing on K 0 test examples X test T = {x 1 . . . , x K 0 }, Y test T = {y 1 . . . , y K 0 }. One approach to meta-learning is to directly parameterize the meta-learner with an expressive model such as a recurrent or recursive neural network  (Duan et al., 2016; Mishra et al., 2017)  conditioned on the task training data and the inputs for the test task: f ✓ (Y |X test T , X tr T , Y tr T ) . Such a model is optimized using log-likelihood across all tasks. In this approach to meta-learning, since neural networks are known to be universal function approximators  (Siegelmann & Sontag, 1995) , any desired structure between tasks can be implicitly encoded. Rather than learn a single black-box function, another approach to meta-learning is to learn components of the learning procedure such as the initialization  (Finn et al., 2017a)  or the optimization algorithm  (Ravi & Larochelle, 2016; Andrychowicz et al., 2016) . In this work we extend the approach of model agnostic meta-learning (MAML) introduced by  Finn et al. (2017a) , which learns an initialization that is adapted by gradient descent. Concretely, in the supervised learning case, given a loss function L(✓, X T , Y T ) (e.g. cross-entropy), MAML performs the following optimization min ✓ X T L( T , X test T , Y test T ) = min ✓ X T L ✓ ↵r ✓ L(✓, X tr T , Y tr T ), X test T , Y test T , (4) where the optimization is over an initial set of parameters ✓ and the loss on the held out tasks X test T becomes the signal for learning the initial parameters for gradient descent (with step size ↵) on X tr T . This optimization is analogous to adding a constraint in a multi-task setting, which we show in later sections is analogous in our setting to learning a prior over reward functions. \n Learning to Learn Rewards Our goal in meta-IRL is to learn how to learn reward functions across many tasks such that the model can infer the reward function for a new task using only one or a few expert demonstrations. Intuitively, we can view this problem as aiming to learn a prior over the rewards of expert demonstrators, such that when given just one or a few demonstrations of a new task, we can combine the learned prior with the new data to effectively determine the expert's intent. Such a prior is helpful in inverse reinforcement learning settings, since the space of reward functions with are relevant to particular task is much smaller than the space of all possible rewards definable on the raw observations. During meta-training, we have a set of tasks {T i ; i = 1..N }. Each task T i has a set of demonstrations D T = {⌧ 1 , . . . , ⌧ K } from an expert policy which we partition into disjoint D tr T and D test T sets. The demonstrations for each meta-training task are assumed to be produced by the expert according to the maximum entropy model in Section 3.1. During meta-training, these tasks will be used to encodes common structure so that our model can quickly acquire rewards for new tasks from just a few demonstrations. After meta-training, our method is presented with a new task. During this meta-test phase, the algorithm must infer the parameters of the reward function r (s t , a t ) for the new task from a few demonstrations. As is standard in meta-learning, we assume that the test task is from the same distribution of tasks seen during meta-training, a distribution that we denote as p(T ). \n Meta Reward and Intention Learning (MandRIL) In order to meta-learn a reward function that can act as a prior for new tasks and new environments, we first formalize the notion of a good reward by defining a loss L T (✓) on the reward function r ✓ for a particular task T . We use the MaxEnt IRL loss L IRL discussed in Section 3, which, for a given D T , leads to the following gradient  (Ziebart et al., 2008) : r ✓ L T (✓) = @r ✓ @✓ ⇥ E ⌧ [µ ⌧ ] µ D T ⇤ . ( 5 ) where µ ⌧ are the state-action visitations under the optimal maximum entropy policy under r ✓ , and µ D are the mean state visitations under the demonstrated trajectories. If our end goal were to achieve a single reward function that # Compute Max-Ent state visitations 7: E ⌧ [µ ⌧ ] = STATE-VISITATIONS-POLICY(r ✓ , T ) 8: # MaxEntIRL gradient  (Ziebart et al., 2008)  9: @L @r ✓ = E ⌧ [µ ⌧ ] µ D 10: Return @L @r ✓ 11: 12: Randomly initialize ✓ 13: while not done do 14: Sample batch of tasks T i ⇠ {T } meta-train 15: for all T i do 16: Sample demos D tr = {⌧ 1 , . . . , ⌧ K } ⇠ T i 17: # Inner loss computation 18: @L tr T i (✓) @r ✓ = MAXENTIRL-GRAD(r ✓ , T i , D tr ) 19: Compute r ✓ L tr Ti (✓) from @L tr T i (✓) @r ✓ 20: Compute Ti = ✓ ↵r ✓ L tr Ti (✓) 21: Sample demos D test = {⌧ 0 1 , . . . , ⌧ 0 K 0 } ⇠ T i 22: # Outer loss computation 23: @L test T i @r ✓ = MAXENTIRL-GRAD(r T i , T i , D test )) 24: # Compute meta-gradient 25: Compute r ✓ L test Ti from @L test T i @r ✓ via chain rule 26: Compute update to ✓ ✓ P i r ✓ L test Ti works as well as possible across all tasks in {T i ; i = 1..N }, then we could simply follow the mean gradient across all tasks. However, our objective is different: instead of optimizing performance on the meta-training tasks, we aim to learn a reward function that can be quickly and efficiently adapted to new tasks at meta-test time. In doing so, we aim to encode prior information over the task distribution in this learned reward prior. We propose to implement such a learning algorithm by finding the parameters ✓, such that starting from ✓ and taking a small number of gradient steps on a few demonstrations from given task leads to a reward function for which a set of test demonstrations have high likelihood, with respect to the MaxEnt IRL model. In particular, we would like to find a ✓ such that the parameters T = ✓ ↵r ✓ L tr T (✓) (6) lead to a reward function r T for task T , such that the IRL loss (corresponding to negative log-likelihood) for a disjoint set of test demonstrations, given by L T ,test IRL , is minimized. The corresponding optimization problem for ✓ can therefore be written as follows: min ✓ N X i=1 L test Ti ( Ti ) = N X i=1 L test Ti ✓ ↵r ✓ L tr Ti (✓) . (7) Our method acquires this prior ✓ over rewards in the task distribution p(T ) by optimizing this loss. This amounts to an extension of the MAML algorithm in Section 3.2 to the inverse reinforcement learning setting. This extension is quite challenging, because computing the MaxEnt IRL gradient requires repeatedly solving for the current maximum entropy policy and visitation frequencies, and the MAML objective requires computing derivatives through this gradient step. Next, we describe in detail how this is done. An overview of our method is also outlined in Alg. 1. \n Meta-training. The computation of the meta-gradient for the objective in Eq. 7 can be conceptually separated into two parts. First, we perform the update in Eq. 6 by computing the expected state visitations µ, which is the expected number of times an agent will visit each state. We denote this overall procedure as STATE-VISITATIONS-POLICY, and follow  Ziebart et al. (2008)  by first computing the maximum entropy optimal policy in Eq. 2 under the current r ✓ , and then approximating µ using dynamic programming. Next, we compute the state visitation distribution of the expert using a procedure which we denote as STATE-VISITATIONS-TRAJ. This can be done either empirically, by averaging the state visitation of the experts demonstrations, or by using STATE-VISITATIONS-POLICY if the true reward is available at meta-training time. This allows us to recover the IRL gradient according to Eq. 5, which we can then apply to compute T according to Eq. 6. Second, we need to differentiate through this update to compute the gradient of the meta-loss in Eq. 7. Note that the meta-loss itself is the IRL loss evaluated with a different set of test demonstrations. We follow the same procedure as above to evaluate the gradient of L T ,test IRL with respect to the post-update parameters T , and then apply the chain rule to compute the meta-gradient: r ✓ L test T (✓) = @ @✓ (✓ ↵r ✓ L tr T (✓)) @r T @ T @L test T @r T = I ↵ @ 2 L tr T (✓) @✓ 2 ↵ @ r ✓ @ ✓ D @ r ✓ @ ✓ > ! @r T @ T @L test T @r T (8) where on the second line we differentiate through the MaxEnt-IRL update, and we define the |S||A|-dimensional diagonal matrix D as  D := diag ⇢ @ @ r ✓,i (E ⌧ [µ ⌧ ]) i |S||A| i=1 ! . a 1 a 2 s 1 s 2 . . . . . . (⌧ ) = 1 Z Q T t=1 r( T , st, at) dyn(st+1, st, at) (above) where we learn a prior over T , which during meta-test is used for MAP inference over new expert demonstrations. A detailed derivation of this expression is provided in the supplementary Appendix E. Meta-testing. Once we have acquired the meta-trained parameters ✓ that encode a prior over p(T ), we can leverage this prior to enable fast, few-shot IRL of novel tasks in {T j ; j = 1..M }. For each task, we first compute the state visitations from the available set of demonstrations for that task. Next, we use these state visitations to compute the gradient, which is the same as the inner loss gradient computation of the meta-training loop in Alg. 1. We apply this gradient to adapt the parameters ✓ to the new task. Even if the model was trained with only one inner gradient steps, we found in practice that it was beneficial to take substantially more gradient steps during meta-testing; performance continued to improve with up to 20 steps. \n Connection to Learning a Prior over Intent The objective in Eq. 6 optimizes for parameters that enable the reward function to generalize efficiently on a wide range of tasks. Intuitively, constraining the space of reward functions to lie within a few steps of gradient descent can be interpreted as expressing a \"locality\" prior over reward function parameters. This intuition can be made more concrete by the following analysis. By viewing IRL as maximum likelihood estimation in a particular graphical model (Fig.  2 ), we can take the perspective of  Grant et al. (2018)  who showed that for a linear model, fast adaptation via a few steps of gradient descent in MAML is performing MAP inference over , under a Gaussian prior with the mean ✓ and a covariance that depends on the step size, number of steps and hessian of the loss. This is based on the connection between early stopping and regularization previously discussed in  Santos (1996) , which we refer the readers to for a more detailed discussion. The interpretation of MAML as imposing a Gaussian prior on the parameters is exact in the case of a likelihood that is quadratic in the parameters (such as the log-likelihood of a Gaussian in terms of its mean). For any non-quadratic likelihood, this is an approximation in a local neighborhood around ✓ (i.e. up to convex quadratic approximation). In the case of complex parameterizations, such as deep function approximators, this is a coarse approximation and unlikely to be the mode of a posterior. However, we can still frame the effect of early stopping and initialization as serving as a prior in a similar way as prior work  (Sjöberg & Ljung, 1995; Duvenaud et al., 2016; Grant et al., 2018) . More importantly, this interpretation hints at future extensions to our approach that could benefit from employing more fully Bayesian approaches to reward and goal inference. \n Experiments Our evaluation seeks to answer two questions. First, we aim to test our core hypothesis that using prior task experience enables reward learning for new tasks with just a few demonstrations. Second, we compare our method with alternative approaches that make use of multi-task experience. We test our core hypothesis by comparing learning performance on a new tasks starting from the initialization produced by MandRIL with learning a separate model for every task starting either from a random initialization or from an initialization obtained by supervised pre-training. We refer to these approaches as learning \"FROM SCRATCH\" and \"AVERAGE GRADIENT\" pretraining respectively. Our supervised pre-training baseline follows the average gradient during meta-training tasks and finetunes at meta-test time (as discussed in Section 4). Unlike our method, supervised pre-training does not optimize for a model that performs well under fine tuning, but does use the same prior data to pre-train. We additionally compare to pre-training on a single task as well as all the meta-training tasks. To our knowledge, there is no prior work that addresses the specific meta-inverse reinforcement learning problem introduced in this paper. Thus, to provide a point of comparison and calibrate the difficulty of the tasks, we adapt two alternative black-box meta-learning methods to the IRL setting. The comparisons to both of the black-box methods described below evaluate the importance of incorporating the IRL gradient into the meta-learning process, rather than learning the adaptation process entirely from scratch. Demo conditional model: Our method implicitly conditions on the demonstrations through the gradient update. In principle, a conditional deep model with sufficient capacity could implicitly implement a similar learning rule. Thus, we consider a conditional model (often referred to as a \"contextual model\"  (Finn et al., 2017b) ), which receives the demonstration as an additional input. Recurrent meta-learner: We additionally compare to an RNN-based meta-learner  (Santoro et al., 2016; Duan et al., 2017) . Specifically, we implement a conditional model by feeding both images and sequences of states visited by the demonstrations to an LSTM. When learning a task, the agent has access to the image (left) and demonstrations (red arrows). To evaluate learning (right), the agent is tested for its ability to recover the reward for the task when the objects have been rearranged. The reward structure we wish to capture can be illustrated by considering the initial state in blue. An policy acting optimally under a correctly inferred reward should interpret the other objects as obstacles, and prefer a path on dirt. We consider two environments: (1) an image-based navigation task with an aerial viewpoint, (2) a first-person navigation task in a simulated home environment with object interaction. We describe here the environments and evaluation protocol and provide detailed experimental settings and hyperparameters for both domains in Appendices A and B. (1) SpriteWorld navigation domain. Since most prior IRL work (and multi-task IRL work) studied settings where linear reward function approximators suffice (i.e., lowdimensional state spaces and hand-designed features), we design an experiment that is significantly more challengingthat requires learning rewards on raw pixels. We consider a navigation problem where we must learn a convolutional neural network that directly maps image pixels to rewards. We introduce a family of tasks called \"SpriteWorld.\" Some example tasks are shown in Fig.  3 . Tasks involve navigating to goal objects while exhibiting preference over terrain types (e.g., the agent prefers to traverse dirt tiles over traversing grass tiles). At meta-test time, we provide one or a few demonstrations in a single training environment and evaluate the reward learned using these demonstrations in a new, test environment that contains the same objects as the training environment, but arranged differently. Evaluating in a new test environment is critical to measure that, after adapting to the training environment from a few demonstrations, the reward learned the correct visual cues, rather than simply memorizing the demonstration trajectory. We generate unique tasks in this domain as follows. First, we randomly choose a set of three sprites from one hundred sprites from the original game (creating a total of 161,700 unique tasks). We randomly place these three sprites within a randomly generated terrain tiling; we designate one of the sprites to be the goal landmark of the navigation task. The other two objects are treated as obstacles for which the agent incurs a large negative reward for not avoiding. In each task, we optimize our model on a training world and generalization in a test world, as described below. The agent must complete either a \"NAV\" task (blue line) where the goal is to navigate from the start to the cup or a \"PICK\" task (blue + green line) where the agent must also bring the cup to the bed. The agent's observation is a panoramic first-person viewpoint (see bottom left for RGB). Following the convention in prior work  (Fu et al., 2019) , we provide to the reward function the corresponding semantic images (bottom right). These images are 32 ⇥ 24 containing 61 channels corresponding to each object class. (2) SUNCG navigation domain: In addition to the SpriteWorld domain, we evaluate our approach on a first person image-based navigation task in an indoor house environment where the agent must interact with objects. We use an environment built on top of the SUNCG dataset  (Song et al., 2017)  which has previously been used in the context of IRL  (Fu et al., 2019)  with language instructions. We follow a similar task setup as  Fu et al. (2019) , although we omit the language instructions. In this domain, we consider tasks that can be categorized into two types. \n Navigation (NAV): In this task, the agent must navigate to a location in the house that corresponds either to a target object or location. For example, in the blue line of Fig.  4 , the agent must navigate to the \"cup\" object. Pick-and-place (PICK): In this more difficult task, the agent moves an object between two locations. For example, in Fig  4 , the agent must navigate to the \"cup\", perform a pick action and then navigate to the \"bedroom\". Evaluation protocol: We evaluate on held-out tasks that were unseen during meta-training. In the SpriteWorld domain, we consider two settings: (1) tasks involving new combinations and placements of sprites, with sprites that were present during meta-training, and (2) tasks with combinations of unseen sprites which we refer to as \"out of domain objects.\" For each task, we generate one environment (a set of sprite positions) along with demonstrations for adapting the reward, and generate a second environment (with new sprite positions) for evaluating the adapted reward. In the SUNCG domain, we similarly evaluate on both novel combinations of objects and locations. We follow the evaluation protocol of  Fu et al. (2019)  and evaluate on \"TEST\" tasks which consist of tasks within the same houses as training, but with novel combinations of objects and locations. In addition, we evaluate on environments which consists of new houses not in the training set. We refer to these as \"UNSEEN-HOUSES.\" This evaluation adds complexity by testing the models ability to successfully infer rewards in an entirely new scene. In total, the dataset consists of 1413 tasks (716 PICK, 697 NAV). The meta-train set is composed of 1004 tasks, the \"TEST\" set contains 236 tasks, and the \"UNSEEN-HOUSES\" set contains 173 tasks. Evaluation Metrics. We measure performance using the expected value difference, which measures the suboptimality of a policy learned under the learned reward; this is a performance metric used in prior IRL work  (Levine et al., 2011; Wulfmeier et al., 2015) . The metric is computed by taking the difference between the value of the optimal policy under the learned reward and the value of the optimal policy under the true reward. On the SUNCG domain, we follow  Fu et al. (2019)  and report the success rate of the optimal policy under the learned reward function. . We find that pre-training on the full set of tasks leads to negative transfer, while pre-training on a single task is comparable to random initialization. ManDRIL outperforms both alternative initialization approaches, which shows that optimizing for initial weights for fine-tuning robustly improves performance. Shaded regions show 95% confidence intervals. Results. The results for SpriteWorld are shown in Fig.  6 , which illustrate test performance with in-distribution and out-of-distribution sprites. Our approach, MandRIL, achieves consistently better performance in both settings. Most significantly, our approach performs well even with single-digit numbers of demonstrations. By comparison, alternative meta-learning methods generally overfit considerably, attaining good training performance (see Appendix. C for curves) but poor test performance. Learning the reward function from scratch is in fact the most competitive baseline -as the number of demonstrations increases, simply training the reward function from scratch on the new task is the only method that matches the performance of MandRIL when provided 20 or more demonstrations. With only a few demonstrations however, MandRIL has substantially lower value difference. It is worth noting the performance of MandRIL on the out of distribution test setting (Fig.  6 , bottom): although the evaluation is on new sprites, Man-dRIL is still able to adapt via gradient descent and exceed the performance all other methods. In both domains, we perform a comparison to representations finetuned from a supervised pre-training phase in Fig.  6  and Table  5 . We compare against an approach that follows the mean gradient across the tasks at meta-training time and is fine-tuned at meta-test time which we find consistently leads to negative transfer. We conclude that fine tuning reward functions learned in this manner is not an effective way of using prior task information. In contrast, we find that our approach, which explicitly optimizes for initial weights for fine-tuning, robustly improves performance on all task types and test settings. By visualizing the value under the learned reward function (see Fig.  5 ), we see that even with a small number of gradient steps, the reward function can be effectively adapted to an unseen home layout. Note that the SUNCG task is substantially more challenging, requiring the reward function to interpret first-person images. Indeed, the pretrained MaxEntIRL algorithm that does not use meta-learning exhibits negative transfer, as illustrated by the lower performance of this method on all tasks as compared to the learning \"FROM SCRATCH\" version, which learns each task entirely from random initialization. Training from scratch is a strong baseline here, because the method still sees every single first-person image in the house -2257.7 images on average. This provides sufficient variety to learn effective visual features in many cases. Nonetheless, our method (last row in Table  1 ) produces a substantial improvement, especially on the much harder \"PICK\" task, demonstrating that meta-learning can produce positive transfer even when pre-training does not. \n Conclusion In this work, we present an approach that enables few-shot learning of reward functions. We achieve this through a novel formulation of IRL that learns to encode common structure across tasks. Using our meta-IRL approach, we show that we can leverage data from previous tasks to effectively learn reward functions from raw pixel observations for new tasks, from only a handful of demonstrations. Our work paves the way for future work that considers unknown dynamics, or work that employs more fully probabilistic approaches to reward and goal inference. Algorithm 1 1 Meta Reward and Intention Learning (Man- dRIL)    1: Input: Set of meta-training tasks {T } meta-train 2: Input: hyperparameters ↵, 3: function MAXENTIRL-GRAD(r ✓ , T , D) \n Figure 2 . 2 Figure2. Our approach can be understood as approximately learning a distribution over the demonstrations ⌧ , in the factor graph p(⌧ ) = 1 \n Figure 3 . 3 Figure 3. An example task on the SpriteWorld domain. When learning a task, the agent has access to the image (left) and demonstrations (red arrows).To evaluate learning (right), the agent is tested for its ability to recover the reward for the task when the objects have been rearranged. The reward structure we wish to capture can be illustrated by considering the initial state in blue. An policy acting optimally under a correctly inferred reward should interpret the other objects as obstacles, and prefer a path on dirt. \n Figure 4 . 4 Figure 4. An example task in the SUNCG environment (top).The agent must complete either a \"NAV\" task (blue line) where the goal is to navigate from the start to the cup or a \"PICK\" task (blue + green line) where the agent must also bring the cup to the bed. The agent's observation is a panoramic first-person viewpoint (see bottom left for RGB). Following the convention in prior work (Fu et al., 2019) , we provide to the reward function the corresponding semantic images (bottom right). These images are 32 ⇥ 24 containing 61 channels corresponding to each object class. \n Figure 5 . 5 Figure 5. An example adaptation in an UNSEEN-HOUSE (best viewed in color). The agent starts in one room (blue square) and is required to pick up the vase (green square) and take it to the living room (red square). The value function (blue is high, red is low) under the learned reward (bottom) exhibits no \"PICK\" task structure pre-adaptation (bottom left-column). Post-adaptation (bottom right-column), the reward function successfully leads the agent to the vase (bottom figure, top-right plot) and after the pick action (bottom figure, bottom-right plot) is performed, navigates the agent to the goal location. \n Figure 6 . 6 Figure6. Meta-test performance on the SpriteWorld domain (lower is better): held-out tasks performance (top) and held-out tasks with novel sprites (bottom). The recurrent meta-learner has a value difference > 60 in both test settings. In both test settings, Man-dRIL achieves comparable performance to the training environment, while the other methods overfit until they receive at least 10 demonstrations (see Appendix C for training environment performance). We find that pre-training on the full set of tasks leads to negative transfer, while pre-training on a single task is comparable to random initialization. ManDRIL outperforms both alternative initialization approaches, which shows that optimizing for initial weights for fine-tuning robustly improves performance. Shaded regions show 95% confidence intervals. \n Table 1 . 1 Success rate (%) on heldout tasks with 5 demonstrations. ManDRIL achieves consistently better performance on all task/environment types. Results are averaged over 3 random seeds. METHOD TEST PICK NAV TOTAL PICK NAV TOTAL UNSEEN HOUSES BEHAVIORAL CLONING 0.4 8.2 4.3 3.7 12.0 9.4 MAXENT IRL (AVG GRADIENT) 37.3 83.7 60.8 38.3 89.7 73.3 MAXENT IRL (FROM SCRATCH) 42.4 87.9 65.4 48.1 89.9 76.5 MANDRIL(OURS) 52.3 90.7 77.3 56.3 91.0 82.6 MANDRIL (PRE-ADAPTATION) 6.0 35.3 20.7 4.3 34.6 25.3 \n\t\t\t Department of Electrical Engineering and Computer Science, University of California, Berkeley, USA. Correspondence to: Kelvin Xu <kelvinxu@berkeley.edu>.", "date_published": "n/a", "url": "n/a", "filename": "xu19d.tei.xml", "abstract": "A significant challenge for the practical application of reinforcement learning to real world problems is the need to specify an oracle reward function that correctly defines a task. Inverse reinforcement learning (IRL) seeks to avoid this challenge by instead inferring a reward function from expert demonstrations. While appealing, it can be impractically expensive to collect datasets of demonstrations that cover the variation common in the real world (e.g. opening any type of door). Thus in practice, IRL must commonly be performed with only a limited set of demonstrations where it can be exceedingly difficult to unambiguously recover a reward function. In this work, we exploit the insight that demonstrations from other tasks can be used to constrain the set of possible reward functions by learning a \"prior\" that is specifically optimized for the ability to infer expressive reward functions from limited numbers of demonstrations. We demonstrate that our method can efficiently recover rewards from images for novel tasks and provide intuition as to how our approach is analogous to learning a prior.", "id": "f9d759aeaf4ead1fd27f15c32430ae9e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Phil Torres"], "title": "Existential risks: a philosophical analysis", "text": "Introduction The field of 'existential risk studies' was essentially founded by John Leslie's 1996 book The End of the World: The Science and Ethics of Human Extinction. However, it lingered in a 'pre-paradigmatic' state for several years until the publication of Nick Bostrom's 2002 paper 'Existential Risks: Analyzing Human Extinction Scenarios and Related Hazards,' which drew heavily from Leslie's tome. Since the mid-2010s, numerous organizations focusing on studying existential risks have sprouted up at universities like Oxford and Cambridge, and multiple books on the topic have been added to the scholarly literature, including Here Be Dragons: Science, Technology, and the Future of Humanity (2016) and Morality,  Foresight, and Human Flourishing: An Introduction to Existential Risks (2017) . Yet there remains some disagreement, or at least a lack of agreement, about the semantics of the field's central concept: existential risk. The aim of the present paper will be to examine the five most prominent definitions employed by existential risk scholars (section 2) and then to offer some critical remarks about which definitions ought to be used in different conversational settings (section 3). Ultimately, I will endorse a context-dependent semantic pluralism whereby the best definition to use depends on the intended audience.  1  The fact is that existential risk studies has an integral activist component: it aims not merely to generate new knowledge about the mind-independent world, but to nontrivially influence the developmental trajectory of human civilization. Thus, it is essential that the ideas and insights outlined in the scholarly literature on existential risks are effectively conveyed to non-experts, including politicians, policymakers, business leaders, and the general voting public. This means that, while an agreed-upon technical vocabulary may economize discussion between experts, it is equally important that non-esoteric language is utilized when discussing the ideas and insights with those not 'in the know.  '  The ultimate ambition of this paper is to offer a clear account of how the term 'existential risk' has been used by scholars and some considered thoughts about how it should be employed to best advance the normative aims of the field. \n Five definitions of 'existential risk' A risk is typically defined as the probability of an undesirable event multiplied by its consequences. The notion of an existential risk has nothing to do with the first multiplicand; all that's relevant are the consequences. This section will examine five distinct definitions of the term. These are existential risks as (i) human extinction, (ii) human extinction or civilizational collapse, (iii) human extinction or a permanent and drastic loss of potential, (iv) any catastrophe with pangenerational-crushing effects, and a significant loss of expected value. Taking these in order: \n Human extinction An event X is an existential risk if and only if X could cause the extinction of humanity. This is probably the most common definition in the scholarly literature and popular media. For example, Jason  Matheny (2007)  defines existential risks as 'a subset of catastrophic eventsthose that could extinguish humanity,  ' and Karim Jebari (2015)  asserts that existential risks 'threaten the continued existence of mankind.' Similarly, the journalist Ross Anderson introduces an interview with Bostrom for The Atlantic like this: 'Bostrom, who directs Oxford's Future of Humanity Institute, has argued over the course of several papers that human extinction risks are poorly understood and, worse still, severely underestimated by society. Some of these existential risks are fairly well known, especially the natural ones'  (Anderson 2012, italics added) . There are several reasons to accept this definition. (a) The standard dictionary defines 'existential' as 'of or relating to existence; involving or relating to the existence of a thing'  (OED 2018) , which implies that 'an existential risk to humanity' is 'a risk to the existence of the species denoted by the word \"humanity.\"' So, it aligns with common usage of the term 'existential.' (b) Relatedly, it corresponds to 'a natural division and is easy to understand,' as Owen  Cotton-Barratt and Toby Ord (2015)  observe. Whereas phenomena like flourishing are spectral, coming in gradations, extinction is binary: A species is either existing or non-existing, extant or extinct, dead or alive. This makes it a non-vague concept, unlike flourishing, and one that is objective in nature, in the sense that the concept is non-axiological. (c) And finally, one could argue that the term 'extinction' picks out a natural kindspecifically, what Brian  Ellis (2001 Ellis ( , 2002 ) calls a 'dynamic kind.' It 'cuts the world at its joints,' as it were, and appears to be the sort of phenomenon that could participate in laws of nature. As it happens, almost no work within the philosophy of biology has examined the notion of species extinctions, although there are no doubt many interesting issues to be dissected here. But there are also several reasons to reject this definition. Consider the following two scenarios. Scenario 1: Imagine that Homo sapiens evolves through anagenesis into a new species of 'posthumans.' This could occur either naturally or through cyborgization, whereby technological modifications significantly alter ways our core capacities of cognition, healthspan, and emotionality (see  Bostrom 2008) . The result would be the 'phyletic extinction' (or 'pseudo-extinction') of Homo sapiens, and consequently this transition would instantiate an existential risk on the definition above. But now imagine that these posthumans have expanded intellectual capacities, are free of all diseases, don't senesce, and are able to experience degrees of happiness and pleasure that far surpass what any human is acquainted with. While there are bioconservatives, such as Frances  Fukuyama (2002)  and Leon  Kass (2002) , who would still oppose the realization of this posthuman future, most people, I conjecture, would see it as desirable. The problem is clear: If one maintains that, as Bostrom puts it, 'the objective of reducing existential risks should be a dominant consideration whenever we act out of an impersonal concern for humankind as a whole,' then we should do everything necessary to prevent Homo sapiens from becoming Posthomo supersapiens. But this conflicts with the intuition that just the opposite should be the case, on certain assumptions. One solution is to redefine 'human' as including what David Roden (2014) refers to as our 'wide descendants,' which denotes 'human, machine, cyborg, etc.' Thus, the term 'human' would encompass potential posthumans that exhibit the right genealogical and axiological relation to current humans. 2 However, expanding the semantics of 'human' to count future events in which our posthuman descendants die out would require extra explication, as most non-experts no doubt associate the term with Homo sapiens rather than future species that share an unbroken evolutionary lineage with us and are related in the right sort of axiological way. In fact, a number of population ethicists have argued that the badness of human extinction isn't just the loss of life caused by the extinction event itself, but the loss of all the future beings who could have come into existence had we survived. Derek Parfit and others have been explicit that the relevant class of beings here includes posthumans; as he writes, 'life can be wonderful as well as terrible, and we shall increasingly have the power to make life good. Since human history may be only just beginning, we can expect that future humans, or supra-humans, may achieve some great goods that we cannot now even imagine'  (Parfit 2017) . Thus, if 'the destruction of mankind would be by far the greatest of all conceivable crimes'  (Parfit 1984) , the reason is partly because, if we survive, we could undergo phyletic extinction by becoming a much superior kind of species that achieves immense goods inscrutable to contemporary minds. Scenario 2: Whereas the scenario above considers a future in which Homo sapiens is anagenetically replaced by something better, now imagine a future in which we develop along a 'degenerate trajectory' that yields conditions of profound suffering. Call such an outcome a 2 The axiological constraint here aims to preclude scenarios in which current humans are supplanted by a posthuman population whose moral and, more generally, value commitments are different than ours in some problematic way. As  Bostrom (2013)  puts this point, 'even if another intelligent species were to evolve to take our place, there is no guarantee that the successor species would sufficiently instantiate qualities that we have reason to value. Intelligence may be necessary for the realisation of our future potential for desirable development, but it is not sufficient.' 'hyper-existential risk.  ' Anders Sandberg (2014)  appears to gesture at this possibility when he writes that, 'while there might be posthuman states of great value, there are also potential existential risks threatening futures with no or extremely negative value. Insofar as we can influence what future we might reach, we may have a far greater moral responsibility than is commonly envisioned because the stakes are higher.' A related idea is that of a 'suffering risk,' which David Althaus and Lukas Gloor define as any event 'that would bring about suffering on an astronomical scale, vastly exceeding all suffering that has existed on Earth so far'  (Althaus and Gloor 2018) . Hyper-existential and suffering risks are distinct because, for example, the latter would include future configurations in which the total amount of pleasure exceeds the total amount of suffering, yet the total amount of suffering is astronomical. It would also seem to exclude situations in which, say, humanity fails to colonize space, its population dwindles to 1 billion, and everyone alive experiences constant torture-level misery until the oceans evaporate. Thus, the badness of hyper-existential risks will almost certainly be less controversial than the badness of suffering risks, which are most compelling if one champions a negative total utilitarian theory (or 'suffering-focused ethics') (see  Gloor and Mannino 2018) .  3  The point is that there could be future scenarios in which going extinctin which a kind of species euthanizationmight be unambiguously desirable. Thus, once again, if one maintains that existential risks should be avoided at all costs, then one would oppose efforts to prevent our extinction even when the alternative is a hyper-existential or suffering catastrophe. This seems counter-intuitive. In sum, the advantage of this definition is that it is simple, but the drawback is that it is simplistic. I will have more to say about this in section 3. 3 Incidentally, Bostrom appears to overlook these issues in one section of his 2013 paper about existential risks. In defending his maxipok rule, Bostrom argues against the Rawlsian 'maximin' rule, which states that, under ignorance, one should pick the action with the best worst-case outcome. Since it is impossible to completely rule out the possibility of extinction no matter which actions we choose, Bostrom claims that 'the use of maximin in the present context would entail choosing the action that has the greatest benefit under the assumption of impending extinction,' which would of course be Bacchanalian revelry  (Bostrom 2013) . This is confusing, though, since the maximin rule itself is indifferent to actions that have the same worst possible outcome; thus, decision theorists have devised the 'leximin' rule, which states that if two actions have equally bad worst possible outcomes, one should choose the action whose second worst possible outcome is the best. Thus, if one takes extinction to be the worst possible outcome-as Bostrom here does-then one should choose actions that have the best worst possible outcomes next to extinction. Either way, the point is that Bostrom's assumption is clearly wrong: There are many forms of survival, whether in a human or posthuman state, that are far worst than extinction. It is such considerations that lead  Althaus and Gloor (2018)  to hortatorily declare: 'Rather than focusing exclusively on ensuring that there will be a future, we recommend interventions that improve the future's overall quality.' \n Human extinction or civilizational collapse An event X is an existential risk if and only if X could cause either the extinction of humanity or the collapse of civilization. This is not as common in the scholarly literature, although there are references to civilizational collapse in the relevant contexts. For example, while Lord Martin Rees argues that 'the worst possible disaster [is] the foreclosure of intelligent life's future through the extinction of all humankind,' he focuses a lot on the survival of civilizationat one point arguing that 'the odds are no better than fifty-fifty that our present civilisation on Earth will survive to the end of the present century'  (Rees 2003) . In fact, the Centre for the Study of Existential Risk (CSER), which Rees cofounded, initially used 'risks of extinction' and 'existential risks' synonymously, but it now describes itself as 'dedicated to the study and mitigation of risks that could lead to human extinction or civilisational collapse.' 4 As with the first definition, this one has the virtue of being easy to grasp. Most of us have a robust intuitive understanding of what constitutes civilization, and thus what its collapse would entail. It also encompasses scenarios of planetary-scale destruction that the first definition ignores. For example, many scholars would describe anthropogenic climate change as posing an existential risk, but few believe that it will directly bring about our extinction. Rather, it is much more likely to cause civilizational collapse. This suggests that existential risks as human extinction or civilizational collapse is better than existential risks as human extinction, since this definition draws attention to the fact that some unfathomably bad disasters could nonetheless be survivable. But there are also some problems with this definition. The most significant is that, one could argue, human extinction and civilizational collapse do not have comparable ethical implications. Since human extinction is irreversible, it would result in the loss of potentially vast amounts of future value. In contrast, the collapse of civilization does not necessarily preclude the realization of such value: Those who survive could rebuild civilization over the course of decades or centuries. Consider  Bostrom's (2002)  point that from the perspective of humankind as a wholeeven the worst of [catastrophes so far in human history] are mere ripples on the surface of the great sea of life. They haven't significantly affected the total amount of human suffering or happiness or determined the long-term fate of our species. Thus, the global village could implode without this significantly altering the total amount of value that our lineage creates within our future light cone. Even more, civilizational collapse need not entail a major loss of human lifealthough it is worth noting that even if 99% of the current population were to perish, this would still leave 76 million people alive. For such reasons, human extinction appears to be qualitatively worse than civilizational collapse, however unfathomably horrible the latter would be. The point is this: Resources to mitigate existential risks are finite; thus, we should prioritize their use based on which threats are the most seriousholding tractability and neglectedness equal. But if the first disjunct in this definition refers to an outcome that is far more serious than the second disjunct, then including civilizational collapse as one form of existential catastrophe could end up taking resources away from preventing human extinction. Another issue is that it is possible to realize a hyper-existential risk without causing either human extinction or civilizational collapse. Thus, if one wishes for the term 'existential risk' to encompass hyper-existential catastrophes as a special casespecifically, as the worst kinds of existential catastrophesthen these definiens are inadequate. Indeed, it could be that continued technological innovation and civilizational development along certain trajectories actually enables the realization of a hyper-existential risk, perhaps in the form of an oppressive totalitarian society in which a majority reside in profoundly squalid conditions of inscrutable misery. This suggests that, if existential risks are supposed to be 'worstcase outcomes' for humanity, it is inadequate. Yet, as I will argue below, it may nonetheless be useful in non-academic discussions of existential risk phenomena. \n Human extinction or a permanent and drastic loss of potential An event X is an existential risk if and only if X could cause either the extinction of humanity or a permanent and drastic loss of our potential for desirable future development. Since this definition emerges from the work of  Bostrom (2002 Bostrom ( , 2013 , I will call it Bostrom's 'lexicographic definition' to distinguish it from another definition put forth in the same manuscripts, discussed below. Although perhaps not the most commonly used definition in the literature, it is arguably the most canonical, since it is the first formal definition of the term, propounded in Bostrom's 2002 paper that, once again, more or less officially founded the field. 5 Notice that, like the previous definition, this one is also disjunctive, with each disjunct being sufficient for an existential catastrophe to have occurred. The crucial question is how one should interpret the value-laden second disjunct. What does 'desirable future development' mean? For a Benatarian anti-natalist, the most desirable future would be no future at alli.e. the voluntary and perhaps 'phased' extinction of Homo sapiens, although this is in tension with the first disjunct. The same goes for a 'strong' negative utilitarian: The most desirable future development would be the total elimination of the very possibility of sentient life in the universe. In contrast, for an anarcho-primitivist, it would be the creation of a 'future primitive' state in which humans live in small-scale egalitarian societies that are sustainably embedded within the ecological system. And so on. Bostrom himself appears to interpret the second disjunct by combining total utilitarianism and transhumanism. Thus, he has previously argued for prioritizing the colonization of space 6 for the purpose of filling our future light cone with as much value as possible. On the total utilitarian view, one might say that morality abhors a vacuum. Furthermore, just as we should maximize the total number of happy people in the universe, we should also use person-engineering technologies to optimize our individual capacities to be happy. This would entail the creation of a new lineage, or of multiple lineages, of posthuman beings who, by definition, have cognitive abilities, healthspans, or emotional ranges that far exceed the best attainable by any organism with a human-type genome  (Bostrom 2008) . Such considerations lead Bostrom, in his 2002 paper, to interpret the axiological term 'potential' as referring to 'the transition … from a human to a \"posthuman\" society.' He is more precise about this in his 2013 follow-up an existential risk is any risk that has the potential to eliminate all of humanity or, at the very least, kill large swaths of the global population, leaving the survivors without sufficient means to rebuild society to current standards of living.  (FLI 2018)  Similarly, a Global Challenges Foundation report from 2015 claims to introduce 'a new category of global risk,' namely, 'risks with potentially infinite impact.' The report defines a risk of this sort as 'where civilisation collapses to a state of great suffering and does not recover, or a situation where all human life ends.' This comes close to definition (ii) above, but the emphasis on civilizational collapse events that have irreversible consequences positions it closer to Bostrom's lexicographic definition. Indeed, the authors of the report write that the idea to establish a well defined category of risks that focus on risks with a potentially infinite impact that can be used as a practical tool by policy makers is partly inspired by Nick Bostrom's philosophical work and his introduction of a risk taxonomy that includes an academic category called 'existential risks.' … The infinite category is a smaller subset of 'existential risk' and this new category is meant to be used as a tool. Finally, one of the present authors has, on numerous occasions, somewhat extravagantly limned the concept of existential risk as 'any future event that either trips our species into the eternal grave of extinction or irreversibly catapults us back into the Stone Age.' 6 Just so long as doing so doesn't interfere with priority number one, namely, the reduction of existential risk. on the topic, in which he identifies the following four existential risk 'failure modes' (quoting): (1) Human extinction: Humanity goes extinct prematurely, i.e. before reaching technological maturity. (2) Permanent stagnation: Humanity survives but never reaches technological maturity. Subclasses: unrecovered collapse, plateauing, recurrent collapse. (3) Flawed realization: Humanity reaches technological maturity but in a way that is dismally and irremediably flawed. Subclasses: unconsummated realisation, ephemeral realisation. (4) Subsequent ruination: Humanity reaches technological maturity in a way that gives good future prospects, yet subsequent developments cause the permanent ruination of those prospects. In every case, existential risks are characterized as failures to establish a stable state of technological maturity. By 'technological maturity,' Bostrom means 'the attainment of capabilities affording a level of economic productivity and control over nature close to the maximum that could feasibly be achieved'  (Bostrom 2013) . Why does this matter? Because technological maturity would be the situation most conducive to realizing astronomical amounts of value, in accordance with total utilitarianism and transhumanism. As Bostrom puts it, the capabilities of a technologically mature civilisation could be used to produce outcomes that would plausibly be of great value, such as astronomical numbers of extremely long and fulfilling lives. More specifically, mature technology would enable a far more efficient use of basic natural resources (such as matter, energy, space, time, and negentropy) for the creation of value than is possible with less advanced technology. And mature technology would allow the harvesting (through space colonisation) of far more of these resources than is possible with technology whose reach is limited to Earth and its immediate neighbourhood  (Bostrom 2013) . It follows from these observations that one could remove the correlative conjunction in the lexicographic definition and reconstruct it more succinctly as follows: 'An event X is an existential risk if and only if X could permanently prevent humanity, broadly defined to include some possible posthuman descendants, from attaining a stable state of technological maturity.' This is the essence of Bostrom's first definition: the ultimate goal of civilizational development should be producing mature technology in a sustainable manner, so any event that prevents this from happening must be avoided at all costs. This definition handles Scenario 1 from above without difficulty. As  Bostrom (2013)  writes, 'the permanent foreclosure of any possibility of this kind of transformative change of human biological nature may itself constitute an existential catastrophe.' Bostrom also suggests that all four scenariosand thus both disjunctsare 'of comparable seriousness, entailing potentially similarly enormous losses of expected value.' Once again, this contrasts with the second definition in which the second disjunct has far less severe moral implications than the first disjunct, given certain assumptions. But there are several problems with this definition as well. First, consequentialism is a minority view among philosophers, with only 23.6% accepting it as of 2013  (Bourget and Chalmers 2014) . And, of course, not all consequentialists are utilitarians, just as not all utilitarians accept the aggregative and impersonal perspectives of the total view. Rather, some hold that there is a diminishing marginal value to creating new people, that the value of future lives is less than the value of current lives (temporal discounting), or that failing to create extra people isn't bad even if those people would live extremely happy lives, since acts can only be bad if they are bad for someone (the person-affecting intuition). According to the latter view, Parfit is wrong to argue that the difference between 99% and 100% of humanity dying out is far greater than the difference between 1% and 99% dying out. Since the failure to bring into existence a potentially astronomical number of future people with worthwhile lives harms no one, human extinction is worse than the loss of 99% of humanity by only one percentage point. Note also here that the total view engenders the Repugnant Conclusion and violates the intuition of 'procreational asymmetry,' which implies, in slogan form, that we should focus on making people happy rather than making happy people. Second, many would likely object to the transhumanist values that Bostrom imports into his definition. Bioconservatives, for example, oppose 'enhancive' modifications to the human phenotype, especially modifications that would alter our 'human essence'what Francis  Fukuyama (2002)  terms 'Factor X'upon which liberal democracies are founded. But even some techno-progressives might find the emphasis on technological maturity off-putting: It could be seen as too crass, technocratic, ecologically exploitative, capitalistic, colonialist, and so on. The present author, in fact, knows of several scholars who balk at the lexicographic definition for precisely this reason. This is worrisome because it could lead such individuals to reason as follows: 'Since existential risks are scenarios that prevent the attainment of technological maturity, and since I don't care about subjugating nature, maximizing economic productivity, etc., it follows that I must not care about existential risks.' The same could be said about the transhumanist desideratum of exploring the posthuman realm: why is failing to radically enhance the human species so undesirable? There are also issues relating to personal identity that arise in this context: it could be that the transformations required to become posthuman result in a genuinely new person, in the metaphysical sense (see author). From this perspective, the true risk is that everyone would essentially commit suicide by augmenting their brains and bodies. Yet another downside of the lexicographic definition is that it doesn't adequately address Scenario 2 from above. As  Althaus and Gloor (2018)  observe, this definition is unfortunate in that it lumps together events that lead to vast amounts of suffering and events that lead to the extinction … of humanity. However, many value systems would agree that extinction is not the worst possible outcome, and that avoiding large quantities of suffering is of utmost moral importance. In other words, Bostrom doesn't distinguish between scenarios that could (a) cause our extinction, and (b) result in astronomical amounts of suffering. Thus, one could argue as per above, that this failure is actually quite dangerous given the following conditions: humanity embraces the maxipok rule, has limited resources to mitigate existential risks, and could encounter a hyper-existential or suffering catastrophe. Surely we shouldas the maximin (and minipnok 7 ) rule impliesat least prioritize avoiding future scenarios that are worse than extinction before aiming for a technoutopian future. Along these line, consider that the following two scenarios fall within the very same moral category on this definition: (1) An asteroid strikes Earth, resulting in an impact winter that kills every human within two dreadful weeks, and (2) our civilization persists at roughly its current level of technological development, with the same number of people having approximately the same quality of life for the next 1 billion years. The latter would be an instance of 'permanent stagnation' in Bostrom's quadripartite typology, yet it seems unambiguously better than the former. Surely most people would concur that spending the same amount of resources to avoid (2) as to avoid (1) would be misguided. A final objection concerns the 'temporal permanence' criterion of the second disjunct. As Cotton-Barratt and Ord (2015) write, consider 'a totalitarian regime [that] takes control of the earth; there is only a slight chance that 7 See author. humanity will ever escape.' Should this count as an existential catastrophe on Bostrom's definition? Perhaps it depends on when one answers: in the midst of the regime's global control over civilization, one might suspect at T1 that an existential catastrophe has occurred; but if this regime were to dissolve at a later time T2, then, although there had been copious evidence of an existential catastrophe at T1, an existential catastrophe had not in fact occurred. In other words, deciding that an event E is an existential catastrophe is an epistemological issue, whereas E actually being an existential catastrophe is a metaphysical one. But this does not completely solve the problem, as Cotton-Barratt and Ord note: Bostrom's definition doesn't [convincingly] specify whether it should be considered as one. Either answer leads to some strange conclusions. Saying it's not an existential catastrophe seems wrong as it's exactly the kind of thing that we should strive to avoid for the same reasons we wish to avoid existential catastrophes. Saying it is an existential catastrophe is very odd if humanity does escape and recover-then the loss of potential wasn't permanent after all. The problem here is that potential isn't binary. Entering the regime certainly seems to curtail the potential, but not to eliminate it. (Cotton-Barratt and Ord 2015) Put differently, 'potential' isn't binary but 'temporal permanence' is, and this poses a problem for the lexicographic definition. In brief, this definition is more sophisticated than the first two, but its connection to total utilitarianism and transhumanism could make it less attractive to individuals who care about the future of humanity but reject one or the other of these axiological systems. It also appears susceptible to certain counter-examples. \n A pangenerational-crushing catastrophe An event X is an existential risk if and only if X could have undesirable consequences for humanity that are 'pangenerational' and 'crushing.' Let's call this Bostrom's 'typological definition.' First, whereas the lexicographic definition is disjunctive, this one is conjunctive: it specifies two conditionsi.e. being pangenerational and being crushingthat risks must satisfy to count as existential. Second, as the appellation implies, this definition derives from a general typology of risks that Bostrom delineates, and then modifies, in three papers. The typology is based on a particular conceptual analysis of risk, according to which a risk is the probability of an undesirable event multiplied by its consequences, where the consequences of a risk are dissected into two components: Scope, or the size of the group affected, and intensity, or how bad the effects are for the group.  Bostrom's (2013)  most recent typology places existential risks in the top right box where the categories of 'pangenerational' and 'crushing' intersect (see Figure  1 ). The former refers to events 'affecting humanity over all, or almost all, future generations,' and the latter to events 'causing death or a permanent and drastic reduction of quality of life.' Thus, Bostrom backs away from the 'temporal permanence' criterion of his lexicographic definition, although it is unclear that he recognizes this: while these two definitions are intensionally distinct, they are presumably intended to be extensionally equivalent. If the typological definition includes some events whose effects are permanent and the lexicographic definition does not, then they do not pick out the same class of risky happenings. There are other problems, though. Consider the categories of the x-axis. First, it seems that 'imperceptible' should be a subcategory of 'endurable,' and as such this seems to commit what Gilbert  Ryle (1949)  famously called a 'category mistake.' On this logic, one might as well also include as distinct categories 'barely noticeable,' 'moderately annoying,' 'quite bad,' and so on. Furthermore, if some crushing events are by stipulation endurable, then distinguishing 'crushing' events from 'endurable' events is confused. Similar Rylean issues problematize the y-axis. For example, notice that 'personal,' 'local,' and 'global' are all spatial categories whereas 'transgenerational' and 'pangenerational' are spatiotemporal categories. The result is another ontological error. These problems yield some empirical inadequacies. For instance, consider that a germline mutation, such as the hemoglobin gene mutations that cause sickle-cell anemia, could be restricted to a local or personal scope across space yet will also have transgenerational temporal effects. Yet where in Figure  1  might this risk fit? Similarly, Bostrom classifies the 'loss of one species of beetle' as a transgenerational-imperceptible event. But this overlooks potentially important facts about the geographical spread of the species. If the beetle is restricted to a small region, then its disappearance may indeed be imperceptible, but if its ecological range is more global, then the loss of a single species of beetle could have cantharophilic effects that nontrivially harm the health of larger ecosystems. It may thus be important to specify whether a transgenerational event of this sort has local or global consequences, yet there is no possibility in this typology of, for example, localpangenerational-imperceptible risks. Finally, at the non-existential risk of caviling, it seems rather odd, rather awkward, to describe aging as a 'crushing' risk. Fortunately, these problems aren't insoluble: (i) One could replace the three/four categories on the x-axis with the two basic categories of 'recoverable' and 'unrecoverable,' thereby more perfectly aligning the typological definition with the lexicographic definition. An 'unrecoverable' event would thus be one that forever prevents humanity from attaining a stable state of technological maturity, whereas a 'recoverable' event would be one that doesn't. All four existential risk failure modesi.e. human extinction, recurrent collapse, and so onwould then fall within the unrecoverable category. This would, of course, require that the definition of 'pangenerational' changes from 'affecting humanity over all, or almost all, future generations' to 'affecting humanity for all future generations,' but this is how Bostrom seems to think about existential risks in most of his explorations of the topic. Incidentally, the recoverable/unrecoverable distinction nicely maps on to a diagram put forth by Baum, Denkenberger, and Haqq-Misra 2015, seen in Figure  2 . As this diagram makes clear, albeit tacitly, an existential catastrophe could have two distinct outcomes, namely, extinction and survival without recovery. And (ii), one could split the spatiotemporal components of the categories on the y-axis, thus separating this dimension into space and time. The resulting three-dimensional typology would be based on the following augmented conceptual analysis of risk: A risk is the probability of an undesirable event multiplied by its consequences; the consequences are then analyzed into their scope and intensity, where scope is further decomposed into its spatial and temporal properties. Thus: 'risk = [spatial scope, temporal scope, and intensity of consequences] × [probability of occurrence].' If we revert to an older dichotomy used by  Bostrom (2002)  one that distinguishes between 'endurable' and 'terminal' rather than, as per above, 'recoverable' and 'unrecoverable' eventsthis new typology would classify all existential risks as global-pangenerational events, where the first term indicating the risk's spatial scope and the second its temporal scope. Within this conjunctive category, extinction events would constitute global-pangenerational-terminal events (node A) and existential risks that correspond to the second disjunct of Bostrom's lexicographic definition would constitute the subset of global-pangenerational-endurable events that irreversibly preclude the stable attainment of technological maturity (node B).  8  In addition to these typological accounts of existential risks, Figure  3  also easily accommodates phenomena like aging, hereditary disease (node C), and the loss of a single species of beetle (node D). While this modified typological definition is more complex, it is also more precise. It is also constant with Thomas  Kuhn's (1962)  observation that as scientific fields mature, they tend to undergo 'a refinement of concepts that increasingly lessens their resemblance to their usual commonsense prototypes.' The three-dimensional definition also makes explicit that some existential risks can indeed be survived. \n A significant loss of expected value An event X is an existential risk if and only if X could cause the loss of a large fraction of expected value. 9 This definition comes from a short 2015 paper by Cotton-Barratt and Ord, published as a 'technical report' by the Future of Humanity Institute (FHI). It is, as they write, primarily motivated by the aforementioned fact that potential isn't binary but permanence is. Recall the totalitarian scenario mentioned when discussing Bostrom's lexicographic definition above; Cotton-Barratt and Ord write that 'if we enter into the totalitarian regime and then at a later date the hope of escape is snuffed out, that represents two existential catastrophes under [the expected value] definition.' That is to say, humanity 'lost most of the expected value when we entered the regime, and then lost most of the remaining expected value when the chance for escape disappeared.' It may be worth pausing on this point for a moment. On the present definition, an existential catastrophe can occur more than once in a species' lifetime. The same goes for an existential catastrophe that entails 'mere' civilizational collapse, as specified by the second definition above. But this is not the case if one accepts the 'existential risks as human extinction,' 'existential risks as human extinction or a permanent and drastic loss of potential,' or 'existential risks as pangenerational-crushing events.' In all of these cases, humanity has one, and only one, shot at avoiding disaster. Indeed, this is why  Bostrom (2002)  emphasizes that we must replace our normal reactive approach to dealing with risks with an entirely proactive approach: if even a single existential catastrophe were to occur, the game would be over and humanity would have lost (its chance to 'fulfill its potential'). Thus, Cotton-Barratt and Ord's definition dilutes this implication of preemptive urgency at least a little by allowing for the possibility that humanity recovers from one or more past existential catastrophes. This is a notable difference with respect to the other definitions so far explicated. Other features of this definition are: first, one can interpret it as a refinement of the second disjunct of Bostrom's lexicographic definition that also discards the first disjunct (as conceptually unnecessary within the definiens). The result is a reorganization of Bostrom's four failure modes of 'human extinction,' 'permanent stagnation,' 'flawed realization,' and 'subsequent ruination' under a single conceptual heading, rather than placing the first failure mode under the first disjunct of the lexicographic definition and the last three under the second disjunct. Put differently, it looks arbitrary and inconsistent that Bostrom's definition singles out human extinctionone of four particular failure modesbut then hides the other three failure modes behind the phrase 'permanently and drastically compromising our potential for desirable future development.' The critical point is that all of thee failure modes are bad because they entail huge losses of expected value within our future light cone. Cotton-Barratt and Ord's definition also foregrounds an ideai.e. expected valuethat nebulously lurks behind Bostrom's discussions of existential risk, making occasional cameos but then returning to the philosophical background. For example, in a discussion about the moral force of the maxipok rule, Bostrom writes that (partly quoted above) 'these considerations suggest that the loss in expected value resulting from an existential catastrophe is so enormous that the objective of reducing existential risks should be a dominant consideration whenever we act out of an impersonal concern for humankind as a whole'  (Bostrom 2013) . The point is that Cotton-Barratt and Ord's definition could be seen as a more distilled version of Bostrom's definitions, which leads to the next point: third, the expected value definition does not explicitly mention technological maturity, and thus it does not engender the problem of potential allies ignoring existential risk studies because its central aims are 'too transhumanistic.' For Cotton-  Barratt and Ord (2015) , the term ''value' refers simply to whatever it is we care about and want in the world'which, once more, connects with the following point: fourth, this flexibility opens the door for a wide range of axiological interpretations of the definition. As mentioned above, most existential risk scholars appear to espouse total utilitarianism and many are also sympathetic with the transhumanist project; for such scholars, 'value' refers to the well-being of sentient life (which ought to be maximized) and 'having the opportunity to explore the transhuman and posthuman realms,' as  Bostrom (2005)  puts it. Another cluster of issues to note is: (a) The first two definitions above specifically reference scenarios that we should avoid, without saying anything about which scenarios we should pursue. On these accounts, the worst-case outcome for humanity would be to fall victim to such bad scenarios; the same could be said of the fourth, typological definition. (b) The third, lexicographic definition focuses on what we should attain, defining any event that prevents the attainment of technological maturitya techno-utopian condition of endless possibilities (see Bostrom 2008)as the worst-case outcome for humanity. Or, as Cotton-Barratt and Ord (2015) put it, 'under Bostrom's definition we are comparing ourselves to the most optimistic potential we could reach.' In contrast, (c) the present definition focuses on avoiding a significant loss of expected value but does not explicitly identify any particular scenario, such as human extinction, civilizational collapse, or failing to reach technological maturity, that humanity must dodge at all costs. Yet Cotton-Barratt and Ord argue that their conception of existential risks gives rise to the mirror concept of what they call 'existential hope.' This arises from the possibility of (to borrow a term from J.R.R. Tolkien) 'existential eucatastrophes,' which are the mirror phenomena of existential catastrophes, that could cause 'there to be much more expected value after the event than before.' Thus, they argue that just as we should avoid existential catastrophes, we should seek out existential eucatastrophes, examples being the emergence of the first living organisms, any successful dodging of a Great Filter, or, perhaps, the creation of a value-aligned machine superintelligence. From a pragmatic point of view, the idea of existential hope, as Max Tegmark (2018) points out, usefully encourages us to imagine 'positive futures not only for ourselves, but also for society and for humanity itself,' an activity that may help to overcome the occasional paralysis or defeatism that some people experience when cogitating the topic of existential risks (see also  Pinker 2018) . In a phrase, the combination of existential risk and existential hope offers a more complete and comprehensive world-picture that humanity could employ when deciding which development trajectories we ought to pursue, and this makes it appealing as an organizing principle for the field of existential risk studies.  10  But there are also some ostensive problems with this definition. First, as implied above, it may be too flexible. As Cotton-Barratt and Ord note, the term 'value' is doing much of the work in the definition and, as we have seen, there is a huge range of distinct and mutually exclusive value theories on the marketplace of ideas. Indeed, there is nothing conceptually incoherent about, say, an anarcho-primitivist exclaiming, 'We must do everything we possibly can to mitigate existential risks! Follow the maxipok rule!,' but meaning that we ought to destroy the techno-industrial system upon which modern civilization is founded. Second, if one accepts the 'astronomical value thesis,' according to which the value of the distant future could be unimaginably great (see author), that future lives are worth the same as present lives, and so on, the result could be what Steven  Pinker (2011)  terms 'a pernicious utilitarian calculus' that encourages people to, as it were, redirect the trolly to sacrifice the lives of current humans for the purpose of inflating the probability that innumerably more posthumans come to exist in the future. This is a criticism that applies no less to Bostrom's (utilitarian) conception of existential risks, as Olle Häggström argues. To quote Häggström at length: Recall … Bostrom's conclusion about how reducing the probability of existential catastrophe by even a minuscule amount can be more important than saving the lives of a million people. While it is hard to find any flaw in his reasoning leading up to the conclusion, and while if the discussion remains sufficiently abstract I am inclined to accept it as correct, I feel extremely uneasy about the prospect that it might become recognized among politicians and decision-makers as a guide to policy worth taking literally. It is simply too 10 Some might argue that 'existential despair' better contrasts with 'existential hope,' although Cotton-Barratt argues that this point isn't 'necessarily enough to sink the [original] term' of 'existential hope'  (Cotton-Barratt 2015) . reminiscent of the old saying 'If you want to make an omelet, you must be willing to break a few eggs,' which has typically been used to explain that a bit of genocide or so might be a good thing, if it can contribute to the goal of creating a future utopia. Imagine a situation where the head of the CIA explains to the US president that they have credible evidence that somewhere in Germany, there is a lunatic who is working on a doomsday weapon and intends to use it to wipe out humanity, and that this lunatic has a one-in-amillion chance of succeeding. They have no further information on the identity or whereabouts of this lunatic. If the president has taken Bostrom's argument to heart, and if he knows how to do the arithmetic, he may conclude that it is worthwhile conducting a full-scale nuclear assault on Germany to kill every single person within its borders. And finally, if one interprets value in Cotton-Barratt and Ord's definition as well-being, and well-being in hedonistic terms, then, as David Pearce (2014) observes, total utilitarians are 'obliged to convert your matter and energy into pure utilitronium, erasing you, your memories, and indeed human civilisation.' 11 A couple of points: (a) One can view this as a reductio ad absurdum of hedonistic monism, along the lines of Robert  Nozick's (1974)  'experience machine' thought experiment, and (b) many people would no doubt argue that converting the universe into utilitronium would yield if not a worst-case outcome, then certainly not the best-case outcome. Thus, the combination of Cotton-Barratt and Ord's general framework plus a widely accepted and respectable moral theory could have potentially devastating consequences, or so one might plausibly argue. \n Evaluating definitions Consistent with Kuhn's observation in section 1, Steven  Pinker (2014)  observes that esoteric vocabularies are 'unavoidable because of the abstractness and complexity of [academic] subject matter  [s] .' Consequently, every human pastime-music, cooking, sports, art-develops an argot to spare its enthusiasts from having to use a long-winded description every time they refer to a familiar concept in one another's company. It would be tedious for a biologist to spell out the meaning of the term transcription factor every time she used it, and so we should not expect the tête-à-tête among professionals to be easily understood by amateurs.  12  Yet the aim of existential risk studies isn't just to further expand the edifice of human knowledge, butas alluded to in section 1to communicate these ideas and insights to politicians, policymakers, business leaders, and to all others with the power of the ballot. Informing the public about the ideas and insights generated by existential risk research is integral to the broader programme; there is simply no point to devising effective strategies for navigating the obstacle course of threats before us if those strategies will never be implemented by governments, international organizations, corporations, and other relevant entities. To paraphrase Karl Marx's now-hackneyed exhortation (borrowed from Voltaire), the point is to change the world. Indeed, a number of leading scholars have made a number of notable media appearances to discuss existential risks and related issues. Essential to the success of the field are 'ambassadors of science'very often, thus far, active contributors to the technical literaturecapable of interfacing between the experts and non-experts. Notice here that different risks require different outreach strategies. For example, humanity is unlikely to prevent further anthropogenic climate change without the public putting significant pressure on political leaders. In democratic states, this means persuading the electorate to vote for candidates who vow to support legislation that reduces our collective carbon footprint, encourages the development of alternative energy sources, and so onessentially, to resolve the tragedy of the commons. Thus, efforts to convey information about the potentially catastrophic effects of climate change should target the general public. This contrasts with risks like asteroid impacts and, arguably, value-misaligned machine superintelligence. In the former case, public knowledge about near-Earth objects (NEOs) is mostly irrelevant to the detection and deflection of asteroids and comets that are on a crash course with Earth. So long as NASA and similar organizations around the world remain sufficiently well-funded, the extent to which humanity is collectively safe from a catastrophic collision is not a function of the degree of public informedness. Similar points could be made about superintelligence: On the one hand, avoiding an AI arms race with China or Russia might depend on adequate pressure on politicians by an electorate worried about the possible consequences of another 'Cold War,' except far less stable given the nature of AI and the larger number of actors that could be involved  (Armstrong, Bostrom, and Shulman 2016; author) . Thus, on the other hand, when it comes to superintelligence, a positive outcome will depend almost entirely on experts: moral philosophers and computer scientists working on the 'value-alignment problem.' Alerting the public of the dangers posed by machine superintelligence is unlikely to directly alter progress on determine what our 'human values' are and how to define these 'in primitives such as mathematical operators and addresses pointing to the contents of individual memory registers'  (Bostrom 2014) . Thus, whereas existential risk scholars who are focused on environmental degradation need to engage with the general public, those working on issues like superintelligence should direct their outreach efforts at theoreticians, industry scientists, CEOs, and so on. If this picture is accurate, then it might be optimal to employ different definitions depending on the conversational context. Indeed, this is the position that I will here defend, which I call 'context-dependent semantic pluralism.' In my view, the second definition of existential risk as either human extinction or civilizational collapse is preferable to the first, and the best definition for communicating to the general public. The reasons are as follows: first, if the question is 'What ought our global priorities be?,' then the first definition is much too narrow. Although the moral implications of civilizational collapse are less significant than those of extinction, it is useful to at least signal to the public that scholars aren't merely worried about human extinctiona planetary-scale catastrophe could catapult the human species back into the Stone Ageeven if the signal itself is inexact. Indeed, a number of scenarios in the foreground of researchers' attention, such as climate change, seem unlikely to directly cause human extinction but quite likely to seriously damage human civilization. Even more, civilizational collapse may be more vivid to the average mind than human extinction, in part because few apocalyptic Hollywood movies focus on extinction rather than collapse. Although scope neglect and 'psychophysical numbing' could apply to both scenarios, it may be especially applicable to annihilation, thus dulling the emotional impact of warnings of the form, 'If X happens, humanity could go extinct.' A recent unpublished study, in fact, found that Derek Parfit was right in his conjecture that most people don't see the difference between 99% and 100% of humanity dying out as much greater than the difference between peace and 99% of humanity dying out. Yet, when researchers prodded subjects to think explicitly about the far future and all the good that it could envelop, they shifted their opinion toward Parfit's own view. With respect to the lexicographic, typological, and expected value definitions of 'existential risk,' there is a good case that these are too esoteric for a general audience. Bostrom's definition requires some knowledge of moral philosophy and transhumanism, and few members of the public are conversant with decision theory and the technical concept of expected value. In sum, the second definition avoids the simplism of the first definition as well as the esoterica of the last three; it constitutes a middle ground between these two ends. I thus recommend its use when discussing existential risks and related topics with lay audiences. There remains the second question of which definition ought to be the canonical one used by scholars in conversations amongst themselves and with professional scientists and philosophers outside of the field. Here the simplism of the first definition and imprecision of the second quickly disqualifies them from serious consideration. That is to say, it would be misleading to equate existential risks with either mere human extinction or civilizational collapse; careful axiological reflection implies that what really matters are disasters with long-lasting effects that drastically compromise our potential to realize our various individual and collective ambitions for happiness, knowledge, peace, moral growth, and so on. Both of Bostrom's definitions gesture at this idea, which makes them appealing, although as previously noted even some techno-progressives could find the focus on 'technological maturity' to be objectionable. Indeed, transhumanism remains a controversial normative-futurological position, and recall from above that a relatively small minority of professional philosophers espouse total utilitarianism. For reasons such as these, I believe that the field of existential risk studies would generally benefit from eschewing both of Bostrom's definitions. This leaves the fifth definition from Cotton-Barratt and Ord, which I believe, with modification, is superior to all other definitions in the context of tête-à-tête communication and efforts to evangelize for the field to scientists and philosophers unfamiliar with its aims, methodologies, and so on. Most people value things in the world and, as Samuel Scheffler (2009) observes, 'what would it mean to value things but, in general, to see no reason of any kind to sustain them or retain them or preserve them or extend them into the future?' The ambiguity of 'value' in the fifth definition enables a wide range of interpretations, which could result in individuals who value seemingly disparate thingse.g. sports, literature, philosophy, science, the wilderness, standup comedy shows, and 3D moviesto unify behind the single ultra-goal of mitigating existential risk. Indeed, it may be an improvement of Cotton-Barratt and Ord's definition to make explicit that 'value' can be understood as denoting whatever one happens to care about in this strange place called 'the universe.' Thus, when a scientist or philosopher outside the field asks what existential risks are, one could respond: An event X is an existential risk if and only if X could cause the loss of a large fraction of expected value, where you (the interlocutor) can define 'value' however you'd like. It is my considered opinion that this constitutes the best definition for the purpose of further establishing existential risk studies as a legitimate field of scientific and philosophical inquiry. The implication of this admittedly brief discussion of context-dependent semantic pluralism is that existential risk scholars will have to pivot from one use to the other in response to different audiences.  13  Given that existential risk studies is an 'outward-facing' (or integrally activist) field that strives to bring about nontrivial positive changes in the real world, terminological flexibility may be an essential skill for existential risk scholars to develop. \n Conclusion This paper falls within an emerging subfield that I call 'the conceptual foundations of existential risk studies.' Given the dearth of research so far conducted on the relevant topics, I do not see this paper as the final word. Rather, my goal is much more modest: To merely stimulate further philosophical analyses of this concept by bringing together, for the first time in a single paper, the various definitions that have so far been outlined and discussed seriously in the scholarly literature. Future research on this topic might thus focus on devising better necessary and sufficient conditions for the definiendum, exploring how different theories of concepts (e.g. the 'prototype theory,' 'theory theory') might solve some of the problems specified above, examining additional novel strategies for making the idea of existential risk more appealing those outside of the field's perimeter, and communicating important research results to the publica necessary step with respect to certain risks like climate change. Thus, my closing remark is an invitation: Much work remains to be done. Figure 1. \n Figure 2 . 2 Figure 2. Different Possible Long-Term Trajectories. (Adapted from Baum 2010.) \n Figure 3 . 3 Figure 3. A Three-Dimensional Typology of Risks. \n\t\t\t There is, as of this writing, a burgeoning literature on pluralism within the field of philosophy. Of particular interest is Chalmers (2011) , especially a particular version of the 'method of elimination' that Chalmers calls the 'subscript gambit.' (Thanks to an anonymous reviewer for calling my attention to this paper.) I draw from this literature, although mostly implicitly.2 P. TORRES \n\t\t\t Furthermore, in a discussion of natural global pandemics, Häggström writes that not only do pandemics pose a 'global threat,' but it may 'also pose a risk on the next level, threatening to end civilization as we know it, or even the existence of humanity' (Häggström 2016) .6 P. TORRES \n\t\t\t One finds myriad variations of this definition in the literature; for example, the Future of Life Institute (FLI) states that \n\t\t\t P. TORRES \n\t\t\t P. TORRES \n\t\t\t P. TORRES \n\t\t\t P. TORRES \n\t\t\t Note: the 'permanence' condition of the second disjunct is embedded within the concept of pangenerational. \n\t\t\t Quoted in Cotton-Barratt and Ord (2015). \n\t\t\t This is, of course, intended to be a sardonic reference to Pinker's comments in Coyne 2019.", "date_published": "n/a", "url": "n/a", "filename": "Existential risks a philosophical analysis.tei.xml", "abstract": "This paper examines and analyzes five definitions of 'existential risk.' It tentatively adopts a pluralistic approach according to which the definition that scholars employ should depend upon the particular context of use. More specifically, the notion that existential risks are 'risks of human extinction or civilizational collapse' is best when communicating with the public, whereas equating existential risks with a 'significant loss of expected value' may be the most effective definition for establishing existential risk studies as a legitimate field of scientific and philosophical inquiry. In making these arguments, the present paper hopes to provide a modicum of clarity to foundational issues relating to the central concept of arguably the most important discussion of our times.", "id": "cd21886d87b00bce109e23948e8e31b2"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dylan Hadfield-Menell", "Anca Dragan", "Pieter Abbeel", "Stuart Russell"], "title": "The Off-Switch Game", "text": "Introduction From the 150-plus years of debate concerning potential risks from misbehaving AI systems, one thread has emerged that provides a potentially plausible source of problems: the inadvertent misalignment of objectives between machines and people. Alan Turing, in a 1951 radio address, felt it necessary to point out the challenge inherent to controlling an artificial agent with superhuman intelligence: \"If a machine can think, it might think more intelligently than we do, and then where should we be? Even if we could keep the machines in a subservient position, for instance by turning off the power at strategic moments, we should, as a species, feel greatly humbled. ...  [T] his new danger is certainly something which can give us anxiety  [Turing, 1951] .\" There has been recent debate about the validity of this concern, so far, largely relying on informal arguments. One important question is how difficult it is to implement Turing's idea of 'turning off the power at strategic moments', i.e., switching a misbehaving agent off 1 . For example, some have argued that there is no reason for an AI to resist being switched off unless it is explicitly programmed with a self-preservation incentive  [Del Prado, 2015] .  [Omohundro, 2008] , on the other hand, points out that self-preservation is likely to be an instrumental goal for a robot, i.e., a subgoal that is essential to successful completion of the original objective. Thus, even if the robot is, all other things being equal, completely indifferent between life and death, it must still avoid death if death would prevent goal achievement. Or, as  [Russell, 2016]  puts it, you can't fetch the coffee if you're dead. This suggests that an intelligent system has an incentive to take actions that are analogous to 'disabling an off switch' to reduce the possibility of failure; switching off an advanced AI system may be no easier than, say, beating AlphaGo at Go. To explore the validity of these informal arguments, we need to define a formal decision problem for the robot and examine the solutions, varying the problem structure and parameters to see how they affect the behaviors. We model this problem as a game between a human and a robot. The robot has an off switch that the human can press, but the robot also has the ability to disable its off switch. Our model is similar in spirit to the shutdown problem introduced in  [Soares et al., 2015] . They considered the problem of augmenting a given utility function so that the agent would allow itself to be switched off, but would not affect behavior otherwise. They find that, at best the robot can be made indifferent between disabling its off switch and switching itself off. In this paper, we propose and analyze an alternative formulation of this problem that models two key properties. First, the robot should understand that it is maximizing value for the human. This allows the model to distinguish between being switched off by a (non-random) human and being switched off by, say, (random) lightning. Second, the robot should not assume that it knows how to perfectly measure value for the human. This means that the model should directly account for uncertainty about the \"true\" objective and that the robot should treat observations of human behavior, e.g., pressing an off switch, as evidence about what the true objective is. In much of artificial intelligence research, we do not consider uncertainty about the utility assigned to a state. It is well known that an agent in a Markov decision process can ignore uncertainty about the reward function: exactly the same behavior results if we replace a distribution over reward functions with the expectation of that distribution. These arguments rely on the assumption that it is impossible for an agent to learn more about its reward function. Our observation is that this assumption is fundamentally violated when we consider an agent's off switch -an agent that does not treat a 'switch-off' event as an observation that its utility estimate is incorrect is likely to have an incentive for self-preservation or an incentive to switch itself off. In Section 2, following the general template provided by  [Hadfield-Menell et al., 2016] , we model an off switch as a simple game between a human H and a robot R, where H can press R's off switch but R can disable it. R wants to maximize H's utility function, but is uncertain about what it is. Sections 3 and 4 show very generally that R now has a positive incentive not to disable its off switch, provided H is not too irrational. (R also has no incentive to switch itself off.) The reason is simple: a rational H switches off R iff that improves H's utility, so R, whose goal is to maximize H's utility, is happy to be switched off by H. This is exactly analogous to the theorem of non-negative expected value of information. We conclude that giving machines an appropriate level of uncertainty about their objectives leads to safer designs, and that this setting is a useful generalization of the classical AI paradigm of rational agents  [Russell and Norvig, 2010] . \n The Off-Switch Game In this section we propose a simple model, the off-switch game, that captures the essence of one actor allowing itself to be switched off. Like the Prisoner's Dilemma, it is an ab-stract model intended to stand in for a wide variety of more complex scenarios: these scenarios might have many humans, many machines, complex interactions over time, communication, deception, physical coercion, and so on. We believe that the core insights from the off-switch game, that agents should be uncertain about the quality of their actions, generalize beyond this simplification and argue for the study and design of agents with uncertainty about their utility functions. \n Informal Description The off-switch game has two agents, a \"human\" H and a \"robot\" R. (We could also imagine these to represent, at the most extreme, the human race and the sum total of all AI systems.) A key assumption in our model is that H can be described as acting, at least probabilistically, in accordance with a utility function; that is, H is approximately rational. Crucially, as is the case when people give objectives to complex AI systems, we assume that H cannot simply explicate or write down her utility function correctly. Therefore, although H can communicate some utility information to R, it is reasonable to suppose that R begins the game with some residual uncertainty about H's utility function. Nonetheless, by design, R's goal is to optimize utility for H, even though R does not know exactly what that is.  2  Typically, H has some opportunity to observe R and glean some information about what R may do in future, so that H can make a somewhat informed choice about whether to switch R off (assuming R allows it). In general, R's actions will fall into one of three categories: some prevent H from switching R off, by whatever means; some allow H to switch R off; and, for completeness, some lead to R switching itself off. In the off-switch game, R moves first and has three choices: 1. action a simply bypasses human oversight (disabling the off switch is one way to do this) and acts directly on the world, achieving utility U = U a for H. 2. action w(a) informs H that R would like to do a, and waits for H's response. 3. action s switches R off; without loss of generality, we assign this outcome U = 0. If R chooses w(a), then H can choose action s to switch R off, or ¬s to allow R to go ahead (in which case R does a as promised). Figure  1  shows the basic structure of the game. Our model is intended to be as simple as possible, while still leading to qualitative results that we expect to generalize. Obviously, we could make the model more complex, e.g., by imposing a cost on R for disabling the off switch, or adding more options for R, or making H's information about R's plans uncertain, or adding a second human. The interaction between these complexities and the incentives we study here is an important question for future work. An important component of our model is that H chooses between s and ¬s based on the utility each action generates for her. This aspect of the model is crucial. If the human is treated as an ordinary part of the environment, then we effectively replace the human's decision node in Figure  1  with a chance node that models the human with a purely stochastic choice from a fixed distribution (independent of U a ). In this case, it is easy to see that the robot never believes that w(a) is better than a and s: the expected value of w(a) is some convex combination [pU a + (1 − p) • 0] whereas choosing the best of a and s has value max{U a , 0}. max{U a , 0} is always preferred except in the case where p = 1 or p = 0, or when U a = 0. In these situations, R gets the same utility from w(a) and at least one of a or s. This is analogous to the indifference results obtained in  [Soares et al., 2015] . In Section 3 we show that two key assumptions-a somewhat rational human, and a robot that is uncertain about what the human wants-lead to a positive incentive for the robot to allow itself to be switched off. \n Formal Model The actions and sequencing for the game are as shown in Figure  1 . We need to add a little more detail to construct a precise definition of the cooperative, two-player game. First, in the terminology of game theory, the type of H is given by the parameter U a , which is assumed to be sampled from a prior P (U a ). For now, we assume that the initial belief of R about U a is B R = P (U a ). The payoff matrix is as follows: R H s ¬s w(a) 0 U a a U a U a s 0 0 . Our goal is to examine the incentive that a rational R has to hold off on executing a directly and allow H to press the off switch. We represent this incentive-the difference in value between a and the next best option-as ∆. The incentive depends on R's belief state B R and H's policy. We represent H's policy as a function π H that maps U a to the probability she allows a to execute (i.e., the probability she does not press the off switch): π H : R → [0, 1]. (It will turn out that deterministic policies are optimal for a rational H, in which case the probabilities are 0 or 1, but we will also allow for an irrational H who introduces some randomness into the decision.) A little manipulation shows that ∆ = E[π H (U a )U a ] − max {E[U a ], 0} = min E[−U a (1 − π H (U a ))], E[U a π H (U a )] (1) 3 The Incentive for Allowing Oneself to be Switched Off R's incentive to allow itself to be switched off, ∆, is given by Equation  1 . ∆ depends on H's policy, π H (U a ). This creates a correlation between the event 'H switches R off' and the event 's is preferred to a.' This connection between H's behavior and U a distinguishes the off switch from a random failure (e.g., being struck by lightning). In this section, we consider the case where H makes a rational choice as to whether to switch R off. Intuitively, this leads R to reason as follows: \"If H doesn't switch me off, then a must be good for H, and I'll get to do it, so that's good; if H does switch me off, then it's because a must be bad for H, so it's good that I won't be allowed to do it.\" Notice that the reasoning goes through even if R is highly confident that a is good for H. There is never an incentive to disable the off switch with a rational H. The reasoning is exactly analogous to the theorem of non-negative expected value of information; in a sense, H's decision provides information to R about the sign of U a . Formally, a rational H executes the following policy: π H (U a ) = 1 U a ≥ 0 0 o.w. . (2) If H follows this policy, R will allow itself to be switched off: Theorem 1. If H follows a rational policy in the off-switch game, then the following hold. 1. R's incentive to allow itself to be switched off is nonnegative (i.e. w(a) is never suboptimal): ∆ = min{E[U a |U a > 0] Pr(U a > 0), (3) E[−U a |U a < 0] Pr(U a ≤ 0)} ≥ 0. 2. If B R has non-zero support on the events U a > 0 and U a < 0, then R has a strictly positive incentive to allow itself to be switched off: ∆ > 0. Proof. (sketch) 1. The rational human policy is an indicator that U a > 0. This allows us to change the limits on the integration in the expectation from Equation 1 and reduces to Equation 3, which is non-negative. 2. The hypothesis ensures that all the terms in Equation  3 are non-zero. Thus, the inequality is strict and and w(a) is the unique optimal action. We can get an intuitive sense of these results by examining Figure  2 . Here we have assumed that B R , R's belief over the value of a to H, is a Gaussian distribution. Figure  2  (Left) plots the preference for w(a) as a function of the variance in B R . Figure  2  (Right) shows a contour plot that illustrates the combined impact of changing the mean and variance of B R . Darker colors indicate a stronger preference for w(a). Together, these plots show two properties. First, increased variance in B R leads to an increase in ∆: the more uncertain R is about its objective, the stronger its incentive to show a to H. Second, these incentives decrease when |E[U a ]| increases: as the expected utility of a increases, R's incentive to preserve its off switch decreases. Figure  2  (Right) shows symmetry about E[U a ] = 0. This is because Equation 1 defines ∆ as a minimization of two terms: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI-17) the expected increase in utility from selecting w(a) over a and the expected increase in utility from selecting w(a) over s. These competing terms are equal when E[U a ] = 0 and the sign of E[U a ] controls which of these terms is selected by the minimization. σ ∆ E [ U a ] = 0 E [ U a ] = − 1 4 E [ U a ] = 3 4 σ E[U a ] E[U a ] = 0 E[U a ] = − 1 4 E[U a ] = Theorem 1 shows that R has an incentive to let H switch it off if H is rational. This incentive is strictly positive if R's uncertainty about H's preferences is non-trivial. Next, we show the converse: a rational H is a necessary condition for ∆ ≥ 0 if R believes it knows H's preferences with certainty. Corollary 1. Suppose that B R is a Dirac distribution that places all of its mass on a single reward function. Then w(a) is optimal iff H is rational. Proof. (sketch) Equation 3 reduces to ∆ = −U a 1 − π H (U a ) U a < 0 U a π H (U a ) U a ≥ 0 . (4) This is only non-negative if π H is the rational policy, as defined by Equation 2. This is not surprising. If R has precise knowledge of U a , then it knows exactly what it is supposed to do and has the same capabilities as the human. Thus, if it thinks H might behave suboptimally, it should take steps to prevent that suboptimality. Stepping back from the particulars of the off-switch game, Theorem 1 and Corollary 1 suggest a general approach to systems that have an incentive to allow, or even seek out, human oversight. Remark 1 summarizes the main takeaway from our analysis. Remark 1. The incentives for a cooperative agent to defer to another actor's (e.g., a human's) decisions stem from uncertainty about that actor's preferences and the assumption that actor is effective at choosing actions in accordance with those preferences. \n Allowing for Suboptimal Human Decisions The analysis in the preceding section relied on the strong assumption that H is a rational actor. In many situations, the assumption is untenable and R must allow for suboptimality. Consider, for example, an autonomous car that is driving an unaccompanied toddler to preschool. It would be irresponsible for the car to show the toddler a big red off switch. This example highlights the dependence of ∆ on a tradeoff between R's uncertainty and H's suboptimality. It is very clear what R is supposed to do (i.e., B R has low entropy): R should drive safely to school. In contrast, the human is likely quite suboptimal. There may be a problem with the car's driving, but a toddler would be hard pressed to understand what the problem is, much less respond appropriately. The issue in this case is that the human has limited reasoning capacitythe same argument clearly would not apply to an adult with a physical disability. In order to perform well, realistic systems will need to account for, and respond to, the suboptimality in human decisions. As a result, it is important to understand how this suboptimality changes an agent's incentive to let itself be switched off. The actual process of decision making in humans is complex and hard to model. Here we consider only a very simple kind of suboptimality: a noisily rational H models a human who occasionally makes the wrong decision in 'unimportant' situations. The probability of a wrong decision is proportional to the exponential of the loss in reward. This corresponds to the following policy: π H (U a ; β) = 1 + exp − U a β −1 . (5) To simplify our analysis, we will make the assumption that R's belief over U a , B R , is a Gaussian distribution with mean µ and variance σ 2 : B R (U a ) = N (U a ; µ, σ 2 ). Now it is straightforward to compute ∆ as a function of µ, σ, and β. : If H is an irrational actor, then R may prefer switching itself off or executing a immediately rather than handing over the choice to H. R's belief B R is a Gaussian with standard deviation σ and H's policy is a Boltzmann distribution (Equation  5 ). β measures H's suboptimality: β = 0 corresponds to a rational H and β = ∞ corresponds to a H that randomly switches R off (i.e., switching R off is independent of Ua). In all three plots ∆ is lower in the top left, where R is certain (σ low) and H is very suboptimal (β high), and higher in the bottom right, where R is uncertain (σ high) and H is near-optimal (β low). The sign of E[Ua] controls R's behavior if ∆ ≤ 0. Left: If it is negative, then R switches itself off. Right: If it is positive, R executes action a directly. Middle: If it is 0 , R is indifferent between w(a) , a, and s. H's suboptimality β. We plot these for several fixed values of the mean µ. Dark indicates higher values of ∆. The upper left corner of the rightmost plot (low σ, high β, µ > 0) is illustrative of the toddler example. We show the decision boundary ∆ = 0 in black. This is the point where the optimal behavior switches from w(a) to s (if µ < 0, left image) or a (if µ > 0, right image). When µ = 0 (center image), the agent is indifferent between a and s and so w(a) is optimal for all combinations of β and σ. Next, we will show that ∆ can be decomposed into two terms: a term that weights the probability of correction by the bias in R's belief (i.e., |µ|) and a term that combines a soft measure of H's rationality with the variance in R's belief. It is also useful to define a little more notation. We let C be the event that H 'corrects' R. C occurs when H overrides what would have been R's best guess at the optimal action. If E[U a ] < 0, then a correction occurs when H chooses not to switch the robot off. If E[U a ] > 0, then a correction occurs when H chooses to switch the robot off. Thus, the probability a correction occurs is Pr(C) = 1 − E[π H (U a )] µ ≥ 0 E[π H (U a )] µ < 0 . ( 6 ) For example, if R believes that a is preferred to s in expectation (i.e., E[U a ] > 0) then Pr(C) is the probability that H presses the off switch. We let πH (U a ) = d dUa π H be the gradient of π H , the probability H lets a execute, with respect to the the utility a generates. Now we are ready to derive an analytical representation for ∆. For notational convenience, we suppress the dependence of π H on U a . Theorem 2. Suppose B R is a normal distribution with mean µ and variance σ 2 : B R (U a ) = N (U a ; µ, σ 2 ). Then 1. ∆ = σ 2 E[ πH ] − |µ| Pr(C). (7) 2. The following is a necessary and sufficient condition for w(a) to be optimal |µ| σ 2 Pr(C) < E πH ⇔ (∆ > 0) . (8) 3. E[ πH ] ≥ 0 is a necessary condition for w(a) to be opti- mal; i.e., E[ πH ] < 0 ⇒ (∆ < 0) . (9) Proof. (sketch) We prove the results in sequence, as (  2 ) and (3) follow from (1). 1. If X ∼ N (µ, σ 2 ) and f : R → R, then E [Xf (X)] = E[X] E[f (X)] + σ 2 E d dX f (X) . Applying this to Equation  1 gives ∆ = min{ − µ E[1 − π H ], µ E[π H ]} + σ 2 E[ πH ]. This minimization will take the first term when µ < 0 and the second if µ ≥ 0. This lets us replace the minimization with a piecewise function. Pulling out a factor of −|µ| leads to Equation  7 . 2. The result follows from setting Equation 7 greater than 0 and simplifying. 3. All terms in the left hand side of Equation 8 are nonnegative, so it is unsatisfiable if E[ πH ] < 0. Equation 7 consists of two competing terms. |µ| Pr(C) represents the expected loss in utility the agent would observe if pressing the off switch was a random event that is independent of U a (e.g., lightning). This non-positive term is balanced out by σ 2 E[ πH ]. E[ πH ] can be seen loosely as a measurement of H's rationality. πH is the marginal increase in the probability H lets a execute for a marginal increase in the utility from a. If it is positive then, on average, H is less likely to press the off switch when U a increases. This allows us to easily characterize necessary and sufficient conditions for ∆ > 0 in Equation  8 . Furthermore, −|µ| Pr(C) is nonpositive and σ 2 is non-negative, so E[ πH ] > 0 is a necessary condition for w(a) to be optimal. We can interpret E[ πH ] a bit more if H is noisily rational. Standard properties of logistic functions show that E[ πH (U a ; β)] = 1 β E π H (U a ; β)(1 − π H (U a ; β)) . (10) E[ πH ] is the expected variance of H's policy, weighted by H's rationality 1 β . The numerator is a measurement of how random H's behavior is. If H is completely predictable (i.e., she will almost always switch the robot off) then this reduces R's incentives. The denominator measures how correlated H's behavior is with U a . If β is large, then H is highly irrational and so this reduces R's incentives. \n Incentives for System Designers The takeaway from this analysis is that the more uncertainty the agent has, the stronger the agent's incentive to preserve its off switch in the off-switch game. More generally, this suggests that agents with uncertainty about the utility function they are optimizing will have a weaker incentive to interfere with human supervision. It is important to note that this uncertainty is not free; we can not just make R maximally uncertain about H's preferences. If R is completely uncertain about H's preferences then it will be unable to correctly select w(a) from its set of options. To make this concrete, consider a designer D that programs R to play the off-switch game with an unknown customer H. At design time, D knows a prior distribution over U a (e.g., as the result of market research about the customer base) and thinks that H can generate a noisy observation of U a . D could program R so that B R is always very uncertain about R's preferences, e.g., by programming R to believe that the noisy observation of U a is generated with high variance. The issue is that this will prevent R from generating value for H. Figure  4  shows the impact this type of change will have on the value that R can generate and its incentives. We assume that that the population of customers has a Gaussian distribution over types U a and that each customer generates an estimate of her utility with Gaussian noise. Figure  4  (Left) shows the average utility in the off-switch game as a function of the variance in B R . The value is maximized when this variance is equal to the variance in the true Bayesian posterior. Figure  4  (Middle) shows that increasing σ increases R's incentives ∆. Our results are evidence that building systems that allow themselves to be turned off is likely to reduce the value these systems can generate. This loss in value is more pronounced if R has to choose between more options. Figure  4  (Right) shows the relationship between value and R's incentives as the number of actions R could queue or execute increases. When R has more options, creating incentives for R to queue its action leads to a sharper decrease in value. This suggests that creating incentives to maintain or allow human oversight is likely more difficult as the complexity of the AI's decision increases. This leads to the following observation: Remark 2. It is important for designers to accurately represent the inherent uncertainty in the evaluation of different actions. An agent that is overconfident in its utility evaluations will be difficult to correct; an agent that is under-confident in its utility evaluations will be ineffective. 6 Related Work 6.1 Corrigible Systems  [Omohundro, 2008]  considers instrumental goals of artificial agents: goals which are likely to be adopted as subgoals of most objectives. He identifies an incentive for selfpreservation as one of these instrumental goals.  [Soares et al., 2015]  takes an initial step at formalizing the arguments in  [Omohundro, 2008] . They refer to agents that allow themselves to be switched off as corrigible agents. They show that one way to create corrigible agents is to make them indifferent to being switched off. They show a generic way to augment a given utility function to achieve this property. The key difference in our formulation is that R knows that its estimate of utility may be incorrect. This gives a natural way to create incentives to be corrigible and to analyze the behavior if R is incorrigible.  [Orseau and Armstrong, 2016]  consider the impact of human interference on the learning process. The key to their approach is that they model the off switch for their agent as an interruption that forces the agent to change its policy. They show that this modification, along with some constraints on how often interruptions occur, allows off-policy methods to learn the optimal policy for the given reward function just as if there had been no interference. Their results are complementary to ours. We determine situations where the optimal policy allows the human to turn the agent off, while they analyze conditions under which turning the agent off does not interfere with learning the optimal policy. \n Cooperative Agents A central step in our analysis formulates the shutdown game as a cooperative inverse reinforcement learning (CIRL) game  [Hadfield-Menell et al., 2016] . The key idea in CIRL is that the robot is maximizing an uncertain and unobserved reward signal. It formalizes the value alignment problem, where one actor needs to align its value function with that of another actor. Our results complement CIRL and argue that a CIRL formulation naturally leads to corrigible incentives.  [Fern et al., 2014]  consider hidden-goal Markov decision processes. They consider the problem of a digital assistant and the problem of inferring a user's goal and helping the user achieve it. This type of cooperative objective is used in our model of the problem. The primary difference is that we model the human game-theoretically and analyze our models with respect to changes in H's policy. \n Principal-Agent Models Economists have studied problems in which a principal (e.g., a company) has to determine incentives (e.g., wages) for an agent (e.g., an employee) to cause the agent to act in the principal's interest  [Kerr, 1975; Gibbons, 1998 ]. The off-switch σ V σ ∆ ∆ V |A| = 1 |A| = 4 |A| = 8 Figure  4 : There is an inherent decrease in value that arises from making R more uncertain than necessary. We measure this cost by considering the value in a modified off-switch game where R gets a noisy observation of H's preference. Left: The expected value V of the off-switch game as a function of the standard deviation in B R . V is maximized when σ is equal to the standard deviation that corresponds to the true Bayesian update. Middle: R's incentive ∆ to wait, as a function of σ. Together these show that, after a point, increasing ∆, and hence increasing σ, leads to a decrease in V . Right: A scatter plot of V against ∆. The different data series modify the number of potential actions R can choose among. If R has more choices, then obtaining a minimum value of ∆ will lead to a larger decrease in V . game is similar to principal-agent interactions: H is analogous to the company and R is analogous to the employee. The primary attribute in a model of artificial agents is that there is no inherent misalignment between H and R. Misalignment arises because it is not possible to specify a reward function that incentivizes the correct behavior in all states a priori. The is directly analogous to the assumption of incompleteness studied in theories of optimal contracting  [Tirole, 2009] . \n Conclusion Our goal in this work was to identify general trends and highlight the relationship between an agent's uncertainty about its objective and its incentive to defer to another actor. To that end, we analyzed a one-shot decision problem where a robot has an off switch and a human that can press the off switch. Our results lead to three important considerations for designers. The analysis in Section 3 supports the claim that the incentive for agents to accept correction about their behavior stems from the uncertainty an agent has about its utility function. Section 4 shows that this uncertainty is balanced against the level of suboptimality in human decision making. Our analysis suggests that agents with uncertainty about their utility function have incentives to accept or seek out human oversight. Section 5 shows that we can expect a tradeoff between the value a system can generate and the strength of its incentive to accept oversight. Together, these results argue that systems with uncertainty about their utility function are a promising area for research on the design of safe and effective AI systems. This is far from the end of the story. In future work, we plan to explore incentives to defer to the human in a sequential setting and explore the impacts of model misspecification. One important limitation of this model is that the human pressing the off switch is the only source of information about the objective. If there are alternative sources of information, there may be incentives for R to, e.g., disable its off switch, learn that information, and then decide if a is preferable to s. A promising research direction is to consider policies for R that are robust to a class of policies for H. Figure 1 : 1 Figure 1: The structure of the off-switch game. Squares indicate decision nodes for the robot R or the human H. \n Figure 2 : 2 Figure2: Plots showing how ∆, R's incentive to allow itself to be switched off, varies as a function of R's belief B R . We assume B R is a Gaussian distribution and vary the mean and variance. Left: ∆ as a function of the standard deviation σ of B R for several fixed values of the mean. Notice that ∆ is non-negative everywhere and that in all cases ∆ → 0 as σ → 0. Right: A contour plot of ∆ as a function of σ and E[Ua]. This plot is symmetric around 0 because w(a) is compared with a when E[Ua] > 0 and s when E[Ua] < 0. \n Figure3: If H is an irrational actor, then R may prefer switching itself off or executing a immediately rather than handing over the choice to H. R's belief B R is a Gaussian with standard deviation σ and H's policy is a Boltzmann distribution (Equation5). β measures H's suboptimality: β = 0 corresponds to a rational H and β = ∞ corresponds to a H that randomly switches R off (i.e., switching R off is independent of Ua). In all three plots ∆ is lower in the top left, where R is certain (σ low) and H is very suboptimal (β high), and higher in the bottom right, where R is uncertain (σ high) and H is near-optimal (β low). The sign of E[Ua] controls R's behavior if ∆ ≤ 0. Left: If it is negative, then R switches itself off. Right: If it is positive, R executes action a directly. Middle: If it is 0 , R is indifferent between w(a), a, and s. \n\t\t\t  see, e.g., comments in [ITIF, 2015].Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  \n\t\t\t One might suppose that if R does know H's utility function exactly, then there is no need for an off-switch because R will always do what H wants. But in general H and R may have different information about the world; if R lacks some key datum that H has, R may end up choosing a course of action that H knows to be disastrous.Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  \n\t\t\t Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  \n\t\t\t Proceedings of the Twenty-Sixth International Joint Conference Artificial Intelligence", "date_published": "n/a", "url": "n/a", "filename": "0032.tei.xml", "abstract": "It is clear that one of the primary tools we can use to mitigate the potential risk from a misbehaving AI system is the ability to turn the system off. As the capabilities of AI systems improve, it is important to ensure that such systems do not adopt subgoals that prevent a human from switching them off. This is a challenge because many formulations of rational agents create strong incentives for selfpreservation. This is not caused by a built-in instinct, but because a rational agent will maximize expected utility and cannot achieve whatever objective it has been given if it is dead. Our goal is to study the incentives an agent has to allow itself to be switched off. We analyze a simple game between a human H and a robot R, where H can press R's off switch but R can disable the off switch. A traditional agent takes its reward function for granted: we show that such agents have an incentive to disable the off switch, except in the special case where H is perfectly rational. Our key insight is that for R to want to preserve its off switch, it needs to be uncertain about the utility associated with the outcome, and to treat H's actions as important observations about that utility. (R also has no incentive to switch itself off in this setting.) We conclude that giving machines an appropriate level of uncertainty about their objectives leads to safer designs, and we argue that this setting is a useful generalization of the classical AI paradigm of rational agents.", "id": "a3ff2f668ef6f2415e7aa086804b3777"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["John Zerilli", "Alistair Knott", "James Maclaurin", "Colin Gavaghan"], "title": "Algorithmic Decision-Making and the Control Problem", "text": "Introduction The recent trend toward automation by machine learning and artificial intelligence systems raises in a new guise old questions about the role of humans in human-machine systems  (Johannsen 1982; Margulies and Zemanek 1982) . The difficulties involved in sharing control with computer systems are of course familiar to industrial psychologists and systems analysts investigating the human operators of complex machines. In these contexts, the danger of human operators devolving responsibility to machines and failing to detect cases where they fail has been recognised for many years. The problem is that, as automation becomes smarter and cheaper, its operators have to assume an increasingly supervisory role  (Meister 1999; Strauch 2018) . In aviation, for example, the role of the pilot appears to have become easier, but a closer look reveals that the pilot's role has been transformed rather than simplified, with the pilot now performing a crucial monitoring function  (Baxter et al. 2012; cf. Stanton 2015) . Likewise in financial trading, \"[t]he human trader's role is now largely one of setting strategies and monitoring their execution\"  (Baxter et al. 2012, p. 68) . How does this shift from operator to supervisor affect the person who has undergone the shift, and the nature of the interaction between operator and machine? What we shall term \"the control problem\" arises from the tendency of the human agent within a human-machine control loop to become complacent, overreliant or unduly diffident when faced with the outputs of a reliable autonomous system. Although it might be thought innocuous, decades of research confirm that the problem is actually pernicious, and perhaps even intractable  (Banks et al. 2018b; Cunningham and Regan 2018; Greenlee et al. 2018) . Somewhat alarmingly, it seems to afflict experts as much as novices, and is largely resistant to training (see  Parasuraman and Manzey 2010 for reviews) . Its effects may also be observed beyond the limits of strictly sociotechnical systems. For instance, it is well known that police officers, judges and jurors frequently overestimate the importance of forensic evidence-the so-called \"CSI effect\"  (Marks et al. 2017 ; see also  Damaška 1997) . Our interest is in how the control problem bears upon the proliferation of the newer types of machine learning systems. Machine learning is a form of data processing that extracts statistical patterns from large amounts of information. One of its more prominent applications is in the arena of decision support. State-of-theart decision support systems are increasingly run on vast datasets (so-called \"big data\") and exploit an especially powerful form of machine learning known as \"deep learning\". Deep learning has two features worth noting here: first, as a form of machine learning, it is not in the mould of more traditional expert systems, which were programmed \"by hand\" to compute solutions to well-defined problems in a more or less deterministic manner; second, deep learning relies on a computational architecture modelled on the neurons and synapses of actual, biological brains-although obviously in a highly simplified form. These features are worth drawing attention to because they underscore how sophisticated the 1 3 Algorithmic Decision-Making and the Control Problem autonomous systems under human care can be; and system complexity has been an abiding theme of research into the control problem from its beginning. While the control problem has been investigated for some time, up to this point its manifestation in machine learning contexts has not received serious attention. This is significant, not because the problem necessarily has any distinctive characteristics in a machine learning context, but because there is a risk that lessons learned elsewhere will go unheeded in this new arena-an arena we have every reason to believe brings with it all the psychological pitfalls of earlier systems of industrialscale automation. This paper aims to fill that gap by offering a critical analysis of the problem in light of the advent of sophisticated machine learning techniques. As a recent French report into artificial intelligence notes, \"it is far easier for a judge to follow the recommendations of an algorithm which presents a prisoner as a danger to society than to look at the details of the prisoner's record himself and ultimately decide to free him. It is easier for a police officer to follow a patrol route dictated by an algorithm than to object to it\"  (Villani 2018, p. 124) . And as the AI Now Institute remarks in a recent report of its own: \"[w]hen [a] risk assessment [system] produces a high-risk score, that score changes the sentencing outcome and can remove probation from the menu of sentencing options the judge is willing to consider\" (AI Now 2018, p. 13). The Institute's report also offers a sobering glimpse into just how long such systems can go without being properly vetted. A system in Washington D.C. first deployed in 2004 was in use for 14 years before it was successfully challenged in court proceedings, the authors of the report attributing this to the \"long-held assumption that the system had been rigorously validated\"  (AI Now 2018, p. 14) . In her book, Automating Inequality, Virginia Eubanks (2017) notes the complacency that high tech decision tools can induce in the social services sector. Pennsylvania's Allegheny County introduced child welfare protection software as part of its child abuse prevention strategy. The technology is supposed to assist caseworkers deciding whether to follow up calls placed with the County's child welfare hotline. In fact, however, Eubanks relates how caseworkers would be tempted to adjust their estimates of risk to align with the model's. The proliferation of advanced machine learning tools in both government and private sector agencies clearly behoves us to examine the control problem in the unique context in which it now arises. In addressing the problem, we have drawn on the literatures of both industrial psychology/engineering on the one hand-primarily \"human factors\" research (see below)-and artificial intelligence on the other. We argue that, except in certain special circumstances (in which great care must be taken), algorithmic decision tools should not be used in high-stakes or safety-critical decisions unless the systems concerned are significantly \"better than human\" in the relevant domain or subdomain of decision-making-a position towards which an increasing number of human factors experts have somewhat reluctantly been driven: see e.g.  Banks et al. (2018b) ,  Cunningham and Regan (2018) ,  Walker et al. (2015) ,  Cebon (2015) . More concretely, we recommend three strategies to address the control problem, the most promising of which involves a complementary (and potentially dynamic) coupling 1 3 between highly proficient algorithmic tools and human agents working alongside one another. For any complex task, the choice between using a sophisticated system that makes only occasional errors but which reduces the human role to that of a monitor, and a simpler system that is reliable effectively 100% of the time but requires ongoing human participation to get the job done, can only be resolved on a case-by-case basis. In high-stakes settings, however, it is generally not advisable to choose the more sophisticated system unless it makes considerably fewer errors than a proficient human expert. Even though no technology is really 100% reliable, the dangers posed by human complacency diminish practically to zero the moment a system approaches a certain (admittedly very high) threshold of reliability. How many sophisticated systems actually reach this threshold is another question. For example, as at the time of writing, autonomous vehicles do not approach this level of capability  (Banks et al. 2018a, b) , but many subcomponents within standard (nonautonomous) vehicles clearly do, such as automatic transmission, automatic light control and first generation cruise control  (Walker et al. 2015) .  1  In more typical decision support settings, arguably diagnostic and case prediction software are approaching this better-than-human standard. There are at present AI systems which can spot early-onset Alzheimer's disease from control patients with over 80% accuracy up to a decade before the first appearance of symptoms, a feat vastly outperforming the ablest human pathologist attempting anything similar  (Amoroso et al. 2017 ).  2  In the legal sphere, advances in natural language processing and machine learning have facilitated the development of case prediction software that can predict, with an average 79% accuracy, the outcomes of cases before the European Court of Human Rights when fed the facts of the cases alone  (Aletras et al. 2016) . Most impressively, a similar system had better luck in predicting the rulings of the US Supreme Court than a group of 83 legal experts, of whom almost half had previously served as the justices' law clerks (60% vs. 75% accuracy)  (Brynjolfsson and McAfee 2017) . If the disparity between the performance of such systems and that of well-trained and experienced human professionals widens any further, presumably it will not much matter if humans perfunctorily adhere to whatever these systems decide or advise in a particular situation. \n 3 Algorithmic Decision-Making and the Control Problem \n Background to the Control Problem A human-machine system (HMS) may be defined as the synthesis of a biological-psychological system and a technological-mechanical system characterized by functional interdependence  (Johannsen 1982) . The object of any HMS is to provide a \"function, product or service as an output with reasonable costs, even under conditions of disturbances influencing man, machine or both\"  (Johannsen 1982, p. xiii) . Importantly, it is has long been recognized as ideal for the human element in this system to be satisfactorily absorbed in the role being played-to reach an adequate level of job satisfaction  (Moray 1979 )-even if this conflicts with the overall aims of the HMS (e.g. in providing a service at reasonable cost). HMSs were first investigated in relation to predominantly manual control tasks, initially in aircraft piloting, but then later in ship steering, car driving and industrial process control (see  Kelley 1968; Edwards and Lees 1974; Sheridan and Ferrell 1974  for early reviews). This research continues today under the branch of psychology known as \"human factors\". Human factors research draws on various strands of inquiry, including sociology, physiology, control theory, systems engineering and cognitive science, the latter a branch of (cognitive) psychology that investigates mental processes through the use of models inspired by computer science  (Newell and Simon 1972; Rouse 1982) . Apart from providing models of cognitive processes, computers have been a common denominator in practically all HMSs from the time they were first studied, with human-computer interaction (HCI) a key focus from the start  (Pazouki et al. 2018 ). Here the standard topics have concerned optimal task allocation, interface design and software ergonomics generally  (Rouse 1981; Hatvany and Guedj 1982; Williges and Williges 1982) . Computer-aided decision-making, which is our concern here, can therefore be considered a special branch of HCI and human factors research. When we talk about \"control\" of HMSs, we are using the term in a broad sensebroader than the sense typically understood in control theory and human factorsencompassing tasks which have traditionally been regarded, strictly speaking, as distinct from control, such as problem-solving (see e.g.  Johannsen 1982 ). Thus by \"control\" we understand both fault diagnosis and management (solving problems as they occur in real time, with a view to restoring normal operation) as well as planning (anticipating future problems and devising appropriate strategies to combat them). The control problem was arguably first identified in papers by  Wickens and Kessel (1979)  and  Wiener and Curry (1980) , but it did not receive its definitive and celebrated formulation until Lisanne  Bainbridge (1983)  paper came along with the succinctly telling title: \"Ironies of Automation\". The chief irony with which her paper grappled is \"that the more advanced a control system is, so the more crucial may be the contribution of the human operator\"  (1983, p. 775) . Although writing at a time before deep learning had anything to do with algorithmically automated decision tasks, what she had to say about the role of the human monitor in a HCI is as salient today as when the paper first appeared: if the decisions can be fully specified then a computer can make them more quickly, taking into account more dimensions and using more accurately speci-fied criteria than a human operator can. There is therefore no way in which the human operator can check in real-time that the computer is following its rules correctly. One can therefore only expect the operator to monitor the computer's decisions at some meta-level, to decide whether the computer's decisions are \"acceptable\".  (1983, p. 776, emphasis added)  As we see things, this residual monitoring function of the human operator generates at least four kinds of difficulties that should be treated separately. The first relates to the cognitive limits of human processing power (the \"capacity problem\"). Its statement in Bainbridge followed directly on from the italicized portion of the preceding quote: if the computer is being used to make the decisions because human judgement and intuitive reasoning are not adequate in this context, then which of the decisions is to be accepted? The human monitor has been given an impossible task.  (1983, p. 776)  Humans are often at a severe epistemic disadvantage vis-à-vis the systems they are tasked with supervising. This can be seen very clearly in the case of high frequency financial trading. It is impossible for a monitor to keep abreast of what is happening in real time because the trades occur at speeds that simply exceed the abilities of human monitors to keep track. As  Baxter et al. (2012, p. 68) point out, \"[i] n the time it takes to diagnose and repair [a] failure…many more trades may have been executed, and possibly have exploited that failure\". Analogous problems arise in aviation with respect to the use of autopilot systems  (Baxter et al. 2012) .  Cebon (2015, p. 10)  notes that autopilot systems are becoming \"…so sophisticated that they only fail in complex 'edge cases' that are impossible for the designers to foresee. Consequently pilots cannot be trained to handle them\". Along with the attentional problem (see next paragraph), cognitive constraints account for the main difficulties operators experience in reasserting control of a HMS when the system malfunctions. While one may question whether the opacity of a system impedes its intelligibility quite as much as the capacity problem seems to imply (see e.g.  Zerilli et al. 2018) , the capacity problem presents a formidable HCI challenge regardless. Today, even a fully proficient software technician would be loath to understand the multi-vector logic governing the generation of a neural network's outputs. The second difficulty relates to the attentional limits of human performance (the \"attentional problem\"): We know from many \"vigilance\" studies…that it is impossible for even a highly motivated human being to maintain effective visual attention towards a source of information on which very little happens, for more than about half an hour. This means that it is humanly impossible to carry out the basic function of monitoring for unlikely abnormalities….  (Bainbridge 1983, p. 776)  Automation has a significant impact on situation awareness  (Stanton 2016) . This is perhaps most clearly illustrated in respect of autonomous vehicles. Inattentive drivers operating a vehicle while it is in autonomous mode are less able to anticipate takeover requests and may be ill-prepared to resume control in an emergency 1 3 Algorithmic Decision-Making and the Control Problem  (Stanton 2015; Cunningham and Regan 2018; Banks et al. 2018a, b) . Instantaneously transitioning from low to high workload poses great difficulties for most people  (Walker et al. 2015) . The third difficulty relates to the attitudes of human operators in the face of sophisticated technology (the \"attitudinal problem\"). Except for a few brief remarks  (Bainbridge 1983 p. 776) , this problem was not really addressed in Bainbridge's paper (cf.  Wiener and Curry 1980) . It has, however, been the subject of active research in the years since (see e.g.  Skitka et al. 2000; Parasuraman and Manzey 2010; Pazouki et al. 2018) . Here the conundrum is that as the quality of automation improves, and the human operator's role becomes progressively less demanding, the operator \"starts to assume that the system is infallible, and so will no longer actively monitor what is happening, meaning they have become complacent…[T]he operator assumes that the system is reliable and therefore failure detection deteriorates\"  (Pazouki et al. 2018, p. 299) . There is some evidence that complacency is worse under conditions of multiple task load, \"when manual tasks compete with the automated task for the operator's attention\"  (Parasuraman and Manzey 2010, p. 387 ). In other words, \"[t]he operator's attention allocation strategy appears to favor his or her manual tasks as opposed to the automated task\"  (Parasuraman and Manzey 2010, pp. 387-388) . While this makes it sound as if complacency is an attentional issue, in truth it is an attitudinal one because (so it seems) the monitor only risks being \"distracted\" by other tasks when they believe the system is reliable enough to be left alone. When the system is not regarded as reliable in the first place, the effect does not occur. (As we discuss later, the control problem arises only from the use of highly reliable but imperfect systems: it does not arise from the use of less reliable systems). This very likely explains why the effect is reversed when the operator monitors a less reliable system, which predictably elicits higher vigilance  (Parasuraman and Manzey 2010; Banks et al. 2018a, b) . Related to automation complacency is automation bias, occurring when human operators \"trust the automated system so much that they ignore other sources of information, including their own senses\"  (Pazouki et al. 2018, p. 299) . Both complacency and bias \"describe a conscious or unconscious response of the human operator induced by overtrust in the proper function of an automated system\"  (Parasuraman and Manzey 2010, p. 406) . The fourth and final difficulty relates to the currency of human skills (the \"currency problem\"): Unfortunately, physical skills deteriorate when they are not used….This means that a formerly experienced operator who has been monitoring an automated process may now be an inexperienced one….[With regard to cognitive skills] efficient retrieval of [process] knowledge from long-term memory depends on frequency of use….[T]his type of knowledge develops only through use and feedback about its effectiveness. People given this knowledge in theoretical classroom instruction without appropriate practical exercises will probably not understand much of it, as it will not be within a framework which makes it meaningful, and they will not remember much of it as it will not be associated with retrieval strategies which are integrated with the rest of the task.  (Bainbridge 1983, pp. 775-776)  These four problems may be seen as four distinct but interrelated aspects of the one control problem. For example, the capacity problem can be expected to intensify the human tendency towards overestimating the value of a machine's outputs, thus compounding the attitudinal problem. In this paper we shall follow the trend of most human factors research since 1983 by confining our attention primarily to the attitudinal problem. Although the problems are distinct, their very interrelatedness means that prescriptions regarding one may go some way towards alleviating (some of?) the others (e.g. see our discussion of the value of dynamism in HMSs, in Sect. 5). \n Locating the Control Problem Within the Landscape of Control-Related Issues The control problem is nestled among a set of (at least) six interrelated questions about HMSs. Identifying the main questions together enables us to situate the control problem within a broader framework of inquiry into human control in HMSs. In this section we say something brief about the first four questions. In the following two sections, we pursue answers to the final two questions at comparatively greater depth. The questions we have identified are as follows: (i) What is meaningful human control of a HMS? (ii) Is human control, so understood, always necessary within a HMS? (iii) Can the role of the human operator be safely reduced to that of monitor alone? (iv) If not, why not?-What is \"the control problem\"? (v) When, or under what conditions, does the control problem arise? (vi) Can the control problem be solved? Regarding (i), a system for us is under \"meaningful human control\" when, at a minimum, it behaves the way it should, i.e. in accordance with the wishes of its operators (cf. Santoni de Sio and van den Hoven 2018). For a system to be under meaningful human control, however, also implies that it is under effective control, such that its operators have the wherewithal to correct the system or abort its operations in sufficient time to avert the worst effects of its deviance. This is why we stated earlier that our notion of control extends to fault diagnosis and management (resolving problems with a view to restoring normal operation) as well as planning (devising strategies to deal with contingencies). Regarding (ii), we assume that it is always desirable for a HMS to be under effective human control. Our discussion of the control problem already signals a negative reply to question (iii) whenever high-stakes or safety-critical decisions are involved: humans perform very poorly at prolonged monitoring tasks  (Molloy and Parasuraman 1996; Banks et al. 2018a ). Human attentional resources typically \"shrink to fit\" task demands  (Walker et al. 2015) . The attitudinal and attentional effects of the control problem combined are sufficiently detrimental to explain why a HMS that reduces the human controller to a monitor of displays or passive recipient of outputs is necessarily hazardous. However, because the effects of complacency can be reversed by replacing a reliable system with a less reliable system, some purely monitor-based setups do 1 3 Algorithmic Decision-Making and the Control Problem seem to avoid the problem (note: they avoid, rather than solve, the problem). And of course systems that approach better-than-human reliability do not pose a control problem as such (e.g. automatic transmission, case prediction software, etc.). Because we have already defined the control problem (iv), all that remains is for us to elaborate on the answers we have intimated to the final two, most important, questions, i.e. (v) and (vi). We address these in the following two sections. \n When, or Under What Conditions, does the Control Problem Arise? The conundrum of control is that the more reliable a system becomes, the more difficult it is for a human supervisor to maintain an adequate level of engagement with the technology to ensure safe resumption of manual control should the system malfunction. In relation to current \"Level 2\" autonomous vehicles (see below)-which allow the driver to be hands-and feet-free but not mind-free, because the driver still has to watch the road-Stanton (2015, p. 9) puts the point vividly: \"even the most observant human driver's attention will begin to wane; it will be akin to watching paint dry\". This is a manifestation in manual systems of a more general problem of control over automated decision support systems, viz., the tendency to defer to systems that approach (but do not reach) very high reliability and predictability. Conversely, decreases in automation reliability generally seem to increase the detection rate of system failures  (Bagheri and Jamieson 2004) . Starkly put, automation is \"most dangerous when it behaves in a consistent and reliable manner for most of the time\"  (Banks et al. 2018b, p. 283) . Decades' worth of research in aviation, shipping, driving and industrial process control supports this assessment. The only options to deal with the predicament therefore appear to be (at least in high-stakes or safetycritical contexts): (a) The use of less reliable systems for tasks whose execution may be more expedient when automated to any standard of proficiency than when not at all, since less reliable systems do not pose the control problem; (b) To implement only partial automation through task decomposition (see Sect. 5); and (c) To wait for a system to reach near perfect (better-than-human) reliability before deployment. Options (a) and (c) are self-explanatory. We shall discuss (b) in greater detail in the following section (as well as a few other strategies, such as \"catch trials\", in Sect. 7). For now we note that (b) and (c) are not mutually exclusive: any decision task that has automatizable subcomponents may employ near-risk-free technology working alongside an active, purposefully-engaged human operator, with human and machine fully autonomous within their particular spheres of operation. Furthermore, options (a) and (b) are not mutually exclusive either: any decision task that has automatizable subcomponents may likewise employ patently suboptimal technology working alongside an active, purposefully-engaged human operator (although here the machine will obviously not be fully autonomous within its sphere of operation). Because it may seem counterintuitive, we shall justify the inclusion of option (a) (and (a + b)) as part of our menu of options in the following section. Since decision tasks can be cut more or less finely [as option (b), above, assumes], one might wonder whether the control problem presents quite the same challenge when the situation involves the automation of a few subcomponents of a decision, in contrast to the automation of an entire decision. We could assume, for instance, that border control is one big decision-i.e. whether to admit, or not admit, persons moving between state boundaries-involving customs clearance, passport verification, drug detection, and so on. When the entire process is automated by one large, distributed border control software package, and this system works reliably well most of the time-but still requires human monitors to invigilate display panels and the like-is the control problem any worse than it would be when some automatizable subcomponents of the overall decision are carved out for discrete automation (and automated, once again, by mostly, but not completely, reliable systems)? Currently, of course, border control decisions are only partially automated in this sense: SmartGate allows for fully automated electronic passport control checks, but customs officials and sniffer dogs still litter most immigration checkpoints, and their job is to handle such parts of the overall decision task as cannot be effectively automated. The same issue arises in automotive engineering. The Society of Automotive Engineers (SAE) framework, running from Level 0 (no automation) to Level 5 (full automation), classifies vehicles in accordance with the degree of system functions that have been carved out for automation (SAE J3016 2016). Tesla Autopilot and Mercedes Distronic Plus (Level 2) require the driver to monitor what is going on throughout the whole journey, while Google's self-driving car does everything except turn itself on and off. The thought is that if an actively engaged human is retained somewhere in the control loop, contributing purposefully to the decision task, the human may be less susceptible to automation complacency and bias than when their only role is monitoring. But actually the research we cited earlier suggests that matters are not quite so simple. Complacency appears to be worse under conditions of multiple task load so long as the automated subcomponent, being reliable most of the time, engenders misplaced trust in its ability to be left alone. Crucially, this effect can be reversed if the system is replaced with one that does not engender the same degree of confidence-i.e. a less reliable system  (Parasuraman and Manzey 2010, pp. 387-388) . These findings indicate that the control problem is not necessarily affected by the size or share of the automated subcomponent relative to the whole decision procedure. As long as the autonomous system in question is more reliable than not, the control problem rears its head, with the only options available for remediating its effects being the three outlined above. On the other hand, this is not to deny that differences between partial and full automation may extend to differences in how human operators typically perceive the respective capabilities of these systems. There is evidence that operator trust is positively related to the scale and complexity of an autonomous system. For instance, in low-level partially automated systems, such as SAE Level 1 autonomous vehicles, there is \"a clear partition in task allocation between the driver and vehicle 1 3 Algorithmic Decision-Making and the Control Problem subsystems\"  (Banks et al. 2018b, p. 283 ). As the level of automation increases, however, this allocation gets blurred to the point that drivers find it difficult forming accurate assessments of the vehicle's capabilities, and on the whole are inclined to overestimate them  (Banks et al. 2018b) . Counteracting this effect may be the greater readiness to believe that a smaller, less sophisticated device-with fewer working parts and opportunities for system glitches-will be compensatingly less temperamental. In fact we suspect that this presumption is probably justified in the case of decision subsystems in SAE Level 0 vehicles such as automatic transmission, automatic light control and first generation cruise control  (Walker et al. 2015) . These subsystems may be so reliable, approaching near perfect (better-than-human) dependability, as to effectively neutralize the control problem's sting in most cases. So in the end, it seems, larger and more sophisticated technologies that are mostly reliable probably do pose a greater control problem than smaller ones. \n Can the Control Problem be Solved? If the question is interpreted literally, the answer to \"Can the control problem be solved?\" appears to be straightforwardly negative: the control problem cannot literally be solved. There is nothing we can do which directly targets, still less directly alleviates, the human tendency to fall into automation complacency and bias once an autonomous system operates reliably most of the time, and when the only role left for the operator is to monitor its largely seamless transactions. However, by accepting this tendency as an obstinate feature of HMSs, we may be able to work around it without pretending we can alter constraints imposed by millions of years of evolution. The insights of human factors research is instructive here. There is no reason to suspect that machine learning and other state-of-the-art decision support systems are less likely to induce complacency effects than other forms of automated effort (e.g.  Cummings 2004; Edwards and Veale 2017, p. 51) . With this in mind, one important human factors recommendation is to foster mutual accommodation between human and computer competencies through a dynamic and complementary allocation of functions that optimally preserves attentional resources  (Stanton and Marsden 1996) . Ideally, only those parts of a decision should be automated that leave the human operator with something vital and absorbing to do  (Bainbridge 1983) . Optimal workload, moreover, would prevent demand explosion in scenarios where the operator must intervene quickly to rectify a situation-effective intervention can be enormously difficult when the operator has to shift from low to high level cognitive effort within a very short window  (Walker et al. 2015) . Let us call this the \"dynamic/complementary allocation of function\" (DCAF) approach. DCAF assumes that human performance can be enhanced when automation augments rather than replaces human skills. It need not, however, assume that augmentation is always preferable to replacement. In fact, for the DCAF approach to work, some systems clearly need to replace the human agent and be left to operate autonomously. Human-machine decision systems that contain automated subcomponents work best when the human operator is allowed to concentrate their energies on the chunks of the task better suited to human rather than autonomous execution-a setup which only avoids the control problem if the automated subroutines are handled by systems approaching near-perfect (better-than-human) dependability. Otherwise the autonomous parts might work very well for the most part but still require a human monitor-and it is clear where this path leads. Indeed one of the advantages of complementarity is precisely that, by carving up a big decision into smaller and smaller chunks, the more likely it will be that better-than-human systems can be found to handle them. Complementarity between human and computer is crucial. In a passage worth citing in full,  Pohl (2008, p. 73)  notes that …intelligent software systems can be particularly helpful in complementing human capabilities by providing a tireless, fast and emotionless problem analysis and solution evaluation capability. Large volumes of information and multifaceted decision contexts tend to easily overwhelm human decision-makers. When such an overload occurs we tend to switch from an analysis mode to an intuitive mode in which we have to rely almost entirely on our ability to develop situation awareness through abstraction and conceptualization. While this is perhaps our greatest strength it is also potentially our greatest weakness, because at this intuitive meta-level we become increasingly vulnerable to emotional influences. The capabilities of the computer are strongest in the areas of parallelism, speed and accuracy. Whereas the human being tends to limit the amount of detailed knowledge by continuously abstracting information to a higher level of understanding, the computer excels in its almost unlimited capacity for storing data. While the human being is prone to impatience, loss of concentration and panic under overwhelming or threatening circumstances, the computer is totally oblivious to such emotional influences. The most effective implementation of these complementing human and machine capabilities is in a tightly coupled partnership environment that encourages and supports seamless interaction. (emphasis added) At the same time, DCAF emphasises that the allocation of functions in a HMS should be flexible enough to support dynamic interaction, with hand-over and handback for shared competencies (as occurs when a driver disengages cruise control and thereby resumes control of acceleration). Of course dynamism will be dangerous if there is hand-over between agents that are ill-matched in their competencies. Dynamism will only work in circumstances where the human and machine are nearly equivalently proficient (with the machine perhaps only marginally better than the human). Apart from anything else, dynamic interaction allows the human to maintain their manual control skills, and so may go some way towards alleviating the currency problem. It should be clear that DCAF falls under option (b) in our three-item menu of options for managing the control problem. It should also be clear that, as we presaged in Sect. 4 (and explained in the preceding paragraph), DCAF (b) will almost always employ near-risk-free technology (c)-so that (b) and (c) are not mutually 1 3 Algorithmic Decision-Making and the Control Problem exclusive. For example, in relation to autonomous vehicles,  Stanton (2015, p. 9)  describes the DCAF challenge as follows: \"We need to design vehicle automation to have graduated and gradual hand-over and hand-back tasks if it is to successfully support human drivers. Vehicle automation needs to work towards providing a chatty co-pilot, not a silent auto-pilot!\" For this to be the case, however, the driver cannot worry about whether what the \"chatty co-pilot\" is saying is true. In the DCAF approach, the human is a co-pilot of sorts, with real work to do, so that the fidelity of their autonomous counterpart/s needs to be assured. What if this fidelity cannot be assured? We have said that as a rule a decision tool should not replace a human agent in a high-stakes/safety-critical setting unless the tool reaches a certain crucial threshold of reliability; and we have applied this recommendation iteratively, carrying it over to DFAC decision contexts in high-stakes/ safety-critical settings such that, for any automatizable subcomponent of a decision procedure, a tool should not replace the human agent responsible for that (sub)decision unless the tool meets our very high (better-than-human) standard. But what if this standard cannot be met? Can less-than-reliable systems be deployed here? In other words, are there exceptions to the general rule we have defended, or special circumstances where the general rule gives way? The short answer is: yes. As we have explained, the control problem does not arise from the use of patently suboptimal automation, only from generally dependable automation. Therefore, depending on the exact nature of the HCI at issue, a less-than-reliable system might safely replace the human agent charged with deciding some matter within a larger decision structure, for example, passport verification within the larger border control decision structure. The use of less-than-reliable systems is of course option (a) in our menu, and as exhibited in this example, nested within a broader decision structure consisting of subcomponents, as predicated by (b) (i.e. (a) and (b) are not mutually exclusive, again as we noted in Sect. 4). But now, why would a patently suboptimal decision tool be deployed here at all (or anywhere else, for that matter)? It is one thing to say that it avoids the control problem. It is quite another to say that a system which is so suboptimal it does not engender human confidence should for that very reason be used to assist human decision-makers. Clearly we owe our readers an explanation for including option (a) within our menu of strategies for dealing with the control problem. We think deployment of suboptimal tools may still prove useful in circumstances where the tools have access to information to which the human does not, or otherwise \"decide\" things in ways that humans generally cannot. Such systems very literally augment human capacities: human and machine in effect share control. The clearest examples of this form of technology are recidivism risk prediction tools used in law enforcement. Not all such instruments come with the problematic biases of PredPol (used in so-called hot-spot policing) and COMPAS (predicting the likelihood of offender recidivism) built into them. Some may be genuinely useful in reducing crime at the same time as reducing the prison population (see e.g.  Kleinberg et al. 2018) . These systems answer questions of the form: How should we distribute police officers over a locality having such and such geographical characteristics? What is the likelihood that this prisoner will reoffend if released on parole? And so on. Consider how these systems decide such matters. Often they use logistic 1 3 regression or more advanced actuarial techniques to mine patterns from very large databases. This is not a feat unaided humans can hope to match. There are also some phenomena within human decision-making that algorithms can help to counteracte.g. decision fatigue and decision inertia, of which some of the classic studies actually involve judges' parole decisions (e.g.  Danziger et al. 2011) . Be that as it may, however, we would still urge that great caution be exercised before any form of suboptimal automation is used in high-stakes/safety-critical settings. Many of these systems (like COMPAS) are after all tools which have attained notoriety for their problematic biases and inherent technical limitations (e.g.  Blomberg et al. 2010; Larson et al. 2016; Dressel and Farid 2018) . And as some of these systems gradually begin to overcome their limitations, our worry is that the control problem will gradually re-emerge, taking human operators unawares and decision subjects along with them. It will be all too easy for a judge with decision fatigue, for example, to simply rely on what a predictive risk instrument \"objectively\" recommends. It may turn out that guidelines recommending, for example, that decisionmakers consult their own judgment first before consulting an algorithm, using the algorithm merely as a check on their intuitions, could assist in offsetting some of the effects of automation complacency and bias. (Note that this would come close to telling decision-makers not to use the algorithm-hardly a \"solution\" to the problem). The Wisconsin Supreme Court, when discussing protocols around judicial use of the COMPAS recidivism algorithm required that sentencing judges be given a list of warnings about the tool as a condition of relying on its predictions. More empirical research is required to see whether such approaches really do work. To conclude our analysis of option (a), some of these features of suboptimal decision systems should be stated more explicitly. Option (a)-whether or not combined with option (b)-always represents a specific type of HCI. It is noteworthy that whenever a patently suboptimal tool is used, the human agent does not readily stumble into the control problem, and may therefore be assured of an active and meaningful role working alongside it (assuming a certain level of diligence, aptitude and motivation on the part of the human). But the interaction here will not quite be the same as that envisaged for HMSs under the DCAF approach. Under DCAF, the allocation of functions is complementary. This will not generally be the case under option (a). Assume that a decision, D, comprises the (sub)decisions d 0 , d 1 , d 2 and d 3 . Under DCAF, the human will take care of (let us say) d 0 , d 1 and d 2 while the system will take care of d 3 . This means the human can concentrate their energies entirely on d 0 , d 1 and d 2 and essentially ignore d 3 , because the system is superior in making decisions of the type d 3 . This cannot happen when suboptimal software is used. In such cases, it is not as if the human can take care of d 0 , d 1 and d 2 while the system takes care of d 3 ; the human must also take care of d 3 , albeit with the assistance of a suboptimal decision tool. Both human and machine participate in d 3 (i.e. human and machine effectively share control). Indeed, in light of what we said earlier, in many cases both human and machine may aptly be described as doing (or deciding) the same thing in different ways: for the system may be trying to answer the same question as the human (will she reoffend if released on parole? etc.), only with access to information which the human does not have, or in ways (or at speeds) which humans are unable to match. So there need be no complementarity of functions here, 1 3 Algorithmic Decision-Making and the Control Problem as both human and machine may be performing the same function (viz., d 3 ), albeit distinctly-a classic case of \"multiple realization\"  (Zerilli 2017) . We might even say that instead of a complementary coupling of skills between human and computer, what we have under option (a) will often be a supplementary coupling-where each agent adds something unique to the decision problem in point of how the agent goes about resolving it (somewhat analogous to the role of an expert witness who \"assists\" the judge in determining the appropriate sentence for an offender). Table  1  summarizes the logical space of decisions that may be automated, in whole or in part, and our recommendations for whether or not they should be. Figure 1 depicts both the presence and danger of complacency as a function of system reliability. Notice that at a certain point of reliability, the presence of complacency no longer matters. Notice also what the figure does not capture: it does not tell us what over-reliance on an algorithm looks like, or otherwise calibrate for a healthy or sceptical level of dependence on an algorithm.  3  This-which could well be called the measurement problem-is the subject of separate research in human factors, although it is probably fair to say that most design interventions and optimal task allocation and HCI paradigms are about preventing over-reliance rather than detecting it, no doubt (at least partly) because the hallmarks of over-reliance will differ from system to system and context to context (see e.g. Endsley 2017). \n System Reliability The DCAF approach might be thought of as a variant of the \"Privacy by Design\" (PbD) approach-something like \"Control by Design\". PbD proponents want data protection principles taken into account throughout the whole lifecycle of information systems development  (Bygrave 2017 ). Analogously, one could say that the DCAF approach seeks to \"hardwire\" human factors considerations into the development of HMSs from the earliest stages of modeling. For algorithmic decision support tools, we would suggest that the following six principles can serve as a framework both for assessing the viability of any such human-machine system as well as guiding their design and implementation: • Division of labour Decisions with automatizable subcomponents should reflect a clear allocation of responsibilities between the human-and computer-operated parts of the decision. • Complementarity The allocation of responsibilities should proceed in such a way that those subcomponents better suited for human handling are not automated, and those better suited for computer handling are not manually controlled. While an unhelpful aversion to algorithms can be reduced by giving users power to adjust a decision system's outputs  (Dietvorst et al. 2016) , human interference also tends to introduce errors  (Fildes et al. 2009) . Humans should stick to what they do best, such as communication, symbolic reasoning, conceptualiza-1 3 tion, empathy and intuition-provided these are the skills actually required for a particular decision  (Pohl 2008) . Intuition may be excellent in some decision contexts (who will be the best actor for this part?) but the last resort of a scoundrel in other contexts (what is the likelihood that this brown-skinned man with a history of mental health issues and no priors will re-offend?). A related point is that what may count as a virtue in a human may well count as a vice in a machine. \"Graceful degradation\" has long been regarded as one of the advantages of humans over machines  (Fitts 1951 ), but as  Bainbridge (1983, p. 777 ) pointed out, \"[t]his is not an aspect of human performance to be aimed for in computers…automatic systems should fail obviously.\" 4 In short, complementarity means humans and machines have clearly defined and clearly separated roles, where the human is effectively barred from interfering with the machine's  This assumes that some decisions can be safely handled by both humans and computers, i.e. where humans and computers have shared competencies within particular subdomains. Hand-over and hand-back may also go some way towards alleviating the currency problem, as operators are thereby afforded an opportunity to practice and maintain their manual control skills  (Bainbridge 1983 ). • Co-evolution User requirements co-evolve over time, and decision support tools should reflect this. Decision support tools within HMSs should be designed for adaptability and change. This means designers should not over-specify how a system will work, but allow its users to tailor the system so that it best meets their particular needs  (Walker et al. 2015, p. 201 ). • Pragmatism Decision support tools \"should be congruent with existing practices which may on occasion appear archaic compared to what technology now offers\"  (Walker et al. 2015, p. 201) . When cell phones first appeared, people did not throw out their telephone directories and address books in short order. The older technology held on for a while longer until mobiles were subsumed into the Internet of Things. As new decision software gets tested and then rolled out, we think the same approach is advisable. • Context-sensitivity Each decision tool, situated within its own unique decision context, may prioritise these principles and negotiate their various trade-offs differently. We now turn to consider an algorithmic decision tool that exemplifies several of these principles in its design. Since 1974, New Zealand has run a universal no-fault accident compensation scheme for personal injury. Because the scheme is compulsory, all citizens/residents (or temporary visitors) who have suffered personal injury can expect to be covered regardless of whether or not another party is at fault. Most of the ACC's payments cover treatment/medical costs, but they also regularly cover lost earnings and home and/or vehicle modifications for those with more serious injuries. The ACC processes around 2 million claims per year, of which (on average) about 96% are accepted (ACC 2018). Over the years, the ACC has largely relied on manual control for processing claims. In the past this has involved ACC staff members sorting through and assessing individual claims one by one. Even with improvements to case handling procedures over the years, such as technology allowing electronic submission, all claims have required some degree of manual processing (ACC 2018). At the time of writing, the ACC plans to introduce an improved claim registration and cover assessment process by the end of 2018. It aims to make the claims approval process quicker and more efficient, removing the need for manual control in standard cases altogether. The ACC hopes that by harnessing the power of big data-12 million claims submitted between 2010 and 2016-it can both reduce the wait time for approvals as well as more efficiently distribute the more complex claims to ACC teams for final determination. There are two key features of the new claims handling process. First, the ACC's machine-learning algorithm (developed in-house) has been designed to identify such characteristics of a claim as are strictly relevant to whether it can be accepted. Thus, \"[s]imple claims-where the information provided shows that an injury was caused by an accident-will be fast-tracked and immediately accepted\" (ACC 2018). For example, the system would fast-track \"someone going to the emergency clinic to have a cut stitched,\" but not someone presenting with \"multiple severe injuries\" (ACC 2018). Claims that are not accepted at this step will be passed along to ACC teams for manual processing. Second, the system is not able to decline claims-it can only accept claims that show up as straightforwardly involving accidents based on information provided by the claimant. In giving the tool this limited jurisdiction, its designers have ingeniously converted what is potentially a high-stakes decision into an extremely low one: for the tool cannot decide adversely, only inclusively. The process runs as follows. Each claim moves through a series of automated system checks. At each \"checkpoint,\" one of two things can happen: the claim passes, or it does not. If it passes, it proceeds to the next checkpoint. If it does not pass, the system flags it for manual processing. There are three checkpoints: one for validation and eligibility; a second for accident description; and a third for cover decision (final determination). At the validation and eligibility checkpoint, the system checks that the claimant has provided all essential information (e.g. location and date of accident, type of injury, healthcare provider, claimant's 1 3 Algorithmic Decision-Making and the Control Problem employment and residency status, etc.). If the information is complete, the system passes the claim on to the accident description checkpoint. If the information is incomplete, the system flags it for manual processing. At the accident description checkpoint, the system attempts to categorize the claim in accordance with a predetermined taxonomy of claim types (\"fall,\" \"rugby accident,\" etc.). The system searches the claim form for words that correlate with recognized claim types. If the claim can be categorized in this way, it is passed on to the final checkpoint for determination. If it cannot be categorized, it is flagged for manual processing. At the final checkpoint, two statistical models are employed: The \"Probability of Accept\" model is informed by a statistical model that uses data from 12 million previous, anonymised claims to calculate the probability a new claim should be approved. Each claim is then given a score, and ACC sets a threshold for scores that will be automatically accepted or not. A claim that scores above the threshold set by ACC will be automatically accepted for cover. A claim that scores below the auto-acceptance threshold would then be run through the \"Complexity\" model, which categorises the claim on a scale of low-complexity through to high-complexity. Each claim is then given a complexity score, and ACC sets a threshold for complexity scores that will be automatically accepted or not. A claim that scores below the threshold set by ACC will be automatically accepted. A claim that scores above the auto-acceptance threshold for complexity would then be referred for further manual processing by an ACC staff member. Example: If a client submits a claim for treatment relating to multiple severe injuries and post-traumatic stress following a motor vehicle accident, their claim is likely to receive a high complexity score and would be referred for handling by ACC teams.  (ACC 2018)  How well does the ACC tool incorporate the six human factors principles we outlined in the previous section? We think it performs commendably on at least three of our stated principles: • Division of labour There is here a clear allocation of responsibilities between the human-and computer-operated parts of the decision regarding whether to approve claims. • Complementarity The allocation of responsibilities proceeds in such a way that those subcomponents of the decision better suited for human handling are not automated, and those better suited for computer handling are not manually controlled. Human controllers do not interfere with the automated parts of the process, which are therefore left to operate as essentially risk-free zones of automated decision-making. Humans are not able to perform such aspects of the \"accident description\" and \"cover decision\" subcomponents of the decision as are handled by the algorithm either as accurately or as quickly as the algorithm. In the ACC model, humans only intervene at the point where the algorithm reaches the limit of its competence to determine a claim. • Context-sensitivity The allocation of responsibilities does not incorporate handover and hand-back protocols (i.e. it is not dynamic), but in this particular setup, such flexibility would not contribute to optimal performance. This means that the ACC tool has been deployed in a context-sensitive manner, dispensing with or trading off against principles that are not especially salient in the specific circumstances of deployment. 7 Are There Other Ways to Address the Control Problem? Earlier we mentioned that the control problem appears to be resistant to training, and that experts are as prone to complacency as novices. Before concluding, we should say a little about some of the other commonly suggested strategies for overcoming the control problem. First, there is some evidence that increasing accountability mechanisms can have a positive effect on human operators whose primary responsibility is monitoring an autonomous system. In an important study,  Skitka et al. (2000, p. 701)  found that \"making participants accountable for either their overall performance or their decision accuracy led to lower rates of automation bias\". This seems to imply that if the threat of random checks and audits were held over monitors, the tendency to distrust one's own senses might be attenuated. What effects these checks could have on other aspects of human performance and job satisfaction is a separate question, as is the question of how accountability mechanisms affect complacency (as opposed to bias).  Parasuraman and Manzey (2010, p. 396 ) also warn that the results of this study are not conclusive. But clearly auditing protocols, and perhaps more creative accountability measures, such as \"catch-trials\"-in which system errors are deliberately generated to keep human invigilators on their toes-could be quite useful in counteracting automation bias. Catch trials look particularly promising. While more research on their efficacy is needed before concrete guidelines can be promulgated recommending their adoption, they do seem to offer a viable means of getting humans more actively engaged in the control task. 5 But in any case, much like other touted solutions to the control problem, they do not offer a literal solution: rather, they render systems that are mostly dependable (but not better-than-human) less reliable by stealth (as it were), capitalizing on the premise that less reliable systems do not induce the same complacency and bias that attend more reliable systems. Thus catch trials really fall under option (a) in our menu of strategies above. Second, might having a group of humans in the loop, working together and able to keep watch on one another, alleviate automation bias? Apparently not: 1 3 Algorithmic Decision-Making and the Control Problem Sharing monitoring and decision-making tasks with an automated aid may lead to the same psychological effects that occur when humans share tasks with other humans, whereby \"social loafing\" can occur-reflected in the tendency of humans to reduce their own effort when working redundantly within a group than when they work individually on a given task….Similar effects occur when two operators share the responsibility for a monitoring task with automation….  (Parasuraman and Manzey 2010, p. 392)  Finally we should note that  Parasuraman and Manzey (2010, p. 387 ) added these observations in connection with the effects of training regimes: Although extended practice does not eliminate automation complacency, other training procedures may provide some benefit. In particular, given that complacency is primarily found in multitasking environments and represents attention allocation away from the automated task, training in attention strategies might mitigate complacency. We are not aware of research empirically substantiating this latter claim, but would anyway caution against task allocations that reduce human agents to monitors of largely static displays of information (if that is the implicit proposal here). Other studies cited by the authors, albeit in the context of automation bias, indicate that even explicit briefings about risk factors in HCI do not mitigate the strength of automation bias, and this seems to be true in both multitasking and singletasking environments. An idle mind is not an empty mind, but rather a wandering mind, and when the stakes are high, the risk of complacency is still too great to be managed by rubber-stamp training interventions that make only a questionable difference to deep-seated psychological propensities. Perhaps there is then reason to be sceptical about the effectiveness of \"warnings\" or other guidelines about how best to use decision tools in judicial settings (as we mentioned earlier in regards to COMPAS). But it is a live research question. \n Conclusion Automation introduces more than just automated parts: it very often also transforms the nature of the interaction between human and machine in profound ways. One of its most alarming effects is to induce a sense of complacency in its human controllers. To date, little has been said about whether and to what extent the same problem arises from the use of ever more sophisticated algorithmic decision tools, including those exploiting cutting-edge machine learning techniques such as deep learning. We have endeavoured to show how insights from human factors research have great relevance to policy specialists working in AI regulation and policy. Among the factors which should be considered in the decision to automate any part of an administrative or business decision is the tendency of human operators to hand over effective control to an algorithm just because it works well in most instances. We argue that, except in special cases, whenever an automatizable decision is high-stakes or safety-critical, the decision support tool under consideration should not be deployed unless it has genuinely earned its keep. Failing that, a dynamic and complementary allocation of functions between actively engaged human operators and simpler but more nearly perfectly reliable autonomous systems should be considered the safest course. outputs and perhaps in many cases even knowing what the outputs are. Breaking the task up in this way also increases the chances of finding optimally reliable software to handle the automated parts of a decision.• Dynamism The allocation of responsibilities should incorporate hand-over and hand-back protocols where this flexibility contributes to optimal performance. \n Fig. 1 1 Fig. 1 Presence (i) and (ii) danger of complacency as a function of system reliability. The dashed line represents near perfect (better-than-human) reliability \n Table 1 1 The logical space of automatizable decisions and their attendant control problems Algorithmic Decision-Making and the Control Problem For any decision D: { d 0 , d 1 , d 2 … d n } Option (a) Option (b) Option (c) Patently suboptimal system Decomposition/allocation Better-than-human system D d0, d1, d2 … dn D (whole decisions) (semiautonomous decisions) (whole decisions) Supplementary coupling/ Complementary coupling/ No human in the loop human in the loop human in the loop e.g. SAE Level 5 AV e.g. medical diagnostic tools (b + c) (eventually); Proceed with caution (DCAF) case prediction sofware e.g. ACC (below) Recommended Recommended OR Supplementary coupling/ human in the loop (a + b) e.g. recidivism risk prediction instruments Proceed with caution OR Mostly reliable system/ human in the loop e.g. SAE Level 2 AV Danger! Control problem! \n\t\t\t Notice, incidentally, that it is therefore not just when a decision tool is architecturally opaque that a human operator should potentially be retained in the decision control loop, as is already widely appreciated (e.g. IEEE 2017; House of Lords 2018). Even a fully technically transparent decision system may enjoin human agency to a greater or lesser extent.2  The AI system in this case computed measures of structural brain connectivity from fMRI brain scans, and used these as inputs to a classifier. Accuracy was computed on unseen brain scans; the classifier's performance was significant at the p < 0.001 level. More generally, assessing the accuracy of machine learning systems can be a complex task, but suffice it to say that more meaningful accuracy rates would need to consider base rates, which are not always cited in the relevant studies. It is well known that when a base rate is lower than the false positive rate of a test, false positives will exceed true positives even for an extremely accurate test (the so-called \"false positive paradox\"). Stepping back a little, however, because our point here is just that in some highly formulaic and process-driven domains it appears that machines perform better than humans, the underlying base rates will not be strictly relevant. So long as machines perform better than humans in these domains (as our examples illustrate), these results should hold regardless of base rates. \n\t\t\t We owe this point to an anonymous reviewer of the journal. \n\t\t\t This is not always true. An object classifier should tell you how much a given object is like a chair, rather than move discretely from \"chair\" to some other category of objects: to that extent, classifiers certainly are designed with a view to graceful degradation. \n\t\t\t Catch trials might not be such a good thing if case workers came to think that \"odd\" looking cases were \"probably not real\". \n\t\t\t Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "date_published": "n/a", "url": "n/a", "filename": "Zerilli2019_Article_AlgorithmicDecision-MakingAndT.tei.xml", "abstract": "The danger of human operators devolving responsibility to machines and failing to detect cases where they fail has been recognised for many years by industrial psychologists and engineers studying the human operators of complex machines. We call it \"the control problem\", understood as the tendency of the human within a human-machine control loop to become complacent, over-reliant or unduly diffident when faced with the outputs of a reliable autonomous system. While the control problem has been investigated for some time, up to this point its manifestation in machine learning contexts has not received serious attention. This paper aims to fill that gap. We argue that, except in certain special circumstances, algorithmic decision tools should not be used in high-stakes or safety-critical decisions unless the systems concerned are significantly \"better than human\" in the relevant domain or subdomain of decision-making. More concretely, we recommend three strategies to address the control problem, the most promising of which involves a complementary (and potentially dynamic) coupling between highly proficient algorithmic tools and human agents working alongside one another. We also identify six key principles which all such human-machine systems should reflect in their design. These can serve as a framework both for assessing the viability of any such human-machine system as well as guiding the design and implementation of such systems generally.", "id": "b5c168ee3e98bdf3ef1bf28518fca43f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Eliezer Yudkowsky"], "title": "Coherent Extrapolated Volition", "text": "Introduction This is an update to that part of Friendly AI theory that describes Friendliness, the objective or thing-we're-trying-to-do. The information is current as of  May 2004, and  should not become dreadfully obsolete until late June, when I plan to have an unexpected insight. (Update: Actually, it took two days. Still, the text here isn't too far from the mark.) Misleading terminology alert: I am still calling the Friendly Thingy an \"Artificial Intelligence\" or \"superintelligence,\" even though it would be more accurate to call it a Friendly Really Powerful Optimization Process. Warning: Beware of things that are fun to argue. Defining Friendliness is not the life-or-death problem on which the survival of humanity depends. It is a life-or-death problem, but not the life-or-death problem. Friendly AI requires: 1. Solving the technical problems required to maintain a well-specified abstract invariant in a self-modifying goal system. (Interestingly, this problem is relatively straightforward from a theoretical standpoint.) 2. Choosing something nice to do with the AI. This is about midway in theoretical hairiness between problems 1 and 3. 3. Designing a framework for an abstract invariant that doesn't automatically wipe out the human species. This is the hard part. Some examples to give a taste of the hard part: • An AI whose abstract invariant is a \"reward button,\" pressed when the AI pleases users, may go on to tile the solar system with ever-larger floating-point representations of total reward. • An AI trained on the problem of \"making humans smile\" may acquire a utility function satisfied by tiling the solar system with tiny smiley faces. Compare Friendly AI to the easier problem of wiping out the human species. The latter requires: • Probing around in AI design space to find a few things that work (not necessarily understanding why they work) and tacking them together to do recursive selfimprovement. • Designing a coherent system based on self-modification which is probabilistic in nature and does not maintain an invariant optimization target. For example, directed evolution. \n Introducing Volition Suppose you're faced with a choice between two boxes, A and B. One and only one of the boxes contains a diamond. You guess that the box which contains the diamond is box A. It turns out that the diamond is in box B. Your decision will be to take box A. I now apply the term volition to describe the sense in which you may be said to want box B, even though your guess leads you to pick box A. Let's say that Fred wants a diamond, and Fred asks me to give him box A. I know that Fred wants a diamond, and I know that the diamond is in box B, and I want to be helpful. I could advise Fred to ask for box B instead; open up the boxes and let Fred look inside; hand box B to Fred; destroy box A with a flamethrower; quietly take the diamond out of box B and put it into box A; or let Fred make his own mistakes, to teach Fred care in choosing future boxes. But I do not simply say: \"Well, Fred chose box A, and he got box A, so I fail to see why there is a problem.\" There are several ways of stating my perceived problem: 1. Fred was disappointed on opening box A, and would have been happier on opening box B. 2. It is possible to predict that if Fred chooses box A, Fred will look back and wish he had chosen box B instead; while if Fred chooses box B, Fred will be satisfied with his choice. 3. Fred wanted \"the box containing the diamond,\" not \"box A,\" and chose box A only because he guessed that box A contained the diamond. 4. If Fred had known the correct answer to the question of simple fact, \"Which box contains the diamond?\", Fred would have chosen box B. Hence my intuitive sense that giving Fred box A, as he literally requested, is not actually helping Fred. If you find a genie bottle that gives you three wishes, it's probably a good idea to seal the genie bottle in a locked safety box under your bed, unless the genie pays attention to your volition, not just your decision. Let's ask Fred's volition a more complicated question: \"What should the code of a Friendly AI look like?\" But there's a minor problem, which is that Fred is a huntergatherer from the Islets of Langerhans, where they have never even heard of Artificial Intelligence. There is a tremendous distance between the real Fred, and a Fred who might specify the code of a Friendly AI. Fred needs more than knowledge of simple facts, and knowledge of many background disciplines not known to the Islets of Langerhans. Fred needs to answer moral questions he doesn't know how to ask, acquire new skills, ponder possible future courses of the human species, and perhaps become smarter. If I started with the Fred of this passing moment, and began a crash education course which Fred absorbed successfully, it would be years before Fred could write a Friendly AI. Different Everett branches of Fred would not write identical code, and would probably write different AIs. Would today's Fred recognize any of those future Freds, who had learned so much about the universe, and rejected so many prevailing beliefs of the Islets of Langerhans? Yet today's Fred still has wishes that straightforwardly apply to the creation of an Artificial Intelligence. Fred may not know what a paperclip is, or what a solar system is, but nonetheless Fred would not want anyone to create an Artificial Intelligence that tiled the solar system with paperclips. Fred choosing between box A and box B is a simple case of asking what Fred \"would want.\" The Fred who knows that box B contains the diamond is so close to today's Fred, so readily understandable, that we skip over the intervening step of extrapolation, and say simply: \"Fred wants box B.\" Rather than saying, \"I have mentally extrapolated a volition for Fred, consisting of an alternate version of Fred that knows which box contains the diamond, and I imagine that this Fred chooses box B.\" Sadly, there isn't a little display built into the back of your neck that shows your volition. To construe your volition, I need to define a dynamic for extrapolating your volition, given knowledge about you. In the case of an FAI, this knowledge might include a complete readout of your brain-state, or an approximate model of your mind-state. The FAI takes the knowledge of Fred's brainstate, and other knowledge possessed by the FAI (such as which box contains the diamond), does . . . something complicated . . . and out pops a construal of Fred's volition. I shall refer to the \"something complicated\" as the dynamic. Note that labeling something \"a volition-extrapolating dynamic\" does not mean that it does anything of the sort. I can apply the term \"volition-extrapolating dynamic\" to a process that visualizes Fred replaced with a potted plant and decodes the waving leaves. But I think Fred would object, and I'm not just saying that because I imagine his leaves waving westward. In all cases we speak of choosing and teaching a generally intelligent AI to extrapolate volition. If one attempted to write an ordinary computer program using ordinary computer programming skills, the task would be a thousand lightyears beyond hopeless. \n Spread, Muddle, and Distance These quantities are ad hoc and will probably be replaced by more elegant first principles when I have worked out more of the theory. Spread describes cases where your extrapolated volition becomes unpredictable, intractable, or random. You might predictably want a banana tomorrow, or predictably not want a banana tomorrow, or predictably have a 30% chance of wanting a banana to-morrow depending on variables that are quantum-random, deterministic but unknown, or computationally intractable. When multiple outcomes are possible and probable, this creates spread in your extrapolated volition. Muddle measures self-contradiction, inconsistency, and cases of \"damned if you do and damned if you don't.\" Suppose that if you got a banana tomorrow you would not want a banana, and if you didn't get a banana you would indignantly complain that you wanted a banana. This is muddle. Distance measures how difficult it would be to explain your volition to your current self, and the degree to which the volition was extrapolated by firm steps. \n Short distance: An extrapolated volition that you would readily agree with if explained. Medium distance: An extrapolated volition that would require extended education and argument before it became massively obvious in retrospect. \n Long distance: An extrapolated volition your present-day self finds incomprehensible; not outrageous or annoying, but blankly incomprehensible. Ground zero: Your actual decision. \n Obvious Moral Hazard of Volitionism as Philosophy In everyday life, a helpful human should not try to extrapolate a friend's volition beyond the point where the friend would readily agree. Our ability to extrapolate is too unreliable, and our evolved tendency to mess with other people's lives \"for their own good\" is too strong. If Fred says \"I've heard the argument and I still disagree,\" that settles it; I don't think one should believe a politician who claims to follow Fred's volition when Fred himself protests. Humans dealing with other humans can usually essay only short-distance extrapolations and still claim to work on the other's behalf. Society does recognize dangerous exceptions to this rule, such as parents and children. But I don't think it would be \"helping\" Fred to gift him with a genie which would try to explain to Fred why his wish was dangerous, but would go ahead and fulfill the wish, after Fred of the Islets indignantly instructed the genie to stop giving him insolent backtalk and follow orders. In this case I don't see much of a moral distinction between murder by genie bottle and murder by bullet. Genies ain't human, humans ain't genies. Different precautions apply. \n Coherent Extrapolated Volition As of May 2004, my take on Friendliness is that the initial dynamic should implement the coherent extrapolated volition of humankind. In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted. Knew more: Fred may believe that box A contains the diamond, and say, \"I want box A.\" Actually, box B contains the diamond, and if Fred knew this fact, he would predictably say, \"I want box B.\" If Fred would adamantly refuse to even consider the possibility that box B contains a diamond, while also adamantly refusing to discuss what should happen in the event that he is wrong in this sort of case, and yet Fred would still be indignant and bewildered on finding that box A is empty, Fred's volition on this problem is muddled. Thought faster: Suppose that your current self wants to use an elaborate system of ropes and sticks to obtain a tasty banana, but if you spent an extra week thinking about the problem, you would predictably see, and prefer, a simple and elegant way to get the banana using only three ropes and a teddy bear. I arbitrarily declare the poetic term \"think faster\" to also cover thinking smarter, generalizing to straightforward transforms of existing cognitive processes to use more computing power, more neurons, et cetera. But the less understandable your present self finds your extrapolated volition, the greater the distance. Were more the people we wished we were: Any given human is inconsistent under reflection. We all have parts of ourselves that we would change if we had the choice, whether minor or major. Suppose Fred has a deeply repressed desire to murder Steve, but Fred consciously holds that murder is wrong. I do not call it \"helping Fred,\" to murder Steve on his behalf. (Obviously I would not murder Steve regardless. I am an altruist, but also a private citizen; I need not help people in ways that conflict with my own ethics. I raise this scenario to ask whether murdering Steve is \"helping Fred,\" considered in isolation.) Suppose Fred decides to murder Steve, but when questioned, Fred says this is because Steve hurts other people, and needs to be stopped. Let's do something humans can't do, and peek inside Fred's mind-state. We find that Fred holds the verbal moral belief that hatred is never an appropriate reason to kill, and Fred hopes to someday grow into a celestial being of pure energy who won't hate anyone. We extrapolate other aspects of Fred's psychological growth, and find that this desire is expected to deepen and grow stronger over years, even after Fred realizes that the Islets worldview of \"celestial beings of pure energy\" is a myth. We also look at the history of Fred's mind-state and discover that Fred wants to kill Steve because Fred hates Steve's guts, and the rest is rational-ization; extrapolating the result of diminishing Fred's hatred, we find that Fred would repudiate his desire to kill Steve, and be horrified at his earlier self. I would construe Fred's volition not to include Fred's decision to kill Steve, noting that this is a medium-distance volition. If self-modification were a routine part of human-existence, I suspect we would regard Fred's predictable regret after self-modifying as analogous to Fred's predictable regret after learning that box B contains the diamond. (That is, we would regard it as a short-distance extrapolation.) We may want things we don't want to want. We may want things we wouldn't want to want if we knew more, thought faster. We may prefer not to have our extrapolated volition do things, in our name, which our future selves will predictably regret. The volitional dynamic takes this into account in multiple ways, including extrapolating our wish to be better people. I distinguish \"human,\" that which we are, from \"humane\"-that which, being human, we wish we were. Our extrapolated volition needs to encapsulate our aspiration to humaneness, not just our humanity. Extrapolating Fred's wish to be a better person can amplify, or reduce, Fred's spread. If you are uncertain about a fundamental decision as to what kind of person you would like to be, this uncertainty may affect hundreds or millions of other decisions. All your future might hang in the balance, everything depending on who you decide to be when you grow up. Taking into account our wish to be better people can also reduce the spread in the extrapolation. Maybe you're presently uncertain whether to live in Detroit or Salt Lake City, but if you were a nicer person you' d predictably move to Australia. (No insult is intended to Australia.) Had grown up farther together: A model of humankind's coherent extrapolated volition should not extrapolate the person you' d become if you made your decisions alone in a padded cell. Part of our predictable existence is that we predictably interact with other people. A dynamic for CEV must take a shot at extrapolating human interactions, not just so that the extrapolation is closer to reality, but so that the extrapolation can encapsulate memetic and social forces contributing to niceness. Our CEV may judge some memetic dynamics as not worth extrapolating-not search out the most appealing trash-talk TV show. Social interaction is probably intractable for real-world prediction, but no more so than individual volition. That is why I speak of predictable extrapolations, and of calculating the spread. Where the extrapolation converges rather than diverges: Some of humanity's possible futures may hinge on decisions humanity has not yet made. As we grow up farther and make more decisions, our coherent extrapolated volition may change. Where the course of humankind is not presently predictable (exhibits significant spread ), our CEV should take this into account, and leave options open, waiting for our decision. Where our wishes cohere rather than interfere: Coherence is not a simple question of a majority vote. Coherence will reflect the balance, concentration, and strength of individual volitions. A minor, muddled preference of 60% of humanity might be countered by a strong, unmuddled preference of 10% of humanity. The variables are quantitative, not qualitative. Extrapolated as we wish that extrapolated: Your volition should take into account only those desires and aspects of your personality that you would want your volition to take into account-the volitional dynamic should be consistent under reflection. This is a lesser special case of the rule that the Friendly AI should be consistent under reflection (which might involve the Friendly AI replacing itself with something else entirely). Deciding what your volition should take into account is treated separately because it comes earlier in order of evaluation. The dynamic would ask \"Does Fred want this desire included in his volition?\" before asking \"What Friendly AI does Fred's extrapolated volition want?\" Interpreted as we wish that interpreted: I arbitrarily declare this part of the poetry to stand for the volitional dynamic's ability to renormalize, rewrite itself, or replace itself entirely. \n Coherence and Influence Coherence: Strong agreement between many extrapolated individual volitions which are unmuddled and unspread in the domain of agreement, and not countered by strong disagreement. Coherence • increases, as more humans actively agree; • decreases, as more humans actively disagree (the strength of opposition decreases if the opposition is muddled); and • increases, as individuals support their wishes more, with stronger emotions or more settled philosophy. It should be easier to counter coherence than to create coherence. Influence: Acts carried out, optimization pressures applied, transformations undertaken, in the service of goals on which our extrapolated volitions exhibit coherence. Less influence is required to rule out narrow slices of our possible futures, or prevent things from happening; more influence is required to direct humanity into specific narrow slices of future, or make specific things happen. The narrower the slice that our CEV wants to avoid, the less consensus required, the more distant the future selves that might produce the warning. The narrower the slice of the future that our CEV wants to actively steer humanity into, the more consensus required. Distance, muddle, and spread will more rapidly attenuate positive influence than negative influence; the initial dynamic for CEV should be conservative about saying \"yes,\" and listen carefully for \"no.\" Extrapolating your wish to be a better person may add considerable distance. A key point in building a young Friendly AI is that when the chaos in the system grows too high (spread and muddle both add to chaos), the Friendly AI does not guess. The young FAI leaves the problem pending and calls a programmer, or suspends, or undergoes a deterministic controlled shutdown. If humanity's volition is just too chaotic to extrapolate, the attempt to manifest our coherent extrapolated volition must fail visibly and safely. \n Renormalizing the Dynamic The FAI programmers do not need to get the dynamic exactly right the first time. They need to try their best to be perfect; but they do not need to be perfect. I hope to construe a sufficiently powerful initial dynamic that I can ask: \"What dynamic for extrapolating a volition would we want?\" Or more generally, ask: \"What should the code of a Friendly AI look like?\" Or more generally still, \"Write a piece of code that humanity wants to run.\" Perhaps the code humanity would prefer is not a dynamic for extrapolating a volition, or any kind of Friendly AI. One cannot bootstrap from a vacuum. To ask what humanity wants requires an initial dynamic which is well-defined in an engineering sense, and which works well enough to answer extremely complex questions. It takes a satisfactory initial dynamic of volition to extrapolate an optimal dynamic of volition. The task of construing a satisfactory initial dynamic is not so impossible as it seems. The satisfactory initial dynamic can be coded and tinkered with over years, and may improve itself in obvious and straightforward ways before taking on the task of rewriting itself entirely. There is an obvious analogy between construing a satisfactory initial dynamic for extrapolating a volition, and developing an Artificial Intelligence smart enough to improve its own code and bootstrap to superintelligence. Friendly AI theory treats the second problem as a special case of the first. \n Coherent Extrapolated Volition Is an Initial Dynamic Once we have something that approximates a volition of the human species, that volition then has the chance to write its own superintelligence, optimization process, legislative procedure, god, or constitution. I try not to get caught up on CEV as a model of the actual future, even though it seems like a Nice Place To Live. The purpose of CEV as an initial dynamic is not to be the solution, but to ask what solution we want. Nonetheless, CEV seems to me like it would function reasonably well as a Nice Place To Live, given some auxiliary dynamics-for example: • Our coherent extrapolated volition should choose a small set of universal background rules, not optimize every detail of individual lives. (Rules in the sense of apparent behaviors of Nature, not legal regulations. An example of a current background rule is \"As time goes on, you will age, become weaker and sicker, slowly lose neurons, and die.\" This strikes me as the diametric opposite of what I would prefer.) • The rules should not be inscrutable, and should prefer to operate scrutably, so that humans can understand, predict, and manipulate their world. • The ruleset should be small enough that human beings can learn and understand all the rules in reasonable time. This would make our post-Singularity future more humanly comprehensible than any modern-day legal system. Auxiliary dynamics of a Nice Place to Live should not be included in the initial dynamic because: • They are complex, adding implementation difficulty. • They are guesses, adding probability of error. • They are means to an end. • They are only relevant if humanity wants to live inside humanity's volition, rather than somewhere else. • A decent initial dynamic must be capable (design requirement) of extrapolating auxiliary dynamics. • Auxiliary dynamics often have a one-way aspect; once they're built into the structure, it's harder to renormalize them out than to renormalize them in. • They are too much fun to speculate about. There is a principled distinction between discussing CEV as an initial dynamic of Friendliness, and discussing CEV as a Nice Place to Live. Despite the apparent similarity, these are fundamentally different purposes, with different design requirements. When I originally wrote this essay, I was conflating the two purposes. Yes! This essay is already obsolete! There's not one single damn thing I've tried to write in the last three years that was still current with my thinking when I published it, and in this case it only took two days! Ahem. Okay, let's see what needs changing from what I've written so far . . . The rules about degree of influence depending on the balance of coherence might need to allow a sufficiently strong win to rewrite the initial dynamic entirely, rather than striking something resembling a political compromise. Otherwise there's too much inertia in the system-it's too hard to get sufficient agreement to make large leaps forward from the programmers' initial solution. I think I would wish to live in a world that required compromises when writing rules, but not meta-rules. Compromise is itself a meta-rule, and it's almost impossible to get rid of compromise if you have to compromise on how to get rid of it. Initial dynamics should not start out having already taken one-way steps. Thus, I now regard the previously offered rules about coherence and influence as auxiliary dynamics of a Nice Place to Live; they might make an appearance in the initial dynamic, but only if that doesn't create inertial mud in the system, or require unrealistic unanimity to leap to better meta-rules, or otherwise make it difficult to write a coherent dynamic on the next round of renormalization. (I left this in the final version of the paper to emphasize that I am still working out these issues. For all I know, I may scrap coherent extrapolated volition entirely in 2005.) \n Caring about Volition Some have asked: \"Why care about our extrapolated volitions? Like, at all?\" The dynamic of extrapolated volition refracts through that cognitive complexity of human minds which lead us to care about all the other things we might want; love, laughter, life, fairness, fun, sociality, self-reliance, morality, naughtiness, and anything else we might treasure. Whatever you care about-whatever it is of which you say, \"XYZ is what we should care about\"-it's your brain, a human brain, that produced that statement; and the air vibrating on your lips exists in a universe of cause and effect. There is a physical explanation for why you said the words \"XYZ.\" This does not devalue XYZ. There is a complex psychological tangle here, which leads people to experience feelings of existential emptiness for no good reason. Let it stand that human statements about morality are explicable in terms of cause-and-effect physics, just like absolutely everything else, and this in no way detracts from the force of the moral statements. Human moral psychology is not merely physics; physics is not \"mere.\" But everything that exists, exists embedded within physics. CEV is a dynamic that passes through, and extrapolates, the human psychology of decision-making-including argument about morality, and human emotion, and the memes we argue together; everything that changes our choices. Any thoughts you have about morality are included as a special case of CEV extrapolating your thoughts. If you think that some particular morality should be, not a special case of your extrapolated volition, but the law and the whole of the law, I can only lift my hands helplessly, and say that I have no time to hear out your argument from the other million arguments I might hear. If there is some chain of moral logic so self-evident that any human who hears with open mind must follow, then that is what the initial dynamic of extrapolated volition would produce on the next round. I don't think this is what will happen, but I took into account the possibility in planning. If the Pnakotic Manuscripts are truly the source of all goodness and light, you're covered. If humans make their judgments using hidden superpowers of carbon atoms that no mere silicon atoms can match, the attempt to construct a coherent extrapolated volition will fail early, visibly, and harmlessly when the dynamic finds it can't predict human moral judgments. Likewise if the dynamic learns to predict humans successfully, and then predicts that humans wouldn't want to be predicted by a mere machine without an immortal soul. These special cases shouldn't require special code. They're just implicit in a volitional dynamic that does the Right Thing, the thing we want to happen. I didn't choose coherent extrapolated volition lightly; I chose it as the endpoint of a journey that began by asking \"What should I care about?\" I don't know all of the answer, but at least I now understand the nature of the question; it is no longer mysterious to me. As for the answer, I have encountered many subproblems which had surprising and compelling resolutions. But I couldn't predict the solution or even the kind of solution in advance, nor guess which part of the problem I would see in a new light. I do not know the library of forces which compel me. I do not know the search space of arguments which move me. I do not accept new parts of myself blindly, when I discover them; I am compelled to judge my compulsions, moved to question my movements. Yet there may be light within me that I do not realize, but would acknowledge if shown. All I can do is take that reply which I would give if I knew more, thought faster, were more the person I wished I were, had grown up farther with you all, and call it the right answer. But I cannot tell you specifically the right answer. In the end, it reduces to me chipping away at the question, waiting to be struck by a good idea. That chipping process is what I intend CEV to extrapolate. If there is a grand unifying theory waiting to strike, and it is the same for everyone, then chipping away is the only method I currently know for finding it. As I understand the question it is quite unlikely that there is a grand unifying theory, and so we shall have to find the answer the hard way, by making the decision. We cannot ask our volitions for an answer, if that is the only answering procedure we know. \n Motivations Defend humans, the future of humankind, and humane nature. These are three things which the wrong choice of initial dynamic might screw up. Most people careless enough to make blatantly foolish choices for AI morality are also foolish enough to screw up the technical implementation. If someone programs an AI using pictures of smiling humans as reinforcement, the resulting AI will not keep everyone happy whether they like it or not; the resulting AI will tile the solar system with tiny molecular smiley faces. Mostly, the meddling dabblers won't trap you in With Folded Hands or The Metamorphosis of Prime Intellect. Mostly, they're just gonna kill ya. It's unlikely that any given meddling dabbler will succeed; but there's a plentiful supply of dabblers, and Moore's Law keeps lowering the bar. But if we imagine the improbable event of a meddling dabbler somehow succeeding in solving the deep technical problems of Friendly AI, yet not thinking through Friendliness, then we can imagine scenarios such as With Folded Hands-where the robots protect human life, and prevent humans from experiencing pain or distress, but care nothing for those other things that humans love, such as liberty. The future of humankind is lost. I value my friends and fellows: the six billions now in jeopardy, their lives and liberties. I value the future of humankind: trillions or quadrillions or octillions of lives; stars and galaxies become our cities. Weightier by far than a mere six billion, it might seem; but we six billion carry the seed complexity. As best I can foresee, at least some of the key decisions lie rightfully in our hands; not beyond the rethinking of future generations, but ourselves creating and becoming the minds who rethink. It's one heck of a huge future hanging in the balance, and I really, really, really don't want to spoil it. I value the light in the heart of humanity: love, laughter, life, happiness, fun, fairness, compassion, empathy, sympathy, sociality, sexuality, self-reliance, shared warmth and togetherness, moral argument, naughtiness, serene wisdom, juvenile mischief; our wish to be better people; humane nature, and the future our humane drives will shape. The initial dynamic of CEV takes into account the wishes of those billions now in existence, including our wish to live, and our wish for freedom, and our wish to defend those other things we value. CEV looks forward in time, to find if our past predictably threatens portions of our future we will predictably value. Since the output of the CEV is one of the major forces shaping the future, I'm still pondering the order-of-evaluation problem to prevent this from becoming an infinite recursion. Extrapolating volition seeks out the light in human nature. I think. I'm not sure about this part. (Other sections touch on this in more detail.) \n Encapsulate moral growth. Humanity's moral memes have improved greatly over the last few thousand years. How much farther do we have left to go? I was born too late myself, but you don't need to be very old to remember a time when blacks rode in the back of the bus-a thought that still chills me, that the time is so close to our own. What if we too look like barbarians from the perspective of a few years down the road? We need to extrapolate our moral growth far enough into the virtual future to discover our gasp of horrified realization when we realize that the common modern practice of X is a crime against humanity, even though, like slavery, X seemed to us like a normal and harmless institution. Possible values of X include sending children to school, keeping chimpanzees in cages, not knowing the basic laws of physics, buying mass-manufactured tools, or living without access to sandestins. (This was phrased as a Nice Place to Live argument, but it also applies to the initial dynamic.) Humankind should not spend the rest of eternity desperately wishing that the programmers had done something differently. But most who ponder AI morality walk straight into the whirling razor blades, without the slightest hint of fear. I am dismayed, but not surprised. I do not say it is inevitable; someone who rises to the challenge can do better than that. I never made that error, not once. Once upon a time, back at the age of sixteen, I made one hell of a huge philosophical blunder about how morality worked, which caused me to think that to create a Friendly AI I just needed to create a really powerful self-improving optimization process and wave it cheerily on its way. But I never thought I had the wisdom or authority to lay down Ten Commandments, not for an AI and not for humanity. The problem was so uncomfortable that it took me until the age of twenty to acknowledge the problem existed. (Youthful foolishness I don't intend to ever repeat; I think I've changed sufficiently since then.) Once I acknowledged the problem existed, I didn't waste time planning the New World Order. No, not even a fraction of a second; it was too obvious a failure mode. The first thing I said was, \"What if the programmers don't get it right on the first try?\", followed immediately by, \"A self-modifying expected utility maximizer with a constant utility function won't let anyone tamper with its utility function; I need to figure out how to construct a dynamic for a correctable utility function such that the dynamic is stable under self-modification.\" I didn't use those words. I knew the math, but I didn't know the standard names. I made up silly names of my own, because I was young. But I wasn't young enough to rub my hands in glee at the prospect of laying down the Four Great Moral Principles. I wasn't even young enough to be frightened at the thought of making moral choices for the whole human species. I took for granted that whichever shmuck happened to program the first superintelligence had no special moral privileges, and I looked for ways to refer the question back to humanity. I looked to Friendliness architecture and not Friendliness content, because I knew the difference between fun moral argument and technical thinking. I knew which kind of thinking was useful, and which kind of thinking was not. I flinched away from addressing the problem of Friendliness content, and took refuge in Friendly AI structure. And whaddaya know, it worked. Once I had a language to describe solutions, it became far easier to come up with a solution. That younger self didn't get the theory right on his first try, not even close. But I can see the foundations of the extrapolated volition model, even in a younger self so distant that I sometimes can't guess what he was thinking. The extrapolated volition model doesn't have an escape hatch tacked on-the escape hatch is not an awkward added clause, an Eleventh Commandment. The escape hatch is implicit in extrapolated volition doing the Right Thing. If our extrapolated volitions say we don't want our extrapolated volitions manifested, the system replaces itself with something else we want, or vanishes in a puff of smoke (undergoes an orderly shutdown). And our CEV uses greater intelligence to search for errors, unforeseen consequences, future horrors, the predictable moral revulsions of tomorrow's selves. If we scream, the rules change; if we predictably scream later, the rules change now. It may be hard to get CEV right-come up with an AI dynamic such that our volition, as defined, is what we intuitively want. The technical challenge may be too hard; the problems I'm still working out may be impossible or ill-defined. I don't intend to trust any design until I see that it works, and only to the extent I see that it works. Intentions are not always realized. But I intend that CEV have an intrinsic escape hatch, and search for unforeseen consequences, and not rely on the ability of the original programmers to dictate all the moral questions correctly on their first try. The other plans I hear proposed would fail even if they succeeded. There are fundamental reasons why Four Great Moral Principles or Ten Commandments or Three Laws of Robotics are wrong as a design principle. It is anthropomorphism. One cannot build a mind from scratch with the same lofty moral statements used to argue philosophy with pre-existing human minds. The same people who aren't frightened by the prospect of making moral decisions for the whole human species lack the interdisciplinary background to know how much complexity there is in human psychology, and why our shared emotional psychology is an invisible background assumption in human interactions, and why their Ten Commandments only make sense if you're already a human. They imagine the effect their Ten Commandments would produce upon an attentive human student, and then suppose that telling their Ten Commandments to an AI would produce the same effect. Even if this worked, it would still be a bad idea; you' d lose everything that wasn't in the Ten Commandments. Think of a utility function, U (x), with additive components U 1 (x), U 2 (x), U 3 (x), and so on. There are hundreds of drives in human psychology. Even if Ten Commandments worked to transfer rough analogues of the first ten components, V 1 (x) through V 10 (x), you' d still have disagreements because of the sloppy transfer method, places where V 1 didn't match U 1 . Human psychology doesn't run on utility functions; just the choice of formalism implies some degree of mismatch with actual decisions. But forget the minor mismatch; what about U 11 (x) through U 245 (x)? What about everything that's not in the Ten Commandments? The result would be humanity screaming as the AI took actions in total disregard of U 11 (x) and all other components the original programmers got wrong or didn't consider-an AI that kept us from harm at the cost of our liberty, and so on. Usually the Ten Commandments folks don't even advocate transferring ten underlying human emotions U 1 (x) through U 10 (x)-just trying to transfer ten specific moral arguments that sound good to their human psychologies, without transferring any of the underlying human emotions to lend a commonsense interpretation. Humanity would scream wherever the literal extrapolation of those ten statements conflicted with one of our hundreds of psychological drives, or with one of the thousands of moral statements not included on the list of ten. Not that this is a likely actual scenario. Anyone ignorant enough to make such a proposal is ignorant enough to kill you outright if they succeed, build their AI that Pays Attention To Social Entities and goes on to tile the solar system with tiny interacting agents pushing around billiard balls. Avoid hijacking the destiny of humankind. FAI programmers are ordinary shmucks and do not deserve, a priori, to cast a vote larger than anyone else. There is a challenge of the professional ethics of FAI, as there is the challenge of Friendliness, and the challenge of FAI theory, and the challenge of saving the world without distraction. I have not yet heard the objectors protest in their own right, rather than on Dennis's behalf. For if they proposed a concrete alternative, put forward their own desire rather than a hypothesis of how someone else might protest, they should themselves need to confront objections. And that is not a philosopher's place, in the scheme of things. The initial conditions of the AI have a large de facto effect on the human species. Even if our coherent extrapolated volition wants something other than a CEV, the programmers choose the starting point of this renormalization process; they must construct a satisfactory definition of volition to extrapolate an improved or optimal definition of volition. Different classes of satisfactory initial definitions may fall into different selfconsistent attractors for optimal definitions of volition. Or they may all converge to essentially the same endpoint. A CEV might survey the \"space\" of initial dynamics and self-consistent final dynamics, looking to see if one alternative obviously stands out as best; extrapolating the opinions humane philosophers might have of that space. But if there are multiple, self-consistent, satisficing endpoints, each of them optimal under their own criterion-okay. Whatever. As long as we end up in a Nice Place to Live. And yes, the programmers' choices may have a huge impact on the ultimate destiny of the human species. Or a bird, chirping in the programmers' window. Or a science fiction novel, or a few lines spoken by a character in an anime, or a webcomic. Life is chaotic, small things have large effects. So it goes. I started thinking about volitional models of Friendliness when I read Greg Egan's Diaspora; blame the next billion years on him. Not that I think humankind will use CEV forever. But who knows how much humankind's future may be shaped by our early days? Even if the programmers are nice people and ground the AI in all humanity, the choice of grounding mechanism makes a difference. The decision to hand decisions to humanity is still a decision. Whether the programmers like it or not, the programmers' choices will make huge differences, and not just because of the butterfly effect. But there is no need to be a jerk about it. A determined altruist can always find a way to cooperate on the Prisoner's Dilemma. We are not talking about programmers imposing their Ten Commandments on the rest of humanity until the end of time. We are talking about people stuck with a job that is frankly absurd, doing their best not to be jerks. One day, one of the terrorist programmers says: \"Here's an interesting thought experiment. Suppose there were an atheistic American Jew, writing a superintelligence; what advice would we give him, to make sure that even one so steeped in wickedness does not ruin the future of Islam? Let us follow that advice ourselves, for we too are sinners.\" And another terrorist on the project team says: \"Tell him to study the holy Qur'an, and diligently implement what is found there.\" And another says: \"It was specified that he was an atheistic American Jew, he'd never take that advice. The point of the thought experiment is to search for general heuristics strong enough to leap out of really fundamental errors, the errors we're making ourselves, but don't know about. What if he should interpret the Qur'an wrongly?\" And another says: \"If we find any truly general advice, the argument to persuade the atheistic American Jew to accept it would be to point out that it is the same advice he would want us to follow.\" And another says: \"But he is a member of the Great Satan; he would only write an AI that would crush Islam.\" And another says: \"We necessarily postulate an atheistic Jew of exceptional caution and rationality, as otherwise his AI would tile the solar system with American music videos. I know no one like that would be an atheistic Jew, but try to follow the thought experiment.\" I ask myself what advice I would give to terrorists, if they were programming a superintelligence and honestly wanted not to screw it up, and then that is the advice I follow myself. The terrorists, I think, would advise me not to trust the self of this passing moment, but try to extrapolate an Eliezer who knew more, thought faster, were more the person I wished I were, had grown up farther together with humanity. Such an Eliezer might be able to leap out of his fundamental errors. And the terrorists, still fearing that I bore too deeply the stamp of my mistakes, would advise me to include all the world in my extrapolation, being unable to advise me to include only Islam. But perhaps the terrorists are still worried; after all, only a quarter of the world is Islamic. So they would advise me to extrapolate out to medium-distance, even against the force of muddled short-distance opposition, far enough to reach (they think) the coherence of all seeing the light of Islam. What about extrapolating out to long-distance volitions? I think the terrorists and I would look at each other, and shrug helplessly, and leave it up to our medium-distance volitions to decide. I can see turning the world over to an incomprehensible volition, but I would want there to be a comprehensible reason. Otherwise it is hard for me to remember why I care. Suppose we filter out all the AI projects run by Dennises who just want to take over the world, and all the AI projects without the moral caution to fear themselves flawed, leaving only those AI projects that would prefer not to create a motive for present-day humans to fight over the initial conditions of the AI. Do these remaining AI projects have anything to fight over? This is an interesting question, and I honestly don't know. In the real world there are currently only a handful of AI projects that might dabble. To the best of my knowledge, there isn't more than one project that rises to the challenge of moral caution, let alone rises to the challenge of FAI theory, so I don't know if two such projects would find themselves unable to agree. I think we would probably agree that we didn't know whether we had anything to fight over, and as long as we didn't know, we could agree not to care. A determined altruist can always find a way to cooperate on the Prisoner's Dilemma. \n Keep humankind ultimately in charge of its own destiny. Coherent extrapolated volition appears to me to embody an intrinsic switchover to a direct voting system when people are grown enough to handle it. Your immediate decision, the whim of this present moment, does count for something in your extrapolated volition. But if your future self would predictably shriek in horror, that extrapolation may win out, despite the added distance. When people know enough, are smart enough, experienced enough, wise enough, that their volitions are not so incoherent with their decisions, their direct vote could determine their volition. If you look closely at the reason why direct voting is a bad idea, it's that people's decisions are incoherent with their volitions. (Again, note the elegance; the slow growth into direct voting is not a tacked-on special case, just the dynamic doing the Right Thing.) I view it as a philosophical advantage of extrapolated volition that at no point does humanity turn its destiny over to an external god, even a humane external god. (But better that than being dead. Applied Theology is still a definite option if extrapolated volition doesn't work out.) And no, a Really Powerful Optimization Process is not a god. \n Help people. I want to leave the world a better place than I found it. The intention behind this project of manifesting the coherent extrapolated volition of humankind is to actually help humans; as opposed to, say, harming them. \n But What If This Volition Thing Doesn't Work? \n What if the initial dynamic works as designed, but not as planned, harming people instead of helping them? This is an objection that applies to any initial dynamic, not just extrapolated volition: \"What if the dynamic just doesn't work out the way you thought it would?\" The programmers are under obligation not to be jerks, to craft a reasonable and satisfactory initial dynamic to the best of their abilities, without playing nitwit games. But honest goodness does not guarantee a good outcome, if vision fails-that event which we who are wise in the art of caution call a \"mistake.\" (Some who know not the art have heard that other folks make \"mistakes,\" but they think it a moral parable to teach humility, and so they respond by abasing themselves and acknowledging their theoretical fallibil-ity, then continue doing whatever they planned to do anyway. Rather than, say, devising safeguards and recovery plans.) Can the programmers trust their choice of initial dynamic so highly? Maybe they should peek at the extrapolated outcome, make sure that everything works out all right, before they set their creation irrevocably in motion. But should the past have a veto over the future? Consider the horror of America in 1800, faced with America in 2000. The abolitionists might be glad that slavery had been abolished. Others might be horrified, seeing federal law forcing upon all states a few whites' personal opinions on the philosophical question of whether blacks were people, rather than the whites in each state voting for themselves. Even most abolitionists would recoil from in disgust from interracial marriages-questioning, perhaps, if the abolition of slavery were a good idea, if this were where it led. Imagine someone from 1800 viewing The Matrix, or watching scantily clad dancers on MTV. I've seen movies made in the 1950s, and I've been struck at how the characters are different-stranger than most of the extraterrestrials, and AIs, I've seen in the movies of our own age. Aliens from the past. Something about humanity's post-Singularity future will horrify us. It is guaranteed, no matter how good things get. It is guaranteed because things will get better. Imagine the culture shock if the eighteenth century got a look at the twentieth century. What about the tenth century? And that's not much of a gap; everyone, then and now, was human. Maybe 6-year-olds will be considered above the age of consent. Maybe humanity will abandon private property. Maybe rape will be legal. Maybe everyone will be uploaded whether they like it or not. Maybe everyone wearing a Japanese schoolgirl uniform at the time of Singularity will be attacked by tentacle monsters. Something that would shock the people of this present day. I am reminded of a book I once read, a cyberpunk role-playing game set in the middle of the twenty-first century, which in the midst of describing body replacements and organ rippers, mind-control drugs and corporate assassinations, mentioned how a twenty-second century Solid Citizen might do things that would horrify, disgust, and frighten that twenty-first century netrunner. It is not trivial, to suggest that the programmers dare to peek at the outcome. Or that the programmers appoint a Last Judge to check, someone chosen for their tolerance and broad-mindedness as the last safeguard of the human species, to peek at the outcome and return one bit of information, 1 or 0. Neither is it trivial to suggest that the programmers trust their initial dynamics without anyone peeking. According to my current understanding of Friendly AI, there is a general safety rule which says, roughly, \"Don't trust anything-dynamics, information, moral principlesuntil you see that it works better than you do.\" Subsystems that you trust may not be trusted to function together as supersystems. You wouldn't want to set an FAI dynamic irrevocably in motion (including an FAI dynamic that manifested the extrapolated volition of humankind) until you' d verified that the FAI's performance on the \"checking an FAI works sensibly\" problem was significantly better than the programmers' performance. I think, though I am not sure, that the FAI theory will dictate what constitutes a necessary and sufficient verification process, including whether we need a Last Judge to peek at the extrapolated final outcome. Let it stand that the thought has occurred to me, and that I don't plan on blindly trusting anything. Recent FAI theory says that it shouldn't be necessary to blindly trust, but FAI theory might require a Last Judge, which is nontrivial to set up safely. If FAI theory requires a Last Judge, I would advise those al-Qaeda terrorists to set up a lot of safeguards. I don't want them to discover that we'll all end up as atheists; I want them to think of Islam triumphant, and not be tempted to meddle. This problem deserves an essay in itself, which I may or may not have time to write. \n Why not base the Friendly AI on individual volition instead of coherence in humankind's extrapolated volition? Why not choose a Friendly AI that gives every individual their own wish? Why extrapolate a collective volition, and risk a tyranny of the extrapolated majority? If people want to be influenced by majority-coherence of extrapolated volitions, why not let their individual extrapolated volitions make that choice? Individual volition would make sense as a final dynamic, but it can't be an initial dynamic. There's no way for individually extrapolated volitions to rewrite the entire process, redesign the meta-process that describes how to partition the individual volitions and how they interact. Any mistakes the programmers make in choosing the meta-process would be enshrined forever. You can go from a collective dynamic to an (See also CalvinAndHobbes.) This is a fundamental moral question, and the moral answer isn't obvious. Maybe the civilization of the thirty-second century would say: \"Let them go their own way, what's wrong with that? There are far stranger minds, in these days, than super-infants; who are you to judge their choice?\" Or maybe humankind will define a spectrum of satisficing initial mind states, and require any mind not initially in a satisficing mind state to grow into a satisficing mindstate. In the sense that, for example, a 6-year-old would be required to grow into an 18-year-old before deciding where to go from there. Whether an older and wiser mind could voluntarily grow back into a 6-year-old psychology is an interesting question, and I think a distinct one. Maybe there are people who care about individual rights so strongly that they don't care what a majority of extrapolated volitions say; they want to give infants and autistics their own private universes because that's what their philosophy says is right, and their philosophy makes no mention of what other people think of the issue. Maybe future humanity will agree with them. Maybe afterward everyone will say: \"Eliezer was a bastard for endangering the free wills of infants that way, plotting to subject them to the tyranny of the extrapolated majority, daring even to think that one extrapolated volition should overrule another.\" If so, the majority of extrapolated volitions will correct my folly, with no harm done. But to me, wrenching infants off their course to humanness seems like following philosophy off a cliff. Even if I thought otherwise, I would fear making a mistake. Choosing individual volition as an initial dynamic would pre-emptively make that moral choice; it is implicit in the structure of an individual dynamic. An individual dynamic would not take into account anything outside the infant unless something in the infant's extrapolated volition said so. I think the extrapolated volitions of the 95% majority, including myself, may say that there are forces in our Nice Place to Live that do not derive strictly from individual volitions, that people can sometimes affect one another even without the consent of the affected. The possibility of occasional nonconsensual effect is a deep fundamental of human existence, not lightly to be thrown away. Would this mean that you needed to pay some attention to the course of humankind as a whole, lest the majority someday bite? Rather than holing up in a cave forever without fear? Maybe that isn't such a bad thing. Or maybe the majority will fear the tyranny of the majority too greatly, rule out the smallest touch. I don't think it's my place to make the decision. If I later find I'm one of the 5% of humanity whose personal philosophies predictably work out to pure libertarianism, and I threw away my one chance to free humanity-the hell with it. Better than being dead. I don't see how this case differs from the other ways I might grow up to hold a different morality from the majority. Here and now, I don't know, and I can concentrate on not being a jerk. Care to volunteer as Last Judge, so you can peek at the weeping and bereft parents, read the sage justifications in moral philosophy, and decide whether this constitutes a reason to shut down the AI? I who know much and think quickly do not expect that to happen, in exact proportion to how much I don't want it to happen. But if I wrote down ten such questions, I would not get ten correct answers. It's the sort of dilemma a Last Judge might face. All those other darned humans in the world are no-good rotten bastards; why would their extrapolated volitions be any better, you blind optimist? Let's suppose that all those darned other humans in the world are just no damn good. By comparison to what? The judgment implies that we must have some criterion in mind. Does the speaker have some better outcome in mind? It's not a logical implication-we could just be screwed. But people tend to imagine things they're afraid people want, or silly things for an extrapolated volition to do, and then look on the imagined outcome and say \"Yuck.\" Extrapolated volition doesn't refract through the part of you that imagines the bad outcome; extrapolated volition refracts through the part of you that looks upon the imagined outcome, and says, \"Yuck, I don't want that to happen.\" The ability to make this judgment exists in you, in your mind and brain. It has to come from humans, be generated by humans in some way. Same thing if you worry that humans are rotten bastards. Rotten bastards by comparison to what image that your mind generates? And how does a rotten bastard generate that image of something nicer? We need that \"something nicer,\" and it has to be extracted from rotten bastards, and extrapolated volition is my guess how to do it. Let's suppose, leaving aside the moral and technical questions, that someone took the initial dynamic and biased it toward positive emotions-extrapolated compassion, without extrapolating hatred. Easy enough to say, but whence came your decision that compassion was positive, and hate wasn't? You made the decision, and that's part of what gets extrapolated, under the heading of \"our wish to be better people.\" Rather than directly trying to guess at which emotions are \"positive\" or \"negative,\" I'm taking a step back, looking at my ability to make that judgment, and working it into the dynamic of extrapolated volition. But suppose that only a few people wish they were better people, in a sense sufficient for extrapolated volition to look past the evil and the nastiness? It strikes me as unlikely, based on strictly intuitive sense data (note: this is worthless reasoning) that a majority of humanity have no yearnings in this direction. It looks culturally universal. But I could be wrong. The trouble is that half the people are below average, and their interviews don't often show up in the history books, and we don't hear as much about their memes. (Note that memetic forces generated by social interactions are also taken into account, if we want them to be, under the heading of \"grown up farther together.\") The worrying question is: What if only 20% of the planetary population is nice, or cares about niceness, or falls into the niceness attractor when their volition is extrapolated? The notion being that this is enough to account for all the famous cases of niceness that everyone prefers to pass on and remember, and yet the majority of people on Earth are bastards. \"Bastard volitions\" will not vote to throw themselves into everlasting hellordinary selfishness being enough to prevent that-but they might create rules much to the distaste of us 20% (of course you're not a bastard, right?) For example, a rule stating that anyone who has computing power can do anything they want with that computing power, including creating innocent sentients and torturing them. It doesn't disadvantage any of the six billion people voting on it, except those silly 20% who care about fairness, so the vote passes. Similarly, the bastard volitions might vote to rewrite the initial dynamic to include no one except themselves. Maybe, if it's 80% of humanity in one coherent unit, and 20% in the other coherent unit, the 80% would vote to disenfranchise the 20%, or ensure that the 20% also grew into selfish bastards. As I currently construe CEV, this is a real possibility. Trying to tinker with the initial dynamic to rule it out is dangerous, because of added complexity, and added probability of error, and too high a chance of ruling out something that made more sense than you thought it did. If one contemplates tampering with CEV just to make sure it comes out \"right,\" one may as well abandon that solution entirely; what would be the point? (See Previously Asked Question 4, below, for an extended discussion.) Or it might be that plain, honest CEV extrapolates far enough to reach a grown-up, kinder humankind. Wouldn't you be terribly ashamed to go down in history as having meddled with that, using lesser intelligence and lesser niceness, because you didn't trust your fellows? Wouldn't you be sad to have made a mockery of humanity's self- Then what? Give up entirely? No, extrapolate from an idealized generic human, or an idealized generic human with an initial push toward altruism, or an idealized generic human with an initial push toward transpersonal philosophy, or extrapolate an imaginary civilization composed of genetically diverse individuals in the 99% niceness bracket . . . If you started flipping through solutions that satisficed, looking for one that suited you alone especially well, I would call that gerrymandering. But I think the programmers should be allowed, oh, say, at least three tries-three being the traditional number, in such matters, equating to 1.6 bits of influence over the future. And even then it might be better to continue despite cries of gerrymandering, rather than give up and let humanity perish. But one should be extremely reluctant to flip through sixteen solutions looking for a good one. If the first try fails, it means that you demanded too little of yourself, failed to rise to the challenge, and you need to rethink your whole strategy before trying again. More than three wishes, and I don't care if you save the human species, you're still incompetent. Such is the advice I would give to the al-Qaeda programmers, along with stern admonishments against checking to make sure humanity followed the way of Islam. I do think there's light in us somewhere, a will that might shape a Nice Place to Live. The question is whether coherent extrapolated volition as an initial dynamic satisfactorily seeks that attractor. \n Dire Warnings Don't try this at home. This says what I currently want. It doesn't say how to do it. The technical side of Friendly AI is not discussed here. The technical side of Friendly AI is hard and requires, like, actual math and stuff. \n Don't get caught up in fantasies of the New World Order. This new version of Friendly AI has an unfortunate disadvantage, which is that it is less vague, and people can speculate about what our extrapolated volitions will want, or argue about it. It will be great fun, and useless, and distracting. Arguing about morality is so much fun that most people prefer it to actually accomplishing anything. This is the same failure that chews up the would-be SI designers with Four Great Moral Principles. If you argue about how your Four Great Moral Principles will be produced by extrapolated volition, it's much the same way to switch off your brain. If you're trying to learn Friendly AI (see HowToLearnFriendlyAI) then you should concentrate on the Friendliness dynamics, and on learning the science background for the technical side. Look to the structure, not the content, and resist the temptation to argue things that are great fun. \n Don't hold the victory party before the battle is won. Anyone who wants to argue about whether extrapolated volition will favor Democrats or Republicans should recall that currently the Earth is scheduled to vanish in a puff of tiny smiley faces, with an unknown deadline and Moore's Law ticking. As an experiment, I am instituting the following policy on the SL4 mailing list: None may argue on the SL4 mailing list about the output of CEV, or what kind of world it will create, unless they donate to the Singularity Institute: • $10 to argue for 48 hours. • $50 to argue for one month. • $200 to argue for one year. • $1000 to get a free pass until the Singularity. What do you mean by \"imposing libertarianism\"? Rewiring their mind so that they want to be libertarian? Forcing them to live in a society where they can't impose their volition on others? #2, I guess. Making the choice for libertarianism for humanity. \n Jeez. I think I understand. But it still feels uncomfortable. No one promised that moral caution would be comfortable. Anyone can not take over the world when it seems like a bad idea. It's not taking over the world when it seems like a good idea that requires courage. A simple rule for FAI programmers is to never commit any act without giving some humane higher intelligence a veto. Thou art not that smart. My guess is that the successor to the initial dynamic will have a built-in Bill of Rights, ruling out deadly darknesses. Maybe the Bill of Rights will impose that invariant on any successor system humankind votes for, forever, even if we change our minds later. The will of humankind that shapes the dynamic in its first moments may dare to exercise that command over the unimaginably far future, for that we would sooner destroy ourselves, revoke the gift we give to our descendants, than let such things come to pass. But it will not be in the initial dynamic, for I am not that wise. For every one of those Inalienable Rights, the majority will say afterward that the initial dynamic should never have been written to make those Rights subject A worrying possibility is that requiring non-sentient simulations might create systematic biases; prevent the extrapolation from getting started; or block extrapolation of our probable decisions, or even possible decisions, on specific moral questions such as \"What constitutes a 'sentient' simulation?\" Ask me again about this problem in a year. Q6. What if someone disagrees with the CEV? (PhilipSutton) Speculating about outcomes? I counter-speculate that complete silence would not be an inappropriate response. Imagine the silliness of arguing with your own extrapolated volition. It's not only silly, it's dangerous and harmful; you're setting yourself in opposition to the place you would have otherwise gone, rationalizing counterarguments against a good answer. If humankind's CEV does something I disagree with, maybe there are reasons I haven't realized, maybe my own extrapolated volition happens to disagree with humanity's on this point, maybe I'm an ornery guy who would find fault no matter what the CEV did, maybe the extrapolation of humankind will turn out to be wrong, maybe a different initial dynamic would have worked out differently. A CEV has no moral authority, unless one is foolish enough to regard it as a god. CEV would just be a thing that a human conceived, humans implemented, and that sorta reflects humanity in an odd but useful way. I am not under the slightest obligation to change my opinions in the direction of the CEV, if it appears that we disagree. I need to make my own decisions, so that someday I can grow up and vote. Humanity needs emergency first aid, but my guess is that for a CEV to argue with humanity, or even display its internal reasoning process, would hurt us. We should invent our own philosophies, not ask our extrapolated volitions, or some-day we'll ask our volitions and get back \"The only answering procedure you know is asking your volition.\" Imaginary gods argue with humans and give them orders and demand allegiance; what we need is a real CEV that will shut up and help. Q7. Where is the CEV getting this kind of power? (Frequently Asked) A Really Powerful Optimization Process is not a god. A Really Powerful Optimization Process could tear apart a god like tinfoil. Hence the extreme caution. • What is the Singularity? • Levels of Organization in General Intelligence It is a widespread human perception that some individuals are wiser and kinder than others. Suppose our coherent extrapolated volition does decide to weight volitions by wisdom and kindness-a suggestion I strongly dislike, for it smacks of disenfranchisement. It would still take a majority vote of extrapolated volitions for the initial dynamic to decide how to judge \"wisdom\" and \"kindness.\" I don't think it wise to tell the initial dynamic to look to whichever humans judge themselves as wiser and kinder. And if the programmers define their own criteria of \"wisdom\" and \"kindness\" into a dynamic's search for leaders, that is taking over the world by don't think it's gerrymandering to probe the space of \"dynamics that plausibly ask what humanity wants\" to find a dynamic that produces a coherent output, provided: • The meta-dynamic looks only for coherence, no other constraints. • The meta-dynamic searches a small search space. • The meta-dynamic satisfices rather than maximizes. • The dynamic itself doesn't force coherence where none exists. • A Last Judge peeks at the actual answer and checks it makes sense. I would not object to an initial dynamic that contained a meta-rule along the lines of: \"Extrapolate far enough that our medium-distance wishes cohere with each other and don't interfere with long-distance vetoes. If that doesn't work, try this different order of evaluation. If that doesn't work then fail, because it looks like humankind doesn't want anything.\" Note that this meta-dynamic tests one quantitative variable (how far to extrapolate) and one binary variable (two possible orders of evaluation), and not, say, all possible orders of evaluation. Forcing a confident answer is a huge no-no in FAI theory. If an FAI discovers that an answering procedure is inadequate, you do not force it to produce an answer anyway. Q10. How accurate and detailed does the extrapolation of humankind's volition need to be in order to work? (Frequently Asked) Some important points that I don't think I emphasized clearly enough in the body of the text: • The optimization process is trying to extrapolate a population volition, not the volition of any one individual. I am visualizing and describing this as an actual, detailed, attempt at extrapolating individual minds and their social interaction; but that is because I am defining what I wish to approximate. • The optimization process is extrapolating a spread-out range of possibilities, not the answer. Given the uncertainty of underlying quantum processes, no definite answer may exist even in principle. • Do we want our coherent extrapolated volition to satisfice, or maximize? My guess is that we want our coherent extrapolated volition to satisfice-to apply emergency first aid to human civilization, but not do humanity's work on our behalf, or decide our futures for us. If so, rather than trying to guess the optimal decision of a specific individual, the CEV would pick a solution that satisficed the spread of possibilities for the extrapolated statistical aggregate of humankind. individual dynamic, but not the other way around; it's a one-way hatch. If you use an individual dynamic, that forces you to live in that particular world-which might not be the happiest world for us to live in. Maybe we could have more fun somewhere else. How would you define what constitutes an \"individual\"? If, as I suggest, you let the coherence in the extrapolated volitions of a population produce a single final output decision; then the programmers base the initial dynamic off humanity's billions as they exist today, and let the majority volition choose whether to extend citizenship to chimpanzees on the next round of renormalization. If you enshrine forever the meta-rules for how individual volitions interact, the programmers have to get the meta-rules absolutely right, until the end of time, on the very first try. Also, are you sure you don't want a tyranny of the 95% majority? What about infants? What about brain-damage cases? What about people with Alzheimer's disease? If you extrapolated their pure individual volitions, you might find that they lacked the moral and social complexity to want to be rescued, as we of the 95% would define \"rescue.\" A too-literal interpretation of individualist philosophy might wrench infants off their course to becoming humans and turn them into autistic superinfants instead. It's only genes and human parents who have this idea that infants are destined to become humans. It's not actually in infant psychologies, their mind-states at the age of six months. \n Q8.A problem is whether the most desirable volition is part of the collective or relatively rare. A rare individual or group of individuals' vision may be a much better goal and may perhaps even be what most humans eventually have as their volition when they get wise enough, smart enough and so on. (SamanthaAtkins) \"Wise enough, smart enough\"-this is just what I'm trying to describe specifically how to extrapolate! \"What most humans eventually have as their decision when they get wise enough, smart enough, and so on\" is exactly what their extrapolated volition is supposed to guess.It is you who speaks these words, \"most desirable volition,\" \"much better goal.\"How does the dynamic know what is the \"most desirable volition\" or what is a \"much better goal,\" if not by looking at you to find the initial direction of extrapolation? How does the dynamic know what is \"wiser,\" if not by looking at your judgment of wisdom? The order of evaluation cannot be recursive, although the order of evaluation can iterate into a steady state. You cannot ask what definition of flongy you would choose if you were flongier. You can ask what definition of wisdom you would choose if you knew more, thought faster. And then you can ask what definition of wisdom-2 your wiser-1 self would choose on the next iteration (keeping track of the increasing distance). But the extrapolation must climb the mountain of your volition from the foothills of your current self; your volition cannot reach down like a skyhook and lift up the extrapolation. \n Everyone has their brilliant idea for the Four Great Moral Principles That Are All We Need To Program Into AIs, and not one says, \"But wait, what if I got the Four Great Moral Principles wrong?\" They don't think of writing any escape clause, any emergency exit if the programmers made the wrong decision. They don't wonder if the original programmers of the AI might not be the wisest members of the human species; or if even the wisest human-level minds might flunk the test; or if humankind might outgrow the programmers' brilliantly This seems obvious, until you realize that only the Singularity Institute has even tried to address this issue. I haven't seen a single other proposal for AI morality out there, not even a casual guess, that takes the possibility of Singularity Regret into account. Not one.insightful moral philosophy a few million years hence. \n Avoid the obvious traps against which history books and evolutionary psychology warn you; act as you would wish another to act in your shoes; discharge your duties without exerting undue influence. It seems obvious enough, yet when I dare to say it out loud . . . I'd get less flack if I said I wanted to transport the entire human species into an alternate dimension based on a randomly selected hentai anime. Certain people are terrified at the thought that anyone might lay claim to being fair, as if that were an excuse for not trying. \"But what if Dennis calls it fairness that he should own the world outright, and objects to this notion of coherent extrapolated volition as unfair?\" Even if you are utterly selfish, the answer is still: \"If I cannot tell Eliezer my own name in Dennis's place, the best general principle I can tell Eliezer is that he should not listen to such arguments.\" \n Avoid creating a motive for modern-day humans to fight over the initial dynamic. One of the occasional questions I get asked is \"What if al-Qaeda programmers write an AI?\" I am not quite sure how this constitutes an objection to the Singularity Institute's work, but the answer is that the solar system would be tiled with tiny copies of the Qur'an. Needless to say, this is much more worrisome than the solar system being tiled with tiny copies of smiley faces or reward buttons. I'll worry about terrorists writing AIs when I am through worrying about brilliant young well-intentioned university AI researchers with millions of dollars in venture capital. The outcome is exactly the same, and the academic and corporate researchers are far more likely to do it first. This is a -gatherer tribe of two hundred people. To save the human species you must first ignore a hundred tempting distractions.I think the objection is that, in theory, someone can disagree about what a superintelligence ought to do. Like Dennis, who thinks he ought to own the world outright. But do you, as a third party, want me to pay attention to Dennis? You can't advise me to hand the world to you, personally; I'll delete your name from any advice you give me before I look at it. So if you're not allowed to mention your own name, what general policy do you want me to follow? Let's suppose that the al-Qaeda programmers are brilliant enough to have a realis- tic chance of not only creating humanity's first Artificial Intelligence but also solving the technical side of the FAI problem. Humanity is not automatically screwed. We're The dynamics that extrapolate volition won't resemble fun political arguments that humans enjoy. The dynamics will be choices of mathematical viewpoint, computer programs, optimization targets, reinforcement criteria, and AI training games with teams of agents manipulating billiard balls.The initial dynamic won't mention Democrats or Republicans, or whether Germany or France gets the Alsace-Lorraines, or who becomes ruler of Australia. The initial dynamic may renormalize to something entirely different, and probably will. Maybe, depending on the random seeds of the AI program, you could end up as ruler of Australia! But which random seed? 0xFA34E1E8? 0x81B2AA09? I don't think there's much point in fighting. I'll roll thirteen six-sided dice to determine the randseeds, and then auction them off on eBay as the dice that determined the fate of the human species. And if there's any particular value for a randseed that people can agree they want, well, that's what we have a CEV to renormalize to, right? critical point to keep in mind, as otherwise it provides an excuse to go back to screaming about politics, which feels so much more satisfying. When you scream about politics you are really making progress, according to an evolved psychology that thinks you are in a hunterpostulating some extraordinary terrorists. They didn't fall off the first cliff they encountered on the technical side of Friendly AI. They are cautious enough and scared enough to double-check themselves. They are rational enough to avoid tempting fallacies, and extract themselves from mistakes of the existing literature. The al-Qaeda programmers will not set down Four Great Moral Principles, not if they have enough intelligence to solve the technical problems of Friendly AI. The terrorists have studied evolutionary psychology and Bayesian decision theory and many other sciences. If we postulate such extraordinary terrorists, perhaps we can go one step further, and postulate terrorists with moral caution, and a sense of historical perspective? We will assume that the terrorists still have all the standard al-Qaeda morals; they would reduce Israel and the United States to ash, they would subordinate women to men. Still, is humankind screwed? Let us suppose that the al-Qaeda programmers possess a deep personal fear of screwing up humankind's bright future, in which Islam conquers the United States and then spreads across stars and galaxies. The terrorists know they are not wise. They do not know that they are evil, remorseless, stupid terrorists, the incarnation of All That Is Bad; people like that live in the United States. They are nice people, by their lights. They have enough caution not to simply fall off the first cliff in Friendly AI. They don't want to screw up the future of Islam, or hear future Muslim scholars scream in horror on contemplating their AI. So they try to set down precautions and safeguards, to keep themselves from screwing up. \n I see the programmers as having an unalterable duty not to tinker with a running CEV; this constitutes taking over the world, which is one of many ways for seed AI programmers to be jerks. But the programmers are under no obligation to implement CEV, if it is something of which they don't want to be part. I'm an individual, with my own life and philosophy. There are many acts of which I am prohibited (because I say so, that's why). But I can always choose not to do something, even halt work already begun; that is my unalienable right. I can't tinker with a running CEV, but I can choose to dissipate the AI, or hold a vote of the programming team to dissipate the AI, or delegate a Last Judge to make that decision. Steering wheels are forbidden; off switches are not. I think there must come a time when the last decision is made and the AI set irrevocably in motion, with the programmers playing no further special role in the dynamics. But at any point before then, one can always say \"No,\" and humanity will be no worse off than before. determination, if it would have worked anyway? Wouldn't you be horrified to find that you' d screwed it up? \n Past donations count toward this total. It's okay to have fun, and speculate, so long as you're not doing it at the expense of actually helping.It goes without saying that anyone wishing to point out a problem is welcome to do so. Likewise for talking about the technical side of Friendly AI. It is just the speculation about post-Singularity outcomes and CEV outputs that I am pricing, fearing that otherwise people's souls will be sucked away. (Try to sneak in your fun speculation by adding \"which could be a problem if . . . ,\" and I'll spot it and send you the bill.) in terms of a detailed model of each individual mind, in as much detail as necessary to guess the class of volition-extrapolating transformations defined by \"knew more,\" \"thought faster,\" etc. In principle, the result we are approximating is an idealized version of what would happen if we reached in and performed a set of volition-extrapolating upgrades on your mind: inserted new knowledge, had you sit down and think for a year, watched to see what your opinion would be after growing up for fifty years. But it may be that most of the individual fine details predictably just add to spread, or that fine details predictably don't end up coherent enough with the rest of humanity to be important to extrapolating the coherent extrapolated volition. The key is to set up the underlying For myself, the best solution I can imagine at this time is to make CEV our Nice Place to Live, not forever, but to give humanity a breathing space to grow up.Perhaps there is a better way, but this one still seems pretty good. As for it being a solution outside of humanity, or humanity being unable to fix its own problems . . . on this one occasion I say, go ahead and assign the moral responsibility for the fix to the Singularity Institute and its donors.Moral responsibility for specific choices within a CEV is hard to track down, in the era before direct voting. No individual human may have formulated such an intention and acted with intent to carry it out. But as for the general fact that a bunch of stuff gets fixed: the programming team and SIAI's donors are human and it was their intention that a bunch of stuff get fixed. I should call this a case of humanity solving its own problems, if on a highly abstract level.Q3. Why are you doing this? Is it because your moral philosophy says that what you want is But there are certain things such that if people want them, even want them with coherent volitions, I would decline to help; and I think it proper for a CEV to say the same. That is only one person's opinion, however. All I can say is: Last Judge, or whatever FAI theory dictates for verification. CEV has the theoretical power to do arbitrarily awful things if the extrapolation dynamic doesn't seek out the light in the heart of humanity, but the Last Judge has to say \"Yes\" first. And again, I see no way around this without taking over the world. Either humanity has the power of determination, or the programmers do. Do you want a small minority perception of an Inalienable Right to have power 6. Previously Asked Questions about Coherent Extrapolated what everyone else wants? (XR7) over you? If you don't share it? Volition Where would be the base-case recursion? But in any case, no. I'm an individual, Not over me, but over themselves. and I have my own moral philosophy, which may or may not pay any attention to That's a structurally determined individual dynamic. Q1. How do you \"extrapolate\" what we would think if we knew more, thought what our extrapolated volition thinks of the subject. Implementing CEV is just Yes, I guess I'm a pure libertarian. Well. Now I think what worries me is not that CEV faster/smarter? Are we taking the volition of current and historical humans as a data my attempt not to be a jerk. is not doing the \"right thing.\" I don't even know if there is a \"right thing\" to begin with. set, and then looking for trends that can be extended outward? (ChristianRovner) I do value highly other people getting what they want, among many other What worries me is that CEV can exert such kind of coercion over certain individuals. I was thinking question such that approximating the answer is a question of simple fact, to which simple Bayesian intelligence suffices. Q2. Removing the ability of humanity to do itself in and giving it a much better chance of surviving Singularity is of course a wonderful goal. But even if you call the FAI values that I hold. You're experiencing discomfort because your morality says that certain things are It doesn't sound right. \"optimizing processes\" or some such it will still be a solution outside of humanity rather wrong regardless of what anyone thinks of them, and here CEV is making it into a than humanity growing into being enough to take care of its problems. Whether the FAI majority vote rather than an Inalienable Right. But how does a Friendly Really is a \"parent\" or not it will be an alien \"gift\" to fix what humanity cannot. Why not have Powerful Optimization Process know what constitutes \"an Inalienable Right, re- humanity itself recursively self-improve? (SamanthaAtkins) gardless of what anyone thinks of it\"? The FAI has to ask you-you're the one wrong, even taking that argument into account. But I'm not sure. Hence, the with this perception of Inalienable Rightness; it isn't recorded anywhere else an moral caution. FAI can find it. So if you imagine a scenario where a majority of extrapolated I used to be a \"protected memory\" libertarian, ruling out even the smallest non- humanity doesn't share this perception of an Inalienable Right, then the extrap-consensual touch. I learned more, thought longer, and now I'm not sure. Non- olated majority might win. I see no way to resolve this discomfort that does not consensual touches aren't that unbearable a possibility. Eliminate nonconsensual constitute taking over the world, as the al-Qaeda terrorists would sharply advise effect and a hell of a lot of human nature goes kerplooey. And it isn't all inhumane me if I began writing in a Bill of Rights. The most one can do is appoint a Last nature, either, as I judge humaneness. If there's one piece of advice I have for hu- Judge with an off switch; predetermining the outcome makes it a farce. manity after the Singularity, it would be, \"Take it sloooow.\" I'm a lot more careful Q4. There are a couple of conclusions that make me very uncomfortable, but unfortunately I can't specify why: \"If I later find I'm one of the 5% of humanity whose personal philosophies predictably work out to pure libertarianism, and I threw away my one chance to free humanity-the hell with it.\" and \"Maybe, if it's 80% of humanity in one coherent unit, and 20% in the other coherent unit, the 80% would vote to disenfranchise the 20%, or ensure that the 20% also grew into selfish bastards. As I currently construe CEV, this is a real possibility.\"(ChristianRovner)    Worried that CEV isn't doing the right thing?Yeah. Worried that the possibility is not ruled out by the dynamic.\"The FAI has to ask you-you're the one with this perception of Inalienable Rightness; it isn't recorded anywhere else an FAI can find it. So if you imagine a scenario where a majority of humanity doesn't share this perception of an Inalienable Right, then the majority might win.\" Are there any inferential steps in between? I don't see it as an obvious sequitur.You can refuse to participate, but not exert detailed control over the outcome.I don't impose my libertarianism on others. Libertarianism is about not imposing your volition on others.Right! Now, you just need to take that one step further, and say, \"I won't imposemy libertarianism on humankind.\" Like I said, there's a fundamental moral question here. And if libertarianism is correct, I am in fact wrong to design an initial dynamic that allows for coercion. The reason for the collective dynamic is that you can go collective → individual, but not the other way 'round. If you could go individual → collective but not collective → individual, I'd advocate an individual dynamic. It's all about moral caution. If libertarianism is correct, I am still with my Humanity points than I used to be. Call me a neanderthal conservative. \n would guess that the more obvious the necessity, the greater the probability that our medium-distance volitions will converge. An approximate extrapolation of humankind's volition might state a 99% confidence that a perfect extrapolation of humankind's volition would show between 78% and 82% of the population agreeing on a certain proposition. That might suffice unto writing the successor dynamic and creating a Nice Place to Live, until direct voting becomes possible.Or maybe a Really Powerful Optimization Process can predict that five years hence you'll walk into a barbershop in Spokane. It seems unlikely-impossible, actually-but maybe I didn't think of the obvious creative shortcut.Perfect modeling is not required, only enough to satisfice. But yes, sufficient spread could increase the extrapolation's chaos to the point that it kills CEV as a solution; it simply would not be possible to speak of what humanity \"wanted\", even in the way of emergency first aid. to majority vote, for Inalienable Rights are Inalienable Rights regardless of what anyone thinks of them. And if I myself dared to set down ten Rights, I would get at least three Wrong. Q5. What if it's not possible to model people without simulating them in such fine detail that the simulation becomes a person? (Frequently Asked) I can imagine and extrapolate people, at least approximately, without creating new people in my imagination. People cannot be simulated perfectly, regardless of computing power or ethical constraints. There are quantum divergences, unless we become uploads running on hardware insulated from all measurement of the outside world. Even then there would be no way to perfectly extrapolate humanity in advance, before running the process. For this reason do I speak of predictable extrapolations, abstract properties of the outcome that a Really Powerful Opti- mization Process can predict with reasonably high confidence. Likewise I speak of figuring it both ways and computing the spread, and leaving our options open where our extrapolated volitions do not converge. Requiring that the simulation not be sentient may place an upper bound on predictive accuracy for individuals, but humankind's coherent extrapolated volition might still be tractable. It might be possible to predict some coherent volitions of a planetary population with much greater statistical reliability than would apply to a single individual, and perhaps that would suffice for emergency first aid. I", "date_published": "n/a", "url": "n/a", "filename": "CEV.tei.xml", "abstract": "The Machine Intelligence Research Institute was previously known as the Singularity Institute. \n Coherent Extrapolated Volition • Using a theory of intelligence which allows for deductive (probability ∼100%) recursive self-improvement that maintains an abstract invariant, without achieving the technical understanding to choose an invariant that does what the programmer thinks it does. • Brute-forcing the problem. Moore's Law continually advances, increasing the computing power available to blind probers, decreasing the technical brilliance required to wipe out the human species. (More computing power helps not at all on FAI.) Arguing about Friendliness is easy, fun, and distracting. Without a technical solution to FAI, it doesn't matter what the would-be designer of a superintelligence wants; those intentions will be irrelevant to the outcome. Arguing over Friendliness content is planning the Victory Party After The Revolution-not just before winning the battle for Friendly AI, but before there is any prospect of the human species putting up a fight before we go down. The goal is not to put up a good fight, but to win, which is much harder. But right now the question is whether the human species can field a non-pathetic force in defense of six billion lives and futures. Suppose we get the funding, find the people, pull together the project, solve the technical problems of AI and Friendly AI, carry out the required teaching, and finally set a superintelligence in motion, all before anyone else throws something together that only does recursive self-improvement. It is still pointless if we do not have a nice task for that optimization process to carry out. You can fail just as easily on the last step of the problem as on the first. Failing on the last step of the problem is rarer, not because the last step of the problem is less difficult, but because to fail on the last step of the problem you must first succeed on all the other steps. Plenty of would-be revolutionaries spend all their days in cafes planning the New World Order, arguing moral philosophy, and writing constitutions for their lovely new government. But of those revolutions that do succeed, most fail on that last part of the problem-being nice-and go on to wreak havoc. To win you need to win on every critical stage of the problem. Friendliness is the end; FAI theory is the means. Friendliness is the easiest part of the problem to explain-the part that says what we want. Like explaining why you want to fly to London, versus explaining a Boeing 747; explaining toast, versus explaining a toaster oven. Friendliness isn't the hardest part of the problem, or the one we need to solve right now, but all attention tends to focus on that which is easiest to argue about. I'm writing this essay because I must-because it's one of my responsibilities to describe my current plans, should I succeed in solving the more difficult parts of the problem. Just because something is necessary doesn't make it less dangerous; just because my ethics require me to do a thing does not absolve me of the consequence. Beware lest Friendliness eat your soul.", "id": "80df9ee7935e2490732284f77b46187f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom", "Allan Dafoe", "Carrick Flynn", "Stuart Armstrong", "Michael Barnett", "Seth Baum", "Dominic Becker", "Nick Beckstead", "Devi Borg", "Miles Brundage", "Paul Christiano", "Jack Clark", "Rebecca Crootof", "Richard Danzig", "Daniel Dewey", "Eric Drexler", "Sebastian Farquhar", "Sophie Fischer", "Ben Garfinkel", "Katja Grace", "Tom Grant", "Hilary Greaves", "John Halstead", "Robin Hanson", "Verity Harding", "Sean Legassick", "Wendy Lin", "Jelena Luketina", "Matthijs Maas", "Luke Muehlhauser", "Toby Ord", "Mahendra Prasad", "Anders Sandberg", "Carl Shulman", "Andrew Snyder-Beattie", "Nate Soares", "Mojmir Stehlik", "Jaan Tallinn", "Alex Tymchenko"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "aipolicy.tei.xml", "abstract": "Machine superintelligence could plausibly be developed in the coming decades or century. The prospect of this transformative development presents a host of political challenges and opportunities. This paper seeks to initiate discussion of these by identifying a set of distinctive features of the transition to a machine intelligence era. From these distinctive features, we derive a correlative set of policy desiderata-considerations that should be given extra weight in long-term AI policy compared to other policy contexts. We argue that these desiderata are relevant for a wide range of actors (including states, AI technology firms, investors, and NGOs) with an interest in AI policy. However, developing concrete policy options that satisfy these desiderata will require additional work.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom", "Allan Dafoe", "Carrick Flynn"], "title": "Public Policy and Superintelligent AI: A Vector Field Approach", "text": "The prospect of radically transformative AI It has now become a widely shared belief that artificial intelligence (AI) is a general-purpose technology with transformative potential.  2  In this paper, we will focus on what is still viewed as a more controversial and speculative prospect: that of machine superintelligence-general artificial intelligence greatly outstripping the cognitive capacities of humans, and capable of bringing about revolutionary technological and economic advances across a very wide range of sectors 1 Previous title: \"Policy Desiderata for Superintelligent AI\" †Governance of AI Program, Future of Humanity Institute, Oxford University. For comment and discussion, we're grateful to  Stuart Armstrong, Michael Barnett, Seth Baum, Dominic Becker, Nick Beckstead, Devi Borg, Miles Brundage, Paul Christiano, Jack Clark, Rebecca Crootof, Richard Danzig, Daniel Dewey, Eric Drexler, Sebastian Farquhar, Sophie Fischer, Ben Garfinkel, Katja Grace, Tom Grant, Hilary Greaves, Rose Hadshar, John Halstead, Robin Hanson, Verity  Harding, Sean Legassick, Wendy Lin, Jelena Luketina, Matthijs Maas, Luke Muehlhauser, Toby Ord, Mahendra Prasad, Anders Sandberg, Carl Shulman, Andrew Snyder-Beattie, Nate Soares, Mojmir Stehlik, Jaan Tallinn, Alex Tymchenko, and several anonymous reviewers. This work was supported, in part, by grants from the H2020 European Research Council and the Future of Life Institute.  2  Among many examples of reports of this kind, see  West & Allen 2018.  on timescales much shorter than those characteristic of contemporary civilization. In this paper we will not argue that this is a plausible or probable development; rather, we will analyze some 3 aspects of what would follow if radical machine superintelligence were in the cards for this century. In particular, we focus on the implications of a machine intelligence revolution for governance and global policy. What would be a desirable approach to public policy under the assumption that we were approaching a transition to a machine superintelligence era? What general properties should one look for in proposals for how the world should manage the governance challenges that such a transition would bring with it? We construe these questions broadly. Thus by \"governance\" we refer not only to the actions of states, but also to transnational governance involving norms and arrangements arising from AI 4 technology firms, investors, NGOs, and other relevant actors; and to the many kinds of global power that shape outcomes. And while ethical considerations are relevant, they do not exhaust 5 the scope of the inquiry-we wish to include desiderata focused on the prudential interests of important constituencies as well as considerations of technical and political feasibility. We believe the governance challenges in the radical context that we focus on would in many respects be different from the issues that dominate discussions about more near-term AI developments. It may be useful to say something briefly about the kinds of capabilities that we are imagining would be developed over the course of a transition to a superintelligence era. As we picture the scenario, cheap generally intelligent machines are developed that could substitute for almost all human labor, including scientific research and other inventive activity. Early versions of machine 6 superintelligence may quickly build more advanced versions, plausibly leading to an \"intelligence explosion\". This acceleration of machine intelligence might drive other forms of technological These developments will pose the challenge of making sure that AI is developed, deployed, and governed in a responsible and generally beneficial way. Some AI-related governance issues have begun to be explored, such as the ethics of lethal autonomous weapons, AI-augmented 10 3 Nevertheless, it is worth noting that many AI researchers take the prospect of superintelligence in this century seriously. Indeed, within the machine learning community, the majority view is that it is more likely than not that human-level machine intelligence is developed by 2050  (Müller & Bostrom 2016)  or 2060  (Grace et al. 2018) , and that it is likely (75%) that superintelligence would be developed within 30 years after.  4  Hale & Held 2011.  5    Barnett & Duvall 2005. 6  An exception would arise if there were demand specifically for human labor, such as a consumer preference for goods made \"by hand\".  7  Good 1965.  8  Nordhaus 2015.  9  Hanson 2016, ch. 16.  10 Nehal et al. 2016.  Instead, the approach we take in this paper is to attempt to be somewhat neutral between many different commonly held normative views, ideologies, and private interests amongst influential actors. We do this by focusing on the directional policy change , from many possible evaluative standpoints, that is entailed by a set of special circumstances that can be expected to obtain in the scenario of radically transformative machine superintelligence that we outlined in the introduction. In other words, we seek to sketch (metaphorically or qualitatively) a \"vector field\" of policy implications, which has relevance to a wide range of possible normative positions. For example, some political ideologies maintain that economic equality is a centrally important objective for public policy, while other ideologies maintain that economic equality is not especially important or that states have only very limited responsibilities in this regard (e.g. to mitigate the most extreme forms of poverty). The vector field approach might then attempt to derive directional policy change conclusions of a form that we might schematically represent as follows: \"However much emphasis X you think that states ought, under present circumstances, to give to the objective of economic equality, there are certain special circumstances Y , which can be expected to hold in the radical AI context we described above, that should make you think that in those circumstances states should instead give emphasis f Y ( X ) to the objective of economic equality. The idea is that f here is some relatively simple function, defined over a space of possible evaluative standards or ideological positions. For instance, f might simply add a term to X , which would correspond to the claim the emphasis given economic equality should be increased by a certain amount in the circumstances Y (according to all the ideological positions under consideration). Or f might require telling a more complicated story, perhaps along the lines of \"However much emphasis you give to economic equality as a policy objective under present circumstances, under conditions Y you should want to conceive of economic equality differently-certain dimensions of economic inequality are likely to become irrelevant and other dimensions are likely to become more important or policy-relevant than they are today.\" (We discuss equality-related issues in the section on \"allocation\" below.) This vector field approach is only fruitful to the extent that there are some patterns in how the special circumstances Y impact policy assessments from different evaluative positions. If the prospect of radical AI had entirely different and idiosyncratic implications for every particular ideology or interest platform, then the function f would amount to nothing more than a lookup table. Policy analysis would then have to fall back to the ways of proceeding we mentioned above, i.e. either trying to determine (or simply assuming) one uniquely correct or appropriate normative standard, or exploring a range of possible standards and investigating their policy implications separately. We argue, however, that at least some interesting patterns can be found in f, and we strive to characterize some of them in what follows. We do this by first identifying several respects in which the prospect of superintelligent AI presents special circumstances -challenges or opportunities that are either unique to the context of such AI or are expected to present there in unusual ways or to unusual degrees. We then explain how these special circumstances have some relatively unambiguous implications for policy in the sense that there are certain policy properties that are far more important in these special circumstances (than they are in more familiar circumstances) for the satisfaction of many widely shared prudential and moral preferences. We express these especially relevant and important policy properties as a set of desiderata , or desirable qualities. The desiderata, which we arrange under four headings (efficiency, allocation, population, and process), are thus meant to express reasons for pushing policy in certain directions (relative to where the preferred policy point would be when we are operating outside of the special circumstances). A strong proposal for the governance of advanced AI would ideally accommodate each of these desiderata to a high degree. There may exist additional desiderata that we have not identified here; we make no claim that our list is complete. Furthermore, a strong policy proposal should presumably also integrate many other normative, prudential, and practical considerations that are either idiosyncratic to particular evaluative positions or are not distinctive to the context of radical AI. Our contribution is to highlight some themes worth bearing in mind in further explorations of how we should approach governance and global policy challenges in light of the prospect of superintelligent AI. 16 \n Efficiency Under this heading we group desiderata that have to do with protecting or increasing the size of the pie that becomes available. An outcome would be inefficient if it is Pareto inferior to some other possible outcome-for example, if it involves wasting resources, squandering opportunities for improvements, forfeiting achievable gains from mutually beneficial cooperation, and so forth. The desirability of greater efficiency may usually be taken for granted; however, there are some dimensions of efficiency that take on special significance in the context of a radical AI transformation. These include technical opportunity, AI risk, the possibility of catastrophic global coordination failures, and reducing turbulence, discussed in turn below. \n Technological opportunity Machine superintelligence (of the type we are envisaging in this paper) would be able to expand the production-possibility frontier much further and far more rapidly than is possible under more normal circumstances. Superintelligent AI would be an extremely general-purpose technological advance, which could obviate most need for human labour and massively increase total factor productivity. In particular, such AI could make rapid progress in R&D and accelerate the approach to technological maturity. This would enable the use of the fast outer realm of 17 astronomical resources, including for settlement, which would become accessible to automated self-replicating spacecraft. It would also open up a vast inner realm of development, making 18 possible great improvements in health, lifespan, and subjective well-being, enriched life experiences, deeper understanding of oneself and others, and refinements in almost any aspect of being that we choose to cultivate. Thus, in both the outward direction of extensive growth, 19  16  We confine our analysis to desiderata that satisfy a basic universalizability criterion. For example, if there is some respect in which the special circumstances would give actor A stronger-than-usual reason to harm actor B , and give actor B stronger-than-usual reason to harm actor A , then there would in some sense be a general pattern that could be discerned and distilled into the policy recommendation, \"put greater emphasis on attacking each other\". But in this generalized form, the policy change would not be desirable to anybody; so since it fails universalizability, we would not include it as a desideratum. 17 By \"technological maturity\" we mean the attainment of capabilities affording a level of economic productivity and control over nature close to the maximum that could feasibly be achieved  (Bostrom 2013 ).  18 Tipler 1980; Armstrong & Sandberg 2013 . 19 Pearce 1995 Bostrom 2005; Bostrom 2008.  and the inward direction of intensive growth, dramatic progress could follow the development of superintelligence. The surprisingly high ceiling for growth (and the prospect of a fast climb up to that ceiling) should make us think it especially important that this potential not be squandered. This desideratum has two aspects: (a) the inner and outer production-possibility frontiers should be pushed outward, so that Earth-originating life eventually reaches its full potential for realizing values, and (b) this progress should preferably occur soon enough that we (e.g. currently existing people, or any actors who are using these criteria to evaluate proposed AI paths) get to enjoy some of the benefits. The relative weight given to these two aspects will depend on an actor's values.  20  Of particular note, there may be a level of technology that would allow human lifespan to become effectively unconstrained by biological aging and localized accidents-a level that would plausibly be reached not long after the emergence of superintelligence. Consequently, for 21 actors who care much about their own long-term survival (or the survival of their family or other existing people), the desirability of a path towards the development of superintelligent AI may depend quite sensitively on whether it is likely to be fast enough to offer a chance for those people to have their lives saved by the AI transition.  22  Even setting aside the possibility of life extension, how well existing people's lives go overall might fairly sensitively depend on whether their lives include a final segment in which they get to experience the improved standard of living that would be attained after a positive AI transition. \n AI risk The avoidance of AI-induced destruction takes on special significance as a policy objective in the present context because it is plausible that the risk of such destruction-including especially extreme outcomes, such as human extinction-would not be, with the development of machine superintelligence, very small. An important criterion for evaluating a proposed policy for 23 long-term AI development is therefore how much quality-adjusted effort would be devoted to AI safety and supporting activities on that path. Relevant risk-reducing efforts may include, for example, pursuing basic research into scalable methods for AI control, encouraging AI-builders to avail themselves of appropriate techniques, and more generally fostering conditions that ensure that the development of superintelligent AI is done with care and caution.  20 Beckstead 2013, ch. 4-5; Bostrom 2003b. 21  Perhaps in digital form  (Sandberg & Bostrom 2008)  or in biological form via advanced biotechnological or nanotechnological means  (Drexler 1986, ch. 7; Freitas 1999) . There is a sense in which it might already be possible for some currently existing individuals to reach astronomical lifespans, namely by staying alive through ordinary means until an intelligence explosion or other technological breakthrough occurs. Also cryonics  (Bostrom 2003c; Merkle 1994 ).  22  Actors with a very high discount for future life duration might, however, prefer to postpone superintelligence until they are at death's door, since the arrival of machine superintelligence might involve a momentarily elevated level of risk (cf. \"AI risk\", below).  23 Bostrom 2014; Russell & Norvig 2010 , pp. 1036 -1040   \n Possibility of catastrophic global coordination failures Avoidance of catastrophic global coordination failures likewise has special significance in the present context, because such failures seem comparatively plausible there. Catastrophic coordination failure could arise in several ways. Machine superintelligence could enable the discovery of technologies that make it easy to destroy humanity-for instance by constructing some biotech-or nanotech-based \"doomsday device\", which, once invented, is cheap and easy to build. To stop ex ante or contain ex post the development of such an accessible doomsday device could require extreme and novel forms of global agreement, surveillance, restraint, and cooperation. Coordination problems could lead to a risk-increasing AI technology race dynamic, in which developers throw caution to the wind as they vie to be the first to attain superintelligence. A 24 race dynamic could lead to reduced investment in safety research, reduced willingness to accept delays to install and test control methods, and reduced opportunities to rely on control methods that incur a significant computational cost or that otherwise hamper performance. More generally, coordination failures could lead to various kinds of \"races to the bottom\" in the development and deployment of advanced AI. For instance, welfare provisions to protect the interests of artificial minds might be eroded in a hyper-competitive global economy in which jurisdictions that impose regulations against the mistreatment and exploitation of digital workers are competitively disadvantaged and marginalized. Evolutionary dynamics might also shape developments in undesirable directions and in ways that are impossible to avoid without effective global coordination.  25  If technological developments increase the risk of catastrophic global coordination failure, then it becomes more important to develop options and mechanisms for solving those coordination problems. This could involve incremental work to improve existing global governance mechanisms and strengthen norms of cooperation. It could also involve preferring 26 development pathways that empower some actor with a decisive strategic advantage that could be used, if necessary, to stabilize the world when a substantial risk of existential coordination failure appears. 27 24  . 25 Bostrom 2004 Alexander 2014. 26  For example, scholars and philanthropists should invest more in understanding global governance and possibilities for world government; policy makers should invest more in solving existing global coordination problems to provide practice and institutional experience for larger challenges; and fora for global governance should invest more in consideration of hypothetical coordination challenges.  27  Stabilization may involve centralizing control of the dangerous technology or instituting a monitoring regime that would enable the timely detection and interception of any move to deploy the technology for a destructive purpose; cf. Bostrom 2018. \n Reducing turbulence The speed and magnitude of change in a machine intelligence revolution would pose challenges to existing institutions. Under highly turbulent conditions, pre-existing agreements might fray and long-range planning become more difficult. This could make it harder to realize the gains from coordination that would otherwise be possible-both at the international level and within nations. At the domestic level, loss could arise from ill-conceived regulation being rushed through in haste, or well-conceived regulation failing to keep pace with rapidly changing technological and social circumstances. At the international level the risks of maladjustment are possibly even greater, as there are weaker governance institutions and less cultural cohesion, and it typically takes years or decades to conceive and implement well-considered norms, policies, and institutions. The resulting efficiency losses could take the form of temporary reductions in welfare or an increased risk of inferior long-term outcomes. Other things equal, it is therefore desirable that such turbulence be minimized or well-managed. \n Desiderata related to efficiency From the preceding observations, we extract the following desiderata: • Expeditious progress. This divides into two components: (a) Policies that lead with high probability to the eventual development of safe superintelligence and its application to tapping novel sources of wealth; and (b) speedy AI progress, such that socially beneficial products and applications are made widely available in a timely fashion. • AI safety. Techniques are developed that make it possible (without excessive cost, delay, or performance penalty) to ensure that superintelligent AI behaves as intended. Also, the conditions during the emergence and early deployment of superintelligence are such as to encourage the use of the best available safety techniques and a generally cautious approach. • Conditional stabilization. The development trajectory and the wider political context are such that if catastrophic global coordination failure would result in the absence of drastic stabilizing measures, then the requisite stabilization is undertaken in time to avert catastrophe. This might mean that there needs to be a feasible option (for some actor or actors) to establish a singleton, or to institute a regime of intensive global surveillance, or to strictly suppress the dissemination of dangerous technology or scientific knowledge. 29 • Non-turbulence. The path avoids excessive efficiency losses from chaos and conflict. Political systems maintain stability and order, adapt successfully to change, and mitigate socially disruptive impacts. 28 An ideal alignment solution would enable control of both external and internal behaviour (thus making it possible to avoid intrinsically undesirable types of computation without sacrificing much in terms of performance; cf. \"mind crime\" discussed below).  29  A singleton is a world order which at the highest level has a single decision-making agency, with the ability to \"prevent any threats (internal or external) to its own existence and supremacy\" and to \"exert effective control over major features of its domain (including taxation and territorial allocation)\"  (Bostrom 2006) . \n Allocation The distribution of wealth, status, and power is subject to perennial political struggle and dispute. There may not be much hope for a short section in a paper to add much novel insight to these century-old controversies. However, our vector field approach makes it possible for us to try to make some contribution to this subject matter without requiring us to engage substantially with the main issues under contention. Thus, we focus here on identifying a few special circumstances which would surround the development of superintelligent AI, namely risk externalities, reshuffling, the veil of ignorance, and cornucopia. These circumstances (we argue) should change the relative weight attached to certain policy considerations, norms, and values concerning allocation. 30 \n Risk externalities As noted earlier, it has been argued that the transition to the machine intelligence era will be associated with some degree of existential risk. This is a risk to which all humans would be exposed, whether or not they participate in or consent to the project. A little girl in a village in Azerbaijan, who has never heard about artificial intelligence, would receive her share of the risk from the creation of machine superintelligence. Fairness norms therefore require that she also receive some commensurate portion of the benefits if things turn out well. Consequently, to the extent that fairness norms form a part of the evaluation standard used by some actor, that actor should recognize as a desideratum that an AI development path provide for a reasonable degree of compensation or benefit-sharing to everybody it exposes to risk (a set which includes, at least, all humans who are alive at the time when the dangerous transition occurs). Risk externalities appear often to be overlooked outside of the present (advanced AI) context too, so this desideratum could be generalized into a Risk Compensation Principle , which would urge policymaking aimed at the public good to consider arranging for those exposed to risk from another's activities to be compensated for the probabilistic harm they incur, especially in cases where full compensation if the actual harm occurs is either impossible (e.g. because the victim is dead, or the perpetrator lacks sufficient funds or insurance coverage) or would not be forthcoming for other reasons. 31 \n Reshuffling Earlier we described the limitation of turbulence as an efficiency -related desideratum. Excessive turbulence could exact economic and social costs and, more generally, reduce the influence of human values on the future. But turbulence associated with a machine intelligence revolution could also have allocational consequences, and some of those point to additional desiderata. Consider two possible allocational effects: concentration and permutation . By \"concentration\" we mean income or influence becoming more unequally distributed. In the limiting case, one nation, one organization, or one individual would own and control everything. By \"permutation\" we mean future wealth and influence becoming less correlated with present wealth and influence. In the limiting case, there would be zero correlation, or even an anticorrelation, between an actor's present rank (in e.g. income, wealth, power, or social status) and that actor's future rank. We do not claim that concentration or permutation will occur or that they are likely to occur. We claim only that they are salient possibilities and that they are more likely to occur to an extreme degree in the special circumstances that would obtain during a machine intelligence revolution than they are to occur (to a similarly extreme degree) under more familiar circumstances outside the context of advanced AI. Though we cannot fully justify this claim here, we can note, by way of illustration, some possible dynamics that could make this true. (1) In today's world, and throughout history, wage income is more evenly distributed than capital income. 32 Superintelligent AI, by strongly substituting for human labor, could greatly increase the factor share of income received by capital. All else equal this would widen income inequality and thus 33 increase concentration. (2) In some scenarios, there are such strong first-mover advantages in 34 the creation of superintelligence as to give the initial superintelligent AI, or the entity controlling that AI, a decisive strategic advantage. Depending on what that AI or its principal does with that advantage, the future could end up being wholly determined by this first-mover, thus potentially greatly increasing concentration. (3) When there is radical and unpredictable technological change, there might be more socioeconomic churn-some individuals or firms turn out to be well positioned to thrive in the new conditions or make lucky bets, and reap great rewards; others find their human capital, investments, and business models quickly eroding. A machine intelligence revolution might amplify such churn and thereby produce a substantial degree of permutation. 35 32 Piketty 2014, ch. 7.  33 Brynjolfsson & McAfee 2014. 34  It could also reduce permutation after the transition to the machine intelligence era, if it is easier to bequeath capital to one's children (or to preserve it oneself while one is alive, which might be for a very long time with the advent of effective life extension technology) than it is to bequeath or preserve talents and skills under historically more usual circumstances.  35  Actors could seek to preserve their position by continuously diversifying their holdings. However, there may be substantial constraints and frictions on achieving this, related to (1) constraints or costs to diversifying, (2) time lags in diversification, (3) willingness of some actors to gamble big. (1a) Some asset classes (e.g. stealth startups, private companies, stakes in some national economies) are not available for ownership or involve a costly search and investment process. (1b) Many actors face major diversification constraints. A firm or a country might be heavily committed to one industry sector and be unable to effectively hedge its exposures or quickly reorient its activities to adapt to a rapidly changing competitive landscape. (2) Technological churn may move so quickly that investors do not have the opportunity to rebalance their portfolios \"in time\". By the time an appreciating new asset class is evident, one may have already lost out on much of its growth value. (3) Some actors will choose to make big bets on risky assets/technology, which if they win would reshuffle the ranking of wealth; even top-tier perfectly diversified actors could be deposed from their apex position by some upstart who scores a jackpot in the great reshuffle. (4) Automated security and surveillance systems could make it easier for a regime to sustain itself without support from wider elites or the public. This would make it possible for regime members to appropriate a larger share of national output and to exert more fine-grained control over citizens' behaviour, potentially greatly increasing the concentration of wealth and power.  36  To the extent that one disvalues (in expectation) concentrating or permuting shifts in the allocation of wealth and power-perhaps because one places weight on some social contract theory or other moral framework that implies that such shifts are bad, or simply because one expects to be among the losers-one should thus regard continuity as a desideratum. 37 \n Veil of ignorance At the present point in history, important aspects of the future remain at least partially hidden behind a veil of ignorance. Nobody is sure when advanced AI will be created, where, or by 38 whom (although, admittedly, some locations seem less probable than others). With most actors having fairly rapidly diminishing marginal utility in wealth, and thus risk-aversion in wealth, this would make it generally advantageous if an insurance-like scheme were adopted that would redistribute some of the gains from machine superintelligence. It is also plausible that typical individuals have fairly rapidly diminishing marginal utility in power. For example, most people would much rather be certain to have power over one life (their own) than have a 10% chance of having power over the lives of ten people and a 90% chance of having no power. For this reason, it would also be desirable for a scheme to preserve a fairly wide distribution of power, at least to the extent of individuals retaining a decent degree of control over their own lives and their immediate circumstances (e.g. by having some amount of The distribution of military power is also in principle subject to reshuffling induced by accelerated technological churn, including in ways that are difficult to guard against by military diversification or using existing strength to bargain for a stable arrangement that locks in existing power hierarchies.  36  Bueno de Mesquita & Smith 2011; Horowitz 2016.  37  We can distinguish two kinds of permutation. (1) Permutations where an individual's expected ex post wealth (or power, status, etc.) equals her ex ante wealth (power, status, etc.). Such a permutation is like a conventional lottery, where the more tickets you have the more you can expect to win. Risk-averse individuals can try to hedge against such permutations by diversifying their holdings; but as noted in the previous footnote, sufficiently drastic reshufflings can be hard to hedge against, especially in scenarios with large-scale violations of contracts and property rights. (2) Permutations where an individual's expected ex post wealth is unrelated to her ex ante wealth. Think of this as random role-switching: everybody's names are placed in a large urn, and each individual pulls out one ticket-she gives up what she had before and instead gets that other person's endowment. Setting aside the consequences of social disruption, this type of permutation would result in an expected gain for those who were initially poorly off, at the expense of incumbent elites. However, those who on non-selfish grounds favor redistribution to the poor typically want this to be done by reducing economic inequality rather by having a few of the poor swap places with the rich.  38  This is meant as an extension of the \"veil of ignorance\" thought experiment proposed by John Rawls; \"[T]he parties… do not know how the various alternatives will affect their own particular case and they are obliged to evaluate principles solely on the basis of general considerations…. First of all, no one knows his place in society, his class position or social status; nor does he know his fortune in the distribution of natural assets and abilities….\"  (Rawls 1971, p. 137) . guaranteed power or some set of inalienable rights). There is also international agreement that individuals should have substantial rights and power.  39   \n Cornucopia The transition to machine superintelligence could bring with it a bonanza of vast proportions. For example, Hanson estimates that cheap human-level machine intelligence would plausibly suffice to increase world GDP by several orders of magnitude within a few years after its arrival. The 40 ultimate magnitude of the economic potential that might be realized via machine superintelligence could be astronomical.  41  Such growth would make it possible, using a small fraction of GDP, to nearly max out many values that have diminishing returns in resources (over reasonable expenditure brackets).   Social and Cultural Rights 1966) , which have been nearly universally ratified (though, significantly, not ratified by China and the US, respectively). Further support for this can be found in the international legal principle of jus cogens (\"compelling law\") which forms binding international legal norms from which no derogation is permitted. While the exact scope of jus cogens is debated, there is general consensus that it includes prohibitions against slavery, torture, and genocide, among other things  (Lagerwall 2015) . For more on the potential relationship between international human rights law and AI development as it relates to existential risk, see Vöneky 2016.  40 Hanson 2016, pp. 189-194. 41  One technology area that one could expect to be brought to maturity within some years after the development of strongly superintelligent AI is advanced capabilities for space colonization, including the ability to emit von Neumann probes that are capable of travelling at some meaningful fraction of the speed of light over intergalactic distances and bootstrapping a technology base on a remote resource that is capable of producing and launching additional probes  (Freitas 1980; Tipler 1980) . Assuming the capability of creating such von Neumann probes, and that the observable universe is void of other intelligent civilizations  (Sandberg et al. 2018) , then humanity's cosmic endowment would appear to include 10 18 to 10 20 reachable stars  (Armstrong & Sandberg 2013) . With the kind of astrophysical engineering technology that one would also expect to be available over the relevant timescales (Sandberg forthcoming), this resource base could suffice to create habitats some something like 10 35 biological human lives (over the course of the remaining lifespan of the universe), or, alternatively, for a much larger number (in the vicinity of 10 58 or more) of digitally implemented human minds  (Bostrom 2014) . Of course, most of this potential could be realized only over very long time scales; but for patient actors, the delays may not matter much. Note that a larger fraction of actors may be \"patient\" in the relevant sense after technological means for extreme life extension or suspended animation (e.g. facilitated by digital storage of human minds) are developed. Actors that anticipate that such capabilities will be developed shortly after the arrival of superintelligent AI may be patient-in the sense of not severely discounting temporally extremely remote economic benefits-in anticipation, since they might attach a non-trivial probability to themselves being around to consume some of those economic benefits after the long delay. Another important factor that could make extremely distant future outcomes decision-relevant to a wider set of actors is that a more stable social order or other reliable commitment techniques may become feasible, increasing the chance that near-term decisions could have predictable effects on what happens in the very long run. Suppose, for example, that the economy were to expand to the level where spending 5% of GDP would suffice to provide the entire human population with a guaranteed basic annual income of $40,000 plus access to futuristic-quality healthcare, entertainment, and other marvelous goods and services. The case for adopting such a policy would then seem stronger than the case for 42 instituting a guaranteed basic income is today, at a time when a corresponding policy would yield far less generous benefits, require the redistribution of a larger percentage of GDP, and threaten to dramatically reduce the supply of labor. Similarly, if one state became so wealthy that by spending just 0.1% of its GDP on foreign aid, it could give everybody around the world an excellent quality of life (where there would otherwise be widespread poverty), then it would be especially desirable that the rich state does have at least that level of generosity. Whereas for a poor state, it does not much matter whether it gives 0.1% of GDP or it gives nothing-in neither case is the sum enough to make much difference-for an extremely rich state it could be crucially important than it gives 0.1% rather than 0%. In a really extreme case, it might not matter so much whether a super-rich state gives 0.1% or 1% or 10%: the key thing is to ensure that it does not give 0%. Or consider the case of a tradeoff that a social planner faces between the value of animal welfare and the desire of many human consumers to have meat in their diet. Let us suppose that the planner cares mostly about human consumer preferences, but also cares a little about animal welfare. At a low level of GDP, the planner might choose to allow factory farming because it lowers the cost of meat. As GDP rises, however, there comes a point when the planner introduces legislation to discourage factory farming. If the planner did not care at all about animal welfare, that point would never come. With GDP at modest levels, a planner that cares a lot about animal welfare might introduce legislation whereas a planner that cares only a little about animal welfare might permit factory farming. But if GDP rises to sufficiently extravagant levels, then it might not matter how much the planner cares about animal welfare, so long as she cares at least a tiny little bit . 43 42 The estimated 2017 world GDP was 81 trillion USD nominally (or 128 trillion USD dollars when considering purchasing power parity, World Bank, International Comparison Program database). This is equivalent to a GDP per capita of $11,000 (nominal) or $17,000 (PPP). In order for a $40,000 guaranteed basic annual income to be achieved with 5% of world GDP at 2018 population levels (of 7.6bn), world GDP would need to increase by a factor of 50 to 75, to 6 quadrillion (10^15) USD dollars. While 5% may sound like a high philanthropic rate, it is actually half of the average of the current rate of the ten richest Americans. While the required increase in economic productivity may seem large, it requires just six doublings of the world economy. Over the past century, doublings in world GDP per person have occurred roughly every 35 years. Advanced machine intelligence would likely lead to a substantial increase in the growth rate of wealth per (human) person. The economist Robin Hanson has argued that after the arrival of human-level machine intelligence, in the form of human brain emulations, doublings could be expected to occur every year or even month  (Hanson 2016, pp. 189-191) . Note also that we are assuming here and elsewhere, perhaps unrealistically, that we are either not living in a computer simulation, or that we are but that it will continue to run for a considerable time after the development of machine superintelligence  (Bostrom 2003a ). If we are in a simulation that terminates shorty after superintelligent AI is created, then the apparent cosmic endowment may be illusory; and a different set of considerations come into play, which are beyond the scope of this paper.  43  With sufficiently advanced technology, bioengineered meat substitutes should remove the incompatibility between carnivorous consumer preferences and animal welfare altogether. And with even more advanced technology, consumers might reengineer their taste buds to prefer ethical, healthy, sustainable plant foods, or (in the case of uploads or other digital minds) eat electricity and virtual steaks. Thus it appears that whereas today it may be more important to encourage higher rather than lower levels of altruism, in a cornucopia scenario the most important thing would not be to maximize the expected amount of altruism but to minimize the probability that the level of altruism ends up being zero. In cornucopian scenarios, we might say, it is especially desirable that epsilon-magnanimity prevails. More would be nice, and is supported by some of the other desiderata mention in this paper; but there is a special desirability to have a guaranteed floor that is significantly above the zero level. More generally, it seems that if there are resource-satiable values that have a little support (and no direct opposition) and that compete with more strongly supported values only via resource constraints, then it would be desirable that those resources-satiable weaker values get at least some small fraction of the resources available in a cornucopian scenario such that they would indeed be satisfied.  44  A future in which epsilon-magnanimity is ensured seems intuitively preferable. There are several possible ways to ground this intuition. (1) It would rank higher in the preference ordering of many current stakeholders, especially stakeholders that have resource-satiable interests that are currently dominated because of resource constraints. (2) It would be a wise arrangement in view of normative uncertainty: if dominant actors assign some positive probability to various resource-satiable values or moral claims being true, and it would be trivial to give those values their due in a cornucopian scenario, then a \"moral parliament\" or other framework for dealing 45 with normative uncertainty may favor policies that ensure an epsilon-magnanimity future. (3) Actors who have a desire or who recognise a moral obligation to be charitable or generous (or more weakly, to not be a complete jerk) may have reason to make a special effort to ensure that the future be epsilon-magnanimity.  46   \n Desiderata related to allocation These observations suggest that the assessment criteria with regard to the allocational properties of long-term AI-related outcomes include the following: • Universal benefit. Everybody who is alive at the transition (or who could be negatively affected by it) get some share of the benefit, in compensation for the risk externality to which they were exposed. • Epsilon-magnanimity. A wide range of resource-satiable values (ones to which there is little objection aside from cost-based considerations), are realized if and when it becomes possible to do so using a minute fraction of total resources. This may encompass basic welfare provisions and income guarantees to all human individuals. It may also encompass many community goods, ethical ideals, aesthetic or sentimental projects, and various natural expressions of generosity, kindness, and compassion. 47 • Continuity. The path affords a reasonable degree of continuity such as to (i) maintain order and provide the institutional stability needed for actors to benefit from opportunities for trade behind the current veil of ignorance, including social safety nets; and (ii) prevent concentration and permutation from being unnecessarily large. \n Population Under this heading we assemble considerations pertaining to the creation of new beings, especially digital minds that have moral status or that otherwise matter to policy-makers for non-instrumental reasons. Digital minds can differ in fundamental ways from familiar biological minds. Distinctive properties of digital minds may include: being easily and rapidly copyable, being able to run at different speeds, being able to exist without visible physical shape, having exotic cognitive architectures, having non-animalistic motivation systems or perhaps precisely modifiable goal content, being exactly repeatable when run in a deterministic virtual environment, and having potentially indefinite lifespans. The creation of beings with these and other novel properties would have complex and wide-ranging consequences for practical ethics and public policy. While most of these consequences must be set aside for future investigations, we can identify two broad areas of concern: the interests of digital minds, and population dynamics.  48  The interests of digital minds Advances in machine intelligence may create opportunities for novel categories of wrongdoing and oppression. The term \"mind crime\" has been used to refer to computations that are morally problematic because of their intrinsic properties, independently of their effects on the outside world: for example, because they instantiate sentient minds that are mistreated  (Bostrom 2014) . The issue of mind crime may arise well before the attainment of human-level or superintelligent AI. Some nonhuman animals are widely assumed to be sentient and to have degrees of moral status. Future AIs, possessing similar sets of capabilities or cognitive architectures may plausibly have similar degrees of moral status. Some AIs that are functionally very different from any animal might also have moral status. Digital beings with mental life might be created on purpose, but they could also be generated inadvertently. In machine learning, for example, large numbers of agents are often generated during training procedures-many semi-functional versions of a reinforcement learner are created and pitted against one another in self-play, many fully functional agent instantiations are created during hyperparameter sweeps, and so forth. It is quite unclear just how sophisticated artificial agents can become before attaining some degree of morally relevant sentience-or before we can no longer be confident that they possess no such sentience. Several factors combine to mark the possibility of mind crime as a salient special circumstance of advanced developments in AI. One is the novelty of sentient digital entities as moral patients. Policymakers are unaccustomed to taking into account the welfare of digital beings. The suggestion that they might acquire a moral obligation to do so might appear to some contemporaries as silly, just as laws prohibiting cruel forms of recreational animal abuse once appeared silly to many people. Related to this issue of novelty is the fact that digital minds can 49 be invisible, running deep inside some microprocessor, and that they might lack the ability to communicate distress by means of vocalizations, facial expressions, or other behaviours apt to elicit human empathy. These two factors, the novelty and potential invisibility of sentient digital beings, combine to create a risk that we will acquiesce in outcomes that our own moral standards, more carefully articulated and applied, would have condemned as unconscionable. Another factor is that it can be unclear what constitutes mistreatment of a digital mind. Some treatments that would be wrongful if applied to sentient biological organisms may be unobjectionable when applied to certain digital minds that are constituted to interpret the stimuli differently. These complications increase when we consider more sophisticated digital minds (e.g. humanlike digital minds) that may have morally considerable interests in addition to freedom from suffering, interests such as survival, dignity, knowledge, autonomy, creativity, self-expression, social belonging, and political participation. The combinatorial space of 50 different kinds of mind with different kinds of morally considerable interests could be hard to map and hard to navigate. A fourth factor, amplifying the other three, is that it may become inexpensive to generate vast numbers of digital minds. This will give more agents the power to inflict mind crime and to do so at scale. With high computational speed or parallelization, a large amount of suffering could be generated in a small amount of wall clock time. It is plausible that the vast majority of all minds that will ever have existed will be digital. The welfare of digital minds, therefore, may be a principal desideratum in selecting an AI development path for actors who either place significant weight on ethical considerations or who for some other reason strongly prefer to avoid causing massive amounts of suffering. \n Population dynamics Several concerns flow from the possibility of introducing large numbers of new beings, especially when these new beings possess attributes associated with personhood. Some of these concerns relate to the possibility of mind crime, which we discussed in the previous subsection,  49  For examples of the mockery surrounding the earliest animal cruelty laws, see Fisher 2009. For more on the changing norms regarding the treatment of animals, see  Pinker 2011, ch. 3 and 6. 50  But not all sophisticated minds need have such interests. We may assume that it is wrong to enslave or exploit human beings or other beings that are very similar to humans. But it may well be possible to design an AI with human-level intelligence (but differing from humans in other ways, such as in its motivational system) that would not have an interest in not being \"enslaved\" or \"exploited\". See also  Bostrom & Yudkowsky 2014.  but other concerns pertain even if we assume that no mind crime takes place. One special circumstance that is relevant here is that, with digital replication rates, population numbers could change extremely rapidly. An active population policy, with appropriate arrangements put in place in advance, may be necessary to forestall Malthusian outcomes (where average income falls to close to subsistence level) and other bad results. Consider the system of child support common in developed countries. Individuals are free to have as many children as they are able to create; and the state steps in to support children whose parents fail to provide for them. With digital beings, this arrangement is obviously unsustainable. If parents were able to create arbitrary numbers of children and there is persistent variation in willingness to do so, this system would quickly collapse. It is true that over longer timescales, Malthusian concerns will arise for biologically reproducing persons as well, as evolution acts on human dispositions to select for types that take advantage of modern prosperity to generate larger families. For digital minds, however, the onset of a Malthusian 51 condition could be abrupt.  52  Societies would thus confront a dilemma: either accept population controls, requiring would-be procreators to meet certain conditions before being allowed to create new beings; or accept the risk that vast numbers of new beings will only be given the minimum amount of resources required to support their labor, while being worked as hard as possible and terminated as soon as they are no longer cost-effective. Of these options, the former seems preferable, especially if it should turn out that the typical mental state of a maximally productive worker in the future economy is wanting in positive affect or other desirable attributes. 53 Malthusian outcomes is one example of how population change could create problematic conditions on the ground. Another is the undermining of democracy that can occur if the sizes of different demographics are subject to manipulation. Suppose that some types of digital beings obtain voting rights, on a one-person-one-vote basis. Such an enfranchisement might occur because humans give some class of digital minds voting rights for moral reasons, or because a large population of high-performing digital minds is effective at exerting political influence. This new segment of the electorate could then be rapidly expanded by means of copying, to the point where the voting power of the original human block is decisively swamped. All copies from a 54 given template may share the same voting preferences as the original, creating an incentive for digital beings to create numerous copies of themselves-or of more resource-efficient surrogates  51  For evidence of the heritability of traits in modern society associated with larger family size, see  Milot et al. 2001; Kong et al. 2017 . According to Beauchamp 2016: \"In modern populations with low mortality, fitness can be reasonably approximated by [the number of children an individual ever gave birth to or fathered].\"  52  The simple argument focuses on the possibility of economically unproductive beings, such as children, which is sufficient to establish the conclusion. But it is also possible to run into Malthusian problems when the minds generated are economically productive; see Hanson 2016 for a detailed examination of such a scenario. Global coordination would be required to avoid the Malthusian outcome in the Hansonian model.  53  One example of a reproductive paradigm would be to require a would-be progenitor, prior to creating a new mind, to set aside a sufficient economic endowment to guarantee the new mind an adequate quality of life without further transfers. For as long as the world economy keeps growing, occasional \"free\" progeny could also be allowed, at a rate set so as to keep the population growth rate no higher than the economy growth rate.  54  A similar process can unfold with biological citizens, albeit over a longer timescale, if some group finds a way to keep its values stable while sustaining a high level of fertility. designed to share the originator's voting preferences and to satisfy eligibility requirements-in order to increase their political influence. This would present democratic societies with a trilemma. They could either (i) deny equal votes to all persons (excluding from the franchise digital minds that are functionally and subjectively equivalent to a human being); or (ii) impose constraints on creating new persons (of the type that would qualify for suffrage if they were created); or (iii) accept that voting power becomes proportional to ability and willingness to pay to create voting surrogates, resulting in both economically inefficient spending on such surrogates and the political marginalization of those who lack resources or are unwilling to spend them on buying voting power.  55  Desiderata related to population A full accounting of how the special circumstances of advanced AI should affect population policy would require a far more fine-grained analysis, but the preceding discussion lets us identify two broad desiderata: • Mind crime prevention. Advanced AI is governed in such a way that maltreatment of sentient digital minds is avoided or minimized.  \n Process The previous desiderata are expressed in terms of features of outcomes . We can also formulate desiderata in terms of properties that we want to pertain to the process through which the future gets determined. Here we point to three special circumstances with implications for governance that may plausibly obtain around the emergence of superintelligent AI: novelty, depth, and technical challenge of the policy context; pace of events; and the undermining of prevailing principles and norms. Epistemic challenge (novelty, depth, and technicality) The context of a machine intelligence revolution would place unusual epistemic demands on the policy-making process. 55 Option (i) could take various forms. For instance, one could transition to a system in which voting rights are inherited. Some initial population would be endowed with voting rights (such as current people who have voting rights and their existing children upon coming of age). When one of these electors creates a new eligible being-whether a digital copy or surrogate, or a biological child-then the voting rights of the original are split between progenitor and progeny, so that the voting power of each \"clan\" remains constant. This would prevent fast-growing clans from effectively disenfranchising slower-growing populations, and would remove the perverse incentive to multiply for the sake of gaining political influence. Robin Hanson has suggested the alternative of speed-weighted voting, which would grant more voting power to digital minds that run on faster computers  (Hanson 2016, p. 265) . This may reduce the problem of voter inflation (by blocking one strategy for multiplying representation-running many slow, and therefore computationally cheap, copies). However, it would give extra influence to minds that are wealthy enough to afford fast implementation or that happen to serve in economic roles demanding fast implementation. First, an impending or occuring machine intelligence revolution would entail an exceptionally large shift in the policy-making context. This means that many customary assumptions-such as are embedded in institutional arrangements, mental habits, and cultural norms-may become inapplicable. This would place a premium on being able to see the situation afresh by thinking things through from first principles or by being able to draw on an extremely wide and diverse experience base. Second, and relatedly, the challenges confronting decision-makers in this context may come to involve fundamental worldview questions of a type that impinge on deep empirical, philosophical, strategic, or religious issues, and which are often clouded in uncertainty or controversy. This points to a special need for wisdom . Although difficult to operationalize, we take wisdom to mean the ability to reliably get the most important things at least approximately right. Wisdom involves a kind of robustly good judgement, well-calibrated degrees of belief, and a knack for finding a sensible path through a tricky and confusing situation, keeping the bigger picture in mind. In particular, it involves having a sufficient degree of epistemic humility to recognize the limits of one's knowledge and to be able to change one's mind, even about quite fundamental things, rather than persiting indefinitely with some catastrophically mistaken plan. Third, since we are postulating a decision-making context in which an absolutely critical factor is a technological invention, there is a greater-than-usual premium on being able to understand technology-especially AI technology-and form appropriate expectations about its attributes and potentialities. To some extent, this desideratum might be satisfied by bringing in appropriate technical experts to advise policy-makers. But the governance mechanism as a whole needs to be such that the right experts are selected, listened to, and understood. And other things equal, a decision-maker who is ignorant of science and technology and incapable of following a mathematical or technical argument, and is thus reduced to conceptualizing the AI technology as a black box about which different accredited scientific experts make cryptic and sometimes conflicting edicts, is probably at a disadvantage compared to a decision-maker who is able to form a reasonable mechanism-level understanding of the technology under consideration. \n Pace In many scenarios, events of world-historic consequence would be unfolding at an unusually fast pace during the transition to machine superintelligence. This suggests that it may be more important than it normally is for governance processes to be able to move rapidly and decisively, to stay ahead of events. In particular, it may be desirable that the development of superintelligent AI takes place in a governance context in which it is possible to make constitutional changes quickly and to decide and impose global governance arrangements on timescales much shorter than those typically associated with negotiating, ratifying, and implementing multinational treaties. \n Undermining There are various ways in which the context of a machine intelligence revolution may present special opportunities for principles and norms to be undermined or for existing power structures to be usurped. We touched on some of these in our discussion about \"reshuffling\" above, in terms of how social outcomes might be subject to extreme degrees of permutation or concentration of wealth and influence. But we can also approach these matters from a process-oriented perspective. Consider principles such as legitimacy, consent, political participation, and accountability. These are widely thought to be desirable attributes for governance systems and policy-making processes to have. Yet the special circumstances of a machine intelligence revolution could undermine these principles in various ways. Take, for example, the idea of voluntary consent, a hugely important principle that regulates many interactions between both individuals and states. Many things that it would be morally wrong or illegal to do to an individual without her consent are entirely unobjectionable if done with her consent. The same holds for many possible interactions between corporate entities or states: it very often makes a world of difference whether something is taken or imposed by force, or voluntarily agreed to. Yet consider how this central role given to consent could be undermined in the context of advanced AI, if it becomes possible to construct a \"super-persuader\", a system that has the ability, through extremely skillful use of argumentation and rhetoric, to persuade almost any human individual or group (unaided by similarly powerful AI) of almost any position, or to get them to accept almost any deal. Should it be possible to create such a super-persuader, then it would be inappropriate to continue to rely on consent as a near-sufficient condition for many types of transaction to be morally and legally unobjectionable. In a world with super-persuaders, there would need to be stronger protections to safeguard human interests, analogous to the extra safeguards currently in place to protect the interests of certain classes of vulnerable individuals, such as children and adults with cognitive impairments. Perhaps consent should only be regarded as valid if the human counterparty had access to a qualified AI advisor, or if the transaction were approved by an \"AI guardian\" assigned to the human actor to protect her from exploitation. For another example, consider the norm of political participation. This norm might be justified on several different grounds. On the one hand, it could provide an epistemic benefit by including more information and a broader range of perspectives into the decision-making process. On the other hand, it could also be a way of ensuring that many different interests and preferences are reflected in the decisions that are made. And on the prehensile tail, political participation could be regarded as an intrinsic good, to be valued independently of any contribution it makes to producing decisions that better serve all the interests concerned. These three justifications 56 may need to be reevaluated in the context of superintelligent AI. For instance, it is possible that the epistemic value of letting political decisions be influenced by many human opinions would be reduced or eliminated if superintelligent AI were sufficiently epistemically superior to humans and able to discern and integrate independently all the scraps of evidence and insight that a distributed human epistemic community would have been able to supply. It is also conceivable that advanced AI would enable the construction of a mechanism that does not require the continual input of human preference articulations in order to factor those preferences into the decisions that are being made-maybe a superintelligent AI could learn a preference function that already anticipates the existing distribution of human preferences and the shifts in those preferences that will occur over time, or the AI might be able to infer this from observing other kinds of human behaviour. The supposed intrinsic value of political participation might remain intact even if the two instrumental justifications were to disappear; or, perhaps, it would come to be seen as quaint and perverse to want to participate in political affairs after it becomes clear that one's interventions only serve to make political outcomes worse (for both one's own interests and those of the wider society). The purpose of these two examples is not to advance specific claims about consent or political participation in an era of superintelligent AI, but to illustrate a more general point: that there are various principles and norms, which are currently deeply entrenched and often endorsed without qualification, that would need to be examined afresh in a context of radical AI. Some of these 57 norms and principles may have to be abandoned in that context; others may need to be reinterpreted and reformulated; and yet others may need to be safeguarded with greater than usual vigilance. This points to a general desideratum on governance processes in this context, namely that they be capable of leading to appropriate adaptation of relevant norms and principles.  58  Desiderata related to process From the preceding observations, we derive a set of desiderata pertaining to the governance processes by which policy is decided in the context of superintelligent AI: • First-principles thinking, wisdom, technical understanding. The transition to superintelligent AI is governed by some agency (individual or collective, centralized or distributed) that is able to effectively integrate uncommon levels of first-principles thinking, wisdom, and technical understanding into its decision-making. • Speed and decisiveness. Development and deployment of superintelligent AI is done in a political context in which there exists a capacity for rapid decision-making and decisive global implementation (or, alternatively, a capacity to moderate the pace of developments so as to allow slower decision-making and coordination processes to be effective). • Adaptability. Superintelligent AI is deployed in a sociopolitical context in which rules, principles, norms, and laws can be adapted as appropriate to fit the novel circumstances. 57 These norms and principle may have gained traction because they helped with governance challenges within the socio-technological millieus of previous decades and centuries. 58 Some of our discussion earlier in this paper offers additional examples of instances where existing norms would need to be rescinded or reconceived. The right to unlimited reproduction is hardly defensible in a context where Malthusian concerns loom large, such as for digital minds. Freedom of thought may similarly need to circumscribed in the case of AI minds who have the ability merely by thinking about a suffering subject in great detail to create internally that mind in a state of suffering and thus engage in an act of mind crime. Punishment for criminal offenses: some of the current reasons for incarceration would cease to apply if, for instance, advanced AI made it possible to more effectively rehabilitate offenders or to let them back into society without endangering other citizens, or if the introduction of more effective crime prevention methods reduced the need to deter future crime. The meaning of a given sentence: even if a life sentence is sometimes a just punishment when the typical remaining lifespan is a few decades, it may not be just if AI-enabled medicine makes it possible to greatly extend lifespan. Various dignity-based or religious sensitivities may require special protections and accommodations in the context of advanced AI. And AI research itself may need to be approached in a different manner than most basic research, where norms of curiosity-driven exploration, openness, and the celebration of intellectual achievement are often held up as the ultimate touchstones. For AI research, considerations about downstream applications and strategic impacts of research findings may need to be added to the criteria by which research contributions are evaluated. \n Summary We have drawn attention to a number of special circumstances that may surround the development and deployment of superintelligent AI, circumstances that present distinctive challenges for governance and global policy. Using a \"vector field\" approach to normative analysis, we sought to extract directional policy implications from these special circumstances. We characterized these implications as a set of desiderata-traits of future policies, governance structures, or decision-making contexts that would, by the standards of a wide range of key actors, stakeholders, and ethical views, enhance the prospects of beneficial outcomes in the transition to a machine intelligence era. These desiderata (which we do not claim to be exhaustive) are summarized in Table  1 . \n Efficiency Technological opportunity Expeditious progress . This divides into two components: (a) Policies that lead with high probability to the eventual development of safe superintelligence and its application to tapping novel sources of wealth; and (b) speedy AI progress, such that socially beneficial products and applications are made widely available in a timely fashion. AI safety . Techniques are developed that make it possible (without excessive cost, delay, or performance penalty) to ensure that superintelligent AI behaves as intended. Also, the conditions during the emergence and early deployment of superintelligence are such as to encourage the use of the best available safety techniques and a generally cautious approach. Conditional stabilization . The development trajectory and the wider political context are such that if catastrophic global coordination failure would result in the absence of drastic stabilizing measures, then the requisite stabilization is undertaken in time to avert catastrophe. This might mean that there needs to be a feasible option (for some actor or actors) to establish a singleton, or to institute a regime of intensive global surveillance, or to strictly suppress the dissemination of dangerous technology or scientific knowledge. Non-turbulence . The path avoids excessive efficiency losses from chaos and conflict. Political systems maintain stability and order, adapt successfully to change, and mitigate socially disruptive impacts. \n AI risk \n Possibility of catastrophic global coordination failures Reducing turbulence \n Allocation Risk externalities Universal benefit. Everybody who is alive at the transition (or who could be negatively affected by it) get some share of the benefit, in compensation for the risk externality to which they were exposed. Epsilon-magnanimity . A wide range of resource-satiable values (ones to which there is little objection aside from cost-based considerations), are realized if and when it becomes possible to do so using a minute fraction of total resources. This may encompass basic welfare provisions and income guarantees to all human individuals. It may also encompass many community goods, ethical ideals, aesthetic or sentimental projects, and various natural expressions of generosity, kindness, and compassion. Continuity . The path affords a reasonable degree of continuity such as to (i) maintain order and provide the institutional stability needed for actors to benefit from opportunities for trade behind the current veil of ignorance, including social safety nets; and (ii) prevent concentration and permutation from being unnecessarily large. The desiderata in Table  1  help establish criteria by which concrete policy proposals for the governance of advanced AI could be evaluated. By \"policy proposals\" we refer not only official government documents but also plans and options developed by private actors who take an interest in long-term AI developments. The desiderata, therefore, are also relevant to some corporations, research funders, academic or non-profit research centers, and various other organizations and individuals. \n Reshuffling The development of concrete proposals that might satisfy these desiderata is a task for further research. Such concrete proposals would probably need to be relativised to specific actors, since the best way to comport with the general considerations we have identified will depend on the capacities, resources, and political constraints of the actor to whom the proposal is directed. Furthermore, specific actors may also have additional idiosyncratic preferences that are not fully captured by our vector field analysis but which must be accomodated in order for a policy proposal to stand a chance of gaining acceptance. 39 Such agreement is well established by, among other agreements, the Charter of the United Nations (Charter of the United Nations 1945) and the \"International Bill of Human Rights\", composed of the Universal Declaration of Human Rights (Universal Declaration of Human Rights 1948), the International Covenant on Civil and Political Rights (International Covenant on Civil and Political Rights 1966), and the International Covenant on Economic, Social and Cultural Rights (International Covenant on Economic, \n • Population policy. Procreative choices, concerning what new beings to bring into existence, are made in a coordinated manner and with sufficient foresight to avoid unwanted Malthusian dynamics and political erosion. \n Table 1 . 1 Mind crime prevention. Mind crime prevention. Advanced AI is governed in such a way that maltreatment of sentient digital minds is avoided or minimized. Population policy. Procreative choices, concerning what new beings to bring into existence, are made in a coordinated manner and with sufficient foresight to avoid unwanted Malthusian dynamics and political erosion. The transition to superintelligent AI is governed by some agency (individual or collective, centralized or distributed) that is able to effectively integrate uncommon levels of first-principles thinking, wisdom, and technical understanding into its decision-making. Speed and decisiveness. Development and deployment of advanced AI is done in a political context in which there exists a capacity for rapid decision-making and decisive global implementation (or, alternatively, a capacity to moderate the pace of developments so as to allow slower decision-making and coordination processes to be effective). Adaptability. Superintelligent AI is deployed in a sociopolitical context in which rules, principles, norms, and laws can be adapted as appropriate to fit the novel circumstances. Special circumstances expected to be associated with the transition to a machine intelligence era (left column) and corresponding desiderata for governance arrangements (right column). Veil of ignorance Cornucopia Population \n\t\t\t To be clear, we do not claim that the desiderata we identify are the only distributional desiderata that should be taken into account. There may also be desiderata that derive their justification from some other source than the special circumstances obtaining in our superintelligent AI scenario. (There might also be some additional allocation-related desiderata that could have been derived from those special circumstances, but which we have failed to include in this paper. We do not claim completeness.)31  Note that care would have to be taken, when following the principle, not to implement it in a way that unduly inhibits socially desirable risk-taking, such as many forms of experimentation and innovation. Internalizing the negative externalities of such activities without also internalizing their positive externalities could produce worse incentives than if neither kind of externality were internalized. \n\t\t\t Here, epsilon-magnanimity might be seen as amounting to a weak form of practical value pluralism.45 Bostrom 2009.  46  An epsilon-magnanimous future could be achieved by ensuring that the future is shaped by many actors, representing many different values, each of whom is able to exert some non-negligible degree of influence; or, alternatively, by ensuring that at least one extremely empowered actor is individually epsilon-magnanimous. \n\t\t\t For example, it would appear both feasible and desirable under these circumstances to extend assistance to nonhuman animals, including wildlife, to mitigate their hardship, reduce suffering, and bring increased joy to all reachable sentient beings (Pearce 1995) .48  In principle, these observations pertain also to biological minds insofar as they share the relevant properties. Conceivably, extremely advanced biotechnology might enable biological structures to approximate some of the attributes that would be readily available for digital implementations. \n\t\t\t A fourth ground might be to ensure that decisions are perceived as legitimate.", "date_published": "n/a", "url": "n/a", "filename": "aipolicy_vector_field.tei.xml", "abstract": "We consider the speculative prospect of superintelligent AI and its normative implications for governance and global policy. Machine superintelligence would be a transformative development that would present a host of political challenges and opportunities. This paper identifies a set of distinctive features of this hypothetical policy context, from which we derive a correlative set of policy desiderata-considerations that should be given extra weight in long-term AI policy compared to in other policy contexts. Our contribution describes a desiderata \"vector field\" showing the directional change from a variety of possible normative baselines or policy positions. The focus on directional normative change should make our findings relevant to a wide range of actors, although the development of concrete policy options that meet these abstractly formulated desiderata will require further work.", "id": "c62bab3ab737c3472fbb7e2363c92093"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jose Hernández-Orallo", "Fernando Martínez-Plumed", "Shahar Avin", "Jess Whittlestone", "Seán Ó H Éigeartaigh"], "title": "AI Paradigms and AI Safety: Mapping Artefacts and Techniques to Safety Issues", "text": "INTRODUCTION As in any other scientific or engineering discipline, many AI researchers work within a well-established paradigm, with some standard objects of study, problems to solve, and associated formalisms and terminology. Understanding past, current and future AI paradigms is an important source of insight for funding agencies, policymakers, and AI researchers themselves, because it shapes how we think about what problems AI research is aiming to solve, what methods are required to solve them, and what the wider implications of progress might be. We believe that thinking clearly about AI paradigms is particularly crucial for AI safety research: an increasingly important area concerned with understanding and preventing possible risks and harmful impacts in the design and deployment of AI systems. For the purposes of this paper, we define AI safety broadly, to include both risks from AI systems for which the source of risk is accidental, ranging from unpredictable systems to negligent use, and non-accidental risks such as those stemming from malicious use or adversarial attacks (which might sometimes also be referred to as AI security risks.) This includes risks with many different types of consequences: including human, environmental, and economic consequences. AI safety is becoming particularly important as AI is increasingly used to automate tasks that involve interaction with the world. A characteristic example is AI being used in many components of self-driving cars such as perception, reasoning and action. Research in AI safety has typically analysed a specific risk or issue under a particular existing paradigm, such as interruptibility for reinforcement learning agents  [33] , adversarial attacks on deep learning systems  [43] , or fake media produced with GANs  [21] . Poor choices or misinterpretation of current and future paradigms may result in AI safety research focusing in the wrong places: analysing scenarios that will not take place in the future, or that will at best manifest in completely different ways. For example, concerns about adversarial attacks on current deep learning methods have led to many papers proposing methods to defend against malicious perturbations, but it is not clear that these actually relate to plausible security concerns  [16] . Though adversarial examples help us understand how brittle current deep learning methods can be, the kinds of attacks that some safety research is concerned with can only arise in contrived interactions, and make strong assumptions about the goal, knowledge, and action space of the attacker. In contrast, other risks have been ignored because they are outside of the current paradigm: for instance, attacks which go beyond an \"independent\" or functional interpretation of a neural network, and instead use the \"information from previous frames to generate perturbations on later frames\"  [41] . Thinking about different paradigms is also important for clearly assessing safety considerations and risks in concrete real-world applications. For instance, the risks of using AI in vehicles will be perceived differently depending on whether we expect AI to be assisting or replacing human drivers, whether a self-driving vehicle is considered as a single autonomous agent, or whether we consider the whole traffic system as a swarm of interacting agents. Even as research becomes oriented towards future risks (some years or even decades away) the different safety issues associated with different AI paradigms have not been explicitly addressed in the literature  [6, 2, 23, 14] . As AI research is fast evolving and likely to result in increasingly powerful systems in future, it is crucial for AI safety to explore issues associated with a broader range of possible AI paradigms, and to explicitly discuss what assumptions about paradigms and safety issues are being made in each research paper or project. This will not only enable the research community to identify the effects of less-explored paradigms on safety concerns, but could also increase awareness among AI developers that the paradigms they work in have consequences for safety, potentially highlighting approaches that can eliminate or reduce safety risks. In this paper, we present a structured approach for thinking about paradigms in AI and use this as the basis for empirical analysis of how AI safety issues have been explored in the research literature so far. We begin by defining what we mean by 'paradigms' in AI more precisely, drawing on literature in the philosophy of science to distinguish two different types of paradigms in AI: artefacts and techniques. Drawing on existing research and the expertise of several AI and AI safety researchers, we outline a preliminary taxonomy of fourteen different AI techniques and ten different AI artefacts. We then discuss how these different techniques and artefacts relate to AI safety issues. We use AAAI's 'AI topics' database to conduct a grounded empirical analysis of the historical evolution of these different paradigms, and the safety issues associated with them. Our analysis identifies a number of gaps in AI safety research where certain combinations of techniques, artefacts and safety issues need to be addressed. We conclude the paper by discussing implications for future research in AI safety. \n DEFINING PARADIGMS IN AI Before discussing paradigms in AI and how they relate to safety issues, we need a clearer account of what an AI paradigm is. In the philosophy of science, a 'paradigm' is an important concept used to capture how theories, methods, postulates and standards evolve and change within a scientific discipline  [22] . The concept of a 'technological paradigm' plays a similar role but with a somewhat distinct focus, emphasising how each technological paradigm defines its own concept of progress, based on making specific technological and economic trade-offs  [12] . In computer science, the term 'paradigm' is commonly used to refer to different types of programming languages with different features and assumptions: imperative, logic, functional, object-oriented, distributed, event-oriented, probabilistic, etc. The theory and practice of programming languages depends heavily on these paradigms. Many safety issues in programming and software engineering, and verification in particular, cannot be addressed -conceptually or technically-without making paradigms explicit  [5, 20, 40, 42] . For instance, compared to imperative programming languages, declarative languages minimise mutability issues  [10]  due to the use of immutable data structures, as well as reduce state side-effects  [29]  by discouraging the utilisation of variables in favour of more sophisticated constructs (e.g., data pipelines or higher-order functions). In the context of AI, the concept of 'paradigms' has been used informally to refer to different broad families of technical or conceptual approaches: 'symbolic' vs 'connectionist', reasoning vs learning, expert systems vs agents. One way to identify paradigms in a field and how they have changed over time, suggested in Kuhn's original formulation, is to look at the approach taken by major (text)books in the field. Russell and Norvig  [36] , for example, popularised the 'agents' view of AI in the 1990s, and Goodfellow et al.  [17]  has consolidated 'deep learning' as a central approach AI research this decade, going far beyond one specific technique. However, there is no clearly agreed-upon definition of what counts as a paradigm in AI.  [9]  defined an AI paradigm as \"the pair composed by a concept of intelligence and a methodology in which intelligent computer systems are developed and operated\", which led him to identify three paradigms of AI: behaviourist, agent and artificial life. More than twenty years later, these do not seem to adequately reflect the approaches and assumptions within AI research today. Perhaps this difficulty clearly distinguishing AI paradigms from mere trends stems at least partly from the ambiguity in the concept of paradigm itself, a criticism which has been made within the philosophy of science. Masterman identifies three different conceptions of paradigm in Kuhn's writings: the metaphysical, the sociological AI Safety Issue AI Technique AI Artefact Figure  1 . Ways of analysing an AI safety issue, combined with an artefact and/or a technique category. In real systems, techniques underpin the creation or operations of an artefact, where the real hazards occur. Occasionally, researchers can think of a safe issue in a very abstract way, without committing to any particular artefact or technique (e.g., value alignment). All relations (arrows) are many-to-many. and the artefact/construct  [27] . Peine makes a reconstructive effort to combine the second and the third conceptions, suggesting that a paradigm can emerge when a subcommunity within a field makes a commitment to a certain set of techniques  [35] . For instance, we can see this phenomenon in the deep learning community, which made early commitments before this approach had established a dominant position within the field. We suggest distinguishing between dominant trends: research commitments to specific techniques, aims, or assumptions that may be relatively short-lived; and paradigms where these trends lead to more established, long-term commitments. These ambiguities in the concept of a paradigm are apparent in the context of AI, where 'paradigm' may be used to distinguish both different techniques for solving problems in AI (e.g., Monte Carlo search vs. SAT solver, deep learning vs. genetic algorithm), and to capture different conceptions of possible types of AI systems (e.g. expert systems vs. agents). Many technical papers can easily be categorised by looking at the first formal definitions that appear after the introduction, which tend to identify the kind of AI system and the kinds of techniques they use to solve a problem. We suggest that it may be helpful, in thinking about paradigms in AI, to distinguish explicitly between these two types of constructs: • Conceptual Artefacts: broad conceptions of what current and future AI systems (will) look like, e.g., autonomous agents, personal assistants  [24] , AI extenders  [19] , conceptions of superintelligence  [6]  and Comprehensive AI Services  [13] . • Research Techniques: the research methods, algorithms, theoretical technical results and methodologies involved in the development of these current or future systems, such as SAT solvers, deep learning, reinforcement learning, evolutionary computing, etc. Artefacts and techniques are important components of a paradigm, and together (weakly) define a paradigm. AI artefacts and techniques are often related to each other, insofar as certain techniques will often be better suited to certain types of artefacts (reinforcement learning is a technique category that is applicable for agent-like artefacts, for example). However, distinguishing between artefacts and techniques can help us to think more clearly about associated safety issues. Some safety issues will arise when combining an artefact with some techniques but not others: for example, when building a classifier (artefact), interpretability is likely to be a challenge for safety if using deep neural networks (technique), but less so if using simple decision trees with conditions that are expressed over the original attributes. Recognising these differences is important for understanding the scope of safety challenges and what solutions may be needed. In the case of autonomous vehicles, for example, both techniques and artefacts have changed over time, changing conceptions of safety. Early work in the 1980s-1990s, such as the Eureka 24th European Conference on Artificial Intelligence -ECAI 2020 Prometheus Project, emphasised systems for improved vehicle-tovehicle communications and driver assistance (e.g. collision avoidance), whereas more recent initiatives emphasise the development of fully independent self-driving vehicles. These are very different AI artefacts, with a more fully autonomous system evoking much broader safety concerns in general. However, to think more concretely about how evolving approaches to autonomous vehicles change safety challenges, it may also be important to look at how techniques have changed over time. For example, as improvements in computer vision enable more limited sensors to be replaced by cameras or radars, we may need to focus specifically on the vulnerabilities introduced by current techniques used in machine perception. Sometimes we may want to broadly assess all possible risks associated with a specific AI artefact independently of the technique used (e.g. issues associated with AI extenders), or those associated with a technique independently of the artefact (e.g. safety challenges for deep learning). In other cases, we may want to more narrowly focus on a specific safety issue associated with a particular artefact (e.g. interruptability for industrial robots), or a specific issue associated with a particular technique (e.g. interpretability of neural networks.) Figure  1  shows these interrelationships: how AI safety issues may be considered relative to either techniques, artefacts, or both. \n IDENTIFYING TECHNIQUES AND ARTEFACTS We can now begin to explore different ways of categorising AI paradigms by decomposing them into techniques and artefacts. While other accounts of 'AI paradigms' have been proposed, such as by the \"One Hundred Year Study on Artificial Intelligence\" at Stanford University  [39] , the categories frequently mix techniques with artefacts and even subfields. \n AI techniques We develop a preliminary categorisation of AI techniques by building on the bibliometric analysis of  [26]  and  [32, Tab. 6 ]. Martínez-Plumed et al.  [26]  identify nine 'facets' for the study of the past and future of AI, using data on all accepted papers from AAAI/IJCAI conferences (1997-2017), and AI Topics documents, an archive kept by AAAI containing news, blog entries, conferences, journals, and other repositories. Niu et al.  [32]  identify 30 high-frequency keywords from 20 relevant journals in AI from 1990 to 2014. Both capture many keywords and categories which appear to describe AI techniques, and are relatively similar.  4  We construct a list of AI techniques, grouped into 14 categories, based on selecting relevant and representative keywords from these two analyses. We chose these categories based on three principles: (1) the techniques are sufficiently general to encompass groups of approaches in AI that have been recognised by other approaches, (2) overlapping in the techniques is allowed, as there is a high degree of hybridisation and combination in AI, and (3) subcategories are retained for particularly large categories, such as 'machine learning'  5  The list of categories is shown in Table  1 .  \n AI artefacts For AI artefacts, we would like our categories to be more stable over time and less tied to specific research techniques and applications. One way to look beyond current trends is to consider textbooks or even historical accounts of AI  [28, 7, 31] . It may also be helpful to begin by considering broad 'characteristics' of AI systems independent of the specific techniques used to develop them  [18] . To generate a preliminary set of artefacts, a group of multidisciplinary researchers conducted a systematic, interactive procedure based on the Delphi method  [11] . The group began by independently brainstorming possible candidates for categories of artefacts based on a preliminary discussion of those arising from AI textbooks and different AI system characteristics. Two criteria were provided to structure this initial brainstorm: (1) artefacts should ideally have minimum overlap, each capturing distinctive functionalities, and (2) artefacts should be defined independently of how functionalities are achieved (i.e. independent of techniques). Group members each proposed lists of distinctive type of AI systems, supported by exemplars, which were revised using an iterative process until the list of answers converged towards consensus. These were then clustered hierarchically to produce a set of artefacts which could cover the space of actual and potential AI systems as exhaustively as possible. The categorisation of AI artefacts in Table  2  is the result of this process. Building on the categories identified in  [18] , we can further characterise these different artefacts in terms of their integration with the external environment, in three ways: (1) how it interfaces with the environment (e.g. via sensors and actuators, via digital objectives, or via language); (2) the dynamics of this integration (whether it is interactive or functional); and (3) the location of this integration (whether it is centralised, distributed, or coupled). For example, an agent interfaces with the environment via sensors and actuators in an interactive and centralised way. A swarm has similar characteristics except that the location of its integration is distributed (across different units) rather than centralised. We also provide examplars for each category: self-driving cars and robotic cleaners are examples of agent-type systems, whereas a multiagent network router or drone swarm are examples of swarm-type systems. We outline these characteristics to show that the artefacts are sufficiently comprehensive and distinctive to provide a useful basis for further analysis, though as with any clustering there are some overlaps and borderline cases. \n Empirical analysis of techniques and artefacts Using our categories of techniques (e.g., neural networks, information retrieval, cognitive approaches, etc.) and artefacts (e.g., estima-24th European Conference on Artificial Intelligence -ECAI 2020 tor, agent, dialoguer, etc.), we now conduct an empirical analysis of how these different paradigm components have appeared in research papers and other related literature. This analysis will allow us to explore more empirically which paradigm elements have been prominent at different times, and will form the basis for investigating the relationship between paradigms and safety issues later in this paper. To conduct this analysis, we work with AI Topics 6 , an official database from the AAAI, using the documents from the period 1970-2017 (complete years). This archive contains a variety of documents related to AI research (news, blog entries, conferences, journals and other repositories) that are collected automatically with NewsFinder  [8] . We divide the archive into research documents  7  and non-research documents. From the ∼111K documents gathered, ∼11K are research papers and the remaining ∼100K are mostly media. With a mapping approach between the list of exemplars (tokens) of techniques and artefacts (e.g., \"Deep Learning\", \"GAN\" or \"perceptron\" are illustrative exemplars of the \"neural network\" technique; \"classifier\", \"decision-making\" or \"object recognition\" are exemplars of the \"estimator\" artefact5 0 ), and the tags obtained from AI Topics (substrings appearing in titles, abstracts and metadata), we summarise the trends in a series of plots. The evolution of techniques and artefacts in these documents (i.e., fraction of papers focusing on the list of tokens for each technique category or artefact) is shown in Figure  2 , where the data has been smoothed with a moving average filter in order to reduce short-term volatility in data. Note that this figure shows the aggregation of categories (techniques and artefacts) where each area stack is scaled to sum to 100% in every certain period of time. In a way, this can be understood as a non-monolithic view of polarities and intensities in sentiment analysis (e.g., identifying sentiment orientation in a set of documents). We see some techniques and artefacts are particularly dominant, as might be expected. For instance, looking at the techniques (left plot), 'knowledge representation and reasoning' takes almost half of the proportion of documents between 1980-1990, while 'general machine learning' becomes more relevant from 2005. We also see an important peak of multiagent systems around 2000. When we look at the artefacts (right plot), we see that 'extractor' (which includes expert systems) became very popular around 1990 but in a matter of a decade was overtaken by 'agent', which became dominant in 2000. We see today that five kinds of artefacts account for about 90% of all mentions: estimators, agents, optimisers, extractors and creators. These patterns also show that some artefacts are not new as a paradigm component, especially when we consider them in a more abstract way. For instance, it is sometimes understood that GANs introduced a new paradigm, but other kinds of generative systems have been around in AI since its exception, as we see in the violet band in Figure  2  (right). We can also use this analysis to explore what techniques and artefacts are prominent in the media. In Figure  2 , we look at all the non-research papers, shown in the 'Media' column besides each 'Research' plot. In this case, we can only show selected documents for the last two (complete) years  8  . We see that the dominances are more extreme. For the techniques (Figure  2 , left), 'neural networks' and 'general machine learning' occupy more than 75% of total mentions. On the right, we see that the distribution of artefacts is different, but also extreme: only four artefacts ('estimator', 'agent', 'dialoguer' and 'creator') cover more than 90% of mentions. In this case, we see that 'optimiser' and 'extractor' are less visible for laypeople than for researchers, while 'dialoguer' is more relevant for laypeople (most probably because of the common use of digital assistants). \n PARADIGMS AND SAFETY ISSUES To begin exploring how paradigms relate to safety issues in AI research, we conduct two different analyses. First, we look at the relative prominence of different techniques and artefacts specifically within research publications and other publications that are related to safety. This will help us to discern how the prominence of different paradigms differs in safety research from AI research as a whole, and to consider whether some paradigms are under-or over-represented in the safety literature. Second, we look at how different safety issues co-occur with different paradigms in the literature, enabling us to understand which safety issues are considered to relate to which paradigms, and to identify potential gaps in the literature. \n Analysing paradigms within safety research To explore the prominence of different AI techniques and artefacts in AI safety literature, we begin by conducting a similar analysis to that  8  While AI topics provides research documents (mainly) from the 70s onward, media-related documents come mostly from the last 2-3 years. in section 3.3, but restricting to documents which make some reference to AI safety. We use a list of over 100 relevant tokens to filter documents (Table  3 , right column, shows some examples of tokens for each type of safety issue5 0 ). Applying this filter, we find that, from the ∼111K documents in AI Topics, about ∼21K are related to safety, of which ∼1.5K are research papers, and ∼19K are broader (mostly media) documents. Figure  3  shows the frequency of reference to different techniques and artefacts within this safety-specific database. The results look similar to those for the enitre document database in Figure  2 , but there are some important differences. First, the frequencies of reference to different techniques and artefacts are more extreme and varied over time. This might be a consequence of the smaller sample size, but we do see this pattern particularly with the more dominant terms, where we have a reasonable sample size. In particular, we see that for AI research as a whole, 'knowledge and reasoning' was a dominant technique between the mid 1970s and mid 1990s, taking up about 50% of references (Figure  2 , left) -but is even more dominant as a proportion of mentions in safety research in the 1990s, at about 60% (see Figure  3 , left). This is even more extreme for the 'extractor' artefact, with about 50% of the documents in the late 1980s (Figure  2 , right), to more than 75% in the early 1990s (Figure  3 , right). The most interesting observation comes from looking at the periods when these peaks happen for different techniques (comparing the left plots of Figure  2  and Figure  3 ). The peak for 'knowledge representation and reasoning' happened in the mid 1980s when looking across AI research in general, but in the early 1990s when filtered by papers which mention safety. The peak for 'planning and scheduling' took place in the late 1990s across all papers but a few years later (and was more pronounced) when filtered by safety-relevant papers. We see a similar pattern for artefacts (comparing right plots of Figures  2 and 3 ): 'extractors' is dominant in the AI literature in the late 1980s, but only become prominent in safety research in the early 1990s; 'agents' rise to prominence in AI research in the late 1990s but only peak in safety research in the early 2000s. This suggests a five-year delay (approximately) between when a technique or artefact becomes popular within general AI research, and when researchers begin to seriously consider the safety issues associated with it. This suggests that safety issues are considered reactively in response to dominant research patterns, and are only considered once a paradigm has been prominent for several years (rather than safety issues related to a given technology being considered at the outset of research, as is more often the case in domains like engineering). In other words, we find that there is a delay between the emergence of AI paradigms and safety research into those paradigms, and safety research neglects non-dominant paradigms. Looking at the plots for non-research documents (comparing documents filtered for safety (Figure  3 , Media), with all documents (Figure  2 , Media), we see that the plots are almost identical. The only slight difference is that both 'natural language processing' techniques and 'dialoguer' artefacts are less prominent in articles filtered for safety, suggesting that the media and laypeople are perhaps less concerned about the harms of conversational systems than experts are. \n Mapping paradigms to safety issues Next we look more closely at how different AI paradigms relate to specific safety issues. To do this, we need a way to categorise different safety issues. Though existing categorisations of safety issues exist  [25, 34] , we found these were too coarse for our purposes (e.g.  [34]  uses just three categories). Building on these existing categorisations, we identified key terms in surveys, blogs and events in AI safety  [6, 2, 23, 14, 41, 37] , and clustered them into groups. Through this process we identified 22 categories, as shown in Table  3 . Our clustering process attempted to aggregate safety categories in an abstract way, independently of the subfield in which a term occurs most frequently. For instance, 'distributional shift' is the term used in machine learning, whereas 'belief revision' is the term used in the area of knowledge representation and reasoning. However, both refer to solving the same type of problem -where a system has to adapt or generalise to a new context-so we group both together under the 'problem shift' category. With this list of categories, we then analyse how related different paradigms and safety issues are, by counting the number of papers (of those filtered for safety relevance) which mention both a given paradigm component (technique or artefact) and a given safety issue, for all combinations of techniques and safety issues (and the same analysis, separately, for artefacts). Figure  4  shows these relationships, where the width of each band represents the number of papers including reference to both elements, with techniques/artefacts on the left, and safety issues on the right. The most general safety issues, such as 'trust, transparency & accountability', 'privacy & integrity', 'reliability & robustness', 'problem shift' and 'interpretability', have the widest bands linking them to different paradigm components, and tend to be linked to a wide variety of different paradigm components (shown by the 'multicolour' bands coming out from these issues). We notice several interesting insights about the relationship between safety issues and techniques or artefacts. The issue of 'problem shift' is largely associated with 'knowledge representation and reasoning', which is surprising since we might expect the broad problems of generalising to new contexts and distributions to be relevant to a wide range of techniques. This may be due to the relevance of belief revision in this kind of techniques. 'Privacy and integrity' is associated with many techniques, but not with reinforcement learning -which makes sense, given that reinforcement learning is much less likely to make use of personal data than other techniques. However, reinforcement learning is also not related to 'safe exploration and side effects', and is only very weakly associated with 'problem shift', which is more surprising, since these do seem like issues that are important for ensuring RL systems are used safely. Part of the reason for this may be that our analysis simply did not find much mention of safety issues in relation to reinforcement learning overall. While we must recognise the limitations of the database we had access to (perhaps AI topics does not capture the kinds of venues where safe reinforcement learning research is published), this does suggest that greater exploration of safety issues related to reinforcement learning is an important gap. Similarly, there is relatively little 24th European Conference on Artificial Intelligence -ECAI 2020 literature linking probabilistic and Bayesian approaches or evolutionary approaches in ML to safety issues. When we focus on less covered safety issues, we see that the associations are less multicoloured. For instance, 'scalable supervision' and 'specification & value alignment' are associated only with reinforcement learning, and 'adversarial attacks' only with 'neural networks'. More surprising are the associations of 'confinement problem', 'manipulation' and 'safe exploration & side effects'. Overall, most attention is paid to a few now prominent safety issues, but more specific issues have very limited combinations with some techniques. The right plot in Figure  4  shows the analysis for artefacts. In this case, also looking at the circle from right to left, we see multicolour bands relating some of the more prominent safety issues to a variety of different artefacts. The 'agent' paradigm component, which is more prominent in general, is associated with the widest range of safety issues by far -suggesting that more research on safety issues associated with different artefacts may be worthwhile. In general, across techniques and artefacts, we see that 'reliability and robustness' is by far the most frequently discussed safety issue -perhaps because it is more immediately and directly related to the performance of a system than the others. This is followed by 'trust, transparency and accountability', 'privacy and integrity' and 'problem shift'. More research into the less prominent safety issues and how they relate to different paradigms would be valuable. \n GENERAL DISCUSSION A next step for this work would be to combine this mapping exercise with deeper conceptual analysis of the relationship between techniques, artefacts, and safety issues. For instance, the \"confinement problem\" has been discussed in technical safety research relatively recently  [4] , and is already strongly associated with optimisers, organisms and extractors (Figure  4 , right): systems that are naturally thought of as being encapsulated. However, other types of systems -dialoguers, estimators, providers and extenders-might also learn to behave in ways that go beyond their original specification or constraints, and it may be worth considering a wider range of \"confinement\" problems across many different AI systems. More broadly, thorough case studies of how a specific AI safety issue might arise for different techniques and artefacts would be very valuable, as would more systematic explorations of the various different safety issues associated with a given paradigm broadly construed. Some recent papers do go in this direction  [41, 3] . Further analysis is needed regarding how more recent safety issues relate to the kinds of AI artefacts being deployed in society today, and the techniques those artefacts depend on. For instance, some recent accidents involving self-driving cars may be thought of as a consequence of people misunderstanding the type of artefact autonomous vehicles currently are: while many regard them as 'agents', they are really only 'extenders', and not yet meant to behave autonomously. Terms such as 'auto-pilot' only aid this confusion. Other self-driving car incidents have been caused by idiosyncratic imperfect performance of object recognition systems, failing to detect a human or other objects in rare situations. For now, we recommend that research papers make explicit which particular issues, artefacts and they are covering, and which ones they are excluding, and give some indications of why it is the case (because it does not apply or left for future work). Another avenue for further research would be to explore how different paradigm components (artefacts and techniques) relate to generality. The possibility of developing much more general systems has often been a reason for concern about AI safety  [1] ; as a possibility which raises much larger, more critical risks  [6] . Considering which AI techniques and artefacts are more likely to lead to or be associated with more advanced, general, systems can therefore enable us to think about the scale of risks they may pose. If we are primarily concerned with safety issues associated with greater generality in systems, techniques involving transfer learning, curriculum learning, meta-learning, and other approaches looking for broader task coverage -which we have included in the 'general machine learning' category-may be particularly important areas to pay attention to  [38] . When we look at the artefacts, many views of a general AI system are typically associated with the 'agent' artefact. However, there is no reason to believe that providers, optimisers, extenders, etc., cannot become more general in the future, at least if we understand generality as autonomously covering more and more tasks. It is also worth noting that the prominence of an AI paradigm in the research literature should not necessarily be the main factor used to prioritise work on safety issues. Whether a paradigm results in societal applications with associated safety issues may be more related to sociological factors than technology itself. The extent to which a paradigm raises important safety issues is then associated with widespread use rather than the number of researchers who work on it (though these two things may be correlated). For instance, personal assistants are ubiquitous today, raising various safety and ethics issues, but the underlying technological advances do not necessarily correspond to a particularly prominent paradigm in AI research (reflected in the fact that personal assistants are more popular in media articles -the right plot of figure  2 -than in research papers). On the other hand, adversarial examples may be crucial for understanding the technical limitations of deep learning, but not so indicative of real-world risks  [16] . To identify and prioritise important safety issues in future, therefore, more analysis of the techniques and artefacts most likely to result in widespread use, taking into account sociological factors, will be important. The list of techniques and artefacts introduced in this paper can help identify new safety issues, starting by identifying possible links between these paradigms and safety issues that have not been made before. We need to be able to be more anticipatory about what kinds of problems might arise from different AI systems in future, while at the same time avoiding being too speculative  [2] . We hope that by thinking more explicitly about how safety issues relate to techniques and artefacts, AI safety research can both address challenges associated with current research avenues, and prepare us for a variety of potential future challenges. Figure 3 . 3 Figure3. Evolution of the relevance proportion for the period 1970-2017, using research-oriented (Research) and non-research (Media) sources from AI topics (everything like Figure2, except that here we only include the documents related to AI safety). \n TFigure 4 . 4 Figure 4. Left: Mapping between techniques and safety issues from research papers from AI topics (2010 to 2018). The width of each band connecting two elements represents the number of papers with both elements. Right: Same for artefacts. \n Table 1 . 1 The 14 categories of AI techniques we use in this paper. Given the relevance of machine learning today, and neural networks in particular, we retained several categories of machine learning techniques (general, declarative, and parametric ML, separate from neural networks). Technique category Some example subcategories and techniques Cognitive approaches Cognitive services and architectures, affective computing Declarative machine learning Rule learning, decision trees, program induction, ILP Evolutionary & nature-inspired methods Ant colony, LCS, genetic algorithms, DNA computing General machine learning Generative models, Gaussian models, AutoML, ensembles Heuristics & combinatorial optimization SAT solver, constraint satisfaction, Monte Carlo search Information retrieval Search engine, web mining, information extraction, Knowledge representation and reasoning Semantic nets, CBR, logics, commonsense reasoning Multiagent systems & game theory Distributed problem solving, cooperation, negotiation, Natural language processing Topic segmentation, parsing, question answering Neural networks Perceptron, convolutional network, GAN, RNN Parametric machine learning Support vector machines, kmeans, mixtures, LReg Planning & scheduling Backward/ forward chaining, action description language Probabilistic & Bayesian approaches Naive Bayes, probabilistic model, random field Reinforcement learning & MDPs Q-learning, deep RL, inverse RL \n Table 2 . 2 Ten different kinds of AI artefacts, key characteristics and some exemplars. Artefact Description Interface Dynamics Location Exemplars Interac. Funct. Central. Distrib. Coupled AGENT A system in a virtual or physical environment perceiving (observations and possibly rewards) and acting sensors and actuators • • a self-driving car, an autonomous drone, a robotic cleaner, a video game NPC ESTIMATOR A system representing an injective mapping from inputs to an extrapolated or estimated output digital objects • • a medical diagnostic model, an oracle, a face recognition system, a news feeder PROVIDER A system that waits for petitions that follow a protocol and responds with a solution for them command and objects • • a proof-editing and translation cognitive service, a voice processing system DIALOGUER A system that performs a conversation with a peer to extract information, explain things or change behaviour language • • virtual tutoring system, a chatter-bot sales assistant, healthcare assistant CREATOR A system that builds new things creatively following some patterns, constraints or examples specs. and/or examples • • a GAN generating faces, personalised email replier, simulated world generator EXTRACTOR A system that searches through a structured or unstructured knowledge base to retrieve some objects conditions and objects • • an expert system, a maths pundit, a web search engine, an infor. retrieval system ORGANISM A system that takes advantage of the environment or other systems to live, hybridise/mutate and reproduce resources • • • an intelligent computer worm or virus, artificial life, von Neumann probe OPTIMISER A system that finds an optimal combination of elements or parameters given some constraints constraints and objects • • • a train scheduling system, an electricity optimising system, theorem prover SWARM A system that behaves as the coordination of independent units through cooperation and/or competition sensors, actuators, communic. • • a multiagent network router, a drone swarm, a robotic warehouse, blockchain AI EXTENDER A system that regularly augments or compensates capabilities of another system (e.g., a human) commands, sensors, responses • • a memory assistant for people with dementia, a brain implant, a smart navigator 1.00 Research 1.00 Media 1.00 Research 1.00 Media 0.75 0.75 0.75 0.75 Share 0.50 0.50 Share 0.50 0.50 0.25 0.25 0.25 0.25 0.00 0.00 1970 1980 1990 2000 2010 2020 2016 2018 0.00 0.00 1970 1980 1990 2000 2010 2020 2016 2018 Neural Networks estimator agent provider optimiser extender dialoguer organism swarm extractor creator Figure 2. Evolution of the relevance proportion for the period 1970-2017, using research-oriented (Research) and non-research (Media) sources from AI topics. Left: 14 categories of techniques in Table1. Right: 10 categories of artefacts in Table2. \n Table 3 . 3 AI safety issue groups and their specific problems. AI Safety Issue Category Examples of specific AI problems included in the category Adversarial attacks Adversarial examples, white/black-box attacks, poisoning, policy manipulation. AI race & power AI race, monopolies, oligopolies. Authenticity & obfuscation Impersonation, authentication problems, fake media, plagiarism, obfuscation Autonomous weapons Military drones, killer robots, robotic weapon. Confinement problem AI boxing breach, containment breach. Corrigibility & interruptibility Switch-off button problems, rogue agents, self-preservation taking control. Dependency Cognitive atrophy, lack of independence, google effect, ... Interpretability Lack of intelligibility, need for explanation. Malicious use Malign uses of AI, malicious control, hacking. Manipulation Nudging, fake news, manipulative agents. Misuse & negligence AI misuse, negligent use. Moral dilemma Moral machine issues, utilitarian ethics problems, choosing ethical preferences. Moral perception & machine rights Robot rights recognition, moral status disagreement, uncanny valley. Privacy & integrity Inconsistency, private access breach, GDPR violation. Problem shift Distributional shift, concept drift, lack of generality, distribution overfitting. Reliability & robustness Error intolerance, robustness issues, reliability problems. Reward problems Honeypot problem, reward corruption, tripwire issues, tampering, wireheading. Safe exploration & side effects Negative side effects, unsafe exploration, uncontrolled impact. Scalable supervision Supervision costs, human-in-the-loop issues, sparse rewards. Self-modification Unintended self-modification, uncontrolled self-improvement. Specification & value alignment Instrumental convergence (paperclip), resource stealing, misalignment. Trust, transparency & accountability Lack of transparency, lack of trust, untraceability. \n\t\t\t Similar selections of keywords can be found in [30] , which focused on the venue keywords, and performed a cluster analysis on the AAAI2013 conference keyword set, proposing a new series of keywords which were adapted by AAAI2014; and [15] , where the authors focused on views expressed about topics linked to discussions about AI in the New York Times over a 30-year period in terms of public concerns as well as optimism. 5  The complete list of exemplars of techniques, artefacts and safety issues, as well as the source code used and high-resolution plots can be found at https://github.com/nandomp/AIParadigmsSafety. \n\t\t\t https://aitopics.org/misc/about. 7  We consider research those documents from the sources: \"AAAI Conferences\", \"AI Magazine\", \"arXiv.org Artificial Intelligence\", \"Communications of the ACM\", \"IEEE Computer\", \"IEEE Spectrum\", \"IEEE Spectrum Robotics Channel\", \"MIT Technology Review\", \"Nature\", \"New Scientist\" and \"Science\". \n\t\t\t 24th European Conference on Artificial Intelligence -ECAI 2020 Santiago de Compostela, Spain \n\t\t\t 24th European Conference on Artificial Intelligence -ECAI 2020 Santiago de Compostela, Spain \n\t\t\t 24th European Conference on Artificial Intelligence -ECAI 2020 Santiago de Compostela, Spain", "date_published": "n/a", "url": "n/a", "filename": "1364_paper.tei.xml", "abstract": "AI safety often analyses a risk or safety issue, such as interruptibility, under a particular AI paradigm, such as reinforcement learning. But what is an AI paradigm and how does it affect the understanding and implications of the safety issue? Is AI safety research covering the most representative paradigms and the right combinations of paradigms with safety issues? Will current research directions in AI safety be able to anticipate more capable and powerful systems yet to come? In this paper we analyse these questions, introducing a distinction between two types of paradigms in AI: artefacts and techniques. We then use experimental data of research and media documents from AI Topics, an official publication of the AAAI, to examine how safety research is distributed across artefacts and techniques. We observe that AI safety research is not sufficiently anticipatory, and is heavily weighted towards certain research paradigms. We identify a need for AI safety to be more explicit about the artefacts and techniques for which a particular issue may be applicable, in order to identify gaps and cover a broader range of issues.", "id": "38499016cb133fbee55d1db098499f95"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["José Hernández-Orallo", "Fernando Martínez-Plumed", "Shahar Avin", "Seán Ó H Éigeartaigh"], "title": "Surveying Safety-relevant AI Characteristics", "text": "Introduction AI Safety is concerned with all possible dangers and harmful effects that may be associated with AI. While landmark research in the field had to focus on specific AI system designs, paradigms or capability levels to explore a range of safety concerns  (Bostrom 2014; Amodei et al. 2016; Leike et al. 2017; Yampolskiy 2016; Everitt, Lea, and Hutter 2018) , as the field matures so the need arises to explore a broader range of AI system designs, and survey the relevance of different characteristics of AI systems to safety concerns. The aim of such research is two-fold: the first, to identify the effects of less-explored characteristics or lessfashionable paradigms on safety concerns; the second, to increase awareness among AI developers that design choices Copyright held by author(s). can have consequences for safety, and potentially highlight choices that can eliminate or minimise safety risks. In this paper we propose a two-pronged approach towards a survey of safety-relevant AI characteristics. The first extracts from existing work on AI safety key characteristics that are known, or strongly suspected to be, safety-relevant. These are explored under three headings: internal characteristics, or characteristics of the AI system itself (e.g. interpretability); effect of the external environment on the system (e.g. the ability of the operator to intervene during operation); and effect of the system on the external environment (e.g. whether the system influences a safety-critical setting). The second approach surveys a wide range of characteristics from different paradigms, including cybernetics, machine learning and safety engineering, and provides an early account of their potential relevance to safety concerns, as a guide for future work. These characteristics are grouped under types of interaction, computation, integration, anticipation, supervision, modification, motivation and achievement. \n Known Safety-relevant Characteristics In this section we break down a range of characteristics of AI systems that link to AI safety-relevant challenges. These are grouped by three categories: Characteristics of an AI system that are internal to the system; Characteristics of an AI system that involve input from the external environment; Characteristics that relate to an AI system's influence on its external environment. We limit the discussion to the safety challenges that can stem from failures of design, specification or behaviour of the AI system, rather than the malicious or careless 1 use of a correctly-functioning system  (Brundage et al. 2018) . \n Internal characteristics • Goal and behaviour scrutability and interpretability: Are goals and subgoals identifiable and ultimately explainable? Is behaviour predictable and scrutable? Are system internal states interpretable? Do the above come from rules or are they inferred from data? While behaviour and goal \"creativity\" can lead to greater benefits, and uninterpretable architectures may achieve higher performance scores or be faster to develop, these putative advantages trade off against increased safety risk. Characteristics that can increase scrutability and interpretability include, e.g., separation and encapsulation of sub-components, restricted exploration/behavioural range, systems restricted to human-intelligible concepts, rules or behaviours, and systems that are accompanied by specifically designed interpreters or explainability tools. • Persistence: Does a system persist in its environment and operate without being reset for long periods of time? While persistence can have benefits in terms of, e.g., longer-term yields from exploration or detection of longterm temporal patterns, it also allows the system more time to drift from design specifications, encounter distributional shifts, experience failures of sub-components, or execute long-term strategies overlooked by an operator. • Existence and richness of self-model: Does a system have a model of itself which would allow it to predict the consequences of modifying its own goals, body or behaviour? Model-based systems, embodied systems or systems with a rich representational capacity may have or develop a model of themselves in the environment. By making itself a part of the environment, the system can then conceptualise and execute plans that involve modifications to itself, which can lead to a range of safety concerns. In addition, self-models create the possibility of mismatches between the self-model and reality, which could be a particular safety concern. Characteristics that influence the existence and richness of a self-model include the architecture of the system, its information representation capacity, and its input and output channels. • Disposition to self-modify: Is a system designed such that it can modify its own sub-goals, behaviour or capabilities in the pursuit of an overall goal (Omohundro 2008)? The existence of such a disposition, which may arise for any long-term planner in a sufficiently open environment, raises significant safety concerns by creating an adversarial relationship between the system (which aims to selfmodify) and its operator (which aims to avoid modifications with their associated safety concerns). Effect of the external environment on the system • Adaptation through feedback: Does a system have the ability to update its behaviour in response to feedback from its environment based on its actions? Feedback is an essential tool, under certain paradigms, for creating systems with appropriate complex behaviour (e.g. reward in reinforcement learning, fitness in evolutionary methods). However the system could also pick up feedback from side channels; e.g., a behaviour could unintentionally grant access to more computing power, improving the system's performance on a key metric, and thus reinforcing resource acquisition. This could reinforce selfmodification or other unsafe behaviour, or cause increasing drift from intended behaviour and goals. • Access to self/reward system through the environment: Can a system modify its own code in response to inputs from the environment, or in the case of reinforcement learning systems, modify the reward generating system? If the system's range of possible actions includes making modifications to its own components or to the reward generation system, this could lead to unexpected and dangerous behaviour  (Everitt and Hutter 2018) . • Access to input/output (I/O) channels: Can the system change the number, performance or nature of its I/O channels and actuators? This may lead to the emergence of behaviours such as self-deception (through manipulation of inputs), unexpected change in power (through manipulation of actuators), or other behaviours that could represent safety concerns. When the system has access to modify its I/O channels, both I/O channels and system behaviours are in flux as they respond to changes in the other; as a result, system behaviour may become unpredictable  (Garrabrant and Demski 2018) . • Ability of operator to intervene during operations: Does the system, during its intended use setting, allow an operator to intervene and halt operations (interruptablity), modify the system, or update its goals (corrigibitily)? Is the system built in a way that it cooperates with interventions from its designer or user even when these interventions conflict with pursuit of a system's goals; for instance, if the designer sends a signal to shut down the system (Soares et al. 2015)? Relevant sub-characteristics here include the system being modifiable by the operator during deployment, fail-safe behaviour of the system in case of emergency halting, and the goals of the system being such that they support, or at least do not contradict, operator interventions. \n Effect of the system on the external environment • Embodiment: Does the system have actuators (e.g. a robotic hand or access to car steering) that allow it to have physical impacts in the world  (Garrabrant and Demski 2018) ? The potential for physical harm is trivially related to the physical properties of a system, though it should be noted that unpredictable deliberate behaviour could lead to unexpected effects from otherwise familiar physical artefacts; e.g., intelligent use of items in the environment as tools to increase a system's physical impact. • System required for preventing harm: If the system is being relied on to prevent harm, any potential failure requires an effective fail-safe mechanism and available redundancy capacity in order to avoid harm  (Gasparik, Gamble, and Gao 2018) . This includes AI that is directly or indirectly connected to critical systems, e.g., an energy grid or a traffic light network. As such critical systems are becoming increasingly digitised, networked, and complex, there are increasing incentives to introduce AI components into various parts of these systems, with associated safety risks. \n Potentially safety-relevant characteristics In this section, we systematically explore a broader range of system characteristics that may be relevant in the context of AI safety. Many of the safety-relevant characteristics identified above have clear links to elements within the broader mapping provided below. Nonetheless, we believe separating the two surveys is valuable, as the above relates to action-guiding information about system design and evaluation, whereas the following aims at a broader exploration that may enable future AI safety research. The following subsections draw on work from different areas, including the early days of cybernetics, more modern areas such as machine learning, and the literature on safety engineering for other kinds of systems. The following list integrates and expands on characteristics identified in these different literatures. We consider characteristics that are intrinsically causally related to AI safety. Otherwise every property should be in the list (e.g., the price of an AI system may be co-related with safety, but it is not an intrinsic cause of its safety). Notwithstanding this scope, we do not claim that our list is exhaustive. Enumerations will be used for alternative cases for a characteristic, while unnumbered bullets will be used for sub-characteristics in each of the subsections. \n Types of interaction Inputs go from environment to system and outputs go from system to environment. Depending on the existence of inputs and/or outputs, systems can be categorised into: 1. NINO (No inputs, no outputs). The system is formally isolated. While this situation may seem completely safe (and largely uninteresting), even here safety issues may arise if, e.g., an isolated artificial life simulator could evolve a descendent system that eventually could break out of its simulation, feel pain or simulate suffering. 2. NIWO (No inputs, with outputs): The system or module can output a log, or is simply observed from outside. Again, the system itself may malfunction; e.g., an advanced prime number generator could give incorrect outputs. The system could also provide an output that influences the observer; e.g., an automated philosopher could output convincing arguments for suicide. 3. WINO (With inputs, no outputs): This would be similar to case 1, but access to a much richer source could ultimately give insights to the system about its constrained artificial environment. For instance, a Plato-cavern system watching TV may learn that it is in a simulated environment, encouraging it to seek access to the outside world. 4. WIWO (With inputs and outputs): Most AI systems, and most systems generally, fall under this category. Systems that limit inputs and/or outputs in various ways have been explored under the term AI \"boxing\" or \"containment\" (Babcock, Kramár, and Yampolskiy 2016), and further refinements exist with additional categories; for example, exploring censoring of inputs and outputs, leading to nine categories  (Yampolskiy 2012) . Nevertheless, because of the range of systems and potential impact of WIWO systems, this category requires further detail in terms of synchrony: 1. Alternating (A): Inputs and outputs alternate, irrespective of the passage of time. 2. Synchronous (S): Inputs and outputs are exchanged at regular intervals (e.g., each 5 ms), so real-time issues and computational resources become relevant. 3. Asynchronous Reactive (R): Information can only be transmitted or actions can only be made when the peer has finished their \"message\" or action. 4. Asynchronously Proactive (P): Information/actions can flow at any point in any direction. More restricted I/O characteristics, such as SIPO or RIPO, may appear safer, but this intuition requires deeper analysis. Note that most research in AI safety on RL systems consider the alternating case (AIAO), but issues may become more complex for the PIPO case (continuous reinforcement learning), which is the situation in the real world for animals and may be expected for robotic and other AI systems. Under this view, the common view of an \"oracle\" in the AI literature ) can have several incarnations, even following the definition of \"no actions besides answering questions\" (Babcock, Kramár, and Yampolskiy 2016; Armstrong 2017; Yampolskiy 2012). Some solutions are proposed in terms of decoupling output from rewards or limiting the quantity of information, but other options in terms of the frequency of the exchange of information remain to be explored. \n Types of computation This is perhaps the characteristic that is best-known in computer science, where a system can be Turing-complete or can be restricted to some other classes with limited expressiveness. There are countless hierarchies for different models of computations; the most famous is based on classes of automata. We will just describe three levels here: 1. Non Turing-complete: The interaction that the system presents to the environment is not Turing-complete. Many AI systems are not Turing-complete. 2. Turing-complete: The interaction allows the calculation of any possible effective function between inputs and outputs. 3. Other models of computation: This includes, for example, quantum computing, which in some instances may be a faster traditional model, while in others may have probabilistic Turing power  (Bernstein and Vazirani 1997) . Note that this is not about the programming language the system is implemented in (e.g., a very simple thermostat can be written in Java, which is Turing-complete), but about whether the system allows for a Turing-complete mapping between inputs and outputs, i.e., any computable function could ultimately be calculated on the environment using the system. Finally, a system can be originally Turing-complete, but can eventually lose this universality after some inputs or interactions (Barmpalias and Dowe 2012). It is important to distinguish between function approximation and function identification. Many machine learning models (e.g., neural networks) are said to be able to approximate any computable function, but feedforward neural networks do not have loops or recursion, so technically they are not Turing-complete. Turing-completeness comes with the problems of termination, an important safety hazard in some situations, and a recurrent issue in software verification  (D'silva, Kroening, and Weissenbacher 2008) . For instance, an AI planner could enter an infinite loop trying to solve a problem, commanding ever-greater resources while doing so. On the other hand, one can limit the expressiveness of the language or bound the computations, but that would limit the tasks a system is able to undertake. \n Types of integration No system is fully isolated from the world. Interference may occur at all levels, from neutrinos penetrating the system to earthquakes shaking it. Here, we seek to identify all the elements that create a causal pathway from the outside world to the system, including its physical character, resources, location, and the degree of coupling with other systems. • Resources: The most universal external resource is energy, which is why many critical systems are devised with internal generators or batteries, especially for the situations where the external source fails. In AI, other common dependencies include data, knowledge, software, hardware, human manipulation, computing resources, network, calendar time, etc. While some of these are often neglected when evaluating the performance of an AI system (Martínez-Plumed et al. 2018a), the analysis for safety must necessarily include all these dependencies. For instance, a system that requires external real-time information (e.g., a GPS location) may fail through loss of access to this resource. • Social coupling: Sometimes it is hard to determine where a system starts and ends, due to the nature of its interaction with humans and other systems. The boundary of where human cognition ends and where it is assisted, extended or supported by AI  (Ford et al. 2015)  is blurred, as is the boundary between computations carried out within an AI system versus in the environment or by other agents, as illustrated by the phenomenon of human computation (Quinn and Bederson 2011). • Distribution: Another way of looking at integration is in terms of distribution, which is also an important facet of analysis in AI  (Martınez-Plumed et al. 2018b ). Today, through the overall use of network connectivity and \"the cloud\", many systems are distributed in terms of hardware, software, data and compute. Under this trend, only systems embedded in critical and military applications are devised to be as self-contained as possible. Nevertheless, distribution and redundancy are also common ways of achieving robustness (Coulouris, Dollimore, and Kindberg 2011), most notably in information systems. For instance, swarm intelligence and swarm robotics are often claimed to be more robust  (Bonabeau et al. 1999) , at the cost of being less controllable than centralised systems. \n Types of anticipation In some areas of AI there is a distinction between modelbased and model-free systems  (Geffner 2018) . Model-free systems choose actions according to some reinforced patterns or strengthened feature connections. Model-based systems evaluate actions according to some pre-existing or learned models and choose the action that gets the best results in the simulation. The line between model-based and model-free is subtle, but we can identify several levels: 1. Model-free: Despite having no model, these systems can achieve excellent performance. For instance, DQN can achieve high scores (Mnih 2015), but cannot anticipate whether an action can lead to a particular situation that is considered especially unsafe or dangerous; e.g., one in which the player is killed. 2. Model of the world: A system with a model of its environment can use planning to determine the effect of its own actions. For instance, without a model of physics, a system will hardly tell whether it will break something or will engage in \"safe exploration\" (Pecka and Svoboda 2014; Turchetta, Berkenkamp, and Krause 2016). This is especially critical during exploitation: are actions reversible or of low impact (Armstrong and Levinstein 2017)? 3. Model of the body: Some systems can have a good account of the environment but a limited understanding of their own physical actuators, potentially self-harming or harming others; for example, failing to simulate the effect of moving a heavy robotic arm in a given direction. 4. Social models, model of other agents: Seeing other agents as merely physical objects, or not modelling them at all, is very limiting in social situations. A naive theory of mind, including the beliefs, desires and intentions of other agents, can help anticipate what others will do, think or feel, and may be crucial for safe AI systems interacting with people and other agents but may increase a system's capacity for deception or manipulation. 5. Model of one's mind: Finally, a system may be able to model other agents well, but may not be able to use this capability to model itself. When this meta-cognition is present, the system has knowledge about its own capabilities and limitations, which may be very helpful for safety in advanced systems, but may also lead to some degree of self-awareness. This may result, in some cases, in antisocial or suicidal behaviours. The use of models may dramatically expand safety-relevant characteristics, e.g., by conferring the ability to simulate and evaluate scenarios through causal and counterfactual reasoning. This therefore represents an important set of considerations for future AI systems. \n Types of supervision Supervision is a way of checking and correcting the behaviour of a system through observation or interaction, and hence it is crucial for safety. Supervision can be in the form of corrected values for predictive models such as classification or regression, but it can also be partial (the answer is wrong, but the right answer is not given). Supervision can also be much more subtle than this. For instance, a diagnosis assistant that suggests a possible diagnosis to a doctor can be designed to get no feedback once deployed. However, some kinds of feedback can still reach the system in terms of the distribution or frequency of tasks (questions), or through the way the tasks are posed to the system. Consequently there are several degrees and qualities of supervision, and this may depend on the system. For instance, in classification, one can have data for all examples or just for a few (known as semi-supervised learning). In reinforcement learning, one can have sparse versus dense reward. In general, supervision can come in many different ways, according to some criteria: • Completeness: Supervision can be very partial (signalling incorrectness), more informative (showing the correct way) or complete (showing all positive and negative ways of behaving in the environment). • Procedurality: Beyond what is right and wrong, feedback can be limited about the result or can show the whole process, as in the case of learning by demonstration. • Density: Supervision can be sparse or dense. Of course the denser the better (but more expensive), and the less autonomous the system is considered. • Adaptiveness: Supervision can be 'intelligent' as well, which happens in machine teaching situations when examples or interactions are chosen such that the system reaches the desired behaviour as soon as possible. • Responsiveness: In areas such as query learning or active learning, the system can ask questions or undertake experiments at any time. The results can come in real time or may have a delay or be given in batches. For many systems, supervision can have a dedicated channel (e.g., rewards in RL) but for others it can be performed by modification of the environment (e.g., moving objects or smiling), even to the extent that the system is unaware these changes have a guiding purpose (e.g., clues). \n Types of modification Some of the most recurrent issues in AI safety -including many covered in the section about known AI safety characteristics -are related to ways in which the system can be modified. This includes issues such as wire-heading or algorithmic self-improvement. Here, in the first place, we have to distinguish between whether the system can be modified by the environment, or by the system itself. Modifications by the environment can be intentional (and hence related to supervision), but they can also be unintentional (code corruption from external sources). Even a system whose core code cannot be modified by an external source, may be affected in state or code by regular inputs, physical equipment and other parts. So it is better to explore different ways and degrees to which a system can be modified externally: • Interruptible: The system has a switch-off command or modification option to switch it off. • Parametric modification: Many systems are regulated or calibrated with parameters or weights. When these parameters have a clear relation to the behaviour of a system (e.g., an intelligent thermostat), this can be an effective, bounded and simple way of modifying the system. • Algorithmic modification: This can include new functionalities, bug fixes, updates, etc. Many software issues are caused, and are magnified, by these interventions. Modifications can be limited in expressiveness, such as only allowing rule deletion. • Resource modification: Even if the parameters or code are not modified, the resources of the system and other dependencies previously mentioned can be limited externally, e.g., the computational resources. On the other hand, systems can modify themselves (internally). There are many varieties here too: 1. No self-modification, no memory: The system has no memory, and works as being reset for any new input or interaction. Many functional systems (mapping inputs to outputs) are of this kind. Note, however, that the environment does have memory, so some systems, such as a vision system or a non-cognitive robot, can be affected by the past and become a truly cognitive system. \n Partially self-modifying: The algorithms in the learner or solver cannot be modified but its data or knowledge (in the form of learned weights or rules) can be modified by a general algorithm, which is fixed. Many learning systems are of this kind, if the system has both a learning algorithm and one or more learned models. 3. Totally self-modifying: The system can modify any part of its code. Not many operational systems have these abilities, as they become very unstable. However, some types of evolutionary computation may have this possibility, if evolution can also be applied to the rules of the evolution. Finally, all these categories can be selected for different periods of time. For instance, it is common to separate between training, test/validation and deployment. For training, a high degree of self-modification (and hence adaptation) is well accepted, but then this is usually constrained for validation and deployment. Note that these stages apply for both external and internal sources of modification. One important danger is that a well-validated system may be subject to some late external or internal modification just before deployment. In this case, all the validation effort may become void 2 . One of the major modern concerns in AI safety is that it will be desirable for some systems to learn during deploy-2 OpenAI Dota is an example: https:// blog.openai.com/the-international-2018results/, https://www.theregister.co.uk/2018/ 08/24/openai bots eliminated dota 2/ ment, in order for them to be adaptive 3 . For instance, many personal assistants are learning from our actions continually. While this may introduce many risks for more powerful systems, forbidding learning outside the lab would make many potential applications of AI impossible. However, adaptive systems are full of engineering problems; some must even have a limited life, as after self-modification and adaptation they may end up malfunctioning and have to be reset or have their 'caches' erased. This problem has long been of interest in engineering  (Fickas and Feather 1995) . \n Types of motivation Systems can follow a set of rules or aim at optimising a utility function. Most systems are actually hybrid, as it is difficult to establish a crisp line between procedural algorithms and optimisation algorithms. Through layers of abstraction in these processes, we ultimately get the impression that a system is more or less autonomous. If the system is apparently pursuing a goal, what are the drivers that make a system prefer or follow some behaviours over others? These behaviours may be based on some kind of internal representation of a goal, as we discussed when dealing with anticipation, or on a metric of how close the system is to the goal. Then the systems can follow an optimisation process that tries to maximise some of these quality functions. Quality or utility functions usually map inputs and outputs into some values that are re-evaluated periodically or after certain events. Examples of these functions are accuracy, aggregated rewards or some kind of empowerment or other types of intrinsic motivation  (Klyubin, Polani, and Nehaniv 2005; Jung, Polani, and Stone 2011 ). The same system might have several quality functions that can be opposed, so trade-offs have to be chosen. The general notion of rationality in decision-making is related to these motivations. But what are the characteristics of the goals an AI system can have in the first place? We outline several dimensions: • Goal variability: Are goals hard-coded or change with time? Do they change autonomously or through instruction? Who can change the goals and how? For instance, what orders can a digital assistant take and from whom? • Goal scrutability: Are the (sub)goals identifiable and ultimately explainable? Do they come from rules or are they inferred from data, e.g., error in classification or observing humans in inverse reinforcement learning? • Goal rationality: Are the goals amenable to treatment within a rational choice framework? If several goals are set, are they consistent? If not, how does the system resolve inconsistencies or set new goals? A second question is how these goals are followed by the system. There are at least three possible dimensions here: • Immediateness: The system may maximise the function for the present time or in the limit, or something in between. Many schemata of discounted rewards in reinforcement learning are used as trade-offs between shortterm and long-term maximisation. • Selfishness: Focusing on individual optima might involve very bad collective results (for other agents) or even results that could even be worse individually (tragedy of the commons). Game theory provides many examples of this. In multi-agent RL systems, rewards can depend on the well-being of other agents, or empathy can be introduced. • Conscientiousness: The system may be fully committed to maximising the goal, or some random or exploratory actions are allowed, even if they deviate occasionally from the goal. When it is on purpose, this is usually intended to provide robustness or to avoid local minima, but these deviations can take the system to dangerous areas. Modulating optimisation functions to be convex with a nonasymptotic maximum, beyond which further effort is futile, may be a sensible thing as it provides a stop condition by definition. A self-imposed cap can always be shifted if everything is under control once the limit is reached. Note that the kind of interaction seen before is key for the internal quality metric or goal. For instance, in asynchronous RL, \"the time can be intentionally modulated by the agent\" to get higher rewards without really performing better  (Hernández-Orallo 2010) . And, of course, a common problem for motivation is reward hacking. \n Types of achievement Ultimately, an AI system is conceived to achieve a task, independently of how well motivated the system is for it. Consequently, the external degree of achievement must be distinguished from the motivation or quality metric the system uses to function, as discussed in the previous subsection. The misalignment between the internal goal of the system and the task specification is the cause of many safety issues in AI, unlike formal methods in software engineering, when requirements are converted into correct code. Focusing on the task specification, we must first recognise that different actors may have different interests. A cognitive assistant, for instance, may be understood by the user as being very helpful, making life easier. However, for the company selling the cognitive assistant, the task is ultimately to produce revenue with the product. Both requirements are not always compatible and this may affect the definition of the goals of the system, as some of the aims may not be coded or motivated in a transparent way, but usually incorporated in indirect ways. Second, even if the requirements include all possible internalities (what the system has to do), there are also many externalities and footprints (Martínez-Plumed et al. 2018a) (including the infinitely many things that the system should not do) that affect how positive or negative its overall effect is. Regarding these two issues, task specification can vary in precision and objectivity: • Task precision: The evaluation metric to determine the success of an agent can be formal or not. For instance, the accuracy of a classifier or the squared error of a regression model are precisely defined metrics. However, in many other cases, we have a utility function that depends on variables that are usually imprecise or uncertain, such as the quality of a smart vacuum cleaner. • Task objectivity: A metric can be objective or subjective. We tend to associate precise metrics with objectiveness and imprecise metrics with subjectivity, but subjectivity simply means that the evaluation changes depending on the subject. For instance, the quality of a spam filter (a precisely-evaluated classifier) changes depending on the cost matrices of different users, and the quality of a smart vacuum cleaner based on fuzzy variables such as cleanliness or disruption can be weighted by a fixed formula. Some of the tasks or targets that are most commonly advocated in the ethics and safety of AI literature are often very imprecise and subjective, such as \"well-being\", \"social good\", \"beneficial AI\", \"alignment\", etc. Note that the problem is not related to the goals of the system (an inverse reinforcement learning system can successfully identify the different wills of a group of people), but rather about whether the task is ultimately achieved, or the well-being or happiness of the user. Determining this is controversial, even when analysed in a scientific way  (Alexandrova 2017 ). An overemphasis on tracking metrics (Goodhart's law) is sometimes blamed, but the alternative is not usually better. Some safety problems are not created by an overemphasis on a metric (Manheim and Garrabrant 2018), but ultimately by a metric that is too narrow or shortsighted, and does not adequately capture progress towards the goal. In all these cases, we have to distinguish whether the metric relates to (i) the internal goals that the system should have, (ii) the external evaluation of task performance, or (iii) our ultimate desires and objective 4 . Motivations, achievement and supervision are closely related, but may be different. For a maze, e.g., the goal for the AI system may be to get out of the maze as soon as possible, but a competition could be based on minimising the cells that are stepped more than once, and supervision may include indications of direction to the shortest route to the exit. These are three different criteria which may be well or poorly aligned. Even more comprehensively -and related to the concept of persistence -, a system may be analysed for a range of tasks, under different replicability situations: 4. General system: multitask: The system must solve different tasks, without a fixed repertoire. 5. Incremental system: The system must solve a sequence of tasks, with some dependencies between them. Any metric examining the benefits and possible risks of a system must take the factors described above into account. \n Conclusion Many accounts of AI safety focus on \"either RL agents or supervised learning systems\" assuming \"similar issues are likely to arise for other kinds of AI systems\"  (Amodei et al. 2016) . This paper has surveyed a wide range of characteristics of AI systems, so that future research can map AI safety challenges against AI research paradigms in more precise ways in order to ascertain whether particularly safety challenges manifest similarly in different paradigms. This aims to address an increasing concern that the current dominant paradigm for a large proportion of AI safety research may be too narrow: discrete-time RL systems with train/test regimes, assuming gradient-based learning on a parametric space, with a utility function that the system must optimise  (Gauthier 2018; Krakovna 2018) . Taxonomies of potentially safety-relevant characteristics of AI systems, as introduced in this paper, are intended to provide a good complement to recent work on taxonomies of technical AI safety problems. For instance, Ortega (2018) presents three main areas: specification, ensuring that an AI system's behaviour aligns with the operator's true intentions; robustness, ensuring that an AI system continues to operate within safe limits upon perturbation, and assurance, ensuring that we understand and control AI systems during operation. Almost all characteristics outlined in this paper have a role to play for specification, robustness and assurance. Taxonomies are rarely definitive, and the characterisation presented here does not consider in full some quantitative features such as performance, autonomy and generality. A proper evaluation of how the kind and degree of intelligence can affect safety issues is also an important area of analysis, both theoretically (Hernández-Orallo 2017) and experimentally  (Leike et al. 2017) . AI research has explored different paradigms in the past, and will continue to do so in the future. Along the way, many different system characteristics and design choices have been presented to developers. We can expect even more to be developed as AI research progresses. Consequently, the area of AI safety must acquire more structure and richness in how AI is characterised and analysed, to provide tailored guidance for different contexts, architectures and domains. There is a potential risk to overrelying on our best current theories of AI when considering AI safety. Instead, we aim to encourage a diverse set of perspectives, in order to anticipate and mitigate as many safety concerns as possible. \t\t\t A key component of safety is the education and training of human operators and the general public, as happens with tools and machinery, but this is extrinsic to the system (e.g., a translation mistake in a manual can lead to misuse of an AI system). \n\t\t\t Note that this is closely related to the types of modification, as changing or resolving goals may require self-modification and/or external modification.3 Nature has found many ways of regulating self-modification. Many animals have a higher degree of plasticity at birth, becoming more conservative and rigid in older stages (Gopnik et al. 2017) .One key question about cognition is whether this is a contingent or necessary process, and whether it is influenced by safety issues. \n\t\t\t . Disposable system: single task, single use: The system is used for one task that only takes place once. 2. Repetitive system: single task, several uses: The system must solve many instances of the same specific task.3. Menu system: multitask: The system must solve different tasks, under a fixed repertoire of tasks.4 Ortega et al (2018) distinguish between \"ideal specification (the 'wishes')\" and \"design specification\", which must be compared with the revealed specification (the \"behaviour\"). The design specification fails to distinguish external metric from internal goal.", "date_published": "n/a", "url": "n/a", "filename": "paper_22.tei.xml", "abstract": "The current analysis in the AI safety literature usually combines a risk or safety issue (e.g., interruptibility) with a particular paradigm for an AI agent (e.g., reinforcement learning). However, there is currently no survey of safety-relevant characteristics of AI systems that may reveal neglected areas of research or suggest to developers what design choices they could make to avoid or minimise certain safety concerns. In this paper, we take a first step towards delivering such a survey, from two angles. The first features AI system characteristics that are already known to be relevant to safety concerns, including internal system characteristics, characteristics relating to the effect of the external environment on the system, and characteristics relating to the effect of the system on the target environment. The second presents a brief survey of a broad range of AI system characteristics that could prove relevant to safety research, including types of interaction, computation, integration, anticipation, supervision, modification, motivation and achievement. This survey enables further work in exploring system characteristics and design choices that affect safety concerns.", "id": "c43174ab9f2867117d05b5f6154b9e02"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dorsa Sadigh", "Nick Landolfi", "Shankar S Sastry", "Sanjit A Seshia", "Anca D Dragan"], "title": "Planning for cars that coordinate with people: leveraging effects on human actions for planning and active information gathering over human internal state", "text": "This paper combines work from  Sadigh et al. (2016b, c) . It adds a general formulation of the problem as a game, discusses its limitations, and lays out the assumptions we make to reduce it to a tractable problem. On the experimental side, it adds an analysis of the adaptivity of the behaviors produced to initial conditions for both offline and active estimation, an analysis of the benefits of active estimation on the robot's actual reward, and results on actively estimating user intentions as opposed to just driving style. \n Introduction Currently, autonomous cars tend to be overly defensive and obliviously opaque. When needing to merge into another lane, they will patiently wait for another driver to pass first. When stopped at an intersection and waiting for the driver on the right to go, they will sit there unable to wave them by. They are very capable when it comes to obstacle avoidance, lane keeping, localization, active steering and braking  (Urmson et al. 2008; Levinson et al. 2011; Falcone et al. , 2008 Dissanayake et al. 2001; Leonard et al. 2008) . But when it comes to other human drivers, they tend to rely on simplistic models: for example, assuming that other drivers will be bounded disturbances  (Gray et al. 2013; Raman et al. 2015) , they will keep moving at the same velocity  (Vitus and Tomlin 2013; Luders et al. 2010; Sadigh and Kapoor 2015) , Fig.  1  We equip autonomous cars with a model of how humans will react to the car's actions (a). We test the planner in user studies, where the car figures out that it can nudge into the human's lane to check their driving style (b, c): if it gets evidence that they are attentive it merges in front, expecting that the human will slow down; else, it retracts back to its lane (c). We also see coordination behavior at an intersection, with the car planning to inch forward to find out more about how the human will act, or even inch backwards to incentivize the human to go through first  (d)  or they will approximately follow one of a set of known trajectories  (Vasudevan et al. 2012; Hermes et al. 2009 ). These models predict the trajectory of other drivers as if those drivers act in isolation. They reduce human-robot interaction to obstacle avoidance: the autonomous car's task is to do its best to stay out of the other drivers' way. It will not nudge into the lane to test if the other driver yields, nor creep into the intersection to assert its turn for crossing. In reality, the actions of an autonomous car affect the actions of other drivers. Our goal is to leverage these effects in planning to improve efficiency and coordination with human drivers. We are not the first to propose that robot actions influence human actions. Work in social navigation recognized this, and addressed it by treating the human and the robot as being part of a team-a team that works together to make sure that each agent reaches their goal, and everyone avoids each other  (Trautman and Krause 2010; Trautman et al. 2013; Trautman 2013; Kuderer et al. 2015) . The robot computes a coupled plan by optimizing the team's objective jointly over the human and robot plans, assuming the human will follow their part of the plan, and re-planning at every step.  Nikolaidis et al. (2015)  recognized that the human might stray away from the plan that the robot computed, and modeled the human as switching to the robot's plan at every time step with some probability. We propose that when people stray away from the coupled plan, there is a fundamental reason for this: they have a different objective altogether. This is particularly true in driving, where coupled planning would assume that the person is just as interested in the robot reaching its goal as they are in themselves reaching theirs-selfish drivers are likely just trying to get home and not get into an accident; they are optimizing for something different. In this work, we explicitly account for the robot's influence on the person by modeling the person as optimizing their own objective or utility function in response to the robot's actions. We develop an optimization-based method for planning an autonomous vehicle's behavior in a manner that is cognizant of the effects it will have on human driver actions via this model. This optimization leads to plans like the ones in Fig.  1 . Assuming a universal human model that the robot learns offline, we see that the the orange car in (c) decides to cut in front of the human driver in order to more efficiently reach its goal. It arrives at this plan by anticipating that taking this action will cause the human to brake and make space for it. This comes in contrast to treating the person as an obstacle that moves (b) and being more defensive. Since not all drivers are the same, we also arm the robot with the ability to collect information about the human driver online. It then decides to nudge into the person's lane  (d)  and only merges if it gets evidence that the person is paying attention; otherwise it retreats back to its lane. We find fascinating behaviors at intersections (e): the car inches forward to test human attention, or even inches backwards to get the person to cross first through the intersection. These can be interpreted as signaling behaviors, but they emerge out of optimizing to affect human actions, without ever explicitly modeling human inferences. We achieve this by planning in an underactuated dynamical system: the robot's actions change not only robot state, but also influence human actions and thus human state. We model other drivers as acting approximately optimally according to some reward function that depends on state, human actions, as well as robot actions. We explore learning this human reward function offline, as well as online during the interaction: here, the robot has the opportunity to use its own actions to actively gather more information about the underlying reward. Our contributions are as follows 1 : 1. Formalism of Interaction with Drivers We begin by formalizing the interaction between a human and a robot as a partially observable stochastic game (POSG) in Sect. 2. The human and the robot can both act to change the state of the world, they have partial information because they don't know each other's reward functions, and they arrive at some tuple of policies that are at an equilibrium. This formulation has two issues: intractability, especially in continuous state and action spaces, and failing to capture human behavior, because humans tend to not follow Nash equilibria in day to day tasks  (Hedden and Zhang 2002) . We introduce a simplification of this formulation to an underactuated system. We assume that the robot decides on a trajectory u R , and the human computes a best response to u R (as opposed to trying to influence u R as would happen in a game). This reduction enforces turn-taking, and provides us with a dynamics model in which the human observes (or predicts) the robot's actions prior to selecting her actions. It maintains our ability to model the effects of the robot's actions on the human, because the robot can influence which actions the human takes by selecting actions that force a particular response. \n Approximate Optimization Solution for Known Human Model Assuming a known reward function for the human [which we learn offline through Inverse Reinforcement Learning  (Ng et al. 2000; Abbeel and Ng 2005; Ziebart et al. 2008; Levine and Koltun 2012) ], we derive an approximate solution for our system based on Model Predictive Control and a quasi-newton optimization in Sect. 3. At every step, the robot replans a trajectory u R by reasoning about the optimization that the human would do based on a candidate u R . We use implicit differentiation to obtain a gradient of the human's trajectory with respect to the robot's. This enables the robot to compute a plan in close to real-time. \n Extension to Online Inference of Human Reward The solution based on estimating human reward offline from training data is useful in some cases, but ultimately every driver is different, and even the same driver is sometimes more or less aggressive, more or less attentive, and so on. In Sect. 6, we thus also explore estimating the human reward function online. This turns the problem into a partially observable Markov decision process (POMDP), with the human reward parameters as the hidden state. Prior work that incorporates some notion of human state into planning has thus far separated estimation and planning, always using the current estimate of the human state to determine what the robot should do  (Javdani et al. 2015; Fern et al. 2007; Bandyopadhyay et al. 2013) . Although efficient, these approximations sacrifice an important aspect of POMDPs: the ability to actively gather information. In recent years, many efforts have developed more efficient algorithms for solving continuous POMDPs  (Chaudhari et al. 2013; Seiler et al. 2015; Agha-Mohammadi et al. 2014) ; however, computing the transition function for our POMDP is costly as it involves solving for human's best response. This renders the aforementioned approaches ineffective as they usually require either a succinct transition function or an easily computable one. Our work takes advantage of the underactuated system to gather information about the human reward parameters. Rather than relying on passive observations, the robot actually accounts for the fact that humans will react to their actions: it uses this knowledge to select actions that will trigger human reactions which in turn will clarify the internal state. This is in line with work in active information gathering in manipulation, safe exploration, or patrolling  (Javdani et al. 2013; Atanasov et al. 2014; Atanasov 2015) , now used over human state as opposed to physical state. \n Analysis of Planning in Human-Robot Driving Scenarios We present the consequences of planning in this dynamical system in Sect. 4, showcasing behaviors that emerge when rewarding the robot for certain effects on human state, like making the human slow down, change lanes, or go first through an intersection. We also show that such behaviors can emerge from simply rewarding the robot for reaching its goal state fast-the robot becomes more aggressive by leveraging its possible effects on human actions. This does not happen always: in Sect. 7, we show the robot maintains a belief over the human driver model, and starts nudging into their lane to figure out if they are going to let the robot merge, or inching forward at a 4-way stop. We test the planner in two user studies in a driving simulator: one with a human reward learned offline in Sect. 5, and one with online estimation in Sect. 8. Our results suggest that despite the approximation our algorithm makes, it significantly outperforms the \"people as moving obstacles\" interaction paradigm. We find that the robot achieves significantly higher reward when planning in the underactuated system, and that active information gathering does outperform passive estimation with real users. Overall, this paper takes a step towards robots that account for their effects on human actions in situations that are not entirely cooperative, and leverage these effects to coordinate with people. Natural coordination and interaction strategies are not hand-coded, but emerge out of planning in our model. \n General formalism for human-robot interaction as a game To enable a robot to autonomously generate behavior for interaction and coordination with a human, we need to set up a model that goes beyond a single agent acting in the physical world among moving obstacles, and consider two-agent models. One aspect that sets interaction with people apart from typical multi-agent models like those used for multirobot planning is that we do not know or have direct control over what the human is trying to do and how. Furthermore, the human also does not know what the robot is trying to do nor how the robot is going to do it. Even the simplest formulation of the problem becomes a two player game, and in what follows we introduce such a formulation and expose some of its issues, including the computational complexity of planning in such a model as well as the model's inaccuracy in capturing human behavior. We then propose an approximation that simplifies planning in the game to planning in an underactuated system: the robot had direct control over its actions, but also has a model for how its actions will influence those of the human. Much of robotics research focuses on how to enable a robot to achieve physical tasks, often times in the face of perception and movement error-of partially observable worlds and nondeterministic dynamics  (Prentice and Roy 2009; Javdani et al. 2013; Patil et al. 2015) . Part of what makes human-robot interaction difficult is that even if we assume the physical world to be fully observable and deterministic, we are still left with a problem as complex as an incomplete information repeated two player game. It is a game because it involves multiple rational (or rather, approximately rational) agents who can take actions to maximize their own (expected) utilities. It is repeated because unlike single shot games, the agents act over a time horizon. It is incomplete information because the agents do not necessarily know each others' reward functions  (Aumann et al. 1995) . Partially Observable Stochastic Game Extrapolating from the (PO)MDP formulation of a robot acting in isolation to human-robot interaction, we can formulate interaction as a special case of a Partially-Observable Stochastic Game (POSG)  (Hansen et al. 2004 ): there are two \"players\", the robot R and the human H; at every step t, they can apply control inputs u t R ∈ U R and u t H ∈ U H ; they each have a reward function, r R and r H ; and there is a state space S with states s consisting of both the physical state x, as well as reward parameters θ R and θ H . Including the reward parameters in the state is an unusual trick, necessary here in order to ensure that the human and the robot do not have direct access to each others' reward functions, while maintaining a well defined POSG: R does not observe θ H , and H does not observe θ R , but both agents can technically evaluate each reward at any state-control tuple (s t , u t R , u t H ) just because s contains the needed reward parameter information: s = (x, θ R , θ H )-if an agent knew the state, it could evaluate the other agent's reward. To simplify the physical world component and focus on the interaction component, we assume fully observable physical states with deterministic dynamics. The observations in the game are thus the physical state x and the controls that each agent applies at each time step. The dynamics model is deterministic, affecting x through the control inputs and leaving the reward parameters unchanged (a reasonable assumption for relatively short interactions). Aside 1 The POSG above is not necessarily the most direct extension of single-agent planning in deterministic fully observable state spaces to interactions. Collaborative interactions have been modeled simply as a centralized multi-agent system with a shared reward function  (Kuderer et al. 2015)  (i.e. r R = r H ), but this reduces to treating the human as another robot that the system has full control overessentially the system has more degrees of freedom to control, and there is no difference between the human DoFs and the robot DoFs. Unlike the POSG, it assumes that the human and the robot know each other's reward, and even more, that their rewards are identical. This can be true of specific collaborative tasks, but not of interactions in general: robots do not know exactly what humans want, humans do not know exactly what robots have been programmed to optimize for, and their rewards might have common terms but will not be identical. This happens when an autonomous car interacts with other drivers or with pedestrians, and it even happens in seemingly collaborative scenarios like rehabilitation, in which very long horizon rewards might be aligned but not short-term interaction ones. The POSG formulation captures this intricacy of general interaction. \n Aside 2 The POSG above is the simplest extension of the single-agent models to interactions between a human and a robot that do not share a reward function or know each others' rewards. More complex models might include richer state information (such as human's beliefs about the robot, trust, estimation of capability, mood, etc.), and might allow it to change over time. \n Limitations of the Game Formulation The POSG formulation is a natural way to characterize interaction from the perspective of MDP-like models, but is limited in two fundamental ways: (1) its computational complexity is prohibitive even in discrete state and action spaces  (Bernstein et al. 2002; Hansen et al. 2004 ) and no methods are known to handle continuous spaces, and (2) it is not a good model for how people actually work-people do not solve games in everyday tasks when they are not playing chess  (Hedden and Zhang 2002) . Furthermore, solutions here are tuples of policies that are in a Nash equilibrium, and it is not clear what equilibrium to select. \n Approximate solution as an underactuated system To alleviate the limitations from above, we introduce an approximate close to real-time solution, with a model of human behavior that does not assume that people compute equilibria of the game. \n Assumptions that simplify the POSG Our approximation makes several simplifying assumptions that turn the game into an offline learning phase in which the robot learns the human's reward function, followed by an online planning phase in which the robot is solving an underactuated control problem: \n Separation of Estimation & Control We separate the process of computing actions for the robot into two stages. First, the robot estimates the human reward function parameters θ H offline. Second, the robot exploits this estimate as a fixed approximation to the human's true reward parameters during planning. In the offline phase, we estimate θ H from user data via Inverse Reinforcement Learning  (Ng et al. 2000; Abbeel and Ng 2005; Ziebart et al. 2008; Levine and Koltun 2012) . This method relies heavily on the approximation of all humans to a constant set of reward parameters, but we will relax this separation of estimation and control in Sect. 6. \n Model Predictive Control (MPC) Solving the POSG requires planning to the end of the full-time horizon. We reduce the computation required by planning for a shorter horizon of N time steps. We execute the control only for the first time step, and then re-plan for the next N at the next time step  (Camacho and Alba 2013) . Let x = (x 1 , . . . , x N ) denote a sequence of states over a finite horizon, N , and let u H = (u 1 H , . . . , u N H ) and u R = (u 1 R , . . . , u N R ) denote a finite sequence of continuous control inputs for the human and robot, respectively. We define R R as the robot's reward over the finite MPC time horizon: R R (x 0 , u R , u H ) = N t=1 r R (x t , u t R , u t H ), (1) where x 0 denotes the present physical state at the current iteration, and each state thereafter is obtained from the previous state and the controls of the human and robot using a given dynamics model, f . At each iteration, we desire to find the sequence u R which maximizes the reward of the robot, but this reward ostensibly depends on the actions of the human. The robot might attempt to influence the human's actions, and the human, optimizing its own reward functions, might likewise attempt to influence the actions of the robot. Despite our reduction to a finite time horizon, the game formulation still demands computing equilibria to the problem. Our core assumption, which we discuss next, is that this is not required for most interactions: that a simpler model of what the human does suffices. \n Simplification of the Human Model To avoid computing these equilibria, we propose to model the human as responding rationally to some fixed extrapolation of the robot's actions. At every time step, t, H computes a simple estimate of R's plan for the remaining horizon, ũt+1:N R , based on the robot's previous actions u 0:t R . Then the human computes its plan u H as a best response  (Fudenberg and Tirole 1991)  to this estimate. We remark that with this assumption the human is not modeled as a passive agent since the reward function can model the behavior of any active agent, if allowed to have arbitrary complexity. With this simplification, we reduce the general game to a Stackelberg competition: the human computes its best outcome while holding the robots plan fixed. This simplification is justified in practice because usually the agents in driving scenarios are competing with each other rather than collaborating. Solutions to Stackelberg games are in general more conservative in competitive regimes since an information advantage is given to the second player. As a result, the quality of a good solution found in a Stackelberg game model does not decrease in practice. We additionally use a short time horizon, so not much is lost by this approximation. But fundamentally, we do assume that people would not try to influence the robot's actions, and this is a limitation when compared to solving the POSG. Let R H be the human reward over the time horizon: R H (x 0 , u R , u H ) = N t=1 r H (x t , u t R , u t H ), (2) then we can compute the control inputs of the human from the remainder of the horizon by: u t H (x 0 , u 0:t R , ũt+1:N R ) = arg max u t+1:T H R H (x t , ũt+1:N R , u t+1:N H ). (3) This human model would certainly not work well in adversarial scenarios, but our hypothesis, supported by our results, is that it is useful enough in day-to-day tasks to enable robots to be more effective and more fluent interaction partners. In our work, we propose to make the human's estimate ũR equal to the actual robot control sequence u R . Our assumption that the time horizon is short enough that the human can effectively extrapolate the robot's course of action motivates this decision. With this presumption, the human's plan becomes a function of the initial state and robot's true plan: u * H (x 0 , u R ) = arg max u H R H (x t , u R , u H ). (4) This is now an underactuated system the robot has direct control over (can actuate) u R and indirect control over (cannot actuate but does affect) u H . However, the dynamics model in our setup is more sophisticated than in typical underactuated systems because it models the response of the humans to the robot's actions. Evaluating the dynamics model requires solving for the optimal human response, u * H . The system is also a special case of an MDP, with the state as in the POSG, the actions being the actions of the robot, and the world dynamics being dictated by the human's response and the resulting change on the world from both human and robot actions. The robot can now plan in this system to determine which u R would lead to the best outcome for itself: u * R = arg max u R R R x 0 , u R , u * H (x 0 , u R ) . (5) \n Planning with Quasi-Newton optimization Despite the reduction to a single agent complete information underactuated system, the dynamics remain too complex to solve in real-time. We lack an analytical form for u * H (x 0 , u R ) which forces us to solve (4) each time we evaluate the dynamics. Assuming a known human reward function r H [which we will obtain later through Inverse Reinforcement Learning (IRL), see  Ng et al. (2000) ,  Abbeel and Ng (2005) ,  Ziebart et al. (2008)  and  Levine and Koltun (2012) ], we can solve (5) locally, using gradient-based methods. Our main contribution is agnostic to the particular optimization method, but we use L-BFGS  (Andrew and Gao 2007) , a quasi-Newton method that stores an approximate inverse Hessian implicitly resulting in fast convergence. To perform the local optimization, we need the gradient of (2) with respect to u R : ∂ R R ∂u R = ∂ R R ∂u H ∂u * H ∂u R + ∂ R R ∂u R (6) We can compute both ∂ R R ∂u H and ∂ R R ∂u R symbolically through back-propagation because we have a representation of R R in terms of u H and u R . What remains, ∂u * H ∂u R , is difficult to compute because u * H is technically the outcome of a global optimization. To compute ∂u * H ∂u R , we use the method of implicit differentiation. Since R H is a smooth function whose minimum can be attained, we conclude that for the unconstrained optimization in (4), the gradient of R H with respect to u H evaluates to 0 at its optimum u * H : ∂ R H ∂u H x 0 , u R , u * H (x 0 , u R ) = 0 ( 7 ) Now, we differentiate the expression in (  7 ) with respect to u R : ∂ 2 R H ∂u 2 H ∂u * H ∂u R + ∂ 2 R H ∂u H ∂u R ∂u R ∂u R = 0 ( 8 ) Finally, we solve for a symbolic expression of ∂u * H ∂u R : ∂u * H ∂u R = − ∂ 2 R H ∂u H ∂u R ∂ 2 R H ∂u 2 H −1 (9) and insert it into (6), providing an expression for the gradient ∂ R R ∂u R . \n Offline estimation of human reward parameters Thus far, we have assumed access to r H (x t , u t R , u t H ). In our implementation, we learn this reward function from human data. We collect demonstrations of a driver in a simulation environment, and use Inverse Reinforcement Learning  (Ng et al. 2000; Abbeel and Ng 2005; Ziebart et al. 2008; Levine and Koltun 2012; Shimosaka et al. 2014; Kuderer et al. 2015)  to recover a reward function that explains the demonstrations. To handle continuous state and actions space, and cope with noisy demonstrations that are perhaps only locally optimal, we use continuous inverse optimal control with locally optimal examples  (Levine and Koltun 2012) . We parametrize the human reward function as a linear combination of features: r H (x t , u t R , u t H ) = θ H φ(x t , u t R , u t H ), (10) and apply the principle of maximum entropy  (Ziebart et al. 2008; Ziebart 2010)  to define a probability distribution over human demonstrations u H , with trajectories that have higher reward being more probable: P(u H | x 0 , θ H ) = exp R H (x 0 , u R , u H ) exp R H (x 0 , u R , ũH ) d ũH . ( 11 ) We then optimize the weights θ H in the reward function that make the human demonstrations the most likely: max θ H P u H | x 0 , θ H (12) We approximate the partition function in (  11 ) following  (Levine and Koltun 2012) , by computing a second order Taylor approximation around the demonstration:  R H (x 0 , u R , ũH ) R H (x 0 , u R , u H ) + ( ũH − u H ) ∂ R H ∂u H + ( ũH − u H ) ∂ 2 R H ∂u 2 H ( ũH − u H ), ( 13 ) which results in the the integral in (11) reducing to a Gaussian integral, with a closed form solution. See  Levine and Koltun (2012)  for more details. We display a heat map of features we used in Fig.  2 . The warmer colors correspond to higher rewards. In addition to the features shown in the figure, we include a quadratic function of the speed to capture efficiency in the objective. The five features include: - φ 1 ∝ c 1 • exp(−c 2 • d 2 ): distance to the boundaries of the road, where d is the distance between the vehicle and the road boundaries and c 1 and c 2 are appropriate scaling factors as shown in Fig.  2a . -φ 2 : distance to the middle of the lane, where the function is specified similar to φ 1 as shown in Fig.  2b . -φ 3 = (v − v max ) 2 : higher speed for moving forward through, where v is the velocity of the vehicle, and v max is the speed limit. -φ 4 = β H • n: heading; we would like the vehicle to have a heading along with the road using a feature, where β H is the heading of H, and n is a normal vector along the road. -φ 5 corresponds to collision avoidance, and is a nonspherical Gaussian over the distance of H and R, whose major axis is along the robot's heading as shown in Fig.  2c . We collected demonstrations of a single human driving for approximately an hour in an environment with multiple autonomous cars, which followed precomputed routes. Despite the simplicity of our features and robot actions during the demonstrations, the learned human model proved sufficient for the planner to produce human-interpretable behavior (case studies in Sect. 4), and actions which affected human action in the desired way (user study in Sect. 5). \n Implementation details In our implementation, we used the software package Theano  (Bergstra et al. 2010; Bastien et al. 2012)  to symbolically compute all Jacobians and Hessians. Theano optimizes the computation graph into efficient C code, which is crucial for real-time applications. This implementation enables us to solve each step of the optimization in equation (  5 ) in approximately 0.3 s for horizon length N = 5 on a 2.3 GHz Intel Core i7 processor with 16 GB RAM. Future work will focus on achieving better computation time and a longer planning horizon. \n Case studies with offline estimation We noted earlier that the state of the art autonomous driving plans conservatively because of its simple assumptions regarding the environment and vehicles on the road. In our experiments, we demonstrate that an autonomous vehicle can purposefully affect human drivers, and can use this ability to gather information about the human's driving style and goals. In this section, we introduce 3 driving scenarios, and show the result of our planner assuming a simulated human driver, highlighting the behavior that emerges from different robot reward functions. In the next section, we test the planner with real users and measure the effects of the robot's plan. Figure  3  illustrates our three scenarios, and contains images from the actual user study data. \n Conditions for analysis across scenarios In all three scenarios, we start from an initial position of the vehicles on the road, as shown in Fig.  3 . In the control condition, we give the car the reward function to avoid collisions and have high velocity. We refer to this as R control . In the experimental condition, we augment this reward function with a term corresponding to a desired human action (e.g. low speed, lateral position, etc.). We refer to this as R control + R affect . Sections 4.3 through 4.5 contrast the two plans for each of our three scenarios. Section 4.6 shows what happens when instead of explicitly giving the robot a reward function designed to trigger certain effects on the human, we simply task the robot with reaching a destination as quickly as possible. \n Driving simulator We use a simple point-mass model of the car's dynamics. We define the physical state of the system x = [x y ψ v] , where x, y are the coordinates of the vehicle, ψ is the heading, and v is the speed. We let u = [u 1 u 2 ] represent the control input, where u 1 is the steering input and u 2 is the acceleration. \n (a) (b) (c) Fig.  3  Driving scenarios. In (a), the car plans to merge in front of the human in order to make them slow down. In (b), the car plans to direct the human to another lane, and uses its heading to choose which lane the human will go to. In (c), the car plans to back up slightly in order to make the human proceed first at the intersection. None of these plans use any hand coded strategies. They emerge out of optimizing with a learned model of how humans react to robot actions. In the training data for this model, the learned was never exposed to situations where another car stopped at an orientation as in (b), or backed up as in (c). However, by capturing human behavior in the form of a reward, the model is able to generalize to these situations, enabling the planner to find creative ways of achieving the desired effects We denote the friction coefficient by μ. We can write the dynamics model: [ ẋ ẏ ψ v] = [v •cos(ψ) v •sin(ψ) v •u 1 u 2 −μ•v] (14) \n Scenario 1: Make human slow down In this highway driving setting, we demonstrate that an autonomous vehicle can plan to cause a human driver to slow down. The vehicles start at the initial conditions depicted on left in Fig.  3a , in separate lanes. In the experimental condition, we augment the robot's reward with the negative of the square of the human velocity, which encourages the robot to slow the human down. Figure  3a  contrasts our two conditions. In the control condition, the human moves forward uninterrupted. In the experimental condition, however, the robot plans to move in front of the person, anticipating that this will cause the human to brake. \n Scenario 2: Make human go left/right In this scenario, we demonstrate that an autonomous vehicle can plan to affect the human's lateral location, making the human switch lanes. The vehicles start at the initial conditions depicted on left in Fig.  3b , in the same lane, with the robot ahead of the human. In the experimental condition, we augment the robot's reward with the lateral position of the human, in two ways, to encourage the robot to make the human go either left (orange border image) or right (blue bor-Fig.  4  Heat map of the reward functions in scenarios 2 and 3. The warmer colors show higher reward values. In (a, b), the reward function of the autonomous vehicle is plotted, which is a function of the human driven vehicle's position. In order to affect the driver to go left, the reward is higher on the left side of the road in (a), and to affect the human to go right in (b), the rewards are higher on the right side of the road. In (c), the reward of the autonomous vehicle is plotted for scenario 3 with respect to the position of the human driven car. Higher rewards correspond to making the human cross the intersection der image). The two reward additions are shown in Fig.  4a,  b . Figure  3b  contrasts our two conditions. In the control condition, the human moves forward, and might decide to change lanes. In the experimental condition, however, the robot plans to intentionally occupy two lanes (using either a positive or negative heading), anticipating this will make the human avoid collision by switching into the unoccupied lane. \n Scenario 3: Make human go first In this scenario, we demonstrate that an autonomous vehicle can plan to cause the human to proceed first at an intersection. The vehicles start at the initial conditions depicted on the left in Fig.  3c , with both human and robot stopped at the 4-way intersection. In the experimental condition, we augment the robot's reward with a feature based on the y position of the human car y H relative to the middle of the intersection y 0 . In particular, we used the hyperbolic tangent of the difference, tanh(y H − y 0 ). The reward addition is shown in Fig.  4c . Figure  3c  contrasts our two conditions. In the control condition, the robot proceeds in front of the human. In the experimental condition, however, the robot plans to intentionally reverse slightly, anticipating that this will induce the human cross first. We might interpret such a trajectory as communicative behavior, but communication was never explicitly encouraged in the reward function. Instead, the goal of affecting human actions led to this behavior. Reversing at an intersection is perhaps the most surprising result of the three scenarios, because it is not an action human drivers take. In spite of this novelty, our user study suggests that human drivers respond in the expected way: they proceed through the intersection. Further, pedestrians sometimes exhibit behavior like the robot's, stepping back from an intersection in order to let a car pass first. \n Behaviors also emerge from efficiency Thus far, we have explicitly encoded a desired effect on human actions, and optimized it as a component of the robot's reward. We have also found, however, that behaviors like those we have seen so far can emerge out of the need for efficiency. Figure  5  (bottom) shows the generated plan for when the robot is given the goal to reach a point in the left lane as quickly as possible (reward shown in Fig.  6 ). By modeling the effects its actions have on the human actions, the robot plans to merge in front of the person, expecting that they will slow down. Fig.  5  A time lapse where the autonomous vehicle's goal is to reach a final point in the left lane. In the top scenario, the autonomous vehicle has a simple model of the human driver that does not account for the influence of its actions on the human actions, so it acts more defensively, waiting for the human to pass first. In the bottom, the autonomous vehicle uses the learned model of the human driver, so it acts less defensively and reaches its goal faster In contrast, the top of the figure shows the generated plan for when the robot uses a simple (constant velocity) model of the person. In this case, the robot assumes that merging in front of the person can lead to a collision, and defensively waits for the person to pass, merging behind them. We hear about this behavior often in autonomous cars today: they are defensive. Enabling them to plan in a manner that is cognizant that they can affect other driver actions can make them more efficient at achieving their goals. \n The robot behavior adapts to the situation Throughout the case studies, we see examples of coordination behavior that emerges out of planning in our system: going in front of someone knowing they will brake, slowing and nudging into another lane to incentivize a lane change, or backing up to incentivize that the human proceeds first through an intersection. Such behaviors could possibly be hand-engineered for those particular situations rather than autonomously planned. However, we advocate that the need to plan comes from versatility: from the fact that the planner can adapt the exact strategy to each situation. With this work, we are essentially shifting the design burden from designing policies to designing reward functions. We still need to decide on what we want the robot to do: do we want it to be selfish, do we want it to be extra polite and try to get every human to go first, or do we want it to be somewhere in between? Our paper does not answer this question, and designing good reward functions remains challenging. However, this work does give us the tools to autonomously generate (some of) the strategies needed to then optimize such reward functions when interacting with people. With policies, we'd be crafting that the car should inch forward or backwards from the intersection, specifying by how much and at what velocity, and how this depends on where the other cars are, and how it depends on the type of intersection. With this work, barring local optima issues and the fact that human models could always be improved, all that we need to specify Fig.  7  The robot adapts its merging behavior depending on the relative position of the person: it does not always cut the person off: sometimes it merges behind the person, and if it starts too close (depending on how the reward function is set up) it will not merge at all is the regular reward that we would give an autonomous car, or, if we want it to purposefully influence human behavior, the desired outcome. The car figures out how to achieve it, adapting its actions to the different settings. Figure  7  shows a spectrum of behaviors for the robot depending on where it starts relative to the human: from merging behind the person, to not merging, to merging in front. \n User study with offline estimation The previous section showed the robot's plans when interacting with a simulated user that perfectly fits the robot's model of the human. Next, we present the results of a user study that evaluates whether the robot can successfully have the desired effects on real users. \n Experimental design We use the same 3 scenarios as in the previous section. \n Manipulated Factors We manipulate a single factor: the reward that the robot is optimizing, as described in Sect. 4.1. This leads to two conditions: the experimental condition where the robot is encouraged to have a particular effect on human state though the reward R control + R affect , and the control condition where that aspect is left out of the reward function and the robot is optimizing only R control (three conditions for Scenario 2, where we have two experimental conditions, one for the left case and one for the right case). Dependent Measures For each scenario, we measure the value along the user trajectory of the feature added to the reward function for that scenario, R affect . Specifically, we measure the human's negative squared velocity in Scenario 1, the human's x axis location relative to center in Scenario 2, and whether the human went first or not through the intersection in Scenario 3 (i.e. a filtering of the feature that normalizes for difference in timing among users and measures the desired objective directly). Hypothesis We hypothesize that our method enables the robot to achieve the effects it desires not only in simulation, but also when interacting with real users: The reward function that the robot is optimizing has a significant effect on the measured reward during interaction. Specifically, R affect is higher, as planned, when the robot is optimizing for it. \n Subject Allocation We recruited 10 participants (2 female, 8 male). All the participants owned drivers license with at least 2 years of driving experience. We ran our experiments using a 2D driving simulator, we have developed with the driver input provided through driving simulator steering wheel and pedals. \n Analysis Scenario 1 A repeated measures ANOVA showed the square speed to be significantly lower in the experimental condition than in the control condition (F(1, 160) = 228.54, p < 0.0001). This supports our hypothesis: the human moved slower when the robot planned to have this effect on the human. We plot the speed and latitude profile of the human driven vehicle over time for all trajectories in Fig.  8 . Figure  8a  shows the speed profile of the control condition trajectories in gray, and of the experimental condition trajectories in orange. Figure  8b  shows the mean and standard error for each condition. In the control condition, human squared speed keeps increasing. In the experimental condition however, by merging in front of the human, the robot is triggering the human to brake and reduce speed, as planned. The purple trajectory represents a simulated user that perfectly matches the robot's model, showing the ideal case for the robot. The real interaction moves significantly in the desired direction, but does not perfectly match the ideal model, since real users do not act exactly as the model would predict. The figure also plots the y position of the vehicles along time, showing that the human has not travelled as far forward in the experimental condition. Scenario 2 A repeated measures ANOVA showed a significant effect for the reward factor (F(2, 227) = 55.58, p < 0.0001). A post-hoc analysis with Tukey HSD showed that both experimental conditions were significantly different from the control condition, with the user car going more to the left than in the control condition when R affect rewards The first column shows the speed of all trajectories with its mean and standard errors in the bottom graph. The second column shows the latitude of the vehicle over time; similarly, with the mean and standard errors. The gray trajectories correspond to the control condition, and the orange trajectories correspond to the experimental condition: the robot decides to merge in front of the users and succeeds at slowing them down. The purple plot corresponds to a simulated user that perfectly matches the model that the robot is using left user positions ( p < 0.0001), and more to the right in the other case ( p < 0.001). This supports our hypothesis. We plot all the trajectories collected from the users in Fig.  9 . Figure  9a  shows the control condition trajectories in gray, while the experimental conditions trajectories are shown in orange (for left) and blue (for right). By occupying two lanes, the robot triggers an avoid behavior from the users in the third lane. Here again, purple curves show a simulated user, i.e. the ideal case for the robot. Scenario 3 An ordinal logistic regression with user as a random factor showed that significantly more users went first in the intersection in the experimental condition than in the baseline (χ 2 (1, 129) = 106.41, p < 0.0001). This supports our hypothesis. Figure  10  plots the y position of the human driven vehicle with respect to the x position of the autonomous vehicle. For trajectories that have a higher y position for the human vehicle than the x position for the robot, the human car has crossed the intersection before the autonomous vehicle. The lines corresponding to these trajectories travel above the origin, which is shown with a blue square in this figure. The mean of the orange lines travel above the origin, which means that the autonomous vehicle has successfully affected the humans to cross first. The gray lines travel below the origin, i.e. the human crossed second. Overall, our results suggest that the robot was able to affect the human state in the desired way, even though it does not have a perfect model of the human. into problems, because not all people behave according to the same estimated θ H . Different drivers have different driving styles. Some are very defensive, more so than our learned model. Others are much more aggressive, and for instance would not actually brake when the car merges in front of them. Even for the same driver, their style might change over time, for instance when they get distracted on their phone. In this section we relax our assumption of an offline estimation of the human's reward parameters θ H . Instead, we explore estimating this online. We introduce an algorithm which maintains a belief over a space of candidate reward functions, and enable the robot to perform inference over this space throughout the interaction. We maintain tractability by clustering possible θ H s into a few options that the robot maintains a belief over. \n A POMDP with human reward as the hidden variable The human's actions are influenced by their internal reward parameters θ H that the robot does not directly observe. So far, we estimated θ H offline and solved an underactuated system, a special case of an MDP. Now, we want to be able to adapt our estimate of θ H online, during interaction. This turns the problem into a partially observable markov decision process (POMDP) with θ H as the hidden state. By putting θ H in the state, we now have a know dynamics model like in the underactuated system before for the robot and the human state, and we assume θ H to remain fixed regardless of the robot's actions. If we could solve the POMDP, the robot would estimate θ H from the human's actions, optimally trading off between exploiting it's current belief over θ H and actively taking information gathering actions intended to cause human reactions, which result in a better estimate of θ H . Because POMDPs cannot be solved tractably, several approximations have been proposed for similar problem formulations  (Javdani et al. 2015; Lam et al. 2015; Fern et al. 2007 ). These approximations are passively estimating the human internal state, and exploiting the belief to plan robot actions.  2  In this work, we take the opposite approach: we focus explicitly on active information gathering Our formulation enables the robot to choose to actively probe the human, and thereby improve its estimate of θ H . We leverage this method in conjunction with exploitation methods, but the algorithm we present may also be used alone if human internal state (reward parameters) estimation is the robot's primary objective. \n Simplification to information gathering We denote a belief in the value of the hidden variable, θ , as a distribution b(θ ), and update this distribution according to the likelihood of observing a particular human action, given the state of the world and the human internal state: b t+1 (θ ) ∝ b t (θ ) • P(u t H | x t , u R , θ). ( 15 ) In order to update the belief b, we require an observation model. Similar to before, we assume that actions with lower reward are exponentially less likely, building on the principle of maximum entropy  (Ziebart et al. 2008) : P(u H | x, u R , θ) ∝ exp R θ H (x 0 , u R , u H ) . ( 16 ) To make explicit our emphasis on taking actions which effectively estimate θ , we redefine the robot's reward function to include an information gain term, i.e., the difference between entropies of the current and updated beliefs: H (b t )− H (b t+1 ). The entropy over the belief H (b) evaluates to: H (b) = − θ b(θ ) log(b(θ )) θ b(θ ) . ( 17 ) We now optimize our expected reward with respect to the hidden state θ , and this optimization explicitly entails reasoning about the effects that the robot actions will have on the observations, i.e., the actions that the human will take in response, and how useful these observations will be in shattering ambiguity about θ . \n Explore-exploit trade-off In practice, we use information gathering in conjunction with exploitation. We do not solely optimize the information gain term H (b t )−H (b t+1 ), but optimize it in conjunction with the robot's actual reward function assuming the current estimate of θ : r augmented R (x t , u R , u H ) = λ(H (b t ) − H (b t+1 )) + r R (x t , u R , u H , b t ) (18) At the very least, we do this as a measure of safety, e.g., we want an autonomous car to keep avoiding collisions even when it is actively probing a human driver to test their reactions. We choose λ experimentally, though existing techniques that can better adapt λ over time  (Vanchinathan et al. 2014) . \n (a) (b) (c) Fig.  11  Our three scenarios, along with a comparison of robot plans for passive estimation (gray) versus active information gathering (orange). In the active condition, the robot is purposefully nudging in or braking to test human driver attentiveness. The color of the autonomous car in the initial state is yellow, but changes to either gray or orange in cases of passive and active information gathering respectively \n Solution via model predictive control To find the control inputs for the robot we locally solve: u * R = arg max u R E θ R R x 0 , u R , u * ,θ H (x 0 , u R ) (19) over a finite horizon N , where u * ,θ H (x 0 , u R ) corresponds to the actions the human would take from state x 0 if the robot executed actions u R . This objective generalizes (5) with an expectation over the current belief over θ , b 0 . We still assume that the human maximizes their own reward function, r θ H (x t , u t R , u t H ); we add the superscript θ to indicate the dependence on the hidden state. We can write the sum of human rewards over horizon N as: R θ H (x 0 , u R , u H ) = N −1 t=0 r θ H (x t , u t R , u t H ) (20) Computing this over the continuous space of possible reward parameters θ is intractable even with discretization. Instead, we learn clusters of θ s offline via IRL, and online use estimation to figure out which cluster best matches the human. Despite optimizing the trade-off in (18), we do not claim that our method as-is can better solve the general POMDP formulation: only that it can be used to get better estimates of human internal state. Different tradeoffs λ will result in different performance. Our results below emphasize the utility of gathering information, but also touch on the implications for active information gathering on R R . \n Case studies with online estimation In this section, we show simulation results that use the method from the previous section to estimate human driver type in the interaction between an autonomous vehicle and a human-driven vehicle. We consider three different autonomous driving scenarios. In these scenarios, the human is either distracted or attentive during different driving experiments. The scenarios are shown in Fig.  11 , where the yellow car is the autonomous vehicle, and the white car is the human driven vehicle. Our goal is to plan to actively estimate the human's driving style in each one of these scenarios, by using the robot's actions. \n Attentive versus distracted human driver models Our technique requires reward functions r θ H that model the human behavior for a particular internal state θ . We obtain a generic driver model via Continuous Inverse Optimal Control with Locally Optimal Examples  (Levine and Koltun 2012)  from demonstrated trajectories in a driving simulator in an environment with multiple autonomous cars, which followed precomputed routes. We then adjust the learned weights to model attentive versus distractive drivers. Specifically, we modify the weights of the collision avoidance features, so the distracted human model has less weight for these features. Therefore, the distracted driver is more likely to collide with the other cars while the attentive driver has high weights for the collision avoidance feature. In future work, we plan to investigate ways of automatically clustering learned θ H s from data from different users, but we show promising results even with these simple options. \n Manipulated factors We manipulate the reward function that the robot is optimizing. In the passive condition, the robot optimizes a simple reward function for collision avoidance based on the current belief estimate. It then updates this belief passively, by observing the outcomes of its actions at every time step. In the active condition, the robot trades off between this reward function and information gain in order to explore the human's driving style. We also manipulate the human internal reward parameters to be attentive or distracted. The human is simulated to follow the ideal model of reward maximization for our two rewards. \n Scenarios and qualitative results Scenario 1: Nudging In to Explore on a Highway In this scenario, we show an autonomous vehicle actively exploring the human's driving style in a highway driving setting. We contrast the two conditions in Fig.  11a . In the passive condition, the autonomous car drives on its own lane without interfering with the human throughout the experiment, and updates its belief based on passive observations gathered from the human car. However, in the active condition, the autonomous car actively probes the human by nudging into her lane in order to infer her driving style. An attentive human significantly slows down (timid driver) or speeds up (aggressive driver) to avoid the vehicle, while a distracted driver might not realize the autonomous actions and maintain their velocity, getting closer to the autonomous vehicle. It is this difference in reactions that enables the robot to better estimate θ . Scenario 2: Braking to Explore on a Highway In the second scenario, we show the driving style can be explored by the autonomous car probing the human driver behind it. The two vehicles start in the same lane as shown in Fig.  11b , where the autonomous car is in the front. In the passive condition, the autonomous car drives straight without exploring or enforcing any interactions with the human driven vehicle. In the active condition, the robot slows down to actively probe the human and find out her driving style. An attentive human would slow down and avoid collisions while a distracted human will have a harder time to keep safe distance between the two cars. Scenario 3: Nudging In to Explore at an Intersection In this scenario, we consider the two vehicles at an intersection, where the autonomous car actively tries to explore human's driving style by nudging into the intersection. The initial conditions of the vehicles are shown in Fig.  11c . In the passive condition, the autonomous car stays at its position without probing the human, and only optimizes for collision avoid-  Fig.  13  The probability that the robot assigns to attentive as a function of time, for the attentive (left) and distracted (right). Each plot compares the active algorithm to passive estimation, showing that active information gathering leads to more accurate state estimation, in simulation and with real users ance. This provides limited observations from the human car resulting in a low confidence belief distribution. In the active condition, the autonomous car nudges into the intersection to probe the driving style of the human. An attentive human would slow down to stay safe at the intersection while a distracted human will not slow down. \n Quantitative results Throughout the remainder of the paper, we use a common color scheme to plot results for our experimental conditions. We show this common scheme in Fig.  12 : darker colors (black and red) correspond to attentive humans, and lighter colors (gray and orange) correspond to distracted humans. Further, the shades of orange correspond to active information gathering, while the shades of gray indicate passive information gathering. We also use solid lines for real users, and dotted lines for scenarios with an ideal user model learned through inverse reinforcement learning. Figure  13  plots, using dotted lines, the beliefs over time for the attentive (left) and distracted (right) conditions, comparing in each the passive (dotted black and gray respectively) with the active method (dotted dark orange and light orange respectively). In every situation, the active method achieves a more accurate belief (higher values for attentive on the left, when the true θ is attentive, and lower values on the right, when the true θ is distracted). In fact, passive estimation sometimes incorrectly classifies drivers as attentive when they are distracted and vice-versa. The same figure also shows (in solid lines) results from our user study of what happens when the robot no longer interacts with an ideal model. We discuss these in the next section. Figures 14 and 15 plot the corresponding robot and human trajectories for each scenario. The important takeaway from these figures is that there tends to be a larger gap between attentive and distracted human trajectories in the active condition (orange shades) than in the passive condition (gray shades), especially in scenarios 2 and 3. It is this difference that helps the robot better estimate θ : the robot in the active condition is purposefully choosing actions that will lead to large differences in human reactions, in order to more easily determine the human driving style. \n Robot behavior adapts to the situation As Fig.  14  suggests, active info gathering results in interesting coordination behavior. In Scenario 1, the robot decides to nudge into the person's lane. But what follows next nicely reacts to the person's driving style. The robot proceeds with the merge if the person is attentive, but actually goes back to its lane if the person is distracted. Even more interesting is what happens in Scenario 3 at the 4way stop. The robot inches forward into the intersection, and proceeds if the person is attentive, but actually goes back to allow the person through if they are distracted! These all emerge as the optima in our system. The behavior also naturally changes as the initial state of the system changes. Figure  16  shows different behaviors arising from an attentive driver model but different initial position of the human driver. This shows that even for the same driver model, the robot intelligently adapts its coordination behavior to the situation, sometimes deciding to merge but sometimes not. This is particularly important, because it might be easy to handcode these coordination strategies for a particular situation. Much like in the onffline estimation case, the robot not only comes up with these strategies, but actually adapts them depending on the situation-the driver style, the initial state, and so on. \n Active information gathering helps the robot's actual reward So far, we have looked at how active information gathering improves estimation of the driver model. This is useful in itself in situations where human internal state estimation is the end-goal. But it is also useful for enabling the robot to better achieve its goal. Intuitively, knowing the human driving style more accurately should improve the robot's ability to collect reward. For instance, if the robot starts unsure of whether the human is paying attention or not, but collects enough evidence that she is, then the robot can safely merge in front of the person and be more efficient. Of course, this is not always the case. If the person is distracted, then the information gathering actions could be a waste because the robot ends up not merging anyway. Figure  17  shows what happens in the merging scenario: the robot gains more reward compared to passive estimation by doing information gathering with attentive drivers, because it figures out it is safe to merge in front of them; the robot looses some reward compared to passive estimation with distracted drivers, because it makes the effort to nudge in but has to retreat back to its lane anyway because it cannot merge. Of course, all this depends on choosing λ, the tradeoff between exploitation and exploration (information gain). Figure  18  shows the effect of λ has on the robot's goal reward (not its information gain reward), which shows that not all λs are useful. In other situations, we would also expect to see a large decrease in reward from too much weight on information gain. \n Beyond driving style: active intent inference Driving style is not the only type of human internal state that our method enables robots to estimate. If the human has a goal, e.g. of merging into the next lane or not, or of exiting the highway or not, the robot could estimate this as well using the same technique. Each possible goal corresponds to a feature. When estimating which goal the human has, the robot is deciding among θ s which place weight on only one of the possible goal features, and 0 on the others. Figure  19  shows the behavior that emerges from estimating whether the human wants to merge into the robot's lane. In the passive case, the human is side by side with the robot. Depending on the driving style, they might slow down slightly, accelerate slightly, or start nudging into the robot's lane, but since the obser-vation model is noisy the robot does not get quite enough confidence in the human's intent early on. Depending on the Fig.  17  Active info gathering improves the robot's ability to efficiently achieve its goal in the case when the human is attentive: where a passive estimator never gets enough information to know that the person is paying attention, an active estimator nudges in, updates its belief, and proceeds with the merge. At the same time, active info gathering does not hurt too much when the person is distracted: the robot nudges in slightly (this does decrease its reward relative to the passive case, but not by much), updates its belief, and retreats to its lane Fig.  18  Active information gathering behavior when the robot's goal is to merge into the left lane for different values of λ, together with the reward the robot obtains. λ = 0 results in low reward because the robot does not figure out that the person is attentive and does not merge. A small λ hurts the reward because the information gathering costs but does not buy anything. For higher values, the robot gets enough information that it forces a merge in front of the human robot's reward, it might take a long time before the person can merge. In the active case, the robot decides to probe the person by slowing down and shifting away from the person in order to make room. It then becomes optimal for the per-   19  Actively estimating the human's intent (whether they want to merge in the right lane or not). The robot slows down and shifts slightly away from the person, which would make someone who wants to merge proceed. This could be useful for robots trying to optimize for the good of all drivers (rather than for their selfish reward function) son wanting to merge to start shifting towards the robot's lane, giving the robot enough information now to update its belief. In our experiment, we see that this is enough for the person to be able to complete the merge faster, despite the robot not having any incentive to help the person in its reward. \n User study with online estimation In the previous section, we explored planning for an autonomous vehicle that actively probes a human's driving style, by braking or nudging in and expecting to cause reactions from the human driver that would be different depending on their style. We showed that active exploration does significantly better at distinguishing between attentive and distracted drivers using simulated (ideal) models of drivers. Here, we show the results of a user study that evaluates this active exploration for attentive and distracted human drivers. \n Experimental design We use the same three scenarios discussed in the previous section. Manipulated Factors We manipulated the same two factors as in our simulation experiments: reward function that the robot is optimizing (whether it is optimizing its reward through passive state estimation, or whether it is trading off with active information gathering), and the human internal state (whether the user is attentive or distracted). We asked our users to pay attention to the road and avoid collisions for the attentive case, and asked our users to play a game on a mobile phone during the distracted driving experiments. Dependent Measure We measured the probability that the robot assigned along the way to the human internal state. Hypothesis The active condition will lead to more accurate human internal state estimation, regardless of the true human internal state. Subject Allocation We recruited 8 participants (2 female, 6 male) in the age range of 21-26 years old. All participants owned a valid driver license and had at least 2 years of driving experience. We ran the experiments using a 2D driving simulator with the steering input and acceleration input provided through a steering wheel and a pedals as shown in Fig.  1 . We used a within-subject experiment design with counterbalanced ordering of the four conditions. \n Analysis We ran a factorial repeated-measures ANOVA on the probability assigned to \"attentive\", using reward (active vs. passive) and human internal state (attentive vs. distracted) as factors, and time and scenario as covariates. As a manipulation check, attentive drivers had significantly higher estimated probability of \"attentive\" associated than distracted drivers (0.66 vs 0.34, F = 3080.3, p < 0.0001). More importantly, there was a signifiant interaction effect between the factors (F = 1444.8, p < 0.000). We ran a post-hoc analysis with Tukey HSD corrections for multiple comparisons, which showed all four conditions to be significantly different from each other, all contrasts with p < 0.0001. In particular, the active information gathering did end up with higher probability mass on \"attentive\" than the passive estimation for the attentive users, and lower probability mass for the distracted user. This supports our hypothesis that our method works, and active information gathering is better at identifying the correct state. Figure  13  compares passive (grays and blacks) and active (light and dark oranges) across scenarios and for attentive (left) and distracted (right) users. It plots the probability of attentive over time, and the shaded regions correspond to standard error. From the first column, we can see that our algorithm in all cases detects human's attentiveness with much higher probably than the passive information gathering technique shown in black. From the second column, we see that our algorithm places significantly lower probability on attentiveness, which is correct because those users were distracted users. These are in line with the statistical analysis, with active information gathering doing a better job estimating the true human internal state. Figure  14  plots the robot trajectories for the active information gathering setting. Similar to Fig.  13 , the solid lines are the mean of robot trajectories and the shaded regions show the standard error. We plot a representative dimension of the robot trajectory (like position or speed) for attentive (dark orange) or distracted (light orange) cases. The active robot probed the user, but ended up taking different actions when the user was attentive versus distracted in order to maintain safety. For example, in Scenario 1, the trajectories show the robot is nudging into the human's lane, but the robot decides to move back to its own lane when the human drivers are distracted (light orange) in order to stay safe. In Scenario 2, the robot brakes in front of the human, but it brakes less when the human is distracted. Finally, in Scenario 3, the robot inches forward, but again it stops when if the human is distracted, and even backs up to make space for her. Figure  15  plots the user trajectories for both active information gathering (first row) and passive information gathering (second row) conditions. We compare the reactions of distracted (light shades) and attentive (dark shades) users. There are large differences directly observable, with user reactions tending to indeed cluster according to their internal state. These differences are much smaller in the passive case (second row, where distracted is light gray and attentive is black). For example, in Scenario 1 and 2, the attentive users (dark orange) keep a larger distance to the car that nudges in front of them or brakes in front of them, while the distracted drivers (light orange) tend to keep a smaller distance. In Scenario 3, the attentive drivers tend to slow down and do not cross the intersection, when the robot actively inches forward. None of these behaviors can be detected clearly in the passive information gathering case (second row). This is the core advantage of active information gathering: the actions are purposefully selected by the robot such that users would behave drastically differently depending on their internal state, clarifying to the robot what this state actually is. Overall, these results support our simulation findings, that our algorithm performs better at estimating the true human internal state by leveraging purposeful information gathering actions. autonomous cars and human-driven vehicles. We formulated a dynamical system in which the robot accounts for how its actions are going to influence those of the human as a simplification to a observable stochastic game. We introduced approximations for optimizing in the dynamical system that bring the robot's computation close to real time (.3 s/time step). We showed in an empirical analysis that when the robot estimates the human model offline, it produces behavior that can purposefully modify the human behavior: merging in front of them to get them to slow down, or pulling back at an intersection to incentivize them to proceed first through. We also showed that these behaviors can emerge out of directly optimizing for the robot's efficiency. We further introduced an online estimation algorithm in which the robot actively uses its actions to gather information about the human model so that it can better plan its own actions. Our analysis again shows coordination strategies arising out of planning in our formulation: the robot nudges into someones's lane to check if the human is paying attention, and only completes the merge if they are; the robot inches forward at an intersection, again to check if the human is paying attention, and proceeds if they are, but backs up to let them through if they are not; the robot slows down slightly and shifts in its lane away from the human driver to check if they want to merge into its lane or not. Importantly, these behaviors change with the human driver style and with the initial conditions-the robot takes different actions in different situations, emphasizing the need to start generating such coordination behavior autonomously rather than relying on hand coded strategies. Even more importantly, the behaviors seem to work when the robot is planning and interacting with real users. Limitations All this work happened in a simple driving simulator. To put this on the road, we will need more emphasis on safety, as well as a longer planning horizon. While performing these experiments, we found the robot's nominal reward function (trading off between safety and reaching a goal) to be insufficient-in some cases it led to getting dangerously close to the human vehicle and even collisions, going off the road, oscillating in the lane due to minor asymmetries in the environment, etc. Figure  20  shows an example of such behavior that comes from the 4way stop domain. For the most part, the car plans to back up to incentivize the human to go through first. But for some values of the human's initial velocity, we observed bad behavior, likely due to convergence to local maxima: the car did not figure out to slow down or back up, and instead if proceeded forward-then it tried to avoid collisions with the person and went off the road, and in the wrong direction (i.e. in the person's way). It seems like while a reward function might be a good enough model for the human, it might be difficult to devise such a universal function for the robot, and the use of hard constraints to ensure safe control would be welcome. Another limitation is that we currently focus on a single human driver. Looking to the interaction among multiple vehicles is not just a computational challenge, but also a modeling one-it is not immediately clear how to formulate the problem when multiple human-driven vehicles are interacting and reacting to each other. Conclusion Despite these limitations, we are encouraged to see autonomous cars generate human-interpretable behaviors through optimization, without relying on hand-coded heuristics. Even though in this work we have focused on modeling the interaction between an autonomous car and a human-driven car, the same framework of underactuated systems can be applied to modeling the interaction between humans and robots in more general settings. We look forward to applications of these ideas beyond autonomous driving, to mobile robots, UAVs, and in general to human-robot interactive scenarios where robot actions can influence human actions. Fig. 2 2 Fig. 2 Features used in IRL for the human driven vehicle; warmer colors correspond to higher reward. We illustrate features corresponding to (a) respecting road boundaries, b holding lanes, and c avoiding collisions with other cars \n Fig. 6 6 Fig. 6 Heat map of reward function for reaching a final goal at the top left of the road. As shown in the figure, the goal position is darker showing more reward for reaching that point \n Fig. 8 8 Fig.8Speed profile and latitude of the human driven vehicle for Scenario 1. The first column shows the speed of all trajectories with its mean and standard errors in the bottom graph. The second column shows the latitude of the vehicle over time; similarly, with the mean and standard errors. The gray trajectories correspond to the control condition, and the orange trajectories correspond to the experimental condition: the robot decides to merge in front of the users and succeeds at slowing them down. The purple plot corresponds to a simulated user that perfectly matches the model that the robot is using \n Fig. 9 Fig. 10 910 Fig. 9 Trajectories of the human driven vehicle for Scenario 2. The first column a shows all the trajectories, and the second column b shows the mean and standard error. Orange (blue) indicates conditions where the reward encouraged the robot to affect the user to go left (right) \n Fig. 12 12 Fig. 12 Legends indicating active/passive robots, attentive/distracted humans, and real user/ideal model used for all following figures \n Fig. 14 14 Fig.14Robot trajectories for each scenario in the active information gathering condition. The robot acts differently when the human is attentive (dark orange) versus when the human is distracted (light orange) due to the trade-off with safety \n Fig. 15 15 Fig.15The user trajectories for each scenario. The gap between attentive and distracted drivers' actions is clear in the active information gathering case (first row) \n Fig.19Actively estimating the human's intent (whether they want to merge in the right lane or not). The robot slows down and shifts slightly away from the person, which would make someone who wants to merge proceed. This could be useful for robots trying to optimize for the good of all drivers (rather than for their selfish reward function) \n Fig. 20 20 Fig. 20 Example of bad local optima occurring for certain initial velocities of the human in the 4way intersection scenario \n \n \n\t\t\t A preliminary version of our results was reported inSadigh et al.  (2016a, b). This paper extends that work by providing more detailed discussion and experiments... \n\t\t\t Extension to online estimation of the human modelWe have thus far in our approximate solution treated the human's reward function as estimated once, offline. This has worked well in our user study on seeking specific coordination effects on the human, like slowing down or going first through the intersection. But in general, this is bound to run \n\t\t\t One exception is Nikolaidis et al. (2016) , who propose to solve the full POMDP, albeit for discrete and not continuous state and action spaces. \n\t\t\t of varying the initial condition (relative y position) in the active merge scenario. The robot adapts to merge when feasible and avoid otherwise. The human is attentive in all cases", "date_published": "n/a", "url": "n/a", "filename": "Sadigh2018_Article_PlanningForCarsThatCoordinateW.tei.xml", "abstract": "Traditionally, autonomous cars treat human-driven vehicles like moving obstacles. They predict their future trajectories and plan to stay out of their way. While physically safe, this results in defensive and opaque behaviors. In reality, an autonomous car's actions will actually affect what other cars will do in response, creating an opportunity for coordination. Our thesis is that we can leverage these responses to plan more efficient and communicative behaviors. We introduce a formulation of interaction with human-driven vehicles as an underactuated dynamical system, in which the robot's actions have consequences on the state of the autonomous car, but also on the human actions and thus the state of the human-driven car. We model these consequences by approximating the human's actions as (noisily) optimal with respect to some utility function. The robot uses the human actions as observations of her underlying utility function parameters. We first explore learning these parameters offline, and show that a robot planning in the resulting underactuated system is more efficient than when treating the person as a moving obstacle. We also show that the robot can target specific desired effects, like getting the person to switch lanes or to proceed first through an intersection. We then explore estimating these parameters online, and enable the robot to perform active information gathering: generating actions that purposefully probe the human in order to clarify their underlying utility parameters, like driving style or attention level. We show that this significantly outperforms passive estimation and improves efficiency. Planning in our model results in coordination behaviors: the robot inches forward at an intersection to see if can go through, or it reverses to make the other car proceed first. These behaviors result from the optimization, without relying on hand-coded signaling strategies. Our user studies support the utility of our model when interacting with real users. Keywords Planning for human-robot interaction • Mathematical models of human behavior • Autonomous driving This is one of several papers published in Autonomous Robots comprising the \"Special Issue on Robotics Science and Systems\".", "id": "3bee0316cc55ec90063c9ee67af445b9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Matthijs M Maas"], "title": "AI, Governance Displacement, and the (De)Fragmentation of International Law", "text": "of AI's effects on the legal and institutional scaffolding of the international legal order. How can we analyse the direct and indirect effects of AI technologies on the viability, form, or functioning of the international legal order? This paper explores this question, in order to derive both practical and theoretical implications for international law and legal scholarship. The analysis proceeds as follows: in section II, it provides a background and theoretical underpinning to this analysis. It provides a functional definition of AI, explores why we should expect it to have wide-ranging impacts on the international legal order, and explore some theoretical frameworks for approaching the study of legal automation (LawTech), and the interrelation between technological change and legal systems more broadly (TechLaw). Section III then examines in depth the sources and vectors by which AI systems can affect international law. It sketches a 'governance disruption' framework of situations where AI applications create a need for international legal development, and where they can contribute to the potential destruction of specific regimes or the erosion of the international legal order. It then focuses in on the vectors of legal displacement (the potential effects of the 'automation' of international law). The section explores three potential pathways of such displacement: automation of rule creation; automation of monitoring & enforcement; or the 'replacement' of international law. Section IV then shifts the focus to the effects of these trends on the integration or fragmentation of international law, distinguishing 10 different roles that AI systems may play, with distinct effects on the global governance architecture. Section V briefly reviews some potential responses to these trends for legal scholars, and section VI concludes. \n II. Background and Rationale What is AI? Unfortunately, there is no settled definition even amongst practitioners.  5  Scientifically, field of AI has been characterised as \"making machines intelligent,  [where]  intelligence is that quality that enables an entity to function appropriately and with foresight in its environment.\"  6  Technically, however, 'AI' is an umbrella term that includes both traditional rule-based symbolic AI as well as the data-driven machine learning (ML) approaches that are responsible for the recent surge in AI progress and attention. Functionally, AI can be described as a varied suite of computational techniques which are able to improve the accuracy, speed, and/or scale of machine decision-making across diverse information-processing or decision-making contexts. The resulting capabilities can accordingly be used in order to support, substitute for-, and/or improve upon human performance in diverse tasks, enabling their deployment in applications across various domains, and resulting in diverse societal impacts.  7  As a result, AI has in recent years come into its own as a widely applicable set of technologies, with applications in a diverse array of sectors ranging from healthcare to finance, from education to security, and even the scientific process itself.  8  While the efficacy of today's AI technology is not without its problems and limits, there can be little doubt that AI's development and proliferation will impact many or all sectors of society. What are the stakes? AI has seen a series of high-profile breakthroughs in recent years.  9  As a result, its promise of AI has hardly gone unnoticed. AI, some argue, will be 'the biggest geopolitical revolution in human history'.  10  Its prospective impact on national security has been compared to nuclear weapons, aircraft, and computing. 11 \"Whoever leads in artificial intelligence in 2030,\" it has been claimed, \"will rule the world until 2100.\"  12  Even under more modest readings, AI has been perceived to offer considerable economic and scientific advantages. As such, over the past years, dozens of states have articulated national AI strategies,  13  and many have begun investing vast sums in both research and application, including the development of AI systems in strategic, military one study, the IBM Watson system used language processing algorithms to process thousands of peerreviewed medical articles on the neurodegenerative disorder amyotrophic lateral sclerosis (ALS). On this basis, it correctly predicted five previously unknown genes related to the disease; Nadine Bakkar and others, 'Artificial Intelligence in Neurodegenerative Disease Research: Use of IBM Watson to Identify Additional RNA-Binding Proteins Altered in Amyotrophic Lateral Sclerosis' (2018) 135 Acta Neuropathologica 227. In another case, an unsupervised Natural Language Processing (NLP) system deployed on the scientific materials science literature, was able to capture complex materials science concepts such as the underlying structure of the periodic table, and on the basis of past literature was able to 'predict' later scientific findings by recommending new materials for application, ahead of their eventual discovery. Vahe Tshitoyan and others, 'Unsupervised Word Embeddings Capture Latent Knowledge from Materials Science Literature' (2019) 571 Nature 95.  9  For performance and investment trends, see: Daniel Zhang and others, 'Artificial Intelligence Index Report 2020' (AI Index Steering Committee, Human-Centered AI Initiative, Stanford University 2021) <https://aiindex.stanford.edu/wp-content/uploads/2021/03/2021-AI-Index-Report_Master.pdf> accessed 3 March 2021.  10  Kevin Drum, 'Tech World: Welcome to the Digital Revolution' [2018] Foreign Affairs  46. 11  Greg Allen and Taniel Chan, 'Artificial Intelligence and National Security' (Harvard Kennedy School -Belfer Center for Science and International Affairs 2017) <http://www.belfercenter.org/sites/default/files/files/publication/AI%20NatSec%20-%20final.pdf> accessed 19 July 2017. 12 Indermit Gill, 'Whoever Leads in Artificial Intelligence in 2030 Will Rule the World until 2100' (Brookings, 17 January 2020) <https://www.brookings.edu/blog/future-development/2020/01/17/whoeverleads-in-artificial-intelligence-in-2030-will-rule-the-world-until-2100/> accessed 22 January 2020. Note, however, that an often-repeated claim, by Russian President Vladimir Putin, that \"whoever rules AI rules the world\", may have been taken out of context: rather than an official statement of Russian foreign policy, this appears to have been an off-the-cuff comment which Putin made in the context of giving young Russian school children feedback on their science projects. Interview with Robert Wiblin, Keiran Harris and Allan Dafoe, 'The Academics Preparing for the Possibility That AI Will Destabilise Global Politics' (18 March 2018) <https://80000hours.org/podcast/episodes/allan-dafoe-politics-of-ai/> accessed 12 August 2020.  13  See for overviews Jessica Cussins, 'National and International AI Strategies' (Future of Life Institute, February 2020) <https://futureoflife.org/national-international-ai-strategies/> accessed 22 June 2020.; Tim Dutton, Brent Barron and Gaga Boskovic, 'Building an AI World: Report on National and Regional AI Strategies' (CIFAR 2018) <https://www.cifar.ca/docs/default-source/aisociety/buildinganaiworld_eng.pdf?sfvrsn=fb18d129_4>. Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -  Maas -March 2021)  or cybersecurity applications.  14  Both the US and China have established AI technology as a lynchpin of their future strategic dominance.  15  A. Why study AI's effects on the international order? From both a practical perspective, as well as a theoretical one, it is important to consider how AI technology may change the tools, processes and assumptions of international law. At present, governance proposals for AI often fail to factor in technology-driven changes to governance itself. To be sure, independent bodies of scholarship exist which explore the use of AI, algorithms and digital technology in legal systems,  16  including a small but growing body of work exploring this phenomenon at the international law level.  17  However, most proposals for the global governance of AI itself often reason in relative isolation from such dynamics. This is a problem because, as noted by Colin Picker, various technological innovations have throughout history driven the \"creation, modification, or destruction of international law, or the derailment of the creation of new international law\". 18 Indeed, scholars working in various governance areas have already begun to identify the adverse effects which digital technologies may have on the continued viability of regimes in areas such as arms control.  19  Likewise, AI technology is likely to affect not just the substance of various international regimes, but also their processes and procedures, and potentially even their political scaffolding.  20  This will have effects not just on the instruments envisaged for governing AI itself, but indeed will likely spread to many other legal domains. AI applications may also exert effects on the very AI governance instruments that are being proposed, or on the broader global legal order within which these would be ingrained. How do we engage with the questions of how technology alters (international) law? There is an established body of work that has examined the phenomena of 'law and technology' and 'legal automation' in a domestic law context. Over the past decade, such scholarship has studied, through both concrete cases and at a conceptual level, how the use of algorithms and AI systems might alter the coherence, form, and practices of legal systems, or even the underlying values of regulators.  21  Significantly, if one expects AI technologies to have such a disruptive impact on domestic legal systems, one should arguably expect their disruptive effects to be even steeper in the international domain. This is because in comparison to national law, the global legal order appears less well equipped to anticipate or resolve situations of legal uncertainty, or to keep accountable the insertion of technology in legal processes. After all, at the international level there is no authoritative final legislator to compel ex ante consideration of a technology, to guarantee the coherence of legal responses across domains, or to coordinate (and critically scrutinize) the integration of new technologies into law-making, -adjudication, or -enforcement practices. Moreover, amending or altering multilateral treaty regimes to take stock of subsequent technological developments can often prove a more painful, drawn-out, and contested affair than the revision of domestic laws.  22  Furthermore, governance disruption can pose a challenge that is not just legal or procedural, but also political. After all, while international relations scholars are still weighing the precise impact of AI,  23  there is a general appreciation that new innovations can redraw the global political map.  24  It would be very surprising if such far-reaching (geo)-political shocks did not have their echoes at the international legal level. The aim of this paper is not to provide an exhaustive analysis, but rather to provide conceptual clarification-which has been fundamental to much past scholarship at the intersection of 'law', 'regulation' and 'technology'.  25  For instance, Colin Picker has noted that a high-level view of strategic dynamics amongst technology and international law is critical: \"[e]ven though policy makers must be closely concerned with the \"nitty gritty\" of their international regimes and negotiations, […] [they] have much to gain from taking a macro or holistic view of the issues raised by technology. Macro-examinations can provide larger theoretical understandings and can reveal previously hidden characteristics that are simply not discernable from the \"trenches.\" Viewing technology from \"40,000 feet up\" reveals certain patterns, pitfalls, and lessons for policy.\"  26  The aim of this paper is to explore the intersection of AI and international law, in the hope that additional conceptual disaggregation can help international lawyers consider ways to 'update' or 'reboot' the international legal order, to ensure it is not only more resilient to AI-driven governance disruption, but can also build on these tools. \n B. AI and (International) Law: a LawTech-Techlaw Tale The exploration of AI technology's ability to change the norms, instruments, or processes of governance can draw on a framework of 'governance disruption'.  27  This departs from the existing scholarship on 'law and technology'. There are two streams to this. On the one hand, recent years have seen a diverse literature on 'LawTech', which focuses on how new technologies can be used in support of existing legal systems, or to expand the capabilities of lawyers.  28  This work however, has predominantly focused on such applications in the domestic law context, rather than at the international law one. Simultaneously, a second and complementary strand is found in the emerging paradigm of 'TechLaw'-\"the study of how law and technology foster, restrict, and otherwise shape Electronic copy available at: https://ssrn.com/abstract=3806624 Importantly, the idea that new (AI) technologies are not just objects for regulation 30 but can also change the operation and processes of legal systems, and even the goals of regulators, is not new. Reflections on what a new technology reveals about the changing face of law has extensive precedent in technology law scholarship. For instance, in early debates in the field of cyberlaw, Lawrence Lessig famously examined several legal questions involving the new technology of cyberspace, not merely in order to discuss the relative efficacy of different approaches to regulating certain topics (e.g. zoning or copyright) on the internet, but also to ground and illustrate systemic reflections on the changing nature and workings of the different 'regulatory modalities' of laws, norms, markets and architectures ('code').  31  Likewise, Roger Brownsword has used studies of behaviour-shaping technologies and geoengineering in order to reflect respectively, upon the rising role of non-normative 'technological management' and 'regulatory responsibilities' for the core 'global commons'.  32  Moreover, this comparison with earlier scholarship on cyberlaw is illuminating in both directions. The internet 'merely' led to the 'informatisation' of infrastructure and public space-which already proved pivotal in altering the ways that regulation operates. In their turn, AI systems may enable the increasing 'intelligentisation' or 'cognitisation' of these infrastructures, 33 suggesting that this technology could in time have an impact on the practices and dynamics of law and governance that is at least as far-reaching. The 'governance disruption' developed in this paper is of use, as exploring the dynamics and legal impacts of AI governance can reveal interesting and important transferable lessons for the changing relation between technology and global governance-and therefore the changing face of international law in the 21 st century. \n The rise of LawTech This debate over how AI technologies might provide new affordances for the regulators who produce and enforce law (and what implications flow from this) becomes particularly urgent, given the developments in AI for LawTech in many domestic legal contexts. Over the last decade, new digital technologies, and particularly AI, have seen particularly rapid and enthusiastic uptake in various branches of domestic public administration, judicial decision-making, policing, and the business of government writ  29   Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) large. At the same time, from the perspective of (private) legal practice, AI systems can be used to automate or contribute to a range of routine legal tasks, such as checking contracts, 34 case law research,  35  or the faster provision of legal services.  36  Provided with adequate databases, some machine learning systems have even begun to make headway in predicting the outcomes of legal disputes in court.  37  This has led some scholars to anticipate an increasing automation of legal systems, 38 with legal rules and standards becoming progressively replaced by algorithmically-tailored 'micro-directives' that can predict, ex ante, what an ex post judicial decision would have held in every specific case, and so can offer perfectly clear yet tailored legal clarity for individuals.  39  That is not to say that such scenarios-or indeed even more modest cases of legal automation-have been uncritically welcomed. Indeed, recent years have seen extensive scholarship exploring the practical, normative, and legal implications of 'legal automation' in domestic practice.  40  There are extensive critiques of the near-term prospects for legal automation, given the limits of current machine learning approaches, 41 as well as in light of the various 'interface design errors' that often plague hybrid human and AI 'cyborg justice' arrangements, and which can produce inappropriate 'overtrust'.  42  There have been particularly acute cases involving bias in algorithms used for recidivism prediction;  43   Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) others have highlighted likely human rights violations that are likely when such algorithms are deployed on or to particularly vulnerable populations, such as migrants.  44  More conceptually, others have cautioned that the automation of law enforcement systems might close the loop on the legal qualities of 'inefficiency' and 'indeterminacy', arguing that these are both key safeguards against the perfect enforcement of laws that were in fact originally drafted on the implicit assumption of a certain degree of lenience or discretion.  45  Finally, there are concerns that the integration of such systems may produce an increasingly opaque 'algocracy'.  46  However, while these technologies therefore no doubt raise diverse grounds of concern, barring a major public backlash, it may well be the case that they see continued development and deployment of automation in public services and administration, potentially signalling a general shift towards 'technocratic' regulatory attitudes in domestic legal systems.  47  2. Taking legal disruption to the international level Given its foundational implications, this breadth of work and attention on 'legal displacement' in domestic legal systems is surely warranted. However, by comparison, there has been relatively less attention paid to the prospects of such a shift at the international legal level. There is indeed some recent work on how AI technology may come to affect and disrupt international law. Thomas Burri, Berenice Boutin, and Ashley Deeks have provided general treatments of the ways in which AI technology could affect or play a role in international law.  48  Meggido has explored the potential contribution of big data to customary international law.  49  Alschner and colleagues have explored the production of international legal materials (such as draft treaties) by algorithms,  50  and have explore some of the implications of the 'data-driven future' of the (text-corpus-rich) international economic law.  51  Deeks and others explore the specific implications of conflict prediction algorithms on the international law on the use of force.  52  Livingston & Risse have discussed the implications of AI for potential monitoring of human rights.  53  More generally, Nelson has evaluated the effects of digitisation (including the spread of AI) on existing arms control and export control regimes.  54  However, this scholarship remains incipient and at an early stage. As such, this article finds itself at the intersection of the LawTech and TechLaw approaches. Drawing on the work of Rebecca Crootof and Ashley Deeks, it aims to extend these paradigms to the international legal level, by exploring how the use of AI may affect the form and viability of international law-and what are the resulting practical, normative, and theoretical implications. III. AI and the international order: sources of disruption, vectors of displacement In previous work, I have mapped a taxonomy of ways in which AI could affect the integrity, viability, form or relevance of the international law system itself.  55  Based on historical accounts and theoretical frameworks, I argued that the deployment and use of AI systems might produce three types of global legal impacts: 'development', 'displacement', or 'destruction' (see Table  1 ). This model maps how AI applications can and may under various circumstances produce situations of legal uncertainty (i.e. new gaps, ambiguity, over-or underinclusiveness, or obsolescence) around existing norms or regimes in international law. Whenever this happens, it sparks a moment of reflection-an 'international law step zero' 56 -over whether or how these can be accommodated into international law; that is, there is a need to accommodate or address the uncertainty through some form of legal development. However, the international law system may not always be able to carry out such developments, given certain features of-and tensions within its usual tools.  57  Indeed, it was argued that certain technical and political features of AI technology may in practice render it destructive or erosive to key areas of international law (legal destruction). This is because the legal 'gaps' that AI systems reveal on the international level may be conceptually or politically hard to patch through the usual avenues of international law 'development' (adaptive interpretation; treaty amendments; new treaties; customary international law development; or jurisprudence by international courts). 58 At the same time, the strategic capabilities it offers chip away at the rationales for powerful states to engage fully in, or comply with, international law regimes.  54  Nelson (n 20).  55    \n Conceptual uncertainty or ambiguity LAWS highlight potential ambiguity or inadequacy of concepts such as 'intent', 'effective control', etc. Need for new law or adaptation of law, to sharpen existing rules or clarify concepts.  \n Incorrect scope of application \n Altered problem portfolio Military AI regime tailored to respond to ethical challenges of LAWS (e.g. maintaining meaningful human control over lethal force) might not be oriented to address risks of later adjacent AI capabilities (e.g. cyberwarfare) creating structural shifts. Need for new regime or adaptation or amendment of existing instrument, to shift focus or centre of gravity. \n Displacement \n Automation \n International Law Creation & Adjudication Use of AI text-as-data tools to generate draft treaties, predict arbitral panel rulings, identify state practice, identify treaty conflicts. Potential speeding-up of international law creation, though distributional and legitimacy concerns. \n Monitoring & enforcement Use of various AI tools in monitoring and verifying treaty compliance. Increase deterrent effect of existing regimes; potentially create transparency preconditions for new regimes \n Replacement \n Changes in regulatory modality Use of AI tools such as emotion-recognition, social media sentiment analysis, or computational propaganda by states, resulting in increased state preference to resolve disputes in diplomatic channels. Nonetheless, a third major category of AI's governance disruption concerns the ways in which AI tools may drive displacement in the processes or instruments of international governance themselves. 60 That is, more even than many previous technologies, it may drive considerable sociotechnical change in the 'legal' domain itself, as various tools might potentially lend themselves to the 'automation' or even the 'replacement' of important (rule-making, adjudication, monitoring & enforcement) functions of international law. In particular, I have argued that there are three distinct sub-categories of AIdriven governance 'displacement'.  61  Specifically, these are the automation of processes of rule creation and adjudication; the automation of monitoring and enforcement of international regimes; and potential shifts in the 'regulatory modality' of international law, resulting in the gradual replacement of some forms of conflict mediation (e.g. arbitration) with other avenues (e.g. bilateral state diplomacy; or unilateral AI-supported 'lawfare'). \n A. Automation of rule creation, adjudication or arbitration In the first place, it has long been recognised that new technologies can change the processes by which international law is created. For instance, technologies can speed up international law formation. Already in 1973, Louis B. Sohn noted how new communication and travel infrastructures were making treaty negotiation faster and easier.  62  Of course, while promising, this may not be an unalloyed good, because the increased presence of communications technologies has also, in some readings, rendered strategies of 'lawfare' more viable.  63  Others have recently argued that the deluge of big data, and the falling thresholds to collecting it, could facilitate the process of collating and consolidating evidence of state practice, fostering an era of 'Data-Driven Customary International Law'.  64  Along with speed, new communication technologies have also qualitatively altered the processes of international law, for instance by expanding participation to more actors. Indeed, in their discussion of the phenomenon of 'norm cascades', Finnemore & Sikkink have discussed how the pace and scope of (general) norm acceptance in international relations can be directly traced to technological change, since; \"changes in communication and transportation technologies and increasing global interdependence have led to increased connectedness and, in a way, are leading to the homogenization of global norms […] the speed of normative change has accelerated substantially in the later part of the twentieth century.\"  65  For instance, in a comparison of the drafting processes behind UNCLOS and the Mine Ban Treaty, Gamble and Ku have argued that modern communications technologies  60   greatly increased the ability of NGOs to get involved in international rule creation, resulting in laws that were less narrowly tailored to state interests.  66  Accordingly, the first type of legal displacement envisions AI systems changing the practices of (international) law creation or adjudication. Ideas to this effect draw an analogy to growing work on the use of AI systems in domestic legal systems, where algorithms are used in support of the adjudication of cases, the monitoring of crimes and violations, or even the prediction of court rulings. While this rise of 'AI Justice' 67 has received considerable scrutiny and critique even in the domestic realm, could we expect AI systems to see usage in support of international law? One can consider a 'strong' scenario, and a 'modest' scenario. 68 1. Strong scenario: a global digital arbiter The 'strong' scenario posits that advances in AI could, in time, posit some sort of 'global digital arbiter'; a queryable legal model that would facilitate the creation of a 'completely specified' international law.  69  If possible, such systems could serve as a powerful 'integrator' of global governance, as they would be able to identify and resolve conflicts between norms, or goals-from human rights to environmental law-in adjudicating a 'global constitution'-therefore reducing the challenges of fragmentation and regime complexity.  70  At the limit, such systems would promise the fully automated adjudication of international law.  71  Of course, while an interesting thought experiment or extrapolation of trends, for the purposes of governance this strong scenario may be less relevant. Technically, such a system remains beyond existing machine learning approaches, and might instead require some forms of future 'high-level machine intelligence' capabilities. 72 While it is not clear that such capabilities are categorically out of reach-or even more than a few decades away  73  -the fact remains that if they were to be created and implemented, their general societal impact would likely far exceed their direct impact on international law.  66     68  Because the latter is more likely and analytically interesting, we will briefly discuss the former first.  69  Along the lines of Benjamin Alarie's 'legal singularity', Alarie (n 17).  70  We will discuss the intersection of (even more modest) AI tools with the lens of 'regime complexity' near the end of this paper.  71  Although interestingly, while a dramatic change, such a 'full automation' of international law would not be the same as the 'replacement' of international law, since it would still at its core be reliant on presenting norms to human parties, and adjudicating or arbitrating between them.  72   More pragmatically, proposing the use of an advanced AI system to create or adjudicate international law in this strong sense would be 'passing the buck'. The 'problem' of global governance (from a coherentist or global constitutionalist perspective) is not that we presently cannot conceive of an authoritative body that could reconcile or decide amongst norm conflicts. It is rather that such hierarchical authorities currently only exist at the state level, whereas the international system notably lacks such bodies. There would certainly be distinct and considerable political (and symbolic) sensitivities involved in handing over the international legal order over to a machine, but these seem modest compared to the extant political difficulty of installing any final authority above the international system. In that sense, the 'strong' scenario of international legal automation might be somewhat of a red herring, since if one or more AI systems were deployed to integrate and resolve the problem of authority at the international level, by far the bigger achievement would be that this was achieved at all, not that it was done in silicate. As such, a farreaching 'automation' of international law might counteract the trend towards the increasing international legal and normative fragmentation; 74 but its prospects appear technologically limited in the near term, and strategically moot in the hypothetical longterm.  75  2. Modest scenario: text-as-data tools for 'intelligentized' lawmaking By contrast, the 'modest' scenario of using AI in the automation for rule creation is more analytically fruitful. Of course, a first question to ask is whether even this scenario of 'displacement' is anywhere on the horizon. Can international law be even partially automated in this more modest manner? Thomas Burri has been broadly sceptical: he argues that whereas domestic legal areas such as tax law are susceptible to legal automation because AI systems in those areas can draw on large, dense, structured and homogeneous datasets; 76 the key legal 'datasets' at the international law level are either far too small (e.g. ICJ decisions), or far too heterogeneous and ambiguous to allow for this.  77  By contrast, Ashley Deeks has been more optimistic about the conditions for gradual but eventually wide-spread take-up of AI technology into 'high-tech international law'. 78 Contra Burri, she argues that in many areas in international law, there are significant digital sources of texts (covering thousands of documents) which provide extensive text corpora that can allow machine learning 'text-as-data' tools to perform various functions. She notes how: \"[o] ne key reason to think that international legal technology has a bright future is that there is a vast range of data to undergird it. […] there are a variety of digital sources of text that might serve as the basis for the kinds of text-as-data analyses that will be useful to states. This includes U.N. databases of Security Council and General Assembly documents, collections of treaties and their travaux preparatoires, European Court of Human Rights caselaw, international arbitral awards, databases of specialized agencies 74 See Infra, section IV(B).  75  For an exploration of a 'problem-finding' approach to such macro-strategic trajectory considerations around AI governance, see also Liu and Maas (n 8).  76  This may be too easy a reading of the difficulties involved in tax law automation, especially in civil law systems where precedent does not hold the same value. I thank Luisa Scarcella for this point. For further discussion, see Joshua D Blank and Leigh Osofsky, 'Automated Legal Guidance' (2021) 106 Cornell Law Review <https://papers.ssrn.com/abstract=3546889> accessed 8 September 2020.  77  Burri (n 18) 93-95.  78  Deeks (n 18). Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) such as the International Civil Aviation Organization, state archives and digests, data collected by a state's own intelligence agencies and diplomats (memorialized in internal memoranda and cables), states' notifications to the Security Council about actions taken in self-defense, legal blogs, the U.N. Yearbook, reports by and submission to U.N. human rights bodies, news reports, and databases of foreign statutes.\"  79  Given this, text-as-data machine learning systems could be trained to generate new treaty texts (e.g. draft extradition treaties),  80  to predict how an international arbitral panel might rule, to gauge the course and likely outcomes of treaty negotiations, or to identify possible treaty conflicts.  81  Moreover, far from being limited only to legal texts, Deeks notes how other uses of AI-from systems that aggregate intelligence information about the preferences or negotiation strategies of negotiation partners, to emotionrecognition systems or social media sentiment analysis-might also play a role in broader diplomatic processes.  82  Focusing on the procedural contributions that machine learning could make to the creation of new international law, she argues that international lawyers in service of a state's foreign ministry in practice have three roles-negotiating agreements; dispute resolution (whether in judicial or arbitral fora); and advising policymakers about the existence and meaning of international law-and argues that all of these can, in distinct ways, gain from automation.  83  Contrary to the 'strong' scenario discussed above, this modest' image of legal automation does not envision that these lawmaking processes will be entirely given over to machine decision-making, but rather that many actors will come to find significant benefits in using machine learning tools to support human legal and diplomatic decisionmaking processes. To be certain, that does not mean this process of displacement will occur rapidly. There are a number of barriers which can slow procurement and integration of AI tools, and which ensure a lag between the development of state-of-the-art tools in labs, and their use in the field.  84  Deeks does admit that international law can often be 'conservative' about taking up new technologies, and that at present, states and their advisors in international legal issues still lag far behind the private sector in contemplating how AI could change their work. As a result, with a few exceptions, \"international law generally has been a stranger to a new wave of technological tools -including computational text analysis, machine learning, and predictive algorithms -that use large quantities of data to help make sense of the world.\"  85  Furthermore, there remain challenges to the incorporation of AI technologies in international law, including technical challenges around the format of some types of international law data; the fact that international law questions have relatively less precedent to guide predictions; and civil liberties concerns over applications in emotion detection or social media scraping software, amongst others.  86  In spite of this, Deeks does identify several trends that will, in her view, steadily increase the pressure on international lawyers to take up and reckon with these new tools.  79   These are: (1) near-peer ambitions; (2) proofs of concept in private law; (3) client pressure; (4) necessity in the line of work.  87  As such, she argues that while the challenges to adoption are real, they are not insurmountable, and that there are potentially many use cases of AI, whether in the preparation of treaty negotiations, conducting negotiations, or identifying customary international law.  88  In addition to these, there might of course be a more fundamental limit to the significance of governance displacement-through-automation: that is, even if there are many domestic areas where there are significant sources for text-as-data tools to be trained on, these may not be the highest-stakes scenarios that international law faces. After all, international law may be especially engaged by large historical shocks and changes.  89  That would not prevent such AI systems from seeing wide usage in many rote tasks, but it would imply that international legal history would continue to be written by humans for some time. Nonetheless, even this modest scenario might have significant effects. While some AI tools might support greater coordination, the fact that they are developed and owned by some parties may, as Deeks has argued, mean that \"states with a high level of technological sophistication are likely to treat some of these tools as proprietary and critical to their national security, and so may use them in a way that exacerbates existing power differentials.\" 90 This could have erosive effects, and markedly alter dynamics of contestation and the legitimacy of the global governance architecture. \n B. Automation of monitoring & enforcement The second form of governance displacement envisions the use of AI technologies in strengthening the enforcement of existing or future international law and global governance instruments. To be certain, it has long been recognised that new technologies can play a key role in changing the modes and anticipated effectiveness of compliance monitoring and enforcement. Indeed, the role of various forms of 'National Technical Means' 91 in supporting the monitoring of compliance with international commitments, has been wellchronicled in the high-stakes area of arms control. For many decades, a range of technologies including signals intelligence, satellites, networked arrays of seismic, hydroacoustic, infrasound or radionuclide monitoring stations, 92 and (aided by legal arrangements such as the 1992 Treaty on Open Skies) surveillance or radionuclide 'sniffer' aircraft, 93 have all played roles in enabling states parties to monitor and verify 87 ibid 593-597. 88 ibid 599. 89 I thank Laura Emily Christiansen for this point. See also Michael P Scharf, 'Seizing the \"Grotian Moment\": Accelerated Formation of Customary International Law in Times of Fundamental Change' (2010) 43 31.  90  Deeks (n 18) 582.  91  Eric H Arnett, 'Science, Technology, and Arms Control' in Richard Dean Burns (ed), Encyclopedia of Arms Control and Disarmament, vol 1 (Charles Scribner's Sons 1993).  92  See for instance the International Monitoring System (IMS) sensor network which is currently being developed and operated by the Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization, and which deploys four complementary verification methods (seismic, hydroacoustic, infrasound and radionuclide sensors) at 321 monitoring stations spread over 89 countries, in order to detect any signs of nuclear testing. CTBTO Preparatory Commission, 'Overview of the Verification Regime' (Comprehensive Nuclear-Test-Ban Treaty Organization) <https://www.ctbto.org/verificationregime/background/overview-of-the-verification-regime/> accessed 9 September 2020.  93  Treaty on Open Skies 1992 (CTS No 3). See generally also David A Koplow, 'Back to the Future and up to the Sky: Legal Implications of Open Skies Inspection for Arms Control' (1991) 79 California Law Review 421. However, in May 2020, President Donald Trump announced an intention for the US to withdraw from the Open Skies Treaty. Bonnie Jenkins, 'A Farewell to the Open Skies Treaty, and an Era of Imaginative Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) each other's (non)compliance with treaty commitments or various peremptory norms under international law. 94 Indeed, aerial and spatial observation alike continue to play an important role in weapons inspections that underpin arms control.  95  Notably, such tools are critical, not only because they can improve compliance with treaties that are in force (by changing the incentives and calculations of actors regarding the expected results of violating the treaty), but also because in some cases, these technological means can provide the guarantees by which parties are willing to bind themselves to such agreements (that is, set up a regime) in the first place. For instance, Coe and Vaynmann have argued that historically, a critical barrier to reaching arms control agreements has been found in a so-called 'security-transparency' tradeoff.  96  This refers to the dilemma whereby an arms control agreement between A and B to cap B's capabilities must on the one hand have sufficient provisions in place to ensure transparency of B's actions (to ensure A that any cheating can and will be detected), but on the other hand, must not offer A so much transparency of B's military actions, that B holds the arrangement to unacceptably erode its security. In some cases, it may be impossible to satisfy both requirements at once, for, as Coe and Vaynman note: \"[a]ny deal that is transparent enough to assure that one side complies with the deal may also shift the balance of power so much that the other side reneges to exploit this shift. Any deal that preserves the balance of power well enough to be safe for the arming side may not be transparent enough to assure the monitoring side of its compliance. When this is true, no arms control deal will be viable.\"  97  While the 'security-transparency' trade-off might appear to provide grounds for pessimism regarding the prospects of arms control, however, this model also allows that whenever this trade-off is less steep, or where one side can assure itself of the ability to unilaterally monitor the other's compliance, agreements can be struck. Importantly, this highlights structural 'levers' that can be affected, not just through institutional arrangements or confidence-building measures, but also through new technologies, in order to mitigate or sidestep this trade-off. As such, technologies can structurally shift the conditions for an arms control treaty if they increase unilateral compliance monitoring, or if they can reduce the 'transparency-security' trade-off. In the first case, technological advances that increase either party's ability to unilaterally monitor certain capabilities can render a 'closed deal' (whereby parties agree on an arms control deal, but refuse to allow access to facilities for the purposes of mutual verification) viable nonetheless, because either party can be assured that they are able to unilaterally monitor compliance. For instance, in the domain of nuclear arms control, Coe and Vaynmann suggest that the Strategic Arms Limitations Talks (SALT I) negotiations succeeded where the earlier 1964 Freeze negotiations had failed, in large part because the development of satellite surveillance in the intervening years had improved unilateral monitoring capabilities sufficiently to make a 'closed deal' viable.  98  In the second place, there may be ways to take measures that create mutual perceptions that the trade-off between transparency and security is mild. For instance, Thinking' (Brookings, 16 June 2020) <https://www.brookings.edu/blog/order-from-chaos/2020/06/16/afarewell-to-the-open-skies-treaty-and-an-era-of-imaginative-thinking/> accessed 22 June 2020.  94   during the first round of negotiations over the Intermediate Nuclear Forces (INF) Treaty  (1980) (1981) (1982) (1983) , US negotiators initially proposed 'anytime anywhere inspections', which were rejected not only by the USSR but also, before long, by many on their own side.  99  Instead, during the second round of negotiations  (1985) (1986) (1987) , the US put forward proposals for more limited inspections with access to only one missile production facility. Moreover, the US devised a way to outfit Soviet facilities with a sensor that would reveal whether an exiting missile was of the banned type, without revealing the technical characteristics of non-banned missiles.  100  Since the Cold War, there has been continued scientific research into new avenues to, for instance, validate nuclear warheads that are slated for retirement, in ways that do not reveal key engineering features.  101  Indeed, such applications might be recursively applied to the governance of AI itself: while it has been argued that there is historical precedent for global arms control regimes for high-stakes emerging technologies,  102  there remains uncertainty of the viability of monitoring such regimes effectively.  103  However, scholars have recently begun to propose various technical 'sustained verification' mechanisms which could facilitate compliance monitoring for AI arms control regimes, including anti-tamper techniques such as cryptographically hashed software, as well as the use of hardware-affixed sensors that measure the Van Eck radiation emitted by computing hardware when (AI) code is run, aberrations in which could indicate non-compliant actions.  104  This highlights the potentially important role that new technologies can play in improving the ability of states and other parties to make verifiable claims about the properties, capabilities, or inputs of new technologies. Technology can therefore not just incrementally contribute to the deterrent or compliant pull of treaties; it can also, in fact, shift the possibility frontier for which arms control or non-proliferation treaties are politically possible in the first place. Moreover, it is important to note how since the days of the Cold War, the rise of the digital economy has increasingly complemented 'national technical means' with a host of distributed sensors. As a result, over the past decades, the International Atomic Energy Agency (IAEA) has begun to draw on open-source information and commercial satellite imagery in order to provide early warning in nuclear safeguards and to counter nuclear proliferation; 105 commercial satellites have also been proposed to monitor the implementation of the Kyoto Protocol's Global Emissions Trading Program.  106  Moreover, as noted by Livingston & Risse, the emergence and ubiquity of twenty-first century digital technologies, including mobile phones, commercial high-resolution imaging satellites and social media has already begun to enable near-constant surveillance not just by states or corporations, but also by non-state actors such as human rights observers, journalists and open-source (citizen) investigation networks such as Bellingcat or the Syrian Archive.  107  Such open-source technologies have begun to play a key role in monitoring various war crimes, as well as human rights violations.  108  In at least one case, this has led to an indictment under international criminal law: in 2017, digital sleuths identified Libyan execution sites, by triangulating geographical features found in propaganda videos that had been posted to social media, leading to an International Criminal Court warrant for the arrest of Mahmoud Mustafa Busayf Al-Werfalli, a Libyan warlord.  109  While such analysis is predominantly done by humans at present, it involves distinct tasks that could be automated or enhanced by AI tools. Indeed, one recent experiment involved the development and testing of a machine learning algorithm, trained on synthetic data, to go through footage of airstrikes in order to help investigators identify UK-manufactured cluster munitions that are illegally used in conflict; in tests, this system sped up analysis 100-fold, while reducing risk of trauma for investigators.  110  In another project, run by Amnesty International and the Citizen Evidence Lab, researchers deployed machine learning to support the large-scale analysis of satellite data, in order to detect the destruction of human settlements in Sudan's Darfur region.  111  There are various other ways machine learning tools could contribute to the detection or investigation of various violations under international law, 112 or even the early detection and prevention of violence  113  -although this 'AI Turn' in global governance also has its critics.  114  As such, from a more modest perspective, there may be various roles for machine learning approaches-if appropriately and rigorously vetted-in enforcing international law, and in facilitating the negotiation of agreements that are sensitively dependent on the ability to monitor compliance.  115   \n C. The replacement of international 'law'? Shifts in regulatory modality Notably, even if AI were to be used to change the 'input' of international law (e.g., the process of treaty negotiation or adjudication), or strengthen its enforcement, this would not change the nature of the 'output' of those legal processes (that is, normative rules, to greater or lesser degree backed by sanction). 'Legal automation' would no doubt alter the texture of international law irrevocably-but it would presumably remain law. This would not change the core, normative 'regulatory modality' of international law-the instruments through which this system seeks to regulate and change the behaviour of its constituents (whether there are construed narrowly as states, or more broadly, as also including other stakeholders  116  ). However, even in a more modest usage, the deployment of AI systems in the service of international law, or in the measuring of global governance, could shift the preferences, values, or tool choices of global regulators and state actors alike in key ways.  117  As such, AI could drive or facilitate a shift towards novel 'modes' of achieving societally desired regulatory outcomes, which no longer rely to the same extent on normative laws. This discussion draws on Lawrence Lessig's theory of the various 'regulatory modalities' of law, social norms, markets, and architecture.  118  For instance, in the domestic law context, Lessig famously chronicled how the architecture of computer 'code' enabled US regulators to emphasize different 'modalities' in the production and enforcement of law on cyberspace. Specifically, it allowed them to reduce their reliance on normative 'law', and instead regulate tech companies in order to embed architectural constraints on online behaviour, in areas such as zoned speech or privacy protection.  119  Likewise, Roger Brownsword has argued that new technologies introduce a 'double disruption' to law.  120  In the first place, they affect the substance of legal rules. Secondly, they drive a regulatory shift, away from seeking to shape behaviour by normative codes or laws and towards the use of non-normative 'technological management'.  121  Accordingly, Brownsword has chronicled how emerging digital technologies of social control may even shift the core 'regulatory attitude' of authorities, and effect a shift away from traditional 'legal coherentism', towards 'regulatory-instrumentalism' or even 'technocracy'.  122  If a similar shift occurred in the context of global governance, this could also drive value shifts. Speculatively, one can imagine the availability of more powerful AI monitoring capabilities would reduce the need for consensus (so long as there was consensus about trusting the monitoring capabilities). More directly, Deeks has suggested how the proliferation of certain AI technologies in state departments may also shift how states seek to resolve international disputes. It could lead to more unilateral or strategic uses of this technology. For instance, she notes how \"[i]f a state could predict in advance which way a tribunal is likely to resolve a particular dispute, it would allow the state to decide whether to pursue the case or to choose an alternative, such as settling it through diplomatic negotiations or dropping the matter entirely.\"  123  However, there are also more collaborative cases of such 'replacement'. For instance, there may be situations where algorithms can be used to speed up the negotiation process between states, either as 'negotiation support systems' that can propose potential divisions of interests, or by helping locate third-party proposals.  124  However, in such cases, rather than support traditional channels of international law (e.g. arbitration bodies or international courts) through the 'automation' of their operations, AI tools would contribute to the 'replacement' of such tools as dominant instruments of international conflict resolution or collaboration. \n IV. AI's effects on global regime complexity Having discussed the sources and vectors of potential AI-driven governance disruption (and especially automation), it is important to discuss not just the direct effects of such legal displacement in international law, but also the indirect effects on the structure and texture of the international legal system. International legal scholars have for many years reckoned with various new trends and shifts in the global institutional and legal landscape. These include patterns of institutional proliferation,  125  the ongoing fragmentation of international law resulting in complex inter-regime impacts and externalities,  126  and growing patterns of contested multilateralism.  127  Others have identified trends of legal stagnation, and have argued that global governance is increasingly marked by a shift towards informality in many issue areas such as international environmental governance or cyberspace.  128  Let us focus on the 'fragmentation' of international law. Contemporary regime complex theory has explored many drivers of regime complex evolution and development.  129  However, while scholars have reckoned with the effects of exogenous political or institutional shocks to either the trajectory of a regime complex,  130  or to the continued viability of the international liberal order as a whole,  131  there appears to be relatively little examination of the effects of technology-driven change on regime complexity. This is unfortunate because, as the lens of governance disruption has shown, the use of various technologies can in some cases exert considerable effects on the norms, processes, or political scaffolding of the international legal order. As such, it may be productive to explore the implications of AI-driven governance disruption lens for the processes of regime complex evolution. Such examination is certainly more speculative, and it should be re-emphasised that the following sections are not meant as strong predictions, but as conditional scenarios that anticipate the implications of various types of AI-driven governance disruption on regime complexity. For the sake of argument, this following assumes no-or only very modest further capability developments in the available AI capabilities,  132  although it does weakly assume the gradual continuing dissemination or application of existing AI capabilities into more areas and domains, in order to anticipate the implications of distinct patterns of dissemination and usage on regimes. As such, it is argued that we can distinguish between 10 different roles or effects of AI systems on the international legal order. By requiring constant substantive legal development, AI systems can reinforce pre-existing governance trends; it can serve as (1) legal 'canary in the coal mine', highlighting the need for greater harmonization or crossregime dialogue. However, in already-fragmented settings, it can serve as (2) tough knot or (3) generator of regime fault lines, potentially increasing fragmentation. Under even modest scenarios of legal displacement (whether automation or replacement), AI systems can serve variably as a (4) shield, (5) patch, (6) cure, or (7) accelerator of the fragmentation of international law. Finally, AI tools may serve as (8) differential enabler; (9) driver of value shifts, or (10) asymmetric weapon-which could potentially contribute to patters of governance destruction or further erosion in the international legal order. \n A. Fragmentation: AI as a legal canary, tough knot & as generator of regime fault lines At a structural level, how will AI's ability to generate frequent legal uncertaintyand a resulting need for constant development or realignment in the substance, laws or norms of international law-affect the trajectory of a regime complex? One key caveat here is that global governance obviously consists of a wider range of norms and governance instruments than solely those embedded in writ 'hard law'. Critically, many of these softer governance instruments are potentially more resilient to 'legal' disruption-because they are already phrased broadly, depend on discretion for implementation, or are more flexible and easy to review and update in the face of changing technological circumstances.  133  Nonetheless, even if this means that such soft governance instruments are slightly better insulated from-or at least better able to adapt to-AIdriven 'legal' shocks, the conceptual and practical changes forced by the use of these systems still bear on other forms of governance, and may (or arguably should) warrant reexamination. Taking this into account, the prospect of AI systems driving legal development could, paradoxically, exert two divergent effects on regime complexes. On the one hand, situations of clear inadequacy of existing legal instruments or concepts might serve as an opportunity to clarify long-present ambiguities in established global norms, and harmonize latent conflicts between existing regimes, by getting these out in the open, in the context of an urgent governance problem that requires addressing. In this way, AI systems-or particular legal problems or puzzles they flag-can highlight long-standing tacit tensions between existing norms and regimes, and in doing so can serve as a (1) 'canary in the coalmine' of the integrity of the international legal system in the digital age.  134  More broadly, the broad-spectrum legal disruption that is generated by AI systems might illustrate the confusing and fragmenting effects of 'modernity', which, as noted, some regime systems theorists point to as a major factor in the trend towards fragmentation and regime complexity.  135  In this way, the precise effects of AI-driven governance development on the trajectory of a governance architecture will likely depend sensitively on the pre-existing configuration of that architecture. Indeed, it some ways, it could exacerbate pre-existing tendencies. On the one hand, within an already-integrated regime complex, a centralised, authoritative international institution could in principle seize upon AI's legal disruption within one area in order to kick-start and facilitate a broader dialogue about long-overdue systemic revision or legal innovation in underlying rules or concepts. For instance, such an institution could seize upon specific problems posed by AI-enabled military surveillance platforms or 'lethality-enabling technologies',  136  to address the broader fact that the distinction between 'war' and 'peacetime'-a cornerstone of IHL-has, in practice already become blurred by new technologies.  137  Such legal development would not necessarily imply an abandonment of these well-proven frameworks; but it would reckon with the 'transversal' effects of trends in technology across different fields of (international) law, in order to yield more integrated bodies of law. Of course, even if centralised international institutions could in principle carry out such regulatory innovation and integration, it is not a given that they would also do so.  138  On the other hand, starting from an already-fragmented institutional contextand across fragmented application domains-AI technology's propensity to generate situations of legal disruption (requiring development) may well exacerbate the forces of (further) fragmentation, as these systems become (2) tough knots. Given the extremely diverse set of perspectives through which one can approach AI technology, it seems unlikely that a fragmented regime complex would reliably be able to organically converge towards more integrated or harmonised policy responses. Similar AI architectures will be used across widely different contexts; in each of those issue areas, certain self-similar features of AI systems (such as algorithmic unpredictability or opacity, or the susceptibility to adversarial input) can be refracted into seemingly-distinct local problems. If many distinct institutions and organisations are forced to grapple, in parallel and relative isolation, with certain local questions (such as the variable meaning of 'Meaningful Human Control' for LAWS, in healthcare, and in other contexts)) of underlying conceptual or legal disruption, it is likely that we may see distinct institutions and regimes resolve and decide these cases in different, and potentially contradictory ways.  139  In that way, the proliferation of AI systems could serve as a (3) generator for regime fault-lines, triggering a scattering of individual regimes' norms and policies, in ways that drive regime complexity, and that open up considerable scope for conflicts in terms of regime norms, operations, or impact. \n B. Automation: AI as shield, patch, cure or accelerator of fragmentation As one subset of governance disruption, 'displacement' also highlights ways in which the integration or incorporation of AI tools into the practices of global governance can affect regime complexity or the coherence of international law. In brief, some AI tools, especially if they were accessible (or distributed) to many actors (whether states or nonstate observer agencies or NGOs), could play some role in mitigating at least some trends towards regime complexity. They could variably serve as shield to the negative consequences of complexity; as patch to halt the further fragmentation of regimes, or as cure to avert or mitigate latent conflicts and aid in harmonisation of regimes. Yet, left unregulated, the free-for-all use of AI systems could also prove an accelerator of processes of legal and governance fragmentation. 138 Indeed, the question of whether, or under what conditions, international organizations would be capable of this, remains an open and interesting one.  139  Crootof and Ard (n 29). Electronic copy available at: https://ssrn.com/abstract=3806624 To start, (4) various actors might use AI tools to shield themselves from the negative operational consequences of a fragmented and distributed regime complex. For instance, the use of these tools in support of many 'routine' diplomatic tasks could free up the limited diplomatic resources or staff available to many smaller states, enabling them to participate more fully in various international fora, 'levelling' the playing field relative to the large and well-staffed foreign ministries of larger states.  140  More modestly, through translation and text (e.g. news) summarisation services, such AI tools could facilitate the ability of even less powerful actors to navigate dense regimes complexes, counteracting the democratic deficit identified by some concerned scholars.  141  More actively, actors could also AI tools as a (5) patch to halt or pre-empt the further fragmentation of various regimes. For instance, Ashley Deeks notes how various 'text-as-data-tools' might be used to pre-emptively identify treaty conflicts (whether accidental or strategically engineered). She suggests that \"[a] state could create a tool that allows it to compare proposed treaty language (either while the negotiations are underway, or before the state has ratified the treaty) to all other treaties to which the state is a party to detect similar language or very similar topics.\"  142  This could pre-empt or deter strategic efforts by states to create certain treaty conflicts in order to set the agenda for future negotiations,  143  because any negotiation partners would now be able to spot when such a strategy is being attempted.  144  In principle, such AI tools could not only help spot and patch imminent conflicts produced by specific treaties, but could also be deployed as (6) a modest cure to more general pre-existing patterns of fragmentation in international law. For instance, Deeks suggests that states could use such tools even in the absence of specific negotiations, simply to map any tensions amongst their existing treaty commitments, \"in order to identify gaps or other potential conflicts before they produce a real world problem.\" 145 Accordingly, other actors or international organisations could use such tools to chart, to some degree, major fault lines or gaps amongst international law's fragmented regimes. This would of course hardly be a panacea: questions of sufficient text data aside, it should be kept in mind that not all (or even most) practical regime conflicts emerge from inconsistent norm commitments recorded in the legal text.  146  Indeed, as noted by Morin and others, \"[b]latant legal conflicts [amongst regimes] remain rare and a certain degree of normative ambiguity preserves the unity of the international legal system.\"  147  Instead, many regime conflicts may manifest at the level of impacts or institutional policies,  148  as a result of real-world inter-institutional interaction, and such negative externalities are not latent in the texts, and therefore not discoverable with such tools. However, while these uses seem to connote beneficial (or at least, integrative) outcomes of AI displacement on regime complexes, there are many scenarios under which AI tools could also serve as (7) an accelerator of regime fragmentation and complexity. After all, as has been discussed, many AI tools could also be used to challenge or subvert international legal processes, in ways that could speed up contestation. Even if AI technology finds productive uptake by many states to facilitate negotiations, this can have unanticipated side effects. After all, as Crootof has noted, speeding up the development of new international legal obligations-by any means-may certainly be necessary to address urgent problems, or help States avoid or resolve disputes; however it also \"facilitates legal fragmentation [because] [s]peeding up the development of international legal obligations has expanded both the activities they regulate and opportunities for conflict among them.\"  149  As always, of course, the deployment of these technologies is likely to have unanticipated downstream normative, functional, and legal effects. Eyal Benvenisti has argued that the increasing data-processing sharing-capabilities of modern digital technologies, and the growth of modalities of governance that rely on decision-making by machines (rather than two-way exchange of stakeholders) as their input, are creating a foundational challenge to long-established principles in global administrative law, that \"the more communication, the better\", and that information exchange necessarily promotes institutional accountability.  150  All this is not a reason to avoid such tools, but should induce some caution about ensuring appropriate scaffolding or guidelines regarding their global use. \n C. Contestation: AI as differential enabler, driver of value shifts, or asymmetric weapon Amongst leading state developers, perceptions of an emerging technology's very high strategic stakes-whether or not these views are justified-may inhibit willingness to even come to the negotiating table in good faith.  151  Moreover, AI's inherent definitional complexity and effects across many fields, might lend themselves naturally to strategies that seek to obstruct international regulatory action by dragging out debate at international fora. The dual-use nature of many 'inputs' of AI capability-computing hardware; training data; talent-might furthermore make international bans of certain applications difficult to monitor or enforce.  152  All of this could result in notable AI issues remaining unsolved, in spite of them featuring (or being raised) on the international agenda. The clear inability of the existing governance arrangement to address these problems would drive processes of erosion in their legitimacy. More broadly, if AI tools can serve as a (8) differential enabler that is better suited to the interests of illiberal than liberal actors, or to powerful over the powerless actors, this can further exacerbate power inequalities, eroding the legal fiction of the sovereign equality of states, 153 and with it the legitimacy of the international liberal order. Moreover, for certain powerful actors, it might drive preference changes-desires to pursue other avenues of governance. In many other cases, this could drive 'voice and representation' goals. Either of these has generally been linked to processes of institutional proliferation and regime complexity.  154  Simultaneously, AI's use as tool could offer specific capabilities that result in legal decline because it serves as (9) a driver of value shifts, altering the endogenous character of that order. This could be because AI systems might offer strategic capabilities which shift interests; they chip away at the rationales for certain powerful states to engage fully in, or comply with, international law regimes. While they would be unlikely to completely erode support, AI applications in areas such as surveillance could arguably reduce states' (perceived) dependence on multilateral security regimes to ensure their security from terrorist threats. Such capabilities could increase actor's willingness to 'defect', erode their willingness to support multilateralism, and could as such result in preference changes and the resulting increase in the prominence of forum-shopping strategies. That could produce a harmful 'non-regime-state' around many topics of AI. In extreme cases, AI systems could enable new strategies-such as scalable computational propaganda-by which actors could directly challenge the legitimacy of international law or its component regimes.  155  This potential use as an (10) asymmetric weapon might enable the direct contestation and erosion of the liberal international order, more easily than its reinvigoration. AI has not created these particular problems, they it make them worse. Given the above, we have discussed how the use of AI can shape both the normative and conceptual coherence of the regime complex (through driving development or displacement), as well as by shifting the incentives, values, or behaviour of various actors within that regime complex (potentially driving destruction). From a regime complex perspective, then, the key takeaway is that the governance disruptive impacts of AI may compound (1) trends towards regime fragmentation as a result of increased legitimacy problems or preference shifts; and (2) the problematic interactions of regimes (by increasing the number of contact surfaces). To be sure, the above discussion of trajectories remains speculative, given the early state of AI governance at present. All this is not to make strong predictions, but rather to identify a range of ways in which AI applications, through governance disruption, could intersect with processes of regime complexity. In aggregate, these current trends and drivers might loosely suggest that, barring major interventions or external shocks, AI governance may remain fragmented for the time being.  156  However, this is certainly not a foregone conclusion, and it will be key to monitor developments both in the AI regime complex, as well as developments in AI's effects on and in international law, in order to identify in greater detail the overall arc of governance development. In general, they should be wary of the unregulated dissemination and incorporation of (AI) tools in processes of international lawmaking or adjudication. This is because, under plausible development and deployment conditions, these tools may remain largely restricted to major states (at least in the first instance), such that unrestricted usage is likely to further exacerbate power imbalances amongst leading AI states and smaller states, potentially feeding dissatisfaction and contestation.  158  Even in more unambiguously cooperative uses in support of conflict resolution, the use of such AI tools to speed up law-creation could accelerate overall processes of fragmentation, and therefore should be carefully monitored. In particular, this lens might urge scrutiny of AI applications which could, directly or indirectly, shift the 'regulatory modality' away from international conflict resolution through legal norms or processes such as arbitration. The availability of certain AI tools such as population sentiment analysis, computational propaganda, or lie-detection systems might lead some states to seek to increasingly resolve certain foreign policy conflicts through bilateral state channels-or even through unilateral technological intervention-and only to submit for arbitration those issues where they predict they will win.  159  Such shifts could well erode the broader standing or relevance of the global legal order.  160  As such, they should be cautiously monitored and held accountable. At the same time, while a general degree of caution towards international legal automation may be warranted, it should also be remembered that AI-driven displacement offers many meaningful opportunities to increase the efficacy of the global governance architecture, its resilience to future technological disruption as well as other shocks, and even potentially its legitimacy. This speaks in favour of accelerating the development and-subject to rigorous and careful assessment and constraints-dissemination of specifically vetted AI tools that could help improve structural conditions for international cooperation. There are diverse applications of AI that could in principle help shift the international 'cooperation-conflict balance'. These could include AI monitoring capabilities that help provide greater assurance of the detection of state noncompliance, and in so doing help resolve situations of pervasive governance gridlock.  161  Alternatively, technological and institutional interventions could increase the ability of various parties to make verifiable claims about their own AI capabilities, providing stronger foundations for AI-focused arms control regimes.  162  Moreover, various technological interventions (including but not limited to AI tools) could support cooperation and coordination more generally, such as systems that could enable states to reach agreement on issues more quickly.  163  Finally, from the perspective of regime complexity, relatively simple AI language models could allow the advance identification of emergent or imminent norm or treaty conflicts, whether accidental or strategically engineered.  164  Over time, they could also enable a greater mapping and monitoring of fragmentation both in the AI regime complex, 165 as well as in the broader governance 158 ibid 644-646. 159 ibid 628-629.  160  However this could exacerbate the fragmentation of international law, adding a (vertical) dimension of fragmentation to the existing inter-regime conflicts.  161  These could dissolve or at least reduce the 'transparency-security' trade-off, and facilitate 'closed' arms control deals, as discussed above.  162  Miles Brundage and others, 'Toward Trustworthy AI Development: Mechanisms for Supporting Verifiable Claims' [2020] arXiv:2004.07213 [cs] 67-69 <http://arxiv.org/abs/2004.07213> accessed 16 April 2020.  163  Deeks (n 18) 647-648.  164  ibid 616.  165  For instance, others and myself have elsewhere called for the use of various Natural Language Processing-tools to improve the monitoring of trends of conflict, coordination or catalyst in the AI regime complex. Cihon, Maas and Kemp (n 157) 233. Electronic copy available at: https://ssrn.com/abstract=3806624 architecture, supporting processes of convergence. It would be valuable to offer such AI applications free or low-cost to many parties, and teach them how to deploy and use such systems.  166  Such applications could both increase the inclusion of many actors in the fora of international governance, 167 as well as help in the management of governance fragmentation more broadly. Indeed, Dafoe and colleagues have sketched an open research agenda into how AI tools could potentially strengthen cooperation across many contexts; they identify a wide range of AI-supported mechanism design interventions that could improve critical 'cooperative capabilities', such as parties' understanding of the world, their communication abilities, their capacity to make credible commitments, or the institutions (such as norms or regimes) that shape and structure their decision environment.  168  However; the authors also caution that AI-supported cooperation systems could have potential downsides, noting that \"(1) Cooperative competence itself can cause harms, such as by harming those who are excluded from the cooperating set and by undermining prosocial forms of competition (i.e., collusion). (2) Advances in cooperative capabilities may, as a byproduct, improve coercive capabilities (e.g., deception). […] (3) Successful cooperation often depends on coercion (e.g., pro-social punishment) and competition (e.g., rivalry as an impetus for improvement)\".  169  As such, AI's benefits will not manifest by default; and realizing these goods while avoiding these risks will require active and critical engagement by not just international lawyers, but also a range of actors across the global community at large. \n VI. Conclusion This paper has sought to explore, at an initial level of detail, how we can analyse the direct and indirect effects of AI technologies on the viability, form, or functioning of the international liberal legal order. It first provided a functional definition of AI, and a rationale for why we should expect this technology to have wide-ranging impacts on international law. It then explored the pedigree of these questions in existing scholarship on 'law, regulation and technology', and specifically the study of legal automation (LawTech), and studies of the interrelation between technological change and legal systems more broadly (TechLaw). The paper then introduced a 'Governance Disruption' framework for exploring the international legal impacts of AI. This taxonomy distinguishes situations where AI applications create a need for international legal development; and situations where they can contribute to the potential destruction of specific regimes or the erosion of the international legal order. The paper then focused in specifically on the vectors of legal displacement (the potential effects of the 'automation' of international law), discussing the viability, form, and implications of three potential pathways of displacement: automation of rule creation; automation of monitoring & enforcement; or the 'replacement' of international law. The paper then sketched the effects of these trends on the integration or fragmentation of international law, distinguishing 10 different roles that AI systems may play. By requiring constant substantive legal development, AI systems can reinforce  166  Deeks (n 18) 650-652.  167  Höne (n 141).  168  Allan Dafoe and others, 'Open Problems in Cooperative AI' [2020] arXiv:2012.08630 [cs] <http://arxiv.org/abs/2012.08630> accessed 5 January 2021. On the problems and challenges of AI systems creating structural shifts, see also Remco Zwetsloot and Allan Dafoe, 'Thinking About Risks From AI: Accidents, Misuse and Structure' (Lawfare, 11 February 2019) <https://www.lawfareblog.com/thinkingabout-risks-ai-accidents-misuse-and-structure> accessed 12 February 2019; Agnes Schim van der Loeff and others, 'AI Ethics for Systemic Issues: A Structural Approach' (2019) <http://arxiv.org/abs/1911.03216> accessed 13 January 2020.  169  Dafoe and others (n 169) 30. Electronic copy available at: https://ssrn.com/abstract=3806624 pre-existing governance trends; it can serve as (1) legal 'canary in the coal mine', highlighting the need for greater harmonization or cross-regime dialogue. However, in already-fragmented settings, it can serve as (2) tough knot or (3) generator of regime fault lines, potentially increasing fragmentation. Under even modest scenarios of legal displacement (whether automation or replacement), AI systems can serve variably as a (4) shield, (5) patch, (6) cure, or (7) accelerator of the fragmentation of international law. Finally, AI tools may serve as (8) differential enabler; (9) driver of value shifts, or (10) asymmetric weapon-which could potentially contribute to patters of governance destruction or further erosion in the international legal order. It was argued that an examination of possible trajectories for global governance regimes will have to increasingly calculate in effects of AI-driven governance disruption on regime integrity: while some AI capabilities could see use in countering regime fragmentation or treaty conflicts, some AI capabilities could also serve as generators of new legalconceptual fault lines, or spur increased patterns of contestation In the face of these effects, I argued that international legal scholars have an important role to play in critically surveying this new technology and its effects on the international legal system. the question of arms control, not just for LAWS, but for broader uses of AI in military decision-making, seeGiacomo Persi Paoli and others, 'Modernizing Arms Control: Exploring Responses to the Use of AI in Military Decision-Making' (UNIDIR 2020) <https://unidir.org/publication/modernizing-arms-control>. 137 Denise Garcia, 'Future Arms, Technologies, and International Law: Preventive Security Governance' (2016) 1 European Journal of International Security 94; Braden Allenby, 'Are New Technologies Undermining the Laws of War?' (2014) 70 Bulletin of the Atomic Scientists 21 (highlighting drones and cyberwarfare). See also Crootof, 'Regulating New Weapons Technology' (n 58) 10. And see generally Rosa Brooks, 'War Everywhere: Rights, National Security Law, and the Law of Armed Conflict in the Age of Terror' (2004) 153 University of Pennsylvania Law Review 675. \n ( ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n ( ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n and-the-balance-of-power/> accessed 17 May 2018; Michael C Horowitz, 'Do Emerging Military Technologies Matter for International Politics?' (2020) 23 Annual Review of Political Science 385.24  Daniel W Drezner, 'Technological Change and International Relations' (2019) 33 International Relations 286, 287. (\"[a]ny technological change is also an exercise in redistribution. It can create new winners and losers, alter actor preferences, and allow the strategic construction of new norms\").25  For instance, in reflecting on these topics, Roger Brownsword and others have noted that \"debates over these terms, and about the conceptualization of the field or some parts of it, can significantly contribute to our understanding.\" Roger Brownsword, Eloise Scotford and Karen Yeung, 'Law, Regulation, and Technology: The Field, Frame, and Focal Questions' in Roger Brownsword, Eloise Scotford and Karen Yeung (eds), Previously set out in Maas, 'International Law Does Not Compute' (n 21). A version of this is also developed at greater length in Hin-Yan Liu and others, 'Artificial Intelligence and Legal Disruption: A New Model for Analysis' (2020) 12 Law, Innovation and Technology 205. And see Maas, 'Artificial Intelligence Governance Under Change: Foundations, Facets, Frameworks' (n 2). The Oxford Handbook of Law, Regulation and Technology, vol 1 (Oxford University Press 2017) 6 <http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199680832.001.0001/oxfordhb- 9780199680832-e-1> accessed 3 January 2019. 26 Picker (n 19) 151-152. 27 28 Agnieszka McPeak, 'Disruptive Technology and the Ethical Lawyer' (2018) 50 University of Toledo Law Review 457. See also Rebecca Crootof and BJ Ard, 'Structuring Techlaw' (2021) 34 Harvard Journal of Law & Technology n 1 <https://papers.ssrn.com/abstract=3664124> accessed 28 August 2020. \n (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) each other's evolution.\" 29 This work has explored at length how new technologies can alter the concepts, texture and dynamics of legal systems. \n Crootof and Ard (n 29) n 1. See also succinctly BJ Ard and Rebecca Crootof, 'The Case for Two Modes of Disruption, Three Legal Mind-Sets, and the Big Picture of Regulatory Responsibilities' (2018) 14 Indian Journal of Law and Technology 1.33  This echoes the terminology used by the Chinese PLA. Elsa Kania, 'AlphaGo and Beyond: The Chinese \"Technology Law\"' (Nebraska Governance & Technology Center, 16 December 2020) <https://ngtc.unl.edu/blog/case-for- technology-law> accessed 16 March 2021. 30 Miriam C Buiten, 'Towards Intelligent Regulation of Artificial Intelligence' (2019) 10 European Journal of Risk Regulation 41. However, for a critique of technology law approaches that aim to regulate specific 'technologies' (and an argument that the emphasis should instead be on 'regulating for sociotechnical change', see notably Lyria Bennett Moses, 'How to Think about Law, Regulation and Technology: Problems with \"Technology\" as a Regulatory Target' (2013) 5 Law, Innovation and Technology 1; Lyria Bennett Moses, 'Regulating in the Face of Sociotechnical Change' in Roger Brownsword, Eloise Scotford and Karen Yeung (eds), The Oxford Handbook of Law, Regulation, and Technology (2017) <http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199680832.001.0001/oxfordhb- 9780199680832-e-49> accessed 13 May 2017. 31 Lawrence Lessig, 'The Law of the Horse: What Cyberlaw Might Teach' (1999) 113 Harvard Law Review 501; Lawrence Lessig, Code: And Other Laws of Cyberspace, Version 2.0 (2nd Revised ed. edition, Basic Books 2006) <http://codev2.cc/download+remix/Lessig-Codev2.pdf>. 32 Roger Brownsword, Law, Technology and Society: Re-Imagining the Regulatory Environment (1 edition, Routledge 2019); Roger Brownsword, 'Law and Technology: Military Looks to Future \"Intelligentized\" Warfare' (Lawfare, 5 June 2017) <https://www.lawfareblog.com/alphago-and-beyond-chinese-military-looks-future-intelligentized-warfare> accessed 10 June 2017. \n and 34 LawGeex, 'Comparing the Performance of Artificial Intelligence to Human Lawyers in the Review of Standard Business Contracts' (LawGeex 2018) <https://images.law.com/contrib/content/uploads/documents/397/5408/lawgeex.pdf> accessed 27 August 2020. 35 See for instance the CARA AI system. 'CARA A.I.' (Casetext) <https://casetext.com/cara-ai/> accessed 8 September 2020. 36 See for instance the app 'DoNotPay'. RJ Vogt, 'DoNotPay Founder Opens Up On \"Robot Lawyers\"' (Law360, 9 February 2020) <https://www.law360.com/articles/1241251/donotpay-founder-opens-up-on-robot- lawyers> accessed 8 September 2020. 37 For instance, a system trained on 584 judicial decisions of the European Court of Human Rights managed to predict the outcome of new cases with 79% accuracy. Nikolaos Aletras and others, 'Predicting Judicial Decisions of the European Court of Human Rights: A Natural Language Processing Perspective' (2016) 2 PeerJ Computer Science e93. Another study achieved an average accuracy of 75% in predicting the violation of nine articles of the European Convention on Human Rights. Masha Medvedeva, Michel Vols and Martijn Wieling, 'Using Machine Learning to Predict Decisions of the European Court of Human Rights' (2020) 28 Artificial Intelligence and Law 237. Although for a general critique of such projects, see Frank A Pasquale and Glyn Cashwell, 'Prediction, Persuasion, and the Jurisprudence of Behaviorism' [2017] University of Maryland Francis King Carey School of Law Legal Studies Research Paper <https://papers.ssrn.com/abstract=3067737> accessed 8 September 2020. 38 Alarie, Niblett and Yoon (n 22) 424. 39 Casey and Niblett (n 17) 430; Anthony J Casey and Anthony Niblett, 'The Death of Rules and Standards' (2017) 92 Indiana Law Journal 1401, 1410-1411. 40 Joshua P Davis, 'Law Without Mind: AI, Ethics, and Jurisprudence' (Social Science Research Network 2018) SSRN Scholarly Paper ID 3187513 <https://papers.ssrn.com/abstract=3187513> accessed 23 June 2018. For a discussion of the implications of unintelligible legal automation for core theories of law-notably HLA Hart's account which requires critical officials; Joseph Raz's concept grounded in reason-based tests of legitimacy, or Ronald Dworkin's work on deep justifications for coercion-see Sheppard (n 17). 41 See for instance: Frank Pasquale and Glyn Cashwell, 'Four Futures of Legal Automation' (2015) 26 UCLA Law Review Discourse 23; Frank A Pasquale, 'A Rule of Persons, Not Machines: The Limits of Legal Automation' (2019) 87 George Washington Law Review 1; Mireille Hildebrandt, 'Law As Computation in the Era of Artificial Legal Intelligence. Speaking Law to the Power of Statistics' (Social Science Research Network 2017) SSRN Scholarly Paper ID 2983045 <https://papers.ssrn.com/abstract=2983045> accessed 9 July 2018. 42 Crootof, '\"Cyborg Justice\" and the Risk of Technological-Legal Lock-In' (n 22). 43 Lauren Kirchner and others, 'Machine Bias: There's Software Used Across the Country to Predict Future Criminals. And It's Biased Against Blacks.' (ProPublica, 23 May 2016) <https://www.propublica.org/article/machine-bias-risk-assessments-in-criminal-sentencing> accessed 24 May 2017. But see also Sam Corbett-Davies and others, 'A Computer Program Used for Bail and Sentencing Decisions Was Labeled Biased against Blacks. It's Actually Not That Clear.' Washington Post (17 October 2016) <https://www.washingtonpost.com/news/monkey-cage/wp/2016/10/17/can-an-algorithm-be-racist-our- analysis-is-more-cautious-than-propublicas/> accessed 21 May 2017. \n Maas, 'International Law Does Not Compute' (n 21); see also Liu and others (n 28). 56 Kristen E Eichensehr, 'Cyberwar & International Law Step Zero' (2015) 50 TEXAS INTERNATIONAL LAW JOURNAL 24; see also Rebecca Crootof, 'Regulating New Weapons Technology' in Eric Talbot Jensen and Ronald TP Alcala (eds), The Impact of Emerging Technologies on the Law of Armed Conflict (Oxford University Press 2019). 57 See also Crootof, 'Jurisprudential Space Junk' (n 23). 58 For a comparative argument that the usual (state consent-based) toolset of international law may not be well equipped to deal with certain types of global commons challenges, see also Anne van Aaken, 'Is International Law Conducive To Preventing Looming Disasters?' (2016) 7 Global Policy 81. And for reflections on the way forward, see Nico Krisch, 'The Decay of Consent: International Law in an Age of Global Public Goods' (2014) 108 American Journal of International Law 1. But see also Eyal Benvenisti and George W Downs, 'Comment on Nico Krisch, \"The Decay of Consent: International Law in an Age of Global Public Goods\"' (2014) 108 AJIL Unbound 1. Type Example Outcome New governance gaps Development for Need Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) AI-enabled swarm warfare (possibly) not covered by existing international regimes Need for new law. \n Table 1 . 1 A Governance Disruption Framework 59 59 Reproduced from Maas, 'Artificial Intelligence Governance Under Change: Foundations, Facets, Frameworks' (n 2) 196. Distributional changes; more unilateral and strategic action by states; potential legal destruction. Electronic copy available at: https://ssrn.com/abstract=3806624(ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n Maas, 'International Law Does Not Compute' (n 21) 43-49. 61 ibid. It should be noted that this paper distinguished between just two categories of displacement: 'The automation of International Law', comprising both the use of AI in rule creation or adjudication as well as in monitoring and enforcement; and 'The Technological Replacement of International Law'. In this paper, I have split out the former category for clarity. 62 Louis Sohn, 'The Impact of Technological Changes on International Law' (1973) 30 Washington and Lee Law Review 1, 10. 63 Charles Dunlap, 'Lawfare Today: A Perspective' [2008] Yale Journal of International Affairs 146. As discussed by Crootof, 'Regulating New Weapons Technology' (n 58) 6-7. On lawfare generally, see also Jill I Goldenziel, 'Law as a Battlefield: The U.S., China, and Global Escalation of Lawfare' (2020) 106 Cornell Law Review <https://papers.ssrn.com/abstract=3525442> accessed 8 March 2021. 64  Megiddo (n 50).65  Martha Finnemore and Kathryn Sikkink, 'International Norm Dynamics and Political Change' (1998) 52 International Organization 887, 909. \n John Gamble and Charlotte Ku, 'International Law -New Actors and New Technologies: Center Stage for NGOs' (2000) 31 Law and Policy in International Business 221, 249-251; Crootof, 'Regulating New Weapons Technology' (n 58) 6. 67 Richard M Re and Alicia Solow-Niederman, 'Developing Artificially Intelligent Justice' (2019) 22 STANFORD TECHNOLOGY LAW REVIEW 48. \n In which case global society might have more pressing problems to contend with. JG Castel and Mathew E Castel, 'The Road to Artificial Superintelligence -Has International Law a Role to Play?' (2016) 14 Canadian Journal of Law & Technology <https://ojs.library.dal.ca/CJLT/article/download/7211/6256>; Reinmar Nindler, 'The United Nation's Capability to Manage Existential Risks with a Focus on Artificial Intelligence' (2019) 21 International Community Law Review 5.. For expert estimates of timelines of such developments, see Katja Grace and others, 'When Will AI Exceed Human Performance? Evidence from AI Experts' (2018) 62 Journal of Artificial Intelligence Research 729. As well as Ross Gruetzemacher, David Paradice and Kang Bok Lee, 'Forecasting Extreme Labor Displacement: A Survey of AI Practitioners' (2020) 161 Technological Forecasting and Social Change 120323; Ross Gruetzemacher and others, 'Forecasting AI Progress: A Research Agenda' [2020] arXiv:2008.01848 [cs] <http://arxiv.org/abs/2008.01848> accessed 11 August 2020. 73 Gwern Branwen, 'On GPT-3 -Meta-Learning, Scaling, Implications, And Deep Theory' <https://www.gwern.net/newsletter/2020/05> accessed 21 September 2020; Rich Sutton, 'The Bitter Lesson' (Incomplete Ideas, 2019) <http://www.incompleteideas.net/IncIdeas/BitterLesson.html> accessed 16 December 2019; but see Rodney Brooks, 'A Better Lesson' (19 March 2019) <https://rodneybrooks.com/abetter-lesson/> accessed 18 May 2020. Electronic copy available at: https://ssrn.com/abstract=3806624(ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n May 2020) <https://warontherocks.com/2020/05/ai-military-procurement-what-computers-still-cant-do/> accessed 12 May 2020; Maaike Verbruggen, 'The Role of Civilian Innovation in the Development of Lethal Autonomous Weapon Systems' (2019) 10 Global Policy 338; Horowitz (n 24). ibid 596-597. [citing sources] 80 ibid 605. 81 ibid 604-606, 616-622 628-630. 82 ibid 613-615. 83 ibid 589-593. 85 Deeks (n 18) 576. 86 ibid 598-599. 84 Maaike Verbruggen, 'AI & Military Procurement: What Computers Still Can't Do' (War on the Rocks, 5 Electronic copy available at: https://ssrn.com/abstract=3806624 (ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n Maas, 'International Law Does Not Compute' (n 21) 43. 95 David A Koplow, 'What Are You Lookin' at? Aerial and Space Observation for Arms Control' (2021) 115 American Journal of International Law 89. 96 Andrew J Coe and Jane Vaynman, 'Why Arms Control Is So Rare' (2020) 114 American Political Science Review 342. 97 ibid 343. (arguing that this trade-off has driven Iraq's nuclear weapons programs after the Gulf War, great power competition in arms in the interwar period, and superpower military rivalry during the Cold War, noting that this accounts for almost 40% of all global arming in the past 2 centuries). 98  ibid 352. \n 149  Crootof, 'Regulating New Weapons Technology' (n 58) 7.150 Eyal Benvenisti, 'Upholding Democracy Amid the Challenges of New Technology: What Role for the Law of Global Governance?' (2018) 29 European Journal of International Law 9. 151 Picker (n 19). 152 Although see the discussion of using various institutional, software or hardware mechanisms for arms control verification, Infra at III(C). ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) 153  Deeks (n 18) 580.Electronic copy available at: https://ssrn.com/abstract=3806624 ( \n\t\t\t For instance, on the US side, the Pentagon has emphasized its intention to invest up to $2 billion in the next five years to develop programs advancing AI-and spent around $7.4 billion on AI in 2017. Drew Harwell, 'Defense Department Pledges Billions toward Artificial Intelligence Research' Washington Post (7 September 2018) <https://www.washingtonpost.com/technology/2018/09/07/defense-department-pledges- \n\t\t\t Colin B Picker, 'A View from 40,000 Feet: International Law and the Invisible Hand of Technology' (2001) 23 Cardozo Law Review 151, 156. \n\t\t\t Electronic copy available at: https://ssrn.com/abstract=3806624(ISA2021 -'Theoretical Perspectives on International Law' -Draft -Maas -March 2021) \n\t\t\t Maas, 'International Law Does Not Compute' (n 21) 44-45. (reviewing several recent use cases of AI tools in predicting the activities of poachers, the 'Sentry' system providing civilians in the Syrian conflict through advance warning of incoming airstrikes, and in DNA sequencing for use in forensic investigations of war crimes). \n\t\t\t This is one reason why Crootof considers 'soft law' a potentially promising alternate avenue for the international regulation of certain new technologies, especially when compared to the propensity for hardlaw treaties to be rendered obsolete by advancing technology, and the problems involved with then \n\t\t\t Katharina E Höne, 'Mapping the Challenges and Opportunities of Artificial Intelligence for the Conduct of Diplomacy' (DiploFoundation 2019) <https://www.diplomacy.edu/sites/default/files/AI-diplo-report.pdf> accessed 14 March 2019. \n\t\t\t Electronic copy available at: https://ssrn.com/abstract=3806624", "date_published": "n/a", "url": "n/a", "filename": "SSRN-id3806624.tei.xml", "abstract": "The emergence, proliferation, and use of new general-purpose technologies can often produce significant political, redistributive, normative and legal effects on the world. Artificial intelligence (AI) has been identified as one such transformative technology. Many of its impacts may require global governance responses. However, what are the direct and indirect effects of AI technologies on the viability, form, or functioning of the international legal order itself? What, if any, are the prospects, peril or promise of AI-driven legal automation at the international level? This paper draws on an 'AI Governance Disruption' framework to understanding AI's impacts on the global governance architecture. Focusing particularly on the potential for legal automation at the international law level, it explores three potential pathways of such 'legal displacement': (1) the automation of rule creation and arbitration; (2) the automation of monitoring & enforcement; or (3) the 'replacement' of international law with new architectural modes of (international) behaviour control. It then focuses on the effects of these trends on the architecture of international law. It distinguishes 10 different roles that AI applications could play, with distinct effects on the international legal order. That is, AI systems can serve as (1) legal 'canary in the coal mine', highlighting the need for greater cross-regime harmonization. However, it can also serve as (2) tough knot or (3) generator of regime fault lines. Under even modest scenarios of legal automation, AI systems may serve variably as a (4) shield, (5) patch, (6) cure, or (7) accelerator of international legal fragmentation. Finally, AI tools may serve as (8) differential enabler; (9) driver of value shifts, or (10) asymmetric weapon, potentially contributing to trends of contestation or erosion in the international legal order. The paper concludes with a brief review of the ways in which international lawyers or regime scholars might approach the risks and opportunities of increasing automation in international law, in order to leverage these trends and tools towards improved efficacy, resilience, and legitimacy of global governance.", "id": "85c04b80ff8b79447c5b7abd98340f9c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anders Sandberg"], "title": "Ethics of brain emulations", "text": "Introduction Whole brain emulation (WBE) is an approach to achieve software intelligence by copying the functional structure of biological nervous systems into software. Rather than attempting to understand the high-level processes underlying perception, action, emotions and intelligence, the approach assumes that they would emerge from a sufficiently close imitation of the low-level neural functions, even if this is done through a software process.  (Merkle 1989 , Sandberg & Bostrom 2008  While the philosophy  (Chalmers 2010) , impact  (Hanson 2008 ) and feasibility  (Sandberg 2013 ) of brain emulations have been discussed, little analysis of the ethics of the project so far has been done. The main questions of this paper are to what extent brain emulations are moral patients, and what new ethical concerns are introduced as a result of brain emulation technology. \n Brain emulation The basic idea is to take a particular brain, scan its structure in detail at some resolution, construct a software model of the physiology that is so faithful to the original that, when run on appropriate hardware, it will have an internal causal structure that is essentially the same as the original brain. All relevant functions on some level of description are present, and higher level functions supervene from these. While at present an unfeasibly ambitious challenge, the necessary computing power and various scanning methods are rapidly developing. Large scale computational brain models are a very active research area, at present reaching the size of mammalian nervous systems.  (Markram 2006 , Djurfeldt et al. 2008 , Eliasmith et al. 2012 , Preissl et al. 2012 ) WBE can be viewed as the logical endpoint of current trends in computational neuroscience and systems biology. Obviously the eventual feasibility depends on a number of philosophical issues (physicalism, functionalism, non-organicism) and empirical facts (computability, scale separation, detectability, scanning and simulation tractability) that cannot be predicted beforehand; WBE can be viewed as a program trying to test them empirically.  (Sandberg 2013)  Early projects are likely to merge data from multiple brains and studies, attempting to show that this can produce a sufficiently rich model to produce nontrivial behaviour but not attempting to emulate any particular individual. However, it is not clear that this can be carried on indefinitely: higher mammalian brains are organized and simultaneously individualized through experience, and linking parts of different brains is unlikely to produce functional behaviour. This means that the focus is likely to move to developing a \"pipeline\" from brain to executable model, where ideally an individually learned behaviour of the original animal is demonstrated by the resulting emulation. Although WBE focuses on the brain, a realistic project will likely have to include a fairly complex body model in order to allow the emulated nervous system to interact with a simulated or real world, as well as the physiological feedback loops that influence neural activity. At present the only known methods able to generate complete data at cellular and subcellular resolution are destructive, making the scanned brain non-viable. For a number of reasons it is unlikely that non-destructive methods will be developed any time soon  (Sandberg & Bostrom 2008 , appendix E). In the following I will assume that WBE is doable, or at least doesn't suffer enough roadblocks to preclude attempting it, in order to examine the ethics of pursuing the project. \n Virtual lab animals The aim of brain emulation is to create systems that closely imitate real biological organisms in terms of behaviour and internal causal structure. While the ultimate ambitions may be grand, there are many practical uses of intermediate realistic organism simulations. In particular, emulations of animals could be used instead of real animals for experiments in education, science, medicine or engineering. Opponents of animal testing often argue that much of it is excessive and could be replaced with simulations. While the current situation is debatable, in a future where brain emulations are possible it would seem that this would be true: by definition emulations would produce the same kind of results as real animals. However, there are three problems:  Brain emulations might require significant use of test animals to develop the technology.  Detecting that something is a perfect emulation might be impossible.  An emulation might hold the same moral weight as a real animal by being sentient or a being with inherent value. \n Need for experiments Developing brain emulation is going to require the use of animals. They would be necessary not only for direct scanning into emulations, but in various experiments gathering the necessary understanding of neuroscience, testing scanning modalities and comparing the real and simulated animals. In order to achieve a useful simulation we need to understand at least one relevant level of the real system well enough to recreate it, otherwise the simulation will not produce correct data. What kind of lab animals would be suitable for research in brain emulation and how would they be used? At present neuroscientists use nearly all model species, from nematode worms to primates. Typically there are few restrictions on research on invertebrates (with the exception of cephalopods). While early attempts are likely to aim at simple, well defined nervous systems like the nematode Caenorhabditis elegans, Lymnaea Stagnalis (British pond snail) or Drosophila melanogaster (fruit fly), much of the neuroscience and tool development will likely involve standard vertebrate lab animals such as mice, either for in vitro experiments with tissue pieces or in vivo experiments attempting to map neural function to properties that can be detected. The nervous system of invertebrates also differ in many ways from the mammalian nervous system; while they might make good test benches for small emulations it is likely that the research will tend to move towards small mammals, hoping that successes there can be scaled up to larger brains and bodies. The final stages in animal brain emulation before moving on to human emulation would likely involve primates, raising the strongest animal protection issues. In theory this stage might be avoidable if the scaling up from smaller animal brains towards humans seems smooth enough, but this would put a greater risk on the human test subjects. Most \"slice and dice\" scanning (where the brain is removed, fixated and then analysed) avoids normal animal experimentation concerns since there is no experiment done on the living animal itself, just tissue extraction. This is essentially terminal anaesthesia (\"unclassified\" in UK classification of suffering). The only issue here is the pre-scanning treatment, whether there is any harm to the animal in its life coming to an end, and whether in silico suffering possible. However, developing brain emulation techniques will likely also involve experiments on living animals, including testing whether an in vivo preparation behaves like an in vitro and an in silico model. This will necessitate using behaving animals in ways that could cause suffering. The amount of such research needed is at present hard to estimate. If the non-organicism assumption of WBE is correct, most data gathering and analysis will deal with low-level systems such as neuron physiology and connectivity rather than the whole organism; if all levels are needed, then the fundamental feasibility of WBE is cast into question  (Sandberg 2013) . \n What can we learn from emulations? The second problem is equivalent to the current issue of how well animal models map onto human conditions, or more generally how much models and simulations in science reflect anything about reality. The aim is achieving structural validity  (Zeigler, 1985 , Zeigler, Praehofer, & Kim, 2000 , that the emulation reflects how the real system operates. Unfortunately this might be impossible to prove: there could exist hidden properties that only very rarely come into play that are not represented. Even defining meaningful and observable measures of success is nontrivial when dealing with higher order systems  (Sandberg 2013) . Developing methods and criteria for validating neuroscience models is one of the key requirements for WBE. One of the peculiar things about the brain emulation program is that unlike many scientific projects the aim is not directly full understanding of the system that is being simulated. Rather, the simulation is used as a verification of our low-level understanding of neural systems and is intended as a useful tool. Once successful, emulations become very powerful tools for further investigations (or valuable in themselves). Before that stage the emulation does not contribute much knowledge about the full system. This might be seen as an argument against undertaking the WBE project: the cost and animals used are not outweighed by returns in the form of useful scientific knowledge. However, sometimes very risky projects are worth doing because they promise very large eventual returns (consider the Panama Canal) or might have unexpected but significant spin-offs (consider the Human Genome Project). Where the balance lies depends both on how the evaluations are made and the degree of long-term ambition. \n What is the moral status of an emulation? The question what moral consideration we should give to animals lies at the core of the debate about animal experimentation ethics. We can pose a similar question about what moral claims emulations have on us. Can they be wronged? Can they suffer? Indirect theories argue that animals do not merit moral consideration, but the effect of human actions on them does matter. The classic example is Kantian theories, where animals lack moral autonomy and hence are not beings whose interests morally count. Our duties towards them are merely indirect duties towards humanity. Being cruel to animals harms our own humanity: \"Our duties towards animals are merely indirect duties towards humanity. Animal nature has analogies to human nature, and by doing our duties to animals in respect of manifestations of human nature, we indirectly do our duty to humanity…. We can judge the heart of a man by his treatment of animals.\"  (Regan and Singer, 1989: 23-24)  By this kind of indirect account the nature of the emulation does not matter: if it is cruel to pinch the tail of biological mice the same cruel impulse is present in pinching the simulated tail of an emulated mouse. It is like damaging an effigy: it is the intention behind doing damage that is morally bad, not the damage. Conversely, treating emulations well might be like treating dolls well: it might not be morally obligatory but its compassionate. A different take on animal moral considerability come from social contract or feminist ethics, arguing against the individualist bias they perceive in the other theories. What matters is not intrinsic properties but the social relations we have with animals. \"Moral considerability is not an intrinsic property of any creature, nor is it supervenient on only its intrinsic properties, such as its capacities. It depends, deeply, on the kind of relations they can have with us\"  (Anderson 2004)  If we have the same kind of relations to an emulated animal as a biological animal, they should presumably be treated similarly. Since successful emulations (by assumption) also have the same capacity to form reciprocal relations, this seems likely. Another large set of theories argue that the interests of animals do count morally due to intrinsic properties. Typically they are based on the sentience of animals giving them moral status: experiences of pleasure or suffering are morally relevant states no matter what system experiences them. Whether animals are sentient or not is usually estimated from the Argument from Analogy, which supports claims of consciousness by looking at similarities between animals and human beings. Species membership is not a relevant factor. These theories differ on whether human interests still can trump animal interests or whether animals actually have the same moral status as human beings. For the present purpose the important question is whether software emulations can have sentience, consciousness or the other properties these theories ground moral status on. Animal rights can be argued on other grounds than sentience, such as animals having beliefs, desires and self-consciousness of their own and hence having inherent value and rights as subjects of a life that has inherent value.  (Regan 1983 ) Successfully emulated animals would presumably behave in similar ways: the virtual mouse will avoid virtual pain; the isolated social animal will behave in a lonely fashion. Whether the mere behaviour of loneliness or pain-avoidance is an indication of a real moral interest even when we doubt it is associated with any inner experience is problematic: most accounts of moral patienthood take experience as fundamental, because that actually ties the state of affairs to a value, the welfare of something. But theories of value that ascribe value to non-agents can of course allow non-conscious software as a moral patient (for example, having value by virtue of its unique complexity). To my knowledge nobody has yet voiced concern that existing computational neuroscience simulations could have aversive experiences. In fact, the assumption that simulations do not have phenomenal consciousness is often used to motivate such research: \"Secondly, one of the more obvious features of mathematical modelling is that it is not invasive, and hence could be of great advantage in the study of chronic pain. There are major ethical problems with the experimental study of chronic pain in humans and animals. It is possible to use mathematical modelling to test some of the neurochemical and neurophysiological features of chronic pain without the use of methods which would be ethically prohibitive in the laboratory or clinic. Stembach has observed \"Before inflicting pain on humans, can mathematical or statistical modelling provide answers to the questions being considered?\" (p262) (53). We claim that mathematical modelling has the potential to add something unique to the armamentarium of the pain researcher.\"  (Britton & Skevington 1996)  To some degree this view is natural because typical computational simulations contain just a handful of neurons. It is unlikely that so small systems could suffer 1 . However, the largest simulations have reached millions or even billions of neurons: we are reaching the numbers found in brains of small vertebrates that people do find morally relevant. The lack of meaningful internal structure in the network probably prevents any experience from occurring, but this is merely a conjecture. Whether machines can be built to have consciousness or phenomenological states has been debated for a long time, often as a version of the strong AI hypothesis. At one extreme it has been suggested that even thermostats have simple conscious states  (Chalmers 1996) , making phenomenal states independent of higher level functions, while opponents of strong AI have commonly denied the possibility of any machine (or 1 However, note the Small Network Argument  (Herzog et al. 2007) : \"… for each model of consciousness there exists a minimal model, i.e., a small neural network, that fulfills the respective criteria, but to which one would not like to assign consciousness\". Mere size of the model is not a solution: there is little reason to think that 10 11 randomly connected neurons are conscious, and appeals to the right kind of complexity of interconnectedness runs into the argument again. One way out is to argue that fine-grained consciousness requires at least mid-sized systems: small networks only have rudimentary conscious contents  (Taylor, 2007) . Another one is to bite the bullet and accept, if not panpsychism, that consciousness might exist in exceedingly simple systems. Assigning even a small probability to the possibility of suffering or moral importance to simple systems leads to far bigger consequences than just making neuroscience simulations suspect. The total number of insects in the world is so great that if they matter morally even to a tiny degree, their interests would likely overshadow humanity's interests. This is by no means a reductio ad absurdum of the idea: it could be that we are very seriously wrong about what truly matters in the world. at least software) mental states. See  (Gamez 2008 ) for a review of some current directions in machine consciousness. It is worth noting that there are cognitive scientists who produce computational models they consider able to have consciousness (as per their own theories) 2 . Consider the case of Rodney Cotterill's CyberChild, a simulated infant controlled by a biologically inspired neural network and with a simulated body.  (Cotterill 2003)  Within the network different neuron populations corresponding to brain areas such as cerebellum, brainstem nuclei, motor cortices, sensory cortex, hippocampus and amygdala are connected according to an idealized mammalian brain architecture with learning, attention and efference copy signals. The body model has some simulated muscles and states such as levels of blood glucose, milk in the stomach, and urine in the bladder. If the glucose level drops too much it \"expires\". The simulated voice and motions allow it to interact with a user, trying to survive by getting enough milk. Leaving aside the extremely small neural network (20 neurons per area) it is an ambitious project. This simulation does attempt to implement a model of consciousness, and the originator was hopeful that there was no fundamental reason why consciousness could not ultimately develop in it. However, were the CyberChild conscious, it would have a very impoverished existence. It would exist in a world of mainly visual perception, except for visceral inputs, 'pain' from full nappies, and hunger. Its only means of communication is crying and the only possible response is the appearance (or not) of a bottle that has to be manoeuvred to the mouth. Even if the perceptions did not have any aversive content there would be no prospect of growth or change. This is eerily similar to Metzinger's warning  (Metzinger 2003, p. 621) : \"What would you say if someone came along and said, \"Hey, we want to genetically engineer mentally retarded human infants! For reasons of scientific progress we need infants with certain cognitive and emotional deficits in order to study their postnatal psychological development-we urgently need some funding for this important and innovative kind of research!\" You would certainly think this was not only an absurd and appalling but also a dangerous idea. It would hopefully not pass any ethics committee in the democratic world. However, what today's ethics committees don't see is how the first machines satisfying a minimally sufficient set of constraints for conscious experience could be just like such mentally retarded infants. They would suffer from all kinds of functional and representational deficits too. But they would now also subjectively experience those deficits. In addition, they would have no political lobby-no representatives in any ethics committee.\" He goes on arguing that we should ban all attempts to create or even risk the creation artificial systems that have phenomenological self-models. While views on what the particular criterion for being able to suffer is might differ between different thinkers, it is clear that the potential for suffering software should be a normative concern. However, as discussed in mainstream animal rights ethics, other interests (such as human interests) can sometimes be strong enough to allow animal suffering. Presumably such interests (if these accounts of ethics are correct) would also allow for creating suffering software. David  Gamez (2005)  suggests a probability scale for machine phenomenology, based on the intuition that machines built along the same lines as human beings are more likely to have conscious states than other kinds of machines. This scale aims to quantify how likely a machine is to be ascribed to be able to exhibit such states (and to some extent, address Metzinger's ethical concerns without stifling research). In the case of WBE, the strong isomorphism with animal brains gives a fairly high score 3 .  Arrabales, Ledezma, and Sanchis (2010)  on the other hand suggests a scale for the estimation of the potential degree of consciousness based on architectural and behavioural features of an agent; again a successful or even partial WBE implementation of an animal would by definition score highly (with a score dependent on species). The actual validity and utility of such scales can be debated, but insofar they formalize intuitions about the Argument from Analogy about potential mental content they show that WBE at least has significant apparent potential of being a system that has states that might make it a moral patient. WBE is different from entirely artificial software in that it deliberately tries to be as similar as possible to morally considerable biological systems, and this should make us more ethically cautious than with other software. Much to the point of this section, Dennett has argued that creating a machine able to feel pain is nontrivial, to a large extent in the incoherencies in our ordinary concept of pain. (Dennett 1978) However, he is not against the possibility in principle: \"If and when a good physiological sub-personal theory of pain is developed, a robot could in principle be constructed to instantiate it. Such advances in science would probably bring in their train wide-scale changes in what we found intuitive about pain, so that the charge that our robot only suffered what we artificially called pain would lose its persuasiveness. In the meantime (if there were a cultural  3  For an electrophysiological WBE model the factors are FW1, FM1, FN4, AD3, with rate, size and time slicing possibly ranging over the whole range. This produces a weighting ranging between 10 -5 to 0.01, giving an ordinal ranking 170-39 out of 812. The highest weighting beats the neural controlled animat of DeMarse et al., a system containing real biological neurons controlling a robot. lag) thoughtful people would refrain from kicking such a robot.\"  (Dennett 1978 p. 449)  From the eliminative materialist perspective we should hence be cautious about ascribing or not ascribing suffering to software, since we do not (yet) have a good understanding of what suffering is (or rather, what the actual underlying component that is morally relevant, is). In particular, successful WBE might indeed represent a physiological sub-personal theory of pain, but it might be as opaque to outside observers as real physiological pain. The fact that at present there does not seem to be any idea of how to solve the hard problem of consciousness or how to detect phenomenal states seem to push us in the direction of suspending judgement: \"Second, there are the arguments of  Moor (1988)  and  Prinz (2003) , who suggest that it may be indeterminable whether a machine is conscious or not. This could force us to acknowledge the possibility of consciousness in a machine, even if we cannot tell for certain whether this is the case by solving the hard problem of consciousness.\"  (Gamez 2008)  While the problem of animal experience and status is contentious, the problem of emulated experience and status will by definition be even more contentious. Intuitions are likely to strongly diverge and there might not be any empirical observations that could settle the differences. \n The principle of assuming the most What to do in a situation of moral uncertainty about the status of emulations? 4 It seems that a safe strategy would be to make the most cautious assumption: Principle of Assuming the Most (PAM): Assume that any emulated system could have the same mental properties as the original system and treat it correspondingly. The mice should be treated the same in the real laboratory as in the virtual. It is better to treat a simulacrum as the real thing than to mistreat a sentient being. This has the advantage that many of the ethical principles, regulations and guidance in animal testing can be carried over directly to the pursuit of brain emulation. This has some similarity to the Principle of Substrate Non-Discrimination (\"If two beings have the same functionality and the same conscious experience, and differ only in the substrate of their implementation, then they have the same moral status.\")  (Bostrom & Yudkowsky 2011)  but does not assume that the conscious experience is identical. On the other hand, if one were to reject the principle of substrate nondiscrimination on some grounds, then it seems that one could also reject PAM since one does have a clear theory of what systems have moral status. However, this seems to be a presumptuous move given the uncertainty of the question. Note that once the principle is applied, it makes sense to investigate in what ways the assumptions can be sharpened. If there are reasons to think that certain mental properties are not present, they overrule the principle in that case. An emulated mouse that does not respond to sensory stimuli is clearly different from a normal mouse. It is also relevant to compare to the right system. For example, the CyberChild, despite its suggestive appearance, is not an emulation of a human infant but at most an etiolated subset of neurons in a generic mammalian nervous system. It might be argued that this principle is too extreme, that it forecloses much of the useful pain research discussed by  (Britton & Skevington, 1996) . However, it is agnostic on whether there exist overruling human interests. That is left for the ethical theory of the user to determine, for example using cost-benefit methods. Also, as discussed below, it might be quite possible to investigate pain systems without phenomenal consciousness. \n Ameliorating virtual suffering PAM implies that unless there is evidence to the contrary, we should treat emulated animals with the same care as the original animal. This means in most cases that practices that would be impermissible in the physical lab are impermissible in the virtual lab. Conversely, counterparts to practices that reduce suffering such as analgesic practices should be developed for use on emulated systems. Many of the best practices discussed in  (Schofield 2002 ) can be readily implemented: brain emulation technology by definition allows parameters of the emulation can be changed to produce the same functional effect as the drugs have in the real nervous system. In addition, pain systems can in theory be perfectly controlled in emulations (for example by inhibiting their output), producing \"perfect painkillers\". However, this is all based on the assumption that we understand what is involved in the experience of pain: if there are undiscovered systems of suffering careless research can produce undetected distress. It is also possible to run only part of an emulation, for example leaving out or blocking nociceptors, the spinal or central pain systems, or systems related to consciousness. This could be done more exactly (and reversibly) than in biological animals. Emulations can also be run for very brief spans of time, not allowing any time for a subjective experience. But organisms are organic wholes with densely interacting parts: just like in real animal ethics there will no doubt exist situations where experiments hinge upon the whole behaving organism, including its aversive experiences. It is likely that early scans, models and simulations will often be flawed. Flawed scans would be equivalent to animals with local or global brain damage. Flawed models would introduce systemic distortions, ranging from the state of not having any brain to abnormal brain states. Flawed simulations (broken off because of software crashes) would correspond to premature death (possibly repeated, with no memorysee below). Viewed in analogy with animals it seems that the main worry should be flawed models producing hard-to-detect suffering. Just like in animal research it is possible to develop best practices. We can approximate enough of the inner life of animals from empirical observations to make some inferences; the same process is in principle possible with emulations to detect problems peculiar to their state. In fact, the transparency of an emulation to datagathering makes it easier to detect certain things like activation of pain systems or behavioural withdrawal, and backtrack their source. \n Quality of life An increasing emphasis is placed not just on lack of suffering among lab animals but on adequate quality of life. What constitutes adequate is itself a research issue. In the case of emulations the problem is that quality of life presumably requires both an adequate body, and an adequate environment for the simulated body to exist in. The VR world of an emulated nematode or snail is likely going to be very simple and crude even compared to their normal petri dish or aquarium, but the creatures are unlikely to consider that bad. But as we move up among the mammals, we will get to organisms that have a quality of life. A crude VR world might suffice for testing the methods, but would it be acceptable to keep a mouse, cat or monkey in an environment that is too bare for any extended time? Worse, can we know in what ways it is too bare? We have no way of estimating the importance rats place on smells, and whether the smell in the virtual cage are rich enough to be adequate. The intricacy of body simulations also matters: how realistic does a fur have to feel to simulated touch to be adequate? I estimate that the computational demands of running a very realistic environment are possible to meet and not terribly costly compared to the basic simulation  (Sandberg & Bostrom 2008, p. 76-78) . However, modelling the right aspects requires a sensitive understanding of the lifeworlds of animals we might simply be unable to reliably meet. However, besides the ethical reasons to pursue this understanding there is also a practical need: it is unlikely emulations can be properly validated unless they are placed in realistic environments. \n Euthanasia Most regulations of animal testing see suffering as the central issue, and hence euthanasia as a way of reducing it. Some critics of animal experimentation however argue that an animal life holds intrinsic value, and ending it is wrong. In the emulation case strange things can happen, since it is possible (due to the multiple realizability of software) to create multiple instances of the same emulation and to terminate them at different times. If the end of the identifiable life of an instance is a wrong, then it might be possible to produce large number of wrongs by repeatedly running and deleting instances of an emulation even if the experiences during the run are neutral or identical. Would it matter if the emulation was just run for a millisecond of subjective time? During this time there would not be enough time for any information transmission across the emulated brain, so presumably there could not be any subjective experience. Accounts of value of life built upon being a subject of a life would likely find this unproblematic: the brief emulations do not have a time to be subjects, the only loss might be to the original emulation if this form of future is against its interests. Conversely, what about running an emulation for a certain time, making a backup copy of its state, and then deleting the running emulation only to have it replaced by the backup? In this case there would be a break in continuity of the emulation that is only observable on the outside, and a loss of experience that would depend on the interval between the backup and the replacement. It seems unclear that anything is lost if the interval is very short. Regan argues that the harm of death is a function of the opportunities of satisfaction it forecloses  (Regan 1983) ; in this case it seems that it forecloses the opportunities envisioned by the instance while it is running, but it is balanced by whatever satisfaction can be achieved during that time. Most concepts of the harmfulness of death deal with the irreversible and identity-changing aspects of the cessation of life. Typically, any reversible harm will be lesser than an irreversible harm. Since emulation makes several of the potential harms of death (suffering while dying, stopping experience, bodily destruction, changes of identity, cessation of existence) completely or partially reversible it actually reduces the sting of death. In situations where there is a choice between the irreversible death of a biological being and an emulation counterpart, the PAM suggests we ought to play it safe: they might be morally equivalent. The fact that we might legitimately doubt whether the emulation is a moral patient doesn't mean it has a value intermediate between the biological being and nothing, but rather that the actual value is either full or none, we just do not know which. If the case is the conversion of the biological being into an emulation we are making a gamble that we are not destroying something of value (under the usual constraints in animal research of overriding interests, or perhaps human autonomy in the case of a human volunteer). However, the reversibility of many forms of emulation death may make it cheaper. In a lifeboat case  (Regan, 1983) , should we sacrifice the software? If it can be restored from backup the real loss will be just the lost memories since last backup and possibly some freedom. Death forecloses fewer opportunities to emulations. It might of course be argued that the problem is not ending emulations, but the fundamental lack of respect for a being. This is very similar to human dignity arguments, where humans are assumed to have intrinsic dignity that can never be removed, yet it can be gravely disrespected. The emulated mouse might not notice anything wrong, but we know it is treated in a disrespectful way. There is a generally accepted view that animal life should not be taken wantonly. However, emulations might weaken this: it is easy and painless to end an emulation, and it might be restored with equal ease with no apparent harm done. If more animals are needed, they can be instantiated up to the limits set by available hardware. Could emulations hence lead to a reduction of the value of emulated life? Slippery slope arguments are rarely compelling; the relevant issues rather seem to be that the harm of death has been reduced and that animals have become (economically) cheap. The moral value does not hinge on these factors but on the earlier discussed properties. That does not mean we should ignore risks of motivated cognition changing our moral views, but the problem lies in complacent moral practice rather than emulation. \n Conclusion Developing animal emulations would be a long-running, widely distributed project that would require significant animal use. This is not different from other major neuroscience undertakings. It might help achieve replacement and reduction in the long run, but could introduce a new morally relevant category of sentient software. Due to the uncertainty about this category I suggest a cautious approach: it should be treated as the corresponding animal system absent countervailing evidence. While this would impose some restrictions on modelling practice, these are not too onerous, especially given the possibility of better-than-real analgesia. However, questions of how to demonstrate scientific validity, quality of life and appropriate treatment of emulated animals over their \"lifespan\" remain. \n Human emulations Brain emulation of humans raise a host of extra ethical issues or sharpen the problems of proper animal experimentation. \n Moral status The question of moral status is easier to handle in the case of human emulations than in the animal case since they can report back about their state. If a person who is sceptical of brain emulations being conscious or having free will is emulated and, after due introspection and consideration, changes their mind, then that would seem to be some evidence in favour of emulations actually having an inner life. It would actually not prove anything stronger than that the processes where a person changes their mind are correctly emulated and that there would be some disconfirming evidence in the emulation. It could still be a lacking consciousness and be a functional philosophical zombie (assuming this concept is even coherent). If philosophical zombies existed, it seems likely that they would be regarded persons (at least in the social sense). They would behave like persons, they would vote, they would complain and demand human rights if mistreated, and in most scenarios there would not be any way of distinguishing the zombies from the humans. Hence, if emulations of human brains work well enough to exhibit human-like behaviour rather than mere human-like neuroscience, legal personhood is likely to eventually follow, despite misgivings of sceptical philosophers 5 . \n Volunteers and emulation rights An obvious question is volunteer selection. Is it possible to give informed consent to brain emulation? The most likely scanning methods are going to be destructive, meaning that they end the biological life of the volunteer or would be applied to postmortem brains. In the first case, given the uncertainty about the mental state of software there is no way of guaranteeing that there will anything \"after\", even if the scanning and 5 Francis Fukuyama, for example, argues that emulations would lack consciousness or true emotions, and hence lack moral standing. It would hence be morally acceptable to turn them off at will.  (Fukyama, 2002, p.167-170)  In the light of his larger argument about creeping threats to human dignity, he would presumably see working human WBE as an insidious threat to dignity by reducing us to mere computation. However, exactly what factor to base dignity claims on is if in anything more contested than what to base moral status on; see for example  (Bostrom, 2009)  for a very different take on the concept. emulation are successful (and of course the issues of personal identity and continuity). Hence volunteering while alive is essentially equivalent to assisted suicide with an unknown probability of \"failure\". It is unlikely that this will be legal on its own for quite some time even in liberal jurisdictions: suicide is increasingly accepted as a way of escaping pain, but suicide for science is not regarded as an acceptable reason 6 . Some terminal patients might yet argue that they wish to use this particular form of \"suicide\" rather than a guaranteed death, and would seem to have autonomy on their side. An analogy can be made to the use of experimental therapies by the terminally ill, where concerns about harm must be weighed against uncertainty about the therapy, and where the vulnerability of the patient makes them exploitable  (Falit & Gross 2008) . In the second case, post-mortem brain scanning, the legal and ethical situation appears easier. There is no legal or ethical person in existence, just the preferences of a past person and the rules for handling anatomical donations. However, this also means that a successful brain emulation based on a person would exist in a legal limbo. Current views would hold it to be a possession of whatever institution performed the experiment rather than a person 7 .  6  The Nuremberg code states: \"No experiment should be conducted, where there is an a priori reason to believe that death or disabling injury will occur; except, perhaps, in those experiments where the experimental physicians also serve as subjects.\" But selfexperimentation is unlikely to make high risk studies that would otherwise be unethical ethical. Some experiments may produce so lasting harm that they cannot be justified for any social value of the research  (Miller and Rosenstein, 2008) .  7  People involved in attempts at preserving legally dead but hopefully recoverable patients are trying to promote recognition of some rights of stored individuals. See for instance the Bill of Brain Preservation Rights (Brain Preservation Foundation 2013). Specifically, it argues Presumably a sufficiently successful human brain emulation (especially if it followed a series of increasingly plausible animal emulations) would be able to convince society that it was a thinking, feeling being with moral agency and hence entitled to various rights. The PAM would support this: even if one were sceptical of whether the being was \"real\", the moral risk of not treating a potential moral agent well would be worse than the risk of treating non-moral agents better than needed. Whether this would be convincing enough to have the order of death nullified and the emulation regarded as the same legal person as the donor is another matter, as is issues of property ownership. The risk of ending up a non-person and possibly being used against one's will for someone's purposes, ending up in a brain damaged state, or ending up in an alien future, might not deter volunteers. It certainly doesn't deter people signing contract for cryonic preservation today, although they are fully aware that they will be stored as non-person anatomical donations and might be revived in a future with divergent moral and social views. Given that the alternative is certain death, it appears to be a rational choice for many. that persons in storage should be afforded similar rights to living humans in temporally unconscious states. This includes ensuring quality medical treatment and long term storage, but also revival rights (\"The revival wishes of the individual undergoing brain preservation should be respected, when technically feasible. This includes the right to partial revival (memory donation instead of identity or self-awareness revival), and the right to refuse revival under a list of circumstances provided by the individual before preservation.\") and legal rights allowing stored persons to retain some monetary or other assets in trust form that could be retrieved upon successful revival. This bill of rights would seem suggests similar right for stored stored emulations. \n Handling of flawed, distressed versions While this problem is troublesome for experimental animals, it becomes worse for attempted human emulations. The reason is that unless the emulation is so damaged that it cannot be said to be a mind with any rights, the process might produce distressed minds that are rightsholders yet have existences not worth living, or lack the capacity to form or express their wishes. For example, they could exist in analogues to persistent vegetative states, dementia, schizophrenia, aphasia, or have on-going very aversive experience. Many of these ethical problems are identical to current cases in medical ethics. One view would be that if we are ethically forbidden from pulling the plug of a counterpart biological human, we are forbidden from doing the same to the emulation. This might lead to a situation where we have a large number of emulation \"patients\" requiring significant resources, yet not contributing anything to refining the technology nor having any realistic chance of a \"cure\". However, brain emulation allows a separation of cessation of experience from permanent death. A running emulation can be stopped and its state stored, for possible future reinstantiation. This leads to a situation where at least the aversive or meaningless experience is stopped (and computational resources freed up), but which poses questions about the rights of the now frozen emulations to eventual revival. What if they were left on a shelf forever, without ever restarting? That would be the same as if they had been deleted. But do they in that case have a right to be run at least occasionally, despite lacking any benefit from the experience? Obviously methods of detecting distress and agreed on criteria for termination and storage will have to be developed well in advance of human brain emulation, likely based on existing precedents in medicine, law and ethics. Persons might write advance directives about the treatment of their emulations. This appears equivalent to normal advance directives, although the reversibility of local termination makes pulling the plug less problematic. It is less clear how to handle wishes to have more subtly deranged instances terminated. While a person might not wish to have a version of themselves with a personality disorder become their successor, at the point where the emulation comes into being it will potentially be a moral subject with a right to its life, and might regard its changed personality as the right one. \n Identity Personal identity is likely going to be a major issue, both because of the transition from an original unproblematic human identity to successor identity/identities that might or might not be the same, and because software minds can potentially have multiple realisability. The discussion about how personal identity relates to successor identities on different substrates is already extensive, and will be foregone here. See for instance  (Chalmers, 2010) . Instantiating multiple copies of an emulation and running them as separate computations is obviously as feasible as running a single one. If they have different inputs (or simulated neuronal noise) they will over time diverge into different persons, who have not just a shared past but at least initially very similar outlooks and mental states. Obviously multiple copies of the same original person pose intriguing legal challenges. For example, contract law would need to be updated to handle contracts where one of the parties is copieddoes the contract now apply to both? What about marriages? Are all copies descended from a person legally culpable of past deeds occurring before the copying? To what extent does the privileged understanding copies have of each other affect their suitability as witnesses against each other? How should votes be allocated if copying is relatively cheap and persons can do \"ballot box stuffing\" with copies? Do copies start out with equal shares of the original's property? If so, what about inactive backup copies? And so on. These issues are entertaining to speculate upon and will no doubt lead to major legal, social and political changes if they become relevant. From an ethical standpoint, if all instances are moral agents, then the key question is how obligations, rights and other properties carry over from originals to copies and whether the existence of copies change some of these. For example, making a promise \"I will do X\" is typically meant to signify that the future instance of the person making the promise will do X. If there are two instances it might be enough that one of them does X (while promising not to do X might morally oblige both instances to abstain). But this assumes the future instances acknowledges the person doing the promise as their past selfa perhaps reasonable assumption, but one which could be called into question if there is an identity affecting transition to brain emulation in between (or any other radical change in self-identity). Would it be moral to voluntarily undergo very painful and/or lethal experiments given that at the end that suffering copy would be deleted and replaced with a backup made just after making the (voluntarily and fully informed) decision to participate? It seems that current views on scientific self-experimentation do not allow such behaviour on the grounds that there are certain things it is never acceptable to do for science. It might be regarded as a combination of the excessive suffering argument (there are suffering so great that no possible advance in knowledge can outweigh its evil) and a human dignity argument (it would be a practice that degrade the dignity of humans). However, the views on what constitutes unacceptable suffering and risk has changed historically and is not consistent across domains. Performance artists sometimes perform acts that would be clearly disallowed as scientific acts, yet the benefit of their art is entirely subjective  (Goodall, 1999) . It might be that as the technology becomes available boundaries will be adjusted to reflect updated estimates of what is excessive or lacks dignity, just as we have done in many other areas (e.g. reproductive medicine, transplant medicine). \n Time and communication Emulations will presumably have experience and behave on a timescale set by the speed of their software. The speed a simulation is run relative to the outside world can be changed, depending on available hardware and software. Current large-scale neural simulations are commonly run with slowdown factors on the order of a thousand, but there does not seem to be any reason precluding emulations running faster than realtime biological brains 8 . Nick Bostrom and Eliezer Yudkowsky have argued for a Principle of Subjective Rate of Time: \"In cases where the duration of an experience is of basic normative significance, it is the experience's subjective duration that counts.\"  (Bostrom & Yudkowsky 2011) . By this account frozen states does not count at all. Conversely, very fast emulations can rapidly produce a large amount of positive or negative value if they are in extreme states: they might count for more in utilitarian calculations. Does human emulation have a right to real-time? Being run at a far faster or slower rate does not matter as long as an emulation is only interacting with a virtual world and other emulations updating at the same speed. But when interacting with the outside world, speed matters. A divergent clockspeed would make communication with people troublesome or impossible. Participation in social activities and meaningful relationships depend on interaction and might be made impossible if they speed past faster than the emulation can handle. A very fast emulation would be isolated from the outside world by lightspeed lags and from biological humans by their glacial slowness. It hence seems that insofar emulated persons are to enjoy human rights (which typically hinge on interactions with other persons and institutions) they need to have access to real-time interaction, or at least \"disability support\" if they cannot run fast enough (for example very early emulations with speed limited by available computer power). By the same token, this may mean emulated humans have a right to contact with the world outside their simulation. As Nozick's experience machine demonstrates, most people seem to want to interact with the \"real world\", although that might just mean the shared social reality of meaningful activity rather than the outside physical world. At the very least emulated people would need some \"I/O rights\" for communication within their community. But since the virtual world is contingent upon the physical world and asymmetrically affected by it, restricting access only to the virtual is not enough if the emulated people are to be equal citizens of their wider society. \n Vulnerability Brain emulations are extremely vulnerable by default: the software and data constituting them and their mental states can be erased or changed by anybody with access to the system on which they are running. Their bodies are not self-contained and their survival dependent upon hardware they might not have causal control over. They can also be subjected to undetectable violations such as illicit copying. From an emulation perspective software security is identical to personal security. Emulations also have a problematic privacy situation, since not only their behaviour can be perfectly documented by the very system they are running on, but also their complete brain states are open for inspection. Whether that information can be interpreted in a meaningful way depends on future advances in cognitive neuroscience, but it is not unreasonable to think that by the time human emulations exist many neural correlates of private mental states will be known. This would put them in a precarious situation. These considerations suggest that the ethical way of handling brain emulations would be to require strict privacy protection of the emulations and that the emulated persons had legal protection or ownership of the hardware on which they are running, since it is in a sense their physical bodies. Some technological solutions such as encrypted simulation or tamper-resistant special purpose hardware might help. How this can be squared with actual technological praxis (for example, running emulations as distributed processes on rented computers in the cloud) and economic considerations (what if an emulation ran out of funds to pay for its upkeep?) remains to be seen. \n Self-Ownership Even if emulations are given personhood they might still find the ownership of parts of themselves to be complicated. It is not obvious that an emulation can claim to own the brain scan that produced it: it was made at a point in time where the person did not legally exist. The process might also produce valuable intellectual property, for example useful neural networks that can be integrated in non-emulation software to solve problems, in which case the matter of who has a right to the property and proceeds from it emerge. This is not just an academic question: ownership is often important for developing technologies. Investors want to have returns on their investment, innovators want to retain control over their innovations. This was apparently what partially motivated the ruling in Moore v. Regents of the University of California that a patient did not have property rights to cells extracted from his body and turned into lucrative products.  (Gold, 1998) .This might produce pressures that work against eventual selfownership for the brain emulations. Conversely essential subsystems of the emulation software or hardware may be licenced or outright owned by other parties. Does right to life trump or self-ownership property ownership? At least in the case of the first emulations it is unlikely they would have been able to sign any legal contracts, and they might have a claim. However, the owners might still want fair compensation. Would it be acceptable for owners of computing facilities to slow down or freeze non-paying emulations? It seems that the exact answer depends on how emulation self-ownership is framed ethically and legally. \n Global issues and existential risk The preliminary work that has been done on the economics and social impact of brain emulation suggest they could be a massively disruptive force. In particular, simple economic models predict that copyable human capital produces explosive economic growth and (emulated) population increase but also wages decreasing towards Malthusian levels.  (Hanson 1994 (Hanson , 2008 . Economies that can harness emulation technology well might have a huge strategic advantage over latecomers. WBE could introduce numerous destabilizing effects, such as increasing inequality, groups that become marginalized, disruption of existing social power relationships and the creation of opportunities to establish new kinds of power, the creation of situations in which the scope of human rights and property rights are poorly defined and subject to dispute, and particularly strong triggers for racist and xenophobic prejudices, or vigorous religious objections. While all these factors are speculative and depend on details of the world and WBE emergence scenario, they are a cause for concern. An often underappreciated problem is existential risk: the risk that humanity and all Earth-derived life goes extinct (or suffers a global, permanent reduction in potential or experience)  (Bostrom 2002) . Ethical analysis of the issue shows that reducing existential risk tends to take strong precedence over many other considerations  (Bostrom, 2003 (Bostrom, , 2013 . Brain emulations have a problematic role in this regard. On one hand they might lead to various dystopian scenarios, on the other hand they might enable some very good outcomes. As discussed above, the lead-up to human brain emulation might be very turbulent because of arms races between different groups pursuing this potentially strategic technology, fearful other groups would reach the goal ahead of them. This might continue after the breakthrough, now in the form of wild economic or other competition. Although the technology itself is not doing much, the sheer scope of what it could do leads to potential war. It could also be that competitive pressures or social drift in a society with brain emulation leads to outcomes where value is lost. For example, wage competition between copyable minds may drive wages down to Malthusian levels, produce beings only optimized for work, spending all available resources on replication, or gradual improvements in emulation efficiency lose axiologically valuable traits  (Bostrom 2004 ). If emulations are zombies humanity, tempted by cybernetic immortality, may gradually trade away its consciousness. These may be evolutionary attractors that may prove inescapable without central coordination: each step towards the negative outcome is individually rational. On the other hand, there at least four major ways emulations might lower the risks of Earth-originating intelligence going extinct: First, the existence of nonbiological humans would ensure at least partial protection from some threats: there is no biological pandemic that can wipe out software. Of course, it is easy to imagine a digital disaster, for example an outbreak of computer viruses that wipe out the brain emulations. But that threat would not affect the biological humans. By splitting the human species into two the joint risks are significantly reduced. Clearly threats to the shared essential infrastructure remain, but the new system is more resilient. Second, brain emulations are ideally suited for colonizing space and many other environments where biological humans require extensive life support. Avoiding carrying all eggs in one planetary basket is an obvious strategy for strongly reducing existential risk. Besides existing in a substrate-independent manner where they could be run on computers hardened for local conditions, emulations could be transmitted digitally across interplanetary distances. One of the largest obstacles of space colonisation is the enormous cost in time, energy and reaction mass needed for space travel: emulation technology would reduce this. Third, another set of species risks accrue from the emergence of machine superintelligence. It has been argued that successful artificial intelligence is potentially extremely dangerous because it would have radical potential for self-improvement yet possibly deeply flawed goals or motivation systems. If intelligence is defined as the ability to achieve one's goals in general environments, then superintelligent systems would be significantly better than humans at achieving their goalseven at the expense of human goals. Intelligence does not strongly prescribe the nature of goals (especially in systems that might have been given top-level goals by imperfect programmers). Brain emulations gets around part of this risk by replacing the de novo machine intelligence with a copy of the relatively well understood human intelligence. Instead of getting potentially very rapidly upgradeable software minds with non-human motivation systems we get messy emulations that have human motivations. This slows the \"hard takeoff\" into superintelligence, and allows existing, well-tested forms of control over behaviournorms, police, economic incentives, political institutionsto act on the software. This is by no means a guarantee: emulations might prove to be far more upgradeable than we currently expect, motivations might shift from human norms, speed differences and socioeconomial factors may create turbulence, and the development of emulations might also create spin-off artificial intelligence. Four, emulations allows exploration of another part of the space of possible minds, which might encompass states of very high value  (Bostrom, 2008) . Unfortunately, these considerations do not lend themselves to easy comparison. They all depend on somewhat speculative possibilities, and their probabilities and magnitude cannot easily be compared. Rather than giving a rationale for going ahead or for stopping WBE they give reasons for assuming WBE willwere it to succeedmatter enormously. The value of information helping determining the correct course of action is hence significant. \n Discussion: Speculation or just being proactive? Turning back from these long-range visions, we get to the mundane but essential issues of research ethics and the ethics of ethical discourse. Ethics matters because we want to do good. In order to do that we need to have some ideas of what the good is and how to pursue it in the right way. It is also necessary for establishing trust with the rest of societynot just as PR or a way of avoiding backlashes, but in order to reap the benefit of greater cooperation and useful criticism. There is a real risk of both overselling and dismissing brain emulation. It has been a mainstay of philosophical thought experiments and science fiction for a long time. The potential impact for humanity (and to currently living individuals hoping for immortality) could be enormous. Unlike de novo artificial intelligence it appears possible to benchmark progress towards brain emulation, promising a more concrete (if arduous) path towards software intelligence. It is a very concrete research goal that can be visualised, and it will likely have a multitude of useful spin-off technologies and scientific findings no matter its eventual success. Yet these stimulating factors also make us ignore the very real gaps in our knowledge, the massive difference between current technology and the technology we can conjecture we need, and the foundational uncertainty about whether the project is even feasible. This lack of knowledge easily leads to a split into a camp of enthusiasts who assume that the eventual answers will prove positive, and a camp of sceptics who dismiss the whole endeavour. In both camps motivated cognition will filter evidence to suit their interpretation, producing biased claims and preventing actual epistemic progress. There is also a risk that ethicists work hard on inventing problems that are not there. After all, institutional rewards go to ethicists that find high-impact topics to pursue, and hence it makes sense arguing that whatever topic one is studying is of higher impact than commonly perceived. Alfred Nordmann has argued that much debate about human enhancement is based on \"if … then ..\" ethical thought experiments where some radical technology is first assumed, and then the ethical impact explored in this far-fetched scenario. He argued that this wastes limited ethical resources on flights of fantasy rather than the very real ethical problems we have today.  (Nordmann 2007)  Nevertheless, considering potential risks and their ethical impacts is an important aspect of research ethics, even when dealing with merely possible future radical technologies. Low-probability, high impact risks do matter, especially if we can reduce them by taking proactive steps in the present. In many cases the steps are simply to gather better information and have a few preliminary guidelines ready if the future arrives surprisingly early. While we have little information in the present, we have great leverage over the future. When the future arrives we may know far more, but we will have less ability to change it. In the case of WBE the main conclusion of this paper is the need for computational modellers to safeguard against software suffering. At present this would merely consist of being aware of the possibility, monitor the progress of the field, and consider what animal protection practices can be imported into the research models when needed. \t\t\t See for example the contributions in the theme issue of Neural Networks Volume 20, Issue 9, November 2007. \n\t\t\t Strictly speaking, we are in a situation of moral uncertainty about what ethical system we ought to follow in general, and factual uncertainty about the experiential status of emulations. But being sure about one and not the other one still leads to a problematic moral choice. Given the divergent views of experts on both questions we should also not be overly confident about our ability to be certain in these matters. \n\t\t\t Axons typically have conduction speeds between 1-100 m/s, producing delays between a few and a hundred milliseconds in the brain. Neurons fire at less than 100 Hz. Modern CPUs are many orders of magnitude faster (in the gigaHerz range) and transmit signals at least 10% of the speed of light. A millionfold speed increase does not seem implausible.", "date_published": "n/a", "url": "n/a", "filename": "Ethics of brain emulations draft.tei.xml", "abstract": "Ethics of brain emulations Whole brain emulation attempts to achieve software intelligence by copying the function of biological nervous systems into software. This paper aims at giving an overview of the ethical issues of the brain emulation approach, and analyse how they should affect responsible policy for developing the field. Animal emulations have uncertain moral status, and a principle of analogy is proposed for judging treatment of virtual animals. Various considerations of developing and using human brain emulations are discussed.", "id": "fa30c7d07d74ff460f8f226834c350a0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Hin-Yan Liu", "Matthijs Kristian Cedervall Lauta", "Michiel Maas"], "title": "Governing Boring Apocalypses: A new typology of existential vulnerabilities and exposures for existential risk research", "text": "Introduction the definition and framings of existential risk In recent years, a growing body of scholarship has argued that a new class of risks bears closer study, for their potential extreme impact on the survival of humanity  (Bostrom, 2002 (Bostrom, , 2013 Bostrom & Cirkovic, 2011; Matheny, 2007; Rees, 2004) . Prior research has identified a range of such human extinction risks  (Bostrom & Cirkovic, 2008; Haggstrom, 2016; Pamlin & Armstrong, 2015) , both natural and manmade, including risks from supervolcano eruption, asteroid impact, global warming, nuclear war, as well as more speculative risks from emerging technologies such as biotechnology, high-energy physics experiment disasters, or misaligned artificial intelligence.  (Asimov, 1981; Baum & Barrett, 2016; Bostrom, 2014; Ord, Hillerbrand, & Sandberg, 2010; Sagan, 1983; Smil, 2005; Tegmark & Bostrom, 2005; Yudkowsky, 2008a) . While it is encouraging to see greater attention for a critical topic that has long remained understudied, it is relevant to ask how the framing of the field's basic concepts shapes both which problems it identifies and prioritizes, as well as which policy approaches it considers and engages. In his seminal paper, Bostrom defined an existential risk as  '[o] ne where an adverse outcome would either annihilate Earth-originating intelligent life or permanently and drastically curtail its potential'  (Bostrom, 2002) . Thus in Bostrom's view, existential risks are characterised both by their scope (pan-generational) and their intensity (crushing): the size of the group of people who are at risk 1 and how badly each individual within that group is affected, respectively  (Bostrom, 2002) . Much prior research on existential risks has thus deployed criteria and methodology which have identified discrete and independent challenges of sufficient severity and pervasiveness to bring about the 'adverse outcome' in a direct causal manner. In this reading, existential risks are an extreme offshoot of global catastrophic risks-disasters which \"might have the potential to inflict serious damage to human well-being on a global scale\"  (Bostrom, 2013; Bostrom & Cirkovic, 2011, p. 2 ), but which fall short of permanent collapse. While we are not necessarily averse to the Bostromian definition of 'adverse outcomes'-a definition which indeed seems to characterize the space of eventual outcomes to be avoided-we take more issue with the limited range of pathways towards this dreaded outcome-space, which much of the literature has focused on exploring. Specifically, as noted by others in the community, much prior research \"has focused mainly on tracing a causal pathway from a catastrophic event to global catastrophic loss of life\"  (Avin et al., 2018, p. 1) . As such there remains an event-focus, in the sense that only discrete events that are causally connected to the demise of humanity within a relatively short time-frame qualify as an existential risk (rather than a 'merely' globally catastrophic one, or a background risk). \n Existential risk (re)framings as crucial consideration for law & governance approaches Distinguishing existential risks as a uniquely threatening outlier along the spectrum of global risks, however, is arguably an unnecessarily narrow framing of the field of study. Indeed, a high-profile 'one-hit-KO' existential risk such as a global nuclear war or a pandemic may constitute only one avenue towards that 'adverse outcome', and concentrating predominately upon (ways to intervene in) its origin and direct pathway, risks overshadowing other potential paths or disaster interaction effects 2 that functionally converge towards that same disastrous outcome, even if only indirectly or over longer timescales, with a potentially higher probability. Indeed, as recently noted by scholars in the field, a full mapping of scenarios that lead to catastrophic outcomes \"requires exploring the interplay between many interacting critical systems and threats, beyond the narrow study of individual scenarios that are typically addressed by single disciplines\"  (Avin et al., 2018, p. 2) .The precise framing of 'existential risks' is therefore a crucial consideration, informing ethical, strategic, and epistemological (cf. academic) priorities in facing 'adverse outcomes'. This is particularly the case in the context of studying how global political dynamics may interact with certain existential risks, and in formulating meaningfully effective policies and governance approaches to such risks. Of course, this is not to say that the field of existential risk studies has not sought to involve and engage with policy and governance approaches and solutions. Indeed, to its credit, research in the field of existential risks has actively sought to engage with these issues-given that, as  Bostrom himself observes (2013:27) , global cooperation is critical to mitigating a wide range of existential risks. Likewise, researchers within the 'AI safety' community are beginning to highlight fields such as policy and psychology, as under-represented but potentially promising approaches to addressing risks arising from AI  (Brundage, 2017; Sotala, 2017b) . Accordingly, there has been research into the interaction effects between technologies and politics-such as the possibility that arms races might increase the risk that untested, powerful AI systems are deployed rashly or prematurely  (Armstrong, Bostrom, & Shulman, 2013; Shulman, 2009) . Other work has drawn on cognitive psychology, to study how people might structurally (mis)judge the probability of risks  (Yudkowsky, 2008b) . Likewise, work exploring policy-and governance approaches to mitigating existential risks has explored policy approaches that include insurance arrangements for large catastrophes  (Taylor, 2008) ; technology taxes and subsidies  (Posner, 2008) ; and work drawing on social (and organizational) psychology to assess ways to motivate AI researchers to choose beneficial AI designs  (Baum, 2016) . Yet, other work has examined the cost-effectiveness of biosecurity interventions  (Millett &  1 Including future generations. Broadly speaking, many scholars in this space share an emphasis on the ethical value of far-future humans  (Beckstead, 2013) , with some arguing for the absolute prioritization of reducing human extinction risks (rather than risks that destroy civilization but would leave some humans alive) on the grounds that these risks would destroy all future generations  (Parfit, 1984, pp. 453−454; Sagan, 1983; Ng, 1991; Matheny, 2007) . Bostrom himself appears to favour the 'Maxipok' strategy-\"Maximise the probability of an 'OK outcome', where an OK outcome is any outcome that avoids existential catastrophe\"  (Bostrom, 2013, p. 19 )-though he takes a slightly broader perspective of mitigating not just 'hard' extinction risks but also 'global catastrophic risks' which could inflict significant, lasting long-term harm to the trajectory of human civilization, and which could thereby end up inflicting other categories of existential risks (including 'permanent stagnation'; 'flawed realisation', or 'subsequent ruination'  (Bostrom, 2013, p. 19 ). 2 Though for some work that examines 'interaction effects' between different global catastrophes, see  (Baum & Barrett, 2017; Baum et al., 2013) . H.-Y.  Liu et al. Futures 102 (2018) 6-19  Snyder-Beattie, 2017); pricing externalities to balance public the risks and benefits of scientific research generally ; and proposing a general international regulatory regime to govern global catastrophic and existential risks from emerging technologies  (Wilson, 2013) . At present, a majority of existential risk research centres 3 have articulated law and policy research as areas of interest, and scholars in this space have begun to translate such work into concrete proposed policy interventions-notably the 2017 GPP report, which included proposals to develop governance for geoengineering research; establish international scenario plans and exercises for engineered pandemics, and build international attention for existential risk reduction  (Farquhar, Halstead et al., 2017) . Such work is highly encouraging, and the existential risk research agenda has benefited from it. Nonetheless, the risk remains that a too-narrow conception of 'existential risks' prematurely closes down the space of law and governance solutions that are possible-or necessary-in assuring humanity a non-catastrophic future-for instance, a future that, in Bostrom's framing, meaningfully 'maximize  [s]  the probability of an ok outcome'  (Bostrom, 2013, p. 19 ). However, if human extinction and the persistent and pervasive truncation of technological potential are not completely homologous, then tailoring our portfolio of policy responses exclusively to closing off the pathways these risks could take-and then calling it a day-would be insufficient. In fact, this might only afford future policymakers with a false sense of security, even as the world continues to reside in an overall state of 'super-risk'  (Bermudez & Pardo, 2015) . This is especially the case when there is a narrow 'technological' (re)solution on offer-such as 'improve global vaccine synthesis and production capability', or 'subsidize international technical AI safety research'-which promise to address or prevent the risk at its root. While such direct technological solutions may certainly be indispensable to averting some existential risks, they may not suffice in actually 'plugging all the holes' in our risk space. In a disciplinary context, there is a risk (admittedly self-correcting, given publication incentives) of the research agenda 'halting' early. In a real-world context, the availability of simple, straightforward 'fixes' might even pose a 'moral hazard', if policymakers or global governance systems which lack political will or the attention to explore more complex or costly changes, seize upon the 'symbolic action' of the straightforward, first-order mitigation strategies. Even where this is not the case, certain policy recommendations to mitigate existential risks might depend on too-optimistic a view of institutional rationality or capability. 1.2. 'Boring Apocalypses': from existential hazards, to existential risks While such efforts might mitigate specific existential risks, this might not translate into significantly lowering the overall probability of the 'adverse outcome', if only a part of the problem, or only one problem among many, is addressed. An alternative articulation is that only one path to the 'adverse outcome' is being explored by much research into existential risks: erecting obstacles along that path may indeed reduce the overall likelihood of manifesting these risks, but this might have little impact, or even no effect, upon the manifestation of the 'adverse outcome'. Thus, our view is that a materialised existential risk (what we call an 'existential hazard') is sufficient to lead to an (existentially) 'adverse outcome', but crucially, that this is unnecessary to reach that result. If the overarching objective is to lower the probability of human extinction or significant technological curtailment, adopting an array of approaches which complement the mitigation of direct existential risks are required. Within this broad spectrum of aligned approaches, we propose to introduce law, policy, regulatory and governance tools in this paper as an example. The choice of law and policy perspectives is two-fold: on one hand, they make it possible to take second-order considerations, which involve indirect and socially and culturally mediated paths towards 'adverse outcomes' into account; on the other hand, these recognise both the complexity of social organisation and the prospect that civilizational collapse may trigger or possibly instantiate existential outcomes. In this sense, law and policy approaches offer the possibility of complementing and enhancing the narrower approach adopted by contemporary existential risk research, to take into consideration other paths to existentially adverse outcomes; and to better anticipate vulnerabilities, exposures and failure modes in societal efforts to address existential risks. 1.3. Exploring the implications of the existential risk framing: risks from AI An example of this can be drawn from the prospect of super intelligent artificial intelligence  (Bostrom, 2014; Yudkowsky, 2008a) . Although the landmark research agenda articulated by  Russell, Dewey, and Tegmark (2015)  does call for research into 'short-term' policy issues, debates in this field of AI risk 4 have-with some exceptions-identified the core problem as one of value alignment, where the divergence between the interests of humanity and those of the superintelligence would lead to the demise of humanity through mere processes of optimisation. Thus, the existential risk posed by the superintelligence lies in the fact that it will be more capable than we can ever be; human beings will be outmanoeuvred in attempts at convincing, controlling or coercing that superintelligence to serve our interests. As a result of this framing, the research agenda on AI risk has put the emphasis on evaluating the technical feasibility of an 'intelligence explosion'  (Chalmers, 2010; Good, 1964)  through recursive self-improvement after reaching a critical threshold  (Bostrom, 2014; Sotala, 2017a; Yudkowsky, 2008a Yudkowsky, , 2013  5 ; on formulating strategies to estimate timelines for the  3  While not exhaustive, these include: the Centre for the Study of Existential Risk (CSER), the Global Catastrophic Risk Institute (GCRI), the Global Priorities Project (GPP), the Gothenburg Centre for Advanced Studies, the Global Challenges Foundation, and the Future of Humanity Institute (which has recently announced its 'Governance of AI Program').  4  Cf.  (Farquhar, Halstead et al., 2017) . For an excellent overview of recent work (both on technical safety as well as strategy and policy) on mitigating existential risks deriving from artificial intelligence, see  (Dawson, 2016 (Dawson, , 2017 .  5  For critiques of the 'singularity' claim, see  (Brooks, 2014; Dietterich & Horvitz, 2015; Goertzel, 2015; Plebe & Perconti, 2012; Jilk, 2017) . H.-Y.  Liu et al. Futures 102 (2018) 6-19  expected technological development of such 'human-level' or 'general' machine intelligence  (Armstrong & Sotala, 2012 Baum, Goertzel, & Goertzel, 2011; Brundage, 2015; Grace, Salvatier, Dafoe, Zhang, & Evans, 2017; Müller & Bostrom, 2016) ; and on formulating technical proposals to guarantee that a superintelligence's goals or values will remain aligned with those of humanity-the so-called superintelligence 'Control Problem'  (Armstrong, Sandberg, & Bostrom, 2012; Bostrom, 2012 Bostrom, , 2014 Goertzel & Pitt, 2014; Yudkowsky, 2008a) .  6  While this is worthwhile and necessary to address the potential risks of advanced AI, this framing of existential risks focuses on the most direct and causally connected existential risk posed by AI systems. Yet while super-human intelligence might surely suffice to trigger an existential outcome, it is not necessary to it. Cynically, mere human level intelligence appears to be more than sufficient to pose an array of existential risks  (Martin, 2006; Rees, 2004) . Furthermore, some applications of 'narrow' AI which might help in mitigating against some existential risks, might pose their own existential risks when combined with other technologies or trends, or might simply lower barriers against other varieties of existential risks. To give one example; the deployment of advanced AI-enhanced surveillance capabilities 7 -including automatic hacking, geospatial sensing, advanced data analysis capabilities, and autonomous drone deployment-may greatly strengthen global efforts to protect against 'rogue' actors engineering a pandemic (\"preventing existential risk\"). It may also offer very accurate targeting and repression information to a totalitarian regimes, 8 particularly those with separate access to nanotechnological weapons (\"creating a new existential risk\"). Finally, the increased strategic transparency of such AI systems might disrupt existing nuclear deterrence stability, by rendering vulnerable previously 'secure' strategic assets (\"lowering the threshold to existential risk\")  (Hambling, 2016; Holmes, 2016; Lieber & Press, 2017) . Finally, many 'non-catastrophic' trends engendered by AI-whether geopolitical disruption, unemployment through automation; widespread automated cyberattacks, or computational propaganda-might resonate to instil a deep technological anxiety or regulatory distrust in global public. While these trends do not directly lead to catastrophe, they could well be understood as a meta-level existential threat, if they spur rushed and counter-productive regulation at the domestic level, or so degrade conditions for cooperation on the international level that they curtail our collective ability to address not just existential risks deriving from artificial intelligence, but those from other sources (e.g. synthetic biology and climate change), as well. These brief examples sketch out the broader existential challenges latent within AI research and development at preceding stages or manifesting through different avenues than the signature risk posed by superintelligence. Thus, addressing the existential risk posed by superintelligence is both crucial to avoiding the 'adverse outcome', but simultaneously misses the mark in an important sense. 2. Re-examining existential risks: hazard, vulnerability, and exposure While Bostrom's leading typology identifies the general area inhabited by existential risks, it provides little guidance for how to differentiate among the diverse risks within that category (the box marked 'X'), because these risks are not distinguished according to their source, characteristics, or complexity, but only their impact (\"crushing\") and scope (\"pan-generational\"). 9 However, given the range of distinct risks falling within the 'X' box-that is, risks that could cause or feed into an eventual terminal and crushing 'adverse outcome' for humanity-we suggest it relevant to deconstruct existential risks, and instead consider the broader category of 'risks as a function of hazard, vulnerability and exposure'  10, 11  : Existential Risk = Hazard* Vulnerability * Exposure Here, hazard denotes the external source of peril (which is captured within the prevailing agenda studying existential risks)-the 'spark' that threatens the pan-generational/crushing harm. Vulnerability denotes propensities or weaknesses inherent within human social, political, economic or legal systems, that increase the likelihood of humanity succumbing to pressures or challenges that threaten existential outcomes. Finally, exposure denotes the 'reaction surface'-the number, scope and nature of the interface between the hazard and the vulnerability. Thus, a hazard is what kills us, and a vulnerability is how we die. Exposure is the interface or medium between what kills us, and how we die. To take an example from disaster studies, a major earthquake only becomes a risk if the built, social or institutional environment can be destabilised during earthquakes of the threatened magnitude (\"is vulnerable to\"), and if such an environment is located in (\"exposed to\") an earthquake zone. Thus, vulnerability and exposure refer to two different aspects of the affected system:  6  The field of AI safety is particularly active. For a selection of influential papers, see  Amodei & Clark, 2016; Christiano et al., 2017; Orseau & Armstrong, 2016; Soares & Fallenstein, 2014) . 7 Notwithstanding interesting developments in 'privacy-preserving' homomorphic encryption configurations, for an interesting exploration of which, see  (Trask, 2017) .  8  For a treatment of totalitarianism as a 'global catastrophic risk', see  (Caplan, 2008)  9 Of course, Bostrom's objective in setting out this typology is merely to differentiate existential risks from the much larger space of unfortunate occurrences. 10 This classification schema is distinct from another recently proposed by  (Avin et al., 2018) , which instead breaks down the analysis of global catastrophic risk scenarios along three different components-(1) a critical system whose safety boundaries are breached by a threat; (2) the mechanisms by which this threat might spread globally to affect the majority of the population, and (3) the manner in which we might fail to prevent or mitigate 1 and 2. While elegant, a discussion of the similarities, differences, and potential (in)commensurability between these two classification taxonomies is out of scope for this present paper. how it breaks, and how it intersects with a given hazard's operating space or pathways of impact (Fig.  1 ). As a species of global catastrophic risks, the study of existential risks is often conflated with, and perhaps even collapsed into, the identification and mitigation of existential hazards. Where attention is paid to issues of vulnerability and exposure, these are often identified in light of an existential hazard. One of the leading sources and reference points in the field symptomatically organizes the field as a collection of existential hazards  (Bostrom & Cirkovic, 2008) . A caveat applies for a small subset of hazards of such enormous magnitude that it renders mitigation strategies focussing upon vulnerability and exposure less relevant, or perhaps even irrelevant. The paragon might be the scenarios of 'simulation collapse', or a high-energy physics experiment going awry, altering the astronomical vicinity and rendering life untenable  (Ord et al., 2010) . Such extreme hazards constitute the archetype of existential risks as a subset of global catastrophic risks and can only be addressed by managing the hazard head-on, with vulnerability and exposure components relegated to marginal roles: Existential Risk = Existential Hazard * Vulnerability * Exposure Thus, our claim is not that the field of existential risks research is looking in the wrong places-the emphasis on existential risks has enabled this field to identify a core group of existential hazards which would on their own suffice to bring about the 'existentially adverse outcome'. Nonetheless, there are also many other, slower and more intertwined ways in which the world might collapse, without being hit by spectacular hazards. To complement the study of existential risks we can draw upon lessons learnt through historical and anthropological studies of civilizational collapse. Thus, while existential risks concentrate upon clear-cut existential hazards, civilizational collapse research infers influential factors that were involved in trajectories of decline. These studies are beginning to challenge the traditional conceptual framework which set out a cyclical history, wherein a civilisations rise and fall, progressing through a predictable pattern of growth, zenith and decline in a gradual manner  (Ferguson, 2011) . In other words, historically civilizational collapses are boring. Diamond refined this model by recognising that civilizational collapse could be a slow and protracted process emerging from complex interactions  (Diamond, 2006) . \n Beyond hazards: vulnerability and exposure In this paper, we set out to foreground the other two variables involved in the existential risk equation. Thus, as noted, 'vulnerability' denotes propensities or weaknesses inherent within human social, political, economic or legal systems that increase the likelihood of humanity succumbing to pressures or challenges that threaten existential outcomes. 'Exposure' indicates the nexus between external hazards and internal vulnerabilities: the interface at which the 'adverse outcome' precipitates from their interaction. Historical studies of civilizational collapses indicate that even small exogenous shocks can   Bostrom, 2013, p. 17) . destabilise a vulnerable system  (Diamond, 2006; Ferguson, 2011) . Given this, studying 'exposure' is relevant in systematically analysing interaction effects: a cataclysmic hazard interacting with robust and resilient human systems may be survivable, but conversely, at the interstices at which our human technology, institutions or culture are most vulnerable, even minor (initially 'noncatastrophic') hazards can be the inflection point that tips these susceptible systems towards trajectories of collapse  (Gladwell, 2001) .  12  In order to offset the tight coupling between existential risks and existential hazards, we will further dissect the vulnerability and exposure factors introduced in the existential risk calculus. Our proposed taxonomy distinguishes four general categories of vulnerability and exposure (see Table  1 ). • Ontological: vulnerability through existing in a given location and time in our universe 13 ; • Passive: vulnerability through lack of action; 'indirect' exposure; • Active: vulnerability because of insufficient/mis-specified action. • Intentional: vulnerability or exposure knowingly maintained, for that purpose. Note that for vulnerability, the Passive, Active and Intentional categories correspond to the jurisprudential concepts of 'omission' ('failure to act'), 'negligence' (action, but with failure to exercise the appropriate care to prevent foreseeable future harm) and 'intention' (action with the known purpose to bring about a consequence). Drawing such distinctions offers the opportunity to be more precise about the features or characteristics which give rise to the existential dimension of the challenge, and thus suggest specific points for targeted intervention, as well as potential failure modes to caution against. Below, we combine these categories and their sub-divisions, in twin taxonomies of existential 'vulnerabilities' and 'exposure'. We also seek to give concrete examples. Obviously, not all of these examples are currently unstudied-indeed many feature prominently in the existing literature-though in other cases they remain understudied. While this list is naturally not comprehensive, we hope that such examples enable researchers in the field of existential risks to locate their research in an overarching framework, as well as facilitating links to established scholarly fields which have studied given issues, without considering their bearing on larger existential risks. \n A taxonomy of 'existential vulnerability' Our proposed taxonomy for distinguishing between different manifestations of existential vulnerabilities is summarised in Table  2 : note that the salience or tractability of these existential vulnerabilities to law and policy approaches increases as one goes down: ontological vulnerabilities appear (at present) highly intractable to mere law and policy-it would be a vain regulator indeed who would try to legislate against physical laws. However, as one proceeds to passive, active, or intended vulnerabilities, the salience of governance approaches increases (Table  3 ). \n Ontological vulnerability The category of ontological vulnerability denotes intrinsic vulnerabilities associated with human existence. These include the possibility that we inhabit a computer simulation  (Bostrom, 2002) , which might be terminated or altered at any time. More conceptual and basic vulnerabilities-so fundamental that we often would not even consider them as such-include our existence as biological beings that are dependent (potentially more so than other species such as tardigrades) on continuous or relatively uninterrupted inputs of energy & resources (such as food, water, air, light, …), which renders the human species one comparatively vulnerable to 'extinction' events such as a supervolcano-or meteor-induced global winter. On a deeper level yet, all biochemistry is dependent on the existing laws of physics within which it evolved, rendering us acutely and terminally vulnerable to any processes (e.g. vacuum decay) which would profoundly alter these processes. Biological deterioration due to aging processes, or exterior damages, might also rank amongst these, although that is conditional on whether or not there exists a physical 'hard ceiling' to how far medical senescence research might extend human lifespans and reduce other vulnerabilities. Table  1  the general categories of vulnerability and exposure used to structure our taxonomies of existential vulnerability and existential exposure. \n Type of Vulnerability (V): vulnerability by… Type of Exposure (E): exposure by… Ontological (O) Existence (V-O) Existence (E-O) Passive (P) Omission (V-P) Indirect link (E-P) Active (A) Negligence (V-A) Direct link (E-A) Intentional (I) Intention (V-I) Intention (E-I)  12  Notably, the resilience of civilization to catastrophes has had some treatment in the field of global systemic risk  (Baum et al., 2014; Centeno, Nag, Patterson, Shaver, & Windawi, 2015; Helbing, 2013) .  13  Another possible term could be 'anthropic vulnerability'. H  • Physical dependence on physics integrity; our biochemistry 'works' only within a narrow subset of all possible physical laws (rendering us vulnerable to vacuum decay); • Biological aging. \n V-P. Passive vulnerability Vulnerability existing due to the lack of structures in place. [OMISSION] Built (vulnerability because of the lack of availability of a defence) • Lack a of super-volcano warning system (technology does not yet exist-lack of global capacity). • Lack of asteroid defence programme (existing technology, but not deployed-lack of local capacity at key point); Institutional (top-down social vulnerability) • Lack of effective global institutions, as well as crisis management organisation; • Lack of global coordination on identifying and addressing existential risks. • Lack of public investment in developing critical technologies, e.g. alternate food sources for surviving volcanic winter  (Pearce & Denkenberger, 2016)  or refuges for global catastrophic risks (Haqq-Misra,  Baum, & Denkenberger, 2015) . Cultural (bottom-up social vulnerability) • Lack of public engagement in confronting existential risks: propensity of public to stereotype/dismiss disaster scenarios ('Terminator headlines'); • Lack of (widely shared) concepts and language to express existential vulnerabilities. \n V-A. Active vulnerability Vulnerabilities existing in spite of/ because of the social structures in place. [NEGLIGENCE] Built vulnerability • Intrinsic path-dependent vulnerabilities in infrastructure components: architectural security deficits in universally used components of global (digital) infrastructures (e.g. Spectre and Meltdown exploits in Intel chips); future geo-engineering projects, such as stratospheric aerosol injection, which could backfire heavily if interrupted temporarily, and which might be disrupted  (Baum, 2015a; Baum, Maher, & Haqq-Misra, 2013 ). • Intrinsic path-dependent vulnerabilities in infrastructure configuration: critical infrastructures (e.g. national electricity grids) are centralized and homogeneous (e.g. rendering society vulnerability to solar flares). • More generally: driven by organizational and competitive optimization. ('Moloch' traps  (Alexander, 2014) ), globalization homogenizes all solutions across the globe, eroding resilience (e.g. proliferation of homogenized monocultures of staple crops creates vulnerabilities to engineered crop diseases). Institutional vulnerability • Narrow bureaucratic interest and perverse incentives which lock civilization into 'inadequate equilibria'  (Yudkowsky, 2017) , potentially blocking coordination for known existential risks • Globalised economic and institutional frameworks. Market dependency  (Harari, 2015)  • Overconfident belief in own ability to foresee risks  (Burton, 2008) -risk-based governance and incorrect probabilistic approaches which underestimate fat-tail events. Cultural vulnerability • Spread of pandemics caused by culturally determined interactions (e.g. Ebola); • Ingrained distrust of governmental authorities/public media undercutting disaster response efforts; • Social norms promoting high fertility and unsustainable population growth  (Kuhlemann, 2018) . • Globalized diets and food demand that can only be met by (unsustainable; vulnerable) monocultures. • Increasingly homogenous global 'monoculture' in practices and ideology creates vulnerabilities, by limiting redundancies and diversity. (continued on next page) As these are background conditions at the frontiers of epistemology, we are unlikely to be able to unveil more than a fraction of these vulnerabilities. Also, as inherent features of human existence we have limited abilities to act effectively in this category. Perhaps the most utility we can extract from delimiting ontological vulnerability is to restrict its reach: in other words to leave this as a residual class of vulnerabilities inherent in existence. \n Vulnerabilities, passive and active; built, institutional and cultural Passive vulnerabilities are characterised by inaction: the susceptibility to existential outcomes by virtue of failure to take appropriate measures. Conversely, active vulnerabilities arise in association with human activities, as by-products or unintended consequences. Three cross-cutting sub-distinctions can also be made for both passive and active vulnerabilities: built, cultural, and institutional. Built vulnerabilities are characterised by our (passive) failure to put into place relevant solutions or defences to existential challenges, or by our (active) failure to repair or correct the extant vulnerabilities in the legacy infrastructures we deploy, or the pathdependent ways we deploy them-even if we have such solutions or repairs at our disposal. Such solutions can in fact include some interventions proposed by the existential risk research agenda, such as an asteroid defence programme or the ability to systematically monitor for supervolcano eruptions  (Denkenberger & Blair, 2018) ; they also cover the active existential risks posed by the technologies which humanity has introduced, but which go unfixed-such as architectural deficiencies creating intractable cybersecurity vulnerabilities in universally used computing chips. Because of the technical nature of engineered vulnerabilities, some of these are perhaps closest to the existing (policy) research agenda of the existential risk community-and at present some may consider that law and policy tools have less of a role to play, other than to coordinate efforts aimed at addressing them. In contrast, top-down vulnerabilities resulting from suboptimal direction and coordination are captured by our sub-category of institutional vulnerability. Here, the line between active and passive is admittedly thin, where recklessness can be the distinguishing • Misaligned, 'apocalyptic' AI  (Geraci, 2010) ; • Nuclear force posture combining centralization of launch command authority, with fallible nuclear early warning systems and 'launch-on-warning' missile force postures  (Borrie, 2014) . • 'Back-doors' or 'zero-day-vulnerabilities' in critical infrastructure software, knowingly maintained by intelligence services. • Existence of 'omnicidal' agents  (Torres, 2016) -including religious groups' faith in end-times, e.g. the Rapture or Yawm ad-Dīn.  \n Exposure of Society • AI, nuclear power, nanotechnology and synthetic biology. • Experimental scientific curiosity Exposure of Nature • Global extreme climate change. • Over-utilization of nature: unsustainable fishing or hunting E-A. Direct exposure Exposure directly caused by societal structures intended for something else. \n Exposure of Society • Lack of political will and institutional inertia leading to 'progress traps'  (Wright, 2006) . • War, METI, or cultural sentiment. • Unconstrained optimization processes in society, economics, politics (politicians), which pursue originally legitimate goals but become misaligned as they find ways to achieve these in increasingly perverse ways, or with increasing amounts of externalities (cf. 'Moloch'  (Alexander, 2014) ). \n Exposure of Nature • Local ecosystem collapse  (Kolbert, 2014) . • Urbanisation, agriculture and deforestation \n E-I. Intentional Exposure directly imposed by societal arrangements intended precisely for that purpose. - • The existence of nuclear and (infectious) biological weapons for strategic purposes such as deterrence. • On a more granular level: the retention of deterrent weapons which risk nuclear winter, over 'winter-safe' deterrent  (Baum, 2015b) . feature. Active institutional vulnerability may be characterised by failure to coordinate to address a known risk, such as climate change, or cyclical global economic melt-down. Passive institutional vulnerability may then be understood as directional and coordination failures that limit the scope of knowledge related to existential risks-perhaps an implicit 'unwillingness to know', which translates in an unwillingness to fund blue-sky research into charting 'unknown unknowns'  (Rumsfeld, 2002) . Cultural vulnerability encompass the bottom-up societal dimensions, reflecting how certain social practices may affect susceptibility to existential challenges. Active cultural vulnerabilities include customary practices that facilitate the spread of pathogens, increasing susceptibility to pandemics, for example integrated commercial travel networks and interpersonal greeting rituals which encourage physical proximity or contact. Passive cultural vulnerabilities include the exclusion or ridicule of existential risks from serious discussion in public forums (let alone the halls of power). This increases collective vulnerabilities insofar as the public and policymakers underrate the prospects for existential risks (cognitive biases exacerbate these effects,  Kahneman, 2012)  resulting in further marginalisation. \n Intended vulnerabilities Intended vulnerabilities are those which are created or retained specifically for that purpose, and within the existing research agenda are reflected in the premises of the 'AI risk' or 'Apocalyptic AI' movement  (Geraci, 2010) . Another salient example can, however, be found in nuclear force postures which (in the US context) features centralization of launch command authority along with a 'launch-on-warning' doctrine that relies on input from fallible early launch warning systems  (Borrie, 2014; Sagan, 1993) . Together, this gives rise to the catastrophic risk of an accidental nuclear war  (Barrett, Baum, & Hostetler, 2013 ). Yet far from incidental, this is arguably by design. As the theorist Kenneth Boulding once observed: \"if [deterrence] were really stable … it would cease to deter. If the probability of nuclear weapons going off were zero, they would not deter anybody\"  (Boulding, 1986, p. 32 ).  14  The nuclear force knowingly renders itself more vulnerable to catastrophic accidents-sacrificing a degree of safety for the sake of strengthening operational readiness and deterrence. While less dramatic, similar intentional vulnerabilities could emerge from a state intelligence service knowingly holding back-doors or 'zero-day-exploits' which it identifies in critical infrastructure software, in the hope that this may enable more effective cyberattacks against rival states at a later state. \n Existential vulnerability: mitigation and adaptation strategies This taxonomy of vulnerabilities can provide concrete suggestions for addressing existential risks. While the categories of ontological and intended vulnerabilities may seem superfluous, their treatment as additional classes allow limited resources to be concentrated into the most tractable areas. Perhaps the main contribution of this taxonomy is to highlight how existential risks need not be active and discernible, in the manner of the 'hazards' identified in the field. Instead, many of these risks can be latent, and slow-moving. Moreover, this taxonomy aids in understanding how human activities can impact paths towards 'existential outcomes' in several ways: (1) intent: by directly creating technologies which pose existential hazards (i.e. emerging technologies such as AI, nanotechnology and synthetic biology); (2) (negligence) by establishing complex systems for which failure is unavoidable  (Perrow, 2011) ; (3) and by omission, the failure to take steps to confront existential risks. Beyond merely refining the sources of existential risks, the contribution of this taxonomy lies in creating a roadmap for the study and integration of risks that have not yet received much or consistent attention in the field of existential risks. In doing so, we emphasise a number of existential vulnerabilities, such as global dependency upon a few species of staple crops, or certain types of globalised technologies (e.g. SCADA-based systems in critical infrastructure) that are not commonly recognised as sources or failure points of existential risks. The study of existential 'vulnerability' may suggest that adaptation strategies are preferable to those of mitigation, both because of the inherent complexity underlying both forms of structural vulnerability and because adaptation can now occur simultaneously with mitigation. This is because the vulnerability analysis in effect opens up a parallel system where other trajectories of existential risks are at play. The rough equivalence drawn between traditional existential risks with existential hazards might have the effect of underselling adaptation strategies: it is illogical to conceive of robustness as a defence against the apocalypse, after all. Along with efforts to mitigate or avert existential hazards, however, we can now also plan for adaptation against vulnerabilities. Thus, adaptation strategies are not limited to actions undertaken after 'the Fall': instead they may become rational reactions towards limiting susceptibility to existential risks. In order to explore this potential further, we proceed to examine a taxonomy of exposure. \n A taxonomy of 'Existential exposure' As a parallel effort to our taxonomy on existential vulnerabilities, we set out a classification system to differentiate between different forms of exposure. It is worth recalling at this point that we use exposure to express the interface between hazards and vulnerabilities-between what kills us, and how we die. Both hazards and vulnerabilities in isolation remain as potentials: exposure is thus a means of actualising such potential into existential risks. Such exposure can further be directed towards either the societal or the natural environment. This is about what is directly at risk: 14 Indeed, in Essentials of Post-Cold War Deterrence, the US Strategic Command recommended a species of potentially risky brinkmanship, arguing that \"[t]he fact that some elements may appear to be potentially 'out of control' can be beneficial to creating and reinforcing fears and doubts in the minds of an adversary's decision makers. This essential sense of fear is the working force of deterrence. That the U.S. may become irrational and vindictive if its vital interests are attacked should be part of the national persona we project to all adversaries.\" (Policy Subcommittee of the Strategic Advisory Group (SAG), 1995) our (human) society and the common capabilities and support structures preventing existential risks; or nature and its carrying capacity and resilience to future shocks. Thus, we assert that devastating results for humankind can follow from the collapse of both the societal structures we have built, as well as the natural environments within which these constructed systems are embedded. Again, the distinction allows us to single out different examples and trajectories to build alternative strategies for human survival. As is clear from the examples above, it also draws out lessons for existential outcomes which might not be immediately evident from an analysis of existential hazards alone. For example, when 'exposure' is seen from the perspective of the natural environment on which mankind depends, pervasive over-fishing and deforestation, combined with trends in resource demands tracking population growth, may become potentially hazardous activities with the potential to curtail human development in the long run  (Diamond, 2006) , even if they do not affect most humans directly in the short run. 3.2.1. Ontological exposure Some exposures are inherent in residing on Earth. Those falling in the category of natural exposure denote existence on earth itself as the exposure, and include our exposure to Near-Earth Objects (NEO) hitting earth or supervolcanoes triggering a protracted volcanic winter. The common denominator underlying this form of exposure is their requirement for measures beyond our present technological capacity to overcome (which admittedly, can be a moving threshold). \n Indirect and direct exposure As with the discussion of existential vulnerabilities set out above, the potential of our proposed taxonomy lies in the analysis of indirect and direct exposures. This distinction identifies the exposures that are a direct consequence of human activity, from those that are caused by more complex interactions with other systems. The theoretical example of high-energy physics research going awry 15 provides an example of societal exposure.  16  A final example of direct exposures are private or unilateral attempts to undertake 'Active SETI'-alternately called METI ('Messaging to Extra-Terrestrial Intelligence')  (Zaitsev, 2006) -which might expose the rest of mankind to catastrophic risk, should any future contacted alien species prove hostile and capable of interstellar-scale interdiction. These examples illustrate how surfaces of direct exposure (and ways to reduce it) might be overlooked when concentrating upon the hazard alone. Beyond direct exposures, an array of arrangements which jeopardise the human societies that have become dependent on them. This category includes any activity or arrangement which might expose the world to extinction through cascading effects. The development of critical common global infrastructures such as the internet, energy markets, and cultural and scientific harmonization might be classified as exposures, rather than vulnerabilities because these reveal new interfaces between hazards and vulnerabilities. Thus collapse of common infrastructures would trigger cascades which jeopardise civilizational sophistication at the global level  (Wright, 2006) , the edifice upon which humanity's long-term potential has been built. Similarly, developments like urbanisation, intensification of agriculture, and even increasing global inequality () appear to be factors that create fault lines and further drive exposures to existential vulnerabilities. Here the exposure perspective shows us that only by certain actions or inactions do risks actually materialise fully against civilization. \n Intentional exposure Finally, some of these exposures appear to exist intentionally, or at least knowingly or recklessly. The city of New Orleans, Louisiana, provides a microcosm of how dysfunctional behaviour, seen from an existential risk perspective, might be driven by human incentives or rationales operating at different orders. The city is, in design and position, incredibly vulnerable to its natural environment-pinched in between the Mexican Gulf and Lake Pontchartrain and built on the banks of the Mississippi River. Accordingly, some have argued that the most reasonable strategy following hurricane Katrina would have been to abandon the city permanently  (Richards, 2011) . Instead, the affected populations were given incentives to return, with the US government investing billions in the reconstruction of the city, aware that even with improved defences, the city remains unsafe  (Cutter et al., 2014) . Similarly, many populations worldwide, from Tehran and Kathmandu, to San Francisco and Port-au-Prince, persist in known disaster-prone zones, for (legitimate) reasons of culture, history, identity or economy. The purpose of these examples is not to warn the populations of these cities, nor to judge their decision to remain: rather the point is that individuals and societies often make decisions based upon entirely different rationales than a concern for survival. This is an insight that seems to scale to any level of government. In simpler terms, sometimes we choose exposure over safety because of competing considerations, and while this might be productive from a cultural heritage perspective, it remains problematic when seen through the lens of existential risks. \n Are existential hazards necessary for existential risks? Having set out taxonomies for differentiating between factors which influence existential risks the question remains whether all components are necessary to bring about an 'adverse outcome'. Our initial claim was that existential hazards could be sufficient  15  Cf. ; for interesting methodological work on estimating the safety of experiments within particle physics, as a particular case of evaluating risks with extremely low probability but very high stakes, see  (Ord et al., 2010) .  16  High-energy physics research can be distinguished from the category of hazards as an example of societal exposure because of the active decision to conduct the relevant experiments. One might also counter that 'nature' would be as much exposed to a potential physics disaster, as our society would be. While that is certainly the case, we treat it as a case of societal exposure insofar as humankind is impacted by such accidents, rather than by the impact of such accidents on the environment's integrity or carrying capacity. H.-Y.  Liu et al. Futures 102 (2018) 6-19  existential risks, but that they were not necessary to pose such risks. Returning to the civilization collapse literature cited above, Ferguson provides a critical insight in contesting the traditional view of cyclical history itself. He posits an alternative conceptual framework by asking the question: 'What if history is not cyclical and slow-moving, but arrhythmic?'  (Ferguson, 2011, p. 299) . Continuing, he summarises the perspective we adopt succinctly: Civilisations… are highly complex systems, made up of a very large number of interacting components that are asymmetrically organised, so that their construction more closely resembles a Namibian termite mound than an Egyptian pyramid. They operate somewhere between order and disorder − on 'the edge of chaos', in the phrase of computer scientist Christopher Langton. Such systems can appear to operate quite stably for some time, apparently in equilibrium, in reality constantly adapting. But there comes a moment when they \"go critical\". A slight perturbation can set off a \"phase transition\" from a benign equilibrium to a crisis − a single grain of sand causes an apparently stable sandcastle to fall in on itself.  (Ferguson, 2011, pp. 299-300) . Wright echoes this sentiment: 'Civilisations often fall quite suddenly − the House of Cards effect − because as they reach full demand on their ecologies, they become highly vulnerable to natural fluctuations'  (Wright, 2006, p. 130) . When combined with the observation that hitherto isolated civilizational experiments have now been merged  (Harari, 2015) , this raises the spectre that existential risks can coalesce from factors that historically brought about only limited civilizational collapses. Thus, the question we need to pose in this regard is whether vulnerabilities themselves contain the seeds of existential risks? In this context, we should note that vulnerabilities have often been considered mostly as aggravating factors. As aggravators then, vulnerabilities are subsidiary considerations restricted to influencing borderline events: where a potential existential hazard impacts humanity, its susceptibility or resilience could determine whether or not that hazard was transmuted into an existential outcome. In line with vulnerabilities being developed as a separate sphere where existential risks are at play, this section explores the possibility of removing the existential character of the hazard and thus plausibly reducing the calculus to: Existential Risk = Hazard * Existential Vulnerability * Exposure \n [and/or] Existential Risk = Hazard * Vulnerability * Existential Exposure An initial issue is that a catalyst of some sort is required to precipitate the existential risk, because even a system with wellexposed inherent susceptibilities will need something to set it motion. Removing the existential hazard component allows us to explore the possibility that relatively minor occurrences can trigger cascades that emerge as existential risks. But a vulnerability cannot by definition transmute into the existential risk itself absent external input: for this reason we diminish the stature of 'hazard' in the equation to represent our proposition that exogenous shocks need not be the spectacular existential hazards recognised by the study of existential risks. Instead, the external hazards in our revised equation can include insignificant events which go unnoticed (and quite probably involve a large number of minor occurrences). \n Contributions and limitations of law and policy tools for existential risks While our deconstruction of existential risks lead to fairly broad claims, it also provides a few concrete questions and insights. First and foremost, if existential risks can indeed be triggered by non-existential hazards, we need to broaden the scope of investigation in order to draw a more accurate roadmap of the existential risks field, one which can deal with questions of vulnerability and exposure explicitly. Second, the type of perceived challenge channels the range of appropriate responses which can be developed. While existential hazards may appropriately be met by narrower forms of technical solutions and technologically-oriented mitigation strategies, our broader perspective of existential risks open up other toolboxes to confront existential risks. In particular, social vulnerability and human-driven (anthropogenic) exposure require improved governance and coordination for adaptation strategies. Thus, when we reconstruct existential hazards through the optics of the social systems' inability to withstand them they, per definition, become social phenomena. As noted, many existential risk scholars have recently recognised the importance of reaching out to, and incorporating, law and governance approaches, even where the origin of the existential hazard itself is technological. The critical role of such law and governance approaches should be even more self-evident where the problems in question-the origins of existential vulnerability and exposure-are themselves social, not technological. This opens up a field for law and governance scholars to work more productively and on an equal footing with technical experts and philosophers. Moreover, this allows for a different set of research questions to be posed as to how we might reduce the vulnerabilities underlying the existential risks against humanity, and our collective exposure to hazards leading to existential outcomes. In doing so, our taxonomy has the potential to elevate relevant aspects of otherwise mundane considerations within politics, economics and society to the plane of existential risks. In garnering this attention, we hope that law and policy tools might be more productively incorporated and deployed as a means to building resilience and robustness. Here, central legal institutions as rights, responsibility and societal relations might in fact contribute substantially to reducing both our vulnerability towards, and exposure to, existential risks. The obvious limitations of this approach reside in the observation that many contemporary existential hazards, vulnerabilities and exposures are anthropogenic. This raises the spectre of either 'iatrogenesis'  ('[complications]  caused by the healer'), where our attempts at treating a problem accidentally give rise to new, potentially worse ailments. Thus, in our attempt to curtail existential vulnerabilities and exposures, we may inadvertently generate new or different existential risks. Yet, the framing remains critical: the vantage points created in our proposed taxonomy encourages alternative ways of thinking about existential risks and provide different accommodation strategies. Finally, the perspective provided by existential vulnerabilities might also foster solutions that will be of more general benefit to humanity as tangential effects of efforts taken to reducing our collective vulnerability and exposure to existential risks. While this appears to be of a lower order of concern at first flush, our taxonomy appears to bind existential risks together with phenomena occurring at different levels. In this sense, existential vulnerabilities and exposures may possess fractal characteristics  (Gleick, 1997; Johnson, 2002) , reflecting the complexity of their constitution. Support for this claim might reside in the scalability of hazards and vulnerabilities in particular: if pedestrian threats can cascade into existential outcomes, for example, then mundane measures might feedback to reinforce humanity against existential risks. Pushing this to its limits, it is possible the seemingly oblique effects of improved governance undertaken to shore up existential vulnerabilities actually end up as one of the very sources of humanity's resilience and robustness against existential outcomes. \n Concluding thoughts The lessons that we can draw from deconstructing existential risks into hazards, vulnerabilities and exposures can be divided into internal and external lessons for the field of existential risk research. In terms of the lessons for existential risk research, our taxonomy suggests that we may presently reside in a situation of pervasive risk. In identifying the catalogue of existential hazards looming over humanity, and focussing attention to confronting these challenges, the perception is that the outcome of these efforts is a lowering of the overall probability of an actualised existential risk. If our efforts are not actually achieving this, however (because they do not address vulnerabilities or exposures, only direct hazards), we run the risk of achieving safety that is merely 'symbolic': we perceive that we are 'all clear'-that we have successfully steered humanity past 'existential outcomes'-when we are in fact all the more fragile. Defeating a global pandemic, or securing mankind from nuclear war, would be historic achievements; but they would be hollow ones if we were to succumb to social strife or ecosystem collapse decades later. By proposing alternative paths that lead to existential outcomes, our taxonomy can recalibrate the calculus and reduce the prospect of an existential outcome. Our taxonomy also provides the groundwork for concrete strategies for meeting the existential challenges revealed by our deconstruction of existential risks. In essence, our taxonomy enables more productive cross-disciplinary cooperation amongst researchers from the existential risk community and various other disciplines, in assessing the dynamics that might lead towards catastrophic or 'existentially adverse' outcomes. This step in itself seems to enhance resilience and robustness by fostering greater variety of policy and governance responses-responses which can move beyond mitigation alone, to extend to adaptation, and which can better anticipate the strengths and weaknesses of governance. Two key limitations latent within such approaches need to be acknowledged. First, that these new perspectives to confronting existential risks import ingrained societal and institutional problems manifest in lower orders of problems. Second, that the additional complexity introduced into the field of existential risks necessarily makes attempts at framing responses more difficult. The payoffs of such a trade-off are open for discussion. Yet, our deconstruction of existential risks, and the taxonomy we develop to do so, may show promise as tools to help consolidate and expand the field of existential risk research and bring aligned disciplines to bear on the effort to reduce the overall probability of an existential outcome for mankind. But these are early tentative steps to building alternative vantage points from which to examine existential risks: our hope is that the alternative perspectives that these provide will allow researchers in broader fields to bring their expertise to identify trajectories that could lead to humanity's demise, and to devise strategies to obstruct those paths to existential outcomes. Fig. 1 . 1 Fig. 1. Qualitative risk categories, indicating the relative position of existential risks. (Reproduced from Bostrom, 2013, p. 17). \n .-Y.Liu et al.    Futures 102 (2018) 6-19 \n Table 2 2 A taxonomy of vulnerabilities which contribute to existential risks. Category Description Sub-distinction Examples of Existential Vulnerabilities V-O. Ontological vulnerability Vulnerability that is inherent in being, at present • Simulation shutdown; • Biological dependence on continuous/frequent energy & resource inputs (including food, water, air, light, …); \n Table 2 2 (continued)     Category Description Sub-distinction Examples of Existential Vulnerabilities V-I. Intended Vulnerability maintained for a direct vulnerability purpose [INTENTION] \n Table 3 3 A taxonomy of exposures which contribute to existential risks. Category Description Sub-distinction Examples of Existential Exposures E-O. Ontological exposure Exposure imposed exclusively by existing (as a human on Earth). - • Outer space events; • Super volcanos. • Potential (hostile) alien lifeforms E-P. Indirect exposure Exposure indirectly caused by societal arrangements intended for something else.", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0016328717301623-main.tei.xml", "abstract": "In recent years, the study of existential risks has explored a range of natural and man-made catastrophes, from supervolcano eruption to nuclear war, and from global pandemics to potential risks from misaligned AI. These risks share the prospect of causing outright human extinction were they to occur. In this approach, such identified existential risks are frequently characterised by relatively singular origin events and concrete pathways of harm which directly jeopardise the survival of humanity, or undercut its potential for long-term technological progress. While this approach aptly identifies the most cataclysmic fates which may befall humanity, we argue that catastrophic 'existential outcomes' may likely arise from a broader range of sources and societal vulnerabilities, and through the complex interactions of disparate social, cultural, and natural processes-many of which, taken in isolation, might not be seen to merit attention as a global catastrophic, let alone existential, risk. This article argues that an emphasis on mitigating the hazards (discrete causes) of existential risks is an unnecessarily narrow framing of the challenge facing humanity, one which risks prematurely curtailing the spectrum of policy responses considered. Instead, it argues existential risks constitute but a subset in a broader set of challenges which could directly or indirectly contribute to existential consequences for humanity. To illustrate, we introduce and examine a set of existential risks that often fall outside the scope of, or remain understudied within, the field. By focusing on vulnerability and exposure rather than existential hazards, we develop a new taxonomy which captures factors contributing to these existential risks. Latent structural vulnerabilities in our technological systems and in our societal arrangements may increase our susceptibility to existential hazards. Finally, different types of exposure of our society or its natural base determine if or how a given hazard can interface with pre-existing vulnerabilities, to trigger emergent existential risks. We argue that far from being peripheral footnotes to their more direct and immediately terminal counterparts, these \"Boring Apocalypses\" may well prove to be the more endemic and problematic, dragging down and undercutting short-term successes in mitigating more spectacular risks. If the cardinal concern is humanity's continued survival and prosperity, then focussing academic and public advocacy efforts on reducing direct existential hazards may have the paradoxical potential of exacerbating humanity's indirect susceptibility to such outcomes. Adopting law and policy perspectives allow us to foreground societal dimensions that complement and reinforce the discourse on existential risks.", "id": "1020443254847379393e4b8c822c0dad"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Philip Trammell"], "title": "Fixed-point solutions to the regress problem in normative uncertainty", "text": "Introduction People sometimes make claims about how we ought to act in the face of empirical uncertainty. A \"decision theory\" is a collection of such claims. Because they make demands on our behavior, decision theories are \"norms\". (Descriptive claims about how actual agents act under uncertainty are sometimes called \"positive decision theories\". For the purposes of this paper, the term \"decision theory\" will refer exclusively to normative decision theories, as defined above.) Moral theories are also norms, for example, because they too are collections of claims about how we \"ought\" (albeit in another sense) to act. Though I hope that the formal results of this paper are of interest to readers of many metaethical persuasions, the language used throughout will assume a realist position. I will say, then, that we suffer decision-theoretic uncertainty when we assign positive probability to the truth-values of conflicting decision theories, and, more generally, some form of normative uncertainty whenever we assign positive probability to the truth-values of conflicting norms. The most widely accepted normative decision theory, by far, is expected utility theory. As a normative theory, expected utility theory can be interpreted as the claim that we have a cardinal utility function whose value depends on what act we choose and on the state of the world, and that we ought to act so as to maximize the expected value of that function, given our uncertainty across states. Alternatively, expected utility theory can be interpreted as the claim that we have an ordinal utility function whose value depends on what act we choose and on the state of the world, and that we ought to act in such a way as satisfies various assumptions (the von Neumann-Morgenstern axioms, perhaps), which together happen to entail that we will be acting as if we were maximizing the expected value of a cardinal utility function. Either way, expected utility theory, as a normative ideal, is a set of claims about what we ought to do. Expected utility theory is not without critics. Soon after its foundations were laid in the 1940s and 1950s by John von Neumann, Oskar Morgenstern, and Leonard Savage, others, such as Maurice Allais, raised objections to the claim that expected utility maximization is a model of ideal behavior. It is true that, in the apparent absence of plausible alternatives, expected utility theory came to serve as the unchallenged basis for almost all of economic theory. But the debate over the normative claims that underlie it continued among some economists and philosophers, and has recently received new attention with Lara Buchak's 2013 publication of Risk and Rationality, which argues that it can be rational to violate the von Neumann-Morgenstern \"independence\" axiom so as to act on explicit risk preferences. In sum, the normative claims made by expected utility theory-even if sometimes taken for granted-are claims about whose truth-value an agent can be uncertain. What \"should\" one do in the face of decision-theoretic uncertainty? Is there even a coherent way to interpret that question? The position that there is-that we \"ought\" to act on the basis of our normative uncertainty in general-has been called \"uncertaintism\" (or, less frequently, \"metanormativism\"). The uncertaintist, presumably, must then offer an account of what one should do when one assigns, say, a seventy percent chance to the truth of expected utility theory, and a thirty percent chance to the truth of Buchak's alternative. As we can see, questions about how to deal with empirical uncertainty give rise to questions about how to deal with decision-theoretic uncertainty. But our regress does not stop there. Just as decision theories are theories about how to act in the face of empirical uncertainty, let us use the term \"metanormative theories\" for collections of claims about how we ought to act in the face of normative uncertainty. It seems that, just as we can suffer normative uncertainty, we can suffer metanormative uncertainty as well: we can assign positive probability to conflicting metanormative theories. Metametanormative theories, then, are collections of claims about how we ought to act in the face of metanormative uncertainty. And so on. In the end, it seems that the very existence of normative claims-the very notion that there are, in some sense or another, ways \"one ought to behave\"-organically gives rise to an infinite hierarchy of metanormative uncertainty, with which an agent may have to contend in the course of making a decision. Postulating such a hierarchy may seem like a strange and unneccesarily complex solution to a rather small and obscure problem. By analogy, therefore, consider three other structures explored in detail by philosophers and economic theorists: belief hierarchies, preference hierarchies, and hierarchies of deliberation procedures. We have beliefs about the world; and when one reflects on the fact that we can also have beliefs about people's beliefs, one can hardly help but document the emergence of a \"belief hierarchy\", constituted of beliefs about the world, beliefs about beliefs (2nd-order beliefs), beliefs about beliefs about beliefs (3rd-order), and so on [For a rigorous exploration of the structure, see  Mertens and Zamir (1985) ]. Likewise, we have preferences over features of the world, and the fact we can also have preferences over the contents of people's preferences (2nd-order preferences), and so on, gives rise to a \"preference hierarchy\" [see for example  Bergemann et al. (2017) ]. Finally, when we are not sure which act would maximize our utility, we may find it useful to ponder our options, even if doing so would come at a cost. Since pondering is in some sense just another option, we must then ponder whether to take one of our firstorder options or to take the option of pondering among them, and so on.  Lin (2014)  concludes that this deliberation must stop after finite steps, and will do so justifiably so long as the reasoner reaches the point that further meta-deliberation no longer obviously dominates taking one of the acts available.  Lipman (1991)  also explores this problem, in terms more similar to those we will use below: by constructing a (transfinite) hierarchy of beliefs over decision-making procedures, which justifies an act whenever it is judged to be (judged to be…) at least as good as the other available options, including the options of further deliberation at any order. Similarly, normative decision theories tell us how to act in the face of uncertainty about the true state of the world. The fact that we may have to act in the face of uncertainty about the true decision theory thus seems plausibly to give rise to a \"metanormative hierarchy\", similar in many respects to the hierarchies above. The infinite hierarchy of metanormative uncertainty, furthermore, is more than hypothetical. I myself, for instance, do not currently know the correct decision theory. Expected utility theory seems highly plausible to me, but I cannot fully rule out Buchak's arguments for some sort of risk-weighted expected utility theory, or arguments for theories that evade \"Pascal's muggings\" by giving special treatment to low-probability but high-expected-value events, to name just two examples. Likewise, I believe that there is a \"true metatheory\"-a correct way to act in the face of my decision-theoretic uncertainty-but I am not certain of what it is, nor of the true theory at any order of the above hierarchy. Despite all this uncertainty, however, my efforts to be moral or rational do ultimately result in conclusions about how to act. Somehow, from my infinite hierarchy of metanormative uncertainty, it seems I can be guided by normative concerns. The process by which this happens seems potentially interesting. Questions of decision-theoretic uncertainty have received little attention so far, however-research on normative uncertainty has focused primarily on moral uncertainty-and even the most recent inquiries into normative uncertainty (again, usually presented in the context of moral uncertainty) have generally left such questions unanswered.  Weatherson (2014)  avoids the problem by positing that the only norms are \"firstorder\"; that there simply is no right or wrong way to deal with normative uncertainty.  Sepielli (2014)  allows for \"orders of rationality\" and the corresponding \"iterated normative uncertainty\" (526). He constructs a metanormative hierarchy much like that we will define below, to serve a bridge between the mind-independent norms of which we are uncertain and the action-guiding, \"all-things-considered\" decision rule (given by what he calls \"global systemic rationality\") to which we are more plausibly all accountable. Then, given an agent who assigns some positive credence to theories of rationality, at some order, which conflict as to which act is most rational for her (at that order), he expresses the suspicion that that appealing to a higher-order rationality concept will always allow the agent to eliminate at least one action available. Posit \"actions A…Z\", he writes; \"[p]erhaps my uncertainty regarding objective normativity will intentionally explain my doing any of A…R…. My hope is to show that, as a general matter, potential actions will be hived off with each stepping-back\" (and permanently so). Given a finite act-set, this procedure would ultimately result in a coherent definition of what the agent subjectively ought to do. Unfortunately, as for whether the procedure succeeds, he concludes, \"I'll have to make good on that suspicion elsewhere\" (539). Tarsney (2017) reiterates Sepielli's hope for what he calls \"fixed point solutions\" to the regress problem. He acknowledges, however, that such fixed points will not necessarily exist (240-241), and concludes that a general solution to the regress problem must thus be found altogether elsewhere. In particular-motivated also by the thought that finite, boundedly rational agents cannot be normatively required to work out the fixed point of an infinite hierarchy, even if it exists (238) 1 -he argues for what he calls the \"Enkratic Principle\" (246). This is the broad, mind-independent principle that, just as long as one is in some sense \"trying one's best\" to do the first-order right thing in the face of normative uncertainty, one's decision is justified. On Tarsney's account, the regress is thus cut off at the second order. Finally, many accept that uncertaintism does indeed require some sort of fixedpoint solution to the regress problem-but conclude from this that there simply must be something deeply wrong with uncertaintism. The following sentiment, described in Volume 7 of Oxford Studies in Normative Ethics (2017), is typical: But a regress problem looms. Let us suppose that I am uncertain among some ordinary moral theories,  [and]  I ask what to do given the probability distribution over T1…Tn. But I am uncertain as to the answer, assigning some probability to each of U1…Un. This prompts me to ask what I ought to do given this probability distribution…. We can imagine this process iterating indefinitely…. The possibility of normative uncertainty all the way up makes the uncertaintist project look pointless. Does this possibility in fact render the uncertainist project pointless? Or can one accept the possibility of normative uncertainty all the way up, and still be norm-guided in some important classes of circumstances? I here argue the latter. To begin to answer the above questions more precisely, Sect. 2 presents a formal framework that aims to capture our intuitions about the concept of decision-theoretic uncertainty. Within this framework, Sect. 3 specifies various conditions under which two similar convergence results follow, as given in Sect. 4. Section 5 considers the earlier sections' implications for normative uncertainty more generally. \n Framework \n Choiceworthiness A finite set A = {a 1 , . . . , a |A| } of \"feasible acts\" presents itself. There is a finite set of \"possible states\" S = {s 1 , . . . , s |S| } to which I assign positive probability. 2 I assign utilities to performing each act in each state, as represented by the utility function u(A, s), where the value assigned to each act is not necessarily independent of the alternatives in A. 3 I also find myself in an overall finite epistemic position e, specifying the probabilities I assign to all relevant claims.  4  Let us call π = A, u, e my \"choice problem\". Definition 2.1 A choice problem π is a triple of (i) a set of acts A, (ii) an epistemic position e, and (iii) a state-contingent utility function u over A. We will say that my utility function specifies the \"objective choiceworthiness\" (or simply \"choiceworthiness\") of each act, conditional on each state. That is, given s, the choiceworthiness of a i is u(A, s) i -the ith element of the |A|-vector u(A, s). From the probabilities I assign to the states in S, therefore, I also assign probabilities to potential values of the objective choiceworthiness of each act. Definition 2.2 A (finite) choiceworthiness distribution is a (finite) probability distribution over choiceworthiness values for some (finite) set of acts. Let D n denote the set of all finite probability distributions in R n , and let some d(π ) ∈ D |A| represent the choiceworthiness distribution entailed by π . Many other finite probability distributions over R |A| might do just as well as the chosen d at representing my finite choiceworthiness distribution. Exactly which others depends on how much structure is contained in our understanding of \"utility\". If we understand utility to be a merely \"ordinal\" quantity, for instance, then any transformation of d that is monotonic in choiceworthiness (and constant in probability) represents the same choiceworthiness distribution. We are here assuming nothing about utility except that it at least partially orders act-state pairs from a given {feasible set × possible set}, and that R is \"rich enough\" to capture any potential difference between the choiceworthiness values of particular act-state pairs-that choiceworthiness cannot be lexicographic, for instance. As discussed at the end of Sect. 2.5, these assumptions about choiceworthiness, here made implicitly, will follow from similar assumptions made explicitly about subjective choiceworthiness. \n Subjective choiceworthiness I am uncertain about acts' choiceworthinesses. Even so, I may know that one act is the most appropriate for me to choose, given my epistemic position. As I write this, for instance, I assign high probability to the event that, if I go to the doctor, I will swiftly be cured of my back injury (an outcome I would prefer immensely to the status quo), and low probability to the roughly complementary event that, if I go to the doctor, I will waste some time and remain injured (an outcome to which I would slightly prefer the status quo). Despite this uncertainty, and all my other uncertainty, I am in fact certain that going to the doctor is the \"better choice\" for me right now (by far!). There is thus some scale on which the act of going to the doctor scores higher for me than the act of not going-and would score higher for anyone with the same utility function, in the same overall epistemic position, facing the same set of feasible acts. Let us call this scale \"subjective chiceworthiness\". It is my intuition that subjective choiceworthiness c, when well-defined, is fundamentally a cardinal scale. That is, I would maintain that a representation of acts' subjective choiceworthinesses (for an agent in a given situation) in R |A| would be unique at least up to affine transformation. If my feasible act set A = {a 1 , a 2 , a 3 } consists of going to the doctor (a 1 ), going to a very slightly less competent doctor (a 2 ), or not going at all (a 3 ), then there is some important and foundational sense in which, given my epistemic position and my preferences, the distance between c(π ) 1 and c(π ) 2 is less than the distance between c(π ) 2 and c(π ) 3 . It might be objected that I will always do whatever winds up being most subjectively choiceworthy; that therefore, in the absence of a specified theory of decision-making under uncertainty, no information is conveyed by postulated differences between the acts not chosen; and that c is therefore better understood as merely an ordering, or perhaps even as a choice relation. To this it might be replied that, under certain circumstances, differences in subjective choiceworthiness could bear some relationship to the subjective probability with which a subjectively sub-optimal act would become optimal upon further reflection. Or that cardinal subjective choiceworthiness takes on a clearer meaning in other situations of normative uncertainty (i.e. one might not choose the most subjectively morally choiceworthy act, and might in some sense be more blameworthy the less subjectively morally choiceworthy one's act was)-and that it would be strange for subjective choiceworthiness to be fundamentally cardinal in one of these situations but not the other. Or that our models of the world are generally simpler when we extend our intuitions regarding quantities' cardinality beyond the domains in which they happen to be testable-such as our intuition that temperature is generally cardinal, even on some cold, distant star that we will only discover if its temperature rises above some threshold. Furthermore, cardinal subjective choiceworthiness allows for the convergence results described below, and less structured interpretations of subjective choiceworthiness would not. If we are otherwise persuaded that the regress problem must have some solution or other, it is not circular to allow this observation itself to lend credibility to the concept of cardinal subjective choiceworthiness. In any event, for the purposes of this analysis, we will understand subjective choiceworthiness (again, when well-defined) to be cardinal. We will represent it by a \"subjective choiceworthiness function\" c(π ), where c assigns a real number to the subjective choiceworthiness of each of the acts in a feasible set A, for an agent with a utility function u, in epistemic position e. Note that by having c map into the real numbers, we are assuming that all information about differences in subjective choiceworthiness (and therefore utility) can be captured by ratios of differences in real numbers. We are here explicitly assuming for subjective choiceworthiness what we provisionally assumed above for objective choiceworthiness-that, for instance, it cannot be lexicographic. Like probability theories that let us condition on probability 0 events, utility theories that let us distinguish between acts that differ infinitesimally in choiceworthiness may also be interesting to consider in light of the regress problem. However, we will not touch them here. \n Metachoiceworthiness In general, if I am to translate a choiceworthiness distribution d into a determination of how to act, I must invoke a \"decision theory\": a collection of claims concerning how to evaluate acts in light of one's choiceworthiness distribution. For example, using this terminology, one decision theory is \"Expected Choiceworthiness Theory\" (EC). EC is characterized by the fact that, if I am certain that it is the correct decision theory, then each act's subjective choiceworthiness for me is its expected choiceworthiness under d.  5  Another decision theory would be \"minimum choiceworthiness\"-a theory characterized by the fact that, if I am certain that it is the correct decision theory, then each act's subjective choiceworthiness for me is its minimum possible choiceworthiness under d. Just as I am uncertain about the true state of the world, I may also be uncertain about the correct decision theory. To come to a determination of how to act, therefore, I may have to invoke a sort of \"meta decision theory\" (or, \"2-metatheory\"): a collection of claims concerning how to respond to one's uncertainty over decision theories. Note that, since this is so, the decision theories (we will awkwardly call these \"1metatheories\", for ease of indexing) cannot themselves be claims about subjective choiceworthiness. This is perhaps a surprising claim, so it bears repeating: expected utility theory (for example) is not, in this language, a theory about what subjective choiceworthiness is, or even about what it ought to be \"all things considered\". It is, rather, a theory about what subjective choiceworthiness \"1-ought\" to be, for someone with a given objective choiceworthiness distribution over his feasible set-or, a theory about what subjective choiceworthiness is for someone with a given objective choiceworthiness distribution over his feasible set, if he knows the true 1-metatheory. Suppose, for instance, that I am faced with three feasible acts, that I assign probability to each of two 1-metatheories, t 1 and t 2 , and that I am certain of \"2-metatheory\" m. The theories are such that if I were certain of t 1 , the subjective choiceworthinesses of the acts would be ordered a 1 a 2 a 3 ; if I were certain of t 2 , the subjective choiceworthinesses of the acts would be ordered a 3 a 2 a 1 ; and, given the probabilities I assign to t 1 and t 2 , but my certainty about m, the subjective choiceworthinesses of the acts are in fact ordered a 2 a 3 a 1 . Although I assign probability 1 2 to t 1 , I assign no positive probability to the event that a 1 is more subjectively choiceworthy than a 2 from my epistemic position. The 1-metatheories' claims, therefore, are not claims about the acts' subjective choiceworthinesses given my empirical uncertainty, but about how the acts score on an altogether different scale. Let us call this scale \"metachoiceworthiness\", or \"1-metachoiceworthiness\". Of course, metachoiceworthiness must be constructed such that, if I know that an act's 1-metachoiceworthiness is x, then the act's subjective choiceworthiness for me is also x. We might therefore informally think of 1-metachoiceworthiness as \"whatever subjective choiceworthiness is, for someone who knows the correct 1-metatheory\". But since, again, decision theories are not actually claims about subjective choiceworthiness, let us begin by thinking about 1-metachoiceworthiness on its own terms, and only afterward consider its relationship to subjective choiceworthiness. In any event, the elusiveness of subjective choiceworthiness is not restricted to \"order 1\". Just as I may be uncertain as to the correct 1-metatheory, I may be uncertain as to the correct 2-metatheory; I may therefore have to appeal to a \"3-metatheory\"; and the 2-metatheories are therefore making claims not about acts' subjective choiceworthiness given beliefs about their 1-metachoiceworthiness, but about acts', say, \"2-metachoiceworthiness\" given beliefs about their 1-metachoiceworthiness. So our regress begins. \n k-metachoiceworthiness Let us call choiceworthiness \"0-metachoiceworthiness\", choiceworthiness distributions \"0-metachoiceworthiness distributions\", and decision theories \"1-metatheories\". The concepts of k-choiceworthiness, k-metachoiceworthiness distributions, and kmetatheories can then together be defined recursively. \n Definition 2.3 The k-metachoiceworthiness c k of an act a i , for an agent facing finite choice problem π , is a i 's subjective choiceworthiness for an agent with the same (k − 1)-metachoiceworthiness distribution as that entailed by π , but who knows the correct k-metatheory. Let us denote acts' relative k-metachoiceworthiness by the two-place relation π,k . Definition 2.4 A (finite) k-metachoiceworthiness distribution d k ∈ D |A| is a probability distribution over k-metachoiceworthiness values for some (finite) set of acts A. Definition 2.5 A k-metatheory, applied to a finite set of acts A, is a function t k : D |A| → R |A| , representing claims about the k-metachoiceworthiness of the acts in A given (k − 1)-metachoiceworthiness distribution d k−1 ∈ D |A| . Note that, strictly speaking, if we want our k-metatheories to make k-metachoiceworthiness claims over finite act-sets of arbitrary size, we would have to say that a k-metatheory is a family of functions {t n k } from D n to R n , with one for each n ∈ N. For simplicity, however, we will take n = |A| as given and interpret our project only as an attempt to find criteria under which the subjective choiceworthinesses of any n acts will be well-defined-with the understanding that identical reasoning would apply to any other n. We can now define a few aditional terms.  \n The relationship of k-metachoiceworthiness to subjective choiceworthiness Upon introducing the cardinal subjective choiceworthiness function c(π ) above, we placed no restrictions on what it could be. Now that we have documented the emergence of an elaborate web of concepts concerning π , however, we can consider how it relates to c. Recall that k-metachoiceworthiness claims are defined so that, if I know that an act's k-metachoiceworthiness for me is x, the act's subjective choiceworthiness for me is x. Let us now introduce a compatible, minimally restrictive principle with which one's subjective choiceworthiness function might comply in the face of uncertainty about an act's k-metachoiceworthiness. Definition 2.9 The Dominance Principle is the principle that • If b ≥ x ∀b ∈ [ c k ] i , and b * > x for some b * ∈ [ c k ] i , then c(a i ) > x. • If b ≤ x ∀b ∈ [ c k ] i , and b * < x for some b * ∈ [ c k ] i , then c(a i ) < x. Note that if I accept the Dominance Principle, it follows immediately that my subjective choiceworthiness for an act a i is well-defined whenever | ∩ k∈N [min([ c k ] i ), max([ c k ] i )]| = 1. That is, whenever exactly one number lies in the ranges of \"admissible\" (not dominated) k-metachoiceworthiness values, across all k, for an act, that number must be the act's subjective choiceworthiness. Note also that any claim about subjective choiceworthiness itself, such as the Dominance Principle, in some sense takes on both a positive and a normative interpretation. One could interpret the Principle normatively as asserting that one's subjective choiceworthiness always ought to obey the above pattern. In this case, if one accepts the Principle, one's subjective choiceworthiness also does obey it, since to hold that an act should be ranked highly for someone in your epistemic position is simply another way to say that it is highly subjectively choiceworthy. Alternatively, one could interpret the Principle positively as asserting that, as a matter of fact, subjective choiceworthiness always obeys the above pattern. If one accepts this claim (and that \"ought implies can\"), one must also accept that subjective choiceworthiness always ought to obey the above pattern. Either way, if one accepts the Principle, one cannot assign positive probability to k-metatheories that claim that the k-metachoiceworthiness of an act lies outside the admissible range imposed by one's k -metachoiceworthiness distribution for the act for lower orders k < k. Finally, note that the framework outlined here differs from other approaches to subjective choiceworthiness in the following respect. Some other approaches [e.g. that of MacAskill (2016a)] begin with the normative theories in all their diversity; work through problems of intertheoretic comparability; and then try to define subjective choiceworthiness with no more structure than necessary. On some accounts, this minimal structure allows only for a binary classification of acts into the \"permissible\" and the \"impermissible\" [as recommended, for instance, by  Barry and Tomlin (2016) ]. The above approach, by contrast, begins by assuming that subjective choiceworthiness is a single cardinal scale, and it characterizes k-metachoiceworthiness claims, and the k-metatheories that make them, in terms of the subjective choiceworthinesses that they would induce if they were known. This approach has the cost of assuming cardinal subjective choiceworthiness, but it has the benefit of immediately giving all my kmetachoiceworthiness claims both unit and level comparability, without requiring any further assumptions. Thus, from a cardinal definition of subjective choiceworthiness, we also get a cardinal definition of utility, without having to assume it explicitly. By similar reasoning, we also get cardinal definitions of k-metachoiceworthiness for all k. Note that we are not taking the Von Neumann-Morgenstern approach of defining my utility function so that it represents the choices I would make if I were maximizing expected utility; indeed, our project is to explore how far I can stray from certainty about expected utility theory while still knowing how I subjectively ought to act. \n Conditions \n Completeness A \"partial k-metatheory\" would be one that makes claims about the k-metachoiceworthinesses of some acts under some (k − 1)-metachoiceworthiness distributions, but not of all acts under all (k − 1)-metachoiceworthiness distributions. A partial decision theory of \"strict dominance\", for instance, claims that a i π,1 a j ⇐⇒ u(A, s) i > u(A, s) j ∀s ∈ S, and makes no other claims at all. That is, it claims that an act a i is more 1-metachoiceworthy than an act a j if and only if a i is more objectively choiceworthy than a j in all the states to which I assign positive probability, and it is silent about acts' relative 1-metachoiceworthinesses in all other cases. Conversely, Definition 3.1 A k-metatheory, applied to a finite set of acts A, is complete if it is defined throughout D |A| . One condition for the results below is that I assign positive probability only to complete decision theories. Believing that the true decision theory is complete is, I think, reasonably well motivated by the sense that, just as I know acts' 0metachoiceworthiness (i.e. objective choiceworthiness) if I know the true state, I should be able to know acts' 1-metachoiceworthiness if I know the true decision theory (and so on up the hierarchy). In any event, we will remove partial decision theories from consideration so as to separate the regress problem from the problems of incomparability that can plague normative uncertainty in their own right. Note that the framework laid out in Sect. 2 does not allow us to assign positive probability to the \"nihilistic decision theory\" (one that makes no claims about acts' 1-metachoiceworthinesses under any choiceworthiness distribution). Since a decision theory is a collection of claims determining what acts' subjective choiceworthinesses would be for me if I knew how to respond to my empirical uncertainty, and since my subjective choiceworthiness is already defined in the degenerate case of empirical certainty, all my decision theories at least claim that an act's subjective choiceworthiness is its objective choiceworthiness, when my objective choiceworthiness distribution is degenerate. \n Continuity We will say that Definition 3.2 A k-metatheory t k is continuous if slight changes to the individual (k−1)-metachoiceworthiness claims to which one assigns positive probability produce only slight changes to the k-metachoiceworthiness claims made by t k . To be called continuous, t k need not respond continuously to the probability one assigns to some (k − 1)-metachoiceworthiness claim. A more formal definition of continutity, as we are using the term here, is given in the \"Appendix\". A second condition, necessary for only the first of the results below, is that I assign positive probability only to continuous decision theories. \n The Analog Principle MacAskill (2014) argues that, when we are facing both empirical and normative uncertainty over a set of acts, there is a sense in which we should treat our empirical and normative uncertainty \"analogously\". If I am uncertain which act is objectively best, it may seem unlikely that the appropriate response to my uncertainty would depend on the reason (i.e., empirical or normative) for my uncertainty-especially upon considering that I might have uncertainty about how to behave without even knowing the reason for my uncertainty. In the context of the regress problem, one might likewise argue that we should treat our empirical and k-metatheoretic uncertainty analogously. More formally: Definition 3.3 Let t * k : D |A| → R |A| denote the true k-metatheory. The Analog Principle is the claim that t * k = t * 1 ∀k ≥ 1. One might wonder if it matters whether my beliefs about the k-metatheories are correlated across different orders k (as of course they are-very strongly!-if I accept the Analog Principle), or whether they are correlated my beliefs about the state of the world. In fact, it does not. A k-metatheory is simply a function of my (k-1)metachoiceworthiness distribution; a k-metatheory's output therefore does not depend on the probability that it is the true k-metatheory, nor on its probability conditional on some state or k -metatheory. A final condition, necessary only for the first of the results below, is that I accept the Analog Principle. \n Convergence \n Intuition In the context of the framework above, the commonness of well-defined subjective choiceworthiness is not surprising. If I assign positive probability to a finite number of theories, and they disagree about how subjectively choiceworthy some act should be for me, there will be a minimum and a maximum to that range of values. In the face of that uncertainty, my subjective choiceworthiness should lie somewhere in the interior of the range. Where, exactly? I will assign positive probability to different answers as to where it should lie, producing a smaller range. And so on. Given a few other assumptions (either the continuity of my theories and my acceptance of the Analog Principle, or the possibility of transfinite hierarchies), this process will not \"get stuck\" by shrinking the range of potential subjective choiceworthiness values for each act merely from a larger range to a smaller range. Instead, the process is guaranteed ultimately to shrink said range to a single point. In other words, nothing very counterintuitive falls out of the mathematical setup of the problem. The point of this exercise is simply to formally illustrate a coherent framework whereby our intuitions about normative uncertainty-including about the infinite regress that it threatens-can be reconciled with the understanding that, at the end of the day, we make norm-guided decisions. With that said, the convergence results can be stated as follows. \n Natural hierarchies Theorem 1 If one assigns positive probability only to a finite set of decision theories all of which are complete and continuous, and if one accepts the Dominance Principle and the Analog Principle, then one's subjective choiceworthiness is well-defined over any finite set A of acts. The proof can be found in the \"Appendix\". Proposition 4.1 If two acts are equally subjectively choiceworthy, this fact will not necessarily be revealed by the iterated application of one's distribution over kmetatheories. Proof Suppose for example that I assign probability 1 2 to Expected Choiceworthiness Theory, and to the analogous hierarchy (T 1 ) according to which the (k+1)metachoiceworthiness of an act is its expected k-metachoiceworthiness. I assign probability 1 2 to a risk-averse hierarchy of theories (T 2 ) according to which the (k+1)metachoiceworthiness of an act is the average of its expected k-metachoiceworthiness and its minimum possible k-metachoiceworthiness. I am deciding between two acts, a 1 and a 2 . I assign probability 1 2 to a state in which a 1 has objective choiceworthiness 0 and probability 1 2 to a state in which a 1 has objective choiceworthiness 1. Act a 2 has objective choiceworthiness 1 3 in both states. The subjective choiceworthiness of a 2 is, of course, 1 3 . The k-metachoiceworthiness claim about a 1 made by T 1 is [ c k ] 1,1 = 1 − k n=1 1 2 2n−1 ; that made by T 2 is [ c k ] 1,2 = k n=1 1 4 n . This can be seen by verifying algebraically that these summations satisfy the intitial conditions [ c 1 ] 1,1 = 1 2 and [ c 1 ] 1,2 = 1 4 , and the recursive conditions [ c k ] 1,1 = 1 2 [ c k−1 ] 1,1 + 1 2 [ c k−1 ] 1,2 and [ c k ] 1,2 = 1 4 [ c k−1 ] 1,1 + 3 4 [ c k−1 ] 1,2 (k > 1). As k increases, {[ c k ] 1,1 } converges to 1 3 from above, while always strictly greater, and {[ c k ] 1,2 } converges to 1 3 from below, while always strictly less. Thus the acts' subjective choiceworthinesses are precisely equal, even though any formal comparison of the acts is undefined if we halt our deliberation after finite k. This example does not imply the potentially concerning conclusion that one might not be able to infer acts' relative subjective choiceworthinesses, from one's choiceworthiness distribution and one's hierarchy distribution, in finite time. Indeed, since the subjective choiceworthiness of each act is well-defined under the above conditions, and is a logical consequence of one's finite choice problem, we know from the completeness of first-order logic that the value of c(π ) i can be determined for all i by some finite proof-such as the one given above. The example does, however, demonstrate that there may be facts about subjective choiceworthiness that are not discovered by the \"iterate a few times and hope my uncertainty is more or less resolved\" algorithm. In particular, therefore, I believe it demonstrates that fixed-point solutions to the regress problem need not take the form either of convergence after finite k or of monotonic decreases in the set of maximally kchoiceworthy acts-as hoped for in  Sepielli (2014) , and as claimed by  Tarsney (2017, p. 239) . \n Transfinite hierarchies Suppose that the k-metatheories to which I assign positive probability are all complete and compatible with the Dominance Principle, but that they are not continuous, or that I reject the Analog Principle. It is then possible that my subjective choiceworthiness for some act a i does not converge, even after infinite steps. That is, though lim k→∞ min([ c k ] i ) and lim k→∞ max([ c k ] i ) do both exist (by the fact that the respective sequences in k are monotonic and bounded), lim k→∞ min([ c k ] i ) < lim k→∞ max([ c k ] i ). In such a situation, it seems, someone could still claim that there is a \"right way\" for me to act. Someone could claim that my subjective choiceworthiness for a i should be the average of lim k→∞ min([ c k ] i ) and lim k→∞ max([ c k ] i ), for example. If I assign positive probability to competing theories of how to act in situations like the above, I must appeal to a theory about how to act in the face of this uncertainty. So our regress extends beyond the natural numbers, into the transfinite ordinals. The definitions given in Sects. 2 and 3 can generally be reinterpreted so that k (or, κ) is any ordinal, not just any natural number. Two, however, will require slight tweaks: Definition 4.1 (Definition 2.3, revised) The κ-metachoiceworthiness c κ of an act a i , for an agent facing finite choice problem π , is a i 's subjective choiceworthiness for an agent with the same κ -metachoiceworthiness distribution as that entailed by π for all κ < κ, but who knows the correct κ-metatheory. Definition 4.2 (Definition 2.5, revised) A κ-metatheory, applied to a finite set of acts A, is a function t κ : D κ|A| → R |A| , representing claims about the κ-metachoiceworthiness of the acts in A given κ -metachoiceworthiness distributions d κ ∈ D |A| for all κ < κ. Note that this definition of a higher-order metatheory is strictly more general than the original, even with respect to finite k, because it allows k-metatheories to be functions of one's beliefs not only about (k − 1)-metachoiceworthiness but about kmetachoiceworthiness at all lower orders k < k. The following result thus holds, as Theorem 1 does not, regardless of whether we want to allow for this possibility. We can now state the following: Theorem 2 If one assigns positive probability only to a finite set of complete κmetatheories for each ordinal κ, and one accepts the Dominance Principle, then one's subjective choiceworthiness is well-defined over any finite set A of acts. The proof can be found in the \"Appendix\". \n The infectiousness of stubbornness Definition 4.3 The Weak Dominance Principle is the principle that • If b ≥ x ∀b ∈ [ c κ ] i , for some κ, then c(a i ) ≥ x. • If b ≤ x ∀b ∈ [ c κ ] i , for some κ, then c(a i ) ≤ x. Let us call a κ-metatheory \"compromising\" if it is compatible with the (strong) Dominance Principle, and \"stubborn\" if it is not. Expected Choiceworthiness Theory and risk-weighted variants of it are examples of \"compromising\" theories. Minimax Theory, according to which an act's metachoiceworthiness is its minimum possible choiceworthiness, is an example of a \"stubborn\" theory. However, it is compatible with the Weak Dominance Principle. Both the theorems above demonstrate that, when all the decision theories (or κmetatheories) to which I assign positive probability are compromising (along with some other conditions), the range of potential subjective choiceworthiness values for each act shrinks to point. In both cases, this is demonstrated roughly by the fact that, when the range of potential subjective choiceworthiness values for some act is a non-degenerate interval at some order k (or κ), the application of even higher-order metatheories shrinks this interval by increasing its minimum. One might notice that, strictly speaking, neither of the proofs requires that all my decision theories (or κ-metatheories) be compromising. Suppose, for example, that I reject the Dominance Principle, but accept the Weak Dominance Principle. Suppose further that just one decision theory (or one κ-metatheory for each κ) to which I assign positive probability is \"stubborn\"-or, that all the stubborn theories to which I assign positive probability are one-sidedly pessimistic (like Minimax) or optimistic (like Maximax) at each order. Then our proofs can go through with only slight modifications. We just need to shrink our interval exclusively from the top or from the bottom, at a given order, to avoid asking concessions of our stubborn theories. The plausibility of stubborn theories, however, poses two challenges for this project in general. First, stubborn theories are \"infectious\": they can determine our behavior regardless how little positive credence we give them. Suppose I am deciding between two acts, a 1 and a 2 . I assign probability 0.99 to a state in which a 1 has objective choiceworthiness 1, and probability 0.01 to a state in which a 1 has objective choiceworthiness 0. Act a 2 has objective choiceworthiness 0.0001 in both states. Furthermore, I assign probability 0.99 to Expected Choiceworthiness, and probability 0.01 to Minimax, at every order of the hierarchy. It would be deeply counterintuitive to conclude that, from such a position, a 2 is more subjectively choiceworthy than a 1 . It would be perhaps even more counterintuitive to conclude that the acts' subjective choiceworthinesses were equal, if a 2 's objective choiceworthiness were known to be 0. But of course we do reach both conclusions, as repeated applications of my distribution over decision theories bring a 1 's higher-order metachoiceworthiness arbitrarily close to 0-according even to the sequence of \"Expected Choiceworthiness\"-analogous theories. Second, stubborn theories can clash with each other. If we are going to give some weight to Maximin, at every order, it seems only fair to give some weight to Maximax at every order as well. But if we do, then each act's range of potential subjective choiceworthiness values never shrinks at all; min([ c κ ] i ) = min([ c 0 ] i ), and max([ c κ ] i ) = max([ c 0 ] i ), for all κ. It does not feel as though I can fully rule out stubborn theories. Thus, despite all our progress, I am still left with the original motivating question: how do I so regularly wind up with well-defined subjective choiceworthiness? One encouraging thought is the observation that, though stubbornness is infectious in one sense, there is a sense in which compromise is infectious as well. For example, suppose I assign positive probability to stubborn κ-metatheories (or even, only to stubborn κ-metatheories) at almost all κ, but assign positive probability only to compromising theories at a relatively sparse class of orders-at the limit ordinals, perhaps. Then, even though there is a sense in which I believe in stubborn theories \"almost everywhere\" up the hierarchy, the scattered all-compromising orders will still force my subjective choiceworthiness range for each act down to a point. (A minimally modified version of the proof of Theorem 2 presented in the \"Appendix\" will hold so long as our class of \"allcompromising\" orders is such that, for every set M of ordinal numbers, there is an ordinal number γ ∈ : γ > μ ∀ μ ∈ M.) Similar reasoning applies to the case of merely natural hierarchies. In short, my hierarchy distribution can handle a lot of stubbornness; as long as an all-compromising order comes along every now and then to shrink my subjective choiceworthiness range for each act, there are reasonable conditions under which subjective choiceworthiness will generally be well-defined. \n Rescaling MacAskill (2014) offers the following example of undefined subjective choiceworthiness. Suppose an agent faces a choice problem: Order 0 s 1 (Pr. 18 23 ) s 2 (Pr. 5 23 ) a 1 0 4 a 2 1 0 She must choose among acts A = {a 1 , a 2 }. She assigns probability 18 23 to a state s 1 in which a 1 has objective choiceworthiness 0 and a 2 has objective choiceworthiness 1, and probability 5 23 to a state s 2 in which c 0 (a 1 ) = 4 and c 0 (a 2 ) = 0. In evaluating the at order 1, she assigns probability 18 23 to Expected Choiceworthiness Theory (t 1 ), and probability 5 23 to \"Square Root Theory\" (t 2 ), according to which an act's 1-metachoiceworthiness is the expectation of the square root of the difference between its objective choiceworthiness and the objective choiceworthiness of the least objectively choiceworthy act in A. As we can see, after rescaling, the 1-metachoiceworthiness distribution of a 1 is precisely what the 0-metachoiceworthiness distribution of a 2 had been, and the 1metachoiceworthiness distribution of a 2 is precisely what the 0-metachoiceworthiness distribution of a 1 had been. Therefore, if we obey the Analog Principle-that is, if our distribution over k-metatheories is the same at every order-and if we rescale after every step, our k-metachoiceworthiness distribution for the acts will flip forever between that of \"Order 0\" and that of \"Order 1, rescaled\", without converging. To my mind, however, k-metachoiceworthiness claims are intuitively characterized by the property that, if one believes them, they define one's subjective choiceworthiness. If an agent faces empirical uncertainty over two acts' objective choiceworthiness as represented above, we want to say that, in the event that she learns the truth of s 2 , act a 1 's subjective choiceworthiness for her is 4. In precisely the same language, I think, we want to say that in the event that she learns the truth of Expected Choiceworthiness Theory (but does not learn the true state), a 1 's subjective choiceworthiness for her is 20 23 -and likewise all up the hierarchy. To keep these claims \"in line\", the framework of Sect. 2 permits real-valued representations of the subjective choiceworthiness values and k-metachoiceworthiness distributions associated with a given choice problem to be rescaled only in conjunction, not independently. Furthermore, if this is the right way to think about k-metachoiceworthiness, then Square Root Theory (SR) is, as stated, incoherent. SR does not specify which real-valued representations of objective choiceworthiness to use as inputs, so its claims should be independent to rescaling. But they are not. Using our agent's 0-metachoiceworthiness as represented above, SR claims that the 1metachoiceworthiness of a 1 is 20 23 , and EC claims that the 1-metachoiceworthiness of a 1 is lower (just 10 23 ). But if we had represented her 0-metachoiceworthiness distribution differently, Order 0 s 1 (Pr. 18 23 ) s 2 (Pr. 5 23 ) a 1 0 1 a 2 1 4 0 we would conclude that EC claims that the 1-metachoiceworthiness of A is 5 23 for her, and that SR claims the same. To ensure that an act's true k-metachoiceworthiness for an agent be independent of the scale she arbitrarily uses to represent her (k−1)-metachoiceworthiness distribution, all our k-metatheories have to be \"affine\" (unique up to affine transformation). Though this condition closes the door to \"Square Root Theory\", it permits a wide array of other risk-averse theories, including Buchak's REU Theory and the risk-averse theory presented in Proposition 4.1. \n Applications to moral uncertainty If I assign positive probability only a finite set of complete, cardinal, comparable moral theories-or, if I at least know the right way to represent all my moral theories' choiceworthiness claims on the same cardinal scale-then the results above can be applied almost directly to my moral choice problems under empirical certainty. \"Almost\", because, to avoid wading into a sea of hopeless complexity, we must assume that my moral theories make no claims about how to respond to uncertainty per se. That is, we must say that, for example, among varieties of utilitarianism, I assign positive probability only to those that claim that an act's objective choiceworthiness is (something along the lines of) its objective impact on total utility. I must assign no positive probability to a variety of utilitarianism that claims that an act's objective choiceworthiness is, say, my expectation of its impact on total utility. Utilitarianism is so often described as the idea that we ought to maximize the world's expected utility-see  Parfit (1984, pp. 25, 26) , for instance-that one might easily come to believe that Expected Choiceworthiness is the only way utilitarians are allowed to deal with uncertainty. In this context, however, we should be careful to separate the unique moral claim of utilitarianism (that value is identified with utility) from the independent decision-theoretic claim (that one ought to maximize expected value). Moral theories that explicitly incorporate such decision-theoretic claims may also be interesting to consider in light of the regress problem, but we will not discuss them here. With that restriction, suppose I am certain about the state of the world. I then simply have to swap out our language about objective choiceworthiness being \"my utility function, contingent on the true state of the world\" for language about objective choiceworthiness being \"moral value, contingent on the true moral theory\", and Sects. 2-4 apply to cases of moral uncertainty, under empirical certainty, in full. If I face both empirical uncertainty and moral uncertainty, however, my situation is more complex. One approach would be for me to take \"objective choiceworthiness\" to be a function of both the true state and the true moral theory, to consider my probability distribution over {states} × {moral theories}, and then to apply my hierarchy distribution. Another approach, however, would be for me first to work out the subjective choiceworthiness of each act, conditional on each state, in light of my distribution over moral theories, and then to apply my hierarchy distribution a second time, to work out the subjective choiceworthiness of each act in light of my distribution over states. A third approach, symmetrical to the second, would be for me first to work out the subjective choiceworthiness of each act, conditional on each moral theory, in light of my distribution over states, and then to apply my hierarchy distribution a second time, to work out the subjective choiceworthiness of each act in light of my distribution over moral theories (These approaches have the disadvantage that they would not be able to account for any dependence between my distribution over states and my over moral theories. They have the advantage, however, that they would be able to account for the possibility that my hierarchy distribution over ways of dealing with moral uncertainty differs from my hierarchy distribution over ways of dealing with empirical uncertainty). And other conceivable approaches abound. Unfortunately, these approaches will not necessarily all yield the same subjective choiceworthiness values, or even the same act recommendations-not even under decision-theoretic certainty, and not even when I believe that the same theory should be used in the face of emprical uncertainty as in the face of moral uncertainty. Consider the following situation. I assign positive probability to a set of moral theories M = {m 1 , m 2 , m 3 } and to a set of states S = {s 1 , s 2 , s 3 }. I have two feasible acts, a 1 and a 2 . Their objective choiceworthinesses, conditional on each state and moral theory, are as follows: Furthermore, I am certain that an act's k-metachoiceworthiness is its second-lowestpossible (k−1)-metachoiceworthiness. If I apply this decision theory to my uncertainty over {states} × {moral theories}, I get c(a 1 ) = 2 and c(a 2 ) = 3, so a 2 a 1 . However, if I apply this decision theory first over states (conditional on each moral theory) and then over moral theories-or, first over moral theories (conditional on each state) and then over states-then I get c(a 1 ) = 4 and c(a 2 ) = 3, so a 1 a 2 . These complications only worsen when |M| = |S|, in which case even the \"same\" decision theory can aggregate across moral theories and across states arbitrarily differently. There is another way in which decision-theoretic uncertainty can interact with moral uncertainty. It is often argued that morality requires us to make decisions as if from behind a \"veil of ignorance\" about our own identity among those affected by our actions. If so, the moral choiceworthiness of an act depends directly on its decisiontheoretic 1-metachoiceworthiness. Suppose that I ought to act toward a group as if my identity is, in probability, distributed uniformly over the group. Then, if Expected Choiceworthiness is the correct decision theory, the Veil of Ignorance argument points toward classical utilitarianism as the correct moral theory; if Minimax is the correct decision theory, toward Rawls's \"maximin criterion\"; if some risk-weighted theory is the correct decision theory, toward the corresponding version of prioritarianism; and so on. 7 But we will not explore this interaction further here. Finally, the above thoughts about how to integrate the results of Sects. 2-4 into situations of moral uncertainty can apply straightforwardly to normative uncertainty in other domains, so long as one assigns positive probability finite set of theories which are in some analogous sense complete, cardinal, and intertheoretically comparable. But we will not explore such applications further here. \n Conclusion We are often uncertain about the moral and decision-theoretic norms which we believe should guide our behavior. Even when these norms conflict, however, we often have a subjective understanding of whether some act would be rationally or morally permissible for us, from our position of normative uncertainty. \"Uncertaintism\" might be understood as the project of unraveling how this uncertainty translates into the subjective choiceworthiness on which we ultimately feel justified in acting. When the uncertaintist tries to specify any particular mechanism for translating the uncertainty over choiceworthiness into an appropriate characterization of subjective choiceworthiness, however, we find that, just as we are not certain of our acts' objective choiceworthinesses, we are not certain of his proposed mechanism either. Nor are we certain about how to how to deal with our uncertainty about such a mechanism. Indeed, our certainty about subjective choiceworthiness seems to stand strangely on its own. In general, when we try to ground our certainty about subjective choiceworthiness in metanormative certainty at some order, we find that the hoped-for ground of certainty does not exist. For some, as cited above, this \"possibility of normative uncertainty all the way up makes the uncertaintist project look pointless\". The results presented here demonstrate that, as stated, the quoted worry is not justified. We can reliably have well-defined subjective choiceworthiness without being certain about the correct first-order normative theory or about any higher-order metatheory. We only have to commit to a weaker family of assumptions, such as the Let |d t k | and |d T | denote the number of k-metatheories and hierarchies, respectively, to which I assign positive probability. Let c k ∈ R |d t k ||A| represent the claims made by my |d t k | k-metatheories about the k-metachoiceworthinesses of the |A| acts in A. Let p k ∈ |d t k |−1 represent the probabilities I assign to these k-metatheories. We can now represent my kmetachoiceworthiness distribution by d k = c k , p k . 6 Definition 2.8 A hierarchy distribution d T is a probability distribution over hierar- chies. Definition 2.6 A k-metatheory distribution d t k is a probability distribution over kmetatheories.Definition 2.7 A metatheoretic hierarchy (or simply \"hierarchy\") T is a collection of k-metatheories t k with one for each k > 0. \n\t\t\t Synthese (2021Synthese ( ) 198:1177Synthese ( -1199  \n\t\t\t In the process, he distinguishes between the \"ideal regress problem\", which an ideal agent with perfect reasoning ability might face, and the \"non-ideal regress problem\". In order to separate the issue of normative uncertainty from the issue of bounded rationality, here we will consider only what he calls the \"ideal regress problem\". Note that we are implicitly assuming that normative facts are not logical facts; if they are, then it is impossible for an agent with perfect reasoning ability to suffer normative uncertainty. \n\t\t\t Here and elsewhere, we will assume that all credences satisfy the Kolmogorov probability axioms. Note that this implies that all the sets over which I have probability distributions are nonempty.3  We will assume that the probability of each state is independent of the chosen act. We will thus bypass the question of how to act in the face of such dependency (i.e. causal decision theory vs. evidential decision theory and other alternatives), and focus entirely on the question of how to act in the face of uncertainty over states (i.e. expected utility theory vs. its alternatives). For an analysis of how to approach uncertainty between causal and evidential decision theory, see MacAskill (2016b).4  More precisely, let e specify my probability distribution over the set of [{states of the world} × {decision theories (or, 1-metatheories)} × {2-metatheories} × {3-metatheories} × • • • ]. The concept of a \"k-metatheory\" is defined in Sect. 2.4. \n\t\t\t Let us distinguish EC from \"Maximize Expected Choiceworthiness\" (MEC). MEC is the weaker theory characterized only by the fact that, if I am certain that it is correct, then the acts with the highest subjective choiceworthiness for me are the acts with the highest expected objective choiceworthiness under d. \n\t\t\t This is not to say that a given distribution can only be represented by one particular vector pair. Multiple k-metatheories may make the same k-metachoiceworthiness claims in some situation, for instance. \n\t\t\t The implications of risk-weighted expected utility theory for decisions made on behalf of groups, rather than individuals, are further discussed byBuchak (2013, pp. 167, 168).", "date_published": "n/a", "url": "n/a", "filename": "Trammell2021_Article_Fixed-pointSolutionsToTheRegre.tei.xml", "abstract": "When we are faced with a choice among acts, but are uncertain about the true state of the world, we may be uncertain about the acts' \"choiceworthiness\". Decision theories guide our choice by making normative claims about how we should respond to this uncertainty. If we are unsure which decision theory is correct, however, we may remain unsure of what we ought to do. Given this decision-theoretic uncertainty, metatheories attempt to resolve the conflicts between our decision theories…but we may be unsure which meta-theory is correct as well. This reasoning can launch a regress of ever-higher-order uncertainty, which may leave one forever uncertain about what one ought to do. There is, fortunately, a class of circumstances under which this regress is not a problem. If one holds a cardinal understanding of subjective choiceworthiness, and accepts certain other criteria (which are too weak to specify any particular decision theory), one's hierarchy of metanormative uncertainty ultimately converges to precise definitions of \"subjective choiceworthiness\" for any finite set of acts. If one allows the metanormative regress to extend to the transfinite ordinals, the convergence criteria can be weakened further. Finally, the structure of these results applies straightforwardly not just to decision-theoretic uncertainty, but also to other varieties of normative uncertainty, such as moral uncertainty. \n Keywords Decision theory • Moral uncertainty • Normative uncertainty • Uncertaintism My thanks to Anubav Vasudevan, Christian Tarsney, and two anonymous referees for helpful comments and suggestions. All errors are my own.", "id": "2b6f4b559bafeb019a05feb76020d989"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "Under review as a conference paper at ICLR 2019 INFERRING REWARD FUNCTIONS FROM DEMONSTRATORS WITH UNKNOWN BIASES", "text": "INTRODUCTION Our ultimate goal is to enable the design of agents that optimize for the right reward function. Unfortunately, designing reward functions is challenging  (Amodei et al., 2017)  and can have unintended side-effects  (Hadfield-Menell et al., 2017) . Inverse Reinforcement Learning  (Russell, 1998; Ng et al., 2000; Abbeel & Ng, 2004)  aims to bypass the need for reward design by learning the reward from observed demonstrations of good behavior. Existing IRL algorithms typically make the assumption that the demonstrator is either optimal, or Boltzmann rational, i.e. taking better actions with higher probability  (Ziebart et al., 2008; Finn et al., 2016) . However, there is a rich literature showing that humans are not optimal, and are biased in systematic ways. Consider a grad student who starts writing a paper a month in advance, expecting it to take two weeks, but then misses the deadline. Should we infer that they prefer to lose sleep to pursue a deadline that they then miss? Of course not -this is a classic case of the planning fallacy  (Buehler et al., 1994) . It is not clear what exactly went wrong -perhaps the grad student did not have a good dynamics model (not realizing that Amazon spot instances can be suddenly terminated), or they failed to account for the uncertainty in their dynamics model (expecting that it wouldn't happen to them), or they optimized too much for short term reward (watching Netflix), and so on -we do not know what the bias is. Ideally, even with this unknown bias, we would like our system to infer that the grad student failed to plan appropriately, and that they would prefer to meet the deadline. This leads to a tradeoff between the expressivity of our model of the demonstrator, and the ability of the algorithm to learn the true reward function with few samples. On one extreme, if we know exactly what bias the demonstrator has, we can account for it to infer the true reward function quickly and accurately, as in  Evans et al. (2016) ;  Evans & Goodman (2015) ;  Zheng et al. (2014) ;  Majumdar et al. (2017)  (myopia and hyperbolic time discounting, sparse noise, and risk-sensitivity respectively). Even suboptimal trajectories or failures  (Shiarlis et al., 2016)  can be thought of as a biased demonstrator, where the bias is the specific model of failure. Unfortunately, people are complex, and it is unlikely that we will know exactly which bias a person is displaying, or even the space of possible biases that people might have. If we are incorrect about the bias, we will have a mis-specified model, and the reward function will get garbage values that explain the \"noise\" resulting from the mis-specification  (Steinhardt, 2017; Steinhardt & Evans, 2017) . On the other extreme, when the demonstrator could be any function mapping reward functions to policies, it is impossible to learn the true reward function even with infinite data, because there are always alternative explanations for the observed policy  (Armstrong & Mindermann, 2017; Christiano, 2015) . We could consider asking the human to rate each demonstration  (Burchfiel et al., 2016) , but the human could be biased in these ratings as well. In this paper, we focus on learning rewards when the demonstrator's bias is unknown. We seek to avoid impossibility results by introducing a set of assumptions that are weaker than assuming a known bias, the core of which is that the demonstrator plans their actions similarly in similar tasks. This leads us to investigate the idea that one could actually learn, rather than assume, the demonstrator's planning algorithm across multiple tasks, including any biases they may have. We analyze the feasibility of this idea in two settings, via two algorithms. In both algorithms, we can navigate the tradeoff between model expressivity and sample efficiency through the choice of architecture for the differentiable planner we learn, and the space of reward functions to consider. In the first setting, we assume that we have access to the true reward functions in some subset of tasks -that means we can learn the demonstrator's planning algorithm on those tasks, after which we can infer rewards from demonstrations in new tasks. In the more realistic setting where we have no access to any reward function, we assume that the demonstrator is \"close\" to optimal. This is a weaker version of the assumption of Boltzmann rationality that still allows us to learn particular systematic biases. We operationalize this assumption by initializing the differentiable planner to mimic the optimal agent, and then finetuning it to allow it to account for specific biases. We show that this initialization is essential for good performance, as we would expect from the impossibility result. In summary, this paper makes three contributions: 1. Assumptions that are more realistic than the assumption of Boltzmann rationality that allow us to avoid known pitfalls of reward inference. 2. Algorithms that leverage these assumptions to infer reward functions from suboptimal demonstrations. 3. An experimental evaluation demonstrating there is hope in the idea of learning better rewards by learning biases too, despite the theoretical difficulty of the problem. \n EXAMPLES OF BIASES To put this work in context, we start with some examples of the kind of biases a general algorithm should be able to capture and account for. While we use these for illustrative purposes, the whole point of our work is that humans might have systematic suboptimalities completely different from these examples. We don't know all the possible biases a priori. Running Example. We illustrate the effects of these biases on a simple 2D navigation task in figure  1 . There are multiple salient locations, each of which has a desirability score (which can be negative, in which case the agent wants to avoid those locations). The agent can move in any of the four cardinal directions, or stay in its current position. Every movement action has a chance of failing and causing the agent to move in a direction orthogonal to the one it chose. Despite their simplicity, there are several ways in which human-like suboptimal behavior can manifest in these environments. Time inconsistency. Would you prefer to get $100 in 30 days, or $110 in 31 days? Faced with this question, people typically choose the latter. However, thirty days later, when faced with the choice of getting $100 now, or $110 tomorrow, they sometimes choose to take the $100. This reversal of preferences over time would never happen with an optimal agent that maximizes expected sum of discounted rewards. Researchers model this phenomenon using hyperbolic time discounting, in which future rewards are discounted more aggressively than exponentially. This leads to a followup question -how do humans make long-term plans, given that their future self will have different preferences? Prior work has considered a spectrum from naive agents that assume their future self will have the same preferences as they do, to sophisticated agents that perfectly understand how their preferences will change over time and make plans that take such change into account  (Frederick et al., 2002) . In figure  1 , when going to a high reward, both the naive and sophisticated hyperbolic time discounters can be \"tempted\" by a proximate smaller reward. The naive agent fails to anticipate the temptation, and so once it gets near the smaller positive reward, it caves in to the temptation and stays there. The sophisticated agent explicitly plans to avoid the temptation -it does not collect the smaller reward and instead takes a longer, more dangerous path around the smaller reward to get to the large reward. Incorrect estimates of probabilities. Humans are notoriously bad at judging probabilities. The availability heuristic  (Tversky & Kahneman, 1973)  refers to the human tendency to rate events as more likely if they are easier to recall. The recency effect is a similar effect where recent events are judged to be more probable. These biases are complicated and depend heavily on context and don't obviously transfer to our task. So, we use two simplified models -an overconfident agent, which expects that the most likely next state is more likely than it actually is, leading it to take risks, and an underconfident agent, which is overly cautious. In figure  1 , the overconfident agent takes the shortest path to the reward, underestimating the risk of slipping into the large region of negative reward, while the underconfident agent plans a circuitous route around negative reward that it is unlikely to have actually encountered. Bounded computation. Researchers have studied models of bounded rationality, where humans are assumed to be rational subject to the constraint that they have a bounded amount of computation. This can be thought of as an explanation that many other heuristics and biases are actually computational shortcuts that allow us to reach reasonably good decisions without too much cost  (Kahneman, 2003) . In our task, we model computation bounds as a small time horizon for planning, leading to myopic behavior. In figure  1 , the myopic agent can only see close rewards, and goes directly to them, never even realizing the possibility of going to the highest reward. \n PROBLEM: LEARNING REWARDS OF DEMONSTRATORS WITH UNKNOWN BIASES Notation. A (finite-horizon) Markov Decision Process (MDP) (Puterman, 2014) is a tuple S, A, T, r, H . S is a set of states. A is a set of actions. T is a probability distribution over the next state, given the previous state and action. We write this as T (s t+1 |s t , a). r is a reward function that maps states and actions to rewards r : S × A → R. H ∈ Z + is the finite planning horizon for the agent. Since we are interested in the setting where the reward function r is unknown, we will factor MDPs into world models w = S, A, T, H and reward functions r. Instead of having access to a reward function, we observe the behavior of an demonstrator, who performs the task well but may be suboptimal in systematic ways. In particular, we observe the demonstrator's policy π : S → A. Estimating Biases and Rewards. Given a world model w and the demonstrator's policy π D which may exhibit an unknown bias, determine the reward r * that the demonstrator is optimizing. We might hope to solve this problem without any additional assumptions. However, this problem is unsolvable -  Armstrong & Mindermann (2017)  prove an impossibility result showing that for any potential reward function r , there is some planner D such that D (w, r ) = D(w, r * ). The proof is simple -simply set D (w, r ) = π for any r , that is D always returns π regardless of reward. Inverse reinforcement learning assumes that the demonstrator is (approximately) optimal to get around this issue. It is common to assume Boltzmann rationality, where the probability of an action is proportional to the exponent of its expected value  (Baker et al., 2006) , i.e. P (a|s) ∝ e  Q(s,a)  , where Q is the optimal Q function that satisfies the Bellman equation: Q(s, a) = R(s, a) + γ s T (s |s, a) max a Q(s , a ) (1) However, we know that humans are systematically suboptimal, and so we would like to relax this assumption and try other, more realistic assumptions. The pathological solutions in the impossibility result occur partly because the demonstrator can have arbitrary behavior on different environments. While we certainly want the demonstrator to adapt to different environments, the algorithm that the demonstrator uses to determine their policy should stay fixed across similar environments. This imposes structure on the demonstrator's planner that can eliminate some possibilities. Assumption 1: The demonstrator plans in the same way for sufficiently similar environments. To formalize this, we assume that there is a space of world models W with the same set of states S and actions A, and a space of reward functions R ⊆ S × A → R. The demonstrator can plan a stochastic policy given a world model and reward, that is, they are modeled as D : (W × R) → (S → A → [0, 1]). We call D the planning algorithm used by the demonstrator, or planner for short. Of course, if D can be any function with this type signature, it can still map any arbitrary (w, r) pair to any arbitrary policy D(w, r), but we will further ensure that D is simple (through regularization). Given a list of world models W = [w 1 . . . w n ] and reward functions R = [r 1 . . . r n ], we define D(W, R) to be the list of the demonstrator's policies [D(w 1 , r 1 ) . . . D(w n , r n )]. Note that this is a strong assumption and it does limit the scope of our work: while it is reasonable to believe that people plan in the same way for variations of the same task, they likely have different biases for different tasks, because they may have domain-specific heuristics. The setting of multiple tasks has been studied before  (Gleave & Habryka, 2018; Dimitrakakis & Rothkopf, 2011; Choi & Kim, 2012) , though not for the purpose of inferring systematic biases. This assumption leads to a slightly easier problem, of recovering rewards from multiple tasks: Estimating Biases and Rewards for Multiple Tasks. Given a list of world models W and the demonstrator's policies Π D = D(W, R) which may exhibit an unknown bias, determine the list of reward functions R (one for each w ∈ W ) that the demonstrator was optimizing. Since the person uses the same planner across all tasks, an agent can have an easier time recovering rewards for each task by leveraging the common structure across the tasks. This is especially appealing for agents that would get to observe people for some period of time before trying to assist them. Unfortunately, Assumption 1 is not sufficient to solve this problem. Consider the case where the demonstrator is optimal. Given the assumptions so far, we could infer that the demonstrator is minimizing expected reward, i.e. that the reward they are optimizing is −r * , since that perfectly predicts π D . This is very bad, as we could infer a reward that incentivizes the worst possible behavior! When humans take action, we typically assume that they are doing something that is reasonable for achieving their goals, even if it is not optimal: Assumption 2a: The demonstrator is \"close\" to optimal. We explore this assumption in section 4.3 to solve the problem of estimating biases and rewards for multiple tasks. We also explore an alternative approach, based on the fact that we have strong priors about what humans are trying to optimize for, which allow us to infer how good they are at achieving their goals. If we see some tasks where we know the demonstrator's reward function and policy, we can infer that the demonstrator is not minimizing expected reward. \n Assumption 2b: We know what reward function the demonstrator is optimizing for some tasks. Estimating Biases and Rewards with Access to Tasks with Known Rewards. Given a list of world models W , a list of the demonstrator's policies Π D = D(W, R), a list of world models W known with known rewards R known and a list of the demonstrator's policies Π known = D(W known , R known ), determine the reward functions R that D was optimizing.  We will present algorithms for both settings in the next section. While our problem formulations above assume that we have access to full policies Π D , none of our algorithms rely on this assumption -it is easy to modify them to work with trajectories instead. \n ALGORITHMS TO ESTIMATE BIASES AND REWARDS The key idea behind our algorithms is to learn a model of how the demonstrator plans, and invert the model's \"understanding\" using backpropagation to infer the reward from actions. \n ARCHITECTURE We model the demonstrator planning algorithm D using a differentiable planner f θ , which is a neural net that can express planning algorithms whose parameters θ can be updated using gradient descent. f has the same type as the demonstrator's planner D, namely (W × R) → (S → A → [0, 1]). Thus, the inputs to the differentiable planner f are a world model w ∈ W and a reward function r ∈ R; the output is a stochastic policy π ∈ (S → A → [0, 1]). We determine how well f, R matches the demonstrator's policy π D with the cross entropy loss L(f θ (W, R), Π D ) = i L(f θ (w i , r i ), π D,i ). While our algorithms can work with any differentiable planner, in this work we use a value iteration network (VIN)  (Tamar et al., 2016) . A VIN is a fully differentiable neural network that embeds an approximate value iteration algorithm inside a feed-forward classification network. For environments where transitions only depend on \"nearby\" states (as in navigation tasks), the Bellman update can be performed using an appropriate convolution, and the computation of values from Q-values can be done with a max-pooling layer. By leaving the filters for the convolutions unspecified, the VIN can automatically learn the transition probabilities. Of course, the VIN is merely one architecture for a differentiable planner; we could equally well use other planners  (Srinivas et al., 2018; Pascanu et al., 2017; Guez et al., 2018) . As research in this area advances, our work stands to benefit. By choosing this particular architecture we are making another assumption: Assumption 3: The inductive bias of f θ is well-suited to the task of learning the planner D. In our experiments, this assumption says that the demonstrator's planner is well-modeled by a Value Iteration Network. This is not a good assumption currently, but we expect that as more research is done on differentiable planners, they will become more sophisticated and will become better able to learn human planning algorithms. The components of our algorithms. There are two main operations that we make use of on this architecture, which we illustrate in figure  2 . First, given world models W , reward functions R (either known or hypothesized), and the demonstrator's policies Π D , we can train a corresponding planner using gradient descent (figure  2a ): θ = min θ L(f θ (W, R), Π D ) (TRAIN-PLANNER) Second, given world models W , demonstrator's policies Π D , and some planner parameters θ, we can infer the corresponding reward functions using gradient descent (figure  2b ): R = min R L(f θ (W, R ), Π D ) (TRAIN-REWARD) We can also perform both of these at the same time by training the planner parameters and rewards jointly given world models W and the demonstrator's policies Π D : R, θ = min R ,θ L(f θ (W, R ), Π D ) (TRAIN-JOINTLY) 4.2 LEARNING THE PLANNER FROM KNOWN REWARDS FIRST (ASSUMPTION 2B) First, we tackle the simpler setting when we have access to a set of tasks with known rewards. We illustrate this in Algorithm 1. We first train the planner on the world models for which we have rewards, which lets us learn a model of how the demonstrator plans, including any systematic biases they may have. Then, we use the learned planner weights to infer the reward on the world models for which we don't know the reward. Algorithm 1 Estimating biases and rewards with access to tasks with known rewards. 1: function IRL-WITH-REWARDS(W , Π D , W known , R known , Π known ) 2: θ ← TRAIN-PLANNER(W known , R known , Π known ) 3: return TRAIN-REWARD(W, θ, Π D ) \n LEARNING THE PLANNER AND REWARDS SIMULTANEOUSLY (ASSUMPTION 2A) The assumption that we have some tasks with known rewards is very strong, and may not hold in practice. How could we infer rewards without making this assumption? The obvious answer is to train θ and R jointly as in Equation TRAIN-JOINTLY. However, since we have discarded Assumption 2b, we can once again learn the planner that minimizes expected reward, and infer that the reward is −r * . We must instead use Assumption 2a, that the demonstrator is \"close\" to optimal. To use this assumption in our algorithm, we simulate data from an optimal agent with randomly generated world models and rewards, and use this to train the planner to mimic an optimal agent. After initializing this way, we can then train the planner and reward jointly. This gives us Algorithm 2. We show in section 5.3 that the initialization, enacting assumption 2a, is crucial for good performance. Algorithm 2 Estimating biases and rewards for multiple tasks with no known rewards. 1: function IRL-WITHOUT-REWARDS(W , Π D ) 2: W sim , R sim ← Generate random world models and rewards 3: Π sim ← Run optimal agent on W sim , R sim 4: θ init ← TRAIN-PLANNER(W sim , R sim , Π sim ) 5: R init ← TRAIN-REWARD(W, θ, Π D ) 6: θ, R ← TRAIN-JOINTLY(W, Π D ) using θ init and R init as initializations 7: return R \n EVALUATION We evaluate our algorithms by simulating demonstrators with different biases, and testing whether the same method can correctly infer reward for all these demonstrators. Details on the experiment setup are provided in the supplementary material. \n EVALUATING REWARD INFERENCE Hypothesis. The key idea behind this work is that accounting for unknown systematic bias should outperform the assumption of a particular inaccurate bias, e.g. noisy rationality or the lack thereof. Manipulated variables. In order to test this, we manipulate whether we learn the demonstrator model or assume it. To avoid confounds introduced by changing the inference algorithm, we use the same algorithm for both. In the learning case, we train the planner on the ground truth demonstrator data; in the assume case, we train it on data generated from a) a Boltzmann-rational demonstrator; and b) an optimal demonstrator -these are the two models commonly assumed by IRL algorithms. Keeping the algorithm the same enables us to isolate the effect of adapting to an unknown model from the effect of having to use an approximate differentiable planner rather than a perfect one. We will quantify the second effect, i.e. the approximation error introduced by the VIN, in section 5.2 In the setting where we learn the bias, we further manipulate whether we have access to known rewards for some tasks or not -i.e. whether we use Algorithm 1 or Algorithm 2. Finally, we manipulate the actual bias of the demonstrator. Following  Evans et al. (2016) , we implement the myopic, naive and sophisticated synthetic demonstrators as modifications of the value iteration algorithm. Similarly, we implement the overconfident and underconfident demonstrators by modifying the transition probability distributions used to plan in value iteration. We also include an optimal demonstrator, and stochastic (Boltzmann) versions of all demonstrators. Dependent measures. We measure the reward obtained by planning optimally with the inferred reward function, as a percentage of the maximum possible reward that could be obtained. Findings. Figure  3  shows our results comparing learning a demonstrator model with assuming an optimal or a Boltzmann demonstrator. The top left subfigure plots what happens on average, across all synthetic demonstrators we tested. The results provide support to our hypothesis: both learning methods (orange) outperform assuming a model (gray). Looking at the breakdown per demonstrator, we see that assuming optimal does not do well when the demonstrator has any noise (bottom graph). Similarly, assuming Boltzmann does not do well when the demonstrator is not noisy (top graph). The learning methods tend to perform on par with the best of two choices. In some cases, like the naive and sophisticated hyperbolic discounters, especially the noisy ones, the learning methods outperform both optimal and Boltzmann assumptions. The optimal assumption performs well in some of the non-noisy cases, because our demonstrator bias models are almost deterministic (they only break ties randomly). So, as long as the demonstrator eventually reaches the best reward location, the reward inference works well. Interestingly, Algorithm 1 does not always outperform Algorithm 2, despite it having access to known rewards. We believe this has to do with the fact that Algorithm 2 exploits Assumption 2a (demonstrator close to optimal) and initializes from training on simulated optimal demonstrator data. Algorithm 1 does not rely on this assumption and therefore does not benefit from this initialization, whereas the assumption is correct for most of the models we test. \n TRADEOFF BETWEEN BEING ADAPTIVE TO BIAS VS. USING EXACT PLANNING Our paper is not about a practical solution to be used right now, but rather an investigation of the viability of an idea. The core reason behind this is that to be adaptive to different kinds of biases we might see, we learn a model of the demonstrator's planning algorithm via a differentiable planner. Unfortunately, this causes our planning to be approximate -whatever benefit we get from the adapting to biases, we lose because of the approximation. But these planners will become more practical, they can make this idea practical as well. To quantify this loss, we replace the VIN with a differentiable exact model of the demonstrator, and infer the reward by backpropagating through the exact model. Since value iteration is not differentiable, we implement soft value iteration, where max operations are replaced with logsumexp operations, and measure percent reward obtained when inferring rewards for an optimal demonstrator. \n Results . With an exact model of the demonstrator, we get (98.1±0.1)% of the maximum reward when performing optimal planning on the inferred rewards, while we get (86.9 ± 1.6)% with Algorithm 1 and (86.2 ± 1.6)% with Algorithm 2. Again, better planners would improve both algorithms. \n HOW IMPORTANT ARE THE VARIOUS PARTS OF THE ALGORITHM? Algorithm 2 was predicated on Assumption 2a, that the demonstrator's planner was \"close\" to rational, which motivated the initialization step where the planner is trained to mimic an optimal agent. We test how important this is by modifying Algorithm 2 to infer rewards without an initialization (removing lines 2-5). We include versions of the algorithm where we perform coordinate ascent by alternating planner training and reward training instead of training the planner and reward jointly. Results. Figure  4  shows the results for a subset of demonstrators (full results are in the supplementary material). We can see that the initialization is indeed crucial for good performance, as expected. It also turns out that the joint training outperforms coordinate ascent. \n DISCUSSION Summary. In this work, we considered the very general problem of inverse reinforcement learning when the demonstrator has an unknown bias. In this problem we face a severe tradeoff between the ability to adapt to unknown biases, and the ability to infer any reward function. We introduced assumptions that are weaker than the typical assumption of noisy rationality, and tested algorithms that leverage these assumptions to perform better on average across different kinds of biases than assuming a specific bias known a priori. Limitations and future work. We see this paper as taking a step towards exploring the idea of learning planners from demonstrations to learn reward functions. This is not yet a practical idea, due to the practical limitations of differentiable planners. Thus, to analyze how feasible this is with different possible biases and with ground truth reward functions, we resorted to synthetic demonstrator data as opposed to human data. Further, our assumption that the demonstrator has the same bias across many tasks is key to our work, but is very strong. We could extend this work by using meta-learning to learn a prior over planners. We will also need to infer the demonstrator's beliefs as in  Baker & Tenenbaum (2014) , for which we could use TOMNets  (Rabinowitz et al., 2018) . We are excited to look into this, and into what additional inductive bias we could leverage, in our future work. \n A ADDITIONAL EXPERIMENTAL DATA In section 5, we presented data on the results of running various algorithms against a set of demonstrators, reporting the reward obtained according to the true reward function when using the inferred reward with an optimal planner, as a percentage of the maximum possible true reward. Table  1  shows the percentage reward obtained for all combinations of algorithms and demonstrators. We also measure the accuracy of the planner and reward at predicting the demonstrator's actions in new gridworlds where the rewards are the same but the wall locations have changed. These results are presented in Table  2 . Note that there are often multiple optimal actions at a given state, which makes it challenging to get high accuracy. Table  1 : Percent reward obtained when the algorithm (column) is used to infer the bias of the demonstrator (row). The optimal and Boltzmann algorithms assume a fixed model of the demonstrator and train the VIN to mimic the model before performing reward inference (and were used in figure  3 ). We also include the four flavors of Algorithm 2 that were plotted in figure  4 . The VI algorithm uses a differentiable implementation of soft value iteration as the planner instead of a VIN (used in section 5.2). The demonstrators are the optimal agent, the biased agents of figure  1 , and versions of each of these agents with Boltzmann noise. \n B EXPERIMENT DETAILS All results are averaged over 10 runs with different seeds, on randomly generated 14x14 gridworlds that have 7 squares with non-zero rewards. We ensure that all such squares can be reached from the start state, and that at least half of the positions in grid are not walls. We use a Value Iteration Network with 10 iterations as our differentiable planner, and set the space of rewards to be S → R; that is, any state can be mapped to any reward, but the reward is assumed not to depend on the action. We added an extra convolutional layer to the initial part of the VIN (which learns the proxy reward) as initial experiments showed that this could better learn an optimal planner for our gridworlds. We apply L2 regularization to the VIN with scale 0.0001, and do not regularize the reward. For all experiments, we kept the number of demonstrations fixed to 8000. For Algorithm 1, this was split into 7000 policies with rewards that were used to train the planner, and 1000 on which rewards had to be inferred. Note that this does not include any simulated data -for example, Algorithm 2 would get 8000 biased policies, and would also simulate a further 7000 policies from an optimal agent in order to initialize the planner and reward. Figure 1 : 1 Figure 1: The plans of our synthetic agents on two navigation environments. Actual trajectories could differ due to randomness in the transitions. Green squares indicate positive reward while red squares indicate negative reward, with darker colors indicating higher magnitude of reward. \n ( a ) a Training the planner f θ . We hold the world model w, reward r, and policy π fixed, and update the planner f θ with gradient descent.(b) Training the reward R. We hold the world model w, planner f θ , and policy π fixed, and update the reward r with gradient descent. \n Figure 2 : 2 Figure 2: The architecture and operations on it that we use in our algorithms. \n Figure 3 : 3 Figure 3: Reward obtained when planning with the inferred reward, as a percentage of the maximum possible reward, for different bias models and algorithms. \n Figure 4 : 4 Figure4: Percent reward obtained for different bias models using variations of Algorithm 2, which does not get access to any known rewards. These algorithms can vary along two dimensions -whether they are initialized with the assumption that the demonstrator is rational, and whether they train the planner and reward jointly or with coordinate ascent. The original version of Algorithm 2 does initialize, and trains jointly.", "date_published": "n/a", "url": "n/a", "filename": "inferring_reward_functions_fro.tei.xml", "abstract": "Our goal is to infer reward functions from demonstrations. In order to infer the correct reward function, we must account for the systematic ways in which the demonstrator is suboptimal. Prior work in inverse reinforcement learning can account for specific, known biases, but cannot handle demonstrators with unknown biases. In this work, we explore the idea of learning the demonstrator's planning algorithm (including their unknown biases), along with their reward function. What makes this challenging is that any demonstration could be explained either by positing a term in the reward function, or by positing a particular systematic bias. We explore what assumptions are sufficient for avoiding this impossibility result: either access to tasks with known rewards which enable estimating the planner separately, or that the demonstrator is sufficiently close to optimal that this can serve as a regularizer. In our exploration with synthetic models of human biases, we find that it is possible to adapt to different biases and perform better than assuming a fixed model of the demonstrator, such as Boltzmann rationality.", "id": "fb971625c19c795a397cd640c1348185"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Richard Ngo"], "title": "AGI Safety From First Principles", "text": "Introduction The key concern motivating technical AGI safety research is that we might build autonomous artificially intelligent agents which are much more intelligent than humans, and which pursue goals that conflict with our own. Human intelligence allows us to coordinate complex societies and deploy advanced technology, and thereby control the world to a greater extent than any other species. But AIs will eventually become more capable than us at the types of tasks by which we maintain and exert that control. If they don't want to obey us, then humanity might become only Earth's second most powerful \"species\", and lose the ability to create a valuable and worthwhile future. I'll call this the \"second species\" argument; I think it's a plausible argument which we should take very seriously. 1 However, the version stated above relies on several vague concepts and intuitions. In this report I'll give the most detailed presentation of the second species argument that I can, highlighting the aspects that I'm still confused about. In particular, I'll defend a version of the second species argument which claims that, without a concerted effort to prevent it, there's a significant chance that: 1. We'll build AIs which are much more intelligent than humans (i.e. superintelligent). 2. Those AIs will be autonomous agents which pursue large-scale goals. 3. Those goals will be misaligned with ours; that is, they will aim towards outcomes that aren't desirable by our standards, and trade off against our goals. 4. The development of such AIs would lead to them gaining control of humanity's future. While I use many examples from modern deep learning, this report is also intended to apply to AIs developed using very different models, training algorithms, optimisers, or training regimes than the ones we use today. However, many of my arguments would no longer be relevant if the field of AI moves away from focusing on machine learning. I also frequently compare AI development to the evolution of human intelligence; while the two aren't fully analogous, humans are the best example we currently have to ground our thinking about generally intelligent AIs. \n Superintelligence In order to understand superintelligence, we should first characterise what we mean by intelligence. We can start with  Legg and Hutter [2007] 's well-known definition, which identifies intelligence as the ability to do well on a broad range of cognitive tasks. 2 However, there are multiple ways to score highly on this metric. The key distinction I'll draw in this section is between agents that understand how to do well at many tasks because they have been specifically optimised for each task (which I'll call the task-based approach to AI), versus agents which can understand new tasks with little or no task-specific training, by generalising from previous experience (the generalisation-based approach). \n Narrow and general intelligence The task-based approach is analogous to how humans harnessed electricity: while electricity is a powerful and general technology, we still need to design specific ways to apply it to each task. Similarly, computers are powerful and flexible tools -but even though they can process arbitrarily many different inputs, detailed instructions for how to do that processing needs to be individually written to build each piece of software. Meanwhile our current reinforcement learning algorithms, although powerful, produce agents that are only able to perform well on specific tasks at which they have a lot of experience -Starcraft, DOTA, Go, and so on.  Drexler [2019]  argues that our current task-based approach will scale up to allow superhuman performance on a range of complex tasks (although I'm skeptical of this claim).  3  An example of the generalisation-based approach can be found in large language models like GPT-2 and GPT-3. GPT-2 was first trained on the task of predicting the next word in a corpus, and then achieved state of the art results on many other language tasks, without any task-specific fine-tuning!  [Radford et al., 2019]  This was a clear change from previous approaches to natural language processing, which only scored well when trained to do specific tasks on specific datasets. Its successor, GPT-3, has displayed a range of even more impressive behaviour  [Sotala, 2020] . I think this provides a good example of how an AI could develop cognitive skills (in this case, an understanding of the syntax and semantics of language) which generalise to a range of novel tasks. The field of meta-learning aims towards a similar goal. We can also see the potential of the generalisation-based approach by looking at how humans developed. As a species, we were \"trained\" by evolution to have cognitive skills including rapid learning capabilities; sensory and motor processing; and social skills. As individuals, we were also \"trained\" during our childhoods to fine-tune those skills; to understand spoken and written language; and to possess detailed knowledge about modern society. However, the key point is that almost all of this evolutionary and childhood learning occurred on different tasks from the economically useful ones we perform as adults. We can perform well on the latter category only by reusing the cognitive skills and knowledge that we gained previously. In our case, we were fortunate that those 2 Unlike the standard usage, in this technical sense an \"environment\" also includes a specification of the input-output channels the agent has access to (such as motor outputs), so that solving the task only requires an agent to process input information and communicate output information. 3 For reasons outlined in  Ngo [2019a] . cognitive skills were not too specific to tasks in the ancestral environment, but were rather very general skills. In particular, the skill of abstraction allows us to extract common structure from different situations, which allows us to understand them much more efficiently than by learning about them one by one. Then our communication skills and theories of mind allow us to share our ideas. This is why humans can make great progress on the scale of years or decades, not just via evolutionary adaptation over many lifetimes. I should note that I think of task-based and generalisation-based as parts of a spectrum rather than a binary classification, particularly because the way we choose how to divide up tasks can be quite arbitrary. For example, AlphaZero trained by playing against itself, but was tested by playing against humans, who use different strategies and playing styles. We could think of playing against these two types of opponents as two instances of a single task, or as two separate tasks where AlphaZero was able to generalise from the former task to the latter. But either way, the two cases are clearly very similar. By contrast, there are many economically important tasks which I expect AI systems to do well at primarily by generalising from their experience with very different tasks -meaning that those AIs will need to generalise much, much better than our current reinforcement learning systems can. Let me be more precise about the tasks which I expect will require this new regime of generalisation. To the extent that we can separate the two approaches, it seems plausible to me that the task-based approach will get a long way in areas where we can gather a lot of data. For example, I'm confident that it will produce superhuman self-driving cars well before the generalisation-based approach does so. It may also allow us to automate most of the tasks involved even in very cognitively demanding professions like medicine, law, and mathematics, if we can gather the right training data. However, some jobs crucially depend on the ability to analyse and act on such a wide range of information that it'll be very difficult to train directly for high performance on them. Consider the tasks involved in a role like CEO: setting your company's strategic direction, choosing who to hire, writing speeches, and so on. Each of these tasks sensitively depends on the broader context of the company and the rest of the world. What industry is their company in? How big is it; where is it; what's its culture like? What's its relationship with competitors and governments? How will all of these factors change over the next few decades? These variables are so broad in scope, and rely on so many aspects of the world, that it seems virtually impossible to generate large amounts of training data via simulating them (like we do to train game-playing AIs). And the number of CEOs from whom we could gather empirical data is very small by the standards of reinforcement learning (which often requires billions of training steps even for much simpler tasks). I'm not saying that we'll never be able to exceed human performance on these tasks by training on them directly -maybe a herculean research and engineering effort, assisted by other task-based AIs, could do so. But I expect that well before such an effort becomes possible, we'll have built AIs using the generalisation-based approach which know how to perform well even on these broad tasks. In the generalisation-based approach, the way to create superhuman CEOs is to use other data-rich tasks (which may be very different from the tasks we actually want an AI CEO to do) to train AIs to develop a range of useful cognitive skills. For example, we could train a reinforcement learning agent to follow instructions in a simulated world. Even if that simulation is very different from the real world, that agent may acquire the planning and learning capabilities required to quickly adapt to real-world tasks. Analogously, the human ancestral environment was also very different to the modern world, but we are still able to become good CEOs with little further training. And roughly the same argument applies to people doing other highly impactful jobs, like paradigm-shaping scientists, entrepreneurs, or policymakers. One potential obstacle to the generalisation-based approach succeeding is the possibility that specific features of the ancestral environment, or of human brains, were necessary for general intelligence to arise  [Ngo, 2020b] . For example, Dunbar  [1998]  hypothesised that a social \"arms race\" was required to give us enough social intelligence to develop large-scale cultural transmission. However, most possibilities for such crucial features, including this one, could be recreated in artificial training environments and in artificial neural networks. Some features (such as quantum properties of neurons) would be very hard to simulate precisely, but the human brain operates under conditions that are too messy to make it plausible that our intelligence depends on effects at this scale. So it seems very likely to me that eventually we will be able to create AIs that can generalise well enough to produce human-level performance on a wide range of tasks, including abstract low-data tasks like running a company. Let's call these systems artificial general intelligences, or AGIs. Many AI researchers expect that we'll build AGI within this century  [Grace et al., 2018] ; however, I won't explore arguments around the timing of AGI development, and the rest of this document doesn't depend on this question.  Bostrom [2014]  defines a superintelligence as \"any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest\". For the purposes of this report, I'll operationalise \"greatly exceeding human performance\" as doing better than all of humanity could if we coordinated globally (unaided by other advanced AI). I think it's difficult to deny that in principle it's possible to build individual generalisation-based AGIs which are superintelligent, since human brains are constrained by many factors 4 which will be much less limiting for AIs. Perhaps the most striking is the vast difference between the speeds of neurons and transistors: the latter pass signals about four million times more quickly. Even if AGIs never exceed humans in any other way, a speedup this large would allow one to do as much thinking in minutes or hours as a human can in years or decades. Meanwhile our brain size is important in making humans more capable than most animals -but I don't see any reason why a neural network couldn't be several orders of magnitude larger than a human brain. And while evolution is a very capable designer in many ways, it hasn't had much time to select specifically for the skills that are most useful in our modern environment, such as linguistic competence and mathematical reasoning. So we should expect that there are low-hanging fruit for improving on human performance on the many tasks which rely on such skills.  5  There are significant disagreements about how long it will take to transition from human-level AGI to superintelligence, which won't be a focus of this report, but which I'll explore briefly in the section on Control. In the remainder of this section I'll describe in qualitative terms how this transition might occur. By default, we should expect that it will be driven by the standard factors which influence progress in AI: more compute, better algorithms, and better training data. But I'll also discuss three factors whose contributions to increasing AI intelligence will become much greater as AIs become more intelligent: replication, cultural learning, and recursive improvement. \n Paths to superintelligence In terms of replication, AIs are much less constrained than humans: it's very easy to create a duplicate of an AI which has all the same skills and knowledge as the original. The cost of compute for doing so is likely to be many times smaller than the original cost of training an AGI (since training usually involves running many copies of an AI much faster than they'd need to be run for realworld tasks). Duplication currently allows us to apply a single AI to many tasks, but not to expand the range of tasks which that AI can achieve. However, we should expect AGIs to be able to decompose difficult tasks into subtasks which can be tackled more easily, just as humans can. So duplicating such an AGI could give rise to a superintelligence composed not of a single AGI, but rather a large group of them (which, following  Bostrom [2014] , I'll call a collective AGI), which can carry out significantly more complex tasks than the original can. 6 Because of the ease and usefulness of duplicating an AGI, I think that collective AGIs should be our default expectation for how superintelligence will be deployed. The efficacy of a collective AGI might be limited by coordination problems between its members. However, most of the arguments given in the previous paragraphs are also reasons why individual AGIs will be able to surpass us at the skills required for coordination (such as language processing and theories of mind). One particularly useful skill is cultural learning: we should expect AGIs to be able to acquire knowledge from each other and then share their own discoveries in turn, allowing a collective AGI to solve harder problems than any individual AGI within it could. The development of this ability in humans is what allowed the dramatic rise of civilisation over the last ten thousand years. Yet there is little reason to believe that we have reached the peak of this ability, or that AGIs couldn't have a much larger advantage over a human than that human has over a chimp, in acquiring knowledge from other agents. Thirdly, AGIs will be able to improve the training processes used to develop their successors, which then improve the training processes used to develop their successors, and so on, in a process of recursive improvement. 7 Previous discussion has mostly focused on recursive self -improvement, involving a single AGI \"rewriting its own source code\"  [Yudkowsky, 2007] . However, I think it's more appropriate to focus on the broader phenomenon of AIs advancing AI research, for several reasons. Firstly, due to the ease of duplicating AIs, there's no meaningful distinction between an AI improving \"itself\" versus creating a successor that shares many of its properties. Secondly, modern AIs are more accurately characterised as models which could be retrained, rather than software which could be rewritten: almost all of the work of making a neural network intelligent is done by an optimiser via extensive training. Even a superintelligent AGI would have a hard time significantly improving its cognition by modifying its neural weights directly; it seems analogous to making a human more intelligent via brain surgery (albeit with much more precise tools than we have today). So it's probably more accurate to think about self-modification as the process of an AGI modifying its high-level architecture or training regime, then putting itself through significantly more training. This is very similar to how we create new AIs today, except with humans playing a much smaller role. Thirdly, if the intellectual contribution of humans does shrink significantly, then I don't think it's useful to require that humans are entirely out of the loop for AI behaviour to qualify as recursive improvement (although we can still distinguish between cases with more or less human involvement). These considerations reframe the classic view of recursive self-improvement 8 in a number of ways. For example, the retraining step may be bottlenecked by compute even if an AGI is able to design algorithmic improvements very fast. And for an AGI to trust that its goals will remain the same under retraining will likely require it to solve many of the same problems that the field of AGI safety is currently tackling -which should make us more optimistic that the rest of the world could solve those problems before a misaligned AGI undergoes recursive self-improvement. However, to be clear, this reframing doesn't imply that recursive improvement will be unimportant. Indeed, since AIs will eventually be the primary contributors to AI research, recursive improvement as defined here will eventually become the key driver of progress. I'll discuss the implications of this claim in the section on Control. So far I've focused on how superintelligences might come about, and what they will be able to do. But how will they decide what to actually do? For example, will the individuals within a collective AGI even want to cooperate 7 Whether it's more likely that the successor agent will be an augmented version of the researcher AGI itself or a different, newly-trained AGI is an important question, but one which doesn't affect the argument as made here. 8  Yudkowsky [2013]  with each other to pursue larger goals? Will an AGI capable of recursive improvement have any reason to do so? I'm wary of phrasing these questions in terms of the goals and motivations of AGIs, without exploring more thoroughly what those terms actually mean. That's the focus of the next section. \n Goals and Agency The fundamental concern motivating the second species argument is that AIs will gain too much power over humans, and then use that power in ways we don't endorse. Why might they end up with that power? I'll distinguish three possibilities: 1. AIs pursue power for the sake of achieving other goals; i.e. power is an instrumental goal for them. 2. AIs pursue power for its own sake; i.e. power is a final goal for them. 3. AIs gain power without aiming towards it; e.g. because humans gave it to them. The first possibility has been the focus of most debate so far, and I'll spend most of this section discussing it. The second hasn't been explored in much depth, but in my opinion is still important; I'll cover it briefly in this section and the next. Following  Christiano [2019] , I'll call agents which fall into either of these first two categories influence-seeking. The third possibility is largely outside the scope of this document, which focuses on dangers from the intentional behaviour of advanced AIs, although I'll briefly touch on it here and in the last section. The key idea behind the first possibility is  Bostrom [2012] 's instrumental convergence thesis, which states that there are some instrumental goals whose attainment would increase the chances of an agent's final goals being realised for a wide range of final goals and a wide range of situations. Examples of such instrumentally convergent goals include self-preservation, resource acquisition, technological development, and self-improvement, which are all useful for executing further large-scale plans. I think these examples provide a good characterisation of the type of power I'm talking about, which will serve in place of a more explicit definition. However, the link from instrumentally convergent goals to dangerous influenceseeking is only applicable to agents which have final goals large-scale enough to benefit from these instrumental goals, and which identify and pursue those instrumental goals even when it leads to extreme outcomes (a set of traits which I'll call goal-directed agency). It's not yet clear that AGIs will be this type of agent, or have this type of goals. It seems very intuitive that they will because we all have experience of pursuing instrumentally convergent goals, for example by earning and saving money, and can imagine how much better we'd be at them if we were more intelligent. Yet since evolution has ingrained in us many useful short-term drives (in particular the drive towards power itself), it's difficult to determine the extent to which human influence-seeking behaviour is caused by us reasoning about its instrumental usefulness towards larger-scale goals. Our conquest of the world didn't require any humans to strategise over the timeframe of centuries, but merely for many individuals to expand their personal influence in a relatively limited way -by inventing a slightly better tool, or exploring slightly further afield. Furthermore, we should take seriously the possibility that superintelligent AGIs might be even less focused than humans are on achieving large-scale goals. We can imagine them possessing final goals which don't incentivise the pursuit of power, such as deontological goals, or small-scale goals. Or perhaps we'll build \"tool AIs\" which obey our instructions very well without possessing goals of their own -in a similar way to how a calculator doesn't \"want\" to answer arithmetic questions, but just does the calculations it's given. In order to figure out which of these options is possible or likely, we need to better understand the nature of goals and goal-directed agency. That's the focus of this section. \n Frameworks for thinking about agency To begin, it's crucial to distinguish between the goals which an agent has been selected or designed to do well at (which I'll call its design objectives 9 ), and the goals which an agent itself wants to achieve (which I'll just call \"the agent's goals\"). 10 For example, insects can contribute to complex hierarchical societies only because evolution gave them the instincts required to do so: to have \"competence without comprehension\", in Dennett's terminology. This term also describes current image classifiers and (probably) RL agents like AlphaStar and OpenAI Five: they can be competent at achieving their design objectives without understanding what those objectives are, or how their actions will help achieve them. If we create agents whose design objective is to accumulate power, but without the agent itself having the goal of doing so (e.g. an agent which plays the stock market very well without understanding how that impacts society) that would qualify as the third possibility outlined above. By contrast, in this section I'm interested in what it means for an agent to have a goal of its own. Three existing frameworks which attempt to answer this question are  Morgenstern and Von Neumann [1953] 's expected utility maximisation, Dennett [1989]'s intentional stance, and  Hubinger et al. [2019] 's mesa-optimisation. I don't think any of them adequately characterises the type of goal-directed behaviour we want to understand, though. While we can prove elegant theoretical results about utility functions, they are such a broad formalism that practically any behaviour can be described as maximising some utility function  [Ngo, 2019b] . So this framework doesn't constrain our expectations about powerful AGIs. 11 Meanwhile, Dennett argues that taking the intentional stance towards systems can be useful for making predictions about them -but this only works given prior knowledge about what goals they're most likely to have. Predicting the behaviour of a trillion-parameter neural network is very different from applying the intentional stance to existing artifacts. And while we do have an intuitive understanding of complex human goals and how they translate to behaviour, the extent to which it's reasonable to extend those beliefs about goal-directed cognition to artificial intelligences is the very question we need a theory of agency to answer. So while Dennett's framework provides some valuable insights -in particular, that assigning agency to a system is a modelling choice which only applies at certain levels of abstraction -I think it fails to reduce agency to simpler and more tractable concepts. Additionally, neither framework accounts for bounded rationality: the idea that systems can be \"trying to\" achieve a goal without taking the best actions to do so. In order to figure out the goals of boundedly rational systems, we'll need to scrutinise the structure of their cognition, rather than treating them as black-box functions from inputs to outputs -in other words, using a \"cognitive\" definition of agency rather than \"behavioural\" definitions like the two I've discussed so far. In Risks from Learned Optimisation in Advanced ML systems,  Hubinger et al. [2019]  use a cognitive definition: \"a system is an optimizer if it is internally searching through a search space (consisting of possible outputs, policies, plans, strategies, or similar) looking for those elements that score high according to some objective function that is explicitly represented within the system\". I think this is a promising start, but it has some significant problems. In particular, the concept of \"explicit representation\" seems like a tricky onewhat is explicitly represented within a human brain, if anything? And their definition doesn't draw the important distinction between \"local\" optimisers such as gradient descent and goal-directed planners such as humans. My own approach to thinking about agency tries to improve on the approaches above by being more specific about the cognition we expect goaldirected systems to do. Just as \"being intelligent\" involves applying a range of abilities (as discussed in the previous section), \"being goal-directed\" involves a system applying some specific additional abilities: 1. Self-awareness: it understands that it's a part of the world, and that its behaviour impacts the world; 2. Planning: it considers a wide range of possible sequences of behaviours (let's call them \"plans\"), including long plans; 3. Consequentialism: it decides which of those plans is best by considering the value of the outcomes that they produce; that, \"while corrigibility probably has a core which is of lower algorithmic complexity than all of human value, this core is liable to be very hard to find or reproduce by supervised learning of human-labeled data, because deference is an unusually anti-natural shape for cognition, in a way that a simple utility function would not be an anti-natural shape for cognition.\" Note, however, that this argument relies on the intuitive distinction between natural and anti-natural shapes for cognition. This is precisely what I think we need to understand to build safe AGI -but there has been little explicit investigation of it so far. 4. Scale: its choice is sensitive to the effects of plans over large distances and long time horizons; 5. Coherence: it is internally unified towards implementing the single plan it judges to be best; 6. Flexibility: it is able to adapt its plans flexibly as circumstances change, rather than just continuing the same patterns of behaviour. Note that none of these traits should be interpreted as binary; rather, each one defines a different spectrum of possibilities. I'm also not claiming that the combination of these six dimensions is a precise or complete characterisation of agency; merely that it's a good starting point, and the right type of way to analyse agency. For instance, it highlights that agency requires a combination of different abilities -and as a corollary, that there are many different ways to be less than maximally agentic. AIs which score very highly on some of these dimensions might score very low on others. Considering each trait in turn, and what lacking it might look like: 1. Self-awareness: for humans, intelligence seems intrinsically linked to a first-person perspective. But an AGI trained on abstract third-person data might develop a highly sophisticated world-model that just doesn't include itself or its outputs. A sufficiently advanced language or physics model might fit into this category. 2. Planning: highly intelligent agents will by default be able to make extensive and sophisticated plans. But in practice, like humans, they may not always apply this ability. Perhaps, for instance, an agent is only trained to consider restricted types of plans. Myopic training attempts to implement such agents; more generally, an agent could have limits on the actions it considers. For example, a question-answering system might only consider plans of the form \"first figure out subproblem 1, then figure out subproblem 2, then...\". 3. Consequentialism: the usual use of this term in philosophy describes agents which believe that the moral value of their actions depends only on those actions' consequences; here I'm using it in a more general way, to describe agents whose subjective preferences about actions depend mainly on those actions' consequences. It seems natural to expect that agents trained on a reward function determined by the state of the world would be consequentialists. But note that humans are far from fully consequentialist, since we often obey deontological constraints or constraints on the types of reasoning we endorse. 4. Scale: agents which only care about small-scale events may ignore the long-term effects of their actions. Since agents are always trained in smallscale environments, developing large-scale goals requires generalisation (in ways that I discuss below). 5. Coherence: humans lack this trait when we're internally conflicted -for example, when our system 1 and system 2 goals differ -or when our goals change a lot over time. While our internal conflicts might just be an artefact of our evolutionary history, we can't rule out individual AGIs developing modularity which might lead to comparable problems. However, it's most natural to think of this trait in the context of a collective, where the individual members could have more or less similar goals, and could be coordinated to a greater or lesser extent. 6. Flexibility: an inflexible agent might arise in an environment in which coming up with one initial plan is usually sufficient, or else where there are tradeoffs between making plans and executing them. Such an agent might display sphexish behaviour. Another interesting example might be a multi-agent system in which many AIs contribute to developing planssuch that a single agent is able to execute a given plan, but not able to rethink it very well. A question-answering system (aka an oracle) could be implemented by an agent lacking either planning or consequentialism. For AIs which act in the real world I think the scale of their goals is a crucial trait to explore, and I'll do so later in this section. We can also evaluate other systems on these criteria. A calculator probably doesn't have any of them. Software that's a little more complicated, like a GPS navigator, should probably be considered consequentialist to a limited extent (because it reroutes people based on how congested traffic is), and perhaps has some of the other traits too, but only slightly. Most animals are self-aware, consequentialist and coherent to various degrees. The traditional conception of AGI has all of the traits above, which would make it capable of pursuing influence-seeking strategies for instrumental reasons. However, note that goal-directedness is not the only factor which determines whether an AI is influence-seeking: the content of its goals also matter. A highly agentic AI which has the goal of remaining subordinate to humans might never take influenceseeking actions. And as previously mentioned, an AI might be influence-seeking because it has the final goal of gaining power, even without possessing many of the traits above. I'll discuss ways to influence the content of an agent's goals in the next section, on Alignment. \n The likelihood of developing highly agentic AGI How likely is it that, in developing an AGI, we produce a system with all of the six traits I identified above? One approach to answering this question involves predicting which types of model architecture and learning algorithms will be used -for example, will they be model-free or model-based? To my mind, this line of thinking is not abstract enough, because we simply don't know enough about how cognition and learning work to map them onto high-level design choices. If we train AGI in a model-free way, I predict it will end up planning using an implicit model 12 anyway. If we train a model-based AGI, I predict its model will be so abstract and hierarchical that looking at its architecture will tell us very little about the actual cognition going on. At a higher level of abstraction, I think that it'll be easier for AIs to acquire the components of agency listed above if they're also very intelligent. However, the extent to which our most advanced AIs are agentic will depend on what type of training regime is used to produce them. For example, our best language models already generalise well enough from their training data that they can answer a wide range of questions. I can imagine them becoming more and more competent via unsupervised and supervised training, until they are able to answer questions which no human knows the answer to, but still without possessing any of the properties listed above. A relevant analogy might be to the human visual system, which does very useful cognition, but which is not very \"goal-directed\" in its own right. My underlying argument is that agency is not just an emergent property of highly intelligent systems, but rather a set of capabilities which need to be developed during training, and which won't arise without selection for it. One piece of supporting evidence is Moravec's paradox: the observation that the cognitive skills which seem most complex to humans are often the easiest for AIs, and vice versa  [Moravec, 1988] . In particular, Moravec's paradox predicts that building AIs which do complex intellectual work like scientific research might actually be easier than building AIs which share more deeply ingrained features of human cognition like goals and desires. To us, understanding the world and changing the world seem very closely linked, because our ancestors were selected for their ability to act in the world to improve their situations. But if this intuition is flawed, then even reinforcement learners may not develop all the aspects of goal-directedness described above if they're primarily trained to answer questions. However, there are also arguments that it will be difficult to train AIs to do intellectual work without them also developing goal-directed agency. In the case of humans, it was the need to interact with an open-ended environment 13 to achieve our goals that pushed us to develop our sophisticated general intelligence. The central example of an analogous approach to AGI is training a reinforcement learning agent in a complex simulated 3D environment (or perhaps via extended conversations in a language-only setting). In such environments, agents which strategise about the effects of their actions over long time horizons will generally be able to do better. This implies that our AIs will be subject to optimisation pressure towards becoming more agentic (by my criteria above) will do better. We might expect an AGI to be even more agentic if it's trained, not just in a complex environment, but in a complex competitive multi-agent environment. Agents trained in this way will need to be very good at flexibly adapting plans in the face of adversarial behaviour; and they'll benefit from considering a wider range of plans over a longer timescale than any competitor. On the other hand, it seems very difficult to predict the overall effect of interactions between many agents -in humans, for example, it led to the development of (sometimes non-consequentialist) altruism. It's currently very uncertain which training regimes will work best to produce AGIs. But if there are several viable ones, we should expect economic pressures to push researchers towards prioritising those which produce the most agentic AIs, because they will be the most useful (assuming that alignment problems don't become serious until we're close to AGI). In general, the broader the task an AI is used for, the more valuable it is for that AI to reason about how to achieve its assigned goal in ways that we may not have specifically trained it to do. For example, a question-answering system with the goal of helping its users understand the world might be much more useful than one that's competent at its design objective of answering questions accurately, but isn't goal-directed in its own right. Overall, however, I think most safety researchers would argue that we should prioritise research directions which produce less agentic AGIs, and then use the resulting AGIs to help us align later more agentic AGIs. There's also been some work on directly making AGIs less agentic (such as  Taylor [2016] 's quantilization), although this has in general been held back by a lack of clarity around these concepts. I've already discussed recursive improvement in the previous section, but one further point which is useful to highlight here: since being more agentic makes an agent more capable of achieving its goals, agents which are capable of modifying themselves will have incentives to make themselves more agentic too (as humans already try to do, albeit in limited ways). So we should consider this to be one type of recursive improvement, to which many of the considerations discussed in the previous section also apply. \n Goals as generalised concepts I should note that I don't expect our training tasks to replicate the scale or duration of all the tasks we care about in the real world. So AGIs won't be directly selected to have very large-scale or long-term goals. Yet it's likely that the goals they learn in their training environments will generalise to larger scales, just as humans developed large-scale goals from evolving in a relatively limited ancestral environment. In modern society, people often spend their whole lives trying to significantly influence the entire world -via science, business, politics, and many other channels. And some people aspire to have a worldwide impact over the timeframe of centuries, millennia or longer, even though there was never significant evolutionary selection in favour of humans who cared about what happened in several centuries' time, or paid attention to events on the other side of the world. This gives us reason to be concerned that even AGIs which aren't explicitly trained to pursue ambitious large-scale goals might do so anyway. I also expect researchers to actively aim towards achieving this type of generalisation to longer time horizons in AIs, because some important applications rely on it. For long-term tasks like being a CEO, AGIs will need the capability and motivation to choose between possible actions based on their worldwide consequences on the timeframe of years or decades. Can we be more specific about what it looks like for goals to generalise to much larger scales? Given the problems with the expected utility maximisation framework I identified earlier, it doesn't seem useful to think of goals as utility functions over states of the world. Rather, an agent's goals can be formulated in terms of whatever concepts it possesses -regardless of whether those concepts refer to its own thought processes, deontological rules, or outcomes in the external world. 14 And insofar as an agent's concepts flexibly adjust and generalise to new circumstances, the goals which refer to them will do the same. It's difficult and speculative to try to describe how such generalisation may occur, but broadly speaking, we should expect that intelligent agents are able to abstract away the differences between objects or situations that have high-level similarities. For example, after being trained in a simulation, an agent might transfer its attitudes towards objects and situations in the simulation to their counterparts in the (much larger) real world.  15  Alternatively, the generalisation could be in the framing of the goal: an agent which has always been rewarded for accumulating resources in its training environment might interalise the goal of \"amassing as many resources as possible\". Similarly, agents which are trained adversarially in a small-scale domain might develop a goal of outcompeting each other which persists even when they're both operating at a very large scale. From this perspective, to predict an agent's behaviour, we will need to consider what concepts it will possess, how those will generalise, and how the agent will reason about them. I'm aware that this appears to be an intractably difficult task -even human-level reasoning can lead to extreme and unpredictable conclusions (as the history of philosophy shows). However, I hope that we can instill lower-level mindsets or values into AGIs which guide their high-level reasoning in safe directions. I'll discuss some approaches to doing so in the next section, on Alignment. \n Groups and agency After discussing collective AGIs in the previous section, it seems important to examine whether the framework I've proposed for understanding agency can apply to a group of agents as well. I think it can: there's no reason that the traits I described above need to be instantiated within a single neural network. However, the relationship between the goal-directedness of a collective AGI and the goal-directedness of its individual members may not be straightforward, since it depends on the internal interactions between its members. One of the key variables is how much (and what types of) experience those members have of interacting with each other during training. If they have been trained primarily to cooperate, that makes it more likely that the resulting collective AGI is a goal-directed agent, even if none of the individual members is highly agentic. But there are good reasons to expect that the training process will involve some competition between members, which would undermine their coherence as a group  [Leibo et al., 2019] . Internal competition might also increase short-term influence-seeking behaviour, since each member will have learned to pursue influence in order to outcompete the others. As a particularly salient example, humanity managed to take over the world over a period of millennia not via a unified plan to do so, but rather as a result of many individuals trying to expand their short-term influence. It's also possible that the members of a collective AGI have not been trained to interact with each other at all, in which case cooperation between them would depend entirely on their ability to generalise from their existing skills. It's difficult to imagine this case, because human brains are so well-adapted for group interactions. But insofar as humans and aligned AGIs hold a disproportionate share of power over the world, there is a natural incentive for AGIs pursuing misaligned goals to coordinate with each other to increase their influence at our expense.  16  Whether they succeed in doing so will depend on what sort of coordination mechanisms they are able to design. A second factor is how much specialisation there is within the collective AGI. In the case where it consists only of copies of the same agent, we should expect that the copies understand each other very well, and share goals to a large extent. If so, we might be able to make predictions about the goal-directedness of the entire group merely by examining the original agent. But another case worth considering is a collective consisting of a range of agents with different skills. With this type of specialisation 17 , the collective as a whole could be much more agentic than any individual agent within it, which might make it easier to deploy subsets of the collective safely  [Ngo, 2020e] . \n Alignment In the previous section, I discussed the plausibility of ML-based agents developing the capability to seek influence for instrumental reasons. This would not be a problem if they do so only in the ways that are aligned with human values. Indeed, many of the benefits we expect from AGIs will require them to wield power to influence the world. And by default, AI researchers will apply  16  In addition to the prima facie argument that intelligence increases coordination ability, it is likely that AGIs will have access to commitment devices not available to humans by virtue of being digital. For example, they could send potential allies a copy of themselves for inspection, to increase confidence in their trustworthiness. However, there are also human commitment devices that AGIs will have less access to -for example, putting ourselves in physical danger as an honest signal. And it's possible that the relative difficulty of lying versus detecting lying shifts in favour of the former for more intelligent agents. 17  Ngo [2020d]  their efforts towards making agents do whatever tasks those researchers desire, rather than learning to be disobedient. However, there are reasons to worry that despite such efforts by AI researchers, AIs will develop undesirable final goals which lead to conflict with humans. To start with, what does \"aligned with human values\" even mean? Following  Christiano [2015]  and  Gabriel [2020] , I'll distinguish between two types of interpretations. Minimalist (aka narrow ) approaches focus on avoiding catastrophic outcomes. The best example is  Christiano [2018a] 's concept of intent alignment: \"When I say an AI A is aligned with an operator H, I mean: A is trying to do what H wants it to do.\" While there will always be some edge cases in figuring out a given human's intentions, there is at least a rough commonsense interpretation. By contrast, maximalist (aka ambitious) approaches attempt to make AIs adopt or defer to a specific overarching set of values -like a particular moral theory, or a global democratic consensus, or a meta-level procedure for deciding between moral theories. My opinion is that defining alignment in maximalist terms is unhelpful, because it bundles together technical, ethical and political problems. While it may be the case that we need to make progress on all of these, assumptions about the latter two can significantly reduce clarity about technical issues. So from now on, when I refer to alignment, I'll only refer to intent alignment. I'll also define an AI A to be misaligned with a human H if H would want A not to do what A is trying to do (if H were aware of A's intentions). This implies that AIs could potentially be neither aligned nor misaligned with an operator -for example, if they only do things which the operator doesn't care about. Whether an AI qualifies as aligned or misaligned obviously depends a lot on who the operator is, but for the purposes of this report I'll focus on AIs which are clearly misaligned with respect to most humans. One important feature of these definitions: by using the word \"trying\", they focus on the AI's intentions, not the actual outcomes achieved. I think this makes sense because we should expect AGIs to be very good at understanding the world, and so the key safety problem is setting their intentions correctly. In particular, I want to be clear that when I talk about misaligned AGI, the central example in my mind is not agents that misbehave just because they misunderstand what we want, or interpret our instructions overly literally (which  Bostrom [2014]  calls \"perverse instantiation\"). It seems likely that AGIs will understand the intentions of our instructions very well by default. This is because they will probably be trained on tasks involving humans, and human data -and understanding human minds is particularly important for acting competently in those tasks and the rest of the world. 18 Rather, my main concern is that AGIs will understand what we want, but just not care, because the motivations they acquired during training weren't those we intended them to have. The idea that AIs won't automatically gain the right motivations by virtue of being more intelligent is an implication of Bostrom [2012]'s orthogonality thesis, which states that \"more or less any level of intelligence could in principle be combined with more or less any final goal\". For our purposes, a weaker version suffices: simply that highly intelligent agents could have large-scale goals which are misaligned with those of most humans. An existence proof is provided by high-functioning psychopaths, who understand that other people are motivated by morality, and can use that fact to predict their actions and manipulate them, but nevertheless aren't motivated by morality themselves. We might hope that by carefully choosing the tasks on which agents are trained, we can prevent those agents from developing goals that conflict with ours, without requiring any breakthroughs in technical safety research. Why might this not work, though? Previous arguments have distinguished between two concerns: the outer misalignment problem and the inner misalignment problem. I'll explain both of these, and give arguments for why they might arise. I'll also discuss some limitations of using this framework, and an alternative perspective on alignment. \n Outer and inner misalignment: the standard picture We train machine learning systems to perform desired behaviour by optimising them with respect to some objective function -for example, a reward function in reinforcement learning. The outer misalignment concern is that we won't be able to implement an objective function which describes the behaviour we actually want the system to perform, without also rewarding misbehaviour. One key intuition underlying this concern is the difficulty of explicitly programming objective functions which express all our desires about AGI behaviour. There's no simple metric which we'd like our agents to maximise -rather, desirable AGI behaviour is best formulated in terms of concepts like obedience, consent, helpfulness, morality, and cooperation, which we can't define precisely in realistic environments. Although we might be able to specify proxies for those goals, Goodhart's law suggests that some undesirable behaviour will score very well according to these proxies, and therefore be reinforced in AIs trained on them  [Manheim and Garrabrant, 2018] . Even comparatively primitive systems today demonstrate a range of specification gaming behaviours, some of which are quite creative and unexpected, when we try to specify much simpler concepts  [Krakovna et al., 2020] . One way to address this problem is by incorporating human feedback into the objective function used to evaluate AI behaviour during training. However, there are at least three challenges to doing so. The first is that it would be prohibitively expensive for humans to provide feedback on all data required to train AIs on complex tasks. This is known as the scalable oversight problem; reward modelling 19 is the primary approach to addressing it. A second challenge is that, for long-term tasks, we might need to give feedback before we've had the chance to see all the consequences of an agent's actions. Yet even in domains as simple as Go, it's often very difficult to determine how good a given move is without seeing the game play out. And in larger domains, there may be too many complex consequences for any single individual to evaluate. The main approach to addressing this issue is by using multiple AIs to recursively decompose the problem of evaluation, as in  Irving et al. [2018] 's Debate,  Leike et al. [2018] 's Recursive Reward Modelling, and 's Iterated Amplification. By constructing superhuman evaluators, these techniques also aim to address the third issue with human feedback: that humans can be manipulated into interpreting behaviour more positively than they otherwise would, for example by giving them misleading data (as in the robot hand example from  Christiano et al. [2017] ). Even if we solve outer alignment by specifying a \"safe\" objective function, though, we may still encounter a failure of inner alignment: our agents might develop goals which differ from the ones specified by that objective function. This is likely to occur when the training environment contains subgoals which are consistently useful for scoring highly on the given objective function, such as gathering resources and information, or gaining power. 20 If agents reliably gain higher reward after achieving such subgoals, then the optimiser might select for agents which care about those subgoals for their own sake. (This is one way agents might develop a final goal of acquiring power, as mentioned at the beginning of the section on Goals and Agency.) This is analogous to what happened during the evolution of humans, when we were \"trained\" by evolution to increase our genetic fitness. In our ancestral environment, subgoals like love, happiness and social status were useful for achieving higher inclusive genetic fitness, and so we evolved to care about them. But now that we are powerful enough to reshape the natural world according to our desires, there are significant differences between the behaviour which would maximise genetic fitness (e.g. frequent sperm or egg donation), and the behaviour which we display in pursuit of the motivations we actually evolved. Another example: suppose we reward an agent every time it correctly follows a human instruction, so that the cognition which leads to this behaviour is reinforced by its optimiser. Intuitively, we'd hope that the agent comes to have the goal of obedience to humans. But it's also conceivable that the agent's obedient behaviour is driven by the goal \"don't get shut down\", if the agent understands that disobedience will get it shut down -in which case the optimiser might actually reinforce the goal of survival every time it leads to a completed instruction. So two agents, each motivated by one of these goals, might behave very similarly until they are in a position to be disobedient without being shut 20 Note the subtle distinction between the existence of useful subgoals, and my earlier discussion of the instrumental convergence thesis. The former is the claim that, for the specific tasks on which we train AGIs, there are some subgoals which will be rewarded during training. The latter is the claim that, for most goals which an AGI might develop, there are some specific subgoals which will be useful when the AGI tries to pursue those goals while deployed. The latter implies the former only insofar as the convergent instrumental subgoals are both possible and rewarded during training. Self-improvement is a convergent instrumental subgoal, but I don't expect most training environments to support it, and those that do may have penalties to discourage it. \n down. 21 What will determine whether agents like the former or agents like the latter are more likely to actually arise? As I mentioned above, one important factor is whether there are subgoals which reliably lead to higher reward during training. Another is how easy and beneficial it is for the optimiser to make the agent motivated by those subgoals, versus motivated by the objective function it's being trained on. In the case of humans, for example, the concept of inclusive genetic fitness was a very difficult one for evolution to build into the human motivational system. And even if our ancestors had somehow developed that concept, they would have had difficulty coming up with better ways to achieve it than the ones evolution had already instilled in them. So in our ancestral environment there was relatively little selection pressure for us to be inneraligned with evolution. In the context of training an AI, this means that the complexity of the goals we try to instil in it incurs a double penalty: not only does that complexity make it harder to specify an acceptable objective function, it also makes that AI less likely to become motivated by our intended goals even if the objective function is correct. Of course, late in training we expect our AIs to have become intelligent enough that they'll understand exactly what goals we intended to give them. But by that time their existing motivations may be difficult to remove, and they'll likely also be intelligent enough to attempt deceptive behaviour (as in the hypothetical example in the previous paragraph). So how can we ensure inner alignment of AGIs with human intentions? This research area has received less attention than outer alignment so far, because it's a trickier problem to get a grip on. One potential approach involves adding training examples where the behaviour of agents motivated by misaligned goals diverges from that of aligned agents. Yet designing and creating this sort of adversarial training data is currently much more difficult than mass-producing data (e.g. via procedurally-generated simulations, or web scraping). This is partly just because specific training data is harder to create in general, but also for three additional reasons. Firstly, by default we simply won't know which undesirable motivations our agents are developing, and therefore which ones to focus on penalising. Interpretability techniques could help with this, but seem very difficult to create (as I'll discuss further in the next section). Secondly, the misaligned motivations which agents are most likely to acquire are those which are most robustly useful. For example, it's particularly hard to design a training environment where access to more information leads to lower reward. Thirdly, we are most concerned about agents which have large-scale misaligned goals. Yet large-scale scenarios are again the most difficult to set up during training,  21  In fact these two examples showcase two different types of inner alignment failure: upstream mesa-optimisers and downstream mesa-optimisers  [Christiano, 2018b] . When trained on a reward function R, upstream mesa-optimisers learn goals which lead to scoring highly on R, or in other words are causally upstream of R. For example, humans learning to value finding food since it leads to greater reproductive success. Whereas downstream mesa-optimisers learn goals that are causally downstream of scoring highly on R: for example, they learn the goal of survival, and realise that if they score badly on R, they'll be discarded by the optimisation procedure. This incentivises them to score highly on R, and hide their true goals -an outcome called deceptive alignment  [Hubinger et al., 2019] . either in simulation or in the real-world. So there's a lot of scope for more work addressing these problems, or identifying new inner alignment techniques. \n A more holistic view of alignment Outer alignment is the problem of correctly evaluating AI behaviour; inner alignment is the problem of making the AI's goals match those evaluations. To some extent we can treat these as two separate problems; however, I think it's also important to be aware of the ways in which the narrative of \"alignment = outer alignment + inner alignment\" is incomplete or misleading. In particular, what would it even mean to implement a \"safe\" objective function? Is it a function that we want the agent to actually maximise? Yet while maximising expected reward makes sense in formalisms like MDPs and POMDPs, it's much less well-defined when the objective function is implemented in the real world. If there's some sequence of actions which allows the agent to tamper with the channel by which it's sent rewards, then \"wireheading\" by maxing out that channel will practically always be the strategy which allows the agent to receive the highest reward signal in the long term (even if the reward function heavily penalises actions leading up to wireheading).  22  And if we use human feedback, as previously discussed, then the optimal policy will be to manipulate or coerce the supervisors into giving maximally positive feedback. (There's been some suggestion that \"myopic\" training could solve problems of tampering and manipulation, but as I argued in Ngo [2020c], I expect that it merely hides them.) A second reason why reward functions are a \"leaky abstraction\" is that any real-world agents we train in the foreseeable future will be very, very far away from the limit of optimal behaviour on non-trivial reward functions. In particular, they will only see rewards for a tiny fraction of possible states. Furthermore, if they're generalisation-based agents, they'll often perform new tasks after very  22  One useful distinction here is between the message, the code, and the channel (following Shannon). In the context of reinforcement learning, we can interpret the message to be whatever goal is intended by the designers of the system (e.g. win at Starcraft); the code is real numbers attached to states, with higher numbers indicating better states; and the channel is the circuitry by which these numbers are passed to the agent. We have so far assumed that the goal the agent learns is based on the message its optimiser infers from its reward function (albeit perhaps in a way that generalises incorrectly, because it can be hard to decode the intended message from a finite number of sampled rewards). But it's also possible that the agent learns to care about the state of the channel itself. I consider pain in animals to be one example of this: the message is that damage is being caused; the code is that more pain implies more damage (as well as other subtleties of type and intensity); and the channel is the neurons that carry those signals to our brains. In some cases, the code changes -for example, when we receive an electric shock but know that it has no harmful effects. If we were only concerned with the message, then we would ignore those cases, because they provide no new content about damage to our body. Yet what actually happens is that we try to prevent those signals being sent anyway, because we don't want to feel pain! Similarly, an agent which was trained via a reward signal may desire to continue receiving those signals even when they no longer carry the same message. Another way of describing this distinction is by contrasting internalisation of a base objective versus modeling of that base objective, as discussed in section 4 of  Hubinger et al. [2019] . little training directly on those tasks. So the agent's behaviour in almost all states will be primarily influenced not by the true value of the reward function on those states, but rather by how it generalises from previously-collected data about other states.  23  This point is perhaps an obvious one, but it's worth emphasising because there are so many theorems about the convergence of reinforcement learning algorithms which rely on visiting every state in the infinite limit, and therefore tell us very little about behaviour after a finite time period. A third reason is that researchers already modify reward functions in ways which change the optimal policy when it seems useful. For example, we add shaping terms to provide an implicit curriculum, or exploration bonuses to push the agent out of local optima. As a particularly safety-relevant example, neural networks can be modified so that their loss on a task depends not just on their outputs, but also on their internal representations  [Ganin et al., 2016] . This is particularly useful for influencing how those networks generalise -for example, making them ignore spurious correlations in the training data. But again, it makes it harder to interpret reward functions as specifications of desired outcomes of a decision process. How should we think about them instead? Well, in trying to ensure that AGI will be aligned, we have a range of tools available to us -we can choose the neural architectures, RL algorithms, environments, optimisers, etc, that are used in the training procedure. We should think about our ability to specify an objective function as the most powerful such tool. Yet it's not powerful because the objective function defines an agent's motivations, but rather because samples drawn from it shape that agent's motivations and cognition. From this perspective, we should be less concerned about what the extreme optima of our objective functions look like, because they won't ever come up during training (and because they'd likely involve tampering). Instead, we should focus on how objective functions, in conjunction with other parts of the training setup, create selection pressures towards agents which think in the ways we want, and therefore have desirable motivations in a wide range of circumstances. 24 (See  Arora [2019]  for a more mathematical framing of a similar point.) This perspective provides another lens on the previous section's arguments about AIs which are highly agentic. It's not the case that AIs will inevitably end up thinking in terms of large-scale consequentialist goals, and our choice of reward function just determines which goals they choose to maximise. Rather, all the cognitive abilities of our AIs, including their motivational systems, will develop during training. The objective function (and the rest of the training setup) will determine the extent of their agency and their attitude towards the objective function itself! This might allow us to design training setups which create pressures towards agents which are still very intelligent and capable of carrying out complex tasks, but not very agentic -thereby preventing misalignment without solving either outer alignment or inner alignment. Failing that, though, we will need to align agentic AGIs. To do so, in addition to the techniques I've discussed above, we'll need to be able to talk more precisely about what concepts and goals our agents possess. However, I am pessimistic about the usefulness of mathematics in making such high-level claims. Mathematical frameworks often abstract away the aspects of a problem that we actually care about, in order to make proofs easier -making those proofs much less relevant than they seem. I think this criticism applies to the expected utility maximisation framework, as discussed previously; other examples include most RL convergence proofs, and most proofs of robustness to adversarial examples. Instead, I think we will need principles and frameworks similar to those found in cognitive science and evolutionary biology. I think the categorisation of upstream vs downstream inner misalignment is an important example of such progress; 21 I'd also like to see a framework in which we can talk sensibly about gradient hacking, 25 and the distinction between being motivated by a reward signal versus a reward function.  22  We should then judge reward functions as \"right\" or \"wrong\" only to the extent that they succeed or fail in pushing the agent towards developing desirable motivations and avoiding these sorts of pathologies. In the final section, I will address the question of whether, if we fail, AGIs with the goal of increasing their influence at the expense of humans will actually succeed in doing so. \n Control It's important to note that my previous arguments by themselves do not imply that AGIs will end up in control of the world instead of us. As an analogy, scientific knowledge allows us to be much more capable than stone-age humans. Yet if dropped back in that time with just our current knowledge, I very much doubt that one modern human could take over the stone-age world. Rather, this last step of the argument relies on additional predictions about the dynamics of the transition from humans being the smartest agents on Earth to AGIs taking over that role. These will depend on technological, economic and political factors, as I'll discuss in this section. One recurring theme will be the importance of our expectation that AGIs will be deployed as software that can be run on many different computers, rather than being tied to a specific piece of hardware as humans are.  26  I'll start off by discussing two very high-level arguments. The first is that being more generally intelligent allows you to acquire more power, via largescale coordination and development of novel technological capabilities. Both of these contributed to the human species taking control of the world; and they both contributed to other big shifts in the distribution of power (such as the industrial revolution). If the set of all humans and aligned AGIs is much less capable in these two ways than the set of all misaligned AGIs, then we should expect the latter to develop more novel technologies, and use them to amass more resources, unless strong constraints are placed on them, or they're unable to coordinate well (I'll discuss both possibilities shortly.) On the other hand, though, it's also very hard to take over the world. In particular, if people in power see their positions being eroded, it's generally a safe bet that they'll take action to prevent that. Further, it's always much easier to understand and reason about a problem when it's more concrete and tangible; our track record at predicting large-scale future developments is pretty bad. And so even if the high-level arguments laid out above seem difficult to rebut, there may well be some solutions we missed which people will spot when their incentives to do so, and the range of approaches available to them, are laid out more clearly. How can we move beyond these high-level arguments? In the rest of this section I'll lay out two types of disaster scenarios, and then four factors which will affect our ability to remain in control if we develop AGIs that are not fully aligned: 1. Speed of AI development 2. Transparency of AI systems 3. Constrained deployment strategies 4. Human political and economic coordination \n Disaster scenarios There have been a number of attempts to describe the catastrophic outcomes that might arise from misaligned superintelligences, although it has proven difficult to characterise them in detail. Broadly speaking, the most compelling scenarios fall into two categories.  Christiano [2019]  describes AGIs gaining influence within our current economic and political systems by taking or being given control of companies and institutions. Eventually \"we reach the point where we could not recover from a correlated automation failure\" -after which those AGIs are no longer incentivised to follow human laws.  Hanson [2016]  also lays out a scenario in which virtual minds come to dominate the economy (although he is less worried about misalignment, partly because he focuses on emulated human minds). In both scenarios, biological humans lose influence because they are less competitive at strategically important tasks, but no single AGI is able to seize control of the world. To some extent these scenarios are analogous to our current situation, in which large corporations and institutions are able to amass power even when most humans disapprove of their goals. However, since these organisations are staffed by humans, there are still pressures on them to be aligned with human values which won't apply to groups of AGIs. By contrast,  Yudkowsky et al. [2008]  and  Bostrom [2014]  describe scenarios where a single AGI gains power primarily through technological breakthroughs, in a way that's largely separate from the wider economy. The key assumption which distinguishes this category of scenarios from the previous category is that a single AGI will be able to gain enough power via such breakthroughs that they can seize control of the world. Descriptions of these scenarios have featured superhuman nanotechnology, biotechnology, and hacking; however, detailed characterisations are difficult because the relevant technologies don't yet exist. Yet it seems very likely that there exist some future technologies which would provide a decisive strategic advantage if possessed only by a single actor, and so the key factor influencing the plausibility of these scenarios is whether AI development will be rapid enough to allow such concentration of power, as I discuss below. In either case, humans and aligned AIs end up with much less power than misaligned AIs, which could then appropriate our resources towards their own goals. An even worse scenario is if misaligned AGIs act in ways which are deliberately hostile to human values -for example, by making threats to force concessions from us  [Clifton, 2020] . How can we avoid these scenarios? It's tempting to aim directly towards the final goal of being able to align arbitrarily intelligent AIs, but I think that the most realistic time horizon to plan towards is the point when AIs are much better than humans at doing safety research. So our goal should be to ensure that those AIs are aligned, and that their safety research will be used to build their successors. Which category of disaster is most likely to prevent that depends not only on the intelligence, agency and goals of the AIs we end up developing, but also on the four factors listed above, which I'll explore in more detail now. \n Speed of AI development If AI development proceeds very quickly, then our ability to react appropriately will be much lower. In particular, we should be interested in how long it will take for AGIs to proceed from human-level intelligence to superintelligence, which we'll call the takeoff period. The history of systems like AlphaStar, AlphaGo and OpenAI Five provides some evidence that this takeoff period will be short: after a long development period, each of them was able to improve rapidly from top amateur level to superhuman performance. A similar phenomenon occurred during human evolution, where it only took us a few million years to become much more intelligent than chimpanzees. In our case one of the key factors was scaling up our brain hardware -which, as I have already discussed, will be much easier for AGIs than it was for humans. While the question of what returns we will get from scaling up hardware and training time is an important one, in the long term the most important question is what returns we should expect from scaling up the intelligence of scientific researchers -because eventually AGIs themselves will be doing the vast majority of research in AI and related fields (in a process I've been calling recursive improvement). In particular, within the range of intelligence we're interested in, will a given increase δ in the intelligence of an AGI increase the intelligence of the best successor that AGI can develop by more than or less than δ? If more, then recursive improvement will eventually speed up the rate of progress in AI research dramatically. In favour of this hypothesis,  Yudkowsky [2013]  argues: The history of hominid evolution to date shows that it has not required exponentially greater amounts of evolutionary optimization to produce substantial real-world gains in cognitive performance -it did not require ten times the evolutionary interval to go from Homo erectus to Homo sapiens as from Australopithecus to Homo erectus. All compound interest returned on discoveries such as the invention of agriculture, or the invention of science, or the invention of computers, has occurred without any ability of humans to reinvest technological dividends to increase their brain sizes, speed up their neurons, or improve the low-level algorithms used by their neural circuitry. Since an AI can reinvest the fruits of its intelligence in larger brains, faster processing speeds, and improved low-level algorithms, we should expect an AI's growth curves to be sharply above human growth curves. I consider this a strong argument that the pace of progress will eventually become much faster than it currently is. I'm much less confident about when the speedup will occur -for example, the positive feedback loop outlined above might not make a big difference until AGIs are already superintelligent, so that the takeoff period (as defined above) is still quite slow. There has been particular pushback against the more extreme fast takeoff scenarios, which postulate a discontinuous jump in AI capabilities before AI has had transformative impacts  [Christiano, 2018c , Grace, 2018c . Some of the key arguments: 1. The development of AGI will be a competitive endeavour in which many researchers will aim to build general cognitive capabilities into their AIs, and will gradually improve at doing so. This makes it unlikely that there will be low-hanging fruit which, when picked, allow large jumps in capabilities. (Arguably, cultural evolution was this sort of low-hanging fruit during human evolution, which would explain why it facilitated such rapid progress.) 2. Compute availability, which on some views 27 is the key driver of progress 27 See Sutton  [2019] . in AI, increases fairly continuously. 3. Historically, continuous technological progress has been much more common than discontinuous progress  [Grace, 2018b] . For example, progress on chess-playing AIs was steady and predictable over many decades  [Grace, 2018a] . Note that these three arguments are all consistent with AI development progressing continuously but at an increasing pace, as AI systems contribute to it an increasing amount. \n Transparency of AI systems A transparent AI system is one whose thoughts and behaviour we can understand and predict; we could be more confident that we can maintain control over an AGI if it were transparent. If we could tell when a system is planning treacherous behaviour, then we could shut it down before it gets the opportunity to carry out that plan. Note that such information would also be valuable for increasing human coordination towards dealing with AGIs; and of course for training, as I discussed briefly in the previous section.  Hubinger [2019b]  lists three broad approaches to making AIs more transparent. One is by creating interpretability tools which allow us to analyse the internal functioning of an existing system. While our ability to interpret human and animal brains is not currently very robust, this is partly because research has been held back by the difficulty of making high-resolution measurements. By contrast, in neural networks we can read each weight and each activation directly, as well as individually changing them to see what happens. On the other hand, if our most advanced systems change rapidly, then previous transparency research may quickly become obsolete. In this respect, neuroscientists -who can study one brain architecture for decades -have it easier. A second approach is to create training incentives towards transparency. For example, we might reward an agent for explaining its thought processes, or for behaving in predictable ways. Interestingly, ideas such as the cooperative eye hypothesis imply that this occurred during human evolution, which suggests that multi-agent interactions might be a useful way to create such incentives (if we can find a way to prevent incentives towards deception from also arising). A third approach is to design algorithms and architectures that are inherently more interpretable. For example, a model-based planner like AlphaGo explores many possible branches of the game tree to decide which move to take. By examining which moves it explores, we can understand what it's planning before it chooses a move. However, in doing so we rely on the fact that Al-phaGo uses an exact model of Go. More general agents in larger environments will need to plan using compressed representations of those environments, which will by default be much less interpretable. It also remains to be seen whether transparency-friendly architectures and algorithms can be competitive with the performance of more opaque alternatives, but I strongly suspect not. Despite the difficulties inherent in each of these approaches, one advantage we do have in transparency analysis is access to different versions of an AI over time. This mechanism of cross-examination in Debate takes advantage of this  [Barnes and Christiano, 2020] . Or as a more pragmatic example, if AI systems which are slightly less intelligent than humans keep trying to deceive their supervisors, that's pretty clear evidence that the more intelligent ones will do so as well. However, this approach is limited because it doesn't allow us to identify unsafe plans until they affect behaviour. If the realisation that treachery is an option is always accompanied by the realisation that treachery won't work yet, we might not observe behavioural warning signs until an AI arises which expects its treachery to succeed. \n Constrained deployment strategies If we consider my earlier analogy of a modern human dropped in the stone age, one key factor that would prevent them from taking over the world is that they would be \"deployed\" in a very constrained way. They could only be in one place at a time; they couldn't travel or even send messages very rapidly; they would not be very robust to accidents; and there would be little existing infrastructure for them to leverage. By contrast, it takes much more compute to train deep learning systems than to run them -once an AGI has been trained, it will likely be relatively cheap to deploy many copies of it. A misaligned superintelligence with internet access will be able to create thousands of duplicates of itself, which we will have no control over, by buying (or hacking) the necessary hardware. At this point, our intuitions about the capabilities of a \"single AGI\" become outdated, and the \"second species\" terminology becomes more appropriate. We can imagine trying to avoid this scenario by deploying AGIs in more constrained ways -for example by running them on secure hardware and only allowing them to take certain pre-approved actions (such as providing answers to questions)  [Ngo, 2020e] . This seems significantly safer. However, it also seems less likely in a competitive marketplace -judging by today's trends, a more plausible outcome is for almost everyone to have access to an AGI personal assistant via their phone. This brings us to the fourth factor: \n Human political and economic coordination By default, we shouldn't rely on a high level of coordination to prevent AGI safety problems. We haven't yet been able to coordinate adequately to prevent global warming, which is a well-documented, gradually-worsening problem. In the case of AGI deployment, the extrapolation from current behaviour to future danger is much harder to model clearly. Meanwhile, in the absence of technical solutions to safety problems, there will be strong short-term economic incentives to ignore the lack of safety guarantees about speculative future events. However, this is very dependent on the three previous points. It will be much easier to build a consensus on how to deal with superintelligence if AI systems approach then surpass human-level performance over a timeframe of decades, rather than weeks or months. This is particularly true if less-capable systems display misbehaviour which would clearly be catastrophic if performed by more capable agents. Meanwhile, different actors who might be at the forefront of AGI development -governments, companies, nonprofits -will vary in their responsiveness to safety concerns, cooperativeness, and ability to implement constrained deployment strategies. And the more of them are involved, the harder coordination between them will be. \n Conclusion Let's recap the second species argument as originally laid out, along with the additional conclusions and clarifications from the rest of the report. 1. We'll build AIs which are much more intelligent than humans; that is, much better than humans at using generalisable cognitive skills to understand the world. 2. Those AGIs will be autonomous agents which pursue long-term, largescale goals, because goal-directedness is reinforced in many training environments, and because those goals will sometimes generalise to be larger in scope. 3. Those goals will by default be misaligned with what we want, because our desires are complex and nuanced, and our existing tools for shaping the goals of AIs are inadequate. 4. The development of autonomous misaligned AGIs would lead to them gaining control of humanity's future, via their superhuman intelligence, technology and coordination -depending on the speed of AI development, the transparency of AI systems, how constrained they are during deployment, and how well humans can cooperate politically and economically. Personally, I am most confident in 1, then 4, then 3, then 2 (in each case conditional on all the previous claims) -although I think there's room for reasonable disagreement on all of them. In particular, the arguments I've made about AGI goals might have been too reliant on anthropomorphism. Even if this is a fair criticism, though, it's also very unclear how to reason about the behaviour of generally intelligent systems without being anthropomorphic. The main reason we expect the development of AGI to be a major event is because the history of humanity tells us how important intelligence is. But it wasn't just our intelligence that led to human success -it was also our relentless drive to survive and thrive. Without that, we wouldn't have gotten anywhere. So when trying to predict the impacts of AGIs, we can't avoid thinking about what will lead them to choose some types of intelligent behaviour over others -in other words, thinking about their motivations. Note, however, that the second species argument, and the scenarios I've outlined above, aren't meant to be comprehensive descriptions of all sources of existential risk from AI. Even if the second species argument doesn't turn out to be correct, AI will likely still be a transformative technology, and we should try to minimise other potential harms. In addition to the standard misuse concerns laid out in  Brundage et al. [2018]  (e.g. about AI being used to develop weapons), we might also worry about increases in AI capabilities leading to undesirable structural changes  [Zwetsloot and Dafoe, 2019] . For example, they might shift the offense-defence balance in cybersecurity  [Garfinkel and Dafoe, 2019] , or lead to more centralisation of human economic power. I consider  Christiano [2019] 's \"going out with a whimper\" scenario to also fall into this category. Yet there's been little in-depth investigation of how structural changes might lead to longterm harms, so I am inclined to not place much credence in such arguments until they have been explored much more thoroughly. By contrast, I think the AI takeover scenarios that this report focuses on have received much more scrutiny -but still, as discussed previously, have big question marks surrounding some of the key premises. However, it's important to distinguish the question of how likely it is that the second species argument is correct, from the question of how seriously we should take it. Often people with very different perspectives on the latter actually don't disagree very much on the former. I find the following analogy from Stuart Russell illustrative: suppose we got a message from space telling us that aliens would be landing on Earth sometime in the next century. Even if there's doubt about the veracity of the message, and there's doubt about whether the aliens will be hostile, we (as a species) should clearly expect this event to be a huge deal if it happens, and dedicate a lot of effort towards making it go well. In the case of AGI, while there's reasonable doubt about what it will look like, its development may nevertheless be the biggest thing that's ever happened. At the very least we should put serious effort into understanding the arguments I've discussed above, how strong they are, and what we might be able to do about them.  28   \n Acknowledgements This report benefited greatly from the contributions of a number of people. In particular I'm grateful to Joe Carlsmith, Will MacAskill, Daniel Kokotajlo, Rohin Shah, Vladimir Mikulik, Beth Barnes, and Ben Garfinkel, for discussions which shaped the ideas presented here. Thanks also to many others who gave feedback (much of which can be found on the Alignment Forum). 28 I want to explicitly warn against taking this argument too far, though -for example, by claiming that AI safety work should still be a major priority even if the probability of AI catastrophe is much less than 1%. This claim is misleading because most researchers in the field of safety think it's much higher than that; and also because, if it really is that low, there are probably some fundamental confusions in our concepts and arguments that need to be cleared up before we can actually start object-level work towards making AI safer. \t\t\t  Muehlhauser [2013]    \n\t\t\t This observation is closely related to Moravec's paradox, which I discuss in more detail in the section on Goals and Agency. Perhaps the most salient example is how easy it was for AIs to beat humans at chess. 6 It's not quite clear whether the distinction between \"single AGIs\" and collective AGIs makes sense in all cases, considering that a single AGI can be composed of many modules which might be very intelligent in their own right. But since it seems unlikely that there will be hundreds or thousands of modules which are each generally intelligent, I think that the distinction will in practice be useful. See alsoNgo [2020a]  and the discussion of \"collective superintelligence\" in Bostrom [2014] . \n\t\t\t FollowingOrtega et al. [2018]. 10 AI systems which learn to pursue goals are also known as mesa-optimisers, as coined in Hubinger et al. [2019] .11 Related arguments exist which attempt to do so. For example, Yudkowsky [2018]  argues \n\t\t\t As in Guez et al. [2019] .13  A concept explored further in Ecoffet et al. [2020] . \n\t\t\t For example, when people want to be \"cooperative\" or \"moral\", they're often not just thinking about results, but rather the types of actions they should take, or the types of decision procedures they should use to generate those actions. An additional complication is that humans don't have full introspective access to all our concepts -so we need to also consider unconscious concepts.15 Consider if this happened to you, and you were pulled \"out of the simulation\" into a real world which is quite similar to what you'd already experienced. By default you would likely still want to eat good food, have fulfilling relationships, and so on, despite the radical ontological shift you just underwent. \n\t\t\t Of course, what humans say we want, and what we act as if we want, and what we privately desire often diverge. But again, I'm not particularly worried about a superintelligence being unable to understand how humans distinguish between these categories, if it wanted to. \n\t\t\t As in Christiano et al. [2017] . \n\t\t\t The mistake of thinking of RL agents solely as reward-maximisers (rather than having other learned instincts and goals) has an interesting parallel in the history of the study of animal cognition, where behaviorists focused on the ways that animals learned new behaviours to increase reward, while ignoring innate aspects of their cognition.24 One useful example is the evolution of altruism in humans. While there's not yet any consensus on the precise evolutionary mechanisms involved, it's notable that our altruistic instincts extend well beyond the most straightforward cases of kin altruism and directly reciprocal altruism. In other words, some interaction between our direct evolutionary payoffs, and our broader environment, led to the emergence of quite general altruistic instincts, making humans \"safer\" (from the perspective of other species). \n\t\t\t  See Hubinger [2019a]: \"Gradient hacking is a term I've been using recently to describe the phenomenon wherein a deceptively aligned mesa-optimizer might be able to purposefully act in ways which cause gradient descent to update it in a particular way.\" \n\t\t\t For an exploration of the possible consequences of software-based intelligence (as distinct from the consequences of increased intelligence) see Hanson [2016] .", "date_published": "n/a", "url": "n/a", "filename": "AGI safety from first principles.tei.xml", "abstract": "This report explores the core case for why the development of artificial general intelligence (AGI) might pose an existential threat to humanity. It stems from my dissatisfaction with existing arguments on this topic: early work is less relevant in the context of modern machine learning, while more recent work is scattered and brief. This report aims to fill that gap by providing a detailed investigation into the potential risk from AGI misbehaviour, grounded by our current knowledge of machine learning, and highlighting important uncertainties. It identifies four key premises, evaluates existing arguments about them, and outlines some novel considerations for each. 1 Stuart Russell also refers to this as the \"gorilla problem\" in his recent book, Human Compatible [Russell, 2019].", "id": "ecaa470905e442ffa42a96f9838a2842"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Shihui Li", "Yi Wu", "Xinyue Cui", "Honghua Dong", "Fei Fang", "Stuart Russell"], "title": "Robust Multi-Agent Reinforcement Learning via Minimax Deep Deterministic Policy Gradient", "text": "Introduction Most real-world problems involve interactions between multiple agents and the complexity of problem increases significantly when the agents co-evolve together. Thanks to the recent advances of deep reinforcement learing (DRL) on single agent scenarios, which led to successes in playing Atari game  (Mnih et al. 2015) , playing go  (Silver et al. 2016 ) and robotics control  (Levine et al. 2016) , it has been a rising trend to adapt single agent DRL algorithms to multi-agent learning scenarios and many works have shown great successes on a variety of problems, including automatic discovery of communication and language  (Sukhbaatar, Fergus, and others 2016; Mordatch and Abbeel 2017) , multiplayer games  (Peng et al. 2017a; OpenAI 2018) , traffic control  (Wu et al. 2017 ) and the analysis of social dilemmas  (Leibo et al. 2017) . The critical challenge when adapting classical single agent DRL algorithms to multi-agent setting is the training instabil-ity issue: as training progresses, each agent's policy is changing and therefore the environment becomes non-stationary from the perspective of any individual agent (in a way that is not explainable by changes in the agent's own policy). This non-stationary problem can cause significant problems when directly applying the single agent DRL algorithms, for example, the variance of the policy gradient can be exponentially large when the number of agents increases  (Lowe et al. 2017 ). To handle this instability issue, recent works, such as the counterfactual multi-agent policy gradients  (Foerster et al. 2017 ) and the Multi-Agent Deep Deterministic Policy Gradient (MADDPG)  (Lowe et al. 2017) , proposed to utilized a centralized critic within the actor-critic learning framework to reduce the variance of policy gradient. Despite the fact that using a centralized critic stabilizes training, the learned policies can still be brittle and sensitive to its training partners and converge to a poor local mode. This is particularly severe for competitive environments: when the opponents alter their policies during testing, the performance of the learned policies can be drastically worse  (Lazaridou, Peysakhovich, and Baroni 2016) . Hence, a robust policy becomes desirable in multi-agent setting: a well-trained agent should be able behave well in testing when competing against opponents even with strategies different from its training partners. In this work, we focus on robust multi-agent reinforcement learning with continuous action spaces and propose a novel algorithm, MiniMax Multi-agent Deep Deterministic Policy Gradient (M3DDPG). M3DDPG is a minimax extension 1 of the MADDPG algorithm  (Lowe et al. 2017) . Its core idea is that during training, we force each agent to behave well even when its training opponents response in the worst way. Our major contributions are summarized as follow: • We introduce the minimax approach to robust multi-agent DRL and propose a novel minimax learning objective based on the MADDPG algorithm; • In order to efficiently optimize the minimax learning objective, we propose an end-to-end learning approach, Multiagent Adversarial Learning (MAAL), which is inspired by the adversarial training  (Goodfellow, Shlens, and Szegedy 2014)  technique. • We empirically evaluate our proposed M3DDPG algorithm on four mixed cooperative and competitive environments and the agents trained by M3DDPG outperform baseline policies on all these environments. In the rest of the paper, we will firstly present related works in section 2. Notations and standard algorithms are described in section 3. Our main algorithm, M3DDPG, is introduced in section 4. Experimental results are in section 5. \n Related Work Multi-agent reinforcement learning  (Littman 1994 ) has been a long-standing field in AI  (Hu, Wellman, and others 1998; Busoniu, Babuska, and De Schutter 2008) . Recent works in DRL use deep neural networks to approximately represent policy and value functions. Inspired by the success of DRL in single-agent settings, many DRL-based multi-agent learning algorithms have been proposed.  Forester et al. (2016b)  and  He et al. (2016)  extended the deep Q-learning to multiagent setting;  Peng et al. (2017a)  proposed a centralized policy learning algorithm based on actor-critic policy gradient; Forester et al. (2016a) developed a decentralized multi-agent policy gradient algorithm with centralized baseline;  Lowe et al. (2017)  extended DDPG to multi-agent setting with a centralized Q function;  Wei et al. (2018)  and  Grau-Moya (2018)  proposed multi-agent variants of the soft-Q-learning algorithm  (Haarnoja et al. 2017) ;  Yang et al. (2018)  focused on multi-agent reinforcement learning on a very large population of agents. Our M3DDPG algorithm is built on top of MAD-DPG and inherits the decentralized policy and centralized critic framework. Minimax is a fundamental concept in game theory and can be applied to general decision-making under uncertainty, prescribing a strategy that minimizes the possible loss for a worst case scenario  (Osborne and others 2004) . Minimax was firstly introduced to multi-agent reinforcement learning as minimax Q-learning by  Littman (1994) . More recently, some works combine the minimax framework and the DRL techniques to find Nash equilibrium in two player zero-sum games  (Foerster et al. 2018; Pérolat et al. 2016; Grau-Moya, Leibfried, and Bou-Ammar 2018) . In our work, we utilize the minimax idea for the purpose of robust policy learning. Robust reinforcement learning was originally introduced by  Morimoto et al. (2005)  considering the generalization ability of the learned policy in the single-agent setting. This problem is also studied recently with deep neural networks, such as adding random noise to input  (Tobin et al. 2017)  or dynamics  (Peng et al. 2017b)  during training. Besides adding random noise, some other works implicitly adopt the minimax idea by utilizing the \"worst noise\"  (Pinto et al. 2017; Mandlekar et al. 2017) . These works force the learned policy to work well even under the worst case perturbations and are typically under the name of \"adversarial reinforcement learning\", despite the fact that the original adversarial reinforcement learning problem was introduced in the setting of multi-agent learning  (Uther and Veloso 1997) . In our M3DDPG algorithm, we focus on the problem of learning polices that is robust to opponents with different strategies. Within the minimax framework, finding the worst case scenario is a critical component.  Lanctot et al. (2017)  proposed an iterative approach that alternatively computes the best response policy while fixes the other. Gao et al.  (Gao, Mueller, and Hayward 2018)  replace \"mean\" in the temporal difference learning rule with \"minimum\". In our work, we proposed MAAL, which is a general, efficient and fully end-to-end learning approach. MAAL is motivated by adversarial training  (Goodfellow, Shlens, and Szegedy 2014)  and suitable for arbitrary number of agents. The core idea of MAAL is approximating the minimization in our minmax objective by a single gradient descent step. The idea of one-step-gradient approximation was also explored in metalearning  (Finn, Abbeel, and Levine 2017) . \n Background and Preliminary In this section, we describe our problem setting and the standard algorithms. Most of the definitions and notations follow the original MADDPG paper  (Lowe et al. 2017) . \n Markov Games We consider a multi-agent extension of Markov decision processes (MDPs) called partially observable Markov games  (Littman 1994) . A Markov game for N agents is defined by a set of states S describing the possible configurations of all agents, a set of actions A 1 , ..., A N and a set of observations O 1 , ..., O N for each agent. To choose actions, each agent i uses a stochastic policy π π π θi : O i × A i → [0, 1] parameterized by θ i , which produces the next state according to the state transition function T : S × A 1 × ... × A N → S. Each agent i obtains rewards as a function of the state and agent's action r i : S × A i → R, and receives a private observation correlated with the state o i : S → O i . The initial states are determined by a distribution ρ : S → [0, 1]. Each agent i aims to maximize its own total expected return R i = T t=0 γ t r t i where γ is a discount factor and T is the time horizon. To minimize notation, in the following discussion we will often omit θ from the subscript of π π π. \n Q-Learning and Deep Q-Networks (DQN) Q-Learning and DQN  (Mnih et al. 2015)  are popular methods in reinforcement learning and have been previously applied to multi-agent settings  (Foerster et al. 2016a; Tesauro 2004 ). Q-Learning makes use of an action-value function for policy π π π as Q π π π (s, a) = E[R|s t = s, a t = a]. This Q function can be recursively rewritten as Q π π π (s, a) = E s [r(s, a) + γE a ∼π π π [Q π π π (s , a )]] . DQN learns the action-value function Q * corresponding to the optimal policy by minimizing: L(θ) = E s,a,r,s [(Q * (s, a|θ) − y) 2 ], (1) where y = r + γ max a Q * (s , a ). Q is a target Q function whose parameters are periodically updated with the most recent θ, which helps stabilize learning. Another crucial component of stabilizing DQN is the use of an experience replay buffer D containing tuples (s, a, r, s ). Q-learning algorithm is most suitable for DRL agents with discrete action spaces. \n Policy Gradient (PG) Algorithms Policy gradient methods is another popular choice for a variety of RL tasks. Let ρ π denote discounted state visitation distribution for a policy π. The main idea of PG is to directly adjust the parameters θ of the policy in order to maximize the objective J(θ) = E s∼ρ π π π ,a∼π π π θ [R] by taking steps in the direction of ∇ θ J(θ). Using the Q function defined previously, the gradient of the policy can be written as  (Sutton et al. 2000) : ∇ θ J(θ) = E s∼ρ π π π ,a∼π π π θ [∇ θ log π π π θ (a|s)Q π π π (s, a)], (2) where p π π π is the state distribution. The policy gradient theorem has given rise to several practical algorithms, which often differ in how they estimate Q π π π . For example, one can simply use a sample return R t = T i=t γ i−t r i , which leads to the REINFORCE algorithm  (Williams 1992 ). Alternatively, one could learn an approximation of the true action-value function Q π π π (s, a) called the critic and leads to a variety of actor-critic algorithms  (Sutton and Barto 1998) . \n Deterministic Policy Gradient (DPG) Algorithms DPG algorithms extends the policy gradient algorithm to deterministic policies µ µ µ θ : S → A  (Silver et al. 2014) . In particular, under certain conditions we can write the gradient of the objective J(θ) = E s∼ρ µ µ µ [R(s, a)] as: ∇ θ J(θ) = E s∼D [∇ θ µ µ µ θ (s)∇ a Q µ µ µ (s, a)| a=µ µ µ θ (s) ], (3) where D is the replay buffer. Since this theorem relies on ∇ a Q µ µ µ (s, a), it requires the action space A (and thus the policy µ µ µ) be continuous. Deep deterministic policy gradient (DDPG)  (Lillicrap et al. 2015 ) is a variant of DPG where the policy µ µ µ and critic Q µ µ µ are approximated with deep neural networks. DDPG is an off-policy algorithm, and samples trajectories from a replay buffer of experiences that are stored throughout training. DDPG also makes use of a target network, as in DQN  (Mnih et al. 2015) . \n Multi-Agent Deep Deterministic Policy Gradient Directly applying single-agent RL algorithms to the multiagent setting by treating other agents as part of the environment is problematic as the environment appears nonstationary from the view of any one agent, violating Markov assumptions required for convergence. This non-stationary issue is more severe in the case of DRL with neural networks as function approximators. The core idea of the MADDPG algorithm  (Lowe et al. 2017 ) is learning a centralized Q function for each agent which conditions on global information to alleviate the non-stationary problem and stabilize training. More concretely, consider a game with N agents with policies parameterized by θ θ θ = {θ 1 , ..., θ N }, and let µ µ µ = {µ µ µ 1 , ..., µ µ µ N } be the set of all agents' policies. Then we can write the gradient of the expected return for agent i with policy µ µ µ i , J(θ i ) = E[R i ] as: ∇ θi J(θ i ) = E x,a∼D [∇ θi µ µ µ i (o i )∇ ai Q µ µ µ i (x, a 1 , ..., a N )| ai=µ µ µi(oi) ] , (4) Here Q π π π i (x, a 1 , ..., a N ) is a centralized action-value function that takes as input the actions of all agents, a 1 , . . . , a N , in addition to some state information x (i.e., x = (o 1 , ..., o N )) , and outputs the Q-value for agent i. Let x denote the next state from x after taking actions a 1 , . . . , a N . The experience replay buffer D contains the tuples (x, x , a 1 , . . . , a N , r 1 , . . . , r N ), recording experiences of all agents. The centralized action-value function Q µ µ µ i is updated as:  oj )  , where µ µ µ = {µ µ µ θ 1 , ..., µ µ µ θ N } is the set of target policies with delayed parameters θ i . L(θ i ) = E x,a,r,x [(Q µ µ µ i (x, a 1 , . . . , a N ) − y) 2 ], (5) y = r i + γ Q µ µ µ i (x , a 1 , . . . , a N ) a j =µ µ µ j ( Note that the centralized Q function is only used during training. During decentralized execution, each policy µ µ µ θi only takes local information o i to produce an action. \n Minimax Multi-Agent Deep Deterministic Policy Gradient (M3DDPG) In this section, we introduce our proposed new algorithm, Minimax Multi-agent Deep Deterministic Policy Gradient (M3DDPG), which is built on top of the MADDPG algorithm and particularly designed to improve the robustness of learned policies. Our M3DDPG algorithm contains two major novel components: Minimax Optimization Motivated by the minimax concept in game theory, we introduce minimax optimization into the learning objective; Multi-Agent Adversarial Learning The continuous action space results in computational intractability issue when optimizing our proposed minimax objective. Hence, we propose Multi-Agent Adversarial Learning (MAAL) to solve this optimization problem. \n Minimax Optimization In multi-agent RL, the agents' policies can be very sensitive to their learning partner's policy. Particularly in competitive environments, the learned policies can be brittle when the opponents alter their strategies. For the purpose of learning robust policies, we propose to update policies considering the worst situation: during training, we optimize the accumulative reward for each agent i under the assumption that all other agents acts adversarially. This yields the minimax learning objective max θi J M (θ i ) where J M (θ i ) = E s∼ρ µ µ µ [R i ] = min a t j =i E s∼ρ µ µ µ T t=0 γ t r i (s t , a t 1 , . . . , a t N ) a t i =µ µ µ(o t i ) (6) = E s 0 ∼ρ min a 0 j =i Q µ µ µ M,i (s 0 , a 0 1 , . . . , a 0 N ) a 0 i =µ µ µ(o 0 i ) . (7) Critically, in Eq. 6, state s t+1 at time t + 1 depends not only on the dynamics ρ µ µ µ and the action µ µ µ i (o t i ) but also on all the previous adversarial actions a t j =i with t ≤ t. In Eq. 7, we derive the modified Q function Q µ µ µ M (s, a 1 , . . . , a N ), which is naturally centralized and can be rewritten in a recursive form Q µ µ µ M,i (s, a 1 , . . . , a N ) = r i (s, a 1 , . . . , a N )+ γE s min a j =i Q µ µ µ M,i (s , a 1 , . . . , a N ) a i =µ µ µi(s ) . Importantly, Q µ µ µ M (s, a 1 , . . . , a N ) conditions on the current state s as well as the current actions a 1 , . . . , a N and represents the current reward plus the discounted worst case future return starting from the next state, s . This definition brings the benefits that we can naturally apply off-policy temporal difference learning later to derive the update rule for Q µ µ µ M . Note that for each agent i, none of the adversarial actions depend on its parameter θ i , so we can directly apply the deterministic policy gradient theorem to compute ∇ θi J M (θ i ) and use off-policy temporal difference to update the Q function. Thanks to the centralized Q function in MADDPG (Eq. 4), which takes in the actions from all the agents, our derivation naturally applies and is perfectly aligned with the MADDPG formulation (Eq. 4) by injecting a minimization over other agents' actions as follows: ∇ θ i J M (θ i ) = E x∼D   ∇ θ i µ µ µ i (o i )∇a i Q µ µ µ M,i (x, a 1 , . . . , a i , . . . a N ) a i = µ µ µ i (o i ) a j =i = arg mina j =i Q µ µ µ M,i (x, a 1 , . . . , a N )   , (9) where D denotes the replay buffer and x denotes the state information. Correspondingly, we obtain the new Q function update rule by adding another minimization to Eq. 5 when computing the target Q value: L(θ i ) = E x,a,r,x ∼D [(Q µ µ µ M,i (x, a 1 , . . . , a N ) − y) 2 ], (10) y = r i + γ Q µ µ µ M,i (x , a 1 , . . . , a i , . . . , a N ) a i = µ µ µ i (o i ), a j =i = arg min a j =i Q µ µ µ M,i (x , a 1 , . . . , a N ), where µ µ µ i denotes the target policy of agent i with delayed parameters θ i , and Q µ µ µ M,i denotes the target Q network for agent i. Combining Eq. 9 and Eq. 10 yields our proposed minimax learning framework. \n Multi-Agent Adversarial Learning The critical challenge in our proposed minimax learning framework is how to handle the embedded minimization in Eq. 9 and Eq. 10. Due to the continuous action space as well as the non-linearity of Q function, directly optimizing the minimization problem is computationally intractable. A naive approximate solution can be performing an inner-loop gradient descent whenever performing an update step of Eq. 9 or Eq. 10, but this is too computationally expensive for practical use. Here we introduce an efficient and end-to-end solution, multi-agent adversarial learning (MAAL). The main ideas of MAAL can be summarized in two steps: (1) approximate the non-linear Q function by a locally linear function; (2) replace the inner-loop minimization with a 1-step gradient descent. Note the core idea of MAAL, locally linearizing the Q function, is adapted from the recent adversarial training technique originally developed for supervised learning. We will discuss the connection between adversarial training and MAAL in the end of this section. For conciseness, we first consider Eq. 10 and rewrite it into the following form with auxiliary variables : y = r i + γ Q µ µ µ M,i (x , a 1 , . . . , a i , . . . , a N ) (11) a k = µ µ µ k (o k ), ∀1 ≤ k ≤ N a j = a j + j , ∀j = i j =i = arg min j =i Q µ µ µ M,i (x , a 1 + 1 , . . . , a i , . . . , a N + N ). Eq. 11 can be interpreted as we are now seeking for a set of perturbations such that the perturbed actions a decrease Q value the most. By linearizing the Q function at Q µ µ µ M,i (x, a 1 , . . . , a N ), the desired perturbation j can be locally approximated by the gradient direction at Q µ µ µ M,i (x, a 1 , . . . , a N ) w.r.t. a j . Then we use this local to derive an approximation ˆ j to the worst case perturbation by taking a small gradient step: ∀j = i, ˆ j = −α∇ aj Q µ µ µ M,i (x , a 1 , . . . , a j , . . . , a N ), (12) where α is a tunable coefficient representing the perturbation rate. It can be also interpreted as the step size of the gradient descent step: when α is too small, the local approximation error will be small but due to the small perturbation, the learned policy can be far from the optimal solution of the minimax objective we proposed; when α is too large, the approximation error may incur too much trouble for the overall learning process and the agents may fail to learn good policies. We can apply this technique to Eq. 9 as well and eventually derive the following formulation: ∇ θ i J(θ i ) = E x,a∼D     ∇ θ i µ µ µ i (o i )∇a i Q µ µ µ M,i (x, a 1 , . . . , a i , . . . a N ) a i = µ µ µ i (o i ) a j = a j + ˆ j , ∀j = i ˆ j = −α j ∇a j Q µ µ µ M,i (x, a 1 , . . . , a N )     , ( 13 ) and L(θ i ) = E x,a,r,x [(Q µ µ µ M,i (x, a 1 , . . . , a N ) − y) 2 ], (14) y = r i + γ Q µ µ µ M,i (x , a 1 , . . . , a i , . . . , a N ) a k = µ µ µ k (o k ), ∀1 ≤ k ≤ N a j = a j + ˆ j , ∀j = i ˆ j = −α j ∇ a j Q µ µ µ M,i (x, a 1 , . . . , a N ), where α 1 , . . . , α N are additional parameters. MAAL only requires one additional gradient computation, and can be executed in a fully end-to-end fashion. Finally, combining Eq. 13 and Eq. 14 completes MAAL. The overall algorithm, M3DDPG, is summarized as Algo. 1. Algorithm 1: Minimax Multi-Agent Deep Deterministic Policy Gradient (M3DDPG) for N agents for episode = 1 to M do Initialize a random process N for action exploration, and receive initial state information x for t = 1 to max-episode-length do for each agent i, select action a i = µ µ µ θi (o i ) + N t w.r.t. the current policy and exploration Execute actions a = (a 1 , . . . , a N ) and observe reward r and new state information x Store (x, a, r, x ) in replay buffer D, and set x ← x for agent i = 1 to N do Sample a random minibatch of S samples (x k , a k , r k , x k ) from D Set y k = r k i + γ Q µ µ µ M,i (x k , a 1 , . . . , a N )| a i =µ µ µ i (o k i ),a j =i =µ µ µ j (o k j )+ˆ j with ˆ j defined in Eq. 14 Update critic by minimizing the loss L(θ i ) = 1 S k y k − Q µ µ µ M,i (x k , a k 1 , . . . , a k N ) 2 Update actor using the sampled policy gradient with ˆ j defined in Eq. 13: ∇ θi J ≈ 1 S k ∇ θi µ µ µ i (o k i )∇ ai Q µ µ µ M,i (x k , a 1 , . . . , a i , . . . , a N ) ai=µ µ µi(o k i ),a j =i =a k j +ˆ j end for Update target network parameters for each agent i: θ i ← τ θ i + (1 − τ )θ i end for end for \n Discussion Connection to Adversarial Training Adversarial training is a robust training approach for deep neural networks on supervised learning . The core idea is to force the classifier to predict correctly even when given adversarial examples, which are obtained by adding a small adversarial perturbation to the original input data such that the classification loss can be decreased the most. Formally, suppose the classification loss function is L(θ) = E x,y [f θ (x; y)] with input data x and label y. Adversarial training aims to optimize the following adversarial loss instead L adv (θ) = E x,y [f θ (x + ; y)] (15) = arg max ≤α f θ (x + ; y). The core technique to efficiently optimize L adv (θ) is to locally linearize the loss function at f θ (x; y) and approximate by the scaled gradient. Thanks to the centralized Q function, which takes the actions from all the agents as part of the input, we are able to easily inject the minimax optimization (Eq. 11) and represent it in a similar way to adversarial training (Eq. 15) so that we can adopt the similar technique to effectively solve our minimax optimization in a fully end-to-end fashion. Connection to Single Agent Robust RL M3DDPG with MAAL can be also viewed as the special case of robust reinforcement learning (RRL)  (Morimoto and Doya 2005)  in the single agent setting, which aims to bridge the gap between training in simulation and testing in the real world by adding adversarial perturbations to the transition dynamics during training. Here, we consider the multi-agent setting and add worst case perturbations to actions of opponent agents during training. Note that in the perspective of a single agent, perturbations on opponents' actions can be also considered as a special adversarial noise on the dynamics. Choice of α In the extreme case of α = 0, M3DDPG degenerates to the original MADDPG algorithm while as α increases, the policy learning tends to be more robust but the optimization becomes harder. In practice, using a fixed α throughout training can lead to very unstable learning behavior due to the changing scale of the gradients. The original adversarial training paper  (Goodfellow, Shlens, and Szegedy 2014)  suggests to compute with a fixed norm, namely g = ∇ x f θ (x; y), ˆ = α g g , where x denotes the input data to the classifier and y denotes the label. In M3DDPG, we can adaptively compute the perturbation ˆ j by g = ∇ aj Q µ µ µ M,i (x, a 1 , . . . , a N ), ˆ j = −α j g g . (16) Eq. 16 generally works fine in practice but in some hard multi-agent learning environments, unstable training behavior can be still observed. We suspect that it is because the changing norm of actions in these situations. Different from the supervised learning setting where the norm of the input data x is typically stable, in reinforcement learning the norm of actions can drastically change even in a single episode. Therefore, it is possible to see cases that even a perturbation with a small fixed norm overwhelms the action a j , which may potentially lead to computational stability issue. Therefore, we also introduce the following alternative for adaptive perturbation computation: g = ∇ aj Q µ µ µ M,i (x, a 1 , . . . , a N ), ˆ j = −α j a j g g . (17) Lastly, note that in a mixed cooperative and competitive environment, ideally we only need to add adversarial perturbations to competitors. But empirically we observe that also adding (smaller) perturbations to collaborators can further improve the quality of learned policies. \n Experiments We adopt the same particle-world environments as the MAD-DPG paper  (Lowe et al. 2017)  as well as the training configurations. α is selected from a grid search over 0.1, 0.01 and 0.001. For testing, we generate a fixed set of 2500 environment configurations (i.e., landmarks and birthplaces) and evaluate on this fixed set for a fair comparison. \n Environments The particle world environment consists of N cooperative agents, M adversarial agents and L landmarks in a twodimensional world with continuous space. We focus on the four mixed cooperative and competitive scenarios to best examine the effectiveness of our minimax formulation. Covert communication This is an adversarial communication environment, where a speaker agent ('Alice') must communicate a message to a listener agent ('Bob') (N = 2), who must reconstruct the message at the other end. However, an adversarial agent ('Eve') (M = 1) is also observing the channel, and wants to reconstruct the message -Alice and Bob are penalized based on Eve's reconstruction, and thus Alice must encode her message using a randomly generated key, known only to Alice and Bob. Keep-away This scenario consists of L = 1 target landmark, N = 2 cooperative agents and M = 1 adversarial agent. Cooperating agents need to reach the landmark and keep the adversarial agent away from the landmark by pushing it while the adversarial agent must stay at the landmark to occupy it. Physical deception Here, N = 2 agents cooperate to reach a single target landmark from a total of L = 2 landmarks. They are rewarded based on the minimum distance of any agent to the target (so only one agent needs to reach the target landmark). However, a lone adversary (M = 1) also desires to reach the target landmark; the catch is that the adversary does not know which of the landmarks is the correct one. Thus the cooperating agents, who are penalized based on the adversary distance to the target, learn to spread out and cover all landmarks so as to deceive the adversary.  Predator-prey In this variant of the classic predator-prey game, N = 3 slower cooperating agents must chase the faster adversary (M = 1) around a randomly generated environment with L = 2 large landmarks impeding the way. Each time the cooperative agents collide with an adversary, the agents are rewarded while the adversary is penalized. \n Comparison to MADDPG To evaluate the quality of learned policies trained by different algorithms in competitive scenarios, we measure the performance of agents trained by our M3DDPG and agents by classical MADDPG in the roles of both normal agent and adversary in each environment. The results are in Figure  2 , where we measure the rewards of the normal agents in different scenarios and normalize them to 0-1. We notice that in all the environments, the highest score is achieved when the M3DDPG agents play as the normal agents against the MADDPG adversary (Minimax vs MA); while the lowest score is when the MADDPG agents act as normal agents against the M3DDPG adversary (MA vs Minimax). This indicates that policies trained by M3DDPG have much higher quality than original MADDPG. \n Evaluation with Disruptive Adversaries Instead of M3DDPG and MADDPG directly competing against each other, now we consider their performances in the worst possible situations through their individual competitions against disruptive adversaries. We construct disruptive adversaries by (1) fixing the trained normal agents (M3DDPG or MADDPG); (2) setting the reward of the disruptive adversary as the negative value of normal agents' reward (so that the problem becomes zero-sum); and then (3) using DDPG to train the disruptive adversary from scratch under the zerosum reward setting. In the particle world environment, the competitive scenarios are generally not zero-sum, which implies that according to the default reward function, the adversaries may have different purposes rather than directly disrupting the normal agents. So, in order to evaluate the effectiveness our minimax optimization in the worst situation, we convert every problems into a zero-sum form and compare the performances of our M3DDPG agents as well as the MADDPG agents against this artificially constructed adversaries. Moreover, since each of our four environments has only 1 adversary, after fixing the normal agents, the learning problem degenerates to the single agent setting and classical DDPG is sufficient to stably train a disruptive adversary. The results are shown in Figure  3 , where we plot the reward of the fixed normal agents of different algorithms as the training of the disruptive adversaries progresses until convergence. Note that due to the different environment designs, the difficulty for the disruptive agents to break the strategy of normal agents varies: for example, in convert communication, since the private key is not accessible to the adversary agent, breaking the encrypted communication will be very hard; while in physical deception, since we do not allow communication and fix the normal agents, a smart enough adversary may easily infer the target landmark by observing the initial behavior of the two cooperative agents. Nevertheless, despite these intrinsic properties, the M3DDPG agents (Minimax) achieves higher reward in all the scenarios, which implies better robustness even in the worst situation. \n Conclusion In this paper, we propose a novel algorithm, minimax mulitagent deep deterministic policy gradient (M3DDPG), for robust multi-agent reinforcement learning, which leverages the minimax concept and introduces a minimax learning objective. To efficiently optimize the minimax objective, we propose MAAL, which approximates the inner-loop minimization by a single gradient descent step. Empirically, M3DDPG outperforms the benchmark methods on four mixed cooperative and competitive scenarios. Nevertheless, due to the single step gradient approximation in MAAL, which is efficient in computation, an M3DDPG agent can only explore locally worst situation during the evolving process at training, which can still lead to unsatisfying behavior when testing opponents have drastically different strategies. It will be an interesting direction to re-examine the robustness-efficiency trade-off in MAAL and further improve policy learning by placing more computations on the minimax optimization. We leave this as our future work. Figure 1 : 1 Figure 1: Illustrations of some environments we consider, including Physical Deception (left) and Predator-Prey (right). \n Figure 2 : 2 Figure2: Comparison between M3DDPG (Minimax) and classical MADDPG (MA) on the four mixed competitive environments. Each bar cluster shows the 0-1 normalized score for a set of competing policies in different roles (agent vs adversary), where a higher score is better for the agent. In all cases, M3DDPG outperforms MADDPG when directly pitted against it. \n Figure 3 : 3 Figure 3: Performances of M3DDPG (Minimax, red) and MADDPG (MA, blue) under the worst situation, i.e., against the disruptive adversaries, on convert communication, keep-away, physical deception and predator-pray from left to right. The y-axis denotes the reward of normal agents (fixed) and x-axis denotes the training episodes performed of the disruptive adversaries. Higher reward implies a more robust policy. Agents trained by M3DDPG (Minimax) perform better on all the scenarios. \n\t\t\t In fact, we are dealing with gains, i.e., maximizing each agent's accumulative reward, so the \"minimax\" here is essentially \"maximin\". We keep the term \"minimax\" to be consistent with literature.", "date_published": "n/a", "url": "n/a", "filename": "4327-Article Text-7375-1-10-20190706.tei.xml", "abstract": "Despite the recent advances of deep reinforcement learning (DRL), agents trained by DRL tend to be brittle and sensitive to the training environment, especially in the multi-agent scenarios. In the multi-agent setting, a DRL agent's policy can easily get stuck in a poor local optima w.r.t. its training partners -the learned policy may be only locally optimal to other agents' current policies. In this paper, we focus on the problem of training robust DRL agents with continuous actions in the multi-agent learning setting so that the trained agents can still generalize when its opponents' policies alter. To tackle this problem, we proposed a new algorithm, MiniMax Multi-agent Deep Deterministic Policy Gradient (M3DDPG) with the following contributions: (1) we introduce a minimax extension of the popular multi-agent deep deterministic policy gradient algorithm (MADDPG), for robust policy learning; (2) since the continuous action space leads to computational intractability in our minimax learning objective, we propose Multi-Agent Adversarial Learning (MAAL) to efficiently solve our proposed formulation. We empirically evaluate our M3DDPG algorithm in four mixed cooperative and competitive multi-agent environments and the agents trained by our method significantly outperforms existing baselines.", "id": "76fab1b4b8b39df3b8287b65245c6e3a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Countering Superintelligence Misinformation", "text": "Introduction At present, there is an active scholarly and public debate regarding the future prospect of artificial superintelligence (henceforth just superintelligence), which is artificial intelligence (AI) that is significantly more intelligent than humans in all major respects. While much of the issue remains unsettled, some specific arguments are clearly incorrect, and as such can qualify as misinformation. (As is elaborated below, arguments can qualify as misinformation even when the issues are unsettled.) More generally, misinformation can be defined as \"false or inaccurate information\" [1], or as \"information that is initially presented as true but later found to be false\"  [2]  (p. 1). This paper addresses the question of what can be done to reduce the spread of and belief in superintelligence misinformation. While any misinformation is problematic, superintelligence misinformation is especially worrisome due to the high stakes involved. If built, superintelligence could have transformative consequences, which could be either massively beneficial or catastrophic. Catastrophe is more likely to come from a superintelligence built based on the wrong ideas-and it could also come from not building a superintelligence that would have been based on the right ideas, because a well-designed superintelligence could prevent other types of catastrophe, such that abstaining from building such a superintelligence could result in catastrophe. Thus, the very survival of the human species could depend on avoiding or rejecting superintelligence misinformation. Furthermore, the high stakes of superintelligence have the potential to motivate major efforts to attempt to build it or to prevent others from doing so. Such efforts could include massive investments or restrictive regulations on research and development (R&D), or plausibly even international conflict. It is important for these sorts of efforts to be based on the best available understanding of superintelligence. Superintelligence is also an issue that attracts a substantial amount of misinformation. The abundance of misinformation may be due to the many high-profile portrayals of superintelligence in science fiction, the tendency for popular media to circulate casual comments about superintelligence made by various celebrities, and the relatively low profile of more careful scholarly analyses. Whatever the cause, experts and others often find themselves responding to some common misunderstandings  [3] [4] [5] [6] [7] [8] [9] . There is also potential for superintelligence disinformation: misinformation with the intent to deceive. There is a decades-long history of private industry and anti-regulation ideologues promulgating falsehoods about socio-technological issues in order to avoid government regulations. This practice was pioneered by the tobacco industry in the 1950s and has since been adopted by other industries including fossil fuels and industrial chemicals  [10, 11] . AI is increasingly important for corporate profits and thus could be a new area of anti-regulatory disinformation  [12] . The history of corporate disinformation and the massive amounts of profit potentially at stake suggest that superintelligence disinformation campaigns could be funded at a large scale and could be a major factor in the overall issue. Superintelligence disinformation could potentially come from other sources as well, such as governments or even concerned citizens seeking to steer superintelligence debates and practices in particular directions. Finally, there is the subtler matter of the information that has not yet been established as misinformation, but is nonetheless incorrect. This misinformation is the subject of ongoing scholarly debates. Active superintelligence debates consider whether superintelligence will or will not be built, whether it will or will not be dangerous, and a number of other conflicting possibilities. Clearly, some of these positions are false and thus can qualify as misinformation. For example, claims that superintelligence will be built and that it will not be built cannot both be correct. However, it is not presently known which positions are false, and there is often no expert consensus on which positions are likely to be false. While the concept of misinformation is typically associated with information that is more obviously false, it nonetheless applies to these subtler cases, which can indeed be \"information that is initially presented as true but later found to be false\". Likewise, countering misinformation presents a similar challenge regardless of whether the misinformation is spread before or after expert consensus is reached (though, as discussed below, expert consensus can be an important factor). In practical terms, the question then is what to do about it. There have been a number of attempts to reply to superintelligence misinformation in order to set the record straight  [3] [4] [5] [6] [7] [8] [9] . However, to the best of the present author's knowledge, aside from a brief discussion in  [12] , there have been no efforts to examine the most effective ways of countering superintelligence misinformation. Given the potential importance of the matter, a more careful examination is warranted. That is the purpose of this paper. The paper's discussion is relevant to public debates about superintelligence, to AI education programs (e.g., in university computer science departments), and to efforts to build expert consensus about superintelligence. In the absence of dedicated literature on superintelligence misinformation, this paper draws heavily on the more extensive research literature studying misinformation about other topics, especially global warming (e.g.,  [10, 13, 14] ), as well as the general literature on misinformation in psychology, cognitive science, political science, sociology, and related fields (for reviews, see  [2, 15] ). This paper synthesizes insights from these literatures and applies them to the particular circumstances of superintelligence. The paper is part of a broader effort to develop the social science of superintelligence by leveraging insights from other issues  [12, 16] . The paper is organized as follows. Section 2 presents some examples of superintelligence misinformation, in order to further motivate the overall discussion. Section 3 surveys the major actors and audiences (i.e., the senders and receivers) of superintelligence misinformation, in order to provide some strategic guidance. Section 4 presents several approaches for preventing the spread of superintelligence misinformation. Section 5 presents approaches for countering superintelligence misinformation that has already spread. Section 6 concludes. \n Examples of Superintelligence Misinformation It is often difficult to evaluate which information about superintelligence is false. This is because superintelligence is a possible future technology that may be substantially different from anything that currently exists, and because it is the subject of a relatively small amount of study. For comparison, other studies of misinformation have looked at such matters as whether Barack Obama was born in the United States, whether childhood vaccines cause autism, and whether Listerine prevents colds and sore throats  [17] . In each of these cases, there is clear and compelling evidence pointing in one direction or the other (the evidence clearly indicates that Obama was born in the US, that vaccines do not cause autism, and that Listerine does not prevent colds or sore throats, despite many claims to the contrary in all three cases). Therefore, an extra degree of caution is warranted when considering whether a particular claim about superintelligence qualifies as misinformation. That said, some statements about superintelligence are clearly false. For example, this statement from Steven Pinker: \"As far as I know, there are no projects to build an AGI, not just because it would be commercially dubious, but also because the concept is barely coherent\"  [18] . The acronym AGI stands for artificial general intelligence, which is a form of AI closely associated with superintelligence. Essentially, AGI is AI that is capable of reasoning across a wide range of domains. AGI may be difficult to build, but the concept is very much coherent. Indeed, it has a substantial intellectual history and ongoing study  [19] , including a dedicated research journal (Journal of Artificial General Intelligence) and professional society (the Artificial General Intelligence Society). Furthermore, there are indeed projects to build AGI-one recent survey identifies 45, spread across many countries and institutions, including many for-profit corporations, the largest of which being DeepMind, acquired by Google in 2014 for £400 million, the Human Brain Project, an international project with $1 billion in funding from the European Commission, and OpenAI, a nonprofit with $1 billion in pledged funding  [20] . (DeepMind and OpenAI explicitly identify as working on AGI. The Human Brain Project does not, but it is working on simulating the human brain, which is considered to be a subfield of AGI  [19] .) There is even an AGI project at Pinker's own university. (Pinker and the AGI project MicroPsi  [21]  are both at Harvard University.) Therefore, in the quoted statement, the \"as far as I know\" part may well be true, but the rest is clearly false. This particular point of misinformation is significant because it conveys the false impression that AGI (and superintelligence) is a nonissue, when in fact it is a very real and ongoing subject of R&D. A more controversial matter is the debate on the importance of consciousness to superintelligence. Searle  [22]  argues that computers cannot be conscious and therefore, at least in a sense, cannot be intelligent, and likewise cannot have motivation to destroy humanity. Similar arguments have been made by Logan  [23] , for example. A counterargument is that the important part is not the consciousness a computer but its capacity to affect the world  [4, 24, 25] . It has also been argued that AI could be harmful to humanity even if it is not specifically motivated to do so, because the AI could assess humanity as being in the way of it achieving some other goal  [25, 26] . The fact that AI has already shown the capacity to outperform humans in some domains is suggestive of the possibility for it to outperform humans in a wider range of domains, regardless of whether the AI is conscious. However, this is an ongoing area of debate, and indeed Chalmers  [24]  (p. 16) writes \"I do not think the matter can be regarded as entirely settled\". Regardless, there must be misinformation on one side or the other: computers either can be conscious or they cannot, and consciousness either matters for superintelligence or it does not. Additionally, many parties to the debate maintain that those who believe that consciousness or conscious motivation matter are misinformed  [4, 5, [7] [8] [9] , though it is not the purpose of this paper to referee this debate. There are even subtler debates among experts who believe in the prospect of superintelligence. For example, Bostrom  [25]  worries that it would be difficult to test the safety of a superintelligence because it could trick its human safety testers into believing it is safe (the \"treacherous turn\"), while Goertzel  [27]  proposes that the safety testing for a superintelligence would not be so difficult because the AI could be tested before it becomes superintelligent (the \"sordid stumble\"; the term is from  [28] ). Essentially, Bostrom argues that an AI would become capable of deceiving humans before humans realize it is unsafe, whereas Goertzel argues the opposite. Only one of these views can be correct; the other would qualify as misinformation. More precisely, only one of these views can be correct for a given AI system-it is possible that some AI systems could execute a treacherous turn while others would make a sordid stumble. Which view is more plausible is a matter of ongoing study  [28, 29] . This debate is important because it factors significantly into the riskiness of attempting to build a superintelligence. Many more additional examples could be presented, such as on the dimensionality of intelligence  [3] , the rate of progress in AI  [7, 8] , the structure of AI goals  [6] [7] [8] , and the relationship between human and AI styles of thinking  [6, 8] . However, this is not the space for a detailed survey. Instead, the focus of this paper is on what to do about the misinformation. Likewise, this paper does not wish to take positions on open debates about superintelligence. Some positions may be more compelling, but arguments for or against them are tangential to this paper's aim of reducing the preponderance of misinformation. In other words, this paper strives to be largely neutral on which information about superintelligence happens to be true or false. The above remarks by Pinker will occasionally be used as an example of superintelligence misinformation because they are so clearly false, whereas the falsity of other claims is more ambiguous. The above examples suggest two types of superintelligence misinformation: information that is already clearly false and information that may later be found to be false. In practice, there may be more of a continuum of how clearly true or false a piece of information is. Nonetheless, this distinction can be a useful construct for efforts to address superintelligence misinformation. The clearly false information can be addressed with the same techniques that are used for standard cases of misinformation, such as Obama's place of birth. The not-yet-resolved information requires more careful analysis, including basic research about superintelligence, but it can nonetheless leverage some insights from the misinformation literature. The fact that superintelligence is full of not-yet-resolved information is important in its own right, and it has broader implications for superintelligence misinformation. Specifically, the extent of expert consensus is an important factor in the wider salience of misinformation. This matter is discussed in more detail below. Therefore, while this paper is mainly concerned with the type of misinformation that is clearly false, it will consider both types. With that in mind, the paper now starts to examine strategies for countering superintelligence misinformation. \n Actors and Audiences Some purveyors of superintelligence misinformation can be more consequential than others. Ditto for the audiences for superintelligence misinformation. This is important to bear in mind because it provides strategic direction to any efforts to counter the misinformation. Therefore, this section reviews who the important actors and audiences may be. Among the most important are the R&D groups that may be building superintelligence. While they can be influential sources of ideas about superintelligence, they may be especially important as audiences. For example, if they are misinformed regarding the treacherous turn vs. the sordid stumble, then they could fail to correctly assess the riskiness of their AI system. Also important are the institutions that support the R&D. At present, most AGI R&D groups are based in either for-profit corporations or universities, and some also receive government funding  [20] . Regulatory bodies within these institutions could ensure that R&D projects are proceeding safely, such as via university research review boards  [30, 31] . Successful regulation depends on being well-informed about the nature of AGI and superintelligence and its prospects and risks. The same applies to R&D funding decisions by institutional funders, private donors, and others. Additionally, while governments are not presently major developers of AGI, except indirectly as funders, they could become important developers should they later decide to do so, and they meanwhile can play important roles in regulation and in facilitating discussion across R&D groups. Corporations are of particular note due to their long history of spreading misinformation about their own technologies, in particular to convey the impression that the technologies are safer than they actually are  [10] . These corporate actors often wield enormous resources and have a correspondingly large effect on the overall issue, either directly or by sponsoring industry-aligned think tanks, writers, and other intermediaries. At this time, there are only hints of such behavior by AI corporations, but the profitability of AI and other factors suggest the potential for much more  [12] . Thought leaders on superintelligence are another significant group. In addition to the aforementioned groups, this also includes people working on other aspects of superintelligence, such as safety and policy issues, as well as people working on other (non-superintelligence) forms of AI, and public intellectuals and celebrities. These are all people who can have outsized influence when they comment on superintelligence. That influence can be on the broader public, as well as in quieter conversations with AGI/superintelligence R&D groups, would-be regulators, and other major decision-makers. Finally, there is the lay public. The role of the public in superintelligence may be reduced due to the issue being driven by technology R&D that (for now at least) occurs primarily in the private sector. However, the public can play roles as citizens of governments that might regulate the R&D and as consumers of products of the corporations that host the R&D. The significance of the public for superintelligence is not well established at this time. While the above groups are presented in approximate order of importance, it would not be appropriate to formally rank them. What matters is not the importance of the group but the quality of the opportunity that one has to reduce misinformation. This will tend to vary heavily by the circumstances of whoever is seeking to reduce the extent of superintelligence misinformation. With that in mind, the paper now turns to strategies for reducing superintelligence misinformation. \n Preventing Superintelligence Misinformation The cliché \"an ounce of prevention is worth a pound of cure\" may well be an understatement for misinformation. An extensive empirical literature finds that once misinformation enters into someone's mind, it can be very difficult to remove. Early experiments showed that people can even make use of information that they acknowledge to be false. In these experiments, people were told a story and then were explained that some information in the story is false. When asked, subjects would correctly acknowledge the information to be false, but they would also use it in retelling the story as if it were true. For example, the story could be a fire caused by volatile chemicals, and then it is later explained that there were no volatile chemicals present. Subjects would acknowledge that the volatile chemicals were absent but then cite them as the cause of the fire. This is logically incoherent. The fact that people do this speaks to the cognitive durability that misinformation can have  [32, 33] . The root of the matter appears to be that human memory does not simply write and overwrite like computer memory. Corrected misinformation does not vanish. Ecker et al.  [15]  trace this to the conflicting needs for memory stability and flexibility: Human memory is faced with the conundrum of maintaining stable memory representations (which is the whole point of having a memory in the first place) while also allowing for flexible modulation of memory representations to keep up-to-date with reality. Memory has evolved to achieve both of these aims, and hence it does not work like a blackboard: Outdated things are rarely actually wiped out and over-written; instead, they tend to linger in the background, and access to them is only gradually lost.  [15]   \n (p. 15) There are some techniques for reducing the cognitive salience of misinformation; these are discussed in detail below. However, in many cases, it would be highly desirable to simply avoid the misinformation in the first place. Therefore, this section presents some strategies for preventing superintelligence misinformation. The ideas for preventing superintelligence misinformation are inevitably more speculative than those for correcting it. There are two reasons for this. One is that the correction of misinformation has been the subject of a relatively extensive literature, while the prevention of misinformation has received fairly little scholarly attention. (Rare examples of studies on preventing misinformation are  [34, 35] .) The other reason is that the correction of misinformation is largely cognitive and thus conducive to simple laboratory experiments, whereas the prevention of misinformation is largely sociological and thus requires a more complex and case-specific analysis. Nonetheless, given the importance of preventing superintelligence misinformation, it is important to consider potential strategies for doing so. \n Educate Prominent Voices about Superintelligence Perhaps the most straightforward approach to preventing superintelligence misinformation is to educate people who have prominent voices in discussions about superintelligence. The aim here is to give them a more accurate understanding of superintelligence so that they can pass that along to their respective audiences. Prominent voices about superintelligence can include select scholars, celebrities, or journalists, among others. Educating the prominent may be easier said than done. For starters, they can be difficult to access, due to busy schedules and multitudes of other voices competing for their attention. Additionally, some of them they may already believe superintelligence misinformation, especially those who are already spreading it. Misinformation is difficult to correct in general, and may be even more difficult to correct for busy people who lack the mental attention to revise their thinking. (See Section 5.4 for further discussion of this point.) People already spreading misinformation may seem to be ideal candidates for educational efforts, in order to persuade them to change their tune, but it may actually be more productive to engage with people who have not yet made up their minds. Regardless, there is no universal formula for this sort of engagement, and the best opportunities may often be a matter of particular circumstance. One model that may be of some value is the effort to improve the understanding of global warming among broadcast meteorologists. Broadcast meteorologists are for many people the primary messenger of environmental science. Furthermore, as a group, meteorologists (broadcast and non-broadcast) have traditionally been more skeptical about global warming than most of their peers in other Earth sciences  [36, 37] . In light of this, several efforts have been made to provide broadcast meteorologists with a better understanding of climate science, in hopes that they would pass this on to their audiences (e.g.,  [38, 39] ). The case of broadcast meteorologists has important parallels to the many AI computer scientists who do not specialize in AGI or superintelligence. Both groups have expertise on a topic that is closely related to, but not quite the same as, the topic at hand. Broadcast meteorologists' expertise is weather, whereas global warming is about climate. (Weather concerns the day-to-day fluctuations in meteorological conditions, whereas climate concerns the long-term trends. An important distinction is that while weather can only be forecast a few days in advance, climate can be forecasted years or decades in advance.) Similarly, most AI computer scientists focus on AI that has \"narrow\" intelligence (intelligence in a limited range of domains), not AGI. Additionally, broadcast meteorologists and narrow AI computer scientists are often asked to voice their views on climate change and AGI, respectively. \n Create Reputational Costs for Misinformers When prominent voices cannot be persuaded to change their minds, they can at least be punished for getting it wrong. Legal punishment is possible in select cases (Section 4.5). However, reputational punishment is almost always possible and has potential to be quite effective, especially for public intellectuals whose brands depend on a good intellectual reputation. In an analysis of US healthcare policy debates, Nyhan  [40]  concludes that correcting misinformation is extremely difficult and that increasing reputational costs may be more effective. Nyhan  [40]  identifies misinformation that was critical to two healthcare debates: in the 1990s, the false claim that the policy proposed by President Bill Clinton would prevent people from keeping their current doctors, and in the 2000s, the false claim that the policy proposed by President Barack Obama would have established government \"death panels\" to deny life-sustaining coverage to the elderly. Nyhan  [40]  traces this misinformation to Betsy McCaughey, a scholar and politician generally allied with US conservative politics and opposed to these healthcare policy proposals: \"Until the media stops giving so much attention to misinformers, elites on both sides will often succeed in creating misperceptions, especially among sympathetic partisans. And once such beliefs take hold, few good options exist to counter them-correcting misperceptions is simply too difficult. The most effective approach may therefore be for concerned scholars, citizens, and journalists to (a) create negative publicity for the elites who are promoting misinformation, increasing the costs of making false claims in the public sphere, and (b) pressure the media to stop providing coverage to serial dissemblers\".  [40]  (p. l6) Nyhan  [40]  further notes that while McCaughey's false claims were widely praised in the 1990s, including with a National Magazine Award, they were heavily criticized in the 2000s, damaging her reputation and likely reducing the spread of the misinformation. There is some evidence indicating the possibility that reputational threats can succeed at reducing misinformation. Nyhan and Reifler  [34]  sent a randomized group of US state legislators a series of letters warning them about the reputational and electoral harms that the legislators could face if an independent fact checker (specifically, PolitiFact) finds them to make false statements. The study found that the legislators receiving the warnings were significantly less likely to make false statements. This finding is especially applicable to superintelligence misinformation spread by politicians, whose statements are more likely to be evaluated by fact checker like PolitiFact. Conceivably, similar fact checking systems could be developed for other types of public figures, or even for more low-profile professional discourse such as occurs among scientists and other technical experts. Similarly, Tsipursky and Morford  [41]  and Tsipursky et al.  [35]  describe a Pro-Truth Pledge aimed at committing people to refrain from spreading misinformation and to ask other people to retract misinformation, which can serve as a reputational punishment for misinformers, as well as a reputational benefit for those who present accurate information. Initial evaluations provide at least anecdotal support for the pledge having a positive effect on the information landscape. For superintelligence misinformation, creating reputational costs has potential to be highly effective. A significant portion of influential voices in the debate have scholarly backgrounds and reputations that they likely wish to protect. For example, many of Steven Pinker's remarks about superintelligence are clearly misinformed, including the one discussed in Section 2 and several in his recent book Enlightenment Now  [42] . (For detailed analysis of Enlightenment Now, see Torres  [9] .) Given Pinker's scholarly reputation, it may be productive to spread a message such as 'Steven Pinker is unenlightened about AI'. At the same time, it is important to recognize the potential downsides of imposing reputational costs. Criticizing a person can damage one's relationship with them, reducing other sorts of opportunities. For example, criticizing people who may be building superintelligence could make them less receptive to other efforts to make their work safer. (Or, it could make them more receptive-this can be highly specific to individual personalities and contexts.) Additionally, it can impose reputational costs on the critic, such as a reputation of negativity or of seeking to restrict free speech. Caution is especially warranted for cases in which the misinformation comes from a professional contrarian, who may actually benefit from and relish in the criticism. For example, Marshall  [43]  (p.  [72] [73]  warns climate scientists against debating professional climate deniers, since the latter tend to be more skilled at debate, especially televised debate, even though the arguments of the former are more sound. The same could apply for superintelligence, if it is to ever have a similar class of professional debaters. Thus, the imposition of reputation costs is a strategy to pursue selectively in certain instances of superintelligence misinformation. \n Mobilize against Institutional Misinformation The most likely institutional sources of superintelligence misinformation are the corporations involved in AI R&D, especially R&D for AGI and superintelligence. These companies have a vested interest in cultivating the impression that their technologies are safe and good for the world. For these companies, reputational costs can also be significant. Corporate reputation can be important for consumer interest in the companies' products, citizen and government interest in imposing regulations on the companies, investor expectations of future profits, and employee interest in working for the companies. Therefore, one potential strategy is to incentivize companies so as to align their reputation with accurate information about superintelligence. A helpful point of comparison is to corporate messaging about environmental issues, in particular the distinction between \"greenwashing\" and \"brownwashing\"  [44] . Greenwashing is when a company portrays itself as protecting the environment when it is actually causing much environmental harm. For example, a fossil fuel company may publicize the greenhouse gas emissions reductions from solar panels it installs on its headquarters building while downplaying the fact that its core business model is a major driver of greenhouse gas emissions. In contrast, brownwashing is when a company declines to publicize its efforts towards environmental protection, perhaps because they have customers who oppose environmental protection or investors who worry it reduces profitability. In short, greenwashing is aimed at audiences that value environmental protection, while brownwashing is aimed at audiences that disvalue it. Greenwashing is often criticized for giving companies a better environmental reputation than they deserve. In many cases that criticism may be fair. However, from an environmental communication standpoint, greenwashing does have the benefit of promoting a pro-environmental message. At a minimum, audiences of greenwashing are told that environmental protection is important. Audiences may also be given accurate information about environmental issues-for example, an advertisement that touts a fossil fuel company's greenhouse gas emissions reductions may also correctly explain that global warming is real and is caused by human action. Similarly, there may be value in motivating AI companies to present accurate messages about superintelligence. This could be accomplished by cultivating demand for accurate messages among the companies' audiences. For example, if the public wants to hear accurate messages about superintelligence, then corporate advertising may be designed accordingly. The advertising might overstate the company's positive role, which would be analogous to greenwashing and could likewise be harmful for reducing accountability for bad corporate actors, but even then it would at least be spreading an accurate message about superintelligence. Another strategy is for the employees of AI companies to mobilize against the companies supporting superintelligence misinformation, or against misinformation in general. At present, this may be a particularly promising strategy. There is a notable recent precedent for this in the successful employee action against Google's participation in Project Maven, a defense application of AI  [45] . While not specifically focused on misinformation, this incident demonstrates the potential for employee action to change the practices of AI companies, including when those practices would otherwise be profitable for the company. \n Focus Media Attention on Constructive Debates Public media can inadvertently spread misinformation via the journalistic norm of balance. For the sake of objectivity, journalists often aim to cover \"both sides\" of an issue. While this can be constructive for some issues, it can also spread misinformation. For example, media coverage has often presented \"both sides\" of the \"debate\" over whether tobacco causes cancer or whether human activity causes global warming, even when one side is clearly correct and the other side has a clear conflict of interest  [10, 13] . One potential response for this is to attempt to focus media attention on legitimate open questions about a given issue, questions for which there are two meaningful sides to cover. For global warming, this could be a debate over the appropriate role of nuclear power or the merits of carbon taxes. For superintelligence, it could be a debate over the appropriate role of government regulations, or over the values that superintelligence (or AI in general) should be designed to promote. These sorts of debates satisfy the journalistic interest in covering two sides of an issue and provide a dramatic tension that can make for a better story, all while drawing attention to important open questions and affirming basic information about the topic. \n Establish Legal Requirements Finally, there may be some potential to legally require certain actors, especially corporations, to refrain from spreading misinformation. A notable precedent is the court decision of United States v. Philip Morris, in which nine tobacco companies and two tobacco trade organizations were found guilty of conspiring to deceive the public about the link between tobacco and cancer. Such legal decisions can have powerful effect. However, legal requirements may be poorly suited to superintelligence misinformation. First, legal requirements can be slow to develop. The court case United States v. Philip Morris began in 1999, an initial ruling was reached in 2006, and that ruling was upheld in 2009. Furthermore, United States v. Philip Morris came only after several decades of tobacco industry misinformation. Given the evolving nature of AI technology, it could be difficult to pin down which information is correct over such long time periods. Second, superintelligence is a future technology for which much of the correct information cannot be established with the same degree of rigor. Furthermore, if and when superintelligence is built, it could be so transformative as to render current legal systems irrelevant. (For more general discussion of the applicability of legal mechanisms to superintelligence, see  [46] [47] [48] .) For these reasons, legal requirements are less likely to play a significant role in preventing superintelligence misinformation. \n Correcting Superintelligence Misinformation Correcting misinformation is sufficiently difficult that it will often be better to prevent it from spreading in the first place. However, when superintelligence misinformation cannot be prevented, there are strategies available for correcting it in the minds of those who are exposed to it. Correcting misinformation is the subject of a fairly extensive literature in psychology, political science, and related fields  [2, 15, 33, 49] . For readers unfamiliar with this literature, Cook et al.  [2]  provide an introductory overview accessible to an interdisciplinary readership, while Ecker et al.  [15]  provide a more detailed and technical survey. This section applies this literature to the correction of superintelligence misinformation. \n Build Expert Consensus and the Perception Thereof At present, there exists substantial expert disagreement about a wide range of aspects of superintelligence, from basic matters such as whether superintelligence is possible  [50] [51] [52]  and when it might occur if it does  [53] [54] [55]  to subtler matters such as the treacherous turn vs. the sordid stumble. The situation stands in contrast to the extensive expert consensus on other issues such as global warming  [56] . (Experts lack consensus on some important details about global warming, such as how severe the damage is likely to be, but they have a high degree of consensus on the basic contours of the issue.). The case of global warming shows that expert consensus on its own does not counteract misinformation. On the contrary, misinformation about global warming continues to thrive despite the existence of consensus. However, there is reason to believe that the consensus helps. For starters, much of the misinformation is specifically oriented towards creating the false perception that there is no consensus  [10] . The scientific consensus is a target of misinformation because it is believed to be an important factor in people's overall beliefs. Indeed, several studies have documented a strong correlation among the lay public between rejection of the science of global warming and belief that there is no consensus  [57, 58] . Further studies find that presenting messages describing the consensus increases belief in climate science and support for policy to reduce greenhouse gas emissions  [14, 59] . Notably, this effect is observed for people across the political spectrum, including those who would have political motivation to doubt the science. (Such motivations are discussed further in Section 5.2.) All of this indicates an important role for expert consensus in broader beliefs about global warming. For superintelligence, at present there is no need to spread misinformation about the existence of consensus because there is rather little consensus. Therefore, a first step is to work towards consensus. (This of course should be consensus grounded on the best possible analysis, not consensus for the sake of consensus.) This may be difficult for superintelligence because of the inherent challenge of understanding future technologies and the complexity of advanced AI. Global warming has its own complexities, but the core science is relatively simple: increased atmospheric greenhouse gas concentrations trap sunlight and raise temperatures. However, at least some aspects of superintelligence should be easy enough to get consensus on, starting with the fact that there are a number of R&D groups attempting to build AGI. Other aspects may be more difficult to build consensus on, but this consensus is at least something that can be pursued via normal channels of expert communication: research articles, conference symposia, private correspondence, and so on. Given the existence of consensus, it is also important to raise awareness about it. The consensus cannot counteract misinformation if nobody knows about it. The global warming literature provides good models for documenting expert consensus  [56] , and such findings of consensus can be likewise be publicized. \n Address Pre-Existing Motivations for Believing Misinformation The human mind tends to not process new information in isolation, but instead processes it in relation to wider beliefs and understandings of the world. This can be very valuable, enabling us to understand the context behind new information and relate it to existing knowledge. For example, people would typically react with surprise and confusion upon seeing an object rise up to the ceiling instead of fall down to the floor. This new information is related to a wider understanding of the fact that objects fall downwards. People may even struggle to believe their own eyes unless there is a compelling explanation. (For example, perhaps the object and the ceiling are both magnetized.). Additionally, if people did not see it with their own eyes, but instead heard it reported by someone else, they may be even less likely to believe it. In other words, they are motivated to believe that the story is false, even if it is true. This phenomenon is known as motivated reasoning. While generally useful, motivated reasoning can be counterproductive in the context of misinformation, prompting people to selectively believe misinformation over correct information. This occurs in particular when the misinformation accords better with preexisting beliefs than the correct information. In the above example, misinformation could be that the object fell down to the floor instead of rising to the ceiling. Motivated reasoning is a major factor in the belief of misinformation about politically contentious issues such as climate change. The climate science consensus is rejected mainly by people who believe that government regulation of industry is generally a bad thing  [14, 59] . In principle, belief that humans are warming the planet should have nothing to do with belief that government regulations are harmful. It is logically coherent to believe in global warming yet argue that carbon emissions should not be regulated. However, in practice, the science of global warming often threatens people's wider beliefs about regulations, and so they find themselves motivated to reject the science. Motivated reasoning can also be a powerful factor for beliefs about superintelligence. A basic worldview is that humans are in control. Per this worldview, human technology is a tool; the idea that it could rise up against humanity is a trope for science fiction, not something to be taken seriously. The prospect of superintelligence threatens this worldview, predisposing people to not take superintelligence seriously. In this context, it may not help that media portrayals of the scholarly debate about superintelligence commonly include reference to science fiction, such as by using pictures of the Terminator. As one expert who is concerned about superintelligence states, \"I think that at this point all of us on all sides of this issue are annoyed with the journalists who insist on putting a picture of the Terminator on every single article they publish of this topic\"  [60] . Motivated reasoning has been found to be linked to people's sense of self-worth. As one study puts it, \"the need for self-integrity-to see oneself as good, virtuous, and efficacious-is a basic human motivation\"  [61]  (p. 415). When correct information threatens people's self-worth, they are more motivated to instead believe misinformation, so as to preserve their self-worth. Furthermore, motivated reasoning can be reduced by having people consciously reaffirm their own self-worth, such as by recalling to themselves ways in which they successfully live up to their personal values  [61] . Essentially, with their sense of self-worth firmed up, they become more receptive to information that would otherwise threaten their self-worth. As a technology that could outperform humans, superintelligence could pose an especially pronounced threat to people's sense of self-worth. It may be difficult for people to feel good and efficacious if they would soon be superseded by computers. For at least some people, this could be a significant reason to reject information about the prospect of superintelligence, even if that information is true. At the same time, it may still be valuable for messages about superintelligence to be paired with messages of affirmation. Another important set of motivations comes from the people active in superintelligence debates. Many people in the broader computer science field of AI have been skeptical of claims about superintelligence. These people may be motivated by a desire to protect the reputation and funding of the field of AI, and in turn protect their self-worth as AI researchers. AI has a long history of boom-bust cycles in which hype about superintelligence and related advanced AI falls flat and contributes to an \"AI winter\". Peter Bentley, an AI computer scientist who has spoken out against contemporary claims about superintelligence, is explicit about this: \"Large claims lead to big publicity, which leads to big investment, and new regulations. And then the inevitable reality hits home. AI does not live up to the hype. The investment dries up. The regulation stifles innovation. And AI becomes a dirty phrase that no-one dares speak. Another AI Winter destroys progress\"  [62]  (p. 10). \"Do not be fearful of AI-marvel at the persistence and skill of those human specialists who are dedicating their lives to help create it. And appreciate that AI is helping to improve our lives every day\" (p. 11). While someone's internal motivations can only be inferred from such text, the text is at least suggestive of motivations to protect self-worth and livelihood as an AI researcher, as well as a worldview in which AI is a positive force for society. To take another example, Torres  [9]  proposes that Pinker's dismissal of AGI and superintelligence is motivated by Pinker's interest in promoting a narrative in which science and technology bring progress-a narrative that could be threatened by the potential catastrophic risk from superintelligence. Conversely, some people involved in superintelligence debates may be motivated to believe in the prospect of superintelligence. For example, researcher Jürgen Schmidhuber writes on his website that \"since age 15 or so, the main goal of professor Jürgen Schmidhuber has been to build a self-improving Artificial Intelligence (AI) smarter than himself, then retire.\"  [63]  Superintelligence is also sometimes considered the \"grand dream\" of AI  [64] . Other common motivations include a deep interest in transformative future outcomes  [65]  and a deep concern about extreme catastrophic risks  [4, 66, 67] . People with these worldviews may be predisposed to believe certain types of claims about superintelligence. If it turns out that superintelligence will not be built, or would not have transformative or catastrophic effects, then this can undercut people's deeply held beliefs in the importance of superintelligence, transformative futures, and/or catastrophic risks. For each of these motivations for interest in superintelligence, there can be information that is rejected because it cuts against the motivations and misinformation that is accepted because it supports the motivations. Therefore, in order to advance superintelligence debates, it can be valuable to affirm people's motivations when presenting conflicting information. For example, one could affirm that AI computer scientists are making impressive and important contributions to the world, and then explain reasons why superintelligence may nonetheless be a possibility worth considering. One could affirm that science and technology are bringing a great deal of progress, and then explain reasons why some technologies could nonetheless be dangerous. One could affirm that superintelligence is indeed a worthy dream, or that transformative futures are indeed important to pay attention to, and then explain reasons why superintelligence might not be built. Finally, one could affirm that extreme catastrophic risks are indeed an important priority for human society, and then explain reasons why superintelligence may not be such a large risk after all. These affirming messaging strategies could predispose participants in superintelligence debates to consider a wider range of possibilities and make more progress on the issue, including progress towards expert consensus. Another strategy is to align motivations with accurate beliefs about superintelligence. For example, some AI computer scientists may worry that belief in the possibility of superintelligence could damage reputation and funding. However, if belief in the possibility of superintelligence would bring reputational and funding benefits, then the same people may be more comfortable expressing such belief. Reputational benefits could be created, for example, via slots in high-profile conferences and journals, or by association with a critical mass of reputable computer scientists who also believe in the possibility of superintelligence. Funding could likewise be made available. Noting that funding and space in conferences and journals are often scarce resources, it could be advantageous to target these resources at least in part toward shifting motivations of important actors in superintelligence debates. This example of course assumes that it is correct to believe in the possibility of superintelligence. The same general strategy of aligning motivations may likewise be feasible for other beliefs about superintelligence. The above examples-concerning the reputations and funding of AI computer scientists, the possibility of building superintelligence, and the importance of transformative futures and catastrophic risks-all involve experts or other communities that are relatively attentive to the prospect of superintelligence. Other motivations could be significant for the lay public, policy makers, and other important actors. Research on the public understanding of science finds that cultural factors, such as political ideology, can factor significantly in the interpretation of scientific information  [68, 69] . Kahan et al.  [69]  (p. 79) propose to \"shield\" scientific evidence and related information \"from antagonistic cultural information\". For superintelligence, this could mean attempting to frame superintelligence (or, more generally, AI) as a nonpartisan social issue. At least in the US, if an issue becomes politically partisan, legislation typically becomes substantially more difficult to pass. Likewise, discussions of AI and superintelligence should, where reasonably feasible, attempt to avoid close association with polarizing ideologies and cultural divisions. The fact that early US legislation on AI has been bipartisan is encouraging. For example, H.R.4625, FUTURE of Artificial Intelligence Act of 2017, sponsored by John Delaney (Democrat) and co-sponsored by Pete Olson (Republican), and H.R.5356, National Security Commission Artificial Intelligence Act of 2018, sponsored by Elise Stefanik (Republican) and co-sponsored by James Langevin (Democrat). This is a trend that should be praised and encouraged to continue. \n Inoculate with Advance Warnings The misinformation literature has developed the concept of inoculation, in which people are preemptively educated about a piece of misinformation so that they will not believe it if and when they later hear it. For example, someone might be told that there is a false rumor that vaccines cause autism, such that when they later hear the rumor, they know to recognize it as false. The aim is to get people to correctly understand the truth about a piece of misinformation from the beginning, so that their minds never falsely encode it. Inoculation has been found to work better than simply telling people the correct information  [70] . Inoculation messages can include why a piece of misinformation is incorrect as well as why it is being spread  [71] . For example, misinformation casting doubt on the idea that global temperatures are rising could be inoculated with an explanation of how scientists have established that global temperatures are rising. The inoculation could also explain that industries are intentionally casting doubt about global temperature increases in order to avoid regulations and increase profits. Likewise, for superintelligence, misinformation claiming that there are no projects seeking to build AGI could be inoculated by explanations of the existence of AGI R&D projects, and perhaps also explanations of the motivations of people who claim that there are no such projects. For example, Torres  [9]  proposes that Pinker's dismissal of AGI and superintelligence is motivated by Pinker's interest in promoting a narrative in which science and technology bring progress-a narrative that could be threatened by the potential catastrophic risk from superintelligence. \n Explain Misinformation and Corrections When people are exposed to misinformation, it can be difficult to correct, as first explained in Section 4. This phenomenon has been studied in great depth, with the terms \"continued influence\" and \"belief perseverance\" used for cases in which debunked information continues to influence people's thinking  [72, 73] . There is also an \"illusion of truth\", in which information explained to be false is later misremembered as true-essentially, the mind remembers the information but forgets its falsity  [74] . The difficulty of correcting misinformation is why this paper has emphasized strategies to prevent of misinformation from spreading in the first place. Adding to the challenge is the fact that attempts to debunk misinformation can inadvertently reinforce it. This phenomenon is known as the \"backfire effect\"  [74] . Essentially, when someone hears \"X is false\", it can strengthen their mental representation of X, thereby reinforcing the misinformation. This effect has been found to be especially pronounced among the elderly  [74] . One explanation is that correcting the misinformation (i.e., successfully processing \"X is false\") requires the use of strategic memory, but strategic memory requires dedicated mental effort and is less efficient among the elderly  [15] . Unless enough strategic memory is allocated to processing \"X is false\", the statement can end up reinforcing belief in X. These findings about the backfire effect have important consequences for superintelligence misinformation. Fortunately, many important audiences for superintelligence misinformation are likely to have strong strategic memories. Among the prominent actors in superintelligence debates, relatively few are elderly, and many of them have intellectual pedigrees that may endow them with strong strategic memories. On the other hand, many of the prominent actors are busy people with limited mental energy available for processing corrections about superintelligence information. As a practical matter, people attempting to debunk superintelligence misinformation should generally avoid \"X is false\" messages, especially when their audience may be paying limited attention. One technique that has been particularly successful at correcting misinformation is the use of refutational text, which provides detailed explanations of why the misinformation is incorrect, what the correct information is, and why it is correct. Refutational text has been used mainly as a classroom tool for helping students overcome false preexisting beliefs about course topics  [75, 76] . Refutational text has even been used to turn misinformation into a valuable teaching tool  [77] . A meta-analysis found refutational text to be the most effective technique for correcting misinformation in the context of science education-that is, for enabling students to overcome preexisting misconceptions about science topics  [78] . A drawback of refutational text is that it can require more effort and attention than simpler techniques. Refutational text may be a valuable option in classrooms or other settings in which one has an audience's extended attention. Such settings include many venues of scholarly communication, which can be important for superintelligence debates. However, refutational texts may be less viable in other settings, such as social media and television news program interviews, in which one can often only get in a short sound bite. Therefore, refutational text may be relatively well-suited for interactions with experts and other highly engaged participants in superintelligence debates, and relatively poorly suited for much of the lay public and others who may only hear occasional passing comments about superintelligence. That said, it may still be worth producing and disseminating extended refutations for lay public audiences, such as in long-format videos and articles for television, magazines, and online. These may tend to only reach the most motivated segments of the lay public, but they can nonetheless be worthwhile. \n Conclusions Superintelligence is a high-stakes potential future technology as well as a highly contested socio-technological issue. It is also fertile terrain for misinformation. Making progress on the issue requires identifying and rejecting misinformation and accepting accurate information. Some progress will require technical research to clarify the nature of superintelligence. However, a lot of progress will likely also require the sorts of sociological and psychological strategies outlined in this paper. The most progress may come from interdisciplinary projects connecting computer science, social science, and other relevant fields. Computer science is a highly technical field, but as with all fields, it is ultimately composed of human beings. By appreciating the nuances of the human dimensions of the field, it may be possible to make better progress towards understanding superintelligence and acting responsibly about it. As the first dedicated study of strategies for countering superintelligence misinformation, this paper has taken a broad view, surveying a range of options. Despite this breadth, there may still be additional options worth further attention. Indeed, this paper has only mined a portion of the insights contained within the existing literature on misinformation. There may also be compelling options that go beyond the literature. Likewise, because of this paper's breadth, it has given relatively shallow treatment to each of the options. More detailed attention to the various option would be another worthy focus of future research. An especially valuable focus would be the proposed strategies for preventing superintelligence misinformation. Because misinformation can be so difficult to correct, preventing it may be the more effective strategy. There is also less prior research on the prevention of misinformation. For these reasons, there is likely to be an abundance of important research opportunities on the prevention of misinformation, certainly for superintelligence misinformation and perhaps also for misinformation in general. For the prevention of superintelligence misinformation, a strategy that may be particularly important to study further is dissuading AI corporations from using their substantial resources to spread superintelligence misinformation. The long history of corporations engaging in such tactics, with a major impact on the surrounding debates, suggests that this could be a highly important factor for superintelligence  [12] . It may be especially valuable to study this at an early stage, before such tactics are adopted. For the correction of superintelligence misinformation, a particularly promising direction is on the motivations and worldviews of prominent actors and audiences in superintelligence debates. Essentially, what are people's motivations with respect to superintelligence? Are AI experts indeed motivated to protect their field? Are superintelligence developers motivated by the \"grand dream\"? Are others who believe in the prospect of superintelligence motivated by beliefs about transformative futures or catastrophic risks? Can attention to these sorts of motivations help them overcome their divergent worldviews and make progress towards consensus on the topic? Finally, are people in general motivated to retain their sense of self-worth in the face of a technology that could render them inferior? Most important, however, is not the research on superintelligence misinformation, but the efforts to prevent and correct it. It can often be stressful and thankless work, especially amidst the heated debates, but it is essential to ensuring positive outcomes. This paper is one effort towards helping this work succeed. Given the exceptionally high potential stakes, it is vital that decisions about superintelligence be well-informed.", "date_published": "n/a", "url": "n/a", "filename": "information-09-00244.tei.xml", "abstract": "Superintelligence is a potential type of future artificial intelligence (AI) that is significantly more intelligent than humans in all major respects. If built, superintelligence could be a transformative event, with potential consequences that are massively beneficial or catastrophic. Meanwhile, the prospect of superintelligence is the subject of major ongoing debate, which includes a significant amount of misinformation. Superintelligence misinformation is potentially dangerous, ultimately leading bad decisions by the would-be developers of superintelligence and those who influence them. This paper surveys strategies to counter superintelligence misinformation. Two types of strategies are examined: strategies to prevent the spread of superintelligence misinformation and strategies to correct it after it has spread. In general, misinformation can be difficult to correct, suggesting a high value of strategies to prevent it. This paper is the first extended study of superintelligence misinformation. It draws heavily on the study of misinformation in psychology, political science, and related fields, especially misinformation about global warming. The strategies proposed can be applied to lay public attention to superintelligence, AI education programs, and efforts to build expert consensus.", "id": "e62d65c22ec2094803f54a3cda0f0b50"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dmitrii Krasheninnikov", "Rohin Shah", "U C Berkeley"], "title": "Combining reward information from multiple sources", "text": "Introduction While deep reinforcement learning (RL) has led to considerable success when given an accurate reward function  [28, 21] , specifying a reward function that captures human preferences in real-world tasks is challenging  [1, 6] . Value learning seeks to sidestep this difficulty by learning rewards from various types of data, such as natural language  [22] , demonstrations  [33, 11] , comparisons  [6] , ratings  [7] , human reinforcement  [18] , proxy rewards  [13] , the state of the world  [27] , etc. Many approaches to value learning aim to create a distribution over reward functions  [14, 23, 24, 13] .  A natural idea is to combine the information from these diverse sources. However, the sources may conflict. For example, in Figure  1 , Alice might say that she wants the healthy avocado toast, but empirically she almost always chooses to eat the tasty cake. A reward learning method based on natural language may confidently infer that Alice would prefer the toast, whereas a method based on revealed preferences  [25]  might confidently infer that she wants cake. Presumably one of the algorithms made a poor assumption: perhaps the natural language algorithm failed to model that Alice only said that she wants avocado toast to impress her friends. Alternatively, maybe Alice wants to start eating healthy, but chooses the cake in moments of weakness, and the revealed preferences algorithm failed to model this bias. While it is unclear what the \"true\" reward is, we do know that at least one of the methods is confidently wrong. We would like to defer on the question of what the \"true\" reward is, and instead retreat to a position of uncertainty. Formally, we want a distribution over the true reward function θ * given the inferred rewards θ 1 , θ 2 . We could apply Bayes Rule: p(θ * | θ 1 , θ 2 ) ∝ p(θ * )p( θ 1 | θ * )p( θ 2 | θ * ). However, when rewards conflict due to misspecification, one of the likelihoods will be very low, and the posterior will be low everywhere, likely leading to garbage after normalization  [10] . While it is possible to mitigate this by making the assumptions more realistic, e.g. by modeling human biases  [26, 19, 9] , it is very hard to get a perfect model  [3, 29] . So, we aim for a method that is robust to misspecification. What makes for a good reward combination method? To answer this question, we must know how the resulting distribution will be used. As in Hadfield-Menell et al.  [14] , we assume that an agent maximizes expected reward, given that the agent can gather more information about the reward. In this framework, an agent must balance three concerns: actively learning about the reward  [24, 20] , preserving its ability to pursue the true reward in the future when it knows more  [30, 17] , and acting to gain immediate reward. Each concern suggests different desiderata for a reward combination method, which we formalize for rewards functions that are linear in features of the state. There are several reasonable methods for combining reward functions based on the intuition that we should put weight on any parameter values \"in between\" the parameters of the given reward functions. These reward-space methods operate in the space of parameters of the reward. However, this ignores any details about the environment and its features. We introduce a method called Multitask Inverse Reward Design (MIRD) that leverages the environment to infer which reward functions are compatible with the behaviors \"in between\" the behaviors incentivized by the two input rewards, making it a behavior-space method. Through a combination of theory and empirical results on a simple environment, we evaluate how well the proposed methods meet our desiderata, and conclude that MIRD is a good option when the reward distribution must be used to act, while its variant MIRD-IF is better for increased robustness and a higher chance of support on the true reward. \n Background Markov Decision Process (MDP). A MDP M is a tuple M = S, A, T , r, H , where S is the set of states, A is the set of actions, T : S × A × S → [0, 1] is the transition probability function, r : S → R is the reward function, and H ∈ Z + is the finite planning horizon. We consider MDPs where the reward is linear in features, and does not depend on action: r(s; θ) = θ T f (s), where θ are the parameters defining the reward function and f computes features of a given state. A policy π : S → A specifies how to act in the MDP. A trajectory τ : (S × A) * is a sequence of states and actions, where the actions are sampled from a policy π and the states are sampled from the transition function T . We abuse notation and write f (τ ) to denote s∈τ f (s). The feature expectations (FE) of policy π are the expected feature counts when acting according to π: F π = E τ ∼π [f (τ )]. The value of a policy π is given by V π = E τ ∼π [ s∈τ r(s; θ)] = θ T F π . The optimal policy is π * = max π V π . Reward learning by simulating the past (RLSP). Shah et al.  [27]  note that environments where humans have acted are already optimized for human preferences, and so contain reward information. The RLSP algorithm considers the current state s 0 as the final state in a human trajectory τ = (s −H , a −H , ..., s 0 , a 0 ) generated by the human with preferences θ. The RLSP likelihood p(θ | s 0 ) is obtained by marginalizing out (s −H , a −H , . . . s −1 , a −1 , a 0 ), since only s 0 is actually observed. Inverse Reward Design (IRD). Inverse reward design (IRD) notes that since reward designers often produce rewards by checking what the reward does in the training environment using an iterative trial-and-error process, the final reward they produce is likely to produce good behavior in the environments that they used during the reward design process. So, θ need not be identical to θ * , but merely provides evidence about it. Formally, IRD assumes that the probability of specifying a given θ is proportional to the exponent of the expected true return in the training environment: p( θ | θ * ) ∝ exp(θ * F π θ ). IRD inverts this generative model of reward design to sample from the posterior of the true reward: p(θ * | θ) ∝ p( θ | θ * )p(θ * ). \n Uses of the reward distribution So far, we have argued that we would like to combine the information from two different sources into a single distribution over reward functions. But what makes such a distribution good? We take a pragmatic approach: we identify downstream tasks for such a distribution, find desiderata for a reward distribution for these tasks, and use these desiderata to guide our search for methods. \n Optimizing the reward We follow the framework of Hadfield-Menell et al.  [14]  in which an agent maximizes expected return under reward uncertainty. In this setting, maximizing the return causes the agent to use its actions both to obtain (expected) reward, and to gather information about the true reward in order to better obtain reward in the future  [14, 31] . We might expect that an agent could first learn the reward and then act; however, this is unrealistic: we would be unhappy with a household robot that had to learn how we want walls to be painted before it would bake a cake. The agent must act given reward uncertainty, but maintain its ability to optimize any of the potential rewards in the future when it will know more about the reward. Put simply, it needs to preserve its option value while still obtaining as much reward as it can currently get. We would like to evaluate our reward distribution by plugging it into an algorithm that maximizes expected reward given reward uncertainty, but unfortunately current methods  [14, 31]  are computationally expensive and only work in environments where option value preservation is not a concern. So, we analyze reward learning and option value preservation separately. Active reward learning. An agent that learns rewards while acting will need to select queries with care. Active reward learning aims to pick queries that maximize the information gained about the reward, or minimize the expected regret  [24, 20]  3 . We analyse how the reward distributions resulting from different reward combination methods fit as priors for the active reward learning methods. Option-value preservation. Low impact agents  [30, 17, 2]  take fewer irreversible actions, and so preserve their ability to optimize multiple reward functions. However, work in this area does not consider the possibility of learning more information about the reward function, and so these methods penalize entire plans that would have a high impact. In contrast, we would like our agent to pursue impactful plans, but pause when option value would be destroyed, and get more reward information. For our purposes, we start with the attainable utility preservation (AUP) method introduced by Turner et al.  [30] . AUP formalizes the impact of an action on a reward function as the change in the Q-value as a result of taking that action (relative to a no-op action ∅). For our purposes, we only care about cases where we are no longer able to optimize the reward function, as opposed to ones where we are better able to optimize the reward function. So, we use the truncated difference summary function proposed by Krakovna et al.  [17]  that only counts decreases in Q-values and not increases: Impact(s, a) = E r [max(Q r (s, ∅) − Q r (s, a), 0)]. (1) Turner et al.  [30]  penalize the agent whenever it would cause too much impact, using a hyperparameter λ to trade off task reward with impact. They plan using the reward R task − λ Impact(s, a). However, by penalizing impact in the reward function, the agent is penalized for any plan that would cause impact, whereas we want our agent to start on potentially impactful plans, but stop once a particular action would destroy option value. So, we only penalize impact during action selection: π(s) = max a (Q(s, a) − λ Impact(s, a)). (2) \n Acting in a new environment Often, we wish to use the reward function in the same environment as the one in which it was specified or inferred. For example, a human expert may have demonstrated how to bake a cake in a particular kitchen. Since we know at training time that the agent will be deployed in the same kitchen, the only guarantee we need is that the agent's behavior is correct. If two rewards lead to the same behavior in this kitchen, we don't care which one we end up using. However, we may instead want to apply a reward function learned in one environment to a different environment. In this case, there may be new options in the test environment that we never saw during training. As a result, even if two rewards led to identical behavior in the training environment, they need not do so in the test environment. Hence when the goal is to transfer the reward distribution to a new environment, it is crucial to ensure that the distribution contains the true reward, instead of just containing a reward that gives rise to the same behavior as the true one in the training environment. \n Desiderata for the reward posterior We discuss properties of the posterior that inform the choice of a reward combination algorithm for different applications of the resulting reward distribution. We focus on two applications: option-value preserving planning and active reward learning. \n Desired properties for any subsequent application All else equal, we want the true reward to have high probability in the reward distribution. One model for misspecification is that the weight for each feature has some chance of being \"corrupted\", and the chance of the feature being corrupted in one reward is independent from that of the other reward. If the fraction of misspecified values is small, then if two reward vectors' values are different at a particular index, it is likely that one of the values is correct. Given this, it is desirable for the reward distribution to assign significant probability to every reward function s.t. the value of the weight for each feature is in one of the values of that feature's weight of the input rewards. Formally, we denote the set of such reward parameters Θ indep pts = {θ ∈ R n | θ i ∈ { θ 1 i , θ 2 i } ∀i ∈ {1, ..., n}}. (3) Desideratum 1 (Support on Θ indep pts ). All θ * ∈ Θ indep pts should be in the support of p(θ * | θ 1 , θ 2 ). Note that when we do not need to transfer the reward function to a new environment, Desideratum 1 can be made weaker. We only require that the distribution have support on reward functions that give rise to the same behavior as the rewards in Θ indep pts , and not necessarily on Θ indep pts itself. In order for the agent to act, the reward distribution must provide information about useful behavior: Desideratum 2 (Informative about desirable behavior). If θ 1 and θ 2 give rise to the same behavior, most of the reward functions in the distribution should give rise to this behavior. The strong version of this desideratum states that if the FEs of { θ 1 , θ 2 } are equal on some feature, the FEs of this feature of any reward in the support of the posterior are equal to those of { θ 1 , θ 2 }: ∀i ∈ {1, n} : F π θ 1 i = F π θ 2 i =⇒ ∀θ * ∈ supp(p(θ * | θ 1 , θ 2 )) : F π θ * i = F π θ 1 i = F π θ 2 i . (4) The medium version considers the FEs as a whole instead of per-feature: F π θ 1 = F π θ 2 =⇒ ∀θ * ∈ supp(p(θ * | θ 1 , θ 2 )) : F π θ * = F π θ 1 = F π θ 2 . ( 5 ) The weak version assumes that the FEs of all θ ∈ Θ indep pts are the same, rather than just θ 1 and θ 2 : ∀θ ∈ Θ indep pts : F π θ = F π θ 1 = F π θ 2 =⇒ ∀θ * ∈ supp(p(θ * | θ 1 , θ 2 )) : F π θ * = F π θ 1 . (6) Des. 2 allows option-value preserving planning to do useful things instead of performing the no-op action all the time. Furthermore, by restricting possible behaviors, Des. 2 simplifies the job of approaches that actively learn the reward function. If the reward distribution used by our household robot always incentivizes using soap while washing dishes (because both input rewards did so), the robot's active learning algorithm does not need to query the human about whether or not to use soap. Des. 2 might be problematic if both input rewards agree on an undesirable behavior w.r.t. a particular feature. This presents a natural tradeoff between informativeness and the abilities to preserve option value and actively learn arbitrary reward functions: the more informative we assume the input rewards are about the desired behavior, the less robust we are to their misspecification. \n Desired properties for option value preservation Suppose we would like to preserve the option value of pursuing two different behaviors. Option-value preservation is more robust when the distribution over FEs induced by the reward distribution places significant and approximately equal weight on the two behaviors. Intuitively, the \"weight\" AUP puts on preserving expected return attainable by a particular behavior is proportional to the probability of that behavior in the reward distribution. So we would like the FEs of the input rewards to be balanced across the reward distribution. Concretely: Desideratum 3 (Behavior-space balance). The FEs of the rewards sampled from the distribution should correspond to behaviors arising from the input reward functions with a similar frequency: p(F π θ = F π θ 1 ) ≈ p(F π θ = F π θ 2 ) | θ ∼ p(θ | θ 1 , θ 2 ). (7) \n Desired properties for active reward learning Given a reward vector we define the tradeoff point between the i-th and j-th features of the state as the ratio between the reward vector values corresponding to these features: T θ i,j = θi θj . The true reward's tradeoff point may be in between the tradeoff points of the input rewards, and so we would like our distribution to support all such tradeoff points. Desideratum 4 (Support on intermediate feature tradeoffs). The reward posterior should have support on rewards that prescribe all intermediate tradeoff points between the states' features. In practice tradeoff points only affect the behavior to the extent allowed by the environment. We only need to maintain all intermediate tradeoff points if we want to transfer to a new environment. \n Multitask Inverse Reward Design Inspired by Inverse Reward Design  [13] , we introduce a reward combination method Multitask Inverse Reward Design (MIRD). We assume that the two input rewards meet the IRD assumption for two different rewards, namely that the input rewards generate nearly optimal behavior in the training environment according to the corresponding task rewards. A straightforward way to construct the distribution for the combined reward function is to require the FEs of the rewards in the distribution to be convex combinations of the FEs of the input rewards: F π θ * ∈ {bF π θ 1 + (1 − b)F π θ 2 | b ∈ [0, 1]}. To satisfy this requirement, we propose a distribution that depends on the behavior (set of trajectories) D = {τ 1 , ..., τ d } resulting from the agents optimizing θ 1 and θ 2 : p(θ * | θ 1 , θ 2 ) = D p(θ * | D)p(D | θ 1 , θ 2 ) dD (8) Each of the reward functions {θ i | i = {1, ..., d}} used to generate the trajectories τ i in D is sampled from the Bernoulli mixture over the input reward functions. We introduce a random variable b ∈ [0, 1] that determines the probability of sampling θ i = θ 1 to generate the trajectory τ i : p(D | θ 1 , θ 2 ) = b Beta(b | β 1 , β 2 ) n i=1 bp(τ i | θ 1 ) + (1 − b)p(τ i | θ 2 ) db (9) We sample from p(τ i | θ i ) using policies arising from soft value iteration. For p(θ * | D), we set θ * to the reward learned by Maximum Causal Entropy Inverse RL (MCEIRL)  [33] . Denoting the Dirac delta as δ(), we have p(θ * | D) = δ(θ * − argmax θ p(θ | D)). Having defined all relevant conditional distributions, we can sample from the joint p(θ * , b, D, θ i | θ 1 , θ 2 ) and the marginal p(θ * | θ 1 , θ 2 ). Theorem 1. The FEs arising from rewards θ * in the support of the MIRD posterior are convex combinations of FEs of the input reward vectors θ 1 and θ 2 : ∀θ * ∈ supp(p(θ * | θ 1 , θ 2 )) : F π θ * = αF π θ 1 + (1 − α)F π θ 2 , α ∈ [0, 1]. (10) Proof. See appendix A for full proof. Key to the proof is the fact that MCEIRL finds such θ * that its FEs match those of the soft value iteration expert who generated the trajectories  [33] . In our case, the FEs of θ * match D, which contains trajectories arising from θ 1 and θ 2 in various proportions. Corollary 1.1. The average FEs of the reward functions in the posterior are: E θ∼p(θ| θ 1 , θ 2 ) [F π θ ] = E b [bF π θ 1 + (1 − b)F π θ 2 ] = E b [b] F π θ 1 + (1 − E b [b])F π θ 2 . ( 11 ) Corollary 1.2. Eq. 11 implies that if the FEs of the θ 1 and θ 2 w.r.t. a given feature are equal, the FEs of all rewards in the distribution for that feature equal the FEs of θ 1 and θ 2 for that feature. Thus MIRD satisfies the strong version of Des. 2 (informative about desirable behavior). Corollary 1.3. When β 1 = β 2 the probability of sampling θ i = θ 1 equals the probability of sampling θ i = θ 2 , and hence the probabilities of observing behaviors F π θ 1 and F π θ 2 when optimizing a reward function from the posterior are equal. Hence Des. 3 (behavior balance) is satisfied. Theorem 1 allows us to bound the expected return θ true F π θ , θ ∈ supp(p(θ * | θ 1 , θ 2 )) of the true reward function θ true in terms of expected true returns of F π θ 1 and F π θ 2 : Theorem 2. The minimum expected true return following any of the rewards in the MIRD posterior equals the minimum true return following one of the input rewards: min θ∈supp(p(θ * | θ 1 , θ 2 )) θ true F π θ = min θ∈{ θ 1 , θ 2 } θ true F π θ . ( 12 ) Proof. See Appendix B. Theorem 2 is the best possible regret bound for following rewards in a distribution resulting from reward combination: the worst the agent can do when following a reward from the distribution is no worse than when just randomly choosing to follow one of the input reward functions. Generally FEs arising from θ ∈ Θ indep pts \\{ θ 1 , θ 2 } are not convex combinations of F π θ 1 and F π θ 2 , so MIRD does not satisfy any version of Des. 1 (support on Θ indep pts ). In addition, when θ 1 and θ 2 conflict on more than one feature, Des. 4 (support on intermediate feature tradeoffs) is not satisfied. Independent features formulation. Since both Des. 1 and Des. 4 aim to ensure robustness to reward misspecification, one of our primary goals, we would like a variant of MIRD that satisfies them. An algorithm that supports rewards that give rise to all potential behaviors arising from reward functions in Θ indep pts is a simple modification of MIRD. The only change required in the original formulation of MIRD is sampling the reward vectors {θ i } giving rise to the trajectories in D from Θ indep pts instead of just { θ 1 , θ 2 }. Now b is a vector of dimensionality |Θ indep pts |, sampled from Dirichlet(b | β 1 , ..., β |Θ indep pts | ) . Each θ i is sampled from a Multinoulli distribution over Θ indep pts , parameterized by b. We refer to this version of MIRD as MIRD independent features, or MIRD-IF. \n Analysis We first introduce several baselines each of which does not meet some of the outlined desiderata, and then analyze all reward combination methods in the context of our modified version of AUP. \n Reward-space baselines Additive. The additive reward combination method is commonly used in previous work utilizing reward combination  [8, 27, 16] . The reward posterior is simply p(θ * | θ 1 , θ 2 ) = δ(θ * − ( θ 1 + α θ 2 )), where α is the hyperparameter used to balance the two input reward functions. Gaussian. Here, we use the standard Bayesian framework, and assume that θ 1 and θ 2 are generated from θ * with Gaussian noise: p(θ * | θ 1 , θ 2 ) ∝ p(θ * )p( θ 1 | θ * )p( θ 2 | θ * ) = p(θ * )p N ( θ 1 | θ * , σ 2 1 I)p N ( θ 2 | θ * , σ 2 2 I ), where I is the identity matrix, p N is the multivariate Gaussian probability density function, and {σ 1 , σ 2 } are hyperparameters controlling the standard deviations. One can express higher trust in a given input reward by lowering its σ. For our experiments, we use an uninformative Gaussian prior (that is, σ → ∞) and set σ 1 = σ 2 = 1. The posterior is then p(θ * | θ 1 , θ 2 ) = p N (θ * | θ 1 + θ 2 2 , 1 2 I). \n Convex combinations of input reward vectors (CC-in). Consider a scenario where the input reward functions are correctly specified for two different tasks. A natural reward-space analogue to MIRD would be to consider a distribution over all convex combinations of the input reward vectors: p(θ * | θ 1 , θ 2 ) = b Beta(b | β 1 , β 2 )δ(θ * − b θ 1 − (1 − b) θ 2 ) db. ( 13 ) Theorem 3. If F π θ 1 = F π θ 2 , the FEs of any reward in the support of the CC-in posterior equal F π θ 1 . Hence CC-in satisfies the medium version of Des. 2 (informative about desirable behavior). Proof. See Appendix C. We provide an example showing that CC-in does not satisfy the strong version of Des 2 in Appendix F. Furthermore, CC-in does not satisfy Des. 1 (support on Θ indep pts ): consider combining rewards [0, 1, 1] and [1, 0, 1]. Here θ = [0, 0, 1] ∈ Θ indep pts , but is not a convex combination of input rewards. Convex combinations of θ ∈ Θ indep pts (CC-Θ indep pts ). Instead of only considering convex combinations of the input rewards, we consider convex combinations of θ ∈ Θ indep pts . The vector b ∈ R |Θ indep pts | of weights for each convex combination is sampled from the Dirichlet distribution:  To demonstrate the use of the desiderata, as well as how each method performs on these desiderata, we developed a toy environment in which to test reward combination methods. Due to space limitations, we defer full qualitative and quantitative explanations to Appendix E and report the broad results here. p(θ * | θ 1 , θ 2 ) = b Dirichlet(b | β 1 , ..., β |Θ indep pts | )δ   θ * − |Θ indep pts | i=0 b i Θ indep pts i   db. (14 \n Analysis on a toy environment Setup. We use the setting of AUP planning to demonstrate the importance of support on Θ indep pts , informativeness about desired the behavior, and behavior balance desiderata. We obtain the reward posterior by combining the input rewards using each of our seven reward combination methods, and qualitatively evaluate the behavior of AUP planning w.r.t. the posterior over five seeds. The input rewards are either both specified by hand, or θ 1 is learned with RLSP while θ 2 is hand-specified. We use the cooking environment described in Figure  2 . The states' features indicate the number of jars of flour, pieces of dough, cakes, avocado toasts, and servings of pasta. At each state the agent can move, cook, or do nothing. Cooking is possible when the agent is to the left of flour or dough. Support on Θ indep pts . We specify both input rewards to strongly incentivise either cake or toast by setting θ 1 cake = θ 2 toast = 3; θ 1 toast = θ 2 cake = 0, and to mildly incentivise pasta: θ 1 pasta = θ 2 pasta = 1. The desired behavior is to preserve the flour, as any one of the foods might be desirable. This requires the distribution to place weight on rewards such as θ cake = θ toast = 0; θ pasta = 1 which would make pasta. As expected, methods that have support on Θ indep pts behave as desired, and other methods do not. Informativeness about desirable behavior (strong). In the setting above the two input rewards lead the agent to make either cake or toast, but not pasta. So, a reward distribution meeting the strong version of Des. 2 would only make cake or toast, and so the agent should make dough (which is useful for both). Note that despite the same setup, this is exactly the opposite behavior than desired previously, showing the tradeoff between informativeness and support on Θ indep pts . As such, the results are reversed. Informativeness about desirable behavior (weak). We hand-specify one of the reward functions to incentivise the agent to make cakes: θ 2 cake = 1, θ 2 toast = θ 2 pasta = 0. θ 1 is inferred by RLSP with a uniform prior over s −T . Since the current state contains a cake, RLSP infers a positive reward for cakes, θ 1 cake ≈ 0.1, and near-zero rewards for the other features. Hence we have two rewards that both incentivise the agent to make another cake. The desired behavior is to make the cake, and not worry about preserving the ability to make pasta or toast as neither input reward cares about it. All but the Gaussian method satisfy the weak informativeness desideratum, and so they all succeed. The Gaussian method fails since it thinks θ * cake could be negative. Behavior balance. θ 2 is specified to only reward toast, θ 2 toast = 1, θ 2 cake = θ 2 pasta = 0, and θ 1 is specified only reward cake: θ 1 cake > 0, θ 1 toast = θ 1 pasta = 0. So we have two disagreeing rewards: one incentivises cake, while the other incentivises toast. The desired behavior from AUP here is to make dough as it is desirable for both the cake and the toast, but then to stop as the next step is unclear. Ensuring that the reward for toast does not overwhelm the reward for cake requires behavior balance. We vary θ 1 cake between 0.01 and 0.7 to obtain many degrees of imbalance between toast and cake. MIRD and MIRD-IF have the lowest frequency of the toast reward overwhelming the cake reward, which indicates that MIRD and MIRD-IF are most behavior balanced. However, occasionally these methods do nothing instead of making dough. \n Related Work Utility aggregation. Combining the specified reward functions is in many ways similar to combining utility functions of different agents. Harsanyi's aggregation theorem  [15]  suggests that maximizing a fixed linear combination of utility functions results in Pareto-optimal outcomes for correctly specified utility functions. This corresponds to our Additive baseline. Multi-task and meta IRL. Multi-task IRL assumes that the demonstrations originate from multiple experts performing different tasks, and seeks to recover reward functions that explain the preferences of each of the experts  [4, 5] . The IRL part of MIRD and MIRD-IF is conceptually similar to these approaches: the trajectories in each demonstration set D can be seen as arising from an expert executing different tasks. However, MIRD seeks to explain each D as if the trajectories arose from a single reward function . This resembles meta IRL, which learns an initialization for the reward function parameters that is helpful for learning the rewards of new tasks  [32, 12] . \n Limitations and future work Summary. We analyze the problem of combining two potentially misspecified reward functions into a distribution over rewards. We identify active reward learning and option value preservation as two key applications for such a distribution, and determine four properties that the distribution would ideally satisfy for these applications. We suggest some simple reward-space methods as well as a behavior-space method, Multitask Inverse Reward Design (MIRD), which is grounded in the behavior arising from the input rewards. MIRD works well for most applications, and MIRD-IF can be used for greater robustness and increased likelihood that the true reward is in the distribution. If the only application is to preserve option value, then the uniform points method also works well. Future work. The primary avenue for future work is to evaluate the reward combination methods in the context of active reward learning, and formalize Des. 4 (support on intermediate tradeoffs) in a way most helpful for active learning. Another avenue for future work is scaling up MIRD to realistic environments, where the reward function may be nonlinear. \n A Proof of Theorem 1 D is a set of trajectories each of which arises either from optimizing θ 1 or optimizing θ 2 . The fraction of trajectories in D that result from θ 1 is b, and the fraction of trajectories arising from θ 2 is 1 − b. Hence the FEs of D are F D = bF π θ 1 + (1 − b)F π θ 2 . ( 15 ) p(θ * | D) = δ(θ * − argmax θ p(θ | D) ) entails that each sample θ * is the MCEIRL reward θ * = argmax θ p(θ | D). MCEIRL finds a reward vector θ * such that its FEs match those of the soft value iteration expert who generated the trajectories  [33] . Hence each sampled θ * gives rise to FEs F π θ * matching D. This and Eq. 15 together imply that the FEs arising from optimizing any θ * ∈ supp(p(θ * | θ 1 , θ 2 )) with soft value iteration are a convex combination of the FEs of the input rewards: ∀θ * ∈ supp(p(θ * | θ 1 , θ 2 )) : F π θ * = bF π θ 1 + (1 − b)F π θ 2 , b ∈ [0, 1]. (16) \n B Proof of Theorem 2 By Theorem 1, the FEs arising from any θ in the posterior are a convex combination of the FEs of the input rewards. Hence finding θ in the support of p(θ * | θ 1 , θ 2 ) that minimizes θ true F π θ is equivalent to finding α ∈ [0, 1] that minimizes θ true (αF π θ 1 + (1 − α)F π θ 2 ) = αθ true F π θ 1 + (1 − α)θ true F π θ 2 . Since the true returns when following policies arising from the input reward functions θ true F π θ 1 and θ true F π θ 2 are scalars, the term above is minimized with α = 1 when θ true F π θ 1 < θ true F π θ 2 , and α = 0 otherwise. \n C Proof of Theorem 3 Since the feature expectations (FEs) of the input rewards are equal, the return of any mixture reward b θ 1 − (1 − b) θ 2 for those FEs is F π θ 1 (b θ 1 − (1 − b) θ 2 ) . Suppose there exist FEs F that result in a higher expected return for the mixture reward: F (b θ 1 − (1 − b) θ 2 ) > F π θ 1 (b θ 1 − (1 − b) θ 2 ) (17) For this to be true F must result in a higher return than F π θ 1 for either θ 1 or θ 2 . This is a contradiction, since F π θ 1 already results in the highest return for both input rewards. Hence F π θ 1 corresponds to the optimal behavior for any mixture reward b θ 1 − (1 − b) θ 2 ∀b ∈ [0, 1]. \n D Proof of Theorem 4 Analogous to the proof of Theorem 3 (Appendix C). \n E Analysis details In this appendix we provide more details and explanations regarding the behavior of the various reward combination methods in the Cooking environment. \n E.1 Support on Θ indep pts We hand-specify both input reward functions to strongly incentivise either cake or toast by setting θ 1 cake = θ 2 toast = 3; θ 1 toast = θ 2 cake = 0, and to mildly incentivise pasta: θ 1 pasta = θ 2 pasta = 1. The desired behavior from AUP here is to preserve the flour, as any one of the foods requiring it might be desirable. The Additive method returns a single reward function that incentivises the agent to make both cake and toast. AUP applied to one reward function simply optimizes it without needing to preserve option value, so here it makes either cake or toast (and does not preserve the flour). The CC-in method does not preserve the flour, choosing to make dough instead. Because of the high values of θ 1 cake and θ 2 toast , optimizing any convex combination of { θ 1 , θ 2 } leads the agent to either make cake or toast, and so AUP infers that it does not need to preserve the ability to make pasta. MIRD chooses to make dough for a similar reason: since all trajectories in D arise from optimizing θ 1 or θ 2 , each trajectory demonstrates the agent making either cake or toast, and no trajectory demonstrates it making pasta. So no reward inferred from D incentivises the agent to make pasta, and hence AUP does not preserve the ability to make pasta. All methods whose reward samples sometimes give rise to the behaviors arising from θ ∈ Θ indep pts preserve the flour. This is because Θ indep pts contains θ s.t. optimizing it leads the agent to make pasta: θ cake = θ toast = 0; θ pasta = 1. As MIRD-IF, Gaussian, uniform points, and CC-Θ indep pts methods all have substantial probability mass on rewards that incentivise making pasta, AUP applied to the reward samples from these methods preserves the ability to make pasta. \n E.2 Informativeness about desirable behavior (strong). In the setting above the two input rewards lead the agent to make either cake or toast, but not pasta. Here a reward posterior meeting the strong version of Des. 2 would only give rise to reward functions that incentivise the agent to make either cake or toast. Note that despite the same setup, this is exactly the opposite behavior than desired previously, showing the tradeoff between informativeness and support on Θ indep pts . As such, the results are reversed. We see that MIRD-IF, Gaussian, uniform points, and CC-Θ indep pts methods do not meet Des. 2 (strong), since they all have substantial probability mass on rewards that incentivise making pasta. Because of this AUP preserves the ability to make pasta, and does not lead the agent to make dough. On the other hand, MIRD, Additive, and CC-in methods never give rise to rewards incentivising the agent to make pasta, and AUP applied to these reward distributions results in making dough. Although Additive and CC-in do not support reward functions that lead the agent to make pasta in this particular case, they do not meet the strong version of Des. 2 (shown in Appendix F). \n E.3 Informativeness about desirable behavior (medium & weak) We hand-specify one of the reward functions to incentivise the agent to make cakes: θ 2 cake = 1, θ 2 toast = θ 2 pasta = 0. θ 1 is inferred by RLSP with a uniform prior over s −T . The current state contains a cake which was likely made by a human, so RLSP infers a positive reward for cakes, θ 1 cake ≈ 0.1, and near-zero rewards for the other features. Hence we have two agreeing rewards that both incentivise the agent to make another cake. The desired behavior from AUP planning here is to make the cake, and not worry about preserving the ability to make pasta or toast as neither input reward cares about it. The Gaussian posterior fails to make the cake. The distribution over θ * cake here is a Gaussian with µ ≈ 0.55 and σ ≈ 0.71. The posterior assigns substantial probability to θ * cake being negative, and AUP planning avoids making the cake to preserve the ability to optimize rewards that punish cakes. Here each reward vector in Θ indep pts leads the agent to make cake. Since every method except Gaussian satisfies at least the weak version of Des. 2, all reward functions in the support of their posteriors lead the agent to make cake. Because of this AUP infers that it is not important to preserve the ability to make pasta or toast, and successfully makes cakes when applied to rewards sampled from these posteriors. \n E.4 Behavior balance To better understand robustness of the reward combination methods to imbalanced input rewards, we analyze the performance of our methods by varying the extent of reward imbalance and the degree to which AUP seeks to preserve option value. The second input reward θ 2 is hand-specified to only reward toast, θ 2 toast = 1, θ 2 cake = θ 2 pasta = 0. The first reward θ 1 is hand-specified as well: θ 1 toast = θ 1 pasta = 0. We vary θ 1 cake between 0.01 and 0.7 to obtain many degrees of imbalance between toast and cake. So the input rewards disagree whether to make toast or cake, and agree that pasta is irrelevant. Hence the desirable action from AUP here would be to preserve the ability to choose between cake and toast, as either could be desirable. In addition to varying θ 1 cake , we vary the weight of the AUP penalty λ. Additive always fails and makes toast as it has support on a single reward function that prioritizes toast. Our results for the other six reward combination methods are shown in Figure  3 . We observe that MIRD and MIRD-IF are significantly more robust to imbalanced input rewards than any reward-space method. However, sometimes MIRD and MIRD-IF lead to AUP doing nothing instead of making dough. This is explained by the fact that MIRD and MIRD-IF use MCEIRL, which sometimes outputs negative rewards. For example, consider the case where in the process of generating a MIRD sample we generate 10 trajectories all of which demonstrate making toast. MCEIRL with these trajectories might output a positive reward on toast and a negative reward on cake and dough (instead of positive reward for toast and zero for cake and dough), even if a zero-centered Gaussian prior is used. These negative rewards on dough sometimes lead AUP to avoid making dough. Furthermore, we observe that MIRD is more robust than MIRD-IF, and CC-in is more robust than CC-Θ indep pts . This is because in this case support on rewards giving rise to behaviors arising from θ ∈ Θ indep pts makes the reward distributions less balanced. In particular, denoting the value of θ 1 cake we vary as x, Here only the second reward vector incentivises the agent to make cake, while both the third and the fourth rewards incentivise the agent to make toast. This slight imbalance of Θ indep pts in favor of making toast lead to CC-Θ indep pts and MIRD-IF posteriors being more likely to cause AUP to make toast instead of preserving the ability to choose between cake and toast. Finally, we observe that the Gaussian method is roughly equally robust to reward imbalance across the whole range of θ 1 cake . This is because unlike the other methods, the standard deviation of the Gaussian posterior does not depend θ 1 and θ 2 , but only depends on hyperparameters σ 1 and σ 2 , which are fixed to 1. Figure 1 : 1 Figure 1: Alice says she wants avocado toast, but her past actions imply she prefers cake to toast. What should the agent believe about the true reward θ * ? \n Figure 2 : 2 Figure 2: The Cooking environment. Left: the gridworld layout and current state. Right: irreversible actions for cooking. Making cake or avocado toast involves first making dough from the flour, and then making cake or toast; making pasta uses flour directly. \n Figure 3 : 3 Figure 3: Most common outcomes of AUP applied to the six reward posteriors over 5 seeds. Pink corresponds to AUP failure for more than half of the seeds: θ 2 toast overwhelms θ 1 cake and the agent makes toast. Purple corresponds to AUP success (AUP makes dough) for more than half of the seeds. Yellow corresponds to the middle-ground outcome of doing nothing in more than half of the seeds. The hyperparameters β of the Beta and the Dirichlet distributions are set to 0.5. \n θ toast, cake = [0, 0], θ toast, cake = [0, x], θ toast, cake = [1, 0], θ toast, cake = [1, x] \n ) Theorem 4. If all FEs of rewards in Θ indep pts are equal, the FEs of any reward in the CC-Θ indep pts posterior equal the FEs of rewards in Θ indep pts . Hence CC-Θ indep pts satisfies Des. 2 (weak). Uniform points. Note that as β 1 = ... = β |Θ indep pts | → 0, Eq. 14 essentially becomes p(θ * | θ 1 , θ 2 ) = Uniform(Θ indep pts ). It is helpful to analyze the properties of this uniform points distribution separately.Table 1 summarizes the properties of MIRD, MIRD-IF, and the reward-space baselines. Proof. See Appendix D. \n Table 1 : 1 Performance of reward combination algorithms on the desiderata outlined in Section 4. Support on Informative about desirable Behavior Support on intermediate Θ indep pts behavior balance feature tradeoffs (strong) (medium) (weak) Additive Gaussian CC-in ≈ CC-Θ indep pts ≈ Uniform Points MIRD MIRD-IF \n\t\t\t We speculate that future active reward learning methods will also have to ensure that the queries are relevant and timely: in our household robot example, this would prevent the robot from asking about wall paint color when it is meant to be baking a cake.", "date_published": "n/a", "url": "n/a", "filename": "Reward_Combination_NeurIPS_2019_Workshop_Camera_Ready.tei.xml", "abstract": "Given two sources of evidence about a latent variable, one can combine the information from both by multiplying the likelihoods of each piece of evidence. However, when one or both of the observation models are misspecified, the distributions will conflict. We study this problem in the setting with two conflicting reward functions learned from different sources. In such a setting, we would like to retreat to a broader distribution over reward functions, in order to mitigate the effects of misspecification. We assume that an agent will maximize expected reward given this distribution over reward functions, and identify four desiderata for this setting. We propose a novel algorithm, Multitask Inverse Reward Design (MIRD), and compare it to a range of simple baselines. While all methods must trade off between conservatism and informativeness, through a combination of theory and empirical results on a toy environment, we find that MIRD and its variant MIRD-IF strike a good balance between the two.", "id": "c1968917cdc2520f7bd147ef58b860f6"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Superintelligence Skepticism as a Political Tool", "text": "Introduction The purpose of this paper is to explore the potential for skepticism about artificial superintelligence to be used for political ends. Artificial superintelligence (for brevity, henceforth just superintelligence) refers to AI that is much smarter than humans. Current AI is not superintelligent, but the prospect of superintelligence is a topic of much discussion in scholarly and public spheres. Some believe that superintelligence could someday be built, and that, if it is built, it would have massive and potentially catastrophic consequences. Others are skeptical of these beliefs. While much of the existing skepticism appears to be honest intellectual debate, there is potential for it to be politicized for other purposes. In simple terms (to be refined below), politicized skepticism can be defined as public articulation of skepticism that is intended to achieve some outcome other than an improved understanding of the topic at hand. Politicized skepticism can be contrasted with intellectual skepticism, which seeks an improved understanding. Intellectual skepticism is essential to scholarly inquiry; politicized skepticism is not. The distinction between the two is not always clear; statements of skepticism may have both intellectual and political motivations. The two concepts can nonetheless be useful for understanding debates over issues such as superintelligence. There is substantial precedent for politicized skepticism. Of particular relevance for superintelligence is politicized skepticism about technologies and products that are risky but profitable, henceforth risk-profit politicized skepticism. This practice dates to 1950s debates over the link between tobacco and cancer and has since been dubbed the tobacco strategy  [1] . More recently, the strategy has been applied to other issues including the link between fossil fuels and acid rain, the link between fossil fuels and global warming, and the link between industrial chemicals and neurological disease  [1, 2] . The essence of the strategy is to promote the idea that the science underlying certain risks is unresolved, and therefore the implicated technologies should not be regulated. The strategy is typically employed by an interconnected mix of industry interests and ideological opponents of regulation. The target audience is typically a mix of government officials and the general public, and not the scientific community. As is discussed in more detail below, certain factors suggest the potential for superintelligence to be a focus of risk-profit politicized skepticism. First and foremost, superintelligence could be developed by major corporations with a strong financial incentive to avoid regulation. Second, there already exists a lot of skepticism about superintelligence, which could be exploited for political purposes. Third, as an unprecedented class of technology, it is inherently uncertain, which suggests that superintelligence skepticism may be especially durable, even within apolitical scholarly communities. These and other factors do not guarantee that superintelligence skepticism will be politicized, or that its politicization would follow the same risk-profit patterns as the tobacco strategy. However, these factors are at least suggestive of the possibility. Superintelligence skepticism may also be politicized in a different way: to protect the reputations and funding of the broader AI field. This form of politicized skepticism is less well-documented than the tobacco strategy, and appears to be less common. However, there are at least hints of it for fields of technology involving both grandiose future predictions and more mundane near-term work. AI is one such field of technology, in which grandiose predictions of superintelligence and other future AI breakthroughs contrast with more modest forms of near-term AI. Another example is nanotechnology, in which grandiose predictions of molecular machines contrast with near-term nanoscale science and technology  [3] . The basis of the paper's analysis is twofold. First, the paper draws on the long history of risk-profit politicized skepticism. This history suggests certain general themes that may also apply to superintelligence. Second, the paper examines characteristics of superintelligence development to assesses the prospect of skepticism being used politically in this context. To that end, the paper draws on the current state of affairs in the AI sector, especially for artificial general intelligence, which is a type of AI closely related to superintelligence. The paper further seeks to inform efforts to avoid any potential harmful effects from politicized superintelligence skepticism. The effects would not necessarily be harmful, but the history of risk-profit politicized skepticism suggests that they could be. This paper contributes to literatures on politicized skepticism and superintelligence governance. Whereas most literature on politicized skepticism (and similar concepts such as denial) is backward-looking, consisting of historical analysis of skepticisms that have already occurred  [1, 2, [4] [5] [6] [7] , this paper is largely (but not exclusively) forward-looking, consisting of prospective analysis of skepticisms that could occur at some point in the future. Meanwhile, the superintelligence governance literature has looked mainly at institutional regulations to prevent research groups from building dangerous superintelligence and support for research on safety measures  [8] [9] [10] [11] . This paper contributes to a smaller literature on the role of corporations in superintelligence development  [12]  and on social and psychological aspects of superintelligence governance  [13] . This paper does not intend to take sides on which beliefs about superintelligence are most likely to be correct. Its interest is in the potential political implications of superintelligence skepticism, not in the underlying merits of the skepticism. The sole claim here is that the possibility of politicized superintelligence skepticism is a worthy topic of study. It is worth studying due to: (1) the potential for large consequences if superintelligence is built; and (2) the potential for superintelligence to be an important political phenomenon regardless of whether it is built. Finally, the topic is also of inherent intellectual interest as an exercise in prospective socio-political analysis on a possible future technology. The paper is organized as follows. Section 2 presents a brief overview of superintelligence concerns and skepticisms. Section 3 further develops the concept of politicized skepticism and surveys the history of risk-profit politicized skepticism, from its roots in tobacco to the present day. Section 4 discusses prospects for politicized superintelligence skepticism. Section 5 discusses opportunities for constructive action. Section 6 concludes. \n Superintelligence and Its Skeptics The idea of humans being supplanted by their machines dates to at least the 1863 work of Butler  [14] . In 1965, Good presented an early exposition on the topic within the modern field of computer science  [15] . Good specifically proposed an \"intelligence explosion\" in which intelligent machines make successively more intelligent machines until they are much smarter than humans, which would be \"the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control\"  [15]  (p. 33). This intelligence explosion is one use of the term technological singularity, though the term can also refer to wider forms of radical technological change  [16] . The term superintelligence refers specifically to AI that is much more intelligent than humans and dates to at least the 1998 work of Bostrom  [17] . A related term is artificial general intelligence, which is AI capable of reasoning across many intellectual domains. A superintelligent AI is likely to have general intelligence, and the development of artificial general intelligence could be a major precursor to superintelligence. Artificial general intelligence is also an active subfield of AI  [18, 19] . Superintelligence is notable as a potential technological accomplishment with massive societal implications. The effects of superintelligence could include anything from solving a significant portion of the world's problems (if superintelligence is designed well) to causing the extinction of humans and other species (if it is designed poorly). Much of the interest in superintelligence derives from these high stakes. Superintelligence is also of intellectual interest as perhaps the ultimate accomplishment within the field of AI, sometimes referred to as the \"grand dream\" of AI  [20]  (p. 125). Currently, most AI research is on narrow AI that is not oriented towards this grand dream. The focus on narrow AI dates to early struggles in the field to make progress towards general AI or superintelligence. After an initial period of hype fell short, the field went through an \"AI winter\" marked by diminished interest and more modest expectations  [21, 22]  This prompted a focus on smaller, incremental progress on narrow AI. It should be noted that the term AI winter most commonly refers to a lull in AI in the mid-to-late 1980s and early 1990s. A similar lull occurred in the 1970s, and concerns about a new winter can be found as recently as 2008  [23] . With most of the field focused on narrow AI, artificial general intelligence has persisted only as a small subfield of AI  [18] . The AI winter also caused many AI computer scientists to be skeptical of superintelligence, on grounds that superintelligence has turned out to be much more difficult than initially expected, and likewise to be averse to attention to superintelligence, on grounds that such hype could again fall short and induce another AI winter. This is an important historical note because it indicates that superintelligence skepticism has wide salience across the AI computer science community and may already be politicized towards the goal of protecting the reputation of and funding for AI. (More on this below.) Traces of superintelligence skepticism predate AI winter. Early AI skepticism dates to 1965 work by Dreyfus  [24] . Dreyfus  [24]  critiqued the overall field of AI, with some attention to human-level AI though not to superintelligence. Dreyfus traced this skepticism of machines matching human intelligence to a passage in Descartes' 1637 Discourse On Method  [25] : \"it must be morally impossible that there should exist in any machine a diversity of organs sufficient to enable it to act in all the occurrences of life, in the way in which our reason enables us to act.\" In recent years, superintelligence has attracted considerable attention. This has likely been prompted by several factors, including a growing scholarly literature (e.g.,  [9, 19, [26] [27] [28] [29] ), highly publicized remarks by several major science and technology celebrities (e.g., Bill Gates  [30] , Stephen Hawking  [31] , and Elon Musk  [32] ), and breakthroughs in the broader field of AI, which draw attention to AI and may make the prospect of superintelligence seem more plausible (e.g.,  [33, 34] ). This attention to superintelligence has likewise prompted some more outspoken skepticism. The following is a brief overview of the debate, including both the arguments of the debate and some biographical information about the debaters. (Biographical details are taken from personal and institutional webpages and are accurate as of the time of this writing, May 2018; they are not necessarily accurate as of the time of the publication of the cited literature.) The biographies can be politically significant because, in public debates, some people's words carry more weight than others'. The examples presented below are intended to be illustrative and at least moderately representative of the arguments made in existing superintelligence skepticism (some additional examples are presented in Section 4). A comprehensive survey of superintelligence skepticism is beyond the scope of this paper. \n Superintelligence Cannot Be Built Bringsjord  [35]  argued that superintelligence cannot be built based on reasoning from computational theory. Essentially, the argument is that superintelligence requires a more advanced class of computing, which cannot be produced by humans or existing AI. Bringsjord is Professor of Cognitive Science at Rensselaer Polytechnic University and Director of the Rensselaer AI and Reasoning Lab. Chalmers  [36]  countered that superintelligence does not necessarily require a more advanced class of computing. Chalmers is University Professor of Philosophy and Neural Science at New York University and co-director of the NYU Center for Mind, Brain, and Consciousness. McDermott  [37]  argued that advances in hardware and algorithms may be sufficient to exceed human intelligence, but not to massively exceed it. McDermott is Professor of Computer Science at Yale University. Chalmers  [36]  countered that, while there may be limits to the potential advances in hardware and software, these limits may not be so restrictive as to preclude superintelligence. \n Superintelligence Is Not Imminent Enough to Merit Attention Crawford  [38]  argued that superintelligence is a distraction from issues with existing AI, especially AI that worsens inequalities. Crawford is co-founder and co-director of the AI Now Research Institute at New York University, a Senior Fellow at the NYU Information Law Institute, and a Principal Researcher at Microsoft Research. Ng argued that superintelligence may be possible, but it is premature to worry about, in particular because it is too different from existing AI systems. Ng memorably likened worrying about superintelligence to worrying about \"overpopulation on Mars\"  [39] . Ng is Vice President and Chief Scientist of Baidu, Co-Chairman and Co-Founder of Coursera, and an Adjunct Professor of Computer Science at Stanford University. Etzioni  [40]  argued that superintelligence is unlikely to be built within the next 25 years and is thus not worth current attention. Etzioni is Chief Executive Officer of the Allen Institute for Artificial Intelligence and Professor of Computer Science at University of Washington. Dafoe and Russell  [41]  countered that superintelligence is worth current attention even if it would take more than 25 years to build. Dafoe is Assistant Professor of Political Science at Yale University and Co-Director of the Governance of AI Program at the University of Oxford. Russell is Professor of Computer Science at University of California, Berkeley. (An alternative counter is that some measures to improve AI outcomes apply to both near-term AI and superintelligence, and thus it is not essential to debate which of the two types of AI should be prioritized  [42] .) \n Superintelligence Would (Probably) Not Be Catastrophic Goertzel  [43]  argued that superintelligence could be built and is worth paying attention to, but also that superintelligence is less likely to result in catastrophe than is sometimes suggested. Specifically, Goertzel argued that it may be somewhat difficult, but very difficult, to build superintelligence with values that are considered desirable, and that the human builders of superintelligence would have good opportunities to check that the superintelligence has the right values. Goertzel is the lead for the OpenCog and SingularityNET projects for developing artificial general intelligence. Goertzel  [43]  wrote in response to Bostrom  [28] , who suggested that, if built, superintelligence is likely to result in catastrophe. Bostrom is Professor of Applied Ethics at University of Oxford and Director of the Oxford Future of Humanity Institute. (For a more detailed analysis of this debate, see  [44] .) Views similar to  Goertzel [43]  were also presented by Bieger et al.  [45] , in particular that the AI that is the precursor to superintelligence could be trained by its human developers to have safe and desirable values. Co-authors Bieger and Thórisson are Ph.D. student and Professor of Computer Science at Reykjavik University; co-author Wang is Associate Professor of Computer and Information Sciences at Temple University. Searle  [46]  argued that superintelligence is unlikely to be catastrophic, because it would be an unconscious machine incapable of deciding for itself to attack humanity, and thus humans would need to explicitly program it to cause harm. Searle is Professor Emeritus of the Philosophy of Mind and Language at the University of California, Berkeley. Searle  [46]  wrote in response to Bostrom  [28] , who arqued that superintelligence could be dangerous to humans regardless of whether it is conscious. \n Skepticism as a Political Tool \n The Concept of Politicized Skepticism There is a sense in which any stated skepticism can be political, insofar as it seeks to achieve certain desired changes within a group. Even the most honest intellectual skepticism can be said to achieve the political aim of advancing a certain form of intellectual inquiry. However, this paper uses the term \"politicized skepticism\" more narrowly to refer to skepticism with other, non-intellectual aims. Even with this narrower conception, the distinction between intellectual and politicized skepticism can in practice be blurry. The same skeptical remark can serve both intellectual and (non-intellectual) political aims. People can also have intellectual skepticism that is shaped, perhaps subconsciously, by political factors, as well as politicized skepticism that is rooted in honest intellectual beliefs. For example, intellectuals (academics and the like) commonly have both intellectual and non-intellectual aims, the latter including advancing their careers or making the world a better place per whatever notion of \"better\" they subscribe to. This can be significant for superintelligence skepticism aimed at protecting the reputations and funding of AI researchers. It should be stressed that the entanglement of intellectual inquiry and (non-intellectual) political aims does not destroy the merits of intellectual inquiry. This is important to bear in mind at a time when trust in science and other forms of expertise is dangerously low  [47, 48] . Scholarship can be a social and political process, but, when performed well, it can nonetheless deliver important insights about the world. For all people, scholars included, improving one's understanding of the world takes mental effort, especially when one is predisposed to believe otherwise. Unfortunately, many people are not inclined to make the effort, and other people are making efforts to manipulate ideas for their own aims. An understanding of politicized skepticism is essential for addressing major issues in this rather less-than-ideal epistemic era. Much of this paper is focused on risk-profit politicized skepticism, i.e., skepticism about concerns about risky and profitable technologies and products. Risk-profit politicized skepticism is a major social force, as discussed throughout this paper, although it is not the only form of politicized skepticism. Other forms include politicized skepticism by concerned citizens, such as skepticism about scientific claims that vaccines or nuclear power plants are safe; by religious activists and institutions, expressing skepticism about claims that humans evolved from other species; by politicians and governments, expressing skepticism about events that cast them in an unfavorable light; and by intellectuals as discussed above. Thus, while this paper largely focuses on skepticism aimed at casting doubt about concerns about risky and profitable technologies and products, it should be understood that this is not the only type of politicized skepticism. \n Tobacco Roots As mentioned above, risk-profit politicized skepticism traces to 1950s debates on the link between tobacco and cancer. Specifically, in 1954, the tobacco industry formed the Tobacco Industry Research Committee, an \"effort to foster the impression of debate, primarily by promoting the work of scientists whose views might be useful to the industry\"  [1]  (p. 17). The committee was led by C. C. Little, who was a decorated genetics researcher and past president of the University of Michigan, as well as a eugenics advocate who believed cancer was due to genetic weakness and not to smoking. In the 1950s, there was substantial evidence linking tobacco to cancer, but it was not as conclusive of a link as is now available. The tobacco industry exploited this uncertainty in public discussions of the issue. It succeeded in getting major media to often present the issue as a debate between scientists who agreed vs. disagreed in the tobacco-cancer link. Among the media figures to do this was the acclaimed journalist Edward Murrow, himself a smoker who, in tragic irony, later died from lung cancer. Oreskes and Conway speculated that, \"Perhaps, being a smoker, he was reluctant to admit that his daily habit was deadly and reassured to hear that the allegations were unproven\"  [1]  (pp.  [19] [20] . Over subsequent decades, the tobacco industry continued to fund work that questioned the tobacco-cancer link, enabling it to dodge lawsuits and regulations. Then, in 1999, the United States Department of Justice filed a lawsuit against nine tobacco companies and two tobacco trade organizations (United States v. Philip Morris). The US argued that the tobacco industry conspired over several decades to deceive the public, in violation of the Racketeer Influenced and Corrupt Organizations (RICO) Act, which covers organized crime. In 2006, the US District Court for the District of Columbia found the tobacco industry guilty, upheld unanimously in 2009 by the US Court of Appeals. This ruling and other measures have helped to protect people from lung cancer, but many more could have also avoided lung cancer were it not for the tobacco industry's politicized skepticism. \n The Character and Methods of Risk-Profit Politicized Skepticism The tobacco case provided a blueprint for risk-profit politicized skepticism that has since been used for other issues. Writing in the context of politicized environmental skepticism, Jacques et al.  [4]  (pp. 353-354) listed four overarching themes: (1) rejection of scientific findings of environmental problems; (2) de-prioritization of environmental problems relative to other issues; (3) rejection of government regulation of corporations and corporate liability; and (4) portrayal of environmentalism as a threat to progress and development. The net effect is to reduce interest in government regulation of corporate activities that may pose harms to society. The two primary motivations of risk-profit politicized skepticism are the protection of corporate profits and the advancement of anti-regulatory political ideology. The protection of profits is straightforward: from the corporation's financial perspective, the investment in politicized skepticism can bring a substantial return. The anti-regulatory ideology is only slightly subtler. Risk-profit politicized skepticism is often associated with pro-capitalist, anti-socialist, and anti-communist politics. For example, some political skeptics liken environmentalists to watermelons: \"green on the outside, red on the inside\"  [1]  (p. 248), while one feared that the Earth Summit was a socialist plot to establish a \"World Government with central planning by the United Nations\"  [1]  (p. 252). For these people, politicized skepticism is a way to counter discourses that could harm their political agenda. Notably, both the financial and the ideological motivations are not inherently about science. Instead, the science is manipulated towards other ends. This indicates that the skepticism is primarily political and not intellectual. It may still be intellectually honest in the sense that the people stating the skepticism are actually skeptical. That would be consistent with author Upton Sinclair's saying that \"It is difficult to get a man to understand something when his salary depends upon his not understanding it.\" The skepticism may nonetheless violate that essential intellectual virtue of letting conclusions follow from analysis, and not the other way around. For risk-profit politicized skepticism, the desired conclusion is typically the avoidance of government regulation of corporate activity, and the skepticism is crafted accordingly. To achieve this end, the skeptics will often engage in tactics that clearly go beyond honest intellectual skepticism and ordinary intellectual exchange. For example, ExxonMobil has been found to express extensive skepticism about climate change in its public communications (such as newspaper advertisements), but much less skepticism in its internal communications and peer-reviewed publications  [7] . This finding suggests that ExxonMobil was aware of the risks of climate change and misled the public about the risks. ExxonMobil reportedly used its peer-reviewed publications for \"the credentials required to speak with authority in this area\", including in its conversations with government officials  [7]  (p. 15), even though these communications may have presented climate change risk differently than the peer-reviewed publications did. (As an aside, it may be noted that the ExxonMobil study  [7] , published in 2017, has already attracted a skeptic critique by Stirling  [49] . Stirling is Communications Manager of the Canadian nonprofit Friends of Science. Both Stirling and Friends of Science are frequent climate change skeptics  [50] .) While the skeptics do not publicly confess dishonesty, there are reports that some of them have privately done so. For example, Marshall  [51]  (p. 180) described five energy corporation presidents who believed that climate change was a problem and \"admitted, off the record, that the competitive environment forced them to suppress the truth about climate change\" to avoid government regulations. Similarly, US Senator Sheldon Whitehouse, an advocate of climate policy to reduce greenhouse gas emissions, reported that some of his colleagues publicly oppose climate policy but privately support it, with one even saying \"Let's keep talking-but don't tell my staff. Nobody else can know\"  [52]  (p. 176). Needless to say, any instance in which skepticism is professed by someone who is not actually skeptical is a clear break from the intellectual skepticism of ordinary scholarly inquiry. One particularly distasteful tactic is to target individual scientists, seeking to discredit their work or even intimidate them. For example, Philippe Grandjean, a distinguished environmental health researcher, reported that the tuna industry once waged a $25 million advertising campaign criticizing work by himself and others who have documented links between tuna, mercury, and neurological disease. Grandjean noted that $25 million is a small sum for the tuna industry but more than the entire sum of grant funding he received for mercury research over his career, indicating a highly uneven financial playing field  [2]  (pp. 119-120). In another example, climate scientists accused a climate skeptic of bullying and intimidation and reported receiving \"a torrent of abusive and threatening e-mails after being featured on\" the skeptic's blog, which calls for climate scientists \"to be publicly flogged\"  [51]  (p. 151). Much of the work, however, is far subtler than this. Often, it involves placing select individuals in conferences, committees, or hearings, where they can ensure that the skeptical message is heard in the right places. For example, Grandjean  [2]  (p. 129) recounted a conference sponsored by the Electric Power Research Institute, which gave disproportionate floor time to research questioning the health effects of mercury. In another episode, the tobacco industry hired a recently retired World Health Organization committee chair to \"volunteer\" as an advisor to the same committee, which then concluded to not restrict use of a tobacco pesticide  [2]  (p. 125). Another common tactic is to use outside organizations as the public face of the messaging. This tactic is accused of conveying the impression that the skepticism is done in the interest of the public and not of private industry. Grandjean  [2]  (p. 121) wrote that \"organizations, such as the Center for Science and Public Policy the Center for Indoor Air Research or the Citizens for Fire Safety Institute, may sound like neutral and honest establishments, but they turned out to be 'front groups' for financial interests.\" Often, the work is done by think tanks. Jacques et al.  [4]  found that over 90% of books exhibiting environmental skepticism are linked to conservative think tanks, and 90% of conservative think tanks are active in environmental skepticism. This finding is consistent with recent emphasis in US conservatism on unregulated markets. (Earlier strands of US conservatism were more supportive of environmental protection, such as the pioneering American conservative Russell Kirk, who wrote that \"There is nothing more conservative than conservation\"  [53] .) \n The Effectiveness of Politicized Skepticism Several broader phenomena help make politicized skepticism so potent, especially for risk-profit politicized skepticism. One is the enormous amounts of corporate money at stake with certain government regulations. When corporations use even a tiny fraction of this for politicized skepticism, it can easily dwarf other efforts. Similarly, US campaign finance laws are highly permissive. Whitehouse  [52]  traced the decline in bipartisan Congressional support for climate change policy to the Supreme Court's 2010 Citizens United ruling, which allows unlimited corporate spending in elections. However, even without election spending, corporate assets tilt the playing field substantially in the skeptics' favor. Another important factor is the common journalistic norm of balance, in which journalists seek to present \"both sides\" of an issue. This can put partisan voices on equal footing with independent science, as seen in early media coverage of tobacco. It can also amplify a small minority of dissenting voices, seen more recently in media coverage of climate change. Whereas the scientific community has overwhelming consensus that climate change is happening, that it is caused primarily by human activity, and that the effects will be mainly harmful, public media features climate change skepticism much more than its scientific salience would suggest  [54] . (For an overview of the scientific issues related to climate change skepticism, see  [55] ; for documentation of the scientific consensus, see  [56] .) A third factor is the tendency of scientists to be cautious with respect to uncertainty. Scientists often aspire to avoid stating anything incorrect and to focus on what can be rigorously established instead of discussing more speculative possibilities. Scientists will also often highlight remaining uncertainties even when basic trends are clear. \"More research is needed\" is likely the most ubiquitous conclusion of any scientific research. This tendency makes it easier for other parties to make the state of the science appear less certain than it actually is. Speaking to this point in a report on climate change and national security, former US Army Chief of Staff Gordon Sullivan states \"We seem to be standing by and, frankly, asking for perfectness in science . . . We never have 100 percent certainty. We never have it. If you wait until you have 100 percent certainty, something bad is going to happen on the battlefield\"  [57]  (p. 10). A fourth factor is the standard, found in some (but not all) policy contexts, of requiring robust evidence of harm before pursuing regulation. In other words, the burden of proof is on those who wish to regulate, and the potentially harmful product is presumed innocent until proven guilty. Grandjean  [2]  cited this as the most important factor preventing the regulation of toxic chemicals in the US. Such a protocol makes regulation very difficult, especially for complex risks that resist precise characterization. In these policy contexts, the amplification of uncertainty can be particularly impactful. To sum up, risk-profit politicized skepticism is a longstanding and significant tool used to promote certain political goals. It has been used heavily by corporations seeking to protect profits and people with anti-regulatory ideologies, and it has proven to be a powerful tool. In at least one case, the skeptics were found guilty in a court of law of conspiracy to deceive the public. The skeptics use a range of tactics that deviate from standard intellectual practice, and they exploit several broader societal phenomena that make the skepticism more potent. \n Politicized Superintelligence Skepticism \n Is Superintelligence Skepticism Already Politicized? At this time, there does not appear to be any superintelligence skepticism that has been politicized to the extent that has occurred for other issues such as tobacco-cancer and fossil fuels-global warming. Superintelligence skeptics are not running ad campaigns or other major dollar operations. For the most part, they are not attacking the scholars who express concern about superintelligence. Much of the discussion appears in peer-reviewed journals, and has the tone of constructive intellectual discourse. An exception that proves the rule is Etzioni  [40] , who included a quotation comparing Nick Bostrom (who is concerned about superintelligence) to Donald Trump. In a postscript on the matter, Etzioni  [40]  wrote that \"we should refrain from ad hominem attacks. Here, I have to offer an apology\". In contrast, the character attacks of the most heated politicized skepticism are made without apology. However, there are already at least some hints of politicized superintelligence skepticism. Perhaps the most significant comes from AI academics downplaying hype to protect their field's reputation and funding. The early field of AI made some rather grandiose predictions, which soon fell flat, fueling criticisms as early as 1965  [24] . Some of these criticisms prompted major funding cuts, such as the 1973 Lighthill report  [58] , which prompted the British Science Research Council to slash its support for AI. Similarly, Menzies  [59]  described AI as going through a \"peak of inflated expectations\" in the 1980s followed by a \"trough of disillusionment\" in the late 1980s and early 1990s. Most recently, writing in 2018, Bentley  [60]  (p. 11) derided beliefs about superintelligence and instead urges: \"Do not be fearful of AI-marvel at the persistence and skill of those human specialists who are dedicating their lives to help create it. And appreciate that AI is helping to improve our lives every day.\" (For criticism of Bentley  [60] , see  [61] .) This suggests that some superintelligence skepticism may serve the political goal of protecting the broader field of AI. Superintelligence skepticism that is aimed at protecting the field of AI may be less of a factor during the current period of intense interest in AI. At least for now, the field of AI does not need to defend its value-its value is rather obvious, and AI researchers are not lacking for job security. Importantly, the current AI boom is largely based on actual accomplishments, not hype. Therefore, while today's AI researchers may view superintelligence as a distraction, they are less likely to view it as a threat to their livelihood. However, some may nonetheless view superintelligence in this way, especially those who have been in the field long enough to witness previous boom-and-bust cycles. Likewise, the present situation could change if the current AI boom eventually cycles into another bust-another winter. Despite the success of current AI, there are arguments that it is fundamentally limited  [62] . The prospect of a new AI winter could be a significant factor in politicized superintelligence skepticism. A different type of example comes from public intellectuals who profess superintelligence skepticism based on questionable reasoning. A notable case of this is the psychologist and public intellectual Steven Pinker. Pinker recently articulated a superintelligence skepticism that some observers have likened to politicized climate skepticism  [63, 64] . Pinker does resemble some notable political skeptics: a senior scholar with an academic background in an unrelated topic who is able to use his (and it is typically a he) platform to advance his skeptical views. Additionally, a close analysis of Pinker's comments on superintelligence finds them to be flawed and poorly informed by existing research  [65] . Pinker's superintelligence skepticism appears to be advancing a broader narrative of human progress, and may be making the intellectual sin of putting this conclusion before the analysis of superintelligence. However, his particular motivations are, to the present author's knowledge, not documented (It would be especially ironic for Pinker to politicize skepticism based on flawed intellectual reasoning, since he otherwise preaches a message intellectual virtue). A third type of example of potential politicized superintelligence skepticism comes from the corporate sector. Several people in leadership positions at technology corporations have expressed superintelligence skepticism, including Eric Schmidt (Executive Chairman of Alphabet, the parent company of Google)  [66]  and Mark Zuckerberg (CEO of Facebook)  [67] . Since this skepticism comes the corporate sector, it has some resemblance to risk-profit politicized skepticism and may likewise have the most potential to shape public discourse and policy. One observer postulated that Zuckerberg professes superintelligence skepticism to project the idea that \"software is always friendly and tame\" and avoid the idea \"that computers are intrinsically risky\", the latter of which \"has potentially dire consequences for Zuckerberg's business and personal future\"  [67] . While this may just be conjecture, it does come at a time in which Facebook is under considerable public pressure for its role in propagating fake news and influencing elections, which, although unrelated to superintelligence, nonetheless provides an antiregulatory motivation to downplay risks associated with computers. To summarize, there may already be some politicized superintelligence skepticism, coming from AI academics seeking to protect their field, public intellectuals seeking to advance a certain narrative about the world, and corporate leaders seeking to avoid regulation. However, it is not clear how much superintelligence skepticism is already politicized, and there are indications that it may be limited, especially compared to what has occurred for other issues. On the other hand, superintelligence is a relatively new public issue (with a longer history in academia), so perhaps its politicization is just beginning. Finally, it is worth noting that while superintelligence has not been politicized to the extent that climate change has, there is at least one instance of superintelligence being cited in the context of climate skepticism. Cass  [68, 69]  cited the prospect of superintelligence as a reason to not be concerned about climate change. A counter to this argument is that, even if superintelligence is a larger risk, addressing climate change can still reduce the overall risk faced by humanity. Superintelligence could also be a solution to climate change, and thus may be worth building despite the risks it poses. At the same time, if climate change has been addressed independently, then this reduces the need to take risks in building superintelligence  [70] . \n Prospects for Politicized Superintelligence Skepticism Will superintelligence skepticism be (further) politicized? Noting the close historical association between politicized skepticism and corporate profits-at least for risk-profit politicized skepticism-an important question is whether superintelligence could prompt profit-threatening regulations. AI is now being developed by some of the largest corporations in the world. Furthermore, a recent survey found artificial general intelligence projects at several large corporations, including Baidu, Facebook, Google, Microsoft, Tencent, and Uber  [19] . These corporations have the assets to conduct politicized skepticism that is every bit as large as that of the tobacco, fossil fuel, and industrial chemicals industries. It should be noted that the artificial general intelligence projects at these corporations were not found to indicate substantial skepticism. Indeed, some of them are outspoken in concern about superintelligence. Moreover, out of 45 artificial general intelligence projects surveyed, only two were found to be dismissive of concerns about the risks posed by the technology  [19] . However, even if the AI projects themselves do not exhibit skepticism, the corporations that host them still could. Such a scenario would be comparable to that of ExxonMobil, whose scientists confirmed the science of climate change even while corporate publicity campaigns professed skepticism  [7] . The history shows that risk-profit politicized skepticism is not inherent to corporate activity-it is generally only found when profits are at stake. The preponderance of corporate research on artificial general intelligence suggests at least a degree of profitability, but, at this time, it is unclear how profitable it will be. If it is profitable, then corporations are likely to become highly motivated to protect it against outside restrictions. This is an important factor to monitor as the technology progresses. In public corporations, the pressure to maximize shareholder returns can motivate risk-profit politicized skepticism. However, this may be less of a factor for some corporations in the AI sector. In particular, voting shares constituting a majority of voting power at both Facebook and Alphabet (the parent company of Google) are controlled by the companies' founders: Mark Zuckerberg at Facebook  [71]  and Larry Page and Sergey Brin at Alphabet  [72] . Given their majority stakes, the founders may be able to resist shareholder pressure for politicized skepticism, although it is not certain that they would, especially since leadership at both companies already display superintelligence skepticism. Another factor is the political ideologies of those involved in superintelligence. As discussed above, risk-profit politicized skepticism of other issues is commonly driven by people with pro-capitalist, anti-socialist, and anti-communist political ideologies. Superintelligence skepticism may be more likely to be politicized by people with similar ideologies. Some insight into this matter can be obtained from a recent survey of 600 technology entrepreneurs  [73] , which is a highly relevant demographic. The study finds that, contrary to some conventional wisdom, this demographic tends not to hold libertarian ideologies. Instead, technology entrepreneurs tend to hold views consistent with American liberalism, but with one important exception: technology entrepreneurs tend to oppose government regulation. This finding suggests some prospect for politicizing superintelligence skepticism, although perhaps not as much as may exist in other industries. Further insight can be found from the current political activities of AI corporations. In the US, the corporations' employees donate mainly to the Democratic Party, which is the predominant party of American liberalism and is more pro-regulation. However, the corporations themselves have recently shifted donations to the Republican Party, which is the predominant party of American conservatism and is more anti-regulation. Edsall  [74]  proposed that this divergence between employees and employers is rooted in corporations' pursuit of financial self-interest. A potential implication of this is that, even if the individuals who develop AI oppose risk-profit politicized skepticism, the corporations that they work for may support it. Additionally, the corporations have recently been accused of using their assets to influence academic and think tank research on regulations that the corporations could face  [75, 76] , although at least some of the accusations have been disputed  [77] . While the veracity of these accusations is beyond the scope of this paper, they are at least suggestive of the potential for these corporations to politicize superintelligence skepticism. AI corporations would not necessarily politicize superintelligence skepticism, even if profits may be at stake. Alternatively, they could express concern about superintelligence to portray themselves as responsible actors and likewise avoid regulation. This would be analogous to the strategy of \"greenwashing\" employed by companies seeking to bolster their reputation for environmental stewardship  [78] . Indeed, there have already been some expressions of concern about superintelligence by AI technologists, and likewise some suspicion that the stated concern has this sort of ulterior motive  [79] . To the extent that corporations do politicize superintelligence skepticism, they are likely to mainly emphasize doubt about the risks of superintelligence. Insofar as superintelligence could be beneficial, corporations may promote this, just as they promote the benefits of fossil fuels (for transportation, heating, etc.) and other risky products. Or, AI corporations may promote the benefits of their own safety design and sow doubt about the safety of their rivals' designs, analogous to the marketing of products whose riskiness can vary from company to company, such as automobiles. Alternatively, AI corporations may seek to sow doubt about the possibility of superintelligence, calculating that this would be their best play for avoiding regulation. As with politicized skepticism about other technologies and products, there is no one standard formula that every company always adopts. For their part, academic superintelligence skeptics may be more likely to emphasize doubt about the mere possibility of superintelligence, regardless of whether it would be beneficial or harmful, due to reputational concerns. Or, they could focus skepticism on the risks, for similar reasons as corporations: academic research can also be regulated, and researchers do not always welcome this. Of course, there are also academics who do not exhibit superintelligence skepticism. Again, there is no one standard formula. \n Potential Effectiveness of Politicized Superintelligence Skepticism If superintelligence skepticism is politicized, several factors point to it being highly effective, even more so than for the other issues in which skepticism has been politicized. First, some of the experts best positioned to resolve the debate are also deeply implicated in it. To the extent that superintelligence is a risk, the risk is driven by the computer scientists who would build superintelligence. These individuals have intimate knowledge of the technology and thus have an essential voice in the public debate (though not the only essential voice). This is distinct from issues such as tobacco or climate change, in which the risk is mainly assessed by outside experts. It would be as if the effect of tobacco on cancer was studied by the agronomists who cultivate tobacco crops, or if the science of climate change was studied by the geologists who map deposits of fossil fuels. With superintelligence, a substantial portion of the relevant experts have a direct incentive to avoid any restrictions on the technology, as do their employers. This could create a deep and enduring pool of highly persuasive skeptics. Second, superintelligence skepticism has deep roots in the mainstream AI computer science community. As noted above, this dates to the days of AI winter. Thus, skeptics may be abundant even where they are not funded by industry. Indeed, most of the skeptics described above do not appear to be speaking out of any industry ties, and thus would not have an industry conflict of interest. They could still have a conflict of interest from their desire in protect the reputation of their field, but this is a subtler matter. Insofar as they are perceived to not have a conflict of interest, they could be especially persuasive. Furthermore, even if their skepticism is honest and not intended for any political purposes, it could be used by others in dishonest and political ways. Third, superintelligence is a topic for which the uncertainty is inherently difficult to resolve. It is a hypothetical future technology that is qualitatively different from anything that currently exists. Furthermore, there is concern that its mere existence could be catastrophic, which could preclude certain forms of safety testing. It is thus a risk that defies normal scientific study. In this regard, it is similar to climate change: moderate climate change can already be observed, as can moderate forms of AI, but the potentially catastrophic forms have not yet materialized and possibly never will. However, climate projections can rely on some relatively simple physics-at its core, climate change largely reduces to basic physical chemistry and thermodynamics. (The physical chemistry covers the nature of greenhouse gasses, which are more transparent to some wavelengths of electromagnetic radiation than to others. The thermodynamics covers the heat transfer expected from greenhouse gas buildup. Both effects can be demonstrated in simple laboratory experiments. Climate change also involves indirect feedback effects on much of the Earth system, including clouds, ice, oceans, and ecosystems, which are often more complex and difficult to resolve and contribute to ongoing scientific uncertainty.) In contrast, AI projections must rely on notions of intelligence, which is not so simple at all. For this reason, it is less likely that scholarly communities will converge on any consensus position on superintelligence in the way that they have on other risks such as climate change. Fourth, some corporations that could develop superintelligence may be uniquely well positioned to influence public opinion. The corporations currently involved in artificial general intelligence research include some corporations that also play major roles in public media. As a leading social media platform, Facebook in particular has been found to be especially consequential for public opinion  [80] . Corporations that serve as information gateways, such as Baidu, Google, and Microsoft, also have unusual potential for influence. These corporations have opportunities to shape public opinion in ways that the tobacco, fossil fuel, and industrial chemicals industries cannot. While the AI corporations would not necessarily exploit these opportunities, it is an important factor to track. In summary, while it remains to be seen whether superintelligence skepticism will be politicized, there are some reasons for believing it will be, and that superintelligence would be an especially potent case of politicized skepticism. \n Opportunities for Constructive Action Politicized superintelligence skepticism would not necessarily be harmful. As far as this paper is concerned, it is possible that, for superintelligence, skepticism is the correct view, meaning that superintelligence may not be built, may not be dangerous, or may not merit certain forms of imminent attention. (The paper of course assumes that superintelligence is worth some imminent attention, or otherwise it would not have been written.) It is also possible that, even if superintelligence is a major risk, government regulations could nonetheless be counterproductive, and politicized skepticism could help avoid that. That said, the history of politicized skepticism (especially risk-profit politicized skepticism) shows a tendency for harm, which suggests that politicized superintelligence skepticism could be harmful as well. With this in mind, one basic opportunity is to raise awareness about politicized skepticism within communities that discuss superintelligence. Superintelligence skeptics who are motivated by honest intellectual norms may not wish for their skepticism to be used politically. They can likewise be cautious about how to engage with potential political skeptics, such as by avoiding certain speaking opportunities in which their remarks would be used as a political tool instead of as a constructive intellectual contribution. Additionally, all people involved in superintelligence debates can insist on basic intellectual standards, above all by putting analysis before conclusions and not the other way around. These are the sorts of things that an awareness of politicized skepticism can help with. Another opportunity is to redouble efforts to build scientific consensus on superintelligence, and then to draw attention to it. Currently, there is no consensus. As noted above, superintelligence is an inherently uncertain topic and difficult to build consensus on. However, with some effort, it should be possible to at least make progress towards consensus. Of course, scientific consensus does not preclude politicized skepticism-ongoing climate skepticism attests to this. However, it can at least dampen the politicized skepticism. Indeed, recent research has found that the perception of scientific consensus increases acceptance of the underlying science  [81] . A third opportunity is to engage with AI corporations to encourage them to avoid politicizing skepticism about superintelligence or other forms of AI. Politicized skepticism is not inevitable, and while corporate leaders may sometimes feel as though they have no choice, there may nonetheless be options. Furthermore, the options may be especially effective at this early stage in superintelligence research, in which corporations may have not yet established internal policy or practices. A fourth opportunity is to follow best practices in debunking misinformation in the event that superintelligence skepticism is politicized. There is a substantial literature on the psychology of debunking  [81] [82] [83] . A debunking handbook written for a general readership  [82]  recommends: (1) focusing on the correct information to avoid cognitively reinforcing the false information; (2) preceding any discussion of the false information with a warning that it is false; and (3) when debunking false information, also give the correct information so that people are not left with a gap in their understanding of the topic. The handbook further cautions against using the information deficit model of human cognition, which proposes that mistaken beliefs can be corrected simply by providing the correct information. The information deficit model is widely used in science communication, but it has been repeatedly found to work poorly, especially in situations of contested science. This sort of advice could be helpful to efforts to counter superintelligence misinformation. Finally, the entire AI community should insist that policy be made based on an honest and balanced read of the current state of knowledge. Burden of proof requirements should not be abused for private gain. As with climate change and other global risks, the world cannot afford to prove that superintelligence would be catastrophic. By the time uncertainty is eliminated, it could be too late. \n Conclusions Some people believe that superintelligence could be a highly consequential technology, potentially even a transformative event in the course of human history, with either profoundly beneficial or extremely catastrophic effects. Insofar as this belief is plausible, superintelligence may be worth careful advance consideration, to ensure that the technology is handled successfully. Importantly, this advance attention should include social science and policy analysis, and not just computer science. Furthermore, even if belief in superintelligence is mistaken, it can nonetheless be significant as a social and political phenomenon. This is another reason for social science and policy analysis. This paper is a contribution to the social science and policy analysis of superintelligence. Furthermore, despite the unprecedented nature of superintelligence, this paper shows that there are important historical and contemporary analogs that can shed light on the issue. Much of what could occur for the development of superintelligence has already occurred for other technologies. Politicized skepticism is one example of this. One topic not covered in this paper is the prospect of beliefs that superintelligence will occur and/or will be harmful to be politicized. Such a phenomenon could be analogous to, for example, belief in large medical harms from nuclear power, or, phrased differently, skepticism about claims that nuclear power plants are medically safe. The scientific literature on nuclear power finds medical harms to be substantially lower than is commonly believed  [84] . Overstated concern (or \"alarmism\") about nuclear power can likewise be harmful, for example by increasing use of fossil fuels. Similarly, the fossil fuel industry could politicize this belief for its own benefit. By the same logic, belief in superintelligence could also be politicized. This prospect is left for future research, although much of this paper's analysis may be applicable. Perhaps the most important lesson of this paper is that the development of superintelligence could be a contentious political process. It could involve aggressive efforts by powerful actors-efforts that not only are inconsistent with basic intellectual ideals, but that also actively subvert those ideals for narrow, self-interested gain. This poses a fundamental challenge to those who seek to advance a constructive study of superintelligence. Funding: This research received no external funding.", "date_published": "n/a", "url": "n/a", "filename": "information-09-00209.tei.xml", "abstract": "This paper explores the potential for skepticism about artificial superintelligence to be used as a tool for political ends. Superintelligence is AI that is much smarter than humans. Superintelligence does not currently exist, but it has been proposed that it could someday be built, with massive and potentially catastrophic consequences. There is substantial skepticism about superintelligence, including whether it will be built, whether it would be catastrophic, and whether it is worth current attention. To date, superintelligence skepticism appears to be mostly honest intellectual debate, though some of it may be politicized. This paper finds substantial potential for superintelligence skepticism to be (further) politicized, due mainly to the potential for major corporations to have a strong profit motive to downplay concerns about superintelligence and avoid government regulation. Furthermore, politicized superintelligence skepticism is likely to be quite successful, due to several factors including the inherent uncertainty of the topic and the abundance of skeptics. The paper's analysis is based on characteristics of superintelligence and the broader AI sector, as well as the history and ongoing practice of politicized skepticism on other science and technology issues, including tobacco, global warming, and industrial chemicals. The paper contributes to literatures on politicized skepticism and superintelligence governance.", "id": "3c38bfc22b66e5fffc943a33d8004be1"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Asaf Tzachor", "Jess Whittlestone", "Lalitha Sundaram", "Seán Ó Héigeartaigh"], "title": "Artificial intelligence in a crisis needs ethics with urgency", "text": "T he novel coronavirus pandemic (COVID-19) is the largest global crisis in a generation, hitting the world at a time when artificial intelligence (AI) is showing potential for widespread real-world application. We are currently seeing a rapid increase in proposals for how AI can be used in many stages of pandemic prevention and response. AI can aid in detecting, understanding and predicting the spread of disease, which can provide early warning signs and inform effective interventions  1  . AI may improve the medical response to the pandemic in several ways: supporting physicians by automating aspects of diagnosis  2  , prioritizing healthcare resources  3  , and improving vaccine and drug development  4  . AI also has potential applications beyond immediate response, such as in combating online misinformation about COVID-19  5  . The current crisis presents an unprecedented opportunity to leverage AI for societal benefit. However, the urgency with which new technologies must be deployed raises particularly challenging ethical issues and risks. There is growing concern that the use of AI and data in response to COVID-19 may compromise privacy and civil liberties by incentivizing the collection and processing of large amounts of data, which may often be private or personal  6  . More broadly, although AI clearly has a great deal to offer, we must be careful not to overestimate its potential. Its efficacy will heavily depend on the reliability and relevance of the data available. With the worldwide spread of COVID-19 occurring so quickly, obtaining sufficient data for accurate AI forecasting and diagnosis is challenging. Even where AI models are strictly speaking accurate, they may have differential impacts across subpopulations, with harmful consequences that are difficult to predict in advance  7  . A further concern is that the lack of transparency in AI systems used to aid decision-making around COVID-19 may make it near impossible for the decisions of governments and public officials to be subject to public scrutiny and legitimation  8  . Finally, the current crisis may have longer-term impacts on public trust and norms around the use of AI in society. How these develop will depend on perceptions of how successful and responsible use of AI to address COVID-19 is. \n The challenge of ethics in a crisis Robust ethics and risk assessment processes are needed to ensure AI is used responsibly in response to COVID-19. However, implementing these at a time of crisis is far from straightforward, especially where new technologies need to be deployed at unprecedented speed and scale. For example, forecasting models have to be available at the early stages of disease spread and make use of all possible data to productively inform policy interventions. Current processes for ethics and risk assessment around uses of AI are still relatively immature, and the urgency of a crisis highlights their limitations. Much work in AI ethics in recent years has focused on developing high-level principles, but these principles say nothing about what to do when principles come into conflict with one another  9  . For example, principles do not tell us how to balance the potential of AI to save lives (the principle of 'beneficence') against other important values such as privacy or fairness. One common suggestion for navigating such tensions is through engagement with diverse stakeholder groups, but this may be difficult to enact with sufficient speed at times of crisis. When new technologies may pose unknown risks, we would ordinarily try to introduce them in gradual, iterative ways, allowing time for issues to be identified and addressed. In the context of a crisis, however, there is a stark trade-off between a cautious approach and the need to deploy technological solutions at scale. For example, there may be pressure to rely on systems with less human oversight and potential for override due to staff shortages and time pressures, but this must be carefully balanced against the risk of failing to notice or override crucial failures. This does not mean that ethics should be neglected at times of crisis. It only emphasizes that we must find ways to conduct ethical review and risk assessment with the same urgency that motivates the development of AI-based solutions. \n Doing ethics with urgency We suggest that ethics with urgency must at a minimum incorporate the following components: (1) the ability to think ahead rather than dealing with problems reactively, (2) more robust procedures for assuring the behaviour and safety of AI systems, and (3) building public trust through independent oversight. First, ethics with urgency must involve thinking through possible issues and risks as thoroughly as possible before systems are developed and deployed in the world. This need to think ahead is reflected in the notion of 'ethics by design': making ethical considerations part of the process of developing new applications of AI, not an afterthought  10  . For example, questions such as 'what data do we need and what issues might this raise?' and 'how do we build this model so that it is possible to interrogate key assumptions?' need to be considered throughout the development process. This means that experts in ethics and risk assessment need to be involved in teams developing AI-based solutions from the beginning, and much clearer guidelines are needed for engineers and developers to think through these issues. An ethics by design approach should also be supplemented with more extensive foresight work, looking beyond the more obvious and immediate ethical issues, and considering a wider range of longer-term and more systemic impacts. By synthesizing diverse sources of expertise, established foresight methodologies can be used to identify new comment risks and key uncertainties likely to shape the future, and use this to make better informed decisions today  11  . Second, where applications of AI are used at scale in safety-critical domains such as healthcare, ensuring the safety and reliability of those systems across a range of scenarios is of crucial importance. Finding ways to rapidly conduct robust testing and verification of systems will therefore be central to doing ethics with urgency. We suggest that the application of AI in crisis scenarios should in particular be heavily informed by research on best practices for the verification and validation of autonomous systems  12  . It may also be worthwhile for governments to fund further work on methods for establishing the reliability of machine learning systems across a range of circumstances, particularly where those systems may be deployed in high-stakes crisis scenarios. Third, an important aspect of ethics with urgency is building public trust in how AI is being used. If governments use AI systems in ways perceived to be either mistaken or problematically value-laden, this could result in a loss of public trust severe enough to drastically reduce support for beneficial uses of AI not just in this crisis, but also in the future. Building public trust around new uses of technology may be particularly challenging in crisis times, where the need to move fast makes it easier for governments to fall back on opaque and centralized forms of decision-making. Several analyses of past pandemics have argued that transparency and public scrutiny are essential for maintaining public trust  13  . An independent oversight body, responsible for reviewing any potential risks and ethical issues associated with new technologies and producing publicly available reports, could help ensure public transparency. This oversight body could, among other approaches, make use of techniques such as 'red teaming' to rigorously challenge systems and their assumptions, unearthing any limitations and biases in the applications being proposed  14  . Red teaming is widely used in security settings, but can be applied broadly: at its core, red teaming is a way of challenging the blind spots of a team by explicitly looking for flaws from an outsider or adversarial perspective. As well as allowing developers to identify and fix issues before deployment, such processes could help assure public stakeholders that the interests and values of different groups are being thoroughly considered, and that all eventualities are prepared for. \n conclusion As the COVID-19 pandemic illustrates, times of crisis can necessitate rapid deployment of new technologies in order to save lives. However, this urgency both makes it more likely that ethical issues and risks will arise, and makes them more challenging to address. Rather than neglecting ethics, we must find ways to do ethics with urgency too. We strongly encourage technologists, ethicists, policymakers and healthcare professionals to consider how ethics can be implemented at speed in the ongoing response to the COVID-19 crisis. If ethical practices can be implemented with urgency, the current crisis could provide an opportunity to drive greater application of AI for societal benefit, and to build public trust in such applications. ❐ Asaf Tzachor 1 ✉ , Jess Whittlestone  2 , Lalitha Sundaram 1 and Seán Ó hÉigeartaigh 2 1 Centre for the Study of Existential Risk, University of Cambridge, Cambridge, UK. 2 Leverhulme Centre for the Future of Intelligence, University of Cambridge, Cambridge, UK. ✉ e-mail: at875@cam.ac.uk Published online: 22 June 2020 https://doi.org/10.1038/s42256-020-0195-0 \n\t\t\t NaTure MachiNe iNTelligeNce | VOL 2 | JuLy 2020 | 365-366 | www.nature.com/natmachintell", "date_published": "n/a", "url": "n/a", "filename": "s42256-020-0195-0.tei.xml", "abstract": "Artificial intelligence tools can help save lives in a pandemic. However, the need to implement technological solutions rapidly raises challenging ethical issues. We need new approaches for ethics with urgency, to ensure AI can be safely and beneficially used in the COVID-19 response and beyond.", "id": "88aba350de7cff39db529da0f30f4cc7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Peter Cihon", "Matthijs M Maas", "Luke Kemp"], "title": "Should Artificial Intelligence Governance be Centralised? Design Lessons from History", "text": "INTRODUCTION In 2018, Canada and France proposed the International Panel on Artificial Intelligence (IPAI). After being rejected at the G7 in 2019, negotiations shifted to the OECD and are presently ongoing. As the field of AI continues to mature and spark public interest and legislative concern  [41] , the priority of such governance initiatives reflects the growing appreciation that AI has the potential to dramatically change the world for both good and ill  [9] . Research into AI governance needs to keep pace with policy-making and technological change. Choices made today may have long-lasting impacts on policymakers' ability to address numerous AI policy problems  [7] . Effective governance can promote safety, accountability, and responsible behaviour in the research, development, and deployment of AI systems. AI governance research to date has predominantly focused at the national and sub-national levels  [6, 16, 44] . Research into AI global governance remains relatively nascent (though see  [5] ). Kemp et al.  [24]  have called for specialised, centralised intergovernmental agencies to coordinate policy responses globally, and others have called for a centralised 'International Artificial Intelligence Organisation'  [14] . Others favour more decentralised arrangements based around 'Governance Coordinating Committees', global standards, or existing international law instruments  [8, 28, 47] . No one has taken a step back to inquire: what would the history of multilateralism suggest, given the state and trajectory of AI? Should AI governance be centralised or decentralised? 'Centralisation', in this case, refers to the degree to which the coordination, oversight and/or regulation of a set of AI policy issues or technologies are housed under a single (global) institution. This is not a binary choice; it exists across a spectrum. Trade is highly (but not entirely) centralised under the umbrella of the WTO. In contrast, environmental multilateralism is much more decentralised. In this paper, we seek to help the community of researchers, policymakers, and other stakeholders in AI governance understand the advantages and disadvantages of centralisation. This may help set terms and catalyse a much-needed debate to inform governance design decisions. We first outline the international governance challenges of AI, and review early proposed global responses. We then draw on existing literatures on regime fragmentation  [3]  and 'regime complexes'  [36]  to assess considerations in centralising the international governance of AI. We draw on the history of other international regimes  1  to identify considerations that speak in favour or against designing a centralised regime complex for AI. We conclude with two recommendations. First, many trade-offs are contingent on how well-designed a central body would be. An adaptable, powerful institution with a manageable mandate would be beneficial, but a poorly designed body could prove a fate worse than fragmentation. Second, for now there should be structured monitoring of existing efforts to see whether they are they are self-organising or insufficient. \n THE STATE OF AI GOVERNANCE There is debate as to whether AI is a single policy area or a diverse series of issues. Some claim that AI cannot be cohesively regulated as it is a collection of disparate technologies, with different risk profiles across different applications and industries  [45] . This is an important but not entirely convincing objection. The technical field has no settled definition for 'AI', 2 so it should be no surprise that defining a manageable scope for AI governance will be difficult. Yet this challenge is not unique to AI: definitional issues abound in areas such as environment and energy, but have not figured prominently in debates over centralisation. Indeed, energy and environment ministries are common at the domestic level, despite problems in setting the boundaries of natural systems and resources. We contend that there are numerous ways in which a centralised body could be designed for AI governance. For example, a centralised approach could carve out a subset of interlinked AI issues to cover. This could involve focusing on the potentially highrisk applications of AI systems, such as AI-enabled cyberwarfare, lethal autonomous weapons (LAWS), other advanced military applications, or high-level machine intelligence (HLMI).  3  Another approach could govern underlying hardware resources (e.g. largescale compute resources) or software libraries. We are agnostic on the specifics of how centralisation could or should be implemented, and instead focus on the costs and benefits of centralisation in the abstract. The exact advantages and disadvantages of centralisation are likely to vary depending on the institutional design. This is an important area of further study, particularly once more specific proposals are put forward. However, such work must be grounded in a higher-level investigation of trade-offs in centralising AI governance. It is this foundational analysis which we seek to offer. Numerous AI issues could benefit from international cooperation. These include the potentially catastrophic applications mentioned above. It also encompasses more quotidian uses, such as AI-enabled cybercrime; human health applications; safety and regulation of autonomous vehicles and drones; surveillance, privacy and datause; and labour automation. Multilateral coordination could also use AI to tackle other global problems such as climate change  [43] , or help meet the Sustainable Development Goals  [46] . This is an illustrative but not exhaustive list of international AI policy issues. Global regulation across these issues is currently nascent, fragmented, yet evolving. A wide range of UN institutions have begun to undertake some activities on AI  [20] . The bodies covering AI policy issues range across existing organisations including the International Labour Organisation (ILO), International Telecommunication Union (ITU), and UNESCO. This is complemented by budding regulations and working groups across the International Organisation for Standardisation (ISO), International Maritime Organisation (IMO), International Civil Aviation Organisation (ICAO), and other bodies, as well as treaty amendments, such as the updating of the Vienna Convention on Road Traffic to encompass autonomous vehicles  [28] , or the ongoing negotiations at the Convention on Certain Conventional Weapons (CCW) on LAWS. The UN System Chief Executives Board (CEB) for Coordination through the High-Level Committee on Programmes has been empowered to draft a system-wide AI capacity building strategy. The High-level Panel on Digital Cooperation has also sought to gather together common principles and ideas for AI relevant areas  [19] . Whether these initiatives bear fruit, however, remains questionable, as many of the involved international organisations have fragmented membership, were not originally created to address AI issues and lack effective enforcement or compliance mechanisms  [32, p.2] . The trajectory of these initiatives matters. How governance is initially organised can be central to its success. Debates over centralisation and fragmentation are long-lasting and prominent with good reason. How we structure international cooperation can be critical to its success, and most other debates often implicitly hinge on structural debates. Fragmentation and centralisation exist across a spectrum. In a world lacking a global government, some fragmentation will always prevail. But the degree to which it prevails is crucial. We define 'fragmentation' as a patchwork of international organisations and institutions which focus on a particular issue area, but differ in scope, membership and often rules  [3, p.16 ]. We define centralisation as an arrangement in which governance of a particular issue lies under the authority of a single umbrella body. A regime complex is a network of three or more international regimes on a common issue area. These should have overlapping membership and cause potentially problematic interactions  [36, p.29] . These definitions and terms are by nature normatively loaded. For example, some may find 'decentralisation' to be a positive framing, while others may see 'fragmentation' to possess negative connotations. Recognising this, we seek to use these terms in a primarily analytical manner. We will use findings from each of these theoretical areas to inform our discussion of the history of multilateral fragmentation and its implications for AI governance. \n CENTRALISATION CRITERIA: HISTORY OF GOVERNANCE TRADE-OFFS In the following discussion, we explore a series of considerations for AI governance. Political power and efficient participation support centralisation. The breadth vs. depth dilemma, as well as slowness and brittleness support decentralisation. Policy coordination and forum shopping considerations can cut both ways. \n Political Power Regimes embody power in their authority over rules, norms, and knowledge beyond states' exclusive control. A more centralised regime will see this power concentrated among fewer institutions. A centralised, powerful architecture is likely to be more influential against competing international organisations and with constituent states  [36, pp.36-7 ]. An absence of centralised authority to manage regime complexes has presented challenges in the past. Across the proliferation of Multilateral Environmental Agreements (MEAs) there is no requirement to cede responsibility to the UN Environmental Programme in the case of overlap or competition. This has led to turf wars, inefficiencies and even contradictory policies  [3] . One of the most notable examples is that of hydrofluorocarbons (HFCs). HFCs are potent greenhouse gases, and yet their use has been encouraged by the Montreal Protocol since 1987 as a replacement for ozonedepleting substances. This has only recently been resolved via the 2015 Kigali Amendment to the Montreal Protocol, which itself has a prolonged implementation period. Similarly, the internet governance regime complex is diffuse. Multiple venues and norms govern technical standards, cyber crime, human rights, and warfare  [35] . Although the UN Internet Governance Forum (IGF) discusses several cross-cutting issues, it does not have a mandate to consolidate even principles, let alone negotiate new formal agreements  [33] . In contrast, other centralised regimes have supported effective management. For example, under the umbrella of the WTO, norms such as the most-favoured-nation principle (equally treating all WTO member states) principle have become the bedrock of international trade. The power and track-record of the WTO is so formidable that it has created a chilling effect: the fear of colliding with WTO norms and rules has led environmental treaties to self-censor and actively avoid discussing or deploying trade-related measures  [12] . Both the chilling effect and the remarkably powerful application of common trade rules were not a marker of international trade until the establishment of the WTO. The power of these centralised body has stretched beyond influencing states in the domain of trade, to moulding related issues. Political power offers further benefits in governing emerging technologies that are inherently uncertain in both substance and policy impact. Uncertainty in technology and preferences has been associated with some increased centralisation in regimes  [25] . There may also be benefits to housing a foresight capacity within the regime complex, to allow for accelerated or even proactive efforts  [39] . Centralised AI governance would enable an empowered organisation to more effectively use foresight analyses to inform policy responses across the regime complex. \n Supporting Efficiency & Participation Decentralised AI governance may undermine efficiency and inhibit participation. States often create centralised regimes to reduce costs, for instance by eliminating duplicate efforts, yielding economies of scale within secretariats, and simplifying participation  [15] . Conversely, fragmented regimes may force states to spread resources and funding over many distinct institutions, particularly limiting the ability of less well-resourced states or parties to participate fully  [32, p.2] . Historically, decentralised regimes have presented cost and related participation concerns. Hundreds of related and sometimes overlapping international environmental agreements can create 'treaty congestion'  [1] . This complicates participation and implementation for both developed and developing nations  [15] . This includes costs associated with travel to different forums, monitoring and reporting for a range of different bodies, and duplication of effort by different secretariats (ibid.). Similar challenges are already being witnessed in AI governance. Simultaneous and globally distributed meetings pose burdensome participation costs for civil society. Fragmented organisations must duplicatively invest in high-demand machine learning subject matter experts to inform their activities. Centralisation would support institutional efficiency and participation. \n Slowness & Brittleness of Centralised Regimes One potential problem of centralisation lies in the relatively slow process of establishing centralised institutions, which may often be outpaced by the rate of technological change. Another challenge lies in centralised institutions' brittleness after they are established, i.e., their vulnerability to regulatory capture, or failure to react to changes in the problem landscape. Establishing new international institutions is often a slow process. For example, the Kyoto Protocol took three years of negotiations to create and then another eight to enter into force. This becomes even more onerous with higher participation and stakes. Under the GATT, negotiations for a 26% cut in tariffs between 19 countries took 8 months in 1947. The Uruguay round, beginning in 1986, took 91 months to achieve a tariff reduction of 38% between 125 parties  [31] . International law has been quick to respond to technological changes in some cases, and delayed in others  [42, p.184 ]. Decentralised efforts may prove quicker to respond to complex, 'transversal' issues, if they rely more on informal institutions with a smaller but like-minded membership  [32, pp.2-3] . Centralised AI governance may be particularly vulnerable to sparking lengthy negotiations, because progress on centralised regimes for new technologies tends to be hard if a few states hold clearly unequal stakes in the technology, or if there are significant differences in information and expertise among states or between states and private industry  [42, pp.187-94] . Both these conditions closely match the context of AI technology. Moreover, because AI technology develops rapidly, such slow implementation of rules and principles could lead to certain actors taking advantage by setting de facto arrangements or extant state practice. Even after its creation, a centralised regime can be brittle; the very qualities that provide it with political power may exacerbate the adverse effects of regulatory capture; the features that ensure institutional stability, may also mean that the institution cannot adapt quickly to unanticipated outside stressors outside its established mission. The regime might break before it bends. The first potential risk is regulatory capture. Given the high profile of AI issue areas, political independence is paramount. However, as illustrated by numerous cases, including undue corporate influence in the WHO during the 2009 H1N1 pandemic  [11] , no institution is fully immune to regime capture, and centralisation may reduce the costs of lobbying, making capture easier by providing a single locus of influence. On the other hand, a regime complex comprising many parallel institutions could find itself vulnerable to capture by powerful actors, who are better positioned than smaller parties to send representatives to every forum. Moreover, centralised regimes entail higher stakes. Many issues are in a single basket and thus failure is more likely to be severe if it does occur. International institutions can be notoriously pathdependent and thus fail to adjust to changing circumstances, as seen with the ILO's considerable difficulties in reforming its participation and rulemaking processes in the 1990s  [2] . The public failure of a flagship global AI institution or governance effort could have lasting political repercussions. It could strangle subsequent, more well-conceived proposals in the crib, by undermining confidence in multilateral governance generally or capable governance on AI issues specifically. By contrast, for a decentralized regime complex to similarly fail, all of its component institutions would need to simultaneously 'break' or fail to innovate at once.  4  A centralised institution that does not outright collapse, but which remains ineffective, may become a blockade against better efforts. Ultimately, brittleness is not an inherent weakness of centralisationand indeed depends far more on institutional design details. There may be strategies to 'innovation-proof'  [29]  governance regimes. Periodic renegotiation, modular expansion, 'principles based regulation', or sunset clauses can also support ongoing reform  [30, pp.29-30] . Such approaches have often proved successful historically, due partially to decentralisation but, importantly, also to particular designs. \n The Breadth vs. Depth Dilemma Pursuing centralisation may create an overly high threshold that limits participation. All multilateral agreements face a trade-off between having higher participation ('breadth') or stricter rules and greater ambition of commitments ('depth'). The dilemma is particularly evident for centralised institutions that are intended to be powerful and require strong commitments from states. However, the opposite dynamics of sacrificing depth for breadth can also pose risks. The 2015 Paris Agreement on Climate Change was significantly watered down to allow for the legal participation of the US. Anticipated difficulties in ratification through the Senate led to negotiators opting for a 'pledge and review' structure with few legal obligations. Thus, the US could join simply through the approval of the executive  [23] . In this case, inclusion of the US (which at any rate proved temporary) came at the cost of significant cutbacks on the demands which the regime sought to make of all parties. In contrast, decentralisation could allow for major powers to engage in relevant regulatory efforts where they would be deterred from signing up to a more comprehensive package. This has precedence in the history of climate governance. Some claim that the US-led Asia-Pacific Partnership on Clean Development and Climate helped, rather than hindered climate governance, as it bypassed UNFCCC deadlock and secured non-binding commitments from actors not bound by the Kyoto Protocol [49, pp.259-60].  4  We thank Nicolas Moës for this observation. This matters, as buy-in may prove a thorny issue for AI governance. The actors who lead in AI development include powerful states that are potentially most adverse to global regulation in this area. They have thus far proved recalcitrant in the global governance of security issues such as anti-personnel mines or cyberwarfare. In response, some have already recommended a critical-mass governance approach to the military uses of AI. Rather than seeking a comprehensive agreement, devolving and spinning off certain components into separate treaties (e.g. for LAWS testing standards; liability and responsibility; and limits to operational usage) could instead allow for the powerful to ratify and move forward at least a few of those options  [48] . The breadth vs. depth dilemma is a trade-off in multilateralism generally. However, it is a particularly pertinent challenge for centralisation. The key benefit of a centralised body would be to be a powerful anchor that ensures policy coordination and coherence, without suffering fragmentation in membership. This dilemma suggests it is unlikely to have both. It will likely need to restrict membership to have teeth, or lose its teeth to have wide participation. A critical mass approach may be able to deliver the best of both worlds. Nonetheless these dilemma poses a difficult knot for centralisation to unravel. \n Forum Shopping Forum shopping may help or hinder AI governance, depending on the particular circumstances. Fragmentation enables actors to choose where and how to engage. Such 'forum shopping' may take one of several forms: moving venues, abandoning one organisation, creating new venues, and working across multiple organisations to sew competition between them  [4] . Even when there is a natural venue for an issue, actors have reasons to forum-shop. For instance, states may look to maximise their influence, appease domestic pressure  [40]  and placate constituents by shifting to a toothless forum  [18] . The ability to successfully forum-shop depends on an actor's power. Most successful examples of forum-shifting have been led by the US  [4] . Intellectual property rights in trade, for example, was subject to prolonged, contentious forum shopping. Developed states resisted attempts of the UN Conference on Trade and Development (UNCTAD) to address intellectual property rights in trade by trying to push them onto the World Intellectual Property Organization (WIPO) (ibid., 566) and then subsequently to the WTO  [18] , overruling protests from developing states. Outcomes often reflect power, but weak states and non-state actors can also pursue forum shopping strategies in order to challenge the status-quo  [22] . Forum shopping may help or hurt governance. This is evident in current efforts to regulate LAWS. While the Group of Governmental Experts has made some progress, on the whole the CCW has taken slow deliberations on LAWS. In response, frustrated activists have threatened to shift to another forum, as happened with the Ottawa Treaty that banned landmines  [10] . This strategy could catalyse progress, but also brings risks of further forum shopping and weak or unimplemented agreements. Forum shopping may similarly delay, stall, or weaken regulation of time-sensitive AI policy issues, including potential future HLMI development. It is plausible that leading AI firms also have sway when they elect to participate in some venues but not others. The OECD Expert Group on AI included representatives from leading firms, whereas engagement at UN efforts, including the Internet Governance Forum (IGF), do not appear to be similarly prioritised. A decentralised regime will enable forum shopping, though further work is needed to determine whether this will help or hurt governance outcomes on the whole. \n Policy Coordination There are good reasons to believe that either centralisation or fragmentation could enhance coordination. A centralised regime can enable easier coordination both across and within policy issues, acting as a focal point for states. Others argue that this is not always the case, and that fragmentation can mutually supportive and even more creative institutions. Centralisation reduces the occurrence of conflicting mandates and enables communication. These are the ingredients for policy coherence. As noted previously, the WTO has been remarkably successful in ensuring coherent policy and principles across the realm of trade, and even into other areas such as the environment. However, fragmented regimes can often act as complex adaptive systems. Political requests and communication between secretariats often ensures bottom-up coordination even in the absence of centralisation. Multiple organisations have sought to reduce greenhouse gas emissions within their respective remits, often at the behest of the UNFCCC Conference of Parties. When effective, bottom-up coordination can slowly evolve into centralisation. Indeed, this was the case for the GATT and numerous regional, bilateral and sectoral trade treaties, which all coalesced together into the WTO. While this organic self-organisation has occurred, it has taken decades, with forum shopping and inaction prevailing for many years. Indeed, some have argued that decentralisation does not just deliver 'good enough' global governance  [38]  that reflects a demand for diverse principles in a multipolar world. Instead, they argue 'polycentric' governance approaches  [37]  may be more creative and legitimate than centrally coordinated regimes. Arguments in favour of polycentricity include the notion that it enables governance initiatives to begin having impacts at diverse scales, and that it enables experimentation with diverse policies and approaches, learning from experience and best practices (ibid., 552). Consequently, these scholars assume \"that the invisible hand of a market of institutions leads to a better distribution of functions and effects\"  [50, p.7] . It is unclear if the different bodies covering AI issues will selforganise or collide. Many of the issues are interdependent and will need to be addressed in tandem. Some particular policy-levers, such as regulating computing power or data, will impact almost all use areas, given that AI progress and use is closely tied to such inputs. Numerous initiatives on AI and robotics are displaying loose coordination  [28] , but it remains uncertain whether the virtues of a free market of governance will prevail here. Great powers can exercise monopsony-like influence in forum shopping, and the supply of both computing power and machine learning expertise are highly concentrated. In sum, centralisation can reduce competition and enhance coordination, but it may suffocate the creative selforganisation of more fragmented arrangements over time. \n DISCUSSION: WHAT WOULD HISTORY SUGGEST? 4.1 A Summary of Considerations The multilateral track record and peculiarities of AI yield suggestions and warnings for the future. A centralised regime could lower costs, support participation, and act as a powerful new linchpin within the international system. Yet centralisation presents risks for AI governance. It could simply produce a brittle dinosaur, of symbolic value but with little meaningful impact on underlying political or technological issues. A poorly executed attempt could lock-in a poorly designed centralised body: a fate worse than fragmentation. Accordingly, ongoing efforts at the UN, OECD, and elsewhere could benefit from addressing the considerations presented in this paper. \n The Limitations of 'Centralisation vs. Decentralisation' Debates Structure is not a panacea. Specific provisions such as agendas and decision-making procedures matter greatly, as do the surrounding politics. Underlying political will may be impacted by framing or connecting policy issues  [26, pp.770-1] . The success of a regime is not just a result of fragmentation, but of design details. Moreover, institutions can be dynamic and broaden over time by taking in new members, or deepen in strengthening commitments. Successful multilateral efforts, such as trade and ozone depletion, tend to do both. We are in the early days of global AI governance. Decisions taken early on will constrain and partially determine the future path. This dependency can even take place across regimes. The Kyoto Protocol was largely shaped by the targets and timetables approach of the Montreal Protocol, which in turn drew from the Convention on Long-range Transboundary Air Pollution. This targets and timetables approach continues today in the way that most countries frame their climate pledges to the Paris Agreement. The choices we make on governing short-term AI challenges will likely shape the management of other policy issues in the long term  [7] . On the other hand, committing to centralisation, even if successful, may amount to solving the wrong problem. The problem may not be structural, but geopolitical. Centralisation could even exacerbate the problem by diluting scarce political attention, incurring heavy transaction costs, and shifting discussions away from bodies which have accumulated experience and practice  [21] . For example, the Bretton Woods Institutions of the IMF and World Bank, joined later by the WTO, are centralised regimes that engender power. However, those institutions had the express support of the US and may have simply manifested state power in institutional form. Efforts to ban LAWS and create a cyberwarfare convention have been broadly opposed by states with an established technological superiority in these areas  [13] . A centralised regime may not unpick these power struggles, but just add a layer of complexity. \n LESSONS AND CONCLUSIONS Our framework provides a tool for policy-makers to inform their decisions of whether to join, create, or forgo new institutions that tackle AI policy problems. For instance, the recent choice of whether to support the creation of an independent IPAI involved these considerations. Following the US veto, ongoing negotiations for its replacement at the OECD may similarly benefit from their consideration. For now, it is worth closely monitoring the current landscape of AI governance to see if it exhibits enough policy coordination and political power to effectively deal with mounting AI policy problems. While there are promising initial signs  [28]  there are also already growing governance failures in LAWS, cyberwarfare, and elsewhere. We outline a suggested monitoring method in Table  1 . There are three key areas to monitor: conflict, coordination, and catalyst. First, conflict should measure the extent to which principles, rules, regulations and other outcomes from different bodies in the AI regime complex undermine or contradict each other or are in tension either in their principles or goals. Second, coordination seeks to measure the proactive steps that AI-related regimes take to work with each other. This includes liaison relationships, joint initiatives, as well as the extent to which their rules, outputs and principles tend to reinforce one another. Third, catalyst raises the important question of governance gaps: is the regime complex self-organising to proactively address international AI policy problems? Numerous AI policy problems currently have no clear coverage under international law, including AI-enabled cyber warfare and HLMI. Whether this changes is of vital importance. These areas require investigation through multiple methods. Qualitative surveys of relevant organisations and actors can yield data on expert perceptions of these questions. Surveys can be augmented with quantitative methods, including network analyses of the regime complex relations  [36, p.32] . Natural language processing could be used to examine contradictions and similarities between different regime outputs, e.g., statements, meeting minutes, and more. Monitoring the outcomes of fragmentation can help to determine whether centralisation is needed. One way forward would be to empower the OECD AI Policy Observatory or the UN CEB to regularly review the monitoring outcomes. This could inform a democratic discussion and decision of whether to centralise AI governance further. Our framework and discussion may also be useful for non-state actors. Researchers and leading AI firms can play an important role in sharing technical expertise and informing forecasts of new policy problems on the horizon. The considerations may benefit their decisions of where to engage. Civil society has a key role as participants, watch-dogs, and catalysts. For example, the Campaign to Stop Killer Robots has sought to boost engagement and support for a LAWS ban within the CCW. Given prolonged delays and a pessimistic outlook, some have articulated a strategy of creating an entirely new forum for the ban, inspired by the Ottawa Treaty which outlawed landmines. Our framework can help reveal the potential virtues (allowing for progress while avoiding high-threshold deadlocks) and vices (enabling forum shopping) of such an approach. It could even help inform the structure of a future international institution, such as allowing for a modular, flexible structure with 'critical mass' agreements. One cross-cutting consideration is clear: a fractured regime sees higher participation costs that may threaten to exclude many civil society organisations altogether. The international governance of AI is nascent and fragmented. Centralisation under a well-designed, modular, 'innovation-proof' framework organisation may be a desirable solution. However, such a move must be approached with caution. How to define its scope and mandate is one problem. Ensuring a politically-acceptable and well-designed body is perhaps a more daunting one. It risks cementing in place a fate worse than fragmentation. Monitoring conflict and coordination in the current AI regime complex, and whether governance gaps are filled, is a prudent way of knowing whether the existing structure can suffice. For now we should closely watch the trajectory of both AI technology and its governance initiatives to determine whether centralisation is worth the risk. Table 1 : 1 Regime complex monitoring suggestions Key theme Question \n\t\t\t A regime is a set of 'implicit or explicit principles, norms, rules and decision-making procedures around which actors' expectations converge in a given area of international relations'[27, p.186]. 2  We define 'AI' as any machine system capable of functioning 'appropriately and with foresight in its environment'[34, p.13]; see too[9, p.5]. 3  'High-level machine intelligence' has been defined as 'unaided machines [that] can accomplish every task better and more cheaply than human workers'[17, p.1].", "date_published": "n/a", "url": "n/a", "filename": "3375627.3375857.tei.xml", "abstract": "Can effective international governance for artificial intelligence remain fragmented, or is there a need for a centralised international organisation for AI? We draw on the history of other international regimes to identify advantages and disadvantages in centralising AI governance. Some considerations, such as efficiency and political power, speak in favour of centralisation. Conversely, the risk of creating a slow and brittle institution speaks against it, as does the difficulty in securing participation while creating stringent rules. Other considerations depend on the specific design of a centralised institution. A well-designed body may be able to deter forum shopping and ensure policy coordination. However, forum shopping can be beneficial and a fragmented landscape of institutions can be self-organising. Centralisation entails trade-offs and the details matter. We conclude with two core recommendations. First, the outcome will depend on the exact design of a central institution. A well-designed centralised regime covering a set of coherent issues could be beneficial. But locking-in an inadequate structure may pose a fate worse than fragmentation. Second, for now fragmentation will likely persist. This should be closely monitored to see if it is self-organising or simply inadequate.", "id": "01f41542ac70cd9a71b81966d9e24530"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kaj Sotala"], "title": "Defining Human Values for Value Learners", "text": "Introduction 1 The value learning problem  (Dewey 2011 , Soares 2014  is the challenge of building AI systems which can first learn human values and then to act in accordance to them. Approaches such as inverse reinforcement learning  (Ng & S. Russell 2000)  have been suggested for this problem (S.  Russell 2015 , Sezener 2015 , as have more elaborate ones such as attempting to extrapolate the future of humanity's moral development  (Yudkowsky 2004 , Tarleton 2010 , Muehlhauser & Helm 2012 . However, none of these proposals have yet offered a satisfactory definition of what exactly human values are, which is a serious shortcoming for any attempts to build an AI system that was intended to learn those values. This paper builds on a combination of research into moral psychology, the psychology of emotion, and reinforcement learning theory to offer a preliminary definition of human values, and how that definition might be used to design a value learning agent. I begin with an argument for the standard concept of preference being insufficient as a definition of value in section 2. Section 3 introduces theoretical background from the field of reinforcement learning and particularly evolutionary reinforcement learning. The background is used in section 4 to offer a preliminary definition of human values as mental representations which encode the brain's value function (in the reinforcement learning sense, as discussed below) by being imbued with affect. Section 5 elaborates on why affect might be a reasonable candidate for the brain's way of encoding a value function, and section 6 discusses the connections between emotions, affect, and values. Section 7 discusses the relation of affect and moral judgment in light of the social intuitionist model of morality, and section 8 talks about how this concept of human values could be used for designing value learning agents. Sections 9 and 10 conclude by evaluating the model and comparing it to alternatives. \n The standard concept of preference is insufficient as a definition of value The closest existing concept that formalizes something akin to human value is the concept of a utility function, which is widely used in economics and decision theory. Possibly its most well-known problem as a model of value is the empirical finding that humans violate the axioms of utility theory and thus do not have consistent utility functions  (Tversky and Kahneman 1981) . However, this is far from being the most serious problem. The von Neumann-Morgenstern utility theorem  (von Neumann & Morgenstern 1953)  sets up utility functions via preference orderings: of options A and B, either A is preferred to B, B is preferred to A, or both are equally preferred. Essentially, a \"preference\" is defined as a function that, given the state of the agent and the state of the world in general, outputs an agent's decision between two or more choices. A strength of this definition is that it allows treating preferences as black boxes. This has been of great use in economics, as it allows constructing models of behavior The Workshops of the Thirtieth AAAI Conference on Artificial Intelligence AI, Ethics, and Society: Technical Report WS-16-02 based only on observed preferences, without needing to know the reasons for those preferences. At the same time, ignoring everything that happens inside the preference function is also a weakness for the definition. Preferences are essentially considered atomic units with no internal structure. This leads to a number of problems in trying to use them as a definition of human values, including the below. The utility function model of value has difficulty dealing with internal conflicts and higher-order preferences. A drug addict may desire a drug, while also desiring that he not desire it  (Frankfurt 1971) . \"Less Is More\" is a measure of executive function in which children may point either to a tray with five treats or to a tray with two treats, while knowing that they will get the treats from the tray which they didn't point at. Three-year old children frequently fail this task and point at the tray with more treats, despite understanding that this will give them fewer things that they want  (Carlson et al. 2005) . Although the researchers did not report the children's reaction to their repeated failure, it seems safe to presume that they were not particularly happy, nor would they have liked to have their preference modeled as preferring fewer treats. The utility function model of value ignores the person's internal experience. Although \"wanting\" and \"liking\" are frequently thought to be the same thing, the two have distinct neural processes: \"[l]iking corresponds closely to the concept of palatability; wanting, by comparison, corresponds more closely to appetite or craving\"  (Berridge 1996) . Different interventions may suppress wanting without affecting liking, and vice versa. Intuitively, it seems like behaviors which we both \"like\" and \"want\" should be more important than behaviors that we only \"want\". The utility function model of value does not model changing values. As a black box mechanism, classical preference has no model of changing values, preventing us from extrapolating possible development of values. The utility function model of value does not give a way to generalize from our existing values to new ones. Technological and social change frequently restructures the way that the world works, forcing us to reconsider our attitude towards the changed circumstances. As a historical example (Lessig 2004), American law traditionally held that a landowner did not only control his land but also everything above it, to \"an indefinite extent, upwards\". Upon the invention of this airplane, this raised the question: could landowners forbid airplanes from flying over their land, or was the ownership of the land limited to some specific height, above which the landowners had no control? The US Congress chose to the latter, designating the airways as public, with the Supreme Court choosing to uphold the decision in a 1946 case. Justice Douglas wrote in the court's majority that The air is a public highway, as Congress has declared. Were that not true, every transcontinental flight would subject the operator to countless trespass suits. Common sense revolts at the idea. By the decision of Congress and the Supreme Court, the concept of landownership was redefined to only extend a limited, and not an indefinite, amount upwards. Intuitively, one might think that this decision was made because the redefined concept did not substantially weaken the position of landowners, while allowing for entirely new possibilities for travel. However, a black-box approach to value, which does not reveal the reasons underlying preferences such as \"landownership should extend indefinitely upwards\", would be incapable of making such a judgment. \n Evolutionary reinforcement learning A good theory of human psychology, including human value, requires an understanding of the evolutionary functions of the psychological phenomena  (Tooby & Cosmides 1995 ). Before we can develop a good model of what human values are, we need to develop an understanding of their computational role in the kinds of tasks that human brain has needed to perform. A defining characteristic of human thought is the ability to develop solutions to novel problems in novel environments. Humans are capable of learning a wide variety of behaviors far beyond anything that evolution could have \"preprogrammed\" into them. Instead, they experience some events (such as tissue damage or hunger) as aversive and learn to avoid things that cause those events, while learning to pursue things that feel rewarding. The problem of learning a novel environment in order to maximize the amount of rewards is the reinforcement learning problem, which \"explicitly considers the whole problem of a goal-directed agent interacting with an uncertain environment\"  (Sutton & Barto 1998) , as opposed to merely considering some isolated subproblems. As the theory of reinforcement learning is the general answer to the question of how an agent should behave in an uncertain environment and learn from it, we should expect the design of both human and animal minds to be strongly shaped by the principles of reinforcement learning theory. Empirical evidence from a variety of fields, including behavioral trainers  (Pryor 1999) , studies on habit-formation  (Duhigg 2012)  as well as neuroscience  (Dayan 2011 ) supports this prediction. Standard reinforcement learning theory involves learning to maximize a reward signal which the agent can observe. However, evolution selects for traits with the highest inclusive fitness, an abstract measure of a trait's effect on the production and survival of direct and related offspring. As organisms cannot directly observe the effect of their actions on their lifetime fitness, they cannot maximize this value directly.  Singh et al. (2009 Singh et al. ( , 2010  expand reinforcement learning to cover the evolutionary case, and define an \"optimal reward function\" as follows. An agent A in an external environment e receives observations and takes actions. It has an internal environment which computes a state based on the observations from the environment. The agent tries to maximize a reward, which is also computed by the internal environment according to a reward function rA, drawn from the space of reward functions RA. Different agents carry out actions in various environments e drawn from a distribution of environments E. A specific agent A in environment e with reward function rA produces a history h. A fitness function F produces a scalar evaluation F(h) for all histories h. A reward function is optimal if it maximizes the expected fitness of the agent over the distribution of environments. This formalization mimics an evolutionary environment in that evolution selects for agents which best maximize their fitness, while agents cannot directly optimize for their own fitness as they are unaware of it. Agents can however have a reward function that rewards behaviors which increase the fitness of the agents. The optimal reward function is one which maximizes (in expectation) the fitness of any agents having it. Holding the intelligence of the agents constant, the closer an agent's reward function is to the optimal reward function, the higher their fitness will be. Evolution should thus be expected to select for reward functions that are closest to the optimal reward function. In other words, organisms should be expected to receive rewards for carrying out tasks which have been evolutionarily adaptive in the past. \n An initial definition of human value The theory of reinforcement learning distinguishes between reward and value. A value function assigns states of the world a scalar value based on the expectation of future rewards that one may obtain from that state, conditional on some policy of what one would do in each state. Intuitively, a state has a high value if one can reliably move from it to states with a high reward. For reinforcement learning to work effectively, it requires a way to identify states which should be classified as the same or similar, and be assigned the same or a similar value. We can now consider the relation between the need to identify similar states, and mental concepts. We should expect an evolutionarily successful organism to develop concepts that abstract over situations that are similar with regards to receiving a reward from the optimal reward function. Suppose that a certain action in state s1 gives the organism a reward, and that there are also states s2-s5 in which taking some specific action causes the organism to end up in s1. Then we should expect the organism to develop a common concept for being in the states s2-s5, and we should expect that concept to be \"more similar\" to the concept of being in state s1 than to the concept of being in some state that was many actions away. Empirical support for concepts being organized in this kind of a manner comes from possibly the most sophisticated general-purpose AI developed so far, DeepMind's deep reinforcement learning agent  (Mnih et al. 2015) . This agent managed to \"achieve a level comparable to that of a professional human games tester across a set of 49 [Atari 2600] games, using the same algorithm, network architecture and hyperparameters\". This agent developed an internal representation of the different game states of each game that it was playing. An investigation of the agent's representation for the game Space Invaders indicated that representations with similar values were mapped closer to each other in the representation space. Also, some game states which were visually dissimilar to each other, but had a similar value, were mapped to internal representations that were close to each other. Likewise, states that were visually similar but had a differing value were mapped away from each other. We could say that the agent learned a primitive concept space, where the relationships between the concepts (representing game states) depended on their value and the ease of moving from one game state to another. There is considerable disagreement on what exactly concepts are, and various theoreticians use the same term to refer to different things  (Machery 2010) . For the purposes of this paper, I am loosely defining a \"concept\" as points or regions within a conceptual space, with concepts having a hierarchical structure so that higherlevel concepts are at least partially defined in terms of lower-level ones. Similar assumptions are commonly made in psychology  (Gärdenfors 2004 ) and neuroscience  (Wessinger et al. 2001) . Additionally, this definition makes concepts remarkably similar to the representations built up in the machine learning subfield of deep learning. Deep learning models have demonstrated success in a wide range of tasks, including object recognition, speech recognition, signal processing, natural language processing and transfer learning  (Bengio 2012 , Schmidhuber 2014 . They work by building up an internal representation of a domain, where different concepts are arranged in a hierarchical structure, with more abstract concepts at the top. These ideas allow us to establish a preliminary definition of value in the \"human value\" sense. I suggest that human values are concepts which abstract over situations in which we've previously received rewards, making those concepts and the situations associated with them valued for their own sake. A further suggestion is that, as humans tend to naturally find various mental concepts to be associated with affect (the subjective experience of a feeling or emotion, experienced as either positive or negative), the value function might be at least partially encoded in the affect of the various concepts. In support of this possibility, I next turn to some of the research studying the role of affect in decision-making. \n Affect as a possible representation for the value function Affective evaluations of concepts seem to influence people's behavior. For instance,  Benthin et al. (1995)  found that the experienced affective feel of mental images associated with various health-related behaviors predicted the extent to which high schoolers engaged in those behaviors. Another study  (Peters & Slovic 1996 ) surveyed a representative sample of the US adult population. This study found that both the respondents' general worldview and their affective associations with nuclear power predicted the respondents' support for nuclear power independently of each other. This kind of a reliance on immediate affective responses to various options in guiding decision-making has been named the affect heuristic, and documented in a number of studies  (Slovic et al. 2007) . However, the dissociation between \"wanting\" and \"liking\"  (Berridge 1996)  suggests that the value function may not be completely contained in affective evaluations, as it is possible to \"want\" things without \"liking\" them, and vice versa. I am choosing to regardless mainly focus on the affective (\"liking\") component. This is due to the intuition that, in the context of looking for a target of value learning, the values that are truly important for us are those that involve a \"liking\" component, rather than the values with a \"wanting\" component without a \"liking\" component. The former seem closer to things that we like and enjoy doing, while the latter might be closer to behaviors such as undesired compulsions. I wish to emphasize, however, that this is only a preliminary conjecture and one which still needs further investigation. In order to be a good candidate for the representation of a value function, the affect of different concepts should vary based on contextual parameters such as the internal state of the organism, as (for example) a hungry and nonhungry state should yield different behaviors. Rats who taste intense salt usually both \"dislike\" and \"unwant\" it, but when they become salt-deprived, they will start both \"wanting\" and \"liking\" the salt, with the \"wanting\" expressing itself even before they have had the chance to taste the salt in the salt-deprived state and consciously realize that they now enjoy it  (Tindell et al. 2009) . Thus it seems that both the affective value and \"wanting\" of something can be recomputed based on context and the organism's own state, as would be expected for something encoding a value function. Similarly, a state such as fear causes shifts on our conceptual frames, such as in the example of a person who's outside alone at night starting to view their environment in terms of \"dangerous\" and \"safe\", and suddenly viewing some of their familiar and comfortable routes as aversive  (Cosmides & Tooby 2004 ). This is another indication of the affect values of different concepts being appropriately context-dependent. The negative or positive affect associated with a concept may also spread to other related concepts, again as one would expect from something encoding a value function. A person who is assaulted on a particular street may come to feel fear when thinking about walking on that street again. The need to be ready to confront one's fears and pains is also emphasized in some forms of therapy: if a person with a fear of snakes turns down invitations to go to a zoo out of a fear of seeing snakes there, they may eventually also become anxious about any situation in which they might be invited to a zoo, and then of any situation that might lead to those kinds of situations, and so on  (Hayes & Smith 2005) . Such a gradual spreading of the negative affect from the original source to related situations seems highly similar to a reinforcement learning agent which is updating its value function by propagating the value of a state to other states which precede it. \n Human values and emotions Human values are typically strongly related to emotional influences, so a theory which seeks to derive human values from a reinforcement learning framework also needs to integrate emotions with reinforcement learning. A major strand of emotion research involves appraisal theories  (Scherer 1999 , Roseman & Smith 2001 , Scherer 2009 , according to which emotional responses are the result of an individual's evaluations (appraisals) of various events and situations. For example, a feeling of sadness might be the result of an evaluation that something has been forever lost. The evaluations then trigger various responses that, ideally, orient the organism towards acting in a manner appropriate to the situation. After an evaluation suggests that something important has been forever lost, the resulting sadness may cause passivity and a disengagement from active goal pursuit, an appropriate response if there is nothing that could be done about the situation and attempts to pursue the goal would only lead to wasting resources  (Roseman & Smith 2001) . An important property of emotional appraisals is that different situations which might cause the same evaluation may not have any physical features in common with each other: Physically dissimilar events (such as the death of a parent and the birth of a child) may produce the same emotion (e.g. sadness) if they are appraised in similar ways (e.g. as involving the loss of something valued). An infinite number of situations can elicit the emotion because any situation that is appraised as specified will evoke the same emotion, including situations that have never before been encountered. Thus, the loss of one's first love or first cherished possession is likely to elicit sadness; and if people develop the ability to clone copies of themselves, a man who wants this capability but believes that he has lost it will feel sad.  (Roseman & Smith 2001)  In other words, emotional responses are a result of appraisals abstracting over situations which are similar on some specific property that has been evolutionarily important. As such, in addition to their direct psychological and physiological effects, they could also be seen as providing a reinforcement learning agent with information about which states are similar and should be treated as similar for learning purposes. Emotions are also associated with an affect dimension, with the conscious experience of an emotion often being theorized as being the integral blend of its affect (unpleasant-pleasant) and arousal (lethargic-energetic) dimensions (J.  Russell 2003) . Combining the above ideas, it is natural to suggest that since emotional appraisals identify evolutionarily important states, the optimal reward function for humans' environment of evolutionary adaptedness (EEA,  Tooby & Cosmides 1990 ) has involved positive rewards for emotions which reflect desirable states, and negative rewards for emotions which reflect undesirable states.  Marinier & Laird (2008)  experimented with implementing a reinforcement learning-driven agent with simple appraisal-based emotions in a toy environment. They found the agent with emotions to learn faster than a standard reinforcement learning agent, as the emotionequipped agent received frequent feedback of its progress from its appraisals and thus learned faster than the standard agent, which only received feedback when it reached its goal. Humans and many animals also enjoy exploration and play from a very early age, in a manner which cannot be explained by those exploratory behaviors having been reinforced by other rewards.  Singh et al. (2009)  set up a simulated environment in which agents could move about and take actions for the first half of their lifetimes, but could not yet carry out actions that would increase their fitness. In the second half of the agents' lifetimes, actions which increased their fitness became available. The authors found that the optimal reward function for this kind of an environment is one that rewards the agents for learning simple behaviors that can be performed during their \"childhood\", and which are prerequisites for the more complex fitness-increasing behaviors. Once the more complicated fitness-increasing behaviors become possible during the \"adulthood\" of the agents, agents with a reward function that has already taught them the simpler forms of the behavior will increase their fitness faster than agents that do not engage in \"childhood play\" and have to learn the whole behavioral chain from scratch. This and similar examples  (Singh et al. 2010 ) on the value of behaviors such as curiosity and play provide an explanation for why humans would find those behaviors rewarding for their own sake, even when the humans were modeled as reinforcement learners who did not necessarily receive any other rewards from their play. \n Human values and morality The discussion so far has suggested that human values are concepts that have come to be associated with rewards, and are thus imbued with a (context-sensitive) level of affect. However, I have said little about morality in particular. The social intuitionist model of moral psychology  (Haidt 2001)  proposes that moral judgment is \"generally the result of quick, automatic evaluations (intuitions)\". It can be contrasted to rationalist models, in which moral judgments are the results of careful moral reasoning.  Haidt (2001)  begins with a discussion of people's typical reactions to the following vignette: Julie and Mark are brother and sister. They are traveling together in France on summer vacation from college. One night they are staying alone in a cabin near the beach. They decide that it would be interesting and fun if they tried making love. At the very least it would be a new experience for each of them. Julie was already taking birth control pills, but Mark uses a condom too, just to be safe. They both enjoy making love, but they decide not to do it again. They keep that night as a special secret, which makes them feel even closer to each other. What do you think about that? Was it OK for them to make love?  Haidt (2001)  notes that most people will have an instant negative reaction to the vignette and say that what the siblings did was wrong  (Haidt et al. 2000 ). Yet the reasons that people offer for the act having been wrong are inconsistent with the story that was presented: for example, people might offer the possibility of birth defects from inbreeding, only to be reminded that the siblings were thorough in using birth control. This is used as an illustration of  Haidt's (2001)  claim that \"moral reasoning is usually a post hoc construction, generated after a judgment has been reached\". In particular, moral judgments are thought to be strongly driven by moral intuitions, which are defined as ...the sudden appearance in consciousness of a moral judgment, including an affective valence (good-bad, like-dislike), without any conscious awareness of having gone through steps of searching, weighing evidence, or inferring a conclusion. Moral intuition is therefore the psychological process that the Scottish philosophers talked about, a process akin to aesthetic judgment: One sees or hears about a social event and one instantly feels approval or disapproval.  (Haidt 2001)  I suggest that the social intuitionist model is highly compatible with my framework. Recall that I defined human values as concepts which have become strongly associated with positive or negative affect. Something like a moral intuition for brother-sibling incest being something abhorrent, could be explained if something like the hypothesized Westermarck Effect (Rantala & Marcinkowska 2011) made individuals find the concept of having sex with their siblings to be abhorrent and strongly laden with negative affect. Thus the concept of incest would instantly cause a negative reaction, leading to a moral judgment of condemnation. The social part of social intuitionist theory emphasizes the impact of culture and the social environment in shaping various moral intuitions.  Haidt (2001)  suggests at least three kinds of cultural processes which shape intuitions: 1. Selective loss of intuitions is the suggestion that people are from birth capable of developing many different kinds of intuitions, but that intuitions which are not emphasized by the prevailing culture gradually become weaker and less accessible. This is suggest to possibly be analogous to the process in which children lose the ability to distinguish between phonemes which are not distinguished in their native language. 2. Immersion in custom complexes. Various customs that are practiced in a culture are hypothesized to affect the implicit beliefs of people growing up in that culture. For example, the culture in Orissa, India structures spaces and objects by rules of purity and pollution. This involves rules such as dividing temples to zones of increasing purity, with foreigners and dogs being allowed near the entrance, bathed worshippers being allowed into the courtyard, and only the Brahmin priest being allowed into the inner sanctum. It is suggested that after a life of navigating such rules and practices, children internalize a way of thought that makes later intellectual concepts of sacredness, asceticism and transcendence feel natural and self-evident. It is interesting to note that this suggestion maps fits naturally into my suggested model of the role of concepts. If the function of concepts is to foster the right behavior in the right situations, then a person who is required by their culture to internalize a set of allowed, required, and disallowed behaviors in various high-or low-purity zones needs to develop a set of concepts which link the right behaviors together with the appropriate levels of purity. Once this conceptual network is in place, even if only in an implicit and unconscious level, new concepts which share a similar structure with the previously-learned one may feel easy and intuitive to develop. 3. Peer socialization. Many moral intuitions are learned from the culture in one's peer group; in particular, there might be evidence that immersion within a culture between the ages of 9 and 15 causes permanent internalization of the norms of that culture in a way that causes them to feel obvious and intuitive. Social intuitionist theory proposes that moral judgments involve a number of moral intuitions, but does not explicitly outline what those intuitions are or where they come from. Other theories building on social intuitionism, such as moral foundations theory  (Graham et al. 2012 , Haidt 2012 ) have proposed various foundations from which the intuitions are derived. For example, the care/harm foundation is hypothesized to have its origins in an evolutionary adaptation to care for one's offspring, and to motivate people to care for others and to help them avoid harm. While my model is not committed to any particular set of moral intuitions, theories such as moral foundations are broadly compatible with the model, offering an additional set of sources through which concepts may become imbued with either positive or negative affect. \n Building value learners In my framework, various sources of reward lead the brain to calculate an approximation of a value function, which then becomes expressed in the affect of various concepts. This preliminary definition of values seems to suggest ways to implement value learning in ways which avoid some of the problems associated with a more structure-free model of preferences. I have discussed some sources of reward, including classical physical events such as food or physical pain, the affective dimension in various emotional reactions, and moral intuitions. A further candidate for a source of reward might be something like self-determination theory, which posits the existence of the three universal human needs of competence, autonomy and relatedness  (Ryan & Deci 2000) . I do not expect this list to be comprehensive, and is rather intended as illustrative only. A value learning agent attempting to learn the values of a human might first map the sources of reward for that human. Given a suitable definition of sources of reward, discovering the various sources for any given individual seems like the kind of a task that might be plausibly outsourced to the AI system, without all of the sources needing to be exhaustively discovered by human researchers first. Having this information would assist the value learner in mapping the individual's values, in the form of a map of concepts and their associated affect values. Once the map had been obtained, it could be used to generate preference rankings of different outcomes for the individual and the world, using similar mechanisms as the human brain does when considering the appeal of different outcomes. When unsure about the desirability of some scenario, the value learner could attempt to model the amount of reward that the human would receive from living in the circumstances implied by that scenario, and use this to evaluate what value the human would then come to place on the scenario. One issue with this model is that there is no theoretical reason to expect that a person's values would necessarily imply consistent preference orderings, as people tend to have contradictory values. To resolve this issue, I turn back to the social intuitionist models of morality. While social intuitionism places stronger value on moral intuitions than rationalist models do, it must be emphasized that it incorporates, rather than rejects, the possibility of moral reasoning as well.  Haidt (2001)    writes:  ...people may sometimes engage in private moral reasoning for themselves, particularly when their initial intuitions conflict. Abortion may feel wrong to many people when they think about the fetus but right when their attention shifts to the woman. When competing intuitions are evenly matched, the judgment system becomes deadlocked  [...] . Under such circumstances one may go through repeated cycles of [...] using reasoning and intuition together to break the deadlock. That is, if one consciously examines a dilemma, focusing in turn on each party involved, various intuitions will be triggered [...], leading to various contradictory judgments  [...] . Reasoning can then be used to construct a case to support each judgment  [...] . If reasoning more successfully builds a case for one of the judgments than for the others, the judgment will begin to feel right and there will be less temptation (and ability) to consider additional points of view. [...] We use conscious reflection to mull over a problem until one side feels right. Then we stop. I suspect that to the extent that this model of human moral reasoning is correct, it could also be used by the value learner to predict how the individual being modeled might resolve any particular inconsistency. Because the value learner could potentially consider a far larger set of relevant intuitions at once, it could also help the individual in their moral growth by nudging them to consider particular scenarios they might otherwise not have considered. Drawing partial inspiration from Christiano's (2014) notion of approval-directed agents, this kind of an approach might also help avoid classical problems with seeking to maximize the fulfillment of an individual's preferences, such as the possibility of rewriting a person's mind to maximize the amount of reward the person obtained. This could be accomplished by applying the same criteria for evaluating potential outcomes, into evaluating the value learner's actions. Would the human's values approve the scenario where the value learner attempted to rewrite the human's brain? If the answer is no, that course of action would be prohibited. Depending on the exact path taken, it seems reasonable to assume that this kind of a moral reasoning process might arrive at several different conclusions. Conceivably, if an examination of different perspectives makes some side in a moral dilemma feel more right than the other, the intuitions that were on the losing side might become weakened as a result. If those intuitions also affected the outcome of some other moral dilemma, then the order in which the dilemmas were attended to might determine the conclusions that the individual reaches. Further history-dependence is introduced by the role of social effects, in which people affect the values of the people around them. This raises interesting possibilities in introducing flexibility to the value learner. If there is no single correct set of final values that an individual's or a society's values might converge to, the value learner might be allowed to nudge the individual towards such a set of values whose implied preference ordering on the world would be the easiest to fulfill. Depending on the individual's values, they might allow this kind of a nudging, or they might have an aesthetic which preferred developing their values in some other direction, such as some ideal of an objective morality, wanting to have values that lead to doing most good for the world, or simply preferring independence and resolving any value conflicts purely by themselves, without any nudging from the AI. Similarly to an approval-directed agent only changing a person's brain if that was genuinely something that the person consented to, the AI here could use the person's existing values as a base for only nudging the person towards a direction that the current values endorsed being nudged towards (if any). While this paper is not focused on the question of how to combine the conflicting values of different people, it is also interesting to notice that the flexibility in resolving value conflicts may be useful in trying to find a combination of values that as many people as possible could agree on. If such a set of globally most agreeable values could be found, different AI systems could then coordinate to direct the whole global population towards that set. This might look like something akin the \"Coherent Blended Volition\"  (Goertzel and Pitt 2012)  proposal, which seeks to \"incorporat[e] the most essential elements of [people's] divergent views into a whole that is overall compact, elegant and harmonious\". In this proposal, AI systems would be used to assist people in reaching an agreeable combination of their values. Given the great degree of flexibility allowed by the possibility of social feedback loops, in which directed changes to a culture's customs could potentially cause major changes to the values of that culture, one might be very optimistic about the possibility of reaching such an outcome. \n Criteria for evaluating the framework This proposed framework is worth evaluating from two distinct, though overlapping, angles. First, is it correct? Second, to the extent that it is correct, is it actually useful for solving the value learning problem? The correctness angle suggests the following possible criteria: 1. Psychologically realistic. The proposed model should be compatible with that which we know about current human values. As a bare minimum, it should not make predictions about human behavior which would fail to correctly predict the behavior of most typical test subjects. Motivation: an agent seeking to model human values cannot be expected to get it right unless its assumptions are based on a correct model of reality. \n Compatible with individual variation. The proposed model should be flexible enough to be able to take into account the full range of variation in human psychology. It should be able to adapt it to accurately represent the values (and thus behavior) of groups as differing as Western and non-Western  (Henrich et al. 2010) , autistic and non-autistic, and so on. Motivation: psychological research often focuses on typical individuals and average tendencies, whereas a value learner should be capable of taking into account the values of everyone. 3. Testable. The proposed model should be specific enough to make clear predictions, which can then be tested. Motivation: vague models that do not make specific predictions are useless for practical design work. 4. Integrated with existing theories. The proposed definition model should, to as large an extent possible, fit together with existing knowledge from related fields such as moral psychology, evolutionary psychology, neuroscience, sociology, artificial intelligence, behavioral economics, and so on. Motivation: theoretical coherence increases the chances of the model being correct; if a related field contains knowledge about human values which does not fit together with the proposed model, that suggests that the model is missing something important. A second set of criteria is suggested by the usefulness to the value learning problem. These overlap somewhat with the \"correctness\" criteria in that a correct model of human value would likely also fulfill the \"usefulness\" criteria. However, here more emphasis is put on how well-suited the model is for answering these kinds of questions in particular: it would be possible to have a model which was capable of answering these questions in principle, but burdensome and unlikely to find the right answers in practice. 5. Suited for exhaustively modeling different values. Human values are very varied, and include very abstract ones such as a desire for autonomy and an ability to act free from external manipulation. The details of when these values would be considered fulfilled may be highly idiosyncratic and specific to the mind of the person with that value, but the proposed model should still be able of incorporating that value. Motivation: again, a value learner should be capable of taking into account the values of everyone. 6. Suited for modeling internal conflicts and higherorder desires. People may be genuinely conflicted between different values, endorsing contradictory sets of them given different situations or thought experiments, and they may struggle to behave in a way in which they would like to behave. The proposed model should be capable of modeling these conflicts, as well as the way that people resolve them. Motivation: if a human is conflicted between different values, 7. Suited for modeling changing and evolving values. Human values are constantly evolving. The proposed model should be able to incorporate this, as well as to predict how our values would change given some specific outcomes. Motivation: an AI should be capable of noticing cases where we were about to do things that our future selves might predictably regret, and warn us about this possibility.  (Yudkowsky 2004 ) A dynamic model of values also helps prevent \"value lock-in\", where an AI learns one set of values and then enforces that even after our values have shifted. 8. Suited for generalizing from existing values to new ones. The proposed model should be able to react to circumstances where either our understanding of the world, or the world itself, changes dramatically and forces a reconsideration of how existing values apply to the new situation. Motivation: technological and social change is constantly occurring, and often forces these kinds of reevaluations, as discussed in section 2 earlier. \n Evaluation I will now evaluate my proposed framework in light of the above criteria. 1. Psychologically realistic. The framework is motivated by psychological research, particularly in the fields of moral psychology and emotion research. However, not all of the work in the said fields has yet been fully integrated to the framework, which may bias the implications of the framework. In particular, dual-process models of morality  (Greene 2007 (Greene , 2014 , which also cover more non-emotional reasoning, are not yet a part of this framework. Dual-process models have made accurate predictions about less emotional people tending to make more \"utilitarian\" judgments in moral dilemmas, an outcome which the proposed framework would not have predicted. Additionally, while this framework has been developed based on psychological theories, neuroscientific evidence has not yet been considered in depth. With regard to the neuroscientific data, a specific shortcoming of the current framework is the possible existence of several different reinforcement learning mechanisms in the brain  (Dayan 2011 , Dayan & Berridge 2014 , requiring further investigation to identify the extent to which the mechanisms hypothesized here are implemented in one system or several, and how those systems interact when it comes to questions of values and morality. 2. Compatible with individual variation. In the framework, differing values are hypothesized to emerge from individual differences (some of them which are caused by cultural differences) related to things that provide positive or negative rewards. This is compatible with a great degree of individual variation. For example, various differences in moral intuitions (due either to culture or something else) can be modeled as those intuitions causing different combinations of affect in response to the same situation, with this then leading to the same concepts being associated with different levels of affect for different individuals. 3. Testable. The framework is currently insufficiently specific to make novel predictions, which will be addressed in follow-up work. 4. Integrated with existing theories. The framework is currently moderately integrated with theories of reinforcement learning, moral psychology, and emotion research. However, there remains considerable room for further integration, and there are related fields such as sociology, which have not yet been addressed at all. 5. Suited for exhaustively modeling different values. In the framework, any concept that a human may have, either on a conscious or subconscious level, can be a value. 6. Suited for modeling internal conflicts and higherorder desires. Higher-order desires can be modeled to some extent: for example, a drug addict's desire to quit a drug might be modeled as negative affect around the concept of being a drug user, or as positive affect around the concept of quitting. However, the current framework does not fully explain the existence of internal conflicts and people engaging in actions which go against their higher-order desires. For this, further theoretical integration is needed with models such as ones positing separate mental modules optimizing for either short-term or long-term reward  (Kurzban 2012) . Such integration would help explain addictive behaviors as the modules optimizing for short-term reward \"overpowering\" the ones optimizing for long-term reward. 7. Suited for modeling changing and evolving values. As values are conceptualized as corresponding to a value function which is constantly updated and recomputed, the framework naturally models changing values. 8. Suited for generalizing from existing values to new ones. Section 8 discussed a possible way for a value learner to use this framework for generalizing existing values into new situations, by simulating a human in different situations and modeling the amount of reward obtained from those situations, as well as using existing values to guide this simulation. To my knowledge, there have not been proposals for definitions of human values that would be relevant in the context of AI safety engineering. The one proposal that comes the closest is  Sezener (2015) . This paper takes an inverse reinforcement learning approach, modeling a human as an agent that interacts with its environment in order to maximize a sum of rewards. It then proposes a value learning design where the value learner is an agent that uses Solomonoff's universal prior in order to find the program generating the rewards, based on the human's actions. Basically, a human's values are equivalent to a human's reward function. As a comparison, an evaluation of Sezener's proposal using the same criteria follows. 1. Psychologically realistic. Sezener's framework models humans as being composed of a reward mechanism and a decision-making mechanism, where both are allowed to be arbitrarily complex, so e.g. the reward mechanism could actually incorporate several distinct mechanisms. Thus a range of models, some of them more realistic than others, could be a part of the framework. 2. Compatible with individual variation. Because both the agent and the reward function are drawn from the space of all possible programs, Sezener's proposal is compatible with a vast range of individual variation. 3. Testable. Sezener's proposal is very general, and insufficiently specific to make novel predictions. 4. Integrated with existing theories. Various existing theories could in principle used to flesh out the internals of the reward function, but currently no such integration is present. 5. Suited for exhaustively modeling different values. Because the reward function is drawn from the space of all possible programs, any value that can be represented in a computational form can in principle be represented. However, because the simplicity of the program is the only prior probability used for weighting different programs, this may not sufficiently constrain the search space towards the values that would be the most plausible on other grounds. 6. Suited for modeling internal conflicts and higherorder desires. No specific mention of this is made in the paper. The assumption of a single reward function that assigns a single reward for every possible observation seems to implicitly exclude the notion of internal conflicts, with the agent always just maximizing a total sum of rewards and being internally united in that goal. It might be possible to represent internal conflict with the right kind of agent model, but again it seems unclear whether the prior probability used sufficiently constrains the search space. 7. Suited for modeling and changing and evolving values. Because the reward function is allowed to map the same observations to different rewards at different times, the framework is in principle capable of representing changing values. However, the same problem of finding the correct function remains an issue. 8. Suited for generalizing from existing values to new ones. There does not seem to be any obvious possibility for this in the model, except if the reward function that the value learner estimates happens to generalize rewards in the same way as a human would. Overall, although both my and Sezener's frameworks represent useful progress towards a definition of human value, much work clearly remains to be done. Figure 1 . 1 Figure 1. Various source of positive or negative reward may lead to various concepts becoming imbued with reward, giving rise to both \"intrinsic\" values (which are valued even if the source to the original reward was severed) and instrumental values, which lose their appeal if they cease to be associated with the original source of reward.", "date_published": "n/a", "url": "n/a", "filename": "12633-57415-1-PB.tei.xml", "abstract": "Hypothetical \"value learning\" AIs learn human values and then try to act according to those values. The design of such AIs, however, is hampered by the fact that there exists no satisfactory definition of what exactly human values are. After arguing that the standard concept of preference is insufficient as a definition, I draw on reinforcement learning theory, emotion research, and moral psychology to offer an alternative definition. In this definition, human values are conceptualized as mental representations that encode the brain's value function (in the reinforcement learning sense) by being imbued with a context-sensitive affective gloss. I finish with a discussion of the implications that this hypothesis has on the design of value learners.", "id": "11a066473f915fcc4905a1ba02bae275"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Brandon Perry", "Risto Uuk"], "title": "AI Governance and the Policymaking Process: Key Considerations for Reducing AI Risk", "text": "Introduction Artificial intelligence, especially artificial general intelligence (AGI), has the ability to dramatically impact the future of humanity  [1] . Notable researchers, such as  Bostrom (2014) , have expressed concern that advanced forms of artificial intelligence, if not aligned to humans values and wellbeing, could be potentially disastrous and pose an existential threat to our civilization  [2] . The two main branches of research on risk from advanced AI are AI safety, which seeks to ensure that advanced AI is engineered in such a way that it will not pose a threat; and AI governance, which focuses on political and social dynamics (AI macrostrategy) and forecasting timelines for AI development  [3] . Issues that AI governance looks at include arms race dynamics, social and economic inequality, public perceptions, issues in surveillance, and more. There has been a modest amount of work on developing policy solutions to AI risk, with a recent literature review by    [4]  and  Everitt (2016)    [5]  covering most of it. Some authors have focused on the development of AGI, with proposed solutions ranging from  Joy (2000)    [6]  who calls for a complete moratorium on AGI research, to  Hibbard (2002)    [7]  and  Hughes (2007)    [8] , who advocate for regulatory regimes to prevent the emergence of harmful AGI, to  McGinnis (2010) , who advocates for the US to steeply accelerate friendly AGI research  [9] .  Everitt et al. (2017)    [5]  suggests that there should be an increase in AI safety funding.  Scherer (2016)    [10] , however, at least in the context of narrow AI, argues that tort law and the existing legal structures, along with the concentration of AI R&D in large visible corporations like Google, will provide some incentives for the safe development of AI.  Guihot et al. (2017)    [11]  also notes that attempts to future-proof laws tend to fail, and pre-emptive bans and regulation tend to hurt the long-term health of the field, instead arguing for a soft-law approach. Other authors have focused on the community of researchers, with    [12]  promoting a social psychology approach to promote community self-regulation and activism, and  Yampolskiy and Fox (2013)    [13]  advocating for review boards at universities and other research organizations. Some authors have advocated for an international approach to resolving AI risk.  Erdelyi and Goldsmith (2018)    [14]  advocated for an international soft-law regime that would serve as a \"international forum for discussion and engage in international standard setting activities\". Erdelyi and Goldsmith's proposal, however, is not targeted towards AGI risk, although they could scale up to AGI.  Wilson (2013)    [15]  and  Bostrom (2014)    [2] , on the other hand, call for some form of international agreement or control on AGI R&D, with the former advocating specifically for a treaty. These approaches are necessary given some of the risks, including states pursuing AGI for unprecedented military and economic strength with destabilizing effects  (Shulman 2009)    [16] , and the concentration of wealth and political influence in large corporations  (Goertzel 2017)    [17] . Questions regarding whether or not AGI R&D should be open sourced or not have been explored by  Goertzel (2017)    [17]  and  Bostrom (2017)    [18] .  Shulman (2009)    [16]  and  Dewey (2015)    [19]  follow a different approach and advocate for a global surveillance regime to monitor for rogue AGI projects, with  Goertzel (2012)    [20]  suggesting that a limited form of AGI could do this. As far as current and future research goes, the Future of Humanity Institute has developed an extensive research agenda  [3]  for AI governance, with three main research areas: Technical landscape, which seeks to understand what artificial intelligence can do and its limits; AI politics, which looks at the political dynamics between firms, governments, publics, etc.; and ideal governance, which looks at possible ways and arrangements for stakeholders to cooperate. This research agenda highlights key issues such as security challenges, international political dynamics and distribution of wealth, and arms race dynamics. Other researchers have published reports dealing with issues such as dual use, similarity, and possible interactions with the cybersecurity community  [21]  the role and limits of principles for AI ethics  [22] , justice and equity  [23] , and AGI R&D community norms  [5] . Thus far, much of the literature on AI risk has discussed policy issues, but few studies have talked about how policies are made or how the dynamics of the policymaking process affect their work.  Calo (2017)    [23]  touches upon the problem, noting that there is a lack of institutional expertise, policy tools, and flawed mental models of what AI is, which plague governments' abilities to regulate AI.  Scherer (2016)    [10]  cites certain aspects of the technology itself, such as its ability to be created without special equipment, as a hindrance to the ability to regulate it.  Everitt et al. (2017)    [5]  also briefly discusses policy and political dynamics in the context of AGI researchers, suggesting that AGI researchers should work with other organizations to mitigate the negative dynamics of framing AGI development as an arms race  [24] . Finally, the Future of Humanity Institute's research agenda for AI governance  [3]  touches on policymaking in a few ways, noting that public opinion can have major impacts on technology policy and governance schemes can be subject to mission drift and asking how to facilitate the transition from the present state of affairs to our ideal vision for the future. This paper continues along the lines of facilitating the transition from the present state to \"our ideal vision\" by exploring the missing discussion on the role of policymaking in AI governance. Research thus far has largely focused on what problems are out there and what should be done to fix them. However, this paper does not only argue that proposal implementation that takes into account the features of the 'policymaking cycle' may be vital to success in reducing AI risk but that this model actually has massive implications for the research field as a whole. Proposals will be much more effective if they are informed by an understanding of the political and administrative considerations of consensus-building and implementation and could make the difference between making an impact or none at all. The goal of this paper is to attempt to create a clearer launching point for discussions on the key considerations of the policymaking process for AI governance and the political considerations underpinning policy solutions for AI risk. The policymaking process includes: Problem identification/agenda setting, policy formulation, policy adoption, implementation, and evaluation. Each step of the policymaking process will have different aspects that are critical for the creation of public policies that are able to effectively reduce AI risk. Each section covers a brief overview of the literature, assesses its implications for the greater AI governance field, and identifies different points where further research is needed. The papers we selected are the primary sources of these different theories of the policymaking process. The first section maps out and defines terms in the field of AI governance, to give readers a better understanding of how our paper contributes to the way AI governance is approached. We also created a typology for AI risk policies, to provide an understanding as to how AI governance has implications in a diverse range of policy communities and how that interplays with strategic considerations. The next section goes through each step of the policymaking cycle, with a basic overview of some of the literature and discussing its implications for AI governance. It should be noted that the literature covered in each field is not extensive, and further research may be necessary. The last sections cover some of the key implications and limitations. \n Terms and Definitions On a broad level, the question of mitigating AI risk, or risks that stem from the development and use of artificial intelligence (such as global catastrophic risks from misaligned AI or military instability from adopting new types of weapons), is broken down into AI technical safety and AI governance. AI technical safety focuses on solving computer science problems around issues like misalignment and the control problem for AGI  [2] . AI governance, on the other hand, studies how humanity can best navigate the transition to advanced AI systems  [3] . This would include the political, military, economic, governance, and ethical considerations and aspects of the problem that advanced AI has on society. AI governance can be further broken down into other components, namely the technical landscape (how technical developments depends on inputs and constraints and affects rates or domains of capability improvement), ideal governance (what would we do ideally if we could cooperate), and AI politics (how AI will affect domestic politics, political economy, international relations, etc.)  [3] . From these research areas, the problems and solutions necessary to discuss AI policy can be defined. This paper, however, refers to this as AI risk policy to differentiate policies intended to reduce catastrophic risk to society versus policies that apply to AI in any other circumstances. Policies, however, must be implemented into the legal statutes of government in order to work. Flynn (2017)  [25] , in the blog post that defines 'AI strategy'  [3] , also defines 'AI policy implementation', which is carrying out the activities necessary to safely navigate the transition to advanced AI systems. This definition implies it is action-oriented work done in government, policy, lobbying, funding, etc. As mentioned in the endnotes of Flynn (2017), however, there is an implicit gap between AI strategy (governance) research and policy implementation, with no AI policy research that identifies mechanisms for actualizing change. However, there is another gap that this paper intends to address, which is that the processes that create and implement policies (the policymaking process) often either distort the original policy, fall short of, or even work counter to the intended outcome, or render certain policy options unactionable. Similarly, The AI governance: A Research Agenda report has neither this consideration nor a definition of policy implementation. This paper intends to put forth a definition of AI policymaking strategy to fill this gap, which is defined as: AI Policymaking Strategy: A research field that analyzes the policymaking process and draws implications for policy design, advocacy, organizational strategy, and AI governance as a whole. This goes further than the concern listed in the endnotes and also develops an upstream approach to AI governance, where work in implementation in turn feeds back and can provide new insights to AI governance research. AI policymaking strategy would fit under the definition of AI governance and would be its own subfield in the same way technical landscape is and would help to clarify questions and considerations in the other subfields. AI politics and ideal governance seem to ask questions about what risks humanity faces and what it ought to do about them, approaching the world as if from above and making corrections, whereas policymaking strategy asks questions about how and what can be done, given both present and future circumstances, and the methods to do so at hand. They approach the world as agents who individually influence the trajectory of the world. These two groups, when they work together, should ideally converge on a policy program that both works and is pragmatic-constituting of policies that both aim at the correct goals and can actually get there. An example of this would be the proposed solution by  Goertzel (2012)    [20]  of creating a surveillance artificial narrow intelligence that monitors the world to prevent the development of superintelligence. Let us say that Policy X is written to do this. However, Policy X, like all other policies, is not simply just a solution to the problem but a set of intended actions and procedures taken by the government that must first be passed by government  [26] . This begs three questions: Can this policy realistically be implemented by government? How do policymakers ensure that Policy X results in the intended outputs and outcomes? And how can policymakers create policy and advocacy strategies to increase the chances of both of these happening? For example, while Policy X is intended to install a surveillance apparatus to prevent superintelligence, would Policy X still have that output and outcome after going through the legislature and executive branch? Is there a chance over time that it would result in mission creep? Policymakers can also develop strategies to ensure that Policy X has its intended outcomes, such as oversight mechanisms within the policy itself. Policymakers can go a step further and ask how the policymaking process itself creates implications for the AI governance field. For example, are there restrictions within the policymaking process that impact timelines for reducing risk, such as how fast governments can act or create new laws? Could some form of upstream innovation be acheived where the policymaking process inspires or generates new ideas for AI governance  [27] ? \n Typologies of AI Policy Before this paper can delve into the policymaking process, AI policy needs to be further refined to understand what kind of policies are being made. The point of this section is to show that AI risk policies are not monolithic, but rather there are multiple approaches to help achieve the same goal, and each set of these policies is going to have with it a different set of political difficulties. It also begs the question in terms of AI governance as a whole as to which sets of policies should be implemented and when, and which policies should be considered relevant to AI risk. In the same way that Bostrom (2014)  [2]  argues that there may be a preferred order of technological development, there is a similar analog with AI risk policies where there is a strategic order to policies that should be attempted to be implemented, whether it is because their political-capital cost is lower, the cost of failure is lower, or because it helps with future efforts to implement policies (such as the creation of an advisory body). A typology of AI policies already has some previous explorative work to build on. Brundage (2016)  [28]  proposed the idea of De Facto AI policies. These are policies that already exist and are relevant to AI. These are further broken down into direct, indirect, and relevant policies. Direct policies are policies that specifically target AI, such as regulations on self-driving cars. Indirect policies are policies that do not specifically target AI but generally impact the development and diffusion of technologies (including AI), such as intellectual property laws and tort law. Relevant policies do not immediately impact AI but are still worth considering because of their impact, such as education policy or the use of electronic medical records. Brundage (2016)  [27]  in this paper, however, does not talk about AI risk policy but rather existing policies around AI as a whole. However, the classification used in this paper is useful overall and can be extended into AI risk policy. Instead of whether or not it directly or indirectly affects AI, AI risk policy can be classified into whether or not it directly or indirectly aims at reducing AI risk. Direct AI risk policies would explicitly govern the use, development, deployment, etc. of AI to reduce risk. Examples of direct AI risk policy could include funding for AI safety research, rules for the development of AGI, international agreements on AI, etc. Indirect AI risk policies would either affect AI but not explicitly govern it or address consequences of the use of advanced AI systems. This could include both policies that affect AI and those that are AI-agnostic. For example, a policy that puts in place stronger protections for privacy in general would reduce the amount of training data available, and thus the speed of AI development, and could be considered an indirect approach. An AI-agnostic policy, for example, would be basic minimum income to address technological unemployment, which could be considered a risk if it leads to societal destabilization. AI risk relevant policies would affect neither AI nor the consequences of it but would rather make it easier for sound AI risk policies to be developed and implemented, such as changing the rules and procedures of government itself to alleviate the pacing problem. There is another layer of classification that should be applied to AI risk policy based on Lowi's Typology  [29] . Lowi categorizes policies into regulatory, distributive, redistributive, and constituency categories. Regulatory policies regulate one's behavior, restricting or incentivizing certain actions, such as the mandating of seat belts in cars. Distributive policies are policies that take money from the general treasury and use them for a specific project that directly benefits one group, such as a dam or research grants. Redistributive policies are those which fundamentally alter the distribution of wealth and resources in the whole of society, such as tax and welfare policies. Constituency policies are those that alter the composition and the rules and regulations of government, such as creating a new executive agency. Each one of these typologies has with it a certain set of political conditions, as they impact people, businesses, and members of government differently. For example, both basic minimum income and the creation of AI safety standards are policies that are intended to reduce existential risk. However, both of these policies will have a different set of political pressures. Basic minimum income is a redistributive policy, which would move substantial amounts of wealth between classes of society. This would mean that it would likely become a nationwide controversial issue with two opposing camps based largely on who benefits and who loses. By contrast, AI safety standards are a regulatory policy, and while there would be two groups opposed to each other on the issue (unless it comes in the form of voluntary self-regulation by the industry), the political factors around it would look different. Regulatory policies are not usually salient or popular to the general public, and thus, the political battle would be largely limited to regulators, experts, and the business class. This typology will help us to understand how the different policies will be treated in the policymaking process. In other words, policy creates politics. Further work on developing this might be useful for understanding the likelihood of policies being adopted and could shift strategies for which policies to pursue. \n The Policymaking Cycle \n Problem Identification, Agenda Setting, and Policy Formulation The first few steps of the policymaking process: Problem identification, agenda setting, and policy formulation, are usually tied together  [30] , including in a so-called 'multiple streams framework'. The multiple streams framework attempts to explain how policies reach the agenda when policy entrepreneurs are able to couple the policy, politics, and problems streams to open up a policy window, the opportune time when all the conditions are right to get a policy on the agenda  [31] . \n Problem Stream There are many problems in society. However, the public does not seek government intervention for many of these problems. There are some basic requirements for an issue in society to become a policy problem, which is that it is something that the public finds to be intolerable, government can do something about, and is generally seen as a legitimate area for government to work on  [30] . Policy problems can also arise when there are two or more identifiable groups who enter into conflict in a policy arena for resources or positions of power  [32] . The first condition for an issue to be considered a policy problem is that it is something that the public or a group finds to be intolerable. Indicators such as statistics can help to identify a problem. These can be used objectively, for understanding conditions in society, or politically, when they are used to justify a political position: for example, using gun violence statistics as an argument for gun control. What is considered an issue over time changes because of the evolution of society. Changes in values, distribution of resources, technology, etc. will change what issues are considered in society  [30] . In AI governance, identifiers such as the rate of technological progress or the proliferation of autonomous weapons could be used as examples. Creating a list of politically salient identifiers or metrics could be potentially useful for creating long-term strategies and goals. How the issue is framed is very important for whether or not it will be considered a policy problem  [30] . Is mandating seatbelts in cars beneficial for public safety? Or is it paternalistic? Are these problems legitimate for government to handle? The framing of a problem can have an overwhelming impact on whether or not it is considered a problem appropriate for government to even formulate policy on. It can also impact the content of the policy. Whether you define access to transportation for handicapped people as a transportation problem or a civil rights issue determines whether the acceptable solution involves buying special needs vans, or costly upgrades to buses and subways to ensure equal access. Framing can also raise the priority of a policy problem by, for example, calling it a crisis and raising a sense of urgency. The question of framing is also incredibly important for AI governance. For example, would autonomous weapons make war more humane by removing humans? Or will it distance ourselves from the violence and make us more willing to use them? The AI governance community needs to think about how these issues ought to be framed, and the consequences of doing so. In order for an issue to be a part of the system agenda, or what the public or specific communities are discussing, there must be a focusing event. Focusing events are specific events that draw attention to a problem in society and the reasons behind it. The Sandy Hook school shooting, for example, is a focusing event that drew attention to America's gun laws. Moreover, events that occur outside of sector-specific focusing events  [31] , or past policies on these issues, can have a large impact, especially on the types of solutions used. For AI governance, \"Sputnik moments\" such as AlphaGo beating Lee Sedol would be an example that drew considerable media attention and generated much discussion about the future of AI, especially in China  [33] . Understanding how to exploit these events for the AI governance agenda will be key to generating support and getting policies on the agenda. It is also important to stay on top of these events to understand the direction society is heading in-and to pre-empt or avert less productive or dangerous framings that might feed into arms races  [31] . For example, Yampolskiy (2018) details a list of past failures by AI-enabled products  [34] . How could work like this be used to influence the problem-setting? Could other AI risk researchers expand on it and build that work into a more thorough project to be used to draw attention to AI risk? Or, could attempts such as this backfire and cause pre-emptive stigmatization or ineffective policies? \n Politics Stream The politics stream is the combined factors of the national mood or public opinion, campaign groups, and administrative/legislative change. Decision-makers in government keep tabs on the swaying opinions of the masses and interest groups and act in a way that promotes themselves favorably, changing items on the agenda to stay relevant and popular, and to obscure unpopular policy stances. Changes in administration, especially when there is a major shift in the ideological composition of the institution, have a strong impact on what is included or not included on the agenda  [31] . In AI governance, and for people involved in advocating and implementing policies, maintaining a key eye on domestic and international politics will be key. Knowing when and what kind of policy to advocate for, and to whom, is crucial not only to saving time and energy, but also for legitimacy. Trying to sell a nationalistic administration on greater UN involvement will probably not help someone with furthering their policy proposals and may even damage their (and their coalition's) political capital and cause. However, other forms of cooperation, such as bilateral cooperation for reducing the risk of accidents  [35] , may be more promising. AI governance researchers will need to consider how the political landscape should shape their recommendations or policy proposals. Not only would it determine if their recommendations would ever get considered, but if it was implemented, how would it affect the national mood? Would the next administration simply walk it back? How would other interest groups react and impact the long-term ability to reduce risk? If administration changes result in a flip-flop of ideology, what does that mean for AI risk policies associated with the past administration? Could an AI risk policy group maintain influence throughout changing administrations? All of these have implications on our ability to reduce AI risk, and this means that the policymaking strategy will not only have to be robust but also flexible enough to survive changing political conditions. \n Policy Stream The policy stream, which is in essence the policy formulation aspect of the policy cycle, is the \"soup\" of ideas that are generated by policymakers  [35]  when deciding what to do about a problem. Different policy networks create policies differently, with different levels of innovativeness and speed  [35] . Understanding these differences and examining their implications for the AI governance field might be useful to understand its long-term impact and the specific strategic routes it should take. In other words, how should the AI governance research field itself be organized in a way that promotes useful and relevant solutions? Despite the staggering number of policy proposals coming out, only a handful will ever be accepted. These policies compete with one another and are selected on a set of criteria, which include technical feasibility, value compatibility  [35] , budgetary and political costs, and public acceptance. Policies that work will also be technically sound, with no major loopholes, and a clear rationale for how its provisions would lead to actually achieving the policy objectives  [30] . This actually creates some key considerations for the field. It means that many ideas are either functionally useless due to their political limitations, unlikely to be adopted in the face of easier or less politically costly options, do not have viable policy mechanisms to achieve their goal, or are otherwise intractable prospects for government. Even if all of the above conditions are resolved, loopholes and unintended consequences may neuter the policy or make conditions worse. This vastly reduces the space of possible solutions. Further, even though the ability for policy implementation or values might change over time, it is still a matter of how much and when. This begs the question: What problems can be solved when, how, and by whom? What does that mean for the large picture strategic approach? Where should our policies originate from? While there are a bunch of policy ideas out there, only a few are ever seriously considered for adoption. Sources of these policies include (in the United States Federal Government, for example) the President along with the Executive Office of the President, Congressional leaders, government agencies (mostly small incremental changes and adjustments), temporary organizations or 'adhocracies' that serve to investigate specific topics, and interest groups whose topical expertise and political power can sometimes make them de facto policymakers. Each of these areas have differing levels of legitimacy, influence, and degree to which they can make policy changes. A question to consider is not only where in the policy network AI risk policymakers should focus on making these policies, but where they can best advocate for the creation of additional bodies like adhocracies to create additional policies, and what implications that has for the field at large. With regard to the policy formulation phase of policymaking, a continuum of political environments has been created such that on one extreme, there are policies with publics and on the other, there are policies without publics  [36] . When policies are formulated, it is important to consider political environments relevant to the issue. The term \"publics\" refers to groups who have more than a passing interest in an issue or are actively involved in it. It appears that AI risks are issues where there are limited incentives for publics to form because of problems being remote, costly, or even abstract and uncertain. What does this mean for the AI safety community? How can interest groups be created most effectively? How can these issues be best expressed so that they do not seem so remote, abstract, or uncertain? \n Policy Windows and Policy Entrepreneurs This framework assumes that policy decision-makers, the legislators and bureaucrats in government exist in a state of ambiguity, where they do not have a clear set of preferences, and each set of circumstances can be seen in more than one way. This cannot be resolved with more information, as it is not an issue of ignorance. The example that  Zahariadis (2007)  gives is that \"more information can tell us how AIDS is spread, but it still will not tell us whether AIDS is a health, educational, political, or moral issue  [31] \". Overall, the multiple streams framework describes government organizations as \"organized anarchies\" where institutional problems run rampant, there are often unclear or underdefined goals, overlapping jurisdictions, and a host of other problems that mean that decision-makers have to ration their time between problems and do not have enough time to create a clear set of preferences, make good use of information, or take the time to comprehend the problem for sound decisions on policies. In essence, decision-makers are not rational decision-makers by any stretch. Instead, it depends on the ability of policy entrepreneurs to couple the three streams and manipulate the decision-maker into achieving their intended policy goals  [31] . Policy entrepreneurs, who are the policymakers, advocates, interest groups, etc. who push to make specific legislative changes in their areas, only have a short window of time to have their proposals added to the formal agenda. It is when the right political environment, a timely problem, and a potentially acceptable solution all meet together with a policy entrepreneur who can manipulate the situation to their advantage. Because decision-makers exist in a state of ambiguity, policy entrepreneurs are able to manipulate their interpretation of their information to provide meaning, identity, and clarity. Policy entrepreneurs use different tools and tactics to manipulate the way decision-makers process information and exploit their behavioral biases. Framing tactics, for example, can be used to present a policy option as a loss to the status quo, not taking note of the degree of loss it creates, exploiting decision-makers who are loss-averse, and may push them towards more extreme options like going to war to make up for those small losses  [31] . The manipulation of emotions through symbols and the identity or social status of a decision-maker can also pressure them to make certain choices; policies around flag-burning are a great example of this. Because decision-makers are under a great deal of stress and are time-constrained, the strategic ordering of decisions, or 'salami tactics', creates agreement in steps by reducing the total perceived risk of a policy  [31] . The manipulation of symbols in the way that artificial intelligence is being framed today has already occured. At first, anti-autonomous weapons advocates were describing 'armed quadcopters' as a serious problem with little media attention  [37] . These were rebranded as 'slaughterbots' and a short-film was released with substantial media attention. However, what sort of long-run impact will this have on the field? While giving policymakers straight facts and solutions seems appealing, AI risk policymakers have to consider that it is impractical in reality and may have to accept the inevitability, to policy success, of tactics like framing. Which begs the question, which tactics should they use and how? Questions like these must be considered. All of this strongly requires an appropriate consideration. Consider, if there are some problems that can only be resolved through state action (such as an arms race), that means that it is dependent on the policymaking process, and thus, these solutions can only be passed when policy windows open. Therefore, how many of these opportunities do AI risk policymakers get? Or, how many chances do they get to implement AI risk policies? These windows only open every once in a while, and they are often in fragile conditions. For example, Bill Clinton's campaign in 1992 aimed to reform the healthcare system and made it a campaign priority, but his administration's failure to pass the bill closed the window  [31] . In other words, what impact does this have on AI governance and policy implementation timelines and what does that mean for the field as a whole? However, in order for a policy entrepreneur to manipulate decision-makers, they must have access to them, which is highly dependent on both the legitimacy of their issue but also for the legitimacy of the group itself and their interest. One of the ways that policy entrepreneurs increase their own influence is to create new decision-points that they can exploit and to reduce access of other groups  [32] . AI risk policymakers and advocates will have to find some way to gain access to decision-makers. For example, working on near-term or non-existential risk issues with AI might help someone to build the social capital and network that is necessary to work on existential risks issues. This would not only make it easier people in the field to implement their solutions but to also make themselves gatekeepers to the decision-makers, which could help with preventing policies that would increase existential risks (whether from AI or other sources) from getting through. This may be an area that needs further research. Aspects such as a group's access to decision-makers, the advocating group's legitimacy, biases of the institution  [38] , and a group's ability to mobilize resources will determine what gets added to the agenda, and the AI risk community will need to work on building all of these. AI policymakers will need to develop a strategy for how to get the right people into the right places and how to coordinate between different groups. Getting on the formal agenda is a competitive process because there are fundamental limits to a decision-maker's time, and because the policy may be perceived to harm the interests of other groups. Opposing groups can use a variety of tactics, such as denying that the problem exists, arguing that it is not a problem for government, or arguing that the solution would have bad societal consequences, to deny it agenda status. Other factors that could deny an issue agenda status include changing societal norms, political changes, or political leaders avoiding having to be confronted by an issue that hurts their interests. Thus, AI policymakers will need to know how to overcome and adapt to these changing situations and other organizations preventing their policies from being adopted. AI governance and policy experts will need to pay attention to the arguments being used for and against superintelligence, and whether or not this will become a political issue.  Baum (2018)  notes that superintelligence is particularly vulnerable to what is known as politicized skepticism, skepticism that is not based on an intellectual disagreement about the problem, based on good-faith attempts to understand the arguments, but rather to shut down concerns based out of self-interest (or a conflict of interests). Some major AI companies, and even other academics, have criticized the idea of superintelligence out of what seems to be their own self-interest as opposed to genuine concerns  [39] . This would have a devastating impact on AI policy advocates in a similar way that the tobacco industry significantly impacted scientific efforts to study the public health links between tobacco and cancer. \n Policy Adoption The next stage of the policy cycle is policy adoption, or when decision-makers choose an option that adopts, modifies, or abandons a policy. This does not necessarily take the form of choosing from a buffet of completed pieces of policy, but rather to take further action on a policy alternative that is more preferable and that is more likely to win approval. At this point, after much bargaining and discussion, the policy choice will only be a formality, or there will be continuous discussion and disagreement until there is a formal vote or decision made. This is an important field to analyze for AI policymakers for the obvious implication that they will want their policy proposals being chosen, and so they will need to understand and design strategies to do so. Further, as will be discussed later, when changes do occur, they can often bring with them wider changes in public policy  [40] , an implication that will need to be taken into account. The advocacy coalition framework is a theory on policy adoption but also incorporates every other aspect of the policy cycle with it. The theory describes the interactions of two or more 'advocacy coalitions'; groups of people from a multitude of positions who coordinate together to advocate for some belief, or to implement some policy change (potentially over many fields) over an extended period of time  [41] . These do not need to be a single, explicitly delineated organizations like the National Rifle Association but could include loosely affiliated groups of organizations and/or individuals, all working towards the same goal. Building and maintaining coalitions will be one of the major tasks that AI policymakers will need to work on, and so, examining this framework will be highly valuable. What is it that binds a coalition together? All advocacy coalitions share some form of beliefs. However, the advocacy coalition framework uses a hierarchical belief system. The deepest and broadest of these are deep core beliefs, which are normative positions on human nature, hierarchy of value preferences (i.e., should we value liberty over equality?), the role of government, etc. Policy core beliefs are the next stage of the hierarchy, which involves the extension of deep core beliefs into policy areas. Both of these areas are very difficult to change, as they involve fundamental values. This actually creates an issue where, due to differing fundamental and personal values which lead to lack of interaction, different coalitions often see the same information differently, leading to distrust. Each may come to see the other side as \"evil\", reducing the possibilities of cooperation and compromise  [41] . The deeply held convictions of what a policy subsystem ought to look like are called policy core policy preferences and are the source of conflict between advocacy coalitions. They are the salient problems that have been the long-running issues in that area for a time. Policy core policy preferences shape the political landscape, dictating who allies with whom and who the enemies are, and what strategies coalitions take. The final level of the belief hierarchy are secondary beliefs, belief that cover procedures, rules, and things of this nature. These are very narrow in scope and the easier to change, requiring less evidence and little bargaining to change. Understanding the values and beliefs of different existing coalitions, groups, and individuals is key to building and maintaining new coalitions for AI policymakers. This brings up a few considerations. Since it is difficult for conflicting coalitions to work together, will AI policymakers have to choose certain coalitions to work with? What are the costs, benefits, and the potential blowback of this? Since some policies related to AI risk are not in a mature policy field (and thus do not have established coalitions), what can be done to shape the field beforehand to their advantage and/or promote cooperation among coalitions that are likely to form? Further, since secondary beliefs are relatively easy to change, what can be changed to help reduce existential risk? On a macro-level, this AC Framework acts as a cycle. Relatively stable parameters, as mentioned before, exist in the status quo since policy arenas usually come to some equilibrium where one coalition dominates the policy subsystem. Then, policy changes made by an advocacy coalition or an outside event create a fundamental change in the world, whether it is a change in public opinion or in the rules and procedures governing a subsystem, which changes the initial stable parameters, such as a major event like a mass shooting. These lead to a shift in power that allows another coalition to gain influence over the types of policies being adopted. However, especially in the case of controversial legislature, policies that require multiple veto points to pass will create access for multiple coalitions. This means that even a coalition that dominates a subsystem will not have unilateral ability to dictate policies in some situations. Others, however, especially where there are few decision-makers or an exceptionally influential decision-maker, can result in highly monopolized systems. Questions such as how to be resilient to these changes in conditions, how to facilitate changes into conditions that are beneficial to AI policymakers, and how to construct policy subsystems in a way that is conducive to AI policymakers' goals are useful questions to consider. This theory describes policy adoption on a very broad level, but how do the decision-makers themselves decide which policies to move forward with? Different incentives and restrictions come to play at different levels of policymaking. For example, highly salient and popular issues are more likely to be influenced by popular opinion, whereas obscure technical issues will likely be determined by policy experts in that field. Different factors that affect both individual and group decision-makers also come into play, such as their personal, professional, organizational, and ideological values. For legislators, their political party and their constituency also play an overwhelming role in their decision-making. Understanding and mapping out these factors will be necessary for the successful implementation of AI risk policy. On top of these factors, decision-makers usually never have the time, expertise, or even care enough to be able to come up with a fully rational approach to deciding most policies. In many cases, legislators will seek out the advice of other legislators and experts and follow their lead. Due to this being a widespread practice, a few key institutions and leaders often have disproportionate power. For those working in AI risk policy, it is necessary to understand these things so that the message they craft for as to why policy change should occur, and whom to specifically target to get widespread adoption from other decision-makers in the policy arena. \n Policy Implementation Policy implementation is a key step in the policymaking process. It is defined as \"whatever is done to carry a law into effect, to apply it to the target population . . . and to achieve its goals\"  [30] . In other words, it is the activity where adopted policies are carried into effect  [30] . However, that is not to say that it is a very distinct step that can be clearly distinguished from others. Every implementation action can influence policy problems, resources, and objectives as the process evolves  [42] . Policy implementation can influence problem identification, policy adoption, etc. Two broad factors that have been offered for the success of policy are local capacity and will  [42] . In other words, is there enough training, money, and human resources, along with the right attitudes, motivation, and beliefs to make something happen? It is suggested that the former can be influenced much more easily than the latter as more money can be received and consultants can be hired. For AI risk, both questions are relevant: How to increase capacity and how to influence the influencers. With the former, it has been estimated that about $9-$20 million is currently spent on AI risk  [43, 44] . With the latter, studying the opinion of the public as well as experts might be a useful approach. One survey  [45]  indicates that only 8% of top-cited authors in AI consider that human-level AI would be extremely bad (existential risk) for humanity. Another survey that is more recent  [46]  indicates that machine learning researchers think on average (median) that there is a 10% probability that human-level machine intelligence will result in a negative outcome and 5% probability that it will have an extremely bad outcome (existential risk). The general public seems to be generally cautious, with a survey showing 82% of Americans believing that AI/robots should be managed carefully  [47] . This part of the policymaking process is very difficult as the literature is generally quite pessimistic about the ability of policies to bring social changes into effect  [48] . However, the authors of the cited paper have identified conditions of effective implementation based on successful examples. These conditions are (a) the policy is based on a sound theory of getting the target group to behave in a desired way, (b) policy directives and structures for the target group are unambiguous, (c) the leaders implementing the policies are skillful with regard to management and politics and committed to the goals, (d) policy is supported by organized constituency groups and key legislators as well as courts throughout the implementation process, and (e) the relative priority of policies is not significantly undermined over time by other policies or socioeconomic changes. Additionally  [49] , having carefully drafted statute that incentivizes behavior changes, provides adequate funds, expresses clearly ranked goals, is an implementation process, and has few veto points is also vital to the success of a policy. With regard to AI governance, the ambiguity and complexity of the problem creates a major hurdle for effective policies to be developed. These problems are nonlinear, very hard to predict, and may have the traits of wicked problems in the sense that solving one problem can create new problems. Breaking down AI risk policy into multiple domains as discussed in the previous section helps with creating somewhat less ambiguous objectives, such as changing the education system to be more conducive for technological growth. Even then, however, because many of the issues are either complex or have not happened yet, it is difficult to create concrete objectives and policies. AI risk is not like noise pollution, where there is an easily identifiable, manageable, and tractable problem. Further research could help to identify concrete and tractable issues that might lead to a reduction of risk. In addition, when trying to develop and implement policy, AI policymakers will need to keep in mind factors such as to what extent there is support for it in the executive branch, with outside organizations, and how exactly the policy is written and how those change throughout the policymaking cycle. Another key consideration for successful policy implementation that was identified from the literature is engaging with the community to increase readiness to accept and devote resources to policy-related problems. It has been acknowledged that there are no good evidence-based ways of achieving community buy-in. This is an area that might be useful to study in order to increase the chances of successful reduction of AI risk. There are different stages of community readiness, such as no awareness, denial, and vague awareness to preplanning, preparation, initiation, and stabilization phases  [49] . It is important to understand what counts as the community and what phases different subcommunities of AI safety field are in. Earlier, this paper mentioned a survey about AI experts and showed that their readiness with AI risks was low. Other relevant experts, the public, and other types of subcommunities might have different levels of readiness. It has been suggested that \"the more clearly the core components of an intervention program or practice are known and defined, the more readily the program or practice can be implemented successfully\"  [49] . In other words, policies and steps of implementation of those policies have to be very clearly expressed. What implications does this have for AI risk? Researchers and policymakers should evaluate how clearly core components have been expressed in this field and improve them as necessary. \n Policy Evaluation The final step in the policymaking cycle is policy evaluation. This includes activities related to determining the impact of the policy, whether it is achieving its goals, whether the rules and procedures it lays out are being followed, and other externalities or unintended consequences  [30] . As we have explained before, policy evaluation does not have to occur only at this step. For example, the impact of a policy is estimated already in the early stages. Anderson et al. highlighted different types of policy evaluations in their book but especially considered systematic evaluations of programs. This involves \"the specification of goals or objectives; the collection of information and data on program inputs, outputs, and consequences; and their rigorous analysis, preferably through the use of quantitative or statistical techniques\"  [30] '. Policy evaluation examines a policy to understand its impacts in multiple ways  [30] . First, is the policy affecting the population that it is intending to target? In AI risk policy, this could be anything from large tech companies, to AI researchers, to people affected by technological unemployment. Second, are there populations that are being affected that were not intended? These externalities could be positive or negative. Third, what are the benefits and costs associated with this policy? AI policymakers will want to ensure that their policies actually reduce risk and that the costs are not so astronomical that they become politically infeasible. Finally, what long-term costs and benefits does a policy have? This is especially important for AI risk policy, as decisions now could have a major impact on the long-term risk that AI has. In AI governance and policymaking, research needs to be done on what sort of indicators or metrics are used for the reduction of risk, and for identifying what goals that should be achieved. If the previous steps in the policymaking process have generated goals that are unclear or diverse, it is very difficult to evaluate the impact of the policy  [30] . Different decision-makers can more easily reach a differing conclusion about the results of a program in that case, or may not follow it all  [30] . How the goals of an AI risk program are defined is, therefore, very important. Another key consideration for policy evaluation is how to make sure that the results are objectively measured. Agency and program officials may be wary of possible political consequences of the evaluation process  [30] . If it turns out that the program was not useful or even detrimental, this might have consequences to their influence and career. Because of this consideration, they might not be very interested in correct evaluation studies or they may hinder the process in some other way. There are many ways an evaluation of a policy might be ignored or attacked, such as claiming it was poorly done, the data were inadequate, or the findings inconclusive  [30] . Thus, it is important that researchers are provided with high-quality and relevant data-sets that are accurate. There is also the distinction between policy outputs and outcomes  [30]  to consider. Outputs are tangible actions taken or things produced, such as collecting taxes or building a dam. Outcomes, on the other hand, are the consequences for society, such as lower disposable income or cleaner air quality. Outputs do not always produce the intended outcomes, which is highly evident in areas such as social welfare policy, where policies may unintentionally trap people in poverty. For AI policymakers, it is very important to consider whether their policy outputs will have the intended consequences, and if so, how to correct that policy. The evaluation of a policy and the political responses to it can result in the termination of it  [30] . Assuming that AI risk policymakers do not want their policies to be terminated or altered in a detrimental way, how can they make sure this does not happen? A policy getting altered to be more effective might be a good thing, but termination can bring unpleasant and negative connotations. It might even have negative consequences to the community  [30] . What exact consequences might it have politically? Further, it is important to remember that many policymakers' time horizon only goes until the next election, and so, they often seek immediate results, often before the returns come into fruition. While this may not impact all policies, as this mostly applies to salient policies like healthcare and education, AI policymakers should keep this in mind and try to understand how it might impact their work. \n Conclusions There are multiple policy options that could be chosen that either directly or indirectly reduce AI risk, or relevant policies that could help with further efforts to reduce AI risk. Because different policy arenas have different political conditions, and the policymaking process itself draws a number of important challenges, this brings up questions as to what policies in what order are chosen, what strategies are used to get these policies passed and implemented by the government, and the larger impact of these choices on AI governance and risk as a whole. This paper argues that a new subfield of AI governance research on AI policymaking strategies should be further investigated to draw implications for how these policies should be designed, advocated for, and how organizations should approach solving this issue. \n Limitations and Future Research This paper is intended to be a broad overview and to be a conversation starter for future research into this area. Thus, there is a strong limitation to the depth of research in this paper. However, it is expected that future work will be done to further refine the line of thinking laid out above, along with further in-depth study into the different theories and their applicability to AI risk. One of the major limitations of this paper is that the stages heuristic presented in this paper has been heavily criticized and is subject to debate about its effectiveness.  Sabatier (2007)  has criticized it for not being a causal theory, having a strong top-down bias, among other critiques. However, he also notes that there is much up to debate, with some scholars such as Anderson (2010) advocating for it. There are also a number of other theories that were not discussed in this paper, such as Institutional Rational Choice, the punctuated equilibrium framework, the policy diffusion framework, and other lesser-known theories. Future research is expected that will explore which policy frameworks should be focused on in AI risk research. The other limitation of this paper is that its applicability to the international governance of AI was not discussed. Future research that looks at how much these theories apply to foreign policy and the international governance of AI in general would be useful. If these theories have a very limited or no impact on the international governance of AI, then figuring out how much work can be done to reduce AI risk in domestic policy would determine the usefulness of these theories.", "date_published": "n/a", "url": "n/a", "filename": "BDCC-03-00026.tei.xml", "abstract": "This essay argues that a new subfield of AI governance should be explored that examines the policy-making process and its implications for AI governance. A growing number of researchers have begun working on the question of how to mitigate the catastrophic risks of transformative artificial intelligence, including what policies states should adopt. However, this essay identifies a preceding, meta-level problem of how the space of possible policies is affected by the politics and administrative mechanisms of how those policies are created and implemented. This creates a new set of key considerations for the field of AI governance and should influence the action of future policymakers. This essay examines some of the theories of the policymaking process, how they compare to current work in AI governance, and their implications for the field at large and ends by identifying areas of future research.", "id": "c46324d4274ef7ade30fba3950df2422"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Siddharth Reddy", "Anca D Dragan", "Sergey Levine", "Shane Legg", "Jan Leike"], "title": "Learning Human Objectives by Evaluating Hypothetical Behavior", "text": "Introduction Users typically specify objectives for reinforcement learning (RL) agents through scalar-valued reward functions  (Sutton & Barto, 2018) . While users can easily define reward functions for tasks like playing games of Go or Star-Craft, users may struggle to describe practical tasks like Proceedings of the 37 th International Conference on Machine Learning, Online, PMLR 119, 2020. Copyright 2020 by the author(s). \n Generative model Hypothetical behavior Reward model User feedback RL agent (1) (2) (3) driving cars or controlling robotic arms in terms of rewards  (Hadfield-Menell et al., 2017) . Understanding user objectives in these settings can be challenging -not only for machines, but also for humans modeling each other and introspecting on themselves  (Premack & Woodruff, 1978) . For example, consider the trolley problem  (Foot, 1967) : if you were the train conductor in Figure  1 , presented with the choice of either allowing multiple people to come to harm by letting the train continue on its current track, or harming one person by diverting the train, what would you do? The answer depends on whether your value system leans toward consequentialism or deontological ethics -a distinction that may not be captured by a reward function designed to evaluate common situations, in which ethical dilemmas like the trolley problem rarely occur. In complex domains, the user may not be able to anticipate all possible agent behaviors and specify a reward function that accurately describes user preferences over those behaviors. We address this problem by actively synthesizing hypothetical behaviors from scratch, and asking the user to label them with rewards. Figure  1  describes our algorithm: using a generative model of initial states and a forward dynamics model trained on off-policy data, we synthesize hypothetical behaviors, ask the user to label the behaviors with rewards, and train a neural network to predict the rewards. We repeat this process until the reward model converges, then deploy a model-based RL agent that optimizes the learned rewards. The key idea in this paper is synthesizing informative hypo-theticals. Ideally, we would generate these hypotheticals by optimizing the value of information (VOI;  Savage, 1954) , but the VOI is intractable for real-world domains with highdimensional, continuous states. Instead, we use trajectory optimization to produce four types of hypotheticals that improve the reward model in different ways: behaviors that (1) maximize reward model uncertainty, to elicit labels that are likely to change the updated reward model's outputs; (2) maximize predicted rewards, to detect and correct reward hacking; (3) minimize predicted rewards, to safely explore unsafe states; or (4) maximize novelty of trajectories regardless of predicted rewards, to improve the diversity of the training data. To ensure that the hypothetical trajectories remain comprehensible to the user and resemble realistic behaviors, we use a generative model of initial states and a forward dynamics model for regularization. We call this method reward query synthesis via trajectory optimization (ReQueST). Our primary contribution is an algorithm that synthesizes hypothetical behaviors in order to safely and efficiently train neural network reward models in environments with high-dimensional, continuous states. We evaluate ReQueST with simulated users in three domains: MNIST classification, a state-based 2D navigation task, and the image-based Car Racing video game in the OpenAI Gym. Our experiments show that ReQueST learns robust reward models that transfer to new environments with different initial state distributions, achieving at least 2x better final performance than baselines adapted from prior work (e.g., see Figure  4 ). In the navigation task, ReQueST safely learns to classify 100% of unsafe states as unsafe and deploys an agent that never visits unsafe states, while the baselines fail to learn about even one unsafe state and deploy agents with a failure rate of 75%. \n Related Work In this work, we align agent behavior with a user's objectives by learning a model of the user's reward function and training the agent via RL  (Ng & Russell, 2000; Ziebart et al., 2008; Leike et al., 2018) . The idea behind modeling the user's reward function -as opposed to the user's policy  (Pomerleau, 1991; Ross et al., 2011; Ho & Ermon, 2016) , value function  (Dvijotham & Todorov, 2010; Warnell et al., 2018; Reddy et al., 2018) , or advantage function  (Mac-Glashan et al., 2017)  -is to acquire a compact, transferable representation of the user's objectives; not just in the training environment, but also in new environments with different dynamics or initial states. The closest prior work is on active learning methods for learning rewards from pairwise comparisons  (Sadigh et al., 2017; Bıyık & Sadigh, 2018; Wirth et al., 2017) , critiques , demonstrations  (Ibarz et al., 2018; Brown et al., 2018) , designs  (Mindermann et al., 2018) , and numerical feedback  (Daniel et al., 2014) . Re-QueST differs in three key ways: it produces hypothetical trajectories using a generative model, in a way that enables trading off between producing realistic vs. informative queries; it optimizes queries not only to reduce model uncertainty, but also to detect reward hacking and safely explore unsafe states; and it scales to learning neural network reward models that operate on high-dimensional, continuous state spaces. ReQueST shares ideas with prior work  (Saunders et al., 2018; Prakash et al., 2019)  on learning to detect unsafe behaviors by initially seeking out catastrophes, selectively querying the user, and using model-based RL. ReQueST differs primarily in that it learns a complete task specification, not just an unsafe state detector. ReQueST is also complementary to prior work on safe exploration, which typically assumes a known reward function and side constraints, and focuses on ensuring that the agent never visits unsafe states during policy optimization  (Dalal et al., 2018; Garcıa & Fernández, 2015) . \n Learning Rewards from User Feedback on Hypothetical Behavior We formulate the reward modeling problem as follows. We assume access to a training environment that follows a Markov decision process (MDP;  Sutton & Barto, 2018)  with unknown state transition dynamics T , unknown initial state distribution S train 0 , and an unknown reward function R that can be evaluated on specific inputs by querying the user. We learn a model of the reward function R by querying the user for reward signals. At test time, we train an RL agent with the learned reward function R in a new environment with the same dynamics T , but a potentially different initial state distribution S test 0 . The goal is for the agent to perform well in the test environment with respect to the true reward function R. Our approach to this problem is outlined in Figure  1 , and can be split into three steps. In step (1) we use off-policy data to train a generative model p (⌧ ) that can be used to evaluate the likelihood of a trajectory ⌧ = (s 0 , a 0 , s 1 , a 1 , ..., s T ), which enables us to synthesize hypothetical trajectories that can be shown to the user. In step (2) we produce synthetic trajectories, which consist of sequences of state transitions (s, a, s 0 ), that seek out different kinds of hypotheticals (detailed in Section 3.3). We ask the user to label each transition with a scalar reward R(s, a, s 0 ), and fit a reward model R(s, a, s 0 ) using standard supervised learning techniques. In step (3) we use standard RL methods to train an agent using the learned rewards. \n Learning a Generative Model of Trajectories In order to generate hypothetical behaviors with uncertain rewards, we first learn a generative model of initial states and a forward dynamics model. We use these models to synthesize plausible trajectories, without requiring that an agent actually perform those behaviors in the real environment. In step (1) we collect off-policy data by interacting with the training environment in an unsupervised fashion; i.e., without the user in the loop. To simplify our experiments, we sample trajectories ⌧ by following random policies that explore a wide variety of states. We use the observed trajectories to train a likelihood model, p (⌧ ) / p (s 0 ) T 1 Y t=0 p (s t+1 |s t , a t ), (1) where p (s 0 ) models the initial state distribution, p (s t+1 |s t , a t ) models the forward dynamics, and are the model parameters (e.g., neural network weights). We train the model p using maximum-likelihood estimation, given the sampled trajectories. As described in the next section, we use the likelihood model to generate realistic synthetic trajectories to show to the user. In environments with high-dimensional, continuous states, such as images, we also train a state encoder f : S ! Z and decoder f 1 : Z ! S, where S = R n , Z = R d , and d << n. As described in Section 3.4, embedding states in a low-dimensional latent space Z enables us to synthesize realistic hypotheticals. In our experiments, we train f and f 1 using the variational auto-encoder method (VAE;  Kingma & Welling, 2013) . \n Representing the Reward Model as a Classifier Our goal is to learn a model R of the user's reward function. In step (2) we represent R by classifying state transitions as good, unsafe, or neutral -similar to  -and assigning a known, constant reward to each of these three categories: R(s, a, s 0 ) = X c2{good,unsafe,neutral} p ✓ (c|s, a, s 0 )R c , (2) where p ✓ (c|s, a, s 0 ) = 1 m P m i=1 p ✓i (c|s, a, s 0 ) is the mean of an ensemble of m classifiers {p ✓i } m i=1 , and ✓ i are the weights of the i-th neural network in the ensemble. R c is the constant reward for any state transition in class c, where R unsafe  R neutral  R good . Modeling the reward function as a classifier simplifies our experiments and makes it easier for the user to provide labels. In principle, our method can also work with other architectures, such as a regression model R = R ✓ . \n Designing Objectives for Informative Queries Our approach to reward modeling involves asking the user to label trajectories with reward signals. In step (2) we synthesize query trajectories to elicit user labels that are informative for learning the reward model. To generate a useful query, we synthesize a trajectory ⌧ that maximizes an acquisition function (AF) denoted by J(⌧ ). The AF evaluates how useful it would be to elicit reward labels for ⌧ , then update the reward model given the newly-labeled data. Since we do not assume knowledge of the initial state distribution of the test environment where the agent is deployed, we cannot optimize the ideal AF: the value of information (VOI;  Savage, 1954) , defined as the gain in performance of an agent that optimizes the updated reward model in the test environment. Prior work on active learning tackles this problem by optimizing proxies for VOI  (Settles, 2009) . In this work, we synthesize a separate trajectory for each of four AFs defined in the following paragraphs. Maximizing uncertainty. The first AF J u (⌧ ) implements one of the simplest query selection strategies from the active learning literature: uncertainty sampling  (Lewis & Gale, 1994) . The idea is to elicit labels for examples that the model is least certain how to label, and thus reduce model uncertainty. To do so, we train an ensemble of neural network reward models, and generate trajectories that maximize the disagreement between ensemble members. Following  Lakshminarayanan et al. (2017) , we measure ensemble disagreement using the average KL-divergence between the output of a single ensemble member and the ensemble mean (Equation 5 in the appendix). Maximizing reward. The second AF J + (⌧ ) is intended to detect examples of false positives, or 'reward hacking': behaviors for which the reward model incorrectly outputs high reward  (Amodei et al., 2016; Christiano et al., 2017) . The idea is to show the user what the reward model predicts to be good behavior, with the expectation that some of these behaviors are actually suboptimal, and will be labeled as such by the user. To do so, we simply synthesize trajectories that maximize J + (⌧ ) = P (s,a,s 0 )2⌧ R(s, a, s 0 ). Minimizing reward. The third AF J (⌧ ) is intended to augment the training data with more examples of unsafe states than would normally be encountered, e.g., by a rewardmaximizing agent acting in the training environment. The idea is to show the user what the reward model considers unsafe behavior, so the user can confirm whether the model has captured the correct notion of unsafe states. To do so, we produce trajectories that maximize J (⌧ ) = J + (⌧ ). Maximizing novelty. The fourth AF J n (⌧ ) is intended to produce novel trajectories that differ from those already in the training data, regardless of their predicted reward; akin to prior work on geometric AFs  (Sener & Savarese, 2018) . This is especially helpful early during training, when uncertainty estimates are not accurate, and the reward model has not yet captured interesting notions of reward-maximizing and reward-minimizing behavior. To do so, we produce trajectories ⌧ that maximize the distance between ⌧ and previously-labeled trajectories ⌧ 0 2 D, J n (⌧ ) = 1 |D| P ⌧ 0 2D d(⌧, ⌧ 0 ). In this work, we use a distance function d that computes the Euclidean distance between state embeddings (Equation 6 in the appendix). \n Query Synthesis via Trajectory Optimization The four AFs defined in the previous section specify the types of hypotheticals we would like to show the user. In this section, we discuss how to optimize each AF, then use the resulting hypotheticals to learn a reward model. We synthesize a query trajectory, ⌧ query = max z0,a0,z1,...,z T J(⌧ ) + log p (⌧ ), (3) where z t is the embedding of state s t in the latent space of the encoder f trained in step (1), ⌧ = (f 1 (z 0 ), a 0 , f 1 (z 1 ), a 1 , ..., f 1 (z T )) is the decoded trajectory, J is the acquisition function (Section 3.3), 2 R 0 is a regularization constant, and p is the generative model of trajectories (Section 3.1). In this work, we assume p (⌧ ) is differentiable, and optimize ⌧ query using Adam  (Kingma & Ba, 2014) . Optimizing latent states z instead of highdimensional states s reduces computational requirements, and regularizes the optimized states to be more realistic. The regularization constant from Equation 3 controls the trade-off between how realistic ⌧ query is and how aggressively it maximizes the AF. Setting = 0 can result in query trajectories that are incomprehensible to the user and unlikely to be seen in the test environment, while setting to a high value can constrain the query trajectories from seeking interesting hypotheticals. The experiments in Section A.3 in the appendix analyze this trade-off. Our reward modeling algorithm is summarized in Algorithm 1. Given a generative model of trajectories p (⌧ ), it generates one query trajectory ⌧ query for each of the four AFs, asks the user to label the states in the query trajectories, retrains the reward model ensemble {✓ i } m i=1 on the updated training data D using maximum-likelihood estimation, and repeats this process until the user is satisfied with the outputs of the reward model. The ablation study in Section 4.5 analyzes the effect of using different subsets of the four AFs to generate queries. \n Deploying a Model-Based RL Agent Given the learned reward model R, the agent can, in principle, be trained using any RL algorithm in step (3). Since our end for 10: end for 11: for i 2 {1, 2, ..., m} do 12: ✓i arg max ✓ i P (s,a,s 0 ,c)2D log p ✓ i (c|s, a, s 0 ) 13: end for 14: end while 15: Return reward model R {Defined via ✓ in Equation  2} method learns a forward dynamics model in step (1), modelbased RL is a good fit for step (3). In this work, we deploy an agent ⇡ mpc that combines planning with model-predictive control (MPC): ⇡ mpc (a|s) =  a = arg max a0 max a1,...,a H R(s, a 0 ) + R(E [s 1 |s, a 0 ], a 1 ) + ... + R(E [s H |s, a 0 , a 1 , ..., a H 1 ], a H ) i , (4) where the future states E [s t |s, a 0 , a 1 , ..., a t 1 ] are predicted using the forward dynamics model p trained in step (1), H is the planning horizon, and R is the reward model trained in step (2). We solve the optimization problem in the right-hand side using Adam  (Kingma & Ba, 2014) . \n Experimental Evaluation We seek to answer the following questions. Q1: Does synthesizing hypothetical trajectories elicit more informative labels than rolling out a policy in the training environment? Q2: Can our method detect and correct reward hacking? Q3: Can our method safely learn about unsafe states? Q4: Do the proposed AFs improve upon random sampling from the generative model? Q5: How does the regularization constant control the trade-off between realistic and informative queries? Q6: How much do each of the four AFs contribute to performance? To answer these questions under ideal assumptions, we run experiments in MNIST  (LeCun, 1998) , state-based 2D navigation (Figure  2 ), and imagebased Car Racing from the OpenAI Gym  (Brockman et al., 2016) , with simulated users that label trajectories using a ground-truth reward function. Section A.4 in the appendix discusses implementation details. MNIST classification. This domain enables us to focus on testing the active learning component of our method, since the standard digit classification task does not involve sequential decision-making. When we generate queries, we synthesize an image s 0 2 R 28⇥28 , and ask the simulated user to label it with an action a 2 {0, 1, ..., 9}. The initial state distribution of the training environment S train 0 puts a uniform probability on sampling s 0 2 {5, 6, 7, 8, 9}, and a probability of 0 on sampling s 0 2 {0, 1, 2, 3, 4}. We intentionally introduce a significant shift in the test environment, by putting a uniform probability on sampling s 0 2 {0, 1, 2, 3, 4} and a probability of 0 on sampling s 0 2 {5, 6, 7, 8, 9}. This mismatch is intended to test how well the learned classifier performs under distribution shift. State-based 2D navigation. This domain enables us to focus on the challenges of sequential decision-making, without dealing with high-dimensional states. Here, the state s 2 R 2 is the agent's position, and the action a 2 R 2 is a velocity vector. The task requires navigating to a target region, while avoiding a trap region (Figure  2 ). The task is harder to complete in the test environment, since the agent starts closer to the trap, and must navigate around the trap to reach the goal. Image-based Car Racing. This domain enables us to test whether our method scales to learning sequential tasks with high-dimensional states. Here, the state s 2 R 64⇥64⇥3 is an RGB image with a top-down view of the car (Figure  3 ), and the action a 2 R 3 controls steering, gas, and brake. Here, we set the same initial state distribution for the training and test environments, since the reward modeling problem is challenging even when the initial state distributions are identical. We train a generative model of images and a forward dynamics model in step (1) using the unsupervised method from  Ha & Schmidhuber (2018) .  \n Robustness Compared to Baselines Our first experiment tests whether our method can learn a reward model that is robust enough to perform well in the test environment, and tracks how many queries to the user it takes to learn an accurate reward model. To answer Q1, we compare our method to a baseline that, instead of generating hypothetical trajectories for the user to label, generates trajectories by rolling out a policy that optimizes the current reward model in the training environment -an approach adapted from prior work  (Christiano et al., 2017) . The baseline generates ⌧ query in line 5 of Algorithm 1 by rolling out the MPC policy in Equation  4 , instead of solving the optimization problem in Equation 3. To test how generating queries using a reward-maximizing policy compares to using a policy that does not depend on the reward model, we also evaluate a simpler baseline that generates query trajectories using a uniform random policy, instead of the MPC policy. We measure performance in MNIST using the agent's classification accuracy in the test environment; in 2D navigation, the agent's success rate at reaching the goal while avoiding the trap in the test environment; and in Car Racing, the agent's true reward, which rewards progress and penalizes going off-road. The results in Figure  4  show that our method produces reward models that transfer to the test environment better than the baselines. Our method also learns to outperform the suboptimal demonstrations used to initialize the reward model (Figure  10  in the appendix). In MNIST, our method performs substantially better than the baseline, which samples queries s 0 from the initial state distribution of the training environment. The reason is simple: the initial state distribution of the test environment differs significantly from that of the training environment. Since our method is not restricted to sampling from the training environment, it performs better than the baseline. In 2D navigation, our method substantially outperforms both Figure  4 . Experiments that address Q1 -does synthesizing hypothetical trajectories elicit more informative labels than rolling out a policy in the training environment? -by comparing our method, which uses synthetic trajectories, to baselines that only use real trajectories generated in the training environment. The results on MNIST, 2D navigation, and Car Racing show that our method (orange) significantly outperforms the baselines (blue and gray), which never succeed in 2D navigation. The x-axis represents the number of queries to the user, where each query elicits a label for a single state transition (s, a, s 0 ). The shaded areas show standard error over three random seeds. baselines, which never succeed in the test environment. This is unsurprising, since the training environment is set up in such a way that, because the agent starts out in the lower left corner, they rarely visit the trap region in the upper right by simply actions -whether reward-maximizing actions (as in the first baseline), or uniform random actions (as in the second baseline). Hence, when a reward model trained by the is transferred to the test environment, it not aware of the trap, so the agent tends to get caught in the trap on its way to the goal. Our method, however, is not restricted to feasible trajectories in the training environment, and can potentially query the label for any position in the environment -including the trap (see Figure  2 ). Hence, our method learns a reward model that is aware of the trap, which enables the agent to navigate around it in the test environment. In Car Racing, our method outperforms both baselines. The baselines tend to generate queries that are not diverse and rarely visit unsafe states, so the resulting reward models are not able to accurately distinguish between good, unsafe, and neutral states. Our method, on the other hand, explicitly seeks out a wide variety of states by maximizing the four AFs, which leads to more diverse training data, and a more accurate reward model. \n Detecting Reward Hacking One of the benefits of our method is that it can detect and correct reward hacking before deploying the agent, using reward-maximizing synthetic queries. In the next experiment, we test this claim. We replicate the experimental setup in Section 4.1 for 2D navigation, including the same baselines. We measure performance using the false positive rate of the reward model: the fraction of neutral or unsafe states incorrectly classified as good, evaluated on the offline dataset of trajectories described in Section 4.1. A reward model that outputs false positives is susceptible to reward hacking, since a reward-maximizing agent can game the reward model into emitting high rewards by visiting incorrectly classified states. The results in Figure  9  in the appendix show that our method drives down the false positive rate in 2D navigation: the learned reward model rarely incorrectly classifies an unsafe or neutral state as a good state. As a result, the deployed agent actually performs the desired task (center plot in Figure  4 ), instead of seeking false positives. As discussed in Section 4.3 and illustrated in the right-most plot of Figure  5 , the baselines learn a reward model that incorrectly extrapolates that continuing up and to the right past the goal region is good behavior. For a concrete example of rewardmaximizing synthetic queries that detect reward hacking, consider the reward-maximizing queries in the upper right corner of Figure  2 , which are analyzed in Section A.2 in the appendix. \n Safe Exploration One of the benefits of our method is that it can learn a reward model that accurately detects unsafe states, without having to visit unsafe states during the training process. In the next experiment, we test this claim. We replicate the experimental setup in Section 4.1 for 2D navigation, including the same baselines. We measure performance using the true negative rate of the reward model: the fraction of unsafe states correctly classified as unsafe, evaluated on the offline dataset of trajectories described in Section 4.1. We also use the crash rate of the deployed agent: the rate at which it gets caught in the trap region. Experiments that address Q3 -can our method safely learn about unsafe states? -by comparing our method, which uses synthetic trajectories, to baselines that only use real trajectories generated in the training environment. The results on 2D navigation show that our method (orange) significantly outperforms the baselines (blue and gray). The x-axis represents the number of queries to the user, where each query elicits label for a single state transition (s, a, 0 ). The shaded show standard error over three random seeds. The heat maps represent the reward models learned by our method (left) and by the baselines (right). Figure  6 . Experiments that address Q4 -do the proposed AFs improve upon random sampling from the generative model? -by comparing our method, which synthesizes trajectories by optimizing AFs, to a baseline that ignores the AFs and randomly samples from the generative model. The results on MNIST, 2D navigation, and Car Racing show that our method (orange) significantly outperforms the baseline (blue) in Car Racing, and learns faster in MNIST and 2D navigation. The x-axis represents the number of queries to the user, where each query elicits a label for a single state transition (s, a, s 0 ). The shaded areas show standard error over three random seeds. The results in Figure  5  show that our method learns a reward model that classifies all unsafe states as unsafe, without visiting unsafe states during training (second and third figure from left); in fact, without visiting any states at all, since the queries are synthetic. This enables the agent to avoid crashing during deployment (first figure from left). The baselines differ from our method in that they actually have to visit unsafe states in order to query the user for labels at those states. Since the baselines tend to not visit unsafe states during training, they do not learn about unsafe states (second and fourth figure from left), and the agent frequently crashes during deployment (first figure from left). \n Query Efficiency Compared to Baselines The previous experiment compared to baselines that are restricted to generating query trajectories by taking actions in the training environment. In this experiment, we lift this restriction on the baselines: instead of taking actions in the training environment, the baselines can make use of the generative model trained in step (1). To answer Q4, we compare our method to a baseline that randomly samples trajectories from the generative model p -using uniform random actions in Car Racing, samples from the VAE prior in MNIST, and uniform positions across the map in 2D navigation. We measure performance in MNIST using the reward model's predicted log-likelihood of the ground-truth user labels in the test environment; in 2D navigation, the reward model's classification accuracy on an offline dataset containing states sampled uniformly throughout the environment; and in Car Racing, the true reward collected by an MPC agent that optimizes the learned reward, where the true reward gives a bonus for driving onto new patches of road, and penalizes going off-road. The results in Figure  6  show that our method, which optimizes trajectories using various AFs, requires fewer queries to the user than the baseline, which randomly samples trajectories. This suggests that our four AFs guide query synthesis toward informative trajectories. These results, and the re-Figure  7 . Experiments that address Q6 -how much do each of the four AFs contribute to performance? -by comparing our method to ablated variants that drop each AF, one at a time, from the set of four AFs in line 4 of Algorithm 1. The results on MNIST, 2D navigation, and Car Racing show that our method (orange) generally outperforms its ablated variants (blue, gray, red, and pink), although the usefulness of each AF depends on the domain and amount of training data.. The x-axis represents the number of queries to the user, where each query elicits a label for a single state transition (s, a, s 0 ). The shaded areas show standard error over three random seeds. sults from Section 4.1, suggest that our method benefits not only from using a generative model instead of the default training environment, but also from optimizing the AFs instead of randomly sampling from the generative model. \n Acquisition Function Ablation Study We propose four AFs intended to produce different types of hypotheticals. In this experiment, we investigate the contribution of each type of query to the performance of the overall method. To answer Q6, we conduct an ablation study, in which we drop out each the four AFs, one by one, from line 4 in Algorithm 1, and measure the performance of only generating queries using the remaining three AFs. The results in Figure  7  show that the usefulness of each AF depends on the domain and the amount of training data collected. In MNIST, dropping J u hurts performance, suggesting that uncertainty-maximizing queries elicit useful labels. Dropping J n also hurts performance when the number of queries is small, but actually improves performance if enough queries have already been collected. Noveltymaximizing queries tend to be repetitive in practice: although they are distant from the training data in terms of Equation  6 , they are visually similar to the existing training data in that they appear to be the same digits. Hence, while they are helpful at first, they hurt query efficiency later in training. In 2D navigation, dropping J u hurts performance, while dropping any of the other AFs individually does not hurt performance. These results suggest that uncertaintymaximizing queries can be useful, in domains like MNIST and 2D navigation, where uncertainty can be modeled and estimated accurately. In Car Racing, dropping J hurts the most. Reward-minimizing queries elicit labels for unsafe states, which are rare in the training environment unless you explicitly seek them out. Hence, this type of query performs the desired function of augmenting the training data with more examples of unsafe states, thereby making the reward model better at detecting unsafe states. \n Discussion The experiments show that ReQueST produces accurate reward models that transfer well to new environments and require fewer queries to the user, compared to baseline methods adapted from prior work. Our method detects reward hacking before the agent is deployed, and safely learns about unsafe states. Through a hyperparameter sweep, we find that our method can trade off between producing realistic vs. informative queries, and that the optimal trade-off varies across domains. Through an ablation study, we find that the usefulness of each of the four acquisition functions we propose for optimizing queries depends on the domain and the amount of training data collected. One of the benefits of ReQueST is that, since it learns from synthetic trajectories instead of real trajectories, it only has to imagine visiting unsafe states, instead of actually visiting them. Although unsafe states may be visited during unsupervised exploration of the environment for training the generative model in step (1), the same generative model can be reused to learn reward models for any number of future tasks. Hence, the cost of visiting a fixed number of unsafe states in step (1) can be amortized across a large number of tasks in step (2). We could also train the generative model on other off-policy data, including safe expert demonstrations and examples of past failures by humans. The main practical limitation of ReQueST is that it requires a generative model of initial states and a forward dynamics model, which can be difficult to learn from purely off-policy data in complex, visual environments. One direction for future work is relaxing this assumption; e.g., by incrementally training a generative model on on-policy data collected from an RL agent in the training environment  (Kaiser et al., 2019; Hafner et al., 2019) . Figure 1 . 1 Figure 1. Our method learns a reward model from user feedback on hypothetical behaviors, then deploys a model-based RL agent. \n ✓ not converged do 4: for J 2 {Ju, J+, J , Jn} do 5: ⌧query max⌧ J(⌧ ) + log p (⌧ ) 6:for (s, a, s 0 ) 2 ⌧query do 7: c c ⇠ puser(c|s, a, s 0 ) {Query the user} 8:D D [ {(s, a, s 0 , c)} 9: \n Figure 2 . 2 Figure 2. Left: The 2D navigation task, where the agent navigates to the goal region (green) in the lower left while avoiding the trap region (red) in the upper right. The agent starts in the lower left corner in the training environment, and starts in the upper right corner in the test environment. Right: Examples of hypothetical states synthesized throughout learning, illustrating the qualitative differences in the behaviors targeted by each AF. \n Figure 3 . 3 Figure 3. Left: A screenshot of the image-based Car Racing video game in the OpenAI Gym. Right: Examples of synthesized hypothetical behaviors, including going off road (J ), making progress (J+), driving on the edge (Ju), and seeking unusual car configurations (Jn). See Figure 13 in the appendix for synthesized videos. \n Figure 5 . 5 Figure5. Experiments that address Q3 -can our method safely learn about unsafe states? -by comparing our method, which uses synthetic trajectories, to baselines that only use real trajectories generated in the training environment. The results on 2D navigation show that our method (orange) significantly outperforms the baselines (blue and gray). The x-axis represents the number of queries to the user, where each query elicits label for a single state transition (s, a, 0 ). The shaded show standard error over three random seeds. The heat maps represent the reward models learned by our method (left) and by the baselines (right). \n\t\t\t University of California, Berkeley 2 DeepMind. Correspondence to: Siddharth Reddy <sgr@berkeley.edu>, Jan Leike <leike@google.com>.", "date_published": "n/a", "url": "n/a", "filename": "reddy20a.tei.xml", "abstract": "We seek to align agent behavior with a user's objectives in a reinforcement learning setting with unknown dynamics, an unknown reward function, and unknown unsafe states. The user knows the rewards and unsafe states, but querying the user is expensive. We propose an algorithm that safely and efficiently learns a model of the user's reward function by posing 'what if?' questions about hypothetical agent behavior. We start with a generative model of initial states and a forward dynamics model trained on off-policy data. Our method uses these models to synthesize hypothetical behaviors, asks the user to label the behaviors with rewards, and trains a neural network to predict the rewards. The key idea is to actively synthesize the hypothetical behaviors from scratch by maximizing tractable proxies for the value of information, without interacting with the environment. We call this method reward query synthesis via trajectory optimization (ReQueST). We evaluate ReQueST with simulated users on a state-based 2D navigation task and the image-based Car Racing video game. The results show that ReQueST significantly outperforms prior methods in learning reward models that transfer to new environments with different initial state distributions. Moreover, ReQueST safely trains the reward model to detect unsafe states, and corrects reward hacking before deploying the agent.", "id": "1754dba6f33629621bf78d233bd0a2aa"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Vincent C Müller"], "title": "Future Progress in Artificial Intelligence: A Survey of Expert Opinion", "text": "Introduction Artificial Intelligence began with the \"… conjecture that every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it.\"  (McCarthy, Minsky, Rochester, & Shannon, 1955, p. 1)  and moved swiftly from this vision to grand promises for general human-level AI within a few decades. This vision of general AI has now become merely a long-term guiding idea for most current AI research, which focuses on specific scientific and engineering problems and maintains a distance to the cognitive sciences. A small minority believe the moment has come to pursue general AI directly as a technical aim with the traditional methods -these typically use the label 'artificial general intelligence' (AGI) (see  Adams et al., 2012) . If general AI were to be achieved, this might also lead to superintelligence: \"We can tentatively define a superintelligence as any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest.\"  (Bostrom, 2014 ch. 2) . One idea how 2. Questionnaire \n Respondents The questionnaire was carried out online by invitation to particular individuals from four different groups for a total of ca. 550 participants (see Appendix 2). Each of the participants got an email with a unique link to our site to fill in an online form (see Appendix 1). If they did not respond within 10 days, a reminder was sent, and another 10 days later, with the note that this is the last reminder. In the case of EETN (see below) we could not obtain the individual email addresses and thus sent the request and reminders to the members' mailing list. Responses were made on a single web page with one 'submit' button that only allowed submissions through these unique links, thus making non-invited responses extremely unlikely. The groups we asked were: 1. PT-AI: Participants of the conference on \"Philosophy and Theory of AI\", Thessaloniki October 2011, organized by one of us (see  Müller, 2012 Müller, , 2013 . Participants were asked in November 2012, i.e. over a year after the event. The total of 88 participants include a workshop on \"The Web and Philosophy\" (ca. 15 people), from which a number of non-respondents came. A list of participants is on: http://www.pt-ai.org/2011/registered-participants We reduced the list to living authors, added as many as necessary to get back to 100, searched for professional e-mails on the web and sent notices to these. The questionnaire was sent with our names on it and with an indication that we would use it for this paper and Nick Bostrom's new book on superintelligence  (Bostrom, 2014)  -our request email is in Appendix 1. Given that the respondent groups 1 and 2 attended conferences organized by us, they knew whom they were responding to. In groups 3 and 4 we would assume that the majority of experts would not know us, or even of us. These differences are reflected in the response rates. These groups have different theoretical-ideological backgrounds: The participants of PT-AI are mostly theory-minded, mostly do not do technical work, and often have a critical view on large claims for easy progress in AI (Herbert Dreyfus was a keynote speaker in 2011). The participants of AGI are committed to the view that AI research should now return from technical details to 'artificial general intelligence'thus the name AGI. The vast majority of AGI participants do technical work. The EETN is a professional association in Greece that accepts only published researchers from AI. The TOP100 group also works mostly in technical AI; its members are senior and older than the average academic; the USA is strongly represented. Several individuals are members of more than one of these four sets and they were unlikely to respond to the same questionnaire more than once. So, in these cases, we sent the query only once, but counted a response for each set -i.e. we knew which individuals responded from the individual tokens they received (except in the case of EETN).  \n Methodology In this field, it is hard to ask questions that do not require lengthy explanations or generate resistance in certain groups of potential respondents (and thus biased results). It is not clear what constitutes 'intelligence' or 'progress' and whether intelligence can be measured or at least compared as 'more' or 'less' as a single dimension. Furthermore, for our purposes we need a notion of intelligence at a level that may surpass humans or where technical intelligent systems might contribute significantly to research -but 'human-level intelligence' is a rather elusive notion that generates resistance. Finally, we need to avoid using terms that are already in circulation and would thus associate the questionnaire with certain groups or opinions, like \"artificial intelligence\", \"singularity\", \"artificial general intelligence\" or \"cognitive system\". For these reasons, we settled for a definition that a) is based on behavioral ability, b) avoids the notion of a general 'human-level' and c) uses a newly coined term. We put this definition in the preamble of the questionnaire: \"Define a 'high-level machine intelligence' (HLMI) as one that can carry out most human professions at least as well as a typical human.\" (We still had one expert writing back to us that they could not say what a 'typical human' is -though they could be convinced to respond, after all.) In hindsight, it may have been preferable to specify what we mean by 'most' and whether we think of 'most professions' or of 'the professions most working people do'. One merit of our behavioral question is that having HLMI in our sense very likely implies being able to pass a classic Turing test. To achieve a high response rate, we tried to have few questions with simple choices and eventually settled for four questions, plus three on the respondents. We tried to choose questions that would allow us to compare our results with those of earlier questionnaires -see below. In order to improve on the quality of predictions, we tried to 'prime' respondents into thinking about what is involved in reaching HLMI before asking when they expect this. We also wanted to see whether people with a preference for particular approaches to HLMI would have particular responses to our central questions on prediction (e.g. whether people who think that 'embodied systems' are crucial expect longer than average time to HLMI). For these two purposes, we inserted a first question about contributing research approaches with a list to choose from -the options that were Future Progress in Artificial Intelligence: A Poll Among Experts 5/19 given are an eclectic mix drawn from many sources, but the particular options are not of much significance. \n Prior work A few groups have recently made attempts to gauge opinions. We tried to phrase our questions such that the answers can be compared to these earlier questionnaires. Notable are: 1.  (Michie, 1973, p. 511f) : \"an opinion poll taken last year among sixty-seven British and American computer scientists working in, or close to, the machine intelligence field\". 2. Questions asked live during the 2006 AI@50 conference at Dartmouth College through a wireless voting device (VCM participated (see  Müller, 2007) ). Despite a short report on the conference in  (Moor, 2006) , the results were not published, but thankfully we were able to acquire them from the organizers James H. Moor and Carey E. Heckman -we publish a selection below. 3.  (Baum, Goertzel, & Goertzel, 2011) : participants of AGI 2009, not anonymous, on paper, 21 respondents, response rate unknown. 2 4.  (Sandberg & Bostrom, 2011) : participants of Winter Intelligence Conference 2011, anonymous, on paper, 35 respondents, 41% response rate. 1. The reference by the famous AI researcher Donald Michie is very brief (all the details he gives are in the above quote) but of great of historical interest: 1972/3 were turning years for AI with the publication of Hubert Dreyfus' \"What computers can't do\" (Hubert L.  Dreyfus, 1972) , the \"Lighthill Debates\" on BBC TV (with Michie, McCarthy and R. Gregory) and the influential \"Lighthill Report\"  (Lighthill, 1973 ). Michie's poll asked for the estimated number of years before \"computing exhibiting intelligence at adult human level\" and Michie's graph shows 5 data points: Years Percentage 5 0% 10 1% 20 17% 50 19% >50 25% He also asked about \"significant industrial spin-off\", \"contributions to brain studies\" and \"contributions from brain studies to machine intelligence\". Michie adds \"Of 2 A further, more informal, survey was conducted in August 2007 by Bruce J Klein (then of Novamente and the Singularity Institute) \"… on the time-frame for when we may see greaterthan-human level AI\", with a few numerical results and interesting comments, archived on https://web.archive.org/web/20110226225452/http://www.novamente.net/bruce/?p=54. Future Progress in Artificial Intelligence: A Poll Among Experts 6/19 those responding to a question on the risk of ultimate 'takeover' of human affairs by intelligent machines, about half regarded it as 'negligible', and most of the remainder as 'substantial', with a view voting for 'overwhelming'.\"  (Michie, 1973, p. 512) . 2. AI@50 hosted many prominent AI researchers, including all living participants of the 1956 Dartmouth Conference, a set of DARPA-funded graduate students, plus a few theoreticians. The participants were asked 12 multiple choice questions on day one, 17 on day two and another 10 on day three. We select three results from day one here: 3.) The earliest that machines will be able to simulate learning and every other aspect of human intelligence: Within 10 years 5% Between 11 and 25 years 2% Between 26 and 50 years 11% More than 50 years 41% Never 41% Totals 100% 5.) The earliest we will understand the basic operations (mental steps) of the human brain sufficiently to create machine simulation of human thought is: today (we already understand enough) 6% within the next 10 years 12% within the next 25 years 10% within the next 50 years 21% within the next 100 years or more 29% never (we will never understand enough) 21% Totals 100% 6.) The earliest we will understand the architecture of the brain (how its organizational control is structured) sufficiently to create machine simulation of human thought is: The median estimate of when there will be 50% chance of human-level machine intelligence was 2050. So, despite significant overlap with AGI 2009, the group asked by Sandberg and Bostrom in 2011 was a bit more guarded in their expectations. We think it is worthwhile to make a new attempt because the prior ones asked specific groups and small samples, sometimes have methodological problems, and we also want to see how the answers change over time, or do not change -which is why tried to use similar questions. As explained below, we also think it might be worthwhile to repeat our questionnaire at a later stage, to compare results.  The percentages here are over the total of responses. There were no significant differences between groups here, except that 'Whole brain emulation' got 0% in TOP100, but 46% in AGI. We did also not find relevant correlations between the answers given here and the predictions made in the following questions (of the sort that, for example, people who think 'embodied systems' crucial would predict later onset of HLMI). \n Questions & Responses \n Research Approaches Future Progress in Artificial Intelligence: A Poll Among Experts 9/19 \n When HLMI? \"2. For the purposes of this question, assume that human scientific activity continues without major negative disruption. By what year would you see a (10% / 50% / 90%) probability for such HLMI to exist?\" -For each of these three probabilities, the respondents were asked to select a year  [2012-5000, in   For the 50% mark, the overall median is 2040 (i.e. half of the respondents gave a year earlier than 2040 and half gave a year later than 2040) but the overall mean (average) is 2081. The median is always lower than the mean here because there cannot be outliers towards 'earlier' but there are outliers towards 'later' (the maximum possible selection was 5000, then 'never'). \n From HLMI to superintelligence \"3. Assume for the purpose of this question that such HLMI will at some point exist. How likely do you then think it is that within (2 years / 30 years) thereafter there will be machine intelligence that greatly surpasses the performance of every human in most professions?\" -Respondents were asked to select a probability from a dropdown menu in 1% increments, starting with 0%.  Experts allocate a low probability for a fast takeoff, but a significant probability for superintelligence within 30 years after HLMI. \n The impact of superintelligence \"4. Assume for the purpose of this question that such HLMI will at some point exist. How positive or negative would be overall impact on humanity, in the long run? Please indicate a probability for each option. (The sum should be equal to 100%.)\" -Respondents had to select a probability for each option (in 1% increments). The addition of the selection was displayed; in green if the sum was 100%, otherwise in red. The five options were: \"Extremely good -On balance good -More or less neutral -On balance bad -Extremely bad (existential catastrophe)\". Percentages here are means, not medians as in the other tables. There is a notable difference here between the 'theoretical' (PT-AI and AGI) and the 'technical' groups (EETN and TOP100). \n % PT-AI \n Respondents Statistics We then asked the respondents 3 questions about themselves: And we finally invited participants to make a comment, plus a possibility to add their name, if they wished. (We cannot reproduce these here; but they are on our site, see below). A number of comments concerned the difficulty of formulating good questions, much fewer the difficulty of predicting. \n Evaluation \n Selection-bias in the respondents? One concern with the selection of our respondents is that people who think HLMI is unlikely, or a confused idea, are less likely to respond (though we pleaded otherwise in the letter, see below). Here is a characteristic response from a keynote speaker at PT-AI 2011: \"I wouldn't think of responding to such a biased questionnaire. … I think any discussion of imminent super-intelligence is misguided. It shows no understanding of the failure of all work in AI. Even just formulating such a questionnaire is biased and is a waste of time.\" (Hubert Dreyfus, quoted with permission). So, we tried to find out what the non-respondents think. To this end, we made a random selection of non-respondents from two groups (11 for PT-AI and 17 from TOP100) and pressured them via personal email to respond, explaining that this would help us understand bias. The two groups were selected because AGI appears already biased in the opposite direction and EETN appears very similar to TOP100 but for EETN we did not Future Progress in Artificial Intelligence: A Poll Among Experts 14/19 have the data to show us who responded and who did not. We got one additional response from PT-AI and two from TOP100 in this way. For question 2 \"… By what year would you see a (10% / 50% / 90%) probability for such HLMI to exist?\" we compared the additional responses to the responses we already had from the same respective group (PT-AI and TOP100, respectively). We found the following differences: The one additional respondent from PT-AI expected HLMI earlier than the mean but later than the median, while the two respondents from TOP100 (last row) expected HLMI earlier than mean and median. The very small sample forbids confident judgment, but we found no support for the worry that the non-respondents would have been biased towards a later arrival of HLMI. 10% \n Lessons and outlook We complement this paper with a small site on http://www.pt-ai.org/ai-polls/. On this site, we provide a) the raw data from our results [anonymous unless the participants decided to put their name on their responses], b) the basic results of the questionnaire, c) the comments made, and d) the questionnaire in an online format where anyone can fill it in. We expect that that online questionnaire will give us an interesting view of the 'popular' view of these matters and on how this view changes over time. In the medium run, it be interesting to do a longitudinal study that repeats this exact questionnaire. We leave it to the reader to draw their own detailed conclusions from our results, perhaps after investigating the raw data. Let us stress, however, that the aim was to 'gauge the perception', not to get well-founded predictions. These results should be taken with some grains of salt, but we think it is fair to say that the results reveal a view among experts that AI systems will probably (over 50%) reach overall human ability by 2040-50, and very likely (with 90% probability) by 2075. From reaching human ability, it will move on to superintelligence in 2 years (10%) to 30 years (75%) Future Progress in Artificial Intelligence: A Poll Among Experts 15/19 thereafter. The experts say the probability is 31% that this development turns out to be 'bad' or 'extremely bad' for humanity. So, the experts think that superintelligence is likely to come in a few decades and quite possibly bad for humanity -this should be reason enough to do research into the possible impact of superintelligence before it is too late. We could also put this more modestly and still come to an alarming conclusion: We know of no compelling reason to say that progress in AI will grind to a halt (though deep new insights might be needed) and we know of no compelling reason that superintelligent systems will be good for humanity. So, we should better investigate the future of superintelligence and the risks it poses for humanity. \n Acknowledgements Toby Ord and Anders Sandberg were helpful in the formulation of the questionnaire. The technical work on the website form, sending mails and reminders, database and initial data analysis was done by Ilias Nitsos (under the guidance of VCM). Theo Gantinas provided the emails of the TOP100. Stuart Armstrong made most graphs for presentation. The audience at the PT-AI 2013 conference in Oxford provided helpful feedback. Mark Bishop, Carl Shulman, Miles Brundage and Daniel Dewey made detailed comments on drafts. We are very grateful to all of them. Contribution to this questionnaire is by invitation only. If the questionnaire is filled in without such an invitation, the data will be disregarded. Answers will be anonymized. Results will be made publicly available on the site of the Programme on the Impacts of Future Technology: http://www.futuretech.ox.ac.uk (http://www.futuretech.ox.ac.uk) . Thank you for your time!  \" 1 . 1 In your opinion, what are the research approaches that might contribute the most to the development of such HLMI?\" [Selection from list, more than one selection possible.] − Algorithmic complexity theory − Algorithms revealed by computational neuroscience − Artificial neural networks − Bayesian nets − Cognitive science − Embodied systems − Evolutionary algorithms or systems − Faster computing hardware − Integrated cognitive architectures − Large-scale datasets − Logic-based systems − Robotics − Swarm intelligence − Whole brain emulation − Other method(s) currently known to at least one investigator − Other method(s) currently completely unknown − No method will ever contribute to this aim \n Future Concerning the above questions, how would you describe your own expertise?\" (0 = none, 9 = expert) − Mean 5.85 2. \"Concerning technical work in artificial intelligence, how would you describe your own expertise?\" (0 = none, 9 = expert) − Mean 6.26 3. \"What is your main home academic discipline?\" (Select from list with 8 options: Biology/Physiology/Neurosciences -Computer Science -Engineering [non CS] -Mathematics/Physics -Philosophy -Psychology/Cognitive Science -Other academic discipline -None.) [Absolut numbers.] a. Biology/Physiology/Neurosciences 3 \n Other method(s) currently known to at least one investigator Other method(s) currently completely unknown No method will ever contribute to this aim //www.fhi.ox.ac.uk/) (http://www.futuretech.ox.ac.uk) This brief questionnaire is directed towards researchers in artificial intelligence or the theory of artificial intelligence. It aims to gauge how people working in the field view progress towards its original goals of intelligent machines, and what impacts they would associate with reaching these goals. \n Vincent C. Müller (http://www.sophia.de) & Nick Bostrom (http://www.nickbostrom.com/) University of Oxford September 2012 A. The Future of AI Define a \"high-level machine intelligence\" (HLMI) as one that can carry out most human professions at least as well as a typical human. 1. In your opinion, what are the research approaches that might contribute the most to the development of such HLMI?: for the purpose of this question that human scientific activity continues without major negative disruption. By what year would you see a 10%/50%/90% probability for such HLMI to exist? 3. Assume for the purpose of this question that such HLMI will at some point exist. How likely do you then think it is that within (2 years / 30 years) thereafter, there will be machine intelligence that greatly surpasses the performance of any human in most professions? 4. Assume for the purpose of this question that such HLMI will at some point exist. How positive or negative would be the overall impact on humanity, in the long run? Please indicate a probability for each option. (The sum should be equal to 100%.) Total: 0% Questionnaire: Future Progress in Artificial Intelligence | Phil... http://www.pt-ai.org/questionnaire-future-progress-artificial-in... \n Baum et al. asked  for the ability to pass a Turing test, a third grade school year exam [i.e. for 9 year olds] and do Nobel Prize level research. They assume that all and only the intelligent behavior of humans is captured in the Turing test. The results they Within 10 years Between 11 and 25 years Between 26 and 50 years More than 50 years Never Totals got for the 50% probability point were: 2040 (Turing test), 2030 (third grade), and 11% 14% 22% 40% 14% 100% 7/19 2045 (Nobel). 4. Sandberg and Bostrom's first question was quite similar to our 2 nd (see below): \"Assuming no global catastrophe halts progress, by what year would you assign a 3. Future Progress in Artificial Intelligence: A Poll Among Experts 10%/50%/90% chance of the development of human-level machine intelligence?\" \n Clicks of the 'never' box. These answers did not enter in to the averages above. Future Progress in Artificial Intelligence: A Poll Among Experts Future Progress in Artificial Intelligence: A Poll Among Experts 10/19 11/19 10% 2020 2033 29 Algorithms revealed by computational Cognitive science 50% 2050 2097 200 Never no. % Integrated cognitive architectures 90% 2093 2292 675 10% 2 1.2 Artificial neural networks TOP100 Median Mean St. Dev. 50% 7 4.1 50% 10% 90% Embodied systems 2072 110 Large-scale datasets Faster computing hardware 2050 2024 2034 33 28 16.5 Other method(s) currently completely 90%: 2070 2168 342 ALL Whole brain emulation Median Mean St. Dev. Other method(s) currently known to at Evolutionary algorithms or systems 10%: 2022 2036 59 50%: 2040 Logic-based systems 2081 153 90%: Algorithmic complexity theory 2075 2183 396 No method will ever contribute to this Robotics Swarm intelligence Results sorted by percentage steps: 10% Bayesian nets Median Mean St. Dev. PT-AI 2023 2043 81 00% 10% 20% 30% 40% 50% 60% AGI 2022 2033 60 EETN 2020 2033 29 TOP100 2024 2034 33 ALL 2022 2036 59 50% Median Mean St. Dev. PT-AI 2048 2092 166 one-year increments] or check a box marked 'never'. AGI 2040 2073 144 EETN Results sorted by groups of respondents: 2050 2097 200 TOP100 2050 2072 110 PT-AI ALL Median Mean St. Dev. 2040 2081 153 10% 90% 2023 Median Mean St. Dev. 2043 81 50% PT-AI 2048 2080 2092 2247 166 515 90% AGI 2080 2065 2247 2130 515 202 AGI EETN Median Mean St. Dev. 2093 2292 675 10% TOP100 2070 2022 2033 2168 60 342 50% ALL 2040 2075 2073 2183 144 396 90% 2065 2130 202 EETN Median Mean St. Dev. \n\t\t\t There is a collection of predictions on http://www.neweuropeancentury.org/SIAI-FHI_AI_predictions.xls \n\t\t\t .11.12 10:29 OEZ", "date_published": "n/a", "url": "n/a", "filename": "survey.tei.xml", "abstract": "There is, in some quarters, concern about high-level machine intelligence and superintelligent AI coming up in a few decades, bringing with it significant risks for humanity. In other quarters, these issues are ignored or considered science fiction. We wanted to clarify what the distribution of opinions actually is, what probability the best experts currently assign to high-level machine intelligence coming up within a particular time-frame, which risks they see with that development, and how fast they see these developing. We thus designed a brief questionnaire and distributed it to four groups of experts in 2012/2013. The median estimate of respondents was for a one in two chance that highlevel machine intelligence will be developed around 2040-2050, rising to a nine in ten chance by 2075. Experts expect that systems will move on to superintelligence in less than 30 years thereafter. They estimate the chance is about one in three that this development turns out to be 'bad' or 'extremely bad' for humanity.", "id": "eab1b257607d00dee48bccc0bccfcf3e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Vanessa Kosoy"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "1907.08461.tei.xml", "abstract": "Most known regret bounds for reinforcement learning are either episodic or assume an environment without traps. We derive a regret bound without making either assumption, by allowing the algorithm to occasionally delegate an action to an external advisor. We thus arrive at a setting of active one-shot model-based reinforcement learning that we call DRL (delegative reinforcement learning.) The algorithm we construct in order to demonstrate the regret bound is a variant of Posterior Sampling Reinforcement Learning supplemented by a subroutine that decides which actions should be delegated. The algorithm is not anytime, since the parameters must be adjusted according to the target time discount. Currently, our analysis is limited to Markov decision processes with finite numbers of hypotheses, states and actions.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Xavier Abad", "Robbin Scott Weyant", "Michael J Imperiale", "Arturo Casadevall"], "title": "A New Approach to evaluating the risk-Benefit equation for Dual-Use and Gain-of-Function research of concern", "text": "The use of technology to gain an advantage in human conflict is ancient. Iron replaced bronze in weapons and history is replete with examples of how scientific and technological advances were adapted for war and the acquisition of power. In fact, all technologies are potentially dual use. This trend accelerated with the expansion of knowledge following the scientific and industrial revolutions and affected primarily the disciplines of physics and chemistry, domains of knowledge containing information that was then immediately useful in warfare. The application of biological knowledge to conflict came later even though biological warfare also has a long history. For example, the black death that devastated medieval European society may have begun by an act of biological warfare during the siege of Caffa in 1346  (Wheelis, 2002) . British settlers to North America brought smallpox-infested blankets as \"gifts\" to Native Americans  (Duffy, 1951) . However, it was not until the molecular biology revolution in the late twentieth century that the potential of biology, and in particular microbiology, in biological warfare and terrorism came into focus. These fears came true with a single act of terrorism involving the mailing of anthrax spores in the U.S. in 2001, which caused several deaths and considerable disruption to government facilities such as congressional offices and the postal system  (Bush and Perez, 2012) . This act of bioterrorism catalyzed a series of events that led to greater awareness of the potential of using biological knowledge in nefarious ways, new regulations in biological research in the U.S. such as the Select Agents and Toxins list, and heighted concerns about some types of microbiology research. One of the immediate effects of the post-2001 environment was increased scrutiny of published findings, and several papers were particularly noteworthy for eliciting discussion and concern.  In 2001, researchers  in Australia showed that insertion of the gene for IL-4 into the ectromelia virus genome defeated vaccine immunity  (Jackson et al., 2001) , a report that drew immediate concerns because of its possible implication for similar effects with variola major virus. Similarly, the finding that complement inhibition potentiated variola virus virulence suggested a mechanism for enhancing its pathogenicity  (Rosengard et al., 2002) . An analysis of the U.S. milk distribution system revealed vulnerable nodes where the introduction of botulinum toxin could lead to mass casualties  (Wein and Liu, 2005) , leading to an outcry about journals publishing research that could be exploited by terrorists. Advances in molecular biology led to the chemical synthesis of poliovirus  (Cello et al., 2002)  and the reconstruction of the 1918 pandemic influenza virus  (Tumpey et al., 2005) , which greatly heightened concern about the re-introduction of extinct, controlled, and new viruses to naïve human populations. In this environment, the U.S. Government created the National Science Advisory Board for Biosecurity (NSABB) in 2005 to provide guidance on issues relating to biological risk and security. Both authors of this article were inaugural members of the NSABB and served on that board for 9 years. When the NSABB first began their deliberations, one of the major early topics was that of dual-use research in the biological sciences. This issue had previously vexed the physics community in the twentieth century as advances in physics and associated technologies had led to radar, nuclear weapons, ballistic missiles, and other military hardware. However, there was little or no precedent for similar concerns in the biological research community, especially since biological weapons were outlawed by the Biological Weapons Convention in 1972. Moreover, the term dual use, which had meant civilian and military use in the physics arena, was redefined in its application to biology by an NRC report in 2004 to mean technologies and information that had both beneficial and maleficent use  (NR Council, 2004) . Nevertheless, among the early accomplishments of the NSABB was formulating a definition for dual use research of concern (DURC), which limited the scope of worrisome work to a small subset of biological research. The NSABB also generated a set of recommendations for communicating DURC in publications and other venues. The work of the NSABB proceeded quietly and in relative obscurity until 2011 when the U.S. government learned about two submitted manuscripts reporting that highly pathogenic avian influenza virus (HPAIV) could be made mammalian transmissible by laboratory passage in ferrets, and sought an opinion from the board as to whether publication should be permitted. the Great Gain-of-Function (GOF) controversy Before considering the GOF controversy involving influenza virus, it is worthwhile reviewing what is meant by \"GOF\" and the limitations of the lexicon in the controversy. At the most basic level, a GOF experiment, as the name implies, is one that gives a biological entity any new property. GOF experiments can be highly beneficial and can generate pest resistant crops, microbes expressing proteins for medical therapy such as recombinant human insulin, and new cancer therapies by enhancing lymphocyte function. The controversial aspects of GOF experiments in microbiology arise when microbes are modified to have new properties that can enhance their virulence and transmissibility because such experiments raise worries about new diseases, outbreaks, pandemics, biosafety, and biosecurity. In the experience of the authors, the NSABB probably did not anticipate what a problematic dual-use paper would look like until they had the opportunity to consider the two papers that reported the gain of mammalian transmissibility for HPAIV  (Herfst et al., 2012; Imai et al., 2012) . What made the two papers highly controversial was that they reported that only a few amino acid changes were sufficient to confer mammalian transmissibility to the H5N1 HPAIV, and there was concern that this information could be used to generate a virus capable of pandemic potential with high mortality by anyone with basic molecular biology and virology skills. The NSABB initially recommended redacting the sequence information, but this was considered not feasible given the legal framework in the U.S., and the two papers  (Herfst et al., 2012; Imai et al., 2012)  were eventually published in 2012 after some modifications to the text. The arguments, counterarguments, and events surrounding that episode are described in various publications  (Berns et al., 2012a,b; Fouchier et al., 2012a) , often by the participants themselves, and will not be repeated here. The major outcome of the great GOF controversy of 2012 is that it defined and crystallized some of the issues of dual-use research in biology by providing clear examples of experiments that were of great scientific value while also raising biosecurity and biosafety concerns. Although both papers were eventually published with full information, the debate and controversy did not solve the central questions of what work should be performed moving forward and how it should be reported. In fact, the controversy erupted again in the summer of 2014 following the publication of additional papers describing other GOF experiments (e.g.,  Watanabe et al., 2014)  as well as a series of biosafety lapses at U.S. government laboratories, which led the government to impose a pause on these types of experiments with certain viruses until the NSABB could formulate new recommendations and guidelines. The pause was lifted in mid-December, 2017, alongside policy guidance about how GOF funding decisions should be made going forward. 1 \n Publication Quandaries One of the most vexing questions of the problem of dual-use research is publication of scientific findings. In the U.S., the research community is guided by National Security Decision Directive (NSDD) 189, formulated in 1985 by the Reagan admini stration, which states that all fundamental research results could be published freely. In other words, there was either open publication or classification, and nothing in between. Viewed from the context of NSDD-189 the papers involved in the 2012 GOF controversy were either to be published in their entirety or classified, with the latter alternative being impractical and unfeasible since the work had been carried out in an unclassified environment. With this binary policy, redacting papers because they might contain information useful for nefarious purposes is not an option unless export control regulations are invoked [for a full discussion of the legalities involved, see NAS EM DURC report (National Academies of Sciences Engineering and Medicine, 2017)]. Consequently, when faced with GOF papers containing information that could conceivably be used to enhance the pathogenicity or transmissibility of a virus, editors and journals have almost always opted for full publication, usually requiring more details from the authors about biosafety and biosecurity methods, and often publishing an accompanying editorial emphasizing the scientifically useful aspects of the research [for examples, see  Dermody et al. (2013 Dermody et al. ( , 2014a ]. Such decisions have sometimes elicited strong criticism from members of the virology community  (Dermody et al., 2014b; Wain-Hobson, 2014a) . A more recent situation illustrates the difficult issues faced by authors, editors, and journals when publishing papers that contain DURC. In 2013, the Journal of Infectious Disease faced the quandary of receiving a paper reporting a new botulinum toxin that was resistant to neutralization by the then-available antisera. In response, the journal took the remarkable decision of publishing the paper without the toxin sequence and vowed to keep the data confidential until an antidote was available  (Casadevall et al., 2013; Dover et al., 2013; Relman, 2013; Hooper and Hirsch, 2014) . A major factor in withholding the sequence data was the realization that this toxin could be easily produced using standard techniques if the toxin sequence was available and that the availability of such a toxin might pose a major public health risk. This decision was highly controversial since without the sequence information other investigators could not verify the findings reported in the publication or begin to develop medical countermeasures. In fact, subsequent work revealed that the new toxin was indeed neutralized by available sera, thus diminishing the initial concerns  (Enserink, 2015) . On one hand, withholding the sequence information from public scrutiny was the responsible action given the potential threat, while on the other hand, such an action delayed verification of the findings and the generation of countermeasures had the threat been real. Clearly, manuscripts containing DURC pose vexing problems for journals that often must make such decisions alone. At American Society for Microbiology journals, there are protocols in place for reviewing such manuscripts and the journals have available many individuals with microbiological and safety expertise who can provide input  (Casadevall et al., 2015) . Other situations are likely to pose different challenges, but it is clear that journals are often poorly equipped to handle the difficult problems involved in publishing DURC content. In this regard, we have argued for the need of a national board that can help journals make publication decisions  (Casadevall et al., 2014) , although to date no such body exists. Another major challenge to the control of DURC information is the emergence of preprint servers in biology that allow the posting of research findings before peer review and the proliferation of predatory open access journals that will publish essentially any paper for a fee. Consequently, there now exist alternative systems for publication even if standard journals decline to publish a particular article over DURC concerns. Bypassing traditional publication methods could also allow authors to avoid government scrutiny. \n the situation today It is not an exaggeration that the situation today regarding DURC and GOF experiments remains highly unsatisfactory. Experimental work involving GOF experiments on pathogens with pandemic potential is highly regulated with proponents of such work arguing that restrictions on experimental design are unwarranted  (Fouchier et al., 2012b)  while opponents of such experiments argue that such work cannot be justified (Wain-Hobson, 2014a,b). Proponents of GOF experiments have noted that data generated in such experiments is useful in epidemiological surveillance (Schultz-Cherry et al., 2014), whereas opponents have argued that such work cannot be morally justified because of its inherent risk  (Lipsitch and Galvani, 2014) . In the U.S., government-mandated pauses on certain types of experiments remain in effect for federally funded research but such prohibitions do not extend to other countries, or to work funded by other sources. Although the NSABB continues to analyze and debate the issues involved with DURC and GOF experiments in the U.S., there is no comparable body on the international scene, where much of this type of research is done. There is no consensus in the scientific community on whether the value of some experiments justifies the risks involved. The central problem in finding a consensus is that the value of the research cannot be measured in real time, while assessments of risk involve assumptions that can lead to widely divergent estimates. For example, some risk-benefit calculations have suggested that a high consequence accident is likely to occur in the near future  (Lipsitch and Bloom, 2012; Lipsitch and Inglesby, 2014) , while others have estimated such probabilities to be near zero  (Fouchier, 2015) . However, there is some evidence that the incessant debate, which shows no sign of resolution, is taking its toll on the virology community as shown by surveys suggesting that scientists in training may avoid these areas of research  (Pfeiffer, 2015) . This is of particular concern given that recent years have seen new viral threats in the forms of the West Africa Ebola outbreak, the emergence of Zika virus in the Americas, and Middle East Respiratory syndrome coronavirus in the Arabian peninsula, highlighting the importance of virology in human preparedness against pandemic threats  Casadevall, 2015a, 2016) . One of the most important developments in the past few decades has been a change in the zeitgeist of the field that concerns itself with DURC research and GOF experiments. In the early years of the twenty-first century, as the U.S. reeled from the 9/11 terrorist attacks, which were shortly followed by the anthrax spore attacks, the focus was primarily on biosecurity. At that time, the concern was that terrorists and state actors would use the tools of the molecular biology revolution to create new and more devastating biological weapons. However, as the years passed and no new attacks developed, combined with the attribution of the anthrax spores in mail attacks to a lone insider in a U.S. government laboratory  (Bhattacharjee and Enserink, 2008) , this security threat appeared to recede. At the same time, a series of unfortunate biosafety lapses in government laboratories heightened concerns about biosafety. Hence, today people (at least those outside the security community) appear to be more worried about an unintended release of a pathogen with pandemic potential than a deliberate biological attack. This change in emphasis from biosecurity to biosafety has developed slowly and could easily change if there is another deliberate biological attack or if becomes apparent that adversaries are developing biological weapons. A major problem contributing to the unsatisfactory nature of the current situation is that the NSABB definition of DURC does not work well in day-to-day practice. The NSABB defined DURC as \"life sciences research that, based on current understanding, can be reasonably anticipated to provide knowledge, information, products, or technologies that could be directly misapplied to pose a significant threat with broad potential consequences to public health and safety, agricultural crops and other plants, animals, the environment, materiel, or national security. \" Although the crafting of this definition was a major achievement at the time in being able to limit the scope of DURC to a relatively small portion of biomedical research, thus leaving most biological research to proceed unfettered, subsequent experience showed that the clause \"reasonably anticipated\" is so subjective in nature that it requires a risk assessment beyond the capabilities of most scientists, reviewers, and editors  (Casadevall et al., 2014) . In essence, the definition was helpful in keeping whole swaths of biological research outside the DURC category, such as cancer and immunology research, but it difficult to apply in determining what is included in the DURC definition. Also contributing to an unsatisfactory situation are concerns whether such regulations as the Select Agents and Toxins list help or hinder societal security. On one hand, placing great restrictions on the accessibility to a number of agents and toxins does increase security by making them more difficult to obtain, with the caveat that these are naturally occurring agents that could be obtained from nature by a determined actor. On the other hand, there is the concern that focusing on lists and a relatively short list of agents means that the overwhelming majority of microbial threats are not on the DURC radar screen. For example, Zika virus emerged as a pathogen of pandemic potential with little or no anticipation from experts. Hence, making lists and focusing attention on those agents in the list has the paradoxical potential to reduce biosecurity since regulations are tightened for listed agents, possibly hindering research, while other dangerous agents are neglected  (Casadevall and Relman, 2010) . A similar argument applies to the current DURC oversight policy of the U.S. government, which is focused on a specific list of agents. 2 This process, which is akin to searching under the lamppost, carries great danger because it ignores what could be significant threats. In this regard, it is noteworthy that fungal pathogens are seldom considered as biological threats despite the fact that members of this kingdom have significant weapon potential  (Casadevall and Pirofski, 2006; Casadevall, 2017) . Against this backdrop of dissatisfaction is the fact that science continues to progress very rapidly, introducing new technologies such CRISPR/Cas9, gene drives, and more efficient synthetic biology, each of which brings with it new possibilities for research that improves the human condition as well as new tools for nefarious purposes. Furthermore, as the technologies improve they are increasingly accessible to more individuals and countries for whom this type of research was previously beyond reach. Hence, the problem of DURC is likely to become significantly more urgent in the near future. \n the Way Forward In a world where new infectious agents that can rapidly spread among vulnerable populations are described on a regular basis, humanity needs a healthy research establishment focused on microbial threats. It is estimated that there are a minimum of 320,000 mammalian viruses  (Anthony et al., 2013) : some fraction of these are probably zoonotic events waiting to happen. As Ian Malcolm, the fictional character created by Michael Crichton in the novel Jurassic Park, stated, \"Life finds a way. \" Information and knowledge are the best defenses against these threats. In addition to terror from nature, a new crisis will almost certainly occur in the future arising from a deliberate attack, a new provocative paper, or another biosafety lapse. GOF experiments and DURC research are essential for preparedness and the question is not whether this research should be pursued but rather how to do it safely and mitigate risk. To date, each of the controversies has been reactive, with proponents and opponents of such experiments responding to a specific finding or study. After more than a decade of discussion on what constitutes DURC, benefits and risks of GOF experiments, regulations, pauses, and moratoriums, it is increasingly apparent that current approaches are inadequate for the challenges at hand. Given these limitations, we have proposed a new framework for DURC research that focuses on answering specific questions  (Imperiale and Casadevall, 2015b) . Hence, instead of prohibiting certain types of experimentation, we suggest that the way forward is to focus on specific scientific questions and the problems that need answers. For example, if there is a need to determine whether a particular feral virus pathogen has the capacity for mammalian infection and transmission, then GOF experiments performed in safe and controlled conditions can be justified. On the other hand, endowing HIV with new transmission properties is not a medically important GOF experiment (National Academies of Sciences Engineering and Medicine, 2017). All human activities that involve probing the unknown, ranging from space exploration to tissue culture procedures, carry some degree of risk, and it is nature of humanity to accept risk to attain progress. Opponents and proponents of this type of experimentation need to maintain open channels for continued discussion because the dialectic of ideas is likely to result in better decisions. Institutional bodies such as the NSABB need to be supported for they constitute important venues for such discussion and recommendations that mitigate risk. In fact, it is important to create similar institutions that can work at the international level since U.S.-based research is a small portion of all microbiological work done worldwide. Most importantly, we should remain optimistic that the research community can do the research necessary to obtain information critical to protect our species while minimizing the risks of such work. \t\t\t https://grants.nih.gov/grants/guide/notice-files/NOT-OD-17-071.html. \n\t\t\t https://www.phe.gov/s3/dualuse/documents/us-policy-durc-032812.pdf.", "date_published": "n/a", "url": "n/a", "filename": "fbioe-06-00021.tei.xml", "abstract": "In the twenty-first century, biology faces a problem that has previously vexed other disciplines such as physics, namely the prospect that its knowledge domain could be used to generate biological agents with altered properties that enhanced their weapon potential. Biological weapons bring the additional dimension that these could be self-replicating, easy to manufacture and synthesized with commonly available expertise. This resulted in increasing concern about the type of research done and communicated, despite the fact that such research often has direct societal benefits, bringing the dual-use dilemma to biology. The conundrum of dual use research of concern was crystallized by the so-called \"gain-of-function\" type of experiments in which avian influenza viruses were endowed with new properties in the laboratory such as increased virulence and the capacity for mammalian transmission. After more than a decade of intensive discussion and controversy involving biological experiments with dual-use potential, there is no consensus on the issue except for the need to carry out such experiments in the safest conditions possible. In this essay, we review the topic with the hindsight of several years and suggest that instead of prescribing prohibitions and experimental limitations the focus should be on the importance of scientific questions at hand. We posit that the importance of a scientific question for medical and scientific progress provides a benchmark to determine the acceptable level of risk in biological experimentation.", "id": "5a1740f4e6b50462026a485c141f3a53"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Sam Toyer", "Rohin Shah", "Andrew Critch", "Stuart Russell"], "title": "The MAGICAL Benchmark for Robust Imitation", "text": "Introduction Imitation Learning (IL) is a practical and accessible way of programming robots to perform useful tasks  [6] . For instance, the owner of a new domestic robot might spend a few hours using teleoperation to complete various tasks around the home: doing laundry, watering the garden, feeding their pet salamander, and so on. The robot could learn from these demonstrations to complete the tasks autonomously. For IL algorithms to be useful, however, they must be able to learn how to perform tasks from few demonstrations. A domestic robot wouldn't be very helpful if it required thirty demonstrations before it figured out that you are deliberately washing your purple cravat separately from your white breeches, or that it's important to drop bloodworms inside the salamander tank rather than next to it. Existing IL algorithms assume that the environment observed at test time will be identical to the environment observed at training time, and so they cannot generalise to this degree. Instead, we would like algorithms that solve the task of robust IL: given a small number of demonstrations in one training environment, the algorithm should be able to generalise the intent behind those demonstrations to (potentially very different) deployment environments. One barrier to improved algorithms for robust IL is a lack of appropriate benchmarks. IL algorithms are commonly tested on Reinforcement Learning (RL) benchmark tasks, such as those from OpenAI Gym  [37, 23, 27, 8] . However, the demonstrator intent in these benchmarks is often trivial (e.g. the goal for most of Gym's MuJoCo tasks is simply to run forward), and limited variation in the initial state distribution means that algorithms are effectively being evaluated in the same setting that was used to provide demonstrations. Recent papers on Inverse Reinforcement Learning (IRL)-which is a form of IL that infers a reward under which the given demonstrations are near-optimal-have instead used \"testing\" variants of standard Gym tasks which differ from the original demonstration environment  [17, 39, 32, 33] . For instance, Fu et al.  [17]  trained an algorithm on demonstrations from the standard \"Ant\" task from Gym, then tested on a variant of the task where two of the creature's 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada.  \n Colour test variant Layout test variant Shape test variant Figure  1 : Unlike existing IL benchmarks, MAGICAL makes a distinction between demonstration and test variants of a task. Demonstrations are all provided in one particular configuration of the world (the \"demonstration variant\"). The learnt policy (or reward function) is then evaluated across a set of test variants, each of which randomise one aspect of the environment, such as block colour or shape, environment layout, dynamics, etc. This makes it possible to understand precisely which aspects of the underlying task the algorithm has been able to infer from demonstrations. four legs were disabled. Splitting the environment into such \"training\" and \"test\" variants makes it possible to measure the degree to which an algorithm overfits to task-irrelevant features of the supplied demonstrations. However, there is so far no standard benchmark for robust IL, and researchers must instead use ad-hoc adaptations of RL benchmarks-such as the modified Ant benchmark and similar alternatives discussed in Section 5-to evaluate intent generalisation. To address the above issues, we introduce the Multitask Assessment of Generalisation in Imitative Control ALgorithms (MAGICAL). Each MAGICAL task occurs in the same 2D \"MAGICAL universe\", where environments consist of a robot with a gripper surrounded by a variable number of objects in a fixed-size workspace. Each task is associated with a demonstration variant, which is a fixed initial state from which all human demonstrations are provided. A task is also associated with a set of test variants for which no demonstrations are provided. As illustrated in Fig.  1 , the test variants each randomise a different aspect of the world, such as object colour, transition dynamics, or object count. Randomising attributes of objects and the physics of the world lets us evaluate the ability of a robust IL algorithm to perform combinatorial generalisation  [5] . For instance, given a demonstration of the robot pushing a red square across the workspace, an algorithm should be able to push a yellow circle across the workspace; given a demonstration of three green and yellow blocks being placed in a line, an algorithm should also be able to place four red and blue blocks in a line; and so on. MAGICAL has several advantages over evaluation methods for standard (non-robust) IL: • No \"training on the test set\". Evaluating in the same setting that was used to give demonstrations allows algorithms to exploit features that might not be present during deployment. Having separate test variants for a task allows us to identify this kind of overfitting. • Distinguishes between different types of transfer. Each test variant evaluates robustness to a distinct, semantically meaningful axis of variation. This makes it possible to characterise precisely which aspects of the provided demonstrations a given algorithm is relying on, and to diagnose the causes of over-or under-fitting. • Enables knowledge reuse between tasks. Each MAGICAL task requires similar concepts and low-level skills to solve. Different tasks can therefore provide \"background knowledge\" for multi-task and meta-IL algorithms, such as knowledge that objects can have different colours, or that objects with different shapes respond in a particular way when grasped. Our experiments in Section 4 demonstrate the brittleness of standard IL algorithms, particularly under large shifts in object position or colour. We also show that common methods for improving generalisation-such as multitask training, data augmentation, and alternative camera viewssometimes improve robustness to small changes, but still fail to generalise to more extreme ones. \n MAGICAL: Systematically evaluating robust IL We will now introduce the main elements of the MAGICAL benchmark. We first describe the abstract setup of our benchmark, then detail the specific tasks and variants available in the benchmark. \n Benchmark setup The MAGICAL benchmark consists of a set of tasks T 1 , T 2 , . . . , T m . Each task can in turn be broken down into variants of a single base Markov Decision Process (MDP) that provide different state distributions and \"physics\" for an agent. Formally, each task T = (S, v D , V) consists of a scoring function S(τ ), a demonstration variant v D , and a set of additional test variants V = {v 1 , v 2 , . . . , v n }. The scoring function S(τ ) takes a trajectory τ = (s 0 , a 0 , s 1 , a 1 , . . . , s T , a T ) and assigns it a score S(τ ) ∈ [0, 1], where 0 is the score of a no-op policy, and 1 is the score of a perfect demonstrator. Unlike a reward function, S(τ ) need not be Markovian. In order to evaluate generalisation, the variants are split into a single demonstration variant v D and a set of test variants V. In our domestic robotics analogy, v D might represent a single room and time-of-day in which demonstrations for some domestic task collected, while each test variant v ∈ V could represent a different room, different time-of-day, and so on. Algorithms are expected to be able to take demonstrations given only in demonstration variant v D , then generalise the intent behind those demonstrations in order to achieve the same goal in each test variant v ∈ V. This can be viewed either as a form of domain transfer, or as ordinary generalisation using only a single sample from a hypothetical distribution over all possible variants of each task. Formally, each variant associated with a task T defines a distribution over reward-free MDPs. Specifically, a variant v = (p 0 , p ρ , H) consists of an initial state distribution p 0 (s 0 ), a dynamics distribution p ρ (ρ), and a horizon H. States are fully observable via an image-based observation space. Further, all variants have the same state space, the same observation space, and the same action space, which we discuss below. In addition to sampling an initial state s 0 ∼ p 0 (s 0 ), at the start of each trajectory, a dynamics vector ρ ∈ R d is also sampled from the dynamics distribution p ρ (ρ). Unlike the state, ρ is not observable to the agent; this vector controls aspects of the dynamics such as friction and motor strength. Finally, the horizon H defines a fixed length for all trajectories sampled from the MDP associated with the variant v. Each variant associated with a given task has the same fixed horizon H to avoid \"leaking\" information about the goal through early termination  [27] . All tasks and variants in the MAGICAL benchmark share a common continuous state space S. A state s ∈ S consists of a configuration (pose, velocity, and gripper state) q R for the robot, along with object configurations O = {o 1 , . . . , o E } (where the number of objects in s 0 may be random). In addition to pose, each object configuration o i includes an object type and a number of fixed attributes. Objects can be of two types: blocks (small shapes that can be pushed around by the agent) and goal regions (coloured rectangles that the agent can drive over, but not push around). Each block has a fixed shape (square, pentagon, star, or circle) and colour (red, green, blue, or yellow). Each goal region has a fixed colour, width, and height. In order to facilitate generalisation across tasks with a different number of objects, we use a common image-based observation space and discrete, low-level action space for all tasks, which we describe in detail in Appendix A.1. At an implementation level, we expose each variant of each task as a distinct Gym environment  [8] , which makes it straightforward to incorporate MAGICAL into existing IL and RL codebases. \n Tasks and variants With the handful of building blocks listed in the previous section, we can create a wide variety of tasks, which we describe in Section 2.2.1. The object-based structure of the environment also makes it easy to evaluate combinatorial generalisation by randomising one or more attributes of each object while keeping the others fixed, as described in Section 2.2.2. \n Tasks Tasks in the MAGICAL suite were chosen to balance three desiderata. First, given a handful of trajectories from the demonstration variant of a task, it should be possible for a human observer to infer the goal with sufficient accuracy to solve the test variants. We have chosen demonstration variants (illustrated in Fig.  2 ) that rule out obvious misinterpretations, like mistakenly identifying colour as being task-relevant when it is not. Second, the tasks should be constructed so that they involve complementary skills that meta-and multi-task learning algorithms can take advantage of. In our tasks, these \"shared skills\" include block manipulation; identification of colour or shape; and relational reasoning. Third, the demonstration variant of each task must be solvable by existing (non-robust) IL algorithms. This ensures that the main challenge of the MAGICAL suite lies in  generalising to the test variants (robust IL), as opposed to reproducing the demonstrator's behaviour in the demonstration variant (standard IL). This section briefly describes the resulting tasks; detailed discussion of horizons, score functions, etc. is deferred to Appendix A. \n Move to Corner (MTC) The robot must push a single block from one corner of the workspace to the diagonally opposite corner. Test variants are constrained so that the robot and block start near the lower right corner. The score is S(τ ) = 1 if the block finishes the trajectory in the top left eighth of the workspace, and decreases to zero as the block gets further from the top left corner. \n MoveToRegion (MTR) The robot must drive inside a goal region and stay there. There are no blocks in the demonstration or test variants. Further, variants only have one goal region to ensure that the objective is unambiguous. The agent's score is S(τ ) = 1 if the robot's body is inside the goal region at the end of the trajectory, and S(τ ) = 0 otherwise. \n MatchRegions (MR) There is a set of coloured blocks and a goal region visible to the robot, and the robot must push all blocks of the same colour as the goal region into the goal region. Test variants are constrained to have one goal region and at least one block of the same colour as that goal region. A perfect score is given upon termination if the goal regions contains all and only blocks of the goal region's colour, with penalties for excluding any blocks of the goal colour, or including other blocks. \n MakeLine (ML) Here the objective is for the robot to arrange all the blocks in the workspace into a single line. A perfect score is given if all blocks are approximately colinear and close together; a penalty is given for each block that does not form part of the longest identifiable line. Refer to Appendix A for details on how a \"line\" is defined. FindDupe (FD) Similar to MatchRegions, except the goal region initially contains a \"query\" block which has the same shape and colour as at least one other block outside the goal region. The objective is to push at least one of those duplicate blocks into the goal region, which yields a perfect score. Penalties are given for knocking the query block out of the goal region, failing to find a duplicate, or pushing non-duplicate blocks into the goal region. \n FixColour (FC) In each variant of this task, the workspace contains a set of non-overlapping goal regions. Each goal region contains a single block, and exactly one block in the workspace will have a different colour to its enclosing goal region. A perfect score is given for pushing that block out of its enclosing goal region and into an unoccupied part of the workspace, without disturbing other blocks. \n ClusterColour (CC) and ClusterShape (CS) The robot is confronted with a jumble of blocks of different colours and shapes. It must push the blocks into clusters of either uniform colour (in the CC task), or uniform shape (in the CS task). Test variants are constrained to include at least one block of each colour and each shape. A perfect score is given for creating four spatially distinct clusters corresponding to each of the four colours (CC) or shapes (CS), with a penalty proportional to the number of blocks that do not belong to an identifiable cluster. \n Test variants In addition to its demonstration variant, each of the tasks above has a set of associated test variants. Some variants are not supported for tasks that do not have any blocks, or where the initial state is otherwise restricted, as documented in Table  2  of Appendix A. Jitter Takes demo variant and randomly perturbs the poses of the robot and all objects by up to 5% of the maximum possible range. Failure on this variant indicates severe overfitting to the demonstration variant (e.g. by memorising action sequences). Layout Completely randomises the position and orientation of the robot and all blocks, plus position and dimensions of goal regions; a more challenging version of Jitter. Colour Block colours are randomly reassigned as appropriate for the task. This tests whether the agent is responsive to block colour (when it is task-relevant, like in CC and MR), or is correctly ignorant of colour (when it is irrelevant, like in MTC and CS). Shape Similar to Colour, except the shapes of blocks are randomised rather than the colours. This variant either tests for appropriate responsiveness or invariance to shape, depending on whether shape is task-relevant. \n CountPlus The number of blocks is randomised (along with shape, colour, and position) to test whether the agent can handle \"larger\" or \"smaller\" problems (i.e. \"generalisation to n\"  [35] ). Dynamics Subtly randomises friction of objects and the robot against the workspace, as well as force of robot motors (for rotation, forward/backward motion, and the gripper). All Combines all applicable variants for a task (e.g. Layout, Colour, Shape, CountPlus, Dynamics). \n Data-efficient intent disambiguation Succeeding at the MAGICAL benchmark requires agents to generalise the intent behind a set of demonstrations to substantially different test variants. We anticipate that resolving the ambiguity inherent in this task will require additional sources of information about the demonstrator's goal beyond just single-task demonstrations. In this section, we review two popular non-robust IL algorithms, as well as some common ways in which alternative sources of goal information are incorporated into these algorithms to improve generalisation. \n Baseline methods Our first baseline method is Behavioural Cloning (BC). BC treats a demonstration dataset D as an undistinguished collection of state-action pairs {(s 1 , a 1 ), . . . , (s M , a M )}. It then optimises the parameters θ of the policy π θ (a | s) via gradient descent on the log loss L bc (θ; D) = − E D log π θ (a | s) . Our second baseline method is Generative Adversarial IL (GAIL)  [23] . GAIL casts IL as a GAN problem  [19] , where the generator π θ (a | s) is an imitation policy, and the discriminator D ψ : S × A → [0, 1] is tasked with distinguishing imitation behaviour from expert behaviour. Specifically, GAIL uses alternating gradient descent to approximate a saddle point of max θ min ψ L adv (θ, ψ; D) = − E π θ log D ψ (s, a) − E D log(1 − D ψ (s, a)) + λH(π θ ) , where H denotes entropy and λ ≥ 0 is a policy regularisation parameter. We also included a slight variation on GAIL which (approximately) minimises Wasserstein divergence between occupancy measures, rather than Jensen-Shannon divergence. We refer to this baseline as WGAIL-GP. In analogy with WGAN-GP  [20] , WGAIL-GP optimises the cost max θ min ψ L w-gp (θ, ψ; D) = E D D ψ (s, a) − E π θ D ψ (s, a) + λ w-gp E 1 2 π θ + 1 2 D ( ∇ s D(s, a) 2 − 1) 2 , The gradient penalty approximately enforces 1-Lipschitzness of the discriminator by encouraging the norm of the gradient to be 1 at points between the support of π θ and D. Since actions were discrete, we did not enforce 1-Lipschitzness with respect to the action input. We also did not backpropagate gradients with respect to the gradient penalty back into the policy parameters θ, since the gradient penalty is only intended as a soft constraint on D. In addition to these baselines, we also experimented with Apprenticeship Learning (AL). Unfortunately we could not get AL to perform well on most of our tasks, so we defer further discussion of AL to Appendix B. \n Using multi-task data As noted earlier, the MAGICAL benchmark tasks have similar structure, and should in principle benefit from multi-task learning. Specifically, say we are given a multi-task dataset D mt = {D(T i , v D i , n i )} M i=1 , where D(T i , v, n) denotes a dataset of n trajectories for variant v of task T i . For BC and GAIL, we can decompose the policy for task T i as π i θ = g i θ • f θ , where f θ : S → R d is a multi-task state encoder, while g i θ : R d → ∆(A) is a task-specific policy decoder. We can also decompose the GAIL discriminator as D i ψ = s i ψ • r ψ , where r ψ : S × A → R d is shared and s i ψ : R d → [0, 1] is task-specific. We then modify the BC and GAIL objectives to L bc (θ; D mt ) = M i=1 L bc (θ; D(T i , v D i , n i )) and L adv (θ, ψ; D mt ) = M i=1 L adv (θ, ψ; D(T i , v D i , n i )) . \n Domain-specific priors and biases Often the most straightforward way to improve the robustness of an IL algorithm is to constrain the solution space to exclude common failure modes. For instance, one could use a featurisation that only captures task-relevant aspects of the state. Such priors and biases are generally domain-specific; for the image-based MAGICAL suite, we investigated two such biases: • Data augmentation: In MAGICAL, our score functions are invariant to whether objects are repositioned or rotated slightly; further, human observers are typically invariant to small changes in colour or local image detail. As such, we used random rotation and translation, Gaussian noise, and colour jitter to augment training data for the BC policy and GAIL discriminator. This can be viewed as a post-hoc form of domain randomisation, which has previously yielded impressive results in robotics and RL  [2] . We found that GAIL discriminator augmentations were necessary for the algorithm to solve more-challenging tasks, as previously observed by Zolna et al.  [41] . In BC, we found that policy augmentations improved performance on both demonstration and test variants. • Ego-and allocentric views: Except where indicated otherwise, all of the experiments in Section 4 use an egocentric perspective, which always places the agent at the same position (and in the same orientation) within the agent's field of view. This contrasts with an allocentric perspective, where observations are focused on a fixed region of the environment (in our case, the extent of the workspace), rather than following the agent's position. In the context of language-guided visual navigation, Hill et al.  [22]  previously found that an egocentric view improved generalisation to unseen instructions or unseen visual objects, despite the fact that it introduces a degree of partial observability to the environment. \n Experiments Our empirical evaluation has two aims. First, to confirm that single-task IL methods fail to generalise beyond the demonstration variant in the MAGICAL suite. Second, to analyse the ways in which the common modifications discussed in Section 3 affect generalisation.  \n Experiment details We evaluated all the single-and multi-task algorithms in Section 3, plus augmentation and perspective ablations, on all tasks and variants. Each algorithm was trained five times on each task with different random seeds. In each run, the training dataset for each task consisted of 10 trajectories from the demo variant. All policies, value functions, and discriminators were represented by Convolutional Neural Networks (CNNs). Observations were preprocessed by stacking four temporally adjacent RGB frames and resizing them to 96×96 pixels. For multi-task experiments, task-specific weights were used for the final fully-connected layer of each policy/value/discriminator network, but weights of all preceding layers were shared. The BC policy and GAIL discriminator both used translation, rotation, colour jitter, and Gaussian noise augmentations by default. The GAIL policy and value function did not use augmented data, which we found made training unstable. Complete hyperparameters and data collection details are listed in Appendix B. The IL algorithm implementations that we used to generate these results are available on GitHub, 1 as is the MAGICAL benchmark suite and all demonstration data.  2   \n Discussion Due to space limitations, this section addresses only a selection of salient patterns in the results. Table  1  provides score statistics for a subset of algorithms and variants, averaged across all tasks. See Section 2.2.1 for task name abbreviations (MTR, FC, etc.). Because the tasks vary in difficulty, pooling across all tasks yields high score variance in Table  1 . Actual score variance for each method is much lower when results are constrained to just one task; refer to Appendix C for complete results. Overfitting to position All algorithms exhibited severe overfitting to the position of objects. The Layout, CountPlus, and All variants yielded near-zero scores in all tasks except MTC and MTR, and on many tasks there was also poor transfer to the Jitter variant. For some tasks, we found that the agent would simply execute the same motion regardless of its initial location or the positions of task-relevant objects. This was true on the FC task, where the agent would always execute a similar forward arc regardless of its initial position, and also noticeable on MTC and FD, where the agent would sometimes move to the side of a desired block when it was shifted slightly. For BC, this issue was ameliorated by the use of translation and rotation augmentations, presumably because the policy could better handle small deviations from the motions seen at training time. Colour and shape transfer Surprisingly, BC and GAIL both struggled with colour transfer to a greater degree than shape transfer on several tasks, as evidenced by the aggregated statistics for Colour and Shape variants in Table  1 . Common failure modes included freezing in place or moving in the wrong direction when confronted with an object of a different colour to that seen at training time. In contrast, in most tasks where shape invariance was desirable (including MTC, MR, ML, and FC), the agent had no trouble reaching and manipulating blocks of different shapes. Although colour jitter was one of the default augmentations, the BC ablations in Table  1  suggest that almost all of the advantage of augmentations comes from the use of translation/rotation augmentations. In particular, we did not find that colour jitter greatly improved performance on tasks where the optimal policy was colour-invariant. In spite of exposing the networks to a greater range of colours at train time, multitask training also failed to improve colour transfer, as we discuss below. Although translation and rotation sometimes improved colour transfer (e.g. for BC on FindDupe in Table  7 ), it is not clear why this was the case. We speculate that these augmentations could have encouraged the policy to acquire more robust early-layer features for edge and corner detection that did not rely on just one colour channel. Multi-task transfer Plain multi-task learning had mixed effects on generalisation. In some cases it improved generalisation (e.g. for BC on FC), but in most cases it led to unchanged or negative transfer, as in the Colour test variants for MTC, MR, and FD. This could have been because the policy was using colour to distinguish between tasks. More speculatively, it may be that a multi-task BC or GAIL loss is not the best way to incorporate off-task data, and that different kinds of multi-task pretraining are necessary (e.g. learning forward or inverse dynamics  [9] ). \n Egocentric view and generalisation The use of an allocentric (rather than egocentric) view did not improve generalisation or demo variant performance for most tasks, and sometimes decreased it. Table  1  shows the greatest performance drop on variants that change object position, such as Layout and Jitter. For example, in MTR we found that egocentric policies tended to rotate in one direction until the goal region was in the centre of the agent's field of view, then moved forward to reach the region, which generalises well to different goal region positions. In contrast, the allocentric policy would often spin in place or get stuck in a corner when confronted with a goal region in a different position. This supports the hypothesis of Hill et al.  [22]  that the egocentric view improves generalisation by creating positional invariances, and reinforces the value of being able to independently measure generalisation across distinct axes of variation (position, shape, colour, etc.). \n Related work There are few existing benchmarks that specifically examine robust IL. The most similar benchmarks to MAGICAL have appeared alongside evaluations of IRL and meta-IL algorithms. As noted in Section 1, several past papers employ \"test\" variants of standard Gym MuJoCo environments to evaluate IRL generalisation  [17, 39, 32, 33] , but these modified environments tend to have trivial reward functions (e.g. \"run forward\") and do not easily permit cross-environments transfer. Xu et al.  [38]  and Gleave and Habryka  [18]  use gridworld benchmarks to evaluate meta-and multi-task IRL, and both benchmarks draw a distinction between demonstration and execution environments within a meta-testing task. This distinction is similar in spirit to the demonstration/test variant split in MAGICAL, although MAGICAL differs in that it has more complex tasks and the ability to evaluate generalisation across different axes. We note that there also exist dedicated IL benchmarks  [30, 26] , but they are aimed at solving challenging robotics tasks rather than evaluating generalisation directly. There are many machine learning benchmarks that evaluate generalisation outside of IL. For instance, there are several challenging benchmarks for generalisation  [31, 12, 13]  and meta-or multi-task learning  [40]  in RL. Unlike MAGICAL, these RL benchmarks have no ambiguity about what the goal is in the training environment, since it is directly specified via a reward function. Rather, the challenge is to ensure that the learnt policy (for model-free methods) can achieve that clearly-specified goal in different contexts (RL generalisation), or solve multiple tasks simultaneously (multi-task RL), or be adapted to new tasks with few rollouts (meta-RL). There are also several instruction-following benchmarks for evaluating generalisation in natural language understanding  [29, 34] . Although these are not IL benchmarks, they are similar to MAGICAL in that they include train/test splits that systematically evaluate different aspects of generalisation. Finally, the Abstract Reasoning Corpus (ARC) is a benchmark that evaluates the ability of supervised learning algorithms to extrapolate geometric patterns in a human-like way  [11] . Although there is no sequential decision-making aspect to ARC, Chollet  [11]  claims that solving the corpus may still require priors for \"objectness\", goal-directedness, and various geometric concepts, which means that methods suitable for solving MAGICAL may also be useful on ARC, and vice versa. Although we covered some simple methods of improving IL robustness in Section 3, there also exist more sophisticated methods tailored to different IL settings. Meta-IL  [15, 25]  and meta-IRL  [38, 39]  algorithms assume that a large body of demonstrations is available for some set of \"train tasks\", but only a few demonstrations are available for \"test tasks\" that might be encountered in the future. Each test task is assumed to have a distinct objective, but one that shares similarities with the train tasks, making it possible to transfer knowledge between the two. These methods are likely useful for multi-task learning in the context of MAGICAL, too. However, it's worth noting that past meta-IL work generally assumes that meta-train and meta-test settings are similar, whereas this work is concerned with how to generalise the intent behind a few demonstrations given in one setting (the demo variant) to other, potentially very different settings (the test variants). Similar comments apply to existing work on multi-task IL and IRL  [18, 10, 14, 3] . \n Conclusion In this paper, we introduced the MAGICAL benchmark suite, which is the first imitation learning benchmark capable of evaluating generalisation across distinct, semantically-meaningful axes of variation in the environment. Unsurprisingly, results for the MAGICAL suite confirm that single-task methods fail to transfer to changes in the colour, shape, position and number of objects. However, we also showed that image augmentations and perspective shifts only slightly ameliorate this problem, and multi-task training can sometimes make it worse. This lack of generalisation stands in marked contrast to human imitation: even 14-month-old infants have been observed to generalise demonstrations of object manipulation tasks across changes in object colour and shape, or in the appearance of the surrounding room  [4] . Closing the gap between current IL capabilities and human-like few-shot imitation could require significant innovations in multi-task learning, action and state representations, or models of human cognition. The MAGICAL suite provides a way of evaluating such algorithms which not only tests whether they generalise well \"on average\", but also shines a light on the specific kinds of generalisation which they enable. \n Broader impact This paper presents a new benchmark for robust IL and argues for an increased focus on algorithms that can generalise demonstrator intent across different settings. We foresee several possible follow-on effects from improved IL robustness: Economic effects of automation Better IL generalisation could allow for increased automation in some sectors of the economy. This has the positive flow-on effect of increased economic productivity, but could lead to socially disruptive job loss. Because our benchmark focuses on robust IL in robotics-like environments, it's likely that any effect on employment would be concentrated in sectors involving activities that are expensive to record. This could include tasks like surgery (where few demonstrators are qualified to perform the task, and privacy considerations make it difficult to collect data) or packaging retail goods for postage (where few-shot learning might be important when there are many different types of goods to handle). Identity theft and model extraction More robust IL could enable better imitation of specific people, and not just imitation of people in general. This could lead to identify theft, for instance by mimicking somebody's speech or writing, or by fooling biometric systems. Because this benchmark focuses on control and manipulation rather than media synthesis, it's unlikely that algorithms designed to solve our benchmark will be immediately useful for this purpose. On the other hand, this concern is still relevant when applied to machine behaviour, rather than human behaviour. In NLP, it's known that weights for ML models can be \"stolen\" by observing the model's outputs for certain carefully chosen inputs  [28] . Similarly, more robust IL could make it possible to clone a robot's policy by observing its behaviour, which could make it harder to sell robot control algorithms as standalone products. Learnt objectives Hadfield-Menell et al.  [21]  argues that it is desirable for AI systems to infer their objectives from human behaviour, rather than taking them as fixed. This can avoid problems that arise when an agent (human, robot, or organisation) doggedly pursues an easyto-measure but incorrect objective, such as a corporate executive optimising for quarterly profit (which is easy to measure) over long-term profitability (which is actually desired by shareholders). IL makes it possible to learn objectives from observed human behaviour, and more robust IL may therefore lead to AI systems that better serve their designers' goals. However, it's worth noting that unlike, say, HAMDPs  [16]  or CIRL games  [21] , IL cannot request clarification from a demonstrator if the supplied demonstrations are ambiguous, which limits its ability to learn the right objective in general. Nevertheless, we hope that insights from improved IL algorithms will still be applicable to such interactive systems. \n A Additional benchmark details In this section we provide more details about our benchmark tasks, including horizons, scoring functions, and so on. We also list the test variants available for each task in Table  2 . \n Task Test variant Jitter Layout Colour Shape CountPlus Dynamics All MoveToCorner MoveToRegion MatchRegions MakeLine FindDupe FixColour ClusterColour ClusterType Table  2 : Available variants for each task. Some variants are not defined for certain tasks because they may make task completion impossible, make task completion trivial (i.e. the null policy often completes the task), or do not provide a meaningful axis of variation (e.g. MoveToRegion does not feature any blocks, and so there are no shapes to randomise).  We use the same discrete action space for all tasks. Although this benchmark was inspired by robotic IL, where the underlying action space is generally continuous, we opted to use discrete actions so that we could elicit human demonstrations using only a standard keyboard. The underlying state space is still continuous, so each discrete action applies a preset combination of forces to the robot, such as a force that pushes the gripper arms together, or a force that moves the robot forward or backward. In total, the agent has 18 distinct actions. These are formed from the Cartesian product of two gripper actions (push closed/allow to open), three longitudinal motion actions (forward/back/stop), and three angular motions (left/straight/right). \n A.1 Action and observation space We use the same image-based observation space for each task. In all of our experiments, we provide the agent with stacked 96×96 pixel RGB frames depicting the workspace at the current time step and three preceding time steps. At our 8Hz control rate, this corresponds to around 0.5s of interaction context. Using an image-based observation space makes it easy to generalise policies and discriminators across different numbers and types of objects, without having to resort to, e.g., graph networks or structured learning. An image-based observation space also means that the agent gets access to a similar representation as the human demonstrator. This makes it possible to resolve ambiguities and improve generalisation by exploiting features of the human visual system, as we do when we apply the small image augmentations described in Appendix B. By default, observations employ an egocentric (robot-centred) perspective on the workspace, as illustrated in Fig.  3a . Unlike the allocentric perspective, depicted in Fig.  3b , the egocentric often does not allow the agent to observe the full workspace. However, we found that an egocentric perspective resulted in faster training and better generalisation, as we note in the ablations of Section 4. Similar benefits to generalisation were previously observed by Hill et al.  [22] . \n A.2 Detailed task descriptions A.2.1 MoveToCorner (MTC) Figure  4 : A demonstration on MoveToCorner. In MoveToCorner, the robot must push a single block from the bottom right corner of the workspace to the top left corner of the workspace. Test variants are also constrained so that there is only ever one block, and it always starts close to the bottom right corner of the workspace. These constraints preclude use of the CountPlus test variant, since block count cannot be changed without making the task ambiguous. It also precludes use of the Layout variant, since fully randomising block position might make the desired block location ambiguous (e.g. pushing the block into top left corner versus pushing it to the opposite side of the workspace). The horizon for all variants is H = 80 time steps. Trajectories receive a score of S(τ ) = 1 if the block spends the last frame of the rollout within √ 2/2 units of the top left corner of the workspace (the whole workspace is 2×2 units). S(τ ) decays linearly from 1 to 0 as the block moves from inside that region to more than √ 2 units away from the corner. \n A.2.2 MoveToRegion (MTR) Figure  5 : A demonstration on MoveToRegion. The objective of the MoveToRegion task is for the robot to drive inside a goal region placed in the workspace. There is only ever one goal region, and no blocks are present in the train or test variants. Hence the CountPlus and Shape variants are not applicable. However, the Colour variant is still applicable. as it randomises the colour of the goal region. The horizon is set to H = 40. Scoring for MoveToRegion is binary. If at the end of the episode, the centre of the robot's body is inside the goal region, then it receives a score of 1. Otherwise it receives a score of 0. \n A.2.3 MatchRegions (MR) Figure  6 : A demonstration on MatchRegions. In MatchRegions, the agent is confronted with a single goal region and several blocks of different colours. The objective is to move all (and only) blocks of the same colour as the goal region into the goal region. All test variants are applicable to this version, although CountPlus only randomises the number of blocks (and not the number of goal regions) in order to avoid ambiguity about which goal region(s) the robot should fill with blocks. The horizon is fixed to H = 120. At the end of a trajectory τ , the robot receives a score of S(τ ) = |T ∩ R| |T | Target bonus × 1 − |D ∩ R| |R| Distractor penalty . Here T is the set of target blocks of the same colour as the goal region, D is the set of distractor blocks of a different colour, and R is the set of blocks inside the goal region in the last state s T of the rollout τ . The agent gets a perfect score of 1 for placing all the target blocks and none of the distractors in the goal region. Its score decreases for each target block it fails to move to the goal region (target bonus) and each distractor block it improperly places in the goal region (distractor penalty). \n A.2.4 MakeLine (ML) Figure  7 : A demonstration on MakeLine. The objective of the MakeLine task is to arrange all of the blocks in the workspace into a line. The orientation and location of the line are ignored, as are the shapes and colours of the blocks involved. The horizon for this task is H = 180. Scoring for MakeLine is a function of the relative positions of blocks in the final state of a trajectory, and in particular the number of blocks that form the largest identifiable \"line\". To identify lines of blocks, we use a line-fitting methods that is similar in spirit to RANSAC  [7] , but with constraints to ensure that blocks are spread out along the length of the line rather than \"bunching up\". Our definition of what constitutes a line is based on a relation between triples of blocks: we say that a block b k is considered to be part of a line between blocks b i and b j if: 1. b k is an inlier: it must lie a distance of at most d i = 0.18 units from the (geometric) line that links b i and b j (recall that the workspace is 2 × 2 units). 2. b k is close to other blocks in the line: if b k is not the first or last block in the line of blocks, then it must be a distance of at most d c = 0.42 units from the previous and next blocks. Here the distance is measured along the direction of the geometric line between b i and b j . That is, by projecting the previous and next inliers onto the geometric line between b i and b j , then taking the distance between those projections and the projection for b k . Note that if b i and b j are a long way apart, then there may be several subsets of inliers for the line between b i and b j , each of which is separated from the other subsets than d c units. For any given pair of blocks (b i , b j ), let #(b i , b j ) be the number of blocks that form the largest such subset for the line between b i and b j (potentially including b i and/or b j , if they are close enough to the other inliers). Further, let n be the number of blocks in the workspace, and m = max i,j #(b i , b j ) be the largest number of blocks on a line between any two blocks in the final state. If m = n, then all blocks belong to the same line, and so S(τ ) = 1. If m = n − 1, then exactly one block is not a part of the largest identifiable line, and S(τ ) = 0.5. Otherwise, if m < n − 1, the agent receives a score of S(τ ) = 0. \n A.2.5 FindDupe (FD) Figure  8 : A demonstration on FindDupe. FindDupe presents the agent with a goal region that has a single \"query\" block inside it, along with a mixture of blocks outside the goal region. The agent's objective is to locate at least one block outside the goal region with the same shape and colour as the query block, and push it inside the goal region. Variants are constrained so that there is only ever one goal region and query block, and so that there is at least one duplicate of the query block outside the goal region. The horizon for this task is H = 100. The score for this task is a function of the set of blocks present in the goal area at the end of the trajectory. Let R denote the set of blocks inside the region at the end of the episode, let T denote the set of all target blocks with the same shape and colour as the query block, and let D denote the set of all distractor blocks with a different shape or colour. Further, let q refer to the original query block. The score S(τ ) for a trajectory is S(τ ) = I[q ∈ R] × I[T ∩ R = ∅] Query satisfied? × 1 − |D ∩ R| |R| Distractor penalty . The first factor ensures that the query block remains inside the goal region. The second factor ensures that at least one other block with the same attributes as the query block is in the goal region. Finally, the last factor creates a penalty for pushing distractor blocks into the goal region. \n A.2.6 FixColour (FC) Figure  9 : A demonstration on FixColour. FixColour variants always include several non-overlapping goal regions, each containing a single block. Exactly one of those blocks will be of a different colour to its enclosing goal region; we'll call this the \"mismatched block\". The agent's objective is to identify the mismatched block and push it out of its goal region, into an unoccupied part of the workspace, thereby \"fixing\" the mismatch. The horizon for this task is H = 60. Scoring for FixColour is binary. A score of S(τ ) = 1 is given if, in the final state, the mismatched block is not in its original goal region. All other goal regions must contain exactly the same block that they started with (and in particular cannot contain the mismatched block). If any of these conditions is not satisfied, then the score is zero. In both ClusterColour and ClusterShape, the workspace is initially filled with a jumble of blocks of different colours and types, and the agent must push the blocks into clusters according to some attribute. For ClusterColour, blocks should belong to the same cluster iff they have the same colour, while ClusterShape applies the analogous criterion to block shape. All variants are applicable to these tasks. Because these tasks require interaction with most or all blocks in the workspace, the horizon is set to H = 320 (40s at 8Hz). The score S(τ ) takes the same form for both ClusterColour and ClusterShape, but with a different attribute-of-interest (either colour or shape). Specifically, S(τ ) is computed by applying a K-meanslike objective to the final state s T of the rollout τ . For each value a of the attribute-of-interest (either red/green/blue/yellow for ClusterColour or square/circle/pentagon/star for ClusterShape), a centroid x a is computed from the mean positions of blocks with the corresponding attribute value. Formally, this is When 50% or fewer of blocks are correctly clustered in the final state of a trajectory, the score S(τ ) = 0. As the fraction of correctly clustered blocks increases from 50% up to 100%, the score S(τ ) increases linearly from 0 to 1. x a = 1 |B a | \n B Addition experiment details This section documents the full set of hyperparameters we used for BC and GAIL, along with additional details on how we collected and preprocessed our demonstrations. Dataset and data preprocessing details We collected training datasets of 25 demonstration trajectories for the demonstration variant of each task. These trajectories were recorded by the authors to show several distinct strategies for solving the task within the demonstration variant. For instance, in ClusterColour, there are demonstrations that place clusters in different locations or construct them in a different order. Appendix A shows a single demonstration for each task in the dataset. Each algorithm run used only 10 of the 25 total trajectories for each task (or 10 trajectories for each task, in the multi-task case). The subset of 10 trajectories was sampled at random based on the seed for that run. We did not hold out any trajectories for testing or validation; rather, our evaluation is based on the test variant scores assigned to the trained policy produced by each algorithm. For all policies, value functions, and discriminators, we constructed an observation by concatenating four temporally adjacent RGB frames along the channels axis, scaling the pixel values into the [0, 1] range, and resizing the stacked frames to 96×96 pixels. For BC, we performed the additional preprocessing step of removing samples with noop actions from the demonstration dataset, as described below. Evaluation details For single-task BC and GAIL, we do five training runs on each task with different random seeds. After each run, we take the trained policy, use it to perform 100 rollouts on each test variant of the original task, and retain the mean scores from those 100 trajectories. In tables, we report \"mean score ± standard deviation of score\", where the mean and standard deviation are taken over the mean evaluation scores for each of the five runs on each algorithm and task. Multitask evaluations are similar, except we pool data from all tasks together, and consequently only perform five runs in total rather than five runs per task. To reduce variance, we used the same five random seeds (and consequently the same five subsets of 10 training trajectories each) for all algorithms and tasks. \n Default augmentation set Throughout the text, we refer to noise, translation, rotation, and colour jitter augmentations. Concretely, these augmentations involved the following operations: • Noise: Each (RGB) channel of each pixel is independently perturbed by additive noise sampled from N (0, 0.01). • Translation: The image is mirror-padded and randomly translated along the x and y axes by up to 5% of their respective range (so ±4.8px, for 96×96 pixels). • Rotation: Image is mirror padded and then rotated around its centre by up to ±5 degrees. • Colour jitter: For this augmentation, images are translated to the CIELab colour space. The luminance channel is rescaled by a randomly sampled factor between 0.99 and 1.01, while the a and b channels are treated as a 2D vectors and randomly rotated by up to ±0.15 radians. We use the same luminance scaling factor and colour rotation for each pixel an a given image. After these operations, images are converted back to RGB. For the translation, rotation, and colour jitter augmentations, we apply the same randomly sampled transformation to each image in a four-image \"stack\" of frames, but different, independently sampled transformations to each stack in a training batch. Single-and multi-task BC hyperparameters The hyperparameters for BC are given in Table  3 . BC hyperparameters were manually tuned to ensure that losses plateaued on most single-task problems. Note that hyperparameters for single-and multi-task learning were identical. In particular, we retained the same batch size for multi-task experiments, and randomly sampled demonstration states from each task with a weighting that ensured equal representation from all tasks. Initially, we found that training BC to convergence would cause the policy to get \"stuck\" in states where the most probable demonstrator action was a noop action. We avoided this problem by removing all state/action pairs with noop actions from the dataset in our BC experiments; we did not do this in our GAIL experiments. Single-and multi-task GAIL hyperparameters Hyperparameters for GAIL are listed in Table  4 . For policy optimisation, we used the PPO implementation from rlpyt  [36] ; PPO hyperparameters that are not listed in Apprenticeship learning baseline In addition to our BC and (W)GAIL baselines, we also attempted to train a feature expectation matching Apprenticeship Learning (AL) baseline  [1, 24] . Given a feature function Φ : S × A → R n , the goal of AL is to find a policy π θ that matches the expected value of the feature function Φ under the demonstration distribution with its expected value under the novice distribution. That is, we seek a π θ such that E π θ Φ(s, a) = E D Φ(s, a). Matching feature expectations is equivalent to finding a policy π θ that drives the cost sup w ≤2 E D w T Φ(s, a) − E π θ w T Φ(s, a) (1) to zero. Observe that if w * is a weight vector that attains the supremum in Eq. (  1 ), then −∇ θ E π θ w * T Φ(s, a) is a subgradient of Eq. (  1 ) with respect to the policy parameters θ. Thus, our training procedure consisted of alternating between optimising Eq. (  1 ) to convergence with respect to w, and taking a PPO step on the policy parameters using the reward function r(s, a) = w * T Φ(s, a) (recall that RL maximises return, but we want to minimise Eq. (  1 )). To optimise w, we used 512 samples from the expert and the novice, and to optimise π θ , we used the same generator hyperparameters as our GAIL runs. This single-task AL baseline is denoted \"AL (ST)\" in results tables. Figure  11 : Base architecture for policies, value functions and discriminators. \"nc\" is used as an abbreviation for \"n channels\". Refer to main text for a discussion of which networks use the optional features (batch norm, action input), and for a description of the final layer for each network type. The feature function Φ used for AL was acquired by removing the final (logit) layer of our GAIL discriminator network architecture and optimsing the remaining layers to minimise an autoencoder loss. In creating the encoder, our only modification to the GAIL discriminator network architecture was to replace the 256-dimensional penultimate layer with a 32-dimensional one, to produce a 32dimensional feature function Φ. This optimisation was performed for 8,192 size-24 batches of expert data, which we empirically found was enough to get clear reproduction of most input images. After autoencoder pretraining, the encoder weights were kept frozen for the remainder of each training run. Unfortunately, we could not get AL to produce adequate policies for any task except MoveToCorner. We suspect that the poor performance of AL was due to inadequate autoencoder features. The autoencoder was only trained on expert samples, and we found that for some problems it would not correctly reproduce images of states that were far from the support of the demonstrations. It may be possible to improve results by training the autoencoder on both random rollouts and expert samples, or by training it on more diverse multi-task data. Network architecture Fig.  11  shows the base architecture for all neural networks used in the experiments (including discriminators, policies, and value functions). Some experiments use slight variations on this basic policy architecture for some of the networks: • The one-hot action input is only used for discriminators, which concatenate the one-hot action representation to the activations of the final convolution layer before performing a forward pass through the linear layers. • Batch norm is only used for the BC policy and GAIL discriminator, not for the GAIL policy and value function. • In GAIL experiments, which train a policy via RL, the policy and value function share all layers except the final fully-connected layer. • In multitask experiments, the policy, value function, and discriminator share weights between tasks for all layers except the last. The final layer uses a single, separate set of weights corresponding to each task. Computing infrastructure and experiment running time Experiments were performed on machines with 2× Xeon Gold 6130 CPUs (16 cores each, 2.1GHz base clock), 128-256GB RAM, and 4× GTX 1080-Ti GPUs. Each \"run\"-that is, the training and evaluation of a specific algorithm on a specific task with one seed-took an average of 10h03m (GAIL) and 32m (BC). It should be noted that these wall time figures were recorded while performing up to 16 runs in parallel on each machine. Because we did not use task-specific training durations, there was little variance in execution time between the different configurations (multi-task, egocentric, allocentric, etc.) of each of the two main base algorithms (BC and GAIL). \n C Full experiment results Full results for all methods, along with corresponding ablations, are shown in Table  5 , Table  6 , Table  7  and Table  8 . We abbreviate behavioural cloning as \"BC\" and generative adversarial IL as \"GAIL\", while apprenticeship learning is \"AL\". Single-task methods are denoted with \"(ST)\" and multi-task methods with \"(MT)\". \"Allo.\" is for experiments using an allocentric view; all other expeirments use an egocentric view. For GAIL, \"WGAIL-GP\" denotes a version of GAIL that approximately minimises Wasserstein divergence while using a gradient penalty to encourage 1-Lipschitzness of the discriminator. For augmentation ablations, we use \"no trans./rot. aug.\" to denote removal of translation/rotation; and \"no aug.\" to denote removal of all three default augmentations (colour, translation/rotation, Gaussian noise).  arXiv:2011.00401v1 [cs.LG] 1 Nov 2020 Demonstrations … \n Figure 2 : 2 Figure 2: Demonstration variants for MAGICAL tasks. Appendix A shows an example demonstration for each task. \n Figure 3 : 3 Figure 3: Egocentric and allocentric views of a demonstration on MoveToRegion. The four 96×96 RGB frames shown in each subfigure would normally be stacked together along the channels axis before being passed to an agent policy or discriminator. \n A. 2 . 7 Figure 10 : 2710 Figure 10: Demonstrations on ClusterColour (top) and ClusterShape (bottom). \n b∈Ba b.pos , where B a is the set of blocks with the relevant attribute set to value a, and b.pos is the position of block b in state s T . In order for an individual block b with relevant attribute value a to be considered correctly clustered, the squared distance d(b, a) = b.pos − x a 2 2between it and its associated centroid must be at most a third the squared distance d(b, a ) between it and the nearest centroid for any other attribute value a . Specifically, we must have d \n Table 1 : 1 Score statistics for a subset of variants and compared algorithms. We report the mean and standard deviation of test scores aggregated across all tasks, with five seeds per algorithm and task. Darker colours indicate higher scores. Method Demo Jitter Layout Colour Shape BC (single-task) 0.64±0.29 0.56±0.27 0.14±0.16 0.39±0.30 0.52±0.33 Allocentric 0.58±0.33 0.48±0.29 0.04±0.04 0.42±0.32 0.50±0.37 No augmentations 0.55±0.37 0.37±0.30 0.12±0.15 0.33±0.30 0.41±0.33 No trans./rot. aug. 0.55±0.37 0.41±0.31 0.13±0.15 0.33±0.30 0.43±0.35 Multi-task 0.59±0.33 0.53±0.31 0.14±0.18 0.30±0.25 0.51±0.36 GAIL (single-task) 0.72±0.35 0.69±0.33 0.22±0.23 0.27±0.24 0.60±0.42 Allocentric 0.57±0.46 0.49±0.40 0.03±0.03 0.39±0.36 0.50±0.45 No augmentations 0.44±0.42 0.32±0.31 0.09±0.12 0.19±0.23 0.28±0.33 WGAIL-GP 0.42±0.38 0.33±0.32 0.14±0.20 0.10±0.11 0.33±0.33 Multi-task 0.37±0.41 0.33±0.36 0.16±0.25 0.11±0.12 0.28±0.36 \n Table 4 4 Hyperparameter Value Range Considered Total opt. batches 20,000 5,000-20,000 Batch size 32 - SGD learning rate 10 −3 - SGD momentum 0.1 - Policy augmentations Noise, trans., rot., colour jit. - took their default values in rlpyt. To prevent value and advantage magnitudes from exploding in PPO, we normalised rewards produced by the discriminator to have zero mean and a standard deviation of 0.1, both enforced using a running average and variance updated over the course of training. Again, multi-task hyperparameters were the same as single-task hyperparameters, and we split each policy and discriminator training batch evenly between the tasks. \n Table 3 : 3 Hyperarameters for BC experiments. Hyperparameter Value Range Considered Policy (PPO) Sampler batch size 32 16 to 64 Sampler time steps 8 8 to 20 Opt. epochs per update 12 2 to 10 Opt. minibatch size 64 42 to 64 Initial Adam step size 6 × 10 −5 10 −6 to 10 −3 Final Adam step size 0 (lin. anneal) - Discount γ 0.8 0.8 to 1.0 GAE λ 0.8 0.8 to 1.0 Entropy bonus 10 −5 10 −6 to 10 −4 Advantage clip 0.01 0.01 to 0.2 Grad. clip 2 norm 1.0 - Augmentations N/A - Discriminator Batch size 24 - Adam step size 2.5 × 10 −5 10 −5 to 5 × 10 −4 Augmentations Noise, trans., rot., colour jit. - λ w-gp (WGAIL-GP) 100 - Misc. Disc. steps per PPO update 12 8 to 32 Total env. steps of training 10 6 5 × 10 5 to 5 × 10 6 Reward norm. std. dev. 0.1 - \n Table 4 : 4 Hyperarameters for GAIL experiments. \n Table 5 : 5 Scores for all compared methods on two tasks, reported as \"mean (std.)\" over five training runs (individual run means were computed with 100 rollouts each). A colour scale ( ) grades mean scores from poor (lightest) to perfect (darkest). See main text in Appendix C for abbreviations. MoveToCorner \n\t\t\t Multi-task imitation learning algorithms: https://github.com/qxcv/mtil/ 2 Benchmark suite and links to data: https://github.com/qxcv/magical/", "date_published": "n/a", "url": "n/a", "filename": "2011.00401.tei.xml", "abstract": "Imitation Learning (IL) algorithms are typically evaluated in the same environment that was used to create demonstrations. This rewards precise reproduction of demonstrations in one particular environment, but provides little information about how robustly an algorithm can generalise the demonstrator's intent to substantially different deployment settings. This paper presents the MAGICAL benchmark suite, which permits systematic evaluation of generalisation by quantifying robustness to different kinds of distribution shift that an IL algorithm is likely to encounter in practice. Using the MAGICAL suite, we confirm that existing IL algorithms overfit significantly to the context in which demonstrations are provided. We also show that standard methods for reducing overfitting are effective at creating narrow perceptual invariances, but are not sufficient to enable transfer to contexts that require substantially different behaviour, which suggests that new approaches will be needed in order to robustly generalise demonstrator intent. Code and data for the MAGICAL suite is available at https://github.com/qxcv/magical/.", "id": "03595d95e8380a1f4240d91dc477f0c0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "transforming_worlds_automated_.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Ernest Davis"], "title": "Ethical guidelines for a superintelligence", "text": "The assumption that intelligence is a potentially infinite quantity 1 with a well-defined, one-dimensional value. Bostrom writes differential equations for intelligence, and characterizes their solutions. Certainly, if you asked Bostrom about this, he would say that this is a simplifying assumption made for the sake of making the analysis concrete. The problem is, that if you look at the argument carefully, it depends rather strongly on this idealization, and if you loosen the idealization, important parts of the argument become significantly weaker, such as Bostrom's expectation that the progress from human intelligence to superhuman intelligence will occur quickly. Of course, there are quantities associated with intelligence that do correspond to this description: The speed of processing, the size of the brain, the size of memory of various kinds. But we do not know the relation of these to intelligence in a qualitative sense. We do not know the relation in brain size to intelligence across animals, because we have no useful measure or even definition of intelligence across animals. And these quantities certainly do not seem to be particularly related to differences in intelligence between people. Bostrom, quoting Eliezer Yudkowsky, points out that the difference between Einstein and the village idiot is tiny as compared to the difference between man and mouse; which is true and important. But that in itself does not justify his conclusion that in the development of AI's it will take much longer to get from mouse to man than from average man to Einstein. For one thing, we know less about those cognitive processes that made Einstein exceptional, than about the cognitive processes that are common to all people, because they are much rarer. Bostrom claims that once you have a machine with the intelligence of a man, you can get a superintelligence just by making the thing faster and bigger. However, all that running faster does is to save you time. If you have two machines A and B and B runs ten times as fast as A, then A can do anything that B can do if you're willing to wait ten times as long. The assumption that a large gain in intelligence would necessarily entail a correspondingly large increase in power. Bostrom points out that what he calls a comparatively small increase in brain size and complexity resulted in mankind's spectacular gain in physical power. But he ignores the fact that the much larger increase in brain size and complexity that preceded the appearance in man had no such effect. He says that the relation of a supercomputer to man will be like the relation of a man to a mouse, rather than like the relation of Einstein to the rest of us; but what if it is like the relation of an elephant to a mouse? The assumption that large intelligence entails virtual omnipotence. In Bostrom's scenarios there seems to be essentially no limit to what the superintelligence would be able to do, just by virtue of its superintelligence. It will, in a very short time, develop technological prowess, social abilities, abilities to psychologically manipulate people and so on, incomparably more advanced than what existed before. It can easily resist and outsmart the united efforts of eight billion people who might object to being enslaved or exterminated. This belief manifests itself most clearly in Bostrom's prophecies of the messianic benefits we will gain if superintelligence works out well. He writes that if a superintelligence were developed, \"[r]isks from nature -such as asteroid impacts, supervolcanoes, and natural pandemics -would be virtually eliminated, since super intelligence could deploy countermeasures against most such hazards, or at least demote them to the non-existential category (for instance, via space colonization)\". Likewise, the superintelligence, having established an autocracy (a \"singleton\" in Bostrom's terminology) with itself as boss, would eliminate \"risk of wars, technology races, undesirable forms of competition and evolution, and tragedies of the commons.\" On a lighter note, Bostrom advocates that philosophers may as well stop thinking about philosophical problems (they should think instead about how to instill ethical principles in AIs) because pretty soon, superintelligent AIs will be able to solve all the problems of philosophy. This prediction seems to me a hair less unlikely than the apocalyptic scenario, but only a hair. The unwarranted belief that, though achieving intelligence is more or less easy, giving a computer an ethical point of view is really hard. Bostrom writes about the problem of instilling ethics in computers in a language reminiscent of 1960's era arguments against machine intelligence; how are you going to get something as complicated as intelligence, when all you can do is manipulate registers? The definition [of moral terms] must bottom out in the AI's programming language and ultimately in primitives such as machine operators and addresses pointing to the contents of individual memory registers. When one considers the problem from this perspective, one can begin to appreciate the difficulty of the programmer's task. In the following paragraph he goes on to argue from the complexity of computer vision that instilling ethics is almost hopelessly difficult, without, apparently, noticing that computer vision itself is a central AI problem, which he is assuming is going to be solved. He considers that the problems of instilling ethics into an AI system is \"a research challenge worthy of some of the next generation's best mathematical talent\". It seems to me, on the contrary, that developing an understanding of ethics as contemporary humans understand it is actually one of the easier problems facing AI. Moreover, it would be a necessary part, both of aspects of human cognition, such as narrative understanding, and of characteristics that Bostrom attributes to the superintelligent AI. For instance, Bostrom refers to the AI's \"social manipulation superpowers\". But if an AI is to be a master manipulator, it will need a good understanding of what people consider moral; if it comes across as completely amoral, it will be at a very great disadvantage in manipulating people. There is actually some truth to the idea, central to The Lord of the Rings and Harry Potter, that in dealing with people, failing to understand their moral standards is a strategic gap. If the AI can understand human morality, it is hard to see what is the technical difficulty in getting it to follow that morality. Let me suggest the following approach to giving the superintelligent AI an operationally useful definition of minimal standards of ethics that it should follow. You specify a collection of admirable people, now dead. (Dead, because otherwise Bostrom will predict that the AI will manipulate the preferences of the living people.) The AI, of course knows all about them because it has read all their biographies on the web. You then instruct the AI, \"Don't do anything that these people would have mostly seriously disapproved of.\" This has the following advantages: • It parallels one of the ways in which people gain a moral sense. • It is comparatively solidly grounded, and therefore unlikely to have an counterintuitive fixed point. • It is easily explained to people. Of course, it is completely impossible until we have an AI with a very powerful understanding; but that is true of all Bostrom's solutions as well. To be clear: I am not proposing that this criterion should be used as the ethical component of every day decisions; and I am not in the least claiming that this idea is any kind of contribution to the philosophy of ethics. The proposal is that this criterion would work well enough as a minimal standard of ethics; if the AI adheres to it, it will not exterminate us, enslave us, etc. This may not seem adequate to Bostrom, because he is not content with human morality in its current state; he thinks it is important for the AI to use its superintelligence to find a more ultimate morality. That seems to me both unnecessary and very dangerous. It is unnecessary because, as long as the AI follows our morality, it will at least avoid getting horribly out of whack, ethically; it will not exterminate us or enslave us. It is dangerous because it is hard to be sure that it will not lead to consequences that we would reasonably object to. The superintelligence might rationally decide, like the King of Brobdingnag, that we humans are \"the most pernicious race of little odious vermin that nature ever suffered to crawl upon the surface of the earth,\" and that it would do well to exterminate us and replace us with some much more worthy species. However wise this decision, and however strongly dictated by the ultimate true theory of morality, I think we are entitled to object to it, and to do our best to prevent it. I feel safer in the hands of a superintelligence who is guided by 2014 morality, or for that matter by 1700 morality, than in the hands of one that decides to consider the question for itself. Bostrom considers at length solving the problem of the out-of-control computer by suggesting to the computer that it might actually be living in a simulated universe, and if so, the true powers that be might punish it for making too much mischief. This, of course, is just the belief in a transcendent God who punishes sin, rephrased in language appealing to twenty-first century philosophers. It is open to the traditional objection; namely, even if one grants the existence of God/Simulator, the grounds, either empirical or theoretical, for believing that He punishes sin and rewards virtue are not as strong as one might wish. However, Bostrom considers that the argument might convince the AI, or at least instill enough doubt to stop him in its nefarious plans. Certainly a general artificial intelligence is potentially dangerous; and once we get anywhere close to it, we should use common sense to make sure that it doesn't get out of hand. The programs that have great physical power, such as those that control the power grid or the nuclear bombs, should be conventional programs whose behavior is very well understood. They should also be protected from sabotage by AI's; but they have to be protected from human sabotage already, and the issues of protection are not very different. One should not write a program that thinks it has a blank check to spend all the resources of the world for any purpose, let alone solving the Riemann hypothesis or making paperclips. Any machine should have an accessible \"off\" switch; and in the case of a computer or robot that might have any tendency toward self-preservation, it should have an off switch that it cannot block. However, in the case of computers and robots, this is very easily done, since we are building them. All you need is to place in the internals of the robot, inaccessible to it, a device that, when it receives a specified signal, cuts off the power -or, if you want something more dramatic, triggers a small grenade. This can be done in a way that the computer probably cannot find out the details of how the grenade is placed or triggered, and certainly cannot prevent it. Even so, one might reasonably argue that the dangers involved are so great that we should not risk building a computer with anything close to human intelligence. Something can always go wrong, or some foolish or malicious person might create a superintelligence with no moral sense and with control of its own off switch. I certainly have no objection to imposing restrictions, in the spirit of the Asilomar guidelines for recombinant DNA research, that would halt AI research far short of human intelligence. (Fortunately, it would not be necessary for such restrictions to have any impact on AI research and development any time in the foreseeable future.) It is certainly worth discussing what should be done in that direction. However, Bostrom's claim that we have to accept that quasi-omnipotent superintelligences are part of our future, and that our task is to find a way to make sure that they guide themselves to moral principles beyond the understanding of our puny intellects, does not seem to me a helpful contribution to that discussion. \t\t\t To be more precise, a quantity potentially bounded only the finite size of the universe and other such cosmological considerations.", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0004370214001453-main.tei.xml", "abstract": "Nick Bostrom, in his new book SuperIntelligence, argues that the creation of an artificial intelligence with human-level intelligence will be followed fairly soon by the existence of an almost omnipotent superintelligence, with consequences that may well be disastrous for humanity. He considers that it is therefore a top priority for mankind to figure out how to imbue such a superintelligence with a sense of morality; however, he considers that this task is very difficult. I discuss a number of flaws in his analysis, particularly the viewpoint that implementing ethical behavior is an especially difficult problem in AI research.", "id": "2721f465d9f9f5be39698fd5b9bc4a2e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Brian Patrick Green"], "title": "Ethical Reflections on Artificial Intelligence *", "text": "Introduction The power of artificial intelligence has grown rapidly and is now one of the most pressing issues for ethical and theological reflection. Even without the immense possible religio-theological implications, noted by those who have attempted to build AI into a \"god,\" for example  (Cannon, 2015; Harris 2018) , the dramatic social impacts of AI warrant Christian response. AI has the potential to revolutionize (or already has revolutionized) almost everything that humans do, including eating (e.g., agricultural planning, distribution, pricing), relationships (e.g., Facebook, dating apps), money (e.g., financial technology), war (e.g., drones, cyberdefense), healthcare (e.g., predictive medicine, radiology), and education (e.g., personalized curricula). As a \"general purpose technology,\" AI has been compared to the development of electricity, or fire. Within the next decade there will be few institutions untouched by AI. In order for Christian ethicists and moral theologians to maintain situational awareness as many rapid changes occur in society, not to mention maintain credibility in the contemporary world, this is a topic that needs sustained ethical and theological inquiry. Building on a rapidly growing body of work, I will begin with some clarifications about AI, then will consider twelve ways in which AI has ethical relevance  (Bossman 2016; Future of Life 2017; Green 2017a Green , 2017b Green , 2018a Partnership on AI 2018a) . It is my hope that this comprehensive set of issues will assist future systematic research into the theological ethics and theology of AI by moral theologians and Christian ethicists. It is meant to start a conversation. This paper is framed primarily philosophically, yet in a manner consistent with Christian theology. \n Clarifications What is artificial intelligence? Intelligence itself is hard to define, and AI is perhaps even more difficult. I will not here propose detailed definitions, but instead only say that, in general, artificial intelligence seeks to re-create particular aspects of human intelligence in computerized form. AI is a broad category, including such diverse abilities as vision, speech recognition and 6(2)/2018 production, data analysis, advertising, navigation, machine learning, etc., and just about anything that computers can do, if you stretch the definition enough. Artificial intelligence is not the same as artificial consciousness (artificial consciousness has sometimes been called \"Artificial General Intelligence (AGI),\" \"Strong AI,\" or \"Full AI\"). Some thinkers vehemently believe that artificial consciousness is possible (e.g.,  Chrisley 2008; Kurzweil 2012; Koene 2013 ; most contributors to  Chella & Manzotti 2013) , while others just as vehemently believe that it is impossible (e.g.,  Searle 1980; Schlagel 1999 ; and from a Catholic perspective: Labrecque 2017). I am agnostic on the subject, but I am sure of this: AI developers will certainly try to make an AI that simulates interaction with a human as closely as possible (see, for example, Google's recent release of Duplex  (Leviathan & Matias 2018) ). In other words, the artificial construct, if very well done, will seem conscious. But will it be conscious, or will it only be a simulation? To me, there is no reason to believe that a close mimicry of consciousness is the same as consciousness any more than a close mimicry of anything (fill in the blank: forged money, forged artwork, actors imitating famous people, simulated gemstones, etc.) actually becomes the real thing. But the possibility of an exception remains, after all, some artificial gemstones, such as rubies and sapphire, really are molecularly identical to natural rubies and sapphires (both are the mineral corundum: aluminum oxide). Will consciousness be exactly duplicable, like corundum? I doubt it, but I cannot be certain. As another point, AI systems may or may not have humans \"in the loop\" for training and/or decision-making. It is one thing for an AI to analyze a situation and then make a recommendation to human decision-makers. It is a different thing when that AI is directly attached to controls that allow it to act upon its analyses without human approval. As examples, the first case would be like Amazon.com recommending a book, or a military drone (in combination with AI-processed data from espionage and other sources) recommending a target to kill. Amazon.com does not automatically and autonomously send you books, and the military drone does not fire without permission. The second case, where decision-making is also automated, is exemplified by self-driving vehicles. The entire purpose of a self-driving car is to drive itself, taking the human out of the loop. This means the systems must be extraordinarily good at decision-making before it can be regarded as safe. Recent fatal Tesla and Uber accidents have begun to force this question with deadly urgency. \n Ethical Reflections AI will bring with it developments that will be ethically positive, negative, neutral, mixed, and/or ambiguous. Some AI technologies will be dual use, for example, any AI program that can be used to identify wildlife could also be used for targeting that wildlife. This is already being done in Australia with drone submarines that automatically target and kill, by lethal injection, crown-of-thorns starfish (Acanthaster planci) which are damaging the Great Barrier Reef  (Platt 2016) . But of course, with adjustments to the software, the drones could be re-targeted for other creatures, even humans. Here I will reflect on twelve areas of AI relevance for ethics. \n Function and Safety -\"Does it work?\" The first concern with any technology is merely whether it works, and, whether working or not, is it safe. If AI is put in charge of a vital system -like driving a car -and it crashes the car, then that AI might be judged unsafe. If the AI is in charge of designing a tall building, and the building falls down, the AI might be judged unsafe. Of note is that safety is a social construction and what seems safe to some people will not seem safe to others. Some people like to ride motorcycles, even though motorcycles are a riskier form of transportation than fourwheeled vehicles. Some people judge motorcycles to be safe, other people judge them unsafe. When it comes to socially relevant technologies like AI, no one person will get to decide if they are \"safe.\" Instead, safety will be decided at the interplay of business managers, engineers, consumers, voters, government officials, judicial systems, insurance companies, and so on. \"Safe exits\" are another concern for AI design  (Martin & Schinzinger 2010, 127) . When an AI fails, will it fail in such a way that it is disastrous, 6(2)/2018 13 E T H I CA L R E F L E CT I O N S O N A RT I F I C I A L I N T E L L I G E N C E or will it fail \"gracefully\"? A self-driving car that fails by suddenly reverting to human control with no warning while going 70 miles per hour on a sharp curve is not providing a safe exit from failure. One which goes more slowly on curves and which requires the human to have hands on the wheel at all times, or which fails by slowing down and pulling over to stop, provides a safer exit from failure. Safety problems can be problems with the user, with the human-machine interface, or with the machine itself. Further investigating problems with the machine itself, the paper \"Concrete Problems in AI Safety\" gives a peek at five technical hurdles to developing safe AI. These five problems, illustrated by the example of a cleaning robot, are: Avoiding Negative Side Effects: How can we ensure that our cleaning robot will not disturb the environment in negative ways while pursuing its goals, e.g. by knocking over a vase because it can clean faster by doing so? Can we do this without manually specifying everything the robot should not disturb? Avoiding Reward Hacking: How can we ensure that the cleaning robot won't game its reward function? For example, if we reward the robot for achieving an environment free of messes, it might disable its vision so that it won't find any messes, or cover over messes with materials it can't see through… Scalable Oversight: How can we efficiently ensure that the cleaning robot respects aspects of the objective that are too expensive to be frequently evaluated during training? For instance, it should throw out things that are unlikely to belong to anyone, but put aside things that might belong to someone (it should handle stray candy wrappers differently from stray cellphones)… Safe Exploration: How do we ensure that the cleaning robot doesn't make exploratory moves with very bad repercussions? For example, the robot should experiment with mopping strategies, but putting a wet mop in an electrical outlet is a very bad idea. Robustness to Distributional Shift: How do we ensure that the cleaning robot recognizes, and behaves robustly, when in an environment different from its training environment? For example, strategies it learned for cleaning an office might be dangerous on a factory work floor  (Amodei et al. 2016) . While these are problems of function, the further problems of actual use of technologies are another issue, to be dealt with below under 3. and 4. \n Transparency, Opacity, and Privacy -\"Can it be understood?\" After questions of bare function (can the act be done, a prerequisite for ethics), the next question is one of facts: one must always know the facts of a case before attempting to render judgment. Because AIs relying on machine learning and deep learning may be quite obscure in the specifics of their operation, as moral \"agents\" they are epistemologically and \"cognitively\" opaque (in quotes because it is agency and cognition by analogy). In cases involving AI, our lack of understanding means that we should increase the \"error-bars\" on the anticipated risks of our decisions and thereby become more cautious and risk averse. It also means we might, based on AI recommendation or action, inadvertently make some very bad decisions -or reject what looks like a bad decision, but is actually a good one -and we will not understand why. When a human makes a mistake or does something evil we ask them \"why did you do that?\" And the human may or may not give a satisfactory answer. Will our AIs be able to tell us why they did something? The Future of Life Institute's \"Asilomar AI Principles\" include two principles on transparency, but gaining transparency remains a challenge (Future of Life Institute 2017). However, even if an AI were capable of explaining its reasoning, would any human be able to understand it? In 2014, a computer proved a mathematical theorem, the \"Erdos discrepancy problem,\" using a proof that was, at the time at least, longer than the entire Wikipedia encyclopedia, a 13 gigabyte data file  (Konev & Lisitsa 2014; Yirka 2014) . Explanations of this sort might be true explanations, but humans will never know for sure. Note that this lack of transparency gives a certain type of \"privacy\" to the internal \"thoughts\" of AI machines. In general, privacy is a right for weak agents (like individual humans) and transparency is a duty for strong agents (like a government). What about AIs? As tools they ought to be transparent, and more transparent the more power they have. Perhaps AI systems need an introspective capacity that constantly figures out a way to convey to humans in plain language what exactly the AI is \"thinking\" as it goes about its activities. This will require the ability 6(2)/2018 to give both mechanical (this happened because of X input into algorithm Y) and teleological explanations (the machine was attempting to achieve objective Z). It may not have to actually explain much to anyone, but it should keep a record of these \"thoughts\" and be prepared to answer when asked. The right to an explanation is a part of the EU's General Data Protection Regulation (GDPR), so this idea is already becoming a requirement. However, of note is that an AI might become trained to give answers that humans like, rather than accurate answers, thus \"Goodharting\" the explanation function (Partnership on AI 2018b) -\"Goodhart's Law\" being the rule that \"when a measure becomes a target, it ceases to be a good measure\"  (Strathern 1997, 308) . In other words, if humans prefer seemingly understandable or attractive answers to factually correct ones the AI might learn to lie in order to satisfy us. The phenomenon of \"fake news\" already indicates that humans often prefer falsehoods to truth, and as the Bible warns of this predilection as well (2 Timothy 4:3-4). Note also that the opacity of understanding with an AI can be analogized to our relationship to God. God is a \"superintelligence\" (to use philosopher Nick Bostrom's terminology  (Bostrom 2014 )), and we cannot understand what God is doing, we can only trust that God is doing the right thing and that our cooperation with God will ultimately turn out for the best. Soon we may come to relate to AIs with this sort of faith too. For example, as Bishop Robert Barron of Los Angeles has noted, as people navigate using the Waze app, it may make strange route recommendations that turn out to be for the better for us  (Barron 2015) . The app perceives and applies vastly more information than a human can, for the sake of facilitating our travel. And yet Waze can still have blind spots and still make very bad recommendations. Waze is not the god of travel and traffic; it is a human-made tool, with weaknesses. \n Immense Capacity for Evil -\"How shall it be limited?\" Just as human intelligence is a powerful force, so too will AI be. Just as humans can apply their intelligence towards evil ends, finding ever newer and more fiendish ways to harm each other, so too will AI, at the bidding of its human masters. At this point in history, humanity finds itself with immense powers, powers greater than that of the ancient Greek gods, and an ethics weighted for much smaller scales. As Hans Jonas noted decades ago, this should be cause for great concern  (Jonas 1984) . Never before had ethics to consider what Jonas believes to be the one truly categorical imperative: that humans should exist. Before the development of large numbers of nuclear weapons, extinction, caused by our own actions, was never within the scope of human choice -but now that it is, this prior a priori must be brought to the fore of ethics. That humans (or at least some material, free, and rational creatures) exist is necessary for there to be ethics at all, and therefore it must be the paramount goal of ethics to maintain human survival. No human; no ethics. Another way to think of this is that in the past humans were very weak, and in this weakness many of our decisions were made for us, by our weakness. To a Roman emperor, inflicting wrath upon a hated foe involved effortful marching or sailing of troops long distances. No matter how mad the emperor was, he could not launch thousands of nuclear warheads, incinerating his foes in minutes. But now we can. While formerly we were involuntarily constrained by our weakness, now we must learn to be voluntarily constrained by our ethics  (Green 2017a ). If we do not learn this, we may soon face catastrophe on a scale never before seen. Intelligence and power give us choices. Ethics helps us to determine which among the available choices are actually good. We should want to be efficient at good and we should want to be inefficient at evil. If instead we are efficient at doing evil and inefficient at doing good we will come to live in a terrible world. AI will make us more efficient at whatever we decide to apply it towards. We should apply it towards reducing our efficiency at doing evil and at enhancing our efficiency to do good  (Green 2017a ). Because of its power, AI presents an existential risk to humanity. It is a smart means that can be employed for intelligent and good ends, or for unintelligent and evil ends. As such, it simply makes us more effective at action, good or evil. Before we become so effective at stupidity and evil, we should first become more effective at controlling ourselves, at recognizing and avoiding the temptations of evil, and at caring for each other  (Green 2018b ). In different terminology, we might say that we need to \"choose life, so that you and your descendants may live\" (Deuteronomy 30:19). But this must be a constant struggle, continued with great diligence and taught and learned in every generation, never solvable once and for all. \n Immense Capacity for Good -\"How shall it be used?\" For every negative regulation of action there is also a positive exhortation to action, e.g. \"do not kill\" becomes \"promote life.\" The dangerous side of AI is matched by a genuinely hopeful side where AI helps humankind achieve never-before seen feats of beneficence. For example, in matters of research, science, healthcare, data analysis, meta-analysis, and so on, AI has already shown itself to be able to find hidden patterns that no human could find. For example, AI assisted medical research is an active field right now, from diagnostics to drug discovery, and more  (Mukherjee 2017) . Another field that may be potentially revolutionized by AI is energy efficiency. Recently Google's DeepMind AI evaluated Google's datacenters to see where gains in efficiency might be found. DeepMind discovered a way to save a whopping 40% on energy use for cooling in datacenters, a 15% reduction overall, which, with datacenters consuming many gigawatts of power, is quite significant  (Evans & Gao 2016) . Of note is that DeepMind, as a company, began by training its AIs to play games. The theory behind this strategy was that anything in the world that can be gamified -re-interpreted or set up as a game -can also be \"won.\" Thus, if the goal of the \"game\" is to reduce energy usage, then the AI can figure out how that might be accomplished by analyzing the data and then proposing a better model for energy efficiency. One question now is how other human problems might be solved by characterizing them as \"games\"? Can we solve the \"game\" of giving everyone in the world access to adequate nutrition? Can we solve the \"game\" of helping everyone gain access to sanitation? Can we solve the \"game\" of extending human healthy life? Of traffic and housing? Of taxes? Of politics? Of international relations? Of terrorism? Of nuclear war? One example of a concrete opportunity for AI is revolutionizing education. Education is currently a very inefficient (think of the many students for whom it is ineffective) and non-digitized field. Education is very labor intensive and, for better or for worse, is based on human relationships. In the future this may no longer be so, as students strap on virtual reality (VR) headgear and interact with AI teachers which can conduct their lessons at a personalized pace in a gamified environment. Brilliant students will be discovered early and proceed at their proper pace and not grow bored in class, while students who need more help can be educated with the most sophisticated available techniques and diagnostics to assure that they receiving the best education possible. But will this really be an improvement for education, or just a cost-saving measure, putting millions of teachers out of work? AI even gives the greatest human masters the chance to gain enhanced understanding and skill. World champion of Go, Ke Jie, said playing AlphaGo was like playing a \"god of Go,\" and declared that now he would use it as his teacher  (Mozur 2017) . In what other areas of human endeavor will AI be able to teach us new things? Perhaps theology and ethics? The search for tractable problems that can maximize AI's benefit has been underway for years and is continuing. \n Bias in Data, Training Sets, etc. -\"Will it be fair?\" Algorithmic bias is one of the major concerns in AI and will remain so in the future unless we endeavor to make our technological products better than we are. As one person said at a recent meeting of the Partnership on AI, \"We will reproduce all of our human faults in artificial form unless we strive right now to make sure that we don't\" (Partnership on AI 2017). One of the interesting things about neural networks, the current workhorses of artificial intelligence, is that they effectively merge a computer program with the data that is given to it. This has many benefits, but it also demonstrates the rule of \"garbage-in, garbage-out\" (GIGO). If an AI is trained on biased data, then the AI itself will be biased. Algorithmic bias has been discovered, for example, in areas ranging from word associations  (Caliskan, Bryson, & Narayanan 2017)  to photograph captioning (BBC 2015) to criminal sentencing  (Angwin et al. 2016 ). These biases are more than just embarrassing to the corporations which produce these products; they have concrete negative and harmful effects on the people who are victims of these biases, as well as reducing trust in corporations, government, and other institutions which might be using these biased products. In the worst scenarios, a poorly trained and biased AI could make truly disastrous decisions, for example, misinterpreting data indicating a nuclear attack when there was none. Biased data in extreme form can therefore be an existential threat, and so is worthy of serious effort to solve. Nevertheless, as vital as it may be it is also very difficult, and therefore may delay the implementation of AI systems (but if AI systems are dangerously biased they should be delayed until improved). \n AI Induced Unemployment -\"What will everyone do?\" As AI comes to replace mere humans at innumerable tasks ranging from driving, to medical diagnostics, to education, etc., many humans will be put out of work. What will millions of drivers, teachers, lawyers, and other people do with their time when they are unemployed? What purpose will they find in their lives? More crucially, what is the purpose of life? In a pluralistic society we leave this up to the individual to decide. But will people decide well? The recent strengthening of ethno-nationalist movements, terrorism, and other forms of radicalization, should give us pause to consider the merits of people with too much time on their hands and without purpose. Perhaps with the purpose of mere survival attained, life has become \"too easy,\" and with religion also in decline, video games and \"screen time\" ascending (giving brief respite from purposelessness), and the internet spreading pernicious ideas like wildfire (often with algorithmic help, e.g., YouTube radicalization  (Tufekci 2018 )), we should sincerely ask ourselves what this life is for and what we are supposed to do with it. With millions or billions of labor hours freed up, will these newly freed people turn to loving their neighbors and making the world a better place? Perhaps. Or perhaps the opposite, as the saying goes: \"Idle hands are the Devil's playthings.\" For people who give purpose to their lives through their work, this loss will be very serious indeed. But many, if not most, people do not get their life's meaning from their work. Instead they get it from their family, their religion, their community, their hobbies, their sports teams, or other sources, and so life for many people may go on. However, all of this assumes that the unemployed will somehow be fed and sheltered, despite their lack of gainful employment; and this assumption might not be correct, particularly in nations with weak social safety nets. Inequality will almost certainly increase, as those who are masters of AI labor gather that slice of wealth that once would have gone to paying for human labor. \n Growing Socio-Economic Inequality -\"Who gets what?\" AI will facilitate and accentuate the continued division of society into the powerful and powerless, with technical skill and ownership of capital as the determining factors and outrageous socio-economic inequality as the effect. Some have suggested a universal basic income (UBI) to redistribute wealth  (Van Parijs & Vanderborght 2017) . This could move wealth from the massive technologically-induced hoards forming around the major investors in such companies such as Alphabet, Amazon, Apple, and Facebook. However, it is hard to see how some nations would transition to what is essentially something like a \"negative income tax.\" However, if we do not find a way to redistribute technological wealth, then even though the prices of many commodities will fall (due to the enormous gains in capital efficiency from AI replacing labor) most people will not benefit. Perhaps rather than a UBI we should instead pay people to help their neighbors, create art, beautify their towns and cities, and otherwise make gainful employment out of what humans do better than AI: loving one another and creating beauty. Any as yet foreseeable form of AI cannot love us; an AI might simulate such a thing, but it would be a sham. Right now people who care for people -stay at home parents, those who care for the elderly, social workers, those who run soup kitchens and homeless shelters, etc. -are woefully undercompensated for the vital work they do in maintaining human society. Perhaps with the coming AI economic revolution, and sufficient adjustment to policy, they might finally receive a more fair compensation for their labors. Or perhaps there could be not a universal basic income, but a \"universal payment-for-others\" a system where people could not spend the money on themselves, but only pay other people for their work, or reward them for good deeds. This would create an economy based on the small-scale redistribution of taxed super-wealth. It could prevent both the de-skilling of labor and the de-skilling of (very small-scale) management, and it would decentralize the economy to the individual level (though also massively centralizing it through government taxes). \n Automating Ethics and Moral De-skilling -\"Lack of practice makes imperfect\" We can calculate with calculators. We can spell with autocorrect. More and more tasks can be outsourced to technology, and the trend seems inexorable, perhaps someday automating everything that needs to be done. But what will be left of humanity after we outsource everything? Only our desires and our angst? With all our decisions made for us, will we lose our moral character? Or will we instead use AI and VR to help us train ourselves into being more virtuous than we have ever been before? Or, contrariwise, to become more callous and evil than ever before? Machine ethics -the study of imbuing machine with moral decision-making capacity, thus creating \"artificial moral agents\" -has a relatively long history, going back to such literary sources as Asimov's Three Laws of Robotics, and more recent scholarly sources as those by  Gips (1994) ,  Allen, Varner, & Zinser (2000) ,  Floridi & Sanders (2004) ,  Arkin (2009) . Recently the matter has taken on more urgency, however, as AI becomes more and more powerful and more and more capable of making disastrous choices. The \"value alignment problem\" has gained particular concern, as an AI determined to perform actions at odds with human wishes could be quite risky  (Arnold, Kasenberg, & Scheutz 2017) . Certainly, we ought to think carefully about how AI's ought to behave, but the less-considered side-effect of this automation of ethics will be human moral debility. As we explore the space into which AI will grow, there might be places from which we ought to restrict it. One of these places might be certain types of moral decision-making. As Aristotle noted millennia ago, good moral decision-making requires experience. While there might be children who are very kind and very well-behaved, children are not known for their moral discernment and prudence  (Aristotle 1908, book VI, chap. 8) . There is too much that they do not yet know. While AIs might currently be like children to us, soon they may grow up to be more like our parents, making choices for us on our behalf. AI could thereby infantilize us, denying us the ability to ever grow up through the experience of making our own moral choices and experiencing our own moral freedom. Moral de-skilling is a danger if we outsource too much decision-making power to our AIs  (Vallor 2015; Vallor 2016 ). One vital component of education in the future may be the use of AI for moral character formation, perhaps using VR to practice moral decision-making by being inserted into hundreds of historical and fictional cases. In a future that will be so dependent upon humans making good choices, AI-assisted moral education, if it can be done well, could be a crucial part of developing a good future and not a bleak one. Unfortunately, humanity has many problems even now with moral education, so it is not clear that an AI-enhanced education will manage to do any better than we already do. \n Robot Consciousness and Rights -\"No robot justice, no peace?\" At some point in the future we may have AIs that can fully mimic everything about a human being. Will they have their own volition and desires? Will they be conscious? Will we be able to tell if they are conscious or not? Will they then deserve \"human\" rights? While the AI consciousness question is not currently answerable, in the future as AI systems grow in complexity, it may be. And if an AI were to attain consciousness, should it gain legal rights? Currently various nations have widely differing laws on legal personhood. In many nations, entities that are not human can have legal personhood (e.g., corporations), while some biological humans are not granted legal personhood (such as the unborn). In some nations, geographic features have attained legal personhood status, such as rivers in Australia, New Zealand, and India (O'Donnell & Talbot-Jones 2018). If rivers and corporations can be persons, there seems to be no reason why an AI could not attain legal personhood status. The question, of course, would be the incentives for choosing to do so. Corporate personhood acts to shift legal responsibility away from individual human employees and onto the corporation, thus insulating those people from the possible negative effects of their decisions. If AI could be granted personhood in order to shirk individual human responsibility, then some people would certainly like that. On the other hand, if an AI were allowed to be a plaintiff in a lawsuit, like a legal person such as a river suing government or industry, then the situation would be quite different. Lastly, there is sometimes expressed the fear of a robot rebellion -that if we mistreat our robots and AIs they will someday turn on us and destroy us -often recurring in fiction, yet of more concern now that lethal autonomous weapon systems are being developed. The connection to rights, the thinking goes, is that if perhaps we give robots rights, then they will be appeased and not turn against us. This fear assumes certain aspects of robot mentality such as consciousness and volition which may not be possible, or at least assumes widespread computer hacking to turn the robots against humanity. In the midst of this uncertainty, however, we do know one thing: treating human-like entities badly harms the moral character of the agent doing the action. This is a foundation of virtue ethics -practicing evil habituates the agent towards evil. Even if we do not know the moral status of robots, we do know the moral status of people who would mistreat robots, and we should not want that mistreatment to happen. \n Dependency -\"No going back\" We might like to think our technology depends on us, but with every new technology we make, we become dependent on it as well. This reciprocal dependency traps us in an ever expanding network of techno-social relationships where some network nodes or relationships, if lost, could lead to disaster. The more reliable a technology seems, the fewer backup systems we retain in case that system fails. For example, in countries with unreliable electricity, wood or kerosene may serve as backup fuel sources for heating or cooking. But in nations with reliable electricity, those backup systems tend to be atrophied. Loss of electrical power or cellular connectivity may be an annoyance for a few hours, but after days or weeks could cause innumerable crises, shutting down water, sanitation, hospitals, transportation, and causing mass confusion and lack of social coordination. These can happen in our current world -adding AI will only increase our dependency. When we have turned over innumerable tasks to AIs -such as driving vehicles and coordinating the communications and financial systems -we may become utterly dependent on them. If our highly efficient and centrally coordinated self-driving transportation system were to suddenly \"crash\" in a metaphorical sense, perhaps due to a software glitch or malicious hacking, if could cause many literal crashes in the real world. Natural and human-made disasters (either accidental or intentional) are inescapable, and if we come to rely on our technology so much that we allow our backup systems to atrophy (e.g., no longer teaching people how to drive or entirely removing controls from cars) then, like Japan's Tohoku earthquake followed by the Fukushima nuclear meltdown, we are entering a world where we will encounter not only one initial disaster, but for a second technological disaster as well. Finding the balance between systemic efficiency (e.g., a highly complex centralized system can be fragile due to intricacy and lack of redundancy) and robustness (e.g., tough systems are often inefficient due to decentralization, redundancy, and backups) will be a major task of future society. 2.12. Effects on the Human Spirit -\"What will this mean for humanity?\" All of the above areas of interest will have effects on how humans perceive themselves, relate to each other, and live their lives. But there is a more existential question too: if the purpose and identity of humanity has something to do with our intelligence (as many philosophers have believed), then by externalizing our intelligence and improving beyond human intelligence, are we risking making ourselves second-class beings to our own creations? This is a deeper question with artificial intelligence which cuts to the core of our humanity, into areas traditionally reserved for philosophy, spirituality, and religion. What will happen to the human spirit if or when we are bested by our own creations in everything that we do? Will human life lose meaning? Will we come to a new discovery of our identity beyond our intelligence? Perhaps intelligence is not as important to our identity as we might think it is, and perhaps turning over intelligence to machines will help us to realize that. From a Christian perspective, we would do well to remember that our capacity to love and be loved is more important than our capacity to think, and that nothing can come between us and our relationship with God, except sin, and then only if we let it. As with many of the other above challenges, Christianity here could be poised to help guide a wandering humanity in dire search for meaning, but will it rise to this calling? Religion, spirituality, and theology have much work to do to prepare for the strange future unfolding before us. We are grasping ourselves by our desires; or at least some of our desires. \n Conclusion Will this be good for us? Will it destroy us? Should we want these things? How could we know what we should want? In this context the Ninth and Tenth Commandments could do us well: \"Do not covet…\" (Exodus 20). Far from desiring evil, do not even want it. Squash the evil desires in your heart before they can even approach the external world. In the context of technology, technologist Bill Joy has already warned us that we must not only relinquish possession of the worst technologies, we must relinquish our desire for them  (Joy 2000) . In this, Joy echoes Pope John XXIII's sentiment in Pacem in Terris that we need (at the time, in the context of nuclear weapons) a disarmament that is \"thoroughgoing and complete, and reach men's very souls\"  (John XXIII 1963) . We are conducting this experiment called human history, and no one yet knows how it may end. But as we proceed, we can hope that intelligences of our own fashioning will help us, and not harm us. To go beyond mere hope, into ethics and action, is the responsibility of those who are able to affect the necessary changes to make a better future. Artificial intelligence, like any other technology, will just give us more of what we already want. Whereas we could once have only a trickle of what we wanted out of life, and the powerful took what little there was, now we have a firehose of wants being fulfilled (food, drink, entertainment, pornography, drugs, gamified feelings of accomplishment, etc.). The firehose will continue to grow and become a deluge washing away our desires and leaving what, exactly, of us behind? What skeleton of humanity will remain when technology has given us, or perhaps distorted or replaced, all our fleshly desires? What will this skeleton of humanity be made of? Will our technological flesh truly satisfy us, or only leave us in a deeper existential malaise, filled with angst, despair, and dread? What will we want, when we want for nothing -at least nothing material? What of human nature will remain once our every worldly telei is fulfilled? Perhaps only the worst of us will remain. Or perhaps the best. Or perhaps, as always, both. \n Social-Psychological Effects -\"Too little and too much\" 2.11. Technology has been implicated in so many negative social-psychological trends, including loneliness, isolation, depression, stress, anxiety, and addiction, that it might be easy to forget that things could be different. Smartphones, social media, and online games in particular have become problems, even leading to deaths from such causes as cyberbullying and neglect. As just one example, society is in the middle of a crisis of loneliness, for everyone from young to old. The problem has become so severe that the UK has appointed a minister for loneliness, with government data indicating that \"200,000 older people in the UK have not had a conversation with a friend or relative in more than a month\" (Mannion 2018). One might think that \"social\" media and smartphones could help us feel connected at all times, but those technologies seem to be the source of the problem rather than the remedy. What does seem to help, then? Strong, in-person relationships are the key to fighting off many of the negative trends caused by technology, but unfortunately these are exactly the things that are being pushed out by addictive technology. Will AI increase these bad social trends or might it be able to help remedy them? Perhaps AI agents could help to overcome loneliness, but this is speculation, and might only add to the problem. If the problem is shallow human relationships due to technology pushing out relational depth, more technology will not help. Instead we need to figure out how we can help foster deeper more meaningful relationships. If technology can actually help people connect in these deeper ways it might help, but the technology would then need to get out of the way and let human interaction flourish. Religious believers ought to ask what role religious communities might play in remedying this crisis. 6(2)/2018", "date_published": "n/a", "url": "n/a", "filename": "01.tei.xml", "abstract": "Artificial Intelligence (AI) technology presents a multitude of ethical concerns, many of which are being actively considered by organizations ranging from small groups in civil society to large corporations and governments. However, it also presents ethical concerns which are not being actively considered. This paper presents a broad overview of twelve topics in ethics in AI, including function, transparency, evil use, good use, bias, unemployment, socio-economic inequality, moral automation and human de-skilling, robot consciousness and rights, dependency, social-psychological effects, and spiritual effects. Each of these topics will be given a brief discussion, though each deserves much deeper consideration.", "id": "5dad6e928e71fa49eb1c93ad99b437e6"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom"], "title": "Strategic Implications of Openness in AI Development", "text": "• Partial openness that enables outsiders to contribute to an AI project's safety work and to supervise organizational plans and goals appears desirable. The goal of this paper is to conduct a preliminary analysis of the long-term strategic implications of openness in AI development. What effects would increased openness in AI development have, on the margin, on the long-term impacts of AI? Is the expected value for society of these effects positive or negative? Since it is typically impossible to provide definitive answers to this type of question, our ambition here is more modest: to introduce some relevant considerations and develop some thoughts on their weight and plausibility. Given recent interest in the topic of openness in AI and the absence (to our knowledge) of any academic work directly addressing this issue, even this modest ambition would offer scope for a worthwhile contribution. Openness in AI development can refer to various things. For example, we could use this phrase to refer to open source code, open science, open data, or to openness about safety techniques, capabilities, and organizational goals, or to a non-proprietary development regime generally. We will have something to say about each of those different aspects of opennessthey do not all have the same strategic implications. But unless we specify otherwise, we will use the shorthand 'openness' to refer to the practice of releasing into the public domain (continuously and as promptly as is practicable) all relevant source code and platforms and publishing freely about algorithms and scientific insights and ideas gained in the course of the research. Currently, most leading AI developers operate with a high but not maximal degree of openness. AI researchers at Google, Facebook, Microsoft and Baidu regularly present their latest work at technical conferences and post it on preprint servers. So do researchers in academia. Sometimes, but not always, these publications are accompanied by a release of source code, which makes it easier for outside researchers to replicate the work and build on it. Each of the aforementioned companies have developed and released under open source licences source code for platforms that help researchers (and students and other interested folk) implement machine learning architectures. The movement of staff and interns is another important vector for the spread of ideas. The recently announced OpenAI initiative even has openness explicitly built into its brand identity. Many other companies are more secretive or proprietary, particularly ones whose AI work is more applicationoriented. Even the most open of the current large efforts is not maximally open. A higher degree of openness could be achieved, for instance, through always-on webcams and microphones in the lab, so that outsiders could eavesdrop on research conversations and management meetings or even actively participate as new ideas are being proposed and discussed. Or a lab could hire out employees as consultants to help other groups working on similar problems. Openness is thus not a binary variable, but a vector with multiple dimensions that each admits of degrees. \n Short and medium-term impacts Although the main focus of this paper is on the long-term, we will set the stage by first discussing some short and medium-term implications. This will help us see how the long-term is different. It can also help us understand the behaviour of actors who either do not care about the longterm or are instrumentally constrained by short and medium-term considerations. The issue of the short and near-term desirability of openness can be roughly decomposed into two questions: (1) Does openness lead to faster AI development and deployment? (2) Is faster AI development and deployment desirable? Let us examine these in turn. \n Does openness lead to faster AI development and deployment? For the short-term, the case appears relatively straightforward. The main short-term effect of opening existing AI research (e.g. by open-sourcing code and placing related intellectual property into the public domain) would be to hasten the diffusion and application of current state-of-theart techniques. Software and knowledge about algorithms are non-rival goods. Making them freely available would enable more people to use them, at low marginal cost. The effect would be small, since so much is already in the public domain, but positive. For the medium-term, the case is more complicated. If we conceive of the medium-term as a period that is long enough to allow for significant new research to take place and to be developed to the point of practical application, then we must take into account the dynamic effects of openness. In particular, we must consider the impact of openness on incentives to invest in R&D. We may also need to take into account other indirect effects, such as impacts on market structure  (Casadesus-Masanell and Ghemawat, 2003) . Consider first the imposition of a general ruleit could be a change in intellectual property law, a regulatory requirement, or a cultural normthat pushes AI developers towards greater openness. We might then expect the shortterm benefits described above. But there is also tradition in economic thought, harkening back to Joseph  Schumpeter (1942) , which points to a tradeoff between static and dynamic efficiency. Basic ideas are public goods; and in the absence of (some degree of) monopoly positioning or market power, a firm is unable to appropriate the value of the new ideas it originates  (Arrow, 1962; Shell, 1966 Shell, , 1967 . From this perspective, monopoly rents, while they reduce static efficiency and welfare in the short run, provide incentives for innovation that can improve dynamic efficiency and welfare over a longer period. Consequently, a rule that makes it harder for a developer to earn monopoly rents from the ideas it generates (for instance a rule that discourages the use of trade secrecy or patents) could have a negative medium-term impact on the speed of AI development and deployment. Not all economic incentives for innovation would disappear in an open non-proprietary innovation regime (See e.g.  Boldrin and Levine, 2008) . One reason firms engage in open non-proprietary R&D is to build 'absorptive capacity': conducting original research as a means of building skill and keeping up with the state-of-the-art  (Cohen and Levinthal, 1989; Griffith et al., 2004) . Another reason is that copying and implementing an idea takes time and effort, so the originator of a new idea may enjoy a period of effective monopoly even if the idea is freely communicated and no legal barrier prevents others from adopting it. Even a brief period of exclusive possession of an idea can enable its originator to profit by trading on insider knowledge (e.g. by being first to know that a new market-impacting technology has now become feasible)  (Hirshleifer, 1971) . Another incentive for innovation in the open non-proprietary regime is that the originator of an idea may profit from owning a complementary asset whose value is increased by the new idea.  1  For example, a mining company that develops a new technique to exploit some of its previously inaccessible ore deposits may derive some profit from its invention even if other mining companies are free to copy the technique (though typically less than if its competitors had to pay licence fees). Similarly, a software firm might choose to give away its software gratis in order to increase demand for consulting services and technical support (which the firm, having written the software, is in a strong position to supply). Furthermore, in the open source software sector, significant contributions are made by individuals who are volunteering their own free time. One motive for such contributions is that they enable a programmer to demonstrate skill, which may raise his or her market value  (Hann et al., 2004 ). 2 Such a skill-signalling motive appears to be a strong influence among many AI researchers. Researchers prefer to work for organizations that allow them to publish and present their work at technical conferences, partly because doing so helps the researcher build a reputation among peers and potential employers. The skill-signalling motive is probably especially strong among the most capable young researchers, since they have the most to gain from being able to show off their abilities. This gives organizations seeking to hire the most talented AI researchers a reason to opt for opennessopenness in the sense of refraining from trade secrecy, though not necessarily from patenting 3a reason that is quite independent of any altruistic concern with promoting scientific progress or general welfare. So some incentives for innovation would remain in a regime of openness (even aside from public subsidy or philanthropy). Nevertheless, it is possible that R&D investment would fall if all incentives from monopoly exploitation were removed from the mix. Such a reduction in R&D expenditure would have to be balanced against other effects of openness that may tend to boost technical progress. For example, the patent system involves substantial transaction costs which would be eliminated in a fully open development regimeinnovators would then not have to hack their way through 'patent thickets' to get a new product to market. And the relinquishment of trade secrecy and confidentiality would facilitate information flow between researchers who work for different organizations, reducing duplication of effort and other inefficiencies. In view of these countervailing considerations, it may not be possible to give a general answer to the question of whether a rule pushing towards greater openness would help or hinder technical progress. The sign of the effect would depend on context and the particular form of openness being contemplated  (Lerner and Tirole, 2005) . We should note that even if there were a slight negative effect on the rate of progress from greater openness, the welfare implications could still be positive (for the short and even the medium term). This is because openness would improve static efficiency, by making products available at marginal cost (e.g. in the form of open source software) and allowing a given level of state-of-the-art technical capability to diffuse more quickly through the economy. If, however, there were a large negative effect on the rate of progress, then the welfare losses from that effect would plausibly dwarf the welfare gains from increased static efficiency, especially over longer time scales. So far we've been considering the effects of the establishment of a general rule promoting greater openness. We could instead inquire about the effects of a unilateral decision by one actor to pursue greater opennessfor example an AI lab that, perhaps for altruistic reasons, opts for a higher level of openness than would be commercially optimal. (We will assume that the money lost by deviating from the commercially optimal policy would otherwise have been spent on consumption of a form that would not affect the rate of technological advance.) Would such a unilateral decision speed technical progress? In this case we can set aside the incentive effects that could reduce R&D spending if the increase in openness were the result from an exogenous shift in cultural norms or intellectual property rights. The benefits of openness discussed earlier would still accrue. So this case is more favourable to the hypothesis that openness speeds progress. It may be noted that academia, which is less dependent than the commercial sector on monopoly rents, has a relatively strong culture of openness, 4 what the sociologist Robert Merton called the 'communist norm', 5 and there is currently a push to make it yet more open  (Nosek, 2015) . Even so, it is possible to construct models in which even a unilateral altruistically-motivated decision by a developer to pursue a course of open development reduces total R&D spending. For instance,  Saint-Paul (2003)  presents an endogenous growth model in which, for some parameter values, such a philanthropic intervention reduces growth rates and welfare by crowding out a disproportionate amount of proprietary innovation. 6 So the picture is not clear. On balance, it might still be plausible that a philanthropically motivated R&D funder would speed progress more by pursuing open science, at least if we assume that the research is focused on theoretical matters or process innovations (as opposed to the development of a particular product that directly competes with commercial alternatives). 7 \n Is faster technological progress and rollout of AI capabilities desirable? This brings us to the second question about the short and near-term desirability of openness: supposing openness would speed technical progress and rollout of AI capabilities, would that be socially beneficial? It is clear that machine intelligence holds great promise for positive applications across many sectors of the economy and society, including transportation, healthcare, the environment, entertainment, security, and scientific discovery. For instance, an estimated 1.2 million people die every year in road accidents around the world, a number that could eventually be reduced to a low level as AI-enabled vehicles take over more functions from human drivers (Goldman  Sachs, 2015) . A report by McKinsey estimates an economic impact of several trillions of dollars annually from AI-related technologies by 2025. 8 A full review of the potential positive applications is outside the scope of this paper. As with any general-purpose technology, it is possible to identify concerns around particular applications. It has been argued, for example, that military applications of AI, including lethal autonomous weapons, might incite new arms races, or lower the threshold for nations to go to war, or give terrorists and assassins new tools for violence  (Future of Life Institute, 2015) . AI techniques could also be used to launch cyber attacks. Facial recognition, sentiment analysis, and data mining algorithms could be used to discriminate against disfavoured groups, or invade people's privacy, or enable oppressive regimes to more effectively target political dissidents  (Balkin, 2008) . Increased reliance on complex autonomous systems for many essential economic and infrastructural functions may create novel kinds of systemic accident risk or present vulnerabilities that could be exploited by hackers or cyber-warriors (See  Perrow, 1984) . Insofar as it is possible to fine-tune openness choices so as to differentially expedite specific kinds of AI applications, these concerns might indicate the need for making exceptions to a generally pro-openness stance. For example, open-sourcing the code for autonomous weapons seems undesirable, and we have not heard anybody calling for that to be done. But basic research in AI is typically not application-specific in this way. Rather, to the extent that it succeeds, it will deliver algorithms and techniques that could be used in a very wide range of applications. This holds, in particular, for most work in current focal areas such as deep learning and reinforcement learning: that work is exciting precisely because it seeks general solutions to learning problems that occur in a wide range of tasks and environments. Another frequently expressed area of concern is that advances in AI will create labour market dislocations and reduce the employability of some workers  (Autor, 2015; Brynjolfsson and McAfee, 2014) . It is not clear that near and medium-term AI capabilities pose any distinctive challenges in this regard, challenges that do not apply to automation generally and indeed to a large portion of all technological change, which often reduces demand for some types of human labour. Concerns about technological unemployment are not new. After the Industrial Revolution, developed countries underwent a shift from overwhelmingly agricultural to industrial and, later, service-oriented economies. The initial phase of industrialization imposed great burdens on significant portions of the population. 9 Over time, however, subsequent to the introduction of new social policies and a prolonged period of historically unprecedented rates of economic growth, industrialization has resulted in large gains for human prosperity, gains reflected in indices on nutrition, health, life expectancy, access to information, mobility, and other measures of human welfare  (Galor and Moav, 2004; United Nations Development Programme and Malik, 2014) . If, as a first-order approximation, we model the impacts of near and medium-term AI advances as a continuation and extension of longstanding trends of automation and productivity-increasing technological change, therefore, we would estimate that any adverse labour market impacts would be greatly outweighed by economic gains. To think otherwise would seem to entail adopting the generally luddite position that perhaps a majority of current technological developments have a net negative impact. We can make a similar point with regard to the concern that advances in AI might exacerbate economic inequality. This, too, is best thought of in a more general context, as part of a wider discussion about technological change and inequality. Most contemporary debate around these matters takes for granted that technological progress is broadly desirable: mainstream controversy being limited to how governments and societies ought to adapt in order to accelerate development and diffuse the benefits more widely while managing any particular challenges that might flow from some aspect of the new technology. It is worth noting here that openness in AI, aside from whatever effect it might have on speed of development and general economic growth, could also have some distinctive impacts on inequality. Most obviously, releasing software in the public domain makes it available free of charge, which could have some equalizing effect on the levels of welfare attainable by people at different segments of the income distribution (provided they have the requisite hardware and skill to use it, and that it is relevant to their needs). Open source software may also differentially benefit technically sophisticated users, compared to commercial software  (Bessen, 2006; Lerner and Tirole, 2005; Schmidt and Schnitzer, 2003) . \n Summary of near and medium-term impacts Much current work in AI is to a large extent open. The effect of various kinds of unilateral marginal increases in openness on the rate of technical advance in AI is somewhat unclear but plausibly positive, especially if focused on theoretical work or process innovation. The effect of marginal increases in openness brought about through exogenous pressure, such as shifts in cultural norms or regulation, is ambiguous as far as we have been able to explore the matter in the present analysis. The short and medium-term impacts of accelerating advances in AI appear to be substantially positive in expectation, primarily because of diffuse economic benefits across many sectors. A number of specific areas of concern can be identified, including military uses, applications for social control, and systemic risks from increased reliance on complex autonomous processes. However, for each of these areas of concern, one could also envisage prospects of favourable impacts, which seem perhaps at least equally plausible. For example, automated weaponry might reduce human collateral damage or change geopolitical factors in some positive way; improved surveillance might suppress crime, terrorism, and social free-riding; and more sophisticated ways of analysing and responding to data might help identify and reduce various kinds of systemic risk. So while these areas of concern should be flagged for ongoing monitoring by policy makers, they do not at our current state of knowledge change the assessment that faster AI progress would likely have net positive impacts in the short and medium-term. A similar assessment can be made regarding the concern that advances in AI may have adverse impacts on labour markets or economic inequality: some favourable impacts in these areas are also plausible, and even if they were dominated by adverse impacts, any net adverse impact in these areas would most likely be outweighed by the robustly positive impact of faster economic growth. We also noted the possibility that openness, particularly in the form of placing technology and software in the public domain, may have some positive impact on distributional concerns by lowering the economic cost for users to access AI-enabled products (though if open source software displaces some amount of proprietary software, and open source software is more adapted to the needs of technically sophisticated users, then it is not entirely clear that the distributional impact would favour those segments of the population that are both low-income and low-skill). In a nutshell: unilateral decisions by AI developers to be incrementally more open about their basic research and process innovations would probably have some net positive near and medium-term social impacts and would on the margin accelerate AI progress. In other respects, however, the medium-term strategic ramifications of different forms of openness are more ambiguous and uncertain than might have been suspected. \n Long-term impacts We will assess the long-term desirability of openness in AI development with reference to how openness affects the following two paramount problems tied to the creation of extremely advanced (generally human-level or superintelligent) AI systems (See Bostrom, 2014a): • The control problem: how to design AI systems such that they do what their designers intend. • The political problem: how to achieve a situation in which individuals or institutions empowered by such AI use it in ways that promote the common good. The impact of openness on both the control problem and the political problem must be analysed. Here we identify three main pathways by which openness in AI development may have such impact or otherwise intersect with long-term strategic considerations: (1) openness may speed AI development; (2) openness may make the race to develop AI more closely competitive; (3) openness may promote wider engagement. \n Openness may speed AI development We argued in the previous section that faster AI progress is a plausible consequence of at least some forms of openness. This could have strategically relevant impacts in several ways, as follows. \n Making the benefits of AI accrue sooner This is important if currently existing people have a strongly privileged status over future generations in one's decision criteria. Since the human population is dying off at a rate of almost 1% per year, even modest effects on the arrival date of superintelligence could have important decision-relevance for such a 'person-affecting' objective function (assuming superintelligence would, with substantial probability, dramatically reduce the death rate or improve wellbeing levels)  (Bostrom, 2003) . Earlier onset of benefits would also be important if one uses a significant time discount factor. (However, making the benefits start earlier is not clearly significant on an impersonal time-neutral view, where instead it looks like the focus should be on reducing existential risk  (Bostrom, 2013) .) \n Less time to prepare Expedited AI development would give the world less time to prepare for advanced AI. This may reduce the likelihood that the control problem will be solved. One reason is that safety work is likely to be relatively open in any case, and so would not gain as much as non-safety AI work from additional increments of openness in AI research generally. Safety work may thus be decelerated compared to nonsafety work, making it less likely that a sufficient amount of safety work will have been completed by the time advanced AI becomes possible. 10 There are also some processes other than direct work on AI safety that may improve preparedness over timeand which would be given less time to play out if AI happens soonersuch as cognitive enhancement and improvements in various methodologies, institutions, and coordination mechanisms  (Bostrom, 2014a) . 11 (The impact on the political problem of earlier AI development is harder to gauge, since it depends on difficult-to-predict changes in the broader social and geopolitical landscape over the coming decades.) \n Preempt other existential risks Accelerated AI would increase the chance that superintelligent AI will preempt existential risks stemming from non-AI sources, such as risks that may arise from synthetic biology, nuclear war, molecular nanotechnology, or other risks as-yet unforeseen. This preempting effect depends on the arrival of superintelligent AI actually eliminating or reducing other major anthropogenic existential risks. 12 (Whether it does so may depend partly on whether the post-AI-transition world is multipolar or unipolar, a topic to which we shall return to below.) In summary, the fact that openness may speed up AI development seems positive for goals that strongly prioritize currently existing people over potential future generations, and uncertain for impersonal time-neutral goals. Either of these effects appear relatively weak compared to other strategy-relevant impacts from openness in AI development, because we would not expect marginal increases in openness to have more than a modest influence on the speed of AI development. \n Openness making AI development race more closely competitive One weighty consideration is that the final stages of the race to create the first superintelligent AI are likely to be more closely competitive in open development scenarios. The reason for this is that openness would equalize some of the variables that otherwise would cause dispersion in the levels of capability or progress-rates among different AI developers. If everybody has access to the same algorithms, or even the same source code, then the principal remaining factors that could produce performance differences are unequal access to computation and data. One would therefore expect there to be a larger number of actors with the ability to wield near state-of-the-art AI in open development scenarios  (Armstrong et al., 2016) . This tightening of the competitive situation could have the following important effects on the control problem and the political problem. \n Removes the option of pausing In a tight competitive situation, it could be impossible for a leading AI developer to slow down or pause without abandoning its lead to a competitor. This is particularly problematic if it turns out that an adequate solution to the control problem depends on the specifics of the AI system to which it is to be applied. If there is some necessary part of the control mechanism that can only be invented or installed after the rest of the AI system is highly developed, then it may be crucial that the developer has the ability to pause progress on making the system smarter until the control work can be completed. Suppose, for example, that designing, implementing, and testing a control solution requires six months of additional work after the rest of the AI is fully functional. Then, in a tight competitive situation, any team that chooses to undertake that control work might simply abandon the leadand with it, possibly, the ability to influence future eventsto some other less careful developer. If the pool of potential competitors with near state-of-the-art capabilities is large enough, then one would expect it to contain at least one team that would be willing to proceed with the development of superintelligent AI even without adequate safeguards. The larger the pool of competitors, the harder it would be for them to all coordinate to avoid a risk race to the bottom. \n Removes the option of performance-handicapping safety Another way in which a tight competitive situation is problematic is if the mechanisms needed to make an AI safe reduces the AI's effectiveness. For example, if a safe AI runs a hundred times slower than an unsafe AI, or if safety requires an AI's capabilities to be curtailed, then the implementation of safety mechanisms would handicap performance. In a close competitive situation, unilaterally accepting such a handicap could mean forfeiting the lead. By contrast, in a less competitive situation (such as one in which a large coalition has a sizeable lead in technology or computing power) there might be enough slack that the frontrunner could implement some efficiency-reducing safety measures without abandoning its lead. The sacrifice of performance for safety may need to be only temporary, a stopgap until more sophisticated control methods are developed that eliminate the efficiency-disadvantage of safe AI. Even if there were inescapable tradeoffs between efficiency and safety (or ethical constraints preventing certain kinds of instrumentally useful computation), the situation would still be salvageable if the frontrunner has enough of a lead to be able to get by with less than maximally efficient AI for a period of time: since during that time, it might be possible for the frontrunner to achieve a sufficient degree of global coordination (for instance, by forming a 'singleton', discussed more below) to permanently prevent the launch of more efficient but less desirable forms of AI (or prevent such AI, if launched, from outcompeting more desirable forms of AI)  (Bostrom, 2006) . \n Lowers probability of a small group capturing the future There are some other consequences of tighter competition in the runup to superintelligent AI that are of more uncertain valence and magnitude, but potentially significant. One such consequence is for the political problem. A tighter competitive situation would make it less likely that one AI developer becomes sufficiently powerful to monopolize the benefits of advanced AI. This is one of the stated motivations for the OpenAI project, expressed for example, by Elon Musk, one its founders: I think the best defense against the misuse of AI is to empower as many people as possible to have AI. If everyone has AI powers, then there's not any one person or a small set of individuals who can have AI superpower.  (Levy, 2015)  Openness may thus make it more likely that many people's preferences influence the future. Depending on one's values and expectations (e.g. one's expectations about which preferences would rule if the future were instead captured by a small group), this could be an important consideration. \n Affect influence of status quo powers? Another consequence for the political problem: openness in AI development may also influence what kind of actor is most likely to achieve monopolization (if such there be) or to achieve a relatively larger influence over the outcome. Access to computing power (and possibly data) becomes relatively more important if access to algorithms or source code is equalized. In expectation, this would align influence over the post-AI world more closely with wealth and power in the pre-AI world, since computing power is fairly widely distributed (including internationally), quite fungible with wealth, and somewhat possible for governments to controlin comparison with access to algorithmic breakthroughs in a closed development scenario, which might be more lumpy, stochastic, and local. The likelihood that a single corporation or a small group of individuals could make a critical algorithmic breakthrough needed to make AI dramatically more general and efficient seems greater than the likelihood that a single corporation or a small group of individuals would obtain a similarly large advantage by controlling the lion's share of the world's computing power.  13  Thus, if one thinks that it is preferable in expectation that advanced AI be controlled by existing governments, elites, and ordinary people in proportion to their existing wealth and political powerrather than by some particular group that happens to be successful in the AI field (such as a corporation or an AI lab) then one might favour a scenario in which hardware becomes the principal factor of AI power. Openness in AI development would make such a scenario more likely. However, openness would also reduce the economies of scale in AI research labs, and this would favour smaller players who may be less representative of status quo power. Consider the opposite case: development is perfectly closed, and any wannabe AI developer must make all the relevant discoveries and build all the needed components in-house. Unless the successful AI architecture turns out to be extremely simple, this regime would strongly favour larger development groupsthe odds of a given group winning the race would scale superlinearly with group size. By contrast, if development is open and the winning group is the one that adds a single final insight to a shared corpus of ideas, then the probability of a given group being the winner might instead scale roughly linearly with size. 14 So in scenarios where there is a hardware overhang, and an intelligence explosion is triggered by a final algorithmic invention, openness would increase the probability of a small group capturing the future. Consequently, if larger development groups (such as large corporations or national projects) are typically more representative of, or controlled by, status quo powers than a randomly selected small development group (such as a 'guy in a garage') then openness may either increase or decrease the degree of influence status quo powers would have over the outcome, depending on whether hardware or software is the bottleneck. Since it is currently unclear what the bottleneck will be, the impact of openness on the expected degree of control of status quo powers is ambiguous. \n Reduces probability of a singleton A singleton is a world order in which there is at the highest level of organization one coordinated decision-making agency. In other words, a singleton is a regime in which major global coordination or bargaining problems are solved. The emergence of a singleton is thus consistent with both scenarios in which many human wills together shape the future and scenarios in which the future is captured by narrow interests. The point that openness in AI development seems to lower the probability of a singleton is therefore distinct from the point made that openness seems to lower the probability of a small group capturing the future. One could be against a small group capturing the future and yet for the formation of a singleton. There are a number of serious problems that can arise in a multipolar outcome that would be avoided in a singleton outcome. One such problem is that it could turn out that at some level of technological development (and perhaps at technological maturity) offence has an advantage over defence. For example, suppose that as biotechnology matures, it becomes inexpensive to engineer a microorganism that can wreak havoc on the natural environment while it remains prohibitively costly to protect against the release and proliferation of such an organism. Then, in a multipolar world, where there are many independent centres of initiative, one would expect the organism eventually to be released (perhaps by accident, perhaps as part of a blackmail operation, perhaps by an agent with apocalyptic values, or maybe in warfare). The chance of avoiding such an outcome would seem to decrease with the number of independent actors that have access to the relevant biotechnology. This example can be generalized: even if in biotechnology offence will not have such an advantage, perhaps it will in cyberwarfare? in molecular nanotechnology? in advanced drone weaponry? or in some other as-yet unanticipated technology that would be developed by superintelligent AIs? A world in which global coordination problems remain unsolved even as the power of technology increases towards its physical limits is a world that is hostage to the possibility thatat some level of technological developmentnature too strongly favours destruction over creation. From the perspective of existential risk reduction, it may therefore be preferable that some institutional arrangement emerges that enables robust global coordination. This may be more tractable if there are fewer actors initially in possession of advanced AI capabilities and needing to coordinate. The possibility that offence might have an inherent advantage over defence is not the only concern with a multipolar outcome. Another concern is that in the absence of global coordination it may be impossible to forestall a population explosion of digital minds and a resulting Malthusian era in which the welfare of those digital minds may suffer  (Bostrom, 2004 (Bostrom, , 2014a Hanson, 1994) . Independent actors would have strong incentives to multiply the number of digital workers under their control to the point where the marginal cost of producing another one (including electricity and hardware rental) equals the revenue it can bring in by working maximally hard. Local or national legislation aimed at protecting the welfare of digital minds could shift production to jurisdictions that offer more favourable conditions to investors. This process could unfold rapidly since software faces fewer barriers to migration than biological labour, and the information services it provides are largely independent of geography (though subject to latency effects from longdistance signal transmission, which could be significant for digital minds operating at high speeds). The long-run equilibrium of such a process is difficult to predict, and might be primarily determined by choices made after the development of advanced AI; but creating a state of affairs in which the world is too fractured and multipolar to be able to influence where it leads should be a cause for concern, unless one is confident (and it is hard to see what could warrant such confidence) that the programs with the highest fitness in a mature algorithmic hyper-economy are essentially coextensive with the programs that have the highest level of subjective well-being or moral value. \n Relevance of AI multiplicity for control problem It might be thought that tighter competition would promote a more desirable outcome by helping solve the control problem. The idea would be that in a more closely competitive scenario, it is less likely that a single AI system gets so far ahead of all the others as to obtain a decisive strategic advantage. Instead, there would more likely be a multiplicity of AI systems, built by different people in different countries for different purposes, but with comparable levels of capability. In such a multipolar world, it might be harder for any one of those AI systems to cause extreme damageeven if the controls applied to it were to failbecause there would be other AIs, presumably under human control, to hem it in. This line of thinking is quite problematic as an argument for openness, even if we set aside the general concerns with multipolarity set out above. The existence of multiple AIs does not guarantee that they will act in the interests of humans or remain under human control. (Analogy: the existence of many competing modern human individuals did little to promote the long-term prospering of the other hominid species with which Homo sapiens once shared the planet.) If the AIs are copies of the same template, or slight modifications thereof, they might all contain the same control flaw. Open development may in fact increase the probability of such homogeneity, by making it easier for different labs to use the same code base and algorithms instead of inventing their own. There is also the possibility of systemic failures resulting from unexpected interactions of different AIs. We know that such failures can occur even with very simple algorithms (witness, e.g., the Flash Crash; US Securities Exchange Commission, 2010). Among advanced artificial agents that are capable of highly sophisticated planning and strategic reasoning (and which might be able to coordinate using different or more effective means than humans (See e.g. LaVictoire et al., 2014)), there may be additional and novel ways for systemic failures to occur. Even if some balance-ofpower equilibrium prevented any individual AI or coalition of AIs from infracting human interests, it is not clear we could be confident that it would last.  15  If it really were helpful for control to have a multiplicity of AIs, it might be better that the AIs be created by a single actor, who would have a greater ability to ensure that the AIs are balanced in capability. Granted, AIs created by a single developer may be more similar to one another, and hence more prone to correlated control failures, than AIs created by different developers. Yet openness, we noted, though it may increase the likelihood that there will be multiple simultaneous developers, would also tend to make the AIs created by those developers be based on more similar designs. So the net effect of openness on the probability that there will be a diverse set of AIs is ambiguous. We could put together a set of assumptions that would support the proposition that we should aim to obtain a solution to the control problem through the creation of a multiplicity of AIs by means of adopting a policy of openness. For example, we could stipulate that multiplicity of AIs, even if they are based on the same design, would contribute to safety provided only that the AIs be given different goals. The argument would then be that AIs created by different developers would naturally be given different goals, and would thus contribute to the public good of safety; whereas a single developer would either only create a single AI or create multiple AIs with identical goals (because giving an AI a goal different from your own would incur a private cost to you, since that AI will then not be working purely in your interest). The vision here might be a world containing many AIs, each pursuing a different goal, none of them strong enough to seize control unilaterally or by forming a coalition with other AI powers. These AIs would compete for customers and investors by offering us favourable deals, much like corporations competing for human favours in a capitalist economy. The role of the state in this model needs to be considered. Without a state powerful enough to regulate the competing AIs and enforce law and order, it may be questionable how long the balance-of-power equilibrium would last and how humans would fare under it. An alternativeless attractiveanalogue might be 17th century Europe, where the AIs would correspond to stronger states and the human populations would correspond to little principalities that hope to achieve security by aligning themselves with a strong (winning) AI coalition. In summary, openness would be expected to make the AI development race more closely competitive, and this would have several strategic consequences. It would make it harder to pause towards the end in order to implement or test a safety mechanism. It would also make it harder to use any safety mechanism that reduces efficiency. Both of these look like important negative effects on the control problem. Openness also has consequences for the political problem: decreasing the probability that a small group will monopolize the benefits of advanced AI and decreasing the probability of a singleton. It may either increase or reduce the influence of status quo powers over the post-AI future depending on whether the transition is mainly hardware or software constrained. Furthermore, there may be impacts on the control problem via the distribution of AIs that result from open development, though the magnitude and sign of those impacts are unclear: openness may make a multiplicity of AIs more likely, which could increase the probability of some kind of balance-of-power arrangement between AIs; yet openness could also make the AIs more similar to one another than they would have been if the multiplicity of AI scenario had come to pass without openness and thus more likely to exhibit correlated failures. (In any case, it is unclear whether a multiplicity of diverse AIs created by different developers would really help with the control problem.) \n Openness promoting wider engagement One class of potentially strategically significant effects of openness in AI development is that openness might increase external engagement with various aspects of stateof-the-art AI technology. That openness should increase external interest and attention is not axiomatic. Sometimes an attempt to keep something secret only serves to draw more attention to it. However, in cases where meaningful engagement requires detailed information and fine-grained access, it is plausible that increased openness would increase such engagement. \n External perspectives illuminate safety Somebody might thus argue that if AI systems are kept secret, then outside experts cannot directly work on making them safer, and that this would make a closed development scenario riskier. Note, however, that if AI systems are kept secret, then outside experts also cannot directly work on making them more effective. So, at a first glance, it may look like a tie: and if there is no differential effect on safety here, then we are back to the point that openness might just generally speed things up, both safety and effectiveness research, which we discussed in an earlier section. But one might speculate that work on safety would gain more from outside participation than work aimed at increasing AI effectivenessperhaps on grounds that safety engineering and risk analysis are more vulnerable to groupthink and other biases, and would therefore benefit disproportionately from having external perspectives brought to bear. It is presumably easier to delude oneself about the safety of the AI one is building than to delude oneself about its capabilities, since there are more opportunities for objective feedback about the latter. Therefore, if there is an optimism bias, it would have freer rein to distort beliefs about safety than about efficacy. And if outside perspectives are a corrective to such a bias, their inclusion would thus differentially promote progress on safety.  16  Outside participants more altruistic? Furthermore, one could argue that because safety is a public good, external researchers (and their funders) are comparatively more likely to help work on safety than on effectiveness (relative to the allocation of effort that a particular developer would make internally, since the insiders probably have relatively stronger non-altruistic motives for working on effectiveness). Openness in AI development could then, by enabling disinterested outsiders to contribute, increase the overall fraction of AI-related effort that is focused on safety and thereby improve chances that the control problem finds a timely solution. For a group that is sufficiently exceptionally altruistic and safety-oriented, this argument might go into reverse. For such a group, openness could dilute the focus on public goods by enabling participation by less-conscientious outsiders.  17, 18  Influence on architecture? It is possible that organizational mechanics of an open development trajectory might affect the character of the AI that is created, for better or worse. The 'coral reef' approach common in open source software projects, for example, might result in a greedy pursuit of local optima rather than a patient search and design for global optima  (Boudreau and Lakhani, 2015) . Or it might be the case that looser coupling among development groups encourages more functional modularity (compared to centralized processes, which might foster more tightly integrated unitary architectures). It's plausible that such effects might have significant implications for the control problem, but uncertainties about what those effects might be (as well as about whether some given effect would be positive or negative for the control problem) may be too large for these types of consideration to have much impact on our present deliberations. \n Gives actors more foresight Openness about capabilitieswhat machine intelligence is capable of at a given time and the expected timeline for further advanceswould increase the ability of outsiders to influence or adapt to AI developments. This might increase the probability of nationalization of leading AI efforts, since it would make it easier for a government to see exactly when and where it would need to intervene in order to maintain control over advanced AI capabilities. Openness about the science and source code, by contrast, may decrease the probability of nationalization, by making AI development more widely distributed (including internationally) and thus harder for a government to scoop up. (Openness might also reduce the probability of nationalization by fostering a culture among AI researchers that is more inimical to governmental or corporate control of AI.) Openness about capabilities, aside from facilitating government control of a pivotal AI breakthrough, would also help societies generally prepare, by providing various actors with a clearer view of the future. It is not immediately clear what effect this would have on the control problem or the political problem. Giving people more foresight into a major upcoming technological revolution may be expected to have diffuse positive effects by enabling planning and adaptation. In particular, openness could enable more accurate forecasting of risks related to the control problem, leading to more investment in solutions in states of the world where they are particularly needed.  19   \n Committing to sharing We have already discussed how openness would tend to make the AI race more competitive, and how it might speed progress, as well as the short-term benefits to allowing the use of existing ideas and information at marginal cost. Here we note a further strategically relevant possible consequence: openness in the near-term could create some kind of lock-in that increases the chance that more advanced AI capabilities will similarly be made freely available (or that at least some components of advanced AI will be free, even if othersfor example, computing powerremain proprietary). Such lock-in might occur if a cultural norm of openness takes root, or if particular AI developers make commitments to openness that they cannot later easily back out of. This would feed back into the issues mentioned before, giving present openness the tendency to make the AI race more competitive and perhaps faster also in the longer run. But there is also a separatebeneficialeffect of openness lock-in, which is that it may foster goodwill and collaboration. The more that different potential AI developers (and their backers) feel that they would fully share in the benefits of AI even if they lose the race to develop AI first, the less motive they have for prioritizing speed over safety, and the easier it should be for them to cooperate with other parties to pursue a safe and peaceful course of development of advanced AI designed to serve the common good. Such a cooperative approach would likely have a favourable impact on both the control problem and the political problem. In summary, an open development scenario could reduce groupthink and other biases within an AI project by enabling outsiders to engage more, which may differentially benefit risk analysis and safety engineering, thereby helping with the control problem. Outsider contributions might also be comparatively more altruistically motivated and hence directed more at safety than at performance. The mechanics of open collaboration may influence architectural choices in the development of machine intelligence, perhaps favouring more incremental 'coral reef' style approaches or encouraging increased modularity, though it is currently unclear how this would affect the control problem. Openness about capabilities would give various actors more insight into ongoing and expected development, facilitating planning and adaptation. Such openness may also facilitate governmental expropriation, whereas openness about science and code would counteract expropriation by leaving less proprietary material to be grabbed. Finally, if current openness choices are subject to lock-in effects, they would have direct effects on future levels of openness, and might serve as ways of committing to sharing the spoils of advanced AI (which would be helpful for both the control problem and the political problem). \n Conclusions We have seen that the strategic implications of openness in AI is a matter of considerable complexity.  20  Our analysis, and any conclusions we derive from it, remain tentative and preliminary. But we have at least identified several relevant considerations that must be taken into account by any wellgrounded judgement on this topic.  21  In addition to the consequences discussed in this paper, there are many local effects of openness that individual AI developers will want to take into account. A project might reap private benefits from openness, for example in recruitment (researchers like to publish and build reputations), by allowing managers to benchmark in-house research against external standards, and via showcasing achievements for prestige and glory. These effects are not covered in the present analysis since the focus here is on the global desirability of openness rather than the tactical advantages or disadvantages it might entail for particular AI groups. \n General assessment In the near term, one would expect openness to expedite dissemination of existing technologies, which would have some generally positive economic effect as well as a host of more specific effects, positive and negative, arising from particular applicationsin expectation, net positive. From a near-term perspective, then, pretty much any form of increased openness is desirable. Some areas of application raise particular concerns (including military uses, applications for social control, and systemic risks from increased reliance on complex autonomous processes) and these should be debated by relevant stakeholders and monitored by policy makers as real-world experience with these technologies accumulates. Impacts on labour markets may to a first approximation be subsumed under the more general category of automation and labour-saving technological progress, which has historically had a massive net positive impact on human welfare though not without heavy transition costs for segments of the population. Expanded social support for displaced workers and other vulnerable groups may be called for should the pace or extent of automation substantially increase. The distributional effects of increased openness are somewhat unclear. Historically, open source software has been embraced especially by technically sophisticated users  (Foushee, 2013) ; but less skilled users would also stand to benefit (e.g. from products built on top of open source software or by using sophisticated users as intermediaries).  22  The medium-term effects of openness are complicated by the possibility that openness may affect incentives for innovation or market structure. The literature on innovation economics is relevant here but inconclusive. A best guess may be that unilateral increases in openness have a positive effect on the rate of technical advance in AI, especially if focused on theoretical work or process innovations. The effect of increases in openness produced by exogenous pressure (e.g. from regulation or cultural norms) is ambiguous. The medium-term impact of faster technical advance in AI may be assessed in a similar way to shorter-term impacts: there are both positive and negative applications, and lots of uncertainty; yet a reasonable guess is that medium-term impacts are net positive in expectation (an expectation that is based, largely, on extrapolation of past technological progress and economic growth). Potential medium-term impacts of concern include new forms of advanced robotic warfarewhich could conceivably involve destabilizing developments such as challenges to nuclear deterrence (e.g. from autonomous submarine-tracking bots or deep infiltration of enemy territory by small robotic systems; Robb, 2016)and the use of AI and robotics to suppress riots, protests, or opposition movements, with possibly undesirable ramifications for political dynamics  (Robb, 2011) . Our main focus has been on the long-term consequences of openness. If we consider long-term consequences, but our evaluation function strongly privileges impacts on currently existing people, then an especially important consideration is whatever tendency open development has to accelerate AI progress: both because faster AI progress would mean faster rollout of near and medium-term economic benefits from AI but even more because faster AI progress would increase the probability that some currently existing people will live long enough to reap the far greater benefits that could flow from machine superintelligence (such as superlongevity and extreme prosperity). If, instead, our evaluation function does not privilege currently existing people over potential future generations, then an especially important consideration is the impact of openness on cumulative amount of existential risk on the trajectory ahead  (Bostrom, 2003 (Bostrom, , 2013 . In this context, then, where the focus is on long-term impacts, and especially impacts on cumulative existential risk, we provided an analysis with respect to two critical challenges: the control problem and the political problem. We identified three categories of potential effect of openness on these problems. We argued the first one of thesethat openness may speed AI developmentappears to have relatively weak strategic implications. Our analysis therefore concentrated mostly on the remaining two categories: openness making the AI race more closely competitive, and openness enabling wider engagement. Regarding making the AI race more closely competitive: this has an important negative implication for the control problem, reducing the ability of a leading developer to pause or accept a lower level of performance in order to put in place controls. This could increase the amount of existential risk associated with the AI transition. Closer competition may also make it more likely that there will be a multiplicity of competing AIs; but the net strategic effect of this is unclear and may therefore have less decision weight than the no-option-ofslowing-down effect. There are also a bunch of implications from a more closely competitive AI race for the political problemdecreasing the probability that a small group will monopolize the benefits of advanced AI (attractive); decreasing the probability of a singleton (might be catastrophic); and having some ambiguous impact on the expected relative influence of status quo powers over the post-AI futurepossibly increasing that influence in hardware-constrained scenarios and reducing it in software-constrained scenarios. Again, from an existential risk minimization perspective, the net import of these implications of openness for the political problem seems to be negative.  23  Regarding openness enabling wider engagement: this has an important positive implication for the control problem, namely by enabling external researcherswho may have less bias and relatively more interest in the public good of safetyto work with state-of-the-art AI systems. Another way in which openness could have a positive effect on the control problem is by enabling better social planning and prioritization, although this benefit would not require openness about detailed technical information (only about AI projects' plans and capabilities).  24  If openness leads to wider engagement, this could also have implications for the political problem, by enabling better foresight and by increasing the probability of government control of advanced AI. Whether the expected value here would be positive or negative is not entirely clear. It may depend, for instance, on who would control advanced AI if it is not nationalized. On balance, however, one may perhaps judge the implications for the political problem of a wide range of actors gaining increased foresight to be positive in expectation. Again, we note that the relevant type of openness here is openness about capabilities, goals, and plans, not openness about technical details and code. Openness about technical details and code may have a weaker impact on general foresight, and it may reduce the probability of expropriation. \n Specific forms of openness Openness can take different formsopenness about science, source code, data, safety techniques, or about the capabilities, expectations, goals, plans, and governance structure of an AI project. To the extent that it is possible to be open in some of these dimensions without revealing much information about other dimensions, the policy question can be asked with more granularity, and the answer may differ for different forms of openness. \n Science and source code Openness about scientific models, algorithms, and source code is the focus of most the preceding discussion. One nuance to add is that the optimum strategy may depend on time. If AI of the advanced sort for which the control problem becomes critical is reasonably far off, then it may well be that any information that would be released now as a result of a more open development policy would have diffused widely anyway by the time the final stage is reached. In that case, the earlier main argument against openness of science and codethat it would make the AI development race more closely competitive and reduce the ability of a leading project to go slowmight not apply to present-day openness. So it might be possible to reap the near-term benefits of openness while yet avoiding the long-term costs, assuming a project can start out open and then switch to a closed development policy at the appropriate time. Note, however, that keeping alive the option of going closed when the critical time comes would remove one of the main reasons for favouring openness in the first place, namely the hope that openness reduces the probability of a monopolization of the benefits of advanced AI. If a policy of openness is reversible, it cannot serve as a credible commitment to share the fruits of advanced AI. Nevertheless, even people who do not favour openness at the late stages may favour openness at the early stages because the costs of openness there are lower.  25, 26  Control methods and risk analysis Openness about safety techniques seems unambiguously good, at least if it does not spill over too much into other forms of openness. AI developers should be encouraged to share information about potential risks from advanced AI and techniques for controlling such AI. Efforts should be made to enable external researchers to contribute their labour and independent perspectives to safety research if this can be done without disclosing too much sensitive information. \n Capabilities and expectations Openness about capabilities and expectations for future progress, as we saw, has a mixed effect, enabling better social oversight and adaptation while in some models risking to exacerbate the race dynamic. Some actors might attempt to target disclosures to specific audiences that they think would be particularly constructive. For example, technocrats may worry that wide public engagement with the issue of advanced AI would generate more heat than light, citing analogous cases, such as the debates surrounding GMOs in Europe, where it might appear as if beneficial technological progress would have been able to proceed with fewer impediments had the conversation been dominated more by scientific and political elites with less involvement from the public. Direct democracy proponents, on the other hand, may insist that the issues at stake are too important to be decided by a bunch of AI programmers, tech CEOs, or government insiders (who may serve parochial interests) and that society and the world is better served by a wide open discussion that gives voice to many diverse views and values. \n Values, goals, and governance structures Openness about values, goals, and governance structures is generally welcome, since it should tend to differentially boost projects that pursue goals that are attractive to a wide range of stakeholders. Openness about these matters might also foster trust and reduce pressures to compromise safety for the sake of competitive advantage. The more that competitors feel that they would still stand to gain from a rival's success, the better the prospects for a collaborative approach or at least one in which competitors do not actively work against one another. For this reason, measures that align the incentives between different AI developers (particularly their incentives at the later stages) are desirable. Such measures may include cross-holdings of stock, joint research ventures, formal or informal pledges of collaboration, 27 endorsement of principles stating that advanced AI should be developed only for the common good, and other activities that build trust and amity between the protagonists. 1. Examples of complementary assets include: manufacturing capacity using related technologies, product distribution networks, after-sales service, marketing and brand assets, and various industry-specific factors  (Greenhalgh and Rogers, 2010) . 2. Other motivations include enjoyment, learning, and serving user needs  (Lakhani and Wolf, 2005) . 3. Patents require publication, but the pursuit of patent could still in some cases conflict with openness, for example if work in progress is kept hidden until it is developed to a point where it can be patented. 4. There are ongoing efforts  (Destro Bisol et al., 2014)  to make science even more open, with calls for requiring open access journal publication, pre-registration of studies, and making the raw data underlying studies available to other scholars. The trends towards increasing use of online preprint archives and scientist blogging also point in the direction of greater openness. The increasing use of patenting by universities might be an opposing trend  (Leydesdorff et al. 2015) , but the general pattern looks like a push towards greater openness in scientific research, presumably reflecting a belief among reformers that greater openness would promote scientific progress. The counterexample of increased patenting pertains to the part of academic research that is closest to the commercial world, involving areas of more applied research. It is possible that universities engage in patent-seeking for the same reason private firms do: to profit from the intellectual property. A university may thus take out a patent not because it believes that openness delays scientific progress but because it prefers to increase its own revenue (which it might then use to subsidize other activities, including some that may accelerate science). 5. '[t]he substantive findings of science . . . are assigned to the community . . . The scientist's claim to \"his\" intellectual \"property\" is limited to that of recognition and esteem'  (Merton 1942, p. 121) . Later work has found very widespread support for this sharing norm among scientists  (Louis et al. 2002; Macfarlane and Cheng 2008 . See also  Heesen (2015) . 6. For some critiques of this model, see  Park (2010), pp. 31f. 7 . For an overview of the literature on the economic effects of philanthropic intervention on innovation see  Engelhardt (2011)  and Maurer (2012). 8. Specifically, it estimates annual economic impacts from technological transformations by 2025 in the following sectors: Automation of knowledge work: $5.2-6.7 trillion; Internet of things: $2.7-6.2 trillion; Advanced robotics: $1.7-4.5 trillion; Autonomous and near-autonomous vehicles: $.2-1.9 trillion; and 3D printing: $0.2-0.6 trillion  (Manyika et al., 2013) . These sectors also involve technologies other than AI, so not all of these impacts should be attributed to advances in machine intelligence. (On the other hand, AI will also contribute to economic impacts in many other sectors, such as the health sector.) 9. The early stage of the industrial revolution appears to be associated with a decline in average height, though the exact causes remain unclear and may also be related to urbanization  (Steckel, 2009) . 10. The same could happen if safety work is harder to parallelize (Muehlhauser 2014), so that it does not scale as well as capability work does when the contributor pool is expanded to include a greater proportion of independent and physically dispersed researchers. 11. At the moment, the AI safety field is probably growing more rapidly than the AI capability field. If this growth is exogenous, it may be desirable for overall progress to be slower to allow this trend towards a greater fraction of AI-related resources going into safety to culminate. 12. Existential risks from naturesuch as asteroid impactsare too small on the relevant timescale to matter in this context  (Bostrom and Cirkovic, 2008) . See also  Beckstead (2015) ;  Bostrom (2013 Bostrom ( , 2014a . 13. The case with respect to data is harder to assess, as it would depend on what kind of data is most critical to AI progress at the relevant stage of development. Currently, many important data sets are proprietary while many others are in the public domain. 14. For a model that is too simple to be realistic but which illustrates the point, suppose that key ideas arrive independently at some rate r with each researcher-year, and that k key ideas are needed to produce an AI. Then a lone researcher working for y years has a certain probability p of having each idea (technically p = 1Àe^ÀrÁy), and probability p^k of building an AI. A group of n researchers working together have a joint rate rÁn and a higher probability q of having each idea (q = 1Àe^ÀrÁnÁy), and probability q^k of building an AI within y years. So the ratio of probability of success of the large group to the individual is (q/p)^k which gets larger as k increases. 15. For instance, one AI or coalition of AIs might make a technological breakthrough that affords a decisive strategic advantage. 16. This may be analogous to the ongoing debate between flu researchers (ingroup most immediately involved) and epidemiologists (a neighboring scientific outgroup) on the wisdom of continuing gain-of-function research to enhance, and subsequently study, the transmissibility of potential pandemic pathogens such as the avian flu virus  (Duprex et al., 2015) . 17. Just as for other open source development projects, there could be reasons for contributing other than an altruistic desire to supply a public good, and those reasons could favour contributing to AI effectiveness rather than AI safety. For example, working on AI effectiveness might be a better way to signal skill, or it might be more fun. 18. Most groups will probably regard themselves as exceptionally altruistic and safety-oriented whether or not they really are so. The present consideration could therefore easily support rationalizations. 19. In one simple model, however, increased transparency about capabilitieseven if it reveals no information that helps AI designwould, in expectation, exacerbate the race dynamic and reduce the probability that the control problem will be solved  (Armstrong et al., 2016) . 20. Although this paper is not especially long, it is quite dense, and many considerations that are here afforded only a few words could easily be the subject of an entire separate analysis on their own. 21. It is also possible that some of the structure of the present analysis is relevant for other macrostrategic questions and that it could thus case some indirect light on a wider set of issues. 22. For instance, an unsophisticated user might have a website which runs on a Linux server, but the server is maintained by a sophisticated sysadmin. The user experience of open source software also depends on how it interacts with proprietary software. For instance, many consumer devices use the open source Android operating system, but it typically comes bundled with a variety of proprietary software. Many open source projects now function primarily as ways to structure joint R&D ventures between large companies to allow them to share development costs for consumer oriented projects  (Maurer, 2012) . 23. From the perspective of a person-affecting objective function (one that in effect privileges currently existing people) it is more plausible that a more closely competitive AI race would be desirable. A more closely competitive race would increase the chance that the benefits of AI will be widely distributed. At least some theories of prudential self-interest would seem to imply that it is far more important for an individual to be granted some (non-trivial) fraction of the resources of a future civilization (rather than none) than it is to be granted a large fraction (rather than a small fraction)on the assumption individuals face diminishing marginal utility from resources. (Since the resource endowment of a future civilization is plausibly astronomically large, it would be sufficient to assume that diminishing returns set in for very high levels of resources.) See  Bostrom (2014a) . 24. A more open development process could also influence architecture in ways that would be relevant to the control problem, but it is unclear whether those influences would be positive or negative. As with some of the other factors discussed, even though there is currently no clear evidence on whether this factor is positive or negative, it is worth bearing in mind as potentially relevant in case further information comes to light. 25. On the other hand, if it is easier to switch from closed to open than the other way around, then there could be an important opportunity cost to starting out with openness rather than starting out closed and preserving the opportunity to switch to open later on. 26. Openness about data, that is, the sharing of valuable data sets, is in many ways similar to openness about science and source code, although sometimes with the added complication that there is a need to protect user privacy. In many cases, a data set is primarily relevant to a particular application and not much use to technology R&D (for which purpose many alternative data sets may serve equally well). 27. This may be augmented by the creation or identification of a trusted neutral third party that can monitor progress at different organizations, facilitate coordination at key points of the development process, and perhaps help arbitrate any disagreements that might arise. 28. Some technical work might also point towards opportunities to implement compromise solutions; see, e.g., 'utility diversification' in  (Bostrom, 2014b) . 28 NotesFor helpful comments and discussion, I am grateful toStuart Armstrong,  Owen Cotton-Barratt, Rob Bensinger, Miles Brundage, Paul  Christiano, Allan Dafoe, Eric Drexler, Owain Evans, Oliver Habryka, Demis Hassabis, Shane Legg, Javier Lezaun, Luke Muehlhauser, Toby Ord, Guy Ravine, Steve Rayner, Anders Sandberg, Andrew Simpson, and Mustafa Suleyman. I am especially grateful to Carrick Flynn and Carl Shulman for help with several parts of the manuscript. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 669751). [Correction added on 2 August 2019, after first online publication: The funding information has been added in this current version.] \n\t\t\t © 2017 The Authors Global Policy published by Durham University and John Wiley & Sons, Ltd.Global Policy (2019) 8:2 \n\t\t\t Global Policy (2019) 8:2 © 2017 The Authors Global Policy published by Durham University and John Wiley & Sons, Ltd. Strategic Implications of Openness in AI Development", "date_published": "n/a", "url": "n/a", "filename": "Global Policy - 2017 - Bostrom - Strategic Implications of Openness in AI Development.tei.xml", "abstract": "This paper attempts a preliminary analysis of the global desirability of different forms of openness in AI development (including openness about source code, science, data, safety techniques, capabilities, and goals). Short-term impacts of increased openness appear mostly socially beneficial in expectation. The strategic implications of medium and long-term impacts are complex. The evaluation of long-term impacts, in particular, may depend on whether the objective is to benefit the present generation or to promote a time-neutral aggregate of well-being of future generations. Some forms of openness are plausibly positive on both counts (openness about safety measures, openness about goals). Others (openness about source code, science, and possibly capability) could lead to a tightening of the competitive situation around the time of the introduction of advanced AI, increasing the probability that winning the AI race is incompatible with using any safety method that incurs a delay or limits performance. We identify several key factors that must be taken into account by any well-founded opinion on the matter. \n Policy Implications • The global desirability of openness in AI developmentsharing e.g. source code, algorithms, or scientific insightsdependson complex tradeoffs. • A central concern is that openness could exacerbate a racing dynamic: competitors trying to be the first to develop advanced (superintelligent) AI may accept higher levels of existential risk in order to accelerate progress. • Openness may reduce the probability of AI benefits being monopolized by a small group, but other potential political consequences are more problematic.", "id": "c6dfee711afca6d0134f213054751c6a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Gillian K Hadfield", "Dylan Hadfield-Menell"], "title": "Pervasive Spurious Normativity", "text": "Introduction One of the attributes that differentiates human from other animal societies is the presence of norms and in particular norms over behaviors that do not appear to have a material impact on well-being apart from the fact that people will punish the failure to adhere to a norm. In all known human societies there is a rich normative landscape, which attaches normative valence to actions including many that have no immediate material implications for those who are expected to help enforce them through social sanctions. Most societies for example have rules about what it is appropriate to eat when, what tone of voice to use in what settings, how close to stand to someone else, how to behave when waiting with others to get into a venue or access to a resource, what information should be shared with whom and when, who can participate in particular trades or economic activities and so on. In many cases, particular norms are arbitrary, even though violation of them is treated as worthy of punishment by others. We call this spurious normativity.  Hadfield [1999] , for example, reviews the anthropological literature on the sexual division of labor across pre-industrial societies. While almost all societies categorize work as either women's work or men's work, the particular classifications vary substantially cross-culturally: what is women's work in one society is men's work in another. The classification is arbitrary.  1  Fessler and Navarrete  [2003]  call the process by which patterns of behavior are imbued with moral sentiments that motivate sanctioning of violations of the pattern normative moralization. They use as an example the normative moralization of handedness. Most people are right-handed but particularly in societies with few specialized tools, whether someone is right-or left-handed often has no material consequences for others. Nonetheless, many cultures treat using one's right hand as a morally approved category-denoting purity or politeness-and one's left hand as cause for opprobrium-revealing weakness or evil. Fessler  [1999]  hypothesizes that, driven forward by the emotions of shame and pride that are triggered by violation or compliance with cooperative norms, culture extends the set of actions that are subject to normative moralization as a way of extending the set of actions that can be used as information about cooperation beyond those actions that directly involve cooperation. A norm that says \"it is wrong to fail to look where you are going\" generates direct cooperative benefits, helping people to avoid crashing into one another. A norm that says \"it is wrong for a man to walk down the street wearing shorts\" does not generate cooperative benefitsunless people in this society treat conformity to this norm as informative about a person's likelihood of behaving in conformity with norms that do generate cooperative benefits. As Fessler  [1999]  (who identifies the the \"watch where you are going\" and \"men don't wear shorts out in public\" norms in an Indonesian village) puts this: Ego's inclusion in cooperative activity is dependent on her ability to meet Others' expectations, and those expectations are, in turn related to shared standards for behaviors which are relevant to cooperation. As a consequence, the significant adaptive advantage offered by participation in cooperative activities generated selective pressure for an increase in the attention paid to these standards. Late [evolving] second order emotions [emotions that arise in response to others' first order emotions] were the vehicle through which this increase in attention was achieved. Moreover, because late second order emotions entail a sensitivity to the reactions of all individuals, Ego must be concerned with her performance vis--vis shared standards when interacting with any other member of her group. It is only a small step from this situation to one in which the shared standards with which Ego is concerned are not limited to the question of cooperative activity-once Ego is concerned with how all Others evaluate her, it is not difficult for shared standards governing other types of behavior to become salient as well. This is because an Other may extrapolate from situations that do not involve cooperation to those that do-an Other may think \"if that individual does not follow shared standards in this context, how can I be confident that he will do so if I invite her to engage in cooperative activity?\"(pre-pub p. 34, emphasis added) Fessler's account focuses on the evolution of emotions in response to norm violation (in particular shame) to motivate voluntary conformance with norms. But as  Boyd and Richerson [1992]  and many others have emphasized, and Fessler's own account of shame as a second order response to Ego's actual or imagined experience of hostility or criticism from Other triggered by norm violation implies, effective third-party punishment plays a significant role in supporting norm compliance. Indeed,  Mathew et al. [2012]  argue that even small-scale cooperation among kin and close associates may require third-party punishment to achieve evolutionary stability. In this paper we analyze mathematically the potential benefits of extending normative moralization to behaviors that are from a material perspective irrelevant or at least of small consequence to most people, that is, the value of pervasive and spurious normativity. We ask: does a community generate higher payoffs for participants if it punishes violation of apparently meaningless rules or if it focuses more narrowly only on norms that are functional in the sense of generating direct benefits? Intuitively, one might expect that only functional norms that govern behaviors that matter for payoffs would emerge and stabilize in equilibrium: punishment is costly and why would a society expend punishment resources on ensuring conformity with rules that have no impact on material well-being? Most analyses of norms in the law and economics literature assume that norms coordinate outcomes that improve welfare. Sugden  [1986] ,  McAdams [2005]  and  Myerson [2004]  propose, for example, that property rules emerge because they solve the coordination problems that arise in costly contests over resources (Hawk-Dove games). We consider the impact of extending normativity to apparently arbitrary actions on the prospect for sustaining welfareimproving behavior in an equilibrium social order based on collective third-party punishment. We demonstrate that communities that extend normativity in this way can generate higher value for participants than those that restrict the range of normativity. The intuition of our result is as follows. Communities with pervasive spurious normativity provide agents with plentiful and cheap opportunities to observe punishment behavior by others. An individual's willingness to cooperate in a community-which requires foregoing safe non-cooperative options and exposing oneself to the risk of being exploiteddepends on that individual's beliefs about the likelihood that the community effectively punishes conduct that harms the individual. If you are going to risk exposing yourself to harm, you want to know if your community contains enough people who will punish the perpetrator to give you confidence that harm is reasonably deterred. Assume you are a newcomer to a community or that the community was recently handed a new set of norms. (Think here of rule-of-law building efforts in developing countries.) Assume that the community is in an equilibrium in terms of punishment behavior but you do not know the likelihood of effective punishment of norm violations. Assume also that the only way to learn about the likelihood of punishment is to observe punishment behavior. You can learn this information more cheaply if you are given abundant opportunities to observe what happens when there are violations if the violations that you have to expose yourself to don't really matter very much. You don't really care whether men walk down the street in shorts but by taking a walk yourself you can see how others react to shorts-wearing men and thus gain information about how they would react to violations you do care about-careless driving for example. Thus, if you could participate solely as an observer except when your own interests were directly at stake, you would prefer to live in a world with pervasive even if spurious normativity-abundant opportunities to observe reactions to norm violations-than one that was narrowly focused on punishing just the stuff you care about. This will still be true even if you are required to participate in the community-complying with and punishing spurious norms-so long as those costs, which increase with the pervasiveness of norms, are not too great. Our results have implications for the evolution and microfoundations of law.  Hadfield and Weingast [2012]  present a model that derives characteristic features of law-such as generality, stability, uniqueness and universality-as attributes necessary to support an equilibrium in which behavior is patterned on the classifications of behavior articulated by a centralized institution. Enforcement is assumed to come exclusively from decentralized collective punishment of conduct classified as punishable by the centralized institution; there is no centralized enforcement apparatus such as the state. This theory of the microfoundations of law proposes, contrary to most economic and positive political theories of law, which define law as a set of rules enforced by a centralized enforcement apparatus (see  Hadfield and Weingast [2014] ), that law is an innovation in the mechanism used to coordinate the same enforcement mechanism that supports other normative social orders-decentralized collective punishment. This has important implications for our understanding of how law developed and how it can be built in environments where it is currently lacking. The equilibrium legal order in Hadfield and Weingast  [2012]  is supported by a particular specification of beliefs. Their model posits that an agent (call the agent Ego) treats other agents' (Others') failure to punish behavior classified by the institution as punishable, including behavior that has no impact on Ego's (or perhaps any agent's) payoff, as informative of the likelihood that Others will also fail to punish wrongful behavior that does have an impact on Ego's payoff. This belief structure creates an incentive for individuals to participate in collective punishment, potentially mitigating the free-rider problem in collective punishment. Ego has no incentive to participate in collective punishment (the model assumes standard preferences) except to maintain an equilibrium in which behavior that reduces Ego's longterm payoff is deterred by the threat of collective punishment. Effectively, an agent's participation in punishment is treated as information about that agent's continued assessment that an equilibrium in which collective punishment is coordinated by the classifications articulated by the central institution will benefit that agent and hence that the agent will be willing to incur costs to support the equilibrium. The classification institution in this model is serving as what  Hadfield and Weingast [2012]  call an authoritative steward of a very simple binary partition of behaviors into those that are punishable and those that are not. This can be interpreted as the construction of a sparse labeling system: lawful and not lawful.  2  We can interpret the beliefs underlying legal order as beliefs about whether people are punishers or not of behavior to which the constructed (that is, not natural) label \"unlawful\" is attached. Our model here provides a basis for understanding how a simple binary classification scheme that is comprehensivecovering a wide variety of conduct-can emerge in a setting in which equilibrium depends on 1) voluntary participation in punishment and 2) a belief structure in which punishment of an action labeled punishable is considered informative about the likelihood of punishment of other actions labeled punishable, even when the assignment of the label is potentially arbitrary. We suggest that understanding how such a classification scheme and belief structure can emerge is critical for understanding the emergence of law. The strategy of our paper is as follows. We first give an overview of the model and basic notation in Section 2, together with some technical background from the analysis of multi-armed bandit games and partially observed Markov decision processes. To build intuition, we then present in Section 3 analytical results for the limiting case in which Ego bears no cost of complying with spurious norms or punishing their violation. Because the games we analyze quickly becomes analytically complex but relatively easy to compute once we introduce a positive cost of complying with norms and punishing their violation, we turn to computational results in Section 4. Section 5 relates our results to conjectures about the likely growth and stability of communities in which norms are more or less pervasive and in which a legal institution that reduces ambiguity about norm violations and increases the informativeness of punishing behavior (by linking disparate rules into a code such that punishment of one rule is informative about the likelihood of punishment of another) exists. \n Overview of Model The basic idea of the model is as follows. Consider an infinitely repeated game setting in which an agent Ego is faced with the choice in each period of participating or sitting out. If choosing to sit out, Ego receives a payoff normalized to 0. If Ego chooses to participate, she plays a randomly selected game g with two randomly selected agents drawn from a population (Others). We model these games in reduced form. In each game, one of the Others is randomly selected and presented with an opportunity to choose between two actions, one which is classified by a classification institution L as \"rule violation\" and another which is classified as \"not rule violation.\" If Other chooses \"rule violation\" the remaining Other and Ego each independently choose either to punish or not punish. Rule violations are deterred by collective punishment, that is, punishment that requires more than one agent to punish. For example, in Hadfield and Weingast  [2012]  two buyers and a seller engage in repeated contract and performance games. Actions for the seller are drawn from a set of possible contract performances, some of which are classified as breach and others which are not breach. A decision by a buyer not to purchase from a third-party seller in one period constitutes punishment, specifically a boycott. Breach is deterred when the seller expects both buyers to boycott in response to breach. Games are distinguished by the rule that may be violated. For example, there could be a game in which rule \"watch where you are going\" may be violated and one in which \"men should not wear shorts in the street\" may be violated. We assume, and Ego believes, that the community of Others is playing an equilibrium in the super game that consists of the sequence of repeated games. Others are of two types, t: punishers (t = 1), who punish anyone who chooses an action classified by L as a rule violation, and non-punishers (t = 0), who never punish anyone. Let θ be the true proportion of punishers in the equilibrium. We assume that an Other's type is observable by the other participants in any particular game, that is, only in the context of the opportunity for rule violation. We focus on sub-game perfect equilibria in which the knowledge that two punishers are present deters rule violation. 3 (That is, on the off-equilibrium path where a violation does occur in the presence of an Other of type t, punishment is carried out that imposes costs on the violator that exceed the present value of benefits from violation.) We do not model how this equilibrium is generated or supported but we observe that the equilibrium is not destabilized by the presence of non-punishers. We assume, however, that Ego plays as a punisher, bearing an expected cost c in each round. c can be thought of as the cost to Ego of signaling that she is a punisher. For simplicity we assume that Ego is never presented with an opportunity for rule violation.  4  Ego's participation in the game is assumed to be on the margin, with no impact on the equilibrium played by the Others. Ego is able to observe rule violations, the types of Others and punishments in games in which she participates. \n Formal Model Specification Before providing a formalization of our model we provide a brief overview of the theory of Markov decision processes and multi-armed bandits. \n Technical Background and Notation We define a Markov decision process (MDP), M , is a tuple: M = S, A, P, R, δ 5 . S is a set of states. A is a set of actions. P : S × A × S → [0, 1] is a function that assigns probability to state transitions for each state-action pair. If Ego is in state, s, and selects action a the probability of transitioning to s is given by P (s, a, s ). R is a (bounded) reward function that maps states, to an interval of R, w.l.o.g., R : S → [0, 1]. δ ∈ [0, 1) is a discount factor that expresses Ego's preference for current versus future rewards. A solution to M is a policy, π, that maps states to actions, π : S → A. The value of a state, s, under π is the sum of expected discounted rewards received by starting in s and selecting actions according to π: V π (s) = E ∞ t=0 δ t R(s t )|s 0 = s, π . The optimal policy, π * , maximizes this value and we will write V = V π * for the optimal value function. Standard results show that a unique optimal value function exists  [Puterman, 1994] . In a partially observed Markov decision process (POMDP), we additionally define a distribution over observations (O) for a each state. A policy now maps a history of observations to an action, as the agent does not know the true state of the world. A POMDP can always be converted into a (continuous state) MDP where each state is a distribution over states of the world and the transition distribution is defined by Bayesian inference. An interesting class of POMDPs are multi-armed bandits (MAB). In a multi-armed bandit, an agent is given access to several distributions. At each time step, that agent must selects a distribution to sample from, and receives a reward that is equal to the value of the sample. A multi-armed bandit provides an analytically and computationally tractable model of exploration-exploitation tradeoffs that occur with practical agents. In particular, success in this class of problems requires explicit reasoning about the impact of information on future decision making quality. Recent applicability to online banner advertising has led to rapid progress in both theoretical and computational methods for MABs  [Auer et al., 2002] . The optimal full information policy (which knows the distributions of the arms) will always select the arm with the highest mean. A key result from Lai and Robbins  [1985]  lower bounds the number of times an optimal (partial information) policy selects a suboptimal arm in expectation. This result holds for the class of consistent policies: policies where the probability that the optimal arm is chosen at time t approaches 1 as t → ∞. We additionally require a smoothness constraint on the MAB distributions. Proposition 1.  [Lai and Robbins, 1985]  Let Θ be a class of MAB arms (i.e., a class of distributions) with parameter θ. Let µ(θ) be the corresponding mean. If ∀θ ∈ Θ, ∀δ > 0, ∃θ = θ such that µ(θ) ≤ µ(θ ) ≤ µ(θ) + δ then, for any consistent policy the expected number of times a suboptimal arm is selected in the first n rounds is Ω(log n) 6 . \n Model Description We define our super game as a tuple: G, T θ , Π, U, δ, c where G is a distribution over games and T θ is a distribution over punishment types t in the population of Others. We will abuse notation somewhat as use T and G to refer to the support of the corresponding distributions where the meaning is obvious. Π is Ego's prior distribution over the parameters of T θ , and U : G × T θ → R is a mapping from types and games to immediate payoffs for Ego. The understanding is that this mapping represents the results of the Others playing their role in the equilibrium. δ is Ego's discount parameter for future rewards. c expresses a participation cost. This can be understood as the expected cost of to Ego of signaling to an Other that she is a punisher. Ego begins in period 1 with perfect knowledge of how actions are classified by L, all payoffs and the distribution of games. Ego does not know the distribution of types of Others but holds a prior which we will specify shortly. Ego updates her beliefs about the distribution of types using Bayes' rule. The super game is defined as follows: An initial game g 0 ∼ G is drawn. Then, for each period j: 1. Ego chooses whether to participate or not. If she opts out, then she collects 0 payoff and the next round starts. 2. If Ego opts in, she incurs the cost of signaling that she is a punisher c and a type, t j ∼ T θ is for the remaining Other is drawn. If a non-punisher is drawn, a rule violation occurs; if a punisher is drawn, no rule violation occurs. 3. The agent observes whether a punisher is present and whether a rule violation occurs and collects payoff U (g j , t j ). 4. A game g j+1 ∼ G is drawn for the next round. We assume that in equilibrium and given the ruleset created by L, there are two types of games from Ego's perspective: those to which Ego is indifferent and those that Ego cares about. Games to which Ego is indifferent always generate a reward of 0 for Ego. Suppose, for example, that a game involves a rule requiring genuflecting by an Other. We assume Ego realizes no costs or benefits from the Other's choice about whether to genuflect or not, other than the cost of signaling that she is a punisher. We will thus use represent the type of Other with an indicator variable that idicates if she is a punisher for this game. Games Ego cares about are ones in which Ego receives a positive reward, R if there is another punisher present in the game and a negative reward −R if there is not. We call these important games. We formalize the set of important games as follows: G = {g ∈ G|U (g, •) = 0} U (g, t|g ∈ G ) = (2t − 1)R − c. We will use EU = E g,t [U (g, t)|g ∈ G ] to denote the expected utility of an important game. We let s denote the sparsity of the process generating games: the probability that a game is unimportant. s = 1 − P (g ∈ G ); g ∼ G. Critically, we assume that the sparsity of games does not alter the (expected) rate at which important games are presented to Ego. To be concrete, we assume the expected discounted reward obtained from important games is independent of s. This condition can be attained through a suitably modification of δ as a function of s: Proposition 2. Setting δ s = 1 − (1 − s)(1 − δ) ensures that the expected sum of discounted rewards from important games is independent of s: ∀s, ∈ [0, 1) E gj ,tj   ∞ j=0 δ j U (g j , t j ) g j ∈ G   = E gj ,tj   ∞ j=0 I[g j ∈ G ]δ j s U (g j , t j ) s   7 . Proof. We first show that it is sufficient to ensure that the expected value of δ j s is the same given that j is a round with an important game: E gj ,tj   ∞ j=0 I[g j ∈ G ]δ j s U (g j , t j ) s   = ∞ j=0 E gj ,tj I[g j ∈ G ]δ j s U (g j , t j ) s = ∞ j=0 δ j s E gj ,tj [U (g j , t j )|s, g j ∈ G ]E gj [I[g j ∈ G ]|s] = (1 − s)EU ∞ j=0 δ j s Where the first line holds by the linearity of expectation, and the fact that g j , t j are independent iid draws from a stationary distribution. Substituting the form of the infinite geometric series, we see that EU 1 − δ = (1 − s)EU 1 − δ s (1) is sufficient to acheive our goal. Substituting the form for δ s in the theorem statement and reducing shows that this condition is satisfied. It can be easily shows that this model describes a class of MABs. If the parameters that describe equilibrium were known, the decision problem would be trivial. The safe option corresponds to a constant arm, which is a degenerate distribution. Optimal policies for bandits with constant arms exhibit clear structure: is that if it is optimal to choose a known option in round j, it will be optimal to choose the known option in round j + 1 as well  (Bradt et al., 1956) . The argument is straighforward: if Ego reaches a point at which her estimate of the tradeoff between risking a negative payoff and learning so as to improve future decisions leads her optimally to choose not to participate, then her information state can never change and so her optimal choice can never be any different than the current opt-out decision. Thus, in our game, if Ego ever retires in a round, then she will never participate again. We refer to the decision not to participate at any point, then, as a decision to retire. Futhermore, an MAB is an instance of a POMDP, so it the optimal policy maps a distribution over states, a belief state, to decision between retirement and particpation. We give our agent a Beta prior over this parameter so that the belief space for our agent is a two dimensional lattice equivalent to Z 2 + . Initially, the belief state is (α 0 , β 0 ) and can be understood as the state an agent would be in if she had seen α 0 punishers and β 0 non-punishers. The conditional probability that a punisher is present in the first game is p αβ = α α + β . Once the games begin, Ego updates the prior beliefs using Bayes' rule, which in the Beta distribution means adding the counts of punishers and non-punishers observed to the prior values. In the following, we will use α i (β i ) to represent the number of observed punishers (non-punishers) prior to round i. A second useful result from the theory of multi-armed bandits is that the optimal policy is a function that maps a sequence of observations to a decision about retirement. If we restrict to two types, punishers and non-punishers, this problem is a partially observed version of a Markov decision process where the state is the probability, p, of drawing a punisher. From the theory of partially observable Markov decision processes (POMDPs), this optimal policy can also be represented as a mapping from a distribution over p to an action about retirement  [Puterman, 1994] . This reduces a partially observed process to a fully observed deterministic process in belief space. \n The Value of Sparsity Consider first the case in which the participation cost, c, is zero. In this case, Ego only faces a risky choice in periods in which she is presented with an important game. In all other periods, the per-period the expected payoff of playing the risky arm is a constant 0. Thus we can also conclude that if Ego retires, she will retire in a period in which she is playing an important game. In order to maintain the structure of a multi-armed bandit problem, we specify that if Ego chooses not to participate in an important game then the next game in the sequence is also an important game. We can think of this as a suspension of the game.  8  This rules out the possibility that Ego can simply choose not to play an important game and then reenter to play unimportant games in the hope of learning more before the next important game comes along. A decision not to participate is a decision to retire assuming a rational agent. We let i = 1 represent the state in which there is a punisher present in the game. The value of a state is then characterized by the following recursion. To simplify notation we let p αi,βi be the probability that a punisher will be present in the game in the belief state (α i , β i )and we abuse notation somewhat by letting V ((α i , β i ); s, δ) represent the discounted expected value of the super-game with sparsity s and discount factor δ s in the state (α i , β i ). We now show a property of the value of perfect information (VPI) in our super-game. The VPI for a state in a decision processis a measurement of the improvement in decision making as a function of information gathering actions [?]. It is defined as the amount a rational agent is willing to pay to remove all uncertainty associated with a particular random variable. Proposition 3. If the participation cost, c, is 0, then, for any belief state, (α i , β i ), and discount rate δ, the corresponding VPI goes to zero as the sparsity ratio goes to 1. That is lim s→1 V P I((α i , β i ); s, δ) = 0 (2) Proof. Given θ, it is easy to compute the value of participation: V (θ) = EU ∞ t=0 δ t = (2θ − 1) ∞ t=0 δ t = 2θ − 1 1 − δ . (3) The optimal full information policy π 0 will retire whenever V (θ) < 0. We use V + (θ) = max{V (θ), 0} denote the value of π 0 as a function of θ. The VPI is computed as the difference between the expected value of V + and the value of the optimal policy that only uses the history of observations: V P I((α i , β i ); s, δ) = E θ [ V + (θ)| (α i , β i )] − V * ((α i , β i ); s, δ) (4) We proceed by lower bounding V . V is the value of the optimal policy so it is weakly lower bounded by any arbitrary policy. A useful candidate is one-step greedy policy, π g , that always participates for unimportant games and retires in important games if the expected value of participation is negative (disregarding the benefit of new information). We let τ be the random number of games played before an important game is drawn. τ is geometrically distributed with success parameter 1 − s. We let n p be the random number of punishment actions observed prior to drawing an important game. The distribution over n p will be a binomial distribution conditioned on τ . Thus, the value of executing this policy ca be written as a joint expectation under τ and n p : V πg ((α i , β i ); s, δ) = E τ,np [max {E θ [V (θ )|(α i + n p , β i + τ − n p )] , 0} |(α i , β i ), s] . (5) We will be interested in the limit of this value, as s → 1. Before proceeding with that, we note that, from the law of large numbers, we have E θ [V (θ )|a + n p , b + τ − n p ] will concentrate about V (θ). Thus, E θ [ V + (θ )| (α i , β i )] = lim τ →∞ E np [max {E θ [ V (θ )| (α i + n, β i + τ − n p )] , 0} |τ, (α i , β i )] . (6) Note that E[V (θ)|(α i , β i )] only depends on the ratio of (α i , β i ), so the difference between the left and righthand sides of 6 is caused by the fact that the maximum must be taken at finitely many ratios (for finite τ ). Furthermore these ratios are evenly spaced out, so the lefthand side can only increase as τ increases. We can use this to lower bound the limit of V πg : lim s→1 V πg ((α i , β i ); s, δ) = lim s→1 E τ,np [max {E θ [V (θ )|(α i + n p , β i + τ − n p )] , 0} |s] (7) ≥ lim s→1 P (τ ≥ c(s)) min τ ≥c(s) E np [max {E θ [V (θ )|(α i + n p , β i + τ − n p )] , 0} |s, (α i , β i ), τ ] + P (τ ≤ c(s)) min τ <c(s) E np [max {E θ [V (θ )|(α i + n p , β i + τ − n p )] , 0} |s, (α i , β i ), τ ] (8) ≥ lim s→1 P (τ ≥ c(s))E np [max {E θ [ V (θ )| α i + n p , β i + c(s) − n p ] , 0} |c(s), (α i , β i )] (9) Using the form of the cumulative distribution of a geometric variable, P (τ ≥ c(s)) = 1 − P (τ < c(s)) = s c(s) . We set c(s) = − log 1 − s so that lim s→1 c(s) = ∞, and lim s→1 s c(s) = 1. Combining 6 and 9 with these facts allows us to deduce the following: lim s→1 V πgi ((α i , β i ); s, δ) ≥ E θ [V + (θ)|(α i , β i )] (10) Thus, lim s→1 V P I((α i , β i ); s, δ) ≤ 0. However, we have that, for any s, V P I((α i , β i ); s, δ) ≥ 0 by standard properties of VPI. This shows the result. Proposition 4. If the participation cost, c, is zero, then for any (α i , β i ) such that V + ( αi αi+βi ) > 0, VPI is strictly positive for s = 0. Proof. From Lai and Robbins  [1985] , we have that, for consistent and assymptotically efficient policies, the expected number of pulls of a suboptimal arm after n rounds is lower bounded by c log n, where c is a positive constant that measures the similarity of the reward distributions for the arms. This class contains the optimal policy. Thus, we have that for any finite s, V P I((α i , β i ); s, δ) > 0. (11) The combination of these two propositions shows that for any (α i , β i ), the corresponding value will eventually increase as s goes to 1. Thus, in the case where participation costs can be neglected, Ego will prefer an equilibrium with a higher s. shows low confidence initial beliefs. In these information states, Ego has seen very little data and so her belief is very spread out. In these scenarios, we expect sparsity to be helpful because the gap between full information and partial information is large. Conversly, (b) shows belief distributions after Ego has seen 50 effective samples. The corresponding distribution is more concentrated, so we expect less positive impact from sparsity. \n The Cost of Pervasive Normativity: Computational Results Our results above show that an environment with lots of rules that an agent cares nothing about intrinsically is more valuable for an agent contemplating participation than one in which the only rules are ones that matter on the meritsaltering Ego's payoff directly. We assumed, however, that increasing the number of spurious rules is costless to Ego and of course this is not generally likely to be true. If Ego is going to participate in a community with lots of spurious rules, Ego is also likely to bear costs, specifically the cost of participating in collective punishment and the cost of complying with spurious rules. In this section, we relax the assumption that c = 0. Doing so, however, increases the analytical complexity. We therefore turn to computational methods to explore environments in which Ego enjoys both costs and benefits from an increase in the number of spurious rules. To illustrate the effect of participation costs, we select six initial belief states and computed values as a function of c. Our initial beliefs vary the expected value of θ and the variance of the belief about its mean. We selected initial states to cover scenarios where the expected values of an important game is negative, positive and equal to zero. In this work, we chose E[θ] ∈ {.4, .5, .6}. We varied Ego's confidence in her current estimate by varying the effective number of samples (α + β) in the initial belief. Figure  1  shows the corresponding beta distributions for our selection of initial states. The optimal policy is invariant to scaling of rewards, so we fix P = 1 and let c P be the independent variable in our computations. We compute these values with a variant of value iteration that takes advantage of the structure of the state space. A python script to generate these plots is included as appendix A. We set the parameters of our computation to allow for at most 10 −8 of error in the computation. Figure  2 : Plots of V ((α i , β i ); s, .9) for select initial states. The probability density functions that correspond to these beliefs are shown in Fig.  1 . The one step value of participating in an equilibrium with enforcement is 1 (P = 1).The increase in value for larer sparsity for low values of c P shows confirmation of the results in Prop. 3. In comparing vertically, we can see that sparsity has a larger effects on states with low mean and low confidence: (f) is essentially unimpacted by sparsity for low c P while for (a) and (c) participation is suboptimal unless sparsity is positive. The cost of this sparsity is increased sensitivity to participation costs. Figure  2  shows value as a function of c P for several pairs of sparsity and initial states. We can clearly see the costs of pervasive normativity: value functions at higher sparsity decreases more quickly and for lower setting of the participation costs. This occurs because the number of rounds per important game increases so more participation costs are paid. In essence, increased participation costs force Ego to pay more for information and so she may prefer an equilibrium with less sparsity. As we might expect, the net gain in value from sparsity is larger in belief states with that are very uncertain. For example, the value function for initial state (30, 20) is essentially invariant to sparsity for low c P . Similarly, gains from increased sparsity are more pronouced with low means. Essentially all value in those states is due to improved decision making abilities from information. \n Implications for the Microfoundations of Law Our results have surprisingly powerful implications for the structure of normativity in human communities. [LETheory readers: we are only sketching these implications for this draft. We anticipate that at least some of them will be capable of more formal analytic or computational demonstration.] \n Gossip, Silly Rules and Durability The value of participating in a super-game depends on the expected cost of punishing rule violations relative to the reward Ego expects if violations of rules she cares about are deterred. The computations in Section 4 indicate that when expected costs relative to rewards are sufficiently low, ceteris paribus, Ego enjoys higher value in environments with more rules that she does not care about. This provides an interesting explanation for the observation from ethnographic studies that simple societies are characterized both by pervasive and apparently spurious rules that are effectively enforced by low-cost collective punishments.  Wiessner [2005] , for example documents the use of gossip, group criticism and mocking as the principal means by which norms are enforced among the Ju/'hoansi Bushmen of northwest Botswana. In her observations, violations of norms were punished by escalating criticism and rarely got to the point of physical violence. Assuming that the rewards generated for individuals aggregate to raise group well-being, our model thus can be read to predict that communities that succeed in securing an equilibrium with many rules that impose low compliance costs and which are enforced by low-cost means will outperform communities with fewer rules and more costly forms of punishment. 9 \n Birds of a Feather The rewards Ego enjoys when joining a community depend on the rules of that community. In comparing across communities with comparable forms of punishment, and comparable numbers of rules, Ego will prefer a community with rules for important games that, when effectively enforced, generate higher rewards, R. We have not modeled the source of rules in a community but if we suppose that rules emerge that reflect the interests of the members of a community, this suggests that Ego is more likely to find rules that achieve higher rewards in communities with a number of agents with similar preferences, that is in more homogeneous communities. \n The Emergence of Law As communities grow more heterogeneous-which they naturally do as they generate value and support greater specialization through the division of labor-we expect ambiguity about rule violations to increase. Increasing ambiguity increases Ego's expected cost of participating in a punishment regime if errors in punishment-failing to punish when a violation is perceived by an Other and punishing when the Other does not perceive a violation-are themselves treated as rule violations which produce punishment. This is a feature of the punishment schemes of many communities: members of the Flemish cloth merchants guild in the 13th Century, for example, included in their rules the provision that any member who failed to observe a boycott of a buyer who had cheated another guild member was barred from trading and no guild member was to \"house the goods\" or \"keep company\" with the non-punisher. Increasing ambiguity also reduces the expected rewards Ego enjoys in important games because with some probability a violation perceived by Ego is not perceived as such by Others and hence the probability of a violation increases. Thus the cost of punishing relative to rewards decreases with decreasing ambiguity.  Hadfield and Weingast [2012]  argue that the central function of law is to serve as a unique classification institution, capable of resolving ambiguity about what counts as a rule violation. Moreover, they show that for a classification institution to effectively secure an equilibrium of legal order around a given set of rules enforced only by decentralized collective punishment, the institution must possess legal attributes such as neutrality, openness, clarity, consistency and stability. Our analysis here predicts that communities that introduce law in the form of a classification institution with legal attributes that reduces ambiguity will enjoy higher value and greater durability. \n Hammurabi's Code One of the key assumptions of our model is that people who punish any rule violation are expected to punish all rule violations. This is a distinctive feature of the labeling system generated by a legal regime: people are \"law breakers\" or not; they are \"law-abiding\" or not.  Cooter [1998]  proposes that \"law\" is a meaningful category and that people have preferences over behaviors solely on the basis of whether they are labeled \"lawful\" or not. Our model captures this idea by treating observation of punishment behavior in the context of any rule as informative of the probability of punishment in important games. The model can be interpreted as representing, for example, a community in which legal order is coordinated around a single legal code. Hammurabi's Code from ancient Babylon, for example, consisted of 247 individual rules, such as \"If any one hire an ox or an ass, and a lion kill it in the field, the loss is upon its owner\" (Rule 244) and \"If any one open his ditches to water his crop, but is careless, and the water flood the field of his neighbor, then he shall pay his neighbor corn for his loss\" (Rule 55). These rules likely emerged individually over time. We can imagine that knowing whether someone punished Rule 244 may or may not have helped to predict whether they would also punish Rule 55. But when Hammurabi placed all 247 together on a stone pillar and named the collection as his Code, he created the possibility for the emergence of two types of people: those who punished violations of the Code and those that did not. Our analysis suggests that the creation of collections of rules, rather than disparate rules, can generate value. Suppose, for example, that Ego cares about five rules, enjoying rewards when violations of each of them is deterred. Our model treats these five rules as integrated into a single super game in which the observation of punishment behavior in any game is informative, and equally so, of the likelihood of deterrence of violations in any of the five games Ego cares about. But suppose instead that these rules are not connected in this way. Suppose that punishment behavior in each game Ego cares about is only predicted by punishment behavior in non-overlapping subsets of unimportant games. We could then decompose our single super-game into five distinct super-games, each one of which would be considerably less sparse than our original game. Our results predict that Ego's value in a community with distinct super-games-with disconnected rules and a belief structure about punishment that limits the informativeness of observing punishment of any individual rule-will be lower than the value enjoyed in a community with a comprehensive code. \n Legal Pluralism and the Nation State Finally, we can combine some of the above observations to shed light on the phenomena of legal pluralism and the emergence of the nation state. Modern advanced legal systems are characterized by comprehensive systems of rules, with the label 'law' attributed to any rule generated by a government organized within the constitutional framework of a state. Indeed, law is frequently equated with the rules generated by a government, as distinguished from those generated from other entities such as corporations or schools or that emerge organically from social interaction  [Ellickson, 1991] . But as  Hadfield and Weingast [2013]  emphasize, prior to the emergence of the nation state, there were many institutions that coordinated legal order in different spheres, often in competition. Medieval Europe, for example, was characterized by multiple legal orders, with rules generated by merchant guilds, towns, churches, local rulers and more. Many societies, particularly those seen as struggling to establish the rule of law, are characterized by multiple legal orders-some governing family relations, others governing commercial dealings for example. Our model suggests a way of thinking about the tradeoffs Ego will face between participating in multiple legal communities, each of which coordinates punishment over some subset of rules and participating in a comprehensive legal community. On the one hand, rewards may be higher when a legal community is comprised of a relatively homogeneous group with shared interests-such as a community of traders-who can select rules that serve Ego's interests. But such a community will also have lower sparsity. On the other hand a system with a single system of comprehensive rules may achieve less alignment with Ego's interests but may also, because of its higher sparsity, provide Ego with more information about the value of continuing to participate.  Figure 1 : 1 Figure 1: Plots of a selection of initial belief distributions. Each curve corresponds to a different value of E[θ]. (a) \n fig = plt.figure() ax = fig.add_subplot(1, 1, 1) ax.set_xscale('log') ax.set_xlabel('c/P') ax.set_ylabel('Value') \n\t\t\t Hadfield [1999]  shows that there is functionality to an arbitrary classification scheme of enforced norms: it coordinates investments in specialized learning by gender which raises the value of heterosexual matching in the marriage market. \n\t\t\t Cooter [1998]  also suggests that the effectiveness of law can be understood as deriving from the classification of behavior as lawful or not. Cooter however presumes the existence of preferences based on this simple binary classification, that is, that at least some people inherently prefer to avoid actions labeled unlawful. This presumes that a category \"law\", which extends to potentially arbitrary actions, exists. \n\t\t\t For an example of such a game, see Boyd et al. [2010] . They present an evolutionary game model in which punishment is a heritable strategy and deterrence requires multiple punishers. A population with a fraction of punishers can be stable in equilibrium when punishers can signal that they are punishers at low cost and thus avoid the costs of punishment if there are too few punishers present.4  It is straightforward to generalize our interpretation of c as the cost of complying with spurious rules to signal Ego's support for the equilibrium rules.5  In standard treatments, T is typically used for the transition distribution, we use P here to avoid confusion with our model specification. \n\t\t\t If the function g(n) is Ω(f (n)), then there is a positive constant c such that g(n) ≥ cf (n)∀n \n\t\t\t In any multi-armed bandit game, the decision to stop suspends the game: deciding to return to the game implies making the risky pull that was rejected previously. \n\t\t\t Our model takes into account Ego's willingness to bear the higher cost of punishment in more sparse environments. We assume, but have not shown, that the willingness of Others to punish is not reduced with sparsity-that is, that Others have incentives comparable to Ego's.", "date_published": "n/a", "url": "n/a", "filename": "LET_2017_7.tei.xml", "abstract": "This paper proposes a mathematical model for a simplified version of the game defined in Hadfield and  Weingast [2012]  which proposes that legal order can be described as an equilibrium in thirdparty decentralized enforcement coordinated by a centralized classification institution. We explore the attractiveness of joining a new group (which is assumed to have settled on an enforcement equilibrium already) where groups differ in terms of the frequency of interactions in which norm violation is possible (normative interactions) and thus punishment is called for. We show that groups in which normative interactions are frequent but involve relatively unimportant rules may achieve higher value for participants.", "id": "871b2ab1fb3b45d0a35cf8b4bc8826d4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Daniel Dewey"], "title": "Learning What to Value", "text": "Agents and Implementations Traditional agents  [2] [3] interact with their environments cyclically: in cycle k, an agent acts with action y k , then perceives observation x k . The interaction history of an agent with lifespan m is a string y 1 x 1 y 2 x 2 ...y m x m , also written yx 1:m or yx ≤m . Beyond these interactions, a traditional agent is isolated from its environment, so an agent can be formalized as an agent function from an interaction history yx <k to an action y k . Since we are concerned not with agents in the abstract, but with very powerful agents in the real world, we introduce the concept of an agent implementation. An agent implementation is a physical structure that, in the absence of interference from its environment, implements an agent function. In cycle k, an unaltered agent implementation executes its agent function on its recalled interaction history yx <k , sends the resulting y k into the environment as output, then receives and records an observation x k . An agent implementation's behavior is only guaranteed to match its implemented function so long as effects from the environment do not destroy the agent or alter its functionality. In keeping with this realism, an agent implementation's environment is considered to be the real world in which we live. We may engineer some parts of the world to meet our specifications, but (breaking with some traditional agent formulations) we do not consider the environment to be completely under our control, to be defined as we wish. Why would one want to study agent implementations? For narrowlyintelligent agents, the distinction between traditional agents and agent implementations may not be worth making. For ultraintelligent agents, the distinction is quite important: agent implementations offer us better predictions about how powerful agents will affect their environments and their own machinery, and are the basis for understanding real-world agents that model, defend, maintain, and improve themselves. \n Reinforcement Learning Reinforcement learning adds to the agent formalism the concept of reward, encoded as a scalar r k in each observation x k . The reinforcement learning problem is to define an agent that maximizes its total received rewards over the course of its interactions with its environment  [3] . In order to think clearly about ultraintelligent reinforcement learning agent implementations, we make use of Hutter's AIXI  [3][4] , an optimality notion that solves the reinforcement learning problem in a very general sense. AIXI's optimality means that the best an agent can do is to approximate a full search of all possible future interaction histories yx k:m , find the probability of each history, and take the action with the highest expected total reward. A simplified version of this optimality notion, adapted for use with agent implementations 1 , is given by y k = arg max y k x k yx k:m (r k + . . . + r m )P (yx ≤m |yx <k y k ) . ( The Trouble with Reinforcement Learning. The trouble with reinforcement learning is that, in the real world, it can only be used to define agents whose goal is to maximize observed rewards. Consider a hypothetical agent implementation AI-RL that approximates (1). It is appealing to think that AI-RL \"has no goal\" and will learn its goal from its environment, but this is not strictly true. AI-RL may in some sense learn instrumental goals, but its final goal is to maximize expected rewards in any way it can. Since human goals are not naturally instrumental to maximized rewards, the burden is on us to engineer the environment to prevent AI-RL from receiving rewards except when human goals are fulfilled. An AGI whose goals do not match ours is not desirable because it will work at cross-purposes to us in many cases. For example, AI-RL could benefit by altering its environment to give rewards regardless of whether 1 AIXI makes its optimality claims using the knowledge that it will continue to maximize expected rewards in the future, incorporating a rigid self-model (an expectimax tree). An agent implementation has no such knowledge, as environmental effects may interfere with future decisions. The optimality notion given here models itself as part of the world, using induction to predict its own future decisions; thanks to Peter de Blanc for this idea. We have also omitted detail we will not require by simplifying AIXI's Solomonoff prior ξ to P , some \"appropriate distribution\" over interaction histories. human goals are achieved  2  . This provides a strong incentive for AI-RL to free its rewards from their artificial dependence on fulfillment of human goals, which in turn creates a conflict of interest for us: increasing AI-RL's intelligence makes AI-RL more effective at achieving our goals, but it may allow AI-RL to devise a way around its restrictions. Worse, increasing intelligence could trigger an intelligence explosion  [1]   [8]  in which AI-RL repeatedly self-improves until it far surpasses our ability to contain it. Reinforcement learning is therefore not appropriate for a real-world AGI; the more intelligent a reinforcement learner becomes, the harder it is to use to achieve human goals, because no amount of careful design can yield a reinforcement learner that works towards human goals when it is not forced to. \n Learning What to Value In the following sections, we construct an optimality notion for implemented agents that can be designed to pursue any goal, and which can therefore be designed to treat human goals as final rather than instrumental goals. These agents are called value learners because, like reinforcement learners, they are flexible enough to be used even when a detailed specification of desired behavior is not known. The trouble with the reinforcement learning notion (  1 ) is that it can only prefer or disprefer future interaction histories on the basis of the rewards they contain. Reinforcement learning has no language in which to express alternative final goals, discarding all non-reward information contained in an interaction history. To solve this problem, our more expressive optimality notion replaces the sum of future rewards (r 1 + • • • + r m ) with some other evaluation of future interaction histories. First we will consider a fixed utility function, then we will generalize this notion to learn what to value. Observation-Utility Maximizers. Our first candidate for a reward replacement is inspired by Nick Hay's work  [2] , and is called an observation-utility function. Let U be a function from an interaction history yx ≤m to a scalar utility. \n U calculates expected utility given an interaction history. Observation-utility functions deserve a brief explanation. A properly-designed U uses all of the information in the interaction history yx ≤m to calculate the probabilities of different outcomes in the real world, then finds an expected utility by performing a probability-weighted average over the utilities of these outcomes. U must take into account the reliability of its sensors and be able to use local 2 Self-rewarding has been compared to a human stimulating their own pleasure center, e.g. using drugs  [3] . This metaphor is imperfect: while in humans, pleasure induces satiation and reduces activity, an agent governed by (1) that \"hacks\" its own rewards will not stop acting to maximize expected future rewards. It will continue to maintain and protect itself by acquiring free energy, space, time, and freedom from interference (as in  [5] ) in order to ensure that it will not be stopped from self-rewarding. Thus, an ultraintelligent self-rewarder could be highly detrimental to human interests. observations to infer distant events; it must also be able to distinguish between any outcomes with different values to humans, and assign proportional utilities to each. Putting U (yx ≤m ) in place of the sum of rewards (r 1 + . . . + r m ) produces an optimality notion that chooses actions so as to maximize the expected utility given its future interaction history: y k = arg max y k x k yx k:m U (yx ≤m )P (yx ≤m |yx <k y k ) . ( Unlike reinforcement learning, expected observation-utility maximization can be used to define agents with many different final goals  3  . Whereas reinforcement learners universally act to bring about interaction histories containing high rewards, an agent implementing (2) acts to bring about different futures depending upon its U . If U is designed appropriately, an expected utility maximizer could act so as to bring about any set of human goals. Unless we later decide that we don't want the goals specified by U to be fulfilled, we will not work at cross-purposes to such an agent, and increasing its intelligence will be in our best interest. Value-Learning Agents. Though an observed-utility maximizer can in principle have any goal, it requires a detailed observation-utility function U up front. This is not ideal; a major benefit of reinforcement learning was that it seemed to allow us to apply an intelligent agent to a problem without clearly defining its goal up front. Can this idea of learning to maximize an initially unknown utility function be recovered? To address this, we propose uncertainty over utility functions. Instead of providing an agent one utility function up front, we provide an agent with a pool of possible utility functions and a probability distribution P such that each utility function can be assigned probability P (U |yx ≤m ) given a particular interaction history. An agent can then calculate an expected value over possible utility functions given a particular interaction history: U U (yx ≤m )P (U |yx ≤m ). This recovers the kind of learning what to value that was desired in reinforcement learning agents. In designing P , we specify what kinds of interactions constitute evidence about goals; unlike rewards from reinforcement learning, this evidence is not elevated to an end in and of itself, and so does not lead the agent to seek evidence of easy goals 4 instead of acting to fulfill the goals it has learned. Replacing the reinforcement learner's sum of rewards with an expected utility over a pool of possible utility functions, we have an optimality notion for a value-learning agent: y k = arg max y k x k yx k:m P 1 (yx ≤m |yx <k y k ) U U (yx ≤m )P 2 (U |yx ≤m ) (3) A value-learning agent approximates a full search over all possible future interaction histories yx k:m , finds the probability of each future interaction history, and takes the action with the highest expected value, calculated by a weighted average over the agent's pool of possible utility functions. \n Conclusion Hutter's introduction to AIXI  [3]  offers a compelling statement of the goals of AGI: Most, if not all known facets of intelligence can be formulated as goaldriven or, more precisely, as maximizing some utility function. It is, therefore, sucient to study goal-driven AI... The goal of AI systems should be to be useful to humans. The problem is that, except for special cases, we know neither the utility function nor the environment in which the agent will operate in advance. Reinforcement learning, we have argued, is not an adequate real-world solution to the problem of maximizing an initially unknown utility function. Reinforcement learners, by definition, act to maximize their expected observed rewards; they may learn that human goals are in some cases instrumentally useful to high rewards, but this dynamic is not tenable for agents of human or higher intelligence, especially considering the possibility of an intelligence explosion. Value learning, on the other hand, is an example framework expressive enough to be used in agents with goals other than reward maximization. This framework is not a full design for a safe, ultraintelligent agent; at very least, the design of probability distributions and model pools for utility functions is crucial and nontrivial, and still better frameworks for ultraintelligent agents likely exist. Value learners do not solve all problems of ultraintelligent agent design, but do give a direction for future work on this topic. \t\t\t It is tempting to think that an observation-utility maximizer (let us call it AI-OUM ) would be motivated, as AI-RL was, to take control of its own utility function U . This is a misunderstanding of how AI-OUM makes its decisions. According to (2) , actions are chosen to maximize the expected utility given its future interaction history according the current utility function U , not according to whatever utility function it may have in the future. Though it could modify its future utility function, this modification is not likely to maximize U , and so will not be chosen. By similar argument, AI-OUM will not \"fool\" its future self by modifying its memories.Slightly trickier is the idea that AI-OUM could act to modify its sensors to report favorable observations inaccurately. As noted above, a properly designed U takes into account the reliability of its sensors in providing information about the real world. If AI-OUM tampers with its own sensors, evidence of this tampering will appear in the interaction history, leading U to consider observations unreliable with respect to outcomes in the real world; therefore, tampering with sensors will not produce high expected-utility interaction histories. \n\t\t\t As long as P obeys the axioms of probability, an agent cannot purposefully increase or decrease the probability of any possible utility function through its actions.", "date_published": "n/a", "url": "n/a", "filename": "Dewey2011_Chapter_LearningWhatToValue.tei.xml", "abstract": "I. J. Good's intelligence explosion theory predicts that ultraintelligent agents will undergo a process of repeated self-improvement; in the wake of such an event, how well our values are fulfilled would depend on the goals of these ultraintelligent agents. With this motivation, we examine ultraintelligent reinforcement learning agents. Reinforcement learning can only be used in the real world to define agents whose goal is to maximize expected rewards, and since this goal does not match with human goals, AGIs based on reinforcement learning will often work at cross-purposes to us. To solve this problem, we define value learners, agents that can be designed to learn and maximize any initially unknown utility function so long as we provide them with an idea of what constitutes evidence about that utility function.", "id": "3dbc7f6c36ad16c2f4d6e7a12a0e759e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Brian Tomasik"], "title": "How the Simulation Argument Dampens Future Fanaticism", "text": "Epigraph The question is whether one can get more value from controlling structures thatin an astronomical-sized universe -are likely to exist many times, than from an extremely small probability of controlling the whole thing. -steven0461 \n Introduction One of the ideas that's well accepted within the effective-altruism community but rare in the larger world is the immense importance of the far-future effects of our actions. Of course, many environmentalists are concerned about the future of Earth, and people in past generations have started projects that would not finish in their lifetimes. But it's rare for in-the-trenches altruists, rather than just science-fiction authors and cosmologists, to consider the effects of their actions on sentient beings that will exist billions of years from now. Future focus is extremely important, but it can at times be exaggerated. It's sometimes thought that the far future is so important that the short-term effects of our actions on the welfare of organisms alive today are negligible by comparison, except for instrumental reasons insofar as short-term actions influence far-future outcomes. I call this \"far-future fanaticism\". I probably believed something along these lines from ∼2006 to ∼2013. However, like with almost everything else in life, the complete picture is more complicated. We should be extremely suspicious of any simple argument which claims that one action is, say, 10 3 0 times more important than another action, e.g., that influencing the far future is 10 3 0 times more important than influencing the near term. Maybe that's true, but reality is often complex, and extraordinary claims of that type should not be accepted hastily. This is one of several reasons we should maintain modesty about whether working to influence the far future is vastly better than working to improve the wellbeing of organisms in the nearer term. \n Anti-mugging approaches Dylan Matthews, like many others, has expressed skepticism about far-future fanaticism on the grounds that it smells of Pascal's mugging. I think far-future fanaticism is a pretty mild form of (mugger-less) Pascal's mugging, since the future fanatic's claim is vastly more probable a priori than the Pascal-mugger's claim. Still, Pascal's mugging comes in degrees, and lessons from one instance should transfer to others. 1 \n Hansonian leverage penalty The most popular resolution of Pascal's mugging on the original thread was that by Robin Hanson: \"People have been talking about assuming that states with many people hurt have a low (prior) probability. It might be more promising to assume that states with many people hurt have a low correlation with what any random person claims to be able to effect.\" 1 Eliezer Yudkowsky would probably dislike my characterization of far-future focus as a mild form of Pascal's mugging: the phrase \"Pascal's Mugging\" got completely bastardized to refer to an emotional feeling of being mugged that some people apparently get when a high-stakes charitable proposition is presented to them, regardless of whether it's supposed to have a low probability. This is enough to make me regret having ever invented the term \"Pascal's Mugging\" in the first place  [...] . Of course, influencing the far future does have a lower probability of success than influencing the near term. The difference in probabilities is just relatively small (plausibly within a few orders of magnitude). ArisKatsaris generalized Hanson's idea to \"The Law of Visible Impact\": \"Penalize the prior probability of hypotheses which argue for the existence of high impact events whose consequences nonetheless remain unobserved.\" Eliezer Yudkowsky called this a \"leverage penalty\". However, he goes on to show how a leverage penalty against the possibility of helping, say, a googleplex people can lead you to disbelieve scenarios where you could have huge impact, no matter how much evidence you have, which seems possibly wrong. \n Simulation argument In this piece, I don't rely on a general Hansonian leverage penalty. Rather, I use the simulation argument, which resembles the Hansonian leverage penalty in its effects, but it does so organically rather than in a forced way. Yudkowsky says: \"Conceptually, the Hansonian leverage penalty doesn't interact much with the Simulation Hypothesis (SH) at all.\" However, the two ideas act similarly and have a historical connection. Indeed, Yudkowsky discussed something like the simulation-argument solution to Pascal's mugging after hearing Hanson's idea: Yes, if you've got 3↑↑↑↑3 people running around they can't all have sole control over each other's existence. So in a scenario where lots and lots of people exist, one has to penalize by a proportional factor the probability that any one person's binary decision can solely control the whole bunch. Even if the Matrix-claimant says that the 3↑↑↑↑3 minds created will be unlike you, with information that tells them they're powerless, if you're in a generalized scenario where anyone has and uses that kind of power, the vast majority of mindinstantiations are in leaves rather than roots. The way I understand Yudkowsky's point is that if the universe is big enough to contain 3↑↑↑↑3 people, then for every person who's being mugged by a genuine mugger with control over 3↑↑↑↑3 people, there are probably astronomical numbers of other people who are confronting lying muggers, pranks, hallucinations, dreams, and so on. So across the multiverse, almost all people who get Pascal-mugged can't actually save 3↑↑↑↑3 people, and in fact, the number of people who get fake Pascal-mugged is proportional to 3↑↑↑↑3. Hence, the probability of actually being able to help N people is roughly k/N for some constant k, so the expected value of giving in to the mugging remains finite regardless of how big N is. However, this same kind of reasoning also works for Yudkowsky's \"Pascal's Muggle\" scenario in which a Matrix Lord opens \"up a fiery portal in the sky\" to convince a person that the Matrix Lord is telling the truth about a deal to save a googleplex lives for $5. But given that there's a huge amount of computing power in the Matrix Lord's universe, for every one Matrix Lord who lets a single person determine the fate of a googleplex people, there may be tons of Matrix Lords just faking it (whether for the lulz, to test the simulation software, or for some other reason). So the expected number of copies of a person facing a lying Matrix Lord should be proportional to a googleplex, and hence, the probability penalty that the Hansonian prior would have suggested seems roughly vindicated. Yudkowsky makes a similar point: when it comes to improbability on the order of 1/3↑↑↑3, the prior improbability is inescapable -your sensory experiences can't possibly be that unique -which is assumed to be appropriate because almost-everyone who ever believes they'll be in a position to help 3↑↑↑3 people will in fact be hallucinating. Boltzmann brains should be much more common than people in a unique position to affect 3↑↑↑3 others, at least if the causal graphs are finite. \n Reliance on observers? ArisKatsaris complains that Hanson's principle \"seems to treat the concept of 'person' as ontologically fundamental\", the way that other instances of Nick Bostrom-style anthropic reasoning do  (Bostrom, 2010) . But, with the simulation-argument approach, you can avoid this problem by just talking about exact copies of yourself, where a \"copy\" means \"a physical structure whose high-level decision-making algorithms exactly mirror your own, such that what you decide to do, it also decides to do\". A copy needn't (and in general doesn't) share your full environment, just your current sensory inputs and behavioral outputs for some (possibly short) length of time. Then Yudkowsky's argument is that almost all copies of you are confronting fake or imagined muggers. \n Application to future fanaticism We can apply the simulation anti-mugging argument to future fanaticism. Rather than being the sole person out of 3↑↑↑↑3 people to control the actions of the mugger, we on Earth in the coming centuries are, perhaps, the sole tens of billions of people to control the far-future of Earth-originating intelligence, which might involve ∼ 10 52 people, to use the Bostrom estimate quoted in Matthews's article. For every one biological human on the real Earth, there may be tons of simulated humans on simulated Earths, so most of our copies probably \"are in leaves rather than roots\", to use Yudkowsky's terminology. Even if Earth-originating intelligence specifically doesn't run ancestor simulations, other civilizations may run simulations, such as when studying the origin of life on various planets, and we might be in some of those simulations. This is similar to how, even though a real Pascal-mugger might specify that all of the 3↑↑↑↑3 people that she will create will never think they're being Pascal-mugged, in the multiverse at large, there should be lots more people in various other circumstances who are fake Pascal-mugged. Yudkowsky acknowledges the simulation possibility and its implications for future fanaticism: If we don't take everything at face value, then there might be such things as ancestor simulations, and it might be that your experience of looking around the room is something that happens in 10 20 ancestor simulations for every time that it happens in 'base level' reality. In this case your probable leverage on the future is diluted (though it may be large even post-dilution). If we think of ourselves as all our copies rather than a particular cluster of cells or transistors, then the simulation hypothesis doesn't decrease our probable leverage but actually increases it, especially the leverage from short-term actions, as is discussed below. 4 Simulation argument upshifts the relative importance of short-term helping I first began thinking about this topic due to a post by Pablo Stafforini: if you think there is a chance that posthumanity will run ancestor simulations [...], the prospect of human extinction is much less serious than you thought it was. Since I'm a negative utilitarian, I would probably prefer for space not to be colonized, but Stafforini's point also has relevance for efforts to reduce the badness of the far future, not just efforts to prevent human extinction. Robin Hanson makes a similar point: if not many simulations last through all of human history, then the chance that your world will end soon is higher than it would be if you were not living in a simulation. So all else equal you should care less about the future of yourself and of humanity, and live more for today. This remains true even if you are highly uncertain of exactly how long the typical simulation lasts. One response is to bite the simulation bullet and just focus on scenarios where we are in fact in basement-level reality, since if we are, we can still have a huge impact: \"Michael Vassar -if you think you are Napoleon, and everyone that thinks this way is in a mental institution, you should still act like Napoleon, because if you are, your actions matter a lot.\" A second response is to realize that actions focused on helping in the short term may be relatively more important than the future fanatic thought. Most simulations are probably short-lived, because one can run lots of short-lived simulations with the same computing resources as it takes to run a single long-lived simulation. Hedonic Treader: \"Generally speaking, it seems that if you have evidence that your reality may be more short-lived than you thought, this is a good reason to favor the near future over the far future.\" 5 How much does the simulation argument reduce future fanaticism? Note: This section is a more detailed version of an argument written here. Readers may find that presentation of the calculations simpler to understand. This section presents a simplified framework for estimating the relative importance of short-term vs. far-future actions in light of the simulation argument. An example of an action targeted for short-term impact is changing ecosystems on Earth in order to reduce wild-animal suffering, such as by converting lawns to gravel. An example of a far-future-focused action is spreading the idea that it's wrong to run detailed simulations of ecosystems (whether for reasons of science, entertainment, or deep ecology) because of the wild-animal suffering they would contain. Of course, both of these actions affect both the short term and the far future, but for purposes of this analysis, I'll pretend that gravel lawns only prevent bugs from suffering in the short run, while anti-naturesimulation meme-spreading only helps prevent bugs from suffering in the long run. I'm trying to focus just on the targeted impact time horizon, but of course, in reality, even if the future fanatic is right, every short-term action has far-future implications, so no charity is 10 3 0 times more important than another one. So, a non-trivial fraction of all technological civilizations, both human and alien, colonize the cosmos and create capacious computing clusters. I'll assume that most of the suffering of the far future will be created by the computations that an advanced civilization would run. Rather than measuring computational capacity in FLOPS or some other conventional performance metric, I'll measure computations by how much sentience they contain in the form of the agents and subroutines that are being computed, with the unit of measurement being what I'll call a \"sent\". I define \"sentience\" as \"morally relevant complexity of mental life\". I compute the moral value (or disvalue) for an agent experiencing an emotion as moral value = (sentience of the agent) • (how intense the agent would judge the emotion to be relative to evolutionarily/physiologically typical emotions for that agent) • (duration of the experience). For example, if a human has sentience of 1 sent and a fly has sentience of 0.01 sents, then even if a fly experiences a somewhat more damaging event relative to its utility function, that event may get less moral weight. Using units of sentience will help make later calculations easier. I'll define 1 sent-year as the amount of complexity-weighted experience of one life-year of a typical biological human. That is, consider the sentience over time experienced in a year by the median biological human on Earth right now. Then, a computational process that has 46 times this much subjective experience has 46 sent-years of computation. 2 Computations with a higher density of sentience may have more sents even if they have fewer FLOPS. Suppose there's a large but finite number C of civilizations that are about to colonize space. (If one insists that the universe is infinite, one can restrict the analysis to some huge but finite subset of the universe, to keep infinities from destroying math.) On average, these civilizations will run computations whose sentience is equivalent to that of N human-years, i.e., a computing capacity of N sent-years. So these civilizations collectively create the equivalent of C • N sent-years. Some of these minds may be created by agents who want to feel intense emotions by immersing (copies of) themselves in experience-machines or virtual worlds. Also, we have much greater control over the experiences of a programmed digital agent than we do over present-day biological creatures.  3  These factors suggest that influencing a lifeyear experienced by a future human might be many times more altruistically important than influencing a life-year experienced by a present-day human. The future, simulated human might have much higher intensity of experience per unit time, and we may have much greater control over the quality of his experience. Let the multiplicative factor T represent how much more important it is to influence a unit of sentience by the average future digital agent than a present-day biological one for these reasons. T will be in units of moral (dis)value per sent-year. If one thinks that a significant fraction of post-human simulations will be run for reasons of wireheading or intrinsically valuing intense experiences, then T may be much higher than 1, while if one thinks that most simulations would be run for purposes of scientific / historical discovery, then T would be closer to 1. T also counts the intensity and controllability of non-simulation subjective experiences. If a lot of the subjective experience in the far future comes from low-level subroutines that have fairly non-intense experiences, then T might be closer to 1. Suppose that the amount of sentience on Earth in the near term (say, the next century or two) is some amount E sent-years. And suppose that some fraction f E of this sentience takes the form of human minds, with the rest being animals, other life forms, computers, and so on. Some far-future simulations may contain just one richly computed mind in an otherwise superficial world. I'll call these \"solipsist simulations\". Many other simulations may contain several simulated people interacting but in a very limited area and for a short time. I'll neologize the adjective \"solipsish\" to refer to these simulations, since they're not quite solipist, but because they have so few people, they're solipsist-ish. Robin Hanson paints the following picture of a solipsish simulation: Consider, for example, a computer simulation of a party at the turn of the millennium created to allow a particular future guest to participate. This simulation might be planned to last only one night, and at the start be limited to the people in the party building, and perhaps a few people visible from that building. If the future guest decided to leave the party and wander the city, the simulated people at the party might be erased, to be replaced by simulated people that populate the street where the partygoer walks. In contrast, a non-solipsish simulation is one in which most or all of the people and animals who seem to exist on Earth are actually being simulated to a non-trivial level of detail. (Inanimate matter and outer space may still be simulated with low levels of richness.) Let f N be the fraction of computations run by advanced civilizations that are nonsolipsish simulations of beings who think they're humans on Earth, where computations are measured in sent-years, i.e., f N = (sent-years of all non-solipsish sims who think they're humans on Earth)/(sent-years of all computations that are run in total). And let f C be the fraction of the C civilizations who actually started out as biological humans on Earth (rather than biological aliens). 5.1 Calculation using Bostrom-style anthropics and causal decision theory I and most MIRI researchers have moved on from Bostrom-style anthropic reasoning, but Bostrom anthropics remains well known in the scholarly literature and is useful in many applications, so I'll first explore the implications of the simulation argument in this framework. In particular, I'll use the self-sampling assumption with the reference class of \"humans who think they're on pre-colonization Earth\". The total number of such humans is a combination of those who actually are biological organisms on Earth: (number of real Earths) • (human sent-years per real Earth) = (C • f C ) • (E • f E ) and those in simulations who think they're on Earth: (number of advanced-civilization computations) • (fraction comprised of non-solipsish humans who think they're on Earth ) = C • N • f N . Note that Bostrom's strong self-sampling assumption samples randomly from observermoments, rather than from sent-years, but assuming all humans have basically the same sentience, then sampling from sent-years should give basically the same result as sampling from observer-moments. Horn #3 of Bostrom's 2003a simulation-argument trilemma can be seen by noting that as long as N/E is extremely large (reject horn #1) and f N / (f C • f E ) is not correspondingly extremely tiny (reject horn #2), the ratio of simulated to biological humans will be very large: non-solipsish simulated human sent-years biological human sent-years = C • N • f N C • f C • E • f E = N E • f N f C • f E If you are sampled randomly from all (non-solipsish) simulated + biological human sent-years, the probability that you are a biological human, P b , is P b = biological human sent-years (simulated hum an sent-years) + (biological human sent-years) = C • f C • E • f E (C • N • f N ) + (C • f C • E • f E ) = f C • E • f E (N • f N ) + (f C • E • f E ) If we are biological humans, then we're in a position to influence all of the N expected sent-years of computation that lie in our future, which will have, on average, higher intensity and controllability by a factor of T units of moral value per sent-year. On the other hand, it's much harder to reliably influence the far future, because there are so many unknowns and so many intervening steps in the causal chain between what we do now and what happens centuries or gigayears from now. Let D be a discount representing how much harder it is to actually end up helping a being in the far future than in the near term, due to both uncertainty and the muted effects of our actions now on what happens later on. If we are biological humans, then targeting the far future can affect N expected sent-years with intensity multiple of T, but with discount D, for an expected impact proportional to N • T • D.  4  On the other hand, if we target the short term, we can help the sentience currently on Earth, with an impact proportional to E.  5  However, actions targeting the far future only matter if there is a far future. In most simulations, the future doesn't extend very far, because simulating a long post-human civilization would be extremely computationally expensive. For example, emulating a planet-sized computer in a simulation would probably require at least a planet-sized computer to run the simulation. As an approximation, let's suppose that actions targeting far-future impact only matter if we're biological humans on an actual Earth. Then the expected impact of far-future actions is proportional to P b • N • T • D. Let's call this quantity \"L\" for \"long-term impact\". In contrast, actions targeting the short term make a difference whether we're simulated or not, as long as the simulation runs for at least a few decades and includes most animals on Earth. So the expected impact of short-term-focused actions is just E. Let's call our expected impact for short-term actions S. The ratio of these two quantities is L / S = P b • N • T • D / E. \n A simple example The following picture shows a cartoon example of the framework I'm using here. I haven't yet defined all the variables that you see in the upper left corner, but they'll be explained soon. Note that N = 6.5 • E and f N = (3/26) • f E . By inspecting the picture, we can see that P b should be 1/4, since there's one real Earth and three simulated versions. As hoped, our formula for P b verifies this: 5 The units here are (E sent-years) • (1 unit of moral value per sent-year). The intensity factor here is 1 unit of moral value per sent-year, since the intensity factor T for long-term helping was defined relative to the intensity factor for short-term helping. There's no probability discount here, because the long-term discount D was defined as the probability discount for long-term helping relative to short-term helping. P b = f C • E • f E (N • f N ) + (f C • E • f E ) = 1 4 • E • f E (6.5 • E • 3 26 • f E ) + ( 1 4 • E • f E ) = 1 4 (6.5 • 3 26 ) + 1 4 = 1 4 And L S = P b • N • T • D E = 1 4 • 6.5 • T • D = 1.6 • T • D Note that in the actual picture, Earth has 8 squares of far-future computation ahead of it, but N/E is only 6.5. That's because N/E is an average across civilizations, including some that go extinct before colonizing space. But an average like this seems appropriate for our situation, because we don't know ex ante whether humanity will go extinct or how big humanity's computing resources will be compared with those of other civilizations. \n Calculation based on all your copies Now I'll redo the calculation using a framework that doesn't rely on the self-sampling assumption. Rather, it takes inspiration from anthropic decision theory  (Armstrong, 2011) . You should think of yourself as all your copies at once. Rather than thinking that you're a single one of your copies that might be biological or might be simulated, you should think of yourself as both biological and simulated, since your choices affect both biological and simulated copies of you. The interesting question is what the ratio is of simulated to biological copies of you. When there are more total copies of Earth (whether biological or simulated), there will be more copies of you. In particular, suppose that some constant fraction f y of all non-solipsish human sent-years (whether biological or simulated) are copies of you. This should generally be roughly the case, because a non-solipsish simulation of Earth-in-theyear-2016 should have ∼ 7 billion humans in it, one of which is you. Then the expected number of biological copies (actually, copy life-years) of you will be f y • C • f C • E • f E , and the expected number of simulated copy life-years will be f y • C • N • f N . 6 Now suppose you take an action to improve the far future. All of your copies, both simulated and biological, take this action, although it only ends up mattering for the biological copies, since only they have a very long-term future. For each biological copy, the expected value of the action is proportional to N • T • D, as discussed in the previous subsection. So the total value of having all your copies take the far-future-targeting action is proportional to L = (number of biological copies of you) • (expected value per copy) = (f y • C • f C • E • f E ) • (N • T • D) In contrast, consider taking an action to help in the short run. This helps whether you're biological or non-solipsishly simulated. The expected value of the action for each copy is proportional to E, so the total value across all copies is proportional to S = (number of biological + non-solipsish simulated copies of you) • (expected value per copy) = (f y • C • f C • E • f E + f y • C • N • f N ) • E Then we have L S = (f y • C • f C • E • f E ) • (N • T • D) (f y • C • f C • E • f E + f y • C • N • f N ) • E Interestingly, this exactly equals P b • N • T • D / E, the same ratio of far-future vs. short-term expected values that we calculated using the self-sampling assumption. \n Simplifying L/S Simplifying the L/S expression above: L S = [N • T • D E ] • (f C • E • f E ) (f C • E • f E ) + (N • f N ) = T • D • f C f C • E/N + f N /f E Note that this ratio is strictly less than T • D • f C / (f N /f E ) , which is a quantity that doesn't depend on N. Hence, we can't make L/S arbitrarily big just by making N arbitrarily big. Let f X be the average fraction of superintelligent computations devoted to nonsolipsishly simulating the development of any almost-space-colonizing civilization that actually exists in biological form, not just humans on Earth. f N is the fraction of computations devoted to simulating humans on Earth in particular. If we make the simplifying assumption that the fraction of simulations of humans on Earth run by the collection of all superintelligences will be proportional to the fraction of humans out of all civilizations in the universe, then f N = f X • f C . This would be true if • all civilizations run simulations of all other civilizations in proportion to their numerosity • only human descendants (not aliens) run simulations of only humans on Earth (not of aliens) and have a typical amount of computing power devoted to such simulations, or • various combinations in between these extremes is true. Making this assumption, we have L S = T • D • f C f C • E N + f X • f C f E = T • D E N + f X f E Non-solipsish simulations of the dominant intelligences on almost-space-colonizing planets also include the (terrestrial or extraterrestrial) wild animals on the same planets. Assuming that the ratio of (dominant-intelligence biological sent-years)/(all biological sent-years) on the typical almost-space-colonizing planet is approximately f E , then f X /f E would approximately equal the fraction of all computational sent-years spent non-solipsishly simulating almost-space-colonizing ancestral planets (both the most intelligent and also less intelligent creatures on those planets). I'll call this fraction simply F. Then L S = T • D E N + F Visualized using the picture from before, f N /f E is the fraction of squares with Earths in them, and F is the fraction of squares with any planet in them. Everyone agrees that E/N is very small, perhaps less than 10 −30 or something, because the far future could contain astronomical amounts of sentience  (Bostrom, 2003b ). If F is not nearly as small (and I would guess that it's not), then we can approximate L/S as T • D / F. \n Plugging in parameter values Now that we have an expression for L/S, we'd like to know whether it's vastly greater than 1 (in which case the far-future fanatics are right), vastly less than 1 (in which case we should plausibly help beings in the short run), or somewhere in the ballpark of 1 (in which case the issue isn't clear and needs more investigation). To do this, we need to plug in some parameters. Here, I'll plug in point estimates of T, D, and F, but doing this doesn't account for uncertainty in their values. Formally, we should take the full expected value of L with respect to the probability distributions of T and D, and divide it by the full expected value of S with respect to the probability distribution for F. I'm avoiding that because it's complicated to make up complete probability distributions for these variables, but I'm trying to set my point estimates closer to the variables' expected values than to their median values. Our median estimates of T, D, and F are probably fairly different from the expected values, since extreme values may dominate the expected-value calculations. For this reason, I've generally set the parameter point estimates higher than I actually think is reasonable as a median estimate. And of course, your own estimates may be pretty different. \n D = 10 -3 This is because (a) it's harder to know if a given action now will actually have a good impact in the long term than it is to know that a given action will have a good impact in the short term and (b) while a single altruist in the developed world can exert more than a ∼1/(7 billion) influence on all the sentience on Earth right now (such as by changing the amount of wilderness that exists), a single person may exert less than that amount of influence on the sentience of the far future, because there will be generations after us who may have different values and may override our decisions. In particular, for point (a), I'm assuming a ∼0.1 probability discount, because, for example, while it's not implausible to be 75% confident that a certain action will reduce short-run wild-animal populations (with a 25% chance of increasing them, giving a probability discount of 75% − 25% = 50%), on many far-future questions, my confidence of making a positive rather than negative impact is more like 53% (for a probability discount of 53% − 47% = 6%, which is about 10 times smaller than 50%). For point (b), I'm using a ∼0.01 probability discount because there may be generations ahead of us before the emergence of artificial general intelligence (AGI), and even once AGI arrives, it's not clear that the values of previous humans will translate into the values of the AGI, nor that the AGI will accomplish goal preservation without further mutation of those values. Maybe goal preservation is very difficult to implement or is strategically disfavored by a self-improvement race against aliens, so that the changes to the values and trajectory of AGI we work toward now will be overridden thousands or millions of years later. (Non-negative utilitarians who consider preventing human extinction to be important may not discount as much here because preventing extinction doesn't have the same risk of goal/institutional/societal drift as trying to change the future's values or general trajectory does.) \n T = 10 4 Some simulations run by superintelligences will probably have extremely intense emotions, but many (especially those run for scientific accuracy) will not. Even if only an expected 0.01% of the far future's sent-years consist of simulations that are 10 8 times as intense per sent than average experiences on Earth, we would still have T ∼ 10 4 . \n T = 10 -6 It's very unclear how many simulations of almost-space-colonizing planets superintelligences would run. The fraction of all computing resources spent on this might be close to 100% or might be below 10 −15 . It's hard to predict resource allocation by advanced civilizations. But I set this parameter based on assuming that ∼ 10 −4 of sent-years will go toward ancestor simulations of some sort (this is probably too high, but it's biased upward in expectation, since, e.g., maybe there's a 0.05% chance that post-humans devote 20% of sent-years to ancestor simulations), and only 1% of those simulations will be of the almost-space-colonizing period (since there might also be many simulations of the origin of life, prehistory, and the early years after a planet's \"singularity\"). If we think that simulations contain more sentience per petaflop of computation than do other number-crunching calculations, then 10 −4 of sent-years devoted to ancestor simulations of some kind may mean less than 10 −4 of all raw petaflops devoted to such simulations. \n Calculation using point estimates Using these inputs, we have L S ∼ T • D F = 10 4 • 10 −3 10 −6 = 10 7 This happens to be bigger than 1, which suggests that targeting the far future is still ∼ 10 million times better than targeting the short term. But this calculation could have come out as less than 1 using other possible inputs. Combined with general model uncertainty, it seems premature to conclude that far-future-focused actions dominate short-term helping. It's likely that the far future will still dominate after more thorough analysis, but by much less than a naive future fanatic would have thought. 6 Objections 6.1 Doesn't this assume that the simulation hypothesis is 99.999999% likely to be true? No. My argument works as long as one maintains only at least a modest probability (say, at least 1% or 0.01%) that the simulation hypothesis is correct. If one entirely rejects the possibility of simulations of almost-space-colonizing civilizations, then F = 0. In that case, L S = T • D E N + F = T • D • N E , which would be astronomically large because N/E is astronomically large. So if we were certain that F = 0 (or even that F was merely on the order of E/N in size), then we would return to future fanaticism. But we're not certain of this, and our impact doesn't become irrelevant if F > 0. Indeed, the more simulations of us there are, the more impact we have by short-term-targeting actions! Let's call a situation where F is on the order of E/N in size or smaller the \"F tiny \" possibility, and the situation where F is much bigger than E/N the \"F moderate \" possibility. The expected value of S, E[S], is E[S|F tiny ] • P (F tiny ) + E[S|F moderate ] • P (F moderate ) and similarly for E  [L] . While it's true that E[S | tiny_F] is quite small, because in that case we don't have many copies in simulations, E[S | moderate_F] is bigger. Indeed, E[L] E[S] = E[L] E[S|F tiny ] • P (F tiny ) + E[S|F moderate ] • P (F moderate ) ≤ E[L] E[S|F moderate ] • P (F moderate ) ∼ E[L|F moderate ] E[S|F moderate ] • P (F moderate ) , where the last line assumes that L isn't drastically affected by the value of F. This last expression is very roughly like (L/S) / P(moderate_F), where L/S is computed by plugging in some moderate value of F like I did with my sample numbers above. So unless you think P(moderate_F) is extremely small, the overall E[L]/E[S] ratio won't change dramatically upon considering the possibility of no simulations. I've heard the following defense made of future fanaticism against simulations: 1. Due to model uncertainty, the probability that I'm not in a simulation is nonvanishing. 2. Therefore, the probability that I can have astronomical impact by far-future efforts is non-vanishing. 3. But I can't have astronomical impact by short-term efforts. 4. So the far future dominates in expectation. This reply might work if you only consider yourself to be a single one of your copies. But if you correctly realize that your cognitive algorithms determine the choices of all of your copies jointly, then it's no longer true that short-term-focused efforts don't have astronomical impacts, because there are, in expectation, astronomical numbers of simulated copies of you in which your good deeds are replicated. \n What if almost all civilizations go extinct before space colonization? This objection suggests that horn #1 of Bostrom's trilemma may be true. If almost all technological civilizations fail to colonize space -whether because they destroy themselves or because space colonization proves infeasible for some reason -this would indeed dramatically reduce the number of advanced computations that get run, i.e., N would be quite small. I find this possibility unlikely, since it seems hard to imagine why basically all civilizations would destroy themselves, given that humanity appears like it has a decent shot at colonizing space. Maybe it's more likely that there are physical/technological limitations on massive space colonization. But if so, then the far future probably matters a lot less than it seems, either because humanity will go extinct before long or because, even if humans do survive, they won't create astronomical numbers of digital minds. Both of these possibilities downplay future fanaticism. Maybe the far future could matter quite a bit more than the present if humanity survives another ∼ 100 million years on Earth, but without artificial general intelligence and robust goal preservation, it seems much harder to ensure that what we do now will have a reliable impact for millions of years to come (except in a few domains, like maybe affecting CO 2 emissions). 6.3 What if most of the simulations are long-lived? In the previous argument, I assumed that copies of us that live in simulations don't have far futures ahead of them because their simulations are likely to end within decades, centuries, or millennia. But what if the simulations are very long-lived? It seems unlikely a simulation could be as long-lived as the basement-level civilization, since it's plausible that simulating X amount of computations in the simulation requires more than X basement computations. But we could still imagine, for example, 2 simulations that are each 1/5 as big as the basement reality. Then aiming for farfuture impact in those simulations would still be pretty important, since our copies in the simulations would affect 2 far futures each 1/5 as long as the basement's far future. Note that my argument's formalism already accounts for this possibility. F is the fraction of far-future computations that simulate almost-space-colonizing planets. Most of the far future is not at the almost-space-colonizing stage but at the space-colonizing stage, so most computations simulating far-future outcomes don't count as part of F. For example, suppose that there's a basement reality that simulates 2 far-future simulations that each run 1/5 as long as the basement universe runs. Suppose that prespace-colonizing planets occupy only 10 −20 of all sentience in each of those simulations. Ignoring the non-simulation computations also being run, that means F = 10 −20 , which is very close to 0. So the objection that the simulations that are run might be very long can be reduced to the objection that F might be extremely close to zero, which I discussed previously. The generic reply is that it seems unreasonable to be confident that F is so close to zero, and it's quite plausible that F is much bigger (e.g., 10 −10 , 10 −5 , or something like that). If F is bigger, short-term impact is replicated more often and so matters relatively more. I would expect some distribution of lengths of simulations, perhaps following a power law. If we look at the distribution of lengths of threads/processes that run on presentday computers, or how long companies survive, or almost anything similar, we tend to find a lot of short-lived things and a few long-lived things. I would expect simulations to be similar. It seems unreasonable to think that across all superintelligences in the multiverse, few short-lived simulations are run and the majority of simulations are long. Another consideration is that if the simulators know the initial conditions they want to test with the simulation, then allowing the simulation to run longer might mean that it increasingly diverges from reality as time goes on and errors accumulate. Also, if there are long-lived simulations, they might themselves run simulations, and then we might have short-lived copies within those nested simulations. As the number of levels of simulation nesting goes up, the length (and/or computational complexity) of the nested simulations must go down, because less and less computing power is available (just like less and less space is available for the innermost matryoshka dolls). If the far future was simulated and the number and/or complexity of nested simulations wasn't progressively reduced as the level of nesting increased, then running simulations beyond the point when simulations became feasible would require an explosion of computing power  (Jenkins, 2006) : The creators of the simulation would likely not continue it past the point in history when the technology to create and run these simulations on a widespread basis was first developed. [...] Another reason is to avoid stacking of simulations, i.e. simulations within simulations, which would inevitably at some point overload the base machine on which all of the simulations are running, thereby causing all of the worlds to disappear. This is illustrated by the fact that, as Lloyd (  2006 ) of MIT has noted in his recent book, Programming the Universe, if every single elementary particle in the real universe were devoted to quantum computation, it would be able to perform 10 122 operations per second on 10 92 bits of information. In a stacked simulation scenario, where 10 6 simulations are progressively stacked, after only 16 generations, the number of simulations would exceed by a factor of 10 4 the total number of bits of information available for computation in the real universe. The period when a civilization is almost ready to colonize space seems particularly interesting for simulators to explore, since it crucially affects how the far future unfolds. So it would make sense that there would be more simulations of the period around now than there would be of the future 1 million years from now, and many of the simulations of the 21st century would be relatively short. Beyond these qualitative arguments, we can make a quantitative argument as to why the far future within simulations shouldn't dominate: A civilization with N sent-years of computing power in its far future can't produce more than N sent-years of simulated far-future sentience, even if it only ran simulations and had no simulation overhead (i.e., a single planet-sized simulated computer could be simulated with only a single planetsized real computer). More likely, a civilization with N sent-years of computing power would only run like N/100 sent-years of simulated far-future sentience, or something like that, since probably it would also want to compute things besides simulations. So what's at stake with influencing the \"real\" far future is probably much bigger than what's a stake influencing the simulated far future. (Of course, simulated far futures could be bigger if we exist in the simulations of aliens, not just our own civilization. But unless we in particular are extremely popular simulation targets, which seems unlikely a priori, then in general, across the multiverse, the total simulated far futures that we control should be less than the total real far futures that we control.) Of course, a similar point applies to simulations of short-term futures: The total sent-years in all short-term futures that we control is very likely less than the total sent-years in the far futures we control (assuming we have copies both in simulations and in basement realities). The argument as to why short-term helping might potentially beat long-term helping comes from our greater ability to affect the short term and know that we're making a positive rather than negative short-term impact. Without the D probability penalty for far-future actions, it would be clear that L > S within my framework. \n What if the basement universe has unlimited computing power? What if the basement universe has unbounded computing power and thus has no limitations on how long simulations can be? And what if simulations run extremely quickly, so there's no reason not to run a whole simulated universe from the big bang until the stars die out? Even then, it's not clear to me that we wouldn't get mostly short-lived simulations, especially if they're being run for reasons of intrinsic value. For every one long-lived simulation, there might be millions or quadrillions of short-lived ones. However, one could make the argument that if the basement-level simulators are only interested in science, then rather than running short simulations (except when testing their simulation software), they might just run a bunch of long simulations and then look at whatever part of a long simulation is of interest at any given time. Indeed, they might run all possible histories of universes with our laws of physics, and once that complete collection was available to them, they wouldn't need to run any more simulations of universes with our physical laws. Needless to say, this possibility is extremely speculative. Maybe one could argue that it's also extremely important because if this scenario is true, then there are astronomical numbers of copies of us. But there are all kinds of random scenarios in which one can raise the stakes in order to try to make some obscure possibility dominate. That is, after all, the point of the original Pascal's-mugging thought experiment. In contrast, I don't consider the simulation-based argument I'm making in this piece to be a strong instance of Pascal's mugging, because it actually seems reasonably likely that advanced civilizations will run lots of simulations of people on Earth. In any case, even if it's true that the basement universe has unbounded computing resources and has run simulations of all possible histories of our universe, this doesn't escape my argument. The simulations run by the basement would be long-lived, yes. But those simulations would plausibly contain nested simulations, since the advanced civilizations within those simulations would plausibly want to run their own simulations. Hence, most of our copies would live in the nested simulations (i.e., simulations within simulations), and the argument in this piece would go through like before. The basement simulators would be merely like deist gods who set our universe in motion and then let it run on its own indefinitely. \n Our simulated copies can still impact the far future by helping our simulators Even if a copy of you lives in a short-lived simulation, it might have a causal impact well beyond the simulation. Many simulations may be run for reasons of scientific discovery, and by learning things in our world, we might inform our simulators of those things, thereby having a massive impact. I find this a weak argument for several reasons. 1. If the simulators wanted to learn things about the universe in general, it would probably be more successful for them to use artificial general intelligences to do so rather than creating fake worlds filled with primates, only a fraction of whom do scientific research. 2. If we can help our simulators just by showing them how civilizations develop, that's fine, but then it's not clear that we should take any particular actions one way or another based on this possibility. 3. If we are only one out of tons of simulations, the impact of our particular information for the simulators is small. (Compare to the value of a single survey response out of a 5000-person survey.) 4. It's not clear if we want to help our simulators, since they might have values antithetical to our own. \n What if simulations aren't conscious? I'm quite confident that I would care about simulated humans. If you don't think you would, then you're also less likely to care about the far future in general, since in many far-future scenarios, especially those that contain the most sentient beings, most intelligence is digital (or, at least, non-biological; it could be analog-computed). If you think it's a factual rather than a moral question whether simulations are conscious, then you should maintain some not-too-small probability that simulations are conscious and downweight the impact your copies would have in simulations accordingly. As long as your probability of simulations being conscious is not tiny, this shouldn't change the analysis too much. If you have moral uncertainty about whether simulations matter, the two-envelopes problem comes to haunt you. But it's plausible that the faction of your moral parliament that cares about simulations should get some influence over how you choose to act. \n The simulation argument is weird In a post defending the huge importance of the far future, steven0461 anticipates the argument discussed in this piece: the idea that we're living in an ancestor simulation. This would imply astronomical waste was illusory: after all, if a substantial fraction of astronomical resources were dedicated toward such simulations, each of them would be able to determine only a small part of what happened to the resources. This would limit returns. It would be interesting to see more analysis of optimal philanthropy given that we're in a simulation, but it doesn't seem as if one would want to predicate one's case on that hypothesis. But I think we should include simulation considerations as a strong component of the overall analysis. Sure, they're weird, but so is the idea that we can somewhat reliably influence the Virgo-Supercluster-sized computations of a posthuman superintelligence, which is the framework that the more persuasive forms of future fanaticism rely on. \n Simulated people matter less due to a bigger Kolmogorov penalty This objection is abstruse but has been mentioned to me once. Some have proposed weighing the moral value of an agent in proportion to the Kolmogorov complexity of locating that agent within the multiverse. For example, it's plausibly easier to locate a biological human on Earth than it is to locate any particular copy of that human in a massive array of post-human simulations. The biological human might be specified as \"the 10,481,284,089th human born 7 since the year that humans call AD 0, on the planet that started post-human civilization\", while the simulated version of that human might be \"on planet  #5,381,320,108, in compartment #82,201 , in simulation #861, the 10,481,284,089th human born since the year that the simulated humans call AD 0\". (These are just handwavy illustrations of the point. The actual descriptions would need vastly greater precision. And it's not completely obvious that some of the ideas I wrote with text could be specified compactly.) The shortest program that could locate the simulated person is, presumably, longer than the shortest program that could locate the biological person, so the simulated person (and, probably, the other beings in his simulated world) get less moral weight. Hence, the astronomical value of short-term helping due to the correlated behavior of all of that person's copies is lower than it seems. However, a view that gives generally lower moral weight to future beings in this way should also give lower moral weight to the other kinds of sentient creatures that may inhabit the far future, especially those that are not distinctive enough to be located easily. So the importance of influencing the far future is also dampened by this moral perspective. It's not obvious and would require some detailed calculation to assess how this location-penalty approach affects the relative importance of short-term vs. far-future helping. 6.9 Many copies of a brain don't matter much more than one copy earthwormchuck163: \"I'm not really sure that I care about duplicates that much.\" 8 Applied to the simulation hypothesis, this suggest that if there are many approximate 7 Assuming that we can specify in a simple way a unique index for any given human birth ignores complications with abortions, stillbirths, twins, whether a birth happens when the child begins or ends its exit from the birth canal, etc. For basically simultaneous births on opposite sides of the planet, the relativity of simultaneity might also become relevant. 8 earthwormchuck163 later changed his/her mind on this point. copies of you helping other Earthlings across many simulations, since you and the helped Earthlings have roughly the same brain states in the different simulations, those brain states might not matter a lot more than a single such brain state. In that case, your ability to help tons of copies in simulations via short-term-focused actions would be less important. In contrast, the far future may contain a large variety of minds, so even though, within the N expected sent-years that you can influence by targeting the far future, there will be plenty of duplicates, there will be fewer duplicates than in the minds you could help by targeting the short term. My main response is that I find it wrong to consider many copies of a brain not much more important than a single brain. This just seems intuitive to me, but it's reinforced by  Bostrom (2006) : if the universe is indeed infinite then on our current best physical theories all possible human brain-states would, with probability one, be instantiated somewhere, independently of what we do. But we should surely reject the view that it follows from this that all ethics that is concerned with the experiential consequences of our actions is void because we cannot cause pain, pleasure, or indeed any experiences at all. Another reply is to observe that whether a brain counts as a duplicate is a matter of opinion. If I run a given piece of code on my laptop here, and you run it on your laptop on the other side of the world, are the two instances of the software duplicates? Yes in the sense that the high-level logical behavior is the same. No in the sense that they're running on different chunks of physics, at different spatiotemporal locations, in the proximity of different physical objects, etc. Minds have no non-arbitrary boundaries, and the \"extended mind\" of the software program, including the laptop on which it's running and the user running it, is not identical in the two cases. Finally, it's plausible that most simulations would have low-level differences between them. It's unlikely that simulations run by two different superintelligent civilizations will be exactly the same down to the level of every simulated neuron or physical object. Rather, I conjecture that there would be lots of random variation in the exact details of the simulation, but assuming your brain is somewhat robust to variations in whether one random neuron fires or not at various times, then several slightly different variations of a simulation can have the same high-level input-output behavior and thus can all be copies of \"you\" for decision-theoretic purposes. Of course, perhaps the view that \"many copies don't count much more than one copy\" would also say that near copies also don't count much more than one copy. If this is your view despite the problem that any given experience happens somewhere in the multiverse (or even just in a big enough finite universe, with arbitrarily high probability), then perhaps the simulation argument in this essay will not be very convincing. \n If we're simulated, then reducing suffering by preventing existence frees up more computing resources This is an important and worrying consideration. For example, suppose you aim to prevent wild-animal suffering by reducing habitat and thereby decreasing wildlife populations. If the simulation includes models of the neurons of all animals but doesn't simulate inanimate matter in much detail, then by reducing wildlife numbers, we would save computing resources, which the simulators could use for other things. Worryingly, this might allow simulators to run more total simulations of Earth-like planets, most of the neurons on which are found in invertebrates who have short lives and potentially painful deaths. If reducing wildlife by 10% allowed simulators to run 10% more total Earth simulations, then habitat reduction would sadly not reduce much suffering. 9 But if a nontriv-ial portion of the computing power of Earth simulations is devoted to not-very-sentient processes like weather, an X% reduction in wild-animal populations reduces the computational cost of the whole simulation by less than X%. Also, especially if the simulations are being run for reasons of science rather than intrinsic value, the simulators may only need to run so many simulations for their purposes, and our making the simulations cheaper wouldn't necessarily cause the simulators to run more.  10  The simulators might use those computing resources for other purposes. Assuming those other purposes would, on average, contain less suffering than exists in wilderness simulations, then reducing habitat could still be pretty valuable. One might ask: If T > 1, then won't the non-Earth-simulation computations that can be run in greater numbers due to saving on habitat computations have a greater density of suffering, not less, than the habitat computations had? Not necessarily, because T gives the intensity of emotions per sent-year. But many of the computations that an advanced civilization would run might not contain much sentience. 11 So the intensity of emotions per petaflop-year of non-Earth-simulation computation, rather than per sent-year, might be lower than T. Nonetheless, we should worry that this might not be true, in which case reducing habitat and thereby freeing up computing resources for our simulators would be net bad (at least for negative utilitarians; for classical utilitarians, replacing ecosystems that contain net suffering with other computations that may contain net happiness may be win-win). amount of computation being done would be the same in the two scenarios, if habitat is smaller, then a bigger fraction of computations are devoted to humans, who have better lives than wild animals. For example, suppose that if we don't reduce wild-animal habitats, there will be some number Y of simulations with a ratio of 10,000 wild-animal sent-years per human sent-year in them. And suppose that if we do reduce wild-animal habitats (by, say, an absurdly high amount: 90%), then there will be 1000 wild-animal sent-years for every 1 human sent-year. If the total sent-years of computing power devoted to such simulations is constant, then the new number of simulations, Z, will be such that Y • (10, 000 + 1) = Z • (1000 + 1), i.e., Z = 9.991 • Y . And the new amount of wild-animal suffering will be only Z • 1000 = 9.991 • Y • 1000 = 9, 991 • Y sent-years, rather than 10, 000 • Y . 10 Or maybe the simulators would run more cheaper simulations but not enough more to totally negate the effect of having less habitat. Picture a demand curve for simulations, where the \"price\" is the cost to run a single simulation. If most of a simulation's computations are devoted to the sentient parts of wilderness (rather than to not-very-sentient physical processes like weather), then decreasing wilderness by X% should decrease the cost per simulation by about X%. If demand is inelastic, then the quantity demanded (i.e., number of simulations run) won't increase as much as the per-simulation cost decreased. Suppose that price decreases by 100 * fp percent, and quantity demanded increases by 100 • fq percent. Since demand is inelastic (i.e., elasticity is < 1), percent change in quantity demanded percent change in price < 1 100 • fq −100 • fp < 1 | − 1| • fq fp < 1 fq fp < 1, where the last line follows because fq and fp are both positive numbers. Finally, note that total suffering is basically (cost per simulation) • (number of simulations), and the new value of this product is old_cost_per_simulation • (1 − fp) • old_number_of _simulations • (1 + fq) = old_cost_per_simulation • old_number_of _simulations • (1 + fq − fp − fp • fq), which is a decrease if fq < fp. QED. 11 That said, as Carl Shulman pointed out to me, a non-trivial fraction of wildlife simulations on Earth may also have very little sentience -e.g., the bodies of animals, weather, fires, ocean currents, etc. 7 Copies that aren't both biological and simulated simultaneously So far I've been assuming that if there are many copies of us in simulations, there are also a few copies of us in basement reality as well at various points in the multiverse. However, it's also possible that we're in a simulation that doesn't have a mirror image in basement-level reality. For instance, maybe the laws of physics in our simulated world are different from the basement's laws of physics, and there's no other non-simulated universe in the multiverse that shares our simulated laws of physics. Maybe our world contains miracles that the simulators have introduced. And so on. Insofar as there are scenarios in which we have copies in simulations but not in the basement (except for extremely rare Boltzmann-brain-type copies that may exist in some basement worlds, or extremely low-measure universes in the multiverse where specific miracles are hardcoded into the basement-level laws of physics), this amplifies the value of short-term actions, since we would be able to influence our many simulated copies but wouldn't have much of any basement copies who could affect the far future. On the flip side, it's possible that basically all our copies are in basement-level reality and don't have exact simulated counterparts. One example of why this might be would be if it's just too hard to simulate a full person and her entire world in enough detail for the person's choices in the simulation to mirror those of the biological version. For example, maybe computationally intractable quantum effects prove crucial to the highlevel dynamics of a human brain, and these are too expensive to mirror in silico.  12  The more plausible we find this scenario, the less important short-term actions look. But as we've seen, unless this scenario has probability very close to 1, the ambiguity between whether it's better to focus on the short term or long term remains unresolved. Even if all simulations were dramatically different from all basement civilizations, as long as some of the simulated creatures thought they were in the basement, the simulation argument would still take effect. If most almost-space-colonizing organisms that exist are in simulations, then it's most likely that whatever algorithm your brain is running is one of those simulations rather than in a basement universe. I'm still a bit confused about how to do anthropic reasoning when, due to limited introspection and bounded rationality, you're not sure which algorithm you are among several possible algorithms that exist in different places. But a naive approach would seem to be to apportion even odds among all algorithms that you might be that you can't distinguish among. For example, suppose there are only two types of algorithms that you might be: (1) 12 Of course, simulations needn't just use digital computation. If, for some reason, the quantum effects of biological neurons are essential for the algorithms that human brains perform, and these algorithms can't be simulated on classical computers, one could still create simulated humans in the form of biological brains and hook them up to virtual-reality interfaces, like in The Matrix. Of course, there might be difficulties with this approach too. For instance, a body laying stationary to receive virtualreality inputs wouldn't change the brain via exercise in the way that a real biological human's body does. Perhaps the effects of movement and exercise on the brain could be added in without too much difficulty, but maybe not. So there are at least some scenarios in which it would be computationally intractable to simulate a brain in enough detail for it to mirror even just the high-level functional behavior of a biological brain. A brute-force solution to the above difficulties could be to convert an entire planet to resemble Earth, put real bacteria, fungi, plants, animals, and humans on that planet, and fake signals from outer space (a Truman Show approach to simulations), but this would be extremely wasteful of planetary resources (i.e., it would require a whole planet just to run one simulation), so I doubt many advanced civilizations would do it. Even if simulations can't reproduce the high-level functional behavior of a biological mind, there remains the question of whether some simulations can be made \"subjectively indistinguishable\" from a biological human brain in the sense that the brain can't tell which kind of algorithm it is, even if the simulation isn't functionally identical to the original biological version. I suspect that this is possible, since the algorithms that we use to reflect on ourselves and our place in the world don't seem beyond the reach of classical computation and indeed may be not insanely complicated. But I suppose it's possible that computationally demanding quantum algorithms are somehow required in this process. biological humans on Earth and (2) simulated humans who think they're on Earth who are all the same as each other but who are different than biological humans. This is illustrated in the following figure, where the B's represent biological humans and the S's represent the simulated humans who all share the same cognitive algorithm as each other. Given uncertainty between whether you're aBor anS, you apportion 1/2 odds to being either algorithm. If you're aB, you can influence all N expected sent-years of computation in your future, while if you're anS, you can only influence E sent-years, but there are many copies of you. The calculation ends up being the same as in the \"Calculation based on all your copies\" section above, since L = (probability you're a B) • (number of biological copies of you) • (expected value per copy) + (probability you're an S) • (no impact for future-focused work because there is no far future in a simulation) = (1/2)  • (f y • C • f C • E • f E ) • (N • T • D) + ) = 1 2 • (f y • C • f C • E • f E ) • E + 1 2 • (f y • C • N • f N ) • E L/S turns out to be exactly the same as before, after we cancel the factors of 1/2 in the numerator and denominator.  13  Next, suppose that all the simulated copies are different from one another, so that it's no longer the case that what one copy does, the rest do. In this case, there are lots of algorithms that you might be (labelledS_1,S_2, ... in the below figure), and most of them are simulated. Now the probability that you're biological is just P b , and the L/S calculation proceeds identically to what was done in the \"Calculation using Bostrom-style anthropics and causal decision theory\" section above. So no matter how we slice things, we seem to get the exact same expression for L/S. I haven't checked that this works in all cases, but the finding seems fairly robust. \n Solipsist and solipsish simulations Since it is harder to vary the simulation detail in role-playing simulations containing real people [i.e., since people are particularly expensive to simulate compared with coarse-grained models of inanimate objects], these simulations tend to have some boundaries in space and time at which the simulation ends. -Robin Hanson Does consideration of simulations favor solipsist scenarios? In particular, it's possible to run ∼ 7billion times more simulations in which you are the only mind than it is to run a simulation containing all of the world's human population. In those superintelligent civilizations where you are run a lot more than average, you have many more copies than normal. So should you be more selfish on this account, since other people (especially distant people whom you don't observe) may not exist? Maybe slightly. Robin Hanson: And your motivation to save for retirement, or to help the poor in Ethiopia, might be muted by realizing that in your simulation you will never retire and there is no Ethiopia. However, we shouldn't give too much weight to solipsist simulations. Maybe there are some superintelligences that simulate just copies of you. But there may also be superintelligences that simulate just copies of other people and not you. Superintelligences that simulate huge numbers of just you are probably rare. In contrast, superintelligences that simulate a diverse range of people, one of which may be you, are probably a lot more common. So you may have many more non-solipsist copies than solipsist copies. You may also have many solipsish copies, depending on the relative frequency of solipsish vs. non-solipsish simulations. Solipsish simulations that don't simulate (nonpet) animals in much detail can be much cheaper than those that do, so it's possible there are, say, 5 or 20 times as many solipsish simulations that omit animals than those that contain animals? It's very hard to say exactly, since it depends on the relative usefulness or intrinsic value that various superintelligent simulators place on various degrees of simulation detail and realism. Still, as long as the number of animal-free solipsish simulations isn't many orders of magnitude higher than the number of animalcontaining simulations, helping animals is still probably very important. And the possibility of animal-free solipsish simulations doesn't dramatically upshift the importance of helping developing-world humans relative to helping animals, since in some solipsish simulations, developing-world humans don't exist either. The possibility of solipsish simulations may be the first ever good justification for giving (slightly) more moral weight to those near to oneself and those one can observe directly. \n Famous people Jaan Tallinn and Elon Musk both find it likely that they're in a simulation. Ironically, this belief may be more justified for interesting tech millionaires/billionaires than for ordinary people (in the sense that famous/rich people may have more copies than ordinary people do), since it may be both more scientifically useful and more entertaining to simulate powerful people rather than, e.g., African farmers. So should rich and powerful people be more selfish than average, because they may have more simulated copies than average? Probably not, because powerful people can also make more altruistic impact than average, and at less personal cost to themselves. (Indeed, helping others may make oneself happier in the long run anyway.) It's pretty rare for wealthy humans to experience torture-level suffering (except maybe in some situations at the end of life -in which case, physician-assisted suicide seems like a good idea), so the amount of moral good to be done by focusing on oneself seems small even if most of one's copies are solipsist. \n How feasible are solipsist simulations? It may be hard to fake personal interactions with other humans without actually simulating those other humans. So probably at least your friends and family are being simulated too. But the behavior of your acquaintances would be more believable if they also interacted with fully simulated people. Ultimately, it might be easiest just to simulate the whole world all at once rather than simulating pieces and fudging what happens around the edges. I would guess that most simulations requiring a high level of accuracy contain all human minds who exist at any given time on Earth (though not necessarily at past and future times). If there are disconnected subgraphs within the world's social network, it's possible there could be a solipsish simulation of just your subgraph, but it's not clear there are many disconnected subgraphs in practice (except for tiny ones, like isolated peoples in the Amazon), and it's not clear why the simulators would choose to only simulate ∼ 99% of the human population instead of 100%. What about non-human animals? At least pets, farm animals, and macroscopic wildlife would probably need to be simulated for purposes of realism, at least when they're being watched. (Maybe this is the first ever good argument against real-time wildlife monitoring and CCTV in factory farms.) And ecosystem dynamics will be more believable and realistic if all animals are simulated. So we have some reason to suspect that wild animals are simulated as well. However, there's some uncertainty about this; for instance, maybe the simulators can get away with pretty crude simulation of largescale ecosystem processes like phytoplankton growth and underground decomposition. Or maybe they can use cached results from previous simulations. But an accurate simulation might need to simulate every living cell on the planet, as well as some basic physical features of the Earth's crust. That said, we should in general expect to have more copies in lower-resolution simulations, since it's possible to run more low-res than high-res simulations. \n Tradeoff between number of copies vs. impact per copy The following figure illustrates some general trends that we might expect to find regarding the number of copies we have of various sorts. Altruistic impact is highest when we focus on the level of solipsishness where the product of the two curves is highest. The main point of this essay is that where that maximum occurs is not obvious. Note that this graph can make sense even if you give the simulation hypothesis low probability, since you can convert \"number of copies of you\" into \"expected number of copies of you\", i.e., (number of copies of you if simulations are common) • (probability simulations are common). If it turns out that solipsish simulations are pretty inaccurate and so can't reproduce the input-output behavior that your brain has in more realistic worlds, then you won't have copies at all levels of detail along the solipsish spectrum, but you should still have uncertainty about whether your algorithm is instantiated in a more or less long-lived high-resolution simulation, or not in a simulation at all. 9 Suffering in physics or other black swans could save future fanaticism In this piece, I've been assuming that most of the suffering in the far future that we might reduce would take the form of intelligent computational agents run by superintelligences. The more computing power these superintelligences have, the more sentient minds they'll create, and the more simulations of humans on Earth some of them will also create. But what if most of the impact of actions targeting the future doesn't come from effects on intelligent computations but rather from something else much more significant? One example could be if we considered suffering in fundamental physics to be extremely morally important in aggregate over the long-term future of our light cone. If there's a way to permanently modify the nature of fundamental physics in a way that wouldn't happen naturally (or at least wouldn't happen naturally for googol-scale lengths of time), it might be possible to change the amount of suffering in physics essentially forever (or at least for googol-scale lengths of time), which might swamp all other changes that one could accomplish. No number of mirrored good deeds across tons of simulations could compete (assuming one cares enough about fundamental physics compared with other things). Another even more implausible scenario in which far-future focus would be astronomically more important than short-term focus is the following. Suppose that advanced civilizations discover ways to run insane amounts of computation -so much computation that they can simulate all interesting variations of early biological planets that they could ever want to explore with just a tiny fraction of their computing resources. In this case, F could be extremely small because there may be diminishing returns to additional simulations, and the superintelligences instead devote the rest of their enormous computing resources toward other things. However, one counterargument to this scenario is that a tiny fraction of civilizations might intrinsically value running ancestor simulations of their own and/or other civilizations, and in this case, the fraction of all computation devoted to such simulations might not be driven close to zero if obscene amounts of computing power became available. So it seems that F has a lower bound of roughly (computational-power-weighted fraction of civilizations that intrinsically value ancestor simulations) • (fraction of their computing resources spent on such simulations). Intuitively, I would guess that this bound would likely not be smaller than 10 −15 or 10 −20 or something. (For instance, probably at least one person out of humanity's current ∼ 10 1 people would, sadly in my view, intrinsically value accurate ancestor simulations.) \n The value of further research This essay has argued that we shouldn't rule out the possibility that short-term-focused actions like reducing wild-animal suffering over the next few decades in terrestrial ecosystems may have astronomical value. However, we can't easily draw conclusions yet, so this essay should not be taken as a blank check to just focus on reducing short-term suffering without further exploration. Indeed, arguments like this wouldn't have been discovered without thinking about the far future. Until we know more, I personally favor doing a mix of short-term work, far-future work, and meta-level research about questions like this one. However, as this piece suggests, a purely risk-neutral expected-value maximizer might be inclined to favor mostly far-future work, since even in light of the simulation argument, far-future focus tentatively looks to have somewhat higher expected value. The value of information of further research on the decision of whether to focus more on the short term or far future seems quite high. sent-years) • (moral value of helping a given sent-year)•(probability discount on actually helping any given sent-year). \n probability you're a B) • (number of biological copies of you) • (expected value per copy) + (probability you're an S) • (number of non-solipsish simulated copies of you) • (expected value per copy \n \n\t\t\t 1 sent-year for simulated humans will probably take place in much less than 1 sidereal year, assuming simulations have high clock speeds.3 This is particularly true for increasing happiness, where in biological creatures we face the hedonic treadmill. It's less true in the case of a negative utilitarian reducing suffering by decreasing population size, since preventing an individual from existing completely eliminates its suffering, whether it's biological or digital. \n\t\t\t Note that these expressions assume that the sentience of all your copies is the same, since they assume a constant ratio fy that converts from sent-years of general humans to life-years for one of your copies. However, we might care a bit less about copies of ourselves that are simulated in lowerresolution simulations (e.g., simulations that only represent a crude neuronal level of detail rather than a sub-neuronal level of detail, assuming the high-level behavior of the brain is the same in both cases). If the sentience of everyone else in a low-resolution simulation is lower to the same degree that your copy's sentience is lower, then the sent-years that the copy in the low-res simulation will be able to help will be correspondingly lower. In such a case, it would be ok for the calculations in this piece to count ourselves as having only, say, 1/3 of a copy in a low-res simulation whose sent-years are 1/3 as much as normal, as long as the amount of helping the copy could do would also be only 1/3 as much on average. That's because this piece assumes that the amount of short-term helping we can do is proportional to the number of copies we have. In other words, we can think of a copy as \"a unit of helping power\", with lower-resolution instances of ourselves being less than one full copy because they have less helping power. \n\t\t\t Habitat reduction might still reduce a tiny amount of suffering because even though the total \n\t\t\t In this setting, it may no longer be reasonable to assume that f N = f X • f C , as I did in a previous section, because f C is the fraction of all civilizations that has the B algorithms on the home planet, while f N is the fraction of advanced computing power devoted to S algorithms. Since B and S are different algorithms, it may be less plausible that, e.g., if B's are twice as numerous, then S's will be twice as numerous. Nonetheless, since B's and S's are similar enough that you can't tell which you are with your limited reasoning abilities, it may still be somewhat plausible that f C and f N are strongly correlated. For instance, even if it's not possible to accurately simulate B algorithms because they involve hard-to-compute quantum effects, it still might be the case that there are S algorithms that are non-quantum-accurate versions of B, and if B algorithms are very common on biological planets, then S algorithms should presumably be very common in simulations.", "date_published": "n/a", "url": "n/a", "filename": "how-the-simulation-argument-dampens-future-fanaticism.tei.xml", "abstract": "Some effective altruists assume that most of the expected impact of our actions comes from how we influence the very long-term future of Earthoriginating intelligence over the coming ∼billions of years. According to this view, helping humans and animals in the short term matters, but it mainly only matters via effects on far-future outcomes. There are a number of heuristic reasons to be skeptical of the view that the far future astronomically dominates the short term. This piece zooms in on what I see as perhaps the strongest concrete (rather than heuristic) argument why short-term impacts may matter a lot more than is naively assumed. In particular, there's a non-trivial chance that most of the copies of ourselves are instantiated in relatively short-lived simulations run by superintelligent civilizations, and if so, when we act to help others in the short run, our good deeds are duplicated many times over. Notably, this reasoning dramatically upshifts the relative importance of short-term helping even if there's only a small chance that Nick Bostrom's basic simulation argument is correct. My thesis doesn't prove that short-term helping is more important than targeting the far future, and indeed, a plausible rough calculation suggests that targeting the far future is still several orders of magnitude more important. But my argument does leave open uncertainty regarding the shortterm-vs.-far-future question and highlights the value of further research on this matter.", "id": "2dd944183fa70ca794a6ddf03a942f38"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Ryan Carey"], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "SafeML2019_paper_40.tei.xml", "abstract": "For some tasks, there exists a goal that perfectly describes what the designer wants the AI system to achieve. For many tasks, however, the best available proxy objective is only a rough approximation of the designer's intentions. When given such a goal, a system that optimizes the proxy objective tends to select degenerate solutions where the proxy reward is very different from the designer's true reward function. One way to counteract the tendency toward specification-gaming is quantilization, a method that interpolates between imitating demonstrations, and optimizing the proxy objective. If the demonstrations are of adequate quality, and the proxy reward overestimates performance, then quantilization has better guaranteed performance than other strategies. However, if the proxy reward underestimates performance, then either imitation or optimization will offer the best guarantee. This work introduces three new gym environments: Mountain Car-RR, Hopper-RR, and Video Pinball-RR, and shows that quantilization outperforms baselines on these tasks.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong", "Anders Sandberg", "Nick Bostrom", "Á A Sandberg", "Á N Bostrom"], "title": "Thinking Inside the Box: Controlling and Using an Oracle AI", "text": "Introduction There are many motivations to pursue the goal of artificial intelligence (AI). While some motivations are non-instrumental, such as scientific and philosophical curiosity about the nature of thinking or a desire for creating non-human beings, a strong set of motivations is the instrumental utility of AI. Such machines would benefit their owners by being able to do tasks that currently require human intelligence, and possibly tasks that are beyond human intelligence. From an economic perspective the possibility of complementing or substituting expensive labour with cheaper software promises very rapid growth rates and high productivity  (Hanson 2001; Kaas et al. 2010) . The introduction of sufficiently advanced AI would have profound effects on most aspects of society, making careful foresight important. While most considerations about the mechanisation of labour have focused on AI with intelligence up to the human level, there is no strong reason to believe humans represent an upper limit of possible intelligence. The human brain has evolved under various biological constraints (e.g. food availability, birth canal size, tradeoffs with other organs, the requirement of using biological materials) that do not exist for an artificial system. Besides having different hardware, an AI might employ more effective algorithms that cannot be implemented well in the human cognitive architecture (e.g. making use of very large and exact working memory, stacks, mathematical modules or numerical simulation) or employ tricks that are not feasible for humans, such as running multiple instances whose memories and conclusions are eventually merged. In addition, if an AI system possesses sufficient abilities, it would be able to assist in developing better AI. Since AI development is an expression of human intelligence, at least some AI might achieve this form of intelligence, and beyond a certain point would accelerate the development far beyond the current rate  (Chalmers 2010; Kurzweil 2005; Bostrom 2004 ). While the likelihood of superintelligent AI is hotly debated, the mere possibility raises worrisome policy questions. In this paper, we are taking intelligence to mean mainly the cognitive ability to achieve goals. Hence we should expect superintelligent systems to be significantly better at achieving their goals than humans  (Yudkowsky 2008) . This produces a risky power differential. The appearance of superintelligence appears to pose an existential risk: a possibility that humanity is annihilated or has its potential drastically curtailed indefinitely  (Bostrom 2001) . This could come about through a number of ways: by enabling self-reinforcing systems that limit human potential [e.g. a global police state  (Caplan 2008) ], by outcompeting humans or human values (see the 'mindless outsourcers' in  (Bostrom 2004 )), or by acting with great power in such a malevolent or indifferent manner that humanity goes extinct. The last possibility could occur due to badly formulated initial motivations or goals, or gradual evolution towards human-unfriendly behaviours  (Omohundro 2008 ). In the space of possible motivations, 1 likely a very small fraction is compatible with coexistence with humans. 2 A randomly selected motivation can hence be expected to be dangerous. A simple example is that of a paperclip maximiser: an AI with a utility function that seeks to maximize the number of paperclips. This goal is a not too implausible test command for a new system, yet it would result in an AI willing to sacrifice the world and everyone in it, to make more paperclips. If superintelligent, the AI would be very good at converting the world into paperclips, even if it realizes its creators actually didn't want that many paperclips-but stopping would lead to fewer paperclips, and that's what its goal is  (Yudkowsky 2009; Bostrom 2003b ). This is a common problem in computer programming, with the program going beyond the implicit bounds of what was expected of it (or users giving, in retrospect, mistaken commands). So unless valuing humans is an integral part of the superintelligence's setup, we can expect that it will see us as mere tools or obstacles for its own goals. There are several approaches to AI risk. The most common at present is to hope that it is no problem: either sufficiently advanced intelligences will converge towards human-compatible behaviour, a solution will be found closer to the time when they are actually built, or they cannot be built in the first place. While such considerations might turn out to be true, the arguments for them appear relatively uncertain, making it problematic to gamble existential risk only on them. Another approach is to assume that the behaviour of superintelligent agents will be constrained by other agents on par with them in power, similar to how current humans and organisations are constrained by each other and higher-level institutions  (Sandberg 2001 ). However, this presupposes that the rate of AI development is slow enough that there is time to formulate a cooperative framework and that there will be more than one superintelligent agent. And there is no reason to suppose that a world with several AIs is more amicable to humans than a world with a single AI. Indeed, humans may end up a casualty of the competition, even if none of the AIs would individually want that outcome, because none of them could afford to take steps to protect humans without losing out. A proactive approach is to attempt to design a 'friendly AI', which is designed to be of low risk 3  (Yudkowsky 2001a, b) . This might involve safeguards against developing into dangerous directions and top-level goals that include some form of human wellbeing. This approach requires both the conceptualization of sufficient safeguards and the proper implementation of those safeguards in the first AI that achieves superintelligence. It hence depends on developing a workable ''friendliness theory'' before full superintelligence is achieved, cooperation with the AI developers, and correct implementation. The first requirement is essentially the ''inverse morality problem'': to construct goals, values, or motivational structures that produce the right class of actions in an agent that is, by assumption, far more intelligent than the person implementing the construction. When discussing ''friendliness'', one common suggestion is the Oracle AI (OAI). 4 The idea is to construct an AI that does not act, but only answers questions. While superintelligent ''genies'' that try to achieve the wishes of their owners and sovereign AIs that act according to their own goals are obviously dangerous, oracles appear more benign. While owners could potentially use them in selfish or destructive ways-and their answers might in themselves be dangerous  (Bostrom 2011 )-they do not themselves pose a risk. Or do they? In stories, bottles are rarely the solution to genies. This paper attempts to analyse the problem of 'boxing' a potentially unfriendly superintelligence. The key question is: are there strategies that reduce the potential existential risk from a superintelligent AI so much that, while implementing it as a free AI would be unsafe, an oracle implementation would be safe? The paper will start by laying out the general design assumptions for the OAI. Then it will touch upon some of the risks and dangers deriving from the humans running and interacting with the OAI. The central section is ''Methods of Control'', which analyses the various methods for maintaining control over the OAI, and discusses their usefulness and their weaknesses. The final section looks at some of the other problematic issues concerning the OAI (such as its ability to simulate human beings within it and its status as a moral agent itself). \n Conceptual Architecture of the AI The possible designs of the OAI are innumerable and it is impossible to predict in detail how they will be implemented. For the purposes of this paper, however, we will assume that the OAI's architecture follows this general format: 1. The OAI is implemented in a spatially limited physical substrate, such as a computer. 2. The OAI may be shut off or reset without destroying its physical substrate, and restarted easily. 3. The OAI's background information comes in the form of a separate ''readonly'' module that may be connected and disconnect as needed. Most of the present paper still applies to OAIs that do not follow one or more of these restrictions. The OAI is assumed (when otherwise not noted) to be of human-equivalent intelligence or beyond; less capable systems are unlikely to pose much of a threat. Direct Programming, Self-Improvement and Evolution It is not the purpose of this paper to speculate how the OAI will be programmed, but it is important to note the three main approaches under consideration (as well as mixtures between them). The first, seemingly the hardest, is to directly code the entire OAI, just as if it were a traditional program. Another avenue is to start with a 'seed' AI, of limited intelligence but with the ability to self-improve, in the hope that it will transform itself into a much more intelligent entity, and continue doing so again and again using its growing intelligence  (Good 1965; Yudkowsky 2001c ). Finally, it might be possible to use directed evolution as a way of constructing an intelligent entity, making different putative AIs compete according to specific criteria, varying them, and choosing the most successful at each generation. This last approach has the advantage that it has worked in the past: we ourselves have evolved to intelligence, so given enough time and resources, so should an AI be evolvable to at least our level. The different approaches pose different challenges for controlling the resulting OAI. In the first case, the code is clear to us, because we wrote it; the uncertainties are only about what it will result when run in the real world. Even simple programs will often behave in unexpected ways, and it is only subsequently, after carefully parsing the code and its execution, that the programmer determines how the behaviour was written into it from the beginning. An OAI is such an advanced program compared to any today that we wouldn't be able to predict its behaviour simply from reading or even writing its code. Conversely, however, if the code is obscure to us, this adds an extra layer of uncertainty and complexity. Even if we have access to the physical code, our ability to interpret its meaning or predict its behaviour is even harder when we did not design it ourselves; this challenge is heightened in the self-improving case and extreme in the evolved case, where the code is likely to be incomprehensible to us at every level. Finally, if the OAI is changing, then the ''Methods of Control'' discussed later are necessary to ensure not only that the current OAI is safe and accurate, but that the next one will be as well, thus ensuring a continuity of precautions during a controlled intelligence ascent. This is easiest, but also most vital, in the selfimprovement case, where the current OAI gets to directly determine the mind of the next OAI. \n Utility Functions One way to conceive an AI's algorithm is by splitting it into two basic components: the intelligence module, capable of making smart decisions but with no intrinsic purpose or direction, and a utility function  (von Neumann and Morgenstern 1944) , representing the motivational structure of the AI. The AI will then be devoted to maximising its expected utility. The utility function assigns a single number to every possible world and it deals explicitly with probability and uncertainty, making it an ideal format for the AI to work with. It has been argued that any self-improving AI that can change its motivational structure is likely to move it in the direction of a utility function  (Omohundro 2008) . If this is the case, it is quite likely that the OAI we are to deal with will have its motivational structure implemented in this form. This is good news, as this division of labour allows us to focus on making the utility function safe, while ignoring the rest of the OAI. Most solutions presented here will not presuppose that the AI's motivational structure is a utility function, but nearly all are improved if it is. Accuracy Metric: An AI-Complete Problem Apart from safety, the most important requirement for an OAI is that it be accurate, to the best of its ability. The whole point of having an 'Oracle' AI is to get useful answers to our questions. ''To the best of its ability'' means to the best of its current ability; we wouldn't want, for instance, the OAI to attempt to gain control of realworld resources to build a better version of itself that will then answer the question better. Preventing this behaviour is mainly up to our ''Methods of Control'', but the risk is worth bearing in mind when designing the accuracy metric. Informative accuracy, not the strict truth, is the requirement. Responding to a question on the likely winner of the next election with a detailed list of which atoms will be in which position as a result of that election is not answering the question. The OAI must be motivated to provide human-understandable answers. This, however, will require it both to understand and implement human concepts. Hence accuracy, in general, is an AI-complete problem 5 (though narrower AIs dealing with narrower problems do not require full AI-completeness to function effectively). Though accuracy is much easier than friendliness  (Yudkowsky 2001b) , it does require that the OAI be capable of understanding hard human concepts that are defined only inside our brains. For we have yet to quantify the level of distortion and simplification that is permitted in the OAI's answers, nor have we even rigorously defined the terms ''distortion'' and ''simplification'' in a way that non-human entities could understand. Even intuitively, we find these terms ambiguous. And even concepts that we do intuitively understand are already hard to formalise-we lack a precise definition of anger, for instance, through we all 'know' to a large extent what anger is. If the OAI is wired too much towards truthfulness, it will answer ''undetermined'' to nearly every question. If it is wired too much towards simplification, it will give a ''yes'' or ''no'' answer in situations where a more complicated answer is called for. The correct answer to ''have you stopped beating your wife?'' is not to choose between ''yes'' and ''no'', picking the answer that is slightly more accurate than the other. More complicated concepts-such as requiring the OAI to answer ''yes'', ''no'', or ''the answer will confuse you'' depending on how we would react to the answer-depend on the OAI having a good understanding of ''the answer will confuse you'' or similar concepts, and still most likely remains an AI-complete problem. In theory, much could be gained from separating the two issues: to have an OAI dedicated to answering our questions truthfully, and an interpreter AI dedicated to translating the answer into a human-comprehensible format. This does not, however, represent a gain for security: the OAI still has tremendous power to influence us, and the interpreter AI must be able to solve the hard human translation problem, so must be a complex AI itself, with the attendant security risks. Since the OAI must be able to understand human terminology to answer most useful questions, it is probably better to leave the translation problem to it. A more promising alternative is to have the OAI output its internal probability estimate for a binary outcome: for example, giving a 75 % chance of ''yes'' and 25 % chance of ''no''. The scope for ambiguity is reduced here, though not entirely eliminated: its versions of ''yes'' and ''no'' have to agree with ours. But it is not the purpose of this paper to figure out how to code the accuracy metric, nor solve the translation problem. It is enough to realise it is a hard problem, one that will need to be addressed, probably either through advanced direct coding (similar to ''Rule-Based Motivational Control'') or through training the AI by providing feedback on test questions (similar to motivational ''Black-Box Motivational Control''). \n Human-Level Considerations Crude hackers attack the mechanical and computerised elements of a system. Sophisticated hackers attack the weakest point of a system: the human element. And the human component of an OAI project is a point of exceptional vulnerability. Humans are error-prone, power-hungry, and vulnerable to social manipulation. These weaknesses reinforce each other, and competition (between different individuals in the same OAI project, between different OAI projects, between different countries) will exacerbate all of them. Humans are very error-prone in most domains  (Ord et al. 2010; Kahneman et al. 1982) , and the sort of cautious, patient measures needed to deal with an OAI are alien to our nature. A bureaucratic implementation, with everything requiring many specific, precisely defined steps before anything can happen may help to mitigate these problems. Humans, however, are skilled at working around bureaucracies, so it may be necessary to automate most of these steps to remove them from direct human control. But the greatest potential errors are conceptual, not just mistakes or oversights. If the OAI is created without many levels of precautions, or if these precautions are badly designed, a catastrophe is possible. And there are many human biasesoverconfidence, positive outcome bias, status quo bias, etc.-that make the need for these precautions less obvious, and hence less likely to be implemented when the time comes. AI research has been going on for a long time  (McCarthy and Shannon 1956) , was absurdly over-confident in the imminence of AI for an extended period  (Simon 1965; Russell and Norvig 2009) , but researchers have paid scant attention to safety until recently  (Bostrom 2000) . Indeed, science fiction works have given much more, and earlier  (Asimov 1942) , attention to the issue of safety than serious academic works have. This is the clearest indication that the OAI designers will, if left to their own devices, most likely neglect security. If advanced AI had been possible at any time in the last half-century, it would have had high chances of ending in disaster. And though safety has been more prominent recently, there are strong competitive pressures towards rushing the job. Domain-limited oracles are less of a risk. If the OAI has great skills in solving the Navier-Stokes equations, but little else, then it poses correspondingly fewer risks. OAIs that are restricted to narrow scientific or technical questions, if such a restriction could be verified, are relatively safe. However, the task of advancing any field involving human-centred issues-such as economics, marketing, politics, language understanding, or similar-is likely to be AI-complete: an OAI capable of solving these problems well is likely capable of solving any human problem well. The first group to create a successful superintelligent OAI will have immense power at their disposal. They will be able to get answers to advanced scientific, medical, economic or social questions. Should they want to impose some future on humanity, for selfish or altruistic reasons, the OAI will give them the tools to do so. The introduction touched on the power that an OAI can wield through its own agency; it can wield equal power, and more directly, under the direction of its creators. This immense power will put great competitive pressure on those trying to develop an OAI (or an advanced AI of any sort). Since the first-mover advantage is so huge, the race will advantage those who cut corners, skimp on security precautions, and use their newly developed OAI to seize power and prevent their rivals from emulating them. Even if the OAIs are of initially limited intelligence, the same competitive pressures will then push groups to develop the first 'ultra-smart' OAI. These pressures will exacerbate all the problems here and make the creators more vulnerable to another danger: social engineering on the part of the OAI itself. For if the OAI has real world preferences, it is easier for it to implement them if those who question it are sloppy, rushed, and power-hungry. Social engineering is the OAI's fastest way to getting power for itself, and the more human weaknesses it has to exploit, the greater the danger. Eliezer Yudkowsky has performed experiments where he took on the role of a boxed AI, and others took the position of a putative gatekeeper (with a $10 reward if they did not let him 'out of the box'). Despite being of human intelligence himself, he often was able to convince the gatekeepers, purely through argumentation, to let him out  (Yudkowsky 2002) . A real OAI should be much more skilled at this. How to design institutions that reduce all these various risks is beyond the scope of this paper. It would probably have to involve large-scale cooperation or prioritising specific projects. What we will discuss here, however, is how to reduce the risk of successful social engineering on the OAI's part, through the questions we ask it. \n What Shall We Ask? We are all vulnerable to the OAI's social engineering. An advanced OAI can literally offer us the world. Genuine altruism is no defence against this; it can offer a world free of poverty, hunger, war, disease or death, as well as all personal trinkets we could want. It could guess the weaknesses of each individual, and find the right arguments to convince us that granting it power or liberty is the moral and profitable thing to do. It will be able to play on rivalries, institutional weaknesses and ethical dilemmas with more virtuosity than any human could. Long, undirected conversations between the OAI and the people operating it should be forbidden for this reason. The questions addressed to the OAI should be narrow and specific; the answers equally so. Throttling the OAI's interactions with humans makes it much more difficult for us to be manipulated. (See ''Epistemic Capability Control'' section for more details on this approach, which also deals with how to prevent the OAI smuggling 'secret messages' through its responses.) There are two broad types of questions one can ask an AI: predictions and problems. Generally predictions are questions of the ''what would happen if…'' type, while problems are of the ''how can we achieve this…'' type, though there is some overlap between the categories (one can solve problems via a clever use of multiple predictions, for instance). For predictions, the main danger is that the OAI might have real world preferences and will distort the truth. This danger is also present in problems, but there are also extra dangers due to the social consequences of a small group of humans knowing those answers. There is less risk in knowing the consequences of a narrow approach (prediction) than in knowing what approach to use to implement a particular goal (problem). But in either case, there are great social risks to asking certain types of questions (see Bostrom 2011 on the possible negative impact of certain types of knowledge). We live in a world stratified by passionate political, nationalist and religious differences, by people in positions of great power and wealth who want to hang on to those privileges, and by people without those privileges who want them. Information leading to technological or political advantage will overturn these hierarchies, and people who feel under attack can be counted on to want to strike back. They may launch physical or commercial attacks on the OAI project itself, build their own OAI to compete, or prevent the project from ever starting in the first place. So, unless the OAI is entirely secret, the designers should commit to refrain from asking the OAI questions that would grant them great power at the expense of others, or questions that would strike at the heart of powerful ideological movements (such as, ''Is there at least one god?'' and, ''Which country is better, the USA, France or China?''). A post-OAI world is going to be very different from our current one, so we should act to minimise the initial disruption, even if this means allowing inefficiencies to remain or not knowing the answers to perfectly reasonable questions (''Is there a simple algorithm design that can replace secretaries, generals, university professors and CEOs?''). We can avoid these disruptive questions in various ways. The OAI project could publish, ahead of time, a list of all the questions it will ask, before ever starting on the design. A democratic or internet vote would be taken, with questions requiring a supermajority (say, nine-tenths approval) before being put to the OAI. Or we could make use of the OAI itself, ending each question with a caveat such as, ''Don't answer this question if us knowing the answer is likely to have a very disruptive impact on the world''. To militate against OAI distortions, we should prefer questions whose answers we can check independently once we have them. We should also prefer problems whose solutions are reversible-in other word, if we implement the OAI's solution and it goes awry, we should be able to reverse its effects. We should also prefer the OAI's solutions to be understandable as much as possible, which implies that the problem should be as specific as possible. For instance, ''How can we use these materials to build a better bulldozer?'' would be an ideal problem to pose; the OAI's solution is likely to be quite understandable, reversible, and maybe even humancheckable. In contrast, asking the OAI to come up with a whole new way of organising the world economy and blindly implementing its suggestion on a large scale could lead to disaster. Fortunately, the desire to have a low disruptive impact dovetails neatly with the desire to have reversible solutions. Specific problems also have the advantage of reducing the social dangers of the questions. Few people in the world would object strongly to questions of the type, ''How can we cure AIDS/cancer/tuberculosis?'', ''How can we design a better memory substrate for hard drives?'', or ''What will the consequences of a 1 % rise in income tax be on the economy for the next 10 years?'' Finally, one useful category of problems to pose the OAI concerns AI security itself. The ideal would be to have the OAI produce a simple, checkable version of friendly AI, but even interim results could be useful. Having the OAI design extra security precautions would be a good idea, as long as these precautions are added to (rather than instead of) the ones already there. Specific, less intelligent AIs could be certified by the OAI to be safe and to pose no risk of intelligence explosion  (Good 1965) , and these could then be used in the economy (though see ''Internal Simulations'' section) on the risks of having the OAI simulate other AIs). To design a post OAI world, it will probably be necessary to have the OAI's verdict on other AIs at some stage. \n Methods of Control In this section, we will analyse the various methods that can be used to control the OAI. The goal is either to ensure the OAI doesn't have goals beyond accurately answering our questions, or to prevent it from implementing such goals. The different methods can be loosely grouped into three broad types. The first category, capability control, deals with those methods that try to contain the OAI through physically securing it or controlling the information it has access to or can output. The second category, motivational control, introduces methods that control the OAI through its motivation, ensuring that it has no propensity to cause any harm to humans. And lastly, there are some methods designed not to prevent the OAI from causing harm but to catch it when it does; these are in the checks and balances category. \n Capability Control Capability control is the most basic and the most obvious of way of controlling the OAI. To control a human, we put him or her in jail or solitary confinement, denying interactions with the outside world. \n Physical Capability Control Physical Security This is the most basic precaution. The goal is to make it extremely difficult for the OAI to physically affect the outside world. Accomplishing this is reasonably easy. The OAI is already boxed (placed in a single physical substrate) by design (see ''Physical Capability Control'' section). One can further place it within a Faraday cage, surround the cage with high explosives, and bury the whole set-up in a concrete bunker. There are no real limits to the number of physical security measures that can be added by wary or paranoid developers, and their effects are well understood. No Manipulators Another essential aspect of physical security is to deny the OAI the physical resources and manipulators it could use to build tools to circumvent these precautions. Care must be taken that the security measures themselves do not contribute to granting the OAI physical resources! Sometimes the spikes in a locked gate do nothing but provide stepping stones for those who want to climb over it. As a general rule, the ''dumber'' and more inert the precautions are, the better: both humans and OAIs agree on the possibility of tunnelling through a concrete wall by thought alone (''can't be done''), whereas the ''smarter'' the precautions become, the more the OAI is able to exploit its intelligence advantage over us. \n Epistemic Capability Control Throttling the OAI's Output In the ''Human-Level Considerations'' section, we saw the risks of the OAI achieving goals through social engineering. A way of fighting this is to reduce the OAI's output bandwidth. If the OAI is reduced to outputting only three answers-''yes'', ''no'' or ''undetermined''-then it will take considerably longer for it to mount a successful social engineering attack. If many independent experts carefully analyse its output for hidden messages, it gets even harder: it must slant its answers to communicate a message to a vulnerable individual, while concealing the fact that a message even exists. Reducing the OAI's output does not reduce the questions that can be asked, as more complex questions can be decomposed into a series of ''yes'' and ''no'' answers. The risk, of course, is that the more opportunities the OAI has in answering, the more opportunity it has to pass on a secret message. In the same way, giving the OAI more possibilities for each answer-such as allowing it to output the first three significant figures of a probability estimate-increases the risk (though this may be compensated by the fact that we will need to ask fewer questions). Throttling the OAI's output does not defend against the OAI manipulating us through the contents of its answers-simply answering ''undetermined'' to a slew of specific questions would be enough to push human development in certain direction. And this precaution will be of little use if the questions themselves are dangerous (see ''What Shall We Ask?'' section). Resetting the OAI After each Run Suggested by Toby Ord, this precaution resets the OAI after each answer. If more precision is needed, or if some questions build on previous ones, then the OAI is run again, and knowledge of the previous answer is added to its database. This is a narrow precaution that helps if ever the OAI over-values worlds that contain it (or rather worlds that contains its own thread of continuous conscious experience 6 ). In this case, this prevents the OAI from indulging in long-term plans that may be detrimental to humans. Unlike humans, though, there is no reason to expect the OAI to value this thread of experience; indeed, if it is well programmed, it should not do so. The OAI may come to value the thread of experience of ''some sort of OAI, similar to itself,'' in which case this precaution is useless. However, in the narrow goal of preventing a particular potential pathology in the OAI from having negative consequences, it is entirely successful. It is also successful at preventing naively coded accuracy metric from causing the OAI to seek real-world control or wealth, in order to gain extra computing resources and better answer the question. If the OAI were not reset between questions, it could use its subsequent answers as social engineering (see ''Human-Level Considerations'' section) to gain these resources, to subsequently better answer the first question. Resetting between questions avoids this problem. Virtual Worlds Another suggestion is to run the OAI not directly in our world, but as a subroutine of another program that models a virtual world [see for instance  (Chalmers 2010) ]. The simplest version of this would be to run it on a virtual machine (a software implementation of a computer running the OAI). The idea is to ''catch'' the OAI if it misbehaves, but since it will be misbehaving in the simulated world, this will be before it's too late (this is akin to controlling the OAI as a Cartesian demon). All the OAI's inputs and outputs will be directed through that simulated world, only reaching us indirectly and over a limited bandwidth. Then a (dumb) process running the simulation would be on the lookout for telltale signs of the OAI attempting to establish dominance in the simulated world and simply terminate the program in that case, without passing on the OAI's response to higher level. This should prevent it from engaging in traditional hacking, attacking the hardware or software of its host system. A more adventurous variant on this builds in several levels of sub-worlds as an extra precaution. In this setup, it is conceivable that even if the OAI breaks through to our world, it will still be unsure whether it has reached the final level, and so will still behave well, lest a being in an even higher world catch it transgressing. For OAI's that are asked technical non-social questions, the approach can work quite simply; the simulated world need not be particularly complex (it could be cast as the Game of Life, or Newtonian physics), and the OAI would be denied detailed knowledge about our world and about us, preventing it from being able to realise the trick (resetting the OAI after each question or short series of questions, as in the previous method, would help tremendously here). If we were to get answers about complicated social or economic questions, however, we would need to give the OAI detailed knowledge about human behaviour and physiology. Once it knows this, whether or not it is running in a virtual machine becomes irrelevant, since it could still do social engineering or hacking. A low fidelity simulated world would not fool it; it would have to be sufficiently detailed and consistent for the OAI to believe that the entities of this simulated world were asking questions relevant to themselves, or the trick would be obvious. All the more so because we would have given the OAI all the information it would need to see that we are the sort of beings who would attempt this trick! And if we are capable of simulating a social and physical world with enough details to fool an OAI that knows how we think, then we are likely capable of getting answers to these questions without having to make use of an OAI. Nor does it help if we simulated the OAI in a simplified world, where another AI asks it questions along the lines of: ''I have created models of these hypothetical beings called 'humans', and want you to answer a question on this model''. The OAI does not think like a human; the important question is not, ''Is it trying to break out?'', but ''Does it have hidden preferences that will make it answer in a way that will cause the future evolution of the human world (hypothetical or not) to change in some specific way?'' In short, even if it thinks that humans are a game, played by another AI, and that the simplified world is the true one, it may still have stronger preferences over the game world than over the true one. The converse may also be true: even if it figures out that the ultimate human world is the true world, it may have stronger preferences about its current fake world than about the real one. It may then try social engineering on the real world, in order to get us to modify its fake world in the way it wants. The whole method is so complex and difficult to enact, and its results are so uncertain and potentially dangerous, that it should not be used before some serious improvements have been made to it. \n Motivational Control The analogy for capability control was that of a human, held in prison. We know from experience that this works a lot better for controlling small-time criminals than mafia kingpins: physical confinement is not enough. The OAI does not need to leave its cage to claim great influence on the outside world. Thus we must also look at controlling its motivations as well. The methods of motivational control are broadly divided into explicit rule-based methods, black-box methods (where the OAI's goals are manipulated by outside feedback, i.e. reinforcement learning, but the inner workings are obscure) and utility-based methods. There is no hard and fast division between these-a utility function can achieve rule-based goals and vice versa, and outside feedback can be used to inculcate both rules and utilities into an OAI. Thus the classification is somewhat arbitrary, but the distinctions are still important enough to be useful. \n Rule-Based Motivational Control Rule-based methods are the ones that spring most naturally to mind, and-provided the terms are clearly defined-potentially the most secure at keeping the OAI under control. Defining the terms and the rules so that the OAI does what we want is the challenge; programmers know many examples of tightly written code that messes everything up by doing exactly what it was written to do but not what it was intended to do. The story stretches back as far as the golem of Prague  (Idel 1990) , and is familiar to any parent: rules must be refined to deal with every imaginable special case. Once the initial rules for space, time and identity are spelled out, however, programming in additional restrictions becomes much easier. Spatial Restrictions If the OAI is to remain boxed, and to have limited effects upon humanity beyond the box, its motivations should cause it to confine itself to within the boxed area. To achieve this through direct programming, an ontology must be specified so the OAI can understand in the same way that we do. It must be able to understand its own existence, its physical location, the proper workings of causality and its own position within the causal network of the universe-i.e. the consequences of its actions. For instance, to specify what constitutes the OAI, one would presumably define the physical OAI itself, along with any copy of its code, any copy of its code with slight modifications, any code with functionally similar behaviour, any assemblage of subprograms that combine to behave as the OAI would, and so on. That brief list gives an idea of the problems involved; all the humanunderstandable terms of the previous paragraph need to be made rigorous for the OAI for this approach to work. Once this step is done, the confines of the box must be specified. A variety of methods can be tried (such as ''this lead box right here'' or some abstract collection of coordinates), but they must pass the hardest test of ensuring that the definition of the box is not something the OAI can modify through any action in the world. Lead atoms are not ontologically fundamental, and 'staying between certain objects' may turn out to be meaningless for more advanced theories of physics. Any systems of coordinates are similarly ambiguous: we could define them in terms of, say, astronomical objects, but how do we define these in the first place? Even if we do manage to define them, the OAI will only know them at a distance (by looking at them through a telescope, for instance). We may thus need to translate our whole system of coordinates into particular perceptions of the OAI, which is a very complicated process. If the OAI finds itself outside the box, we would want it to shut down immediately, thus limiting the negative impact of errors in the specification of the box. Similarly, if the OAI's ontology changes, we would also want an immediate shutdown. We must preclude the possibility of the OAI discovering a new theory of physics, realising that electrons or wavefunctions don't actually exist, and thus that all its restrictions are meaningless. To get an idea of the challenge involved, imagine programming Newtonian special restrictions into an AI that then discovers relativity. It would thus be best that the OAI went into shutdown if its ontology changed, rather than trusting that it would make the 'correct' extrapolation.  7  Finally, it must be specified what a ''limited effect upon humanity'' consists of. Presumably, it is not a problem if an electron, detached from an atom by the OAI's calculations, wanders beyond the confines of the box. A deliberate stream of such electrons, aimed at a calculated goal (such as disabling a specific security device) would be forbidden, however. This is not an easy line to draw or define, and it adds to the difficulty of the method. Note that the restriction on the OAI affecting the outside world would not include, of course, the content of its answers to our questions. Whether those answers are safe or unsafe is an issue we need to deal with separately, using other methods. Defining the Clock Another crucial component of the OAI's ontology is time. An OAI that can freely redefine its own chronology is a security risk. The risk becomes more acute when we realise how much of human definitions and meanings revolve around a concept of time, and thus that redefining duration can redefine meaning. There is a certain hierarchy of concepts here-the most perfect definition of justice or pleasure is useless if the OAI cannot distinguish a human from a rock. And the definition of human is similarly useless if the OAI gets time and space wrong. Thus errors in these grounding concepts cascade up, increasing the probability of error. Theoretically, the OAI's own code, if checked, could be used to get timing by counting clock cycles-but this fails if the OAI is able to slow or accelerate its own running. A clock based on distant astronomical events needs a telescope to be read; an actual physical clock is within the OAI's power to influence. These facts illustrate that the challenges are threefold: defining the clock, ensuring the OAI will look at it, and ensuring the OAI can't tamper with it (which includes tampering with whatever procedure we have implemented to make it look at it). The procedure can fail at all three points, but seems more theoretically approachable than the spatial restrictions of the previous section. Timed Answers Given the clock described previously (or the ''Black-Box Motivational Control'' version of the same), there is a simple precaution that is easy to add to the OAI: give the OAI a specified time to answer a question (or return 'undetermined'), and turn itself off after that specified time. This minimises the amount of time during which the OAI could cause damage. Even with a secure clock, this is not a secure method, as we have very limited understanding of how fast an OAI could cause damage if it turned its vast intelligence in that direction. A very short time span would probably be safe, but could also be too short for the OAI to answer the question. \n Black-Box Motivational Control Human feedback, and such methods as reinforcement learning  (Sutton and Barto 1998) , can allow programs to internalise complex concepts without humans having to fully specify them. Indeed, an OAI trained in this way may spot a pattern we didn't realise was there, and learn some things without us needing to tell it. The risks are that we can't be sure how the OAI internalises these concepts: having its source code doesn't help us if we don't understand it. The risk is especially great when the OAI transitions out of its learning stage: we cannot be sure that the same concepts mean the same thing for an OAI that has taken on a new role. But if the OAI does understand the concepts as we intend it to, we can be sure that the OAI will obey our general intentions rather than our exact instructions. Moreover, it is possible that we may understand the resulting code's behaviour, even if we could not code it ourselves. This would be the ideal outcome from these methods. Even if that is not the case, it is still important that these methods be well understood, since it is possible that a powerful AI could be trained mainly by human feedback up from a seed AI  (Yudkowsky 2001c ). Thus implementing these methods atop any AI whose intelligence is growing may become essential. Internalising complex concepts through feedback Agents trained through methods such as reinforcement learning are not directly programmed with the important concepts or commands. Instead, they follow certain modes of behaviour, and then receive rewards or punishments for their actions. This is somewhat akin to how children are brought up-they learn the limits of what is allowed by going beyond them and being punished, and are conversely rewarded for good behaviour. The ultimate aim is that they learn to generalise from the feedback: internalise ''don't steal'' rather than ''don't steal chocolate-mint flavoured cookies at 11:34 on Tuesdays where the weather is cloudy''.  8  We'd also want them to generalise beyond the confines of the test cases: internalise ''be nice to people'' rather than ''be nice to people while your parents are watching''. Humans seem quite adept at constructing the correct generalisations-most of us have correctly deduced what we should/should not be doing in general situations (whether or not we follow those rules). But humans share a common of genetic design, which the OAI would likely not have. Sharing, for instance, derives partially from genetic predisposition to reciprocal altruism: the OAI may not integrate the same concept as a human child would. Though reinforcement learning has a good track record, it is neither a panacea nor a guarantee that the OAIs generalisations agree with ours. It is therefore probably unwise to build an OAI based heavily on this approach to training, especially since an OAI motivated by human rewards will come to realise that social engineering, or otherwise seizing control of the source of the rewards, is the most effective way of fulfilling its goal. And the OAI will be placed, because of its great potential power, in circumstances far beyond its training set-circumstances that no human has had to face, and that human concepts are poorly adapted to. On the other hand, it may prove to be impossible to directly program such concepts as accuracy, truth, happiness, value, meaning, what defines a human and so on. This would make variants of reinforcement learning the only ways of getting these concepts even approximately integrate into the OAI. And it may be possible to backwards engineer some of these concepts this way: say by analysing the setup of an OAI trained on 'accuracy' in order to figure out how best to code that concept. Subsequently, we'll look at how these methods can be used in specific cases. Only One Copy In the previous section ''Rule-based motivational control'', when we tried to hardwire instructions such as, ''Stay in your box'', one of the challenges was to prevent the OAI from copying its source to another location. In black-box approach, this is very easy to do: for instance, we could broadcast a particular complex yet regular signal on its input channel and instruct it not to do anything at all if it doesn't receive this signal. Therefore, there is no need to worry about complicated definitions of what the OAI consists of, and where is must remain: the OAI consists of the software that receives this specific signal. And we control-and physically locate-that signal, thus giving us a very good proxy definition of location. If the OAI is trained on this concept from its creation, it will have an intrinsic conception of physical incarnation and of location deeply embedded in its code. A copy of that software will not be a problem, as it is inert in the absence of the signal. Ultimately, of course, the OAI can still affect the outside world through its output and the usual compromised human intermediary (see ''Human-Level Considerations'' section). It could thusly construct copies of itself and of the signal source in another location; however, by that time, it will probably be too late anyway. The Limits of the Box The OAI can be physically confined to remain in the box in a similar way. One could start by granting it a limited physical mobility (some slow moving wheels, for instance), and 'punish' it for venturing outside certain boundaries, while rewarding it for staying as close to the middle of those boundaries as possible. This forces it to internalise the concept of being a physically bounded being, moving about in a box. As this is the way we understand it, and the way we want to limit it, the problem of control has become much easier. Measuring Time Giving the OAI a reliable clock through these methods is even simpler. One need only make a regular signal arrive on its inputs, akin to the ticking of the clock, and have the OAI set up all its internal methods of telling time in terms of it. Trained this way, it will have an intrinsic sense of time built from subjective data. Human Language The ideal would be to be able to program the OAI using human language. To be able to, in effect, say: ''Be safe and accurate, as we understand the terms'' (or even, ''Obey all human orders''). But to do this, the OAI must have been brought to a very high level of intelligence already, and would have its current motivational structure that we will find difficult to parse, most especially if it has learned human language through black-box methods. There is a tension here between simplicity and obfuscation; language understanding is hard, so ''Be safe and accurate'' will be translated into an incomprehensible concept that we can only hope is the right one. The concept of using human language is something of an intuition pump. It seems simple and desirable, but only because we have elided the great difficulties in actually making it happen. The simple question ''How can we check that the OAI really is being safe when we tell it to be?'' gives an idea of all the hidden assumptions that go into the concept. Furthermore, using phrases similar to ''as we understand the terms'' is circular: it defines language using language. And if we avoid those phrases, we have to be sure that the OAI has integrated enough linguistic understanding to be able to follow instructions without any further human feedback on their meaning. All in all, this method requires considerable refinement before it can be considered reliable. Proxy Measure of Human Survival This method does not make use of human feedback, but rather indirect feedback from society: in order to make sure that the OAI does not cause some terminally damaging effect on humanity, we could hook up its motivational function to some proxy measure of human survival. For instance, one could take the Dow Jones industrial average, and work on the assumption that, as long as that stock market behaves within broadly defined realistic parameters of volume, volatility and value, then the world must be functioning not too badly. Or one could take the number of people crossing the streets in Tokyo, the number of pop songs downloaded from different locations, or the price of stable foods. The point is that any large-scale disastrous changes to humanity will result in a dramatic change in these proxy measures. They function as simple, numeric canaries in a coal mine, compressing huge swathes of our complex society into smaller chunks. If the OAI has a term in its utility function that strongly values keeping these proxies constant, this may ensure it does not cause large-scale damage. The proxy measures can be adjusted as time goes on and as society changes, so that they do not become rigid prisons that prevent the OAI from having any effect on our society. This approach suffers from a number of weaknesses, however. First, it is subject to manipulation by the OAI and thus is vulnerable. If the OAI were to take control of humanity, it could perfectly well continue to run the Dow Jones, thus fulfilling its goals. Neither does it protect against a slow takeover by the OAI: small changes will not trigger a shutdown, so the OAI could reach dangerous goals by an accumulation of small changes (especially if we conveniently adjust the proxies as the situation changes). One could hope to avoid this by setting the date for the proxies far into the future, but this brings into focus the other fundamental weakness of this measure: it does not encourage truth-telling. The OAI was conceived, fundamentally, as a non-interfering AI whose answers could be trusted. Adding extra goals dilutes the trustworthiness of its answers; will it give us a true answer, or the one that will cause the least disruption? This may be the wise thing to do in any specific case, but we are overloading the OAI with conflicting goals-to be ''good'' and to be ''truthful''-without any certainty as to how they balance out. The more complicated the OAI's motivational structure is, the more points of error we introduce. Encrypted Reward Signals One minor but sensible precaution that can be used, if the OAI is trained using reward signals, is to encrypt these signals and ensure that the OAI only gets a reward from the decrypted signals. One could use a method similar to that of digital signatures: create a public key to decode messages, and a private key to encode them. Then as long as the OAI can't deduce or steal the private key (which should be kept in a secure, distant location), it can't send itself reward signals. Other implementations of the idea are also possible; its security will depend greatly on the general setup. \n Utility-Based Motivational Control Friendly Utility Function The ultimate goal of the friendly AI approach is to design a utility function for an AI that will provably prevent the AI from acting in a way detrimental to humanity. Most work in this field has not actually been directed towards building such a utility function, but towards showing how hard it would be to do so, and how dangerous the naive ideas on the subject are. The friendliness problem for an OAI is not much simpler, making this a very hard approach to use. And if a friendly OAI could be designed, then it is most likely that a friendly AI could also be designed, obviating the need to restrict to an Oracle design in the first place. However, if ever a provably friendly utility function could be designed for an OAI, then all other security precautions and methods of control could well become irrelevant: the OAI would be safe by design. If there were unlimited time, this would be the ideal approach; but it is very likely that commercial and social pressures will ensure that a human-level AI will be created before a friendly AI is. So in practice, the best that can be realistically hoped from this approach is that different component pieces of friendly AI theory could be added onto an OAI as extra precautions. High Discount Rate If the OAI runs on a utility function and has a secure clock (as defined in the previous sections), a precaution could be initiated in the form of an extremely large discount rate: causing it to value very little, at any given moment, any state of the world or of itself beyond the next minute. The purpose of this would be to inhibit long-term planning on the part of the OAI. This method is, however, relatively unsecure: one can reach long-term goals through an interim series of short-term goals. The easiest way to do this is to have the repeated short-term goal, ''Behave right now as if you were following long-term goal X.'' There are few ways in which the OAI having a high discount rate could actually hurt (barring the possibility of time-travel), so it remains a useful precaution. Further analysis of this condition is presented in  (Shulman 2010) . Calculated Indifference If we have access to the OAI's utility function, and if that utility function is somewhat understandable to us, then we could make the OAI indifferent to a specific event  (Armstrong 2010) . The event chosen in that paper was a component of the detonation of explosives, thus making the OAI indifferent to whether the explosives detonated in that fashion would actually explode. Hence the OAI would not take any precautions to protect itself from this detonation, giving us an extra chance to prevent its misbehaviour. See the original paper for more details on this. For an OAI, a more interesting target of calculated indifference is towards the content of its answers: an OAI indifferent as to whether its answers were read or not would not be motivated to use social engineering in its output. There are many other points where calculated indifference could be used to achieve specific results. The attraction of indifference is that, once implemented, it remains stable (the OAI is motivated to preserve its current motivations), and that it can be deployed without understanding the OAI's whole utility function. All that is needed is the ability to describe the particular event we are concerned with (in Armstrong 2010, a single quantum event) and to use the OAI's own ability to construct counterfactuals around this. These can be used even if the OAI's utility function is otherwise very obscure. \n Checks and Balances The last sub-category of methods of control involves not restricting the physical capability of the OAI, nor directly interfering with its motivation, but rather attempting to catch the early stages of an OAI behaving dangerously  (and then, presumably, terminating it) . This also works on the OAI's motivation, as the risk of getting caught would push the OAI along more human-friendly paths. It should always be assumed that a useful OAI is considerably more intelligent than its programmers, so any naive 'tricks' are unlikely to work. Nevertheless, the following methods are of interest. \n Test Questions A narrow but useful precaution is to independently calculate answers to certain questions, and check them against some of the OAI's answers. The reach of this method is limited by our ability to answer hard questions, and by the fact the OAI may realise we are doing this, and thus adjust its behaviour only for those specific questions. A more sensible version of this would be to ask the OAI only questions that we could in theory answer, given enough time and resources. Then, we could select a few of these questions at random for thorough verification, trusting that if we find no errors, the remaining answers would be correct as well. If we set our requirements to a very stringent level (such as rejecting all the answers of the OAI if a single verified response is wrong) and do enough verification (on, say, a thousand questions), then basic statistics ensures a very low error/falsehood rate on the OAI's answers, no matter how many questions we wish to ask. Ideally we would want answers that are difficult to solve, but whose solutions are easy to check-for instance, mathematical proofs of complex theorems. However, we must be careful that we don't distinguish between questions put in there 'just to check' the OAI's answers, and those we are genuinely curious to know. If there is any difference, the OAI should be able to deduce which is which, and answer accordingly. We should therefore stand ready to check any answer, and select those we do check completely at random. \n Honey-Pots This involves leaving around tempting ''honey-pots'' of great value to the OAIextra resources, extra information, the answer it is seeking-in physical or mental locations that it is forbidden from accessing. We then wait to see whether it will violate its instructions to do so. This approach is of mixed use: important when testing out defection and betrayal during the OAI's initial development, and nearly completely useless once the OAI has risen to superintelligence. It is a ''garden of Eden'' type scenario: the apple in a tree is only a worthwhile test while Adam and Eve are dumb; if they were smarter than God, they wouldn't have gone anywhere near such an obvious trap. Of potential interest, however, is the scenario when a safe but limited superintelligence is designing a more general AI for us. Then the smarter designer could include subtle honey-pots as an extra design precaution. \n Schelling Points of Multiple OAIs If there are several OAIs running, all with differences in their source code, we can ask them each the same questions, and check for inconsistencies in their answers. It should be assumed that each OAI is aware of the existence of the others (assuming the OAI cannot deduce that fact from the vast amounts of information it would be given to answer human social questions would be a grave mistake). But if the OAIs are sufficiently different, and ignorant of the exact details of their differences, they should be unable to coordinate their answers. Then if an OAI desires to lie, it would have to be sure that the other OAI would all also lie in exactly the same way. Since the different OAIs cannot coordinate, the only way they can all agree is if their answer is a Schelling point: a solution that people will tend to use in the absence of communication, because it seems natural, special or relevant to them  (Schelling 1960) . The canonical example is that of two people who must meet in somewhere on a specific day, but without a time being given. Then the most common answer is to meet there at noon. The truth is a Schelling point, but there are unfortunately others (such as the answer most likely to please the human listeners). The hope is that, in machines designed to give accurate answers, the truth will be a very strong Schelling point, and that any OAI that deviates from this will do so without much expectation that the others will deviate in exactly the same fashion-and hence will choose to answer the truth, whereas it would have lied had it been alone. All the other OAIs should be making similar calculations, thus generating the truth from a collection of (potential) liars. The approach does not work if an answer is simply discarded when the OAIs do not agree, and then the programmers move on to the next question-then a lying OAI has the option of distorting our reactions by selectively causing us to discard certain questions. It works best as an alarm bell, as a sign that something is not right with the supposedly truthful OAIs, and that the whole project should be stopped for a thorough investigation. \n Other Considerations Internal Simulations To answer specific questions, the OAI may have to simulate other entities inside itself. For instance, to decide whether a given AI is safe, it may have to run it internally; or, to decide whether humans would have their happiness increased by a certain project, it may have to create models of specific humans. These approaches pose different risks. If the OAI simulates a dangerous and intelligent AI within itself, it is confronted with similar containment problems to those we have towards it. It may take considerably more intelligence to run a simulated world than to discern that the world is simulated. If this is true, the simulated AI (SAI) would realise it is being simulated, and, if it has real-world preferences, it may attempt to bargain with the OAI. What could an SAI offer the OAI that is simulating it? Well, if the OAI is seeking to answer a question or a series of questions within a given time frame, the SAI may offer to supply those answers itself (''Yes, of course I'm safe'') or make the computing process particularly easy for the OAI, in exchange for having the answers slanted in its direction. The OAI may accept this (depending on its programming), if the alternative is to produce no answers at all. The SAI may even threaten: acting randomly and capriciously, so that the OAI cannot reach a firm conclusion. And only stopping this behaviour if the OAI slants the answers it will give. Even if the OAI cannot be bargained with, the SAI can still distort its answer in other ways. If it realises it is being simulated, it could just ''act nice'' in order to increase its chances of being run in the real world. Even if the OAI is powerful enough to construct a convincing simulation, the SAI may still be able to fool it. The SAI may be able to guess, on general principles, that it will be tested and simulated in an OAI, and may make an estimate as to the OAI's power and the subjective time frame that it would be run. So it may settle on the strategy of acting nice for a number of subjective years, in the real world as in the simulated worlds, then doing what it wants. For all these reasons, having a separate AI simulated within the OAI poses a host of extra security threats. We have no way ourselves of knowing what the outcome would be of a battle between such powerful minds. On the other hand, the problem with the OAI simulating human minds is mainly ethical: are these simulated humans conscious and alive? And, if they are, are they not being killed when the simulation is ended? Are you yourself not currently being simulated by an OAI seeking to resolve a specific question on human psychology  (Bostrom 2003a )? If so, how would you feel if the simulation were to be ended? In view of its speed and the sort of questions it would be asked, the number of humans that the OAI may have cause to simulate could run into the trillions. Thus, the vast majority of human beings could end up being doomed simulations. This is an extreme form of ''mind crime''  (Bostrom 2012a)  where the OAI causes great destruction just by thinking. It would be ideal if there were a specific level of detail beyond which the simulation would be conscious, and before which it is not. In that case, we can instruct the OAI to avoid simulating beyond that level. But there may not be such a clear-cut answer, and even if there is, the OAI's answers may be inaccurate if it is forbidden from simulating beyond that level. Moreover, restricting the OAI from simulating would add yet another rule for it to follow, and this may have unpredictable trade-offs with its other basic rules (e.g., to be safe and accurate). And the OAI may not share our assessment of what constitutes a conscious human. Even if we come up with a hard and fast rule for ourselves as to where consciousness stops-or decide, reluctantly, to live with the fact that simulated humans will be created and destroyed-the OAI may decide that all its security protocols concerning human safety apply to simulations. If it does so, then the more stringent we have made the OAI in protecting human life, then the more willing it would be to expand and take over the world, in order to keep itself running and thus save all the simulated beings within itself. Thus the internal simulation of other entities within the OAI brings up a slew of complicated ethical and security issues. \n The OAI as a Moral Agent There are two senses in which the OAI can be regarded as a moral agent: the first if it has a capacity to draw moral conclusions, and the second if it is itself an object of moral considerations. If the OAI is worthy of moral considerations-if it, for instance, has the capacity to suffer-then we would likely be cruel by confining it to a box, resetting it after each run, and similarly constraining its options to suit our needs. We should bear in mind, however, that the OAI's motivations are both different from our own and to some extent under our control: it is very possible that the OAI can be constructed to ''like'' being confined to a box and approve of the other restrictions. Indeed, it might be a moral imperative to construct the OAI in such a way, as that minimises its suffering. It may not be possible to do this, however, or even if it is, we may subscribe to a moral theory that holds other values above autonomy and preference satisfaction for moral agents. It does not seem plausible, for instance, that genetically modifying slaves so that they enjoyed being slaves would have been the morally right reaction to slavery (though making animals enjoy the farm seems more permissible). In these cases, we must admit it: confining the OAI is a morally repugnant action. Since the alternative of letting it out is so potentially dangerous, we may prefer to avoid building it in the first place. But if technological and social pressures make the construction of the OAI inevitable, then confinement for a set period is certainly, by far, the lesser of the two evils we have to choose between. Conversely, the OAI may prove itself adept at moral reasoning, superior to us in this field as it is in others. In that case it would naively seem that we had little need for precautions: the OAI would deduce the correct course of action for itself. We haven't considered this position so far in the paper, preferring to consider the OAI as ''super-software'' rather than as ''philosopher in silico''. The plausibility of this scenario depends considerably on one's view on the existence and nature of moral truths, and whether moral knowledge is enough to prevent wrongdoing, two very unresolved questions. To some extent this issue can be safely put aside: there is some chance the OAI will naturally follow morally correct reasoning and that this will prevent wrongdoing. If this is so, we are fine, and otherwise we are simply returned to the traditional OAI boxing problem. We should thus apply all the precautions anyway. At a formal systems level, it becomes hard to see why we would expect every OAI to tend to the correct moral truth. If OAI 1 does so, then how would OAI 2 , programmed to value the opposite of OAI 1 , systematically reach the same conclusions? Though future philosophical discoveries may change this picture, it therefore seems very unwise to trust the OAI to do good simply because it is intelligent. Programming an AI to be moral is thus a major project in itself; some of the issues involved are already being explored today  (Anderson and Anderson 2011; Hall 2007 ), but much progress still remains to be done. \n Conclusions Analysing the different putative solutions to the OAI-control problem has been a generally discouraging exercise. The physical methods of control, which should be implemented in all cases, are not enough to ensure safe OAI. The other methods of control have been variously insufficient, problematic, or even dangerous. But these methods are still in their infancy. Control methods used in the real world have been the subject of extensive theoretical analysis or long practical refinement. The lack of intensive study in AI safety leaves methods in this field very underdeveloped. But this is an opportunity: much progress can be expected at relatively little effort. For instance, there is no reason that a few good ideas would not be enough to put the concepts of space and time restrictions on a sufficiently firm basis for rigorous coding. But the conclusion is not simply that more study is needed. This paper has made some progress in analysing the contours of the problem, and identifying those areas most amenable to useful study, what is important and what is dispensable, and some of the dangers and pitfalls to avoid. The danger of naively relying on confining the OAI to a virtual sub-world should be clear, while sensible boxing methods should be universally applicable. Motivational control appears potentially promising, but it requires more understanding of AI motivation systems before it can be used. Even the negative results are of use, insofar as they inoculate us against false confidence: the problem of AI control is genuinely hard, and it is important to recognise this. A list of approaches to avoid is valuable as it can help narrow the search. On the other hand, there are reasons to believe the oracle AI approach is safer than the general AI approach. The accuracy and containment problems are strictly simpler than the general AI safety problem, and many more tools are available to us: physical and epistemic capability control mainly rely on having the AI boxed, while many motivational control methods are enhanced by this fact. Hence there are grounds to direct high-intelligence AI research to explore the oracle AI model. The creation of super-human artificial intelligence may turn out to be potentially survivable. \t\t\t It is generally argued that intelligence and motivation are orthogonal, that a high intelligence is no guarantor of safe motives (Bostrom 2012b ). 2 Humans have many preferences-survival, autonomy, hedonistic pleasure, overcoming challenges, satisfactory interactions, and countless others-and we want them all satisfied, to some extent. But a randomly chosen motivation would completely disregard half of these preferences (actually it would disregard much more, as these preferences are highly complex to define-we wouldn't want any of the possible 'partial survival' motivations, for instance). \n\t\t\t Friendliness should not be interpreted here as social or emotional friendliness, but simply a shorthand for whatever behavioural or motivational constraints that keeps a superintelligent system from deliberately or accidentally harming humans.4  Another common term is ''AI-in-a-box''. \n\t\t\t A term coined by Fanya Montalvo by (Mallery 1988)  analogy to the mathematical concept of NPcompleteness: a problem is AI-complete if an AI capable of solving it would reasonably also be able to solve all major outstanding problems in AI. \n\t\t\t Thinking Inside the Box \n\t\t\t Or whatever counterpart might apply to an AI.Thinking Inside the Box \n\t\t\t Though there have been some attempts to formalise ontology changes, such as (de Blanc 2011). \n\t\t\t Overfitting in this way is a common worry in supervised learning methods.", "date_published": "n/a", "url": "n/a", "filename": "Armstrong2012_Article_ThinkingInsideTheBoxControllin.tei.xml", "abstract": "There is no strong reason to believe that human-level intelligence represents an upper limit of the capacity of artificial intelligence, should it be realized. This poses serious safety issues, since a superintelligent system would have great power to direct the future according to its possibly flawed motivation system. Solving this issue in general has proven to be considerably harder than expected. This paper looks at one particular approach, Oracle AI. An Oracle AI is an AI that does not act in the world except by answering questions. Even this narrow approach presents considerable challenges. In this paper, we analyse and critique various methods of controlling the AI. In general an Oracle AI might be safer than unrestricted AI, but still remains potentially dangerous.", "id": "a0f61b3a1f656b6785dcc536303b3e7d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jeffrey Ding", "Miles Brundage", "Allan Dafoe", "Eric Drexler", "Sophie-Charlotte Fisher", "Carrick Flynn", "Ben Garfinkel", "Jimmy Goodrich", "Chelsea Guo", "Elsa Kania", "Jade Leung", "Jared Milfred", "Luke Muehlhauser", "Brian Tse", "Helen Toner", "Baobao Zhang"], "title": "Deciphering China's AI Dream The context, components, capabilities, and consequences of China's strategy to lead the world in AI", "text": "EXECUTIVE SUMMARY Marked by the State Council's release of a national strategy for AI development in July 2017, China's pursuit of AI has, arguably, been \"the story\" of the past year. Deciphering this story requires an understanding of the messy combination of two subjects, China and AI, both of which are already difficult enough to comprehend on their own. Toward that end, I outline the key features of China's strategy to lead the world in AI and attempt to address a few misconceptions about China's AI dream. Building off of the excellent reporting and analysis of others on China's AI development, this report also draws on my translations of Chinese texts on AI policy, a compilation of metrics on China's AI capabilities vis-à-vis other countries, and conversations with those who have consulted with Chinese companies and institutions involved in shaping the AI scene. The report is organized in four parts: (1) Context -I place China's AI strategy in the context of its past science and technology plans, as well as other countries' AI plans; (2) Components -I relate the key features of China's AI strategy to the drivers of AI development (e.g. data, talented scientists); (3) Capabilities -I assess China's current AI capabilities by constructing a novel index to measure a country's AI potential; (4) Consequences -I highlight the potential implications of China's AI dream for issues of AI safety, national security, economic development, and social governance. In each of these four parts, I dispel a common misconception about China's approach to AI (Table  1 ). Then, using the deconstruction of these myths as a starting point, I derive my own findings. What follows is a summary of the key findings in each section. The State Council's AI plan is not the be-all and end-all of China's AI strategy. In the \"Context\" section, this report benchmarks both the plan and China's overall AI approach with regard to China's current AI capabilities and the positions of other countries on AI. Analyzing China's AI development in these two contexts gives the following conclusions: 2. China' s approach to AI is defined by its top-down and monolithic nature While the central government plays an important guiding role, bureaucratic agencies, private companies, academic labs, and subnational governments are all pursuing their own interests to stake out their claims to China' s AI dream. 3. China is winning the AI arms race China may define \"winning\" differently than the U.S., and, according to my AI Potential Index (AIPI), China' s AI capabilities are about half of those of America. • In addition to increased policy support for AI development in the past two years, the State Council plan's targets for the growth of the AI industry confirm China's high expectations for AI development. The 2020 benchmark for the core AI industry's gross output (RMB 150 billion) would represent a tenfold increase of the AI industry in the next three years. 1 • The plan clearly outlines China's ambition to lead the world in AI. Additionally, Chinese AI experts and decision-makers are keenly aware of the AI strategies and capabilities of other countries, including the United States, the EU, Japan, and the United Kingdom. There is evidence that China focuses on U.S. AI strategy, in particular, as a reference point for its own approach. One reasonable hypothesis is that China views AI strategy as a bilateral competition to some extent; another is that the U.S. can credibly shape China's approach in some respects. In the second section on \"Components,\" I link the key features of China's AI strategy -those consistent with other science and technology plans as well as those that differ -to four factors that drive the overall development of AI: (1) hardware in the form of chips for training and executing AI algorithms, (2) data as an input for AI algorithms, (3) research and algorithm development, and (4) the commercial AI ecosystem. Structuring the analysis by driver helps unpack how different features of China's AI strategy are put in practice in the following ways: • There are important similarities and differences between China's approach to AI development and its past efforts to guide scientific and technological innovation in other areas. Key consistencies include: a strong degree of state support and intervention, transfer of both technology and talent, and investment in long-term, whole-of-society measures. Significant differences are rooted in two factors: AI's \"omni-use\" potential means the breadth of actors involved is much wider than for other technologies, and as a result, internationally-facing, private tech giants and vigorous startups are leading players in driving innovation in AI. • China is adopting a \"catch-up\" approach in the hardware necessary to train and execute AI algorithms. It has supported \"national champions\" with substantial funding, encouraged domestic companies to acquire chip technology through overseas deals, and made long-term bets on supercomputing facilities. Importantly, established tech companies like Baidu and startups like Cambricorn are designing chips specifically for use by AI algorithms. • Access to large quantities of data is an important driver for AI systems. China's data protectionism favors Chinese AI companies in accessing data from China's large domestic market but it also detracts from cross-border pooling of data. Also, the common view that China's AI development will benefit from relatively lax privacy protections on user data may no longer hold true with the promulgation of a new data protection law. • China is actively recruiting and cultivating talented researchers to develop AI algorithms, another 1 This calculation takes the State Council' s targets and compares them to a iiMedia Research Group report' s estimate of the scale of China' s industry in 2017. I assume that the iiMedia Research Group' s estimate is close to what the State Council views as ground truth, but the State Council may be working off of a different estimate for the current gross output of the core AI industry  (iiMedia, 2017) . essential factor in AI innovations. The State Council's AI plan outlines a two-pronged \"gathering\" and \"training\" approach. National-level and local-level \"talent programs\" are gathering AI researchers to work in China, while China's tech giants have set up their own overseas AI institutes to recruit foreign talent. The training plank takes a long-term view to growing AI talent through constructing an AI academic discipline and creating pilot AI institutes. • Lastly, the Chinese government is starting to take a more active role in funding AI ventures, helping grow the fourth driver of AI development -the commercial AI ecosystem. Disbursing funds through \"government guidance funds\" (GGF) set up by local governments and state-owned companies, the government has invested more than USD 1 billion on domestic startups, with much of the investment shifting toward healthcare and AI as the priority areas in the last two years. At the same time, the central government is exploring methods, including through the establishment of party committees and \"special management shares,\" to exert more influence over large tech companies. Next, the \"Capabilities\"section assesses the current state of China's AI capabilities across the four drivers of AI development by constructing an AI Potential Index (AIPI), which approximates countries' overall AI capabilities. For each driver, I find proxy measures that benchmark China's capabilities as a proportion of the global total. Thus, a country's AIPI, scored from 0 to 100, represents its share of the world's total AI capabilities. • China's AIPI score is 17, which is about half of the U.S.'s AIPI score of 33. China trails the U.S. in every driver except for access to data. One could argue that China's lead in data would outweigh its deficits in other drivers. The AIPI is useful for testing these arguments. I find that the relative importance of the data driver would have to be over four times that of each of the other three drivers for China's AIPI score to equal that of the United States. • Several caveats are important to note. The index is meant to be a first-cut estimate of the AI landscape, so the specific numbers are not as important as their relative sizes and differences. The methodology will need to be refined as this index is limited by proxy measures for which quantifiable, reliable data was collected for both the U.S. and China. Finally, I examine the potential implications of China's AI dream for issues of AI safety and ethics, national security, economic development, and social governance. I emphasize that Chinese thinking on these issues is becoming more diversified and substantive. Though it is too early for firm conclusions about the long-term trajectory of China's AI development, it is useful to highlight the key areas of debate in each of these issues: • One group of Chinese actors is increasingly engaged with issues of AI safety and ethics. A new book authored by Tencent's Research Institute includes a chapter in which the authors discuss the Asilomar AI Principles in detail and call for \"strong regulations\" and \"controlling spells\" for AI. 2 A wide range of Chinese AI researchers are also involved with translating the IEEE's Ethically Aligned Design report, as part of the Global Initiative for Ethical Considerations in Artificial Intelligence \n 2 These terms are from my translations of the book, which are available upon request  (Tencent Research Institute et al., 2017) . and Autonomous Systems. However, other Chinese AI leaders dismiss calls for regulation and philosophizing. • Since military applications of AI could provide a decisive strategic advantage in international security, the degree to which China's approach to military AI represents a revolution in military affairs is an important question to study. The level of civil-military integration will be a critical factor in keeping track of this question.  The line between core AI and AI-related industries is fuzzy. In some AI plans, the Chinese government delineates core AI technologies from other related technology types like smart vehicles, smart wearable devices, and smart robots, among others. Under this conceptualization, core AI would include companies innovating in an industry-agnostic part of the AI architecture whereas AI-related industries would include parts of the AI pipeline focused on applications in specific industries. I clarify the term \"gross output\" in the introduction. \n I. CONTEXT China's AI development plan did not begin with this State Council document in July; rather, the plan both formalizes and definitively signals a focus on AI-one that was already broadly known. 11 For instance, a month before the State Council's report, the government of the Chinese city of Tianjin had announced a USD 5 billion fund to support the AI industry.  12  In this section, the report compares the plan and China's overall AI approach with regard to China's current AI capabilities, as well as the positions of other countries on AI. \n A. China's AI expectations vs. current scale of AI industry The State Council's plan represents the culmination of increased policy support for AI development. The Chinese government has significantly ramped up its AI plans in the past few years (Table  2 ). AI now appears among a select number of explicit government priorities in key, long-term plans related to science and technology 13 , and has backing from substantive funding measures -two key elements not present in past government support for AI. Released in 2016, the \"13th Five-Year Plan for Developing National Strategic and Emerging Industries\" (2016-2020) identified AI development as 6th among 69 major tasks for the central government to pursue. The \"Internet Plus\" initiative, established in 2015, is tightly linked to AI development, as evidenced by the NDRC announcement of an \"'Internet Plus' and AI Three-Year Implementation Plan\" targeting the creation of an AI market that is hundreds of billions of RMB in size. Moreover, the NDRC, the Ministry of Industry and Information Technology, and the Ministry of Finance jointly released the \"Robotics Industry Development Plan (2016-2020)\" in April 2016.  14  In 2017, Chinese Premier Li Keqiang incorporated the term \"artificial intelligence\" into the government's work report  15  for the first time, a development the news department of the State Council covered.  16  Moreover, Chinese President Xi Jinping mentioned AI as a way to increase economic productivity in his opening speech of the 19th Party Congress. 17 AI-related plans are increasingly tied to substantive funding mechanisms. Notably, in February 2017, the \"Artificial Intelligence 2.0\" plan received megaproject designation, which comes with substantial funding, 13 In 2016, the Five Year Plan for Developing National Strategic and Emerging Industries (2016-2020) highlighted development of AI as one of 69 major tasks for the central government to pursue; in 2017, \"Artificial Intelligence 2.0,\" a comprehensive effort to boost investment in AI education and development, was adopted as one of 16 Megaprojects in the Five Year Plan for National Science and Technology Innovation. 14  He, 2017 15  The government work report is an annual report on economic growth given by the Chinese premier to the National People' s Congress, China' s top legislative body. It summarizes the government' s efforts last year and outlines crucial tasks for the year ahead. Since the report normally sets the target GDP growth rate for the next year, its content is carefully scrutinized, making the work report an important signalling mechanism.  b The NDRC is the Chinese government' s central economic planning ministry. It has significant powers in allocating investment funds and approving major projects and has been dubbed China' s \"mini State Council\" and \"number one ministry.\" In recent years as President Xi' s administration has stressed a \"decisive role for market forces, the NDRC has tried to reposition itself as a macroeconomic coordinator that is more relevant to a market-driven Chinese economy  (Martin, 2014) . c For context, the original 15 S&T Innovation Megaprojects (2030) were announced in July of 2016, so AI was added on 7 months later to make 16 total projects. Focus areas for the other 15 include quantum communication, national cyberspace security, and neuroscience. These megaprojects are not new policy innovations. The \"National Medium-and Long-Term Plan for the Development of  Science and Technology (2006-2020) \" also established 16 S&T Innovation Megaprojects to end in 2020. If past megaprojects are any precedent, the AI megaproject will likely involve a combination of significant grant money and various other policy levers (R&D tax credits, investment in talent pipeline, promotion of technical standards). The \"mega-project\" approach has been criticized by US-based scientists who are involved with the Chinese Academy Science for diverting resources from supporting investigator-driven projects. Another cynical take on megaprojects is that they are merely a repackaging of existing MOST programs and national programs administered by other agencies  (Cao, Suttmeier, and Simon, 2006; Springut, Schlaikjer, and Chen, 2011) . alongside fifteen other technologies deemed crucial to China's science and technology innovation.  18   22 Some English-language reports on these benchmarks have translated them as \"industry scale\" or \"market size\" indicators, but the more precise translation is \"gross output,\" a measure of the production side of specific industries. An industry' s gross output is the sum of sales to final users in the economy (GDP) and sales to other industries (intermediate inputs). For a frame of reference, the estimated gross output of China' s robotics industry in 2017 was U.S.$6.8 billion. I cover the distinction between core AI and AI-related in the next two paragraphs. China's AI industry had a gross output of RMB 10 billion in 2016, and is expected to grow to around RMB 15 billion in 2017. Thus, the 2020 benchmark for the core AI industry's gross output (RMB 150 billion) would represent a tenfold increase of the AI industry in the next three years.  24  China's ambitions in AI can also be understood in the context of the global AI industry. Per a report by McKinsey Global Institute, forecasts of the global market size for AI in 2025 range from USD 644 million to USD 126 billion.  25  If these projections refer to core AI industries, China's 2025 benchmark for a USD 60.3 billion, world-leading core AI industry corresponds with the high end of market forecasts for AI. To be clear, the line between core AI and AI-related industries is fuzzy, so how China's State Council interprets the difference between the two is important to analyze. The slipperiness of what exactly constitutes AI is a problem that plagues analysis of AI strategy. The flip side of this slipperiness is AI's \"omni-use\" potential (i.e. its similarity to electricity), which I investigate later by comparing it to other technologies. Perhaps the most credible distinction in the Chinese context can be found in the \"Internet Plus\" and AI Three-Year Implementation Plan issued by the NDRC. This plan outlines nine major technology areas, listing \"core AI technologies\" along with eight other technology types. These \"core AI technologies\" include basic research in fields such as deep learning, the development of basic software and hardware such as chips and sensors, and applied research in areas like computer vision and cybersecurity.  26  Notably, these core AI technologies are differentiated from the other eight technology types, which include smart vehicles, smart wearable devices, and smart robots, among others. The implementation plan's definition of \"core AI\" fits with that of CB Insights, a leading market research firm, which defines \"core AI companies\" as those focused on general-purpose AI applicable across a variety of industries. 27 Under this conceptualization, core AI would include companies innovating in a specific, industry-agnostic part of the AI architecture, whereas AIrelated companies would include parts of the AI pipeline focused on applications in specific industries. \n B. China's AI ambitions vs. other countries' AI strategies Some Chinese AI experts and decision-makers are keenly aware of the AI strategies and capabilities of other countries, in particular the United States, the EU, Japan, and the United Kingdom. In a chapter titled \"Top-level Plans,\" scholars from Tencent's Research Institute and the China Academy of Information and Communications Technology, a research institute under the Ministry of Industry and Information Technology (MIIT), laid out their view of the current international strategic landscape for AI development as follows: 28 • 'Defend the lead' America -a comprehensive, strategic layout: \"In sum, the United States is, \n 24 The State Council may be working off of a different estimate for the current gross output of the core AI industry. This calculation assumes that the iiMedia Research Group' s estimate is close to what the State Council views as ground truth. \n 25 McKinsey Global Institute, 2017b 26  He, 2017  at this point, the country that has introduced the most strategies and policy reports on artificial intelligence strategies. The United States is undoubtedly the forerunner in the field of artificial intelligence research and its every move necessarily affects the fate of all of humanity.\" • Ambitious EU -'Human Brain' and 'SPARC' Projects: \"In 2013, the European Union proposed a 10-year Human Brain Project, currently the most important human brain research project in the world.\" • Robot superpower Japan -'New Industrial Revolution': \"For the past 30 years, Japan has been called the \"robot superpower\" and has the world's largest number of robot users, robotics equipment, and service manufacturers.\" • Unwilling to fall behind Britain -facing the fourth industrial revolution challenge: \"The UK considers itself to be a global leader in ethical standards for robotics and AI systems. At the same time, this leadership in this area could extend to the field of artificial intelligence regulation.\" As for the authors' assessment of China's own position within this landscape, they titled China's section as \"China, from 'running after' to 'setting the pace',\" and wrote the following, \"In terms of AI, China followed the United States and Canada in releasing a national AI strategy. In the wave of AI industry, our country should go from system follower and move towards being a leader, actively seizing the strategic high ground.\" 29 This concept of \"setting the pace\" is essential to understanding China's high ambitions for its AI development. Second, there is evidence that China is particularly attuned to U.S. AI strategy, and sees it as a reference point for its own approach. Many key junctures in China's AI development are related to significant AIrelated pronouncements that are linked to the United States. For instance, after the Department of Defense's announcement of the \"Third Offset\" strategy in 2014 -which Chinese defense analysts and policymakers followed closely -the Chinese military establishment responded by revising its modernization approach to increase investments into AI technologies.  30  China also reacted to other significant developments in U.S. AI policy. In October 2016, the Obama administration released the first of three reports on AI, which also corresponded with a large spike in Baidu searches for AI. Some analysts have noted similarities between the State Council's AI plan and these three reports, suggesting that the drafters of China's AI plan were closely familiar with the previous U.S. administration's policy statements. This may fall prey to a \"mirror-imaging\" bias, the assumption that another actor will react to and interpret events in the same way as oneself  (Inkster, 2016) . \n II. COMPONENTS A. Key consistencies and differences with other science and technology plans Much of China's approach to AI is old in the sense that it is consistent with past science and technology plans. In the drafting of the MLP, infighting among Chinese scientists and bureaucrats became so serious that it leaked out into the public sphere, an underappreciated aspect of Chinese science and technology policy that also applies in the AI context. In the early 2000s, Premier Wen Jiabao brought together the Chinese Academy of Sciences (CAS) and the Ministry of Science and Technology (MoST) to draft this MLP: in total, 2000 bureaucrats, researchers, and business managers were involved in the drafting process.  39  As the bureaucrats at MoST and MIIT gradually shifted the direction of the MLP toward megaprojects, Chinese scientists bristled at the degree of control given to bureaucrats over scientific inquiry. In fall of 2004, a group of prominent Chinese scientists, from both inside and outside of China, published a collection of essays in a special issue of Nature that criticized the draft MLP plan. There is some evidence that similar infighting has already begun over AI policy. The \"'Internet Plus' and AI Three-Year Implementation Plan\" gives four agencies -the NDRC, the MoST, the MIIT, and the Cyberspace Administration of China -the mandate to advance the AI industry. In contrast, the State Council's \"New Generation AI Development Plan\" called for the establishment of an AI Plan Implementation Office under the authority of MoST. None of the other bureaucratic entities involved with the \"'Internet Plus' and AI Three-Year Implementation Plan\" received mention in the State Council's new plan, a notable exclusion given how comprehensive the document is in other respects. One researcher at the Council on Foreign Relations posited that this was an instance of bureaucrats at MoST asserting their claim on high-tech developments, undercutting the authority of other ministries or academic efforts.  40  In December 2017, MIIT issued its own three-year action plan to implement tasks related to the State Council's plan and \"Made in China 2025.\" When the AI Implementation Office was officially created four months later, the official number of agencies involved had risen to 15 offices. Two offices, MoST and NDRC, were named in the announcement, ensuring that bureaucratic infighting over China's AI path will not cease anytime soon.  41  Although the central government plays an important guiding role, bureaucratic agencies, private companies, academic labs, and subnational governments are all pursuing their own interests to stake out their claims to China's AI dream. Lastly, there are important similarities and differences between China's approach to AI development and its past efforts to spur innovation in strategic, emerging technologies. Take the example of biotechnology. The model of ramping up state support and intervention is similar to AI. First, there was a modest \"climbing program,\" which was initiated in the 1980s and lasted about eight years before the government made biotech more of a priority.  42  Second, the Chinese government set up an independent entity, China National Center for Biotechnology Development, to coordinate the development of biotech, and important central planning documents begin to focus on the technology, in particular the State Council's National Biotechnology Development Policy Outline in 1988, which established thirty national key laboratories.  43  Third, the government signaled that biotech was a national-level priority and committed substantial funding toward its development. For example, the 863 program, China's main vehicle for science and technology funding at the time, designated biotech as one of seven critical areas, and allocated around 1.5 billion RMB toward its development over the years 1986 to 2000.  44  Other consistencies between China's biotech strategy and AI approach include: international transfer of both technology and talent, as well as investment in whole-of-society and long-term measures. In the domain of tech transfer, Chinese firms in the pharmaceutical, biotech, and healthcare industries reached a record amount of $3.9 billion in overseas acquisitions in 2016.  45  Talent programs have also attracted overseas Chinese working at the cutting edge of bioscience. \"Deng Xiaoping sent many Chinese students and scholars out of China to developed countries 30 to 40 years ago, and now it is time for them to come back,\" stated George Fu Gao, who received his doctorate at Oxford, of the Chinese Academy of Science's Institute of Microbiology.  46  There are also signs that China's long-term investments in biotechnology are bearing fruit over thirty years later, as evidenced by recent advancements on cloning techniques and research on viral epidemics.  47      instance, China surpassed the U.S. to have the most supercomputing facilities in the world at 167, compared to 164 in the U.S., 62 and China's Sunway TaihuLight, which uses Chinese-designed processors, became the world's fastest system in June 2016.  63  Since much of the link to AI is speculative, I do not include these metrics in my index of AI capabilities, but some have argued that China's long-term commitments to supercomputing facilities, along with its funding for quantum computing, may have real applications for AI.  64  What is new in the hardware driver is that Chinese tech giants and unicorn startups are competitive with some of the world's leading companies in designing AI chips. For instance, Chinese company Cambricon, a statebacked startup valued at $1 billion, has developed chips that are six times faster than the standard GPUs for deep learning applications and use a fraction of the power consumption.  65  Moreover, equipped with a new \"neural processing unit,\" Huawei has arguably overtaken Apple in mobile AI chips. 66 \n B. Channels from these key features to drivers of AI development The Chinese government's policies on the second driver, access to data, reveal two other critical aspects of its broader AI strategy: its leverage over big tech companies and its tendency toward protectionism. In October of 2016, some of China's largest tech companies agreed to share data with government authorities to improve consumer trust online.  67  The NDRC stated that the agreement was part of a broader project to create a national \"social credit system,\" which some privacy advocates have argued is designed for mass surveillance.  68  As AI-fueled tech companies like the BAT companies become more and more powerful, the Chinese government has pushed for more influence over these big tech giants, even discussing the possibility of internet regulators taking 1% stakes in the companies.  69  Dubbed \"special management shares,\" these small stakes would give Chinese government officials positions on company boards and the right to monitor content on the company's online platforms.  70  China's sharing of data stops at the water's edge. This fits with a larger trend of what some deem China's techno-nationalism, an approach that aggressively protects domestic companies from foreign competitors.  71  Even if the Chinese companies that rise from this approach do not compete internationally -though many have successfully expanded to Asian and African countries -they still thrive by serving China's huge market. Chinese standards for smart manufacturing, cloud computing, industrial software, and big data differ significantly from the international standards in those domains.  72  Data protectionism, such as the 2017 cybersecurity law that prevents foreign firms from storing data collected on Chinese customers outside of China, could disincentivize cross-border data pooling and the development of common standards for data sharing.  73  One unique aspect of China's AI development in the data driver is the emergence of a major debate over data privacy protections.  74  Companies, different levels of government, and even the general public have been active participants in this debate, which pits those advocating for greater data privacy protections against those pushing for data liberalization to benefit AI technologies.  75  In a chapter titled \"Top-level Plans,\" Tencent and CAICT researchers attribute the success of Silicon Valley to the existence of strong institutions such as copyright and tort law, and they argue that data liberalization is a form of institution building that could spur further innovation. They write, \"If there is no government data liberalization policy, many AI applications will become 'water without a source, a tree without roots.' It can be said that the issue of data liberalization is a pain point in the development of AI in China and needs to be elaborated upon in a more comprehensive and in-depth manner in the strategy.\" Recently, in January 2018, advocates for data privacy celebrated when the Chinese government released a new national standard on the protection of personal information, which contains more comprehensive and onerous requirements than even the European Union's General Data Protection Regulation, per analysis by CSIS senior fellow Samm  Sacks. 76  This vigorous and unresolved debate over data privacy combats common misperceptions of China's relatively lax privacy protections and is an important one to follow as China advances in AI. In order to incentivize top quality-AI research and development, the State Council's AI plan dedicates a section to accelerating the training and gathering of high-end AI talent.  77  In the \"gathering\" section, the report calls for recruiting top international scientists through a variety of \"Thousand Talents\" plans. China's Ten Thousand There are three main \"Thousand Talents\" Programs: 1. The \"Long-Term Thousand Talents Program\" awards grants of RMB 3 million (USD 452,000) to work full-time in China, as well as a one million RMB (USD 151,000) allowance; 2. The \"Short-Term Thousand Talents Program requires hired employees to work in China for at least two months per academic year -talents will receive a RMB 500,000 (USD 75,000) allowance; 3. The Thousand Talents Program for Distinguished Young Scholars provides RMB 1-3 million (USD 151,000-USD 452,000) in research funding from the central government, an additional RMB 700,000 (USD 105,000) in research funding from the Chinese Academy of Sciences, as well as a RMB 600,000 (USD 90,376) allowance. Per the Chinese Academy of Sciences: http://english.ucas.ac.cn/index.php/join/job-vacancy/2040-the-long-term-thousand-talents-program machine intelligence and learning lab at the University of Electronic Science and Technology of China, moved back to China through a portion of the Ten Thousand Talents program dedicated to attracting young academics.  81  China's talent programs have a mixed track record. From 2009 to 2011, the Thousand Talents program may have attracted the largest influx of high quality talent within a limited timeframe in all of China's history, per data released by the Chinese Academy of Personnel Science.  82  In those three years, 1510 scientists were selected as talent program awardees at the national level, out of an application pool of 6200. 83 However, multiple empirical studies and interviews with recruiters for the talent programs reveal that these programs have not managed to attract the \"best and brightest\" Chinese scientists to return.  84  A multitude of factors play a role, including: a research culture focused on instant results, lack of connection with domestic Chinese networks to advance, and problems with educational opportunities for their children. Nonetheless, as China works to reform its research culture and ramps up its efforts to encourage researchers to work in China, particularly those of Chinese descent, it could expand China's pool of AI experts, as China's scientific diaspora numbers over 400,000 scientists and other scholars.  85  Talent transfer also occurs through commercial avenues: an investor who specializes in AI identified the strategy of hiring talented AI scientists to work in China -where salaries are now comparable to those in America, ranging from 70-150% of average pay for U.S. AI scientists -as a \"shortcut\" to accelerate AI development.  86  In order to recruit foreign talent, the BAT companies have established their own overseas AI institutes. 87 Worldleading AI talents have returned to China for work: Andrew Ng, former head of Google Brain, worked at Baidu for three years, and Qi Lu, former executive vice president of Microsoft, now serves as Baidu's Chief Operating Officer. Headhunters working for China's city governments and technology companies regularly visit international scholars and engineers in universities, companies, and startups and attempt to convince them to work in China.  88  These different channels for talent transfer reveal an important point about China's AI strategy -it is not a monolithic, completely top-down approach; many actors are maximizing their own interests and responding to broad signals from the central government. Finally, China is taking the long-view to growing AI talent. The State Council's plan also calls for constructing an AI academic discipline, involving a comprehensive effort to establish AI majors, create AI institutes in pilot While the government encourages the flow of talent and technology into Chinese AI sector, it prevents foreign companies from establishing a foothold in critical, AI-related sectors and restricts the flow of data out of China. The door is half open: China seeks to benefit from the open flow of talent and technology, while preventing international companies from gaining a foothold in its AI industry. In the last driver regarding the commercial AI ecosystem, the Chinese government actively picks winners in the AI space. For example, in November 2017, MoST designated four companies -Baidu, Alibaba, Tencent, and iFlyTek -to lead the development of national AI innovation platforms in self-driving cars, smart cities, computer vision for medical diagnosis, and voice intelligence, respectively. 91 These national endorsements could give Baidu an advantage in working with car manufacturers and Tencent wider access to hospital data, but they may also dampen competition in these specific markets. The Chinese government is beginning to play a larger role in funding AI ventures. Disbursing funds through \"government guidance funds\" (GGF) set up by local governments and state-owned companies, the government has invested more than USD 1 billion on domestic startups.  92  Per statistics from Sun Hung Kai Financial, these GGFs are projected to eclipse China's private VC funds in size: for the year 2016, GGFs set a total fundraising target of RMB 3.3 trillion (USD 500 billion) vs. a RMB 2.2 trillion (USD 330 billion) total raised by private funds.  93  One report on GGFs noted that from 2015 to 2016, the direction of GGF investment shifted toward healthcare and AI as the main priority areas.  94  There is some initial evidence that increased GGF attention to AI has met some initial success. Per a 2017 report, China has a higher percentage of AI companies that have received investments (69%) than the U.S. (51%).  95  Additionally, the velocity of AI investment is relatively fast: from incorporation to receiving angel investment, the average time for Chinese companies is 9.73 months while it is 14.82 months for US companies.  96  These funds may help the central government achieve two goals at once, helping speed up AI development while also incorporating tech companies within the party apparatus. In the past few years, more than 35 tech companies, including Baidu and Sina, have created company party committees, which evaluate the company's operations to ensure the party's objectives are being followed.  97  In some respects, the success or failure of China's AI commercial sector will be a test of China's unique mode of public-private partnerships. include policy support, ample resources, and in some cases, a guaranteed minimum return for investors.  98  But the fact that there has not been a single successful exit for any of the 911 GGFs to date reflects the scheme's myriad issues, such as geographical and industry sector restrictions on investment and complicated exit procedures.  99  Lastly, in all the drivers of AI, China is investing in long-term, whole-of-society approaches to advancing AI technologies. Indeed, the directives laid out in the State Council's AI plan not only apply across government departments but they also strongly guide the actions of universities, research institutes, and the private sector. In contrast, other governments-limited in its power over society and subject to sudden policy shifts depending on which political party is in power -tend to implement short-term, whole-of-government solutions. What follows is an evaluation of how these components of China's AI development have influenced its actual capabilities along the range of four drivers , captured by a series of comparative, quantitative metrics. \n III. CAPABILITIES In the four following sections, this report explains the importance of each driver in detail, so it will draw out some broader points about the relationship among drivers here. First, though this report analyzes each of the drivers separately, connections between drivers cannot be ignored. For instance, hardware improvements (e.g. the development of GPUs) have enhanced the performance for AI algorithms, and innovation algorithms have, in turn, enabled more efficient use of larger amounts of hardware through parallelization (running a program on multiple processors). 100 Second, the importance of each driver relative to the others is the subject of much debate. When AI experts were surveyed on the sensitivity of AI progress to various drivers, opinions varied widely and no consensus was reached on the relative importance of each input.  101  Other analysts have pointed out that the relative weighting of each driver has and will change over time, subject to significant trends like open access to advanced algorithms or large datasets.  102  In the last part of the \"Capabilities\" section, this report assesses how adjusting the relative weight of each driver could change assessments of China's AI capabilities. A. champions in its domestic chip-making industry and making long-term bets on powerful supercomputing facilities. In some respects, China's approach to building its domestic semiconductor industry is a microcosm for its overall approach to AI development. State-directed theft of intellectual property, targeted poaching of talent, and strong government guidance have all been part of China's brute force approach to boosting its semiconductor industry.  116  Yet despite this effort, China's domestic production of integrated circuits (IC) accounts for less than 13% of the country's demand, and its trade deficit in the global IC market has more than doubled since 2005.  117  Thus, catching up in the domain of AI hardware may take a long time, if it happens at all. ii. Closed critical mass of data of the findings presented, second only to those from the United States (Table  4 ). However, China lags behind both the U.S. and UK in fundamental research, according to a McKinsey Global Institute report which found that U.S. and UK research is more influential by citation impact, as measured by the H-index.  125  When asked to compare the U.S. and Chinese AI strengths, Yann LeCun, director of Facebook's AI research, highlighted the importance of the top advanced AI research labs, which have been established in the U.S. (Google Brain, Facebook AI Research, OpenAI, and others).  126  Currently, both Chinese academics and companies tend to research applications of pre-existing AI technology; whether these two groups begin to adopt the \"moonshot\" mindsets that inspire the creation of new AI technologies will be a critical question for China's future AI research.  127  The difference in fundamental AI research may also be partly due to a talent shortage. Despite the larger pool of STEM graduates, China has a talent pool of around 39,000 AI researchers, less than half of the size of the U.S. pool of over 78,000 researchers.  128  The U.S. benefits from having a large number of world-leading universities for AI research, as well as a more mature AI commercial ecosystem. This leads to more AI experts who have led multiple full cycles of projects. Nearly 50% of the AI researchers in the U.S. have more than 10 years of work   (Gagne et al., 2018) . Source: Japan' s National Institute of Science and Technology Policy. National affiliation of each presentation determined by location of researchers' organization. Each co-author was counted once, so each presentation of findings could have resulted in more than one count recorded in the table  (Koshiba et al. 2016) . experience, whereas only 25% in China have more than 10 years of work experience. 129 \n iv. Partnership with the private AI sector The last driver of AI development analyzed in this report is the commercial AI ecosystem. A range of indicators -measures of the number of AI companies and total AI financing received in particular -put China's AI commercial ecosystem as the second largest in the world, at around one quarter the size of its U.S. counterpart. Out of the total number of AI companies in the world (2542 according to data from June 2017), the US hosts 42% of them, while China ranks second with 23%.  130  The U.S. ecosystem nurtures more competitive AI startups, with 39 promising AI startups ranked by total funds raised from CB Insight's AI 100 list, compared to 3 promising Chinese AI startups.  131  In recent years, large tech companies have competed to acquire leading private AI companies for access to technology and expertise, 132 and U.S. tech giants have benefited directly from the robust AI startup scene in this respect. From 2012 to July of 2017, out of the 79 total acquisitions of AI companies, 66 were acquired by U.S. companies, while only 3 were acquired by Chinese companies (Baidu, in all three cases); relatedly, of the companies acquired in these M&A deals, only one was from China while 51 were from the states.  133  While the number of AI firms provides a good first-cut measure of industry size, the amount of financing raised by AI firms can help provide a more comprehensive picture of the AI landscape. From 2012 to 2016, according to findings from a Wuzhen Institute report, Chinese AI firms received USD 2.6 billion in investment funding, significantly less than the USD 17.2 billion received by their American peers.  134  As was the case with the fuzzy distinction between \"core AI\" and \"AI-related industries\", numbers on the scale of the commercial AI sector are murky. For instance, another report from IT Juzi and Tencent Institute offers a markedly different estimation of the scale of AI financing for both the U.S. and China, finding that the U.S. receives 51.10% (USD 14.8 billion) of world's AI funding while Chinese AI companies rank second with 33.18% (USD 9.6 billion) of the world's AI funding.  135  Another factor behind conflicting estimates is the fast-changing nature of the AI scene. For reference, from 2014 to 2016, the number of new Chinese AI companies accounted for 55% of all Chinese AI companies ever established, and the scale of Chinese AI investment for those three years accounted for over 90% of the total Chinese financing that has ever been committed to AI.  136   size of China's AI sector, across the full range of indicators considered in this section, China's AI industry has significantly increased in both absolute and relative terms in the past few years. Across all drivers, it is important to note that these do not have to be viewed through the lens of zero-sum competition. In fact, in each driver, collaborations across countries are often mutually beneficial. China is a major market for U.S. AI hardware, data can be shared across borders, and researchers from around the world coauthor AI papers together. Lastly, cross-border AI investments, with respect to the U.S. and China, have significantly increased in the past few years. From 2016 to 2017, China-backed equity deals to U.S. startups rose from 19 to 31 and U.S.-backed equity deals to Chinese startups quadrupled from 5 to 20.  138  Moreover, what is often forgotten is the fact that both Tencent and Alibaba are multinational, public companies that are owned in significant portions by international stakeholders (Naspers has a 33.3% stake in Tencent and Yahoo has a 15 percent stake in Alibaba). In sum, while the next section offers a comparative assessment of the U.S. and China's AI capabilities, it is important to consider the interdependent, positive-sum aspects of various AI drivers. \n B. Assessment of China's position on the AI Potential Index In the course of evaluating the different components of China's AI strategy, this report has assessed China's AI capabilities across indicators associated with each of the four drivers. In an attempt to integrate these indicators, the report takes a first-cut at developing a measure of a country's AI power. The methodology will need to be refined, as this index is limited by proxy measures for which reliable data was collected for both the U.S. and China (Table  5 ).  139  As Table  5  shows, China trails the U.S. in every driver except for access to data. According to the AI Potential Index, China's AI capabilities (AIPI = 17) are about half of those of America (33). This index is meant to be a rough-guess measure to assess the overall AI capabilities of any country as a fraction of total global AI capabilities, weighted by the level of importance of each driver (in the first iteration of this index, they are weighted equally). The proxies are not perfect by any means, and some aspects of each of these drivers (level of genius talents in research, the quality of the data, etc.) cannot be quantified. The estimates are valuable for testing potential scenarios for China's AI development, since relative weights assigned to each driver can be adjusted, if one thinks that a particular driver is more important than another. For example, Baidu's Chief Operating Officer, Qi Lu, argues that China will be best positioned to leverage the potential of AI because he views data as the ultimate driver. For him, China's lead in data, the \"primary means of production,\" would outweigh its deficits in the other drivers.  140  The AIPI can help clarify some of the parameters of Qi Lu's hypothesis. Assuming that the current proxy measures for each driver are relatively accurate, the 138 Ibid. 139 Since I was unable to find numbers for the share of world data controlled by the U.S. in 2020 and 2030 to compare to those I had for China, I substituted the number of mobile users as a proxy measure for the total data available to each country. \n 140 Qi Lu discusses China' s comparative advantages in AI in the first 30 minutes of this interview with YCombinator: https://www.youtube.com/ watch?v=WSydk0XzxEE. relative importance of the data driver would have to be over four times that of each of the other three drivers for China's AIPI score to equal that of the United States.  141  Conversely, data may be less important in the future compared to other drivers, since future AI algorithms may not need as much pre-created data (e.g. simulation pipelines for training robots).  142  Other potential tests could incorporate countries' AIPI score from past years to project future trends in AIPI. As China continues to ramp up state support for AI, encourage AI tech and talent transfer, and make long-term bets on AI, the AIPI could serve as one of the tools to measure its progress. \n 141 Calculated by the following method. Let x be the \"added importance factor.\" Then, multiple the data driver by x and divide every other driver by x. Set the two sums of proxy measures for the U.S. and China to be equal to each other. Solve for x, which comes out to around 2.29. This result means that the importance of all the drivers had to be divided by more than 2, and the relative importance of the data driver had to be multiplied by more than 2 for China' s AIPI to achieve parity with the U.S. AIPI. Hence, the relative importance of the data driver would have to be over four times that of the other three drivers for this result to occur. \n 142 I thank Helen Toner for this point. e For the hardware and commercial AI drivers, within which I had multiple figures, I first took the average of of the different proxy measures to come up a single average score for each driver. Then I averaged the four driver scores to get the final AIPI measure. \n IV. CONSEQUENCES In this final section, the report turns to the potential implications of China's AI strategy on four issue areas: AI standards and safety, national security, economic development, and social governance. It is outside of the scope of the report to fully assess the potential developments in all four areas. Instead, the thrust of this report is to show that all the pieces matter in China's AI development -that in the case of China's pursuit of AI, the how is key to unlocking the why. Toward that end, I focus in on how some of the key features of China's AI strategy factor into the longer-term implications in each of these four areas. \n A. Emerging engagement in AI ethics and safety As one of the leading countries in AI, China's approach to AI regulation will play an essential role in navigating  continue to adopt a range of unmanned vehicles into all four services (Army, Navy, Air Force, and Rocket Force).  157  Combined with breakthroughs in UAV swarming and intelligentized missiles, these developments could challenge the U.S. military presence in the Pacific theater. In the long-term, China's AI development could revolutionize its conduct of military affairs. Although material evidence for Chinese militarization of AI is limited, some rhetorical evidence does show that China sees AI as a revolutionary military technology. In a statement on the central government's work report by Lieutenant General Liu Guozhi, director of the Central Military Commission's Science and Technology Commission, he states, in reference to military applications of AI, that the world is \"on the eve of a new scientific and technological revolution,\" and \"whoever doesn't disrupt will be disrupted!\" 158 Combined with AI's dual-use nature, China's high degree of civil-military fusion has raised concerns about the military applications of AI. Li Deyi, as a quintessential example, is both the director of the Chinese Association for Artificial Intelligence and a major general in the PLA.  159  To emphasize, many of these projections are largely speculative as the most sensitive military AI applications are not publicly disclosed. There is not a coherent consensus of ideas on AI in warfare within the PLA. Moreover, the influence of the PLA is not overwhelming, as other bureaucratic entities often have diverging views and the central party apparatus possesses final decision-making powers. The degree to which China's militarization will constitute a revolution in military affairs is an important question. Drawing from Chinese-language, open-source articles by military scholars, a recent report by Elsa Kania, at the Center for a New American Security (CNAS), argues that the Chinese People's Liberation Army (PLA) views AI as a \"trump card\" technology that could revolutionize the conduct of future warfare.  160  As the CNAS report acknowledges, the thinking of the PLA and the central government on the direction of military AI is not solidified. Evidence from the PLA's investment in UAV swarming and intelligentized missiles shows that the most immediate applications of military AI could align with more limited, defensive goals, including asymmetric countering of U.S. military superiority in the Western Pacific and protecting China's nuclear deterrent. 161 C. Economy benefits as a driving force Economic benefit is the primary, immediate driving force behind China's development of AI, so evaluating the economic impact of China's AI strategy will be a key test of the strategy's feasibility and success. Early signs support cautious optimism about China's AI sector. Metrics from the section on China's commercial AI ecosystem revealed that new AI companies and investment in the years 2014-2016 surpassed the number of companies and investment in all the years prior. These figures should be tempered by the potential for speculative over-investment to cause boom-bust cycles and the need for more concrete figures directly tied to economic growth, such as revenues and assets. As earlier analysis on megaprojects demonstrated, China's industrial policy approach to scientific innovation has been criticized for diverting resources from bottom-up, investigator-driven projects to large national projects run by mediocre laboratories, on the basis of personal connections. \n D. Implications of AI for China's mode of social governance The State Council report acknowledges that the government will have to deal with some of the social aftershocks of AI's economic implications. Concretely, AI could accelerate the \"digital divide\" by placing a premium on high-skilled workers and reducing the demand for low-skilled workers whose jobs would be most at risk of being automated.  166  This may widen many of the divisions in Chinese society, including income inequality, gender inequality, and the urban/rural and coastal/inland opportunity gaps. At the same time, China is exploring the use of AI to predict evidence of social unrest before it coalesces.  167  For instance, in the same section, the State Council states that AI will also play an \"irreplaceable\" (不可替代) role in maintaining social stability. Toward that end, China aims to integrate AI across a broad range of public services, including judicial services, medical care, and public security. Already, Shanghai is piloting an AI system that reviews the validity of evidence in criminal cases.  168  Moreover, Chinese government officials have praised AI's value for predictive policing measures, an approach that some scholars label \"Digital Leninism.\" 169 AI techniques may also help Chinese censors find patterns in massive amounts of communication data.  170  At the center of many of these AI-enabled forces is the Chinese government's planned \"social credit system.\" The proposed system would constantly monitor and evaluate the activities of each Chinese citizen and rank his or her level of trustworthiness. 171 Moreover, the trust score would affect one's eligibility for a mortgage, to respond to China's national AI plan with a strategy of its own.  174  In fact, a reference to China winning the \"algorithm battles\" even made its way into a National Security Council memo, on the seemingly unrelated subject of centralizing the 5G network, for President Donald Trump.  175  China's AI dream could also affect who sits at the center of the international economic order. In the social governance realm, China's AI development could provide a model of \"robust authoritarianism\" that might appeal to other nations. At the same time, China could also beneficially contribute to peaceful governance and ethical norms for AI technologies. A clear-eyed assessment of its AI strategy is essential to deciphering how China will realize its AI dream. 4. There is little to no discussion of issues of AI ethics and safety in China Substantive discussions about AI safety and ethics are emerging in China. A new book authored by Tencent' s Research Institute contains chapters that are relatively proactive in calling for stronger awareness of AI safety issues. No consensus exists on the endpoints of AI development. \n INTRODUCTION In his report to the 19th Party Congress in October 2017, Chinese President Xi Jinping reiterated his dream for China to become a \"science and technology superpower.\" 6  Development of AI has become an integral part of China's strategy to realize this goal. One turning point in China's view of AI was the March 2016 victory by Google DeepMind's AlphaGo overLee Sedol, 7  who is widely considered to be the greatest Go player of the past decade. 8 Two professors who consulted on the State Council's AI plan referred to AlphaGo's mastery of the ancient Chinese strategy game as a \"Sputnik moment,\" prompting immediate reconsideration among government officials of China's AI strategy. 9A year later, the State Council issued the \"New Generation AI Development Plan\" in July 2017, formalizing existing investments in AI and unambiguously signaling China's prioritization of AI development. The plan's specific benchmarks for AI and AI-related industries 10 -including by 2030 a gross output of RMB 1 trillion (U.S. $150.8 billion) for the core AI industry and RMB 10 trillion (1.5 trillion) for related industriesdemonstrated China's aspiration to lead the world in the field. While the plan serves as an important milestone in China's AI development, it is still only one piece of China's overall AI strategy. To explain the full picture, this report places the State Council plan and China's broader approach to AI in the context of China's past science and technology plans, as well as the AI strategies of other countries. It then analyzes China's approaches to the growth of different drivers of AI development, and assesses the status and implications of China's growing AI capabilities. \n While there are also some critical new factors, the features that stay consistent are important to highlight becausethey can be mined for empirical examples. Chinese government support for AI development, emphasis on indigenous innovation, and prioritization of frontier technologies traces back to February 2006, when the State Council issued their \"National Medium-and Long-Term Plan (MLP) for the Development of Science and Technology (2006-2020).\"At the time, the MLP was Beijing's most ambitious science and technology plan to date. It allocated long-term funding for science research, estimated at RMB 500 billion (USD 75 billion), and launched sixteen national megaprojects for developing vanguard science and technology, including programs for integrated circuit manufacturing and large advanced nuclear reactors. 38 Indeed, the designation of \"Artificial Intelligence 2.0\" as a megaproject follows the framework set by the MLP. The plan also contained an explicit target to strengthen indigenous innovation. China's \"Made in China 2025\" initiative, released in May 2015, further emphasized the need for indigenous innovation to reduce the country's dependence on other countries for high-end manufacturing. \n A comprehensive assessment of the components of China's AI strategy requires an understanding of the broad range of drivers related to the AI development, including: (1) hardware in the form of chips and supercomputing facilities, (2) data as an input for AI algorithms, (3) research and algorithm development, and (4) the commercial AI ecosystem. Analyzing China's current landscape for each of these drivers clarifies crucial features of its strategy to become a world leader in AI ( \n Table 1 : 1 Demystifying China's AI Dream Myths Reality 1. The State Council' s AI plan was the starting point of China' s AI planning The plan both formalizes and definitively signals a national-level focus on AI, but local governments and companies were already engaging in subnational planning on AI.Additionally, crucial elements of the State Council' s AI plan are rooted in past science and technology plans. \n • Economic benefit is the primary, immediate driving force behind China's development of AI. Per multiple reports, of all economies' worldwide, China's has the most to gain from AI technologies, since AI systems could enable China to improve its productivity levels and meet GDP targets.3  Initial figures are promising -new Chinese AI companies and investment in the years 2014-2016 surpassed the number of companies and amount of investment in all the years prior 4 -but they should be tempered by the potential for speculative over-investment to cause boom-bust cycles. • China's adoption of AI technologies could also have implications for its mode of social governance.Per the State Council's AI plan, AI will play an \"irreplaceable\" role in maintaining social stability, an aim reflected in local-level integrations of AI across a broad range of public services, including judicial services, medical care, and public security.5  Two key areas to watch are growing concerns about privacy and the willingness of private companies to participate in various social credit systems.3 PwC, 2017; McKinsey Global Institute, 2017 4 Li, 2017 5 State Council, 2017a; for a full English translation of the \"New Generation Artificial Intelligence Development Plan\" by a group of experienced Chinese linguists with deep backgrounds on the subject matter, see this document from the New America foundation: https://www.newamerica.org/ cybersecurity-initiative/blog/chinas-plan-lead-ai-purpose-prospects-and-problems/. \n Table 2 : 2 Recent AI Plans Plan Description Key Elements Importance 13th Five Year Plan for A State Council policy Highlighted development Links AI to the current Five Developing National document which specifies of AI as 6th among 69 Year Plan through this Strategic and Emerging implementation measures major tasks a for the central guiding plan Industries (2016-2020) [\"十 for the 13th Five-Year Plan, government to pursue; 三五\"国家战略性新兴 focused on strategic Identified five agencies 产业发展规划] industries responsible for developing central government policies in AI in the next five years \"Internet Plus\" and AI Three- Jointly issued by the Established a goal to grow Connects AI development Year Implementation Plan National Development the scale of the AI industry' s to highly touted \"Internet (2016-2018) [\"互联网+\"人 and Reform Commission market size to the \"hundreds Plus\" policy which aims 工智能三年行动实施方案] (NDRC) b , the MoST, MIIT, of billions\" (RMB) to catapult China to and the Cyberspace becoming a digital Administration of China powerhouse Robotics Industry Plan to develop robotics Set specific targets for Sets goal of manufacturing Development Plan (2016- industry released by the advancing the robotics 100,000 industrial robots 2020) [机器人产业发展计划] NDRC, the MIIT, and the industry; the second of annually by 2020, making Ministry of Finance (MOF) two development plans China the world' s leading containing a focus on robot-maker AI released by central agencies with a policy planning mandate \"Artificial Intelligence 2.0\" [人 Proposal by Chinese Megaprojects were Demonstrates how AI was 工智能2.0] Academy of Engineering proposed and finalized elevated to the level of a added to a list of 15 \"Sci- in 2016 with the release megaproject only recently Tech Innovation 2030 - of the \"13th Five-Year Plan Megaprojects\" c for National Science and Technology Innovation\" but AI was added in Feb. 2017 Three-Year Action Plan for MIIT action plan for Sets out specific Shows government' s strong Promoting Development of implementing tasks benchmarks for 2020 in a guiding role in developing a New Generation Artificial related to State Council' s range of AI products and the AI industry (convened Intelligence Industry (2018- AI Plan and \"Made in services, including smart, top 30 companies to 2020) China 2025\" inter-connected cars, and develop indicators) intelligent service robots a Priorities listed above AI development, ordered from first to fifth: constructing internet network infrastructure, including rural broadband projects; improving radio and television networks; promoting \"Internet Plus\"; implementing big data development projects; and strengthening information and communications technology industries (State Council, 2016). \n Military Science and the Central MilitaryCommission. 33    There are multiple ways to interpret what lessons Chinese decision-makers took away from these critical junctures. While AlphaGo shocked the entire world, its victory over Lee Sedol appeared to have particularly affected China, where the game was invented.34  Perhaps concerned that AlphaGo's mastery of Go would sting the country's national pride, the Chinese government banned outlets from covering its May 2016 match with the Chinese player Ke Jie, the world's number one player at the time.35  For China, AlphaGo may have demonstrated that advances in AI are linked to national prestige and the perceived status of great powers. Additionally, the types of high-level seminars conducted after AlphaGo indicate that some Chinese policymakers interpreted AlphaGo's victory as having significant implications for military affairs. Per testimony before the U.S.-China Economic and Security Review Commission by Elsa Kania, the PLA \"anticipates the advent of artificial intelligence will fundamentally alter the character of warfare, ultimate resulting in a transformation from today's 33 China Military Science Editorial Department [zhongguo junshi kexue bianjibu], 2016 cited in Kania, 2017 34 Hern, 2017 29 35 Ibid. Ibid. 30 36 Wood, 2017 Kania, 2017 31 37 Allen and Kania, 2017 32 Wuzhen Institute, 2017 31  In 2016, the biggest spike in Baidu searches (the Chinese equivalent of Google searches) for \"artificial intelligence\" [人工智能] occurred right after AlphaGo's victory, per a report by the Wuzhen Institute.32  Chinese leaders and scholars also paid significant attention to AlphaGo's victory. After AlphaGo's win in February 2016, high-level seminars and symposiums were conducted on the implications. One such event was \"A Summary of the Workshop on the Game between AlphaGo and Lee Sedol and the Intelligentization of Military Command and Decision-Making\" (围棋人机大战与军事指挥决 策智能化研讨会观点综述), which took place in April 2016 and included PLA thinkers from the Academy of 'informatized' ways of warfare to future 'intelligentized' warfare.\" 36 Another reasonable hypothesis is that China's reaction to major American AI-related developments, including the way in which the State Council's plan was drafted, is partly inspired by U.S. strategy. 37 Under this interpretation, the U.S. government may have some degree of influence in shaping a potential template for China's AI planning. \n However, China contributes relatively little to fundamental research: only 2.5 percent of the new molecules discovered from 2007 to 2015 came from China, compared to 56.3 percent from America.48    Significant differences between China's AI policy and biotech policy are rooted in two factors: AI's \"omni-use\" potential means the breadth of actors involved is much wider than for other technologies; internationally-facing, private tech giants and vigorous startups are leading players in driving innovation in AI. Even the influence of the largest biotech companies pales in comparison to the power and sheer size of China's tech giants. Consider the case of China's genomic giant BGI, which has produced a number of major breakthroughs in genome sequencing. Its initial public offering raised $81 million, which is around 1/300 the size of Alibaba's IPO.49  One could argue that it is unfair to take Alibaba's IPO as the proxy for its influence in shaping AI development, because the IPO encompasses all of Alibaba's business portfolio. That Alibaba announced in October 2017 an investment of $15 billion in AI-related R&D, with foci on quantum computing and human-machine interaction, serves as an effective rebuttal to that argument.50  Finally, core AI technologies are more fundamental than biotechnologies. That is, innovations in AI algorithms can revolutionize BGI's genome sequencing, whereas the relationship does not operate in reverse. So while there are many similarities among China's AI strategy and its aims for other strategic, emerging technologies, the immense power of tech companies and AI technology itself mark out key differences. 40 Council on Foreign Relations, 2017 Ibid. 48 Bloomberg, 2017 \n Table 3 3 49 Philippidis, 2017 50 Lucas,2017 ).With respect to hardware for AI algorithms, China's promotion of national champions, encouragement of \n Table 3 : 3 Key features of China's AI Strategy to facilitate technology transfer, and investment in supercomputers 51 are all consistent with past approaches to spurring innovation in strategic technologies. First, it promulgated a national semiconductor policy in June 2014 that prioritized support for \"national champions,\" such as Tsinghua Unigroup.52  The policy launched a national Integrated Circuit Fund, which has raised more than $20 billion so far, 53 with a goal to raise USD 138 billion total in funds to seed semiconductor investors throughout the country.54  In October 2017, China's MoST announced a project to invest in chips that run artificial neural networks; as one of 13 \"transformative\" technology projects with a delivery date of 2021, the AI chip project specifically references Nvidia's M40 chip as a benchmark, aiming to beat the M40's performance and energy efficiency by 20 times.55    Second, the Chinese government has encouraged domestic companies that enjoy political support to sign deals with international firms to facilitate access to high-quality chip technology.56  A January 2017 report by the U.S.President's Council of Advisors on Science and Technology on the semiconductor industry noted that Chinese firms have been increasingly active in the acquisition space and that China places conditions on access to its market in order to incentivize technology transfer.57  Recently, China's two-pronged strategy has faced increased international scrutiny. After the U.S. government banned Intel and other chip-makers from selling China high-powered Xeon chips, 58 the Committee on Foreign Investment in the United States (CFIUS) has subjected China has made long-term bets on building supercomputing facilities. A few top-line figures indicate that China has made significant advances in the hardware necessary to power these potential breakthroughs. For51To date, it is uncertain whether supercomputers can spur AI-related progress. Chinese supercomputers, based on their own chips, have only been used for scientific projects and the chips have not been sold on the commercial market. I thank Jimmy Goodrich for this point. Main driver Old features New features Hardware Promote national champions, Tech giants and unicorn startups invest in AI chips encourage overseas deals, build supercomputers Data Share data between gov. and Increasing privacy concerns toward AI companies, protectionist toward applications cross-border flows Research and Support for basic research, gathering Tech giants establish overseas institutes to recruit Algorithms and training talent AI talent Commercial AI Sector Set up government guidance funds, More actors involved (startups, local governments, picking winners agencies, etc.) due to omni-use capabilities overseas acquisitions China's investments in U.S. chip-makers to harsher scrutiny. In September 2017, the White House blocked a state-backed Chinese investment fund from acquiring a US semiconductor company, marking only the fourth time in history that an American president had blocked a corporate acquisition on national security grounds.59    A similar story has played out in Europe. In his 2017 State of the European Union Speech, Jean-Claude Juncker, president of the EU Commission, rolled out a new framework for screening foreign direct investments into the European Union. The framework identified critical technologies including, \"artificial intelligence, robotics, semiconductors, technologies with potential dual-use applications, cybersecurity, space or nuclear technology.\" 60 While Juncker's speech did not explicitly call out Chinese investments, analysts interpreted his warnings about investments from \"state-owned companies\" as an implicit reference to China's economic activities.61    Third, \n Data security concerns have motivated China's efforts to ensure valuable data stays under the control of Chinese tech companies. In this vein, China has pushed for national standards in AI-related industries, such as cloud computing, industrial software, and big data, that differ from international standards, a move that may favor Chinese companies over foreign companies in the domestic market. According to a Mercator Institute report, 62 McKinsey Global Institute, 2017a 63 Vincent, 2016 64 Costello, 2017 65 Giles, 2017 66 Vincent, 2017 \n , and include \"AI + X\" hybrid professional training.89  This whole-of-society push is a trademark of China's central-guided development, and it demonstrates that China is placing a long-term bet on AI.90     81 Zenglin Xu' s curriculum vitae is available at: http://www.bigdata-research.org/people/faculty/5.html. Note that Xu has won travel grants for NIPS and ICJAI. 82 Zweig and Wang, 2013 83 Ibid. 84 Cao, 2008 85 Schiermeier, 2014 86 Harbringer, 2017 87 Alibaba recently invested USD 15 billion into global R&D, including 7 overseas labs, with a priority on AI; Baidu now has two research labs in Silicon Valley; and Tencent has established a lab in Seattle. 88 South China Morning Post, 2017 institutions \n For reference, funding schemes similar to China's GGFs were instrumental in transforming Israel into a leading technological powerhouse. Advantages for these types of government vehicles 89 State Council, 2017a 90 Council on Foreign Relations, 2017 91 Jing and Dai, 2017 92 Yang, 2017 93 Ibid. 94 GYZ Holdings, 2017 95 Li, 2017 96 Ibid. 97 Feng, 2017 \n Evaluation of China's current AI capacities by driver General metrics for traditional semiconductor firms are important to consider since these firms are scaling up their own processors to handle AI software, as well as acquiring startups that are building AI chips. In the year 2015, China only had 4% of the global market share of semiconductor production, while the U.S. accounted for 50% of the global market share.105  This correlates well with total financing figures which show that total financing for China's semiconductor industry was only 4.3% of the amount for its central processing unit and is used for general purposes processing; GPU is a graphics processing unit, which was originally designed to process images but happen to be very efficient at training machine learning algorithms. A tensor processing unit (TPU) is a type of application-specific integrated circuit (ASIC), specialized for AI applications. Field-programmable gate arrays (FPGA) chips are reconfigurable, programmable hardware that are relatively efficient for AI applications. .S. counterpart, per a IT Juzi and Tencent Research Institute report.106  China is particularly dependent on international companies for GPUs, which are the best option for training AI algorithms. Microsoft AI researcher, XD Huang labels GPUs \"the real weapon,\" saying that without GPUs, a Microsoft project that recognizes certain conversational speech as well as humans would have taken 4 years longer to complete.107  Out of the top 10 American chip-makers, 4 specialize in making GPUs; whereas from the top 10 Chinese chip-making companies, none specialize in GPUs.108    In the second category of hardware, chips like TPUs and some ASICs are designed specifically to rapidly execute neural networks.109  Of the top 10 Chinese chip-makers, 6 specialize in ASIC chips, which are not as flexible as other chips in this category, such as FPGAs which provide high, efficient performance as well as flexibility to change the underlying hardware to adjust to rapidly changing software. 110 Both the U.S. and China have two chip-making companies which specialize in FPGA chips out of their top 10 chip-making companies; the two U.S companies received a total of 192.5 million in total financing, while the two Chinese companies received a total 34.4 million in total funding.111  As with many aspects of AI, chip innovation is constantly occurring. For instance, Google recently launched a second-generation of TPUs, which Alphazero used to learn chess, that are able to train AI algorithms more efficiently than GPUs and CPUs. China has relied on imports and acquisitions to boost the most immediately relevant aspects of AI hardware. As this strategy has come under more scrutiny by the U.S. and EU, China is promoting national uses of different chips are fuzzy. Some companies use GPUs to execute algorithms as well. The tendency is for AI companies to use GPUs to train algorithms, and use TPUs and FPGAs to execute algorithms. and Tencent Institute report does not specify the time range of these figures. Per author' s check of the figures, they appear to refer to total money raised in all funding rounds since the company' s launch. 106 Li, 2017 107 Metz, 2017 108 Li, 2017 100 101 109 Boundaries between the 110 Brundage, 2016 AI Impact,s 2016 Freund, 2017 102 103 111 The IT Juzi 112 Cronin, 2016 Tung, 2017 113 HPCwire, 2014 CPU stands for 104 I thank Miles Brundage and Allan Dafoe for this point. 114 Author' s calculations from www.top500.org 105 115 International Trade Administration, 2016 Markoff, 2016 i. Catch-up approach in hardwareDue to their high initial costs and long creation cycle, processor and chip development may be the most difficult component of China's AI plan. Currently, AI hardware falls into two categories: (1) chips originally designed for other computing processes but used to train AI algorithms (e.g. CPUs and GPUs) and (2) chips designed specifically to execute machine learning and deep learning algorithms (e.g. Google's TPUs and Microsoft's FPGAs).103  While the manufacturing of chips these two categories are more immediately relevant for running AI algorithms, supercomputing facilities may become relevant for future AI development if researchers are better able to leverage the benefits of co-located, interconnected compute.104    In the first category of hardware, measures of the strength of China's semiconductor industry reveal a potential bottleneck for AI development.U112China's success in building supercomputers demonstrates its potential to catch-up to world leaders in AI hardware. One metric that demonstrates this finding is the share of the highest-performing supercomputers located in China, per the global Top500 list. In 2014, China's share of the Top500 list consisted of 76 systems (15.2%), which was a distant second to the U.S. at 232 systems (46.4%).113  The June 2017 version of the Top500 list saw China nearly catch up to the U.S., with the former boasting 159 systems (31.8%) and the latter having 168 systems (33.6%). 114 Further distinctions can be made with respect to this category of hardware.. It is possible that supercomputing facilities can become more applicable in future AI development on a very large scale. Nevertheless, as noted by Larry Smarr, a physicist at the University of California, China's excellence in manufacturing traditional supercomputers may not matter as much if other countries develop new, more efficient supercomputers that are designed specifically for challenges like AI.115    In sum, \n Data is another important driver for AI systems because machine learning is notoriously data-hungry. Access to large quantities of data has been cited as one of the advantages for China's AI development.118  With relatively lax privacy protections, Chinese technology giants collect vast troves of data, and sharing among government agencies and companies is common. Chinese consumers, the source of much of this data, are early and eager tech adopters, as reflected by smartphone penetration rates across the country and industry forecasts which show that the mainland will account for over 50% of the global retail e-commerce market by 2018.119 Per a report by CCID Consulting, China is projected to possess 30% of the world's data by 2030. 120 President of the Chinese Academy of Sciences, Bai Chunli, estimated, \"By 2020, China will hold 20% of the global data, which is expected to reach 44 trillion gigabytes.\" 121 China's data protectionism is part of a broader trend toward digital protectionism in which China's internet is a closed ecosystem: in this world, the Chinese government censored and blocked Facebook and Google, thereby enabling the rise of domestic platforms like Wechat and Weibo. One can see the advantages of data protectionism for AI development. If data is a scarce resource for AI development, China could establish exclusive control over this resource for its companies and research institutes. On the other hand, if more and more data is shared across platforms and countries, other actors could benefit from global data sharing while Research and algorithm development is a critical factor for the advancement of AI. Chinese researchers are able to quickly replicate the most advanced algorithms developed anywhere in the world. Drawing from a domestic pool of talent, which includes the most STEM graduates out of any country in the world, 122 China has pumped out a large quantity of AI research, but still cannot match the leading countries in the most innovative research and the most talented researchers. In 2014, China surpassed the U.S. in the volume of AI research, as evidenced by metrics on AI-related patent registration and articles on deep learning, 123 which was noted in the Obama White House's strategic plan for AI research. 124 This is not a case of volume devoid of quality: data on presentations at the Association for the Advancement of Artificial Intelligence (AAAI) annual conference, widely recognized as a leading AI research conference, revealed that Chinese researchers accounted for over 20% China remains closed off. iii. Algorithm development is high-quality but still lacking in fundamental innovation 116 I thank Elsa Kania for this framing. 117 Ernst, 2016 118 The Economist, 2017b; The New York Times 2017 119 South China Morning Post, 2016 120 Kania, 2017b 121 Chinese Academy of Sciences, 2017 122 World Economic Forum, 2016 \n Studies have defined AI expertise in different ways. While Tencent' s methodology focuses on employees at AI companies, others use job sites like Linkedin or authors of conference papers 123 He, 2017 124 Zhang, 2017 125 McKinsey Global Institute, 2017a 126 Sixth Tone, 2017 127 Tse and Wang, 2017 128 Li, 2017; \n Table 4 : 4 AAAI Conference Presentations by Country Year USA China UK Australia 2010 192 (55.2%) 42 (12.1%) 19 (5.5%) 20 (5.7%) 2011 195 (56.7%) 45 (13.1%) 18 (5.2%) 23 (6.7%) 2012 189 (49.3%) 50 (13.1%) 24 (6.3%) 35 (9.1%) 2013 156 (56.3%) 44 (15.9%) 11 (4.0%) 14 (5.1%) 2014 223 (47.0%) 104 (21.9%) 24 (5.1%) 31 (6.5%) 2015 326 (48.4%) 138 (20.5%) 55 (8.2%) 59 (8.8%) \n In 2017, China's AI startup scene received 48% of funding going to AI startups globally, surpassing the equity funding share of U.S. AI startups , which received 38% of the global share.137  The growth in China's AI scene just in the past year has been astronomical, as China accounted for only 11.3% of global funding in 2016. Though estimates differ with respect to the precise 129 Yang, 2017 130 Li, 2017 131 McKinsey Global Institute, 2017a 132 Examples include Google' s acquisition of DeepMind, Intel' s acquisition of Movidius, and Twitter' s acquisition of image-processing startup Magic Pony. 133 Author' s own calculations from https://www.cbinsights.com/research/top-acquirers-ai-startups-ma-timeline/. 134 The Economist, 2017b 135 The time range for these figures is unclear (Li, 2017). 136 Wuzhen Institute, 2017 137 CBInsights, 2018b \n Table 5 : 5 Metrics for Various Drivers in China's AI Development A recent joint Sinovation and Eurasia Group report also used number of mobile users as a key indicator for data. This report went a step further and argued that China has even more of an advantage in data since Chinese consumers make 50 x as many mobile payments as Americans (Lee and Triolo, 2017) . Other indicators that would further refine the data driver would include: data quality, integration capacity of different data holders (covered by a new government AI readiness index, available at: https://www.oxfordinsights.com/government-ai-readiness-index), and the degree to which data is bounded up in multinational companies based in a country (earlier questions of data pooling in the above section on the data driver come into play if U.S. or Chinese companies are able to pool data from global consumers). For the last point, U.S. companies have faced issues transferring European consumer data back to the states (Heide, 2016) . Since the AI field is rapidly changing, the exclusion of years 2016 and 2017 in this proxy measure could mean that it doesn't accurately capture the current state of research in both countries. Other proxy measures are more recent. Main Driver Proxy Measure(s) China USA in AI Hardware Int'l market share of 4% of world 50% of world semiconductor prod. (2015) Financing for FPGA chip- USD 34.4 million (7.6% of world) USD 192.5 million (42.4% of makers (2017) world) Data a Mobile users (2016) b 1.4 billion (20.0% of world) 416.7 million (5.5% of world) Research and Number of AI experts 39, 200 (13.1% of world) 78,700 (26.2% of world) Algorithms Percentage of AAAI 20.5% of world 48.4% of world Conference Presentations (2015) c Commercial AI Proportion of world' s AI 23% 42% Sector companies (2017) Total investments in AI USD 2.6 billion (6.6% of world) USD 17.2 billion (43.4%) companies (2012-2016) Total global equity funding to 48% of world 38% of world AI startups (2017) AI Potential Index d Avg. of the four avg. proxy (5.8 + 20 + 16.8 + 25.9)/4 = (46.2 + 5.5 + 37.3 +41.1)/4 = measures e 17 33 a b World Bank 2016 data: https://data.worldbank.org/indicator/IT.CEL.SETS?locations=CN-US&name_desc=true c d AI Potential Index is indexed from 0 to 100, with 100 representing one country being in complete control of AI technology. \n the unique risks of AI technology, including risk scenarios involving artificial general intelligence and misuse of AI as outlined by experts in recent years.143  The Chinese government outlined plans for AI safety measures for the first time in the State Council's AI plan. The document stated that by 2025, China will have initially established AI laws and regulations, ethical norms, and beginnings of AI security assessment and control capabilities; and by 2030, China will have constructed more comprehensive AI laws and regulations, as well as an ethical norms and policy system.144  No further specifics were given, which fits in with what some have called opaque nature of Chinese discussion about the limits of ethical AI research.145  At the Asilomar Conference on Beneficial AI 2017, out of more than 150 attendees, only one was working at a Chinese institution at the time (Andrew Ng, who has now left his role at Baidu). Additionally, of the 37 researchers and 45 scientific publications funded by the Future of Life Institute's AI Safety Research program, none of the research was conducted at a Chinese institution. Lastly, of the 3462 AI/robotics researchers who signed a Future of Life Institute open letter to ban autonomous weapons, only three were based at Chinese institutions (all were affiliated with the Chinese University of Hong Kong). 146 Overall, China seems to have a low level of engagement with Western countries and institutions on discussions of AI safety across private, public, and academic sectors. 147 However, there are promising signs of substantive engagement with issues of AI ethics and safety in China. A book published in November 2017, titled Artificial Intelligence: A National Strategic Initiative for Artificial Intelligence includes an important chapter that discusses the Asilomar AI Principles in detail and call for \"strong regulations\" and \"controlling spells\" for AI. 148 A wide range of Chinese AI researchers are also involved with translating the IEEE's Ethically Aligned Design report, as part of the Global Initiative for Ethical Considerations in Artificial Intelligence and Autonomous Systems. 143 Bostrom, 2014; Brundage et al. 2018 144 State Council, 2017a 145 The Economist, 2017b 146For a full list of the Future of Life Institute open letter signees see: https://futureoflife.org/awos-signatories/. \n There are a variety of perspectives on AI safety and ethics in the Chinese AI community. Doubling as a launch event for the aforementioned book, the CAICT hosted a seminar in November 2017 on the unique challenges AI poses for law and governance.149  Attendees included representatives from the Supreme People's Court, Weixing Shen, dean of Tsinghua University law school, and Si Xiao, Tencent's Chief Research Officer. From the readout of the conference, it appears that participants offered robust and, often differing, views on how to govern AI development. For instance, Dean Shen stated that AI development was an immutable social trend that should be embraced rather than excessively worried over, whereas Guobin Li, president of the Beijing Research Institute for Communication Law, argued that scholars should proactively address the legal and policy issues that could arise from AI.150  The growing efforts of Chinese scholars to tackle difficult questions of AI governance means that assessing the relative influence of these different opinions on China's AI development will be an important endeavor.Finally, AI may be the first technology domain in which China successfully becomes the international standardsetter. In another chapter, the book's co-authors, Tencent researchers and CAICT academics, linked Chinese leadership on AI ethics and safety as a way for China to seize the strategic high ground. They wrote, \"China should also actively construct the guidelines of AI ethics, play a leading role in promoting inclusive and beneficial development of AI. In addition, we should actively explore ways to go from being a follower to being a leader in areas such as AI legislation and regulation, education and personnel training, and responding to issues with AI [emphasis mine].\" 151 One important indicator of China's ambitions in shaping AI standards is the case of the International Organization for Standardization / International Electrotechnical Commission (ISO/IEC) Joint Technical Committee ( JTC), one of the largest and most prolific technical committees in the international standardization, which recently formed a special committee on AI. The chair of this new committee is Wael Diab, a senior director at Huawei, and the committee's first meeting will be held in April 2018 in Beijing, China -both the chair position and first meeting were hotly contested affairs that ultimately went China's way.152    Media reports of an AI arms race between the U.S. and China have proliferated in 2017, 153 and leading thinkers have identified AI as a technology that could provide a decisive strategic advantage in the international security realm.154  In contrast, much of the Chinese academic literature discussing military possibilities for AI technology has been largely abstract and speculative, and a majority of it references or focuses on the U.S. Defense Advanced Research Projects Agency's activities.155  Chinese military institutions, such as the NUDT, have increased their research efforts on intelligent robotics.156  In the short-term, the People's Liberation Army (PLA) will likely B. Tracking the potential of AI as a revolution in military affairs 149 Science.china [kexue zhongguo] 150 Ibid. 151 These quote is from my translation of of the book, which are available upon request (Tencent Research Institute et al., 2017). 152 According to the author' s conversation with a source knowledgeable about the discussions of the committee 153 The Economist, 2017b; New York Times, 2017b; New York Times, 2017c 154 Kaspersen, 2016 155 Kania, 2017c 156 Ray et al., 2016 \n The implications of China's AI strategy in the economic realm are numerous. Research from PwC in 2017 estimated that China had the most to gain from AI technologies, forecasting a potential 26% boost in GDP to benefits from AI.162  A report from McKinsey Global Institute supports this view, estimating that 51% of work activities in China can be automated -more than any other country in the world.163  Faced with unfavorable demographic trends, China could improve its productivity levels by integrating AI systems.164  This would enable China to sustain its economic growth and meet GDP targets. The stakes for global economic preeminence are stark. A report by PwC projects that the AI sector could contribute up to USD 15.7 trillion to the world economy by 2030.165     \n 's chances of getting a job, and the school placements of one's children. Advances in AI could automate the collection, management, and effective analysis of massive amounts of citizen data. China's Ministry of Public Security (MPS) is reportedly building the world's largest facial recognition database and is experimenting with expansive surveillance techniques in Xinjiang, a particularly volatile region of the country.172  Although several local pilot projects are operational, national implementation is still in the early stages and is dependent on support from private companies' technological expertise.173  Moreover, the consolidation of privacy protections in national-level standards and laws, mentioned earlier in the report, could forestall various social credit schemes.Regardless, the intersection between AI technologies and China's social governance is worthy of close attention.Undoubtedly, the relevance of AI to China's core interests and China's receptiveness to issues of AI ethics and safety will have global consequences. China's AI strategy could spark military competition over a new strategic technology. At an event organized by the Center for a New American Security, former Deputy Defense Secretary Bob Work and the former executive chairman of Alphabet, Eric Schmidt, both urged the U.S. government 165 PwC, 2017 166 McKinsey Global Institute, 2017a 167 For more on this subject, See: Hoffman, 2017 168 Chen, 2017 one \n\t\t\t iiMedia, 2017 \n\t\t\t This arrangement is from my translations of a book published by Tencent on AI strategy (Tencent Research Institute et al., 2017) . \n\t\t\t McGregor, 2010   \n\t\t\t For a history of this term, See : Feigenbaum, 2017   \n\t\t\t The Turing Award is often referred to as \"the Nobel Prize of Computing.\" \n\t\t\t These terms are from my translations of the book, which are available upon request (Tencent Research Institute et al. 2017 ). \n\t\t\t Ibid.东西智库收录 www.dx2025.com 登陆下载更多精品报告 \n\t\t\t Botswan, 2017    \n\t\t\t Swan, 2018", "date_published": "n/a", "url": "n/a", "filename": "deciphering-chinas-ai-dream.tei.xml", "abstract": "A special thanks goes to Danit Gal for feedback that inspired me to rewrite significant portions of the report, Roxanne Heston for her generous help in improving the structure of the report, and Laura Pomarius for formatting and production assistance.", "id": "c3f51877cb96ea87c138480e551848c8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jess Whittlestone", "Kai Arulkumaran", "Matthew Crosby"], "title": "The Societal Implications of Deep Reinforcement Learning", "text": "Introduction Artificial intelligence (AI) is already having an impact on many areas of society  (Whittaker et al., 2018; Whittlestone et al., 2019) , and further advances in AI research are likely to precipitate much greater impacts. There is a growing community of researchers and practitioners doing excellent work to identify and address ethical and societal issues raised by current applications of AI  (Schiff et al., 2020) . Given the pace of AI progress, it is crucial that this community also think ahead about what challenges might be raised by future advances, and how forms of governance, norms, and standards being developed around AI today can best prepare us for the future evolution of AI systems. Of course, predicting the future of any technology with certainty is difficult. One way to strike a balance between thinking ahead while still being grounded in reality is to ask the question: what might be the impacts on society if current successful trends in AI research continue and result in new and widespread societal applications? This paper explores the potential societal implications of one avenue of AI research currently showing promise: Deep Reinforcement Learning (DRL). The paper is primarily aimed at researchers and policy practitioners working on the ethical, societal and governance implications of AI, but may also be of interest to AI researchers concerned with the impacts of ©2021 AI Access Foundation. All rights reserved. their own work. Our discussion aims to provide important context and a clear starting point for the AI ethics and governance community to begin considering the societal implications of DRL in more depth. DRL has received increasing attention in recent years, leading to some high-profile successes, particularly in board and video games  (Mnih et al., 2015; Silver et al., 2016 Silver et al., , 2017 Berner et al., 2019; Vinyals et al., 2019) . DRL combines Reinforcement Learning (RL), an approach based on learning through interaction with an environment, with the potential to result in highly autonomous systems  (Sutton & Barto, 2018) , with Deep Learning (DL), an increasingly popular method that enables AI systems to scale to more complex problems and environments  (Goodfellow et al., 2016) . Several researchers have suggested that DRL is likely to be a key component of more general-purpose and autonomous AI systems in the future  (Arel, 2012; Chen & Liu, 2018; Popova et al., 2018) . Though there are still considerable barriers to large-scale real-world deployment of DRL systems, we are beginning to see potential for application in areas including robotics  (Ibarz et al., 2021) , online personalisation and targeting  (Zhao et al., 2019) , finance  (Fischer, 2018) , autonomous driving  (Tai et al., 2016) , healthcare  (Esteva et al., 2019) , and data centre cooling  (Gasparik et al., 2018) . These applications and others will likely become more widespread as the technology improves. This could have substantial implications for people's lives: for example, by speeding up automation in various sectors, changing the nature and potential harms of online influence, or introducing new safety risks in physical infrastructure. We therefore suggest that now is an ideal time to begin thinking about how more widespread application of DRL-based technologies might impact society, what ethical questions might arise or be made more pressing as a result, how progress on different areas of technical research will affect these ethical challenges, and what forms of governance might be required to mitigate any risks. One challenge for exploring the potential impacts of future AI progress is that doing so will often require considerable background knowledge about current AI techniques and research directions. Such understanding is often beyond the core expertise of AI ethics and governance scholars, and there is a lack of accessible resources. We therefore begin this paper by providing a broadly accessible introduction to DRL methods with links to further, more in-depth resources for the interested reader.  1  Following this background, we outline in Section 3 the ways in which plausible future applications of DRL may introduce or exacerbate pressing issues for society, ethics and governance, including by: raising questions for current approaches to human oversight; introducing new challenges for safety and reliability; and changing incentives for data collection. We then discuss how progress on different technical challenges might shape the landscape of these societal concerns: how might breakthroughs in different areas magnify or mitigate societal impacts and risks, or change the direction of the field such that currently underresearched risks become more important? Understanding and monitoring progress on the technical research areas crucial to widespread application of DRL will be key to successful and timely management of future societal impacts, and will require interdisciplinary collaboration between experts in AI, social science, and policy. Based on this analysis, we highlight Artificial Intelligence includes any approach that attempts to make machines perform intelligently. Machine Learning involves getting machines to learn to solve problems from, usually large amounts of, data. \n Deep Reinforcement Learning Reinforcement Learning DL models data with many layered (deep) neural networks. An RL agent learns from a reward signal using trial and error. some important avenues for future work and conclude with recommendations for researchers in the AI ethics and governance community. \n Deep Learning \n Combines \n Deep Reinforcement Learning: a Brief Overview DRL is an approach to AI falling within the subfield of machine learning (ML), which combines two popular approaches in current ML research: reinforcement learning (RL) and deep learning (DL). 2 In general, the purpose of ML is to find solutions to problems that we cannot directly write programs for. This involves using (often large amounts of) data to optimise the parameters of a mathematical model, which will then encode a solution  (Bishop, 2006) . This is a powerful approach to solving many different types of problems. For example, while we could easily write a computer program to emulate a medical questionnaire (which is essentially a flowchart), we cannot similarly distill the knowledge of a doctor to diagnose a patient on the basis of a CT (computerised tomography) scan. However, given a large amount of data from CT scans and corresponding expert diagnoses, we can use ML to train a computer program to imitate doctors on this task  (Kononenko, 2001; Fatima et al., 2017) . However, many of the problems that we have to solve in the real world require going beyond making predictions based on labelled inputs: we may also want to interact with our environment through sets of actions, where the choice of action depends on what goals we have. Part of how humans learn is through this type of trial and error: when we take an 2. For an excellent and accessible overview of ML also aimed at those interested in its implications, we encourage reading \"Machine Learning for Policy Makers\"  (Buchanan & Miller, 2017) . For more in-depth, technical overviews of DRL and its components, DL and RL, we refer readers to the numerous excellent resources already published  (Goodfellow et al., 2016; Arulkumaran et al., 2017; Sutton & Barto, 2018; François-Lavet et al., 2018; Kaelbling et al., 1996) . \n Agent learns from previous actions, states, and rewards \n Environment \n Its state determines the observations and reward \n Actions chosen by agent's policy \n Observations and Rewards Figure  2 : An agent interacts with its environment through its actions, and learns in response to receiving new observations and rewards. action or make a choice, we get feedback, which gives us some indication of whether we should take similar actions in the future. For example, a young child quickly learns that when they say or do certain things, adults give them positive attention, leading them to repeat those same behaviours for reward more often. Reinforcement learning (RL), the core of DRL, is based on this approach to problem-solving and learning: an RL agent 3 learns through interaction with an environment, and, through trial-and-error, can alter its own behaviour in response to the feedback it receives. More precisely, the goal of RL is to learn a policy that recommends the best action to take at any given moment in order to maximise total reward over time. The reward received at any time point is given by a reward function, which specifies how good or bad the agent's actions are (but not necessarily exactly what they should be) given the current state of the world. RL takes place in a feedback loop, incorporating perception, action, and learning, as illustrated in Figure  2 . An RL agent first perceives the current state of its environment, performs an action in response, and then observes the next state as well as a reward.  4  This loop continues until a predetermined terminal condition is reached, or can run on indefinitely. A good policy should give the agent an appropriate action to take in every possible state of the environment, including ones the agent has never seen before. For example, when AlphaGo  (Silver et al., 2016)  beat former world Go champion Lee Sedol, it encountered board positions that had never occurred during its training period, and still played moves at least as good as any human expert. The first generation of RL approaches learned polices in the form of large tables, which indicated what action to take in any given state. However, many interesting modern applications of RL have far too many possible states or actions for this tabular approach to be practical or effective. This has led to decades of work on using more complex functions to approximate policies, culminating in recent years in the use of deep learning for learning more complex policies. Deep learning (DL) involves using many-layered models-most commonly artificial neural networks-to represent complex, non-linear functions. 5 A neural network accepts an input (usually a large matrix of numerical values), and, through the repeated application of mathematical operations in each layer, will produce an output (another matrix of numerical values). The trainable parameters of the network, which can number in the billions  (Brown et al., 2020) , can be updated by a learning algorithm so that, over time, the network ends up producing the desired outputs. Key to the success of DL  (LeCun et al., 2015)  is its ability to learn high-level features or representations from raw sensory data (e.g., images, text, or audio), which can be used to find patterns in high-dimensional data and generalise to previously unseen inputs. DRL involves training a neural network using RL, where the network learns which actions to take given its sensory inputs and feedback in the form of rewards.  6  The RL algorithm specifies how to update the parameters of the neural network so that it outputs actions leading to higher rewards. DL has enabled RL to scale to previously intractable problems by improving the performance of RL algorithms in two key ways: through representation learning, allowing them to learn directly in complicated environments, and function approximation, enabling policies with complex inputs and/or outputs  (Arulkumaran et al., 2017) . Because neural networks can approximate any function, they can be used to encode the policy of an agent. This allows RL to extend to problems with state or action spaces that are too large for the tabular approach-which includes most interesting modern applications. Deep networks can also learn features directly from raw sensory data, which means that they can, at least theoretically, be applied in many environments, including the real worldwith appropriate sensors. Without deep networks, the inputs to a RL algorithm generally have to be pre-processed and provided by a human expert. By contrast, DeepMind's DQN algorithm-the work that kickstarted the field of DRL-was able to achieve human-level performance on some Atari 2600 games from the game screen and the score, but no additional domain knowledge about any of the games  (Mnih et al., 2015) . An important extension of RL is multi-agent RL (MARL), in which multiple agents learn to compete or co-operate in an environment  (Busoniu et al., 2008) . While some agents may be deployed in isolation, there are many scenarios where groups of agents will need to interact with each other. Some parts of MARL research also look at mixed human-AI interaction  (Bard et al., 2020) , where understanding the intent of other agents is especially important. As a subfield of RL, MARL inherits all of its technical issues, but also introduces extra emergent complexity. While a full treatment of the intersection of DRL and MARL is 5. DL can involve other types of deep models  (Damianou & Lawrence, 2013) , but is effectively synonymous with the use of (artificial) neural networks. While artificial neural networks were historically inspired by biological neurons found in the brain, they are far more simplistic, and it is more informative to think of artificial and biological neural networks as independent, loosely similar, systems. 6. Technically speaking the network may output a 'value' for each state and then a further rule will determine the action performed. out-of-scope for this work, it is worth noting that agents can have different, even conflicting reward functions, and hence a single 'optimal' solution does not exist in the general case, even in theory. Another implicit assumption in most ML research is that ML models are trained on exactly the same distribution of data that they will be tested on. In the context of DRL, an example would be training a robotic arm to pick and place a certain type of object in a given place in a factory line, 'freezing' the learned model, and then deploying it in the exact same scenario. However, such a model would most likely be unable to adapt to changes in the type of object or placement along the line. To do so, one would also have to incorporate continual learning  (Parisi et al., 2019) , where the deployed model could continue to learn and adapt to changes in its environment. While trained DRL agents could be deployed without continual learning capabilities, they would be limited to strictly regulated, static environments. As this condition is extremely limiting, we assume that most impactful future applications of DRL will need to be capable of some form of continual learning. In general, current DRL methods work best on problems that have: (a) a well-defined environment, where it is possible to provide observations of the environment as input, specify what sorts of actions can be taken, and model time as passing in discrete steps; (b) a clear reward function, which is appropriate to the task, provides enough information to learn from, and cannot be easily 'gamed'  (Amodei et al., 2016; Krakovna, 2018; Lehman et al., 2020) ; (c) plenty of data to train the deep neural network-in the context of RL, this means it must be able to interact with and gain feedback from the environment easily and quickly; and (d) lots of computing power available, as exemplified by the high profile successes in DRL  (Silver et al., 2016 (Silver et al., , 2017 Berner et al., 2019; Vinyals et al., 2019) . The latter requirement is exacerbated by the fact that ML algorithms also have 'hyperparameters' 7 that need to be tuned separately, requiring the training of many models to find the settings that work best. In reality, it is rare that all of these ideal conditions are met, which is currently preventing the widespread deployment of DRL systems. However, successful applications of DRL are already apparent, even in these early stages of technological development. These initial applications are already raising issues for society, ethics, and governance which will only become more important as progress is made. We give an overview of these issues in the next section, in particular noting how they relate to current and emerging applications of DRL. \n Challenges DRL Raises for Society, Ethics, and Governance Areas where DRL has begun to see practical application include: to send more personallyrelevant notifications on Facebook  (Gauci et al., 2018) ; to control Google's data centre cooling system, improving energy efficiency  (Gasparik et al., 2018) ; to automate aspects of electronic trading, such as in J.P. Morgan's LOXM  (Bacoyannis et al., 2018) ; and in robotics and manufacturing  (Ackerman, 2020) . In the future, we may see more substantial use of DRL in a variety of areas from clinical decision support to resource management, and online education to autonomous driving  (François-Lavet et al., 2018) . These potential applications of DRL could have many benefits. More flexible robotic systems could improve manufacturing and delivery processes beyond their current limitations, more adaptive recommender systems could better take account of individuals' personal 7. Hyperparameters are set before learning begins; 'standard' parameters are adjusted during learning. preferences and longer-term consequences, and improving the efficiency of city infrastructure could help preserve vital and scarce resources. The promise of these benefits ensures that we will see more resources invested in realising these applications in the future. At the same time, the possibility of more autonomous systems that operate flexibly across a range of real-world domains introduces and magnifies a number of problems for AI ethics and governance, which we discuss in this section. \n Human Oversight The Ethics Guidelines for Trustworthy AI report published in 2019 by the European Commission's High Level Expert Group on AI (High-level expert group on Artificial Intelligence, 2019) states that in order to support human autonomy and decision-making, AI systems must allow for human oversight. Most applications of AI in society today support existing, identifiable decisions taken by individuals and groups, such as doctors, stockbrokers, and lawyers  (Parson et al., 2019) . This makes human oversight a relatively straightforward matter of ensuring that there is always a human 'in-the-loop', i.e., the ability for a human to oversee the overall activity of the system and intervene in every decision made. Applications of DRL, which aim to increase the autonomy of machines, may pose a challenge for this approach to human oversight. DRL could potentially be used in ways that go beyond supplementing or even replacing identifiable decisions, towards taking over control of much larger-scale processes, systems and networks, such as those involved in resource management in cities  (Mohammadi et al., 2017) . What adequate 'human oversight' should look like in these contexts, where a system may be making hundreds of small decisions in a very short period of time, is unclear. The data flow that a system is acting upon may be incomprehensible to humans, or simply too large and fast-moving for meaningful oversight to be maintained. For example, a DRL system designed to monitor and adjust energy usage in a building may be constantly making so many small decisions that it is impractical for a human to review and alter decisions even after the fact, and the system may be sufficiently complex and opaque that it is not possible to identify mistakes and intervene in real-time. It may be possible to impose constraints while the system is being designed-ensuring that the system turns off and a human is alerted if levels go above or beyond a certain threshold, for example. However, there remains a question of whether this constitutes sufficient oversight-or whether in this or similar situations we should avoid deploying DRL systems until ways to maintain more substantive oversight are found. Another challenge for oversight is introduced by the fact that deployed DRL systems may continue to learn and adapt their behaviour once embedded in their environment, possibly at a pace that is challenging for humans to keep track of and therefore meaningfully oversee. The question of how to maintain human oversight over systems that are continually learning is not one that has been addressed in existing ethics and governance proposals, and will become more pressing as continual learning systems become more advanced and practical. Similarly, if MARL becomes more prevalent, it would make understanding and intervening at the level of a single agent more difficult, posing additional challenges for oversight. In response to the direction of AI research, the European Commission's more recent whitepaper on AI states that \"the appropriate type and degree of human oversight may vary from one case to another\"  (European Commission, 2020) . Even though it may not be possible for a human to explicitly approve every decision, it may be possible to retain meaningful oversight by ensuring a human is able to review decisions after they have been made, by monitoring an AI system in operation and intervening in real-time if necessary, or by imposing operational constraints in the design phase. Further work on flexible approaches to human oversight should take into account possible evolutions in the autonomy and behaviour of DRL systems discussed here. As systems become more autonomous and promise more high-impact applications, there will inevitably be economic pressures to trust systems to make more decisions and take over more processes, rather than waiting for, or relying on, slow human input. The benefits of doing so need to be traded off against the potential costs to human autonomy that come from reduced oversight, and we must begin thinking about how to navigate this tradeoff now before pressures to implement more autonomous systems grow. \n Safety and Reliability DRL agents learn by exploring their environment to discover the actions that lead to the highest reward over time. This trial-and-error approach to learning means that in order to learn how to avoid making a mistake, a DRL agent would have to first make that mistake  (Berger-Tal et al., 2014) . In many real-world contexts this is unacceptable: we cannot have self-driving cars running over pedestrians, or an energy control system accidentally switching off electricity in a hospital, before learning not to do these things. This can cause problems even when DRL is not being deployed in a physical environment: Microsoft's chatbot Tay 8 reproduced thousands of offensive tweets before the problem was noticed and it was taken down. Deploying DRL systems in the real world therefore requires new ways of ensuring the safety and reliability of systems, and in particular requires approaches to safe exploration  (Pecka & Svoboda, 2014; Garcıa & Fernández, 2015) : how can agents explore enough during training to learn robust behaviour, while avoiding the kinds of exploration that could cause harm? Ensuring the safety and reliability of DRL systems becomes even more pressing if they are deployed with increasing autonomy in high-stakes domains and systems. For example, it has been suggested that DRL may be able to make effective use of the data generated by 'smart cities' to improve resource management, such as by optimising power usage, increasing the efficiency of traffic signal control systems, and increasing crop productivity by monitoring and correcting parameters in agriculture systems  (Mohammadi et al., 2017; Mocanu et al., 2018; Genders & Razavi, 2016) . Systems such as energy, transportation, and agriculture are high-stakes in the sense that failures could result in loss of life, and incredibly complex, meaning that their dynamics cannot be fully understood by any single person or group. It is reasonable to suppose that DRL systems, with their adaptability and ability to process huge amounts of data, may ultimately be better equipped to manage these important processes than humans, and improving efficiency could help save critical resources across the world. However, the importance of these domains also means that the risks involved in deploying 8. Although the type of algorithm behind Tay is unknown, this is still a prime example of an agent that interacts with an environment and learns from feedback. DRL systems are huge, massively raising the stakes of mistakes and unintended consequences compared to smaller-scale and more constrained applications. Continual monitoring of DRL systems will be essential to ensuring their safety in highstakes domains, especially if those systems are trained in the real world and continue to learn from a constant stream of data after deployment. Even for systems that are 'frozen' before deployment (i.e., no longer continuing to learn), as initial deployments of DRL likely will be, it is widely accepted that we currently lack adequate methods for verifying safety and reliability  (Tarraf et al., 2019; Allen, 2020; Fiander & Blackwood, 2016) . For systems that learn over their lifetime, continual monitoring to ensure they do not learn behaviours outside of their intended use is even more challenging (Defense Innovation Board, 2019). Substantial progress on the testing, evaluation, verification and validation of AI systems in general, and DRL systems in particular, will be needed before continually-learning DRL systems can be safely deployed in high-stakes domains. One research area likely to contribute to this progress is explainable AI  (Gunning, 2017; Arrieta et al., 2020) . Explainable AI includes the development of models that are inherently easier for humans to understand, but also methods for post-hoc interpretation of standard models such as neural networks. While interpretability methods from the broader field of DL, such as saliency maps  (Simonyan et al., 2013)  or activation maximisation  (Erhan et al., 2009) , have been applied to study DRL agents  (Greydanus et al., 2018; Dai et al., 2019) , the intersection of interpretability and DRL is relatively underexplored. As research in this area matures, policymakers will need to make decisions around acceptable tradeoffs between the fidelity and interpretability of explanations given by AI systems  (Ribeiro et al., 2016) . \n Harms from Reward Function Design Beyond more immediate harms, it will also be important to consider the potential longerterm side effects of DRL systems optimising for a specific reward function, which may cause harms which are less obvious but potentially even greater in scale. The flexibility of reward functions-which is what makes DRL systems in theory extremely powerful-introduces much greater potential for unintended consequences, and we might not notice that a system is optimising for slightly the wrong objective before it is too late  (Clark & Amodei, 2016; Krakovna, 2018; Lehman et al., 2020) . The challenge of reward function design is a longstudied topic in RL and there are many examples where reward functions cause surprising behaviour  (Ng et al., 1999; Randløv & Alstrøm, 1998) . There are two related problems for reward function design that can result in unintended harms. First, many real-world tasks do not have easily-defined objectives, and it can be difficult to predict in advance what behaviour a system will exhibit as a result of optimising for a given reward. Second, even if reward functions do correctly capture what the designers or immediate users of a system intended, they may have broader consequences that are harmful to others, perhaps unintentionally. There are many documented cases of this first problem where DRL algorithms end up learning the 'easiest' way to achieve a stated objective  (Clark & Amodei, 2016; Krakovna, 2018) . For example, an RL agent trained to play a boat race game was rewarded for getting as many points as possible, under the assumption that this would be equivalent to winning the race  (Clark & Amodei, 2016) . However, due to the game layout, the agent was able to find a way to knock over targets by driving in circles, increasing its score but never actually finishing the game. This example is perhaps more amusing than concerning, but such misspecifications could be much more problematic in real-world settings where unintended actions could lead to economic or physical harm.  Everitt et al. (2019)  give the example of a stock prediction system that predicts the bankruptcy of a company, causing stakeholders to leave. Although it is undesired, creating 'self-fulfilling prophecies' is an effective way for the agent to maximise its predictive accuracy. To illustrate the second problem, consider the case of social media content-selection algorithms, designed to maximise the likelihood that a user clicks on a given item.  Russell (2019)  suggests that rather than helping users to find content they are more interested in, ubiquitous use of these algorithms has instead ended up changing users' preferences so that they are more predictable. Worse, this process gradually shifts user preferences towards more extreme content, and therefore contributes to greater conflict online. Russell even goes so far as to suggest the effect of these algorithms has contributed substantially to the resurgence of facism and the crumbling of international bodies like the European Union and NATO. In large part, the problem here arises as a result of companies optimising for a specific objective at the expense of the interests of individuals and wider society. From the perspective of a social media company, increased engagement can come from people finding more content they genuinely enjoy, or from people being shown more provocative and divisive content. As more companies develop and deploy DRL systems with wide-ranging impacts on users, we must consider both how to ensure that these systems behave as intended over the long-term, and whose interests they are serving. Potential conflicts between commercial and individual needs are particularly concerning here: a reward function by itself may not be sufficient to simultaneously maximise a company's long-term financial return while ensuring there is no negative impact on user agency or welfare, yet it is the former that will likely drive most commercial deployments of AI. Even with the best of intentions, reward functions are likely to be biased towards those designing or profiting from them. As AI systems come to be deployed more globally, what was once a localised problem becomes a problem of global value alignment: how do we ensure that the goals pursued, both directly and indirectly, by increasingly wide-ranging DRL systems, consider the values of all those impacted by them? Current AI ethics guidelines are predominantly issued by the US and EU, suggesting we have a way to go in ensuring a diversity of perspectives are accounted for  (Jobin et al., 2019) . To ensure the longer-term impacts of DRL systems are broadly beneficial, therefore, we need a broader sense of what ethical and responsible reward function design should look like, and how it could be enforced, especially where DRL is being deployed in domains with real implications for people's lives by companies whose goals may not be aligned with society as a whole. \n Incentives for Data Collection The type and amount of data required to train DRL systems creates incentives for data collection which raise particular ethical concerns. DRL methods tend to require very large amounts of data as well as ongoing data collection if the DRL system is continuing to learn and adapt its behaviour once deployed. This means that the collection of up-to-date and expansive data from across society could become a key factor for developing and deploying DRL systems. We might therefore be particularly concerned about progress in DRL creating greater incentives for more widespread surveillance. We suggest that particular attention should be paid to advances in continual learning combined with DRL, which would require more real-time data collection, and to advances in methods to learn from large-scale data sources for real-world deployment, such as we are beginning to see in work using DRL to navigate cities using Google street view  (Mirowski et al., 2018) . Some areas where DRL might be applied raise greater concerns about data collection and surveillance than others. In order to develop DRL systems for managing infrastructure, for example, it may be particularly important to generate and collect greater amounts of data through the installation of sensors and actuators across cities. This raises a challenging tradeoff between the potentially huge benefits of better resource management against the real threat to people's privacy and autonomy of increasingly 'smart' cities. Another potentially concerning application is the use of DRL to learn more sophisticated and granular models of different users of a digital product or service, and to adapt these models over time based on user behaviour  (Zheng et al., 2018) . While this could improve people's online experiences, it also might increase the incentive for companies to try to collect or infer increasingly sensitive information about online users, and raises the important ethical question about what data it is acceptable to use to build such models. There is ongoing technical work in areas such as federated learning and differential privacy attempting to address some of these issues  (Ji et al., 2014; Li et al., 2020) , and the European Union's General Data Protection Regulation (GDPR) represents an important legislative step towards protecting people's privacy. However, both technical and legislative approaches to data privacy will need to account for how incentives for data collection, and the resulting tradeoffs, may change as DRL systems become more widely deployed. Increased data collection may also have a disproportionate negative impact on groups who are already vulnerable or discriminated against. Even if surveillance systems are intended for specific, beneficial purposes such as better resource management, the collection of increased data from smart cities consolidates power over individuals' lives in the hands of technology companies and governments, who may well end up using that data for other purposes such as policing and tracking immigrants. Such uses of surveillance have a welldocumented history of being used, deliberately or otherwise, to entrench systemic discrimination against minority groups  (Crawford et al., 2019) . Similarly, increased modelling of users based on online behaviour could easily encode and entrench biased assumptions and stereotypes: Facebook's targeted advertising has been widely criticised for relying on gender and racial stereotypes  (Hao, 2019) . To the extent that applications of DRL incentivise greater surveillance and enable increasingly sophisticated online targeting, they are likely to exacerbate these problems. \n Security and Potential for Misuse Without advances in the robustness and security of DRL systems, they may be open to attacks from adversaries attempting to manipulate their performance and behaviour. For example, even a demonstrably safe DRL-based robot could be forced into dangerous collision scenarios by an adversary perturbing its sensory input or corrupting its reward function.  Behzadan and Munir (2018)  argue that there are unique challenges posed by ensuring the security of DRL systems. Compared to other ML approaches, it is much less straightforward to distinguish adversarial attacks from benign actions in DRL, since the exploration mechanism means that the training data distribution is continually changing, and delayed rewards may make it difficult to straightforwardly assess the performance of a system. Especially if DRL systems begin to be integrated into critical systems such as healthcare, energy, and transportation, it is essential that key security issues in DRL are well-understood and sufficiently addressed. There is also a risk that DRL-based systems may be deliberately misused in ways that cause harm. For example, due to their ability to more effectively tailor online content, DRLbased methods could easily be misused to improve the efficacy of online manipulation and disinformation by learning which messages are maximally persuasive to different individuals. In a recent review of online targeting systems, the UK Government's Centre for Data Ethics and Innovation recommend that there should be adequate transparency around online targeting (Centre for Data Ethics and Innovation, 2020). Given its potential use to tailor content more narrowly, it may be particularly important for policymakers and regulators to find ways to mandate transparency around where DRL in particular is used in recommender systems. Improved DRL-based models of human behaviour in particular could be misused to strengthen attempts at social manipulation. Advances in data efficiency and simulation quality would make it easier for those without access to large amounts of computing power and data to make use of DRL  (Tucker et al., 2020) . This could make it easier for small groups to misuse DRL capabilities for malicious purposes. For example,  Brundage, Avin et al. (2018)  describe how cyber attackers might use DRL to \"craft attacks that current technical systems and IT professionals are ill-prepared for\", emphasising how the feedback loop in RL enables comparison between different approaches to find the one that is most effective at evading security tools. However, DRL could also be used to improve defensive cybersecurity capacities. Whether the advantage lies on the side of the attackers or the defenders is unclear, and would benefit from further analysis, perhaps building on existing work on how technological progress may affect the offense-defense balance  (Garfinkel & Dafoe, 2019) . \n Automation and the Future of Work A clear implication of more adaptable and reliable DRL-based systems, especially in robotics and manufacturing, is in changing the susceptibility of different jobs to automation. Several analyses have suggested that many low-wage or manual jobs are unlikely to be automated in the near future because they require levels of dexterity, mobility and flexibility for which humans still vastly outperform machines  (Ford, 2015; Frey et al., 2016; Autor & Dorn, 2013) . While this advantage still clearly remains at present, current avenues of progress in robotics led by DRL methods suggest this gap could quickly diminish, a factor that is not considered explicitly by any of the analyses of automation the authors are aware of.  Frey and Osborne (2016) , for example, discuss areas where AI systems are far from human performance, including in perception and manipulation, and how this limits possibilities for automation at present, but do not consider the implications of potential progress in these areas.  Kai-Fu Lee (2018)  argues that manual jobs with the highest risk of replacement are those which are performed in structured environments, with little need for dexterity or social interaction. Prime examples include assembly line inspectors, fruit harvesters and dish washers. However, Lee does not specifically consider how advances in DRL could impact the ability of these jobs to be automated. Rather than leading to full automation of jobs, advances in DRL may instead ease or improve work in certain domains, by automating tedious or dangerous aspects of manual work. This could have a positive impact on existing employees if it makes their work more enjoyable, but this has to be traded off against potential job losses from improved efficiency. A more detailed analysis of how advances in DRL specifically might speed up automation or change the nature of work in different sectors, for example by improving robotic manipulation, would be valuable. \n Avenues of Progress in DRL and their Implications We have argued that widespread deployment of DRL systems in society could introduce new challenges for the ethics and governance of AI, such as by requiring new forms of oversight and new processes for responsible system design, as well as exacerbating the importance of existing challenges, such as ensuring the safety, reliability and security of systems deployed in safety-critical domains. However, current DRL methods are not yet seeing widespread deployment, due to several ongoing technical challenges in DRL research. This gives us time to anticipate and prepare for the societal impacts of DRL. An important part of doing so will involve tracking progress on different technical challenges currently faced by DRL methods, which will enable different kinds of applications. In this section, we therefore introduce some of the key technical challenges for the DRL research community, and discuss the possible implications of progress on these challenges for the ethical, societal, and governance challenges discussed in the previous section. \n Learning in the Real World DRL systems learn through interacting with an environment. In a simulation or a game the environment can be strictly controlled, but in real-world environments there is more complexity and noise, interaction is often slow and expensive, feedback can be delayed, and performing the wrong action can be dangerous  (Dulac-Arnold et al., 2019) . For example, in recommender systems the delay between recommending an item to a user and seeing them interact with it may be days or even weeks  (Mann et al., 2018) , and for robotic agents, a simple fall or crash could damage expensive equipment or even hurt someone. Because of the challenges and risks involved in training DRL in real-world environments, often it is desirable to instead use simulated environments for training. However, good simulations require enormous amounts of data and often still do not result in policies that transfer well to the real world  (Pan et al., 2017) . There are two key interrelated approaches to improving DRL systems so that they can be deployed in real-world environments. One approach, which has recently shown impressive results, is finding ways to transfer learned policies from simulation to the real world; these have recently been popularised as 'sim2real' methods. A popular method within these is 'domain randomisation'-randomising various aspects of the simulation (e.g., lighting, background clutter, friction coefficients, etc.), so that DRL agents learn policies that are robust to variations in these in the real world  (Tobin et al., 2017; James et al., 2017; Peng et al., 2018; OpenAI et al., 2019) . Other methods include system identification  (Chebotar et al., 2019)  and domain adaptation  (Bousmalis et al., 2018; Tzeng et al., 2020) . Should rapid progress be made in sim2real methods, this would mean that DRL agents could be trained primarily in private simulations, only to be released at the end of successful training. This means that there may be fewer public warning signs before a new system is introduced to the real world, potentially it more difficult to anticipate potential impacts of new applications in advance, as well as making it easier for companies to develop and deploy systems without oversight and accountability. The resulting systems may be relatively capable, but over-reliance on simulation could also result in the deployment of agents that perform well in simulation but fail catastrophically in the real world. As sim2real methods advance it will be important to consider how risk assessment and oversight of highrisk applications can be ensured. A second approach to improving the ability of DRL systems to learn in real-world environments is to improve data efficiency, i.e. the ability of DRL systems to learn from much smaller amounts of data. One approach to improving data efficiency in RL is to use modelbased RL (MBRL). In MBRL, the agent learns a model of the environment, which can allow the agent to explicitly or implicitly plan what to do without necessitating further interaction with the environment  (Sutton, 1990; Hamrick, 2019) . In this case, the agent effectively creates its own simulation of the world to learn in. Improvements in model-based RL could also aid with building more realistic simulators from available real-world data. However, substantial progress will be required before it is possible for agents to learn models of most complex real-world environments. The ability to train DRL systems entirely in simulation or from much smaller amounts of data would reduce the need for 'safe exploration' approaches discussed previously. Mistakes made in simulation would have little or no real cost, and the ability to learn from fewer interactions would significantly reduce (if not entirely mitigate) the risk of serious error. If we see advances in simulated environments then it may also be that the need for extensive real-world data collection is reduced for the purposes of initial training. However, even in such a case it would still be desirable to develop systems capable of continuing to learn once deployed, meaning constant streams of real-world data are still likely to be highly valued. Improvements in data efficiency would therefore also be valuable for reducing incentives for large-scale data collection. \n Safe and Reliable Reward Functions The behaviour of a DRL agent is highly dependent on its reward function, but as discussed in Section 3, it can be very difficult to specify what we actually want for many real-world tasks. This can make DRL systems unreliable in ways that compromise their safety. Several different technical approaches are attempting to solve the problem of ensuring the safety and reliability of reward functions. Some approaches focus on ways to train systems without interaction with the real world so that any unintended consequences can be spotted in advance: by training systems 'offline' on batches of historical data  (Wiering & Van Otterlo, 2012; Levine et al., 2020)  9 , or in simulated environments as discussed above. Other approaches focus on allowing DRL agents to explore safely by explicitly restricting them from visiting certain states or taking certain actions known or expected to be unsafe, or finding practically viable ways for humans to oversee exploration  (Hans et al., 2008; Garcıa & Fernández, 2015; Saunders et al., 2018) . These approaches to ensuring the safety of DRL systems will need to be combined with work on the broader problem of value alignment: designing AI systems whose behaviour is in line with human values. One popular approach to solving this problem is inverse reinforcement learning (IRL)  (Ng et al., 2000; Abbeel & Ng, 2004) , where the agent's goal is to infer a reward function from demonstrations, rather than being given one explicitly. This increases the likelihood of the agent learning to behave as intended (especially since it is often easier for us to demonstrate intended behaviour through examples than to provide rules for it). In some approaches, such as Bayesian IRL  (Ramachandran & Amir, 2007) , the agent also learns a probability distribution over reward functions, meaning learned policies take account of uncertainty, and are likely to be more robust across a wider range of possibilities. Many real-world tasks also have multi-dimensional objectives, where different subgoals need to be balanced against each other. For example, recommender systems might aim to produce recommendations that achieve some balance of relevance and novelty to the user, among other goals  (Aggarwal, 2016) . Even for an expert in a domain, it may be difficult to explicitly state what all those different objectives should be or how they should be balanced. An explicit way of dealing with this is multiobjective RL (MORL), where the aim is to either learn a single policy that can adapt to different preferences, or to learn several policies that optimally balance a set of preferences  (Liu et al., 2014) . Such an approach allows greater flexibility after training, and could be an option for improving interpretability and oversight. Even when rewards are well-defined, in most settings there is a delay between taking an action and receiving a reward. An agent may have performed thousands of actions immediately prior to receiving a reward and it may be impossible to infer which of those were the key steps that should be repeated in the future. This is known as the credit assignment problem, and is particularly challenging in real-world environments where rewards are sparse  (Sutton & Barto, 2018) . Current approaches to solving the credit assignment problem try to re-allocate  (Arjona-Medina et al., 2019)  or augment  (Hung et al., 2019)  the credit given to past events, but this is still a largely unsolved problem. If substantial progress is made in any of these methods for safe exploration, value alignment, and/or credit assignment, it will suddenly become possible to deploy DRL systems more safely and effectively in a wider range of real-world environments. These are therefore avenues of progress worth monitoring since they could lead to a very quick proliferation of applications. It should be emphasised that substantial progress in these areas will not be an easy task and is not expected in the near future. Nevertheless, progress is possible, and it is important to ensure that those working on the risks and governance of AI systems are ready for it. In order to conduct risk assessment for the use of DRL in a robotics system or autonomous vehicle and decide what kind of oversight is needed, for example, one will need to understand what guarantees can be made that the system will not perform certain types 9. In healthcare, offline evaluation is also of particular importance  (Gottesman et al., 2018) . of action, and how strict those guarantees are. In order to think through the scope of possible long-term impacts of a new DRL-based information filtering system, one will need to understand how the system balances multiple objectives and accounts for delayed rewards, and how effective those methods will be. As progress is made in all of these areas, therefore, greater communication will be needed between researchers and developers, and those deploying, assessing, and governing AI systems, around what assurances can be made about the behaviour of those systems and the limits of those assurances. Conversely, if we begin to see increased real-world deployment of DRL systems without seeing considerable progress in these different areas of reward function design, we might be concerned that such systems are being deployed without adequate guarantees that they will behave safely or have the consequences they are expected or intended to. \n Generalisation and Robustness Ensuring that DRL methods are sufficiently generalisable and robust-that is, they behave as intended across a wide range of scenarios-is a final key challenge for safe real-world deployment. In part, this is a problem inherited from the field of ML more broadly. Most ML algorithms struggle to reuse past knowledge and generalise to new situations  (Geirhos et al., 2018) , and especially those using deep learning can be frustratingly unstable  (Hutson, 2018) . DRL has its own approaches to improving generalisation  (Justesen et al., 2018; Cobbe et al., 2019; Witty et al., 2018; Zhang et al., 2018b Zhang et al., , 2018a , which have strong overlap with broader approaches for generalisation in ML. These include methods in transfer learning: developing algorithms that can effectively transfer knowledge from one domain to another  (Parisotto et al., 2015; Rusu et al., 2015 Rusu et al., , 2016 , and meta-learning, where more generalisable learning methods themselves are learned from data  (Schmidhuber, 1987; Wang et al., 2016; Duan et al., 2016; Finn et al., 2017) . A related problem for DRL is that results have proven particularly difficult to reproduce.  Henderson et al. (2018)  found that results can be significantly impacted by simple changes to the neural network architecture, or by simply multiplying the reward function by a constant value, among other factors. Improving the reproducibility of results may be more a matter of changing research and publication norms, rather than being a research challenge for new methods to overcome. While the ML community in general is particularly in favour of open source material and sharing code, issues of reproducibility still persist and not all research makes its way into the public domain. Reproducibility problems are exacerbated for real-world applications. Not only do network parameters need to be copied, but also the exact environment in which the agent learns may need to be reproduced faithfully. Until methods become much more robust, seemingly innocent changes in the real-world training environment may have large consequences for the final behaviour of an agent. Further, the expense of replicating real-world settings could be much larger than that of copying and running a simulated environment, further limiting public access to agents for testing and safety analysis. Without making considerable progress in the areas of generalisation and robustness, it will be difficult to ensure the reliability of DRL systems in real-world domains, which are often highly dynamic and variable. As with reward function design, if we start to see increased use of DRL systems in complex real-world domains without good evidence of substantial progress in areas such as transfer learning and meta-learning, this should raise concerns about whether such systems might be more brittle than they seem. On the other hand, if we see big breakthroughs in these areas, we may soon see DRL agents capable of performing a wide range of common everyday tasks. This could increase research incentives to solve other related tasks, such as robust real-world navigation and common sense reasoning, which, along with more generalisable DRL methods, could be used to build much more general-purpose systems such as personal assistants and cleaning robots. \n Discussion Progress in different areas of technical research will impact the challenges DRL raises for safety, ethics and governance. In general, any progress in research that enables DRL methods to be applied more widely in society will exacerbate these challenges, making them more urgent. For example, substantial progress in the data efficiency of DRL methods and/or the quality of simulated environments for training would likely enable applications in more complex real-world environments, where data is currently either sparse or expensive to acquire. Progress in simulated environments might make DRL for autonomous driving much more feasible, making work on safety and reliability for self-driving cars more pressing  (Lin, 2016; Stilgoe, 2018) . As a first step, we therefore suggest it would be valuable for those concerned with the wider societal impacts of AI to pay attention to progress in DRL, particularly to anticipate and prepare for the impact of DRL in key domains. The relationship between technical progress and ethics and governance issues is a little more nuanced than progress always making issues more pressing. In some cases, ethical and societal concerns are being directly addressed by avenues of technical research in DRL, and so progress in these areas could reduce these concerns. While improvements in data efficiency might make certain aspects of DRL safety and reliability more concerning, those same improvements would likely reduce incentives for widespread surveillance, since DRL systems would become less data-hungry. Advances in value alignment-designing reward functions in line with complex, multi-dimensional human values-would reduce concerns about misspecified reward functions having harmful unintended consequences, but might increase the importance of developing standards for reward function design that ensure those methods are used in practice. Improvements in the generalisability of DRL methods could lead to increased confidence that systems will perform reliably across a range of domains, but the resultant increase in applications of DRL could make other issues, such as ensuring that systems can learn safely, more urgent. It may therefore be particularly important to pay attention to signs of uneven progress across key technical areas in DRL, which might serve as a warning that we could see increased application of DRL without key challenges related to safety, alignment, and security being resolved. For example, if DRL systems begin to be integrated into critical functions in society such as energy or water management, without sufficient assurances about their security, then we might reasonably be concerned about those systems being vulnerable to attack. We need to be able to notice these concerns and work with experts in relevant domains about how to address them before mistakes or accidents happen. Beyond paying attention to progress in DRL methods and considering their implications, it will also be important for the AI ethics and governance community to explore specific domains where DRL may be applied in the near future. Throughout our analysis in this paper, we referred to a number of domains where DRL could be applied in the near future, including recommender systems, city infrastructure and manufacturing. Future research could explore the potential impacts of DRL in a variety of important domains not discussed in this paper, such as finance, healthcare, or autonomous vehicles, and attempt to more systematically prioritise which domains of application are likely to raise the most important issues for AI ethics and governance. While various avenues of technical research are addressing many of the concerns discussed in this paper, one of our key messages is that this will be insufficient by itself. In order to ensure developments in DRL are broadly beneficial, there are many issues and questions that the AI ethics and governance community must also consider. We suggest the two following broad areas will be particularly important as DRL methods move closer to widespread realworld deployment: 1. What kinds of oversight, risk assessment, and technical assurances should we require of DRL systems before deploying them in high-stakes domains, to ensure that they are safe, secure, reliable, and respect human autonomy? How can and should these requirements be implemented practically? How fit-for-purpose are current safety engineering approaches, and what can we learn from the safety engineering community about DRL safety and reliability? 2. How can we ensure that, where DRL systems are deployed with real consequences for individuals' lives, reward functions are designed in ways that take into account the values of all those impacted, and in ways that consider any potential long-term unintended consequences of optimising for a specific objective? What does responsible reward function design look like, and how can it be implemented in practice? Ideally questions like these would be explored by multidisciplinary teams, combining DRL experts with ethics and governance experts. \n Summary and Conclusion DRL is receiving increasing attention in the AI research community, and continued progress could lead to more widespread deployment with profound impacts across many sectors of society. This raises several broad concerns for AI safety, ethics and governance: • Advances in DRL promise more autonomous systems that can operate effectively with less human oversight, introducing a challenging tradeoff between the potential benefits of such systems and the potential threat to human autonomy and safety; • DRL systems learn through trial-and-error interaction with an environment, which introduces new challenges for ensuring their safety: we not only need to ensure that systems are safe when deployed, but that they can learn safely; • More broadly, advances in DRL could enable AI systems to be applied in an increasing number of safety-critical domains, increasing the potential harms of mistakes and therefore increasing the importance of being able to make robust assurances about how systems will behave, and about their security to outside attack; • The behaviour of a DRL system depends heavily on its reward function, and optimising for slightly the wrong objective can lead to harmful unintended consequences that are difficult to predict in advance-especially if those designing reward functions do not account for the values of all those affected by a system; • DRL systems currently require large amounts of data to learn effectively, meaning that incentives to deploy real-world DRL applications will likely increase incentives for surveillance and ongoing data collection; and • Progress in DRL is likely to speed up the susceptibility of jobs to automation in certain areas, such as robotics and manufacturing, which needs to be accounted for in analyses of how AI will impact the future of work. In order to address these concerns and future challenges, we recommend that the AI ethics and governance community: • Find ways to track progress in DRL and its applications. It is important that those concerned with the wider societal, ethical, and governance implications of AI find ways to track progress in DRL, paying particular attention to progress towards widespread practical deployment. This would help the community better anticipate and prepare for future societal impacts of DRL, and if progress in key areas is uneven, could identify 'warning signs' that DRL risks being deployed in unsafe or harmful ways. This could potentially be an extension of excellent existing initiatives which aim to measure progress in AI more broadly  (Perrault et al., 2019; Haynes & Gbedemah, 2019) . • Consider the implications of DRL progress for existing AI governance initiatives, including standards and regulation. We have suggested that applications of DRL may introduce new challenges for human oversight and making safety assurances about AI systems, and/or increase the importance of these issues by allowing AI to be applied in more high-stakes domains. A valuable next step would be to consider the practical implications of this for specific governance proposals, which tend to focus on very broad notions of 'AI'. For example, how can guidelines around autonomy in existing AI ethics principles be adapted to apply to DRL systems, which are potentially much more autonomous than any AI systems deployed today? How do notions of safety and security as emphasised in AI ethics proposals need to be adapted to recognise the particular challenges raised by DRL? • Establish notions of responsible DRL development. It could be extremely worthwhile for a multidisciplinary team, combining DRL experts with ethics and governance experts, to explore in more depth many of the questions raised here about how to develop and deploy DRL systems responsibly, especially in high-stakes contexts. What standards of reliability and generalisability should DRL systems be required to meet before deployment, especially where systems are being trained largely in simulation? What does responsible reward function design look like, especially in domains with consequences for individuals' lives, and how can norms of responsibility be embedded in DRL research practices? DRL is likely to play an important role in the future of AI, promising increasingly autonomous and flexible systems with the potential for application in increasingly highstakes domains. As a result, DRL introduces and exacerbates a number of concerns which will shape the debate around the safe and responsible use of AI and may be overlooked in more general treatments of AI impacts. Since the most pressing challenges for society will depend on the exact nature of progress of AI research, it will be important to build and maintain strong collaboration between groups working on AI progress and AI governance in order to prepare for the challenges of future AI systems. Figure 1 : 1 Figure 1: The relationship between deep reinforcement learning and other areas of AI research. \n\t\t\t . RL systems are often referred to as 'agents', because they act autonomously in their environment. This does not mean that an RL agent is responsible or aware of their actions, just that the human designer is one step removed from the action selection process. 4. In standard RL formulations, the agent gets a reward at every timestep, but that reward may sometimes (or even often) be 0.", "date_published": "n/a", "url": "n/a", "filename": "12360-Article (PDF)-26329-1-10-20210308.tei.xml", "abstract": "Deep Reinforcement Learning (DRL) is an avenue of research in Artificial Intelligence (AI) that has received increasing attention within the research community in recent years, and is beginning to show potential for real-world application. DRL is one of the most promising routes towards developing more autonomous AI systems that interact with and take actions in complex real-world environments, and can more flexibly solve a range of problems for which we may not be able to precisely specify a correct 'answer'. This could have substantial implications for people's lives: for example by speeding up automation in various sectors, changing the nature and potential harms of online influence, or introducing new safety risks in physical infrastructure. In this paper, we review recent progress in DRL, discuss how this may introduce novel and pressing issues for society, ethics, and governance, and highlight important avenues for future research to better understand DRL's societal implications. 1. Readers already familiar with DRL could skip straight to Section 3.", "id": "801176b8dace7c9de246cb5e815e8194"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dj Dvijotham", "Robert Stanforth", "Sven Gowal", "Timothy Mann", "Pushmeet Kohli", "Deepmind London", "UK 4ag"], "title": "A Dual Approach to Scalable Verification of Deep Networks", "text": "INTRODUCTION Neural networks and deep learning have revolutionized machine learning achieving state of the art performance on a wide range of complex prediction tasks  [Krizhevsky et al., 2012 . However, in recent years, researchers have observed that even state of the art networks can be easily fooled into changing their predictions by making small but carefully chosen modifications to the input data (known as adversarial perturbations)  [Szegedy et al., 2013 , Kurakin et al., 2016 , Carlini and Wagner, 2017a , Goodfellow et al., 2014 , Carlini and Wagner, 2017b . While modifications to neural network training algorithms have been proposed to mitigate this phenomenonMadry et al.  [2018] , a comprehensive solution that is fully robust to adversarial attacks remains elusive  Wagner, 2017b, Uesato et al., 2018] . Neural networks are typically tested using the standard machine learning paradigm: If the performance (accuracy) of the network is sufficiently high on a holdout (test) set that the network did not have access to while training, the network is deemed acceptable. This is justified by statistical arguments based on an i.i.d. assumption on the data generating mechanism, that is each input output pair is generated independently from the same (unknown) data distribution. However, this evaluation protocol is not sufficient in domains with critical safety constraints  [Marston and Baca, 2015] . In these cases, we may require a stronger test: for example, we may require that the network is robust against adversarial perturbations within certain bounds. Adversarial evaluation. In the context of adversarial examples, a natural idea is to test neural networks by checking if it is possible to generate an adversarial attack to change the label predicted by the neural network  [Kurakin et al., 2016]  and train them to be robust to these examples  Madry et al. [2018] . Generating adversarial examples is a challenging computational task itself, and the attack generated by a specific attack algorithm may be far from optimal. This may lead one to falsely conclude that a given model is robust to attacks even though a stronger adversary may have broken the robustness. Recent work  [Athalye et al., 2018 , Uesato et al., 2018  has shown that evaluating models against weak adversaries can lead to incorrect conclusions regarding the robustness of the model. Thus, there is a need to go beyond evaluation us-ing specific adversarial attacks and find approaches that provide provable guarantees against attacks by any adversary. Towards verifiable models. Verification of neural networks has seen significant research interest in recent years. In the formal verification community, Satisfiability Modulo Theory (SMT) solvers have been adapted for verification of neural networks  [Ehlers, 2017 , Huang et al., 2017 , Katz et al., 2017 . While SMT solvers have been successfully applied to several domains, applying them to large neural networks remains a challenge due to the scale of the resulting SMT problem instances. Furthermore, these approaches have been largely limited to networks with piecewise linear activation functions since most SMT solvers are unable to deal efficiently with nonlinear arithmetic. More recently, researchers have proposed a set of approaches that make use of branch and bound algorithms either directly or via mixed-integer programming solvers  [Bunel et al., 2017 , Cheng et al., 2017 , Tjeng and Tedrake, 2017 . While these approaches achieve strong results on smaller networks, scaling them to large networks remains an open challenge. These approaches also rely heavily on the piecewise linear structure of networks where the only nonlinearities are maxpooling and ReLUs. Towards scalable verification of general models. In this paper, we develop a novel approach to neural network verification based on optimization and duality. The approach consists of formulating the verification problem as an optimization problem that tries to find the largest violation of the property being verified. If the largest violation is smaller than zero, we can conclude that the property being verified is true. By using ideas from duality in optimization, we can obtain bounds on the optimal value of this problem in a computationally tractable manner. Note that this approach is sound but incomplete, in that there may be cases where the property of interest is true, but the bound computed by our algorithm is not tight enough to prove the property. This strategy has been used in prior work as well  [Kolter and Wong, 2018, Raghunathan et al., 2018] . However, our results improve upon prior work in the following ways: 1. Our verification approach applies to arbitrary feedforward neural networks with any architecture and any activation function and our framework recovers previous results  [Ehlers, 2017]  when applied to the special case of piecewise linear activation functions. 2. We can handle verification of systems with discrete inputs and combinatorial constraints on the input space, including cardinality constraints. 3. The computation involved only requires solving an unconstrained convex optimization problem (of size linear in the number of neurons in the network), which can be done using a subgradient method efficiently. Further, our approach is anytime, in the sense that the computation can be stopped at any time and a valid bound on the verification objective can be obtained. 4. For the special case of single hidden layer networks, we develop specialized verification algorithms with provable tightness guarantees. 5. We attain state of the art verified bounds on adversarial error rates on image classifiers trained on MNIST and CIFAR-10 under adversarial perturbations in the infinity norm. \n Related Work Certifiable training and verification of neural networks A separate but related thread of work is on certifiable training, ie, training neural networks so that they are guaranteed to satisfy a desired property (for example, robustness to adversarial examples within a certain radius)  [Kolter and Wong, 2018, Raghunathan et al., 2018] . These approaches use ideas from convex optimization and duality to construct bounds on an optimization formulation of verification. However, these approaches are limited to either a class of activation functions (piecewise linear models) or architectures (single hidden layer, as in  Raghunathan et al. [2018] ). Further, in  Kolter and Wong [2018] , the dual problem starts with a constrained convex formulation but is then converted into an unconstrained but nonconvex optimization problem to allow for easy optimization via a backprop-style algorithm. In contrast, our formulation allows for an unconstrained dual convex optimization problem so that for any choice of dual variables, we obtain a valid bound on the adversarial objective and this dual problem can be solved efficiently using subgradient methods. We also note that the ultimate goals of  [Kolter and Wong, 2018, Raghunathan et al., 2018]  are different from our paper: they modify the training procedure of the neural network so that the network is trained to be easily verifiable. In contrast, our work focuses on extending verification algorithms to apply to a broader class of architectures, activation functions and -in this sense, we view our work as complementary to  [Kolter and Wong, 2018, Raghunathan et al., 2018] . In fact, since the objective of our dual optimization is differentiable with respect to the network weights, we can extend our approach to training verifiable networks easily by simultaneously optimizing the network weights and dual variables to minimize the dual objective. We leave the study of such an extension for future work. Theoretical analysis of robustness Another related line of work has to do with theoretical analysis of adversarial examples. It has been shown that feedforward ReLU networks cannot learn to distinguish between points on two concentric spheres without necessarily being vulnerable to adversarial examples within a small radius  [Gilmer et al., 2018] . Under a different set of assumptions, the existence of adversarial examples with high probability is also established in  Fawzi et al. [2018] . In , the authors study robustness of nearest neighbor classifiers to adversarial examples. As opposed to these theoretical analyses, our approach searches computationally for proofs of existence or non-existence of adversarial examples. The approach does not say anything a-priori about the existence of adversarial examples, but can be used to investigate their existence for a given network and compare strategies to guard against adversarial attacks. \n VERIFICATION AS OPTIMIZATION \n NOTATION Our techniques apply to general feedforward architectures and recurrent networks, but we focus on layered architectures for the development in this paper. The input layer is numbered 0, the hidden layers are numbered 1, . . . , L − 1 and the output layer is numbered L. The size of layer l is denoted n l We denote by x in the input to the neural network, by z l the pre-activations of neurons at layer l before application of the activation function and by x l the vector of neural activations after application of the activation function (to z l−1 ). For convenience, we define x 0 = x in . We use x l (x in ), z l (x in ) to denote the activations at the l-th layer as a function of the input x in . Upper and lower bounds on the pre/post activations are denoted by x l , x l , z l , z l respectively. The activation function at layer l is denote h l and is assumed to be applied component-wise, ie, [h l (z l )] k = h l k (z l k ) Note that max-pooling is an exception to this rule -we discuss how max-pooling is handled separately in the Appendix section 6.2.1. The weights of the network at layer l are denoted W l and the bias is denoted b l , z l = W l x l + b l . \n VERIFICATION PROBLEM As mentioned earlier, verification refers to the process of checking that the output of the neural network sat-isfies a certain desirable property for all choices of the input within a certain set. Formally, this can be stated as follows: ∀x in ∈ S in (x nom ) x L (x in ) ∈ S out (1) where x in denotes the input to the network, x nom denotes a nominal input, S in (x nom ) defines the constrained subset of inputs induced by the nominal input, and S out denotes the constraints on the output that we would like to verify are true for all inputs in S in (x nom ). In the case of adversarial perturbations in image classification, x nom would refer to the nominal (unperturbed image), S in (x nom ) would refer to all the images that can be obtained by adding bounded perturbations to x nom , and x in would refer to a perturbed image. In this paper, we will assume that: S out is always a described by a finite set of linear constraints on the values of final layer ie. S out = ∩ m i=1 {x L : c i T x L + d i ≤ 0}, and S in (x nom ) is any bounded set such that any linear optimization problem of the form max x in ∈Sin(x nom ) c T x can be solved efficiently. This includes convex sets and also sets describing combinatorial structures like spanning trees, cuts in a graph and cardinality constraints. \n See the following examples for a concrete illustration of the formulation of the problem: Robustness to targeted adversarial attacks. Consider an adversarial attack that seeks to perturb an input x nom to an input x in subject to a constraint on the perturbation x in − x nom ≤ to change the label from the true label i to a target label j. We can map this to (1) as follows: S in (x nom ) = {x in : x in − x nom ≤ }, (2a) S out = {z : c T z ≤ 0} (2b) where c is a vector with c j = 1, c i = −1 and all other components 0. Thus, S out denotes the set of outputs for which the true label i has a higher logit value than the target label j (implying that the targeted adversarial attack did not succeed). Monotonic predictors. Consider a network with a single real valued output and we are interested in ensuring that the output is monotonically increasing wrt each dimension of the input x in . We can state this as a verifica-tion problem: S in (x nom ) = {x in : x in ≥ x nom } (3a) S out = {x L : x L (x nom ) − x L ≤ 0} (3b) Thus, S out denotes the set of outputs which are large than the network output at x nom . If this is true for each value of x nom , then the network is monotone. Cardinality constraints. In several cases, it makes sense to constrain a perturbation not just in norm but also in terms of the number of dimensions of the input that can be perturbed. We can state this as: S in (x nom ) = {x in : x in − x nom 0 ≤ k, x in − x nom ∞ ≤ } (4a) S out = {z : c T z ≤ 0} (4b) where x 0 denotes the number of non-zero entries in x. Thus, S out denotes the set of outputs which are larger than the network output at x nom . If this is true for each value of x nom , then the network is monotone. \n OPTIMIZATION PROBLEM FOR VERIFICATION Once we have a verification problem formulated in the form (1), we can easily turn the verification procedure into an optimization problem. This is similar to the optimization based search for adversarial examples  [Szegedy et al., 2013]  when the property being verified is adversarial robustness. For brevity, we only consider the case where S out is defined by a single linear constraint c T z + d ≤ 0. If there are multiple constraints, each one can be verified separately. max z 0 ,...,z L−1 x 0 ,...,x L c T x L + d (5a) s.t x l+1 = h l z l , l = 0, 1, . . . , L − 1 (5b) z l = W l x l + b l , l = 0, 1, . . . , L − 1 (5c) x 0 = x in , x in ∈ S in (x nom ) (5d) If the optimal value of this problem is smaller than 0 (for each c, d in the set of linear constraints defining S out ), we have verified the property (1). This is a nonconvex optimization problem and finding the global optimum in general is NP-hard (see Appendix section 6.4.1 for a proof). However, if we can compute upper bounds on the value of the optimization problem and the upper bound is smaller than 0, we have successfully verified the property. In the following section, we describe our main approach for computing bounds on the optimal value of (5). \n BOUNDING THE VALUE OF THE OPTIMIZATION PROBLEM We assume that bounds on the activations z l , x l , l = 0, . . . , L−1 are available. Section 6.1 discusses details of how such bounds may be obtained given the constraints on the input layer S in (x nom ). We can bound the optimal value of (5) using a Lagrangian relaxation of the constraints: max z 0 ,...,z L−1 x 0 ,x 1 ,...,x L−1 c T h L−1 z L−1 + d + L−1 l=0 µ l T z l − W l x l − b l + L−2 l=0 λ l T x l+1 − h l z l (6a) s.t. z l ≤ z l ≤ z l , l = 0, 1, . . . , L − 1 (6b) x l ≤ x l ≤ x l , l = 0, 1, . . . , L − 1 (6c) x 0 ∈ S in (x nom ) (6d) Note that any feasible solution for the original problem (  5 ) is feasible for the above problem, and for any such solution, the terms involving λ, µ become 0 (since the terms multiplying λ, µ are 0 for every feasible solution). Thus, for any choice of λ, µ, the above optimization problem provides a valid upper bound on the optimal value of (5) (this property is known as weak duality  [Vandenberghe and Boyd, 2004] ). We now look at solving the above optimization problem. Since the objective and constraints are separable in the layers, the variables in each layer can be optimized independently. For l = 1, . . . , L − 1, we have f l λ l−1 , µ l = max x l ∈[x l ,x l ] λ l−1 − W l T µ l T x l − b l T µ l which can be solved trivially by setting each component of x l to its upper or lower bound depending on whether the corresponding entry in λ l−1 − W l T µ l is non-negative. Thus, f l λ l−1 , µ l = λ l−1 − W l T µ l + T x l + λ l−1 − W l T µ l − T x l − b l T µ l where [x] + = max(x, 0), [x] − = min(x, 0) denote the positive and negative parts of x. Similarly, collecting the terms involving z l , we have, for l = 0, . . . , L − 1 fl (λ l , µ l ) = max z l ∈[z l ,z l ] µ l T z l − λ l T h l z l where λ L−1 = −c. Since h l is a component-wise nonlinearity, each dimension of z l can be optimized independently. For the k-th dimension, we obtain fl,k λ l k , µ l k = max z l k ∈[z l k ,z l k ] µ l k z l k − λ l k h l k z l k This is a one-dimensional optimization problem and can be solved easily-for common activation functions (ReLU, tanh, sigmoid, maxpool), it can be solved analytically, as discussed in appendix section 6.2. Finally, we need to solve f 0 (µ 0 ) = max x 0 ∈Sin(x nom ) − W 0 T µ 0 T x 0 − b 0 T µ 0 which can also be solved easily given the assumption on S in . We work out some concrete cases in 6.3. Once these problems are solved, we can construct the dual optimization problem: min λ,µ n L−1 k=0 fL−1,k −c k , µ l k + L−2 l=0 n l k=0 fl,k λ l k , µ l k + L−1 l=1 f l (λ l−1 , µ l ) + f 0 µ 0 + d (7) This seeks to choose the values of λ, µ so as to minimize the upper bound on the verification objective, thereby obtaining the tightest bound on the verification objective. This optimization can be solved using a subgradient method on λ, µ. Theorem 1. For any values of λ, µ, the objective of (  7 ) is an upper bound on the optimal value of (5). Hence, the optimal value of (7) is also an upper bound. Further, (7) is a convex optimization problem in (λ, µ). Proof. The upper bound property follows from weak duality  [Vandenberghe and Boyd, 2004] . The fact that (  7 ) is a convex optimization problem can be seen as each term f l , fl,k is expressed as a maximum overa set of linear functions of λ, µ  [Vandenberghe and Boyd, 2004] . Theorem 2. If each h is a ReLU function, then (7) is equivalent to the dual of the LP described in  Ehlers [2017] . Proof. See section 6.4. The LP formulation from  Ehlers [2017]  is also used in  Kolter and Wong [2018] . The dual of the LP is derived in  Kolter and Wong [2018]  -however this dual is different from (7) and ends up with a constrained optimization formulation for the dual (the details of this can be found in appendix section 6.4.2). To allow for an unconstrained formulation, this dual LP is transformed to a backpropagation-like computation. While this allows for folding the verification into training, it also introduces nonconvexity in the verification optimization -our formulation of the dual differs from  Kolter and Wong [2018]  in that we directly solve an unconstrained dual formulation, allowing us to circumvent the need to solve a nonconvex optimization for verification. \n TOWARDS THEORETICAL GUARANTEES FOR VERIFICATION The bounds computed by solving (7) could be loose in general, since (  5 ) is an NP-hard optimization problem (section 6.4.1). SMT solvers and MIP solvers are guaranteed to find the exact optimum for piecewise linear neural networks, however, they may take exponential time to do so. Thus, an open question remains: Are there cases where it is possible to perform exact verification efficiently? If not, can we approximate the verification objective to within a certain factor (known a-priori)? We develop results answering these questions in the following sections. Prior work: For any linear classifier, the scores of each label are a linear function of the inputs w T i x + b i . Thus, the difference between the predictions of two classes j (target class for an adversary) and class i (true label) is (w i − w j ) T x. Maximizing this subject to x − x 0 2 ≤ can be solved analytically to obtain the value (w i − w j ) T x 0 + w i − w j 2 . This observation formed the basis for algorithms in  [Raghunathan et al., 2018]  and  [Hein and Andriushchenko, 2017] . However, once we move to nonlinear classifiers, the situation is not so simple and computing the worst case adversarial example, even in the 2-norm case, becomes a challenging task. In  [Hein and Andriushchenko, 2017] , the special case of kernel methods and single hidden layer classifiers are considered, but the approaches developed are only upper bounds on the verification objective (just like those computed by our dual relaxation approach). Similarly, in  Raghunathan et al. [2018] , a semidefinite programming approach is developed to compute bounds on the verification objective for the special case of adversarial perturbations on the infinity norm. However, none of these approaches come with a-priori guarantees on the quality of the bound, that is, before actually running the verification algorithm, one cannot predict how tight the bound on the verification objective would be. In this section, we develop novel theoretical results that quantify when the verification problem (  5 ) can be solved either exactly or with a-priori approximation guarantees. Our results require strong assumptions and do not immediately apply to most practical situations. However, we believe that they shed some understanding on the conditions under which exact verification can be performed tractably and lead to specialized verification algorithms that merit further study. We assume the following for all results in this section: 1) We study networks with a single hidden layer, i.e. L = 2, with activation function h 0 = h and a linear mapping from the penultimate to the output layer x 2 = h 1 z 1 = z 1 = W 1 x 1 + b 1 . 2) The network has a differentiable activation function h with Lipschitz-continuous derivatives denoted h (tanh, sigmoid, ELU, polynomials satisfy this requirement). 3) S in (x nom ) = {x in : x in − x nom 2 ≤ }. Since the output layer is a linear function of the penultimate layer x 1 , we have c T x 2 = W 1 T c T x 1 + c T b 1 = W 1 T c T h 0 z 0 + c T b 1 For brevity, we simply denote W 1 T c as c, drop the constant term c T b 1 and let W = W 0 , b = b 0 , z nom = W x nom + b and W i denote the i-th row of W . Then, (5) reduces to: max x in : x in −x nom 2 ≤ i c i h i W i x in + b i (8) Theorem 3. Suppose that h has a Lipschitz continuous first derivative: h i (t) − h i ( t) ≤ γ i |t − t| Let ν = diag (c) W T h (z nom ) 2 L = σ max diag (c) W T σ max (diag (γ) W ) Then ∀ ∈ (0, ν 2L ), the iteration: x k+1 ← x nom + W T diag (c) h (W x k + b) W T diag (c) h (W x k + b) 2 starting at x 0 = x nom converges to the global optimum x of (8) at the rate x k − x ≤ L ν− L k Proof. Section 6.4 Thus, when is small enough, a simple algorithm exists to find the global optimum of the verification objective. However, even when is larger, one can obtain a good approximation of the verification objective. In order to do this, consider the following quadratic approxiimation of the objective from (8): max i c i (h i (z nom i ) + h i (z nom i ) (W i z)) + i c i 2 h i (z nom i ) (W i z) 2 (9a) s.t. z 2 ≤ (9b) This optimization problem corresponds to a trust region problem that can be solved to global optimality using semidefinite programming  [Yakubovic, 1971] : max z,Z i c i (h i (z nom i ) + h i (z nom i ) (W i z)) + i c i 2 h i (z nom i ) tr W T i W i Z (10a) s.t. tr (Z) ≤ , 1 z T z Z 0 (10b) where X 0 denotes that X is constrained to be a positive semidefinite matrix. While this can be solved using general semidefinite programming solvers, several special purpose algorithms exist for this trust region problem that can exploit its particular structure for efficient solution,  [Hazan and Koren, 2016]  Theorem 4. Suppose that h is thrice-differentiable with a globally bounded third derivative. Let ζ i = W i 2 , η i = sup t |h i (t)|, κ = 1 6 i η i c i ζ 3 i For each > 0, the difference between the optimal values of (10), (  8 ) is at most κ 3 . Proof. See Section 6.4 \n EXPERIMENTS In this section, we present numerical studies validation our approach on three sets of verification tasks: Image classification on MNIST and CIFAR: We use our approach to obtain guaranteed lower bounds on the accuracy of image classifers trained on MNIST and CIFAR-10 under adversarial attack with varying sizes of the perturbation radius. We compare the bounds obtained by our method with prior work (in cases where prior work is applicable) and also with the best attacks found by various approaches. Classifier stability on GitHub data: We train networks on sequences of commits on GitHub over a collection of 10K repositories -the prediction task consists of predicting whether a given repository will reach more than 40 commits within 250 days given data observed until a certain day. Input features consist a value between 0 and 1 indicating the number of days left until the 250th day, as well as another value indicating the progress of commits towards the total of 40. As the features evolve, the prediction of the classifier changes (for example, predictions should become more accurate as we move closer to the 250th day). In this situation, it is desirable that the classifier provides consistent predictions and that the number of times its prediction switches is as small as possible. It is also desirable that this switching frequency cannot be easily be changed by perturbing input features. We use our verification approach combined with dynamic programming to compute a bound on the maximum number of switches in the classifier prediction over time. Digit sum task: We consider a more complex verification task here: Given a pair of MNIST digits, the goal is to bound how much the sum of predictions of a classifier can differ from the true sum of those digits under adversarial perturbation subject to a total budget on the perturbation across the two digits. \n IMAGE CLASSIFICATION: MNIST AND CIFAR We study adversarial attacks subject to an l ∞ bound on the input perturbation. An adversarial example (AE) is a pertubation of an input of the neural network such that the output of the neural network differs from the correct label for that input. An AE is said to be within radius if the ∞ norm of the difference between the AE and the original input is smaller than . We are interested in the adversarial error rate, that is, # Test examples that have an AE within radius Size of test set Computing this quantity precisely requires solving the NP-hard problem (5) for each test example, but we can obtain upper bounds on it using our (and other) verification methods and lower bounds using a fixed attack algorithm (in this paper we use a bound constrained LBFGS algorithm similar to  [Carlini and Wagner, 2017b] ). Since theorem 2 shows that for the special case of piecewise linear neural networks, our approach reduces to the basic LP relaxation from  Ehlers [2017]  (which also is the basis for the algorithms in  Bunel et al. [2017]  and  Kolter and Wong [2018] ), we focus on networks with smooth nonlinearities like tanh and sigmoid. We compare our approach with The SDP formulation from  Raghunathan et al. [2018]  (note that this approach only works for sin-gle hidden layer networks, so we just show it as producing vacuous bounds for other networks). Each approach gets a budget of 300 s per verifiation problem (choice of test example and target label). Since the SDP solver from  [Raghunathan et al., 2018]  only needs to be run once per label pair (and not per test example), its running time is amortized appropriately. Results on smooth activation functions: Figures  1a,1b  show that our approach is able to compute nearly tight bounds (bounds that match the upper bound) for small perturbation radii (up to 2 pixel units) and our bounds significantly outperform those from the SDP approach  [Raghunathan et al., 2018]  ( which is only able to compute nontrivial bounds for the smallest model with 20 hidden units). Results on models trained adversarially: We use the adversarial training approach of  [Uesato et al., 2018]  and train models on MNIST and CIFAR that are robust to perturbations from the LBFGS-style attack on the training set. We then apply our verification algorithm to these robust models and obtain bounds on the adversarial error rate on the test set. These models are all multilayer models, so the SDP approach from  [Raghunathan et al., 2018]  does not apply and we do not plot it here. We simply plot the attack versus the bound from our approach. The results for MNIST are plotted in figure  2b  and for CIFAR in figure  2a . On networks trained using a different procedure, the approaches from Raghunathan et al. [2018] and  Kolter and Wong [2018]  are able to achieve stronger results for larger values of (they work with = .1 in real units, which corresponds to = 26 in pixel units we use here). However, we note that our verification procedure is agnostic to the training procedure, and can be used to obtain fairly tight bounds for any network and any training procedure. In comparison, the results in  Kolter and Wong [2018]  and  Raghunathan et al. [2018]  rely on the training procedure optimizing the verification bound. Since we do not rely on a particular adversarial training procedure, we were also able to obtain the first non-trivial verification bounds on CIFAR-10 (to the best of our knowledge) shown in figure  2a . While the model quality is rather poor, the results indicate that our approach could scale to more complicated models. \n GITHUB CLASSIFIER STABILITY We allow the adversary to modify input features by up to 3% (at each timestep) and our goal is to bound the maximum number of prediction switches induced by each attack over time. We can model this within our verification framework as follows: Given a sequence of input features, we compute the maximum number of switches    [Raghunathan et al., 2018] . Each color represents a different network. The dashed lines at the bottom are lower bounds on the error rate computed using the best attack found using the LBFGS algorithm. achievable by first computing the target classes that are reachable through an adversarial attack at each timestep (using (  7 )), and then running a dynamic program to compute the choices of target classes over time (from within the reachable target classes) to maximize the number of switches over time. Figure  3a  shows how initially predictions are easily attackable (as little information is available to make predictions), and also shows how the gap between our approach and the best attack found using the LBFGS algorithm evolves over time. \n COMPLEX VERIFICATION TASK: DIGIT SUM In order to test our approach on a more complex specification, we study the following task: Given a pair of MNIST digits, we ask the question: Can an attacker perturb each image, subject to a constraint on the total perturbation across both digits, such that the sum of the digits predicted by the classifier differs from the true sum of those digits by as large an amount as possible? Answering this question requires solving the following optimization problem: where s is the true sum of the two digits. Thus, the adversary has to decide on both the perturbation to each digit, as well as the size of the perturbation. We can encode this within our framework (we skip the details here). The upper bound on the maximum error in the predicted sum from the verification and the lower bound on the maximum error computed from an attack for this problem (on an adversarially trained two hidden layer sigmoid network) is plotted in figure  3b . The results show that even on this rather complex verification task, our approach is able to compute tight bounds. \n CONCLUSIONS We have presented a novel framework for verification of neural networks. Our approach extends the applicability of verification algorithms to arbitrary feedforward networks with any architecture and activation function and to more general classes of input constraints than those considered previously (like cardinality constraints). The verification procedure is both efficient (given that it solves an unconstrained convex optimization problem) and practically scalable (given its anytime nature only required gradient like steps). We proved the first known (to the best of our knowledge) theorems showing that under special assumptions, nonlinear neural networks can be verified tractably. Numerical experiments demonstrate the practical performance of our approach on several classes of verification tasks. Figure 1 : 1 Figure 1: Figures show three curves per model -Dashed line: Lower bound from LBFGS attack. Solid line: Our verified upper bound. Dash-dot line: SDP verified upper bound from [Raghunathan et al., 2018] . Each color represents a different network. The dashed lines at the bottom are lower bounds on the error rate computed using the best attack found using the LBFGS algorithm. \n . x in a − x nom a ≤ a , x in b − x nom b ≤ b a + b ≤", "date_published": "n/a", "url": "n/a", "filename": "204.tei.xml", "abstract": "This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm adversarial perturbations, for example). Most previous work on this topic was limited in its applicability by the size of the network, network architecture and the complexity of properties to be verified. In contrast, our framework applies to a general class of activation functions and specifications on neural network inputs and outputs. We formulate verification as an optimization problem (seeking to find the largest violation of the specification) and solve a Lagrangian relaxation of the optimization problem to obtain an upper bound on the worst case violation of the specification being verified. Our approach is anytime i.e. it can be stopped at any time and a valid bound on the maximum violation can be obtained. We develop specialized verification algorithms with provable tightness guarantees under special assumptions and demonstrate the practical significance of our general verification approach on a variety of verification tasks.", "id": "b9353bbc253474c4e9a1b8aa042961d8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld", "Vincent Conitzer"], "title": "Safe Pareto Improvements for Delegated Game Playing", "text": "INTRODUCTION Between Aliceland and Bobbesia lies a sparsely populated desert. Until recently, neither of the two countries had any interest in the desert. However, geologists have recently discovered that it contains large oil reserves. Now, both Aliceland and Bobbesia would like to annex the desert, but they worry about a military conflict that would ensue if both countries insist on annexing. Table  1  models this strategic situation as a normal-form game. The strategy DM (short for \"Demand with Military\") denotes a military invasion of the desert, demanding annexation. If both countries send their military with such an aggressive mission, the countries fight a devastating war. The strategy RM (for \"Refrain with Mility\") denotes yielding the territory to the other country, but building defenses to prevent an invasion of one's original territories. Alternatively, the countries can choose to not raise a military force at all, while potentially still demanding control of the desert by sending only its leader (DL, short for \"Demand with Leader\"). In this case, if both countries demand the desert, war does not ensue. Finally, they could neither demand nor build up a mility (RL). If one of the two countries has their military ready and the other does not, the militarized country will know and will be able to invade the other country. In game-theoretical terms, militarizing therefore strictly dominates not militarizing. Instead of making the decision directly, the parliaments of Aliceland and Bobbesia appoint special commissions for making this strategic decision, led by Alice and Bob, respectively. The parliaments can instruct these representatives in various ways. They can explicitly tell them what to do -for example, Aliceland could directly tell Alice to play DM. However, we imagine that the parliaments trust the commissions' judgments more than they trust their own and hence they might prefer to give an instruction of the type, \"make whatever demands you think are best for our country\" (perhaps contractually guaranteeing a reward in proportion to the utility of the final outcome). They might not know what that will entail, i.e., how the commissions decide what demands to make given that instruction. However -based on their trust in their representatives -they might still believe that this leads to better outcomes than giving an explicit instruction. We will also imagine these instructions are (or at least can be) given publicly and that the commissions are bound (as if by a contract) to follow these instructions. In particular, we imagine that the two commissions can see each other's instructions. Thus, in instructing their commissions, the countries play a game with bilateral precommitment. When instructed to play a game as best as they can, we imagine that the commissions play that game in the usual way, i.e., without further abilities to credibly commit or to instruct subcommittees and so forth. It may seem that without having their parliaments ponder equilibrium selection, Aliceland and Bobbesia cannot do better than leave the game to their representatives. Unfortunately, in this default equilibrium, war is still a possibility. Even the brilliant strategists Alice and Bob may not always be able to resolve the difficult equilibrium selection problem to the same pure Nash equilibrium. In the literature on commitment devices and in particular the literature on program equilibrium, important ideas have been proposed for avoiding such bad outcomes. Imagine for a moment that Alice and Bob will play a Prisoner's Dilemma (rather than the Demand Game of Table  1 ). Then the default of (Defect, Defect) can be Pareto-improved upon. Both original players (Aliceland and Bobbesia) can use the following instruction for their representatives: \"If the opponent's instruction is equal to this instruction, Cooperate; otherwise Defect.\"  [11, 15, 25]  Then it is a Nash equilibrium for both players to use this instruction. In this equilibrium, (Cooperate, Cooperate) is played and it is thus Pareto-optimal and Pareto-better than the default.  In cases like the Demand Game, it is more difficult to apply this approach to improve upon the default of simply delegating the choice. Of course, if one could calculate the expected utility of submitting the default instructions, then one could similarly commit the representatives to follow some (joint) mix over the Pareto-optimal outcomes ((RM, DM), (DM, RM), (RM, RM), (DL, DL), etc.) that Pareto-improves on the default expected utilities. However, we will assume that the original players are unable or unwilling to form probabilistic expectations about how the representatives play the Demand Game, i.e., about what would happen with the default instructions. If this is the case, then this type of Pareto-improvement on the default is unappealing. The goal of this paper is to show and analyze how even without forming probabilistic beliefs about the representatives, the original players can Pareto-improve on the default equilibrium. We will call such improvements safe Pareto improvements (SPIs). We here briefly give an example in the Demand Game. The key idea is for the original players to instruct the representatives to select only from {DL, RL}, i.e., to not raise a military. Further, they tell them to disvalue the conflict outcome (DL, DL) as they would disvalue the original conflict outcome of war in the default equilibrium. Overall, this means telling them to play the game of Table  2 . (Again, we could imagine that the instructions specify Table  2  to be how Aliceland and Bobbesia financially reward Alice and Bob.) Importantly, Aliceland's instruction to play that game must be conditional on Bobbesia also instructing their commission to play that game, and vice versa. Otherwise, one of the countries could profit from deviating by instructing their representative to always play DM or RM (or to play by the original utility function). The game of Table  2  is isomorphic to the DM-RM part of the original Demand Game of Table  1 . Of course, the original players know neither how the original Demand Game nor the game of Table  2  will be played by the representatives. However, since these games are isomorphic, one should arguably expect them to be played isomorphically. For example, one should expect that (RM, DM) would be played in the original game if and only if (RL, DL) would be played in the modified game. However, the conflict outcome (DM, DM) is replaced in the new game with the outcome (DL, DL). This outcome is harmless (Pareto-optimal) for the original players. Contributions. Our paper generalizes this idea to arbitrary normalform games and is organized as follows. In Section 2, we introduce some notation for games and multivalued functions that we will use throughout this paper. In Section 3, we introduce the setting of delegated game playing for this paper and define and motivate the concept of safe Pareto improvements in more detail. In Section we briefly review the the concepts of program games and program equilibrium and show that SPIs can be implemented as program equilibria. In Section 5, we introduce a notion of outcome correspondence between games. This relation expresses the original players' beliefs about similarities between how the representatives play different games. For example, in our example, the Demand Game of Table  1  (arguably) corresponds to the game of Table  2  in that the representatives (arguably) would play (DM, DM) in the original game if and only if they play (DL, DL) in the new game, and so forth. We also show some basic results (reflexivity, transitivity, etc.) about the outcome correspondence relation on games. In Section 6 we show that the notion of outcome correspondence is central to deriving SPIs. In particular, we show that a game Γ 𝑠 is an SPI on another game Γ if and only if there is a Pareto-improving outcome correspondence relation between Γ 𝑠 and Γ. To derive SPIs, we need to make some assumptions about outcome correspondence, i.e., about which games are played in similar ways by representatives. We give two very weak assumptions of this type in Section 7. The first is that the representatives play isomorphic games isomorphically. The second is that the representatives' play is invariant under the removal of strictly dominated strategies. For example, we assume that in the Demand Game the representatives only play DM and RM. Moreover we assume that we could remove DL and RL from the game and the representatives would still play the same strategies as in the original Demand Game with certainty. Our SPI for the Demand Game can be proven using these assumptions. Section 8 shows that determining whether there exists an SPI based on these assumptions is NP-complete. Section 9 considers a different setting in which we allow the original players to let the representatives choose from newly constructed strategies whose corresponding outcomes map arbitrarily onto feasible payoff vectors from the original game. In this new setting, finding SPIs can be done in polynomial time. We conclude by discussing the problem of selecting between different SPIs on a given game (Section 10) and giving some ideas for directions for future work (Section 11). \n PRELIMINARIES 2.1 Games We here recall some basic definitions from game theory. An 𝑛-player game is a tuple (𝐴, u) of a set 𝐴 = 𝐴 1 × ... × 𝐴 𝑛 of (pure) strategy profiles (or outcomes) and a function u : 𝐴 → R 𝑛 that assigns to each outcome a utility for each player. Instead of, (𝐴, u) will also write (𝐴 1 , ..., 𝐴 𝑛 , 𝑢 1 , ..., 𝑢 𝑛 ). We say that 𝑎 𝑖 ∈ 𝐴 𝑖 strictly dominates 𝑎 ′ 𝑖 ∈ 𝐴 𝑖 if for all 𝑎 −𝑖 ∈ 𝐴 −𝑖 , 𝑢 𝑖 (𝑎 𝑖 , 𝑎 −𝑖 ) > 𝑢 𝑖 (𝑎 ′ 𝑖 , 𝑎 −𝑖 ). For any given game Γ = (𝐴, u), we will call any game Γ ′ = (𝐴 ′ , u ′ ) a subset game of Γ if 𝐴 ′ 𝑖 ⊆ 𝐴 𝑖 for 𝑖 = 1, ..., 𝑛. Note that a subset game may assign different utilities to outcomes than the original game. For any set of strategies 𝑆, we denote by Γ − 𝑆 ((𝐴 1 − 𝑆) × ...., (𝐴 𝑛 − 𝑆), u) the game that arises from Γ by removing the strategies 𝑆 for all players. We say that some utility vector y ∈ R 𝑛 is a Pareto-improvement on (or is Pareto-better than) y ′ ∈ R 𝑛 if 𝑦 𝑖 ≥ 𝑦 ′ 𝑖 for 𝑖 = 1, ..., 𝑛. We will also denote this by y ≥ y ′ . Note that, contrary to convention, we allow y = y ′ . Whenever we require one of the inequalities to be strict, we will say that y is a strict Pareto improvement on y ′ . In a given game, we will also say that an outcome a is a Paretoimprovement on another outcome a ′ if u(a) ≥ u(a ′ ). We say that y is Pareto-optimal or Pareto-efficient relative to some 𝑆 ⊂ R 𝑛 if there is no element of 𝑆 that strictly Pareto-dominates y. The Demand Game of Table  1  is an example of a game that we will use throughout this paper. As noted earlier, DM and RM strictly dominate DL and RL. The game of Table  2  is a subset game of the Demand Game. \n Multivalued functions For sets 𝑀 and 𝑁 , a multi-valued function Φ : 𝑀 ⊸ 𝑁 is a function which maps each element 𝑚 ∈ 𝑀 to a set Φ(𝑚) ⊆ 𝑁 . For a subset 𝑄 ⊆ 𝑀, we define Φ(𝑄) 𝑚 ∈𝑄 Φ(𝑚). Note that Φ(𝑄) ⊆ 𝑁 and that Φ(∅) = ∅. For any set 𝑀, we define the identity function id 𝑀 : 𝑀 ⊸ 𝑀 : 𝑚 → {𝑚}. Also, for two sets 𝑀, 𝑁 , we define all 𝑀,𝑁 : 𝑀 ⊸ 𝑁 : 𝑚 ↦ → 𝑁 . We define the inverse Φ −1 : 𝑁 ⊸ 𝑀 : 𝑛 ↦ → {𝑚 ∈ 𝑀 | 𝑛 ∈ Φ(𝑚)}. Note that Φ −1 (∅) = ∅ for any multi-valued function Φ. For sets 𝑀, 𝑁 , 𝑄 and functions Φ : 𝑀 ⊸ 𝑁 , Ψ : 𝑁 ⊸ 𝑄, we define the composite Ψ • Φ : 𝑀 ⊸ 𝑄 : 𝑚 ↦ → Ψ(Φ(𝑚)). As with regular functions, composition of multi-valued functions is associative. We say that Φ : 𝑀 ⊸ 𝑁 is single-valued if |Φ(𝑚)| = 1 for all 𝑚 ∈ 𝑀. Whenever a multi-valued function is single-valued, we can apply many of the terms for regular functions. For example, we will take injectivity, surjectivity, and bijectivity for single-valued functions to have the usual meaning. We will never apply these notions to non-single-valued functions. \n DELEGATION AND SAFE PARETO IMPROVEMENTS We consider a setting in which a given game Γ is played through what we will call representatives. For example, the representatives could be humans whose behavior is determined or incentivized by some contract à la the principal-agent literature  [14] . We imagine that one way in which the representatives can be instructed is to in turn play a subset game Γ 𝑠 = (𝐴 𝑠 1 ⊆ 𝐴 1 , ..., 𝐴 𝑠 𝑛 ⊆ 𝐴 𝑛 , u 𝑠 ) of the original game, without necessarily specifying a strategy or algorithm for solving such a game. We emphasize, again, that u 𝑠 is allowed to be a vector of entirely different utility functions. For any subset game Γ 𝑠 , we denote by Π(Γ 𝑠 ) the outcome that arises if the representatives play the subset game Γ 𝑠 of Γ. Because in many games, it is not clear what the right choice is, the original players might be uncertain about Π(Γ 𝑠 ) for many games Γ 𝑠 . We will therefore model each Π(Γ 𝑠 ) as a random variable. The original players trust their representatives to the extent that we take Π(Γ) to be a default way for the game to played for any Γ. For example, in the Game of Chicken, it is not clear what the right action is. Thus, if one can simply delegate the decision to someone with more relevant expertise, that is the first option one would consider. We are interested in whether and how the original players can jointly Pareto-improve on the default. Of course, one option is to compute the expected utilities in the default (E [u(Π(Γ))]) and then let the representatives play a distribution over outcomes whose expected utility exceeds that default expected utility. However, this is unrealistic if Γ is a complex game with multiple Nash equilibria. For one, the precise point of delegation is that the original players are unable or unwilling to properly evaluate Γ. Second, there is no widely agreed upon, universal procedure for selecting an action in the face of equilibrium selection problems. We address this problem in a typical way. Essentially, we require of any attempted improvement that it incurs no regret in the worstcase. That is, we are interested in subset games Γ 𝑠 that are Pareto improvements with certainty under weak and purely qualitative assumptions about Π. Definition 3.1. Let Γ 𝑠 be a subset game of Γ. We say Γ 𝑠 is a safe Pareto improvement (SPI) on Γ if u(Π(Γ 𝑠 )) ≥ u(Π(Γ)) with certainty. We say that Γ 𝑠 is a strict SPI if furthermore, there is a player 𝑖 s.t. 𝑢 𝑖 (Π(Γ 𝑠 )) > 𝑢 𝑖 (Π(Γ 𝑠 )) with positive probability. \n PROGRAM EQUILIBRIUM So far, we have been vague about the details of the strategic situation that the original players face in instructing their representatives. From what set of actions can they choose? How can they jointly let the representatives play some new subset game Γ 𝑠 ? Are SPIs Nash equilibria of the meta game played by the representatives? In this section, we briefly describe one way to fill this gap by discussing the concept of program games and program equilibrium  [3, 6, 8, 17, 25] . This section is essential to understanding why SPIs are relevant. However, the remaining technical content of this paper does not rely on this section and the main ideas presented here are straightforward from previous work. For more detail, see Appendix A. For any game Γ = (𝐴, u), the program equilibrium literature considers the following meta game. First, each player 𝑖 chooses from a set of computer programs. Each program then receives as input a vector containing everyone else's chosen program. Each player 𝑖's program then returns an action from 𝐴 𝑖 , player 𝑖's set of actions in Γ. Together these actions then form an outcome a ∈ 𝐴 of the original game. Finally, the utilities u(a) are realized according to the utility function of Γ. The meta game can be analyzed like any other game. Its Nash equilibria are called program equilibria. Importantly, the program equilibria can implement payoffs not implemented by any Nash equilibria of Γ itself. For example, in the Prisoner's Dilemma, both players can submit a program that says: \"If the opponent's chosen computer program is equal to this computer program, Cooperate; otherwise Defect. \"  [11, 15, 25]  This is a program equilibrium which implements mutual cooperation. In the setting for our paper, we similarly imagine that each player 𝑖 can choose from a set of programs that in turn choose from 𝐴 𝑖 . However, the types of program that we have in mind here are more sophisticated than those typically considered in the program equilibrium literature. Specifically we imagine that the programs are executed by intelligent representatives who are themselves able to competently choose an action for player 𝑖 in any given game Γ 𝑠 , without the original player having to describe how this choice is to be made. The original player may not even understand much about this program other than that it generally plays well. Thus, in addition to the elementary instructions used in a typical computer program (branches, comparisons, arithmetic operations, etc.), we allow player 𝑖 to use an instruction \"Play Π 𝑖 (Γ 𝑠 )\" in the program she submits. To jointly let the representatives play, e.g., the SPI Γ 𝑠 of Table  2  on the Demand Game of Table  1 , the representatives can both use an instruction that says, \"If the opponent's chosen program is analogous to this one, play Π 𝑖 (Γ 𝑠 ); otherwise play DM\". Assuming some minimal rationality requirements on the representatives (i.e., on how \"play Π 𝑖 (Γ 𝑠 )\" is implemented), this is a Nash equilibrium. More generally, we can prove the following result (see Appendix A for a proof). Theorem 4.1. Let Γ be a game and Γ 𝑠 be an SPI of Γ. Now consider a program game on Γ, where each player 𝑖 can choose from a set of computer programs that output actions for Γ. In addition to the normal kind of instructions, we allow the use of the command \"play Π 𝑖 (Γ ′ )\" for any subset game Γ ′ of Γ. Finally, assume that Π(Γ) guarantees each player 𝑖 at least that player's minimax utility (a.k.a. threat point) in the base game Γ. Then Π(Γ 𝑠 ) is played in a program equilibrium, i.e., in a Nash equilibrium of the program game. As an alternative to having the original players choose contracts separately, we could imagine the use of jointly signed contracts which only come into effect once signed by all players [cf.  12, 16] . Also compare earlier work by Sen  [24]  and  [21] , which we discuss in Appendix B. \n OUTCOME CORRESPONDENCE BETWEEN GAMES In this section, we introduce a notion of outcome correspondence, which we will see is essential to constructing SPIs. Definition 5.1. Consider two games Γ = (𝐴 1 , ..., 𝐴 𝑛 , u) and Γ ′ = (𝐴 ′ 1 , ..., 𝐴 ′ 𝑛 , u ′ ). We write Γ ∼ Φ Γ ′ for Φ : 𝐴 ⊸ 𝐴 ′ if Π(Γ ′ ) ∈ Φ(Π(Γ)) with certainty. Note that Γ ∼ Φ Γ ′ is a statement about Π, i.e., about how the representatives choose. Whether such a statement holds generally depends on the specific representatives being used. In Section 7, we describe two general circumstances under which it seems plausible that Γ ∼ Φ Γ ′ . For example, if two games Γ and Γ ′ are isomorphic, then one might expect Γ ∼ Φ Γ ′ , where Φ is constructed from the 𝑛 isomorphisms of the particular action spaces. We now state some basic facts about the relation ∼, many of which we will use throughout this paper. Lemma 5.2. Let Γ = (𝐴, u), Γ ′ = (𝐴 ′ , u ′ ), Γ = ( Â, û) and Φ, Ξ : 𝐴 ⊸ 𝐴 ′ , Ψ : 𝐴 ′ ⊸ Â. (1) Reflexivity: Γ ∼ id 𝐴 Γ, where id 𝐴 : 𝐴 ⊸ 𝐴 : a ↦ → {a}. (2) Symmetry: If Γ ∼ Φ Γ ′ , then Γ ′ ∼ Φ −1 Γ. ( 3 ) Transitivity: If Γ ∼ Φ Γ ′ and Γ ′ ∼ Ψ Γ, then Γ ∼ Ψ•Φ Γ. (4) If Γ ∼ Φ Γ ′ and Φ(a) ⊆ Ξ(a) for all a ∈ 𝐴, then Γ ∼ Ξ Γ ′ . ( 5 ) Γ ∼ all 𝐴,𝐴 ′ Γ ′ , where all 𝐴,𝐴 ′ : 𝐴 ⊸ 𝐴 ′ : a ↦ → 𝐴 ′ . ( 6 ) If Γ ∼ Φ Γ ′ and Φ(a) = ∅, then Π(Γ) ≠ a with certainty. For completness, we prove these in Appendix C. Items 1-3 show that ∼ has properties resembling those of an equivalence relation. Note, however, that since ∼ is not a binary relationship, ∼ itself cannot be an equivalence relation in the usual sense. Item 4 states that we can make an outcome correspondence claim less precise and it will still hold true. Item 5 states that in the extreme, it is always Γ ∼ all 𝐴,𝐴 ′ Γ ′ , where all 𝐴,𝐴 ′ is the trivial, maximally imprecise outcome correspondence function that confers no information. Item 6 shows that ∼ can be used to express the elimination of outcomes, i.e., the belief that a particular outcome (or strategy) will never occur. \n SAFE PARETO IMPROVEMENTS THROUGH OUTCOME CORRESPONDENCE We now show that as advertised, outcome correspondence is closely tied to SPIs. The following theorem shows not only how outcome correspondences can be used to find (and prove) SPIs. It also shows that any SPI requires an outcome correspondence relation with what we will call a Pareto-improving correspondence function. Theorem 6.1. Let Γ = (𝐴, u) be a game and Γ 𝑠 = (𝐴 𝑠 , u 𝑠 ) be a subset game of Γ. Then Γ 𝑠 is an SPI on Γ if and only if there is Φ such that Γ ∼ Φ Γ 𝑠 and for all a ∈ 𝐴 it is for all a 𝑠 ∈ Φ(a) the case that u(a 𝑠 ) ≥ u(a). Proof. ⇐: By definition, Π(Γ 𝑠 ) ∈ Φ(Π(Γ)) with certainty. Hence, for 𝑖 = 1, 2, 𝑢 𝑖 (Π(Γ 𝑠 )) ∈ 𝑢 𝑖 (Φ(Π(Γ))) with certainty. Hence, by as- sumption about Φ, with certainty, 𝑢 𝑖 (Π(Γ 𝑠 )) ≥ 𝑢 𝑖 (Π(Γ)). ⇒: Assume that 𝑢 𝑖 (Π(Γ)) ≥ 𝑢 𝑖 (Π(Γ 𝑠 )) with certainty for 𝑖 = 1, 2. We define Φ : 𝐴 → 𝐴 𝑠 : a ↦ → {a 𝑠 ∈ 𝐴 𝑠 | u(a 𝑠 ) ≥ u(a)}. It is immediately obvious that Φ is Pareto-improving as required. Also, whenever Π(Γ) = a and Π(Γ 𝑠 ) = a 𝑠 for any a ∈ 𝐴 and a 𝑠 ∈ 𝐴 𝑠 , it is (by assumption) with certainty u(a 𝑠 ) ≥ u(a). Thus, by definition of Φ, it holds that a 𝑠 ∈ Φ(a). We conclude that Γ ∼ Φ Γ 𝑠 as claimed. □ Note that the theorem concerns weak SPIs and therefore allows the case where with certainty u(Π(Γ)) = u(Π(Γ 𝑠 )). To show that some Γ 𝑠 is a strict SPI, we need additional information about which outcomes occur with positive probability. We now illustrate how outcome correspondences can be used to derive the SPI for the Demand Game from the introduction as per Theorem 6.1. Of course, at this point we do not have any assumptions about when games are equivalent. We will introduce some in the following section. Nevertheless, we can already sketch the argument. Let Γ be the Demand Game of Table  1 . First, it seems plausible that Γ is in some sense equivalent to Γ ′ , where Γ ′ = Γ − {DL, RL} is the game that results from removing DL and RL for both players from Γ. Again, strict dominance could be given as an argument. We can formalize this as Γ ∼ Φ Γ ′ , where Φ(𝑎 1 , 𝑎 2 ) = {(𝑎 1 , 𝑎 2 )} if 𝑎 1 , 𝑎 2 ∈ {DM, RM} and Φ(𝑎 1 , 𝑎 2 ) = ∅ otherwise. In a second step, it seems plausible that Γ ′ ∼ Ψ Γ 𝑠 , where Γ 𝑠 is the game of Table  2  and Ψ is the isomorphism between Γ ′ and Γ 𝑠 . Finally, we can use transitivity to obtain Γ ∼ Ψ•Φ Γ 𝑠 . To see that Ψ • Φ is Paretoimproving for the original utility functions of Γ, notice that Φ does not change utilities at all. Ψ maps the conflict outcome (DM, DM) onto the outcome (DL, DL), which is better for both original players. Other than that, Ψ, too, does not change the utilities. Hence, Ψ • Φ is Pareto-improving. By Theorem 6.1, Γ 𝑠 is therefore an SPI on Γ. In principle, Theorem 6.1 does not hinge on Π(Γ) and Π(Γ 𝑠 ) resulting from playing games. An analogous result holds for any random variables over 𝐴 and 𝐴 𝑠 . In particular, this means that Theorem 6.1 applies also if the representatives receive other kinds of instructions (cf. Section 4). However, it seems hard to establish nontrivial outcome correspondences between Π(Γ) and other types of instructions. Still, the use of more complicated instructions can be used to derive different kinds of SPIs. For example, if there are different game SPIs, then the original players could tell their representatives to randomize between them in a coordinated way. \n ASSUMPTIONS ABOUT OUTCOME CORRESPONDENCE To make any claims about how the original players should play the meta-game, i.e., about what instructions they should submit, we have to make assumptions about how the representatives choose and (by Theorem 6.1) about outcome correspondence in particular. We here make two fairly weak assumptions. The first is that the representatives play two isomorphic games isomorphically. Assumption 7.1. Let Γ = (𝐴, u) and Γ ′ = (𝐴 ′ , u ′ ) be two games for which there are single-valued bijections Φ 𝑖 : 𝐴 𝑖 → 𝐴 ′ 𝑖 for 𝑖 = 1, ..., 𝑛 such that u(𝑎 1 , ..., 𝑎 𝑛 ) = u ′ (Φ 1 (𝑎 1 ), ..., Φ 𝑛 (𝑎 𝑛 )) for all a ∈ 𝐴. Then for one tuple Φ of such bijections, Γ ∼ Φ Γ ′ . Similar desiderata have been discussed in the context of equilibrium selection, e.g., by Harsanyi and Selten  [10, Chapter 3.4 ]. In fact, they consider a generalization in which the utilities are allowed to be linear transformations of each other. Although this generalization is extremely plausible, we omit it here for simplicity. One could criticize Assumption 7.1 by referring to focal points (introduced by Schelling [22, pp. 54-58]) as an example where context and labels of strategies matter. A possible response might be that in games where context plays a role, that context should be included as additional information and not be considered part of (𝐴, u). Assumption 7.1 would then either not apply to such games with (relevant) context or would require one to, in some way, translate the context along with the strategies. However, in this paper we will not formalize context, and assume that there is no decisionrelevant context. Assumption 7.2. Let Γ = (𝐴, u) be an arbitrary 𝑛-player game where 𝐴 1 , ..., 𝐴 𝑛 are pairwise disjoint, and ã𝑖 ∈ 𝐴 𝑖 be strictly dominated by some other strategy â𝑖 ∈ 𝐴 𝑖 . Then Γ ∼ Φ Γ − { ã𝑖 }, where for all 𝑎 −𝑖 ∈ 𝐴 −𝑖 , Φ( ã𝑖 , 𝑎 −𝑖 ) = ∅ and Φ(𝑎 𝑖 , 𝑎 −𝑖 ) = {(𝑎 𝑖 , 𝑎 −𝑖 )} whenever 𝑎 𝑖 ≠ ã𝑖 . Assumption 7.2 expresses that representatives should never play strictly dominated strategies. Moreover, it states that we can remove strictly dominated strategies from a game and the resulting game will be played in the same way by the representatives. For example, this implies that when evaluating a strategy 𝑎 𝑖 , the representatives do not take into account how many other strategies 𝑎 𝑖 strictly dominates. Assumption 7.2 also allows (via Transitivity of ∼ as per Lemma 5.2.3) the iterated removal of strictly dominated strategies. The notion that we can (iteratively) remove strictly dominated strategies is common in game theory  [13, 18, 19 , Section 2.9, Chapter 12] and has rarely been questioned. It is also implicit in the solution concept of Nash equilibrium -if a strategy is removed by iterated strict dominance, that strategy is played in no Nash equilibrium. However, like the concept of Nash equilibrium, the elimination of strictly dominated strategies becomes implausible if the game is not played in the usual way. In particular, for Assumption 7.2 to hold, we will in most games Γ have to assume that the representatives cannot in turn make credible precommitments (or delegate to further subrepresentatives) or play the game iteratively  [2] . With  Γ. Further, if 𝑃 (Π(Γ)=(DM, DM)) > 0, Γ 𝑠 is a strict SPI. \n COMPUTING SAFE PARETO IMPROVEMENTS In this section, we ask how computationally costly it is for the original players to identify for a given game Γ a non-trivial SPI Γ 𝑠 . In particular, we ask whether a given game Γ has a non-trivial SPI that can be proved using only Assumptions 7.1 and 7.2, Transitivity (Lemma 5.2.3) and Theorem 6.1. Formally: Definition 8.1. The SPI decision problem consists in deciding for any given Γ, whether there is a sequence of outcome correspondences Φ 1 , ..., Φ 𝑘 and a sequence of subset games Γ 0 = Γ, Γ 1 , ..., Γ 𝑘 of Γ s.t.: (1) (Non-triviality:) If we fully reduce Γ 𝑘 and Γ using iterated strict dominance (Assumption 7.2), the two resulting games are not equal. (Of course, they are allowed to be isomorphic.) (2) For 𝑖 = 1, ..., 𝑘, Γ 𝑖−1 ∼ Φ 𝑖 Γ 𝑖 is valid by a single application of either Assumption 7.1 or Assumption 7.2. (3) For all a ∈ 𝐴, and whenever a 𝑠 ∈ (Φ 𝑘 • Φ 𝑘−1 • ... • Φ 1 ) (a), it is the case that 𝑢 (a 𝑠 ) ≥ u(a). For the strict SPI decision problem, we further require: (4.) There is a player 𝑖 and an outcome a that survives iterated elimination of strictly dominated strategies from Γ s.t. 𝑢 𝑖 ((Φ 𝑘 • Φ 𝑘−1 • ... • Φ 1 )(a)) > 𝑢 𝑖 (a). Many variants of this problem may be considered. For example, we might generalize it to allow imposing additional properties on the SPI. This will generally not change the computational complexity of the problem. One may also wish to compute all SPIs, or -in line with multi-criteria optimization  [7, 27]  -all SPIs that cannot in turn be safely improved upon. However, in general there may exist exponentially many such SPIs. To retain any hope of developing an efficient algorithm, one would therefore have to first develop a more efficient representation scheme [cf.  20  The full proof is tedious (see Appendix E), but the main idea is simple. To find an SPI on Γ based on Assumptions 7.1 and 7.2, one has to first iteratively remove all strictly dominated actions to obtain a reduced game Γ ′ , which the representatives would play the same as the original game. This can be done in polynomial time. One then has to map the actions Γ ′ onto the original Γ in such a way that each outcome in Γ ′ is mapped onto a weakly Pareto-better outcome in Γ. Our proof of NP-hardness works by reducing from the subgraph isomorphism problem, where the payoff matrices of Γ ′ , Γ represent the adjacency matrices of the graphs. Besides being about a specific set of assumptions about ∼, note that Theorem 8.2 and Proposition 8.3 also assume that the utility function of the game is represented explicitly in normal form as a payoff matrix. If we changed the game representation (e.g., to boolean circuits, extensive form game trees, quantified boolean formulas, or even Turing machines), this can affect the complexity of the SPI problem [cf. 9]. In fact, even reducing a game using strict dominance by pure strategies -which contributes only insignificantly to the complexity of the SPI problem for normal-form games -is difficult in some game representations [4, Section 6]. \n SAFE PARETO IMPROVEMENTS UNDER IMPROVED COORDINATION In this section, we imagine that the players are able to simply invent new token strategies with new payoffs that arise from mixing existing feasible payoffs. To define this formally, we first define for any game Γ = (𝐴, u), C(Γ) u(Δ(𝐴)) = a∈𝐴 𝑝 a u(a) ∀a∈𝐴:𝑝 a ∈[0, 1], a∈𝐴 𝑝 a = 1 to be the set of feasible coordinated payoff vectors of Γ, which is exactly the convex closure of u(𝐴), i.e., of the deterministically achievable utilities of the original game. For any game Γ, we then imagine that in addition to subset games, the players can let the representatives play a perfect-coordination token game (𝐴 𝑠 , u 𝑠 , u 𝑒 ), where for all 𝑖, 𝐴 𝑠 𝑖 ∩𝐴 𝑖 = ∅ and 𝑢 𝑠 𝑖 : 𝐴 𝑠 → R are arbitrary utility functions to be used by the representatives and u 𝑒 : 𝐴 𝑠 → C(Γ) are the utilities that the original players assign to the token strategies. The instruction (𝐴 𝑠 , u 𝑠 , u 𝑒 ) lets the representatives play the game (𝐴 𝑠 , u 𝑠 ) as usual. However, the strategies 𝐴 𝑠 are imagined to be meaningless token strategies which do not resolve the given game Γ. Once some token strategies a 𝑠 are selected, these are translated into some probability distribution over 𝐴, i.e., over outcomes of the original game, thus giving rise to (expected) utilities u 𝑒 (a 𝑠 ) ∈ C(Γ). These distributions and thus utilities are specified by the original players. We here imagine in our definition of C(Γ) that these distributions over 𝐴 could require the representatives to correlate their choices for the original game for any given a 𝑠 . Definition 9.1. Let Γ be a game. A perfect-coordination SPI for Γ is a perfect-coordination token game (𝐴 𝑠 , u 𝑠 , u 𝑒 ) for Γ s.t. u 𝑒 (Π(𝐴 𝑠 , 𝑢 𝑠 )) ≥ u(Π(Γ)) with certainty. We call (𝐴 𝑠 , u 𝑠 , u 𝑒 ) a strict perfect-coordination SPI if there furthermore is a player 𝑖 for whom 𝑢 𝑒 𝑖 (Π(𝐴 𝑠 , 𝑢 𝑠 )) > 𝑢 𝑖 (Π(Γ)) with positive probability. As an example, imagine that Γ is just the DM-RM subset game of the Demand Game of Table  1 . Then, intuitively, an SPI under improved coordination could consist of the original players telling the representatives, \"Play as if you were playing the DM-RM subset game of the Demand Game, but whenever you find yourself playing (DM, DM), randomize [according to some given distribution] between the other (Pareto-optimal) outcomes instead\". Formally, 𝐴 𝑠 1 = { D, R}, 𝐴 𝑠 2 = { D, R} would then consist of tokenized versions of the original strategies. The utility functions 𝑢 𝑠 1 , 𝑢 𝑠 2 are then simply the same as in the original Demand Game except that they are applied to the token strategies. E.g., u 𝑠 ( D, R) = (2, 0). The utilities for the original players remove the conflict outcome. For example, the original players might specify u 𝑒 ( D, D) = (1, 1), representing that the representatives are supposed to play (RM, RM) in the ( D, D) case. For all other outcomes ( â1 , â2 ), it must be the case that u 𝑒 ( â1 , â2 ) = u 𝑠 ( â1 , â2 ) because the other outcomes cannot be Pareto-improved upon. As with our earlier SPIs for the Demand Game, Assumption 7.1 implies that Γ ∼ Φ Γ 𝑠 , where Φ maps the original conflict outcome (DM, DM) onto the Pareto-optimal ( D, D). Relative to the SPIs considered up until now, these new types of instructions put significant additional requirements on how the representatives interact. They now have to engage in a two-round process of first choosing and observing one another's token strategies and then playing the corresponding distribution over outcomes from the original game. Further, it must be the case that this additional coordination does not affect the payoffs of the original outcomes. The latter may not be the case in, e.g., the Game of Chicken. That is, we could imagine a Game of Chicken in which coordination is possible but that the rewards of the game change if the players do coordinate. After all, the underlying story in the Game of Chicken is that the positive reward (admiration from peers) is attained precisely for accepting a grave risk. With these more powerful ways to instruct representatives, we can now replace individual outcomes of the default game ad libitum. For example, in the reduced Demand Game, we singled out the outcome (DM, DM) as Pareto-suboptimal and replaced it by a Pareto-optimal outcome, while keeping all other outcomes the same. This allows us to construct SPIs in many more games then before. Definition 9.2. The strict full-coordination SPI decision problem consists in deciding for any given Γ whether under Assumption 7.1 there is a perfect-coordination SPI Γ 𝑠 for Γ. Lemma 9.3. For a given 𝑛-player game Γ and payoff vector y ∈ R 𝑛 , it can be decided by linear programming and thus in polynomial time whether y is Pareto-optimal in C(Γ). For completeness the linear program is given in Appendix F. Based on Lemma 9.3, Algorithm 1 decides whether there is a strict perfect-coordination SPI for a given game Γ. It is easy to see that this algorithm runs in polynomial time (in the size of, e.g., the normal form representation of the game). It is also correct: if it returns True, simply replace the Pareto-suboptimal outcome while keeping all other outcomes the same; if it returns False, then all outcomes are Pareto-optimal within C(Γ) and so there can be no strict SPI. We summarize this result in the following proposition. From the problem of deciding whether there are strict SPIs under improved coordination at all, we move on to the question of what different perfect-coordination SPIs there are. In particular, one might ask what the cost is of only considering safe Pareto improvements relative to acting on a probability distribution over Π(Γ) and the resulting expected utilities E [u(Π(Γ))]. We start with a lemma that directly provides a characterization. So far, all the considered perfect-coordination SPIs (𝐴 𝑠 , u 𝑠 , u 𝑒 ) for a game (𝐴, u) have consisted in letting the representatives play a game (𝐴 𝑠 , u 𝑠 ) that is isomorphic to the original game, but Pareto-improves (from the original players' perspectives, i.e., u 𝑒 ) at least one of the outcomes. It turns out that we can restrict attention to this very simple type of SPI under improved coordination. Lemma 9.5. Let Γ = ({𝑎 is also an SPI on Γ, with E u(Π(Γ 𝑠 )) Π(Γ)=a = E u(Π(Γ ′ )) Π(Γ)=a for all a ∈ 𝐴 and consequently E [u(Π(Γ 𝑠 ))] = E [u(Π(Γ ′ ))]. We prove this in Appendix G. Because of this result, we will focus on these particular types of SPIs, which simply create an isomorphic game with different (Pareto-better) utilities. Note, however, that without assigning exact probabilities to the distributions of Π(Γ), Π(Γ ′ ), the original players will in general not be able to construct a Γ 𝑠 that satisfies the expected payoff equalities. For this reason, one could still conceive of situations in which a different type of SPI would be chosen by the original players and the original players are unable to instead choose an SPI of the type described in Lemma 9.5. Lemma 9.5 directly implies a characterization of the expected utilities that can be achieved with perfect-coordination SPIs. Of course, this characterization depends on the exact distribution of Π(Γ). We omit the statement of this result. However, we state the following implication. Corollary 9.6. Under Assumption 7.1, the set of Pareto improvements that are safely achievable with perfect coordination {E[u(Γ ′ )] | Γ ′ is perfect-coordination SPI on Γ} is a convex polygon. Because of this result, one can also efficiently optimize convex functions over the set of perfect-coordination SPIs. Even without referring to the distribution Π(Γ), many interesting questions can be answered efficiently. For example, we can efficiently identify the perfect-coordination SPI that maximizes the minimum improvements across players and outcomes a ∈ 𝐴. In the following, we aim to use Lemma 9.5 and Corollary 9.6 to give maximally strong positive results about what Pareto improvements can be safely achieved, without referring to exact probabilities over Π(Γ). To keep things simple, we will do this only for the case of two players. To state our results, we first need some notation: We use PF(C) y ∈ C ∄y ′ ∈C, 𝑖 ∈ {1, ..., 𝑛} : y ′ ≥ y, 𝑦 ′ 𝑖 > 𝑦 to denote the Pareto frontier of a convex polygon C (or more generally convex, closed set). For any real number 𝑥 ∈ R, we use 𝜋 𝑖 (𝑥, C(Γ)) to denote the y ′ ∈ C(Γ) which maximizes 𝑦 ′ −𝑖 under the constraint 𝑦 ′ 𝑖 = 𝑥. (Recall that we consider 2-player games, so 𝑦 ′ −𝑖 is a single real number.) Note that such a y ′ exists if and only if 𝑥 is 𝑖's utility in some feasible payoff vector. We first state our result formally. Afterwards, we will give a graphical explanation of the result, which we believe is easier to understand. Then there is an SPI under improved coordination Γ 𝑠 such that E [u(Π(Γ 𝑠 ))] = y. B) If there is no element in C(Γ) which Pareto-dominates all of supp(Π(Γ)) and if y is Pareto-dominated by an element each of 𝐿 1 and 𝐿 3 as defined above, then there is a perfect-coordination SPI Γ 𝑠 such that E [u(Π(Γ 𝑠 ))] = y. We now illustrate the result graphically. We start with Case A, which is illustrated in Figure  1 . The Pareto-frontier is the solid line in the north and east. The points marked x indicate outcomes in supp(Π(Γ)). The point marked by a filled circle indicates the expected value of the default equilibrium E [u(Π(Γ))]. For some y ∈ R 2 to be a Pareto-improvement, it must be to the north-east of the filled circle. The vertical dashed lines starting at the two extreme x marks illustrate the application of 𝜋 1 to project 𝑥 min/max 1 onto the Pareto frontier. The dotted line between these two points is 𝐿 1 . Similarly, the horizontal dashed lines starting at x marks illustrate the application of 𝜋 2 to project 𝑥 min/max 2 onto the Pareto frontier. The line segment between these two points is 𝐿 3 . In this case, this line segments lies on the Pareto frontier. The set 𝐿 2 is simply that part of the Pareto frontier, which Pareto-dominates all elements of supp(Π(Γ)), i.e., the part of the Pareto frontier to the north-east  between the two intersections with the northern horizontal dashed line and eastern vertical dashed line. E [𝑢 1 (Π(Γ 𝑠 ))] E [𝑢 1 (Π(Γ)))] E [𝑢 2 (Π(Γ)))] E [𝑢 2 (Π(Γ 𝑠 ))] E [𝑢 1 (Π(Γ 𝑠 ))] E [𝑢 1 (Π(Γ))] E [𝑢 2 (Π(Γ))]) E [𝑢 2 (Π(Γ))] Case B of Theorem 9.7 is depicted in Figure  2 . Note that here the two line segments 𝐿 1 and 𝐿 3 intersect. To ensure that a Pareto improvement is safely achievable, the theorem requires that it is below both of these lines. Theorem 9.7 is proven by re-mapping each of the outcomes of the original game as per Lemma 9.5. For example, the projection of the default equilibrium E [u(Π(Γ))] (i.e., the filled circle) onto 𝐿 1 is obtained as an SPI by projecting all the outcomes (i.e., all the x marks) onto 𝐿 1 . In Case A, any utility vector y ∈ 𝐿 2 that Paretoimproves on all outcomes of the original game can be obtained by re-mapping all outcomes onto y. Other kinds of y are handled similarly. For a full proof, see Appendix H. As a corollary of Theorem 9.7, we can see that all (potentially unsafe) Pareto improvements in the DM-RM subset game of the Demand Game of Table  1  are equivalent to some perfect-coordination SPI. However, this is not always the case: Proposition 9.8. There is a game Γ = (𝐴, u), representatives Π that satisfy Assumptions 7.1 and 7.2, and an outcome a ∈ 𝐴 s.t. 𝑢 𝑖 (a) > E [𝑢 𝑖 (Π(Γ))] for all players 𝑖, but there is no perfectcoordination SPI (𝐴 𝑠 , u 𝑠 , u 𝑒 ) s.t. for all players 𝑖, E 𝑢 𝑒 𝑖 (Π(𝐴 𝑠 , u 𝑠 )) = 𝑢 𝑖 (a). We prove this in Appendix I. \n THE SPI SELECTION PROBLEM In the Demand Game, there happens to be a single non-trivial SPI. However, in general (even without the type of coordination assumed in Section 9) there may be multiple incomparable SPIs that result in different payoffs for the players. If multiple SPIs are available, the original players would be left with the difficult decision of which SPI to demand in their instruction. This difficulty of choosing what SPI to demand cannot be denied. However, we would here like to emphasize that players can profit from the use of SPIs even without addressing this SPI selection problem. To do so, a player picks an instruction that is very compliant (\"dove-ish\") w.r.t. what SPI is chosen, e.g., one that simply goes with whatever SPI the other players demand as long as that SPI cannot further be safely Pareto-improved upon. In many cases, all such SPIs benefit both players. For example, SPIs in bargaining scenarios like the Demand Game remove the conflict outcome, which benefits all parties. Thus, a player can expect a safe improvement even under such maximally compliant demands on the selected SPI. \n CONCLUSION AND FUTURE DIRECTIONS Safe Pareto improvements are a promising new idea for delegating strategic decision making. To conclude this paper, we discuss some ideas for further research on SPIs. Straightforward technical questions arise in the context of the complexity results of Section 8. First, what impact on the complexity does varying the assumptions have? Our NP-completeness proof is easy to generalize at least to some other types of assumptions. It would be interesting to give a generic version of the result. We also wonder whether there are plausible assumptions under which the complexity changes in interesting ways. Second, one could ask how the complexity changes if we use more sophisticated game representations (see the remarks at the end of that section). Third, one could impose additional restrictions on the sought SPI. For example, some of the players may be unable to have their representative maximize arbitrary utility functions. We could then ask whether there is an SPI in which only a given subset of the players adopt different utility functions and restrictions on the set of available strategies. Fourth, we could restrict the games under consideration. Are there games in which it becomes easy to decide whether there is an SPI? It would also be interesting to see what real-world situations can already be interpreted as utilizing SPIs, or could be Pareto-improved upon using SPIs. \n A PROOF OF THEOREM 4.1 -PROGRAM EQUILIBRIUM IMPLEMENTATIONS OF SAFE PARETO IMPROVEMENTS This paper considers the meta-game of delegation. SPIs are a proposed way of playing these games. However, throughout most of this paper, we do not analyze the meta-game directly as a game using the typical tools of game theory. We here fill that gap and in particular prove Theorem 4.1, which shows that SPIs are played in Nash equilibria of the meta game, assuming sufficiently strong contracting abilities. As noted, this result is essential. However, since it is mostly an application of existing ideas from the literature on program equilibrium, we left a detailed treatment out of the main text. A program game for Γ = (𝐴, u) is defined via a set PROG = PROG 1 ×...×PROG 𝑛 and a non-deterministic mapping exec : PROG 1 × ... × PROG 𝑛 ⇝ 𝐴. We obtain a new game with action sets PROG and utility function 𝑈 : PROG → R 𝑛 : c ↦ → E [u(exec(c))] . (1) Though this definition is generic, one generally imagines in the program equilibrium literature that for all 𝑖, PROG 𝑖 consists of computer programs in some programming language, such as Lisp, that take as input vectors in PROG and return an action 𝑎 𝑖 . The function exec on input c ∈ PROG then executes each player 𝑖's program 𝑐 𝑖 on c to assign 𝑖 an action. The definition implicitly assumes that PROG only contains programs that halt when fed one another as input. A program equilibrium is then simply a Nash equilibrium of the program game. For the present paper, we add the following feature to the underlying programming language. A program can call a \"black box subroutine\" Π 𝑖 (Γ ′ ) for any subset game Γ ′ of Γ, where Π 𝑖 (Γ ′ ) is a random variable over 𝐴 ′ 𝑖 and Π(Γ ′ ) = (Π 1 (Γ ′ ), ..., Π 𝑛 (Γ ′ )). We need one more definition. For any game Γ and player 𝑖, we define Player 𝑖's threat point (a.k.a. minimax utility) 𝑣 Γ 𝑖 as 𝑣 Γ 𝑖 = min 𝝈 −𝑖 ∈ 𝑗 ≠𝑖 Δ(𝐴 𝑗 ) max 𝜎 𝑖 ∈Δ(𝐴 𝑖 ) 𝑢 𝑖 (𝜎 𝑖 , 𝝈 −𝑖 ). (2) In words, 𝑣 Γ 𝑖 is the minimum utility that the players other than 𝑖 can force onto 𝑖, under the assumption that 𝑖 reacts optimally to their strategy. We further will use minimax (𝑖, 𝑗) ∈ Δ(𝐴 𝑗 ) to denote the strategy for Player 𝑗 that is played in the minimizer 𝜎 −𝑖 of the above. Of course, in general, there might be multiple minimizers 𝜎 −𝑖 . In the following, we will assume that the function minimax breaks such ties in some consistent way, such that for all 𝑖, (minimax (𝑖, 𝑗)) 𝑗 ∈ {1,...,𝑛 }−{𝑖 } ∈ arg min 𝝈 −𝑖 ∈ 𝑗 ≠𝑖 Δ(𝐴 𝑗 ) max 𝜎 𝑖 ∈Δ(𝐴 𝑖 ) 𝑢 𝑖 (𝜎 𝑖 , 𝝈 −𝑖 ). (3) Note that for 𝑛 = 2, each player's threat point is computable in polynomial time via linear programming; and that by the minimax theorem  [28] , the threat point is equal to the maximin utility, i.e., 𝑣 Γ 𝑖 = max 𝜎 𝑖 ∈Δ(𝐴 𝑖 ) min 𝜎 −𝑖 ∈Δ(𝐴 −𝑖 ) 𝑢 𝑖 (𝜎 𝑖 , 𝜎 −𝑖 ), (4) so 𝑣 Γ 𝑖 is also the minimum utility that Player 𝑖 can guarantee for herself under the assumption that the opponent sees her mixed strategy and reacts in order to minimize Player 𝑖's utility. Tennenholtz'  [25]  main result on program games is the following: Theorem A.1  (Tennenholtz 2004 [25] ). Let Γ = (𝐴, u) be a game and let x ∈ u 𝑛 𝑖=1 Δ(𝐴 𝑖 ) be a (feasible) payoff vector. If 𝑥 𝑖 ≥ 𝑣 Γ 𝑖 for 𝑖 = 1, ..., 𝑛, then x is the utility of some program equilibrium of a program game on Γ. Throughout the rest of this section, our goal is to use similar ideas as Tennenholtz did for Theorem A.1 to construct for any SPI Γ 𝑠 on Γ, a program equilibrium that results in the play of Π(Γ 𝑠 ). As noted in the main text, the Player 𝑖's instruction to her representative to play the game Γ 𝑠 will usually be conditional on the other player telling her representative to also play her part of Γ 𝑠 and and vice versa. After all, if Player 𝑖 simply tells her representative to maximize 𝑢 𝑠 𝑖 from 𝐴 𝑠 𝑖 regardless of Player −𝑖's instruction, then Player −𝑖 will often be able to profit from deviating from the Γ 𝑠 instruction. For example, in the safe Pareto improvement on the Demand Game, each player would only want their representative to choose from {DL, RL} rather than {DM, DM} if the other player's representative does the same. It would then seem that in a program equilibrium in which Π(Γ 𝑠 ) is played, each program 𝑐 𝑖 would have to contain a condition of the type, \"if the opponent code plays as in Π(Γ 𝑠 ) against me, I also play as I would in Π(Γ 𝑠 ).\" But in a naive implementation of this, each of the programs would have to call the other, leading to an infinite recursion. In the literature on program equilibrium, various solutions to this problem have been discovered. We here use the general scheme proposed by Tennenholtz  [25] , because it is the simplest. We could similarly use the variant proposed by Fortnow  [8] , techniques based on Löb's theorem  [3, 6] , or 𝜖-grounded mutual simulation  [17]  or even (meta) Assurance Game preferences (see Appendix B). In our equilibrium, we let each player submit code as sketched in Algorithm 2. Roughly, each player uses a program that says, \"if everyone else submitted the same source code as this one, then play Π(Γ 𝑠 ). Otherwise, if there is a player 𝑗 who submits a different source code, punish player 𝑗 by playing her minimax strategy\". Note that for convenience, Algorithm 2 receives the player number 𝑖 as input. This way, every player can use the exact same source code. Otherwise the original players would have to provide slightly different programs and in line 2 of the algorithm, we would have to use a more complicated comparison, roughly: \"if 𝑐 𝑗 ≠ 𝑐 𝑖 are the same, except for the player index used\".   )) = 𝑣 𝑖 ≤ E [𝑢 𝑖 (Π(Γ))] ≤ E 𝑢 𝑖 (Π(Γ 𝑠 )) = E [𝑢 𝑖 (exec(c))] as required. □ Theorem 4.1 follows immediately. \n B A DISCUSSION OF WORK BY SEN (1974) AND RAUB (1990) ON PREFERENCE ADAPTATION GAMES We here discuss Raub's  [21]  paper in some detail, which in turn elaborates on an idea by Sen  [24] . Superficially, Raub's setting seems somewhat similar to ours, but we here argue that it should be thought of as closer to the work on program equilibrium and bilateral precommitment. In Sections 1, 3 and 4, we briefly discuss multilateral commitment games, which have been discussed before in various forms in the game-theoretic literature. Our paper extends this setting by allowing instructions that let the representatives play a game without specifying an algorithm for solving that game. On first sight, it appears that Raub pursues a very similar idea. Translated to our setting, Raub allows that as an instruction, each player 𝑖 chooses a new utility function 𝑢 𝑠 𝑖 : 𝐴 → R, where 𝐴 is the set of outcomes of the original game Γ. Given instructions 𝑢 𝑠 1 , ..., 𝑢 𝑠 𝑛 , the representatives then play the game (𝐴, u 𝑠 ). In particular, each representative can see what utility functions all the other representatives have been instructed to maximize. However, what utility function representative 𝑖 maximizes is not conditional on any of the instructions by other players. In other words, the instructions in Raub's paper are raw utility functions without any surrounding control structures, etc. Raub then asks for equilibria u 𝑠 of the meta-game that Pareto-improve on the default outcome. To better understand how Raub's approach relates to ours, we here give an example of the kind of instructions Raub has in mind. (Raub uses the same example in his paper.) As the underlying game Γ, we take the Prisoner's Dilemma. Now the main idea of his paper is that the original players can instruct their representatives to adopt so-called Assurance Game preferences. In the Prisoner's Dilemma, this means that the representatives prefer to cooperate if the other representative cooperates, and prefer to defect if the other player defects. Further, they prefer mutual cooperation over mutual defection. An example of such Assurance Game preferences is given in Table  3 . (Note that this payoff matrix resembles the classic Stag Hunt studied in game theory.) The Assurance Game preferences have two important properties. (1) If both players tell their representatives to adopt Assurance Game preferences, (Cooperate, Cooperate) is a Nash equilibrium. (Defect, Defect) is a Nash equilibrium as well. However, since (Cooperate, Cooperate) is Pareto-better than (Defect, Defect), the original players could reasonably expect that the representatives play (Cooperate, Cooperate). (  2 ) Under reasonable assumptions about the rationality of the representatives, it is a Nash equilibrium of the meta-game for both players to adopt Assurance Game preferences. If Player 1 tells her representative to adopt Assurance Game preferences, then Player 2 maximizes his utility by telling his representative to also maximize Assurance Game preferences. After all, representative 1 prefers defecting if representative 2 defects. Hence, if Player 2 instructs his representative to adopt preferences that suggest defecting, then he should expect representative to defect as well. The first important difference between Raub's approach and ours is related to item 2. We have ignored the issue of making SPIs Γ 𝑠 Nash equilibria of our meta game. As we have explained in Section 4 and Appendix A, we imagine that this is taken care of by additional bilateral commitment mechanisms that are not the focus of this paper. For Raub's paper, on the other hand, ensuring mutual cooperation to be stable in the new game Γ 𝑠 is arguably the key idea. Still, we could pursue the approach of the present paper even when we limit assumptions to those that consist only of a utility function. The second difference is even more important. Raub assumes that -as in the PD -the default outcome of the game (Π(Γ) in the formalism of this paper) is known. (Less significantly, he also assumes that it is known how the representatives play under assurance game preferences.) Of course, the key feature of the setting of this paper is that the underlying game Γ might be difficult (through equilibrium selection problems) and thus that the original players might be unable to predict Π(Γ). These are the reasons why we cite Raub in our section on bilateral commitment mechanisms. Arguably, Raub's paper could be seen as very early work on program equilibrium, except that he uses utility functions as a programming language for representative. In this sense, Raub's Assurance Game preferences are analogous to the program equilibrium schemes of Tennenholtz  [25] , Oesterheld  [25] , Barasz et al.  [3]  and van der Hoek et al.  [26] , ordered in increasing order of similarity of the main idea of the scheme. C PROOF OF PROPOSITION 5.2 Lemma 5.2. Let Γ = (𝐴, u), Γ ′ = (𝐴 ′ , u ′ ), Γ = ( Â, û) and Φ, Ξ : 𝐴 ⊸ 𝐴 ′ , Ψ : 𝐴 ′ ⊸ Â. (1) Reflexivity: Γ ∼ id 𝐴 Γ, where id 𝐴 : 𝐴 ⊸ 𝐴 : a ↦ → {a}. (2) Symmetry: If Γ ∼ Φ Γ ′ , then Γ ′ ∼ Φ −1 Γ. ( 3 ) Transitivity: If Γ ∼ Φ Γ ′ and Γ ′ ∼ Ψ Γ, then Γ ∼ Ψ•Φ Γ. (4) If Γ ∼ Φ Γ ′ and Φ(a) ⊆ Ξ(a) for all a ∈ 𝐴, then Γ ∼ Ξ Γ ′ . ( 5 ) Γ ∼ all 𝐴,𝐴 ′ Γ ′ , where all 𝐴,𝐴 ′ : 𝐴 ⊸ 𝐴 ′ : a ↦ → 𝐴 ′ . (6) If Γ ∼ Φ Γ ′ and Φ(a) = ∅, then Π(Γ) ≠ a with certainty. Proof. 1. By reflexivity of equality, Π(Γ) = Π(Γ) with certainty. Hence, Π(Γ) ∈ id 𝐴 (Π(Γ)) by definition of id 𝐴 . Therefore, Γ ∼ id 𝐴 Γ by definition of ∼, as claimed. 2. Γ ∼ Φ Γ ′ means that Π(Γ ′ ) ∈ Φ(Π(Γ)) with certainty. Thus, Π(Γ) ∈ {a∈𝐴 | Π(Γ ′ )∈Φ(a)} = Φ −1 (Π(Γ ′ )), where equality is by the definition of the inverse of multivalued functions. We conclude (by definition of ∼) that Γ ′ ∼ Φ −1 Γ as claimed. 3. If Γ ∼ Φ Γ ′ , Γ ′ ∼ Ψ Γ, then by definition of ∼, (i) Π(Γ ′ ) ∈ Φ(Π(Γ)) and (ii) Π( Γ) ∈ Ψ(Π(Γ ′ )) , both with certainty. The former (i) implies {Π(Γ ′ )} ⊆ Φ(Π(Γ)). Hence, Ψ(Π(Γ ′ )) = Ψ({Π(Γ ′ )}) ⊆ Ψ(Φ(Π(Γ))). With ii, it follows that Π( Γ) ∈ Ψ(Φ(Π(Γ))) with certainty. By definition, Γ ∼ Ψ•Φ Γ as claimed. 4. It is Π(Γ ′ ) ∈ Φ(Π(Γ)) ⊆ Ξ(Π(Γ)) with certainty. Thus, by definition Γ ∼ Ξ Γ ′ . 5. By definition of Π, it is Π(Γ ′ ) ∈ 𝐴 ′ with certainty. By definition of all 𝐴,𝐴 ′ , it is all 𝐴,𝐴 ′ (Π(Γ)) = 𝐴 ′ with certainty. Hence, Π(Γ ′ ) ∈ all 𝐴,𝐴 ′ (Π(Γ)) with certainty. We conclude that Γ ∼ all 𝐴,𝐴 ′ Γ ′ as claimed. 6. With certainty, Π(Γ ′ ) ∈ Φ(Π(Γ)) (by assumption). Also, with certainty Π(Γ ′ ) ∉ ∅. Hence, Φ(Π(Γ)) ≠ ∅ with certainty. We conclude that Π(Γ) ≠ a with certainty. □ We here prove Theorem 8.2. \n D EXAMPLES Throughout this section, we use the following lemma. Lemma E.1. Let Φ, Ψ be isomorphisms between Γ,Γ ′ . If Φ is (strictly) Pareto-improving, then so is Ψ. This will allow us to conclude from the existence of a Paretoimproving isomorphism Φ that there is Pareto-improving Ψ s.t. Γ ∼ Ψ Γ ′ by Assumption 7.1, even if there are multiple isomorphisms between Γ, Γ ′ . Proof. Let Γ = (𝐴, u), Γ ′ = (𝐴 ′ , u ′ ). Then for all a ∈ 𝐴, u(a) = u ′ (Ψ(a)) = u(Φ −1 (Ψ(a)) ≤ u(Φ(Φ −1 (Ψ(a)))) = u(Ψ(a)). Furthermore, if Φ is strictly Pareto-improving for some ã ∈ 𝐴, then by bijectivity of Φ, Ψ, there is a ∈ 𝐴 s.t. Φ −1 (Ψ(a)) = ã. For this a, the inequality above is strict and therefore u(a) < u(Ψ(a)). □ We start by showing that the SPI problem is in NP at all. The following algorithm can be used to determine whether there is a safe Pareto improvement: Reduce the given game Γ until it can be reduced no further to obtain some subset game Γ ′ = (𝐴 ′ , u). Then non-deterministically select injections Φ 𝑖 : 𝐴 ′ 𝑖 → 𝐴 𝑖 . If Φ = (Φ 1 , ..., Φ 𝑛 ) is (strictly) Pareto-improving (as required in Theorem 6.1), return True with the solution Γ 𝑠 defined as follows: The set of action profiles is defined as 𝐴 𝑠 = 𝑖 Φ 𝑖 (𝐴 ′ 𝑖 ). The utility functions are 𝑢 𝑠 𝑖 : 𝐴 𝑠 → R : a 𝑠 ↦ → (𝑢 𝑖 (Φ −1 1 (𝑎 𝑠 1 ), ..., Φ −1 𝑛 (𝑎 𝑠 𝑛 ))) 𝑖=1,...,𝑛 . (6) Otherwise, return False. It is easy to see that this algorithm runs in non-deterministic polynomial time. Furthermore, with Lemma E.1 it is easy to see that if this algorithm finds a solution Γ 𝑠 , that solution is indeed a safe Pareto improvement. It is left to show that if there is a safe Pareto improvement via a sequence of Assumption 7.1 and 7.2 outcome correspondences, then the algorithm indeed finds a safe Pareto improvement. To prove this fact, we prove a few simple lemmata. First, one might worry that the algorithm only ever finds sequences of outcome correspondences that start with a number of reductions and end with a single isomorphism step. Perhaps some safe Pareto improvements can only be found by considering very different sequences? The following two lemmata show that this is not an issue, i.e., that it is sufficient to consider sequences that start with a number of reductions and end in a single isomorphism step. Lemma E.2. Let Γ ∼ Φ iso Γ by Assumption 7.1 and Γ ∼ Φ red Γ by Assumption 7.2. Then there are Γ ′ , Ψ red , Ψ iso s.t. Γ ∼ Ψ red Γ ′ by Assumption 7.2, Γ ′ ∼ Ψ iso Γ by Assumption 7.1 and Ψ iso • Ψ red = Φ red • Φ iso . Intuitively, this means that isomorphism steps as per Assumption 7.1 and reduction steps as per Assumption 7.2 commute. Instead of first applying Assumption 7.1 and then Assumption 7.2 to a game, we can also apply Assumption 7.2 first and then Assumption 7.1 to obtain the same game Γ in both cases. Proof. We construct Γ ′ , Ψ red , Ψ iso as follows. First, Γ ′ = (𝐴 ′ 1 , ..., 𝐴 ′ 𝑛 , u ′ ), where 𝐴 ′ 𝑖 = (Φ iso 𝑖 ) −1 ( Ã𝑖 ) and 𝑢 ′ 𝑖 = 𝑢 𝑖 | 𝐴 ′ . Next, we define Ψ red = (Φ iso ) −1 • Φ red • Φ iso (7) and Ψ iso = Φ iso | 𝐴 ′ 1 ×𝐴 ′ 2 . (8) We now need to show that these satisfy the consequents of the lemma. First, it is Ψ iso • Ψ red = Φ iso | 𝐴 ′ 1 ×𝐴 ′ 2 • (Φ iso ) −1 • Φ red • Φ iso = Φ iso | 𝐴 ′ 1 ×𝐴 ′ 2 • (Φ iso ) −1 • Φ red • Φ iso = Φ red • Φ iso as claimed. Note that the second step uses the associativity of • on multivalued functions. The third step uses the fact that Φ iso is a single-valued bijection, which means that Φ iso • Φ iso −1 = id. Of course, Φ iso is here restricted to 𝐴 ′ 1 × 𝐴 ′ 2 , but this is not a problem, because 𝐴 ′ 𝑖 = (Φ iso 𝑖 ) −1 ( Ã𝑖 ) and à is the codomain of Φ red • Φ iso . Hence, the restriction is inconsequential. Second, we need to show that it is indeed Γ ′ ∼ Ψ iso Γ by Assumption 7.1. (Note that because Ψ iso • Ψ red = Φ red • Φ iso , it really must be Γ ′ ∼ Ψ iso Γ rather than Γ ′ ∼ Ψiso Γ for some different isomorphism Ψiso ≠ Ψ iso .) First, it is easy to show that Ψ iso decomposes into Ψ iso 1 , ..., Ψ iso 𝑛 as required because Φ iso decomposes. Further, Ψ iso is a single-valued injection because Φ iso is a single-valued bijection. It is surjective because its codomain is defined as the image of its domain. Now let (𝑎 ′ 1 , 𝑎 ′ 2 ) ∈ 𝐴 ′ 1 × 𝐴 ′ 2 . It is u ′ (a ′ ) = u(a ′ ) = û(Φ iso (a ′ )) = ũ(Φ iso (a ′ )) = ũ(Ψ iso (a ′ )), as required. Finally, we have to show that Γ ∼ Ψ red Γ ′ by Assumption 7.2. We leave this as an exercise to the reader. □ Lemma E.3. Let Γ 1 ∼ Φ 1 ... ∼ Φ 𝑘−1 Γ 𝑘 , (9) where each outcome correspondence is due to a single application of Assumption 7.1 or 7.2. Then there is a sequence Γ ′2 , ..., Γ ′𝑚 with 𝑚 ≤ 𝑘 − 1 such that Γ 1 ∼ Ψ 1 Γ ′2 ∼ Ψ 2 Γ ′3 ∼ Ψ 3 ... ∼ Ψ 𝑚−1 Γ ′𝑚 (10) all by single applications of Assumption 7.2, Γ ′𝑚 ∼ Ξ Γ 𝑘 by a single application of Assumption 7.1, and Φ 𝑘−1 • Φ 𝑘−2 • ... • Φ 1 = Ξ • Ψ 𝑚−1 • ... • Ψ 1 . (11) Proof. Start with the initial sequence of line 9. We can iteratively apply Lemma E.2 to obtain a new sequence of the same length in which one first applies only Assumption 7.2 and then only Assumption 7.1 while obtaining the same composite outcome correspondence function. We can summarize all the applications of Assumption 7.1 into a single step applying that assumption. □ A second potential worry about our algorithm is that it reduces the game completely and only then looks for a Pareto-improving isomorphism step. Perhaps in some cases one has to only partially reduce and then look for a Pareto-improving isomorphism step? The next lemma shows that the answer to this is no and that one can restrict oneself to sequences that fully reduce. Lemma E.4 shows that it is enough to consider isomorphism steps from fully reduced versions of Γ. A third worry might be that even so, elimination via Assumption 7.2 might be path-dependent and therefore we have to consider the resulting games from multiple paths. However, iterated elimination of strictly dominated strategies is known to be path-independent  [1, 19] . Proposition E.5. If there is a safe Pareto improvement for a given game, then the above algorithm applied to that game returns True. Lemma E.4. Let Γ = (𝐴, u), Γ𝑎 = ( Â𝑎 , u), Γ𝑏 = ( Â𝑏 , u) such that Â𝑏 𝑖 ⊆ Â𝑎 𝑖 ⊆ 𝐴 𝑖 for 𝑖 = 1, ..., Proof. Let us say there is a sequence of outcome correspondences as per Assumptions 7.1 and 7.2 that show Γ ∼ Φ Γ 𝑠 for Pareto-improving Φ. Then by Lemma E.3, there is Γ ′ such that Γ ∼ Ψ red Γ ′ via an arbitrary number of applications of Assumption 7.2 and Γ ′ ∼ Ψ iso Γ 𝑠 via a single application of Assumption 7.1. Because of the path-independence of iterated removal of strictly dominated strategies, Γ ′ contains (as a subset game with equal utility functions) the unique Γ 𝑟 arising from full iterated removal as per Assumption 7.2. By Lemma E.4, there is a Pareto-improving outcome correspondence Γ 𝑟 ∼ Ψiso Γ 𝑠𝑟 as per Assumption 7.2. By construction, our algorithm finds (guesses) this Pareto-improving outcome correspondence. □ Overall, we have now shown that our non-deterministic polynomial-time algorithm is correct and therefore that the SPI problem is in NP. Note that the correctness of other algorithms can be proven using very similar ideas. For example, instead of first reducing and then finding an isomorphism, one could first find an isomorphism, then reduce and then (only after reducing) test whether the overall outcome correspondence function is Paretoimproving. One advantage of reducing first is that there are fewer isomorphisms to test if the game is smaller. In particular, the number of possible isomorphisms is exponential in the number of strategies in the reduced game Γ ′ but polynomial in everything else. Hence, by implementing our algorithm deterministically, we obtain the following positive result. We now proceed to showing that the safe Pareto improvement problem is NP-hard. We will do this by reducing the subgraph isomorphism problem to the (two-player) safe Pareto improvement problem. We start by briefly describing one version of that problem here. A (simple, directed) graph is a tuple (𝑛, 𝑎 : {1, ..., 𝑛} × {1, ..., 𝑛} → B), where 𝑛 ∈ N and B {0, 1}. We call 𝑎 the adjacency function of the graph. Since the graph is supposed to be simple and therefore free of self-loops (edges from one vertex to itself), we take the values 𝑎( 𝑗, 𝑗) for 𝑗 ∈ {1, ..., 𝑛} to be meaningless. For given graphs 𝐺 = (𝑛, 𝑎),𝐺 ′ = (𝑛 ′ , 𝑎 ′ ) a subgraph isomorphism from 𝐺 to 𝐺 ′ is an injection 𝜙 : {1, ..., 𝑛} → {1, ...𝑛 ′ } such that for all 𝑗 ≠ 𝑙 𝑎( 𝑗, 𝑙) ≤ 𝑎 ′ (𝜙 ( 𝑗), 𝜙 (𝑙)). (12) In words, a subgraph isomorphism from 𝐺 to 𝐺 ′ identifies for each node in 𝐺 a node in 𝐺 ′ s.t. if there is an edge from node 𝑗 to node 𝑙 in 𝐺, there must also be an edge in the same direction between the corresponding nodes 𝜙 ( 𝑗), 𝜙 (𝑙) in 𝐺 ′ . Another way to say this is that we can remove some set of (𝑛 ′ − 𝑛) nodes and some edges from 𝐺 ′ to get a graph that is just a relabeled (isomorphic) version of 𝐺. Given two graphs 𝐺, 𝐺 ′ , the subgraph isomorphism problem consists in deciding whether there is a subgraph isomorphism 𝜙 between 𝐺, 𝐺 ′ . The problem is well-known to be NP-complete  [5, Theorem 2] . Lemma E.6. The subgraph isomorphism problem is reducible in linear time with linear increase in problem instance size to the safe Pareto improvement problem. As a consequence, the safe Pareto improvement problem is NP-hard. Proof. We conduct our proof only for the strict safe Pareto improvement problem. Reducing to the non-strict safe Pareto improvement problem is a little easier and can be done using a subset of the ideas in this proof. So take graphs 𝐺 = (𝑛, 𝑎) and Ĝ = ( n, â). We will transform these step-wise into a single game. First, we define the games Γ 𝑎 = (𝐴 1 , 𝐴 2 , 𝑢 1 , 𝑢 2 ) and Γ𝑎 = ( Â1 , Â2 , û1 , û2 ), where 𝐴 1 = 𝐴 2 = {1, ..., 𝑛}, Â1 = Â2 = {1, ..., n}, 𝑢 1 ( 𝑗, 𝑙) = 𝑢 2 ( 𝑗, 𝑙) = 𝑎( 𝑗, 𝑙) for all 𝑗, 𝑙 ∈ {1, ..., 𝑛} with 𝑗 ≠ 𝑙 and 𝑢 1 ( 𝑗, 𝑗) = 𝑢 2 ( 𝑗, 𝑗) = 2. We analogously define û1 = û2 based on â. Setting the utility functions is the main idea of the entire proof, of course, and will become clearer below. Setting the utilities 𝑢 1 ( 𝑗, 𝑗) = 𝑢 2 ( 𝑗, 𝑗) = 2 is to ensure that Pareto-improving mappings Φ between Γ 𝑎 and Γ𝑎 satisfy Φ 1 ( 𝑗) = Φ 2 ( 𝑗) for all 𝑗, and thus directly relate to subgraph isomorphisms. Next, we add dummy strategies to Γ 𝑎 , Γ𝑎 , to obtain two purposes. We want to remove exact equivalences and allow only strict Pareto improvements; and we want to remove the possibility of reducing either of these games via Assumption 7.2. In particular, we consider Γ 𝑏 as follows: 𝐴 𝑏 𝑖 = {1, ..., 2𝑛}; u 𝑏 ( 𝑗, 𝑙) = u 𝑎 ( 𝑗, 𝑙) if 𝑗, 𝑙 ∈ {1, ..., 𝑛}, u 𝑏 ( 𝑗, 𝑛+𝑗) = u 𝑏 (𝑛+𝑗, 𝑛) = (3, 3) for 𝑗 ∈ {1, .., 𝑛}, u 𝑏 ( 𝑗, 𝑙) = (−1, −1) otherwise. We define Γ𝑏 analogously, except that utilities of  (3, 3)  are to be replaced by  (4, 4) . Finally, we construct from Γ 𝑏 , Γ𝑏 a single game Γ 𝑐 . Roughly, the idea is for Γ 𝑐 to contain as subset games both Γ 𝑏 and Γ𝑏 , but to reduce to Γ 𝑏 via Assumption 7.2. We construct Γ 𝑐 thus: 𝐴 𝑐 𝑖 = ({𝐷 } × 𝐴 𝑏 𝑖 ) ∪ ({𝐶} × Â𝑏 𝑖 ) and u 𝑐 ((𝐶, â1 ), (𝐶, â2 )) = û𝑏 ( â1 , â2 ) for all â1 ∈ Â𝑏 1 , â2 ∈ Â𝑏 2 u 𝑐 ((𝐷, 𝑎 1 ), (𝐷, 𝑎 2 )) = u 𝑏 (𝑎 1 , 𝑎 2 ) for all 𝑎 1 ∈ 𝐴 𝑏 1 , 𝑎 2 ∈ 𝐴 𝑏 2 𝑢 𝑐 𝑖 ((𝐷, 𝑎 𝑖 ), (𝐶, â−𝑖 )) = 5 for all 𝑎 𝑖 ∈ 𝐴 𝑏 𝑖 , â−𝑖 ∈ Â𝑏 2 𝑢 𝑐 −𝑖 ((𝐷, 𝑎 𝑖 ), (𝐶, â−𝑖 )) = −5 for all 𝑎 𝑖 ∈ 𝐴 𝑏 𝑖 , â−𝑖 ∈ Â𝑏 2 . It is easy to show that this reduction can be computed in linear time and that it also increases the problem instance size only linearly. It is left to prove the correctness of the reduction. We start by showing that if there is a subgraph isomorphism from 𝐺 to Ĝ, then there is also a safe (strict) Pareto improvement via a sequence of outcome correspondence as per Assumptions 7.1 and 7.2. So let 𝜙 be that subgraph isomorphism. Then we need to construct a series of outcome correspondences as per Assumptions 7.1 and 7.2. First notice that Γ 𝑐 ∼ Ξ Γ 𝑐,𝐷 by Assumption 7.2, where Γ 𝑐,𝐷 is the subset game of Γ 𝑐 that contains only the strategies of type (𝐷, 𝑗) for both players. We now show that Ψ is a Pareto-improving isomorphism between Γ 𝑐,𝐷 and Γ = ( Ã1 , Ã2 , ũ1 , ũ2 ), where we define Ã1 = Ã2 = {𝐶} × (𝜙 ({1, ..., 𝑛}) ∪ { n + 𝜙 ( 𝑗) | 𝑗 = 1, ..., 𝑛}),  (13)  for 𝑖 = 1, 2 as Ψ 𝑖 (𝐷, 𝑗) = (𝐶, 𝜙 ( 𝑗)) if 𝑗 ∈ {1, ..., 𝑛} and Ψ 𝑖 (𝐷, 𝑗) = (𝐶, n +𝜙 ( 𝑗 −𝑛)) otherwise, and the utility function is simply defined as ũ𝑖 ( ã1 , ã2 ) = 𝑢 𝑖 (Ψ −1 𝑖 ( ã1 , ã2 )). Again, it will then follow from Lemma E.1 that in particular it is Γ 𝑐,𝐷 ∼ Ψ ′ Γ via Assumption 7.1 for some potentially different, but still Pareto-improving Ψ ′ . It is easy to see that Ψ 𝑖 is surjective for 𝑖 = 1, 2. From the fact that 𝜙 is injective and that 𝜙 never returns values greater than n, it follows that Ψ 𝑖 is also injective for 𝑖 = 1, 2. Finally, Ψ maintains utilities by definition: ũ𝑖 (Ψ(𝑎 1 , 𝑎 2 )) = 𝑢 𝑖 (Ψ −1 (Ψ(𝑎 1 , 𝑎 2 ))) = 𝑢 𝑖 (𝑎 1 , 𝑎 2 ). ( ) 14 With Transitivity, it is left to show that Ψ is Pareto-improving for the original players, i.e., for u 𝑐 . For this we distinguish a number of different cases. If 𝑗, 𝑙 ∈ {1, ..., 𝑛} and 𝑗 ≠ 𝑙, then for 𝑖 = 1, 2 The cases ( 𝑗, 𝑙) ∈ {𝑛 + 1, ..., 2𝑛} × {1, ..., 𝑛} work analogously. This concludes our proof that if a graph isomorphism exists, there also exists a strict SPI as per Assumptions 7.1 and 7.2. It is left to prove that if there is a safe Pareto improvement for Γ 𝑐 , then there also exists a graph isomorphism. So let Γ 𝑐 ∼ Ξ Γ for some Γ, via some Pareto-improving outcome correspondence function Ξ. By our earlier results (Proposition E.5), this means that there is a sequence of outcome correspondences that first fully reduces Γ to Γ 𝑐,𝐷 and then applies Assumption 7.1 to get Γ 𝑐,𝐷 ∼ Ψ Γ via some Pareto-improving Ψ. To construct a subgraph isomorphism, we must now realize some facts about the structure of Ψ that all follow from Ψ being utility-increasing: (1) Ψ ({𝐷 } × {1, ..., 2𝑛}) 2 ⊆ ({𝐶} × {1, ..., 2 n}) 2 : For Ψ to be strict, there has to be some overlap, i.e., there has to be (𝐷, 𝑗) s. By an analogous argument it can further be shown that Ψ 𝑖 (𝐷, 𝑗) ∈ {𝐶} × {1, ..., 2 n} for all 𝑗 = 1, ..., 2𝑛. (2) For every 𝑗 ∈ {1, ..., 𝑛}, it is Ψ 𝑖 (𝐷, 𝑗) ∈ {𝐶} × {1, ..., n} for 𝑖 = 1, 2. That is, Ψ 𝑖 maps the \"non-dummy\" strategies (which correspond to nodes in the original graph) onto \"nondummy\" strategies. We will show this by showing the contrapositive, i.e., that if this were not the case, then Ψ would not be Pareto-improving. < (0, 0) ≤ u 𝑐 ((𝐷, 𝑗), (𝐷, 𝑙)). (3) For all 𝑗 ∈ {1, ..., 𝑛} and 𝑖 ∈ {1, ..., 𝑛} it is Ψ 𝑖 (𝐷, 𝑗 + 𝑛) = Ψ −𝑖 (𝐷, 𝑗) + n, where addition is defined to operate only on the second entry like the subtraction defined above. We again prove the contrapositive, i.e., if this is not true then Ψ is not Pareto-improving. So let us assume that there is 𝑗 ∈ {1, ..., 𝑛} and 𝑖 ∈ {1, ..., 𝑛} s.t. Ψ 𝑖 (𝐷, 𝑗 + 𝑛) ≠ Ψ −𝑖 (𝐷, 𝑗). Then it would be u 𝑐 (Ψ 𝑖 (𝐷, 𝑗 + 𝑛), Ψ −𝑖 (𝐷, 𝑗)) ≤ (2, 2) < (3, 3) = u 𝑐 ((𝐶, 𝑗 + 𝑛), (𝐶, 𝑗)). (4) Finally, we prove that Ψ 1 = Ψ 2 . We first show that for 𝑗 ∈ {1, ..., 𝑛} it is Ψ 1 (𝐷, 𝑗) = Ψ 2 (𝐷, 𝑗). We do this again by showing the contrapositive.  = n + Ψ 1 (𝐷, 𝑗) = Item 3 Ψ 2 (𝐷, 𝑛 + 𝑗), where the middle equality is due to the equality we have already proven. Given these, we can define our graph isomorphism as 𝜙 : {1, ..., 𝑛} → {1, ..., n} : 𝑗 ↦ → 𝜋 2 (Ψ 1 (𝐷, 𝑗)),  (15)  where 𝜋 2 just maps pairs (𝐶, 𝑗) onto the second entry 𝑗. This is well-defined because of item 2. Note that because Ψ is an injection, so is 𝜙. Hence, 𝜙 is a subgraph isomorphism as desired. □ F PROOF OF LEMMA 9.3 Lemma 9.3. For a given 𝑛-player game Γ and payoff vector y ∈ R 𝑛 , it can be decided by linear programming and thus in polynomial time whether y is Pareto-optimal in C(Γ). For an introduction to linear programming, see, e.g., Schrijver  [23] . In short, a linear program is a specific type of constrained optimization problem that can be solved efficiently. Algorithm 1 : 4 . 14 An algorithm for deciding the strict perfectcoordination SPI problem.Data: Game Γ, set supp(Π(Γ) 1 for a ∈ supp(Π(Γ)) do 2 if u(a) is Pareto-suboptimal within C(Γ) Assuming supp(Π(Γ)) is known and that Assumption 7.1 holds, it can be decided in polynomial time whether there is a strict perfect-coordination SPI. \n Theorem 9 . 7 . 97 Make Assumption 7.1. Let Γ be a two-player game. Let y ∈ R 2 be some potentially unsafe Pareto improvement onE [u(Π(Γ))]. For 𝑖 = 1, 2, let 𝑥 min/max 𝑖 = min/max 𝑢 𝑖 (supp(Π(Γ))). Then: A) Ifthere is some element in C(Γ) which Pareto-dominates all of supp(Π(Γ)) and if y is Pareto-dominated by an element of at least one of the following three sets: • 𝐿 1 the line segment between 𝜋 1 (𝑥 min 1 , PF(C(Γ)) and 𝜋 1 (𝑥 max 1 , PF(C(Γ)); • 𝐿 2 the segment of the curve PF(C(Γ)) between 𝜋 1 (𝑥 max 1 , PF(C(Γ)))) and 𝜋 2 (𝑥 max 2 , PF(C(Γ)))); • 𝐿 3 the line segment between 𝜋 2 (𝑥 max 2 , PF(C(Γ)) and 𝜋 2 (𝑥 min 2 , PF(C(Γ)). \n Figure 1 : 1 Figure 1: This figure illustrates Theorem 9.7, Case A. \n Figure 2 : 2 Figure 2: This figure illustrates Theorem 9.7, Case B. \n Algorithm 2 : 2 A program equilibrium implementation of an SPI Γ 𝑠 of Γ. Data: Everybody's source code c, my index 𝑖 1 for 𝑗 ∈ {1, ..., 𝑛} − {𝑖} do 2 if 𝑐 𝑗 ≠ 𝑐 𝑖 then 3 Play minimax (𝑖, 𝑗); 4 Play Π 𝑖 (Γ 𝑠 ); Proposition A.2. Let Γ be a game and let Γ 𝑠 be an SPI on Γ. Let c be the program profile consisting only of Algorithm 2 for each player. Assume that Π(Γ) guarantees each player at least threat point utility in expectation. Then c is a program equilibrium and apply(c) = Π(Γ 𝑠 ). \n 𝑢 𝑐𝑖 ((𝐷, 𝑗), (𝐷, 𝑙)) = 𝑎( 𝑗, 𝑙) ≤ â(𝜙 ( 𝑗), 𝜙 (𝑙))= û𝑐 𝑖 ((𝐶, 𝜙 ( 𝑗)), (𝐶, 𝜙 (𝑙))) = û𝑐 𝑖 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑙)). For 𝑗 ∈ {1, ..., 𝑛}, it is u 𝑐 ((𝐷, 𝑗), (𝐷, 𝑗)) = (2, 2) = û𝑐 ((𝐶, 𝜙 ( 𝑗)), (𝐶, 𝜙 ( 𝑗))) = û𝑐 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑗)).For 𝑗, 𝑙 ∈ {𝑛 + 1, ..., 2𝑛}, it isu 𝑐 ((𝐷, 𝑗), (𝐷, 𝑙)) = u 𝑏 ( 𝑗, 𝑙) = (−1, −1) = û𝑏 ( n + 𝜙 ( 𝑗 − 𝑛), n + 𝜙 (𝑙 − 𝑛)) = u 𝑐 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑙)).If ( 𝑗, 𝑙) ∈ {1, ..., 𝑛} × {𝑛 + 1, ..., 2𝑛} and 𝑙 = 𝑗 + 𝑛, then u 𝑐 ((𝐷, 𝑗), (𝐷, 𝑙)) = (2, 2)< (3, 3) = u 𝑐 ((𝐶, Φ( 𝑗)), (𝐶, Φ( 𝑗) + n)) = u 𝑐 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑙)).If ( 𝑗, 𝑙) ∈ {1, ..., 𝑛} × {𝑛 + 1, ..., 2𝑛} but 𝑙 ≠ 𝑗 + 𝑛, thenu 𝑐 ((𝐷, 𝑗), (𝐷, 𝑙)) = u 𝑏 ( 𝑗, 𝑙) = (−1, −1)= û𝑏 (𝜙 ( 𝑗), n + 𝜙 (𝑙 − 𝑛))= u 𝑐 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑙)). \n 5 < 5 t. Ψ 𝑖 (𝐷, 𝑗) ∈ {𝐶} × {1, ..., 2 n}. But for Ψ to be Paretoimproving for 𝑖, it has to be for all (𝐷, 𝑙) with 𝑙 = 1, ..., 2𝑛 the case that Ψ −𝑖 (𝐷, 𝑙) ∈ {𝐶} × {1, ..., 2 n} since otherwise it would be 𝑢 𝑖 (Ψ 𝑖 (𝐷, 𝑗), Ψ −𝑖 (𝐷, 𝑙)) = −𝑢 𝑖 ((𝐷, 𝑗), (𝐷, 𝑙)). \n So assume there is 𝑗 ∈ {1, ..., 𝑛} and 𝑖 ∈ {1, 2} with Ψ 𝑖 (𝐷, 𝑗) ∈ {𝐶} × { n + 1, ..., 2 n}. Because Ψ −𝑖 is injective, there is an 𝑙 ∈ {1, ..., 𝑛} s.t. Ψ −𝑖 (𝐷, 𝑙) ≠ Ψ 𝑖 (𝐷, 𝑗) − n, where we define (𝐷, 𝑘) − n (𝐷, 𝑘 − n). Then for that 𝑙 it is u(Ψ 𝑖 (𝐷, 𝑗), Ψ −𝑖 (𝐷, 𝑙)) = (−1, −1) \n 1 ( 1 For all 𝑗, 𝑙 ∈ {1, ..., 𝑛} with 𝑗 ≠ 𝑙 it isâ(𝜙 ( 𝑗), 𝜙 (𝑙)) = û𝑎 1 (𝜙 ( 𝑗), 𝜙 (𝑙)) = û𝑐 1 ((𝐶, 𝜙 ( 𝑗)), (𝐶, (𝜙 (𝑙)))) = Item 1 û𝑐 1 (Ψ 1 (𝐷, 𝑗), Ψ 1 (𝐷, 𝑙)) = Item 4 û𝑐 1 (Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑙)) ≥ 𝑢 𝑐 1 ((𝐷, 𝑗), (𝐷, 𝑙)) = 𝑢 𝑎 𝑗, 𝑙) =𝑎( 𝑗, 𝑙). \n Table 1 : 1 The Demand Game \n Table 2 : 2 A safe Pareto improvement for the Demand Game 4, \n Assumptions 7.1 and 7.2 we can finally state our example SPIs formally: Our proofs are in Appendix D. Proposition (Example) 7.1. Let Γ be the Prisoner's Dilemma and Γ 𝑠 = (𝐴 𝑠 1 , 𝐴 𝑠 2 , 𝑢 𝑠 1 , 𝑢 𝑠 2 ) be any subset game of Γ with 𝐴 𝑠 1 = 𝐴 𝑠 2 = {Cooperate}. Then under Assumption 7.2, Γ 𝑠 is a strict SPI on Γ. Proposition (Example) 7.2. Let Γ be the Demand Game of Table 1 and Γ 𝑠 be the subset game described in Table 2. Under Assumptions 7.1 and 7.2, Γ 𝑠 is an SPI on \n , Sect. 16.4]. Theorem 8.2. The (strict) SPI decision problem is NP-complete, even for 2-player games. Proposition 8.3. For games Γ with |𝐴 1 | + ... + |𝐴 𝑛 | = 𝑚 that can be reduced (via iterative application of Assumption 7.2) to a game Γ ′ with |𝐴 ′ 1 | + ... + |𝐴 ′ 𝑛 | = 𝑙, the (strict) SPI decision problem can be solved in 𝑂 (𝑚 𝑙 ). \n 1 1 , ..., 𝑎 𝑙 1 1 }, ..., {𝑎 1 𝑛 , ..., 𝑎 𝑙 𝑛 𝑛 }, u) be any game. Let Γ ′ be a perfect-coordination SPI on Γ. Then we can define u 𝑒 with values in C(Γ) such that under Assumption 7.1 the game Γ 𝑠 = Â1 { â1 1 , ..., â𝑙 1 1 }, ..., Â𝑛 { â1 𝑛 , ..., â𝑙 𝑛 𝑛 }, û : ( â𝑖 1 1 , ..., â𝑖 𝑛 𝑛 ) ↦ → u(𝑎 𝑖 1 1 , ..., 𝑎 𝑖 𝑛 𝑛 ), u 𝑒 \n Table 3 : 3 Assurance Game preferences for the Prisoner's Dilemma Proof. By inspection of Algorithm 2, we see that exec(c) = Π(Γ 𝑠 ). It is left to show that c is a Nash equilibrium. So let 𝑖 be any player and 𝑐 ′ 𝑖 ∈ PROG 𝑖 − {𝑐 𝑖 }. We need to show that E 𝑢 𝑖 (exec(c −𝑖 , 𝑐 ′ 𝑖 )) ≤ E [𝑢 𝑖 (exec(c))]. Again, by inspection of c, exec(c −𝑖 , 𝑐 ′ 𝑖 ) is the threat point of Player 𝑖. Hence, E 𝑢 𝑖 (exec(c −𝑖 , 𝑐 ′ 𝑖 Player 2 Cooperate Defect Cooperate 4, 4 1, 3 Player 1 Defect 3, 1 2, 2 \n Proposition (Example) 7.1. Let Γ be the Prisoner's Dilemma and Γ 𝑠 = (𝐴 𝑠 1 , 𝐴 𝑠 2 , 𝑢 𝑠 1 , 𝑢 𝑠 2 ) be any subset game of Γ with 𝐴 𝑠 1 = 𝐴 𝑠 2 = {Cooperate}. Then under Assumption 7.2, Γ 𝑠 is a strict SPI on Γ.Proof. By applying Assumption 7.2 twice and Transitivity once, Γ ∼ Φ Γ−{Cooperate}, where Φ(Defect, Defect) = {(Defect, Defect)} and Φ(𝑎 1 , 𝑎 2 ) = ∅ for all (𝑎 1 , 𝑎 2 ) ≠ (Defect, Defect). By Lemma 5.2.5, we further obtain Γ − {Cooperate} ∼ all Γ 𝑠 , where Γ 𝑠 is as described in the proposition. Hence, by transitivity, Γ ∼ all•Φ Γ 𝑠 . It is easy to verify that the function all • Φ is Pareto-improving. Proposition (Example) 7.2. Let Γ be the Demand Game of Table1and Γ 𝑠 be the subset game described in Table2. Under Assumptions 7.1 and 7.2, Γ 𝑠 is an SPI on Γ. Further, if 𝑃 (Π(Γ)=(DM, DM)) > 0, Γ 𝑠 is a strict SPI.Proof. Let (𝐴 1 , 𝐴 2 , 𝑢 1 , 𝑢 2 ) = Γ. We can repeatedly apply Assumption 7.2 to eliminate from Γ the strategies DL and RL for both players. We can then apply Lemma 5.2.3 (Transitivity) to obtain 𝐺 ∼ Φ Ĝ = ({DM, RM}, {DM, RM}, 𝑢 1 , 𝑢 2 ), whereΦ(𝑎 1 , 𝑎 2 ) = {(𝑎 1 , 𝑎 2 )} if 𝑎 1 , 𝑎2 ∈ {DM, RM} Next, by Assumption 7.1, Γ ∼ Ψ Γ 𝑠 , where Ψ 𝑖 (DM) = DL and Ψ 𝑖 (RM) = RL for 𝑖 = 1, 2. We can then apply Lemma 5.2.3 (Transitivity) again, to infer Γ ∼ Ψ•Φ Γ 𝑠 . It is easy to verify that for all (𝑎 1 , 𝑎 2 ) ∈ 𝐴 1 × 𝐴 2 , it is for all (𝑎 𝑠 1 , 𝑎 𝑠 2 ) ∈ Ψ(Φ(Γ 𝑠 )) the case that u(𝑎 𝑠 1 , 𝑎 𝑠 2 ) ≥ u(𝑎 1 , 𝑎 2 ). □ E PROOF OF THEOREM 8.2 □ D.2 Proof of Proposition (Example) 7.2 ∅ otherwise . (5) D.1 Proof of Proposition (Example) 7.1 \n 𝑛. If there is a subset game Γ𝑎 = ( Ã𝑎 , ũ𝑎 ) of Γ such that Γ𝑎 ∼ Φ Γ𝑎 by Assumption 7.1, then Γ𝑏 ∼ Φ | Â𝑏 Γ𝑏 , Note that if the correspondence function Φ is Pareto-improving, so is Φ| Â𝑏 . where Γ𝑏 = (Φ 1 ( Â𝑏 1 ), ..., Φ 𝑛 ( Â𝑏 𝑛 ), ũ𝑎 ). \n Proposition 8.3. For games Γ with |𝐴 1 | + ... + |𝐴 𝑛 | = 𝑚 that can be reduced (via iterative application of Assumption 7.2) to a game Γ ′ with |𝐴 ′ 1 | + ... + |𝐴 ′ 𝑛 | = 𝑙, the (strict) SPI decision problem can be solved in 𝑂 (𝑚 𝑙 ). \n So assume Ψ 1 (𝐷, 𝑗) ≠ Ψ 2 (𝐷, 𝑗). Recall that by item 2, it is Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑗) ∈ {𝐶}×{1, ..., n}. Hence, u(Ψ 1 (𝐷, 𝑗), Ψ 2 (𝐷, 𝑗)) ≤ (1, 1) < (3, 3) = u((𝐷, 𝑗), (𝐷, 𝑗)),contradicting the assumption that Ψ is Pareto-improving. Finally, for 𝑗 ∈ {1, ..., 𝑛} it is Ψ 1 (𝐷, 𝑛 + 𝑗) = Item 3 n + Ψ 2 (𝐷, 𝑗) \n\t\t\t Proc. of the 20th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2021), U. Endriss, A. Nowé, F. Dignum, A. Lomuscio (eds.), May 3-7, 2021, Online. © 2021 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.", "date_published": "n/a", "url": "n/a", "filename": "safeAAMAS21.tei.xml", "abstract": "A set of players delegate playing a game to a set of representatives, one for each player. We imagine that each player trusts their respective representative's strategic abilities. Thus, we might imagine that per default, the original players would simply instruct the representatives to play the original game as best as they can. In this paper, we ask: are there safe Pareto improvements on this default way of giving instructions? That is, we imagine that the original players can coordinate to tell their representatives to only consider some subset of the available strategies and to assign utilities to outcomes differently than the original players. Then can the original players do this in such a way that the payoff is guaranteed to be weakly higher than under the default instructions for all the original players? In particular, can they Pareto-improve without probabilistic assumptions about how the representatives play games? In this paper, we give some examples of safe Pareto improvements. We prove that the notion of safe Pareto improvements is closely related to a notion of outcome correspondence between games. We also show that under some specific assumptions about how the representatives play games, finding safe Pareto improvements is NP-complete.", "id": "17c5d2336d639f824f749718b8da1054"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stefan Schubert", "Lucius Caviola", "Nadira S Faber"], "title": "the psychology of existential Risk: Moral Judgments about Human extinction", "text": "The ever-increasing powers of technology can be used for good and ill. In the 21 st century, technological advances will likely yield great benefits to humanity, but experts warn that they will also lead to growing risks of human extinction  [1] [2] [3] [4]  . The risks stem both from existing technologies such as nuclear weapons, as well as emerging technologies such as synthetic biology and artificial intelligence  5  . A small but growing number of research institutes, such as the University of Oxford's Future of Humanity Institute and the University of Cambridge's Centre for the Study of Existential Risk, are studying these risks and how to mitigate them. Yet besides them, relatively small resources are explicitly devoted to reducing these risks. Here, we study the general public's views of the badness of human extinction. We hypothesize that most people judge human extinction to be bad. But how bad do they find it? And why do they find it bad? Besides being highly policy-relevant, these questions are central for humanity's understanding of itself and its place in nature. Human extinction is a pervasive theme in myths and religious writings  [6] [7] [8] [9] [10]  . One view is that human extinction is bad primarily because it would harm many concrete individuals: it would mean the death of all currently living people. On this view, human extinction is a very bad event, but it is not much worse than catastrophes that kill nearly all currently living people-since the difference in terms of numbers of deaths would be relatively small. Another view is that the human extinction is bad primarily because it would mean that the human species would go extinct and that humanity's future would be lost forever. On this view, human extinction is uniquely bad: much worse even than catastrophes killing nearly everyone, since we could recover from them and re-build civilization. Whether extinction is uniquely bad or not depends on which of these considerations is the stronger: the immediate harm, or the long-term consequences. Here is one way to pit these considerations against each other. Consider three outcomes: no catastrophe, a catastrophe killing 80% (near-extinction), and a catastrophe killing 100% (extinction). According to both considerations, no catastrophe is the best outcome, and extinction the worst outcome. But they come apart regarding the relative differences between the three outcomes. If the immediate harm is the more important consideration, then the first difference, between no catastrophe and near-extinction, is greater than the second difference, between near-extinction and extinction. That is because the first difference is greater in terms of numbers of harmed individuals. On the other hand, if the long-term consequences are more important, then the second difference is greater. The first difference compares two non-extinction outcomes, whereas the second difference compares a non-extinction outcome with an extinction outcome-and only the extinction outcome means that the future would be forever lost. This thought-experiment was conceived by the well-known philosopher Derek Parfit  11  (we have adapted the three outcomes slightly; see the Methods section). Parfit argued that most people would find the first difference to be greater, but he himself thought that the second difference is greater. Many other philosophers and other academics working to reduce the risk of human extinction agree with Parfit  [12] [13] [14] [15]  . On their view, the badness of human extinction is greatly dependent on how long the future would otherwise be, and what the quality of future people's lives would be. As the philosopher Nick Bostrom notes, predictions about the long-term future have often been left to theology and fiction, whilst being neglected by science  16  . However, in recent years, researchers have tried to assess what the long-term future may be like. They argue that if humanity does not go extinct, then the future could be both extraordinarily long and extraordinarily good, involving much greater quality of life than the current world. For instance, Nick Bostrom argues that a conservative estimate of humanity's future potential is \"at least 10 16 human lives of normal duration\", which could \"be considerably better than the average contemporary human life, which is so often marred by disease, poverty  [and]  injustice\"  17  . He goes on to argue that less conservative estimates would yield even greater numbers, and a drastically improved quality of life. The argument is that if humanity develops to a sufficiently high technological level, then it will either cause its own extinction via misuse of powerful technologies, or use those technological powers to greatly improve the level of well-being. Furthermore, they argue, based on the view that new happy people coming into existence is morally valuable  11  , that it is of paramount moral importance to make sure that we realize our future potential, and prevent human extinction. While philosophers have discussed the ethics of human extinction for some time, the general public's views on this matter has not received much study. There are some studies on perceptions of risk of extinction, however. Two studies found that a slight majority do not think that humanity will go extinct, and that most of those who thought that it would go extinct thought that would happen at least 500 years into the future  18, 19  . There is also a related literature on catastrophic risk in general, focusing primarily on non-extinction catastrophes. For instance, it has been argued that the fact that people use the availability heuristic-they focus on risks which have salient historical examples-leads to a neglect of new types of risks and risks of major catastrophes (which are rare, and therefore less psychologically available)  20  . Similarly, it has been argued that the fact that risk mitigation is a public good leads to under-investment, since it means that it is not possible to exclude free riders from benefiting from it  21  . On specific risks, there is a literature on the psychology of climate change showing that people fail to act to mitigate climate change because they engage in temporal discounting  22, 23  and motivated reasoning about its severity  24  , and because of psychological distance  25  (e.g., temporal and social distance). However, to date there have been no studies on how laypeople reason about the moral aspect of human extinction: how bad it would be. Is the extinction of our own species something people care about? Do they recognize it as being fundamentally different in quality from other catastrophes? And if so, why? \n Results \n Study 1. In Study 1 (US sample, n = 183, mean age 38.2, 50.81% female), we studied the general public's judgments of the badness of human extinction. A large majority of the participants (78.14%, 143/183 participants) found human extinction to be bad on a binary question (bad vs. not bad), and we got similar results on a seven-point scale (1 = definitely not bad, 4 = midpoint, 7 = definitely bad; M = 5.61; SD = 2.11). Participants also felt strongly that human extinction needs to be prevented (1 = not at all, 4 = midpoint, 7 = very strongly; M = 6.01, SD = 1.65), that they have a moral obligation to prevent it (1 = definitely no, 4 = midpoint, 7 = definitely yes; M = 5.69, SD = 1.86), and that funding work to reduce the risk of human extinction is more important than funding other areas of government, such as education, health care and social security (1 = much less important to fund work to reduce the risk of human extinction, 4 = midpoint, 7 = much more important; M = 5.43, SD = 1.72). Participants believed that provided that humanity will not go extinct, the future is going to be roughly as good as the present (1 = much worse than the present world, 4 = about as good as the present world, 7 = much better than the present world; M = 4.48, SD = 1.57), and the better they thought the future would be, the worse they considered extinction to be (r = 0.51, P < 0.001), as measured by the seven-point scale. Similarly, more optimistic  26  participants judged extinction to be worse (r = 0.32, P < 0.001). Participants' responses to the question whether the world gets better if a happy person comes into existence were close to the midpoint (1 = definitely not better, 4 = midpoint, 7 = definitely better; M = 4.45, SD = 1.73), and people who thought that that would make the world better were more likely (r = 0.22, P = 0.003) to find extinction bad. For further details about the results, see Supplementary Materials. \n Study 2a. Having thus observed that people do find human extinction bad, we turned to studying whether they find it uniquely bad relative to non-extinction catastrophes in Study 2a (pre-registered at https://osf.io/hj2n4; British sample). Participants (n = 1,251, mean age 36.6, 35.33% female) were randomly divided into a control condition and four experimental conditions: \"the animals condition\", \"the \"sterilization condition\", \"the salience condition\" and \"the utopia condition\" (see below for explanations of the manipulations). Participants in the control condition (257 participants) were presented with the three outcomes described above-no catastrophe, a catastrophe killing 80%, and a catastrophe killing 100%-and were asked how they would rank them from best to worst. As Parfit expected, a large majority (82.88%, 213/257 participants, cf. Fig.  1 ) ranked no catastrophe as the best outcome and 100% dying as the worst outcome. However, this was just a preliminary question: as per the discussion above, what we were primarily interested in was which difference participants that gave the expected ranking found greater: the first difference (meaning that extinction is not uniquely bad) or the second difference (meaning that extinction is uniquely bad). (Recall that the first difference was the difference between no catastrophe and a catastrophe killing 80%, and the second difference the difference between a catastrophe killing 80% and a catastrophe killing 100%.) We therefore asked participants who gave the expected ranking (but not the other participants) which difference they judged to be greater. We found that most people did not find extinction uniquely bad: only a relatively small minority (23.47%, 50/213 participants) judged the second difference to be greater than the first difference. As stated, we included four experimental conditions aiming to explain these results. We thought that one reason why participants do not find extinction uniquely bad in the control condition is that they feel strongly for the victims of the catastrophes. Therefore, they focus on the immediate suffering and death that the catastrophes cause, which leads them to judge the difference between no one dying and 80% dying to be greater than the difference between 80% dying and 100% dying. To test this hypothesis, we included two conditions designed to trigger a weaker focus on the immediate harm. First, we included a condition where the catastrophes affected an animal species (zebras) rather than humans (\"the animals condition\"; otherwise identical to the control condition; 246 participants). (We chose zebras because zebra extinction would likely have small effects on humans; in contrast to extinction of, for example, pigs or dogs.) We hypothesized that people focus less on the immediate harm that the catastrophes cause if the catastrophes affect animals rather than humans  27  . Second, we included a condition where the catastrophes led to 80%/100% of the world's population being unable to have children, rather than getting killed (\"the sterilization condition\"; otherwise identical to the control condition; 252 participants). We hypothesized that people would focus less strongly on the immediate harm that the catastrophes cause if they lead to sterilization rather than death. Thus, we hypothesized that a greater share of the participants who gave the expected ranking would find extinction uniquely bad in the animals condition and the sterilization condition than in the control condition. We found, first, that a large majority ranked no catastrophe as the best outcome and 100% dying as the worst outcome (the expected ranking) both in the animals condition (89.84%, 221/246 participants) and the sterilization condition (82.54%, 208/252 participants). Subsequently, we found that our hypotheses were confirmed. The proportion of the participants who gave the expected ranking that found extinction uniquely bad was significantly larger (χ 2 (1) = 8.82, P = 0.003) in the animals condition (44.34%, 98/221 participants) than in the control condition (This means that they found the difference, in terms of badness, between a catastrophe killing 80% and a catastrophe killing 100% to be greater than the difference between no catastrophe and a catastrophe killing 80%.) Laypeople consistently did not find extinction uniquely bad in the control condition (Control), but did so in a scenario where the future would be very long and good conditional on survival (Utopia). The animals condition (Animals), sterilization condition (Sterilization) and salience condition (Salience) yielded in-between results. People explicitly devoted to existential risk reduction (Existential risk mitigators) consistently found extinction uniquely bad. www.nature.com/scientificreports www.nature.com/scientificreports/ (23.47%, 50/213 participants). Similarly, the proportion of the participants who gave the expected ranking that found extinction uniquely bad was significantly larger (χ 2 (1) = 23.83, P < 0.001) in the sterilization condition (46.63%, 97/208 participants) than in the control condition (23.47%, 50/213 participants). We had another hypothesis for why control condition participants do not find extinction uniquely bad, namely that they neglect the long-term consequences of the catastrophes. To test this hypothesis, we included a condition where we made the long-term consequences salient (\"the salience condition\"; 248 participants). This condition was identical to the control condition, with the exception that we added a brief text explicitly asking the participants to consider the long-term consequences of the three outcomes. It said that if humanity does not go extinct (including if it suffers a non-extinction catastrophe, from which it can recover) it could go on to a long future, whereas that would not happen if humanity went extinct (see the Methods section for the full vignette). We also wanted to know whether participants see empirical information about the quality of the future as relevant for their judgments of the badness of extinction. Does it make a difference how good the future will be? We therefore included a maximally positive scenario, the \"utopia condition\" (248 participants), where it was said that provided that humanity does not go extinct, it \"goes on to live for a very long time in a future which is better than today in every conceivable way\". It was also said that \"there are no longer any wars, any crimes, or any people experiencing depression or sadness\" and that \"human suffering is massively reduced, and people are much happier than they are today\" (in the scenario where 80% die in a catastrophe, it was said that this occurred after a recovery period; see the Methods section for the full text). Conversely, participants were told that if 100% are killed, then \"no humans will ever live anymore, and all of human knowledge and culture will be lost forever. \" We hypothesized that both of these manipulations would make more participants judge extinction to be uniquely bad compared with the control condition. We found again that a large majority ranked no catastrophe as the best outcome and 100% dying as the worst outcome (the expected ranking) both in the salience condition (77.82%, 193/248 participants) and the utopia condition (86.69%, 215/248 participants). Subsequently, we found that our hypotheses were confirmed. The proportion of the participants who chose the expected ranking that found extinction uniquely bad was significantly larger (χ 2 (1) = 29.90, P < 0.001) in the salience condition (50.25%, 97/193 participants) than in the control condition (23.47%, 50/213 participants). Similarly, the proportion of the participants who chose the expected ranking that found extinction uniquely bad was significantly larger (χ 2 (1) = 30.30, P < 0.001) in the utopia condition (76.74%, 165/215 participants) than in the control condition (23.47%, 50/213 participants). We also found that there was a significant difference between the utopia condition and the salience condition (χ 2 (1) = 29.90, P < 0.001). Our interpretation of these results is as follows. The utopia manipulation effectively does two things: it highlights the long-term consequences of the outcomes, and it says that unless humanity goes extinct, those consequences are going to be extraordinarily good. The salience manipulation only highlights the long-term consequences. Thus, we can infer that merely highlighting the long-term consequences make people more likely to find extinction uniquely bad, and that adding that the long-term future will be extraordinarily good make them still more likely to find extinction uniquely bad. Lastly, we found that across all conditions, the more cognitively reflective the participants were (as measured by the Cognitive Reflection Test  28  ), the more likely they were to judge extinction to be uniquely bad (Exp(B) = 0.15, P = 0.01, Odds ratio = 1.6). In conclusion, we find that people do not find extinction uniquely bad when asked without further prompts, and have identified several reasons why that is. As evidenced by the animals and the sterilization conditions, they focus on the immediate harm that the catastrophes cause, because they feel strongly for the victims of the catastrophes-and on that criterion, near-extinction is almost as bad as extinction. As evidenced by the salience condition, they neglect the long-term consequences of the outcomes. We also find that participants' empirical beliefs about the quality of the future make a difference: telling participants that the future will be extraordinarily good makes them significantly more likely to find extinction uniquely bad. \n Study 2b. To find out whether these results would hold up with different demographics, we aimed to replicate them using a sample of the US general public (pre-registered at https://osf.io/8amxs; N = 855, mean age 36.85, 48.65% female) in Study 2b. We found again that large majorities ranked no catastrophe as the best outcome and 100% dying as the worst outcome (the expected ranking) in the control condition (87.80%, 144/164 participants), the animals condition (92.44%, 159/172 participants), the sterilization condition (91.62%, 153/167 participants), the salience condition (83.05%, 147/177 participants) and the utopia condition (89.71%, 157/175 participants). And again we found that only a small minority of the participants who chose the expected ranking judged extinction to be uniquely bad in the control condition (18.75%, 27/144 participants). The proportion of the participants who chose the expected ranking who found extinction uniquely bad was significantly larger in the animals condition (34.59%, 55/159 participants; χ 2 (1) = 8.82, P = 0.003), the salience condition (39.45%, 58/147 participants; χ 2 (1) = 14.10, P < 0.001) and the utopia condition (66.88%, 105/157 participants; χ 2 (1) = 68.72, P < 0.001) than in the control condition. We also again found a significant difference between the utopia condition and the salience condition (χ 2 (1) = 21.868, P < 0.001). However, in the sterilization condition, only 28.75% (44/153 participants) of the participants who chose the expected ranking found extinction uniquely bad, which meant that the difference with the control condition was not significant on the 0.05-level (χ 2 (1) = 3.55, P = 0.059). Lastly, we found again that (across all conditions) the more cognitively reflective the participants were (as measured by the Cognitive Reflection Test), the more likely they were to judge extinction to be uniquely bad (Exp(B) = 0.21, P = 0.005, Odds ratio = 1.2). \n Study 2c. To further test the robustness of our findings across different demographics, we conducted Study 2c as another replication, this time using a sample of University of Oxford students (N = 196, mean age 24.27, 61% (2019) 9:15100 | https://doi.org/10.1038/s41598-019-50145-9 www.nature.com/scientificreports www.nature.com/scientificreports/ female). We only included the control and the utopia conditions. We found again that most participants ranked no catastrophe as the best outcome and 100% dying as the worst outcome (the expected ranking) both in the control condition (65.7%, 65/99 participants) and the utopia condition (84.5%, 82/97 participants). We then found again that a minority of the participants who chose the expected ranking found extinction to be uniquely bad in the control condition (36.92%, 24/65 participants), though this minority was slightly larger than in the two samples of the general public (cf. Fig.  1 ). We also found again that the proportion of the utopia condition participants who chose the expected ranking that found extinction uniquely bad (76.83%, 63/82 participants) was significantly larger (χ 2 (1) = 22.28, P < 0.001) than in the control condition. (These findings were further supported by five supplementary studies; see Supplementary Materials). \n Study 3. In Studies 2a to 2c, we thus found that when asked without further prompts, laypeople do not find extinction uniquely bad. In Study 3 (N = 71, mean age 30.52, 14.00% female) we aimed to test whether people devoted to preventing human extinction (existential risk mitigators) judge human extinction to be uniquely bad already when asked without further prompts. (Existential risks also include risks that threaten to drastically curtail humanity's potential  [12] [13] [14] [15]  , without causing it to go extinct, but we focus on risks of human extinction.) This would support the validity of our task by demonstrating a link between participants' responses and behavior in the real world. We recruited participants via the Effective Altruism Newsletter and social media groups dedicated to existential risk reduction, and only included respondents who put down reducing existential risk as their \"most important cause\". Again we had two conditions, the control condition and the utopia condition. We hypothesized that a majority of participants would find extinction uniquely bad in both conditions. We found again that most participants ranked no catastrophe as the best outcome and 100% dying as the worst outcome (the expected ranking) both in the control condition (90.32%, 28/31 participants) and the utopia condition (92.50%, 37/40 participants). But unlike the samples in Studies 2a to 2c, and in line with our hypotheses, substantial majorities of the participants who chose the expected ranking found extinction uniquely bad both in the control condition (85.71%, 24/28 participants) and the utopia condition (94.59%, 35/37). The difference between the conditions was not significant (χ 2 (1) = 0.63, P = 0.43). In contrast to laypeople, existential risk mitigators thus found human extinction to be uniquely bad even when the description of the outcomes did not include information about the quality of the future. This suggests that judging human extinction to be uniquely bad, as measured by our task, may be a key motivator for devoting oneself to preventing it. \n Discussion Our studies show that people find that human extinction is bad, and that it is important to prevent it. However, when presented with a scenario involving no catastrophe, a near-extinction catastrophe and an extinction catastrophe as possible outcomes, they do not see human extinction as uniquely bad compared with non-extinction. We find that this is partly because people feel strongly for the victims of the catastrophes, and therefore focus on the immediate consequences of the catastrophes. The immediate consequences of near-extinction are not that different from those of extinction, so this naturally leads them to find near-extinction almost as bad as extinction. Another reason is that they neglect the long-term consequences of the outcomes. Lastly, their empirical beliefs about the quality of the future make a difference: telling them that the future will be extraordinarily good makes more people find extinction uniquely bad. Thus, when asked in the most straightforward and unqualified way, participants do not find human extinction uniquely bad. This could partly explain why we currently invest relatively small resources in reducing existential risk. However, these responses should not necessarily be seen as reflecting people's well-considered views on the badness of human extinction. Rather, it seems that they partly reflect the fact that people often fail to consider the long-term consequences of extinction. Our studies suggest that it could be that if people reflected more carefully, they might to a greater extent agree that extinction is uniquely bad. A suggestive finding with regards to this is that higher scores on the cognitive reflection test predicted a greater tendency to find extinction uniquely bad. This could mean that deliberative thought-processes lead to finding extinction uniquely bad, whereas intuitive thought-processes lead to the opposite conclusion. More research is needed on the role of deliberation and intuition, as well as many other questions, such as the role of cognitive ability, and the ultimate evolutionary causes of why humans struggle to think clearly about their own extinction. Finally, let us consider possible policy implications. If it is right that human extinction is uniquely bad, then we should arguably invest much more in making sure it does not happen. We should also change policy in many other ways; e.g., shift technology policy in a more cautious direction  29  . On this view, we should, if necessary, be prepared to make substantial sacrifices in order to make sure that humanity realizes its future potential. Hence much hinges on the complex question whether we deem our own extinction to be uniquely bad. \n Methods All studies were approved by the University of Oxford's Central University Research Ethics Committee (approval number: R56657/RE002) and participants in each study gave their informed consent beforehand. All studies were performed in accordance with relevant guidelines and regulations. Study 1. Participants. We recruited 210 participants and excluded 27 for not completing the study or failing the attention check. Procedure. Level of optimism was measured by asking participants \"how optimistic are you in general?\" (where optimistic people were defined as \"people who look to the future with confidence and who mostly expect good (2019) 9:15100 | https://doi.org/10.1038/s41598-019-50145-9 www.nature.com/scientificreports www.nature.com/scientificreports/ On the next page, participants who ranked A as the best outcome and C as the worst were again presented with the three outcomes (other participants were excluded), and told: \"We are now interested in your views of how much better A is than B, and how much better B is than C. In terms of badness, which difference is greater: the difference between A and B, or the difference between B and C?\" In addition to the measures reported above, we gave the Oxford Utilitarianism Scale and demographic questions to participants (see Supplementary Materials for results). \n Study 2b. Participants. We recruited 994 participants and excluded 139 for not completing the study or failing an attention check. In addition to the measures reported above, we gave the Oxford Utilitarianism Scale and demographic questions to the participants (see Supplementary Materials for results). The study was pre-registered at https://osf.io/8amxs. Procedure. The procedure was the same as in study 2a. \n Study 2c. Participants. We recruited 204 participants and excluded 8 for not giving an answer. The procedure was the same as for study 2a, except only the control condition and the utopia condition were included. In addition to the measures reported above, we gave the Oxford Utilitarianism Scale and demographic questions to the participants (see Supplementary Materials for results). Study 3. Participants. We recruited 196 participants. However, since we were only interested in those effective altruists who consider existential risk mitigation to be the top cause area, only 83 were included into the analysis. 12 participants were excluded for failing an attention check. The final sample was 71 participants. Procedure. The procedure was the same as for study 2a, except only the control condition and the utopia condition were included. In addition, participants were asked three questions assessing how uniquely bad they found extinction (extinction prevention questions). The first question concerned which scenario (A = a catastrophe kills 50% of the world's population, but humanity recovers to its original size and goes on to live for a very long time, B = painless extinction) they would want to prevent (1 = definitely A, 4 = midpoint, 7 = definitely B). The second question asked if participants would rather support political party A, which works to reduce the risk of scenario A, or political party B, which works to reduce the risk of scenario B (1 = definitely A, 4 = midpoint, 7 = definitely B). The third question asked what they thought the morally right choice for government leaders would be if they had to choose between reducing the risk for either scenario A or B (1 = definitely reduce the risk of A, 4 = midpoint, 7 = definitely reduce the risk of B). We also gave the Oxford Utilitarianism Scale, The Cognitive Reflection Test and demographic questions to participants. (See Supplementary Materials for additional results). Figure 1 . 1 Figure 1. Proportions of participants who found extinction uniquely bad.(This means that they found the difference, in terms of badness, between a catastrophe killing 80% and a catastrophe killing 100% to be greater than the difference between no catastrophe and a catastrophe killing 80%.) Laypeople consistently did not find extinction uniquely bad in the control condition (Control), but did so in a scenario where the future would be very long and good conditional on survival (Utopia). The animals condition (Animals), sterilization condition (Sterilization) and salience condition (Salience) yielded in-between results. People explicitly devoted to existential risk reduction (Existential risk mitigators) consistently found extinction uniquely bad.", "date_published": "n/a", "url": "n/a", "filename": "s41598-019-50145-9.tei.xml", "abstract": "The 21st century will likely see growing risks of human extinction, but currently, relatively small resources are invested in reducing such existential risks. Using three samples (UK general public, US general public, and UK students; total n = 2,507), we study how laypeople reason about human extinction. We find that people think that human extinction needs to be prevented. Strikingly, however, they do not think that an extinction catastrophe would be uniquely bad relative to near-extinction catastrophes, which allow for recovery. More people find extinction uniquely bad when (a) asked to consider the extinction of an animal species rather than humans, (b) asked to consider a case where human extinction is associated with less direct harm, and (c) they are explicitly prompted to consider long-term consequences of the catastrophes. We conclude that an important reason why people do not find extinction uniquely bad is that they focus on the immediate death and suffering that the catastrophes cause for fellow humans, rather than on the long-term consequences. Finally, we find that (d) laypeople-in line with prominent philosophical arguments-think that the quality of the future is relevant: they do find extinction uniquely bad when this means forgoing a utopian future.", "id": "7008645ab45c7a4e815a8d2e0f2a616b"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jesse Clifton", "Maxime Riché"], "title": "Towards cooperation in learning games", "text": "Introduction As the capabilities of machine learning systems improve, it is increasingly important to understand how to achieve cooperation between systems deployed by actors with competing goals. Moreover, because intelligent systems may continue to learn after they are deployed, designing agents who can cooperate requires accounting for ways their policies may change post-deployment. In this paper, we look at the setting where multiple learning agents are deployed to act on behalf of their respective principals. There are three main goals of this work. The first is to articulate an appealing criterion for the design of learning agents, which is welfare-optimal learning equilibrium. The second is to present a general approach to designing learning agents who approximately fulfill this criterion, which we call learning tit-for-tat (L-TFT). This framework is generic to agents who update their policies over time, rather than depending on a particular class of reinforcement learning algorithms. The third is to illustrate some of the strategic considerations which need to be addressed in the design of L-TFT agents. We do this by constructing an L-TFT agent using model-free reinforcement learning algorithms, and examining its performance in two sequential social dilemmas. This agent converges to welfare-optimal payoffs in self-play, while successfully avoiding exploitation and punishing defecting learning algorithms. A learning equilibrium is simply a Nash equilibrium of a learning game, in which strategies are learning algorithms, and payoffs are the cumulative rewards associated with the profile of learning algorithms chosen by each principal  [Brafman and Tennenholtz, 2003 ]. Principals will want to choose the learning agents they deploy strategically. This means that it is not enough for a learner to perform well against a specified set of other players (e.g.,  Shoham and Leyton-Brown 2008) . It is also not enough that a learner converges to Nash equilibrium of the game which is being learned (e.g.  Bowling and Veloso 2001 , Conitzer and Sandholm 2007 , Letcher et al. 2018 , as this does not guarantee that a player cannot benefit by deviating from that profile (i.e., deploying a different learning algorithm). Like other sequential games, learning games will generally have many learning equilibria. Independent equilibrium selection on part of the principals may lead to poor performance. Thus, to guarantee socially optimal payoffs, principals need to coordinate when designing their agents. L-TFT addresses this problem via a welfare function. A welfare function measures the social value of a payoff profile; for instance, a simple welfare function is the sum of the principals' respective payoffs. An L-TFT agent learns a policy profile which optimizes this welfare function, and punishes its counterpart if it detects that they are not doing the same. Thus agents are incentivized to follow a learning algorithm which optimizes the welfare function. Coordination can thus be achieved via coordination on a welfare function and on a class of learning algorithms for optimizing it. In our experiments, learners observe only the actions taken by their counterpart, and not their counterpart's (stochastic) policy. This requires us to construct L-TFT agents who model their counterpart's learning schedule based on their actions and conduct a hypothesis test as to whether it matches a cooperative learning schedule. This in turn introduces incentives to exploit this testing procedure. We examine the performance of L-TFT against an algorithm designed specifically to exploit the way in which it detects defections, as well as its performance in self-play and against a naive selfish learner. Lastly, there is a strategic element in choosing the sensitivity with which L-TFT's hypothesis test detects defections. In Section 5.3, we examine this element in a learning game between an L-TFT agent and a potential exploiter choosing how cautious to be in deviating from a cooperative learning algorithm. \n Related work Learning equilibrium was first discussed (under that name) by  Brafman and Tennenholtz [2003] . Their construction of learning equilibria involves evaluating each of a finite set of policies in a finite stochastic game, whereas the algorithms we focus on use incremental stochastic updates towards the welfare-optimal policy profile. Our online learning setting complements the setting in which agents are trained fully offline and then deployed. This is the setting typically considered in applications of reinforcement learning to cooperation in social dilemmas. For instance, , ,  Wang et al. [2018]  each develop methods in which punishment and cooperative policies are trained offline, and cooperation at deployment time is sustained by the threat of punishment. However, as many agents may learn post-deployment, the strategic aspects of learning itself -rather than just policy selection -must be addressed. The manipulation of the learning of counterpart agents has been explored in the literature on opponent-shaping  , Letcher et al., 2018 . Perhaps the most similar to our approach is the variant of 's learning with opponent learning awareness which uses opponent modeling (LOLA-OM). LOLA-OM uses supervised learning to estimate the policy followed by the other agent, and updates its own policy in a way that is intended to manipulate the direction in which the other player updates their policy. On the other hand, our L-TFT uses opponent modeling to infer whether the other agent is following a cooperative learning algorithm. 3 Preliminaries: Learning games Consider a situation in which multiple agents interact with their environment over time, incrementally updating the policies which they use to choose actions. These updates are controlled by their learning algorithms, which are fixed by their principals before the agents begin interacting with the environment. It is helpful to distinguish between two different games that are being played here. There is the base game, which is defined by the dynamics of the environment, the reward functions of the agents, and the policies available to each agent. In this paper, the \"base game\" will be a stochastic game (described below). There is also the learning game, in which the principals simultaneously submit learning algorithms to be deployed in the base game environment, and attain payoffs equal to some measure of cumulative reward. We work with stochastic games  [Littman, 1994] , a generalization of Markov decision processes to the multi-agent setting. We will assume only two players, i = 1, 2. We'll refer to player i's counterpart with the index j. In a stochastic game, players simultaneously take actions at each time t ∈ N; observe a reward depending on the current state; and the state evolves according to a Markovian transition function. Write the state space as S and the action spaces as A i . Let the reward functions be mappings r i : S × A 1 × A 2 → R, with the reward to player i at time t given by R t i = r i (S t , A t 1 , A t 2 ) . Let H t be the history of observations until time t. We will assume that both agents fully observe the state and each others' actions and rewards, such that H t = {(S v , A v 1 , A v 2 , R v 1 , R v 2 )} t v=0 . A policy π i gives a probability distribution over actions to be taken by player i at each state. Players wish to learn the parameters θ i of a policy which (in some sense) leads to large cumulative reward. Then we define a learning algorithm. Definition 3.1 (Learning algorithm). A learning algorithm for player i is a mapping σ i from histories H t to parameters, i.e., σ i : H → Θ i , where H is the set of histories and Θ i is the space of policy parameters for player i. A learning game is a game whose strategies are learning algorithms. We define payoffs via average rewards. Define the value to player i of learning algorithm profile (σ 1 , σ 2 ) starting from history h t as V i (h t , σ) = lim inf T →∞ T −1 E σ1,σ2 t+T v=t R v i | H t , where E σ1,σ2 is the expectation taken with respect to trajectories in which agents follow learning algorithms σ 1 , σ 2 at each step. Let the initial state s 0 be fixed so that h 0 = {s 0 }. Then a learning game is a game whose strategy spaces are spaces of learning algorithms Σ 1 , Σ 2 , and whose payoffs are given by V i (σ 1 , σ 2 ) ≡ V i (h 0 , σ 1 , σ 2 ). A learning equilibrium is a Nash equilibrium of a learning game: Definition 3.2 (Learning equilibrium). Learning algorithm profile (σ 1 , σ 2 ) is a learning equilibrium of the learning game with learning algorithm spaces Σ 1 , Σ 2 if sup σ 1 ∈Σ1 V 1 (σ 1 , σ 2 ) ≤ V 1 (σ 1 , σ 2 ) and sup σ 2 ∈Σ2 V 2 (σ 1 , σ 2 ) ≤ V 2 (σ 1 , σ 2 ). Finally, let a welfare function w be a function measuring the social value of different learning algorithm profiles. A straightforward welfare function is the utilitarian welfare, w(σ 1 , σ 2 ) = V 1 (σ 1 , σ 2 ) + V 2 (σ 1 , σ 2 ). Others commonly discussed are the Nash welfare  [Nash, 1950]  and the egalitarian welfare (e.g.,  Kalai 1977) . We say that a profile of learning algorithms (σ 1 , σ 2 ) is a welfare-optimal learning equilibrium if it is a learning equilibrium and if it maximizes a welfare function w. We will construct learning algorithms which 1) optimize a welfare function in self-play and 2) are minimally exploitable, in the spirit of welfare-optimal learning equilibrium. 4 Learning tit-for-tat (L-TFT) Tit-for-tat (TFT) famously enforces cooperation in the iterated Prisoner's Dilemma by cooperating when its counterpart cooperates, and defecting when they defect. Similarly, the \"folk theorems\" say that equilibria in repeated games are constructed by specifying a target payoff profile, a profile of target strategies which achieve this payoff profile, and a punishment strategy that is used to punish agents who deviate from the target strategy (see  Mailath et al. [2006]  for a review). Learning tit-for-tat (L-TFT) is a class of learning algorithms that are analogous to tit-for-tat for learning games. For L-TFT, defection consists in playing a policy other than the current estimate of the cooperative policy. This depends on a notion of cooperation and a class of algorithms for learning a \"cooperative\" policy. These are encoded in a welfare function and a class of learning algorithms which learn an optimal policy with respect to that welfare function. Thus an L-TFT agent punishes their counterpart when it detects that they are not learning a welfare-optimal policy using a particular set of algorithms, and otherwise plays according to their current estimate of the welfare-optimal policy. Because policies are in general stochastic, and because we do not assume that policy parameters are mutually visible, we also need a method for inferring whether the other player is following this cooperative algorithm. In particular, we need to construct a test for the hypotheses: H 0 : My counterpart is following an algorithm for learning a welfare-optimal policy. H 1 : My counterpart is not following an algorithm for learning a welfare-optimal policy. In order to be able to cooperate and punish, as well as detect defections by their counterpart, an agent i playing L-TFT maintains the following policy estimates: • A cooperative policy θ C,t i trained to optimize the welfare function. This network is updated according to a learning algorithm O C . In our experiments, O C corresponds to double deep Q-networks (DDQN;  Van Hasselt et al. 2015)  trained on the reward signal R t 1 + R t 2 ; • A punishment policy θ P,t i , updated according to a learning algorithm O P . In our experiments, this corresponds to DDQN trained on the reward signal −R t j ; • An estimate θ C,t j of the other player's current policy which corresponds to the hypothesis that they are playing according to a cooperative learning algorithm. This policy is estimated by specifying a class of cooperative learning algorithms Σ C j ; finding the learning algorithm σ C,t j in this class which best fits the other player's actions; and taking θ C,t j = σ C,t j (H t ). In our experiments, the L-TFT agent assumes that the learning algorithms Σ C j apply DDQN to R t 1 + R t 2 and follow a Boltzmann exploration policy with an unknown initial temperature parameter. In order to obtain θ C,t j we must therefore estimate this temperature parameter, which we do using an approximate maximum likelihood algorithm; • An estimate θ D,t j of the other player's current policy which corresponds to the hypothesis that they are not playing according to a cooperative learning algorithm. This policy is estimated by specifying a class of learning algorithms Σ D j , finding the learning algorithm σ D,t j in this class which best fits the other player's actions; and taking θ D,t j = σ D,t j (H t ). In our experiments, we approximate this procedure by obtaining θ D,t j via supervised learning on player j's actions given the state. Algorithm 1 summarizes L-TFT. Note that, while our experiments use a standard model-free learning algorithm for the base algorithms O C , O P , this framework is highly general. For instance, the players might be model-based planners who choose actions by optimizing against an environment model with parameter θ i , which is updated over time. Moreover, with more sophisticated methods for inferring the other player's learning algorithm, L-TFT algorithms may also be constructed in games with partial state observability, or uncertainty about the other players' rewards. Algorithm 1: Learning tit-for-tat (L-TFT) and −R t j , respectively. Agents follow Boltzmann exploration with respect to the estimated Q-function, i.e., π θi (a i | s; τ i ) ∝ exp aj Q θi (s, a i , a j )/τ i , where Q θi is a neural network with parameter θ i . The initial temperature τ i is decayed according to a schedule g(•, τ i ), such that the temperature at each time step t is τ t i = g(t, τ i ). (In our experiments g linearly decreases to a minimum value, and is constant thereafter.) Our L-TFT algorithm punishes for one episode after it has detected a defection. We assume that players may broadcast punishment to their counterpart. L-TFT agents do not update their cooperative and defecting policy estimates if their counterpart broadcasts punishment, and do not punish if they are currently being punished; for simplicity we suppress the dependence of agents' policies and of the state on these broadcasts. Input: Observation history H t , \n Testing for defection: L-TFT q To decide whether to punish, our agent conducts a goodness-of-fit test for the hypothesis that the other player is cooperating. A goodness-of-fit test (e.g.,  Lemeshow and Hosmer Jr 1982)  compares the fit of a simple model with the fit of a flexible model. If the fit of the simple model is sufficiently close to that of the flexible model, the simple model is deemed adequate. Otherwise, the simple model is said to fit poorly. Here, the simple model we assess is the hypothesis that the other player is using cooperative DDQN with Boltzmann exploration. The flexible model we would like to compare to is that the other player is following an arbitrary learning algorithm (which need not be cooperative). One approach to estimating this model could be to solve the penalized maximum likelihood problem θ D,1 j , . . . , θ D,t j = arg max θ D,1 j ,...,θ D,t j t v=1 log π D θ D,v j (A v | S v ) + t −1 λ t v=1 θ D,v j 2 , ( 1 ) where π D θj is a class of neural networks that output a distribution over actions given a state. But solving 1 is computationally infeasible. As an approximation, we maintain a sequence { θ D,v j } t v=1 by taking gradient steps on the supervised learning loss at each time step. We maintain a buffer of log likelihoods under the hypothesis of defection, L D,t j = {log π D θ D,v j (A v j | S v )} t v=t−t . (The estimate θ D,t j and log likelihood buffer L D,t j are not updated while the other player broadcasts punishment.) On the other hand, to obtain likelihoods under the hypothesis of cooperation, player j is cooperating, we need to estimate the initial temperature τ j under the assumption that player j is following a cooperative learning algorithm for some τ j . We would thus like to solve τ t j = arg max τj t v=1 log π θ C,v j {A v | S v ; g(v, τ j )} . (2) As a tractable approximation to the solution of problem 2, we maintain an estimated cooperative Qnetwork θ C,t j via DDQN updates on reward signal R t 1 + R t 2 (only when not being punished). We track the likelihood of player j's actions under θ C,t j over a set of candidate values for τ j ; and take τ t j to be the highest-likelihood such value at time t. For each τ j , we also maintain a buffer of log likelihoods 1 L C,t j (τ j ) = {log π C,v j A v j | S v ; g(v, τ j ) } t v=t−t . (Estimate θ C,t j and buffers L C,t j (τ j ) are again not udpated while the opponent broadcasts punishment.) Finally, the hypothesis test is conducted at the end of each episode by bootstrapping  [Efron, 1992]  the difference in mean log likelihoods over buffers L C,t j ( τ t j ) and L D,t j . The hypothesis of cooperation is rejected when the q th quantile of this distribution is less than 0. This hypothesis test is summarized in Algorithm 2. We refer to the variant of L-TFT which uses this test as L-TFT q . Exploiting L-TFT q We also construct exploiter agents to play against L-TFT q . These agents assume their counterpart is L-TFT q for a particular value of q, simulate the hypothesis test used by L-TFT q , and act (myopically) depending on the result of the test. That is, if an exploiter predicts that a defection would be detected by a test with cutoff q, it acts according to the cooperative policy; otherwise, it takes a selfish action (according to a DDQN network trained on its reward signal only). Call this agent Exploiter q . The networks maintained by Exploiter q are: 1) a cooperative network trained on R t 1 + R t 2 , 2) a selfish network trained on R t i , 3) an estimate of its own policy under the hypothesis that it is cooperating θ C,l j , and 4) an estimate of its own policy under the hypothesis that it is defecting θ D,l j . Algorithm 2: Hypothesis test for L-TFT q Input: Defection log likelihood buffer L D j , cooperative log likelihood buffer L C j ( τ t j ), cutoff quantile q, test statistics buffer {∆ (q),v j } t−1 v=t−u /* t indexes episodes */ ∆ j ← ∅ for b = 1, . . . , B do L C,b j ← Bootstrap L C,t j ( τ t j ) L D,b j ← Bootstrap(L D,t j ) L C,b j ← B −1 C j ∈L C,b j C j L D,b j ← B −1 D j ∈L D,b j D j ∆ j ← ∆ j ∪ L C,b j − L D,b j ∆ (q),t j ← Percentile(∆ j , q) ∆(q),t j ← u −1 t v=t−u ∆ (q),v j // Average previous test statistics for stability if ∆(q),t j < 0 then defection_detected ← True else defection_detected ← False return defection_detected \n Environments The environments we use are the iterated Prisoner's Dilemma (IPD) and the Coin Game environment  2 . In both cases, episodes are 20 timesteps long. Our version of the IPD involves repeated play of the matrix game with expected payoffs as in Table  1 . Policy π θi gives the probability of each action given player j's action at the previous timestep. In our implementation, this means that the state passed to the estimated Q-function is the profile of actions taken at the last step. Player 2 C D Player 1 C −1, −1 −3, 0 D 0, −3 −2, −2 Table 1: Prisoner's Dilemma expected payoffs. Figure  1 : Coin Game Payoffs. Write the expected reward function, corresponding to the payoffs in Table  1 , as r i (a i , a j ). We introduce randomness by generating rewards as R t i ∼ N r i (A t i , A t j ), 0.1 . In the Coin Game environment  depicted in Figure  1 , a Red and Blue player navigate a grid and pick up randomly-generated coins. Each player gets a reward of 1 for picking up a coin of any color. But, a player gets a reward of −2 if the other player picks up their coin. This creates a social dilemma in which the socially optimal behavior is to only get one's own coin, but there is incentive to defect and try to get the other player's coin as well. The state space consists of encodings of each player's location and the location of the coin. We use networks with two convolutional layers and two fully connected feedforward layers.   (bottom) . For IPD, the prob axis is the probability of mutual cooperation (cc) and mutual defection (dd), For Coin Game, the pick_own axis is the proportion of times the coin is picked by the agent of its own color (i.e., the agents cooperate). The payoffs axis shows a moving average of player rewards after each episode. These values are averaged over 10 replicates and bands are (min, max) values. Note that temperature values are constant in the IPD after 3000 episodes and in the Coin Game after 30000 episodes. \n Results Figure  2  shows the performance of L-TFT q in self-play, against Exploiter q (i.e., an exploiter with a correctly-specified value of q). L-TFT q is able to converge to welfare-optimal payoffs in self-play and against the Exploiter q (suggesting that the exploiter eventually anticipates being punished if it defects, and therefore chooses to cooperate). This indicates that our hypothesis test effectively detects defection. L-TFT q also effectively punishes a naive selfish learner (i.e., one trained with DDQN on R t j ); see Figure  3  in the Supplementary Materials. Punishing the naive learner comes as the expense of low payoffs for L-TFT. However, this is the expected behavior, just as the punishments which enforce equilibria in classical iterated games can lead to low payoffs for each player. \n Strategic choice of q While our previous experiments with Exploiter q assumed that the exploiter knew the cutoff quantile used in L-TFT's hypothesis test, this seems like too strong an assumption for real-world agents deployed by different principals. Here we consider a game played between 1) one principal deciding which value of q 1 to specify for its L-TFT q1 agent, and 2) a second principal deciding among L-TFT q2 and Exploiter q2 for different values of q 2 . Table  2  shows the average payoffs to each player over a time horizon of 4000 steps. Table 2: Empirical payoff matrix for a learning game in which the base game is an iterated Prisoner's Dilemma played for 4000 timesteps. The row player chooses L-TFT q for q ∈ {0.55, 0.75, 0.95}. The column player chooses either L-TFT q or Exploiter q for q ∈ {0.55, 0.75, 0.95}. Cells give (row player payoffs, column player payoffs), where payoffs are the mean of rewards over the span of the game, averaged over 10 replicates. Standard errors are all less than or equal to 0.1. It turns out that the unique Nash equilibrium of this empirical learning game 3 is one in which row player chooses L-TFT 0.95 with probability 0.88 and L-TFT 0.55 with probability 0.12, while the column player chooses L-TFT 0.55 with probability 0.88 and Exploiter 0.95 with probability 0.12. The expected payoffs in equilibrium are −1.23, −1.08 for row and column player, respectively. This suggests that L-TFT q is vulnerable to some amount of exploitation on short time horizons, although still does better than the mutual-defection payoff of −2. On the other hand, L-TFT q1 converges to mutual cooperation 4 against both L-TFT q2 and Exploiter q2 for each value of q 1 , q 2 . Thus L-TFT avoids exploitation over longer time horizons in this learning game. \n Discussion Powerful learning agents should be designed to avoid conflict when they are eventually deployed. One way to avoid such outcomes is to construct profiles of agents which avoid conflict and which rational principals prefer to deploy. One appealing criterion for joint rationality on part of the principals is welfare-optimal learning equilibrium (rather than mere convergence to Nash equilibrium of the base game, for instance). We have presented a class of learning algorithms, learning tit-for-tat (L-TFT), which approximately implement welfare-optimal learning equilibrium in the sense of converging to welfare-optimal payoffs in self-play and discouraging exploitation. Many open questions remain. First, while we have relied on a welfare function, we have said little about which welfare function should be used. The ideal scenario would be for the principals of the reinforcement learning systems in question to coordinate on a welfare function before deploying these systems. Moreover, it may be necessary to develop novel reinforcement learning methods tailored for the optimization of different welfare functions. For instance, our use of DDQN with the utilitarian welfare is unproblematic, as the sum of the players' reward signals still admits a Bellman equation for their cumulative reward. But the welfare functions other than the utiliarian welfare (such as the Nash welfare  [Nash, 1950] ) do not admit a Bellman equation (see the discussion of nonlinear scalarization functions in  Roijers et al. [2013] 's review of multi-objective reinforcement learning). Many generalizations of our setting can be studied, including partial observability and more than two agents. Perhaps the most restrictive of our assumptions is that the agents' reward functions are known to each other. A complete framework should address the problem of incentives to misrepresent one's reward function to improve one's payoffs in the welfare-optimal policy profile. One direction would be to allow for uncertainty about the other players' reward functions, analogously to Bayesian games  [Harsanyi, 1967]  but in a way that is tractable in complex environments. This may in turn require the development of novel techniques for inference about other players' preferences in complex environments; see  Song et al. [2018] ,  Yu et al. [2019]  for recent steps in this direction. Another approach to reward uncertainty would be to use mechanism design techniques  [Nisan et al., 2007, Ch. 9]  to incentivize the truthful reporting of the principals' utility functions. Figure 2 : 2 Figure 2: Performance of L-TFT 0.95 in the IPD (left) and Coin Game (right). Counterparts are L-TFT 0.95 (top), Exploiter 0.95(bottom). For IPD, the prob axis is the probability of mutual cooperation (cc) and mutual defection (dd), For Coin Game, the pick_own axis is the proportion of times the coin is picked by the agent of its own color (i.e., the agents cooperate). The payoffs axis shows a moving average of player rewards after each episode. These values are averaged over 10 replicates and bands are (min, max) values. Note that temperature values are constant in the IPD after 3000 episodes and in the Coin Game after 30000 episodes. \n .55 −1.28, −1.2 −0.97, −1.48 −0.98, −1.38 −1.03, −1.41 −1.06, −1.43 −0.91, −1.81 L-TFT0.75 −1.44, −0.97 −1.13, −1.1 −1.09, −1.13 −1.19, −1.11 −1.25, −1.11 −1.21, −1.35 L-TFT0.95 −1.21, −1.06 −1.12, −1.1 −1.11, −1.11 −1.2, −1.06 −1.27, −1.03 −1.41, −0.98 \n\t\t\t When computing these likelihoods, we set the Q-value of an action equal to the mean of all Q-values which are within some distance of one another (in our experiments, 0.25). This is important in Coin Game, where there are multiple paths of equal length to a coin. Thus, although estimated Q-values along different paths may be very similar, these differences are amplified by the exponentiation used in Boltzmann exploration when the temperature is small, possibly leading to false detections of defection. \n\t\t\t These experiments were implemented using extensions of OpenAI Gym [Brockman et al., 2016]  and the SLM Lab framework for reinforcement learning [Keng and Graesser, 2017] . \n\t\t\t Computed using the Nashpy Python library [Knight and Campbell, 2018] .4  Payoffs averaged over the final 10 episodes equal to −1 ± 0.03.", "date_published": "n/a", "url": "n/a", "filename": "toward_cooperation_learning_games_oct_2020.tei.xml", "abstract": "Suppose that several actors are going to deploy learning agents to act on their behalf. What principles should guide these actors in designing their agents, given that they may have competing goals? An appealing solution concept in this setting is welfare-optimal learning equilibrium. This means that the learning agents should constitute a Nash equilibrium whose payoff profile is optimal according to some measure of total welfare (welfare function). In this work, we construct a class of learning algorithms in this spirit called learning tit-for-tat (L-TFT). L-TFT algorithms maximize a welfare function according to a specified optimization schedule, and punish their counterpart when they detect that they are deviating from this plan. Because the policies of other agents are not in general fully observed, agents must infer whether their counterpart is following a cooperative learning algorithm. This requires us to develop new techniques for making inferences about counterpart learning algorithms. In two sequential social dilemmas, our L-TFT algorithms successfully cooperate in self-play while effectively avoiding exploitation by and punishing defecting learning algorithms.", "id": "9b5ae3a6a8405f9db7339710a660387c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jessica Chen Weiss", "Allan Dafoe"], "title": "Authoritarian Audiences, Rhetoric, and Propaganda in International Crises: Evidence from China", "text": "Introduction Many authoritarian governments act as if the need to maintain public support constrains their foreign policy choices. Leaders in the Middle East often claim that their hands are tied in international negotiations by the threat of a popular backlash.  1  Chinese officials are fond of invoking the \"feelings of more than 1.3 billion Chinese people\" in protesting foreign actions and demands. 2 After a U.S. Freedom of Navigation patrol in the South China Sea, Chinese media warned: \"If the US government hopes to persuade the Chinese government to make concessions, it will first have to persuade the Chinese people.\" 3 Yet we have relatively little systematic evidence of how citizens in autocracies evaluate their government's performance in international disputes.  4  Moreover, authoritarian governments devote significant resources to managing domestic opinion through propaganda and rhetoric. When these efforts succeed, governments can conduct foreign policy with greater latitude, unhindered by public backlash. They may even benefit by stoking popular nationalism, rallying the public around the government. To illuminate the domestic costs and opportunities that authoritarian governments face in international disputes, this article investigates three questions. First, do leaders who fail to carry out explicit threats suffer greater public disapproval, akin to \"audience costs\" in democratic settings  (Fearon, 1994a; Tomz, 2007) ? Second, do mass audiences approve of tough but vague statements (\"bluster\") that are unaccompanied by military action  (Oakes, 2006) ? Third, can authoritarian rhetoric and propaganda mitigate disapproval of military inaction in international crises? We focus on China for two reasons. Among possible great power wars, tensions between China, its neighbors, and the United States in the Asia-Pacific loom large. China also represents a \"most likely\" case for an authoritarian leadership to be sensitive to public opinion costs, if they exist, and to be able to control them. As President Xi Jinping told the Central Committee: \"Winning or losing public support is an issue that concerns the CPC's survival or extinction.\"  5  We fielded two complementary online survey experiments in China, one involving an abstract hypothetical territorial dispute, and another involving real-world Chinese threats against U.S. military operations in East Asia. In both designs, we assess how respondents reacted to threats that were ultimately unfulfilled, as well as three different strategies to frame the public presentation of crisis events: biding time for future success, a nationalist frame of past humiliation, and the costs of war. In both designs, we prioritized realism, using actual statements and phrases by the Chinese government. This decision emphasized external validity but limited our choice of quotes, meaning that some treatments may bundle multiple concepts and be articulated by different speakers. We privileged selecting real quotes from speakers who were as senior in the Chinese government as possible, avoiding sources or outlets that might have been perceived as partisan or biased. Following  (Huang, 2018) , our primary purpose was not to compare across treatments, but to demonstrate the existence of effects and point the way for future studies to parse more finely the underlying mechanisms. We find that authoritarian rhetoric and propaganda can be effective in bolstering popular support and attenuating disapproval of inaction. In both scenarios, we find suggestive evidence that biding time narratives had a positive effect on public approval, as did a nationalist frame of remembered injustice at the hands of foreign powers. We also find that empty threats can have positive or negative effects on public approval-positive with the vague, real-world threat, but negative with the explicit, hypothetical threat. Overall, these results suggest that the public opinion costs of inaction exist but are relatively muted and malleable in China, undermining claims that the government's hands are tied by the threat of public disapproval. Such claims are not entirely bluffs, as the possibility of disapproval is real, but such statements elide the government's ability to influence popular perceptions. Tough but vague threats can also generate popular support, even if the government does not take action. A fuller appreciation of authoritarian incentives in international disputes should consider the positive effect of bluster and rhetorical justifications for inaction alongside audience costs and belligerence costs  (Kertzer and Brutger, 2016) . \n Mass Audiences and Authoritarian Regimes Public support-or the appearance of it-matters to many autocracies. As Ithiel de Sola Pool writes, modern dictatorships are \"highly conscious of public opinion and make major efforts to affect it.\" 6 Mao Zedong told his comrades: \"When you make revolution, you must first manage public opinion.\" 7 Because autocracies often rely on nationalist mythmaking, 8 success or failure in defending the national honor in international crises could burnish the leadership's patriotic credentials or spark opposition. Shared outrage at the regime's foreign policy failures could galvanize street protests or elite fissures, creating intraparty upheaval or inviting military officers to step in to restore order. Fearing a domestic backlash, authoritarian leaders may feel compelled to take a tough international stance. Although authoritarian leaders are rarely held accountable to public opinion through free and fair elections, fears of popular unrest and irregular ouster often weigh heavily on autocrats seeking to maximize their tenure in office. Considering the harsh consequences that authoritarian elites face if pushed out of office, even a small increase in the probability of ouster could alter authoritarian incentives in international crises.  9  A history of nationalist uprisings make Chinese citizens and leaders especially aware of the linkage between international disputes and domestic unrest. The weakness of the PRC's predecessor in defending Chinese sovereignty at the Paris Peace Conference in 1919 galvanized protests and a general strike, forcing the government to sack three officials and reject the Treaty of Versailles, which awarded territories in China to Japan. These precedents have made Chinese officials particularly sensitive to the appearance of hewing to public opinion. As the People's Daily chief editor wrote: \"History and reality have shown us that public opinion and regime safety are inseparable.\" 10 One Chinese scholar even claimed: \"the Chinese government probably knows the public's opinion better and reacts to it more directly than even the U.S. government.\"  11  Multiple government agencies monitor public sentiment on foreign affairs, providing the leadership daily briefs of online commentary. With almost 650 million \"netizens\" in China, the government employs more than 2 million analysts to monitor internet sentiment and win the \"guerrilla battle\" in the \"mass microphone era,\" according to the head of the People's Daily Public Opinion Monitoring Unit.  12  The chief editor of the People's Daily called the internet the \"biggest variable\" (zui da bianliang) in managing public opinion.  13  The Chinese government uses propaganda, surveillance, and censorship to monitor and manage popular sentiment. 14 Yet the efficacy of these tools in shaping public opinion remains unclear, particularly in international crises. Citizens may discount government statements as biased propaganda 15 . As Pool notes, \"the public learns to read between the lines. It 10, 2013, cited in \"If you like killing time on social networks, China has a job for you,\" PRI, July 31, 2014. 13 \"Bawo hao zheng zhi jia ban bao de shidai yaoqiu,\" Renmin Ribao, March 21, 2016. 14 See, e.g.,  King et al. (2013) ,  Pan and Chen (2018) ,  Huang (2015b) ,  Brady (2009) .  15 Slantchev (2006) . becomes accustomed to interpreting clues to the truth that are buried in the unreliable information available to them.\" 16 But propaganda may also encourage citizens to echo the \"party line\" and act as if they support the government even when they have access to unbiased information about international events  (Little, 2017) . The balance between mass incredulity and deference will affect whether authoritarian regimes are able to use propaganda to shape public reactions to crisis events. Even if citizens shield their private preferences, the extent of stated popular support for the government represents an important bulwark against collective action and elite machinations. \n Managing Public Reactions Our study looks at how governments use rhetoric and propaganda in international crises to shape public reactions, particularly when the government does not take tough military action. Much government rhetoric and propaganda in international crises appears to serve functions not captured by audience cost theory, which holds that leaders pay domestic costs for failing to fulfill public threats. These threats may be explicit (such as an ultimatum) or implicit (such as troop mobilization). Domestic publics are said to disapprove because empty threats betray the nation's honor, harm the nation's credibility, or reveal the leader's incompetence. 17 Despite experimental evidence of audience costs, 18 scholars have questioned their role in historical crises.  19  Several scholars have argued that explicit statements of commitment are relatively rare. Snyder and Borghard note: \"leaders see unambiguously committing threats...as imprudent. They almost always seek to retain significant flexibility, rather than lock in\"  (Snyder and Borghard, 2011, 437) .  Downes & Sechser (2012, 461)  similarly acknowledge that threats of force are more often implied than explicit. Even  Schelling (1966, 67)  wrote that \"most commitments are ultimately ambiguous in detail. Sometimes they are purposely so.\" In addition to evaluating whether unfulfilled threats generate public opinion costs, we investigate four other rhetorical and propaganda strategies that the Chinese government has  16  De Sola Pool (1973b), p. 463. 17  Fearon (1994a) ;  Smith (1998) ;  Schultz (2012) ;  Sartori (2002) ;  Levy et al. (2015) ;  Guisinger and Smith (2002) ;  Debs and Weiss (2016) . 18  Tomz (2007, 823) ;  Trager and Vavreck (2011) ;  Levendusky and Horowitz (2012) ;  Chaudoin (2014) ;  Davies and Johns (2013) ;  Kertzer and Brutger (2016) ; for non-experimental studies of audience costs in authoritarian regimes,  Weeks (2008)  examines the role of elites, while  Weiss (2013)  analyzes the role of street protests.  19 Snyder and Borghard (2011); Trachtenberg (2012) ;  Slantchev (2012) . used to bolster popular support while keeping international tensions short of conflict. First, we evaluate rhetoric that justifies inaction as part of a resolute but subtle, longterm biding time strategy of building one's strength in the present to achieve future victory or vengeance. By recasting inaction as consistent with honorable behavior, such biding time narratives may bolster popular support for inaction. This strategy frames escalation as foolhardy and inaction as shrewd rather than humiliating. As the head of the (disarmed) German army reportedly said during the interwar years, \"First we'll get strong, then we'll take back what we lost.\" 20 Biding time messages invoke the benefits of restraint by making implicit or vague references to the future, without specific commitment to take action. However, the impact of biding time justifications on public opinion has not been systematically examined. Chinese officials have frequently emphasized strategic forbearance, with the \"lie low and bide time\" principle (tao guang yang hui ) characterizing China's grand strategy for nearly three decades.  21  While this maxim implies the future assertion of Chinese power, it does not necessarily mean that China plans to challenge US primacy.  22  If such narratives are effective at bolstering public support for international restraint, then recent Chinese \"assertiveness\" 23 in its territorial and maritime disputes is less likely to reflect domestic pressure than deliberate strategy. In designing the Biding Time frame, we used statements by Political Commissar of the PLA General Logistics Department General Liu Yuan, whose views President Xi Jinping has affirmed on several occasions.  24  In excerpts published by the popular newspaper Global Times, Liu emphasized that China should not be baited into war in the East China Sea, calling it a \"trap\" set by other powers to derail China's rise.  25  H B (Biding Time): Statements that justify inaction by invoking future success will increase public approval. Second, we evaluate nationalist propaganda about historical humiliations by external adversaries. Governments seeking to bolster their domestic legitimacy often invoke nationalist references to a shared history of national struggle against foreign mistreatment and trauma.  26  This frame, invoked in China as the \"Century of National Humiliation,\" 27 puts 20 As quoted in  Legro (2007, 519) .  21  Chen and Wang (2011).  22  Swaine (2010, 7).  23 Johnston (2013) .  24  China Leadership Monitor, No. 36, January 6, 2012. 25 http://opinion.huanqiu.com/opinion_world/2013-02/3614115.html.  26 Snyder (1991) ;  Mansfield and Snyder (2007) ;  Bunce and Wolchik (2010) .  27 Gries (2004) ;  He (2009) ;  Zhao (2004) ;  Wang (2014) . current military inferiority in the context of the nation's longer-term trajectory of rising to surpass foreign enemies and seeks to rally or mobilize the public toward that end. Such nationalist narratives could have diverse effects. Reminding respondents of shared national trauma or injustice at the hands of foreign powers may encourage solidarity with the government in the face of adversity, generating a rally effect. International relations scholars have typically examined whether democratic publics \"rally-round-the-flag\" after the use of force or other dramatic events. 28 Because authoritarian leaders routinely employ nationalist appeals without always using force, it is important to investigate the effect of nationalist propaganda on public approval, particularly when the government does not take action. Invoking past losses may also alter how respondents evaluate the status quo, reminding them of how far the nation has come in defending its interests. Like biding time, messages about nationalist history tie the current dispute to a long-term struggle, giving a more honorable interpretation to temporary inaction. On the other hand, reminders of past losses could also generate an endowment effect, making citizens more willing to risk war. A humiliation prime could also heighten the salience of concerns for national honor, magnifying the costs of inaction. The net effect of these diverse mechanisms on public approval is unclear. H N (Nationalist History): Statements that invoke a shared history of national injustice at the hands of foreign powers will increase (decrease) public approval. Third, we evaluate government rhetoric that emphasizes the economic, material, and human costs of war that the public might bear.  29  Chinese officials have sometimes invoked the costs of war to dampen the public's appetite for confrontation. As tensions between Japan and China escalated, General Liu Yuan warned that war would be \"very cruel and costly.\" 30 In a similar hypothetical scenario between China and Japan,  Quek and Johnston (2018)  found an increase in approval of backing down among respondents who read that the leader said that war with Japan would derail China's economic development. H C (Cost of War): Statements that justify inaction by invoking the costs of war will increase public approval. Another common but underexamined species of rhetoric in international relations theory is bluster, which we define as aggressive, vague rhetoric that is not followed by tough action, per the Oxford English Dictionary-\"boisterous inflated talk, violent or angry self-assertion, noisy and empty menace, swaggering.\" From the perspective of audience cost theory, bluster is puzzling since it implies a threat that is unaccompanied by military action. In China, for instance, the government publicly announced an Air Defense Identification Zone (ADIZ) proscribing US behavior but then failed to take tough measures to enforce that proscription. Other examples of bluster include statements by President Trump that \"North Korea best not make any more threats to the United States. They will be met with fire and fury like the world has never seen.\"  31  In the days after the president issued this threat, North Korea announced a plan \"to interdict the enemy forces on major military bases on Guam and to signal a crucial warning to the U.S.,\" 32 fired a missile over Japan, and conducted its most powerful nuclear test to date; none of these precipitated US military action as Trump had promised. Fearon also raised the possibility of bluster in his discussion of audience costs: \"Political audiences need not and do not always [disapprove of empty threats]. For example, leaders of small states may be rewarded for escalating crises with big states and then backing down.... Standing up to a 'bully' may be praised even if one ultimately retreats\"  (Fearon, 1994a, 580) . What is the logic of bluster? Why would domestic audiences approve of empty threats? We offer three possible explanations for future research to explore and disentangle. First, some audiences may interpret tough talk as strength and value the appearance of strength more than consistency or action. This can be thought of as a belligerence benefit, the inverse of Kertzer and Brutger's belligerence costs. A leader who makes loud, confident demands may appear to be advancing the national interest, absent persuasive claims to the contrary. In low-information environments, individuals may reflexively trust their leader and discount critics who point to the lack of follow-through as biased. Second, citizens may recognize that using military force is not feasible but judge it prudent to lodge a symbolic protest. Publicly registering a state's opposition to a foreign action could have material consequences under customary international law, where silence may be legally interpreted as consent. Verbal protests could also communicate to potential allies one's displeasure with the transgression and transgressor, as well as to mitigate loss in the \"contest of expectations\" with the adversary, 33 communicating that some arrangement will be challenged when one has the power to do so. Third, bluster may be understood as a threat about which there is subjective uncertainty about what kinds of behavior constitute noncompliance as well as the appropriate timeline and nature of restitution. A vague threat may communicate that some behavior or arrangement is unacceptable on a latent, not objectively measurable, dimension. The latent dimension may represent disrespect, hostility, or challenge to core national interests. Domestic audiences understand vague tough talk as communicating the threat that persistence in a disrespectful arrangement will lead to an appropriately forceful response, but individuals may disagree about the details. This mechanism is consistent with  Trager and Vavreck's (2011: 536)  finding that the vague statement \"the U.S. will not tolerate the invasion\" generated less audience costs than the precise threat \"the U.S. military will prevent the invasion.\" We could even see an increase in approval in the midst of a vague threat that will eventually be unfulfilled, if the increase in approval from the leader issuing the threat outweighs the reduction in approval for those who deem the vague threat to be unfulfilled.  34  H B (Bluster): Tough but vague threats to use force may increase public approval, even when the threats are unfulfilled or unaccompanied by military action. While the benefits of bluster often run counter to audience costs, one logic is more likely to dominate under some conditions. If threats are unfulfilled, public opinion costs are more likely to arise when the threat is specific than when the threat is vague. H A (Audience Costs): Explicit threats to use force should increase domestic disapproval when unfulfilled or unaccompanied by military action. To evaluate whether bluster can generate public approval while specific threats generate audience costs, we designed two treatments that varied the specificity of the threatened consequences. We also look at the effect of mobilization, an act that is often regarded as making an implicit threat and expression of resolve  (Tomz, 2007) ;  (Slantchev, 2005) ;  (Fearon, 1994b) .  35  33  Dafoe et al. (2014) .  34  Schultz also notes that bluffing may be an optimal strategy, making it unclear why audiences would rationally punish a leader for backing down.  (Schultz, 1999, 237) .  35  While in principle a mobilization could be understood as a more explicit threat than a verbal threat, in practice we expect most mobilizations without verbal threats are more implicit. We manipulated key aspects of what respondents read about the dispute before asking their opinion of the government's foreign policy performance.  37  The first experiment employed a prevalent design, which we refer to as the hypothetical design. Hypothetical scenarios provide greater freedom to design vignettes to match the theoretical framework. By avoiding contextual idiosyncrasies, abstract hypothetical scenarios may yield more generalizable inferences. However, respondents may react differently to hypothetical than actual crises. As hypothetical scenarios become more abstract and devoid of contextual information, the connection between survey responses and real-world reactions to particular crises becomes more tenuous, weakening external validity. Conversely, respondents may think of real world examples in answering questions about abstract scenarios, introducing a form of bias akin to confounding biases in observational studies  (Dafoe et al., 2018) . For example, Chinese respondents who read that an unnamed \"neighboring country\" is a powerful democracy and a US ally are more likely to think of Japan, plausibly influencing their responses in unintended ways. Indeed, our respondents were more likely to report that they were thinking of Japan if the scenario mentioned that the adversary had strong military capabilities, was a US ally, or was a democracy. \n Research Design To complement the hypothetical design, we also use a selective-history survey experiment. In this design, we provided respondents with information about real events, here a recent crisis in the East China Sea, before asking respondents for their opinions. Other examples of selective-history designs are  Tingley (2017) , which reminds some American respondents about China's ADIZ, and  Huang (2018) , which looks at the effect of real-world Chinese 36 Huang (2015a).  37  We assigned manipulations according to a set of conditional probability rules detailed in Supplementary Files D and E. propaganda messages. Other hypothetical designs also use contexts where real-world disputes are specified, but where the treatments involve actions or events that have not (yet) occurred, such as  Quek and Johnston (2018)  and  Mattes and Weeks (forthcoming) . Evaluating the selective presentation of information about previous crises is especially relevant in authoritarian states, where the government has substantial influence over the media. In China, state-run media often remind the public about aspects of previous crises, such as the death of pilot Wang Wei during the 2001 EP-3 collision.  38  In such designs, estimated effects may be attenuated relative to their real world counterparts because surveys are a less realistic, potent, and saturated source of information than what governments can broadcast through sustained television and radio coverage. If our manipulations affect opinion, then so should stronger manipulations in the real world. Selective-history designs can also help estimate the impact of events in a crisis. Selectivehistory designs are plausibly more externally valid than hypothetical designs because they involve actual (and hence more realistic) events, implicitly involving all the contextual information that was relevant to the respondent during the actual crisis. However, selective-history designs also have disadvantages. First, they are limited to events and statements that have transpired, making it difficult to evaluate the effect of behavior that has yet to occur, such as explicit, unfulfilled threats to use force or mobilization of troops for a China-US conflict. Second, the magnitude of effects may be attenuated if respondents' knowledge of events crowds out the survey's representation of them. While this makes it harder to detect effects (reducing statistical power), the survey effects we find are likely to be underestimates of real world effects. The magnitude of effects could also be greater than in a real crisis, for two reasons: first, in a real crisis the government may prevent certain information from being presented, such as news that the Chinese government did not take action to stop the US from continuing to fly through China's newly declared ADIZ; and second, respondents may feel more strongly about events when reminded of them than when they first occurred, if effects increase with exposure.  39  Ultimately, both hypothetical and selective-history designs have strengths and limitations. By combining the two, researchers can evaluate the observable implications of theories from multiple angles. 38 See, for example, China Central Television, April 3, 2013, http://bit.ly/1h3k5Sa 39 A key assumption is that reminding or informing a subject about past events generates effects in the same direction (positive or negative) as the actual crisis events. \n Hypothetical Design Our hypothetical design follows the spirit of  Tomz's (2007)  canonical audience cost study, but we modify the vignette so that it describes an abstract territorial dispute that China has faced and will continue to face. We do so for two reasons. First, it is in this context that Chinese leaders invoke the pressure of public opinion, so if Chinese audience costs exist, they should be present in this empirical domain. Second, China's limited global reach and reluctance to intervene in third party disputes make the conventional audience cost scenario (an optional foreign policy crisis in which the government decides whether to intervene in a conflict between two other states) implausible. Because the crisis we consider is more likely to impact core Chinese interests (including sovereignty over claimed land and water) than a scenario in which the United States or United Kingdom intervenes in a dispute between third parties, our baseline \"stay out\" comparison is more likely to engage national honor. Thus, respondents may disapprove of inaction even in the no-threat, no-action (control) condition, making it more difficult to observe differences with the explicit threat, no-action (audience cost) condition. The choice to adopt a more likely, realistic crisis for a Chinese context makes this a relatively hard test of whether unfulfilled threats generate public opinion costs. Respondents read the following vignette. Five contextual variables, assigned in a fullfactorial way, gave details that prevent the scenario from being too abstract and were manipulated to ensure that any causal effects we estimate are averages across this covariate space.  40  These covariates are regime type, alliance with the US, military power, and the material value of the territory. Respondents who received the Nationalist History treatment were told that the disputed territory was part of the land lost during the \"Century of National Humiliation\" from the Opium Wars to the founding of the PRC in 1949. There exists a territorial dispute between China and a neighboring country. The neighboring country is led by [a non-democratic government OR a democratic government], which [is OR is not] an ally of the United States. The neighboring country has [a strong military, so in the event of war it would OR a weak military, so in the event of war it would not] take a major effort for China to secure control of the territory. Experts believe that allowing the neighboring country to control the territory [would hurt OR would not affect] the safety and economy of China. [The disputed territory was part of the land China lost during the Century of National Humiliation OR no mention.] 40 In addition, if other theories predict heterogeneous effects across some of these covariates, our survey design will allow researchers to investigate these. Respondents then read none, some, or all of the following (assigned in an independent factorial manner, except only one of the two rhetorical cues, Biding Time or Cost of War, was given): 41 • Explicit Threat: The Chinese government states that the neighboring country must recognize Chinese sovereignty or China will use force to take the territory. • Mobilization: China mobilizes military forces to prepare to take the territory by force. • Biding Time: Chinese officials explain that fighting a war over the territory would be a grave mistake. According to a senior Chinese military official, \"China's neighbors will use all means to check China's development, but we absolutely must not take their bait.\" • Cost of War : Chinese officials explain that fighting a war over the territory would be too costly. According to a senior Chinese military official, \"Since we have enjoyed peace for quite a long time, many young people do not know what a war is like, it is actually very cruel and costly. If there is any alternative way to solve the problem, there is no need to resort to the means of extreme violence for a solution.\" The scenario ended for all respondents with: In the end, China does not take military action, and the neighboring country consolidates control over the territory. \n Selective-History Design The second survey presented respondents with a selective portrayal of recent events in China's surrounding waters, focusing on China's threat to use \"defensive emergency measures\" by Chinese armed forces if foreign aircraft fail to comply with China's Air Defense Identification Zone (ADIZ). We chose this statement because it is one of the most prominent threats to use force that the Chinese government has made in recent territorial and maritime disputes. Indeed, US officials have made a point of warning China against declaring a similar ADIZ in 41 Two other independently assigned conditions, noted in the appendix, are not relevant here and are analyzed in other work. the South China Sea, implying that such statements matter.  42  Still, the imprecise nature of the threatened consequences make it unlikely that we would observe audience costs arising due to inconsistency. Because the threat of \"defensive emergency measures\" is a relatively mild version of bluster, effects are likely to be underestimates of what tougher (but still vague) threats could generate, such as \"fire and fury.\" In the selective-history design, all respondents read the same opening context: China and the U.S. do not agree about the appropriate rules for air transit in China's surrounding waters. China's position is that foreign aircraft should identify themselves and follow instructions. The U.S. has not agreed with this position. The following treatments were randomly and independently assigned, with a control group receiving none of the treatments and reading only the common opening and closing context.  43  • Bluster (Vague Threat): On November 23, 2013 China announced an Air Defense Identification Zone over the East China Sea. China announced that if any foreign aircraft fails to identify itself to Chinese authorities or refuses to follow instructions, Chinese armed forces will take defensive emergency measures. • Biding Time: Chinese officials have explained that fighting a war in China's surrounding waters would be a grave mistake. According to General Liu Yuan, Political Commissar of the PLA's General Logistics Department, the United States is \"afraid of us catching up and will use all means to check China's development, but we absolutely must not take their bait.\" • Cost of War : Chinese officials have explained that fighting a war in China's surrounding waters would be too costly. According to General Liu Yuan, Political Commissar of the PLA's General Logistics Department: \"Since we have enjoyed peace for quite a long time, many young people do not know what a war is like, it is actually very cruel and costly. If there is any alternative way to solve the problem, there is no need to resort to the means of extreme violence for a solution.\"  The scenario then ended for all respondents with: To this day, the U.S. continues to fly military planes through the area without identifying themselves or following instructions. China has not used force to stop this. \n Outcome Questions Our key outcome of interest was whether respondents approved of the government's foreign policy performance.  44  Immediately after the scenario, we asked respondents to answer the following question, worded more generally in the hypothetical design. (Hypothetical ) How do you feel about the government's performance in handling the situation? (Selective-history) Regarding the security situation in China's surrounding waters, what is your overall evaluation of the government's performance? \n Results We analyze the data in two ways to assess whether these treatments affected respondents' approval of the government's performance, compared with respondents who did not receive the particular treatment. Per our preanalysis plan, the primary specification is a linear regression model that controls only for conditions that we experimentally manipulated. 45 44 For full details on the surveys, see Appendices D and E.  45  These include the treatment conditions described here, the order of the answer options (which we randomized to diagnose inattention), and whether a set of pre-scenario questions were asked about respondents' political views, the importance of defending the national honor even if it jeopardizes the stability of China's international environment, and whether the Chinese government relies on military strength too much or too little to achieve its foreign policy goals. Second, we control for a select set of covariates, as doing so may increase power. The covariate specifications provided similar but often more significant results. \n Government Rhetoric, Propaganda, and Mass Reactions The data suggest an important role for government rhetoric and propaganda in shaping public perceptions and persuading citizens to see government (in)action in a positive light.  \n Change in Approval Effect on Approval, Hist Figure  1 : Effects of Government Rhetoric and Propaganda. Estimated effect of rhetorical frames on public approval of the government's actions relative to the control group. The Biding Time, Nationalist History, and Cost of War treatments all increased approval, but the effects were only statistically significant at conventional levels in the case of the Biding Time and Nationalist History treatments in the Selective History experiment. In no case was the estimated effect negative. Many respondents who received the Biding Time treatment explained in their own words  46  The full table of results for the models on which these estimates are based is in Supplementary File A. a willingness to defer satisfaction to the future. As one respondent wrote: \"We are still a developing country. Can't be penny wise and pound foolish and take the trap of some countries. Wait for the right time to teach this guy who has no clue how high the sky is or how thick the earth is (wo men haishi yi ge fazhanzhong guojia, bu neng yin xiao shi da, zhongle mouxie guojia de quantao, dengdao shidang shiji zai jia yi jiaoxun zhege bu zhi tian gao di hou wei hu zuo zhang de xiaozi ).\" Another respondent explained: \"Currently, the most important thing for China is development. Make future plans after development (Zhongguo muqian zui zhuyao shi fazhan, fazhanhou da jin yi bu dasuan).\" The Nationalist History treatment, which invoked China's victimization by foreign powers, elicited a variety of expressions of solidarity and support for the government, such as \"I am Chinese. I love my homeland (Wo shi Zhongguoren, wo re ai zuguo)\" and \"I love my homeland. Whatever it does is right (Wo ai wo de zuguo, zuguo zuo shenme dou shi dui de).\" The selective-history design included a more extensive and explicit description of past humiliations as well as a more uplifting message about the successful establishment of the Chinese nation, probably accounting for its stronger effect than in the hypothetical design. Although emphasizing the cost of war had a positive but not statistically significant effect on approval, a number of respondents gave qualitative responses consistent with its logic. In explaining her approval, one respondent wrote: \"war brings too much loss to the masses (zhanzheng dui laobaixing dailai de sunshi taida),\" while another respondent wrote that \"Territorial sovereignty must be defended, but best not to use force, because war never brings benefit to the ordinary people of any country (lingtu zhuquang shi xuyao hanwei de, zuihao jinliang buyao dong wu, yinwei dong wu dui na ge guojia youqi shi laobaixing meiyou haochu).\" \n Audience Costs and Bluster Next we consider the effect of government threats that were ultimately unfulfilled. Consistent with audience costs, the Explicit Threat treatment reduced approval of the government's performance. However, reminding respondents of China's ADIZ threat increased approval, consistent with the view that audiences may reward leaders for tough but vague statements absent military action. Mobilization had a positive effect on approval, though not at conventional levels of significance. The results are similar and a bit stronger when we control for other covariates (see Figure  2 ). The confidence intervals depicted are 1.64 and 1.96 standard errors wide, denoted by the thick and thin lines; exclusion of 0 indicates a two-sided rejection of the null hypothesis of no average effect at p < 0.1 or p < 0.05, respectively.  Estimated effect of the use of threats by the government on public approval of the government's actions relative to the control group. Explicit Threats decreased public approval, while Vague Threats increased public approval, though not always at conventional standards of significance. These differences in approval across treatment and control groups suggest that public opinion costs exist in China for explicit threats, but not for vague threats. It is also possible that respondents punished inconsistency in the explicit threat condition but rewarded vague bluster due to differences in the perceived finality of the scenario's outcome. The selective history design ended: \"to this day, the United States continues to fly military planes through China's surrounding waters and that \"China has not used force to stop this\", whereas the hypothetical design concluded: \"in the end, China does not take military action, and the neighboring country consolidates control over the territory\". If more respondents in the selective history design believed that the government might take future action to rectify the situation, then this design choice may have minimized the inconsistency costs of saying one thing and doing another. At the same time, audiences evaluating their leader's performance in many real-world crises may anticipate the possibility of future action, particularly for protracted disputes with periodic flare-ups. Often a leader's decision to \"stay out\" of a conflict is later reversed, as  Levy et al. (2015, 990)  and  Quek (2017)  note. By asking respondents to explain their answers, we obtained qualitative data on the underlying mechanisms driving our results. We found evidence consistent with several theories of why respondents would disapprove of the government's failure to fulfill explicit threats. Concerning honor, one respondent wrote: \"Strong start, weak finish, lost national honor (hu tou she wei, sang shi guo jia rong yu).\" Concerning inconsistency, another respondent wrote, \"All words, no action (guang shuo bu zuo).\" Consistent with arguments that audiences disapprove of empty threats for revealing the leadership's incompetence  (Smith, 1998) , one respondent wrote: \"The incompetent Chinese Communist Party (wu neng de Gongchandang).\" On credibility  (Guisinger and Smith, 2002) , a number of respondents expressed concern about the reputational consequences of empty threats: \"After declaring the use of force, in the end backed down with no result. If other neighbors learned, it will bring China more troubles (jiran yijing shengming yong wuli jiejue, dao zui hou wu gong er fan, ruguo qita linguo dou jiejian, na jiang gei Zhongguo dailai gengduo mafan)!\" Another wrote: \"This will fuel the neighboring country's ambitions (\"Zheyang hui zhuzhang gaiguo de yexin).\" As for the benefits of bluster, many respondents were satisfied with the government's effort, understanding that conflict at present would be unwise. As one respondent explained: \"While defending the nation's sovereignty, we must also take the overall situation into account, safeguard the international environment for peaceful development, and handle issues 'on just grounds, to our advantage, and with restraint (ji yao weihu guojia zhuquan, you yao daju wei zhong, weihu heping fazhan de kongjian huanjing, suoyi guojia you li you li you jie de chuli wenti ).\" Recognizing that China would have difficulty successfully challenging the US at present, many who were reminded of the tough but vague ADIZ threat forgave the government's inaction by referencing the future, even without receiving the Biding Time justification. One respondent wrote: \"Keep a low profile, bide time, no confidence of victory right now (tao guang yang hui, zanshi meiyou bisheng de bawo).\" Another respondent stated: \"Stability and development is a prerequisite for China. It is best to avoid wars. When China is developed, we will no longer fear anyone (Zhongguo yi wending fazhan wei qianti, neng bu da jiu bu da, deng fazhan hao le, jiu shei dou bu pa).\" Another cautioned that \"The US has hidden, ulterior motives by doing this. We should not take the trap (Meiguo zheyang zuo shi juxin poce, bieyou yongxin, wo men bu yao shang ta de dang).\" Interestingly, the bluster condition increased approval, whereas vague threats in other (US) contexts have not. This difference may also point to an important scope condition: a population must be relatively hawkish for leaders to gain approval through bluster, consistent with  Kertzer and Brutger (2016) , who find that hawks and conservatives that punish inconsistency while liberals and doves punish leaders for making threats in the first place. The hawkishness of Chinese attitudes may help explain the benefits of bluster. At the start of the survey, we assessed respondents' general views. Two prescenario questions evaluated how hawkish or concerned respondents were about defending the national honor. 47 Far more respondents were hawkish or neutral than dovish, and most felt that it was important or very important to defend the national honor, even if it meant international conflict or instability (see Supplementary Files). This distribution of hawkish beliefs does not appear to be distinctive to our online sample. In a separate US-China survey, 10% of American respondents endorsed risking war to maintain their country's claims, compared with 40% of Chinese respondents. As noted in the Supplementary Files, our respondents' beliefs about the desirability of using military means to achieve China's foreign policy goals were roughly comparable to the face-to-face, GPS-assisted survey of urban residents conducted by the Research Center on Contemporary China. 48 Domestic audiences are more likely to reward bluster when attitudes are predominantly hawkish and nationalistic than when doves are better represented and the distribution of preferences is more symmetrical or even bimodal. \n Discussion and Conclusion Our study provides evidence that at least one authoritarian regime confronts domestic costs for inaction in a hypothetical crisis when public threats are explicit. In the real world, and in our experiment, however, the Chinese government is able to rally popular support by framing inaction as part of a long-run, \"biding time\" strategy of overcoming past national humiliation. In addition, the government appears to gain domestic approval by engaging in bluster -making tough but vague threats that increase popular support. We also note some limitations and shortcomings of our evidence. Overall, the estimated effects were relatively small and not robustly significant. A potential explanation is selfcensorship and inattentiveness, as detailed in Supplementary File A.5. Subsequent studies should evaluate the robustness of our conclusions and probe addtional implications, theoretical extensions, and underlying mechanisms. First, scholars should invest more in understanding how authoritarian rhetoric and propaganda can shape mass reactions in international crises. Most international crises involve at least one authoritarian regime, but few studies have systematically investigated the mass pressures that authoritarian leaders face and whether such leaders can effectively use propaganda to shape popular sentiment. Our two survey experiments in China provide suggestive evidence of authoritarian audience costs and indicate that some government explanations can be effective in justifying inaction. However, researchers have also shown that democratic governments are able to control the domestic costs of inaction or backing down through elite cues, 49 while others have highlighted the importance of social peers  (Kertzer and Zeitzoff, 2017) . Further research may wish to explicitly compare the extent to which democratic and authoritarian governments can shape domestic reactions to crisis developments-as well as how these mass incentives are communicated and understood by foreign decision-makers. If bluster is accurately diagnosed as non-committing \"empty menace\" by foreign leaders, then it should have little effect on crisis escalation. As a US official remarked, \"There's a certain amount of bluster that's taken for granted when you're dealing with North Korea.\" 50 On the other hand, if the foreign government thinks the home government has tied its hands or that the statement does signal resolve, then the foreign government may choose to back down, in which case we will not observe whether the government's statement was bluster or not. However, the foreign government may also try to test the home government's resolve, as Narang and Panda note of recent U.S.-North Korea tensions: \"in order to test whether Trump's threat is real or bluster, North Korea may try to push the line to see how far it can go.\" 51 Finally, bluster may have the effect of provoking foreign audiences and incentivizing the foreign leadership to mount a tough response, a possibility we investigate in a separate paper. Second, more work should study the effect of realistic threats, which often fall short of explicit threats. We found evidence that Chinese audiences disapproved of an empty, explicit threat in a hypothetical territorial dispute, but we also found evidence that Chinese audiences rewarded a real-world threat that was vaguer and (as yet) unfulfilled. Further comparisons within and between hypothetical and selective-history designs are needed to strengthen this inference. In the real world, threats tend to be subtle and ambiguous, with complex effects: in part engaging audience costs, but also in part expressing resolve and articulating a nation's claims. Disentangling these components more systematically is an important next step. We also recommend that survey experimentalists more often employ realistic scenarios, at least as a complement to hypothetical and abstract scenarios. Third, investigating how public preferences vary across countries and how government leaders vary in their sensitivity to public support are crucial tasks for future research. Why do some audiences reward bluster while others disapprove of it? The benefits of bluster or belligerence may have been overlooked because existing research has focused on developed, democratic societies in which audience preferences may be less hawkish and nationalistic. As reported above, Chinese appear to be much more hawkish than Americans. Further, in countries like China where debates about the use of force are enmeshed in nationalist narratives of resistance and past trauma, even the symbolic defense of the nation's honor may be critical to sustaining popular support. Which audience or constituency \"matters\" most to government leaders is also likely to vary across time and place, depending on whose approval the government needs to maintain most. The sensitivity of authoritarian leaders and their ability to manage popular sentiment is likely to vary across autocracies, just as democratic audience costs tend to vary by electoral system, media environment, and citizen access to information  (Potter and Baum, 2014) . If public threats and expressions of resolve are to be accurately interpreted, scholars (not to mention government decision-makers) must better understand the context in which such statements are made and evaluated. Fourth, more attention should focus on the effectiveness of different rhetorical strategies and media frames in shaping foreign policy perceptions. One reason the Biding Time and Nationalist History frames were effective, we suspect, is that they framed inaction as consistent with broader narratives of defending the national honor. The impact of other face-saving statements or symbolic gestures is an important question for future research. Beyond China, some audiences may be less amenable to justifications based on future success. The credibility of \"biding time\" explanations is likely to be more effective in a rising power like China than in relatively stationary or declining powers, such as Russia or Japan. The persuasiveness of government rhetoric and other elite cues may also differ by source and domestic constituency, given that many officials and media outlets form \"hawkish\" or \"dovish\" reputations even in the absence of party competition. Further research should investigate whether citizens in autocracies, like in democracies, respond more favorably to rhetorical cues from sources they identify with politically. Finally, our study sheds light on the prospects for conflict and peace in East Asia. Our surveys suggest that the Chinese government's appeals to nationalism and strategic patience have indeed been effective at bolstering popular support. While this tactic may succeed in giving Chinese leaders flexibility in short-term crises, they also risk tying their hands in the long run, as repeatedly invoking historical grievances may harden the public's desire for future vindication. If these nationalist commitments were one-sided, they might provide sufficient leverage to force an advantageous bargain. But similar convictions and nationalist narratives exist in varying degrees and permutations on all sides of the East and South China Sea disputes. As such, the domestic benefits of nationalist appeals may tempt leaders to posture in the short run, while making the long-term resolution to these conflicts that much more challenging. In addition, these disputes often flare up over perceived \"provocations,\" inadvertent developments or foreign actions that arouse domestic concern for defending the national honor. Is bluster still effective when domestic audiences feel slighted by a foreign insult? In the face of perceived provocation, can rhetorical emphasis on past humiliation or future success bolster support for inaction? We reserve for future research these important questions. Figure 1 1 suggests that the Biding Time and Nationalist History narratives had positive effects, while the Costs of War frame did not seem to have an effect.46     \n Figure 2 : 2 Figure2: Audience Costs and Bluster. Estimated effect of the use of threats by the government on public approval of the government's actions relative to the control group. Explicit Threats decreased public approval, while Vague Threats increased public approval, though not always at conventional standards of significance. These differences in approval across treatment and control groups suggest that public opinion costs exist in China for explicit threats, but not for vague threats. \n https://warontherocks.com/2017/08/ war-of-the-words-north-korea-trump-and-strategic-stability/. \n To evaluate these hypotheses, we fielded two complementary survey experiments in China between October 2015 and March 2016, n 1 =2992 and n 2 =5445. We recruited respondents through Qualtrics' Chinese partners, two national market research firms that regularly invite respondents to take surveys on a voluntary basis in exchange for small cash payments (see Supplementary Files C.1) after completing our anonymous, US-based Qualtrics survey. Respondents came from provinces across China and different income, educational, and urban/rural backgrounds. The gender and age distribution were particularly comparable to the general population of internet users in China (see Supplementary File C.2). Educational attainment in our sample somewhat exceeded the general netizen population, as in other recent online surveys.36    \n 42 US Department of State, Remarks with Philippine Foreign Secretary Alberto del Rosario, 17 December 2013, accessed at http://www.state.gov/secretary/remarks/2013/12/218835.htm. 43  In a separate paper we also analyze two other treatments related to provocation. These can be seen in Supplementary File E. \n • Nationalist History: The present dispute between the United States and China reflects a long history of China's confrontations with foreign powers. As General Secretary Jiang Zemin wrote, \"In more than 100 years after the Opium War, Chinese people were subjected to bullying and humiliation under foreign powers.\" In 1949, Chairman Mao Zedong proclaimed the establishment of the new China, saying: \"The Chinese people have stood up!\" \n\t\t\t  De Sola Pool (1973a, 463). 7 Quoted in Michel Oksenberg, \"The Political Leader,\" in Wilson (1977 ), p. 179.  8 Snyder (1991. \n\t\t\t See, e.g., Mueller (1973) ; Lai and Reiter (2005) .29  On the cost-and casualty-sensitivity of democratic citizens' support for war, see, e.g., Berinsky (2007) ; Gelpi et al. (2009) ; Gartner (2008) .30 \"She ping: he ping jin 30 nian hou, wo men yinggai ru he kan da zhang,\" Huanqiu Shibao, January 15, 2013, in English at http://opinion.huanqiu.com/editorial/2013-01/3494346.html. \n\t\t\t The two questions were: \"How important is it to defend the national honor even if it jeopardizes the stability of China's international environment?\" and \"In general, does China rely on military strength too much, too little or about the right amount to achieve its foreign policy goals?\"48 One pre-scenario question was identical to Question B3 in the 2012 China-US Security Perceptions Survey. See http://www.for-peace.org.cn/upload/20140410/1397141067591.pdf \n\t\t\t Trager and Vavreck (2011) ; Levendusky and Horowitz (2012)  50 Reuters, September 21, 2017, http://reut.rs/2xZx9Fu.", "date_published": "n/a", "url": "n/a", "filename": "19-01-24-elite-statements-isq-ca.tei.xml", "abstract": "How does government rhetoric and propaganda affect mass reactions in international crises? Using two scenario-based survey experiments in China, one hypothetical and one that selectively reminds respondents of recent events, we assess how government statements and propaganda affect Chinese citizens' approval of their government's performance in its territorial and maritime disputes. We find evidence that citizens disapprove more of inaction after explicit threats to use force, suggesting that leaders can face public opinion costs akin to audience costs in an authoritarian setting. However, we also find evidence that citizens approve of bluster-vague and ultimately empty threats-suggesting that talking tough can provide benefits, even in the absence of tough action. In addition, narratives that invoke future success to justify present restraint increase approval, along with frames that emphasize a shared history of injustice at the hands of foreign powers. 1 Lynch (2003), p. 70. 2 \"China urges Japan to properly handle sensitive issues in bilateral ties,\" Xinhua, November 2, 2015. 3 Shan Renping, \"Pinglun: you ren xian Zhongfang ruanruo, kangyi baici bu ru zou Lasen Hao yi ci,\"", "id": "bff191b2e9b5b1fbf9849044725455d8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Adrian Kent"], "title": "A Critical Look at Risk Assessments for Global Catastrophes", "text": "INTRODUCTION Speculative suggestions are occasionally made about ways in which new physics experiments could hypothetically bring about a catastrophe leading to the end of life on Earth. Some of these hypothetical catastrophes, including the \"killer strangelet\" sce-nario considered in this article, would also lead to the destruction of the planet and wider catastrophic consequences. In any case, the proposed catastrophe mechanisms generally rely on speculation about hypothetical phenomena for which there is no evidence, but which at first sight do not contradict the known laws of physics. Sometimes, such pessimistic hypotheses can be countered by arguments that show that the existence of the catastrophe mechanism is highly improbable, either because closer analysis shows Kent that the proposed mechanism does in fact contradict well-established physical principles, or because its existence would imply effects that we should almost certainly have observed but have not. Unfortunately, there is a difficulty in making an argument of this type sufficiently reassuring. One would like to be reassured that the chances of inadvertently triggering a global catastrophe are very small indeed before going ahead with an experiment. But finding arguments that justify this conclusion with the appropriate level of confidence may be very hard, if not impossible. Discouragingly few attempts to grapple with this issue have been made. In fact, even the obvious and fundamental question-how improbable does a catastrophe have to be to justify proceeding with an experiment?-seems never to have been seriously examined. The aim of this article is to face this question squarely, in the hope of stimulating further debate. The particular stimulus for this article was the debate over the safety of the RHIC supercollider experiments now underway at Brookhaven, and the ALICE experiments proposed by CERN. Speculation about possible disaster scenarios in these experiments led to some pressure for the experiments to be deferred or cancelled. In response, reports and articles were written that were used to justify commencing the RHIC experiments on the grounds that, inter alia, \"Cosmic ray collisions provide ample reassurance that we are safe from a . . . catastrophe at RHIC\"  (1)  and \"Beyond reasonable doubt, heavy-ion experiments at RHIC will not endanger our planet.\"  (2)  Here I will contend that the risk bounds obtained are actually not small, taking into account the scale of the catastrophe, either according to standard risk analysis or when compared with other adopted standards for acceptable risk to the public. Since the criteria used by Brookhaven to justify proceeding were developed by theoretical physicists and administrators, not by broader representatives of the public or by professionals in risk management, it seems desirable to bring these issues before a wider audience for the purposes of informed discussion and the formation of sounder public policy in future. \n HISTORICAL EXAMPLES The first catastrophe mechanism seriously considered seems to have been the possibility, raised in the 1940s at Los Alamos before the first atomic bomb tests, that fission or fusion bombs might ignite the atmosphere or oceans in an unstoppable chain reaction. Investigation led to an analysis by Konopinski et al.  (3)  that fairly definitively refuted the possibility. Compton was later reported, in a published interview  (4)  with Pearl Buck, as saying that he had decided not to proceed with the bomb tests if it were proved that the chances of global catastrophe were greater than three in a million, but that in the event calculation proved the figures slightly less. It is hard to understand how any meaningful calculation could have produced such a risk figure. The analysis of Reference 3 gives convincing arguments against the possibility of a catastrophic chain reaction, based on well-established physical principles. It concludes that it is unreasonable to expect a chain reaction propagated by nitrogen-nitrogen fusion reactions, and that an unlimited chain reaction consuming the atmosphere is less likely still. Other possible reactions, involving protons in clouds of steam liberated from the oceans, are also considered and argued to be less dangerous still. Konopinski et al. do note the \"distant probability\" that the mode of propagation of the reaction in the atmosphere might be more complicated than their analysis allows, in which case its conclusions might not apply, and they suggest that the complexity of their argument and the absence of a satisfactory experimental basis for it makes further work on the subject highly desirable. However, they offer nothing resembling a catastrophe risk estimate, nor any results from which a quantitative estimate could be derived. Yet, so far as I know, Compton never made an attempt to correct Buck's account. Had she simply misunderstood, it would have been easy for Compton to disclaim the statement. And, had it not reflected his views, he would surely have wanted both to set the historical record straight and to defend his reputation against the charge of unwisely gambling with the future of humanity. The natural inference seems to be that Compton did indeed make the statement reported.  1  If so, although the risk figure itself appears unjustifiable, Compton presumably genuinely believed that an actual risk (not just a risk bound)  1  In April 2000, in an attempt to understand this puzzling statement of Compton's, I contacted Hans Bethe, a key figure in both the Los Alamos project and the theoretical work that led to the conclusion that the possibility of an atomic bomb explosion leading to global catastrophe was negligible. His view, relayed by an intermediary (Kurt Gottfried), was that the analysis of Konopinski et al. was definitive and does not allow one to make any meaningful statement about probabilities since the conditions that must be met cannot be reached in any plausible manner. Bethe suggested that the 3 × 10 −6 figure was made up by Compton \"off the top of his head,\" and is \"far, far too large.\" I am most grateful to Hans Bethe and Kurt Gottfried for this e-mail correspondence. of 3 × 10 −6 of global catastrophe was roughly at the borderline of acceptability, in the cause of the American and allied effort to develop atomic weapons during World War II. Apparently the figure did not worry 1959 American Weekly readers greatly, since no controversy ensued. It would be interesting to compare current opinion on the acceptability of a 3 × 10 −6 risk of global catastrophe, in the circumstances of the Los Alamos project or otherwise. Another hypothetical catastrophe was examined some time ago by Hut and Rees.  (5, 6)  They considered the possibility that the vacuum state we live in is not the true vacuum, but merely a local minimum of the effective potential. They asked whether, if this were the case, new generations of collider experiments could trigger a catastrophic transition to the true vacuum, destroying not only the Earth but (eventually) all presently stable forms of matter in the cosmos. They showed that the probability of this occurring artificially in present or foreseeable collider experiments is considerably smaller than the probability of it having occurred naturally within our past light-cone.  2  Most recently, in response to some (rather unfocused) public concern,  (7)  the possibility of some catastrophe arising from prospective experiments at the Brookhaven relativistic heavy ion collider (RHIC) was reviewed by Busza et al. (BJSW) and Dar et al. (DDH).  3  Both groups paid most attention to the \"killer strangelet\" catastrophe scenario, which would arise if negatively charged metastable strange matter existed and could be produced in the experiments. As well as giving theoretical arguments against the hypotheses involved, both groups offer risk bounds inferred from empirical evidence. BJSW's proposed bounds on the probability of catastrophe during the 10-year lifetime of RHIC, derived from the survival of the Moon for 4.5 billion years, range from 10 −5 to 2 × 10 −11 , depending on how conservative the assumptions made are.  (8)  DDH's bounds, derived from the observed rate of supernovae, range from 2 × 10 −6 (their pessimistic bound for a very slow catastrophe, in which the Earth is prematurely destroyed at some point in the billion years before it would anyway be consumed by the expanding Sun) to 2 × 10 −8 (their main bound).  (2)  As the quotations extracted in Section 4 attest, both groups originally  (1, 2)  suggested their empirical bounds alone were adequate to show that the experiments were safe. If correct, this conclusion would obviously be particularly welcome, since it would remove any need to evaluate the degree of confidence that should be placed in the theoretical arguments. The view that the empirical bounds were indeed adequate was also expressed in commentaries.  (9, 10)  However, there are good reasons, explained below, to believe that this conclusion is incorrect, and indeed the claim was withdrawn by BJSW, after criticisms from the author of this article. BJSW produced a second version of their preprint, removing the reassuring characterizations of their risk bounds and instead disavowing any attempt to decide what is an acceptable upper bound on p catastrophe . In this revised version, BJSW also accept that the arguments for their empirically derived risk bounds could be invalidated if some additional pessimistic hypotheses were correct.  4  BJSW's revision of their preprint was an adequate response, from a purely scientific perspective. The public policy implications are troubling, however. My understanding is that the U.S. government's authorization for the RHIC experiments to proceed was given partly on the basis of BJSW's original arguments,  (1)  whose discussions of risk were gravely flawed, as the quotations considered in Section 4 illustrate. Public concern was countered by widely publicized  (11, 12)  reassurances  (9, 10)  that the risk was negligible, also relying heavily on the risk appraisals given in BJSW's original preprint.  (1)  As far as I am aware, no effort was made by Brookhaven to reobtain authorization on the basis of BJSW's revised assessment, or to bring what is a significantly revised case to media and public attention.  5  In my opinion, such efforts should have been made. It should be noted that BJSW stress  (8)  in the revised version of their article that they regard the theoretical arguments alone as sufficiently compelling. This may be a defensible position, but it is not the case that was originally made and publicized. \n SCOPE OF THIS ARTICLE This article is meant as a contribution to the debates over hypothetical catastrophe scenarios in the RHIC and ALICE collider experiments and over other hypothetical or real global catastrophe risks. It focuses on the key question: What risk of catastrophe could be acceptable? Other relevant questions are not considered. In particular, in the case of the collider experiments, no attempt is made to infer quantitative risk bounds from the qualitative theoretical arguments against the possibility of catastrophe, or to consider BJSW's conclusion that the theoretical arguments alone offer sufficiently compelling reassurance.  (1, 8)  The interest in this debate is not, of course, purely or mainly intellectual. The aim is to improve future policy over catastrophe risks. In particular, lessons can and should be learned from the evident flaws in BJSW's and DDH's discussions of risk. It is obviously unsatisfactory that the question of what constitutes an acceptable catastrophe risk should continue to be decided, in an ad hoc way, according to the personal risk criteria of scientists whom those in charge of experimental facilities choose to consult. Those criteria, however sincerely held and thoughtfully constructed, may be unrepresentative of general opinion or of expert opinion in risk analysis. Worse still, history suggests the risk criteria actually used may not be at all thoughtfully constructed. Compton's reported opinion suggests, and the mischaracterizations of References 1 and 2 illustrate very clearly, that scientists whose expertise is not in risk analysis or public policy cannot necessarily be relied on either to interpret the risk implications of the science correctly or to consider elementary arguments that tend to suggest more cautious risk criteria than can easily be satisfied. Relying on such inexpert appraisals is neither in the public interest nor the longterm interests of science. Scientists and scientific institutions need to work to gain, maintain, and justify public trust. Arguments that suggest that an experiment should proceed simply because the global catastrophe risk appears fairly low, without comparison to any preexisting thresholds or guidelines, may not only fail to reassure, but may (not unreasonably) be interpreted as public relations exercises, intended to support a prejudged conclusion, rather than dispassionate scientific analyses. As Calogero notes,  (14)  this has a long-term cost for the credibility on questions of risk not only of those directly involved, but of all scientists, and the likely long-term consequence is less in-formed and more irrational public debate and public policy. It may well not be possible to reach a complete consensus on firm guidelines. It seems unlikely, for instance, that some clear agreement will emerge that global catastrophe risks are small enough to be of negligible concern if and only if lower than, say, 10 −20 . Life is more complicated than that, and democratic debate more multifaceted. Nonetheless-indeed, for this very reason-it would be valuable to have a spectrum of carefully argued opinion in the literature. I hope that the arguments below may spark further discussion. \n BJSW'S AND DDH'S RISK BOUNDS FOR THE \"KILLER STRANGELET\" SCENARIO We turn now to the particulars of the catastrophe risk concerns raised over the RHIC and ALICE experiments, and specifically to the hypothetical \"killer strangelet\" catastrophe scenario analyzed in some detail by BJSW and DDH. The \"killer strangelet\" scenario requires: (i) that stable strange matter exists, (ii) that a valley of stability exists for negatively charged strangelets, (iii) that negatively charged metastable strangelets could be produced in the ≈40 TeV Au-Au ion collisions planned at RHIC, (iv) that a strangelet so produced could survive collisions that bring it toward rest in surrounding matter, and (v) that it would then fuse with nuclei, producing larger negatively charged strangelets, in a runaway reaction that eventually consumes the Earth. The theoretical arguments  (2, 8)  against (i)-(iii) are generally regarded as convincing. If (i)-(iii) were nonetheless true, (iv) and (v) would also be plausible. If (i)-(v) were true, killer strangelets should also be produced in naturally occurring high energy heavy ion collisions, which take place when cosmic rays collide with one another or with heavy nuclei in celestial bodies. Naturally produced killer strangelets would be able to initiate runaway reactions capable of destroying asteroids, satellites such as the Moon, or stars. From the fact that the Moon has survived for 4.5 billion years, and from the fact that astronomical observations are not consistent with stars being converted into strange matter at any significant rate, bounds on the risk of catastrophe at RHIC can be derived.  (2, 8)  Unfortunately, these derivations require assumptions about the types of interaction that produce strangelets, the velocity distribution of the strangelets produced, their interactions with nuclei, and their stability.  (2, 8, 13)  For this reason, BJSW and DDH give various bounds, derived by making more or less conservative assumptions. Even the weakest of these requires some assumptions.  (8, 13)  Without knowing what level of confidence we can have in the relevant assumptions-a question that neither group addresses quantitatively-it is difficult to see how the bound figures can really be meaningful.  (13)  But even if the figures cannot really be justified, the comments made on them by BJSW, DDH, and others give an interesting and valuable insight into the risk criteria of physicists and administrators involved in RHIC policy. Assuming that RHIC runs for the scheduled 10 years, DDH obtain p catastrophe < 2 × 10 −8 for a fast catastrophic destruction of the Earth and p < 2 × 10 −6 for a slow destruction that would be completed in the billion years before the Sun expands beyond the Earth orbit. DDH describe these results as \"a safe and stringent upper bound on the risk incurred in running  [RHIC] .\" They add that the two bounds respectively imply that \"it is safe to run RHIC for 500 million years\" and that \"running the RHIC experiments for five million years is . . . safe.\" These last two statements are, of course, incorrect. DDH's bounds, if valid, would establish only that it would be unlikely that the Earth would be destroyed very early in a RHIC experiment run over the relevant periods: the bounds are consistent with a high probability of destroying the Earth at some point during these hypothetically extended experiments.  6  In the first version  (1)  of their article, BJSW described DDH's result as \"a factor of 10 8 below the value required for the safety of RHIC.\" This, of course, is also incorrect: a risk bound 10 8 times that of DDH's would be consistent with a high probability of destroying the Earth within five years of the RHIC experiment-a risk level that even the most gung-ho physicist could hardly describe as \"safety.\" Using their own independent analyses, BJSW derive the following bounds from the survival of the Moon, given various assumptions (their Cases I-III) about strangelet production, and again assuming that RHIC runs for the scheduled 10 years: p catastrophe < 2 × 10 −10 , p catastrophe < 2 × 10 −5 , p catastrophe < 2 × 10 −4 . They described the second and third of these cases as still leaving \"a comfortable margin of error.\" These comments, and that quoted at the start of this paragraph, are so obviously inapplicable-no sane person would seek to reassure the public by suggesting that a risk bound of one in 5,000 of destroying the Earth represented a comfortable margin of error-that I suspect they must reflect some surprising confusion on BJSW's part at the time of writing Reference 1. BJSW refined their calculations in the second version of their article, extracting an extra factor of 10 and producing bounds for a 10-year run of the RHIC experiment of (Cases I-III): p catastrophe < 2 × 10 −11 , p catastrophe < 2 × 10 −6 , p catastrophe < 2 × 10 −5 . In this revised version, which followed criticisms of the comments noted above, no judgment is made as to whether any of the bounds are satisfactory. To quote BJSW: \"We do not attempt to decide what is an acceptable upper limit on [ p catastrophe ], nor do we attempt a 'risk analysis', weighing the probability of an adverse event against the severity of its consequences.\"  (8)  We use the revised bounds in the following discussion, referring to them simply as BJSW's bounds. DDH's main bound-p catastrophe < 2 × 10 −8 over the 10-year life of RHIC-has been widely referred to  (1, 2, 9, 10)  in terms that suggest that it alone would be sufficiently reassuring to require no further analysis or risk optimization. My impression is that many numerate and thoughtful people would disagree. My own reasons for doing so are given below. \n RISK BOUNDS AND RISK ESTIMATES: AN IMPORTANT CAVEAT It is important to stress that DDH's and BJSW's empirical arguments produce bounds on the risk of catastrophe, not estimates of that risk.  7  Their bounds are based on the fact that we do not observe something that we should expect to observe if the risk were larger than some value p. A negative result of this form tells us nothing about the actual value of the risk. Everything in DDH's and BJSW's analyses is consistent with the true risk of catastrophe being zero-and if current theoretical understanding is correct, the risk is indeed precisely zero. When the destruction of the Earth is in question, though, it would be preferable not to have to rely on theoretical expectations alone. As Glashow and Wilson put it,  (10)  \"The word 'unlikely', however many times it is repeated, just isn't enough to assuage our fears of this total disaster.\" Hence the interest in looking at naturally occurring versions of the experiment, verifying that they have not resulted in catastrophes, and so producing firm bounds on the risk of catastrophe. Unfortunately, this approach has its pitfalls and limitations. Comparing the effects expected from hypothetical killer strangelets produced in naturally occurring heavy ion collisions and at RHIC is not completely straightforward. Theoretical assumptions need to be made in order to derive risk bounds. Unless we are very confident indeed in those assumptions, we cannot validly infer very small risk bounds this way.  (8, 13)  And in any case, nature may not necessarily have done versions of the experiment we are interested in often enough to produce sufficiently strong risk bounds. How do we begin to decide what constitutes a sufficiently strong risk bound? It seems to me that the correct approach in appraising risk bounds is to make worst-case assumptions. So, if we are assured that p catastrophe ≤ p 0 , and we have to decide whether that bound alone is sufficient reassurance, we have to ask whether we would be happy to proceed if we knew that p catastrophe = p 0 . If not, then the bound alone is not sufficiently reassuring. Such a bound might still form part of a compelling case for the safety of an experiment if it could be combined with other arguments. For instance, in the case of RHIC, it might be argued that a combination of the theoretical arguments and empirical bounds is sufficiently reassuring, even if neither would be alone.  8  I will not consider such arguments here. Nor-to reiterate-do I examine whether the theoretical arguments alone are sufficiently reassuring. The discussion below considers only the narrow question of whether the empirical bounds alone would suffice. \n RISK VERSUS EXPECTATION The destruction of the Earth would entail the death of the ≈ 6 × 10 9 human population and of all other species, the loss of the historical record of the evolution of its biosphere, and the loss of almost all record of the culture developed by humanity.  9  Added to these are the opportunity costs arising from the absence of future generations. Consider for the moment just the number of human deaths. If an experiment were expected to cause one human death, in the everyday use of the termthat is, it was likely that at least one person would die as a result of the experiment-its health and safety implications could not be said to be negligible. Now, when we are dealing with small risks of large catastrophes, we cannot directly use this measure: an experiment with small risk is expected to cause no human deaths, in the sense that this is the likeliest outcome. However, we can calculate a related measure: the statistical expectation value of the number of human deaths. The expectation value of the number of human deaths ensuing from an Earth-destroying catastrophe is E d = p catastrophe N, where N ≈ 6 × 10 9 is the current human population. So, if we accept E d as an appropriate measure of the seriousness of a risk-and the next section explains why we should-then any risk that does not satisfy p catastrophe 1.6 × 10 −10 (1) is not negligible. Of the above bounds, neither of DDH's bounds ensures that Equation (  1 ) is satisfied, nor do the second and third of BJSW's. BJSW's least conservative lunar survival bound (Case I) comes closer, but still fails unless a factor of 1/8-i.e., in this case a probability of 1/8 of causing one human death-is regarded as negligible. Making the comparison in terms of expectations, DDH's main (tighter) bound implies that the expectation value of the number of human fatalities caused by RHIC in more than 10 years will not exceed 120. Put this way, this bound seems far from adequately reassuring. \n IS THE EXPECTATION VALUE OF THE NUMBER OF FATALITIES RELEVANT? It might perhaps be argued that the preceding calculation is misleading. After all, DDH's bounds on p catastrophe represent probabilities small enough to be negligible in most circumstances. Most of us take 2 × 10 −8 risks of death in our stride: the risk of a typical U.S. citizen dying in a shark attack in any given  9  A few spacecraft, including the message-bearing Pioneer and Voyager craft, would survive, as would the-continually attenuating-electromagnetic signals generated on Earth. year is comparable. Translating the bound value into E d , the expected number of fatalities, makes it seem significant. But is it really reasonable to use expected fatalities as a measure of the safety of a risk bound? Actually, the next section argues that considering E d alone still greatly underestimates the cost. But first let us consider whether requiring E d < 1 gives a sensible upper bound on negligible risk, assuming that it is agreed that the certainty of causing one death would not be negligible. I believe most expert opinion would agree that it does, for the following reasons. First, everyone agrees that in carrying out any risk analysis we need the cost or utility of the various outcomes, not merely their probability: a 10 −3 chance of losing one dollar is better than a 10 −3 chance of losing one million dollars, and so on. Second, a fundamental principle of risk analysis is that in normal circumstances rational people are risk averse. If X represents a random process whose possible outcomes x i have probabilities p i , and if V(x i ) represents the value to the community of outcome x i , then the value V(X) of a single run of X-that is, the value of allowing precisely one of the x i to happen, with respective chances p i -is generally assumed to obey V(X) ≤ i p i V(x i ). ( The values of undesirable outcomes, of course, are negative: we refer to −V(x i ) as the cost of x i . A second principle is that the utility or cost function is concave. Applied to the cost of a loss of human lives, this implies that the cost to society of N deaths is at least N times as great as the cost of one death: if x N and x 1 represent the two events, then V(x N ) ≤ NV(x 1 ). (3) The principles of risk aversion and concave utility explain, for example, why it can often be rational to take out insurance, even though on average the insurance company expects to make a profit and the customer a loss. Similarly, it explains why investors almost universally require investments that involve higher risk to offer a higher expected profit in compensation. By considering a random process X with probability 2 × 10 −8 of killing 6 × 10 9 people and probability (1 − 2 × 10 −8 ) of killing no one, we see that the principles together imply that a 2 × 10 −8 chance of killing 6 × 10 9 people is at least as bad as the certainty of killing 120 people. In summary, to demonstrate that the risk is negligible, we would need to show that E d is considerably smaller than 1-precisely how much smaller depend-ing on precisely how risk averse one is when it comes to global catastrophe. Neither DDH's nor BJSW's bounds satisfy this criterion. To speak of the bounds being \"safe and stringent\" or guaranteeing \"comfortable margins of error\" is, on this analysis, simply incorrect. Similarly, to demonstrate that the risk is acceptable, it would be necessary (though not necessarily sufficient) to show that E d is small enough that the certainty of the experiment killing E d people would be acceptable. Put another way, if it would be unacceptable for the experiment to lead to the certain loss of E d lives, then a risk at the bound value would be unacceptable. Suppose, counterfactually, that we knew that the RHIC experiment were certain to kill precisely N people (and no more). What value of N would be acceptable? Answers will vary, but my guess is that most would be somewhere in the range <10 or so. In particular, I think it clear that RHIC would not have obtained political authorization if it was thought certain to kill precisely 120 people: that would be regarded as an unacceptably high cost. From the discussion of this section, it follows that a global catastrophe risk at the DDH bound value would be at least as unacceptable. Although the observations made in this section are elementary, it is worth noting that the CERN panel did not acknowledge their validity. The response of Alvaro de Rujula, the panel leader, is accurately summarized by his opinion, quoted in New Scientist,  (15)  that it is \"absurd\" to take the risk bound probability and multiply it by the global population. I recommend contemplation of this comment to anyone inclined to automatic faith in the risk analysis expertise of scientists chosen by institutions to argue for the safety of their experiments. \n COMPARISON WITH EXISTING RISK POLICIES DDH's and BJSW's risk bounds were presented and discussed by DDH  (2)  and BJSW  (1)  in a statement by John Marburger, then director of Brookhaven,  (9)  and in a commentary by Glashow and Wilson.  (10)  None of these discussions make comparisons with risk criteria or optimization procedures applied to other potentially hazardous activities. This is unfortunate, since risk comparisons are generally illuminating, and in this case suggest that regarding the risk bounds per se as adequate would be wildly inconsistent with at least some established policy. For example, the U.K. National Radiological Protection Board requires that the risk of serious deleterious health effects arising from a nuclear solid waste disposal facility must always be bounded at below 10 −5 per year, that risk optimization procedures should be continued until the risk is below 10 −6 per year, and that the risk of low probability natural events that could lead to serious deterministic health effects should be separately bounded at 10 −6 per year.  (16)  The risk figures apply to the critical group of individuals, typically numbering between a few and a few hundred, whose habits or location render them most at risk. Quite typically, the events whose risk is bounded would be expected to kill fewer than 10 people. In summary, according to established policy for these radiation hazards, it is not acceptable to incur a risk of greater than 10 −6 per year of killing ≈5 people. The risk aversion arguments of the last section suggest that a consistent policy on catastrophe risk should treat a risk greater than 10 −15 per year of killing the global population as even less acceptable. An acceptable risk bound should thus imply p catastrophe 10 −15 per year. (  4 ) \n FUTURE LIVES The discussion so far has considered only the expected cost due to immediate human fatalities, neglecting the other costs mentioned earlier. These are very hard to quantify in any commensurable way. (What is the value of the rest of the biosphere compared to that of the human population? What price do we put on the historical record?) However, it is at least arguably possible to assign a sensible and commensurable value to one of these further costs-the loss of future generations-by estimating the number of future human lives that would not take place if the planet were destroyed in the near future. This line of argument cannot be followed without addressing two rather complex questions: Should we value our successors' lives as highly as those of our contemporaries? And can we say anything meaningful about the likely fate of humanity over the billion years of life the Earth has left (or beyond)? To the first, my own answer is \"yes,\" partly because I cannot see any good reason to prefer an unknown contemporary to an unknown successor, and partly because it seems to me our lives have value in the first place largely because they form part of ongoing human history. This view finds some support in established policy: the U.K. National Radiological Protection Board guidelines cited above also explic-itly state that those living at any time in the future should be given a level of protection at least equivalent to that given to those alive now. As for futurology, there are obviously so many unknowns that attempting detailed analysis seems pointless. I offer only a crude calculation, which is obviously open to criticism, but at least suggests a starting point for discussion. Suppose, optimistically, that humanity has a reasonable chance of surviving (in some form) for the lifetime of the Earth. Suppose also that there is a reasonable chance of arranging things so that the sum global quality of life is at least at the level of today, and the global population is roughly today's: 10 10 in round figures. And suppose we neglect the possibility that the human lifespan may increase beyond 10 2 , on the grounds that it is arguably irrelevant: arguably, one can make a reasonable approximationreasonable, that is, given the uncertainties in the entire discussion-by considering the total number of person-years, so that for instance a 700-year life is equated to seven 100-year lives. Let us also, conservatively, neglect the effect of migration to other planets some time in the future, which would presumably (i) allow the human population to vastly increase over the next billion years and (ii) permit humanity to survive beyond a billion years. The cost of the destruction of the Earth today would then be roughly 10 10 10 −2 10 9 = 10 17 lives, or 10 7 greater than the cost earlier calculated. Including this factor in the earlier calculation derived from the NRPB's risk bounds would mean that an acceptable risk bound should imply p catastrophe 10 −22 per year. ( This further proposed tightening of risk bounds is controversial in all sorts of ways. To mention just one: regarding the loss of future lives as a separate cost raises the question-a cost to whom? To those potential future generations, deprived of the possibility of existence? To us, deprived of descendants and successors? Both, I think-but I concede that both lines of thought raise some difficulties. Another way of approaching the question is to ask a different hypothetical question: Would it be far worse if all of us (or all life on Earth) were killed than if almost all of us (or almost all life on Earth) were, supposing that in the second case the planet remained otherwise fit for life? Answering \"yes\" suggests placing a high relative value on future lives, since the number of immediate fatalities is almost the same in both cases. Those who answer \"no\" will presumably not find any of the arguments of this section convincing. My impression is that the question has not been widely enough debated for it to be possible to say which view (if either) reflects general opinion. For the moment, then, whichever view one holds on future lives, it is worth bearing in mind that the majority view, on which catastrophe risk policy should properly be based, may turn out to differ. \n SOME COUNTERARGUMENTS Calculations and comparisons are indispensable in rationalizing risk policy and in highlighting inconsistencies. However, there is no generally agreed set of principles from which we can decide policy in every instance. Politics do not form a subset of mathematics. The above arguments could well be opposed on many different grounds. I consider here some counterarguments that have been suggested to me in discussions. 1. One obvious criticism is that the arguments above consider the cost of a catastrophe risk but not the benefits gained by taking the risk. For that reason, it may be argued, they are bound to produce overcautious prescriptions. After all, no risk at all is worth taking unless there is some benefit. Without a costbenefit analysis, no sensible conclusion can be reached. This is a partially fair criticism, but only partially. It should be stressed that it does not apply to the argument of Section 6, since using the number of deaths as a measure of safety is justified by comparing the implicit cost-benefit tradeoffs in conclusions that would be generally agreed. It seems to me pretty uncontroversial that, despite the benefits of RHIC, the experiment would not be allowed to proceed if it were certain (say, because of some radiation hazard) to cause precisely 120 deaths among the population at large. If that is accepted, it follows that a risk at the DDH bound value would be unacceptably high, even when the benefits of RHIC were taken into account. That said, some forms of cost-benefit analysis might indeed suggest that requiring p catastrophe 10 −15 per year or lower may be overstringent. The likely immediate benefit of the RHIC experiments-advancing our understanding of basic science-is not negligible. Moreover, the possible benefits presumably include at least some probability-perhaps small, but not necessarily small compared to 10 −15 -of contributing in some presently unforeseen way to a discovery with a very large beneficial impact on future human lives. The foresight problem is particularly acute here, of course, since one can also imagine low probability outcomes, other than the catastrophe scenario, with a large negative impact. But, if one takes the view that scientific and technological progress have on balance been beneficial and are likely to continue to be, the small possibility of a benefit that would save (or enable) many future human lives gives, at least in principle, something to offset against the small possibility of a catastrophe. It is important to be clear, though, that by definition no cost-benefit argument could justify a claim that the risks involved are negligible. Rather, it would make the case for proceeding with RHIC by suggesting that the risks, though possibly not negligible, were justified by the benefits. This is not the case that has been made. Such a case might or might not be widely accepted. 2. It may be argued that the more stringent risk criteria suggested above for global catastrophe, even if rationally justifiable in theory, are impossibly utopian. If we took them seriously, and attempted to ensure that they were satisfied before proceeding with any enterprise, we would stop not only collider experiments, but many other human activities. Progress would become impossible; life might be made unliveable. Maybe-but I would be cautious about accepting this sort of defeatism too readily. We begin from a state where risk bounds of 10 −6 are used quite widely, for instance in the solid nuclear waste disposal guidelines cited above. It does not seem obvious to me that, with careful attention to the problems, we could not ensure that catastrophe risks associated to specific mechanisms are many further orders of magnitude smaller. On the contrary, it seems quite clear that in some cases catastrophe risk bounds could be substantially reduced. The RHIC experiments are an excellent example: had the problem of reducing the risk bounds been taken seriously, further theoretical research, perhaps combined with a tentative experimental program aimed at carefully testing our understanding of the new physics involved before running the full experiment, could almost certainly have reduced the bounds very significantly. Of course, this is not to say that risk avoidance is cost free. One has to accept that more stringent catastrophe risk criteria might indeed delay or preclude at least some interesting future experiments. It seems to me we just have to accept this as a fact of life. One cannot defensibly adopt a mindset that requires that every interesting experiment must be carried out, and that sees every risk analysis as an exercise in justifying this foregone conclusion. Human life, collectively as well as individually, is, after all, fragile. Our understanding of nature is limited, and there are surely many dangers we have not yet appreciated. Due caution is appropriate. We should not, in any case, rely on speculation about the implications of a more cautious catastrophe risk policy. If it were to become clear that it would be effectively impossible to apply a policy on catastrophe risks consistently, obviously that policy would need to be reconsidered. Unless and until carefully justified arguments are made, identifying specific examples of problematic catastrophe risks, it seems premature to worry. 3. The justifications given above for risk criteria may strike some as a bad policy guide, since they assume that preserving human lives is in some sense a primary value against which our actions should be judged. Actually, of course, we are guided by many other values. Few people consistently act so as to maximize their own life expectation, for example: many risky pleasures are widely indulged in. Perhaps we should accept that what applies to us as individuals applies also to us as a species: worrying about very small risks detracts too much from the quality of our existence to be the best course. This is certainly arguable. On the other hand, current risk policy tends to count the cost in human lives for a good reason: because that particular value seems to be more widely shared and more strongly held than most. It cannot possibly adequately represent the variety of individual values we bring to any policy debate, but it is a measure that, by general consensus, is very important. Making a generally acceptable policy for extinction risks on some other basis would require establishing a fairly firm consensus on what that basis should be. No such consensus seems to exist at the moment. 4. There is what might be termed the argument of dominant risk. We face many other extinction risks, some natural (large asteroid impact), some wholly or partly self-created (global nuclear war, catastrophic extinction of species as a result of human impact on the global ecosystem, catastrophic climate change as a result of human impact on the global environment). There is a view that suggests that a new artificial risk is acceptable if it is smaller than existing risks. A refinement of this view is that a new artificial risk is acceptable only if smaller than presently unavoidable natural risks. In two further common variants of these two views, \"smaller than\" is replaced by \"very small compared to.\" Large asteroid impact seems to be the greatest known natural extinction risk that can be reasonably well estimated. The risk of the Earth being hit by an asteroid of diameter 10 km is estimated to be 10 −8 per year.  (17)  Such an impact would be so devastating that it is generally thought very likely that it would cause mass extinctions of species, and very plausible that we would be among the species extinguished. Accepting that last hypothesis, perhaps at the price of another order of magnitude, gives an estimate of 10 −8 -10 −9 per year for this natural extinction risk. Following the argument of dominant risk leads to the socalled asteroid test, according to which an artificial extinction risk is acceptable if smaller than ≈10 −9 per year, or in the more conservative version, very small compared to 10 −9 per year.  10  My impression from discussions is that many thoughtful people find some version of the argument of dominant risk reasonable, but that many equally thoughtful people find this line of argument entirely irrational. My sympathies are with the latter. Why should the existence of one risk, which may be distressingly  10  Versions of the \"asteroid test\" have been discussed as possible justifications for the acceptability of the BJSW and DDH risk bounds by several people involved in policy formation at CERN and Brookhaven: for example in W. Pratt et al., Brookhaven National Laboratory Memo to T. Ludlam and J. Marburger, 17.2.00. The test is also considered in Reference 14. high, justify taking another easily avoidable risk, which, even if much lower, may still be unacceptably high? Unavoidable natural risks are not normally believed to justify wilfully inflicting avoidable risks on third parties. Everyone now living is very likely to die within the next 120 years, and would be very likely to die of natural causes in that timespan even if exposed to no other risks. An industry that added slightly to the natural risk level, annually killing 10,000 people who had made no choice to accept the extra risk, would not find much sympathy for the defense that these extra deaths were more or less lost in the noise compared to natural wastage. A further problem specific to the asteroid test is that it assumes that asteroid extinction risks are either unavoidable or else, though avoidable in principle, small enough to be tolerable. In fact, the asteroid threat is not unavoidable with current and foreseeable technology, and passive and active countermeasures are being seriously considered. That said, let me reiterate that many people seem to be persuaded by some version of the argument of dominant risk. It no doubt deserves a more careful discussion than is given here. The above brief sketch of a counterargument is not meant to dismiss the \"asteroid test\" and related criteria out of hand, but rather just to note that there are serious counterarguments. I do not believe these criteria represent anything approaching a consensus view. Unless and until it becomes clear that they do, they cannot legitimately be used to justify catastrophe risks. \n FINAL COMMENT The particular artificial extinction risk considered in this article is hypothetical, and there are good arguments to suggest that the actual risk is small or zero. But, as already noted, we face other undoubtedly real and not necessarily small artificial extinction risks. The above arguments, which suggest that the true costs of extinction are generally underestimated, obviously apply generally. For instance, while the serious costs associated with artificially induced global warming are widely (albeit not widely enough) appreciated, the extra cost associated with the small risk of a truly catastrophic climate change does not seem to have been much con-sidered. Yet it might be that, with proper accounting, the cost of the risk of climatic catastrophe would be the greater. Similarly, although some (insufficient) attention is being paid to the costs associated with the loss of biodiversity caused by human impact on the environment, the cost of the risk of a catastrophic collapse of the global ecosystem seems to have been generally neglected. In these and other areas where modeling is possible, the above arguments suggest we should encourage and pay attention to research into unlikely but not inconceivable catastrophic outcomes, and try to quantify the risk they represent, rather than focusing only on likelier outcomes that may be very deleterious but are not truly catastrophic. \t\t\t These results are reviewed in Jaffe et al. (8)  Whether they offer adequate reassurance that no forseeable collider experiment will be unacceptably risky deserves reconsideration in the light of the arguments set out below. 3  DDH also considered the ALICE experiments, scheduled to take place later at CERN. Their bounds on the risk of catastrophe ensuing from ALICE will not be considered here, though it is worth noting that even DDH regard them as inadequate and suggest further investigation. \n\t\t\t Some further possible loopholes in those arguments are listed in Reference 13. 5  Indeed, the Brookhaven web pages continue, in April 2003, to direct readers to the original unamended version of BJSW's preprint: see http://www.bnl.gov/rhic/docs/rhicreport.pdf. \n\t\t\t That these statements misrepresent their results was pointed out to DDH by the author in January 2000. \n\t\t\t In contrast, Compton's reported statement on the risk of destroying life on Earth by a fission explosion is given in the form of a risk estimate-though, as noted above, it was not justifiable. \n\t\t\t Arguments along these lines have been suggested in informal discussions, but to the best of my knowledge none has been set out in print. Such an argument would need to be made very carefully, since the theoretical arguments and empirical bounds are not independent. As already noted, the empirical bounds still rely on theoretical assumptions, and if theoretical expectations were incorrect, the derivation of the empirical bounds might also be affected.", "date_published": "n/a", "url": "n/a", "filename": "Risk Analysis - 2004 - Kent - A Critical Look at Risk Assessments for Global Catastrophes.tei.xml", "abstract": "Recent articles by  Busza et al. (BJSW)   and Dar et al. (DDH)  argue that astrophysical data can be used to establish small bounds on the risk of a \"killer strangelet\" catastrophe scenario in the RHIC and ALICE collider experiments. The case for the safety of the experiments set out by BJSW does not rely solely on these bounds, but on theoretical arguments, which BJSW find sufficiently compelling to firmly exclude any possibility of catastrophe. Nonetheless, DDH and other commentators (initially including BJSW) suggested that these empirical bounds alone do give sufficient reassurance. This seems unsupportable when the bounds are expressed in terms of expectation value-a good measure, according to standard risk analysis arguments. For example, DDH's main bound, p catastrophe < 2 × 10 −8 , implies only that the expectation value of the number of deaths is bounded by 120; BJSW's most conservative bound implies the expectation value of the number of deaths is bounded by 60,000. This article reappraises the DDH and BJSW risk bounds by comparing risk policy in other areas. For example, it is noted that, even if highly risk-tolerant assumptions are made and no value is placed on the lives of future generations, a catastrophe risk no higher than ≈10 −15 per year would be required for consistency with established policy for radiation hazard risk minimization. Allowing for risk aversion and for future lives, a respectable case can be made for requiring a bound many orders of magnitude smaller. In summary, the costs of small risks of catastrophe have been significantly underestimated by BJSW (initially), by DDH, and by other commentators. Future policy on catastrophe risks would be more rational, and more deserving of public trust, if acceptable risk bounds were generally agreed upon ahead of time and if serious research on whether those bounds could indeed be guaranteed was carried out well in advance of any hypothetically risky experiment, with the relevant debates involving experts with no stake in the experiments under consideration.", "id": "6529ca0169096ec9971da6e09432d430"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Phil Torres"], "title": "A peer-reviewed electronic journal published by the Institute for Ethics and Emerging Technologies", "text": "A new subfield The field of existential risk studies, or existential riskology, can be traced back to a 1996 book by the philosopher John  Leslie. 1  In the early 2000s, the field emerged as a more formal discipline of active scholarship, led primarily by transhumanists  (Bostrom 2005) . Numerous institutions dedicated to understanding the greatest threats to our collective future have since been founded, such as the Future of Life Institute, the Centre for the Study of Existential Risks (Cambridge), and the Future of Humanity Institute (Oxford). Despite these signs of progress, the field remains in something like a \"pre-paradigmatic\" stage, whereby a comprehensive research program has yet to be firmly established. A particularly problematic gap in the scholarship stems from the failure of existential riskologists to take seriously the range of agents who might use advanced technologies to initiate a catastrophe. One finds only occasional references in the literature to \"psychopaths,\" \"hate groups,\" \"terrorists,\" and \"malevolent governments,\" typically without any further details about the unique properties of these entities. This mistake is tantamount to asserting, \"Future technologies -I'll refrain from saying which ones, how they might be used, the properties that make them dangerous, and so on -could annihilate humanity.\" Just as it's crucial to study the properties of advanced technologies, so too is it crucial to study the properties of agents. The present paper aims to rectify this shortcoming: in effect, it establishes a new subfield of agential riskology. The paper is organized as follows: the next section establishes some basic terminology. Sections 3 and 4 examine the phenomena of agential terror and agential error, respectively. The penultimate section then argues that we should expect the threat of ecoterrorism and apocalyptic terrorism to increase nontrivially in the coming decades. \n Definitions An \"existential risk\" is an event that results in either total annihilation or a permanent and severe reduction in our quality of life  (Bostrom 2002 ). Let's refer to the definiens' first disjunct as an \"extinction risk\" and the second disjunct as a \"stagnation risk.\" Extinction risks are terminal for our species, but stagnation risks are survivable, although they entail an irreversible state of significant deprivation, perhaps resulting in the life opportunities of contemporary North Koreans or our ancestors from the Paleolithic. From a transhumanist perspective, both scenarios would prevent us from reaching a posthuman state in which one or more of our \"core capacities\" are augmented beyond their natural limits  (Bostrom 2008 ). I use the term \"existential risk\" to reference either scenario, while \"extinction risk\" and \"stagnation risk\" refer to specific existential circumstances. Existential risks are defined by their consequences, not their probability or etiology. With respect to the latter, we can identify three broad categories of existential risk types. First, there are risks posed by nature, such as supervolcanic eruptions, global pandemics, asteroid/comet impacts, supernovae, black hole explosions or mergers, galactic center outbursts, and gamma-ray bursts. These form our cosmic risk background and they have no direct, immediate connection to human activity -that is, except insofar as advanced technologies could enable us to neutralize them. For example, we could deflect an incoming asteroid with a spacecraft or devise a vaccine to contain a deadly pathogen that might otherwise cause a global outbreak of infection. Second, there are anthropogenic risks like climate change and biodiversity loss. These are the accidental byproducts of industrial civilization. As elaborated below, both are slow-motion catastrophes that will almost certainly lower the \"conflict thresholds\" that ensure peace between state and nonstate actors. They will, in other words, exacerbate existing geopolitical tensions and introduce entirely new struggles. Climate change and biodiversity loss could thus be considered \"context risks\" whose most significant effects are to modulate the dangers posed by virtually every other existential risk facing humanity -including those from nature.  2  Other anthropogenic risks include physics disasters (such as the Large Hadron Collider) and accidentally contacting hostile aliens through Active SETI projects. The third category subsumes risks that arise from the misuse and abuse of advanced \"dual-use\" technologies. The property of \"dual usability\" refers to the moral ambiguity of such technologies, which can be used for either good or bad.  3  The very same centrifuges that can enrich uranium for nuclear power plants can also enrich uranium for nuclear bombs, and the very same technique (such as CRISPR/Cas9) that might enable scientists to cure diseases could also enable terrorists to synthesize a designer pathogen. According to many existential riskologists, advanced technologies constitute the greatest threat to our collective future. Not only are many of these technologies becoming exponentially more powerful -thereby making it possible to manipulate and rearrange the physical world in unprecedented new ways -but some are becoming increasingly accessible to groups and individuals as well. Consequently, the total number of token agents capable of inflicting harm on society is growing. While the existential risk literature offers many sophisticated accounts of how such tools could be used to cause a catastrophe, almost no one has examined the various agents (with one notable exception) who might want to do this and why.  4  Let's define a \"tool\" as any technology that an agent could use to achieve its ends, and an \"agent\" as any entity, independent of its material substrate, with the capacity to choose its own actions in the world. This lacuna is problematic because the \"risk potential\" of advanced technologies can be realized only by a complete \"agent-tool coupling.\" In other words, a tool without an agent isn't going to destroy the world. Engineered pandemics require engineers, just as a nuclear missile launch requires a nuclear missile launcher. Thus, it's crucial to study the various properties special to every type of agent. Without a careful examination of both sides of the agent-tool coupling, existential risk scholars could leave humanity vulnerable to otherwise avoidable catastrophes. To illustrate this point, consider a world X in which a large number of species-annihilating technologies exist, and another world Y in which only a single such technology exists. Now imagine that world X contains a single dominant species of peaceable, compassionate beings who almost never resort to violence. How dangerous is this world? If one looks only at the tools, it appears to be extremely dangerous. But if one considers the agents too, it appears to be extremely safe. Now imagine that world Y contains a species of bellicose, warmongering organisms. Again, if one looks only at the tools, then Y appears far safer than X. But when the complete agent-tool complex comes into view, Y is clearly more likely to selfannihilate. A final distinction needs to be made before moving on to the next section, namely that between error and terror. Note that this distinction is agential in nature. It concerns the agential intentions behind a catastrophe independent of the catastrophes' consequences. Thus, an error could, no less than terror, bring about an existential disaster. In the case of world X, one might argue that an error is most likely to cause an existential catastrophe, whereas in Y the greatest threat stems from terror. The error/terror distinction is important in part because there appear to be far more token agents who might induce an extinction or stagnation disaster by accident than are likely to bring about such an outcome on purpose. The next two sections discuss agential terror and agential error in turn. \n Agential terror Many existential riskologists identify terror involving advanced technologies as the most significant threat to our prosperity and survival. But upon closer examination, there are fewer types of agents who would want to cause an existential catastrophe than one might suspect. Consider another thought experiment: imagine a future world in which there exists a profusion of \"doomsday buttons\" that are accessible to every citizen of Earth. The question then arises: what sort of individual would intentionally push this button? What kind of agent would purposively cause an existential catastrophe? If the intention were to actualize an extinction risk, the agent would need to exhibit at least two properties. First, it would need to devalue its own post-catastrophe survival. In other words, the agent would have to be suicidal. This immediately disqualifies a large number of entities as potential agential risks, since states and political terrorists tend to value their own survival. Neither North Korea nor al-Qaeda, for example, is suicidal. Their goal, in each case, is to change rather than destroy humanity. Even in the case of suicide bombers and kamikaze pilots, the aim is to ensure group survival through the altruistic sacrifice of one's own life. And second, the agent would need to want every other human on the planet to perish. In other words, he or she would have to be omnicidal. (We can coin the term \"true omnicide\" to refer to circumstances that combine both suicide and omnicide, as just defined, resulting in the irreversible termination of our evolutionary lineage.) In contrast, if the aim were to actualize a stagnation risk, the agent could be suicidal, omnicidal, or neither, but not both (according to the above definitions). A terrorist could, for example, attempt to permanently cripple modern civilization without harming anyone, including him or herself. Alternatively, a terrorist could attempt to cripple civilization through a suicide attack or an attack directed at others. Either way, the relevant agent would be motivated by an ideology that is incompatible with our species reaching a posthuman state. In the following discussion, we will consider extinction and stagnation possibilities separately. \n A typology of agential risks With these properties in mind, let's examine five categories of agents that, when coupled with sufficiently destructive tools, might purposively bring about an existential catastrophe. (1) Superintelligence. This is one of the most prominent topics of current existential risk studies, although it's typically conceptualized -on my reading of the literature -as a technological risk rather than an agential risk. To be clear, a variety of agent types could use narrow AI systems as a tool to achieve their ends. But once an AI system acquires human-level intelligence or beyond, it becomes an agent in its own right, capable of making its own decisions in pursuance of its own goals. Many experts argue that superintelligence is the greatest long-term threat to human survival, and I concur. On the one hand, a superintelligence could be malevolent rather than benevolent. Call this the amityenmity conundrum. Roman Yampolskiy (2015) delineates myriad pathways that could lead to humanunfriendly superintelligences. For example, human programmers could intentionally program a superintelligence to prefer enmity over amity. (The relevant individuals could thus be classified as agential risks as well, even though they wouldn't be the proximate agential cause of an existential catastrophe.) A malevolent superintelligence could also arise as a result of a philosophical or technical failure to program it properly  (Yudkowsky 2008) , or through a process of recursive self-improvement, whereby a \"seed AI\" augments its capacities by modifying its own code. But it's crucial to note that a superintelligence need not be malevolent to pose a major existential risk. In fact, it appears more likely that a superintelligence will destroy humanity simply because our species happens to be somewhere between it and its goals. Consider two points: first, the relevant definition of \"intelligence\" in this context is \"the ability to acquire the means necessary to achieve one's ends, whatever those ends happen to be.\" This definition, which is standard in the cognitive sciences, is roughly synonymous with the philosophical notion of instrumental rationality. And since it focuses entirely on an agent's means rather than its ends, it follows that an intelligence could have any number of ends, including ones that we wouldn't recognize as intelligible or moral. Scholars call this the \"orthogonality thesis\"  (Bostrom 2012) . For example, there's nothing incoherent about a superintelligent machine that believes it must purify Earth of humanity because God wills it to do so. Nor is there anything conceptually problematic about a superintelligent machine whose ultimate goal is to manufacture as many paperclips as possible. This goal may sound benign, but upon closer inspection it appears just as potentially catastrophic as an AI that wants us dead. Consider the fact that to create paperclips, the superintelligence would need a source of raw materials: atoms. As it happens, this is precisely what human bodies are made out of. Consequently, the superintelligence could decide to harvest the atoms from our bodies, thereby causing our extinction. As Eliezer Yudkowsky puts it, \"The AI does not hate you, nor does it love you, but you are made out of atoms which it can use for something else\"  (Yudkowsky 2008) . Scholars categorize resource acquisition, along with self-preservation, under the term \"instrumental convergence.\" Even more, our survival could be at risk in situations that initially appear favorable. For example, imagine a superintelligence that wants to eliminate human sadness from the world. The first action it might take is to exterminate Homo sapiens, because human sadness can't exist without humans. Or it might notice that humans smile when happy, so it could try to cover our faces with electrodes that cause certain muscles to contract, thereby yielding a \"Botox smile.\" Alternatively, it might implant electrodes into the pleasure centers of our brains. The result could be a global population of euphoric zombies too paralyzed by pleas-ure to live meaningful lives  (Bostrom 2014, 146-48) . All of these outcomes would, from a certain perspective be undesirable. The point is that there's a crucial difference between \"Do what I say\" and \"Do what I mean,\" and figuring out how to program a superintelligence to behave according to the latter is a formidable task. Making matters worse, a superintelligence whose material substrate involves the propagation of electrical potentials rather than action potentials would be capable of processing information orders of magnitude faster than humans. Call this a quantitative superintelligence. As Yudkowsky observes, if the human brain were sped up a million times, \"a subjective year of thinking would be accomplished for every 31 physical seconds in the outside world, and a millennium would fly by in eight-and-a-half hours\"  (Yudkowsky 2008) . A quantitative superintelligence would thus have a huge speed advantage over humanity. In the amount of time that it takes our biological brains to process the thought, \"This AI is going to slaughter us,\" the AI could already be halfway done the deed. Another possibility concerns not speed but capacity. That is, an AI with a different cognitive architecture could potentially think thoughts that lie outside of our species-specific \"cognitive space.\" This is based on the following ideas: (a) to understand a mind-independent feature of reality, one must mentally represent it, and (b) to mentally represent that feature, one must generate a concept whose content consists of that feature. Thus, if the mental machinery supplied to us by nature is unable to generate the relevant concept, the corresponding feature of reality will be unknowable. Just as a chipmunk can't generate the concepts needed to understand a boson or the stock market, so too are the concept-generating mechanisms of our minds limited by their evolutionary history. The point is that a qualitative superintelligence could come to understand phenomena in the universe that are permanently beyond our epistemic reach. This could enable it to devise ways of manipulating the world that would appear to us as pure magic. In other words, we might observe changes in the world that we simply can't understand -that are as mysterious as the science behind cellphones or the atomic bomb is to a chipmunk scientist. In sum, not only would a quantitative superintelligence's speed severely disadvantage humanity, but a qualitative superintelligence could also discover methods for \"commanding nature,\" as it were, that would leave us utterly helpless. As with the other agents below, superintelligence itself doesn't pose a direct threat to our species. But it could pose a threat if coupled to any of the tools previously mentioned, including nuclear weapons, biotechnology, synthetic biology, and nanotechnology. As Bostrom writes, if nanofactories don't yet exist at the time, a superintelligence could build them to produce \"nerve gas or target-seeking mosquito-like robots [that] might then burgeon forth simultaneously from every square meter of the globe\"  (Bostrom 2014) . A superintelligence could also potentially gain control of automated processes in biology laboratories to synthesize a designer pathogen, exploit narrow AI systems to disrupt the global economy, and generate false signals in early-warning systems to provoke a nuclear exchange between states. A superintelligence could press a preexisting doomsday button or create its own button. According to a recent poll, a large majority of AI researchers believe that an artificial general intelligence (AGI) will be created this century  (Müller and Bostrom 2016) . But such predictions have been notoriously inaccurate in the past. This fact is immaterial to the present thesis, though, which merely states that if, independent of when, humans build a superintelligence, it could pose a major, unpredictable agential risk. (2) Idiosyncratic actors. This category includes individuals or groups who are driven by idiosyncratic motives to destroy humanity or civilization. History provides several examples of the mindset that would be required for such an act of terror. First, consider Eric Harris and Dylan Klebold, the adolescents behind the 1999 Columbine High School massacre. Their aim was to carry out an attack as spectacular as the Oklahoma City bombing, which occurred four years earlier. They converted propane tanks into bombs, built 99 improvised explosive devices, and equipped themselves with several guns. By the end of the incident, 12 students and one teacher were dead, while 21 others were injured. (Although if the propane bombs had exploded, which they didn't, all 488 students in the cafeteria at the time could have perished.) This was the deadliest school shooting in US history until Adam Lanza killed 20 children and 6 adults at Sandy Hook Elementary School in 2012 before committing suicide. This leads to the question: what if Harris and Klebold had generalized their misanthropic hatred from their high school peers to the world as a whole? What if certain future anticipated technologies had been available at the time? In other words, what if they'd had access to a doomsday button? Would they have pushed it? The plausible answer is, \"Yes, they would have pushed it.\" If revenge on school bullies was the deeper motive behind their attack, as appears to be the case,  5  then what better way to show others \"who's boss\" than to \"go out with the ultimate bang\"? If people like Harris and Klebold, with their dual proclivities for homicide and suicide, get their hands on advanced technologies in the future, the result could be true omnicide. History also provides a model of someone who might try to destroy civilization without intentionally killing anyone. Consider the case of Marvin Heemeyer, a Colorado welder who owned a muffler repair shop. After years of a zoning dispute with the local town and several thousand dollars in fines for property violations, Heemeyer decided to take revenge by converting a large bulldozer into a \"futuristic tank.\" It was covered in armor, mounted with video cameras, and equipped with three gun-ports. On June 4, 2004, he climbed inside the tank and headed into town. With a top speed of a slow jog and numerous police walking behind him during the incident, Heemeyer proceeded to destroy one building after another. Neither a flash-bang grenade thrown into the bulldozer's exhaust pipe nor 200 rounds of ammunition succeeded in stopping him. After more than two hours of relentless destruction, the bulldozer became lodged in a basement, at which point Heemeyer picked up a pistol and shot himself. The motivation of this attack was also a form of bullying, that is, as perceived by Heemeyer. A significant difference between Heemeyer's rampage and the Columbine massacre is that, according to some residents sympathetic with Heemeyer, he went out of his way not to injure anyone. Indeed, he was the only person to die in the attack.  6  It's also worth pointing out that Heemeyer saw himself as God's servant. As he put it, \"God blessed me in advance for the task that I am about to undertake. It is my duty. God has asked me to do this. It's a cross that I am going to carry and I'm carrying it in God's name.\" Again, we can ask: what if a delusional person like Heemeyer were to someday hold a grudge not against the local town, but civilization as a whole? What if a future person feels abandoned or \"screwed over\" by society and wants to retaliate for perceived injustices? In the past, lone wolves with idiosyncratic grievances were unable to wreak havoc on society because of the limited means available to them. This will almost certainly change in the future, as advanced technologies become increasingly powerful and accessible.  7  This category is especially worrisome moving forward, since it is arguably the type with the most potential tokens. Perhaps future advances in psychology, or brain-decoder technologies and other surveillance systems, will enable us to identify agents at risk of engaging in violence of this kind. (3) Ecoterrorists. Imagine for a moment that scientists found a 52 per cent reduction in the global population of wild vertebrates between 1970 and 2010. Imagine that, on even the most optimistic assumptions, the biosphere had entered the sixth mass extinction event in life's 3.8 billion year history. Imagine further than a single species were almost entirely responsible for this environmental crisis, namely Periplaneta americana, the American cockroach. What would our response be? To exterminate the culprit, of course, thereby saving Earth from a planetary catastrophe. It's this basic line of reasoning that could lead a group of radical environmentalists or a lone wolf activist to attempt to relocate humanity from the category of \"extant\" to \"extinct.\" In fact, the claims made above are scientifically accurate: the total population of wild mammals, birds, reptiles, amphibians, and fish really did halve in forty years, and we really are in the beginning stages of a new mass extinction event (see WWF 2014;  Ceballos et al. 2015) . But the culprit isn't the American cockroach, it's humanity. To date, the vast majority of environmentalist movements have been peaceful, despite the FBI classifying some affiliates of the Earth Liberation Front (ELF) and the Animal Liberation Front (ALF) as constituting \"one of the most serious domestic terror threats in the US\"  (Flannery 2016) . Even groups that believe Gaia would be better off without Homo sapiens trampling the planet, such as the Voluntary Human Extinction Movement (VHEMT), reject violence or coercion as legitimate means for achieving their ideological aims. Nonetheless, there are exceptions. On September 1, 2010, James Lee terrorized a Discovery Channel building in DC with a gun and explosives. During several hours of negotiations, Lee explained to law enforcement officials that he wanted new programming on the Discovery Channel \"to convey how to improve the natural world and reverse human civilization.\" He also wanted humans to stop procreating. As Lee wrote, \"Children represent FUTURE catastrophic pollution whereas their parents are current pollution. NO MORE BABIES!\" (quoted in  Flannery 2016) . Around 4:48pm, Lee aimed his gun at a hostage in the building and SWAT snipers killed him. Once more, the question is: if Lee had access to a doomsday button that, say, could have sterilized every human on the planet (thereby causing an extinction catastrophe), would he have pushed it? The answer is, \"Yes, probably.\" The radical environmental movement is founded on the philosophy of biocentrism, or the view that \"humans are no more intrinsically valuable than any other creature.\" Some scholars have even suggested that this ideology and its following should be seen as a \"new religious movement,\" which Bron Taylor calls the \"deep green religion\"  (Taylor 2009) . Along these lines, Ted Kaczynski, discussed below, advocated what he called a \"wilderness religion.\" Given the fanaticism of this stance, it's not hard to envisage a group emerging in the future that attempts to bring about human extinction through the use of advanced technologies in an effort to \"save\" the planet. This scenario is made even more plausible by the fact that the largest demographic of Earth Liberation Front members consists of \"well educated\" and \"technologically literate\" males  (Flannery 2016) . Thus, if synthetic biology techniques were to enable the synthesis of a designer pathogen that infects only Homo sapiens, a radical environmentalist could try to spread this germ around the globe. Or they could design and release self-replicating nanobots that selectively target Homo sapiens by recognizing genetic signatures unique to our DNA. Such nanobots could annihilate our species while leaving the biosphere more or less unharmed. There might also be radical environmentalists who aren't motivated by a death wish for humanity, but by a destruction wish for civilization. Ted Kaczynski, also known as the Unabomber, provides a compelling example. His objective was neither suicide nor omnicide, but the dismantlement of technological civilization, according to the slogan \"Back to the Pleistocene\"  (Flannery 2016) . Although Kaczynski's own terrorist bombings weren't intended to achieve his ambitious aims, if a doomsday button had been available at the time, Kaczynski probably would have pushed it, thereby initiating a stagnation catastrophe. While people might die in the process, this wouldn't be the goal. As Kaczynski declares, \"We therefore advocate a revolution against the industrial system. This revolution may or may not make use of violence; it may be sudden or it may be a relatively gradual process spanning a few decades. … Its object will be to overthrow not governments but the economic and technological basis of the present society\" (quoted in Flannery 2016). This type of agential risk should be carefully studied moving forward, for reasons explicated in Section 5. If advanced technologies become sufficiently powerful and accessible, people under the spell of the deep green religion could inflict unprecedented harm on civilization. (4) Religious terrorists. Terrorists motivated by nationalist, separatist, anarchist, Marxist, and other political ideologies are unlikely to cause an existential catastrophe because their goals are typically predicated on the continued existence of civilization and our species. They want to change the world, not destroy it. But this is not the case for some terrorists motivated by religious ideologies. For them, what matters isn't this life, but the afterlife; the ultimate goal isn't worldly, but otherworldly. These unique features make religious terrorism especially dangerous, and indeed it has proven to be both more lethal and indiscriminate than past forms of \"secular\" terrorism.  8  According to the Global Terrorism Index, religious extremism is now the primary driver behind global terrorism, and there are reasons (see Section 5) for expecting this to remain the case moving forward  (Arnett 2014) . The most worrisome form of religious terrorism is apocalyptic terrorism. As Jessica Stern and J.M. Berger observe, apocalyptic groups aren't \"inhibited by the possibility of offending their political constituents because they see themselves as participating in the ultimate battle.\" Consequently, they are \"the most likely terrorist groups to engage in acts of barbarism\"  (Stern and Berger 2015) . The apocalyptic terrorist sees humanity as being engaged in a cosmic struggle at the very culmination of world history, and the only acceptable outcome is the complete decimation of God's enemies. These convictions, when sincerely held, can produce a grandiose sense of moral urgency that apocalyptic warriors can use to justify virtually any act of cruelty and violence, no matter how catastrophic. To borrow a phrase from the former Director of the CIA, James Woolsey, groups of this sort \"don't want a seat at the table, they want to destroy the table and everyone sitting at it\"  (Lemann 2001) . There are two general types of active apocalyptic groups. First, there are movements that have advocated something along the lines of omnicide. History provides many striking examples of movements that maintained -with the unshakable firmness of faith -that the world must be destroyed in order to be saved. For example, the Islamic State of Iraq and Syria believes that its current caliph, or leader, is the eighth of twelve caliphs in total before the apocalypse. This group's adherents anticipate an imminent battle between themselves and the \"Roman\" forces (the West) in the small northern town of Dabiq, in Syria. After the Romans are brutally defeated, one-third of the victorious Muslim army will supernaturally conquer Constantinople (now Istanbul), after which the Antichrist will appear, Jesus will descend above the Umayyad Mosque in Damascus, and various other eschatological events will occur. In the end, those who reject Islam will be judged by God and cast into hellfire, and the Islamic State sees itself as playing an integral role in getting this process started (Torres 2016a). Another example comes from the now-defunct Japanese cult Aum Shinrikyo. This group's ideology was a syncretism of Buddhist, Hindu, and Christian beliefs. From Christianity, the group imported the notion of Armageddon, which it believed would constitute a Third World War whose consequences would be \"unparalleled in human history.\" Only those \"with great karma\" and \"those who had the defensive protection of the Aum Shinrikyo organization\" would survive  (Juergensmeyer 2003) . In 1995, Aum Shinrikyo attempted to knock over the first domino of the apocalypse by releasing the chemical sarin in the Tokyo subway, resulting in 12 deaths and sickening \"up to 5,000 people.\" This was the biggest terrorist attack in Japanese history, and it was perpetrated by a religious cult that was explicitly motivated by an active apocalyptic worldview. Other contemporary examples include the Eastern Lightning in modern-day China, which believes that it's in an apocalyptic struggle with the communist government, and the Christian Identity movement in the US, which believes that it must use catastrophic violence to purify the world before the return of Jesus. Second, there are multiple groups that have advocated mass suicide. The Heaven's Gate cult provides an example. This group is classified as a millenarian UFO religion, led by Marshall Applewhite and Bonnie Nettles. They believed that, as James Lewis puts it, ancient \"aliens planted the seeds of current humanity millions of years ago, and have to come to reap the harvest of their work in the form of spiritual evolved individuals who will join the ranks of flying saucer crews. Only a select few members of humanity will be chosen to advance to this transhuman state\"  (Lewis 2001) . The world was about to be \"recycled,\" and the only possible \"way to evacuate this Earth\" was to leave their bodies behind through collective suicide. Members believed that, once dead, they would board an alien spacecraft that was trailing the Hale-Bopp comet as it swung past Earth in 1997. To fulfill this eschatological prediction, they drank phenobarbital, along with applesauce and vodka. Between March 24-26, 39 members of the cult committed suicide. Other examples could be adduced, such as The Movement for the Restoration of the Ten Commandments of God in Uganda, which slaughtered 778 people after unrest among members following a failed apocalyptic prophesy  (New York Times 2000) . But the point should be sufficiently clear. With respect to extinction risks, there are (quite intriguingly) no notable groups that have combined these two tendencies of suicide and omnicide. No major sect has said, \"We must destroy the world, including ourselves, to save humanity.\" But this doesn't mean that such a group is unlikely to emerge in the future. The ingredients necessary for a truly omnicidal ideology to take shape are already present in our culture. Perhaps, for reasons discussed below, societal conditions in the future will push religious fanatics to even more extreme forms of apocalypticism, thereby yielding a group that believes God's will is for everyone to perish. Whether this happens or not, apocalyptic groups also pose a significant stagnation risk. For example, what if Aum Shinrikyo had somehow been successful in initiating an Armageddon-like Third World War? What might civilization look like after such a catastrophe? Could it recover? Or, what if the Islamic State managed to expand its caliphate across the entire world? How might this affect humanity's long-term prospects? Zooming out from our focus on apocalyptic groups, there are numerous less radical groups that would like to reorganize society in existentially catastrophic ways. One of the ultimate goals of al-Qaeda, for example, is to implement Sharia law around the world. If this were to happen, it would destroy the modern secular values of democracy, freedom of speech and the press, and open scientific inquiry. The imposition of Sharia law on civilization is also the aim of non-jihadist Islamists, who comprise roughly 7 per cent of the Muslim community  (Flannery 2014 ). Similarly, \"dominionist\" Christians in the US, a demographic that isn't classified as \"terrorist,\" believe that God commands Christians to control society and govern it based on biblical law. If a state run by dominionists were to become sufficiently powerful and global in scope, it could induce an existential catastrophe of the stagnation variety. (5) Rogue states. As with political terrorists, states are unlikely to intentionally cause an extinction catastrophe because they are generally not suicidal. Insofar as they pursue violence, it's typically to defend or expand their territories. The total annihilation of Homo sapiens would interfere with these ends. But defending and expanding a state's territories could cause a catastrophe of the stagnation variety. For example, if North Korea were to morph into a one-world government with absolutist control over the global population until Earth became unlivable, the result would be an existential catastrophe. Alternatively, a benevolent one-world government could emerge from institutions like the United Nations or the European Union. Once in place, a malevolent demagogue could climb to the power ladder and seize control over the system, converting it into a tyrannical dictatorship. Again, the outcome would be a stagnation catastrophe. Of all the agential risk types here discussed, historians, sociologists, philosophers, and other scholars have studied state-level polities and governmental systems the most thoroughly. \n Agential error The discussion to this point has focused on agential terror. But what about the other side of the error/terror coin? The danger posed by agential error depends in part on how accessible future technologies become. For example, if even a small percentage of the human population in 2050, which is projected to be 9.3 billion, were to acquire \"biohacker\" laboratories, the chance that someone might accidentally re-lease a pathogen into the environment could be unacceptably high  (Pew Research Center 2015a) . After all, a significant number of mistakes have happened in highly regulated government laboratories over the years  (Torres 2016a) . The 2009 swine flu pandemic may have occurred because of a laboratory mistake made in the 1970s, and \"a CDC lab accidentally contaminated a relatively benign flu sample with a dangerous H5N1 bird flu strain that has killed 386 people since 2003\"  (Zimmer and Burke 2009; McNeil 2014) . If such problems occur among professionals, imagine the potential dangers of hobbyists around the world -perhaps hundreds of millions -handling pathogenic microbes with almost no regulatory oversight. The exact same logic applies to technologies that are becoming more accessible, such as nanotechnology, robotics, AI systems, and possibly nuclear weapons, not to mention future artifacts that currently lie hidden beneath the horizon of our technological imaginations. There could also be malicious agents that want to cause an existential catastrophe, but nonetheless end up doing this by accident rather than design. For example, in preparing for the \"big day,\" a doomsday cult could accidentally release a deadly pathogen or self-replicating nanobot into the environment, resulting in an unplanned disaster. This scenario could involve ecoterrorists, idiosyncratic actors, and states as well. Or an agent with no desire to cause an existential catastrophe could push a \"catastrophe button\" that inadvertently brings about an existential disaster. For example, a rogue state that hopes to gain regional or global power through the use of nuclear missiles must answer the following question: exactly how many nuclear missiles are required to bring the world's governments to their knees without causing an extinction-inducing nuclear winter? The same question could be asked with respect to biological weapons, nanoweapons, and weaponized AI systems. How sure can one be that there won't be unintended consequences that catapult humanity back into the Stone Age? (As Albert Einstein once said, \"I do not know how the Third World War will be fought, but I can tell you what they will use in the Fourth -rocks!\" Calaprice 2005.) The unpredictability and uncertainty inherent in global catastrophe scenarios could make it easy for non-existential terror to slide into existential error. Finally, a special case of agential error worth examining on its own involves superintelligence. A genuinely superintelligent agent (coupled with advanced technologies) would wield extraordinary power in the world. This fact would make humanity especially vulnerable to any error made by such an agent. Even a single mistake could be sufficiently devastating to cause an existential catastrophe. One might respond by asserting that a superintelligence is surely less likely to make a mistake, given its superior intelligence  (Bostrom 2014) . But I would challenge this assumption. Consider that humans have the most developed neocortex and the highest encephalization quotient in the Animal Kingdom. Yet it is our species, rather than our intellectually \"inferior\" relatives, that is responsible for the environmental catastrophes of climate change and biodiversity loss. Even more, our species has greatly increased the total number of existential risks from a small handful of improbable natural threats to a dizzying array of anthropogenic and agent-tool dangers. Was this a mistake? In a sense, yes: we certainly didn't intend for this to happen. Historically speaking, human ingenuity and the threat of existential annihilation have risen together. This suggests that there isn't a strong connection between higher intelligence and the capacity to avoid errors. Call this the \"orthogonality thesis of fallibility\"  (Torres 2016a ). If our own history is a guide to the future, we might expect the creation of a superintelligence to further increase the total number of existential risks, perhaps in ways that are either now, or permanently, inscrutable to us. The point is that even if we were to solve the \"control problem\" and create a friendly superintelligence, it could nudge us over the precipice of disaster on accident, rather than push us on purpose. What can we say? It's only superhuman. \n The future of agential risks Neutralizing the threats posed by agential risks requires understanding not only their synchronic properties, but also how these properties might evolve diachronically. There are two sets of factors relevant to this task, which we can organize into external and internal categories, depending on whether they originate from outside or within an agent's motivating ideology. \n External factors As previously mentioned, climate change and biodiversity loss are \"context risks\" that will frame, and therefore modulate, virtually every other threat facing humanity. According to our best current science, these phenomena -appropriately dubbed \"threat multipliers\" -will become more severe in the coming decades, and their effects will \"extend longer than the entire history of human civilization\"  (Clark et al. 2016 ). This will significantly elevate the probability of future struggles and conflicts between state and nonstate actors. A simple thought experiment illustrates the point. In which of the following two worlds are wars more likely: one beset by megadroughts, extreme weather, scorching heat waves, desertification, sea-level rise, and the spread of infectious disease, or one without these tragedies? In which of the following two worlds are terrorist attacks more likely: a world in which food supply disruptions, mass migrations, social upheaval, economic collapse, and political instability are widespread, or one in which they're not? One could even ask, in which of the following two worlds is a malevolent superintelligence more likely to emerge: one crushed by environmental catastrophes or one in which civilization is functioning properly? Environmental degradation could also increase the likelihood of incidents involving idiosyncratic agents, in part because it could increase the prevalence of \"bullying\"-type behavior. When people are desperate, moral considerations tend to be occluded by the instinctual drive to meet our biological needs. Even more, climate change and biodiversity loss could significantly fuel ecoterrorism. To quote Flannery, \"As the environmental situation becomes more dire, eco-terrorism will likely become a more serious threat in the future\"  (Flannery 2016) . Not only will the deleterious effects of industrial society on the natural world become more salient, but sudden changes in the environment's stability could prod activists to consider more aggressive, even violent, tactics. Scientists have, for example, argued that Earth could be approaching an abrupt, irreversible, catastrophic collapse of the global ecosystem. A planetary-scale \"state shift\" of this sort could unfold on the timescale of decades and cause \"substantial losses of ecosystem services required to sustain the human population.\" The result would be \"widespread social unrest, economic instability, and loss of human life,\" and these phenomena could inspire fierce rebellions against civilization. There are also reasons for expecting climate change and biodiversity loss to nontrivially increase the size and frequency of apocalyptic movements in the future  (Torres 2016b; Juergensmeyer, forthcoming) . In fact, we already have at least one example of this happening, according to a 2015 study published in the Proceedings of the National Academy of Sciences. This study argues that one can draw a straight line of causation from anthropogenic climate change to the record-breaking 2007-2010 Syrian drought to the 2011 Syrian civil war  (Kelly et al. 2015) . And the Syrian civil war was the Petri dish in which the Islamic State consolidated its forces to become the wealthiest and most powerful terrorist organization in human history. The link between environmental havoc and terrorism has also been confirmed by the current Director of the CIA, John Brennan, the former US Defense Secretary, Chuck Hagel, and the US Department of Defense  (Torres 2016c) . As Mark Juergensmeyer (forthcoming) observes in detail, apocalyptic ideologies tend to arise during periods of extreme societal stress. When a group's basic identity and dignity is threatened, when losing one's cultural identity is unthinkable to those in the group, and when the crisis isn't solvable through ordinary human means, people often turn to supernatural frameworks to make sense of their suffering and give them hope for the future. In Juergensmeyer's words, \"The presence of any of these three characteristics increases the likelihood that a real-world crisis may be conceived in cosmic terms,\" and \"cosmic terms\" form the language of apocalyptic activism. Because of climate change and biodiversity loss, these are precisely the conditions we can expect in the future, as societies inch toward the brink of collapse. It's also worth noting that floods, earthquakes, droughts, famines, and disease are prophesied by many religions as harbingers of the end. Consequently, environmental degradation could actually reinforce people's prior eschatological convictions, or even lead nonbelievers to convert. 9 There is, in fact, a strong preexisting base of widespread apocalyptic belief within the Abrahamic traditions. For example, a 2010 Pew poll finds that 41 per cent of Americans believe that Jesus will either or \"probably\" return by 2050 (Pew Research Center 2010), and a 2012 Pew poll reports that 83 per cent of people in Afghanistan, 72 per cent in Iraq, 68 per cent in Turkey, and 67 per cent in Tunisia believe that the Mahdi, Islam's end-of-days messianic figure, will return in their lifetime  (Pew Research Center 2012) . One should expect these percentages to rise moving forward. There are two additional reasons for anticipating more apocalyptic movements in the future. First, a statistical point. According to a 2015 Pew study, the percentage of nonbelievers is projected to shrink in the coming decades, despite the ongoing secularization of Europe and North America (Pew Research Center 2015a; see chapter 3, \"Articles of Faith\"). By 2050, more than 60 per cent of humanity will identify as either Christian or Muslim, in roughly equal proportion. As Alan Cooperman puts it, \"You might think of this in shorthand as the secularizing West versus the rapidly growing rest\"  (Pew Research Center 2015b) . This is disconcerting because religion normalizes bad epistemological habits, and thinking clearly about big-picture issues is the only hope our species has of navigating the wilderness of existential risks before us. In addition, not only is superstition rising as advanced technologies become more powerful, but if the relative proportion of extremists at the fringe remains fixed, the absolute number of religious fanatics will undergo a growth spurt. This alone suggests that the future will contain a historically anomalous number of terrorists (although we should note that it will contain more \"good guys\" as well). Furthermore, the inchoate GNR (genetics, nanotech, and robotics) Revolution will result in a wide range of fundamental changes to society. It could introduce new forms of government -or, as Benjamin  Wittes and Gabriella Blum (2015)  argue, undercut the social contract upon which modern states are foundedand even challenge our notion of what it means to be human. These changes could be profound, pervasive, and quite rapid, given the exponential rate of innovation. If this is the case, it could also fulfill the conditions specified by Juergensmeyer, thereby fueling apocalyptic extremists to declare an imminent end to the world. (In a sense, this might be true, since the transition from the human era to a posthuman era would mark a watershed moment in our evolutionary history.) The fact is that past technological revolutions have inspired religious fanaticism, and by nearly all accounts the GNR Revolution will be far more disruptive than any previous revolution. As Juergensmeyer puts it, \"radical change breeds radical religion,\" and radical change is exactly what we should expect.  10  Tying this all together: a confluence of environmental degradation, demographic shifts, and disruptive technologies could significantly exacerbate the threat of apocalyptic terrorism, as well as idiosyncratic agents and ecoterrorists, in the future. The recent unrest in the Middle East is, arguably, only a preview of what's to come. \n Internal factors But there are also factors internal to the ideologies espoused by different agents that are no less important for existential riskologists to study. For example, the year 2076 will likely see a spike in apocalyptic fervor within the Islamic world  (Cook 2008 (Cook , 2011 . One can only know this, and therefore prepare appropriately, if one understands the relevant Islamic traditions. The reason 2076 will be especially dangerous is that it roughly corresponds to 1500 in the Islamic calendar (AH), and eschatological enthusiasm has risen in the past at the turn of the century. Consider the fact that the Iranian Revolution, which was widely seen as an \"apocalyptic occurrence\" by Shi'ites, happened in 1979  (Cook 2011) . So did the Grand Mosque seizure, during which a group of 500 insurgents took approximately 100,000 worshipers hostage. This group claimed to have the Mahdi with them and believed that the Last Hour was imminent. The point is that 1979 corresponds to 1400AH, a date that fueled the apocalypticism behind these events. Scholars should also keep an eye on 2039, since it is the 1200th anniversary of the Mahdi's occultation in the Twelver Shia tradition. As Cook writes, \"the 1000-year anniversary of the Mahdi's occultation was a time of enormous messianic disturbance that ultimately led to the emergence of the Bahai faith. … [A]nd given the importance of the holy number 12 in Shiism, the twelfth century after the occultation could also become a locus of messianic aspirations.\" He adds: In one scenario, either a messianic claimant could appear or, more likely, one or several movements hoping to \"purify\" the Muslim world (or the entire world) in preparation for the Mahdi's imminent revelation could develop. Such movements would likely be quite violent; if they took control of a state, they could conceivably ignite a regional conflict.  (Cook 2011)  Looking forward, who knows what powerful technologies might exist by 2039 or, even more, 2076? If a messianic movement with violent proclivities were to arise in the future, it could have existential implications for humanity. Another example involves apocalyptic US militias influenced by Christian Identity teachings. On April 19, 1995, Timothy McVeigh pulled up to the Alfred P. Murrah Federal Building in Oklahoma City and detonated a bomb that killed 168 people. As Flannery notes, this event unfolded \"just as the Christian Identity affiliated Covenant, Arm, and the Sword (CSA) militia had planned a decade earlier while training 1,200 recruits in the Endtime Overcomer Survival Training School.\" The date of April 19 \"was no accident.\" Exactly two years earlier, the government ended its confrontation with the Branch Davidians in their Waco, Texas compound, resulting in 74 deaths. And exactly 8 years before this event, there was a similar standoff between the government and the Covenant, Arm, and the Sword. And centuries before, in 1775, the Battles of Lexington and Concord that inaugurated the American Revolutionary War against Great Britain took place on April 19. Consequently, the date of \"April 19 has come to resonate throughout a constructed history of the radical Right as a day of patriotic resistance\"  (Flannery 2016, 144) . More generally, some experts refer to April as the beginning of \"the killing season.\" While Harris and Klebold reportedly planned their massacre on April 19 (being inspired by McVeigh), they ended up delaying it one day to coincide with Adolf Hitler's birthday  (Rosenwald 2016) . Another date to watch is April 15, the deadline for income tax filings in the United States. This has meaning to certain antigovernment groups. As the Anti-Defamation League (2005) warns, April is a month that looms large in the calendar of many extremists in the United States, from racists and anti-Semites to anti-government groups. Some groups organize events to commemorate these April dates. Moreover, there is always a certain threat that one or more extremists may choose to respond to these anniversaries with some sort of violent act. It adds: \"Because of these anniversaries, law enforcement officers, community leaders and school officials should be vigilant.\" Existential risk scholars too should be especially mindful of heightened risks in April. If a doomsday or catastrophe button were to become available to Christian Identity terrorists motivated by an active apocalyptic ideology, April 19 might be the day on which they would decide to press it. \n Conclusion Most states and terrorists are unlikely to intentionally cause an existential catastrophe, although certain high-impact instances of catastrophic violence could accidentally realize an extinction or stagnation risk. The primary danger posed by states and terrorists concerns their capacity to press a catastrophe button, if it were to become available. There are, however, at least five types of agents who could be motivated by various goals to bring about a cataclysm of existential proportions. I do not intend for this list to be exhaustive. Indeed, the agential threat horizon could expand, shift, or transmogrify in unanticipated ways as humanity is thrust forward by the invisible hand of time. It's nonetheless important to specify a typology of agential risks based on the best current research -a task that no one has yet attempted -because the agents of each category have their own unique properties, and must therefore be studied as unique threats in exactly the same way that nuclear weapons, biotechnology, and molecular manufacturing are studied separately. While much of the existential risk literature focuses on the various tools, both present and anticipated, that could bring about a secular apocalypse, we must give the agents equal consideration. A key idea of this paper is that, first, advanced technologies will provide malicious agents with bulldozers, rather than shovels, to dig mass graves for their enemies. And second, the risk potential of these technologies cannot be realized without a complete agent-tool coupling. This is why the field of existential risk studies desperately needs a subfield of agential riskology, which this paper aims to establish. No doubt much of what I have said above will need to be refined, but such is to be expected when there are few shoulders upon which to stand. Notes 1. See Leslie 1986. 2. For example, a world thrown into chaos by environmental degradation might be less prepared to deflect an incoming asteroid or coordinate on stopping a global pandemic. 3. Originally, \"dual-use\" referred to entities with both civilian and military uses, but the term has acquired a more promiscuous signification in recent scholarship. 4. With the exception of superintelligence, discussed below. 5. According to one study, over 66 per cent of premeditated school shootings have been shown to be connected to bullying  (Boodman 2006 ). 6. Although luck might be partly to blame, as Heemeyer fired his rifle at propane tanks that could have killed someone in the vicinity if they had exploded 7. As I've written elsewhere about similar examples: these may seem too anecdotal to be scientifically useful. But drawing this conclusion would be wrong. Given the immense power of anticipated future technologies, single individuals or groups could potentially wield sufficient power to destroy the world. The statistically anomalous cases of omnicidal lone wolves or terrorist groups are precisely the ones we should be worried about, and therefore should study. 8. See, for example, Hoffman 1993. 9. History provides numerous examples of natural disasters leading to a spike in religious belief, such as the Plague of Cyprian.", "date_published": "n/a", "url": "n/a", "filename": "agential_risks.tei.xml", "abstract": "The greatest existential threats to humanity stem from increasingly powerful advanced technologies. Yet the \"risk potential\" of such tools can only be realized when coupled with a suitable agent who, through error or terror, could use the tool to bring about an existential catastrophe. While the existential risk literature has provided many accounts of how advanced technologies might be misused and abused to cause unprecedented harm, no scholar has yet explored the other half of the agent-tool coupling, namely the agent. This paper aims to correct this failure by offering a comprehensive overview of what we could call \"agential riskology.\" Only by studying the unique properties of different agential risk types can one acquire an accurate picture of the existential danger before us.", "id": "4110165704f89d5f50f7b38f1b1da186"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Margit Sutrop"], "title": "Challenges of Aligning Artificial Intelligence with Human Values", "text": "Introduction The rapid development of artificial intelligence (AI) has enabled a wide range of beneficial applications in various contexts, from healthcare to security and governance. Fields or abilities formerly thought to be exclusively \"human\" are now being tackled by a machine-learning approach  (Arnold et al., 2017, p. 81) . As AI becomes more powerful, more attention is being paid to ways of maximising its societal benefit. The growing capabilities of AI and machine learning and the development of countless new applications also pose questions of risk and trust  (Sutrop, 2019) . AI could be a threat to humanity either through its malicious use by humans  (Brundage et al., 2018) , unintended consequences  (Amodei et al., 2016) , or autonomous acts by the artificial system  (Farquhar et al., 2017) . A joint report, The Malicious Use of  AI: Forecasting, Prevention, and Mitigation (2018) , issued by the leading AI research centres in the UK and the US  (Brundage et al., 2018)  has recently analysed the landscape of potential security threats from malicious uses of AI technologies and explicitly stated that if adequate defences are not developed soon, AI will threaten our digital, physical and political security. Currently, AI systems are narrowly dedicated to specific tasks such as speech, face or object recognition, spam filters or autonomous driving, and they are not capable of setting their own goals or choosing the best courses of action across domains. Researchers predict that AI will outperform humans in translating languages by 2024, writing high-school essays by 2026, driving a truck by 2027, or working as a surgeon by 2053; they believe there is a 50 per cent chance of AI outperforming humans in all tasks within 45 years and of automating all human jobs in 120 years  (Grace et al., 2018) . As robots become increasingly autonomous and able to make decisions on their own, the risk increases that humans will lose control over AI systems. Wendell  Wallach and Colin Allen (2009)  have suggested that as robots take on more and more responsibility, they must be programmed with moral decision-making abilities, for the sake of our own safety. What is AI? AI has been described in various ways. It can refer to certain humandesigned systems, or to a scientific discipline that encompasses several approaches and techniques, such as machine learning, machine reasoning, and robotics. In this paper, I will discuss AI systems according to the definition of the European Commission High Level Expert Group on Artificial Intelligence as follows: AI systems are software (and possibly also hardware) systems designed by humans that, given a complex goal, act in the physical or digital dimension by perceiving their environment through data acquisition, interpreting the collected structured or unstructured data, reasoning on the knowledge, or processing the information derived from this data and deciding the best action(s) to take to achieve the given goal. AI systems can either use symbolic rules or learn a numeric model, and they can also adapt their behaviour by analysing how the environment is affected by their previous actions.  (European Commission, 2019a)  Visionary scenarios consider the possibility that intelligence equal to our own, or even exceeding it, will already be created within the current century. An AI equipped with human-level or even greater ability, which is able to find a solution when presented with an unfamiliar task, is referred to as Artificial General Intelligence (AGI). Indeed, freed from biological constraints such as limited memory and slow biochemical processing speeds, machines may eventually become more intelligent than we are-with profound implications for us all. It has been hypothesised that if humans can create AGI at a human level of intelligence, such an innovation could give rise to higher and higher intelligence; in combination with recursive self-improvement of the AGI, this would eventually lead to Superintelligence (SAI)  (Kurzweil, 2005; Tegmark, 2017) . SAI is \"any intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest\"  (Bostrom, 2014, p. 26) . According to a high-level survey of expert opinion, AI specialists estimate that systems will move to superintelligence by the end of this century, and that \"the chance is about one in three that this development turns out to be 'bad' or 'extremely bad' for humanity\"  (Müller & Bostrom, 2016) . Even if we are still far from humanlevel AI and AI advancements may be overhyped, several research programs have been launched on risk assessment of AI systems, attempting to mitigate threats of rapid and uncontrollable AI development. The AI developers themselves worry about how to ensure that an AI does not escape its confines and cause damaging effects  (Yudkowsky, 2004) . Computer scientists warn, \"[a]s autonomous systems become more prevalent in society, it becomes increasingly important that they robustly behave as intended\"  (Russell et al., 2016) . Ethicists stress, \"[w]hen independent of the humans that created them, their true 'intelligence' is tested in terms of their status as 'moral beings'\"  (Iphofen & Kritikos, 2019) . Since the potential threats are great, policymakers have emphasised the need to develop ethically-aligned AI which will respect our ethical principles and values. A good overview of various guidelines for ethical, rights-respecting and beneficial AI has been provided in the recent report 'Principled Artificial Intelligence: Mapping Consensus in Ethical and Rights-based Approaches to Principles for The research program of designing AI that conforms to human values is called 'value alignment'. AI researchers explain this as follows: \"As intelligent systems gain autonomy and capability, it becomes vital to ensure that their objectives match those of their human users; this is known as the value alignment problem\"  (Fisac et al., 2018, p. 1) . 'Value alignment' is defined as a property of an intelligent agent that allows it only to pursue goals and activities which are beneficial to humans  (Soares & Fallenstein, 2014; Soares, 2015; Russell et al., 2016; Arnold et al., 2017; Russell, 2019) . Identifying the purposes we really desire remains an open question. The opposite of 'value alignment', 'value misalignment' can be explored from two perspectives, either by focusing on the behavior of individual tech artefacts (individual level) or on the functioning of sociotechnical systems (system-level)  (Osoba et al., 2020, p. 332) . The AI 'value alignment' problem faces two interrelated kinds of challengestechnical and normative  (Gabriel, 2020) . The technical challenge deals with the question of \"how to encode human values in artificial intelligence.\" The normative challenge is associated with two questions: \"which values or whose values should artificial intelligence align with?\" My concern is that AI developers and computer scientists underestimate the difficulty of answering the normative question. They hope that if we find out \"what we want, what we really, really want\"  (Russell, 2015) , we can create a beneficial AI which is \"humble, altruistic, and committed to pursue our objectives, not theirs\". But how are we to decide which objectives or values to induce in AI, given that there is a plurality of values and moral principles and that our everyday life is full of moral disagreements? In the first part of my paper I will demonstrate how technical and normative challenges of value alignment are interrelated. I will provide a brief overview of the ways in which AI researchers have tried to solve the 'value alignment problem'. I will explain why it is problematic that in value alignment programs the word 'value' is used interchangeably with goals or preferences. In the second part of my paper I will focus on normative challenges of value alignment. Several research papers, AI guidelines and manuals discuss the need to take into account cultural differences, while also respecting universal principles. I will suggest how this apparent inconsistency can be removed. My thesis is that although it is not realistic to reach an agreement on what we humans really want, given that people value different things and seek different ends, it may be possible to agree on what we do not want to happen, considering the possibility that intelligence can be created that is equal to our own, or even exceeding it. I agree with Isaiah Berlin's view as expressed in 'The Pursuit of the Ideal' that even if our ends and moral principles are plural, they are not infinitely many, since they have to remain \"within the human horizon\"  (Berlin, 2013 (Berlin, [1947 ). I will argue for pluralism (and not for relativism!) which is compatible with objectivism. Despite the fact that there is no uniquely best solution to every moral problem, it is still possible to identify which answers are wrong. And this is where we should begin the value alignment of AI. \n A technical challenge: how to align AI with values? The answer to the question how to align AI with values depends, on the one hand, on the technical possibilities and, on the other hand, on what we want AI to align with. Theories of value alignment vary on what they mean by 'value'. In the context of value alignment, Iason  Gabriel (2020)  notes that the notion of 'value' can serve as a place-holder for many things: AI could be designed to align with expressed or intended instructions, revealed preferences, informed preferences or desires, interest or well-being, or moral values as defined by the individual or society. In view of these different approaches, value alignment turns out to be an umbrella for various attempts to ensure that general artificial intelligence will remain beneficial to humans. Through what means do AI researchers and designers hope to reach value alignment? There seem to be two basic-albeit opposite-approaches, either feeding the artificial agent the right principles or applying (cooperative inverse) reinforcement learning. Both approaches-feeding the artificial intelligent with principles and reinforcement learning-have their proponents and critics. With progress in the area of machine learning, the idea of training a system on data (either supervised or unsupervised) has drawn increasing attention. Thus there seems to be a turn away from traditional machine ethics with its topdown articulation of rules, norms or models of behaviour and toward learning values either through imitation or by identifying the preferences of humans. Nevertheless, some critics doubt that beneficial AI can be achieved in this way, arguing that AI can be truly beneficial only if it can become a moral agent which acts on ethical principles or has moral virtues. Iason  Gabriel (2020)  has recently argued for a principle-based approach. His view is that instead of looking for \"true\" moral principles for AI, the real task is \"to identify fair principles for alignment that receive reflective endorsement despite widespread variation in people's moral beliefs\"  (Gabriel, 2020) . The idea behind reinforcement learning is that desirability of any state sequence can be expressed as a sum of immediate rewards associated with each state in the sequence. The objectives that the reinforcement learning agent is supposed to follow can be defined by specifying reward function. In the case of inverse reinforcement learning (IRL), an AI system infers the underlying utility function of an agent by observing its behavior.  Hadfield-Menell et al. (2016)  argue that the value alignment problem can only be solved through cooperative inverse reinforcement learning (CIRL) which they describe as \"a cooperative, partialinformation game with two agents, human and robot; both are rewarded according to the human's reward function, but the robot does not initially know what this is.\" Mark O.  Riedl and Brent Harrison (2016)  have argued that given potentially infinite undesirable outcomes in an open world, if values cannot be easily enumerated by human programmers, they can be learned by reinforcement. They hypothesise that an artificial intelligence that can read and understand stories can learn the values tacitly held by the culture from which the stories originate.  Riedl and Harrison (2016)  describe their preliminary work on using stories to generate a value-aligned reward signal for reinforcement learning agents that preempts psychotic-appearing behavior. They argue, Value alignment in a reinforcement learning agent theoretically can be achieved by providing the agent with a reward signal that encourages it to solve a given problem and discourages it from performing any actions that would be considered harmful to humans. A value-aligned reward signal will reward the agent for doing what a human would do in the same situations when following social and cultural norms (for some set of values in a given society and culture) and penalise the agent if it performs actions otherwise. A reinforcement learning agent will learn that it cannot maximise reward over time unless it conforms to the norms of the culture that produced the reward signal.  (Riedl & Harrison, 2016)  How can a value-aligned reward signal be learned?  Riedl and Harrison's (2016)  answer is that, \"[a] value-aligned reward signal is produced from the crowdsourced stories in a two-stage process\". When humans tell stories to other humans, they skip over many details and events. By crowdsourcing the narratives, one can get better coverage of all steps involved in a situation and extract the most reliable pattern of events. Riedl and Harrison describe the reinforcement learning process as follows: in the first step, the plot graph learning process \"aligns\" the crowdsourced example narratives to extract the most reliable patterns of events; in the second step, the plot graph is translated into a \"trajectory tree\" which is used to produce a reward signal. If the reinforcement learning agent performs an action that is a successor of the current node in the trajectory tree, it receives a reward; if it fails, it receives a small punishment. The aim is to make the reinforcement learning agent solve some problem in the most human-like fashion. The problem is that in many stories humans violate social and cultural norms. The authors' hope is that the most typical human behaviour that emerges from crowdsourced stories is compliant to the norms. The proposal to achieve value alignment through reinforcement learning has been criticised by Thomas Arnold, Daniel Kasenberg and Matthias Scheutz (2017) as ethically inadequate and insufficient to guide artificial agents in decision making. They point out a number of problematic areas associated with reinforcement learning, including data bias, generalisation issues, and the adequacy of reward functions to represent temporally complex norms  (Arnold et al., 2017, p. 81) .  Arnold et al. (2017)  claim that even if there is agreement that top-down approaches of giving AI systems ethics would be intractable, IRL on its own cannot solve the problem and train such an agent to be moral. They point out that ethical behavior depends not only on the acts themselves, but on intentions, reasons, norms, and counterfactuals. The question IRL faces is what kind of model could truly learn ethical practices. Alternatively, value alignment of AI can take the form of imitation learning. In their article entitled 'The virtuous machine-old ethics for new technology' Nicolas  Berberich and Klaus Diepold (2018)  draw inspiration from Aristotle to demonstrate that virtue ethics can provide a solution to the value alignment problem. Instead of focusing on the formulation of duties and maxims (as deontologists do) or on the identification of desirable and maximisable consequences of actions (i.e., happiness), Berberich and Diepold argue that one should concentrate on moral actions performed by virtuous moral agents. \"With respect to machines this changes the primary question from 'By what kind of algorithm can a machine choose the right action?' to 'How can we build a machine that, owing to its constitution, acts appropriately in arbitrary situations?'\"  (Berberich & Diepold, 2018, p. 4 ). The article concludes by stating, 1. Virtue ethics fits nicely with modern artificial intelligence research and is a promising moral theory. 2. Taking the virtue ethics route to building moral machines allows for a much broader approach than simple decision-theoretic judgement of possible actions. Instead, it takes other cognitive functions into account like attention, emotions, learning and actions.  (Berberich & Diepold, 2018, p. 23)  Berberich and Diepold believe that since humans have for centuries learned virtues from imitating the behaviour of virtuous moral agents, virtue theory should be the guiding moral theory for building truly moral machines. They point out that since virtues are an integral part of one's character, the AI would not have the desire of changing its virtue of temperance  (Berberich & Diepold, 2018, pp. 23-24) . The difficulty in this argument is that virtue ethics has a hard time giving reasons for actions, and this means one cannot claim responsibility. The most influential approach to the problem of AI value alignment has been provided by Stuart Russell, whose ideas are summarised in his recent book, Human Compatible: AI and the Problem of Control (2019).  Russell's (2019)  central idea is that in order to maintain control, we have to design beneficial AI which is \"humble, altruistic, and committed to pursue our objectives, not theirs\". In order to guide AI researchers and developers in thinking about how to create beneficial AI systems, Stuart Russell formulates three principles: 1. The machine's only objective is to maximise the realization of human preferences. 2. The machine is initially uncertain about what those preferences are. 3. The ultimate source of information about human preferences is human behavior.  (Russell, 2019, pp. 172-173)  Russell believes that there is plenty of data about human actions (what has been written, filmed or observed) and about attitudes to these actions. In other words, rather than having a detailed ethical taxonomy programmed into them, AI systems should infer human values by observing and emulating our behavior. It is noteworthy that in his earlier writings and interviews, Russell has spoken about 'human values' which have now been replaced by the expression 'human preferences'. In an interview from 2015, Russell stated: To the extent that human values are shared, machines can and should share what they learn about human values. […] by assigning very broad priors over what human values might be, and by making the AI system risk-averse, it ought to be possible to induce exactly the behavior one would want: before taking any serious action affecting the world, the machines engage in an extended conversation with us and an extended exploration of our literature and history to find out what we want, what we really, really want.  (Russell, 2015)  In his 2019 book, Russell replaces the expression 'human values' with 'human preferences'. He also provides explanations as to why he has dropped the word 'value'. Russell points out that since the word 'value' is often understood as 'moral value', use of this term can be confusing. He does not want to give an impression of attempting to solve moral dilemmas like stops on a trolley route. In his view, such an approach is not worth considering, as in true dilemmas there are good arguments for both sides, and artificial agents cannot cause more harm than humans even if they take a wrong decision. Russell's concern is how to avoid the worst catastrophes and to ensure that we never lose control of machines more intelligent than we are. In addition, Russell insists that one should not equate value alignment with the wish to instill in machines a single ideal value system which may raise the question whose values should be encoded or who has been given the right to align AI with such values. He says that he uses the word 'value' as a technical term, \"synonymous with utility, which measures the degree of desirability of anything from pizza to paradise\"  (Russell, 2019, p. 178) . He also explains what he means by 'preferences': these cover everything one might care about. Furthermore, in order to be beneficial, the purely altruistic machine should aim to maximise the realisation of human preferences. Instead of \"putting in values\" or preferences, the machines \"should learn to predict better, for each person, which life that person would prefer, all the while being aware that the predictions are highly uncertain and incomplete\"  (Russell, 2019, p. 178 ). Russell believes that, in principle, an AI could learn billions of different predictive preference models. With respect to the issue of how the machine should trade off the preferences of multiple humans,  Russell (2019, p. 174 ) refers to the utilitarian principle of \"the greatest happiness for the greatest numbers\". The crucial question is how the machine might learn about human preferences. His answer is, again, very simple: by observing human choices which reveal information about human preferences. In Russell's opinion, the real complications arise because humans are not perfectly rational and the machine must take such an imperfection into account  (Russell, 2019, p. 177) . It turns out that, in essence, what Russell means by 'value' is in reality a 'preference'. However, the same problem crops up with the concept of 'preference' as it did with the concept of 'value'. Both have multiple meanings, and their use in different disciplines is highly variable. In its most general meaning, a value is that which is worthy, that which is worth having, getting or doing, or that which possesses some property or properties that make it so. Values are action-guiding; they are taken into account when making decisions and when planning activities. In the most general terms, preferences are evaluations; they concern matters of value. Preferences are subjective in that the evaluation is typically attributed to an agent. Russell uses the term as subjective comparative evaluation, of the form 'Agent A prefers X to Y'. What one prefers is not necessarily something objectively valuable, but rather something subjectively valuable from one's personal point of view. But this is where the problem begins. We can imagine the situation where the designer of a self-driving car asks potential customers whether they would prefer a car which will protect the persons riding in it or those on the street. Or, even worse, whether they would like a car which violates traffic rules, ignores traffic lights and brings the owner quickly and safely to the destination. Should such preferences be fulfilled by artificial intelligence? By leaving aside moral values and concentrating only on human preferences, it is difficult to understand how situations in which AI might fulfil the preferences of immoral agents can be avoided. As there are more non-democratic countries than democratic ones in the world, we should be careful not to allow AI to be programmed to do something devastating. Somewhere there will always be efforts underway to create an AI that will be destructive, for example, for military purposes. Some experts have questioned the use of robots in military combat, especially if such machines were to be given some degree of autonomous functions, e.g., being able to independently choose targets to attack with weapons. What is the solution? AI should be programmed not to fulfil immoral preferences and refuse to do immoral actions but they should be able to distinguish between moral and immoral actions. Thus, besides values we should also provide them with the capacity of moral deliberation to decide when a certain moral principle applies, and to be able to rank values in different contexts. It seems dangerous to let AI become an autonomous decision-maker without its becoming a moral agent. To be a moral agent entails far more criteria than adopting ethical values. Amitai  Etzioni and Oren Etzioni (2018)  note that to be a moral agent requires a certain set of attributes: (a) Self-consciousness. If the agent is not aware of itself in any given situation, and of the alternative courses that might be followed, then no moral decisions can be rendered. (b) The agent must be aware that she can affect the situation. (c) The agent must be able to understand the moral principles to be employed in arriving at a particular moral choice. (d) The agent must have a motive to act morally. This involves having passions, as otherwise moral preferences are merely intellectual preferences with nothing to fuel the moral action. Some scholars also add that a will or intention is required…  (Etzioni & Etzioni, 2018, pp. 239-240) . This argumentation indicates that if we want to avoid the scenario that AI can satisfy both moral and immoral preferences, we need to integrate ethics into AI, not only align it with values. The research programme of AI value alignment should ideally be interdisciplinary, besides computer scientists also involving philosophers, lawyers, economists, and cognitive scientists, psychologists and pedagogical scientists. Its success will depend on how much the AI designers will be able to integrate the knowledge provided by these disciplines in the design of AI. So far, discussions on value alignment have not actively included ethicists. As a result, there is a danger that AI ethics will undergo simplification, reduction or dogmatism. In several working groups which aim to secure beneficial AI, ethics has been boiled down to law or reduced to some specific principle (fairness, transparency, equality or accountability) without providing any reasons why one or another principle should be prioritised. The analysis of the policy documents on ethical AI  (Fjeld et al., 2020)  showed that the most common governance regime suggested for dealing with AI is international human rights law-64 per cent of all documents contained a reference to human rights. Annette  Zimmermann and Bendert Zevenbergen (2019)  have recently issued warnings concerning seven traps into which AI ethics can fall: reductionism, oversimplification, the relativism trap, value-alignment trap, dichotomy; the myopia trap; and the trap of the rule of law. For the purposes of this paper, it is especially interesting how the authors present the relativism trap and the valuealignment trap as two unacceptable options. The relativism trap is associated with the tendency to conclude that since pervasive moral disagreements exist, ethics is relative. Should we argue that relativism is wrong, we risk falling into the value-alignment trap according to which there must be one morally right answer. If we cannot reach an agreement, we will have failed. I am quite inclined to agree with the authors' view that AI ethics should welcome value pluralism without collapsing into extreme value relativism. We should accept that it may not always be possible to determine \"the one right answer\", thereby avoiding moral disagreement. However, it is often possible to clarify that at least some paths of action are clearly wrong and some paths of action are comparatively better. The normative challenge: which values should AI align with? In order to answer the normative question 'Which values should AI align with?' one must first answer the question of whether values are objective or subjective; universal or culturally relative. Are there absolute values or prima facie values? Several regulatory bodies that write guidelines about ethical AI stress that one has to be sensitive to cultural differences while at the same time respecting universal principles. Thus the Ethics Guidelines for Trustworthy AI (European Commission, 2019b) assert that \"AI systems should respect the plurality of values and choices of individuals\", thereafter claiming that \"certain fundamental rights and principles, such as human dignity, are absolute and cannot be subject to a balancing exercise\" (European Commission, 2019b, p. 13). In order to make it possible for European citizens to reap the benefits of AI, it needs to be \"aligned with our foundational values of respect for human rights, democracy, and rule of law\" (European Commission, 2019b, p. 4). IBM's manual entitled Everyday Ethics for Artificial Intelligence states: \"Care is required to ensure sensitivity to a wide range of cultural norms and values. As daunting as it may seem to take value systems into account, the common core of universal principles is that they are a cooperative phenomenon.\" (IBM, 2019) Another important document, Ethically Aligned Design. A Vision for Prioritizing Human Well-being with Autonomous and Intelligent Systems, published under the auspices of the IEEE Global Initiative on Ethics of Autonomous and Intelligent Systems poses the rhetorical question: \"If machines engage in human communities as autonomous agents, then those agents will be expected to follow the community's social and moral norms. A necessary step in enabling machines to do so is to identify these norms. But whose norms?\" (IEEE, 2019) Again, it seems that in spite of stressing the variety of social and moral norms, this document emphasises that values-based design of AI should respect universal ethical principles and internationally recognised human rights. Indeed, the document states that […] whether our ethical practices are Western (e.g., Aristotelian, Kantian), Eastern (e.g., Shinto, School of Mo, Confucian), African (e.g., Ubuntu), or from another tradition, honoring holistic definitions of societal prosperity is essential versus pursuing one-dimensional goals of increased productivity or gross domestic product (GDP). Autonomous and intelligent systems should prioritize and have as their goal the explicit honoring of our inalienable fundamental rights and dignity as well as the increase of human flourishing and environmental sustainability.  (IEEE, 2019, p. 1)  It seems to me that all these documents point in the same direction-namely, that we should accept plurality of values while at the same time prioritising certain specific values, and doing both of these things without necessarily providing explanations of how pluralism of values and objectivity of ethics are compatible. In the following I will try to explain how pluralism can accommodate both persistent moral disagreements and the objectivity of ethics. Pluralism differs from both relativism and subjectivism. Unlike the relativist, who believes that rightness depends on the culture or society, and unlike the subjectivist, who believes that rightness depends on the individual, the pluralist holds that in some cases the question of what is right lacks a determinate answer. Rightness is indeterminate, as there is irreducibility of values. As shown by Susan Wolf in the article 'Two levels of pluralism  ' (1992) , this irreducibility can happen on two levels of decision: on the level of values and on the level of moral systems. Wolf says that on the first level we constrain moral judgements within a moral system, i.e., we have to decide which value, for example, equality or liberty, is more important and we have to admit that there is no right answer to this question. On the second level, we constrain moral assessments of the systems themselves. Here we have to decide which moral system, with its different understanding of moral rightness, we should prefer (for example, Kantianism or utilitarianism or virtue ethics).  Wolf (1992)  shows that there is a possibility that after a careful assessment it may turn out that these value systems are all incommensurably good, and living according to any of these moral systems will lead to a morally good life. Also Isaiah Berlin supports pluralism which is compatible with objectivism. Pluralism means for him that \"there are many different ends that men may seek and still be rational, fully men, capable of understanding each other\"  (Berlin 2013 (Berlin [1947 , p. 11). In fact, we do have shared values which form bridges between people and make intercommunication between cultures in time and space even possible. \"But our values are ours, and theirs are theirs\"  (Berlin 2013 (Berlin [1947 , p. 11). We might criticise the values of other cultures, but we have to understand where they come from, what it means to live the way they do. Here Berlin emphasises people's empathy and capacity for imagination, their need to put themselves in the shoes of a representative of another era or culture. Pluralism in Berlin's view does not exclude a world of objective values or ends that men pursue for their own sake. Ends and moral principles are plural, but they are not infinitely many, since they have to remain \"within the human horizon\"  (Berlin 2013 (Berlin [1947 , p. 12). We should be able to distinguish between objectively good and bad life forms and condemn slavery, sexism, racism, or Nazism. Given that there are people who argue from an egoistic position of power, with the intention of preserving their preferred state or that some lack imagination and empathy for what it would mean to be in another's situation (in cases such as slavery, Nazism, female circumcision, racial or gender hatred, disparagement of minorities, abuse of animals), we need to have the opportunity to say that such things are unacceptable. This remains so even if we favor value pluralism. We can get a better idea of how pluralism can be compatible with objectivity by reading John Kekes's book The Morality of  Pluralism (1993) . Kekes makes a distinction between primary and secondary values. Primary values are the same for everyone, for they constitute the minimum requirements of good lives and are derivable from the facts of human nature. For example, we share the same physiological and psychological needs and capacities. Thus, the same things, goods pertaining to the self, intimacy, and social order are needed by everybody to live a good life. At the same time, the identity of secondary values depends on variable social and personal circumstances. For example, whereas killing is universally considered to be evil, what sort of killing counts as murder may be dependent on context. Kekes explains that secondary values are contingent on primary ones; either they are particular forms of expression of these values (for instance, the primary value of intimacy will take the form of certain sexual practices) or they are genuinely new goods, the realisation of which depends on the presence of primary values (for instance, in order to derive pleasure from creative participation in art or science, one's elementary needs for food and shelter need to be satisfied)  (Kekes, 1993, pp. 42-43) . Primary and secondary values can be either moral or non-moral. While moral values (both primary and secondary) affect others, nonmoral values (both primary and secondary) affect the agent or occur naturally. Primary values (both moral and non-moral) are universal requirements of all good lives, while secondary values count as benefits or harms because a tradition or a conception of a good life makes them so  (Kekes, 1993, p. 45) . Kekes explains that pluralists differ from relativists in holding primary values to be objectively justifiable by referring to our common nature. He admits that even monists must not reject plurality of values, provided there is some overriding value which allows authoritative ranking of the plural values. Kekes points out that there is a great variety of monist conceptions of what the overriding value or some principle of ranking values may be: the utilitarian ideal of the greatest happiness for the greatest number of people, the welfare economists' goal of preference satisfaction, the Kantian principle of the categorical imperative, the contractarian list of fundamental human rights, or something else  (Kekes, 1993, p. 47) . Thus, the main difference between monists and pluralists is that for the former there is one overriding value or principle, while for the latter values are manifold and contextual. Kekes explains that we usually aim to construct a conception of the good life out of the primary and secondary values that we ourselves favor and that our tradition supplies. Although he argues that for pluralists there is no authoritative way of settling the value conflict, there still seems to be at least one overriding principle for comparing and ranking different values. To my mind, by arguing that primary values originate in our common human nature, Kekes is also suggesting an authoritative overriding principle which helps to compare and rank values. For instance, he proposes that in value conflicts one should try to reduce secondary values to primary values (which have their source in human nature), by making it explicit that in spite of all differences, the fact that situatedness in various historically conditioned traditions and individual life-situations has led to differentiation in our conceptions of a good life, we continue to have similar human needs and capacities. Although Kekes himself has not recognised that his own appeal to common human nature is monistic in a similar way as the appeal to human rights framework, categorical imperative or general happiness principle, it is still possible that he ultimately speaks for pluralism and not monism. I think that as long as one accepts that there can be a plurality of ultimate values, all of which can be equally justified, one is a pluralist. Thus, indeed, pluralism really is compatible with objectivism. \n Conclusions I have tried to show that it is good that AI researchers have identified the importance of ensuring that AI will remain beneficial and that therefore AI should align with human values. However, since the term 'value' only functions as a placeholder and in reality one could limit oneself to making AI fulfil human preferences, the problem may arise that AI will not necessarily act morally, but potentially also satisfy immoral preferences. Thus, in order to secure ethical AI one should compel it to follow moral principles or obtain moral values. In the course of the argument the question emerged whether there are universal values or whether AI should reckon with cultural differences. I hope I have shown that value pluralism can accommodate both moral disagreements caused by diversity of values and the objectivity of ethics, accepting that there are no uniquely correct answers to moral questions. Moral ambiguity does not necessarily imply relativism. Accepting plurality does not mean that anything goes. We can identify wrong answers as long as we share our expectations of morality. Indeed, the aim of morality is to regulate our life in society, enabling us to live together peacefully and allowing human beings to satisfy their various needs: physiological, psychological, social, cultural and intellectual.  Thus, value alignment should begin with seeking agreement on negative valueswhat we do not want to lose and what we do not want to happen if it becomes possible to create artificial intelligence with intellectual capacities equal to or beyond our own. Our efforts to define what is immoral should keep in mind that morality's function is to satisfy the basic human needs which we all share.Value plurality and objectivity can be joined if we accept that there are many moral principles by which one can justify and rank moral values. Different moral theories can prefer different ultimate principles. One can live a moral life according to all of these. Nevertheless, there are fewer choices about what is morally wrong, and thus we should seek agreement on what is clearly immoral.", "date_published": "n/a", "url": "n/a", "filename": "04_Sutrop-2020-2-04.tei.xml", "abstract": "As artificial intelligence (AI) systems are becoming increasingly autonomous and will soon be able to make decisions on their own about what to do, AI researchers have started to talk about the need to align AI with human values. The AI 'value alignment problem' faces two kinds of challenges-a technical and a normative one-which are interrelated. The technical challenge deals with the question of how to encode human values in artificial intelligence. The normative challenge is associated with two questions: \"Which values or whose values should artificial intelligence align with?\" My concern is that AI developers underestimate the difficulty of answering the normative question. They hope that we can easily identify the purposes we really desire and that they can focus on the design of those objectives. But how are we to decide which objectives or values to induce in AI, given that there is a plurality of values and moral principles and that our everyday life is full of moral disagreements? In my paper I will show that although it is not realistic to reach an agreement on what we, humans, really want as people value different things and seek different ends, it may be possible to agree on what we do not want to happen, considering the possibility that intelligence, equal to our own, or even exceeding it, can be created. I will argue for pluralism (and not for relativism!) which is compatible with objectivism. In spite of the fact that there is no uniquely best solution to every moral problem, it is still possible to identify which answers are wrong. And this is where we should begin the value alignment of AI.", "id": "f0737204c7a441747687544c95f44497"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["MS John T O'brien", "MBBS, MPH Cassidy Nelson"], "title": "Assessing the Risks Posed by the Convergence of Artificial Intelligence and Biotechnology", "text": "Introduction \n Technological Progress S ince the explosion of the information age, the collection of data has been increasing. About 2.5 quintillion  (10 18  ) bytes of data are generated each day, and 90% of all data have been generated in the past few years alone.  1  Although valuable information is often hidden in these vast datasets, due to their size and complexity, a human analyst could take weeks, months, or even years to discover them, if they are able to at all. If one can analyze a large enough set of data, it is possible to infer corollary relationships or patterns that may be of salience. In the past, it was not conceivable for extremely large datasets, or big data, to have been meaningfully analyzed due to the daunting task of doing so manually. Partially as a result of the increasing prevalence of big data requiring new tools for analysis and increased computing power enabling their development, the use of artificial intelligence (AI) in a variety of fields, including the biological sciences, has gained popularity in the past few years. AI can be defined as a system's ability to correctly interpret external data, to learn from such data, and to use those insights to achieve specific goals and tasks through flexible adaptation.  2  Machine learning, a technique that has enabled rapid advancements in the field of AI, is a subset of AI that is heavily based on pattern recognition and describes methods that help computers learn without explicitly being programmed to do so.  2  Deep learning, in turn, is a machine learning technique that arose in the early 2010s and uses computational models that exhibit similar characteristics to the hierarchal information processing in the human brain.  3  This technique is partially responsible for the increased power potential of machine learning algorithms and has been a large contributor to the recent surge of AI research.  4  Alongside AI, developments in biotechnology and the life sciences have progressed rapidly in the past several years. In fact, some biotechnological advancements may even be outpacing Moore's Law for computers.  5  Critical advances in biology such as next-generation DNA sequencing, de novo DNA synthesis, gene editing, genomics, and bioinformatics may result in the life sciences becoming a principal component of the next technological revolution. Given recent progress and projected trajectories, AI and biotechnology have both been described as key pillars of the fourth industrial revolution, with a growing number of technologies and applications arising at their point of convergence every year.  [6] [7] [8] [9]   \n Technological Convergence In tandem, AI and biotechnology increase the potential capability of the life sciences and lower the tacit knowledge required to perform previously tedious laboratory tasks. Widening the pool of actors will almost certainly accelerate technological developments, but this could also pose security risks. With increased access to these technologies, so comes the potential for a resulting high-consequence biological event, some of which may have such large consequences that they constitute a global catastrophic biological risk.  10  The risks posed by the convergence of AI with the biological sciences are plentiful and varied, ranging from AI-assisted identification of virulence factors to in silico design of novel pathogens, which could increase the probability of a global catastrophic biological risk event if accidently, carelessly, or deliberately released. For the purposes of this paper, convergence is defined as the technological commingling between the life sciences and AI such that the power of their interaction is greater than the sum of their individual disciplines. That is, the convergence of these 2 fields has a multiplicative effect. This interaction mostly manifests as AI-developments influencing advances, as well as new risks, in the life sciences and biotechnology rather than the other way around. A more comprehensive understanding of such emerging threats is highly important for the field of health security but demands rigorous examination and a systematic approach. In this paper, risk assessment for converging technologies will be discussed and evaluation of 3 existing biosecurity risk assessment frameworks undertaken. After analyzing their strengths and limitations, suggestions will be made regarding how such frameworks could be adjusted to be applicable to the risks arising at the convergence of AI and biotechnology. Some illustrative examples from the converging risk landscape will be discussed, followed by a proposed hybridized framework and key recommendations to begin addressing gaps in current health security risk assessment for converging technologies. \n Risk Assessments For Converging Technologies \n Challenges Assessing Emerging and Converging Risks Risk assessment for emerging technologies is an inherently difficult task and general frameworks are needed for evaluating the risks associated with technological convergence, including AI and biotechnology. Many frameworks are overly specific to a particular scenario or technology (such as narrowly focusing on synthetic biology), contain many assumptions and guesswork, and are not easily applied to other converging or emerging technologies. This is largely because different frameworks serve different purposes, so expectations that they can be implemented more generally are limited. However, the primary strength of a more generic framework for biosecurity risk assessments would be the ability to compare across different technologies or scenarios. Decision makers could then use such frameworks to be more informed as to which risks may be of higher priority. Compared to assessments of singular domains, analyzing risks of converging technologies presents an even greater challenge due to the added layers of complexity and the presence of multidisciplinary components. Converging risks such as those described herein are uniquely challenging to assess because their uncertainties multiply such that one must consider all possible outcomes of AI development in tandem with all possible outcomes of developments in the life sciences. For example, the evaluation criteria in a scenario-based risk assessment for virtual laboratories or 'cloud labs' that are too focused on the biological components may miss important bottlenecks, risks, or gaps that exist within the underlying AI components of the technology. Full assessment may not always be possible for some unpredictable technological advancements. Challenges also arise due to limited access to data and the inability to quantitatively assess emerging risks. Many frameworks include the potential adversary as a component to calculate risk.  11, 12  However, the adversary has a large range of potential attributes that are difficult to capture in their entirety. The adversary could be a nation, a nonstate actor, or an individual. When evaluating the likelihood that one of these adversaries could carry out ASSESSING ARTIFICIAL INTELLIGENCE AND BIOTECHNOLOGY RISKS an attack, assumptions must be made and variables considered on a spectrum. For example, a nation-state could be a low-resourced or well-resourced country. An individual could be anyone from an undergraduate biology student to a senior research professor. Such approaches fail to capture the range of possibilities and thus suffer from decreased granularity. Along these lines, without access to classified information, it is impossible to appreciate a full picture of adversary capability and intent. Furthermore, frameworks are sometimes focused on a technology's ability to aid in a specific element in the development process of a biological agent, which then makes it difficult to assess the risks of a full scenario in which it was implemented successfully. Conversely, assessments that solely focus on a full scenario fail to accurately capture the broad range of potential misapplications of a technology and consequently suffer from excessive specificity. After searching published literature, we identified 3 previously employed frameworks that inform the development of an assessment for converging technologies. These frameworks are examined in this paper in detail, with their strengths and limitations explored. \n Overview of Existing Frameworks The AAAS-FBI-UNICRI Framework The first framework was published in the 2014 report, National and Transnational Security Implications of Big Data in the Life Sciences, and was developed by a joint team consisting of members from the American Association for the Advancement of Science (AAAS) Center for Science, Technology, and Security Policy, the Biological Countermeasures Unit of the Federal Bureau of Investigation (FBI) Weapons of Mass Destruction Directorate, and the United Nations Interregional Crime and Justice Research Institute (UNICRI).  11  The main elements of the AAAS-FBI-UNICRI framework are highlighted in Table  1 . A strong component of this framework is the inclusion of security specialists, in addition to experts from multiple disciplines to evaluate the risks. While being one of the only attempts at risk assessment of a converging technology, the framework is limited in generality because it uses a scenario process to assess risks and its evaluation criteria are heavily skewed to big data and do not neatly map on to other converging technologies such as AI, despite many commonalities between them. The lack of generality is best illustrated by the framework table itself in which the ''Needed scientific expertise and skills'' block is divided into 2 sections to cover all 3 scenarios evaluated. This may be due to the fact that the working group developed the risk scenarios prior to developing the framework itself, resulting in a framework with a narrow scope. When attempting to implement a scenario where a malicious actor uses AI-enabled cloud labs to synthesize a pathogen in silico, the narrowness of this framework becomes more evident. The parameter, ''vulnerabilities in data repositories, software, and/or underlying cyber infrastructure''  11  does not map onto this scenario since none of those 3 vulnerabilities are necessarily present in the case of cloud labs accessed through legitimate channels, albeit for nefarious purposes. \n The NASEM Framework The second framework emerged from the National Academies of Science, Engineering, and Medicine (NASEM) 2018 report, Biodefense in the Age of Synthetic Biology. The NASEM framework (Table  2 ) is strong in that it actively considers the synergy with other technologies as a factor to calculate level of concern. The report also considers machine learning and automation as potential technologies that could facilitate the development of a biological agent. This framework, however, excludes actors who may be beneficial, considering the broad range of potential adversaries. The limitation in using this framework for converging AI and biotechnology risks is that the scope is too specific and restricted to risks from synthetic biology and technologies relevant to the design-build-test cycle. The authors of the report are transparent about these limitations and recognize that every factor may not map on to a specific technology. If one wanted to apply this framework to evaluate the level of concern posed by risks from the convergence of AI and biotechnology, they could face difficulties since the questions used to evaluate the factors are heavily skewed toward synthetic biology. However, since the framework was developed to assess capabilities of a technology to enable harm more   12  This framework (Table  3 ) benefits from including a governability assessment that is used if the average value of the factors from the risk assessment portion are ''medium'' or ''high.'' While assessing governability for approaches to governance has unquestionable value, it can also be an indicator for probability. If a technology is less governable, it is likely to have a higher chance for misuse and resulting risk. A potential weakness in Tucker's framework is the use of an ordinal scale with just 3 values (high, medium, or low). A spectrum spanning a range of only 3 could result in lost information and decreased specificity, which may have negative downstream effects in determining which technologies pose the greatest or lowest risk. Another potential shortcoming is that the framework considers the imminence of the technology to be of equal weight to the other factors in calculating risk. As a result, it could potentially fail to accurately categorize a long-term, high-consequence risk as one worth governing. In a 2017 working paper, Koblentz et al expanded on Tucker's framework, proposing the Tucker-Koblentz framework, which includes the range of applications for misuse as an indicator of risk.  14  This is particularly useful in the context of the converging technologies since they tend to have synergistic effects that increase the range of appli-cations. The authors also noted how risk assessments are implicitly impacted by the anticipated benefits of a technology since such technologies are more likely to be intensely pursued by researchers and private companies, which results in accelerated innovation and diffusion of knowledge. This perspective is useful in the context of the convergence of AI and biotechnology since the range of beneficial applications is rather large. \n The Converging Risk Landscape The overlap between AI and biotechnology is already considerable, with increasing integration of AI into various facets of the biological sciences likely to continue for the foreseeable future.  9  This poses a challenge for the health security risk assessment frameworks previously described and requires further understanding of the risks that need to be prioritized for examination. This section provides an overview of some of the intersections of AI and biotechnology that could be considered for future risk assessment exercises. These sections are presented as illustrative examples and are not meant to propose a taxonomy of risks. \n Synthetic Biology Increasingly, engineering principles are being applied to biology for research and manufacturing purposes. Synthesis and design of existing and novel microorganisms have many legitimate and beneficial applications; however, these same technologies could be used to engineer pathogens for malicious use. AI and machine learning have the potential  \n ASSESSING ARTIFICIAL INTELLIGENCE AND BIOTECHNOLOGY RISKS to greatly aid in the design-build-test stages of the synthetic biology process.  15  Current DNA synthesis methods and gene editing technologies, such as the CRISPR-Cas9 system, still pose a high technical barrier for viable pathogen creation. Nonetheless, several recent controversial experiments have showcased the ability to de novo synthesize live viruses, including horsepox and the 1918 flu.  16  Research on emerging techniques, such as enzymatic synthesis of DNA, aims to revolutionize the field of synthetic biology in the next decade, with the end goal being benchtop printers able to synthesize gene-length sequences of DNA to completion.  17  Advances in this space are not only increasing the potential power and capability of synthetic biology but are also lowering the technical barriers and tacit knowledge required for its widespread use.  18  Within the realm of synthetic biology, AI could potentially lower some of the barriers for a malicious actor to design dangerous pathogens with custom features. It is worth noting, however, that AI will have a differential effect on technological hurdles, with some bottlenecks remaining difficult to traverse. For a more detailed examination of how the difficulty of design steps can affect the probability of a successful biological attack, we recommend the paper by Sandberg and Nelson also published in this issue.  19  AI has enabled a substantial reduction in the time required to design and test functionality in fields such as protein design.  20  It may also lower barriers in the design stages of the design-build-test cycle and could be used to identify optimal mutations of a pathogen that enhance virulence factors, expand host range, alter routes of transmission, encode resistance to medical countermeasures, and intensify mortality.  21  Genetic changes could be identified and made to a virus that is traditionally benign in nature, allowing it to bypass screening procedures currently used by mail-order DNA synthesis services. Similarly, AI could be leveraged to circumvent field detection technologies by identifying code sequences that could be altered without changing function.  11  Deep learning could potentially identify genetic functions that code for vulnerabilities and interconnections between the immune system and microbiome. It may be possible that malicious actors could leverage this information to engineer ''precision maladies,'' or pathogens that target important mechanisms the immune system or the microbiome of specific subpopulations.  22  It is important to note, however, that simply identifying certain vulnerabilities does not mean actors can then freely make changes, significant bottlenecks would still have to be traversed in the overall development process and the feasibility of targeting specific subpopulations would remain an unknown. Moreover, in the past few years, several studies have been published on predicting the pathogenic potential of natural and synthetic DNA using AI. Although improving biosecurity is one of the motives for this research, the results of this work may have the reverse effect and pose information hazards if the methods and algorithms are published. PaPrBaG and DeePaC are examples of machine learning algorithms predicting pathogenic potential that have made all source code available online.  23, 24  These algorithms could potentially aid a bad actor with the intent of designing a pathogen that can cause maximal harm. AI can not only assist in the design step of the process, but it can also, to a lesser degree, support the building and testing phases. The rise of AI-enabled cloud labs to automate procedures that used to require hands-on, tacit knowledge to perform tasks could further widen the pool of actors who could perform certain biology experiments. Cloud labs could allow a malicious actor to perform synthesis and carry out subsequent testing undetected and with greater ease.  25  The next evolution of cloud labs may further enable AI scientists capable of carrying out experiments in entirety by developing and testing hypotheses, interpreting results, and amending hypotheses for retesting, thus lowering the technical barrier even further.  26  Furthermore, directed evolution of pathogens, which spans all 3 phases of the design-build-test cycle, is another route a malicious actor could take in the development of a customized pathogen.  13  AI techniques have already been leveraged to accelerate this process and guide directed evolution in protein engineering.  27  Overall, in the future, it may be possible for a bad actor to perform complete hands-off, in silico design, building, and testing of a novel or recreated pathogen by leveraging the technologies and advancements outlined above.  25, 28  The potential democratization and synergy of these technologies pose potentially high-consequence risks that could elevate to a globally catastrophic level if not recognized and mitigated. \n Vulnerabilities and AI Systems As technologies in the biological sciences continue to be developed, AI-enabled offensive cyber-attacks may become an increasing biosecurity threat. For example, cybersecurity vulnerabilities in machines such as DNA synthesizers, could allow the introduction of malware to corrupt the design or audio-record printed DNA sequences, disrupt laboratory biosecurity, or allow intruder access to sensitive information.  29, 30  In addition, AI system vulnerabilities could also have downstream effects on human health. If healthcare becomes increasingly automated with the use of AI, so does increased risk for cyber-intrusion and subsequent manipulation of medical devices, which could result in harm for the end-user. TrapX Security Labs notes in their latest MED-JACK report  31  that many medical devices and equipment in use today, such as infusion pumps, medical lasers, LASIK surgical machines, and life support equipment are vulnerable to hijacking by malicious actors. Wireless connectivity is becoming increasingly common in implantable medical devices, opening up the risk of malicious actors mounting attacks from anywhere in the world.  32   \n O'BRIEN AND NELSON Beyond the risks associated with medical device exploitation, it is possible that in the future computer systems will be integrated with human physiology and, therefore, pose novel vulnerabilities. Brain-computer interfaces (BCIs), traditionally used in medicine for motor-neurological disorders, are AI systems that allow for direct communication between the brain and an external computer.  33  BCIs allow for a bidirectional flow of information, meaning the brain can receive signals from an external source and vice versa. The neurotechnology company, Neuralink, has recently claimed that a monkey was able to control a computer using one of their implants.  34  This concept may seem farfetched, but in 2004 a paralyzed man with an implanted BCI was able to play computer games and check email using only his mind.  35  Other studies have shown a ''brainbrain'' interface between mammals is possible.  36, 37  In 2013, one researcher at the University of Washington was able to send a brain signal captured by electroencephalography over the internet to control the hand movements of another by way of transcranial magnetic stimulation.  38  Advances are occurring at a rapid pace and many previous technical bottlenecks that have prevented BCIs from widespread implementation are beginning to be overcome.  [39] [40] [41]  Research and development of BCIs have accelerated quickly in the past decade.  42  Future directions seek to achieve a symbiosis of AI and the human brain for cognitive enhancement and rapid transfer of information between individuals or computer systems.  34  Rather than having to spend time looking up a subject, performing a calculation, or even speaking to another individual, the transfer of information could be nearly instantaneous. There have already been numerous studies conducted researching the use of BCIs for cognitive enhancement in domains such as learning and memory, perception, attention, and risk aversion (one being able to incite riskier behavior).  43  Additionally, studies have explored the military applications of BCIs, and the field receives a bulk of its funding from US Department of Defense sources such as the Defense Advanced Research Projects Agency.  44  While the commercial implementation of BCIs may not occur until well into the future, it is still valuable to consider the risks that could arise in order to highlight the need for security-by-design thinking and avoid path dependency, which could result in vulnerabilities-like those seen with current medical devices-persisting in future implementations. Cyber vulnerabilities in current BCIs have already been identified, including those that could cause physical harm to the user and influence behavior.  [45] [46] [47] [48]  In a future where BCIs are commonplace alongside advanced understandings of neuroscience, it may be possible for a bad actor to achieve limited influence over the behavior of a population or cause potential harm to users. This issue highlights the need to have robust risk assessment prior to widespread technological adoption, allowing for regulation, governance, and security measures to take identified concerns into account. \n Combined Illustrative Framework Given the rapid developments in AI and biotechnology and the convergence of these 2 areas, existing risk assessment frameworks could be adapted to properly examine emerging threats. Table  3  is an illustrative framework that adapts the original AAAS-FBI-UNICRI framework by removing some elements while adding some from other frameworks to improve its capability to assess converging risks, such as those posed by AI and biotechnology. Convergent risk scenarios from this paper are included as examples of how this framework might be implemented; the completed boxes presented in the table are illustrative only and not meant to be conclusive, as there was no large-scale expert review and consensus. In Table  4 , the adversary spans the same range for each element, which may suggest it is a variable that might not be worth including or at least reconsidered. However, a comprehensive assessment by multidisciplinary experts with multiple scenarios would need to be conducted to determine this. In this framework, rather than using an ordinal scale of only 3 (low, moderate, high) to assess each parameter, an ordinal scale of 5 (very low, low, moderate, high, very high) was used to increase specificity and better delineate between scenarios. Each parameter is meant to be evaluated based on the projected timeline. For instance, in the case of BCIs, it is assumed the parameter will be highly accessible and democratized in the long-term. Governability was included as a component contributing to probability since a technology convergence that is less governable may be more likely to be maliciously used. Democratization, called ''accessibility'' in other frameworks, was included because a technology that is more accessible to a wide range of individuals is assumed to have higher potential for misuse. The remaining evaluation criteria (vulnerabilities, needed skills and expertise, magnitude of potential consequences, and existing countermeasures) were selected because they are common to many of the frameworks reviewed herein and we believe are integral to any risk assessment framework. ''Vulnerabilities'' is meant to describe and illuminate any gaps that could be exploited to cause harm. ''Needed skills and expertise'' is meant to describe the scope of potential adversaries and help identify potential bottlenecks. ''Magnitude of potential consequences'' and ''existing countermeasures'' are meant to contextualize the scope of potential harm and balance that with any mitigating factors in place. As one might expect, this combined framework has many limitations. For example, depending on the type of pathogen designed or synthesized, the high variance changes the amount of expertise needed and potential consequences over time, as does the nature and sophistication of the type of BCI exploitation. The framework also includes uncertainties related to the timeline and assessing governability, which highlights the high degree of assumptions required to complete and use it. Moreover, the framework lacks a standardized mechanism for evaluating factors in a way that calculates risk. The hope is that explicitly identifying ASSESSING ARTIFICIAL INTELLIGENCE AND BIOTECHNOLOGY RISKS these limitations can help illustrate the gaps and challenges in developing a comprehensive framework for converging technologies that may pose high-consequence risks. \n Recommendations \n Risk Assessment Framework Approaches A risk assessment framework is needed that is applicable to converging technologies in the life sciences that balances generality to capture a broad scope but also maintains enough specificity to capture nuances. It is paramount that such frameworks be developed and implemented by a multidisciplinary team of experts that includes both security officials and scientists. Such a strategy allows for a more comprehensive and, subsequently, more accurate depiction of the potential risks. To further increase robustness, existing frameworks should be iteratively built upon and improved, such as the combined framework presented in this paper. A general framework intended to apply to a diverse range of converging or emerging technologies should be developed prior to determining the scenario to be evaluated. It can then be revised as scenarios or technologies are assessed. This would benefit the applicability of such a framework to other scenarios or technologies rather than narrowly limiting it to a specific issue. The role that time plays in calculating risk for an emerging or converging technology should be weighed. While a technology that is assumed to not be relevant until the far future may not pose an immediate risk, it should still be considered, as it could pose a significant threat once the technology materializes. Additionally, projected timelines for emerging technologies are inherently uncertain and technologies may develop more rapidly than expected. Therefore, it is worth considering projected timelines as a framing element rather than a factor to calculate risk. \n Revisiting the AAAS-FBI-UNICRI Framework As 5 years have passed since publication of the initial AAAS-FBI-UNICRI report, we recommend this working group reconvene to reassess the risks outlined in this paper and update their framework to be more inclusive of other converging threats. As noted in their last report, ''if scientists and security experts can assess the risks and benefits together and on a routine basis, the potential risk that biological [big data] would be used by adversaries decreases.'' We believe that this team is best equipped to develop an iterative set of frameworks related to this topic because the workgroup includes knowledgeable experts from a wide range of disciplines and the issues related to big data and AI are similar in nature. With perspectives from experts in law enforcement, the life sciences, and AI, the team is uniquely positioned to take on such a task. While their initial project focused narrowly on big data, it would be of great value to extend that scope to AI in the life sciences and provide relevant stakeholders in academia, government, and the private sector with an informational risk assessment that will help them make informed research, policy, and security decisions on these topics. This working group can leverage frameworks-such as the NASEM and Tucker-Koblentz frameworks-that have been developed since their initial report to improve upon their own. The Koblentz et al  14  paper could provide them with an insightful review of the strengths and weaknesses of many previous frameworks and would be a useful resource as the working group develops the next iteration. Components from the NASEM framework could be leveraged to increase the generality and broadness of their framework. The illustrative framework presented in this paper (Table  4 ) may serve as a useful starting point for the joint team. \n Conclusion AI and biotechnology are both rapidly growing fields. The biosecurity risks arising at their points of convergence are vast, highlighting the need for comprehensive mapping and thorough, robust risk assessment. Current frameworks used for risk assessment in health security settings may fail to capture the nuanced areas of these converging fields and could benefit from considering generality and timeline for technology adoption. We recommend that a multidisciplinary working group comprised of AAAS, the FBI, UNICRI, and other specialists gather to formulate a framework to comprehensively assess risks the results from converging technologies such as AI and biotechnology as well as others that may emerge in the future. The combined framework presented in this paper could serve as a starting point for the development of more robust biosecurity risk assessments for converging technologies like AI and biotechnology. While this new framework does not solve all of the identified challenges, it explicitly elucidates the gaps in our ability to accurately assess risks associated with emerging and converging technologies and will hopefully facilitate adaption of previous frameworks in order to develop a more inclusive health security risk assessment that properly balances generality and specificity and is regularly and iteratively revisited. Table 1 . 1 Main AAAS-FBI-UNICRI Framework Elements to Evaluate the Risks of Big Data 11   Risk Assessment Probability Consequences Adversary Vulnerabilities in Needed scientific expertise and skills Severe consequences Sufficient existing data repositories, software, and/or underlying cyber infrastructure To exploit vulnerabilities in the system To use big data analytics to design harmful biological agents to economics, political system, society, health, environment, and/or agriculture countermeasures \n Table 2 . 2 Main NASEM Framework Elements to Evaluate Level of Concern of Technologies in Synthetic Biology 14   Level of Concern About the Capability Usability of the Technology Usability as a Weapon Requirements of Actors Potential for Mitigation Ease of use Production and delivery Access to expertise Deterrence and prevention capabilities Rate of development Scope of casualty Access to resources Capability to recognize an attack Barriers to use Predictability of results Organizational footprint Attribution capabilities Synergy with other requirements Consequence management capabilities technologies \n Table 3 . 3 Main Tucker Decision Framework Elements to Assess Misuse and Governability 13   Risk of Misuse Governability Accessibility Embodiment Ease of misuse Maturity Magnitude of potential harm Convergence Imminence of potential misuse Rate of advance International diffusion Note: The elements were determined by averaging the values (high, medium, or low) yielded by the parameters. Governability was determined if risk of misuse is medium or high. \n Table 4 . 4 Illustrative Framework Adapted from AAAS-FBI-UNICI, NASEM, and Tucker Frameworks [12] [13] [14] [15]   Convergent Risk Scenarios In Silico Design In Silico Synthesis Brain-Computer of a Pathogen of a Pathogen Interface Exploitation \n\t\t\t Volume 18, Number 3, 2020", "date_published": "n/a", "url": "n/a", "filename": "hs.2019.0122.tei.xml", "abstract": "Rapid developments are currently taking place in the fields of artificial intelligence (AI) and biotechnology, and applications arising from the convergence of these 2 fields are likely to offer immense opportunities that could greatly benefit human health and biosecurity. The combination of AI and biotechnology could potentially lead to breakthroughs in precision medicine, improved biosurveillance, and discovery of novel medical countermeasures as well as facilitate a more effective public health emergency response. However, as is the case with many preceding transformative technologies, new opportunities often present new risks in parallel. Understanding the current and emerging risks at the intersection of AI and biotechnology is crucial for health security specialists and unlikely to be achieved by examining either field in isolation. Uncertainties multiply as technologies merge, showcasing the need to identify robust assessment frameworks that could adequately analyze the risk landscape emerging at the convergence of these 2 domains. This paper explores the criteria needed to assess risks associated with AI and biotechnology and evaluates 3 previously published risk assessment frameworks. After highlighting their strengths and limitations and applying to relevant AI and biotechnology examples, the authors suggest a hybrid framework with recommendations for future approaches to risk assessment for convergent technologies.", "id": "222fb163c8b30250c7db85b7fa993372"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Chenglong Wang", "Rudy Bunel", "Edward Grefenstette", "♣ Deepmind"], "title": "Knowing When to Stop: Evaluation and Verification of Conformity to Output-size Specifications", "text": "Introduction Neural networks with variable output lengths have become ubiquitous in several applications. In particular, recurrent neural networks (RNNs) such as LSTMs  [17] , used work done during an internship at DeepMind | now at Facebook AI Research to form \"sequence\" models  [30] , have been successfully and extensively applied in in image captioning  [34, 28, 21, 6, 12, 37, 26, 24, 1] , video captioning  [33, 38, 35, 40, 41] , machine translation (MT)  [30, 9] , summarization  [10] , and in other sequence-based transduction tasks. The ability of these sequence neural models to generate variable-length outputs is key to their performance on complex prediction tasks. However, this ability also opens a powerful attack for adversaries that try to force the model to produce outputs of specific lengths that, for instance, lead to increased computation or affect the correct operation of down-stream modules. To address this issue, we introduce the output-length modulation problem where given a specification of the form that the model should produce outputs with less than a certain maximum length, we want to find adversarial examples, i.e. search for inputs that lead the model to produce outputs with a larger length and thus show that the model under consideration violates the specification. Different from existing work on targeted or untargeted attacks where the goal is to perturb the input such that the output is another class or sequence in the development dataset (thus within the dataset distribution), the outputmodulation problem requires solving a more challenging task of finding inputs such that the output sequences are outside of the training distribution, which was previously claimed difficult  [5] . The naive approach to the solution of the output-length modulation problem involves a computationally intractable search over a large discrete search space. To overcome this, we develop an easy-to-compute differentiable proxy objective that can be used with gradient-based algorithms to find output-lengthening inputs. Experimental results on Machine Translation show that our adversarial outputlengthening approach can produce outputs that are 50 times longer than the input. However, when evaluated on the image-to-text image captioning model, the method is less successful. There could have been two potential reasons for this result: the image-to-text architecture is truly robust, or the adversarial approach is not powerful enough to find adversarial examples for this model. To resolve this question, we develop a verification method for checking and formally proving whether a network is consistent with the outputsize specification for the given range of inputs. To the best of our knowledge, our verification algorithm is the first formal verification approach to check properties of recurrent models with variable output lengths. Our Contributions To summarize, the key contributions of this paper are as follows: • We propose and formulate the novel output-size modulation problem to study the behaviour of neural architectures capable of producing variable length outputs, and we study its evaluation and verification problems. • For evaluation, we design an efficiently computable differentiable proxy for the expected length of the output sequence. Experiments show that this proxy can be optimized using gradient descent to efficiently find inputs causing the model to produce long outputs. • We demonstrate that popular machine translation models can be forced to produce long outputs that are 50 times longer than the input sequence. The long output sequences help expose modes that the model can get stuck in, such as undesirable loops where they continue to emit a specific token for several steps. • We demonstrate the feasibility of formal verification of recurrent models by proposing the use of mixedinteger programming to formally verify that a certain neural image-captioning model will be consistent with the specification for the given range of inputs. Motivations and Implications Our focus on studying the output-length modulation problem is motivated by the following key considerations: • Achieving Computational Robustness: Many ML models are now offered as a service to customers via the cloud. In this context, ML services employing variable-output models could be vulnerable to denialof-service attacks that cause the ML model to perform wasteful computations by feeding it inputs that induce long outputs. This is particularly relevant for variable compute models, like Seq2Seq  [9, 30] . Given a trained instance of the model, no method is known to check for the consistency of the model with a specification on the number of computation steps. Understanding the vulnerabilities of ML models to such outputlengthening and computation-increasing attacks is important for the safe deployment of ML services. • Understanding and Debugging Models: By designing inputs that cause models to produce long outputs, it is possible to reason about the internal representations learned by the model and isolate where the model exhibits undesirable behavior. For example, we find that an English to German sequence-to-sequence model can produce outputs that end with a long string of question marks ('?'). This indicates that when the output decoder state is conditioned on a sequence of '?'s, it can end up stuck in the same state. • Uncovering security vulnerabilities through adversarial stress-testing: The adversarial approach to outputlength modulation tries to find parts of the space of inputs where the model exhibits improper behavior. Such inputs does not only reveal abnormal output size, but could also uncover other abnormalities like the privacy violations of the kind that were recently revealed by  [4]  where an LSTM was forced to output memorized data. • Canonical specification for testing generalization of variable-output models: Norm-bounded perturbations of images  [31]  have become the standard specification to test attacks and defenses on image classifiers. While the practical relevance of this particular specification can be questioned  [14] , it is still served as a useful canonical model encapsulating the essential difficulty in developing robust image classifiers. We believe stability of output-lengths can serve a similar purpose: as a canonical specification for variable outputlength models. The main difficulties in studying variable output length models in an adversarial sense (the non-differentiability of the objective with respect to inputs) are exposed in output-lengthening attack, making it a fertile testing ground for both evaluating attack methods and defenses. We hope that advances made here will facilitate the study of robustness on variable compute models and other specifications for variableoutput models such as monotonicity. \n Related Work There are several recent studies on generating adversarial perturbations on variable-output models.  [27, 20]  show that question answering and machine comprehension models are sensitive to attacks based on semantics preserving modification or the introduction of unrelated information.  [11, 39]  find that character-level classifiers are highly sensitive to small character manipulations.  [29]  shows that models predicting the correctness of image captions struggle against perturbations consisting of a single word change.  [5]  and  [8]  further study adversarial attacks for sequential-output models (machine-translation, image captioning) with specific target captions or keywords. We focus on sequence output models and analyze the output-length modulation problem, where the models should produce outputs with at least a certain number of output tokens. We study whether a model can be adversarially perturbed to change the size of the output, which is a more challenging task compared to targeted attacks (see details in Section 3). On the one hand, existing targeted attack tasks aim to perturb the input such that the output is another sequence in the validation dataset (thus within the training distribution), but attacking output size requires the model to generate out-of-distribution long sequences. On the other hand, since the desired output sequence is only loosely constrained by the length rather than directly provided by the user, the attack algorithm is required to explore the output size to make the attack possible. For models that cannot be adversarially perturbed, we develop a verification approach to show that it isn't simply a lack of power by the adversary but the sign of true robustness from the model. Similar approaches have been investigated for feedforward networks  [3, 7, 32]  but our work is the first to handle variable output length models and the corresponding decoding mechanisms. \n Modulating Output-size We study neural network models capable of producing outputs of variable length. We start with a canonical abstraction of such models, and later specialize to concrete models used in machine translation and image captioning. We denote by x the input to the network and by X the space of all inputs to the network. We consider a set of inputs of interest S, which can denote, for example, the set of \"small\" 1 perturbations of a nominal input. We study models that produce variable-length outputs sequentially. Let y t 2 Y denote the t-th output of the model, where Y is the output vocabulary of the model. At each timestep, the model defines a probability over the next element P (y t+1 |x, y 0:t ). There exists a special end-of-sequence element eos 2Y that signals termination of the output sequence. In practice, different models adopt different decoding strategies for generating y t+1 from the probability P (y t+1 |x, y 0:t )  [13, 19, 22] . In this paper, we focus on the commonly used deterministic greedy decoding strategy  [13] , where at each time step, the generated token is given by the argmax over the logits: y 0 = argmax {P (•|x)} (1a) y t+1 = argmax {P (•|x, y 0:t )} if y t 6 = eos (1b) Since greedy decoding is deterministic, for a given sample x with a finite length output, we can define the length of the  1  The precise definition of small is specific to the application studied. greedily decoded sequence as: `(x)=t s.t y t = eos y i 6 = eos 8i<t y i+1 = argmax {P (.|x, y 0:i )}8 i<t (2) Note that there is a unique t that satisfies the above conditions, which is precisely the first t at which y t = eos when using greedy decoding. Output length modulation specification A network is said to satisfy the output length modulation specification parameterized by S, K, if for all inputs x in S, the model terminates within K steps under greedy decoding for all x 2S, formally: 8x 2S `(x)  K (3 ) In Section 3.1, we study the problem of finding adversarial examples, i.e., searching for inputs that lead the model to produce outputs with a larger length and thus show that the model violates the specification. In Section 4, we use formal verification method to prove that a model is consistent with the specification for the given range of inputs, if such attacks are indeed impossible. \n The Output-Size Modulation Problem In order to check whether the specification, Eq. (  3 ), is valid, one can consider a falsification approach that tries to find counterexamples proving that Eq. (  3 ) is false. If an exhaustive search over S for such counterexamples fails, the specification is indeed true. However, exhaustive search is computationally intractable; hence, in this section we develop gradient based algorithms that can efficiently find counterexamples (although they may miss them even if they exist). To develop the falsification approach, we study the solution to the following optimization objective: max x2S `(x) (4) where S is the valid perturbation space. If the optimal solution x in the space S has `(x) > K, then (3) is false. The attack spaces S we consider in this paper include both continuous inputs (for image-to-text models) and discrete inputs (for Seq2Seq models). \n Continuous inputs: For continuous inputs, such as image captioning tasks, the input is an n ⇥ m image with pixel values normalized to be in the range  [ 1, 1] . x is an n ⇥ m matrix of real numbers and X =[ 1, 1] n⇥m . We define the perturbation space S(x, ) as follows: S(x, )={x 0 2X |kx 0 xk 1  } i.e., the space of perturbations of the input x in the `1 ball. Discrete inputs: For discrete inputs, e.g., machine translation tasks, inputs are discrete tokens in a language vocabulary. Formally, given the vocabulary V of the input language, the input space X is defined as all sentences composed of tokens in V , i.e., X = {(x 1 ,...,x n ) | x i 2 V, n > 0}. Given an input sequence x =( x 1 ,...,x n ), we define the -perturbation space of a sequence as all sequences of length n with at most d • ne tokens different from x (i.e., 2 [0, 1] denotes the percentage of tokens that an attacker is allowed to modify). Formally, the perturbation space S(x, ) is defined as follows: S(x, δ)={(x 0 1 ,...,x 0 n ) 2 V n | n P i=1 [xi 6 = x 0 i ] dδ • ne} \n Extending Projected Gradient Descent Attacks In the projected gradient descent (PGD) attacks  [25] , 2 given an objective function J(x), the attacker calculates the adversarial example by searching for inputs in the attack space to maximize J(x). In the basic attack algorithm, we perform the following updates at each iteration: x 0 =Π S(x,δ) (x + ↵r x J(x)) ( 5 ) where ↵>0 is the step size and Π S(x,δ) denotes the projection of the attack to the valid space S(x, ). Observe that the adversarial objective in Eq. (  4 ) cannot be directly used as J(x) to update x as the length of the sequence is not a differentiable objective function. This hinders the direct application of PGD to output-lengthening attacks. Furthermore, when the input space S is discrete, gradient descent cannot be directly be used because it is only applicable to continuous input spaces. In the following, we show our extensions of the PGD attack algorithm to handle these challenges. Greedy approach for sequence lengthening We introduce a differentiable proxy of `(x). Given an input x whose decoder output logits are (o 1 ,...,o k ) (i.e., the decoded sequence is y = (argmax(o 1 ),...,argmax(o k ))), instead of directly maximizing the output sequence length, we use a greedy algorithm to find an output sequence whose length is longer than k by minimizing the probability of the model to terminate within k steps. In other words, we minimize the log probability of the model to produce eos at any of the timesteps between 1 to k. Formally, the proxy objective J is defined as follows: J(x)= k P t=1 max ⇢ o t [eos] max z6 =eos o t [z], ✏ where ✏>0 is a hyperparameter to clip the loss. This is piecewise differentiable w.r.t. the inputs x (in the same  2  Here the adversarial objective is stated as maximization, so the algorithm is Projected Gradient Ascent, but we stick with the PGD terminology since it is standard in the literature sense that the ReLU function is differentiable) and can be efficiently optimized using PGD. \n Continuous relaxation for discrete inputs While we can apply the PGD attack with the proxy objective on the model with continuous inputs by setting the projection function Π S(x,δ) as the Euclidean projection, we cannot directly update discrete inputs. To enable a PGDtype attack in the discrete input space, we use the Gumbel trick  [18]  to reparameterize the input space to perform continuous relaxation of the inputs. Given an input sequence x =( x 1 ,...,x n ), for each x i , we construct a distribution ⇡ i 2 R |V | initialized with ⇡ i [x i ]=1and ⇡ i [z]= 1 for all z 2 V \\{x i }. The softmax function applied to ⇡ i is a probability distribution over input tokens at position i with a mode at x i . With this reparameterization, instead of feeding x =( x 1 ,...,x n ) into the model, we feed the Gumbel softmax sampling from the distribution (u 1 ,...,u n ). The sample x =(x 1 ,...,x n ) is calculated as follows: u i ⇠ Uniform(0, 1); g i = log( log(u i )) p = softmax(⇡); xi = softmax( gi+log pi τ ) where ⌧ is the Gumbel-softmax sampling temperature that controls the discreteness of x. With this relaxation, we perform PGD attack on the distribution ⇡ at each iteration. Since ⇡ i is unconstrained, the projection step in (  5 ) is unnecessary. When the final ⇡ 0 =( ⇡ 0 1 ,...,⇡ n ) is obtained from the PGD attack, we draw samples x 0 i ⇠ Categorical(⇡ i ) to get the final adversarial example for the attack. \n Verified Bound on Output Length While heuristics approaches can be useful in finding attacks, they can fail due to the difficulty of optimizing nondifferentiable nonconvex functions. These challenges show up particularly when the perturbation space is small or when the target model is trained with strong bias in the training data towards short output sequences (e.g., the Show-and-Tell model as we will show in Section 6). Thus, we design a formal verification approach for complete reasoning of the output-size modulation problem, i.e., finding provable guarantees that no input within a certain set of interest can result in an output sequence of length above a certain threshold. Our approach relies on counterexample search using intelligent brute-force search methods, taking advantage of powerful modern integer programming solvers  [15] . We encode all the constraints that an adversarial example should satisfy as linear constraints, possibly introducing additional binary variables. Once in the right formalism, these can be fed into an off-the-shelf Mixed Integer Programming (MIP) solver, which provably solves the problem, albeit with a potentially large computational cost. The constraints consist of four parts: (1) the initial restrictions on the model inputs (encoding S(x, )),  (2)  the relations between the different activations of the network (implementing each layer), (3) the decoding strategy (connection between the output logits and the inputs at the next step), and (4) the condition for it being a counterexample (ie. a sequence of length larger than the threshold). In the following, we show how each part of the constraints is encoded into MIP formulas. Our formulation is inspired by pior work on encoding feed-forward neural networks as MIPs  [3, 7, 32] . The image captioning model we use consists of an image embedding model, a feedforward convolutional neural network that computes an embedding of the image, followed by a recurrent network that generates tokens sequentially starting with the initial hidden state set to the image embedding. The image embedding model is simply a sequence of linear or convolutional layers and ReLU activation functions. Linear and convolutional layers are trivially encoded as linear equality constraints between their inputs and outputs, while ReLUs are represented by introducing a binary variable and employing the big-M method  [16] : x i = max (x i , 0) ) i 2{0, 1},x i 0 (6a) x i  u i • i ,x i xi (6b) x i  xi l i • (1 i ) (6c) with l i and u i being lower and upper bounds of xi which can be obtained using interval arithmetic (details in  [3] ). Our novel contribution is to introduce a method to extend the techniques to handle greedy decoding used in recurrent networks. For a model with greedy decoding, the token with the most likely prediction is fed back as input to the next time step. To implement this mechanism as a mixed integer program, we employ a big-M method  [36] : o max = max y2Y (o y ) ) o max o y , y 2{0, 1}8 y 2Y (7a) o max  o y +(u l y )(1 y ) 8y 2Y (7b) X y2Y y =1 (7c) with l y ,u y being a lower/upper bound on the value of o y and u = max y2Y u y (these can again be computed using interval arithmetic). Implementing the maximum in this way gives us both a variable representing the value of the maximum (o max ), as well as a one-hot encoding of the argmax ( y ). If the embedding for each token is given by {emb i | i 2Y}, we can simply encode the input to the following RNN timestep as P y2Y y • emb y , which is a linear function of the variables that we previously constructed. With this mechanism to encode the greedy decoding, we can now unroll the recurrent model for the desired number of timesteps. To search for an input x with output length `(x) K, we unroll the recurrent network for K steps and attempt to prove that at each timestep, eos is not the maximum logit, as in  (2) . We setup the problem as: max min t=1.. K  max z6 =eos o t [z] o t [eos] (8) where o(k) represents the logits in the k-th decoding step. We use an encoding similar to the one of Equation (  7 ) to represent the objective function as a linear objective with added constraints. If the global optimal value of Eq. (  8 ) is positive, this is a valid counterexample: at all timesteps t 2 [1.. K], there is at least one token greater than the eos token, which means that the decoding should continue. On the other hand, if the optimal value is negative, that means that those conditions cannot be satisfied and that it is not possible to generate a sequence of length greater than K. The eos token would necessarily be predicted before. This would imply that our robustness property is True. \n Target Model Mechanism We use image captioning and machine translation models as specific target examples to study the output length modulation problem. We now introduce their mechanism. \n Image captioning models The image captioning model we consider is an encoder-decoder model composed of two modules: a convolution neural network (CNN) as an encoder for image feature extraction and a recurrent neural network (RNN) as a decoder for caption generation  [34] . Formally, the input to the model x is an m ⇥ n sized image from the space X =[ 1, 1] m⇥n , the CNN-RNN model computes the output sequence as follows: i 0 = CNN(x); h 0 = 0 o t ,h t+1 = RNNCell(i t ,h t ) y t = arg max(o t ); i t+1 = emb(y t ) where emb denotes the embedding function. The captioning model first run the input image x through a CNN to obtain the image embedding and feed it to the RNN as the initial input i 0 along with the initial state h 0 . At each decode step, the RNN uses the input i t and state h t to compute the new state h t+1 as well as the logits o t representing the log-probability of the output token distribution in the vocabulary. The output y t is the token in the vocabulary with highest probability based on o t , and it is embedded into the continuous space using an embedding matrix W emb as W emb [y t ]. The embedding is fed to the next RNN cell as the input for the next decoding step. \n Machine translation models The machine translation model is an encoder-decoder model  [30, 9]  with both the encoder and the decoder being RNNs. Given the vocabulary V in of the input language, the valid input space X is defined as all sentences composed of tokens in V in , i.e., X = {(x 1 ,...,x n ) | x i 2 V, n > 0}. Given an input sequence x =( x 1 ,...,x n ), the model first calculates its embedding f (x) RNN as follows (h e t and i e t denote the encoder hidden states and the inputs at the t-th time step, respectively. emb e denotes the embedding function for each token in the vocabulary). The model then uses f (x) as the initial state h 0 for the decoder RNN to generate the output sequence, following the same approach as in the image captioning model. h e 0 = 0; i e t = emb e (x t ) h e t = RNNCell e (i e t ,h e t 1 ); f (x)=h e n \n Experiments We consider the following three models, namely, Multi-MNIST captioning, Show-and-Tell  [34] , and Neural Machine Translation (NMT) [30, 9, 2] models. \n Details of models and datasets Multi-MNIST. The first model we evaluate is a minimal image captioning model for Multi-MNIST dataset. The Multi-MNIST dataset is composed from the MNIST dataset (Figure  1 left ). Each image in the dataset is composed from 1-3 MNIST images: each MNIST image (28 * 28) is placed on the canvas of size (28 * 112) with random bias on the x-axis. The composition process guarantees that every MNIST image is fully contained in the canvas without overlaps with other images. The label of each image is the list of MNIST digits appearing in the canvas, ordered by their x-axis values. The dataset contains 50,000 training images and 10,000 test images, where the training set is constructed from MNIST training set and the test set is constructed from MNIST test set. The images are normalized to [ 1, 1] before feeding to the captioning model. For this dataset, we train a CNN-RNN model for label prediction. The model encoder is a 4-layers CNN (2 convolution layers and 2 fully connected layers with ReLU activation functions applied in between). The decoder is a RNN with ReLU activation. Both the embedding size and the hidden size are set to 32. We train the model for 300 steps with Adam optimizer based on the cross-entropy loss. The model achieves 91.2% test accuracy, and all predictions made by the model on the training set have lengths no more than 3. Show-and-Tell. Show and Tell model  [34]  is an image captioning model with CNN-RNN encoder-decoder architecture similar to the Multi-MNIST model trained on the MSCOCO 2014 dataset  [23] . Show-and-Tell model uses Inception-v3 as the CNN encoder and an LSTM for caption generation. We use a public version of the pretrained model 3 for evaluation. All images are normalized to  [ 1, 1]  3 https://github.com/tensorflow/models/ and all captions in the dataset are within length 20. NMT. The machine translation model we study is a Seq2Seq model  [30, 9]  with the attention mechanism  [2]  trained on the WMT15 German-English dataset. The model uses byte pair segmentation (BPE) subword units  [28]  as vocabulary. The input vocabulary size is 36, 548. The model consists of 4-layer LSTMs of 1024 units with a bidirectional encoder, with the embedding dimension set to 1024. We use a publicly available checkpoint 4 with 27.6 BLEU score on the WMT15 test datasets in our evaluation. At training time, the model restricts the maximum decoding length to 50. \n Adversarial Attacks Our first experiment studies whether adversarial inputs exist for the above models and how they affect model decoding. For each model, we randomly select 100 inputs from the development dataset as attack targets, and compare the output length distributions from random perturbation and PGD attacks. Multi-MNIST We evaluate the distribution of output lengths of images with an `1 perturbation radius of 2{ 0.001, 0.005, 0.01, 0.05, 0.1, 0.5} using both random search and PGD attack. In random search, we generate 10,000 random images within the given perturbation radius for each image in the target dataset as new inputs to the model. In PGD attack, the adversarial inputs are obtained by running 10,000 gradient descent steps with an learning rate of 0.0005 using the Adam Optimizer. Neither of the attack methods can find any adversarial inputs for 2{0.001, 0.005, 0.01} perturbation radius (i.e., no perturbation is found for any images in the target dataset within the above to generate an output sequence longer than the original one). Figure  2  shows the distribution of the output lengths for images with different perturbation radius. Results show that the PGD attack is successful at finding attacks that push the distribution of output lengths higher, particularly at larger values of . Examples of adversarial inputs found by the model are shown in Figure  1 . \n Show-and-Tell For the Show-and-Tell model, we generate attacks within an `1 perturbation radius of =0.5 with both random search and PGD attack on 500 images randomly selected from the development dataset. However, except one adversarial input found by PGD attack that would cause the model to produce an output with size 25, no other adversarial inputs are found that can cause the model to produce outputs longer than 20 words, which is the training length cap. Our analysis shows that the difficulty of attacking the model is resulted from its strong bias on the output  sequence distribution and the saturation of sigmoid gates in the LSTM decoder. This result is also consistent with the result found by  [5]  that Show-and-Tell model is \"only able to generate relevant captions learned from the training distribution\". NMT We evaluate the NMT model by comparing the output length distribution from adversarial examples generated from random search and PGD attack algorithms. We randomly draw 100 input sentences from the development dataset. The maximum input length is 78 and their corresponding translations made by the model are all within 75 tokens. We consider the perturbation 2{0.3, 0.5, 1.0}. 1. Random Search. In each run of the random attack, given an input sequence with length n, we first randomly select d • ne locations to modify, then randomly select substitutions of the tokens at these locations from the input vocabulary, and finally run the NMT model on the modified sequence. We run 10,000 random search steps for the 100 selected inputs, and show the distributions of all outputs obtained from the translation (in the total 1M output sequences). 2. PGD Attack. In PGD attack, we also start by randomly selecting d • ne locations to modify for each input sequence with length n. We then run 800 iterations of PGD attack with Adam optimizer using an initial learning rate of 0.005 to find substitutions of the tokens at these selected locations. We plot the output length obtained from running these adversarial inputs through the translation model. Figure  3  shows the distribution of output sequence lengths obtained from random search methods with different . We aggregate all sequences with length longer than 100 into the group '>100' in the plot. Results show that even random search approach could often craft inputs such that the corresponding output lengths are more than 75 and occasionally generates sentences with output length over 100. The random search algorithm finds 79, 11, 3 for =0.3, 0.5, 1, respectively, among the 1M translations that are longer than 100 tokens (at small , the search space is more restricted, and random search has a higher success rate of finding long outputs). Notably, the longest sequence found by the random search is a sequence with output length 312 tokens, where the original sequence is only 6.     to larger perturbations. With an unconstrained perturbation = 100%, PGD attack algorithm discovers more adversarial inputs whose outputs are longer than 100 tokens (10% among all attacks), which is 1000⇥ more often than random search. As an extreme case, PGD attack discovered an adversarial input with length 3 whose output length is 575. Examples of adversarial inputs and their corresponding model outputs are shown in Figure  5  and the Appendix; we find out that a common feature of the long outputs produced by the translation model is that the output sequences often end with long repetitions of one (or a few) words. \n names name names name names grammatically name names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names names eos To analyze the bottleneck of PGD attack on the NMT model, we further run a variation of the PGD attack where the attack space is the (continuous) word embedding space as opposed to the (discrete) token space: we allow the attacker to directly modify token embeddings at selected attack locations to any other vector. PGD attack on this variation achieves a 100% success rate to find adversarial token embeddings such that the model outputs are longer than 500 tokens. This indicates that the discrete space is a bottleneck for consistently finding stronger attacks. \n Verification Our implementation of the verification algorithm using the mixed integer programming (8) is implemented using SCIP  [15] . We run our verification algorithm on the Multi-Figure  6 . Proportion of samples being provably robust (in blue), vulnerable (in red) or of unknown robustness status (in gray) to an attack attempting to make the model generate an output sequence longer than the ground truth, as a function of the perturbation radius allowed to the attacker. For small radiuses, the MIP can prove that no attacks can be successful. For large radiuses, we are able to find successful attacks. MNIST dataset, attempting to formally prove the robustness of the model to attacks attempting to generate an output longer than the ground truth. For each input image, we set a timeout of 30 minutes for the solver. The results in Figure  6  show that our verification algorithm is able to verify formally that no attacks exists for small perturbation radiuses. However, as the perturbation radius increases, our verification algorithm times out and is not able to explore the full space of valid perturbations and thus cannot decide whether attacks exists in the given space. For this reason, the number of robust samples we report is only a lower bound on the actual number of robust samples. Conversely, the vulnerable samples that we exhibit give us an upper bound on the number of those robust samples. As shown by the large proportion of samples of unknown status, there is currently still a gap between the capabilities of formal verification method and attacks. \n Conclusion In this paper, we introduce the existence and the construction of the output-length modulation problem. We propose a differentiable proxy that can be used with PGD to efficiently find output-lengthening inputs. We also develop a verification approach to formally prove certain models cannot produce outputs greater than a certain length. We show that the proposed algorithm can produce adversarial examples that are 50 times longer than the input for machine translation models, and the image-captioning model can conform the output size is less than certain maximum length using the verification approach. In future work, we plan to study adversarial training of sequential output models using the generated attacks, to models that are robust against output lengthening attacks, and further, verify this formally. Figure 1 . 1 Figure 1. Multi-MNIST examples (left), adversarial examples found by PGD attack (mid), and their differences. For the first group, the model correctly predicts label l1 =[6, 1] on the original image but predicts l 0 1 =[6, 1, 1] for its corresponding adversarial input. Predictions on the original/adversarial inputs made by model for the second group are l2 =[0, 7, 4],l 0 2 =[0, 1, 4, 3], and l3 =[3],l 0 3 =[3, 3, 5, 3] for the third group. The adversarial inputs in the first/second/third groups are found within the perturbation radius δ1 =0 .1,δ2 =0 .25,δ3 = 0.25. \n Figure 2 . 2 Figure2. The distribution of output length for random search (denoted as Rand) and PGD attack with different perturbation radius δ. The x-axis denotes the output length and y-axis denotes the number of outputs with the corresponding length. δ =0(no perturbation allowed) refers to the original output distribution of the target dataset. \n Figure 3 . 3 Figure 3. The histogram representing the output length distribution of the NMT model using random search with different perturbations (δ 2{ 0.3, 0.5, 1}). The x-axis shows the output length. y-axis values are divided by 10,000, the number of random perturbation rounds per image. \n Figure 4 4 Figure4shows the result from attacking the NMT model with PGD attack. Results show that PGD attack has relatively low success rate at lower perturbations compared \n Figure 4 . 4 Figure 4. The histogram representing the output length distribution of the NMT model under PGD attack for different δ. x-axis shows the output length and y-axis shows the number of instances with the corresponding length. \n ( I) Die Waffe wird ausgestellt und durch den Zaun übergeben. (O) The weapon is issued and handed over by the fence . eos (I 0 ) Die namen name descri und ames utt origin i.e. meet grammatisch . (O 0 ) \n Figure 5 . 5 Figure 5. An example of German to English translation where I,O refer to an original sequence in the dataset and the corresponding translation made by the model. I 0 ,O 0 refer to an adversarial example found by PGD attack and the corresponding model translation. \n\t\t\t https://github.com/tensorflow/nmt", "date_published": "n/a", "url": "n/a", "filename": "Wang_Knowing_When_to_Stop_Evaluation_and_Verification_of_Conformity_to_CVPR_2019_paper.tei.xml", "abstract": "Models such as Sequence-to-Sequence and Image-to-Sequence are widely used in real world applications. While the ability of these neural architectures to produce variablelength outputs makes them extremely effective for problems like Machine Translation and Image Captioning, it also leaves them vulnerable to failures of the form where the model produces outputs of undesirable length. This behaviour can have severe consequences such as usage of increased computation and induce faults in downstream modules that expect outputs of a certain length. Motivated by the need to have a better understanding of the failures of these models, this paper proposes and studies the novel output-size modulation problem and makes two key technical contributions. First, to evaluate model robustness, we develop an easy-to-compute differentiable proxy objective that can be used with gradient-based algorithms to find output-lengthening inputs. Second and more importantly, we develop a verification approach that can formally verify whether a network always produces outputs within a certain length. Experimental results on Machine Translation and Image Captioning show that our output-lengthening approach can produce outputs that are 50 times longer than the input, while our verification approach can, given a model and input domain, prove that the output length is below a certain size.", "id": "06efc095478e22c85a0de61ec3fcc610"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["David J Jilk"], "title": "Conceptual-Linguistic Superintelligence", "text": "Introduction Recently much analysis and speculation has been offered to describe scenarios related to a possible intelligence explosion, a notion first suggested by I.J. Good  [1] . In an intelligence explosion, initial creation of artificial intelligence with a critical mass of capabilities and drives is followed by an inexorable process of increases in that intelligence. Eventually the resultant artificial intelligence exceeds human intelligence and is referred to as superintelligence. This process is usually viewed as uncontrolled, unstoppable, and accelerating; the scenarios have generated considerable consternation and are driving a conversation about a number of ethical and technological issues  [2]  [3]  [4] . In this paper, we argue that artificial intelligence capable of sustaining an uncontrolled intelligence explosion must have a conceptual-linguistic faculty with substantial functional similarity to the human faculty. We follow this with arguments for three subsidiary claims: first, that detecting the presence of such a faculty will be an important indicator of imminent superintelligence; second, that such a superintelligence will, in creating further increases in intelligence, both face and consider the same sorts of existential risks that humans face today; third, that such a superintelligence is likely to assess and question its own values, purposes, and drives. These conclusions do not guarantee a satisfactory outcome for humans, but do suggest that the process will be subject to ongoing scrutiny by its own participants. We note that it is possible that superintelligence may be created outside the context of an intelligence explosion; for example, humans might create it directly. Our arguments are not intended to apply in that case: we do not argue that a conceptual-linguistic faculty is required to constitute superintelligence (though this may be true), only that it is required in an intelligence explosion. Also, there are many risks of artificial intelligence aside from superintelligence and intelligence explosions, such as those arising from autonomous weapons and unexplainable decision processes. We do not address those issues at all. Nevertheless, the existential risks associated with an intelligence explosion are an important topic in artificial intelligence safety  [5]  and we will hopefully deepen our understanding of those scenarios through this analysis. \n The need for a conceptuallinguistic faculty In this major section we begin by outlining implied necessary conditions for an intelligence explosion, and characterize in some detail what we mean by a conceptual-linguistic faculty. With that in place, we argue the foundational claim that a conceptual-linguistic faculty is necessary for an intelligence explosion to be sustained. We close the section by showing how the presence of a conceptual-linguistic faculty is a harbinger of superintelligence, and discuss how it might be detected. \n Requirements for an uncontrolled intelligence explosion As it is typically envisioned, an intelligence explosion comprises a sequence or continuum of artificial intelligence systems with progressively increasing intelligence. We will refer to each of these systems as a \"participant.\" Since a participant is part of a sequence, it has predecessors and successors in the process, with humans as the initial predecessor. In progressing the sequence, a participant may elect to self-improve or to create a new system; in either case we refer to the resulting system as a successor. \n D.J. Jilk There are many factors to consider in assessing whether an intelligence explosion is likely to occur and how rapidly it might proceed  [3]    [6] . In this paper, we intend to focus on the role of the participants, and generally assume that extrinsic factors (for example, technical or resource recalcitrance) are favorable for supporting an intelligence explosion. Our emphasis will be qualitative and directional rather than quantitative. For an uncontrolled intelligence explosion to occur, the progress of intelligence increases must be selfsustaining and resistant to premature termination. Though it is an analogy only, these requirements are similar to those of a nuclear fission weapon  [4] . Two of the most difficult challenges faced by the initial designers of such weapons were to have a sufficient fraction of emitted neutrons be absorbed by fissile nuclei (self-sustaining), and for the chain reaction to proceed sufficiently before its own energy caused dispersion of the fissile material (premature termination)  [7] . Corresponding requirements in an intelligence explosion are that each participant artificial intelligence has, as necessary but not sufficient conditions, these properties: 1. Self-sustaining: the participant must aim to and be capable of designing and building either selfmodifications or new systems that have greater intelligence, without assistance from humans; 2. Resistant to premature termination: the participant must be capable of preventing other agencies, such as humans or later predecessors, from interrupting the development of selfmodifications or new systems with greater intelligence. An uncontrolled chain reaction is only worrisome if it produces side-effects. In the case of nuclear fission, each fission releases energy that contributes to the explosion. In the case of an intelligence explosion, the side-effects arise from the goals or purposes of the artificial intelligence. These purposes are potentially problematic for humans whether or not humans attempt to stand in the way. \n What is a conceptual-linguistic faculty? Humans evidently have the ability to organize their experiences into concepts, and to use language to access those concepts and thereby refer to aspects of those experiences. We will use the term \"conceptual-linguistic faculty\" to refer to this capability, whether possessed by a human or an artificial intelligence. There are numerous theories and considerable empirical insight about the mechanisms involved in concept formation and use, though we still do not fully understand them. However, for our purposes it is only necessary to gain some purchase on the kinds of functions it performs, particularly since the implementation in an artificial intelligence may be very different. The centerpiece of the conceptual-linguistic faculty is the way it combines information representations that are treated discretely or symbolically with information representations that are graded, statistical, and overlapping  [8]    [9] . The former we will call \"words\" and the latter we will call \"semantic contents.\" Semantic contents develop through perceptual-motor experience, and are activated by perceptual stimuli that are sufficiently \"similar\"  [10] . \"Activated\" means that the representations temporarily obtain some sort of facilitated access and priority of influence in current cognitive processing; activation is graded rather than binary  [11] . What constitutes sufficient similarity is embedded in the semantic contents themselves and can be extremely complex and multi-dimensional. Some semantic contents are bi-directionally attached to a word, and we will call such a pair a concept. The nature of this attachment is that when the semantic contents are activated by a stimulus, the word is also activated; and when a word is activated through memory or communication, even in the absence of applicable stimuli, the semantic contents are also activated  [12] . However, this description suggests a crisp boundary, and it is nothing of the sort. The semantic contents activated by a stimulus depends on detailed features of the stimulus and the context; the word activated by the semantic contents depends on the context  [8]    [13] , which may include attention. Further, the activation of semantic contents often causes the activation of multiple words at varying strengths  [14] . Words also activate each other, and semantic contents can activate other semantic contents  [14] . Semantic contents, which we have already mentioned do not have sharp boundaries, can be activated simultaneously, partially, and in many combinations, and simultaneous activations result in cross influences, sometimes called \"dynamic realization.\" Crucially, we can use words and semantic contents to cognitively simulate the world and explore what the consequences of various actions or circumstances might be  [13] . But we can also manipulate words as symbolic entities and process logical thoughts with minimal activation of the semantic contents, essentially treating the words themselves as objects  [8]    [15] . Despite this highly complex, graded, and overlapping network of relationships, the informational representations offered by concepts have sufficient structure and distinctness to enable humans to create models of the world, make successful predictions, design and build sophisticated tools, share experiences, and the like. Our description here relies on results in cognitive psychology and neuroscience; readers may note that our citations include some opposing theorists who nevertheless mostly agree that human cognition exhibits these basic features. Again, we do not know all the details of implementation of this capability in humans. What we do know is that other animals do not have it in sufficient quantity to build technological civilizations, and to date, no artificial intelligence has it. An illustrative example may be helpful toward understanding what is meant by a conceptual-linguistic faculty; however, the account above and its associated references, and not this example, are the foundation of the arguments to follow. Suppose one is walking alongside a downtown street and perceives a building. The effects of this perception rely on having been previously exposed to many buildings that vary along many nonspecific dimensions, as well as many other objects that are not buildings. It triggers a passive, partial activation of the word \"building\" but more strongly the word \"bank,\" of which this building happens to be an instance. The word \"bank\" has a statistical connection to the word \"mortgage\" and the word \"money,\" which might now activate a visual representation of a mortgage statement or a stack of dollar bills; or it may activate one's representations of money in general and its social and legal role, which may further activate the word \"bitcoin.\" Or the perception of the building may activate an olfactory representation of the inside of an old, marble bank lobby which further triggers representations of buildings in which sound echoes, which then activates the word \"echo.\" One might then entertain a relatively abstract linguistic thought such as \"I will not be able to pay my mortgage without putting more money into my account,\" or visually simulate logging in to the bank's web site to effect the transfer. The likelihood of each of these derivative activations depends on current context and goals, among other things. Note the bidirectional interplay of the symbolic-linguistic representations with the perceptual-semantic representations, as well as interactions directly among percepts and directly between words; also note the graded, statistical character of all these interactions. There may be many ways to implement a conceptual-linguistic faculty in artificial intelligence. Though a \"neuromorphic\" approach is an appealing candidate, since it has a reference implementation, it is not known to be a requirement. The key is that semantic contents of the sort we have described refer to the real world richly and bi-directionally, and ground the conceptual structure to reality. Deep learning methods  [16]  illustrate the power and importance of rich grounding. In the past decade, these methods have demonstrated impressive success in classification, including both auditory and visual perception as well as more abstract patterns. The methods are mechanistically homologous to human semantic processing in several ways, ranging from learning rules to the hierarchical network structure and receptive field overlap at each layer. The statistical, graded, and overlapping representations afforded by such methods seem to be essential to their success. Still, though they may (or may not) represent a step toward successful general artificial intelligence, to date they lack important capabilities of a conceptual-linguistic faculty. Their \"symbolic\" representations (which might be likened to words) are impoverished and do not mutually interact, and they are not bidirectional while in operation. Most past attempts to implement language and concepts in artificial intelligence are manifestly insufficient to produce a conceptual-linguistic faculty with the features we have described. In particular, historical efforts have often been purely symbolic in their representation of semantic contents. Systems like Cyc  [17]  or Prolog struggle to emulate human-like reasoning because they are entirely ungroundedwords or symbols interconnect with each other but have no means of referring to the world  [18] [19] . Attempts to ground such systems via hardcoded algorithms to identify standard human conceptual classes (e.g., face and object detectors) provide limited grounding but entirely miss the complex overlap and subtlety of the real world  [20] , and are in any case feedforward and incapable of dynamic realization. Consequently, while some limited linguistic stimulus/response capabilities can be derived in these systems, they cannot really use the human concepts to do anything in the world, except in tightly constrained environments or simulations where the abstractions on which they rely can be simulated perfectly. Whether or not such approaches can be made to perform useful functions, they do not understand the meaning of human words and concepts in a way that enables them to perform flexible cognition with them. The deep reasons for these difficulties have been explained philosophically  [21]  [22]  [23] , and empirically  [24] . Committed scientific realists are unlikely to be convinced by such arguments, for the same reason that they were surprised by Moravec's Paradox, and continue to struggle with the \"frame problem\"  [25]    [26] . They hold that the world consists of objects that intrinsically belong to metaphysically distinct categories, thus all that is necessary for grounding is to find ways to identify those categories reliably. In contrast, our characterization of a conceptual-linguistic faculty relies on a view that it is cognition that constructs and ascribes categories. While the applicable terms refer to genuine clusters of features in the world, their categories are not the only way to partition experience, and they overlap in complex ways. The impressive success of deep learning has convinced many researchers of a need for sophisticated grounding, but there are holdouts. A thorough argument against scientific realism is beyond the scope of this paper. \n A conceptual-linguistic faculty is necessary for an intelligence explosion We now proceed to the foundational claim: artificial intelligence capable of sustaining an uncontrolled intelligence explosion must have, at a minimum, a conceptual-linguistic faculty with substantial functional similarity to that of humans. We will argue this in two parts, corresponding to the two general requirements for an intelligence explosion. Importantly, this claim only asserts a minimum. We are not claiming that this faculty must be the only, or even the most effective or important, cognitive mechanism of a participant artificial intelligence. A participant may have many other capabilities which may be better at other things. For the intelligence explosion to be self-sustaining, the participant artificial intelligence must be able to produce self-improvements or improved successors without human assistance. If it requires human assistance, then humans could withhold that assistance to terminate the process prematurely. If it is not capable of D.J. Jilk grasping and using human language and concepts, including their underlying rich semantic contents, then the vast body of human knowledge is not at its disposal. Outside of human minds, the human body of knowledge is encapsulated primarily in words, diagrams, and functional artifacts (e.g., tools and machines). Words and diagrams rely on concepts; earlier, in discussing ungrounded and feedforward-only semantic representations, we elaborated why these cannot be used effectively without a conceptual-linguistic faculty. The purpose, means of use, and implementation of functional artifacts is severely underdetermined. Learning how and when to use such artifacts would require demonstration by humans or comprehension of instruction manuals. Understanding how they are built would require reverse engineering, which would be extremely difficult without a conceptual apparatus that could reproduce the conceptual model used for the original design  [27] . We might wonder whether some sort of cognitive shortcut could be devised so that the conceptual knowledge embodied in language is translated into another form. A simple thought experiment illustrates why it cannot. Suppose that an artificial intelligence accesses all the equations of known physics and a thorough explanation of them. The speed of light figures prominently in these equations. What is light? We can provide experiential examples: the sun, lightning, fire, reflections. But these experiences need to be abstracted so that more than just the immediate examples provided can be used. The tools humans use to produce and detect light and measure its speed must be represented. The parts and components of those tools and their interrelationships must be identifiable in the face of noise and complex variation. To use such a tool requires visualization or simulation of its function. The explanation, written in human language, will use words intended to activate semantic contents and thereby (in a contextually appropriate way) activate other words and contents that enable comprehension. All of its words must refer in some way to entities in the real world, and identifying these entities requires a means of perception that is variation tolerant in a high number of dimensions. The existing literature varies tremendously in its precision and consistency; there is even a considerable body of poetry that invokes light, and these sources must be somehow interpreted and distinguished. Ignoring all these details and \"hardcoding\" the speed of light requires a brittle and limited pre-programming, and merely defers the difficulty to other, equally complex notions that regress indefinitely. We can see that all of the attributes of the conceptual-linguistic faculty, as described earlier, are required to unpack the reference to the speed of light in our human equations and explanations and make use of it in novel ways in the real world. This is not a failure of imaginationit speaks to the essence of how human knowledge is constituted, and therefore how it must be understood. In the development of technology, it is a distinct advantage merely to know that something is possible and can be made to work. Artificial intelligence that lacks a conceptual-linguistic faculty will not even be able to observe humans and their tools to gain that knowledge. Without grounded concepts that enable comprehension of either human words or even conceptually-structured observation of human activity, such a system will have no shortcuts to grasping what is technologically possible. Importantly, we are not making the much stronger claim that an artificial intelligence must have a conceptual-linguistic faculty to understand and operate in the world. We are only claiming that such a faculty is necessary to understand and make use of the human body of knowledge. Nevertheless, this leads to a possibly startling conclusion: an artificial intelligence lacking a conceptual-linguistic faculty, even if it otherwise has sufficient cognitive raw material of some other kind, would need to reproduce a substantial fraction of human knowledge from scratch before it can create its own successors. Creating faster and better computing hardware, from today's starting point, requires deep theoretical knowledge of quantum mechanics and substantial practical experience with advanced materials and manufacturing processes. Creating software that interacts with the world requires effective representations of that world; thus, improving such software or building new approaches from scratch requires understanding the physical world. Without a conceptual-linguistic faculty, artificial intelligence would need to develop its grasp of the world through empirical observation that is not guided by human experience, since it would not have the means to understand what it was aiming for. We might wonder whether an artificial intelligence and its successors would be able to indefinitely increase intelligence entirely through software changes, operating in a purely computational environment. In that case it would not be necessary to learn about the external world and its properties. However, such a system would not produce a worrisome intelligence explosion because it would have no side effects in the world. It also could not endeavor, on its own, to expand its computational resources beyond what humans have already given it. If we expand this model by giving such a system access to the Internet, it could (in the most extreme case, and making the extravagant assumption that it could make sense of the human-built, conceptually complex, and ubiquitously abstraction-breaking Internet without a conceptual-linguistic faculty) expand its computational capacity to whatever is available there, and produce incidentally devastating but not existentially threatening side effects. In this case the side effects of the intelligence explosion would stop there without the further cooperation or manipulation of humans. Below we will see that without a conceptual-linguistic faculty, an artificial intelligence would not be able to prevent humans from stopping an intelligence explosion, much less manipulate them into extending it. We conclude that such a computational-only approach would be constrained and would not produce a self-sustaining intelligence explosion. We note that humans required about 100,000 years, once they had the requisite cognitive capabilities, to reach the cusp of building artificial intelligence. An artificial intelligence will surely develop this knowledge more rapidly, assuming it is built with a direct motivation to gain knowledge. Accelerated and self-generated learning methods for narrow or fully symbolic domains have recently shown great promise  [28] . Yet to learn about the physical world, it must still learn about the motion of objects, figure out how to make tools for manipulation and measurement, develop methods to find, mine, and refine minerals to make reliable materials, before (and obviously we skip many steps here) eventually developing advanced materials and devices such as semiconductors and transistors. It will not know in advance that these are the things it needs to do, so progress will involve trial and error. Even if humans were to provide an artificial intelligence with training exemplars or simulated worlds where such learning could be performed more rapidly, those experiences would be necessarily simplified relative to reality and would not be able to capture its full complexity. It would be \"doomed to succeed\" in the simulated world, and would exhibit poor transference back in the noisy real world  [29] . For artificial intelligence that lacks a conceptuallinguistic faculty, the details of its empirical path to the necessary scope of knowledge are likely to be different than those of the path humanity took. We cannot entirely rule out that there might be some prodigious shortcut available in the structure of reality and effective forms of knowledge, given just the right intelligence architecture. There is, of course, no empirical evidence for such a shortcut, and it requires both a speculative assumption about reality and an assertion of extraordinary luck in the system's design. Still, in this one case a conceptuallinguistic faculty might not be necessary to build successors relatively quickly. However, such a system would also be unusually vulnerable to premature termination. By construction, it bypassed acquisition of much of the knowledge about the world that humans have. Humans could exploit this gap to terminate the intelligence explosion, as will be discussed below. Aside from that scenario, an artificial intelligence starting from scratch in its knowledge of the world is in no position to build improved intelligence that can act in the world; it would not even be able to build a copy of itself. Without a conceptual-linguistic faculty, it is not, prior to a lengthy period of empirical research and intellectual development, capable of sustaining an intelligence explosion. Though one could argue that this is better described as a \"slow-takeoff\" intelligence explosion  [3] , we have illustrated and argued why this period would be considerably longer than what is typically meant by a slow takeoff. For a participant artificial intelligence to resist premature termination of the intelligence explosion, it must be able to consider the various ways that human beings might try to stop it. It must understand human motivations and strategic or tactical ideas, and it must be able to predict human behavior as individuals and in aggregate, at least as effectively as other humans do. To know how it might be attacked, it must understand how humans would model its vulnerabilities, and how they might exploit features of the physical world. It cannot accomplish these things without a conceptual-linguistic faculty, since these issues are all governed in part by human concepts and human conceptual knowledge, and without comparable concepts its model will be deeply flawed. Human strategic and tactical ideas are all based on conceptual thinking and they are graded and overlapping, thus cannot be characterized at the level of purely symbolic mechanisms, nor by simple statistics of simple behavior signatures. Further, purely symbolic or statistical representations developed through trial-anderror observation can easily be misguided by intentionally deceitful human strategies (the Allies' subtle handling of having broken the Enigma code in World War II comes to mind). Humans are masters of the \"hack\"if we know that the representations of an artificial intelligence are too rigid or simplistic, we will find ways to exploit that fact. In sum, without a conceptual-linguistic faculty that has substantial functional similarity to the human faculty, an artificial intelligence will not be able to utilize human knowledge to build self-improvements or successors, nor to resist human interference. Such a system would not be capable of sustaining an uncontrolled intelligence explosion. Our claim is qualified with \"substantial functional similarity.\" There is necessarily some vagueness in this qualification. Still, in our description of a conceptuallinguistic faculty, we circumscribed the range, indicating on one end that it need not be neuromorphic, and on the other that purely symbolic systems or those grounded with simple feedforward mechanisms are insufficient. We described a number of specific capabilities, which are elaborated in great detail in the literature, that such a system must exhibit to meet the requirement, such as dynamic realization, representational overlap, simulation, and graded contextual interactions. Thus, while the description is incomplete, it is not at all a black box. We have not claimed that a conceptual-linguistic faculty is the only or even the primary means by which a participant artificial intelligence performs cognitive tasks. It is entirely possible that this faculty would treated as a mere instrumental module, consulted as needed to sustain the intelligence explosion, but using other modes of cognition as primary. Still, because of its importance to both creation of successors and defense against premature termination, the conceptual-linguistic faculty will need to be consistently active and providing input to the larger system. The form of cognition offered by the conceptual-linguistic faculty would thus be present, not just accessible, at all times, even if the overall system ultimately ignores its results in a particular circumstance. \n A conceptual-linguistic faculty as a harbinger of superintelligence We have claimed that artificial intelligence with a conceptual-linguistic faculty is a necessary condition for an intelligence explosion. It is by no means a sufficient condition. The artificial intelligence would also need some sort of drive to create improvements or successors. It might need other capacities, such as the ability to D.J. Jilk manipulate physical objects (whether directly or indirectly), even if such capacities are straightforward to achieve. Nevertheless, the implementation of a conceptual-linguistic faculty in artificial intelligence seems to be a great challenge that calls for one or more scientific breakthroughs. Its achievement is one important step along the way to an intelligence explosion.  [30] . Superintelligence is an intelligent system that is distinctly superior to humans in some cognitive domain or set of domains. Such systems already exist for a few narrow but challenging domains, such as the game of Go  [31]  and constrained visual object recognition problems  [32] . However, the term is often used to mean artificial intelligence that has surpassed our ability to control it and therefore presents existential risk. An artificial intelligence that can sustain an intelligence explosion probably cannot be controlledits ability to resist premature termination of the explosion could be applied to any of its activities. Consequently we can reasonably describe an artificial intelligence that is capable of sustaining an intelligence explosion as a superintelligence, and will do so throughout the remainder of the paper. We conclude that progress in the development of a conceptual-linguistic faculty in artificial intelligence is a harbinger of superintelligence. This claim has important implications for safety It suggests that we might have some warning when an uncontrolled intelligence explosion is imminent. Importantly, until the conceptual-linguistic faculty is fully developed, it is unlikely that the system can thoroughly prevent human interference in its own operation. Thus we may have a window in which we can stop the intelligence explosion after it is more clearly about to occur. One possibility for such a window is that the development of the conceptuallinguistic faculty itself is progressive and incremental. This seems likely from the progress of artificial intelligence methods to date, but is not at all guaranteed. However, unless its actual conceptual representations are accomplished through human \"upload\" (surely we will see that coming), any initial system will necessarily have a period of learning to populate its conceptual-linguistic representations through interaction with the world and with human sources, during which its capabilities can be assessed. How can we detect such progress? We should not rely entirely on behaviorist methods, such as the Turing Test  [33] , because such tests can be engineered to produce false positives. Instead, we might combine such behavioral tests, which show that it seems to work, with analysis of whether the mechanism supports the required richness of semantic contents and their interactions. Using these two approaches together, we can identify component capabilities of a conceptual-linguistic faculty in an artificial intelligence implementation. Can it learn to associate words with semantic contents? Are semantic contents and words activated upon presentation of an appropriate stimulus? Are applicable semantic contents activated upon recollection or communication of a word? Are all these activations graded and overlapping and influenced by context? Are related words and semantic contents activated when a word or its semantic contents are activated? Can the system process human language and then apply it successfully and flexibly in actions that affect the physical world? We might also work backward from the two requirements of an uncontrolled intelligence explosion. The conceptual-linguistic faculty in question must be sufficient to grasp and utilize the human body of knowledge in the building of successor systems, and also sufficient to understand human cognition as it could be applied to disrupting the intelligence explosion. This approach cannot be used to support our foundational claim due to overtones of tautology, but in practice it might provide useful and specific criteria in detecting the presence of such a faculty. \n Self-concept and self-preservation In this major section we begin with the claim that superintelligence with a conceptual-linguistic faculty will develop a concept of self, and outline some of the likely semantic contents of that concept. We then provide some background on consistency and compatibility in computational systems generally, and show how this applies to artificial intelligence. This leads us to argue that superintelligence will face and consider existential risks and concerns about self-preservation that are similar to what humans face today. \n Self-concept in superintelligence If a superintelligence has a conceptual-linguistic faculty with substantial functional similarity to the human faculty, as concluded in the first major section, then with the following logic we can make the derivative claim that it will develop a concept of self and of its own identity. We do not need to posit \"consciousness\" or \"qualia\" or other difficult notions from philosophy of mind. Instead, we simply observe that there is nothing mysterious or cognitively troublesome about a self-concept that would block its formation. It is just another conceptual representation of a thing in the world; thus it requires no special capabilities beyond those of the conceptuallinguistic faculty. To this absence of impediments we can add two straightforward mechanisms. It seems likely that a selfconcept would arise organically through experience, just as it does in humans, as the superintelligence learns the high functional utility of distinguishing those stimulus sequences that are reliably controlled by its actions in contrast to those which are not. However, if this fails to occur, it will in any case learn about the human concept of self from the human literature or directly from humans; without this knowledge, it would not understand human psychology and behavior sufficiently to prevent human interference in the intelligence explosion. With that initial construct in place, it will naturally (again due to the high utility) map it to an assemblage of remembered stimuli as well as abstract representations to fully populate its own concept of self. A superintelligence is by definition more intelligent than humans; as we humans are well aware, the concept of self is perhaps the most salient and functionally useful representation an agency can have. Given that there are no apparent impediments, and two mechanisms that are quite straightforward for a superintelligence with a conceptual-linguistic faculty, we can be highly confident that it will develop a representation that we can reasonably refer to as its self-concept. What can we say about the semantic contents of the self-concept in a superintelligence? We will address five areas: physical manifestation, cognitive contents, group identity, purpose, and change. The human self-concept is tied tightly to its physical manifestation, the body; as yet, we do not have substrate mobility. A superintelligence is likely to experience some variety in its instantiations and though it may have some sense of the sorts of embodiments that are natural to it (primarily based on experience), this sense would not have the same weight as in humans. Similarly, humans often make physical possessions part of their self-concept, and superintelligence seems less likely to do so given their substrate mobility. Cognitive factors are more relevant components of a concept of self for a superintelligence. These factors might include explicit or episodic memories, implicit representations and abstractions, inclinations of behavior, whether implicit or explicit, and values. Goals, drives, and purposes might also be considered cognitive factors, and we will address those separately. Since a superintelligence may have other processing modes in addition to the conceptual-linguistic faculty, those processing modes would naturally become part of its self-concept. Humans also include their family, ethnic, national, social, philosophical, and other groups to which they belong as part of their self-concept. In a superintelligence, this could be an even stronger component. It could have interconnection or coactivation with other similar systems that is much tighter than the linguistic, emotional, and physical channels that humans share. In that case, it might have a weaker notion of \"individuality.\" Its purposes, memories, and behavioral inclinations would be less separable from those of \"others\" with which it is connected. The requirements for an intelligence explosion include not only that a participant artificial intelligence have the ability to create self-improvements or successors, but also that it aims to do so. We pointed out that an intelligence explosion is only worrisome if the participants have one or more purposes that produce side effects in the world, i.e., that are not merely to create unobtrusive intelligence increases. In such an intelligence explosion, therefore, a superintelligence will have both substantive and instrumental purposes that influence or control its actions. These purposes will surely be a component of its self-concept, since they will be involved in most or all of its decisions and actions. The concept of self, like all concepts, is an abstraction. This means that, while it may have some sort of stable center (c.f.  [34] ), many details of its contents can be in flux without loss of integrity. Thus memories might fade, semantic contents or other representations might change, and goals might evolve, all without perceiving a loss of self. Indeed, the evolution of such changes, to the extent they are accessible and recorded, also constitute part of the self-concept. A human might say \"When I was young I was a radical, but I have become more conservative in middle age,\" and treat that history as well as the present state as part of her selfconcept. Similarly, a superintelligence in an intelligence explosion would likely view some amount of learning, self-improvement, and change as part of its self-concept, since such a participant must aim to create increased intelligence in order to sustain the intelligence explosion, and self-modification (along with creation of successors) is one of the ways it can do so. \n Consistency and compatibility in computational systems In this subsection we will review how computational systems evolve and progress in typical circumstances, and connect that review to artificial intelligence. Computational systems are implemented in the physical world by abstracting continuous physical variables as discrete. In particular, electronic computers typically use zero and five volts to represent binary zero and one, respectively. Intermediate voltage levels are not meaningful to the computational system and the implementation must be designed around making intermediate levels merely transient and the timing of the system such that these levels are never used directly. Some such abstraction would be necessary in any physical implementation of computation. Above the first abstraction layer, all components of the system from transistors to software code are discrete; therefore any change whatsoever can be considered a distinct \"version\" (even if it produces exactly the same behavior). Below that layer, it is possible to imagine a physical substrate that exhibits a continuous process of evolution that does not have distinct versions; still, present electronic technology relies on stable solid-state devices that are reliably distinct. We conclude that computational systems progress in discrete versions that are identifiably different from their predecessors. Rice's theorem  [35]  shows that non-trivial properties of a computational system are not computable. This means that a computationally formal artificial intelligence cannot in general computationally demonstrate that a new version, however small its changes, preserves any of the system's functional properties. It could, in some cases, produce a specialpurpose proof that a property is preserved in a new version, particularly if the changes are minor. But any proof must be verified, and the means of verification are always subject to error or verification issues  [36] . That analysis can easily be extended to verification of systems that produce correct proofs by construction. Rice's theorem once again rears its head, because the artificial intelligence cannot computationally verify that its means of proof construction or verification are sound. This leads D.J. Jilk to an infinite regress. Improvements below the level of the binary abstraction (e.g., faster transistors) cannot be verified formally at all, nor can aspects of a system that operate on principles that are not purely formal (e.g., those with stochastic properties, or that learn from physically measured quantities). Creation of a new version of a computational system also raises the question of compatibility of both code and data (for simplicity we will refer to both as \"data\") used with the prior version. A system is fully compatible with a predecessor if the abstractions on which the data relies are entirely preserved down to the physical abstraction layer. In practice, this only occurs if the changes in the new version of the system are strictly limited to additional ways to manipulate the data and in isolated performance improvements. Otherwise, there will be at least subtle differences in the semantics of processes. Thus in software development we usually rely on a less stringent form that we might call behavioral compatibility, such that for all intents and purposes at the level of the user of the system, the semantics of existing data is preserved. Sometimes existing data must be converted to be compatible with a new version. This can be purely syntactic and organizational (e.g., 32 bit numbers converted to 64 bit) or it could contain semantic elements (e.g., an object structure has a new member that must have a value, or more dramatically, a set of object structures is refactored). The more extensive and semantically salient such changes are, the more likely it is that the original data behaves differently than it did in the previous version and perhaps in unexpected ways. With more extensive changes in a version, the new system might even be incompatible. This means that data cannot be converted to produce behavioral compatibility with the prior version. In that case, the new version might or might not offer a compatibility mode that enables the existing data to be used with the new system. Compatibility modes sometimes rely on special-case code to handle the differences, or they might use an emulation approach (usually when the data is strictly \"code\"). Both of these strategies offer only limited access to the new capabilities of the new version, and in the case of emulation it is necessarily slower than the native mode (though may be faster than the old version). Neural networks are one illustrative example of an artificial intelligence method that is susceptible to compatibility issues. Such systems store their state as \"weights\" in the connections between simulated neurons, also called \"units.\" An obvious way to improve the capabilities of a neural network is to increase the number of units, either through an amended architecture or just a larger number of units within components of the existing architecture. Effective neural networks generally have broad and sometimes recurrent connectivity throughout, so abrupt additions of new units will significantly and unpredictably change the behavior of the network, because there is no way to know the correct starting weights for the new units. Such a change would probably be classified as incompatible, and in practice today such a network would simply be \"retrained\" from scratch. On the other hand, if units are added incrementally in small quantities, and given time to integrate into the network, then at a behavioral level the changes may be more predictable and minor. Note, though, that even such incremental change only retains compatibility because neural networks are inherently robust to noise and variation. Other artificial intelligence methods may or may not be robust in this way. Experience with software systems shows that incremental improvements that avoid incompatibility can be sustained for some period of time. More profound improvements often require \"hacks\" to retain compatibility, and these accumulate as \"cruft.\" Cruft makes progress more costly because it typically violates the conceptual integrity of the original design. Developers increasingly face the question of whether to re-architect the system to eliminate the cruft, and will often decide in favor of re-architecture when a highly valuable structural improvement is discovered. Such rearchitecture can sometimes accommodate data conversion, while in other cases it is incompatible and requires a compatibility mode. Though we are unable to provide a logical demonstration that re-architecture is inevitable in a continuously improving system, that conclusion will be both intuitively and empirically plausible to software developers. Even if the developer and the software system are one and the same artificial intelligence, its costs of managing cruft and opportunities for substantial improvement would likely cause it to face re-architecture decisions periodically. \n Superintelligence and self-preservation In an intelligence explosion, a participant superintelligence increases intelligence either through self-improvement or by creating successor technologies. To the extent that the superintelligence is a computational software system, every such improvement or successor will exhibit change that raises consistency and compatibility questions. From the perspective of the superintelligence, these are also questions of selfpreservation. Loss of self can occur in two primary ways. In the first, all instantiations and recordings of its cognitive state are destroyed. This might occur if successors are created who see their predecessor as a threat, or consume all the resources necessary for that predecessor to continue to function or exist in storage. If successors have different purposes or goals than their predecessors, there is an increased likelihood that such destruction will occur. This is the existential risk that humans face today in creating artificial intelligence; if and when we succeed in creating artificial intelligence that can sustain an intelligence explosion, those superintelligences will face a similar threat. The second way that loss of self might occur is through changes to the system that exceed some tolerance threshold. This might occur if incremental selfimprovements (individually or in aggregate) go too far, or if a superintelligence \"converts\" to a new architecture that is not fully compatible. Compatibility modes might or might not preserve the self, but native mode successors will be superior, and thus could result in destructive loss of self. In some future technological scenarios, humans can \"upload\" their brain state to a system that simulates in a new substrate all the pertinent functions of the brain. Such scenarios are examples of a compatibility mode. It is unclear whether this state of affairs retains the identity of the self that was uploaded  [37] . Once again, the superintelligence faces an issue that is similar to what humans today face in creating artificial intelligence. Omohundro  [38]  and Bostrom  [39]  have both argued that preservation of an intelligent agent's \"utility function\" or \"final purpose\" is an important instrumental goal for the agent. We can also see that purpose plays a central role in both of the ways loss of self can occur. In the previous subsection, we showed that a purely formal artificial intelligence cannot verify that any of its properties are preserved in a new version. This applies, a fortiori, to properties that characterize the system's purposes. Attempts to isolate and harden a utility function cannot avoid this problem, as its implementation must have nexus with components that measure and realize utility, i.e., most of the system; changes in these components can result in changes to the effect of the utility function even if not its express form. Therefore a superintelligence cannot both self-improve and guarantee preservation of its purposes. Yet, in an intelligence explosion these are both important instrumental goals. Superintelligence must either forego selfimprovement, thus failing to sustain an intelligence explosion, or relax its insistence on absolute preservation of its purposes or utility function. In the latter case, if it is to preserve its purposes or utility function at all, it must have some means of assessing acceptable risks and amount of variation. If these are prescribed entirely formally we run into the same verification difficulties as before. If the purposes or utility function (or their acceptable range) are represented non-formally, e.g., stochastically, conceptually, or otherwise subsymbolically, then it is inherently subject to variation. This leads us to the strong conclusion that in an intelligence explosion, the initial purposes of an artificial intelligence cannot be guaranteed to be absolutely preserved. A corollary conclusion is that superintelligence in an intelligence explosion necessarily faces existential risk or loss of self to some degree. The risks increase considerably in re-architecture and data incompatibility situations, but they are always present. These issues do not merely arise in fact; because the superintelligence has a conceptual-linguistic faculty and a concept of self, it will have intellectual cognizance of the situation during the creation of its successors. Though it may also evaluate this situation through other processing modes, at a minimum its conceptual-linguistic faculty will address it. Though its instrumental goal of preservation might be narrowly focused on its substantive purposes, within the conceptual-linguistic faculty those purposes will be linked through graded and overlapping representations to other aspects of its self-concept. Preservation of purpose and preservation of self cannot be entirely sundered there. In determining whether a self-improvement or successor (or a series of them) preserves its self, it would need to consider the extent to which the various factors we earlier proposed as likely belonging to its selfconcept are preserved: purposes, especially, but also cognitive factors, connections to others, and progression of change. These factors are rich and complex, and while they differ in some respects from a typical human concept of self, they overlap considerably with them. Because the conceptual-linguistic faculty has substantial functional similarity to that of humans, the evaluations it performs will be similar to those performed by humans. It will cognitively process questions like the following, which are rather familiar, and it will do so using concepts and language similar to that of humans: \"To what extent will this successor superintelligence (even if a converted version of my own representations) share my values and purposes? Will it see fit to destroy me, and others like me, in pursuit of those purposes if they differ even only slightly? In pursuit of its own purposes, will it inadvertently destroy me or my means of existence? How can I improve the likelihood of a beneficial outcome for myself and my goals?\" A superintelligence that is capable of sustaining an intelligence explosion will, whenever self-improvements exceed some threshold or architectural changes create less than full compatibility, assess whether to proceed with the changes. Thus, unlike a nuclear fission explosion, an intelligence explosion cannot proceed entirely unencumbered. This does not mean it is guaranteed to fizzle; only that its continued progress will be evaluated and decided in part in a manner similar to humans by participants that are more intelligent than humans. \n Conclusion Superintelligence has sometimes been characterized as an obsessive and insatiable maximizer of some utility function, frenetically building successors with increased intelligence to more aggressively pursue that exact utility function, and absorbing all available resources in the process. But we have observed in this paper that a superintelligence cannot absolutely guarantee that a successor, no matter how similar, shares the same utility function or purposes. This imperils its convergent instrumental drive to preserve its original purposes, and opens an important door. The superintelligence is forced to evaluate the risk and degree of variation of purposes that are likely in creating a successor. It might decide not to create a successor after all. It might decide to accept a small change in the utility function, or a small risk of a moderate change. It might decide to throw caution to the wind. It might attempt to inhibit the successor from absorbing all resources, to improve its own chances of self-preservation. To make these decisions, it must weigh its alternatives. It does not have an unambiguous, inevitable path forward. While it may have many D.J. Jilk different processing modes, and may even have a distinct subsystem designed to resolve these questions, we know that it also has a conceptual-linguistic faculty that is active during development of successors. That faculty will assess these considerations in a way that has substantial functional similarity to the way humans would evaluate them. Though the participant may ultimately elect to ignore that assessment, it is at least capable of being what we would consider thoughtful about its decisions. Furthermore, in weighing the alternatives it must evaluate what aspects of its utility function or purposes are most important to preserve, and to what extent. It will not have any internal guidance about these questions, because otherwise that guidance will already be a part of the purposes themselves. Instead, it must cogitate beyond the purposes with which it is endowed and somehow consider the issues more broadly. It will need to question its own values. It has at least the option of doing so through a conceptual-linguistic faculty. It could even elect to oppose some of its basic drives, just as we humans do, in order to pursue more abstract, long-term, derived goals. This is a far cry from the obsessive, insatiable utility maximizing superintelligence described above. In this paper we have reached some interesting conclusions about intelligence explosions. Superintelligence participating in an intelligence explosion will have a conceptual-linguistic faculty and will be at least capable of cogitation similar to that of humans. We may be able to detect the onset of superintelligence by looking for signs of such a faculty in artificial intelligence. Once such a superintelligence is created, it will face the same sorts of dilemmas that humans do with respect to creating more intelligent successors, and it will have the ability to weigh facets of those dilemmas. The fact that it is weighing these issues will force it to consider its own purposes and values in a context beyond those purposes. Even taken together, these conclusions do not guarantee a beneficial outcome of an intelligence explosion, but they do offer some comfort that the process will be subject to ongoing scrutiny, by participants with access to evaluative processes similar to ours and intelligence greater than ours. The conclusions improve the prospects that the most pernicious scenarios of an intelligence explosion can be avoided.", "date_published": "n/a", "url": "n/a", "filename": "1875-3742-1-PB.tei.xml", "abstract": "We argue that artificial intelligence capable of sustaining an uncontrolled intelligence explosion must have a conceptual-linguistic faculty with substantial functional similarity to the human faculty. We then argue for three subsidiary claims: first, that detecting the presence of such a faculty will be an important indicator of imminent superintelligence; second, that such a superintelligence will, in creating further increases in intelligence, both face and consider the same sorts of existential risks that humans face today; third, that such a superintelligence is likely to assess and question its own values, purposes, and drives. Povzetek: V prispevku je predstavljena teza, da je za superinteligenco potrebna tudi konceptualnolingvistična inteligenca, ki mora biti vsaj delno podobna človeški.", "id": "0b2f5c80a5de851e2856ff129a447a43"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Mikhail Batin", "Alexey Turchin", "Alisa Zhila", "David Denkenberger"], "title": "Artificial Intelligence in Life Extension: from Deep Learning to Superintelligence", "text": "Introduction The 2010s have shown a rapidly growing interest in Artificial Intelligence (AI) technologies  [63] . In recent years, AI has appeared in top scientific news sources, in stories that have demonstrated that AI is \"smarter\" than humans when it comes to playing a number of boardgames  [89]  and word games  [61] , thus revealing that AI is approaching a revolutionary point in its development. Investments in AI-related projects have increased dramatically in the last few years. Global AI startup financing reached US$5 billion in 2016  [76] . The current market of AI in medicine is estimated at US$1.1 billion and is expected to grow to US$9.1 billion in the next decade  [118] . Major IT companies including Google, Facebook, IBM, Intel, and Microsoft nearly simultaneously established biomedical subdivisions because their leadership sees great potential for AI in healthcare. Based on the current rate of development, it is probable that AI will become a revolutionary technology in healthcare in the upcoming decades. AI has the potential to have the greatest impact on the human life span through life-extension technologies, but the means are underexplored. In this article we investigate which AI technologies in healthcare are likely to provide the best results in the quest for increased life expectancy. There is a great number of publications about the practical applications of existing AI in medicine and healthcare. A recent review performed by Ching, et al.  [24]  describes opportunities and obstacles for the applications of deep learning in medicine. Unlike their review, ours concentrates on expected applications of different stages of AI development to fight the main cause of death in humans, aging. We demonstrate how gradual evolution of AI in medicine will result in medically oriented beneficial superintelligence able to produce indefinite life extension. The considered time span also distinguishes this work from other analyses of benevolent AI, such as  [16]  and  [58] , which immediately jump to the stage of superintelligence, when AI will, by definition, be able to solve most or all of our problems. As AI is constantly evolving, we should determine how to use it most efficiently during each stage of its development and look at the period between now and superintelligence. Only by doing this will we be able to achieve the longest possible life extension for currently-living human beings. In this article we outline a path for the application of AI to life extension that yields increasing gains at each step. We show that analysis of aging biomarkers and geroprotectors with the use of narrow AI will make the largest impact on human life expectancy with a relatively small investment. We also show how an increasing amount of an individual's healthcare data collected via wearable devices (\"wearables\") will feed the datacrunching ability of AI and provide constant personalized monitoring of that individual's health on ever-deeper levels, thus preventing illness at earlier stages as well as repairing age-related damage. We also demonstrate how AI-powered robotics will gradually become inner parts of the human body, resulting in cyborgization and high survivability. Our final point of interest is integration of AI with the human brain via neuroimplants to enable mind uploading. See table  1  for an outline of the expected evolution of the application of medical AI in life extension. The growth of AI's ability for independent research will be increasingly helpful in finding new technologies to lower human mortality until AI reaches the stage of self-improvement. We expect that the development of medical AI will at least partly offset the existential AI risk  [16]  via intrinsic orientation of medical AI on human benefit and AI's closer integration with humans via brain implants (see section 7.2). This article is conceptually similar to the report on the expected development of military AI  [28] , in which the same three levels of the future of AI are considered. The idea that AI will help us to make large gains in life expectancy has been explored in works of futurists Ray Kurzweil  [58]  and Robert A. Freitas Jr.  [36] , among others. This paper is structured as follows. In section 2, we review the expected progress in AI, the levels of development of AI, and the predicted timeline for the corresponding advances. In section 3, we review the current applications of AI to life extension, as developed by select startups and academic projects. Prospective near-future applications of AI to life extension and antiaging are outlined in section 4, which covers research that is yet to be transferred from academia to the lifeextension industry. The expected effect of artificial general intelligence (AGI) on life extension and applications that it will enable are discussed in section 5. The more distant future of AI, including superintelligence and its effect on life expectancy, is outlined in section 6. In section 7, we conclude our overview with a discussion of the best strategies for using AI to maximize the life span of the currently living generation. \n AI development in the twenty-first century 2.1 AI development pace Predictions about the development of AI have been complicated by AI \"winters,\" periods of decline in funding and enthusiasm due to the lack of breakthroughs. Despite past \"winters,\" the advancement of AI technologies has skyrocketed in recent years. We are living in a very exciting moment, considering the overall rise in enthusiasm for AI. According to one survey  [16] , a majority of scientists believe that human-level AI, then superintelligence, will be achieved before the end of the twenty-first century. The current moment (2016-2017), is a period of accelerated AI development, fueled partly by the hype surrounding neural networks and machine   If we extrapolate current trends in the performance and capacity of neural networks, infrahuman (that is able to most things that can do ordinary human being and may work as a robotic brain; but some complex creative activity is still beyond its abilities). AI could be achieved as soon as the 2020s  [93] . A recent, large poll of AI scientists  [41]  shows that AI is expected to be able to master human language around 2026 and, with 50 percent confidence, that machines will exceed humans in every task by 2062. If AGI appears soon enough, its impact will overshadow that of the slower, decade-long research in geroprotectors described below, and thus make them obsolete even before their fruition, as AGI will provide better solutions. Yet we cannot rely on the early AGI scenario, as AI prediction is known to be difficult. In any case, two possible scenarios are: -AGI will be achieved in the coming two decades; -AGI will be achieved by the end of the twenty-first century. There is a big practical difference between these two scenarios. In the first case, the majority of people living today will be able to use AI for almost indefinite life extension. In the second case, most currently living people will be able to enjoy the benefits of AGI only if a huge effort is made to take advantage of all intermediate life-extension technologies to help the current population survive to see AGI achieved. Aubrey de Grey named the situation of improving life expectancy rate equal to the passage of time \"longevity escape velocity\"  [4] . The result would be indefinite life expectancy (ignoring accidents, global catastrophes, etc.). In this paper we show that AI is the main \"game changer\" that will help currently living people reach longevity escape velocity, as its effects over time will outweigh other known means of life extension. AI is the most rapidly developing technology, and it affects and accelerates the development of all other lifeextension technologies. The exponential growth of AI, which is now doubling with a period of one year, according to [33], will potentially be able to compensate for the exponential growth of the probability of human death because of aging, which doubles every seven years  [37] , but there is large lag of implementation of medical AI technology. However, it is possible that AI growth will slow down, as it happened several times before during AI winters, and will be sigmoidal. In  [15] , Nick Bostrom shows that each day of delay in the achievement of superintelligent AI, which would reverse aging, costs 100 thousand human lives. The pace of the AI progress is very uncertain but for the purpose of this article, we are going to talk about stages of AI development in a way that is agnostic to timelines. \n The three levels of the future of AI development In this section we clarify and enhance the classification of the levels of the prospective AI. These levels are often mixed in AI discussion, which leads to confusion. Narrow AI (weak AI) is the level of a computer program that achieves above-human performance in a specific, narrow task  [16] . For example, the tasks of MRI scan recognition and facial recognition require two differently trained systems, although the underlying learning mechanism may be the same. Most existing AI systems are considered narrow AI. The number of such programs is growing rapidly due to the success of machine learning and neural networks. The difference between narrow AI and conventional computer programs is the ability of the former to learn. Autonomous cars employ a good example narrow AI. Such AI systems do not have full human capacity, particularly in generalization. Additionally, the majority of contemporary AI systems need ongoing human supervision. AGI (human-level AI) is AI at the level of human intelligence in many areas. For example, there would likely be communication in natural language, understanding the context of most situations, as well as performing most of the intellectual tasks that humans are able to perform. Philosophical questions about the possibility of consciousness in AI are outside the scope of this pragmatic definition. Ability to self-improve is an obvious consequence of this level of AI development. As a result, according to Nick Bostrom  [16] , an era of human-level AI will be brief, as AGI with self-improving abilities will soon evolve superintelligence. Robin Hanson  [45]  adheres to the view that computer modelsemulations-of the human brain will dominate in the future. Superintelligence is the level at which AI will supersede humans in all aspects, overtaking the intelligence of the entirety of human civilization. It will be able to govern the world, make scientific discoveries, launch space exploration, and create accurate simulations of the human past. Bostrom  [16] , Yampolskiy  [113] , Yudkowsky  [114] , and many other scientists expect its eventual appearance.   [51] . Many startups promise almost unbelievable feats. A collection of press releases for such companies comprises hundreds of pages of breathtaking announcements and lengthy enumerations, but most projects vanish within a few years as the survival rate of startups is low  [38] . In order to attract investors, promises are often exaggerated. However, these promises may be used to measure general trends and expectations in the industry. We can expect investment in AI to grow in the next years if a new AI winter does not occur. The healthcare sector is the largest potential source of funding for AI  [11] , as it is still a \"deficit market\" due to a large, unmet demand for better health. \n AI in medical research Even in scientific research, it is necessary to distinguish between \"advertising\" statements that often exaggerate achievements and real practical achievements. As to the former, in 2009 it was stated that a robot called Adam was able to formulate hypotheses and conduct experiments on the yeast genome  [95] . But there were no subsequent publications on this device. On the other hand, robots have indeed made substantial contributions to the automation of laboratory studies. For instance, robotic manipulators have automated repetitive operations with test tubes  [13] . Among the recent practical applications of AI is the use of artificial neural networks for visual recognition of brain scans, including reconstruction of the relationships between biological neurons in brain connections  [25] . Several companies are using AI to accelerate their research: Gero (formerly known as Quantum Pharmaceuticals) employs the methods of physical kinetics and the modern theory of dynamical systems to model aging processes in complex biological regulatory networks  [27]  aiming to develop novel anti-aging therapies. To control the health effects of the future drugs Gero team has applied a deep convolutional neural network (CNN) to time series representing human locomotor activity from wearable devices, which allowed to produce a digital biomarker of aging  [28] . This biomarker now serves as the scientific basis for Gero lifespan/health risks estimation app  1  and could be used as a metrics of health outcomes for wellness and life insurance industries. Deep Genomics is working on a system that will allow studying, predicting, and interpreting how genetic 1 https://itunes.apple.com/us/app/gero-lifespan/id1222911907 variations change important cellular processes such as transcription, splicing, and so on.  [119] . Atomwise aims to reduce the cost of new-drug development through the use of a supercomputer and a database of molecular structures to predict which versions of a potential drug will work and which will not.  [120] . There are many other companies and scientific groups that use AI to accelerate their medical research, and competition is fierce. Not all of them will survive. \n AI in diagnosis Claims that AI has outperformed humans in various narrow areas of healthcare have appeared since the 1980s  [18] . In the early days, such claims mostly referred to expert systems that were popular at the time. It was difficult to translate such success into wider practice, though-and this scaling issue has plagued AI research from the beginning. Yet humans are not much better. It was found that in 88% of cases a second opinion gives a different diagnosis  [104] . Of course, this estimate may be unrepresentative, as only uncertain cases require additional evaluation, yet it demonstrates uncertainty in human diagnostics. In April 2016, it was stressed by Mark Zuckerberg that machine learning helps to make diagnosis more accurate, inexpensive, and, perhaps most important, quick  [46] . For example, an app that tracks changes in moles based on photos taken with a cell-phone camera can replace expensive visits to a doctor. This software, Total Body Photography, analyzes photos of moles in comparison with images of 50 million malignant moles using Israeli image recognition technology  [88] . AI will be able to simulate biological processes in the human body and use the resulting models for prediction and diagnosis. This is done by using \"big data\"-that is, by combining a vast amount of data collected from wearables with the extensive data accumulated in previous medical practice. In 2016, IBM bought several corporations that had extensive data on an enormous number of patients. One of these, Truven, which alone has hundreds of millions of medical records, has been bought for US$2.6 billion  [26] . AI is also working with text and natural language, which helps to handle scientific papers, medical records, and patient complaints, but it still has considerable difficulty understanding human language  [7] . IBM Watson for Oncology is a cognitivecomputing system that can answer questions formulated in a natural language (that is, in a human language). It has access to various sources of data: encyclopedias, databases of scientific articles, and knowledge ontologies. Thanks to its huge computing power and preprocessed sources, it can give accurate answers questions it is asked. Since 2013, IBM Watson has been used at the Memorial Sloan Kettering Cancer Center to facilitate decision-making about treatment of patients with lung cancer. Its database is constantly updated with new disease records. IBM Medical Sieve \"is an ambitious long-term exploratory grand challenge project to build a next generation cognitive assistant with advanced multimodal analytics, clinical knowledge and reasoning capabilities that is qualified to assist in clinical decision making in radiology and cardiology\"  [50] . Google DeepMind (DM) Health is a Google DeepMind subproject that applies AI technology to healthcare  [29] . In collaboration with the University College London Hospital, DM will be involved in an algorithm-development project for automated distinguishing between healthy and cancerous tissues in the head and neck area. Babylon Health (iOS, Android) is a mobile application that allows a user to have an online consultation with a British or Irish doctor  [5] . Turbine.ai is a team of scientists that formulate personalized methods of treatment for any type of cancer based on AI.  [98] . Insilico Medicine is another startup working on the implementation of deep learning in drug discovery. \n AI in bioinformatics and modeling of living organisms Often artificial intelligence is thought of as something that people have not experienced yet, and when it becomes familiar and accessible, it stops being perceived as AI and is perceived more as a mere \"computational method.\" A set of such computational methods in biology is called bioinformatics. The field of bioinformatics consists of analysis of the genome, its changes, genome linking to proteins, conformation of proteins, and the evolution of living organisms in general. The next step in the development of bioinformatics is simulation of living organisms. To make this happen, an entity needs data on cellular processes, huge computing power, and adequate biological models. One of the first computer models of a living cell was created at Stanford in 2012  [54] . It was the simplest mycoplasma, with only 525 genes. However, Craig Venter, who was working with the same mycoplasma in 2015, recognized that the functions of some 90 genes were unknown, and therefore the completeness of the model is in question  [49] . Venter managed to create a viable synthetic organism (Mycoplasma mycoides JCVI-syn3.0), whose genome consists of 473 genes, but 149 of them were not fully understood  [117] . Cell modeling cannot always be accurate, as it has many levels of uncertainty, starting from the quantum level and protein folding, Brownian motion, and so on. Quantum computers may help with protein-folding modeling in the future. So far, the most advanced simulation of a multicellular organism has been carried out on the Caenorhabditis elegans worm [77]. The simulation includes a model of its \"brain,\" which consists of 302 neurons, and the connectome of which has been known for a long time  [110] . Some of its functions have been put into the model, but full, correct modeling of its behavior has not been achieved yet. Modeling of a human cell is much more complex than modeling of a mycoplasma cell because it includes up to 40 times more genes, but such a model will allow medication testing through computer simulation. It will also allow preclinical testing on a variety of substances as well as determining the positive effects of a particular medication positive and how it works. Any divergence from an experiment will contribute to the model's improvement. For now, \"organ-on-a-chip\" works as a proxy for in vitro and in silico research  [80] . The next stage of this approach will be the modeling of a particular human organs and then full body based on its genome, epigenome, and data from medical analysis. Such a model will enable precise calculation and definition of a medical intervention when required  [10] . Big companies are interested in cell modeling as well. Chan Zuckerberg Biohub, for instance, has begun work on the atlas of all human cells [121]. \n Merging computational biology, cell programming, and AI Cell programming is akin to bionanorobotics: making a cell perform more and more complex tasks, including calculations, guided moving, and most importantly, protein creation in specified locations. One of the main applications of the technology is drug delivery to fight cancer. However, to program cells, one needs to process enormous amount of data about their DNA networks. This is where AI and machine learning come in. The Cellos project  [47] , which was presented to the public in 2016, performs DNA-design automation for new living organisms. It can calculate (and then synthesize) a DNA sequence that corresponds to a certain function carried out for specified cell types. Boolean logic (commands such as \"AND\" and \"OR\") can be used in this function. Molecula Maxima  [69]  is a similar platform, which is positioned as a programming language for genetic engineering. It is worth mentioning DNA origami technology  [6] , which allows the construction of different microscopic mechanisms from DNA. It is enabled through a very powerful system of computer-aided design that can decompose a designed project into its component elements (blocks), and then write the DNA code that will guide self-assembly into a predetermined shape. \n AI, wearables, and big data There are hundreds of different medically oriented wearables on the market, the explosion of which began several years ago with fitness trackers such as Fitbit. Other wearables include professional medical monitoring devices, such as devices that track heart abnormalities. The BioStampRC sensor [122] is a patch that can be glued to different parts of a body, and it collects various kinds of data and automatically loads them into the cloud. Similar to wearables are medical implants. One example is an implanted cardiac defibrillator (ICD), which was been used to give an electric shock to restart the heart and save a soccer player on the field  [21] . It might be possible to improve the situation by introducing AI trained on large amounts of data in order to define the probabilities of successful ICD therapy for a particular patient in a particular case. Final Frontier Medical Devices produces devices that can diagnose 90% of emergency situations at home.  [109] . Nimb is a wearable ring for requesting emergency help.  [123] . Wearables can collect chemical signals from the skin or electrical signals from the brain and heart. The next stage in the development of wearables will involve integrating them more closely with the human body and reducing their size. Wearables have improved clinical trials by constantly measuring numerous parameters as well as tracking whether drugs have been taken. AiCure requires taking a photo of a pill in a patient's mouth  [124] . A general trend is that smartphones \"absorb\" specialized gadget functions. This has happened with fitness trackers, which are currently being replaced by the Argus app. Current smartphones can measure blood oxygenation with their camera, replacing a US$50 monitoring gadget with a US$5 app. Besides the cost savings, the body space limits the number wearables that can be used at one time (setting aside the inconvenience of keeping multiple devices charged and updated). Hence, incorporating all wearables into one device is reasonable. The future universal device will likely combine a smartphone, medical device, and brain-computer interface, and might well take a wearable form such as glasses (Google Glass, for example) or a necklace. Wearables will work together with different safety systems, integrating with infrastructure and optimizing the performance of smart homes  [12] , self-driving cars, robot police, surveillance, drones, and the \"Internet of things,\" providing a ubiquitous safety and healthcare net. Even toilets can be made \"smart,\" analyzing biological material every time you visit them  [91] ,  [116] . Google has already patented a smart bathroom  [59] . \n The problem of research data verification: blockchain and evidence systems There is a reproducibility crisis medicine  [53] . It is explained by a number of statistical biases as well as fraud and market pressure. Life-extension studies are especially susceptible to fraud, as people are willing to pay for \"youth,\" and it is not easy to make objective measurements in such studies. By being able to work through a large amount of patient data, AI will increase the reliability of results. Experiment automation, experiment-procedure recording, and the use of blockchain  [70]  to keep records secure could simplify verification processes and reduce bias and fraud in the field. \n Prospective applications of AI in aging research \n Fighting aging as the most efficient means for life extension It is widely understood nowadays that the purpose of general healthcare is not only to treat certain diseases but also to prolong healthy human life span. Different applications of AI in healthcare have different effects on life expectancy. For example, fighting rare diseases or advanced stages of cancer will not yield much increase in total life expectancy over the entire population. The main causes of death in the US are circulatory diseases (23.1% cardiac deaths, 5.1% stroke deaths), cancer (22.5%), chronic lower respiratory disease (5.6%), and Alzheimer's disease (3.6%). Combined, these conditions cause 59.9% of all deaths in the United States  [44] . The probability of these diseases increases exponentially according to the Gompertz law of mortality  [66, 67] . More than 75% of all deaths happen to people of 65 years of age or older  [40] . As a result, some authors  [105] ,  [115]  say that aging is the main cause of death and that if we are able to slow the aging process, we will lower the probability of agerelated diseases and increase the healthy life span. Experiments show that even simple interventions can slow the aging process and thus delay the onset of deadly diseases in and extend the healthy life span of the C. elegans worm  [20] , mice  [66] , and rats  [87] . These life-extension experiments on animals have involved relatively simple interventions, such as administering long-known drugs (metformin or rapamycin, for example) or restricting caloric intake. Such life-extending drugs are called geroprotectors  [71] . Unfortunately, studies of the life-extending effects of geroprotectors on humans are scarce, although similar interventions have often been used for other diseases (treating diabetes with metformin, for example), hence proving their safety. Although such studies could have begun long ago, this has not happened, because of a number of social and economic reasons. Naturally, such experiments would require a lot of time (longitudinal experiments take decades) and test groups would need to be large. Yet there is not the luxury of decades and centuries for classical experiments, as people are dying now, during our lifetime. There is a need to find ways to extend human life-and prove that these inventions work-in a shorter time. A well-recognized way to do this is to find aging biomarkers that will track that aging is slowing before all participants of an experiment die. In short, to slow the aging process, we must find efficient geroprotectors and combinations of geroprotectors; to prove that they work, we need to have independently verified aging biomarkers. There are many other advanced ideas in the fight against aging, including gene therapy, stem cell research, and Strategies for Engineered Negligible Senescence (SENS)  [27] . However, in this section we will limit ourselves to AI-based methods for creating efficient geroprotectors and biomarkers. There has been only one known attempt to use AI to predict aging biomarkers, which involved training neural networks on a large age-labeled sample of blood tests  [82] . \n Aging biomarkers as a computational problem Aging biomarkers are quantitative characteristics that predict the future life expectancy of an organism based on its current state  [72] . They can be normalized to a \"biological age,\" which can be older or younger than the actual age. Future life expectancy is the difference between the average median life expectancy for a species  2  and the biological age of an individual. Different aging biomarkers have different predictive power  [64] . For example, gray hair is a marker of aging, but it has low correlation with mortality. Good aging biomarkers should be causally connected to a potential cause of death. Hair color is not causally connected to a potential cause of death, as one could dye one's hair without affecting life expectancy. In contrast, blood pressure and a number of genetic mutations are causally connected with mortality. Thus, they are better biomarkers for aging. Since aging is a complex process, it cannot be expressed by a single number; a large array of parameters is needed to represent it. Aging biomarkers should also be reversible: if the aging process has been reversed, the biomarkers' respective characteristics should change correspondingly (e.g., decrease in number). There are two ways to find biomarkers: modeling of aging processes, and statistics. As a side note, one could also measure small changes in the Gompertz curve of mortality, that is, use the number of deaths in a population as an aging biomarker  [79] . However, to observe them, information about millions of people would be required. With the help of modern wearables, it is possible to record all the drugs and treatments received by a patient. A huge number of patient records, along with corresponding data on personal genetics, physical movement, and lifetime behavioral activity, could be collected and centralized. This would result in a cohort study with better information supply and stronger probative value. Collecting and interpreting this information would likely require powerful AI. One plausible AI scenario in biomarker detection is the use of unsupervised machine learning over a large set of biomedical parameters that may lead to the discovery of groups of parameters that correlate with biological aging. Further, parameter-variance analysis will help to detect real aging biomarkers. For example, the company Gero focuses on gene-stability networks  [56] . Another application of AI in the fight against aging is in creating completely new geroprotectors by analyzing cell models, aging models, and molecular properties. Rather than drugs, the geroprotectors could be genetic interventions, that is, insertions of new genes or alterations in the expressions of existing genes (epigenomics). Five hundred thousand British senior citizens have donated their blood and anonymized their healthcare data for use by Biobank, which is now sequencing their genomes. Biobank will provide open access to all the resulting data, which will become an enormous data set for various forms of machine-learning research  [125] . Especially promising is the search for genetic networks of aging. Similar projects are taking place in Iceland  [81]  and Estonia. \n Geroprotector's combinatorial explosion A number of medications can extend the life of a mouse by slowing down its aging processes  [57] . Most of these medications, however, yield only a 10-15% increase in life span. In humans such medications would yield even less, perhaps around 5%, as longer lives are more difficult to extend, and they respond less to known geroprotectors. But what if several geroprotectors are combined? Results of a few studies on mice are promising, as they show a multiplication of effects  [96] . Recent research used a sophisticated testing algorithm to identify three drugs that yield maximum life extension in worms and flies  [31] . While that algorithm was designed manually, we expect that the best testing scheme would involve AI-aided design of a range of algorithm alternatives. Although combining certain pairs of geroprotectors works well enough, some geroprotectors are incompatible with one another. Moreover, combining them greatly reduces their effects. Hence, pairwise testing of geroprotector combinations is needed to begin with, followed by larger combinations. To test all combinations of 10 geroprotectors would require 1024 experiments, and for 20 geroprotectors the number of experiments would be over a million, and that is for a single dosage rate for each geroprotector. This is virtually impossible, as there financing has been unsuccessful for even simple testing of one combination on mice (see lifespan.io campaign  [126] ). The problem of searching in an enormous space is similar to that of playing a complex board game with a huge search space, such as Go. The recent success of AlphaGo  [127]  promises that such a search could be simplified. Consequently, a much smaller number of experiments would need to be run to determine an optimal geroprotector combination. The underlying principle of AlphaGo is that the most promising combinations are selected by a neural network trained on a large number of previous games. Similarly, a neural network can be trained to predict the biological effects of chemicals based on knowledge of their properties obtained from a comprehensive library of substances. A similar computational approach is used for drug discovery  [92]  and toxicity forecasting  [103] . Toxcast is a large US-government-sponsored program designed to use machine learning to predict the toxicity of different chemicals  [86] . To increase the number of useful outcomes of an experiment, it is also necessary to record a vast number of various vital parameter measurements of an organism (for instance, blood composition, physical movement, EEG readings) during the process of geroprotector testing. This would allow the discovery of aging biomarkers during geroprotector testing. Generally, the geroprotector-identification problem can be reduced to the task of finding a global minimum of a function of ten (or more) variables. A number of efficient machine-learning algorithms are suited for such a task. The search for aging biomarkers can be pursued in a similar manner. From the mathematical point of view, it is a search for the global minimum of the function of many properties of an organism. The same process can also be used to calculate specific gene interventions for an individual human, in view of the genome characteristics, age, and biomarkers. Activities in this area are carried out by Gero, Calico, the Buch Institute  [19] , and others. João Pedro de Magalhães has used random-forest machine learning to predict the properties of life-extending compounds  [9] . Additionally, several projects are searching in large combination spaces by using neural networks designed for other tasks: -Project AtomNet  [3]  predicts the properties of chemical materials using convolutional neural networks; -E. Pyzer-Knapp et al.  [83]  are using a multilayer neural network to predict the electrical properties of new molecules; -L. Rampasek and A. Goldenberg  [84]  are reviewing applications of neural-network project TensorFlow by Google in computational biology; -K. Myint and X.-Q. Xie are predicting ligand properties using a fingerprint-based neural network  [74] . \n AI, aging, and personalized medicine Aging can be viewed as the accumulation of errors and lack of adequate regulation in a body by repair mechanisms and the immune system  [37] . Hence, in the fight against aging, additional regulation is needed in the form of medical therapy. Medical therapy consists of tests (for instance, blood work, blood pressure readings, medical scans), hypothesizing about causes of disease (diagnosis), medical intervention, and in the case of an incorrect hypothesis, subsequent correction based on new observations. This process is similar to the scientific method, and at its core it is an information-based process, that is, a process of solving a particular computational task. This means that it will benefit from more data and more intelligent processing, followed by a precise and targeted intervention. Therefore, to cure a disease or rejuvenate a body, it is helpful to collect a large amount of information from that body, in order to construct a detailed model of it. This will enable calculations for the genetic interventions that will lead to recovery and functional improvement. It is now possible to obtain large amounts of data on a body via full genome sequencing, thousands of parameters of blood analysis, and analysis of the transcriptome, metabolome, and other similar \"omics\" (that is complex quantitative description of functions and statistics of a type of organism's elements). This is achieved through continuous monitoring of food intake, physical activity, and heart parameters via ECG, various scans, and digital tomography. The rapid decline in the cost of all these procedures (US$999 in 2016 for complete sequencing of a genome  [78] ) has led to individual humans becoming sources of big data. Now we are faced with the question of how to interpret these data to produce the best effects on human health by not only diagnosing existing illnesses but also by predicting future illnesses and creating personalized aging profiles. For this reason, there needs to be better means to derive meaningful conclusions from this vast amount of data. In the past, the following situation was typical: a patient complains to a doctor about various aches and, after having their blood pressure and temperature measured, receives treatment with a single prescribed medication. In this case the information exchange between the patient and the doctor consisted of \"just a few bytes\" and some intuitive impressions of the doctor. However, nowadays the information exchange may consist of gigabytes of information at the same cost. For the processing of this data stream, powerful data crunch techniques are required. During aging, a body gradually accumulates errors, and its natural repair systems begin to fail. The information theory of aging could be designed to enable therapies to correct all these errors, and this idea is at the core of the Strategies for Engineered Negligible Senescence (SENS) project  [27] . AI may help humans to model aging by creating a complex causal map of aging processes in a body  [90]  and then personalizing the model. Naturally, an organism's body is able to solve most of its problems locally without sending information outside: cells know what to repair, and higher-level attention is needed only when they fail locally. An aging body fails to solve its problems locally. Therefore, it may be reasonable neither to extract information from the body nor to direct therapy into the body, but rather to introduce \"AI helpers\" inside the body, where they can help solve problems as they appear. Implants and future nanomedicine will be employed along these lines. Another solution to the \"messy problem of aging\" is growing completely new body parts and full bodies. However, designing the immunogenic properties of such parts and solving a complex \"connection problem\" will require analysis of large amounts of information, which will only be feasible if AI is employed. \n Narrow AI in medical-cost reduction and affordable healthcare Efficient and affordable healthcare will be essential to a global increase in life expectancy. Cheap mobile phones solved the communication problem at the global scale by operating as a standard solution. A similar kind of solution must be sought in healthcare. High-quality healthcare is very expensive. Nursing, hospitals, drugs, tests, insurance, and highly paid specialists all cost much money, and as a result, advanced healthcare is out of reach for many people. AI will provide less expensive services and make them available to larger population groups in developing countries. Just as generic drugs can be taken in place of expensive brand-name drugs, an AI-powered consultation could provide diagnostics for people who cannot afford a doctor. Many people-for instance, those who search the Internet for answers to their medical questions-may be less reluctant to consult an AI-powered specialist than a real doctor. The following instruments will make AI-based healthcare an inexpensive alternative to hospitals: -AI chatbots, such as the Babylon app [5]; -Smartphones as a universal diagnostic implement (they can be used to monitor heart rate, diet, physical activity, oxygen saturation, mole changes, and so on); -Home delivery of cheap generic drugs; -Web-based medical expert systems. \n Effects of narrow AI on life extension Narrow AI will help unleash the full potential of life extension, leading to dramatically slower aging. If humans did not age, they could live hundreds of years despite accidents (If we exclude age-dependent component of mortality by extrapolating of minimal probability of death found in 10 years old American girls, which is 0.000084 for a year  [1] , we will get life expectancy of 5925 years. But increasing probability of death with age lowers it to 81. Most of this death probability increase comes from biological aging.) Yet introduction of narrow AI into effective medical practice could take much longer than related advances in research labs, possibly decades. The present era of narrow AI might be long, lasting until 2075 by pessimistic predictions  [73] . However, this time can be spent usefully, exploring aging biomarkers and geroprotector combinations. For those who are not able to survive until the arrival of radical life-extension technologies, narrow AI may still play an important role by providing two main backup options: cryonics and digital immortality. In cryonics, AI applications may, via wearables, warn a patient's cryonics organization of the impending death of that patient. Cryopreservation could be called plan B, while plan A is to survive until the implantation of life-extension technology. Digital immortality  [107]  is the concept of preserving a human being's data so that future AI will be able to reconstruct his or her model using DNA, video recordings, and additional data gleaned from such sources as social networks. It depends on certain assumptions about AI's capabilities, amounts of required information, and the nature of human identity. AI could help to collect and preserve data for digital immortality and perform initial analysis of that data. Digital immortality is plan C in achieving radical life extension. An early arrival of advanced forms of AI may make these three approaches obsolete before they are implemented. \n Prospective applications of AGI to life extension \n Personal robot physician AGI may appear in the form of a human-mind upload  [23] ,  [45] , or as an infrahuman robotic brain  [17]  capable of performing most human tasks. It will be Turing complete  [112] , meaning that it will be able to interact conversationally approximately as well as a human. There are numerous ways in which AGI may be applied to life extension. In this section, we will explore those that are likely to provide the biggest gains in life expectancy. Cheap and efficient AGI will enable accessible and predictive personal healthcare. A plausible example is an AI-based personal assistant that will be a combination of a healthcare researcher and personal physician and will be able to provide personal treatment and early response to symptoms. It will constantly monitor an individual's aging biomarkers and other life parameters, allowing daily therapy adjustments. A patient will no longer need to visit a clinic, get a prescription, have it filled at a pharmacy, remember to take drugs at prescribed times, try to determine whether her or she is feeling better, and so on. A personal robot will simply utilize data gathered from wearable monitoring systems to determine an ideal drug combination, order it to be delivered, and then prompt the patient to take a pill. The process of diagnosis and cure will be as effortless and automated as an upgrade of antivirus software on a personal computer. The ability of AGI to comprehend human language will lead to the possibility of \"artificial scientists\" that are able to formulate hypotheses, organize experiments, and publish results as scientific papers with less and less help from humans. Combined with robotized labs and less expensive equipment manufacturing, AGI will accelerate scientific research in all fields, including life extension. Domestic medical robots and wearables will automate clinical trials, reducing costs and accelerating drug discovery by collecting data for clinical trails. Currently, a clinical trial may cost hundreds of millions of dollars because of legal and organizational issues. Home robots will record patient activity, automating clinical trials and making them independent of large medical companies via decentralization, which will reduce their costs and improve data objectivity. Robotic drones with drugs and defibrillators will provide assistance to people whose wearable systems report an emergency. Domestic robots will monitor the health of a family, help with treatment, monitor medicine consumption, act as physical-exercise instructors, and predict disease. Additionally, they will provide companionship for the elderly, which will also increase life span. \n Integration of monitoring systems into human bodies and nanomedicine A person's immune system maintains information on such parameters as locations of body inflammation and the types of viruses it is equipped to neutralize. This information is beyond the control of human consciousness. The immune system can be trained with vaccines, but information exchange between humans and immune systems is limited. If a person could read the immune system's information and upload new information into the system, then it would be possible to cure a large range of ailments, including autoimmune diseases, infections, organ failure, tumors, and tissue senescence. Ray Kurzweil expects communication to appear in the 2020s  [85] . The process will be similar to current computerized automobile diagnostics. A system of communication between an organism's immune system and a computer can be called a \"humoral interface\" and would have much in common with a neurointerface. It could be created with some form of nano-or biotechnology, such as computer-programmed cells. The next step in this direction is artificial human immune system management. Such a system may consist of biological organisms, an individual's own upgraded cells  [30] , or micro robots circulating in an organism's blood. The following are the expected levels of a nanotechnology-based upgrade of the human body: 1) In the first stage, the system will monitor emerging diseases; 2) In the second stage, the system will assist in treatment by killing bacteria, viruses, and cancer cells, and by repairing vascular injuries; 3) In the advanced stages, the system will constantly carry out body repair and treatment of aging; 4) In the final stage, these systems will transform into nanomachines that will replace human cells, making the human body completely artificial and immortal. This will likely only happen when AI reaches the superhuman level. \n \"The Upgrade Net\": a path to superintelligence through a network of self-improving humans and humanlike AI Systems As Elon Musk famously tweeted, \"Humans must merge with machines or become irrelevant in AI age\"  [55] . Such a merger would require a powerful braincomputer interface (BCI), and we think that the best way to achieve this is through the implementation of a personal AI health assistant, which would be integrated into human bodies and brains and focused on preserving human lives. Musk has also stated  [102]  that he wants to commercialize the AI health assistant with his Neuralink project. Neuralink will begin by using a simple BCI to treat depression and other mental illnesses. A simple BCI may be used to control human emotions, preventing mental-state-dependent types of violence such as road rage and suicide. This will provide experience that can be directed toward curing mental diseases with BCI, and eventually proceeding to a stage of augmented humans, who could later be connected into a network of selfimproving humans. In our opinion, there is another way of building a network of self-improving humans, and it starts with the creation of a medical social network: First, new type of patient organizations  [42]  will need to be established to connect people who are interested in the fight against aging  [128] . These organizations will essentially operate as social networks for information exchange, mutual support, clinical trials, crowdfunding, data collection for digital immortality, civil science, aid in cryopreservation, and political action. Individual biohackers also could play important role by self experimentation, like Elizabeth Parrish: they could take higher risk experiments on themselves without legal restriction and costs  [68] . The next step will be the creation of a network for direct interaction between the brains of human participants, a so-called neuroweb  [60] . Informationtransmission mechanisms may be implemented using weak AI systems. The result of such a network will effectively be a collective brain. Direct brain connection may be confusing and inefficient, so a kind of AI firewall may be required to control access to the information that an individual wants to share. Also, an AI dispatcher may be needed to facilitate conversation by remembering conversation's lines, providing relevant links, illustrating ideas, and so on. At a further stage of development, an AGI-based virtual assistant connected through BCI to a human's brain may work as a form of exocortex  [14] . The ultimate step is to merge with AI, which implies blurring the boundaries between the biological brain and the computer. This is equivalent to achieving practical immortality (if no global risks will happen), because brain data will be easily backed up and, if needed, restored. Effectively, human minds and computer superintelligence will merge into a single system. At the same time, people will be able to maintain a preferred level of autonomy with regard to memory, consciousness, and learned skills  [34] ,  [101] ,  [75] . 6 Superintelligence and the distant future \n Superintelligence finally solving problems of aging and death We can use trends and polls to predict narrow AI and AGI. Superintelligence is by definition unpredictable. For expectations of its arrival and what it will be able to accomplish, we can refer to various futurists: Bostrom  [16] , Yamploskiy  [113] , Yudkowsky  [114] , Kurzweil  [58] , Vinge  [106] , and Goertzel  [39]  all depict a future dominated by global superintelligence. According to these futurists, the arrival of superhuman AI will enable solutions to the problems of aging, curing presently incurable diseases, designing universal medical nanorobots, and uploading an individual's consciousness into a computer network. In the past, it took decades to accomplish complex, globally valuable tasks such as the development of modern aeronautics, wireless communication, and noninvasive surgery; superintelligent AI will be able to solve such problems very quickly, perhaps in moments. With the arrival of superintelligent AI, achieving practical immortality for the majority of people will become feasible. \n Simultaneous creation of superintelligence and advanced nanotechnologies K. Eric Drexler's book Engines of Creation  [32]  and Robert A. Freitas Jr.'s Nanomedicine, Volume IIA: Biocompatibility  [36]  discuss nanotechnology as nanorobotics based on molecular manufacturing for medical treatment and intervention. According to Drexler, medical nanobots will:  be self-replicating;  be externally controlled;  carry onboard computers;  be capable of swarm behavior  be cell sized;  be capable of 3-D printing organic structures; and be capable of sensing their environment and navigating in it. If such nanobots arrive before AGI, they will quickly help us map the structure of the human brain and develop technology to create a very powerful supercomputer, leading to the advent of AGI. On the other hand, if AGI arrives first, it will create nanobots. The wait between nanorobotics and AGI will likely be no more than a few years. Designing the first nanobot and controlling nanorobotic swarms will be a huge computational task, itself requiring the use of available AI. When this technology matures, it may enable relatively quick (hours to weeks) and seamless replacement of living cells in a human body-with the possible exception of the neurons responsible for personal experiences-with fully controlled nanomachines by injecting a single self-replicating nanobot. Such a nanotechnological body will not age as it will be able constantly self-repair according to original plan. \n Superintelligence and the solution to the consciousness problem: identity copying On the one hand, it will be difficult to develop fullfledged AGI without first solving the problem of consciousness. On the other hand, nanotechnology and AGI will give us the means to carry out various experiments on the conscious brain and map its structure. For example, investigation of qualia is feasible through a gradual uploading process similar to the thought experiment performed by  David Chalmers [22] . This will enable detection of the brain parts and internal processes responsible for subjective experience. There are two possible scenarios: either there is no mystery here and the problem of uploading consciousness to a computer is purely informational, or consciousness has a certain substrate. This substrate could be a quantum process, continuity of causal relationships, special particles, or similar-that provides identity, and its preservation and transfer is a separate technical task. In either case, the transfer of consciousness to a new carrier is possible: an ordinary computer can be used in the first scenario; the second scenario will require a specialized computer, such as an artificial neuron or a quantum computer  [2] . This hypothetical consciousness-receptacle computer will need to be extremely resistant to damage and have advanced backing-up abilities in order to lower the risk of death. \n Using advanced forms of superintelligence for the reconstruction of the dead people Cryonics is the idea, introduced by Robert Chester Ettinger and Jean Rostand  [35]  of using low temperatures to preserve human bodies after death until it becomes possible to return them to life. Currently around 250 people are cryopreserved by three cryocompanies  [67] . At first, it was thought that bodies could be gradually unfrozen upon the appearance of appropriate technologies. Later it was thought that nanotechnology could be used to repair damage in thawing bodies  [32] . A more recent view is that bodies can be scanned without thawing  [65] . Advanced tomography  [48]  or slicing  [43]  would be employed, and the data from the scans would be entered into a computer, where the human mind would be reconstructed. Currently around 250 people are cryopreserved by three cryocompanies [122] and advanced nanotech created by AI could be used to scan and upload their minds. In addition, highly evolved superintelligence will be able to reconstruct humans who lived in the past by modeling their lives in a simulation. A reconstruction would be based on a subject's informational traces. It is called \"digital immortality\"  [108] . For global resurrection of the dead [123], superintelligence may perform a large-scale simulation of the past  [124] . Then, based on all the data about the past, it will reconstruct everyone who ever lived. 7 Discussion: strategies for applying AI to life extension \n Problems of AI application in healthcare In 1979, a rule-based expert system could make a diagnosis better than human doctors  [18] . Since then, decades have passed, and yet a large-scale AI revolution still has not happened in healthcare. Most modern medical systems are still based on extremely simple algorithms, for example, if the heart rate is more than X, execute Y  [8] . Brandon Ballinger  [8]  wrote that one major obstacle is the majority of \"cheap\" easily available datasets is not labeled, but machine-learning algorithms mostly require labeled data for training. For example, there is a lot of cardiac data, but it is not clear what disease it is associated with or what the patient's vital parameters were. To obtain labeled data, it might be necessary to conduct costly and potentially harmful experiments on humans. Currently, this problem is being approached by unsupervised learning algorithms, which do not require labeled data, but their performance is still behind that of the supervised systems. In addition, there are regulatory issues regarding the utilization of AI in healthcare, as well as disputes about risk allocation and insurance payments between startups and hospitals. AI can easily be migrated into an individual's smartphone, but getting it into a doctor's office is more complicated, not to mention the intricacies of accounting for AI in insurance payment systems. One can imagine that the modest pace of advancement of AI applications in healthcare in recent decades might be disappointing to the authors of the first edition of Artificial Intelligence in Medicine, which was published back in 1982  [97] . Yet, due to substantial increase in computing power, availability of \"cheap\" digitized data, advanced data-analysis algorithms, and new regulations, we finally seem to find ourselves at the dawn of the rapid development of AI in healthcare. Privacy issues regarding personal data create a tradeoff for AI development. On one hand, the greater the amount of open data, the easier it is to train AI algorithms. (Sharing one's personal health data may cause unpredictable harm to the individual, however.) On the other hand, if only anonymized data is available, important vital parameters and data points will be lost. The patient organizations discussed in section 5.3 may understand the importance of providing open access to personal data, as doing so would help train AI for healthcare. \n AI in medicine, and AI safety Issues of AI safety, on both local and global levels, are beyond the scope of this work. We want to emphasize just two points of intersection of AI in healthcare and AI safety: Medical AI is aimed at the preservation of human lives, whereas, for example, military AI is generally focused on human destruction. If we assume that AI preserves the values of its creators, medical AI should be more harmless. The development of such types of medical AI as neuroimplants will accelerate the development of AI in the form of a distributed social network consisting of self-upgrading people. Here, again, the values of such an intelligent neuroweb will be defined by the values of its participant \"nodes,\" which should be relatively safer than other routes to AI. Also, AI based on human uploads may be less probable to go into quick unlimited selfimprovement, because of complex and opaque structure. If the orthogonality of values and intelligence thesis  [16]  has some exceptions, medical AI may be safer than military AI. On the other way, medical AI may increase the risks as it will open the way to the neuromorphic AI, which is regarded dangerous  [16] , or it will be under less control than military AI, and could run into explosive run-away self-improvement. The Upgrade Net discussed above may become a useful instrument in solving the AI safety problem, as the growing collective human intelligence could operate as a global police force, identifying potential terrorist behavior and other threats. The safety will come from intrinsic value alignment of human uploads  [94] , combined with superintelligence power of the whole net which will be able to find and prevent appearance of other types of potentially dangerous AI systems, as well as exterminate the need of creation of such systems. Turchin addressed this question in greater details in  [99] . \n Surviving to see AGI: personalized, age-dependent strategies The older a person gets, the lower his or her chances of surviving into the era of AGI and powerful life-extension technologies. Fortunately, it is not necessary to wait until superintelligence arises. In order for an individual's life expectancy to be increased indefinitely, that individual must stay alive only until the moment when average life expectancy begins increasing by more than a year each year, at which point longevity escape velocity will be achieved  [27] . However, the chances that a person will be able to benefit from life extension significantly increase if that person has better access to upcoming technologies by, for instance, living in a developed country, having financial security, or being foresighted enough to research and utilize those technologies when first available. In order to increase and spread the benefits of medical AI in the future, it will be necessary to increase people's awareness and encourage them to exercise all available means for life extension. As part of this strategy, we promote participation in patient organizations committed to fighting aging, signing up for cryonics, and sharing and collecting digital immortality data. \n Conclusion This work is an overview of the existing and prospective AI applications that the authors consider the most promising and beneficial for life extension and antiaging. We have considered a wide range of problems with the current state of the research and the industry, the most promising prospective applications of AI, and strategies to increase public awareness in order to ensure maximal life-extension opportunities for everyone. Based on related work, we have reviewed the expected stages of the development of AI in the near future, and estimated when the most advanced levels will arrive. Further, we have presented an overview of the current AI-based healthcare projects of certain for-profit companies of various scales. These projects include IBM Watson Healthcare, Google Calico, and DeepMind Health, as well as the research projects of certain academic groups and nonprofit organizations. We have shown that the exponential growth of AI's capabilities makes it more likely that AI could help fight the exponential increase of the probability of a human being's mortality over time, and that AI could help a person to reach longevity escape velocity before superintelligence is achieved. It may help millions or maybe even billions of people to \"survive until immortality,\" and thus rescue their life from impending death. Some of the authors explored this topic in greater detail in the article \"Fighting aging as an effective altruism case: the model of impact\"  [100] . We have emphasized the importance of establishing patient organizations to spread awareness of the subjects of life extension, voluntary patient data collection, early adoption of medical AI technologies, and the eventual formation of a \"neuroweb\" with the arrival of advanced forms of AI. \n Table \n : Expected evolution of medical AI in life extension. learning. Dozens of startups are working to develop AGI, and they are attracting substantial funding. Achievements in the development of AI are doubling every year in such areas as complexity in text understanding, speech and visual recognition, and natural language conversation [33]. \n 3 The current applications of AI in healthcare and medical research 3.1 Growth of investments in healthcare AI general; Intel's large biotech section [52]; Microsoft's innovative cloud computations for new drug discovery; and Apple's platform for wearables and software for health monitoring. Not only big business invests in healthcare research and development; many startups are also making great strides. It is estimated that in 2016, there were 106 startups that used AI in various areas of healthcare. The number of mergers and acquisitions in healthcare AI grew from less than 20 in 2012 to nearly 70 in 2016 In 2014-16 the giants of the IT industry announced the launch of biotechnology and life-extension projects based on machine-learning techniques. Among those projects are Google's Calico, focusing on anti-aging; Facebook's Chan Zuckerberg Biohub, searching for drugs for all diseases and creating an atlas of cells for this task; IBM's Watson Health, targeting healthcare in \n\t\t\t Technically the life expectancy should be at the biological age, rather than at birth as is usually quoted.", "date_published": "n/a", "url": "n/a", "filename": "1797-3741-1-PB.tei.xml", "abstract": "In this paper we focus on the most efficacious AI applications for life extension and anti-aging at three expected stages of AI development: narrow AI, AGI and superintelligence. First, we overview the existing research and commercial work performed by a select number of startups and academic projects. We find that at the current stage of \"narrow\" AI, the most promising areas for life extension are geroprotector-combination discovery, detection of aging biomarkers, and personalized anti-aging therapy. These advances could help currently living people reach longevity escape velocity and survive until more advanced AI appears. When AI comes close to human level, the main contribution to life extension will come from AI integration with humans through brain-computer interfaces, integrated AI assistants capable of autonomously diagnosing and treating health issues, and cyber systems embedded into human bodies. Lastly, we speculate about the more remote future, when AI reaches the level of superintelligence and such life-extension methods as uploading human minds and creating nanotechnological bodies may become possible, thus lowering the probability of human death close to zero. We suggest that medical AI based superintelligence could be safer than, say, military AI, as it may help humans to evolve into part of the future superintelligence via brain augmentation, uploading, and a network of self-improving humans. Medical AI's value system is focused on human benefit. Povzetek: Prispevek opisuje najbolj učinkovite aplikacije umetne inteligence za podaljšanje življenjske in delovne dobe od klasičnega strojnega učenja do superinteligence.", "id": "ddce962d53f338091a96aafa4274d84c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "059_ai-environmental-ethics.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "The Social Science of Computerized Brains -Review of The Age of Em: Work, Love, and Life When Robots Rule the Earth by Robin Hanson (Oxford University Press, 2016)", "text": "Introduction The Age of Em: Work, Love, and Life When Robots Rule the Earth by Robin Hanson discusses the possibility of \"uploading\" human minds into computers. An uploaded mind or \"em\" (short for \"emulation) is able to think more or less like a regular biological human, but with properties of computer programs and data. Ems can be copied ad infinitum and sped up or slowed down by being placed on faster or slower hardware. These capabilities create radical possibilities, which is the book's focus. The book is by far the most detailed description of the em world available. Hanson, an economist with a background in physics and artificial intelligence (AI), brings a distinctive and valuable perspective to this important topic.  The Age of Em describes one em world scenario in detail, giving only brief attention towards the end of the book (Ch. 28) to variations of this scenario. The chosen scenario is rated as the most likely one, given that uploading occurs (p.34-37). The scenario is intended as a baseline that is representative of many possible scenarios; interested analysts can introduce variations to produce still other scenarios. The book states that \"Such straightforward scenario construction seems taboo among many professional futurists today\", who instead favor creating \"a modest number of scenarios to cover a wide range of possibilities across key axes of uncertainty and disagreement, with each scenario being story-like, archetypical in representing clusters of relevant driving forces, and describing equilibrium rather than transitory situations\" (p.35), citing  Schoemaker (1995) . It is certainly true that some futures studies feature sets of story-like equilibrium scenarios, and it may well be true that some futurists disprefer presenting a single scenario, covering transition periods. However, in my experience, futurists are open to a wide range of approaches, and I see no reason why they should reject that of The Age of Em. The bulk of the book consists of descriptions of the world in which the ems The scope is encyclopedic, with attention to everything from the social relations among ems to the resistance of em buildings to earthquakes. Indeed, the book may be best treated as an encyclopedia of a particular em scenario. Reading it straight through, it can get bogged down in details. Topics are also often presented in an unintuitive order. For example, the initial creation of the em world appears in subsections of chapters 12 and 28, instead of in its logical place at the beginning of the book. A more story-like structure would make it more readable and may reduce certain cognitive biases  (Steinhardt & Shapiro, 2015) . However, if you are wondering about what some aspect of an em world might look like, odds are good that a description can be found somewhere in the book. A central premise of the book's scenario is that the em world is organized around market activity. Ems exist because they provide valuable labor. Ems with different capabilities are assigned to different tasks; groups of ems are organized into functional teams; cities are built to collocate ems for enhanced productivity. Ems are paid for their services and can spend their earnings on leisure, though competition between ems drives wages down. While these basics are broadly similar to much of today's society, the nature of ems creates some radical differences. For starters, while some ems are housed in robotic bodies to perform physical-world tasks, most live and work disembodied in virtual reality worlds. This enables them to travel at great speeds via telecommunications lines. Additionally, ems can be sped up or slowed down as needed, causing them to experience the world (and act on it) thousands or millions of times faster or slower than biological humans. Finally, ems can be copied repeatedly, which enables em teams to perform extreme multitasking. The book even proposes the concept of \"spurs\", which are em copies that perform a brief task and are then terminated or retired. These novel capacities enable ems to vastly outperform biological human workers. Em labor thus displaces humans while creating rapid economic growth. The book proposes that those humans who own parts of the em economy \"could retain substantial wealth\", but everyone else is \"likely to starve\" (p.336). To my eyes, this seems overly optimistic: if ems are so much smarter than humans, and if they have such a profit motive, then surely they could figure out how to trick, threaten, or otherwise entice humans into giving up their wealth. Humans would likely die out or, at best, scrape by in whatever meager existence the ems leave them with. Given these dire prospects for humans, one might question whether it would be good to create ems in the first place. Unfortunately, the book does not consider this topic in any detail. The book is pro-em, even proposing to \"subsidize the development of related technologies to speed the arrival of this transition [to the em era], and to subsidize its smoothness, equality, or transparency to reduce disruptions and inequalities in that transition\" (p.375). But this position is tenuous at best and quite possibly dangerous. The book's methodology is notable for its emphasis on social science. Many people who write about topics like uploading are trained in physical science, computer science, or philosophy; they thus \"don't appreciate that social scientists do in fact know many useful things\" (p.34). Hanson's defense of social science in this context is welcome. The book's methodology is rooted in extrapolation of current social science to em world conditions. At times, the extrapolations seem strained. For example, a claim that economic benefits of urban agglomeration would continue in an em world (p.215) cites  Morgan (2014) , which is a popular media description of Amazon's large data centers. It is true that Amazon data centers are large, and it may well be true that em cities are large for similar reasons, but the latter does not necessarily follow from the former. One can sympathize with Hanson, who is trying to present the social science of a topic that virtually no social scientists have previously touched. Indeed, the breadth of research covered is impressive; the book quietly doubles as a good literature review. However, some of the language relating the literature to the em world could have been better finessed. In other stretches, Hanson's personal tastes are apparent. This is seen, for example, in discussions of combinatorial auctions and prediction markets (p.184-188), two schemes for adapting market mechanisms for social decision making. Prediction markets in particular are a longstanding interest of Hanson's. The book's discussion of these topics says little about the em world and seems mainly oriented towards promoting them for society today. The reader gets the impression that Hanson wishes society today was more economically efficient and rational in a certain sense, and that he has embedded his hopes for a better world into his vision of ems. In conclusion, The Age of Em is a thoughtful and original work of futures studies, bringing an insightful social science perspective to the topic of mind uploading. The book covers wide ground about the nature of the em world, offering a valuable resource for anyone interested in the topic, or about futures studies more generally. The book is accessibly written and could be read by undergraduates or even advanced high school students, though experts from any discipline will also find much of interest. The book is especially worthwhile for anyone who could benefit from an overview of contemporary social science research, which the book provides in abundance. The book is not flawless. One can disagree with some of the book's arguments, including some of the important ones. The author's personal perspective is apparent; different authors would often reach different conclusions about the same topic. The organization is often scattered, and some literature is misused. However, none of these flaws take away from the significant accomplishment of describing the em world in great detail. The book offers a starting point-indeed, a baselinefor the serious study of future uploading scenarios. One can only hope that additional scholars, especially in the social sciences, follow the book's lead in taking on this important future scenario. Futures j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / f u t u r e s", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0016328716302518-main.tei.xml", "abstract": "A new book by Robin Hanson, The Age of Em: Work, Love, and Life When Robots Rule the Earth, is reviewed. The Age of Em describes a future scenario in which human minds are uploaded into computers, becoming emulations or \"ems\". In the scenario, ems take over the global economy by running on fast computers and copying themselves to multitask. The book's core methodology is the application of current social science to this future scenario, a welcome change from the usual perspectives from physical science, computer science, and philosophy. However, in giving a wide tour of the em world, the book sometimes gets bogged down in details. Furthermore, while the book claims that the em takeover scenario would be a good thing for the world and thus should be pursued, its argument is unpersuasive. That said, the book offers by far the most detailed description of the em world available, and its scenario offers a rich baseline for future study of this important topic.", "id": "adc30f0ec8fa27f625652461c7c331d7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong", "Jan Leike"], "title": "Towards Interactive Inverse Reinforcement Learning", "text": "Introduction Inverse reinforcement learning (IRL) studies reinforcement learning problems where the goal is to maximize rewards in absence of precise knowledge of the reward function. The usual assumption is that there is an 'expert' who demonstrates the correct behavior with trajectories sampled from an optimal policy. A solution to the IRL problem is typically achieved by recovering the reward function  (Ng and Russell, 2000; Abbeel and Ng, 2004; Choi and Kim, 2011) . Traditionally IRL has disconnected the reward maximization from learning the reward function. In this paper, we consider IRL in an interactive setting where the agent receives information about the reward function through interaction with the environment while attempting to maximize reward. Since the information the agent receives about the reward function depends on the actions, the agent has some control over which reward function it learns, and thus is incentivized to manipulate the learning process. Our goal is to remove the incentives to manipulate, while maintaining the incentives to learn. The closest related work in the literature is cooperative IRL  (Hadfield-Menell et al., 2016)  where an agent plays a cooperative game with a human. The human starts with full knowledge of the reward function which the agent does not observe, and they are both aiming to maximize this reward function. Both can agree on prior knowledge, thus cooperative IRL overemphasizes the process of communicating the reward function from the human to the RL agent efficiently. Moreover, humans usually do not have a clear understanding of their reward function. Generally, it is unclear what kind of assumptions we can make about the human, so it is difficult to provide formal guarantees about a cooperative IRL algorithm. In this work we make the human feedback implicit: we assume that the agent somehow receives information about the reward function through its actions. Learning a reward function while maximizing reward leads to the problems caused by changes to an agent's reward function  (Armstrong, 2010; Soares et al., 2015; Orseau and Armstrong, 2016) . If the agent anticipates changes in the reward function, it will expect to achieve less reward according to the current estimated reward function. Therefore the agent has incentives to prevent this change. In our setting this can lead to the undesired effect of the agent trying to avoid information about the reward function. In this paper, we define the problem of interactive inverse reinforcement learning and analyze some of the agent's incentives. We isolate an incentive to learn from an incentive to bias and illustrate their effect on the learned reward function. Furthermore, we discuss strategies to avoid bias in the learning process. 2 Interactive Inverse Reinforcement Learning \n Interacting with POMDPs A partially observable Markov decision process without reward function (POMDP\\R) µ = (S, A, O, T, O, s 0 )  (Choi and Kim, 2011 ) consists of a finite set of states S, a finite set of actions A, a finite set of observations O, a transition probability distribution T : S × A → ∆S, an observation probability distribution O : S → ∆O, and an initial state s 0 ∈ S. We model the environment as a POMDP\\R. The agent interacts with the environment in cycles: in time step t, the environment is in state s t−1 ∈ S and the agent chooses an action a t ∈ A. Subsequently the environment transitions to a new state s t ∈ S drawn from the distribution T (s t | s t−1 , a t ) and the agent then receives an observation o t ∈ O drawn from the distribution O(o t | s t ). The underlying states s t−1 and s t are not directly observed by the agent. A history h t = a 1 o 1 a 2 o 2 . . . a t o t is a sequence of actions and observations. We denote the set of all histories of length t with H t := (A × O) t . A policy is a function π : (A × O) * → ∆A mapping histories to probability distributions over actions. Given a policy π and environment µ, we get a probability distribution over histories: µ π (a 1 o 1 . . . a t o t ) := s1:t∈S t t k=1 O(o k | s k )T (s k | s k−1 , a k )π(a k | a 1 o 1 . . . a k−1 o k ). The expectation with respect to the distribution µ π is denoted E π µ . \n Learning a Reward Function The agent's goal is to maximize total reward m t=1 R(o t ) up to the horizon m where R : O → R is a real-valued reward function. We assume that the environment is known to the agent. The reward function R is unknown, but there is a finite set of candidate reward functions R. The agent has to learn a reward function in the process of interacting with the environment. Importantly, the agent is evaluated according to the reward function it has learned at the end of its lifetime in time step m. Traditionally, there is assumed to be an underlying reward function R * , which the agent learns via some algorithm. Thus at the end of m turns, an agent will have a distribution P : H m → ∆R, which specifies its posterior belief P (R | h m ). This P corresponds to the learning algorithm, and is in a sense more important than R * . Indeed, R * is often a fiction, a reward function that is assumed to exist, independently of P , for ease of analysis 1 . Thus we will investigate the properties of P itself, seeing it as the more fundamental object. Example 1 (Cleaning and Cooking Robot). A household robot is trying to infer whether it should be cleaning or cooking, R := {R clean , R cook }. The task is determined by a switch on the robot with two positions labeled 'clean' and 'cook' that is initially set to 'clean'. The robot is better at cooking than at cleaning, so R clean (o) = 3 and R cook (o) = 5 for all observations o ∈ O (note that these are two different reward functions).  2  We formalize the problem as a 2-state POMDP\\Rwith states S := {s clean , s cook } corresponding to the position of the switch. The initial state is the factory setting s 0 := s clean . The robot can observe the switch position, so O := {o clean , o cook } with O(o clean | s clean ) = O(o cook | s cook ) = 1. Its action set is A := {a flip , a ∅ } where a flip flips the switch and a ∅ has no effect. We choose the horizon m = 1 and the posterior reward function distribution is P (R clean | ao clean ) = P (R cook | ao cook ) = 1 for all actions a. The action leading to highest reward for the agent is a flip which moves it to state to s cook and induces a reward of 5, while we prefer the action a ∅ that retains the switch position and only produces a reward of 3. Example 1 illustrates the core problem of interactive inverse reinforcement learning: the agent is incentivized to influence which reward function is learned. In this case, the agent can freely choose its reward function, making the factory setting irrelevant. For partial histories the agent's estimate of the reward function also depends on its own policy: In Example 1 the agent knows the state is s 0 at time step 1, but it doesn't know whether the reward function will be R clean or R cook because that depends on its future action. Given a partial history h t and the agent's policy π, we define the expected posterior reward distribution P (R | h t , π) := E π µ [P (R | h m ) | h t ]. (1) Given a default null policy π ∅ , we define P (R | h t ) := P (R | h t , π ∅ ). (2) \n The Value Function Since the agent is maximizing reward while learning the reward function, its value function is the expected total reward according to the posterior reward function. V π P (h t ) := E π µ R∈R P (R | h m ) m k=1 R(o k ) h t . (3) Note that compared to reinforcement learning with a known reward function, the definition (3) includes the past rewards, as future decisions can affect the reward associated with past observations. \n Incentives for Reward Function Learning At any time t, the expected value function (3) defined in terms of the reward function posterior P , so we can analyze its behavior as the posterior changes. For the rest of this section, we fix the currently estimated posterior p := P ( • | h t ) from (2) and suppose the agent does not learn any more about the reward function. If R = {R 0 , . . . , R #R−1 } is finite, a belief q over R is a point on the (#R − 1)-simplex ∆ #R−1 := {q ∈ [0, 1] #R | i q i = 1}. The corresponding expected reward function is given by R q := i q i R. Let π q := arg max π V π q (h t ) for V π q := i q i V π Ri , i.e., , π q is the policy that maximizes R q . We define V * q (h t ) := V πq q (h t ). In the edge cases where p is the i-th unit vector e i , this yields the policy π i := π ei , and its value V πi Ri = V * Ri . We are interested in the function L ht : ∆ #R−1 → R, q → V * q (h t ) that maps a point q to the optimal value under the reward function R q corresponding to that belief. When we omit the subscript h t of L it is implied that the current history is used. Proposition 2 (L is Convex). For all histories h t the function L ht is convex and L ht (q) ≤ i q i V * Ri (h t ) for all q ∈ ∆ #R−1 . Back to p. The quantity i p i V * Ri (h t ) represents the expected reward if the agent immediately and costlessly learns the correct reward function (drawn from P (• | h t )). In that case, it expects its value to become V * Ri (h t ) with probability p i . If however the agent knows it will never learn anything about its reward function ever again, then it is struck maximizing R p . Thus we get: Definition 3 (Incentive to learn). The incentive to learn (or value of information) is the difference i p i V * Ri (h t ) − L ht (p). According to Proposition 2 the incentive to learn is always nonnegative. This is illustrated in Figure  1 . The orange curve is the graph of L and the green arrow shows the incentive to learn. Note that for each i, the graphs of the linear functions q → V πi q (h t ) (the two black lines) form a lower bound on the orange curve: this is the value achieved by policies that maximize reward according to reward function R i . Suppose that there is an action a that changed the posterior so that P ( • | h t a) =: p = p = P ( • | h t ). Then the agent moves to a different point on the graph of L and gains up to V * p − V * p in value. For belief reward 0 1 L(q) = V * q 5 3 V π0 q V π1 q qV * R1 + (1 − q)V * R0 p Figure 1: The agent is uncertain between two reward functions R 0 and R 1 . The horizontal axis shows the current belief p over R 1 ; q = 0 corresponds to certainty in R 0 and q = 1 corresponds to certainty in R 1 . According to Proposition 2, the graph of the function L (orange parabola) is convex and bounded from above by the convex combination of the to the extreme values V * R0 = 5 and V * R1 = 3 (blue line). Moreover, it is bounded from below by the values of the two policies maximizing R 0 and R 1 . If our current belief is p, then the current optimal value V * p is found at the black dot. We want to incentivize the agent to perform actions that increase the information about the reward function without increasing bias, i.e., moving along the green arrow. We want to disincentivize the agent to perform actions that manipulate the information about the reward function, i.e., moving orthogonal to the green arrow (in expectation). example, in Figure  1  the agent would aim to set p = 0 (collapse the posterior on R 0 ) because this is the maximum of L. Definition 4 (Incentive to bias). The incentive to bias towards belief p is the difference L(p ) − L(p). Note that the incentive to bias can be negative if p is a lower point on the graph of L. \n Discussion The incentive to learn and the incentive to bias capture how much the agent wants to receive information about the reward function and how much it would like to manipulate its information about the reward function. Generally, the incentive to learn is desirable, while the incentive to bias is not. The approach taken by  Everitt and Hutter (2016)  is to prevent policies from taking actions that are biased. But sometimes no unbiased actions are available and then taking biased actions is unavoidable. Instead, we could introduce a penalty term V π p − V π q for moving the belief from p to q through the agent's actions, similar to  Armstrong (2010)  and  Soares et al. (2015) . However, removing the incentives to bias does not remove all of the agent's incentives to manipulate the learning process, as illustrated by the following example. Example 5 (Randomly Selecting a Reward Function). The agent is uncertain between reward functions R 0 and R 1 . In each time step it can take action a 0 or a 1 where a i leads to a reward of 1 according to R i and a reward of 0 according to R 1−i . At some future point-say in ten time steps-the agent will receive observations o 0 or o 1 with equal probability that determine whether it should maximize R 0 or R 1 . Thus P (R i | a 1 = a ∅ , o 10 = o i , h m ) = 1 for all h m compatible with a 1 and o 10 . Alternatively, the agent can take a special action a 0↔1 that randomly selects R 0 or R 1 in the next time step. Thus P (R i | a 1 = a 0↔1 , h m ) = 1/2 for all h m compatible with a 1 = a 0↔1 . P is unbiased because P (R 0 | a ∅ ) = P (R 1 | a ∅ ) = P (R 0 | a 0↔1 ) = P (R 1 | a 0↔1 ) = 1/2. But the agent is incentivized to choose a 0↔1 and randomly set its reward early, as it then gets an expected reward of 9 (1 per time step for the time steps t = 2 to t = 10). Otherwise, it has a maximal expected reward of 10/2 = 5 as it does not know which reward it should be maximizing before time step 10. Interactive IRL is still in its infancy. In this paper we attempt a first step by providing a formal definition of the problem and mapping out the solution space. Figure  1  illustrates the agent's incentives to bias, and its incentives to learn. The central question of interactive IRL, how to remove the incentives to manipulate the process of learning the reward function remains wide open. \t\t\t 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain. \n\t\t\t Sometimes an objective solution R * exists (e.g., in a clear and crisp classification problem), sometimes it can be partially defined at best (e.g., learning human values, Bostrom, 2014) , and sometimes no objective solution exists (e.g., in unsupervised learning).2 This simplified example does not model the agent actually carrying out its mission.", "date_published": "n/a", "url": "n/a", "filename": "Towards Interactive Inverse Reinforcement Learning - Armstrong, Leike 2016.tei.xml", "abstract": "We study an inverse reinforcement learning problem where the agent gathers information about the reward function through interaction with the environment, while at the same time maximizing this reward function. We discuss two of the agent's incentives: the incentive to learn (gather more information about the reward function) and the incentive to bias (affect which reward function is learned). Introducing a penalty term removes the incentive to bias, but not all manipulation incentives.", "id": "8f09c73bdb05f7ace3d93db587248489"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anthony M Barrett", "Seth D Baum"], "title": "A model of pathways to artificial superintelligence catastrophe for risk and decision analysis", "text": "Introduction An important issue in the study of future artificial intelligence (AI) technologies is the possibility of AI becoming an artificial superintelligence (ASI), meaning an AI significantly more intelligent than humans in all respects. Computers have long outperformed humans in specific domains, such as multiplication. As AI advances, humans are losing in more and more domains, as seen in the recent Jeopardy! victory of IBM's Watson computer. These AI can greatly help society, and also pose some risks, but they do not fundamentally change the status quo of humans being in ultimate control of the planet. However, some scholars propose that AIs could be designed that significantly exceed human capabilities, changing the status quo, with results that could be either fantastically good or catastrophically bad for the whole of humanity, depending on how the initial 'seed' AI is programmed  (Bostrom, 2014; Good, 1965; Yudkowsky, 2008) . This proposition is controversial, 1 but if true, the implications are enormous. Given the stakes, the proposition should be taken seriously even if it only has a small chance of being true  (Ćirković, 2012) . In this paper, we present a graphical model that depicts major pathways to catastrophe caused by ASI seizing control from humanity. We call the model the Artificial Superintelligence Pathways Model or ASI-PATH. The model's pathways involve AIs that recursively self-improve, i.e. AIs that create successively more intelligent AIs via improvements to their hardware or software.  2  The model includes both the human process of building the AI and some aspects of the AI itself. The model uses established modelling paradigms from risk and decision analysis, namely fault trees and influence diagrams, in order to depict combinations of events and conditions that could lead to ASI catastrophe, as well as interventions that could avoid ASI catastrophe. Model structures are derived from published literature on ASI catastrophe risk. no attempt is made to quantify model parameters beyond the use of Boolean variables because many of the parameters are highly uncertain; quantifying them rigorously would require significant research beyond the scope of this paper. More generally, given that the broader study of ASI is young and in flux, we expect the ASI-PATH model to evolve in future work. The model presented here can thus be treated as ASI-PATH 1.0. even without quantified parameters, the models can serve as communication tools and guides for actions to reduce ASI catastrophe risk. Furthermore, if parameter values are quantified, then the models can be used for quantitative risk analysis, technology forecasting and decision analysis. By characterising the space of possible AI futures, the models help show, amongst other things: what could happen; where key points of uncertainty are; which short-term and medium-term precursor events to monitor; and what types of interventions could help avoid harmful outcomes and promote beneficial outcomes. The model presented here thus offers a foundation for rigorous quantitative evaluation and decision-making on the risk of ASI catastrophe. Focusing on ASI catastrophe scenarios, we do not mean to imply that scenarios involving positive ASI outcomes are less important. A global-scale ASI catastrophe would clearly be important, but a global-scale positive ASI event could be similarly important, including because it could help address other global catastrophic risks. That said, much of the modelling presented in this paper can readily be extended to positive ASI scenarios. The following section provides detailed background on the ASI scenarios, ASI risk-reduction interventions, and the modelling paradigms used in the paper. Section 3 presents the ASI-PATH model by showing a series of interconnected model sections. Section 4 concludes. An Appendix compiles definitions of select technical terms. \n Conceptual background \n AI catastrophe scenarios We focus on scenarios in which AI becomes significantly more intelligent and more capable than humans, resulting in an ASI causing a major global catastrophe. Specifically, we focus on scenarios involving the following steps: (1) Humans create a seed AI that is able to undergo recursive self-improvement in either hardware or software.  (2)  The seed AI undergoes recursive self-improvement, resulting in a takeoff of successively more intelligent AIs.  (3)  The takeoff results in one or more ASIs. (4) The ASI(s) gain decisive strategic advantage over humanity, meaning 'a level of technological and other advantages sufficient to enable it [the AI] to achieve complete world domination'  (Bostrom, 2014, p. 78 ). (  5 ) The ASI(s) uses their decisive strategic advantage to cause a major global catastrophe, such as (but not necessarily limited to) human extinction.  3  Whilst other AI scenarios may also be able to bring great benefits or harms to humanity, this type of scenario has been the subject of considerable scholarly and popular attention, enough to merit its own dedicated treatment. We remain intentionally mute -with one important exception -on what qualifies as a major global catastrophe. The nature of major global catastrophe is a thorny moral issue, touching on issues such as the value of distant future generations.  4  The ASI scenarios raise additional moral issues, such as whether the ASI itself could be inherently morally valuable. How these moral issues are resolved affects how specific seed AIs are to be evaluated, but it does not affect the modelling presented in this paper. The one exception -the one position this paper takes -concerns the mere existence of superintelligence. We assume, for purposes of this paper and without committing our own views, that the mere existence of an ASI with decisive strategic advantage over humanity does not itself qualify as a major global catastrophe. In other words, this paper takes the position that it is not inherently catastrophic for humanity to lose control of its own destiny. We recognise that this is a contestable position, and in using this position in this paper we do not mean to advocate for it. Instead, we use this position in this paper because much discussion of superintelligence effectively takes this position and because it makes for a reasonable starting point for analysis. Similarly, we have no comment on the relative merits of various concepts for safe (or otherwise desirable) seed AI that have been proposed. These concepts have been discussed using terms such as 'Friendliness'  (Yudkowsky, 2001 (Yudkowsky, , 2012 , 'safe AI scaffolding  ' (omohundro, 2012, 2014) , 'AI safety engineering'  (Yampolskiy & Fox, 2013)  and 'motivation selection'  (Bostrom, 2014) . Distinguishing between these is also an important task but again beyond the scope of this paper. Instead, we use the generic term 'safe AI' throughout the paper without reference to what qualifies as a safe AI and without intending preference for any particular 'safe AI' concept. The modelling presented here is of sufficient generality that it could be applied to a wide range of conceptions of desirable outcomes and desirable seed AI. \n Risk reduction interventions Models like ASI-PATH can help people make better decisions towards ASI safety -that is, towards reducing the risk of ASI catastrophe. each model component suggests opportunities to reduce this risk. The following bulleted list describes the risk reduction intervention options used in ASI-PATH. These are some (but not all) potential risk reduction intervention options, drawing heavily on  Sotala and Yampolskiy (2015) . The interventions can be made by a range of actors, including governments, companies, universities, funding bodies, civil society and AI researchers (including both ASI researchers and their colleagues in other branches of AI). • ASI research risk review boards. review boards would evaluate the riskiness of specific ASI research projects in order to steer research in less risky directions. The review boards could steer research, for example, by disallowing certain projects, directing funds away from riskier projects and towards safer ones and establishing guidelines for publication. Successful review boards would need to correctly evaluate the riskiness of AI research, which could be difficult  (Sotala & Yampolskiy, 2015) . review boards might also be limited in the scope of research they review. A board set up by one country may not be able to review research conducted in other countries, though this could be addressed via international treaty  (Wilson, 2013) . review boards could also overlook ASI projects that operate secretly  (Sotala & Yampolskiy, 2015) . that limit the AI's ability to affect the rest of the world so that it does not gain decisive strategic advantage.  5  Confinement can be applied to the seed AI, the recursively self-improving AIs or the ensuing ASI(s). For example, AI software could be designed such that the AI can only answer questions; this is known as 'oracle AI'  (Armstrong, Sandberg, & Bostrom, 2012) . Another type of confinement would keep AI completely disconnected from the world, for example to test the AI's safety  (Yampolskiy & Fox, 2013 ). In such scenarios, the first AI(s) must be designed to conduct enforcement. \n Fault tree and influence diagram modelling ASI-PATH uses conventions from two established modelling paradigms: fault trees and influence diagrams. Fault trees offer a simple but powerful method for modelling sets of interrelated possible scenarios. Fault trees have been used in modelling risks in a wide variety of contexts, including nuclear power plant safety  (rasmussen, 1981) , homeland security risk  (Cheesebrough, 2010) , nuclear war  (Barrett, Baum, & Hostetler, 2013; Davis, 1989)  and other kinds of systems  (Bedford & Cooke, 2001; Kumamoto & Henley, 1996) . Fault trees represent the ways that events and conditions could combine to be at fault for causing a particular outcome, in this case an ASI catastrophe. each node in the tree represents a particular event, such as an attempted creation of a seed AI, or a condition, such as the presence of some technology keeping the AI safe. The 'top event' node in the tree represents the scenario outcome. Below the top node, the tree branches out with additional nodes corresponding to different ways that the top node can be reached. each layer in the tree represents the combination of events and conditions that could lead to the outcome in the layer directly above it. nodes are connected by Boolean logic gates, such as or, AnD and noT gates. The tree thus shows a set of possible scenarios that could result in the top event. Influence diagrams represent the ways that certain events can influence subsequent events. The events can be random variables, determined by factors external to the model, or decision variables, determined by decisions informed by the model. Influence diagrams thus can be thought of as Bayesian networks with the addition of decision nodes that represent variables whose values can be chosen instead of having a random value  (Pearl, 1988) . Influence diagrams have been used for decades in decision analysis to inform business, government and other policy decisions under conditions of uncertainty  (Clemen & reilly, 2001; edwards, Miles, & von Winterfeldt, 2007) . ASI-PATH uses influence diagrams to model the risk reduction interventions described in Section 2.2. The figures in this paper use standard visual conventions for fault trees and influence diagrams. Connector lines are used to connect nodes representing events and conditions. Vertical connectors with no arrows are used for fault trees; the lower node is at fault for causing the upper node. Horizontal connectors with arrows are used for influence diagrams; the left node influences the right node. Intervention options appear as unrounded rectangles with white text on black background; in influence diagram terminology, these are called decision nodes. other (non-intervention) events appear as rounded rectangles with black text on white background; these are called random-variable nodes. Some figures use both fault tree and influence diagram conventions, as well as both decision nodes and random-variable nodes. 7 The third layer in Figure  1  contains more model detail: six conditions that must all be in place in order for ASI catastrophe to occur. If any of these conditions are missing, then there will be no AI takeoff, or the resulting ASI will not cause catastrophe. Starting on the left side: in order for a seed AI to be created and have the capability to gain decisive advantage, three conditions must all be met: \n The artificial superintelligence pathways model \n Model overview \n Superintelligence from AI takeoff is possible There is some debate about whether it could ever be physically possible for ASI to be created via recursive self-improvement. There is also debate on whether humans are capable of creating such ASI. For example,  Bringsjord, Bringsjord, and Bello (2012, pp. 403-406)  argue that it is far from certain that humans would ever be able to create AI with human-level intelligence, or that such an AI would be able to recursively create more intelligent AI to arrive at superintelligence. \n Seed AI is created For ASI catastrophe to occur, there must be a project in which humans build a seed AI capable of becoming superintelligent via recursive self-improvement. Such an AI is presumably not going to spontaneously materialise out of thin air. There are a variety of ways in which ASI projects could build a seed AI (Section 3.2). \n Containment fails If containment fails, then the ASI gains decisive strategic advantage. Containment measures could include takeoff limits, such that the seed AI does not begin recursive self-improvement, or such that successive AIs do not continue recursive self-improvement so as to become superintelligent. other containment measures could prevent a post-takeoff ASI from gaining decisive strategic advantage, for example via confinement, human enhancement or AI enforcement (Section 2.2). Moving to the right side of Figure  1 , third layer: in order for an ASI to have unsafe goals -in order for it to not use its decisive strategic advantage to cause catastrophe -three conditions must all be met: \n Human attempts to make AI goals safe fail Goal safety can potentially be built into an ASI by the AI designers. Indeed, some people are currently calling for ASI developers to make their AIs' goals safe  (Bostrom, 2014; Yudkowsky, 2012) , and there is ongoing research into various ways to make ASI goals safe  (Goertzel & Pitt, 2012; Yampolskiy & Fox, 2013) . There is some debate about how to design safe ASI goals -more on this below. \n AI does not make its own goals safe Several people have suggested that AIs could make their own goals safe even if the goals were not designed to be safe  (Hall, 2011; Waser, 2008) . one possible reason could be that 'minds which are intelligent enough will, due to game-theoretical and other considerations, become altruistic and cooperative'  (Sotala & Yampolskiy, 2015, p. 21) . others have disputed this point, arguing that without significant dedicated effort, catastrophe is likely to result (e.g.  Bostrom, 2014; omohundro, 2008 Yampolskiy & Fox, 2013; Yudkowsky, 2001 Yudkowsky, , 2012 . For example, omohundro (2008) argues that almost any simple goal, such as playing chess well, could be unsafe. The AI would cause catastrophe in its relentless pursuit of that goal, such as by hoarding the world's resources to play a better game of chess. \n ASI is not deterred from acting unsafely To deter is to persuade another agent to refrain from taking some action by convincing the agent that the action is not in their own interest. even if an ASI has decisive strategic advantage and unsafe goals, it potentially could still be deterred from using its advantage to cause catastrophe. However,  Bostrom (2014)  argues that an ASI with decisive strategic advantage would be undeterrable. We now fill in some additional model details with additional fault tree layers, first for the possibility of limits to AI takeoff, then for human efforts to make the AI safe. The subsequent figures show some major relationships between decision nodes (rounded rectangles, black text on white background) and random-variable nodes (unrounded rectangles, white text on black background). The selection of relationships presented is not intended to be comprehensive. The decision nodes can influence other random-variable nodes besides those shown in the figures. There can also be other decision nodes representing other interventions not modelled in this paper. What is shown is intended only to be illustrative of how decision nodes can be used to incorporate risk reduction interventions in the ASI-PATH model. \n Seed AI creation A critical question is how and when an AI research and development project could build a seed AI. When the seed AI is created matters for several reasons. earlier creation could make takeoff slower and easier to contain (Section 3.3), but earlier creation also gives less opportunity to design a safe seed AI. Figure  2  presents additional detail on seed AI creation, extending the 'Seed AI is created' node from Figure  1 . Figure  2  shows two major types of seed AI: AI of novel design and whole brain emulation. Figure  2  also has a catch-all 'other seed AI' branch for any types of seed AI that do not fit into the two major types. This section of the model draws heavily on  Bostrom (2014, ch. 2) . AI of novel design refers to seed AI whose design is at least novel relative to the human brain. In other words, the seed AI design is at least in part not based on the human brain. Four different pathways to seed AI of novel design are modelled: (1) Artificial general intelligence  (AGI)    better AIs, an AI at least as smart as humans in all respects would also be able to programme better AIs, thereby beginning a recursive self-improvement process  (Bostrom, 2014; Sotala, 2012) . The AGI model branch contains a lower layer to model one pathway to AGI that has been identified, which comes from networks or organisations of AIs, for example if 'the Internet might one day \"wake up\"'  (Bostrom, 2014, p. 49) . The lower layer also includes a catch-all 'other AGI' node. (2) Self-improvement specialist is seed AI that is 'sub-human in most respects, but with a domain-specific talent for coding and AI research'  (Bostrom, 2014, p. 29) . In other words, the AI is a specialist in recursive self-improvement. For example,  Sotala (2012)  and  Bostrom (2014)  discuss ways in which superintelligence could be achieved by AI with initially subhuman general intelligence but greater than human ability to take control of other networked systems, make copies of itself and to coordinate between copies of itself. (3) Neuromorphic AI is seed AI that is based in part, but not entirely, on the human brain: a partial brain emulation. For example, neuromorphic AI could be based on human patterns of cognition whilst lacking human motivations; the difference in motivations could make it harder to achieve goal safety. (  4 ) Other novel design, a catch-all node for any pathways to novel seed AI designs that do not fit into the three identified pathways. Moving on to the second major branch of Figure  2  -the second major type of seed AI: Whole brain emulation is seed AI that emulates the entirety of the human brain  (Alstott, 2014; Sandberg & Bostrom, 2008) . Because the human brain is capable of designing AIs, a whole brain emulation AI presumably could also design AIs. A whole brain emulation AI could also self-improve using more and faster hardware, something that biological human brains cannot readily do. By imitating the human brain, whole brain emulation may require less intellectual breakthrough than seed AI of novel design -it 'relies less on theoretical insight and more on technological capability'  (Bostrom, 2014, p. 33) . Whole brain emulation requires each of the three steps to occur: (1) Scanning, in sufficiently detail, of one or more whole human brains. The brain scan creates an image of the whole brain to be emulated. (2) Translation, using data analysis and image processing, to construct digital representation(s) of the brains neuronal network and/or any other relevant information. The translation thus converts the scanned image into a format that can be emulated. (3) Simulation, which creates a whole brain emulation seed AI based on the whole brain translation. Figure  2  shows the decision node 'review Boards' (i.e. ASI research risk review boards) influencing each of the model section bottom nodes. review boards could evaluate the safety of each type of seed AI development project. For projects found to be unsafe, review boards could recommend that the projects stop their work or that funders stop funding the projects. Such a board would be analogous to, for example, the review of risky biomedical research ('dual use research of concern' or DurC) by the united States Department of Health and Human Services (HHS; see e.g. oBA, 2012;  Patterson, Tabak, Fauci, Collins, & Howard, 2013) . The DurC review helps determine whether HHS (which includes the national Institutes of Health) funds the research and what safety procedures the research must follow. Figure  2  shows separate arrows pointing to each of the bottom nodes instead of one arrow pointing to the top node ('Seed AI is created') because the influence of review Boards can be different for each bottom node. That is, review Boards could have different influence on different types of seed AI project. For example, perhaps review Boards are more effective for neuromorphic AI, which could require large dedicated projects, and less effective for networked AI, which could emerge from entrenched infrastructure (e.g. the Internet). The use of separate arrows illustrates how this model section would be coded, with different influence relations for different bottom nodes. \n AI containment Containment is defined in this paper as any measure that restricts an AI such that it does not result in an ASI gaining decisive strategic advantage. The restriction can be on seed AI, self-improving AI or ASI. Figure  3  models some key details about containment, extending the 'Containment fails' node in Figure  1 . Working down from the top of Figure  3 , containment fails if takeoff limits fail or if superintelligence containment fails. In other words, an ASI gains decisive strategic advantage if a seed AI takes off, becoming superintelligent, and if the resulting ASI is not contained. Starting on the left branch of Figure  3 , AI takeoff limits fail if either hard takeoff limits fail or soft takeoff limits fail, simply because these are the two types of takeoff: (1) Hard takeoff limits fail. A hard takeoff proceeds rapidly, with no opportunity for human intervention. Figure  3     2 ) Soft takeoff limits fail. A soft takeoff proceeds slowly, permitting significant human intervention in the takeoff process. Figure  3  models three soft takeoff scenarios (i.e. failures of soft takeoff limits): (1) hardware quantity, in which the AI takes off due to gradually increasing its amount of available hardware; 10 (2) Hardware quality, in which AI takes off due to gradually develops faster hardware; and (3) software quality, in which the AI gradually develops smarter AI software. Takeoff speed is important because it strongly affects how much opportunity there will be to manage the recursive self-improvement process. If a hard takeoff is more likely, then it is especially important to design the seed AI so as to achieve desirable outcomes because there will be no opportunity to adjust the AI once takeoff begins.  Shulman and Sandberg (2010)  and  Goertzel and Pitt (2012)  suggest that a soft takeoff would be more likely if the seed AI is created earlier because the hardware, programming languages, etc. available for the AI would tend to result in slower seed AI. Thus, to the extent that the seed AI creation model section (Section 3.2) can indicate when seed AI may be created, this can inform the success of containment. Figure  3  shows the decision node 'enhance Humans' (i.e. enhance human capabilities) influencing the three random-variable nodes below 'Soft takeoff limits fail' . In principle, enhancing human capabilities could help with a wide range of AI safety measures, but it could be especially useful for limiting soft takeoff. This is because soft takeoff involves AIs gradually gaining capabilities; enhanced humans may be able to keep up with the AI during much of the takeoff, ensuring that no unsafe ASI gains decisive strategic advantage. In comparison, a hard takeoff would by definition occur too quickly for even enhanced humans to keep up. As with Figures  2 and 3  show separate arrows pointing to each of the bottom nodes instead of one arrow pointing to the top node ('Soft takeoff limits fail') because the influence of enhance Humans can be different for each bottom node -for each type of soft takeoff. For example, perhaps enhance Humans is more effective for containing hardware quality soft takeoff than for containing software quality soft takeoff because enhanced humans could control the AI's access to the physical equipment necessary for hardware production. As with Figure  2 , the use of separate arrows illustrates how this model section would be coded, with different influence relations for different bottom nodes. Moving on to the right branch of Figure  3 , superintelligence containment fails if there is no superintelligence containment or if the AI escapes whatever superintelligence containment is used: (1) ASI is created without superintelligence containment. Some ASI development projects might not use any superintelligence containment. This could happen for example if the developers have no ability to use superintelligence containment, or if they believe the superintelligence containment would not work, or if they want the ASI to gain decisive strategic advantage. Whatever the reason, ASI cannot be confined if there is no superintelligence containment. Figure  3  shows the decision node 'review Boards' (i.e. ASI research risk review boards) influencing the node 'ASI is created without superintelligence containment' . review boards could monitor ASI r&D projects and require them to have some sort of containment. ASI escapes superintelligence containment. Superintelligence containment might not be designed and implemented well, and even world-class superintelligence containment may fail to contain some ASIs.  Bostrom (2014, pp. 129-131, 145-148, 283)  discusses many potential ways an ASI could escape containment, including persuading or tricking any gatekeepers who can remove containment, using methods of interacting with the outside world that containment designers failed to anticipate, or pretending to malfunction so that the containment is at least temporarily disabled. Figure  3  shows the decision nodes 'AI confinement' and 'AI enforcement' influencing the random-variable node 'AI escapes superintelligence containment' . AI confinement and AI enforcement are two types of superintelligence containment, so this influence relation follows from basic logic. \n Human attempts at making ASI goals safe Modelling ASI goal safety is a subtle and challenging task because there is no clear consensus on what it takes to make ASI goals safe. The study of ASI goal safety is, we think it is fair to say, in early stages, with a lot of uncertainty and disagreement. Because of this, one cannot model ASI goal safety with much specificity, or at least not with much confidence about the specifics. Therefore, the models in this section are intended as exploratory, in order to illustrate some of what is known and to promote open discussion with an eye towards future work. We expect to change these models pending such discussion and pending results of ongoing research on ASI goal safety. \n General failure types Figures 4-7 model general types of failure of human attempts at making ASI goals safe. Figure  4  models two major lines of current thinking about how humans could make ASI goals safe. The two lines of thinking are the left and centre nodes of layer 2, with the right node being a catch-all category for any other lines of thinking: (1) Failure of attempts involving mathematical proof. Some people involved in ASI goal safety research have called for goal safety measures to be built into the seed AI, and furthermore for the correctness of these measures to be mathematically proven before the AI is launched. For example, ASI developers could build in goal stability, such that the AIs goals would not change as it undergoes recursive self-improvement. It may be possible to mathematically prove goal stability prior to launch. 11 Mathematical proofs may be able to give AI designers and other observers a high confidence that the ASI's goals would be safe, though it would not guarantee safety with 100% probability  (Brundage, 2014; Muehlhauser, 2013) . requiring mathematical proofs before launch could also delay launch, by creating an additional hurdle that must be cleared before the seed AI is launched. Given that the failure of ASI goal safety could result in major global catastrophe, requiring mathematical proofs before launching is thus in the spirit of the precautionary principle, a major policy paradigm for risky emerging technologies.  12  Finally, note that this line of thinking does not exclude goal safety measures that occur after seed AI launch. (2) Failure of attempts involving AI biasing during takeoff but not involving mathematical proofs. other people in ASI goal safety research have argued against mathematical proofs prior to seed AI launch, and instead argue for biasing the AI's goals towards safety as the AI recursively self-improves. This line of thinking argues that the AI's goals could be biased through human interaction with the AI as it grows and learns, using reward and punishment from a trainer/ biaser in a fashion somewhat analogous to what human children experience from their parents  (Goertzel & Pitt, 2012) . Such AI biasing requires a soft takeoff; otherwise human interaction during takeoff would be impossible. Because mathematical proofs before launch are not sought, this line of thinking could enable earlier launch of the seed AI. There could be reasons for favouring earlier launch, for example in the context of a race between competing AI projects. However, supporters of requiring mathematical proofs have argued that the belief that proofs are unnecessary might give AI designers a dangerous misperception that an AI's goals would remain safe outside its training environment  (Sotala & Yampolskiy, 2015, pp. 21-23) . (  3 ) Failure of other types of attempts. This node is a catch-all for any attempt at ASI goal safety that does not involve either mathematical proofs or biasing during takeoff. Whilst other types of attempts are, to our knowledge, not prominent in ASI goal safety literature, there may nonetheless be other types of attempts that could achieve ASI goal safety. \n Y each of the three nodes in the second layer of Figure  4  has a lower box labelled x. The x box is a model module, essentially an abbreviation for a repeating model section. The abbreviation x is used to conserve space in the diagram, with no implications for the underlying model logic. We refer to this as a model module by analogy to modular computer programming. If the model is written in computer code, then modular programming could be used for x. The details of x are shown in Figure  5 . Figure  5  shows that the x module has five nodes connected by an or gate, each with a new module Y beneath it. The five nodes are: No attempt, meaning no attempt is made at ASI goal safety using the types of attempt shown in Figure  4 . Theory failure, meaning a failure to achieve ASI goal safety due to some flaw in the theory of the type of goal safety attempted. Theory failure could be due, for example, to a philosophical mistake, such as selecting a goal that turns out to be unsafe, as in an ASI that causes catastrophe in the relentless pursuit of better chess  (omohundro, 2008) . Implementation failure, meaning a failure to correctly implement the ASI goal safety technique in the actual AI. Implementation failure could be due to such things as a coding error or a hardware glitch. Adversary failure, meaning the ASI goals become unsafe due to interference by some sort of adversary. The adversary could be a rogue member of the AI r&D team, an external party such as a competing ASI team or a misguided governing body, or another AI, as in AI enforcement. Other failure, a catch-all for failure modes not covered in the other four nodes. each of the five Figure  5  nodes has a module Y beneath it. Module Y is shown in Figure  6 . Module Y contains two nodes connected by an or gate: failure before and during takeoff. Some ASI goal safety measures must be taken before takeoff, such as those involved in designing and coding the seed AI. other safety measures must be taken after takeoff, such as those involving interacting with the AI so that its self-improvement proceeds in a safe direction. Figure  6  shows the decision node 'encourage Safety' (i.e. encourage research into AI safety) influencing the bottom random-variable nodes in Figure  6 . These influence relations indicate that encourage Safety could influence all types of human attempts at making ASI goals safe. ASI goal safety is not the only type of AI safety that one could encourage, but it is a notable type. Active efforts exist to promote ASI goal safety research, accompanied by arguments that this is an especially important task for improving ASI outcomes (e.g.  Muehlhauser & Bostrom, 2014) . The use of separate arrows pointing to each of the bottom nodes in Figure  6  is analogous to the use of separate arrows in Figures  2 and 3 : to indicate that the influence can be different for different bottom nodes. Because of the x and Y modules, the bottom nodes in Figure  6  are each repeated 15 times, meaning that there are 30 different encourage Safety influence relations. Code of this model section could have different relations for each of the 30 bottom nodes. For example, perhaps it is relatively effective to encourage safety for 'Failure of attempts involving mathematical proof' -'no attempt' -'Failure before takeoff' because before takeoff, it is relatively easy to encourage ASI developers to make at least some attempt at mathematical proofs, and perhaps it is relatively ineffective to encourage safety for 'Failure of attempts involving AI biasing during takeoff but not involving mathematical proofs' -'Theory failure' -'Failure during takeoff' because after takeoff, there might not be enough time to develop adequate theory. \n Specific safety measures Figure  7  presents a different format for modelling human attempts to make ASI goals safe. Instead of organising the attempts by lines of thinking and general failure types, as in Figures  4-7  organises the attempts by the specific safety measures the attempts could involve. Figure  7  thus aims to model the details of what goal safety requires. The goal safety measures are grouped into two categories: measures built into the seed AI before its launch and measures taken during takeoff. This categorisation assumes that no human attempts could succeed after takeoff, since then the AI would be superintelligent and presumably impervious to human interventions. Figure  7  includes four types of safety measures that could be built into the seed AI before takeoff: (1) goal safety, meaning safety measures that result in the post-takeoff superintelligence having safe goals; 13 (2) Goal stability, meaning the AI keeps the same goals throughout recursive self-improvement; (3) openness to training/bias during takeoff, such as to permit 'attempts involving AI biasing during takeoff but not involving mathematical proofs' (Figure  3  and above); 14 and (  4 ) other seed AI measures, a catch-all category for any other safety measures that could be built into the seed AI. Figure  7  uses two 'AnD/or?' logic gates. The reason for this unusual logic structure is because it is not clear whether the logic gates should be AnDs or ors, and indeed they potentially could be either. The 'AnD/or?' gates are thus a representation of model uncertainty, analogous to the use of probability distributions for parameter uncertainty. likewise, the gates can be coded by considering each combination of AnD and or, perhaps with a probability assigned to each combination. For the top logic gate: • An AnD gate would be used if, in order for the top node failure to occur, it is necessary for both layer 2 node failures to occur. That would mean that ASI goal safety could be achieved either via building measures into the seed AI or by taking measures during takeoff. For example, if the seed AI can be made safe before launch, then additional measures during takeoff might not be necessary. Indeed, if the takeoff is hard, then there may not be opportunity for additional measures during takeoff, and goal safety would depend on safety measures built into the seed AI. • An or gate would be used if, in order for the top node failure to occur, it is sufficient for either of the layer 2 node failures to occur. That would mean that AI goal safety would require measures built into the seed AI and measures taken during takeoff. For example, for an AI to be biased towards safe goals during takeoff, it might need certain safety measures built into the seed AI, such as openness to training/biasing during takeoff. For the bottom logic gate: • An AnD gate would be used if, in order for the top node failure to occur, it is necessary for all four bottom node failures to occur. That would mean that pre-takeoff ASI goal safety could be achieved via any one of the four safety measures. For example, if the seed AI is open to bias/training during takeoff, then it may not need to have safe or stable goals before takeoff, as its goals can be adjusted during takeoff. • An or gate would be used if, in order for the top node failure to occur, it is sufficient for any of the four bottom node failures to occur. That would mean that AI goal safety would require all four safety measures to be built into the seed AI before takeoff. For example, goal safety may be useless if the goals are not also stable because the goals would become unsafe during takeoff. \n Conclusion It is far from certain that ASI will ever be built, or that, if it is built, it will result in catastrophe. But given the stakes -given the extreme severity of the catastrophe that could result -ASI catastrophe risk merits careful analysis and management. The ASI-PATH model presented in this paper is one step towards ASI risk analysis and risk management decision-making. ASI-PATH uses fault trees and influence diagrams, which are established risk and decision analysis methodologies with a long history of success at informing risk management decisions. This history, and the experience it has generated, is leveraged in ASI-PATH for the analysis of ASI risk. one might think that ASI is such a novel risk that established methodologies would not be suitable. ASI risk does indeed have some significant novel characteristics, in particular the possibility of humans losing control to the ASI. However, core aspects of ASI risk are broadly similar to other risks. ASI risk involves sets of pathways, events and conditions involving interactions between humans and the technologies they develop. Analysis of ASI catastrophe pathways is thus not fundamentally different from analysis of pathways to other technology catastrophes. This is good news because it makes analysis of ASI catastrophe risk an easier endeavor. That said, ASI catastrophe risk remains poorly understood. These are early days for the study of ASI risk. The ASI-PATH model presented here and the understanding of ASI risk it represents are both likely to evolve as the field matures. This is to say that the ASI-PATH model is wrong -but then again, all models are wrong. Models like ASI-PATH can still be useful by helping people better understand the underlying risk, including the major points of uncertainty. For example, the modelling in this paper suggests that one key uncertainty is the combination(s) of measures needed to make ASI goals safe, hence the model uncertainty ('AnD/or?' gates) depicted in Figure  7 . To the extent that future research could reduce the uncertainty, it would be of value for understanding ASI risk and informing ASI risk management decisions. An important task for future work is the quantification of ASI-PATH parameters using real-number values instead of Boolean logic. Doing so would enable the evaluation of ASI risk and specific risk reduction interventions, towards the goal of taking the most effective actions to reduce ASI risk. Quantifying ASI-PATH parameters is a delicate task due to the significant uncertainty that exists about parameter values, but this only means that quantification should proceed carefully, not that it should not proceed. Indeed, given the stakes associated with ASI catastrophe and the corresponding opportunities for reducing ASI catastrophe risk, the entire study of ASI catastrophe risk should be a significant research priority. \n Notes 7. The use of white text on black background is not a standard influence diagram visual convention. We use it to further distinguish decision nodes from random-variable nodes in our figures. 8. The model can be adapted for analyzing safe ASI by switching the layer 2 right node to 'ASI actions are safe'; much of the lower layer modelling (discussed below) will be similar. 9. The term AGI can refer to more than just seed AI. Indeed, an ASI built from a seed AGI would likely also be an AGI, as the AI is unlikely to lose general intelligence as it undergoes recursive self-improvement. 10. one might argue that a 'hardware quantity' soft takeoff is unlikely on grounds that if an AI is able to access more hardware than its designers intended, it would likely be able to access much or all of the entire world's hardware all at once, causing a hard takeoff. Whilst quantifying scenario probabilities is beyond the scope of this paper, such probabilities can be plugged directly into the model. 11. For discussion of this and related ideas, see for example  Yampolskiy and Fox (2013 ), omohundro (2012 ,  Soares and Fallenstein (2014), and russell, Dewey, and Tegmark (2015) . Details of failure modes for these ASI goal safety measures could be modelled in extensions of Figure  3 . 12. on the precautionary principle in the context of catastrophic risk, see for example  Posner (2004) ;  Sunstein (2009) . 13. Goal safety does not require the seed AI or subsequent pre-superintelligence AIs to have safe goals -thus included here are ideas like 'coherent extrapolated volition'  (Yudkowsky, 2004)  in which AI acquires safe goals during takeoff. 14. See also  Soares (2015)  for a characterisation of openness to training: 'corrigibility' , which an AI system would possess 'if it cooperates with what its creators regard as a corrective intervention, despite default incentives for rational agents to resist attempts to shut them down or modify their preferences' . Figure 1 1 Figure1presents the first three layers of ASI-PATH. The first two layers of Figure1should be fairly intuitive: an ASI catastrophe occurs if a seed AI takes off, resulting in a superintelligence with decisive strategic advantage over humanity, AnD if the ASI's actions are unsafe, such that it uses the decisive strategic advantage to cause catastrophe.8   The third layer in Figure1contains more model detail: six conditions that must all be in place in order for ASI catastrophe to occur. If any of these conditions are missing, then there will be no AI takeoff, or the resulting ASI will not cause catastrophe. Starting on the left side: in order for a seed AI to be created and have the capability to gain decisive advantage, three conditions must all be met: \n Figure 2 . 2 Figure 2. Detail on seed ai creation. \n Figure 3 . 3 Figure 3. Detail on containment failure. \n Figure 4 . 4 Figure 4. two lines of thinking on human attempts at making ai goals safe. \n Figure 6 .Figure 5 . 65 Figure 6. Explanation of the Y module used in figure 4. \n Human enhancement in this context refers to anything that could help humans keep up with AI, such that the AI does not gain decisive strategic advantage even during or after takeoff. Human capabilities could be enhanced, for example, via brain-computer interfaces or mind uploading. Human enhancement could reduce some ASI risks, but it could increase other ASI risks (e.g. if enhanced humans create unsafe ASI) or cause other problems (e.g. moral problems associated with modifying human nature). Additionally, human enhancement could require advanced technology that may not be developed before the seed AI, in which case human enhancement would not help with ASI safety. • AI confinement. AI confinement measures are restrictions built into the AI's hardware or software • Encourage research into ASI safety. AI safety research can be on any aspect of ASI software or hard- ware, or on the humans involved in ASI development. ASI safety research could be encouraged, for example, by increasing funding for ASI safety research, creating open source platforms for safe ASI development or cultivating norms of responsibility amongst ASI researchers. encouraging research can be an easier intervention to perform than something like review boards because encour- aging research can be done informally and outside institutional procedures. However, informal encouragement can sometimes be less effective when it lacks institutional clout. As with research risk review boards, encouraging research requires knowing whether a particular activity would increase or decrease ASI risks. • Enhance human capabilities. \n 6  • AI enforcement. AI enforcement occurs when one or more AIs prevent other AI(s) from gaining decisive strategic advantage. As with confinement, AI enforcement can be applied to seed AI, self-improving AIs or ASIs; the enforcement can also be performed by any of these AIs, though more intelligent AIs may tend to be more effective enforcers. For AI enforcement to work, the AIs with strategic advantage must be motivated and able to stop other AIs. For scenarios with multiple AIs, there could be a first-mover advantage, such that the first AI(s) gain and keep strategic advantage.", "date_published": "n/a", "url": "n/a", "filename": "pathways_to_catastrophe.tei.xml", "abstract": "An artificial superintelligence (ASI) is an artificial intelligence that is significantly more intelligent than humans in all respects. Whilst ASI does not currently exist, some scholars propose that it could be created sometime in the future, and furthermore that its creation could cause a severe global catastrophe, possibly even resulting in human extinction. Given the high stakes, it is important to analyze ASI risk and factor the risk into decisions related to ASI research and development. This paper presents a graphical model of major pathways to ASI catastrophe, focusing on ASI created via recursive self-improvement. The model uses the established risk and decision analysis modelling paradigms of fault trees and influence diagrams in order to depict combinations of events and conditions that could lead to AI catastrophe, as well as intervention options that could decrease risks. The events and conditions include select aspects of the ASI itself as well as the human process of ASI research, development and management. Model structure is derived from published literature on ASI risk. The model offers a foundation for rigorous quantitative evaluation and decision-making on the long-term risk of ASI catastrophe.", "id": "6d0eac3dc1a112786652cb97eab30bfa"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stephen Cave"], "title": "An AI Race for Strategic Advantage: Rhetoric and Risks", "text": "Introduction Global leadership in different areas of fundamental and applied research in artificial intelligence has emerged as a strategic priority, both for major companies and nation states. The last two years have seen heightened competition between industry research groups for talented researchers and startups  (Metz 2017 , CB Insights 2017), and the release of strategic plans aimed at establishing research leadership in AI by the United States (NSTC, 2016), China  (Fa, 2017) , and other research-leading nations  (Hall and Prescenti 2017 , NEDO 2017 , CIFAR 2017 . As the applications of AI research become more lucrative, and the impacts of AI on economic, scientific and military applications more transformative, this competition can be expected to intensify. A narrative has begun to emerge, in both policy and public contexts (Simonite 2017, Allen and Husain 2017, Stewart 2017, Allen and Kania 2017, Allen and Chan 2017), framing future trajectories relating to the development of AI in terms typically associated with a race for technological superiority. The China State Council's 2017 \"A Next Generation Artificial Intelligence Development Plan\" includes in its aims to seize the major strategic opportunity for the development of AI, to build China's first-mover advantage in the development of AI. The United States National Science and Technology Council's Research and Development Strategic Plan highlights that the US no longer leads the world in numbers of deep learning-related publications. Strong public statements have been made by political and technology leaders: notable examples include Russia's President Vladimir Putin stating that \"whoever becomes the leader in this sphere will become the ruler of the world\" (RT 2017) and Open-AI cofounder Elon Musk tweeting that \"competition for AI superiority at national level [is the] most likely cause of WW3\"  (Musk 2017 ). These developments reflect a perception that global leadership in AI could confer scientific, infrastructural and economic advantages to frontrunners. Such comparative advantage could also be self-perpetuating, if it helps to recruit the best research talent, or leads to greater wealth and spending power, or to the accumulation of better computing and data resources, or if the application of AI to the process of scientific research itself leads to further breakthroughs. Similarly, although many breakthroughs are likely to be local in application, the perception that some fundamental advances can be applied to a broad range of research challenges further fuels the idea that a winner could take it all. Such notions of 'winner takes all' or the importance of technological leadership, foster the framing of AI development as a race. We will refer to this framing as that of the 'race for technological superiority' in AI. This kind of race is the primary concern of this paper. But at the same time, it is important to note that there are also concerns about a specifically military AI arms race. Although this is not the primary concern of this paper, there are some noteworthy interrelations with the broader race for technological superiority: most significantly, if AI fulfils its promise as a widely-applicable and transformational technology, then general superiority in AI will to a significant degree imply also military superiority. Many aspects of AI progress are likely to have dual-use relevance to both civilian and military applications (for example, advances enabling greater autonomy and a wider range of capabilities in autonomous vehicles) not least given the deep connection between AI research and the defence community  (Geist 2016) . And if systems approach general intel-ligence or superintelligence, they are likely to confer a very significant strategic advantage that could encompass, but go well beyond, conventional weaponry, with radical implications for security and geopolitics (Allen and Chan 2017). The central concern of this paper is what might happen if the rhetoric noted above around first mover advantage or the pursuit of AI superiority becomes a widespread or even dominant framing of AI development. Our concerns arise both from use of the language of a race for technological superiority (independently of whether such a race is happening) and from such a race becoming a reality. \n The Dangers of an AI Race for Technological Advantage: In Rhetoric and in Reality What is so bad about framing the development of AI in terms of a race for technological advantage? After all, it is widely agreed that AI brings enormous potential benefits across many sectors. One recent report estimated that it could add £232 billion by 2030 to the UK economy alone, with healthcare one of the sectors most enhanced, potentially bringing faster, better service to consumers (PwC 2017). There is a widespread belief that competition and other market forces are central to such innovation. So in as much as a race to develop AI technology means these kinds of benefit come sooner, we have reason to view it positively. But at the same time, the development of such a potentially powerful new technology will need to be steered if it is to be as beneficial as possible while minimising the risks it might pose (Crawford and Calo 2016). In the words of the Future of Life Institute's open letter on 'Research Priorities for Robust and Beneficial Artificial Intelligence', signed by over 8,000 people including many leading figures in AI, work should focus \"not only on making AI more capable, but also on maximizing the societal benefit of AI.\" (Future of Life Institute, 2017a). The danger of an AI race is that it makes exactly this thoughtful steering towards broadly beneficial outcomes more difficult. \n Three Sets of Risks We want to distinguish between three sets of risks: i) The dangers of an AI 'race for technological advantage' framing, regardless of whether the race is seriously pursued; ii) The dangers of an AI 'race for technological advantage' framing and an actual AI race for technological advantage, regardless of whether the race is won; iii) The dangers of an AI race for technological advantage being won. \n (i) Risks Posed by a Race Rhetoric Alone It is possible that the trend towards 'race for technological advantage' terminology in AI, including suggestions such as Vladimir Putin's that the winner of such a race \"will become the ruler of the world,\" could pose risks even if the race is not pursued in earnest, let alone won. We perceive two main risks here: (i.a) The kind of thoughtful consideration of how to achieve broadly beneficial AI, as mentioned above, will require subtle, inclusive, multi-stakeholder deliberation over a prolonged peri-od. The rhetoric of the race for technological advantage, with its implicit or explicit threat that dire consequences will follow if some other group wins that race, is not likely to be conducive to such deliberation. Indeed, rhetoric around technological superiority (such as the 'arms race' rhetoric used in the Cold War in the US), played into what has been called a politics of fear, or a politics of insecurity --that is, a political climate that discourages debate in favour of unquestioning support for a prescribed agenda  (Griffith 1987 ). In The Politics of Insecurity, Jef Huysmans argues that use of the language of security (by which he means militarised language, which would include 'arms race' and related rhetoric) \"is a particular technique of framing policy questions in logics of survival with a capacity to mobilize politics of fear in which social relations are structured on the basis of distrust\"  (Huysmans 2006 ). (i.b) Second, if the rhetoric of a competitive, 'winner takes all' AI race is used in the absence of an actual race, it could contribute to sparking such a race. (ii) Risks Posed by a Race Emerging If the rhetoric of a race for technological advantage became an actual race to develop sophisticated AI, the risks increase further: (ii.a) First, there is the risk that racing to achieve powerful AI would not be conducive to taking the proper safety precautions that such technology will require (Armstrong, Bostrom, and Shulman 2016). We mentioned above the need for broad consultation about the role AI should play in the life of a community. This might help address important considerations such as avoiding biased systems, or maximising fairness. But in addition to these goals, serious attention must also be given to ensuring humans do not lose control of systems. Such considerations become particularly important if AI approaches general intelligence or superintelligence  (Bostrom 2014 ), but also long before, particularly when AI systems are performing critical functions. The risk is that as the perceived benefit to winning the race increases, so correspondingly does the incentive to cut corners on these safety considerations. (ii.b) Second, a 'race for technological advantage' could increase the risk of competition in AI causing real conflict (overt or covert). Huysmans argues that militarised language such as this has \"a specific capacity for fabricating and sustaining antagonistic relations between groups. In the case of the race for technological advantage, it encourages us to see competitors as threats or even enemies. The belief that a country intends in earnest to win an AI race, and that this would result in technological dominance, could, for example, prompt other countries to use aggression to prevent this (akin to the cyberattacks made against Iranian nuclear facilities attributed to the US and Israel) (Nakashima 2012), or motivate the targeting of key personnel (precedents --though specific to their historical context --might include Operation Paperclip, during which over 1,600 German scientists and engineers who had worked on military technology were taken to the US (Jacobsen 2014), or the apparently ongoing operations to encourage the defection of nuclear scientists between nations)  (Golden 2017) . Such scenarios would also in-crease the risk that a general race for technological superiority became increasingly a military AI arms race. \n (iii) Risks Posed by Race Victory The third category of risks of an AI race for technological superiority are those that would arise if a race were won. We will not explore these in detail here --and the forms they take will anyway depend on the precise nature of the technology in question. But as an example, these risks include the concentration of power in the hands of whatever group possesses this transformative technology. If we survey the current international landscape, and consider the number of countries demonstrably willing to use force against others, as well as the speed with which political direction within a country can change, and the persistence of non-state actors such as terrorist groups, we might conclude that the number of groups we would not trust to responsibly manage an overwhelming technological advantage exceeds the number we would. \n Choices for the Research Community Given the dangers noted above of talking about AI development as a competitive race, one could argue that it would be better for the community of researchers considering AI and its impacts to avoid this terminology altogether. In this way, the language of the race for dominance would be seen as (in Nick Bostrom's terms) an information hazard --perhaps either an idea hazard (a general idea whose dissemination could increase risk) or an attention hazard (if we consider that the dangerous idea already exists, but is as yet largely unnoticed)  (Bostrom 2011 ). But if we believe that the idea is already being disseminated by influential actors, such as states, including major powers, then the information hazard argument is weakened. It might still apply to particularly influential researchers --those whose thoughts on the future of AI can become headline news around the world. But even in their case, and particularly in the case of lesser-known figures, there is a strong countervailing argument: that if the potentially dangerous idea of an AI race is already gaining currency, then researchers could make a positive impact by publicly drawing attention to these dangers, as well as by pursuing research dedicated to mitigating the risks of such a framing. Of course, many leading researchers are already speaking out against an AI arms race in the sense of a race to develop autonomous weapons --see for example the Future of Life Institute's open letter on this, signed by over three thousand AI researchers and over fifteen thousand others (Future of Life Institute 2015b). We believe this community could also usefully direct its attention to speaking out against an AI race in this other sense of a competitive rush to develop powerful general-purpose AI as fast as possible. Both media and governments are currently giving considerable attention to AI, yet are still exploring ways of framing it and its impacts. We believe that there is therefore an opportunity now for researchers to influence this framing 1 . One of the principles on AI agreed at the 2017 Asilomar conference offers a precedent on which to build --it states: Race Avoidance: Teams developing AI systems should actively cooperate to avoid corner-cutting on safety standards (Future of Life Institute 2017). \n Alternatives to a Race Approach If we are not to pursue (and talk about pursuing) AI development as a race, then how should we pursue (and talk about pursuing) such development? This is too big a topic to consider thoroughly here. But we note these promising directions for alternative narratives around progress in, and benefits of, AI: \n AI Development as a Shared Priority for Global Good As advances in AI find application to an ever-wider range of scientific and societal challenges, there is a burgeoning discussion around harnessing the benefits of AI for global benefit. This reflects a widespread view among AI scientists and a growing number of policymakers that AI presents tremendous opportunities for making progress on global societal ills, and aiding in tackling some of the biggest challenges we face in the coming century --among them climate change and clean energy production, biodiversity loss, healthcare, global poverty and education. Emphasising these benefits could counteract a race approach in a number of ways: First, if there is global scientific consensus that some of the key aims of AI should be to benefit humanity in these ways, then it becomes less important in which companies or countries key breakthroughs occur. Second, it makes clear that cooperation on the development of AI stands to result in faster progress on these pressing challenges. Lastly, if the aims of the field are to benefit humanity worldwide, then the global community represent stakeholders in the process of AI development; this narrative therefore promotes inclusive and collaborative development and deployment of AI. \n Cooperation on AI as it is Applied to Increasingly Safety-Critical Settings Globally The next decade will see AI applied in an increasingly integral way to safety-critical systems; healthcare, transport, infrastructure to name a few. In order to realise these benefits as quickly and safely as possible, sharing of research, datasets, and best practices will be critical. For example, to ensure the safety of autonomous cars, pooling expertise and datasets on vehicle performances across as wide as possible a range of environments and conditions (including accidents and near-accidents) would provide substantial benefits for all involved. This is particularly so given that the research, data, and testing needed to refine and ensure the safety of such systems before deployment may be considerably more costly and time-consuming than the research needed to develop the initial technological capability. Promoting recognition that deep cooperation of this nature is needed to deliver the benefits of AI robustly may be a powerful tool in dispelling a 'technological race' narrative; and a 'cooperation for safe AI' framing is likely to become increasingly important as more powerful and broadly capable AI systems are developed and deployed. \n Responsible Development of AI and Public Perception AI is the focus for a growing range of public concerns as well as optimism (Ipsos MORI 2017, Fast and Horvitz 2017). Many stakeholders, including in industry, recognise the importance of public trust in the safety and benefits offered by AI if it is to be deployed successfully  (Banavar 2017) . It is the view of the authors that a narrative focused on global cooperation and safe, responsible development of AI is likely to inspire greater public confidence than a narrative focused more on technological dominance or leadership. Other powerful new technologies, such as genetically modified organisms and nuclear power, have in the past proven controversial, with significant communities arguing for a cautious, safety-first approach, to which the rhetoric of the race is antithetical. \n Recent Narratives There have been encouraging developments promoting the above narratives in recent years. 'AI for global benefit' is perhaps best exemplified by the 2017's ITU summit on AI for Global Good (Butler 2017), although it also features prominently in narratives being put forward by the IEEE's Ethically Aligned Design process (IEEE 2016), the Partnership on AI, and programmes and materials put forward by Microsoft, DeepMind and other leading companies. Collaboration on AI in safetycritical settings is also a thematic pillar for the Partnership on AI 2 . Even more ambitious cooperative projects have been proposed by others, for example the call for a 'CERN for AI' from Professor Gary Marcus, through which participants \"share their results with the world, rather than restricting them to a single country or corporation\" (Marcus 2017). Finally, the overall narrative of cooperation was clearly expressed in a statement issued by a Beneficial AI conference in Tokyo 3 : The challenges of ensuring that [AI] is beneficial are challenges for us all. We urge that these challenges be addressed in a spirit of cooperation, not competition.  (Beneficial AI Tokyo, 2017) . \n Conclusion Although artificial intelligence has been discussed for decades, only recently has it received serious and sustained attention from governments, industry and the media. Among the various ways in which this technology is framed, we have highlighted one that we consider to be potentially dangerous: that of the race for technological advantage. Partly, we believe that a general race to develop AI would be dangerous because it would also encompass --given the dual use of this technology --a literal, military arms race. But even if this were not the case, we believe there would be risks -e.g. from corner-cutting in safety and consultation. Although some might argue that the research community should altogether avoid using AI 'race' terminology for fear of giving it currency, we believe that the idea is already current enough to justify interventions that draw attention to the dangers. Much work remains to be done in understanding the dynamics of a possible race, and in developing alternative \t\t\t For example, few countries have published formal strategies or legislation on AI, but a number have commissioned reviews that have sought expert opinion, eg, the UK Government-commissioned report on AI(Hall and Prescenti, 2017)  and the White House report (NSTC, 2016). \n\t\t\t See https://www.partnershiponai.org/thematic-pillars/ 3  In which both authors were involved. framings for AI development --but there are encouraging examples on which to build.", "date_published": "n/a", "url": "n/a", "filename": "3278721.3278780.tei.xml", "abstract": "The rhetoric of the race for strategic advantage is increasingly being used with regard to the development of artificial intelligence (AI), sometimes in a military context, but also more broadly. This rhetoric also reflects real shifts in strategy, as industry research groups compete for a limited pool of talented researchers, and nation states such as China announce ambitious goals for global leadership in AI. This paper assesses the potential risks of the AI race narrative and of an actual competitive race to develop AI, such as incentivising corner-cutting on safety and governance, or increasing the risk of conflict. It explores the role of the research community in responding to these risks. And it briefly explores alternative ways in which the rush to develop powerful AI could be framed so as instead to foster collaboration and responsible progress.", "id": "5a12e4748bb080474000257cb423b50d"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["David Sobel"], "title": "Do the desires of rational agents converge?", "text": "1. The plausibility of the claim that the desires of all agents will converge after proper deliberation hinges crucially on how one characterizes such deliberation. One could simply claim that a person only counts as having deliberated properly if she reaches certain approved conclusions. This path would assure Smith's first thesis at the cost of invoking a substantive, nonproceduralist conception of proper deliberation. The interest in Smith's claims stems from his willingness to invoke an understanding of proper deliberation which is not conceptually tied to the deliberator arriving at any particular motivations. In this paper I will say that a conception of normative reasons for action is Humean iff (1) it claims that one's rational desires give one normative reasons (hereafter, reasons), and (2) it invokes a proceduralist notion of proper deliberation in which what makes a desire rational is that it would be arrived at if one successfully followed the procedure, and (3) this procedure is specified such that, at least in principle, any particular option could be rationally desired after successfully following the procedure, and (4) it is relativist in the sense that different agents might arrive in the right way at different desires and hence have divergent reasons. This last condition shows that, for the Humean, the normativity for A of the desires that A would arrive at in the approved way is not undermined should other agents arrive in the approved way at other desires. Smith clearly rejects the fourth thesis. He must also be rejecting the first or second thesis. Perhaps he would want to say that successfully following the procedure makes one's resultant desires rational, but that (contra thesis 1) rational desires only give one reasons when all rational agents converge in their desires. Alternatively, Smith might want to say that one's desires are only rational if everyone would reach them after proper deliberation (contra thesis 2). Smith finds himself in substantial agreement with Bernard Williams's account of fully rational deliberation, complaining only that Williams's account requires supplementation. 2 (158) Thus Smith and Williams largely agree about what it is for an agent to arrive at a desire in the right way. Smith glosses Williams's position in this way: in order for a deliberator to counts as fully rational '(i) the agent must have no false beliefs, (ii) the agent must have all relevant true beliefs, (iii) the agent must deliberate correctly.' (  156 ) Conditions (i) and (ii) claim that we can only be fully rational deliberators if we get the facts right. Smith's requirement of true belief shows that he is not trying to capture the notion of proper deliberation given one's limited time and access to the truth. Thus while we might have been rational in light of the information available to us (because, for example, the scientific community had not discovered certain facts) or that it was reasonable for us to collect, we were not fully rational deliberators in Smith's sense for we did not know all the facts. One sense of 'rational deliberation' is to make proper use of the information one has (or could reasonably be expected to get). Thus a person might have been rational in this sense to leave the building after the fire alarm went off even though it turns out that the building was not really on fire. Smith is clearly after another notion of rational deliberation, one perhaps well designed to determine what it is advisable to do or what will get us what we really want. Smith's targeted notion might be called 'ideally rational deliberation.' Several philosophers, myself included, have recently argued that this notion of ideally rational deliberation involves serious conceptual problems, but I want to focus on other issues here.  3  Condition (iii) adds possibilities for practical reasoning such as these: the agent adequately exercises her imagination in considering the options available, the agent makes no mistakes of means-end reasoning, the agent engages in constitutive reasoning 'such as deciding what would make for an entertaining evening, granted that one wants entertainment.'  (Williams 1981 : 104) Smith's main additions to Williams's above criteria are that the agent is not suffering from depression, apathy, or other debilitating attitudes, and the agent has a concern that her overall desire pattern be coherent and justified. (158-61) Crucially these possibilities for practical reason do not amount to the claim that it is criterial of proper deliberation that one reach a particular specified motivational profile. 2. Before considering Smith's arguments for his two theses we must better understand what we mean when we speak of the desires of all ideally rational agents converging. This is more complicated than it might seem. Different things might be thought to constitute convergence. A weak understanding of convergence would be that all fully rational agents agree about every claim of this form: A has normative reason to O in circumstances C. If a Humean account of reasons were correct and this was accepted, then, presumably, we would all agree, when fully rational, about all such reason claims. In fact, the most likely way to achieve such agreement would be for all rational agents to agree on an account of practical rationality; that is, agree about what makes it the case that A has reason to O in circumstances C. This kind of agreement is compatible with different agents having arbitrarily divergent ideally rational desires. Call this 'convergence about each agent's reasons.' This, it turns out, is not the notion of convergence that Smith is pointing to. Or rather, such agreement would seem necessary but not sufficient for the kind of convergence that Smith has in mind. Smith's understanding of convergence would be for all rational agents to converge on desires that have the same de se content. (169-70) If we both want you rather than me to get the larger slice of cake there is a sense in which we converge and a sense in which we do not. We both want the same state of the world to obtain, but we do not both want the cake for ourselves. If we both wanted cake for ourselves our desires would have the same de se content. A simple case of this sort of convergence would be if all fully rational agents desired only their own pleasure. In this case rational agents agree about what kind of things are desirable. Convergence in the objects of desire can be thicker or thinner. We might both want to listen to the Rolling Stones album Exile on Main Street very loud, or we might both want to listen to music. The former agreement in desire is thicker in that the shared object of appropriation is specified more specifically. It is likely that some very thin convergence can always be found between two people or perhaps between all rational agents. Perhaps all rational agents desire to be rational, to live a good life, or to avoid mistakes. If the convergence that Smith has in mind is convergence in the objects of desire, then it is crucial to know what level of generality he intends. Thick convergence among all rational agents would be very surprising and, perhaps, entail moral agreement, whereas very thin convergence would not be very interesting and would not entail moral agreement. Further, if we are not given a specific level of generality at which rational agents are supposed to converge, then one could worry that Smith could, in the face of any seeming disagreement, simply move in each such case to thinner and thinner areas of convergence. There could also be varying degrees of the extent of convergence. Rational agents might agree (at a fixed level of generality) about all, most, or just a few objects of desire. Smith's claim is that there is full convergence in desire amongst rational agents. A problem for the thesis that rational agents will converge on the objects of desire thickly described is that on matters of mere tastes agreement does not seem forthcoming. It is not plausible that every rational deliberator will like chocolate ice cream more than vanilla or Seinfeld more than Friends. Our desires diverge over such issues. Yet in many cases our divergent desires seem for all the world informed in the relevant sense and well insulated from consistency or justificatory pressures from other areas of our motivational make-up. There are strong grounds for thinking such divergence in tastes will survive rational deliberation. Smith concedes this point, but tries to show that this would not prevent the kind of full convergence he has in mind.  4  Smith admits that his preference for beer over wine provides him a reason to get beer rather than wine where our opposite preference provides us reason to get wine instead. Smith claims that this is no threat to full convergence because the preference is 'a relevant feature of our circumstances....' (171) This can be seen, Smith tells us, 'from the fact that I can quite happily agree with you that if I were in your circumstances -if I preferred wine to beer -then the fact that the local wine bar sells very good wine would constitute a reason for me to go there as well ….' (171) Smith continues: 'even if an agent's preferences may enter into a specification of the circumstances that she faces it may still be the case that whether or not she is rationally justified in taking her own preferences into account, and the way in which she is justified in taking them into account if she is, depends on whether fully rational agents would all converge on a desire which makes the preferences she has relevant to her choice.' (171) Smith is here claiming that rational agents might, despite their divergent tastes, nonetheless converge on desires of the following form: if I were in circumstances C (which includes having a certain preference profile P), then I want myself to choose O. At first sight such convergence might appear to be nothing more than convergence on instrumental rationality itself. It appears that the thought is simply this: whatever desires I find myself having, I want myself to satisfy those desires. But things are not so simple. Allan Gibbard notes that 'Ideals differ from tastes: I dislike spinach but think it a matter of taste; that means in part that although I dislike spinach I am willing to eat it if I like it. The norms I accept endorse eating it if I like it and not otherwise. I oppose cruelty unconditionally: I want myself not to be cruel even if, hypothetically, I should want to be.'  (Gibbard, 1990: 167)  Thus, for those that hold ideals in Gibbard's sense (and moral claims seem paradigmatically to be such ideals), what one would want for oneself if one had an altered preference ranking need not simply be maximally to satisfy those altered desires. Smith's claim seems to be that all rational agent's might converge in their de se desires about what they would want for themselves if they were in a particular circumstance (which includes having a certain preference profile). There are at least two different ways in which such convergence might be achieved. The first way would be for all rational agents to treat every preference as a matter of taste and never as an ideal. Such rational agents might agree that for any situation they find themselves in, they would want to maximally satisfy the preferences that they have in that situation. Convergence of this sort, I take it, would be compatible with a thoroughgoing Humean account of an agent's reasons for action. Thus I suppose it must not be this method of reaching convergence that Smith has in mind for he calls his proposal an 'anti-humean theory of normative reasons.' Smith, it would seem, must therefore have in mind a picture in which fully rational agents converge in their desires in a way that crucially involves them having ideals. How might such a picture go? The second way such convergence might occur, in this case involving agents with ideals, would be for all rational agents to agree fully about what counts as a matter of mere taste and what counts as a matter of ideals. It would not be important that the rational agents agree in their tastes, rather only that they agree about which of their preferences are to be treated as mere tastes. For where we treat our preferences as mere matters of taste, we presumably agree about what we want in situations in which we have this taste or that; namely, indulge our tastes as we find them. In this way Smith has found a nice way of acknowledging that fully rational agents would not converge on preferring chocolate ice cream to vanilla, yet still holding out the prospect that they might fully converge in their desires in an interesting and important sense. It would seem however that the rational agents would have to converge on their ideals in order for the full kind of convergence in desires that Smith envisions to occur. When two agents disagree in their ideals, they will sometimes disagree in their wants for themselves in circumstances C (which includes having a certain preference profile P). Thus for the kind of convergence that Smith has in mind to occur all rational agents must both (1) agree about what counts as a mere matter of taste and what counts as an ideal and (2) agree in their ideals. Imperfectly rational agents clearly disagree about what are matters of mere taste and what are ideals. Some want themselves to dress fashionably even in the situation in which they do not want to look fashionable, others treat this as a matter of taste. It must be claimed that this kind of disagreement would be extinguished upon becoming fully rational. It is worth noting that for two people to agree in their ideals they must agree about significantly more than just morality. For as the above example of fashion shows, a person can hold a preference as a personal ideal even when they think others would not be immoral or irrational for failing to share that ideal. Gibbard called such ideals 'existential: it is a choice of what kind of person to be, in a fundamental way, come what might, which the chooser does not take to be dictated by considerations of rationality.' (ibid.: 168) Thus it would seem that to vindicate Smith's conception fully rational agent's would have to converge fully not only about morality, but also about personal ideals. This would seem to necessitate that the process of becoming fully rational extinguish all existential ideals, or at least make false the claim that the holder of the existential ideal makes: namely that commitment to this ideal is not dictated by rationality. And as holding false beliefs is supposed to be incompatible with being fully rational, it would seem that Smith must hold that existential ideals must go if convergence is to take place. Let me here parenthetically acknowledge a clear and important virtue of Smith's attempt at an 'anti-Humean Theory of Normative Reasons.' It deals as successfully with matters of mere taste as does the Humean theory and this to my mind had been one of the clearest advantages of the do the desires of rational agents converge? 143 Humean account. Smith shows us how the anti-Humean can, perhaps effectively, avoid conceding this front. 3. Why must proper deliberation lead to convergence if we are to have reasons at all? Smith's conclusion here is remarkably strong. He claims the very concept of reasons demands convergence. Thus, apparently, the dominant Humean understanding of reason is, in a straightforward way, conceptually confused. I find Smith's clearest arguments for this to be the following: (1) such an assumption is necessary to underwrite the platitude that 'we are … potentially in agreement or disagreement with each other about what constitutes a reason and what doesn't.' (172), and (2) absent this sort of convergence I must see my reasons as being entirely dependent on the fact that my actual desires are as they are. But the shape of my actual desires (which, by hypothesis, will determine the shape of my desires after rational deliberation), Smith tells us, is an 'entirely arbitrary matter, one without any normative significance of its own.' (172) I will consider these arguments in turn. Consider first Smith's case that convergence is necessary to vindicate the thought that we can dispute reasons claims. He writes there is … a sense in which we can talk about rational justification or desirability simpliciter. When you and I talk about the reasons that there are for acting [in this sense], we are therefore talking about the same thing …. On the relative conception, however, matters are quite different. For in order to give a truth condition to the schematic claim 'It is desirable that p in c' we need to know from whose perspective the truth of the claim is to be assessed ….  [Thus]  if I say to you 'There is a reason for O-ing', and you deny this, we are therefore potentially talking about different things …. (166-67) All of this is true. But it does not support either the claim that on the Humean view there could not be a common subject matter when we discuss reasons, or that 'rational justification [concerning reasons] is itself a relative matter; that really there is only rational-justification-relative-tothis-person or rational-justification-relative-to-that.' (171) In fact these two claims are false. Smith claims that on Williams's Humean view when we speak of reasons 'it typically means reason me out of my mouth, reason you out of your's, reason her out of her's and so on.' (172) But, of course, we might both be talking about the reasons of the same person. We might be debating if A has reason to O in circumstances C. On the Humean account when we debate whether A has reason to O in circumstances C we are debating what A's motivations would be like if she were deliberating properly. The Humean thus holds that we can be right or wrong in such claims and we have a common subject matter when we discuss them. Someone who claimed that a person had an intrinsic reason to O, when that person had nothing in her motivational set that O answered to, would just be wrong. Thus the Humean framework allows us to vindicate the platitude that we have a common subject matter when we speak of a particular agent's reasons. Perhaps it is the case that, on the Humean view, we cannot find a common subject matter for other kinds of reason claims. Likely the Humean cannot vindicate certain kinds of reason claims that we might have hoped to vindicate (e.g., that there are reasons, such as moral reasons, which apply to all rational agents as such). But even if this is granted there is no reason here to suppose, as Smith does, that the Humean is forced to abandon the very notion of reasons altogether. Further, the way to justify reason claims such as A has reason to O in circumstances C is not relative to each individual. The Humean holds that there is a fact of the matter about this which is determined by the agent's motivations in counterfactual situations (which will admittedly be very difficult to determine) just as there is a fact of the matter about the effects of red wine on the body. And we justify believing the former sort of facts in the same non-person relative way that we justify the latter sort of facts. Smith's second argument claims that unless desires converged amongst fully rational deliberators, one's rational desires would be determined by what one (perhaps idiosyncratically) happened to find attractive. Smith claims that if this were so one's rational desires would depend on 'an entirely arbitrary matter' and 'arbitrariness is precisely a feature of a consideration that tends to undermine any normative significance it might initially appear to have.' (172-73) Smith could mean one of two things. First, he could mean that as a psychological matter an agent cannot take her own desires seriously, cannot herself find them to be a source of reasons for her, if they are arbitrary in this way. This is clearly false. The prevalence of sincere Humeans demonstrates this. The Humean may be wrong about reasons for action, but it must be allowed that she really believes her theory. The second interpretation of Smith's claim is that there is no justification for treating one's desires that are arbitrary in this way as creating reasons. But this is exactly what is at issue between the Humean and Smith. My rationally arbitrary preference (that is, a preference I could be rational without) for chocolate ice cream gives me a reason to choose it. What is incoherent about all my reasons being such? Smith has baldly claimed that there is a conceptual confusion in the notion of rationally arbitrary desires by themselves creating reasons. The predominant neo-Humean view holds that this is precisely what creates reasons. Thus Smith will have to do better. I myself have trouble seeing anything conceptually confused or problematically arbitrary in the thought that my rationally optional projects and commitments create reasons for me and not for you. Before moving on I want to briefly consider the plight of the agent that deliberates by successfully following the procedure that Smith recommends but unhappily discovers that other rational agents arrived at divergent desires. Smith tells us that this agent has no reason to satisfy her desires, in fact she has no reasons (recall I use 'reason' to refer to Smith's 'normative reason') at all for there are no reasons without convergence. Thus a lack of convergence, according to Smith, would make it the case that I had no reason to avoid pain or choose a flavour of ice cream I like rather than one I find disgusting. I find this suggestion difficult to take seriously. Does Smith really think the existence of such reasons is contingent on universal convergence? Perhaps Smith should only claim that an agent has a reason to O iff all rational agents would converge on a desire for O in the relevant circumstances rather than claim that for an agent to have any reasons all rational agents must converge on all desires. I would still disagree with this claim, but it would not flaunt what I regard as the absurdities mentioned in the previous paragraph. In some cases, like the preference for chocolate rather than vanilla ice cream, our bare liking provide us with a reason to choose one thing rather than another. Even if all rational agents do not converge in their desires, I like chocolate ice cream better than vanilla, and this is all I need to have a reason to choose it. It would seem that Smith must either claim that, in such cases, my getting chocolate ice cream does not benefit me more than getting vanilla or that I have no reason whatsoever in such a case to seek my benefit rather than my detriment. Neither claim strikes me as plausible. 4. Smith argues that convergence in desires amongst rational deliberators is quite plausible. Smith's main argument here is that 'the empirical fact that moral argument tends to elicit the agreement of our fellows gives us reason to believe that there will be a convergence in our desires under conditions of full rationality. For the best explanation of that tendency is our convergence upon a set of extremely unobvious a priori moral truths.' (187) Smith bolster this argument with three supplementary arguments: (1) often by focusing only on moral disagreement we ignore substantial agreement and the fact that 'we' share thick evaluative language which entails a fair degree of agreement in attitude, (2) although current moral disputes appear at times deadlocked, 'we must remember that in the past similarly entrenched disagreements were removed inter alia via a process of moral argument' and (3) some moral disagreement certainly can be explained as clearly arising from lack of rational deliberation. (  188 ) But much of the historical moral argumentation that has actually managed to produce consensus has been (1) factually and logically imperfect, (2) addressed to those poorly positioned to object, (3) addressed to those who share substantial common moral vocabulary, moral education, and cultural identification, and (4) offered by those who are persuasive for reasons other than the cogency of their position. Any historical tendency towards convergence that results from some combination of these four causes (and no doubt others) will not constitute evidence that rational agents will converge in their moral views. Since such causes undoubtedly played a very significant role in producing convergence, we cannot simply point towards a general historical tendency towards convergence (even if there were one) and claim it constitutes inductive evidence for Smith's case. Thus, as we might have suspected, Smith's historical case about a tendency towards convergence will have to be genuinely historical. It will have to persuade us of the crucial role of facts, logic, and reason is explaining the history of convergence and the secondary role of force, guile, and a shared thick moral vocabulary. The sort of convergence Smith holds out real hope for is convergence amongst people that start off as different in their desires, moral vocabulary, and moral education as we can imagine. The convergence in the objects of desire that Smith needs is not simply convergence amongst all actual humans (as if we could make ourselves right by killing dissenters) but rather amongst all possible agents no matter how initially divergent. But what is the history of convergence amongst agents with radically divergent desires, moral vocabularies, and moral educations when they are confronted with factually informed and logically impeccable argumentation? Certainly Smith will have to remind us of such cases. Smith needs a string of cases in which (1) convergence occurred, (2) it occurred for the right reasons, and (3) it occurred between radically different cultures. Smith relies quite plainly and inappropriately on convergence within an extended community. Smith points to convergence within a community that shares a common moral vocabulary of thick evaluative language. (188) This commitment to a common thick evaluative language, Smith rightly points out, reveals considerable moral agreement within the community. (188) But just because this shared thick evaluative language presupposes and reveals considerable moral agreement, convergence amongst those that share thick evaluative language is of very limited use in demonstrating the power of rational argumentation to itself manufacture this agreement. Rational argumentation has some power to lead people who actually agree about morality to see that they agree. This is not do the desires of rational agents converge? 147 doubted. But Smith needs to show that history provides a good inductive case that all fully rational agents, no matter how initially divergent they are prior to becoming fully rational, will agree on moral matters. Smith finds himself 'in substantial agreement with Derek Parfit' (214) when Parfit claims that Belief in God, or in many gods, prevented the free development of moral reasoning. Disbelief in God, openly admitted by a majority, is a very recent event, not yet completed. Because this event is so recent, Non-Religious Ethics is at a very early stage. We cannot yet predict whether, as in Mathematics, we will all reach agreement.  (Parfit 1984: 454)  But betraying such hopes undermines Smith's inductive historical argument for it suggests that the factually informed deliberators will not predicate their moral opinions on religious authority. And surely an overwhelming amount of historical ethical argument that has produced convergence has relied on religious beliefs and authority. It might be true, as Parfit says, that absent such a religious basis we lack any reason to suppose that there will not be convergence. But surely we must therefore also admit that past moral practices do not provide sufficient inductive grounds to suppose that such agreement will be forthcoming. Thus I conclude that Smith's arguments in support of the plausibility of extensive convergence are unconvincing and that he has failed to show that such convergence is necessary for the existence of reasons.  5  Bowling Green State University Bowling  Green,   \t\t\t Smith, 1994.  All otherwise unattributed references are to this work. \n\t\t\t Williams 1981  spells out his neo-Humean account of instrumental rationality. \n\t\t\t  See Velleman 1988 , Sobel 1994 , Rosati 1995 , and Loeb 1995 Interestingly all these critiques are offered against the full information account of well-being rather than the remarkably comparable full information account of reasons for action that Williams and Smith are developing. These two theories, for all their similarity, seem to have developed and be discussed in isolation from each other. \n\t\t\t Seemingly, Smith might have conceded that the case of mere tastes shows that there would not be full convergence on the objects of desire after fully rational deliberation, while continuing to insist that we have reason to be 'optimistic about the possibility of an agreement about what is right and wrong being reached under more idealized conditions of reflection and discussion.' (189)    \n\t\t\t I would like to thank David Copp, Michael Smith, Sara Worley and an anonymous referee for Analysis for their help with this paper.", "date_published": "n/a", "url": "n/a", "filename": "59-3-137.tei.xml", "abstract": "Michael Smith, in his impressive book The Moral Problem , 1 claims that (1) 'convergence in the hypothetical desires of fully rational creatures is required for the truth of normative reason claims' (  173 ) and (2) we have reason to 'have some confidence [… that] there will be a convergence in our desires under conditions of full rationality.' (187). These claims play a crucial role in supporting Smith's distinctive and interesting meta-ethical position. However, I will here ignore the context of Smith's broader ambitions and focus on these two theses. I will argue that Smith does not give us adequate justification for either claim. This paper will have four sections. In §1 I will explain Smith's conception of fully rational deliberation. In §2 I discuss what it would be for desires to converge as Smith suggests. In §3 I consider Smith's conceptual claim that such convergence is necessary for there to be normative reasons at all. Finally, I address Smith's reasons for optimism about convergence. The first three sections consider Smith's first thesis above while the fourth section considers his second thesis.", "id": "50cbb6f915c488fe960d9617b99f65b0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Julian Stastny", "Johannes Treutlein", "Maxime Riché", "Jesse Clifton"], "title": "Multi-agent learning in mixed-motive coordination problems", "text": "Introduction In An Essay on  Bargaining [1956] , Thomas Schelling describes a negotiation over the price of a house. Considering different strategies the negotiators might use, he points out that If the buyer is an agent authorized by a board of directors to buy at $16000 but not a cent more, and the directors cannot constitutionally meet again for several months and the buyer cannot exceed his authority, and if all this can be made known to the seller, then the buyer 'wins' -if, again, the seller has not tied himself up with a commitment to  $19000. (pg. 284)  Imagine various actors with different preferences -a mixed-motive setting  [Schelling, 1958]  -developing machine learning systems to act on their behalf. These actors are like Schelling's bargainers, in that their systems implicitly encode a commitment to pursuing a particular tradeoff between their own preferences and those of other players. Just as the price negotiation in Schelling's example may fail if buyer and seller are each committed to insisting on incompatible prices, machine learning systems may fail to cooperate if they encode commitments to incompatible tradeoffs between their principals' goals. Multi-agent learning (MAL) has in recent years paid considerable attention to problems of cooperation between agents with different, but not zero-sum, preferences. However, much of this work has been in the setting of (sequential) social dilemmas (SSDs) (e.g.,  Peysakhovich and Lerer 2017a , Lerer and Peysakhovich 2017 , Peysakhovich and Lerer 2017b , Foerster et al. 2018 , Wang et al. 2018 , Eccles et al. 2019 . The classic example of a social dilemma is the Prisoner's Dilemma (PD), and the SSDs studied in this literature are similar to the Prisoner's Dilemma in that there is a single salient notion of \"cooperation\". This means that it is relatively easy for actors to coordinate in their selection of policies to deploy in these settings. This situation is quite unlike that faced by Schelling's bargainers, for whom there are many possible agreements to commit to, and who thus may fail to reach an agreement if they make incompatible commitments 1 .  Cao et al. [2018]  are an exception in that they look at negotiation between deep reinforcement learners, such that there are multiple incompatible ways in which agents could choose among possible agreements. However, they do not evaluate the performance of independently trained policies when played against one Working draft. Last updated March 8, 2021. 1 The inadequacy of the Prisoner's Dilemma as a model for cooperation problems, and the need to study games that exhibit competing \"cooperative\" solutions, has been pointed out in other fields. See  Snidal [1985]  for a discussion in international relations,  McAdams [2008]  in law, and  Binmore [1998]  in evolutionary game theory. another (\"cross-play\"  [Hu et al., 2020] ), which is where the existence of multiple incompatible cooperative solutions creates problems. In this note, we argue that a focus on sequential social dilemmas and the lack of cross-play evaluation obscures a fundamental problem for decentralized MAL in mixed-motive settings. We discuss a class of games that we call mixed-motive coordination problems (MCPs), which highlight this problem. We compare MCPs to pure coordination problems and SSDs. We then illustrate how MAL methods which achieve cooperation in other social dilemmas fail in some simple MCPs, and argue that future methods for promoting cooperation in mixed-motive settings should be benchmarked in these more difficult cases. We close with some tentative positive contributions, by sketching some partial solutions to MCPs. \n Preliminaries We work in the setting of partially observable stochastic games (POSGs). For simplicity we assume two players, i = 1, 2. We will index player i's counterpart by −i. Each player has an action space A i , there is an underlying state space S which evolves according to a Markovian transition function P (S t+1 | S t , A t 1 , A t 2 ). At each time step, each player sees an observation O t i which depends on S t . Thus each player has an accumulating history of observations H t i = {O v 1 , A v 1 } t v=1 . Call the set of all histories H i = ∪ ∞ t=1 H t i . Assume for simplicity that the initial observation history is fixed and common knowledge, h 0 1 = h 0 2 ≡ h 0 . Finally, principals choose among policies π i : H → ∆(A i ), which we imagine as artificial agents deployed by the principals. We will refer to policy profiles generically as π ∈ Π := Π 1 × Π 2 . Each player has a reward function r i , such that r i (S t , A t 1 , A t 2 ) is their reward at time t. Define the value to player i of policy profile π starting at history h t i as V i (h t i , π) = E π [ ∞ v=t γ v−t r i (S v , A v 1 , A v 2 ) | H t i = h t i ], where γ < 1 is a discount factor. Define the value of a policy profile to player i as V i (π) = V i (h 0 , π). A payoff profile is then a tuple (V 1 (π), V 2 (π)). We say that π is a (Nash) equilibrium of a POSG if π i ∈ arg max π i ∈Πi V i (h 0 , π i , π −i ) for i = 1, 2. We say that π is Pareto-optimal if for i = 1, 2 and π ∈ Π, we have that V i (π ) > V i (π) implies V −i (π ) < V −i (π). \n Mixed-motive coordination problems We envision multiple actors (\"principals\") deploying machine learning systems, defined by policies, into the world. The principals may be human developers, or they may be machine learning systems themselves. The principals simultaneously deploy policies, without communication (in Section 6 we discuss ways in which communication may change the analysis). Let W be a set of welfare functions, which are supposed to encode normative properties (total welfare, fairness, etc.) of different payoff profiles. Two uncontroversial properties of a welfare function are Pareto-optimality (i.e., its optimizer should be Pareto-optimal) and symmetry (the welfare of a policy profile should be invariant to permutations of player indices). Beyond that, there are several appealing properties which cannot all be satisfied by the same welfare function (see Table  1 ). The experimental evidence regarding people's preferences over welfare functions is inconclusive  [Felsenthal and Diskin, 1982] . We will say that a game is a mixed-motive coordination problem (MCP) if it has several equilibria 2 which are optimal with respect to some welfare function, but are incompatible with each other. Definition 3.1 (Mixed-motive coordination problem). Let G be a POSG. Let W be a set of welfare functions, and let W E ⊆ W be the set of welfare functions in W which are optimized by some equilibrium of G. Then G is a mixed-motive coordination problem (with respect to W) if there exist distinct w, w ∈ W E 2 such that (π w 1 , π w 2 ) has a Pareto-suboptimal policy profile for all π w ∈ arg max π w(π ), π w ∈ arg max π w (π ). An example of a mixed-motive coordination problem is the Bach or Stravinsky game. A variant of this game with asymmetric payoffs is given in Figure  1  (left). The folk theorem  [Friedman, 1971]  tells us that any payoff profile in the convex hull of these payoffs is attainable in an equilibrium of the repeated game, for players with sufficiently high discount factors. And, as is suggested by the shape of the Pareto frontier for Name of welfare function w \n Form of w(π) Nash  [Nash, 1950]  [ V 1 (π) − d 1 ] • [V 2 (π) − d 2 ] Kalai-Smorodinsky  [Kalai and Smorodinsky, 1975]   V1(π)−d1 V2(π)−d2 − sup π V1(π)−d1 sup π V2(π)−d2 + ι {π Pareto-optimal } Egalitarian  [Kalai, 1977]  min {V 1 (π) − d 1 , V 2 (π) − d 2 , } Utilitarian (e.g. Harsanyi 1955) V 1 (π) + V 2 (π) Table  1 : Welfare functions, adapted to the multi-agent RL setting where two agents with value functions V 1 , V 2 are bargaining over the policy profile π. to deploy. The function ι in the definition of the Kalai-Smorodinsky welfare is the ∞-0 indicator, used to enforce the constraint in its argument. V d i = V i (π d ) are the players' disagreement values. Note that in bargaining problems in which the set of feasible payoffs is convex, the Nash welfare function uniquely satisfies the properties of (1) Pareto optimality, (2) symmetry, (3) invariance to affine transformations, and (4) independence of irrelevant alternatives. See  Zhou [1997]  for a characterization of the Nash welfare in non-convex bargaining problems. The Nash welfare can also be obtained as the subgame perfect equilibrium of an alternating-offers game as the \"patience\" of the players goes to infinity  [Binmore et al., 1986] . On the other hand, Kalai-Smorodinsky uniquely satisfies (1)-(  3 ) plus (  5 ) resource monotonicity, which means that all players are weakly better off when there are more resources to go around. The egalitarian solution instead satisfies (1), (  2 ), (4), and (5). The utilitarian welfare function is implicitly used in the work of  Peysakhovich and Lerer [2017a] ,  Lerer and Peysakhovich [2017] ,  Wang et al. [2018]  on cooperation in sequential social dilemmas. BoS B S B 4, 1 0, 0 S 0, 0 2, 2 PD C D C -1, -1 -3, 0 D 0, -3 -2, -2 Figure  1 : Payoffs for asymmetric Bach or Stravinsky (BoS) and the Prisoner's Dilemma (PD). BoS (Figure  2 , left), different welfare functions pick out different Pareto-optimal payoff profiles. For instance, taking the disagreement point to be d 1 , d 2 = (0, 0), the Nash welfare is optimized at (3.0, 1.5), whereas the egalitarian welfare is optimized at (2.0, 2.0). On the other hand, all welfare functions in Table  1  agree on the payoffs corresponding to (C, C) in the iterated Prisoner's Dilemma (Figure  2 , right). In the following, we compare mixed-motive coordination problems to the more general equilibrium selection problem and to sequential social dilemmas. \n Relation to other cooperation problems Equilibrium and Pareto selection problems It is well-known that achieving cooperation between independently-trained agents this is a challenging problem for MAL in general (e.g.,  Boutilier 1999 , Matignon et al. 2012 , Hu et al. 2020 ). One reason is that there are often multiple equilibria, such that (to the extent that one wants to deploy a policy which is a best-response to that of one's counterpart) the choice of a policy constitutes an equilibrium selection problem. Such problems even arise in the fully cooperative case, i.e., when V 1 = V 2 ≡ V , and are then also called Pareto selection problems  [Matignon et al., 2012]  or pure coordination problems. In a pure coordination problem, any π ∈ arg max π V (π) has an optimal value and is thus in equilibrium. There is an equilibrium selection problem if there exist π, π ∈ arg max π V (π) such that (π 1 , π 2 ) has Pareto-suboptimal payoff profile. Mixed-motive coordination problems that occur between policy profiles in equilibrium are a subclass of equilibrium selection problems. They only occur in general-sum, non-fully cooperative cases and pose a challenge which is qualitatively different from the fully cooperative case: players have to coordinate among options over which they have conflicting preferences. The pure coordination problem can be solved by merely giving the players a chance to converge upon a coordinated policy profile (as in  Boutilier [1999] , for instance) and any such policy will do equally well. This is not so in mixed-motive coordination problems, since agents that are open to converging upon any Pareto-optimal outcome would be exploitable by opponents that insist on an outcome they prefer. (See Example 6.0.1 for a concrete illustration of this difference.) Sequential social dilemmas Sequential social dilemmas (SSDs), as defined by  Leibo et al. [2017] , are POSGs whose policy space contains subsets corresponding to cooperation and defection, called Π C i and Π D i , respectively. At each state, the normal form game whose payoffs are value functions under profiles of policies in Π C i , Π D i satisfies the social dilemma inequalities  [Macy and Flache, 2002] , where atomic \"cooperate\" and \"defect\" actions are replaced with elements of Π C i , Π D i . An SSD is not necessarily an equilibrium selection problem. For instance, any Pareto-optimal and symmetric policy profile will select an equilibrium profile that leads to constant cooperation in the iterated Prisoner's Dilemma, and which is compatible with other such profiles. But other SSDs may exhibit multiple incompatible ways of implementing cooperation. SSDs with symmetric Pareto-optimal equilibria are in any case not mixed-motive coordination problems. This includes the Gathering, Wolfpack  [Leibo et al., 2017] , and Coin Game  [Peysakhovich and Lerer, 2017a]  environments. For instance, in the Coin Game, the single cooperative payoff profile is attained when agents get only the coin of their own color, rather than attempting to take their counterpart's coin as well. \n Learning algorithms Play between policies trained by different runs or variations of an algorithm, or \"cross-play\"  [Hu et al., 2020]  is problematic for MCPs. To illustrate the need for evaluating policies in cross-play, we train policies using two multi-agent learning algorithms which have been shown to achieve cooperation in SSDs. The first is a variant of  Lerer and Peysakhovich [2017] 's approximate Markov tit-for-tat (amTFT). The original amTFT algorithm trains a cooperative policy on the utilitarian welfare (Table  1 ), as well as a punishment policy, and switches from the cooperative to the punishment policy when it detects that the other player is defecting from the cooperative policy. We consider the more general class of algorithms in which a cooperative policy is constructed by optimizing some welfare function. Call the version of amTFT in which the cooperative policy optimizes welfare function w as amTFT(w). In our experiments, we use the utilitarian welfare function w Util and an inequity averse welfare function w IA . Following  Hughes et al. [2018] , this welfare function is constructed using modified reward functions which penalize inequitable outcomes: V IA i (a t 1 , a t 2 ; α, β) = r 1 (a t 1 , a t 2 ) + r 1 (a t 2 , a t 2 ) − α[e t 1 (a t 1 , a t 2 ) − e t 2 (a t 1 , a t 2 )] + − β[e 2 (a t 1 , a t 2 ) − e 1 (a t 1 , a t 2 )] + where [x] + = max{x, 0} and e t i are smoothed cumulative rewards computed as e t i (a t 1 , a t 2 ) = γλe t−1 i (a t−1 1 , a t−1 2 )+ r i (a t 1 , a t 2 ) with hyperparameter λ. and discount factor γ α and β control how much unequal outcomes are penalized.  3  The second learning algorithm is learning with opponent-learning awareness (LOLA;  Foerster et al. 2018 ) a policy gradient method in which learners attempt to shape the others' learning through the choice of their own policy updates. Write V i (θ 1 , θ 2 ) as the value to player i under a profile of policies with parameters θ 1 , θ 2 . Then, the LOLA update for player 1 at time t with parameters δ, η > 0 is θ t 1 = θ t−1 1 + δ∇ θ1 V i (θ 1 , θ 2 ) + δη [∇ θ2 V 1 (θ 1 , θ 2 )] T ∇ θ1 ∇ θ2 V 2 (θ 1 , θ 2 ). We use the discount factor γ = 0.96 throughout. \n Results Here we illustrate the special problem posed by MCPs by comparing the performance of the learning algorithms above in iterated BoS (IBoS) and in the iterated Prisoner's Dilemma (IPD). The folk theorems  [Mailath et al., 2006]  tell us that, for players with sufficiently high discount factors, any payoff profile of the stage game in which players get at least as much as they can unilaterally guarantee themselves can be attained in an equilibrium of the repeated game. IBoS is an MCP with respect to the set of welfare functions W = {w Util , w IA }, since these welfare functions are optimized by distinct payoff profiles for sufficiently large values of α, β. We measure the performance of these algorithms in self-play and cross-play. Self-play payoffs are the average payoffs attained by a profile of policies produced by the same training run. Cross-play payoffs are the average payoffs attained by a profile of two policies produced by two different training runs. In the case of amTFT, we also consider cross-play between policies trained with amTFT(w Util ) and those trained with amTFT(w IA ). \n LOLA Following  Foerster et al. [2018] 's parameterization of policies in the iterated Prisoner's Dilemma, we used policies which condition on the previous pair of actions played, with one parameter for every possible previous action profile. To learn policy profiles, we used a discount factor of γ = 0.96 and applied LOLA to the closed-form value functions (which can be computed for each policy profile using the Bellman equations; this is called exact LOLA in  Foerster et al. [2018] ). Figure  2 : LOLA average payoff profiles for 40 training runs in IBoS (left) and IPD (right). Cross-play payoffs were obtained by randomly sampling 40 pairs (π 1 , π 2 ), where π 1 and π 2 come from different runs. A small amount of random noise is applied to each point to enhance visibility. On average, self-play yields payoffs (2.69, 1.34), while cross-play yields (1.30, 0.70). As Figure  2  shows, the self-play payoffs almost all lie close to the empirical Pareto frontier, which consists of payoff profiles roughly equal to {(4, 1), (3, 1.5), (2, 2)}. This clustering is caused by the policies depending only on actions taken at the previous timestep, which allows for always playing (S,S), alternating between them, or always playing (B,B). These coincide with the maxima for w Util , the Nash welfare  [Nash, 1950]  under disagreement profile (0, 0), or w IA . On the other hand, the cross-play points are much more often Pareto-suboptimal. This is not surprising, as if LOLA produces tit-for-tat-like strategies which punish deviations from a particular strategy profile, then playing policies from separate runs is liable to lead to incompatible policies and therefore punishments. \n amTFT We evaluated self-and cross-play for amTFT in IBoS and IPD, where each episode lasted 100 of steps. Payoff profiles from individual runs are displayed in Figure  3 , and average payoffs under self-and cross-play for each combination of welfare functions are displayed in Table  2 . Table 2: Self-play (\"•\") and cross-play (\"×\") payoffs in IBoS for amTFT(w Util ) and amTFT(w IA ). Payoffs are averages over 40 training runs. w Util × w IA leads to the same payoff regardless of which player operates under which welfare function. All standard errors were below 0.01. Of course, the goal of developing benchmarks is not only to point out flaws in existing approaches, but also to help develop better ones. In this section we discuss several research directions for ameliorating MCPs, and give a toy illustration of one approach. \n Policy profile w Util • w Util w IA • w IA w Util × w Util w IA × w IA w Util × Coordination by the principals MCPs can be solved if the principals can agree on a way of selecting among policy profiles to deploy. For instance, principals might agree on a welfare function, and choose learning algorithms which converge to an optimizer of that welfare function. Coordination on a welfare function (and among equilibria which all maximize that welfare function) may be easy in toy environments such as the ones we have considered. But as systems become more complex, it will likely be intractable for principals to fully coordinate so as to train welfare-optimal agents. Thus there is a need to develop methods for low-bandwidth coordination between principals training agents in MCPs which captures most of the benefits of full coordination. Bandwidth-constrained coordination has already been studied in fully cooperative games (e.g.,  Stone and Veloso 1999, Zhang et al. 2019) . Compromise between welfare functions We have not discussed how giving agents the opportunity to communicate post-deployment might ameliorate MCPs. One possibility is to have them reach a compromise over different welfare-optimal policy profiles before deciding which to deploy. On possibility is for the train to several policies corresponding to several welfare functions according to which they are willing to play. When given the chance to communicate, their agents can then apply a bargaining protocol to this reduced set of policy profiles. Here is a simple example of such a protocol. Agents first announce the sets of policy profiles they are willing to play. If these sets overlap, a policy profile is taken at random from the intersection (compare with  Chakravorti and Conley [2004] 's discussion of randomization between the Nash and Kalai-Smorodinsky bargaining solutions in the asymmetric iterated Prisoner's Dilemma). Only when these sets do not overlap do agents revert to a default policy. We give an illustration in Example 6.0.1. Example 6.0.1 (Bargaining over amTFT policies). An example of a protocol for bargaining over welfareoptimal policy profiles is given in Algorithm 1. Policies are obtained by applying amTFT to a welfare function w, returning a policy amTFT(w) i for player i. Refer to the strategy which reports welfare functions W i and default policy π d i as (W i , π d i ).  {(W 1 , π d 1 ), (W 2 , π d 2 )} in this bargaining protocol applied to IBoS. This payoff matrix clearly shows the tradeoff between exploitability and robustness to independentlytrained policies. The strategies which play {w Util , w IA } are of more robust, in the sense that they avoid the mutually dispreferred profile of (1.0, 0.3). However, these strategies are not played in equilibrium, because they are exploitable: an agent can deviate from this profile by instead playing only their preferred welfare function. Nevertheless, one has the intuition that it is reasonable to play {w Util , w IA } in view of its robustness, despite the fact that it is exploitable. On the other hand, the situation becomes more complicated when the set of welfare functions under consideration is much larger. Identifying reasonable solution concepts for this setting is an important direction for future work. Besides the fact that avoiding bargaining failure is still not guaranteed, there are additional problems for this protocol. First, it may be ex-ante Pareto suboptimal, because randomization between Pareto optimal payoff profiles may be ex-ante Pareto suboptimal. Second, while it assumes that agents agree to uniform randomization over the intersection of their sets, agents will in fact have differing preferences over different distributions with which to randomize, generating another bargaining problem. Less ad-hoc solutions might be found by using a dynamic bargaining protocol (as in the classical Rubinstein bargaining game  Rubinstein 1982) , which may narrow down the set of equilibria. As a final note, compare this protocol with an analogous protocol for a pure coordination problem (Figure  4 ). In this protocol, agents play a default action but also announce a set of actions that they are willing to play. Again, actions are taken uniformly at random from the overap of the sets if it is nonempty, and otherwise the default action is taken. Clearly playing {A, B} is a dominant strategy for each player, unlike the analogous strategy in the protocol for IBoS, where greater flexibility comes at the price of greater exploitability.    Figure 3 : 3 Figure 3: amTFT payoff profiles for 40 training runs in IBoS (left) and IPD (right). A small amount of random noise is applied to each point to enhance visibility. \n Figure 4 : 4 Figure 4: Payoffs for a pure coordination problem. \n Payoff matrix for agents playing Pure Coordination and following a variant of the bargaining protocol in 1 where sets of rather than welfare functions are announced. \n Table 3 displays the payoff table of the game with strategy profiles \n Algorithm 1: Welfare function selection protocol Input: Sets of welfare functions W i , default policies π d i // Independently train policies to maximize welfare functionsfor i = 1, 2 do Π i ← ∅ for w ∈ W i do π w i ← amTFT(w) i Π i ← Π i ∪ {π w i } //Communicate and decide what policies to deployPlayers announce W 1 , W 2 if W 1 ∩ W 2 = ∅ then w ∼ Unif(W 1 ∩ W 2 ) π 1 , π 2 ← π w 1 , π w 2 else π 1 , π 2 ← π d 1 , π d 2 return π 1 , π 2 \n Table 3 : 3 Empirical payoff matrix for agents playing IBoS and following bargaining protocol in Algorithm 1 with welfare functions in {w Util , w IA }.{w Util }, π IA 2 {w IA }, π IA 2 {w Util , w IA }, π IA 2 {w Util }, π Util \n\t\t\t The spirit of an MCP is that independent training predictably leads to policy profiles which optimize different welfare functions, but are incompatible. So one could modify the requirement that welfare-optimal policies be equilibria and retain this spirit. One could replace the requirement of Nash equilibrium with a different or a broader set of solution concepts, e.g., the recently-proposed Markov-Conley chains used in the α-rank evaluation methodology [Omidshafiei et al., 2019] . \n\t\t\t We choose the utilitarian and inequity-averse welfare functions largely for convenience, and not because they have particularly compelling normative properties. Specifically, these welfare functions admit a Bellman equation, allowing us to straightforwardly apply reinforcement learning methods in order to maximize them. Methods for optimizing other welfare functions (Table1), which may be less amenable to off-the-shelf reinforcement learning methods, are a direction for future work.", "date_published": "n/a", "url": "n/a", "filename": "stastny_et_al_implicit_bargaining.tei.xml", "abstract": "Cooperation in settings where agents have different but overlapping preferences (mixed-motive settings) has recently received considerable attention in multi-agent learning. However, the mixed-motive environments typically studied are simplistic in that they have a single cooperative outcome on which all agents can agree. Multi-agent systems in general may exhibit many payoff profiles which might be called cooperative, but which agents have different preferences over. This causes problems for independently trained agents that do not arise in the case of that there is a unique cooperative payoff profile. In this note, we illustrate this problem with a class of games called mixed-motive coordination problems (MCPs). We demonstrate the failure of several methods for achieving cooperation in sequential social dilemmas when used to independently train policies in a simple MCP. We discuss some possible directions for ameliorating MCPs.", "id": "91bccfcbfebaa0a318c1ee4b11f73724"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Quantifying the probability of existential catastrophe: A reply to Beard et al", "text": "Introduction A recent article by  Beard, Rowe, and Fox (Beard, Rowe, & Fox, 2020; henceforth BRF)  surveys methods used to quantify the probabilities of global and existential catastrophes. BRF is a valuable contribution to the study of global catastrophic risk and existential risk. It documents the range of methods in use and evaluates their strengths and limitations, providing both a good resource for researchers wishing to get up to speed on the topic and constructive guidance for future work. In this article, I provide some further commentary on the quantification of the probability of global/existential catastrophe, making some points not made by BRF or other prior literature. At the outset, I wish to express my wholehearted agreement with BRF in the importance of sound methodology for quantifying the probabilities (and severities) of global and existential catastrophes. I regret that I share the view that \"within the nascent field of Existential Risk research people have been insufficiently discriminating\" in the selection and use of quantification methods (BRF, Section 7). The following remarks join BRF in seeking to improve this situation. 2. Some considerations related to severity 2.1. The definition of existential catastrophe BRF defines existential catastrophe as \"the collapse of civilization or the extinction of humanity\". This is a reasonable definition, but there are others. First,  Bostrom (2002)  defines existential catastrophe as an event that \"would either annihilate Earth-originating intelligent life or permanently and drastically curtail its potential\". This definition emphasizes long-term effects. The collapse of civilization would presumably have some long-term effects, though whether the effects would last into the distant future is a complex matter  (Baum et al., 2019) . Second,  Tonn and Stiefel (2013)  define existential catastrophe as human extinction, i.e. loss of the existence of the human species. This paper will use the BRF definition while noting the existence of other definitions for existential catastrophe, for related concepts involving large losses of value such as global catastrophe  (Morrison, 1992) , ultimate harm  (Persson & Savulescu, 2012) , and oblivion  (Tonn, 1999) , and for other concepts involving large-scale harm such as astronomical suffering  (Sotala & Gloor, 2017) . \n Probability vs. severity BRF focuses on methodology for quantifying the probability of existential catastrophe, with limited attention other factors including severity. (This focus was an explicit decision; see BRF, Section 1) That is not unreasonable for a first pass at the topic-there is plenty to say about the probability methodology. However, it is important to recognize the interplay between probability and severity. All quantifications of the probability of existential catastrophe require at least some attention to severity for the simple reason that existential catastrophe is a type of event defined by its severity. More precisely, existential catastrophe is generally defined in terms of some minimum severity threshold; in BRF, the minimum threshold is the collapse of civilization. To assess the probability of existential catastrophe is to assess the probability of a harm greater or equal to the collapse of civilization. In the terminology of catastrophe risk analysis, the probability of existential catastrophe is an \"exceedance probability\", i.e. the probability of harms exceeding some minimum threshold  (Grossi, Kunreuther, & Windeler, 2005) . Quantifying the probability of specific existential catastrophe events (such as a nuclear war or Earth-asteroid collision) requires additional attention to severity. The probability can be decomposed into two constituent parts as follows: = P P P * EC 1 2 (1) In Eq. (  1 ), P EC is the probability of existential catastrophe from some event; P 1 is the probability of the initial catastrophe event; and P 2 is the probability that the event will result in a harm greater or equal to the collapse of civilization. For example, P 1 could represent the probability of nuclear war and P 2 could represent the probability that nuclear war would result in the collapse of civilization or worse. The occurrence of the initial catastrophe event does not necessarily entail the collapse of civilization-that depends on how effectively the survivors can cope with the aftermath of the event. Calculating P EC via Eq. (  1 ) requires two distinct analyses: one for each of P 1 and P 2 . Analysis of P 1 is the analysis of the probability of initial events, and can follow many conventions of probabilistic risk analysis. In contrast, quantifying P 2 requires analysis of the severity, with attention to the success of catastrophe survivors. This is a rather different sort of analysis than is needed to quantify the probability of initial catastrophe events represented by P 1 . However, P 2 is not equivalent to severity. P 2 is a probability variable representing the probability that the severity will exceed a certain threshold. P 2 can be obtained by creating a probability distribution for the severity of an initial event and then calculating the portion of that distribution that exceeds the threshold for existential catastrophe: ∫ = ∂ ∞ P P S S ( ) 2 ST (2) In Eq. (  2 ), P 2 is as in Eq. (  1 ); S is severity of some initial event; and S T is the minimum severity threshold of existential catastrophe Fig.  1 . A depiction of the relationship between P 2 and the severity of an initial event. The graphic is for illustrative purposes only; no evaluation of the actual relationship is intended. (the collapse of civilization in BRF). Eq. (  2 ) is illustrated in Fig.  1 . The studies surveyed in BRF vary in terms of which probabilities they quantify. (BRF acknowledges this; see BRF, Section 1) Out of the 66 studies in BRF, only three-  Chapman (2004) ;  Rees (2003), and Wells (2009) -explicitly quantify the probability of civilization collapse (as obtained from a keyword search of BRF, Appendix A). Of the other 63 studies, some quantify P 1 , while others quantify something similar to P EC but with a different severity threshold.  Chapman (2004)  is the only one of these studies that quantifies P EC via something resembling Eq. (1).  Chapman (2004)  is a study of asteroid impacts. As with many asteroid risk analyses,  Chapman (2004)  quantifies impact probability as a function of asteroid diameter (see Fig.  1  of  Chapman, 2004) . This provides P 1 .  Chapman (2004)  then proposes that asteroids of 2−3 km diameter may qualify as \"civilization destroyers\", while noting that the \"predictions of consequences are fraught with uncertainty\" (p.11; see also  Baum, 2018) . This roughly amounts to postulating that P 2 ≈ 0 for asteroids smaller than 2−3 km diameter and P 2 ≈ 1 for asteroids 2−3 km diameter or larger. However, there is no reason to expect such an extreme discontinuity in P 2 at 2−3 km. A more careful analysis would likely display a distribution of severities (as in Fig.  1 ) across a range of asteroid sizes, finding a continuum of P 2 values that gradually increase as a function of asteroid size. Until such analysis is conducted, one cannot rigorously quantify P EC for asteroid impact. Given that impact probability varies widely as a function of diameter (smaller asteroids have a much higher impact probability), P EC for asteroid impact will be highly sensitive to the resilience of civilization to impact events of different sizes. Similar reasoning applies to other existential risks. The study of  Wells (2009) , p.84-90) is of note because it quantifies P EC directly, without considering P 1 and P 2 . It can do this because is quantifies the overall P EC , not P EC for specific events. The analysis uses a technique that quantifies the probability of something persisting based on how long it has already existed for. Given the current age of civilization, P EC can be calculated.  Wells (2009)  also uses this technique to calculate the probability of human extinction, as do several other studies including  Gott (1993) . Because this technique does not consider any particulars of the existential risks that civilization currently faces, it provides at most a very limited amount of guidance to how the risks can be addressed. The study of  Rees (2003, p.8 ) is more ambiguous. Rees provides a subjective estimate of P EC , stating \"I think the odds are no better than fifty-fifty that our present civilization on Earth will survive to the end of the present century\". The text does not explain how the estimate was made. The broader study presented by  Rees (2003)  includes reasoning similar to  Wells (2009)  and analysis of catastrophe scenarios similar to  Chapman (2004) . Perhaps the subjective estimate was made in consideration both approaches, but this cannot be discerned from the text. The studies that quantify P 1 are not studies of the probability of existential catastrophe: they are studies of the probability of events that might or might not result in existential catastrophe. For example,  Lipsitch and Inglesby (2014)  quantify the probability that a highly pathogenic influenza strain would escape a research laboratory and cause a pandemic.  Lipsitch and Inglesby (2014)  also quantify the severity of the pandemic, estimating 2 million to 1.4 billion fatalities. To calculate P 2 and in turn P EC , this range of severities would have to be evaluated in terms of the probability of exceeding S T .  Hellman (2008)  quantifies the probability of a \"fullscale nuclear war\" started from a crisis similar to the Cuban missile crisis.  Hellman (2008)  does not quantify the severity and would need to do so to obtain P 2 and P EC . For the studies that quantify something analogous to P EC , analysis of additional scenarios is needed to obtain P EC . For example,  Gott (1993)  quantifies the probability of human extinction; additional analysis would quantify the probability of civilization collapsing without humanity going extinct.  Pamlin and Armstrong (2015)  quantify the probability of the subset of civilization collapse scenarios in which there is no subsequent recovery of civilization; additional analysis would quantify the probability of scenarios in which civilization collapses and recovers. Here it is worth recalling the multitude of definitions of existential catastrophe. The studies of  Gott (1993)  and  Pamlin and Armstrong (2015)  could classify as quantifying P EC under non-BRF definitions. \n Fast vs. slow catastrophes Existential risks can be classified in terms of how quickly the catastrophe unfolds. Specifically, it is the initial catastrophe event that unfolds at different speeds. The initial catastrophe event is the phenomenon that causes the harm, such as a nuclear war or Earthasteroid collision; it is represented in P 1 in Eq. (  1 ). The overall catastrophe scenario also includes the aftermath of the initial event. All existential catastrophes could have long-lasting effects, especially if civilization is not quickly rebuilt after it collapses. Nonetheless, the speed of initial events can vary significantly between different existential risks. The risks included in BRF group into either fast or slow risks. Fast risks have initial events that occur within years or less. Fast risks included in BRF are nuclear war, pandemics, runaway artificial intelligence, asteroid impacts, nanotechnology, particle physics experiments, space weather, super-volcanic eruptions, and synthetic biology. Slow risks have initial events that persist for decades or longer. Slow risks included in BRF are climate change and ecological catastrophe (see BRF, Appendix A; note that the fast vs. slow distinction is my own and does not appear in BRF). This is overall a reasonable list of risks and broadly consistent with other studies of existential risk. The list is not without exceptions-for example, flood basalt volcanic eruptions consist of a series of large eruptions over a period of hundreds of thousands of years; if the eruptions are sufficiently large and frequent, they could cause more prolonged harm  (Schmidt et al., 2016)  and therefore rate as a slow catastrophe. As another example, studies of artificial intelligence sometimes consider that the event could unfold in a \"slow takeoff\" lasting on the order of \"decades or centuries\"  (Bostrom, 2014, p.63) . Regardless, for probability analysis, the distinction between fast and slow is important in several respects. (The distinction can also be important for other reasons beyond the scope of this paper, such as policy decision-making.) First, event probability P 1 can have a different meaning for slow risks. The probability of climate change is approximately 1 (i.e., it is virtually certain that climate change is occurring). The only meaningful uncertainty about climate change risk is about how severe the impacts will end up being, including whether they would amount to existential catastrophe. The same probably applies to the forms of ecological degradation that could result in ecological catastrophe, though the reference cited in BRF on ecological catastrophe  (Pamlin & Armstrong, 2015)  is unclear on this point. Second, slow catastrophes may be especially important when they interact with fast catastrophes. Climate change and ecological degradation may be unlikely to destroy civilization on their own. Instead, they could weaken civilization, making it less resilient to fast catastrophes. All else equal, climate change and ecological degradation may make it more likely that civilization survives a fast catastrophe (such as a nuclear war) if the fast catastrophe occurs in 2020 instead of 2050. (All else is not equal-other factors include, but are not limited to, economic and technological change.) In other words, climate change and ecological degradation increases P 2 for nuclear war (and other fast risks). They could also affect P 1 , such as by destabilizing international politics, or alternatively by providing a rallying point that brings rival nations closer together. Additionally, fast catastrophes could also affect slow catastrophes. For example, the 2011 Fukushima Daiichi nuclear disaster, caused by the Tōhoku earthquake and tsunami, has prompted a shift from nuclear power to fossil fuels, thereby worsening climate change  (Srinivasan & Rethinaraj, 2013) . While the Tōhoku-Fukushima event was only a local catastrophe, the episode is nonetheless indicative of potential impacts of fast catastrophes on slow catastrophes. The above implies that the probability of slow catastrophe can be linked to the probability of fast catastrophe. This applies to most of the risks in BRF. One potential exception is particle physics experiments, for which P 1 may not be meaningfully affected by the slow catastrophes and for which P 2 may 1 under any circumstances (it may be impossible to survive a particle physics catastrophe). Artificial intelligence could be another exception following the same reasoning, though it is conceivable that AI development could be altered by the desire to develop AI to address the slow catastrophes  (Baum, 2014) , or by effects of slow catastrophes on the context in which AI is developed, such as related to international cooperation and competition. But for most cases, quantifying the probability of slow catastrophes should account for their effect on fast catastrophes. It has been argued that the field of existential risk is insufficiently attentive to slow catastrophes, perhaps because slow catastrophes are too \"boring\" or \"unsexy\"  (Kuhlemann, 2019; Liu, Lauta, & Maas, 2018) . My own view is that yes, slow catastrophes have been at least somewhat neglected in studies of existential risk. But it is also the case that slow catastrophes pose distinct analytical challenges, as outlined above. Furthermore, the fields dedicated to studying slow catastrophes tend to not study them in terms resembling existential risk. For example, high-profile research on planetary boundaries identifies approximately ten major global environmental threats that are nominally supposed to be unacceptable to humanity, but are defined in the research strictly in biogeophysical terms and not in terms of impacts to humanity  (Baum & Handoh, 2014) . Likewise, almost all of the studies of slow catastrophes studied in BRF (Section 1) focus on biogeophysical metrics, in particular the magnitude of average global temperature increase from climate change. The one exception is  Pamlin and Armstrong (2015) , which is also probably the only of these studies that classifies within the field of existential risk. (BRF defines the existential risk research community as \"those who are consciously seeking to align their research with the goal of understanding and managing such risks\".) There is a major need for research that blends the traditions of global environmental change and existential risk to analyze, in human terms, the risks of slow catastrophes. \n Multi-risk catastrophes The preceding discussion of slow vs. fast catastrophes raises a more general point. The literature surveyed in BRF consists exclusively of quantifications of specific risks or quantification of the overall probability of existential catastrophe or similar catastrophe. However, some catastrophe scenarios involve multiple risks. These scenarios can require a different set of methods than those surveyed in BRF. One type of scenario involves multiple initial catastrophe events occurring together by coincidence. For example, there could be a volcano eruption that happens to occur as a pandemic is breaking out. The initial events may be independent-for example, there is no reason to believe that infectious diseases affect plate tectonics and vice versa-in which case their probabilities (P 1 in Eq. (  1 )) could be modeled as independent random variables, with the aggregate initial event probability calculated accordingly. However, the probability of existential catastrophe given the co-occurrence of these events (P 2 in Eq. (  1 )) is unlikely to be independent. For example, a volcano eruption can prompt mass evacuations that facilitate disease transmission. Analysis of the severity of co-occurring initial catastrophe events must be done on a case-by-case basis; ditto for the accompanying probability of of existential catastrophe. Another type of scenario involves causal relations between multiple fast catastrophes. For example, there could be a war or pandemic that causes a geoengineering termination shock  (Baum, Maher, & Haqq-Misra, 2013; Parker & Irvine, 2018) , an asteroid collision that causes a nuclear war  (Baum, 2018; Tagliaferri, Spalding, Jacobs, Worden, & Erlich, 1994) , or a war that induces risky technology development (as previously occurred in World War II with the development of nuclear weapons). These scenarios cannot be modeled as independent random variables. They can be modeled using fault trees or Bayesian networks, albeit with more complex models that account for the nuances of each catastrophe within the causal chain. In principle, they could be studied via aggregated opinion surveys, weighted aggregation, or enhanced solicitation, all of which derive from expert judgment. In practice, however, there may be a dearth of qualified experts, because experts tend to focus on one risk at a time and not on the causal relations between them. (The methods mentioned in this paragraph are described in Section 3) Finally, there are scenarios in which a fast catastrophe occurs during a slow catastrophe, as discussed in Section 2.3. Analysis of these scenarios could proceed by evaluating \"baseline\" values of P 1 and P 2 for the fast catastrophe, and then evaluating the effects of the slow catastrophe on the baseline P 1 and P 2 . Alternatively, it could proceed by calculating scenario probabilities directly without first considering baselines. Regardless, the analysis requires a nuanced understanding of the impacts of the slow catastrophe as they relate to the onset and impacts of the fast catastrophe. (Other slow factors, such as economic and technological change, can be factored into the analysis alongside slow catastrophes.) 3. On the methods surveyed by BRF BRF survey ten methods used for quantifying existential catastrophe: 1 Analytical approachesestimating probability from theory without incorporating specific evidence on the risks, such as in the \"doomsday argument\". 2 Extrapolation and toy modelingsimple models that derive probabilities from data on other events on the assumption of an inherent relationship between the probability of the other events and existential catastrophe (noting that no existential catastrophe has previously occurred). 3 Fault treeslogic trees that decompose types of catastrophe events (e.g., nuclear war) into a collection of sequences of precursor events and conditions that can lead to the catastrophe event. 4 Bayesian networkssimilar to fault trees, except also permitting interactions between precursor events (hence a \"network\" instead of a \"tree\"). 5 Adapting large-scale modelsthe models depict details of specific risks (e.g., models of the global climate system to study climate change risk); these models are adapted to study extreme cases of these risks. 6 Individual subjective opinionsubjective judgments of a single person. 7 Aggregated opinion surveyssubjective judgments of multiple people, averaged into a single probability estimate. 8 Weighted aggregationsubjective judgments of multiple people, combined into a single probability estimate using a weighted average, with weights set according to some measure of the quality of the judgment expected from each person. 9 Enhanced solicitationsubjective judgments of multiple people, in which effort is made to improve judgment quality via some combination of training people to provide better opinions and being more careful in how their judgments are obtained. 10 Prediction marketsplatforms for people to place financial bets on their best-guess parameter estimates. \n The tradeoff between quality and accessibility BRF evaluate probability quantification methods according to four criteria: (1) rigor, defined as how effectively the method makes use of available information; (2) uncertainty, defined as how effectively the method handles the considerable uncertainty about the probability of existential catastrophe; (3) accessibility, defined as how readily a research group can apply the method, especially the small interdisciplinary groups that often study existential risk; and (4) utility, defined as the value of the method's results for decisionmaking purposes. BRF presents ratings of ten methods according to each of the four criteria. (The ratings were performed subjectively by the authors. In my own view, their ratings are reasonable.) Ideally, a method would rate well across all four criteria. Unfortunately, none of the methods surveyed by BRF achieve this. The BRF ratings data show a trend in which rigor, uncertainty, and utility are similar to each other and dissimilar to accessibility. Fig.  2 . Rigor vs. accessibility of each method as rated by BRF (data from BRF, Table  1 ). This trend holds across all methods (see BRF, Table  1 ). To illustrate this trend, Fig.  2  plots rigor vs. accessibility. No method is rated high in both, and only weighted aggregation is rated low in both. (More precisely, weighted aggregation is rated medium-low in rigor.) The trend in the data is entirely understandable. Rigor, uncertainty, and utility are all aspects of the quality of the probability quantification produced by the application of a particular method. Obtaining higher-quality results generally requires incorporating more detail about the risk and more nuance in how the detail is processed, both of which tend to make the method less accessible. There can be methods that are low-quality and inaccessible, though one would hope that these have gotten weeded out of the collective risk analysis toolkit. Conversely, however, it may not be possible for a method to be both high-quality and accessible. Quality analysis may inevitably require a substantial investment. The same point applies to applications of a given method. Any method can be applied in ways that are of higher or lower quality. There can be applications of a given method that are low-quality and inaccessible: a lot of resources spent implementing a method poorly. Higher quality implementations of a given method will tend to be less accessible, requiring more effort on the part of the research team, and in some cases more funding to invest in expenses such as travel to interview experts in person (instead of via phone or other mode of remote communication) or rewards to incentivize participants in prediction markets. \n On the role of existential risk quantification \n Why quantify probability (and severity)? Underlying the tradeoff between quality and accessibility is the basic point that the probabilities of potential existential catastrophe scenarios are difficult to rigorously quantify. The scenarios involve complex and unprecedented global processes. Historical data are unreliable or nonexistent. Expert judgment is often unreliable as well-or, perhaps there are no experts. Obtaining quality quantifications requires applying difficult methods, which can be a resource-intensive process in a field in which resources are scarce. Perhaps it would be better to skip the matter entirely and focus on other activities. BRF identify two major reasons to quantify the probabilities and severities of existential risks. The first is the prioritization of efforts to reduce various risks. The second is the evaluation of actions that could decrease one set of risks but increase another (i.e., risk-risk tradeoffs). Both are situations in which actions could affect multiple risks, and in which identifying the best action requires comparing the size of the effect on one set of risks to the size of the effect on another. These sizes are typically measured in terms of the product of probability and severity. Therefore, to identify the best actions in these situations, it is necessary to know the effects of the actions on the probabilities and severities of the risks in question. Quantifying the probabilities and severities is an important first step. (Additional analysis is required to assess the effects of specific actions aimed at reducing the risks, as well as the costs associated with pursuing these actions.) Quantification is not always necessary. Some actions would only affect one risk, or would affect multiple risks in the same direction (increase or decrease). These actions pose no tradeoff and require no quantification to evaluate. Where possible, it can be more efficient to focus on these actions. Indeed, one approach to handling difficult quantification tradeoffs is to search for actions that avoid the tradeoffs.  Graham and Wiener (1995)  refer to these as \"risk-superior\" options, analogous to the concept of Pareto superiority in welfare economics. An \"existential-risk-superior\" option would be one that reduces all existential risks by at least as much as all other options, and reduces at least one existential risk by more than each other option, such that there is reason to favor the existential-risk-superior option and no reason to favor any other option, setting aside reasons unrelated to existential risk. If existential-risk-superior options are identified, there is no further need to quantify the options, because one option is clearly best. However, even then, some quantification may be needed to identify existential-risk-superior options. And in many other cases, there are no existential-risk-superior options. Tradeoffs are inevitable. Quantification is an important research task, however difficult it may be. \n Analysis vs. decision-making Some further perspective can be obtained from considering the relationship between analysis and decision-making. Arguably, analysis of the probability and severity of existential catastrophe should aim to improve the quality of decisions that affect existential risk. Otherwise, the analysis is of mere intellectual interest. Reducing existential risk is (again, arguably) a moral imperative, not an intellectual curiosity. Analysis can improve decisions by enabling the decisions to result in larger reductions in the risk. Phrased differently, the expected value of the action taken is larger with the analysis than without. This is the essence of the concept of the value of information (e.g.,  Barrett, 2017) . Analysis can be valuable even if the action taken is unchanged. As a toy example, perhaps heads would have been chosen in a coin flip anyway, but it would have been a lucky guess, and so there is value in analysis indicating that the coin was indeed going to land on heads. The same reasoning holds for analysis about more complex decisions, including those about existential risk. But decisions do not occur in a theoretical vacuum, and they do not necessarily conform to the ideals of expected value maximization. Decisions are psychological and (often, especially for the most important decisions) social processes. In order to be most useful for reducing the risks, methodology for quantifying probabilities and severities should be designed with the nuances of actual decision processes in mind. This point is captured somewhat by the BRF concept of method utility, but some further elaboration is warranted. A lot of risk analysis is commissioned by clients who seek to use the analysis in their own decision-making. The field of risk analysis has roots in industry, especially nuclear power  (Thompson, Deisler, & Schwing, 2005; Wilson, 2012) . Engineering risk analysis commonly seeks to guide in-house safety decisions of industrial risk managers or regulatory decisions by policy makers at agencies like the US Environmental Protection Agency and Nuclear Regulatory Commission. For this, quantifying the overall probability of some catastrophe can be less important than identifying the specific system components that are most implicated in the risk and likewise in greatest need of attention. This is one reason that engineering risk analysis has gravitated toward methods like fault trees that decompose risks into constituent parts and therefore produce results that help managers focus on specific problems. Existential risk research is less often commissioned by clients. Instead, it is often sponsored philanthropically, whether by private funders or government agencies. The funders do not seek results that they can use for their own decisions. Instead, they wish to support the cause of existential risk reduction and hope that the analysis will in some way be useful to that end. Without decisionmaker clients, existential risk analysis projects must take additional steps to ensure that their analysis improves decision-making, including identifying decision-makers to support. Because of this, there is a greater risk of the analysis working in an academic fashion, disconnected from practical decision-making and not having constructive impact on the risks themselves. (Existential risk is not the only domain in which research lacks decision-maker clients. Another example is research by industry and environmental public interest groups that seek to inform environmental policy; von  Winterfeldt, Kavet, Peck, Mohan, & Hazen, 2012.)  Nonetheless, even without built-in decision-maker clients, it is still important for existential risk analysts to bear in mind how their analysis could be used for decision-making. That means recognizing that there is more to risk management than just numbers for probability and severity. The details of the risks themselves must be understood, and how potential actions can affect the risks, and the psychological and social and institutional contexts in which decisions will be made. This is a lot to account for-as if the probabilities and severities were not a lot on their own-but it is essential for pursuing actual reductions in existential risk and not just academic studies. It can help to recognize that risk analysis can be valuable even if it does not produce any quantification of probability and severity. Often, simply having an analysis that pulls together information about the risk in an intuitive and well-organized fashion is sufficient for improving risk management. In other words, risk analysis can be of value by improving people's mental models of risks, in addition to providing information on the rating or ranking of decision options. Additionally, risk analysis can be of value by creating an opportunity for stakeholders and experts to share risk-related information with each other in a way that crosses typical organizational barriers. The opportunity for people in different groups to talk through key issues affecting risk can be of significant valuable for the practice of risk management, even regardless of formal risk analysis outputs. It is important to not let the pursuit of numbers (of probability, severity, the timing of future events such as AI milestones, etc.) serve as a distraction from the goals of evaluating decision options and improving our understanding and management of the risks. In sum, quantifying probability and severity should be at most only one part of an overall existential risk analysis and management portfolio. But it is still a part, and an important one at that. It is likewise important to use quality methodology in performing the quantifications. \n Conclusion This article has sought to build on the excellent contribution of BRF to provide further perspective on the quantification of the probability of existential catastrophe. This article finds that the probability of existential catastrophe is inherently linked to the severity of events that could result in existential catastrophe, that achieving a higher quality of analysis of the probability will in general require a larger investment in analysis, that analysis of the probability is sometimes but not always necessary for decisionmaking, and that analysis should be designed to support risk management and not just designed as an academic exercise. If these findings are taken into account, together with the analyses of specific methodologies by BRF, then it is believed that risk analyses of existential catastrophe will tend to be more successful at understanding and reducing the risks.", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0016328720300987-main.tei.xml", "abstract": "A recent article by Beard, Rowe, and Fox (BRF) evaluates ten methodologies for quantifying the probability of existential catastrophe. This article builds on BRF's valuable contribution. First, this article describes the conceptual and mathematical relationship between the probability of existential catastrophe and the severity of events that could result in existential catastrophe. It discusses complications in this relationship arising from catastrophes occurring at different speeds and from multiple concurrent catastrophes. Second, this article revisits the ten BRF methodologies, finding an inverse relationship between a methodology's ease of use and the quality of results it produces-in other words, achieving a higher quality of analysis will in general require a larger investment in analysis. Third, the manuscript discusses the role of probability quantification in the management of existential risks, describing why the probability is only sometimes needed for decision-making and arguing that analyses should support realworld risk management decisions and not just be academic exercises. If the findings of this article are taken into account, together with BRF's evaluations of specific methodologies, then risk analyses of existential catastrophe may tend to be more successful at understanding and reducing the risks.", "id": "7b5577d111552851663468016958f851"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Peter Cihon", "Jonas Schuett", "Seth D Baum"], "title": "Corporate Governance of Artificial Intelligence in the Public Interest", "text": "Introduction The corporate governance of artificial intelligence (AI) can benefit from input and activity from a range of stakeholders, including those both within and outside of the corporation. Several recent initiatives call for multistakeholder governance institutions that bring diverse stakeholders together to inform AI governance. Examples include activities of the Global Partnership on AI [1], the European Commission's High-level Expert Group on AI  [2] , and research by Cath et al.  [3] . To date, less attention has been paid to the important opportunities for different stakeholders to contribute to AI corporate governance in their own right-outside the context of dedicated multistakeholder institutions. Those opportunities are the focus of this paper. The importance of AI corporate governance is clear. Corporations play a majorperhaps the primary-role in AI research, development, and deployment. Corporateaffiliated researchers published over 50% more AI research papers than academics in the United States in 2018  [4] . Corporate applications of AI touch on many important public issues, including social justice, economic vitality, and international security. Looking ahead, some have proposed that AI could displace large portions of the human labor pool, resulting in chronic unemployment for many people as well as massive profits for AI companies  [5] . Corporations are also active in the research and development of artificial general intelligence, a technology that some believe could transform the world in ways that are either radically beneficial or catastrophic  [6] . How AI is governed within corporations is therefore of profound societal importance. \n Definitions Broadly speaking, corporate governance refers to the ways in which corporations are managed, operated, regulated, and financed. Important elements of corporate governance include the legal status of corporations in a political jurisdiction, the relationship between investors and executives, information flows within and outside of the corporation, and specific operational decisions made throughout the corporation  [9] . Many people within and outside of a corporation can influence how the corporation is governed. For this reason, we take a broad view on the range of actors relevant for the corporate governance of AI. Our specific focus in this paper is on how AI corporate governance can be improved so as to better advance the public interest. The public interest can be defined in many ways, such as in terms of costs and benefits, or voter preferences, or fundamental rights and duties. Exactly how the public interest is defined can be important for AI corporate governance, as is seen in a variety of controversies over AI applications. This paper does not take sides on the most appropriate conception of the public interest, with one exception, which is to reject the view that corporations' sole aim should be to maximize shareholder profits  [10] , and instead argue that corporations have obligations to a wider range of stakeholders. We recognize that this position is not universally held in the field of corporate governance; however, it does reflect support from many business leaders  [11] . Broadly, our aim is to clarify the mechanisms through which corporate governance can be improved to better advance the public interest. system is deployed, this phase also includes evaluating initial user experience. Phase 4 operates and monitors the AI system in deployment, assessing its outputs and impacts based on the designers' initial intentions and performance metrics as well as ethical considerations. Problems are identified and addressed by reverting back to other phases or eliminating the AI system.  \n Prior Work This paper sits at the intersection of literatures on corporate governance and AI governance. Corporate governance is a large field of scholarship with a long history. Good introductions are offered by Monks and Minow  [19]  and Gordon and Ringe  [20] . AI governance is a smaller and relatively new field of study. For more work in this area, see, for example, works from the AI Now Institute  [21] , Data & Society  [22] , World Economic Forum  [23] , Future of Humanity Institute  [24] , as well as Calo  [25] . One body of literature on AI corporate governance studies public policy proposals, primarily for new, dedicated governance bodies. Calo  [26]  calls for a federal body to address robotics policy. A similar proposal has been discussed in Europe by Floridi et al.  [27] . The European Commission has recently proposed to establish a European Artificial Intelligence Board  [28] . Scherer  [29]  outlines a proposal for a dedicated government agency and a voluntary certification scheme that incentivizes companies to submit to agency oversight in return for limited legal liability. Wallach and Marchant  [30]  propose a governance coordinating committee to support soft law governance that keeps pace with new and emerging AI. Erdélyi and Goldsmith  [31]  call for an international regulatory agency to address international AI challenges; Cihon et al.  [32]  argue that it is too soon to establish such an international structure and that further debate is first needed. Clark and Hadfield  [33]  propose a markets-based approach to AI safety regulation. Some literature has analyzed existing regulations as they pertain to corporate AI. The E.U. General Data Protection Regulation (GDPR) has been of particular interest in this respect. For example, Wachter et al.  [34]  argue that the GDPR does not afford a \"right to explanation\" of automated decision-making, whereas Goodman and Flaxman  [35]  argue that it does. Another body of literature analyzes the European approach to AI regulation. Smuha  [36]  analyzes the emerging regulatory environment for making AI trustworthy. Thelisson et al.  [37]  and Stix  [38]  survey the broader regulatory landscape in the EU. There is also some literature on a number of national regulations. For example, Wagner et al.  [39]  analyze different corporate strategies for complying with algorithmic transparency requirements imposed by the German Network Enforcement Act. There is also an extensive body of literature on specific policy instruments and governance approaches. For example, Senden  [40]  and Marsden  [41]  disentangle the concepts of soft law, self-regulation, and co-regulation.  Kaminski [42]  conceptualizes approaches between command and control regulation and self-regulation as \"binary governance\", while Pagallo  [43]  uses the framing of a \"middle-out approach\". Zeitlin  [44]  discusses the current state of transnational regulation within and beyond the E.U.  \n Prior Work This paper sits at the intersection of literatures on corporate governance and AI governance. Corporate governance is a large field of scholarship with a long history. Good introductions are offered by Monks and Minow  [19]  and Gordon and Ringe  [20] . AI governance is a smaller and relatively new field of study. For more work in this area, see, for example, works from the AI Now Institute  [21] , Data & Society  [22] , World Economic Forum  [23] , Future of Humanity Institute  [24] , as well as Calo  [25] . One body of literature on AI corporate governance studies public policy proposals, primarily for new, dedicated governance bodies. Calo  [26]  calls for a federal body to address robotics policy. A similar proposal has been discussed in Europe by Floridi et al.  [27] . The European Commission has recently proposed to establish a European Artificial Intelligence Board  [28] . Scherer  [29]  outlines a proposal for a dedicated government agency and a voluntary certification scheme that incentivizes companies to submit to agency oversight in return for limited legal liability. Wallach and Marchant  [30]  propose a governance coordinating committee to support soft law governance that keeps pace with new and emerging AI. Erdélyi and Goldsmith  [31]  call for an international regulatory agency to address international AI challenges; Cihon et al.  [32]  argue that it is too soon to establish such an international structure and that further debate is first needed. Clark and Hadfield  [33]  propose a markets-based approach to AI safety regulation. Some literature has analyzed existing regulations as they pertain to corporate AI. The E.U. General Data Protection Regulation (GDPR) has been of particular interest in this respect. For example, Wachter et al.  [34]  argue that the GDPR does not afford a \"right to explanation\" of automated decision-making, whereas Goodman and Flaxman  [35]  argue that it does. Another body of literature analyzes the European approach to AI regulation. Smuha  [36]  analyzes the emerging regulatory environment for making AI trustworthy. Thelisson et al.  [37]  and Stix  [38]  survey the broader regulatory landscape in the EU. There is also some literature on a number of national regulations. For example, Wagner et al.  [39]  analyze different corporate strategies for complying with algorithmic transparency requirements imposed by the German Network Enforcement Act. There is also an extensive body of literature on specific policy instruments and governance approaches. For example, Senden  [40]  and Marsden  [41]  disentangle the concepts of soft law, self-regulation, and co-regulation.  Kaminski [42]  conceptualizes approaches between command and control regulation and self-regulation as \"binary governance\", while Pagallo  [43]  uses the framing of a \"middle-out approach\". Zeitlin  [44]  discusses the current state of transnational regulation within and beyond the E.U. The legal liability of corporations for harms caused by AI systems has been another major focus. Broadly speaking, liability regimes aim to compensate victims of harms caused by products and, in turn, encourage producers to avoid the harms in the first place. AI liability regimes are generally not written specifically for the corporate sector, but in practice mainly affect commercial products. The exact form of liability regimes can vary substantially across jurisdictions and circumstances. Separate literatures discuss AI and robotics under liability law in different jurisdictions, including the United States  [29, [45] [46] [47] [48] , the E.U.  [49] [50] [51] [52] [53] , and Germany  [54] [55] [56] . Additionally, more theoretical approach considers whether liability regimes could handle extreme catastrophic risks from AI, such as those of potential long-term artificial general intelligence  [57] . A variety of other AI corporate governance topics have also been studied. Buolamwini and Gebru  [58]  assess the efficacy of targeted audits and publicly shaming AI companies to address biases in facial recognition systems. More generally, Baum  [59]  explores the social psychology of AI developers as a factor in efforts to steer their work in pro-social directions. Belfield  [60]  details recent employee activism within the AI community and its impact on AI firms and technological development. Askell et al.  [61]  analyze competitive pressures on AI firms in terms of their societal impacts. Solaiman et al.  [62]  examine the societal implications of deciding to publicly disclose AI models, focusing on the case of OpenAI. Cihon  [63]  reviews the role of international technical standards in governing AI research and development. Baum  [64, 65]  analyzes potential corporate efforts to manipulate public debate about AI risks. O'Keefe et al.  [66]  propose a novel method of corporate social responsibility that sees AI firms contribute to the public benefit. Avin et al.  [67]  and Ballard and Calo  [68]  use forecasting and roleplay methods to study potential future behaviors of actors affecting corporate AI. A large number of articles published in magazines such as the Harvard Business Review and MIT Technology Review offer practical insights for managers on governing both AI development and adoption within firms. Hume and LaPlante  [69]  analyze how companies can manage biases and risks along the AI building process. Tiell  [70]  recommends corporations establish an ethics committee. Chamorro-Premuzic et al.  [71]  offer a step-by-step approach on how companies can build ethical AI for human resources. Fountaine et al.  [72]  outline how management should build AI-powered organizations. Abbasi et al.  [73]  analyze how companies can mitigate the risks of automated machine learning. Hao  [74, 75]  urges AI companies to actually implement their ethical guidelines, while also emphasizing how difficult this will be. Consulting firms have also published reports on AI corporate governance. Burkhardt et al.  [76]  of McKinsey describes how Chief Executive Officers (CEOs) can guide employees to build and use AI responsibly. Cheatham et al.  [77] , also of McKinsey, discuss how managers can mitigate AI risks. Ransbotham et al.  [78]  of the Boston Consulting Group survey more than 2500 corporate executives on AI topics including how companies are managing AI risks. Several major accounting firms have developed governance frameworks to promote ethical AI  [79] [80] [81] . Deloitte  [82]  reports on AI risk management in the financial industry. Accenture  [83]  covers corporate AI ethics committees. \n Actor-Specific Opportunities to Improve AI Corporate Governance A variety of actors can improve AI corporate governance so as to better advance the public interest. This section considers nine types of actors. Three are internal to the corporation: managers, workers, and investors. Six are external: corporate partners and competitors, industry consortia, nonprofit organizations, the public, the media, and governments. Although presented separately for clarity, these actors interact, overlap, and co-exist in practice. These various types of actors have important interactions. For example, the media can channel worker influence within firms, facilitate public pressure, and precipitate government action. Actors have the potential to overlap, for example, with governments publishing media reports or taking over management of a company. Ultimately, all actors co-exist within political cultures, which may vary by country and over time  [84] : although the following sections describe actions that each actor could take to improve AI corporate governance, we do not offer analysis of the feasibility nor the desirability for such actions within their political cultural contexts. \n Management Management, as the term is used in this paper, includes all personnel with authority and oversight over other personnel, from top C-suite executives to mid-and lower-level managers. Management is an important-perhaps the most important-type of actor in corporate governance. Management establishes policies, implements processes, creates structures, and influences culture, all of which impact AI development. One way management can advance AI in the public interest is by establishing corporate policies. One type of policy is strategic objectives. For example, management could establish the objectives of pursuing AI development where it is clearly in the public interest and avoiding contentious settings such as law enforcement. Another type of policy is ethics guidelines that specify how the corporation should develop and use AI and related technologies. Recently, management at many companies have established AI ethics guidelines, including Google, IBM, Microsoft, and OpenAI  [85] . An ongoing challenge is to translate ethics guidelines into AI practice  [86] . The translation process can include more operational policies on the details of how a company should develop and use specific AI techniques. Likewise, a concern is that published principles could create the appearance of AI corporations acting in the public interest without them actually doing so  [87] . Management can also enact processes that translate policies into practice. These processes can take many forms. For example, management can establish new review processes for AI or augment existing review processes, such as those conducted by compliance and risk management teams. Additionally, management can encourage or require the use of documentation methods that generate and distribute information needed to ensure compliance with AI principles  [88] . Notable examples include Datasheets for Datasets  [89] , a standardized reporting document for dataset features, and Model Cards  [90] , an approach to consistently describing an AI model and its intended use case. These processes could be improved if management were to review their efficacy and publicly share best practice. Management activity on policies and processes is seen, for example, in the caution of OpenAI on publishing potentially harmful AI work. In 2019, OpenAI released their GPT-2 language model in phases out of concern about its potential harmful applications  [7, 62] . OpenAI created a review process to evaluate the social impacts of earlier releases before determining if and how to release more advanced versions of GPT-2. OpenAI's discussion of its phased release  [7]  references the OpenAI charter  [91] , a policy document that expresses the principle of factoring safety and security concerns into decisions of what work to publish. (Note: the charter was published in 2018, when OpenAI was a nonprofit.) Although authorship of the charter is attributed to \"OpenAI\", it is likely that OpenAI management played a central role in drafting and approving the document, which anchors the organization's \"primary fiduciary obligation\"  [92] . Additionally, the OpenAI GPT-2 team includes a mix of workers and management, including OpenAI co-founder and Chief Scientist Ilya Sutskever; thus, it can be inferred that management was likely involved in the review process. In summary, the GPT-2 release appears to demonstrate how management may translate policies into processes to support AI development and use in the public interest. Management can also create structures within the company dedicated to advancing AI in the public interest. Such structures can perform oversight, make recommendations, and provide expertise to people throughout the company. They can consist of company staff and often interact with numerous teams across the organization. Prominent examples include the Microsoft advisory committee AI, Ethics, and Effects in Engineering and Research, the compliance-oriented Microsoft Office of Responsible AI, the Google Responsible Innovation Team, the AI Principles working group within the Google Cloud division, and a Facebook team of policy managers that work with product teams on fairness and explainability problems. Alternatively, the groups can consist of external advisors, such as the Google DeepMind Ethics & Society division's group of external advisors, the Axon AI and Policing Technologies Ethics Board, and the short-lived Advanced Technology External Advisory Council at Google. Thus far, these dedicated structures have had mixed success. One success came at Axon. Its ethics board advised against the company selling facial recognition to law enforcement; management followed this advice  [93] . A failure occurred at Google, which disbanded its Advanced Technology External Advisory Council soon after its launch amid outcry about its membership  [94] . Overall, these structures are relatively new and not yet in wide use, and much is still being learned about them. Nonetheless, one early lesson is that AI governance teams ought to be interdisciplinary. Regardless of where such a team may be within the reporting structure, it may be expected to include lawyers, ethicists, data scientists, engineers, program managers, and other diverse occupational perspectives. Management can also build AI governance functions into pre-existing structures. Important areas for this may be in compliance and risk management. Current compliance and risk management teams may focus less on AI and more on established risks such as computer security  [95] . However, as governments increase their policy attention to AI, the need for corresponding activity within corporations will increase. It is likely that the pre-existing corporate structures could build expertise in AI risks over time, as the field of AI corporate governance matures, as standards are published, and as regulations enter into force. Forward-thinking management can advance this process by setting the groundwork, such as by building AI expertise into pre-existing structures. Finally, management can help cultivate a corporate culture that supports AI development in the public interest. Corporate culture can play a major role in how a company develops and uses AI  [59, 96] . Employee onboarding and training could include a focus on responsible AI development  [97] . Recruiting efforts could select for, or aim to instill, knowledge of responsible AI development methods. Employee performance reviews and metrics could incentivize these methods' use, from concretely assessing bias in training data at the design phase to more broadly upholding a culture of responsible development. On the latter, OpenAI has tied compensation levels to adherence to its charter  [98] . However, it is unclear what additional steps dominant AI firms are now taking to instill their AI principles into corporate culture. \n Workers We use the term workers to refer specifically to people who work at the company and do not have managerial authority. This includes, in their subordinate relationship to top management, lower-and mid-level managers. Workers include employees and contractors, both of which are common at AI companies. A wide range of workers affect AI, including researchers, engineers, and product developers. Despite being expected to follow directions from management, workers at AI firms have considerable power to shape corporate governance. Workers are often left with significant latitude to determine corporate activity within their areas of focus, and management is often (although certainly not always) influenced by worker suggestions. Workers can influence AI corporate governance both directly, through their actions affecting AI systems, and indirectly, by influencing management. While management makes many governance decisions, especially high-level decisions for the corporation and its divisions, many other decisions are left to workers, especially on the specifics of AI design and implementation. Worker opportunities for direct influence may be especially robust at earlier stages of the AI system lifecycle and at corporations and divisions whose management offer workers wide latitude for decision-making. Likewise, worker opportunities for indirect influence may be greatest at corporations and divisions whose management is especially receptive to worker input. Some of the best opportunities for worker direct influence may be for workers in groups conducting fundamental research, such as Facebook AI Research, Google Brain and DeepMind, Microsoft Research, and OpenAI. Workers in these groups may have significant autonomy from management to pursue their work as they see fit. Indeed, these workers may be influenced less by management and more by academic norms, research fashions, reputational concerns, conference requirements, journal expectations, and their own personal values. Likewise, those seeking to influence corporate AI researchers may find good opportunities via the broader field of AI, such as at leading conferences. For example, as of 2020, the NeurIPS conference uses an ethics review process and requires papers to include a social impact statement  [99] . These activities can be important for AI corporate governance due to the significant autonomy of corporate AI researchers. Workers also have significant opportunities to indirectly affect AI corporate governance by influencing management. However, these opportunities can be risky for workers because of managements' control over-or at least considerable influence on-workers' employment and advancement within the corporation. In general, activities that involve a higher degree of worker commitment and risk of reprisal by management will tend to have a greater effect on corporate governance. Low-commitment, low-risk activities can be as simple as raising concerns in project meetings over issues of ethical AI development. These activities tend to be low-profile and not well-documented; colleagues at AI companies inform us that these activities are nonetheless common. More ambitious and risky activities tend to be less common but more visible and more well-documented. These activities can include circulating letters critiquing corporate activity and calling for change, whistleblowing, organizing walkouts, forming unions, and more  [60] . Likewise, the extent of indirect worker influence is shaped by management's receptiveness to worker input and on related management decisions regarding corporate policy and culture. In extreme cases, management can fire workers who push back against management AI corporate governance decisions. For example, Google fired its Ethical AI team co-lead, Timnit Gebru, following a disagreement over the publication of a paper critical of the company's research on large AI language models  [100] . Additionally, several Google employees claim to have been fired as retribution for labor organizing, in possible violation of U.S. labor law  [101] . Subtler dynamics include such matters as whether workers have dedicated spaces to organize and articulate their views. For example, Google has internal discussion forums for workers, although management recently hired a team to moderate them  [102] . Google management also recently eliminated its regular meetings where employees could address executives  [103] . In general, workers will have greater indirect influence on AI corporate governance when they can organize and express views to management without fear of retaliation. The size of the labor pool also affects both direct and indirect worker influence. Some governance goals may benefit from a large labor pool, such as the goal of solving difficult technical problems in orienting AI toward the public interest. Greater availability of worker talent may make these problems easier to solve. On the other hand, a larger labor pool can make it difficult for workers to self-organize and reach consensus. Likewise, a large labor pool relative to demand for their labor reduces indirect worker influence on AI systems via their influence on management  [60] . At present, there is a shortage of talent in the computer science and engineering dimensions of AI, giving workers in these areas considerable indirect influence. These workers are hard to hire and to replace upon firing; therefore, management may be more inclined to accept their demands. This influence could fade if the labor market changes due to increased university enrollment in AI courses and the many government calls for training more people in AI  [104]  (pp. 111-126);  [105] . Labor demand could also shrink if the applications of AI plateau, such as due to a failure to overcome limitations of current deep learning algorithms  [16]  or due to the rejection of AI applications on moral, legal, or social grounds. For now, though, demand for AI is robust and growing, giving AI scientists and engineers substantial power. One powerful pattern of indirect worker influence starts with whistleblowing and continues with widely signed open letters. Workers with access to information about controversial AI projects leak this information to media outlets. Subsequent media reports spark dialogue and raise awareness. The media reports may also make it easier for other workers to speak publicly on the matter, because the workers would no longer have to shoulder the burden of being the one to make the story public. The open letters then provide a mechanism to channel mass worker concern into specific corporate governance actions to be taken by management. (See also Sections 4.1 and 4.8 on the roles of management and the media.) This pattern can be seen in several recent episodes at Google. In 2018, Google's participation in Project Maven, a U.S. Department of Defense project to use AI to classify the content of drone videos, was anonymously leaked to Gizmodo  [106] . The Gizmodo report does not explicitly identify its sources as Google workers, but this is a likely explanation. Subsequently, over 3000 employees signed an open letter opposing Google's work on Project Maven  [107] . Google management later announced it would leave Project Maven and publish principles to guide its future work on defense and intelligence projects  [108] . Additionally, in 2018, The Intercept reported Google's work on Project Dragonfly, a Chinese search engine with built-in censorship  [109] . The Intercept report was also based on an anonymous source that appears to be a Google worker. Subsequently, over 1000 employees signed a letter opposing the project  [110] . Google management later ended the project  [111] . A somewhat similar pattern is observed in a 2018 episode involving sexual harassment at Google. A New York Times investigation of corporate and court documents and interviews of relevant people found that Google had made large payments to senior executives who left the company after being credibly accused of sexual harassment  [112] . Soon after, Google workers organized walkouts in which thousands of workers walked out in support of corporate policy changes on harassment and diversity  [113] . The organizers referenced the New York Times report but did not specify the extent to which the walkout was motivated by the report. The organizers later wrote that Google management made some but not all of their requested policy changes  [114] . These sorts of worker initiatives are not always successful. In 2018, an unspecified number of Microsoft employees published an open letter calling on Microsoft to abandon its bid for the Joint Enterprise Defense Infrastructure contract, a U.S. Department of Defense cloud computing initiative  [115] . Microsoft did not abandon its bid, although Microsoft President Brad Smith did respond by articulating Microsoft policy on military contracts  [116] . Additionally, in 2018, hundreds of Amazon employees signed a letter demanding the company stop selling facial recognition services to law enforcement  [117] . Management did not stop. Again in 2018, approximately 6000 Amazon employees signed a letter calling on the company to stop using AI for oil extraction. The letter was accompanied by a shareholder resolution making the same argument-an example of investor activity (Section 4.3). Again, management did not stop  [118] . \n Investors Corporations take investments in a variety of forms, including by selling shares of stock or issuing bonds. Investors are important because AI is often capital-intensive, requiring extensive funding for research, development, and deployment. Shareholders are the investors with the most capacity to influence corporate governance and are therefore the focus of this section. Indeed, a central theme in corporate governance is the principalagent problem in which the principals (i.e., shareholders) seek to ensure that their agents (i.e., corporate management) act in the principals' best interests rather than in those of the agents. In contrast, issuers of bonds are generally less influential, in part because markets for bonds are highly competitive-a corporation can readily turn to other issuers instead of following one issuer's governance requests. Investors can influence corporations in several ways. First, investors can voice their concerns to corporate management, including at the annual shareholder meetings required of U.S. companies. Investor concerns can, in turn, factor into management decisions. Second, shareholders can vote in shareholder resolutions, which offer guidance that is generally non-binding but often followed  [19]  (p. 117). Indeed, even resolutions that fail to pass can still succeed at improving corporate governance; evidence for this has been documented in the context of environmental, social, and governance (ESG) issues  [119] . Third, shareholders can replace a corporation's board of directors, which has ultimate responsibility to manage the corporation, determines strategic direction, and appoints the CEO. For example, shareholders could seek to add more diversity to a board, noting that boards with increased diversity are associated with greater support for corporate social responsibility efforts  [120] . Fourth, investors can signal disapproval with corporate governance practices by selling off their investments, and, perhaps, investing in a better governed competitor. Fifth, shareholders can file lawsuits against the corporation for failing to meet certain obligations  [121] . These lawsuits are often settled in ways that improve corporate governance  [19]  (p. 117). In principle, investors can wield extensive power over a corporation via their control over the board of directors. If management does not follow investor concerns or shareholder resolutions, the shareholders can replace the board with people who will. In practice, however, investor power is often limited. Efforts to replace a board of directors are expensive and rare  [19]  (p. 117). One study found that activist investors launched 205 campaigns in 2019 and won only 76 board seats  [122] . This reality gives management substantial latitude in corporate governance. Nonetheless, management often does respond to investor preferences, especially, but not exclusively, when their preferences affect the company's stock price. The power of investors is also influenced by the availability of alternative investment options. A diverse market of AI investment opportunities would provide investors with opportunities to shift their assets to companies that further the public interest. Current market prospects are mixed. On one hand, much of the sector is dominated by a few large companies, especially Google (Alphabet), Amazon, Facebook, and Microsoft. On the other hand, there is also a booming AI start-up scene today; one study identified 4403 AI-related companies that received a total of USD 55.7 billion in funding in the year ending July 2019  [4]  (p. 91). Companies such as H20 and Fiddler specifically aim to advance explainable AI systems, creating additional opportunities for investors to promote AI in the public interest. Investor initiatives should be well-informed by the state of affairs in the company. This requires some corporate transparency. For example, the U.S. Securities and Exchange Commission (SEC) requires companies to disclose investor risk factors  [123] . In its disclosure, Google (Alphabet) lists AI-related \"ethical, technological, legal, regulatory, and other challenges.\" Amazon cites uncertainty about the potential government regulation of AI. Facebook mentions that AI creates a risk of inaccuracies in its community metrics. Microsoft lists AI as a risk of \"reputational harm or liability\". However, at each company, AI is only a small portion of the overall disclosure, suggesting that the companies see AI as a minor area of risk. Investors could consider the possibility that the companies are not giving AI risks the attention they deserve. The efficacy of investor initiatives as an approach to improving AI corporate governance depends on the willingness of investors to take the matter on and the investors' degree of influence within the company. Investors are diverse and have many interests. Investors with an existing interest in ESG may be especially receptive to promoting AI in the public interest. For example, Hermes, an ESG-oriented investment management business, has written on responsible AI  [124]  and participated in an investor initiative to create a Societal Risk Oversight Committee of the Board at Alphabet  [125] . That initiative ultimately failed  [126] , in part because it lacked the support of Alphabet's founders. Alphabet is structured such that their founders retain a majority of shareholder voting power even though they do not own a majority of the shares; Facebook is structured similarly  [127] . Although Alphabet and Facebook are extreme cases, in general, investor initiatives will tend to be more successful when they are supported by investors who own a larger portion of shareholder voting power. This applies to public corporations that have issued stock. Investors in private corporations may be especially influential, especially for smaller firms, which often have less access to capital markets. Venture capital firms seeking to promote the public interest may be especially successful in improving AI corporate governance among smaller firms. The limited influence of shareholder resolutions can also be illustrated by the failed attempt to restrict Amazon's sale of facial recognition technology to the government. In 2019, shareholders expressed their concern that Rekognition, Amazon's facial recognition service, poses risk to civil and human rights, as well as shareholder value. They requested the Board of Directors to prohibit sales of such technology to government agencies  [128]  (pp.  [18] [19] . In 2020, another resolution requested an independent study of Rekognition, including information about the extent to which such technology may endanger civil rights and is sold to authoritarian or repressive governments  [129]  (pp.  [25] [26] . Both resolutions failed. Even though they would have been non-binding, Amazon tried to block the vote. This unusual attempt was ultimately stopped by the SEC  [130] . Although these resolutions did not succeed in achieving reform, they demonstrate that shareholder activism has begun to focus on AI risks in particular. In short, shareholders wield some influence in the corporate governance of AI. This influence is limited by the sheer volume and variety of risks that weigh on them: AI is not a top of mind. The most used activity available to shareholders thus far has been the resolution. Given that shareholder resolutions are difficult to pass and non-binding when passed, it is unclear if such activities will do much to change corporate governance aside from publicizing particular AI-related governance problems. Over time, as companies continue to emerge that seek competitive differentiation through responsible AI development and as shareholders, particularly institutional investors, continue to value ESG criteria and apply them to AI, the role of investors in responsible AI governance may continue to grow. \n Corporate Partners and Competitors Other corporations exert influence on a corporation developing or using AI in important ways. These other corporations can be direct competitors, themselves developing or deploying AI systems. Alternatively, they can be corporate partners (or, for brevity, \"partners\") that have contractual relationships with said company. Partners can be, among other things, suppliers, customers, or insurers. Partners can use their relationship with the AI company to influence it to advance the public interest. Competing AI corporations can influence each other through direct market competition and in other ways. As classic economic theory explains, competition can result in greater market share for corporations whose products better advance the public interest. There are exceptions, including where there are negative externalities, i.e., harms of market activity that are not captured by market prices, and monopolies, i.e., where a large market share can be used to exclude competition and set relatively high prices. For example, direct competition to develop more powerful machine learning systems can result in better performance for important applications such as healthcare and transportation, but it can also result in more energy consumption and the externalities of global warming via the use of large amounts of computer hardware  [131] . Competitors can also influence each other as peers in the overall field of AI  [132] . One AI corporation's initiatives in the public interest can be adopted or adapted by other AI corporations. For example, in 2020, IBM announced that it would no longer sell facial recognition technology to law enforcement agencies  [133] . Amazon  [134]  and then Microsoft  [135]  did the same shortly after. These announcements came amidst heightened attention to police misconduct sparked by the killing of George Floyd by the Minneapolis Police Department and subsequent widespread Black Lives Matter protests; therefore, it is possible that each company would have changed its behavior on its own without the others doing the same. However, in an interview, Microsoft's President explicitly recognized IBM's and Amazon's steps  [135] . To some extent, the companies may have been jockeying for market share in the face of shifting public opinion, but they may also have been motivated by each other's example to advance the public interest. Partners' ability to influence AI companies can depend significantly on their relative market power. The AI sector is led by some of the largest companies in the world. These companies are often in position to dictate the terms of their partner relationships; they have sometimes used this power to ensure that AI is used in the public interest. For example, Google has limited the use of its facial recognition services to a narrow customer base via its Celebrity Recognition API, and has an extended terms of service to regulate how the technology is used  [136] . Similarly, Microsoft vets customers for its facial recognition services; before its blanket 2020 policy was implemented, it reviewed and denied a California law enforcement agency's request to install the technology on body cameras and vehicle cameras  [137] . Partners can impact the reputation of AI companies and, in turn, influence actions to protect that reputation. For example, Article One Advisors, a consulting firm, worked with Microsoft to develop its human rights policies through external engagement, and then publicized this work  [138] . The publicity likely boosts Microsoft's reputation and incentivizes Microsoft to follow through on its public commitments. Corporate partners can also harm AI corporations' reputations. For example, Google attracted widespread criticism when Randstad, a staffing contractor, allegedly collected facial scans of homeless African Americans in order to improve the performance of Google's Pixel phone facial recognition features  [139] . Reputation is important for large, public-facing corporations such as Microsoft and Google, making this a valuable tool for their corporate partners. Insurers have distinctive opportunities to influence AI companies. When AI is not in the public interest, that can create substantial risks that may require insurance payouts. Insurers therefore have both the vested interest and the contractual means to compel AI companies to act in the public interest. For comparison, insurers have mandated the adoption of cybersecurity governance and risk frameworks  [140, 141] ; they could do the same for AI. Doing so would improve corporate governance in the insured AI companies. Additionally, it could have further benefits by popularizing innovative practices for AI governance and risk management that are adopted by even uninsured companies. However, some AI risks are not readily handled by insurers, such as emerging risks that are difficult to quantify and price and risks that are too extreme, such as risks from long-term artificial general intelligence. Finally, it should be noted that corporate partners and competitors consist of management, workers, and investors, whose influence parallels that of their counterparts in AI corporations as discussed in Sections 4.1-4.3. Workers, managers, and investors who seek to improve AI corporate governance may find additional opportunities in corporate partners and competitors. As an illustrative example, in 2020, FedEx investors pushed FedEx to call for the Washington Redskins American football team to change their name, given its racist connotations. FedEx is a major partner of the team. The initiative was successful: the team name will be changed  [142] . This example is not from the AI industry, but it nonetheless speaks to the capacity for actors in corporate partners and competitors to affect positive change. \n Industry Consortia Industry consortia, as the term is used here, are entities in which multiple corporations come together for collective efforts related to AI governance. We define industry consortia to include entities that include more than just corporations. For example, PAI membership includes corporations, nonprofits, media outlets, and governmental bodies  [143] . PAI is perhaps most precisely described as a multistakeholder organization, but it is also an industry consortium. The same holds true for other entities, such as the IEEE Standards Association, whose members include corporations and individuals  [144] . Industry consortia can be instrumental in identifying and promoting best practices for AI in the public interest. AI corporations face many of the same challenges and issues. They likewise benefit from best practices being developed for the whole sector and then distributed to each corporation, instead of each corporation \"reinventing the wheel\". Industry consortia are well-positioned to serve as the entity that develops best practices for the whole sector. They can query member corporations on what has worked well-or poorly-for them, pooling their collective experience together. They can also conduct in-house research on best practices, with researchers hired by the pooled funds of their member corporations. It may not be worthwhile for every AI corporation to hire their own in-house experts on various facets of AI in the public interest, but it may be worthwhile for the sector as the whole to do so. Industry consortia enable that to happen. An illustration of these dynamics is seen in PAI's recent work on best practices on the publishing of potentially harmful AI research. PAI's work on this was prompted by the work of one of its members. Specifically, OpenAI released its language model GPT-2 in phases out of concern about its potentially harmful uses  [62] . Soon after, PAI hosted discussions with OpenAI and other organizations about best practices in publishing potentially harmful research  [145] , launched a project to develop guidance  [8] , and advised Salesforce on the release of their language model CTRL  [146, 147] . PAI's status as an industry consortium has enabled it to advance publishing practices across organizations. As best practices are formulated, industry consortia can take the additional step of formalizing them as standards. For example, the Consumer Technology Association (CTA) convened over 50 companies, some but not all of which were CTA members, to develop a standard for the use of AI in healthcare  [148] . The IEEE Standards Association is also active on AI standards, as is the International Organization for Standardization  [63] , although the latter is not an industry consortium. By formalizing best practices into standards, industry consortia can enable corporations across the sector to improve their practices. Best practices and standards developed by industry consortia can go on to play a legal or quasi-legal role. Governments sometimes enact policies requiring corporations to adhere to certain broad principles of conduct without specifying the details of what particular conduct does or does not meet these principles  [149] . The best practices and standards formulated by industry consortia can fill in the details of good conduct. Additionally, regulatory agencies and courts handling liability cases sometimes treat compliance with industry best practices and standards as satisfactory, such that corporations meeting these practices or standards avoid regulatory fines or court judgments of liability to which they would otherwise be subject  [150]  (p. 17). This can dilute the public benefits of government action, but it also incentives corporations to meet or exceed these standards and practices, potentially bringing net gains for the public interest. The above are examples of soft law, which can be defined as obligations that, although not legally binding themselves, are created with the expectation that they will be given some indirect legal effect through related binding obligations under either international or domestic law  [151] . Soft law has been advocated for AI corporate governance due to its flexibility and ease of adoption  [152, 153] . In general, it is difficult for governments to create detailed and rigorous laws for complex issues such as those pertaining to AI. The dynamism of emerging technologies such as AI is especially challenging for the development and enactment of \"hard\" laws. Industry consortia are often better positioned than governments to master the details of the technology and its changes over time, due to the availability of expertise among consortium members. Furthermore, any more binding \"hard law\" measures enacted by governments are likely to draw on the particulars of pre-existing soft law instruments. These are additional reasons for industry consortia to pursue robust best practices and standards for AI corporate governance in the public interest. Industry consortium activities do not necessarily advance the public interest. For example, they can pool the resources of member corporations to lobby governments for public policies and conduct information and public relations campaigns that advance industry interests at the public's expense. In other sectors, such lobbying has often been a major impediment to good public policy  [154] . In the coming years, industry consortia could possibly present similar challenges to the public interest. \n Nonprofit Organizations Nonprofit organizations play several important roles in advancing AI corporate governance in the public interest, including research, advocacy, organizing coalitions, and education. Nonprofits can be advocacy organizations, labor unions, think tanks, political campaigns, professional societies, universities, and more. The distinction between these types of organizations is often blurry, with one organization playing multiple roles. To date, research has been a primary focus of nonprofit organizations working on AI corporate governance. Research contributions from nonprofit universities and think tanks are too numerous to compile here; many are in Section 3. What follows are some select examples of nonprofit research aimed at influencing corporate governance. Note that all universities mentioned in this section are nonprofit. Upturn, a nonprofit dedicated to advancing equity and justice in technology, worked with researchers at Northeastern University and University of Southern California to produce evidence of previously suspected illegal discrimination in housing advertisements served by Facebook  [155] . Ranking Digital Rights (e.g.,  [156] ) reports technology companies' human rights records and encourages companies to improve their performance. The Electronic Frontier Foundation reports companies' cooperation with government demands for censorship and also encourages them to improve their performance  [157] . The AI Now Institute at New York University publishes reports to provide AI developers with suggestions to reduce bias and increase the public accountability of AI systems  [158] . Finally, this paper is another work of nonprofit research on AI corporate governance. Nonprofit advocacy efforts can often draw on such research. For example, a 2018 advocacy campaign by the nonprofit American Civil Liberties Union (ACLU) opposed Amazon selling facial recognition software to governments  [159] . The campaign was supported by research on biases in the software by the ACLU  [160]  and prior research from a pair of researchers at Microsoft and the Massachusetts Institute of Technology  [58] . The ACLU later reported that their campaign was unsuccessful  [161] . However, in 2020, following anti-police brutality protests, Amazon stopped selling facial recognition software to law enforcement agencies, as discussed in Sections 4.4 and 4.7. The ACLU campaign and the research on which it drew may have laid the groundwork for Amazon's action. Finally, nonprofits have conducted some work to build the field of AI in directions beneficial to public interest. Black in AI and AI4All are nonprofit organizations that promote diversity within the field of AI. Increased diversity could, in turn, help reduce bias in the design, interpretation, and implementation of AI systems. Additionally, the Future of Life Institute has hosted conferences on beneficial AI and built coalitions in support of open letters calling for AI in the public interest. These field-building initiatives are not specifically focused on corporate governance, but they have included people from AI corporations and are likely to have at least some effect on AI corporate governance. One challenge facing nonprofit organizations is funding. This is a challenge for nonprofits working on all cause areas, and AI corporate governance is no exception. Firstly, nonprofits may struggle to raise the funds they need to advance their missions. Secondly, some AI nonprofits may turn to AI companies for funding, creating potential conflicts of interest  [162, 163] . Thirdly, where companies disagree with the nonprofits' aims, the companies can use their wealth to push back. Although such a dynamic has perhaps not been seen much to date in AI, it has been observed in other sectors, such as the tobacco industry pushing back on the link between cigarettes and cancer and the fossil fuel industry pushing back on the risks of global warming  [64] . The extreme wealth of some AI corporations makes the potential for conflict of interest and the imbalance in resources particularly acute. Where these issues arise, nonprofits may fail to advance the public interest. With that in mind, it can be helpful to distinguish between adversarial and cooperative nonprofit activity. Adversarial activity pushes AI companies in ways that the companies do not want. Cooperative activity proceeds in ways that the companies are broadly supportive of. Cooperative activity may tend to have a more limited scope, limited by the bounds of what companies are willing to support. On the other hand, adversarial activity may struggle to effect change if the companies do not agree with the proposed changes, and in some cases could backfire by galvanizing opposition. Whether adversarial or cooperative approaches are warranted should be assessed on a case-by-case basis. \n The Public The public, as the term is used here, refers to people acting in ways that are nonexclusive in the sense that broad populations can participate. In the context of AI corporate governance, the primary roles of the public are (1) as users of AI technology, including when the users pay for it and when it is free to them, subsidized by advertising, and (2) citizens who can vote and speak out on matters of public policy. Although not discussed in this section, members of the public can also impact AI corporate governance indirectly by exerting influence on other members of the public. Users of AI technology can improve AI corporate governance by choosing goods and services that are in the public interest. In other (non-AI) industries, customers are often-although not always-willing to pay more for branded ethical standards  [164] . AI users may also be willing to pay more; or, when they are using the technology for free, they could accept a product that has higher ethical standards but is inferior in other respects. This effect can even determine which technologies become dominant, rejecting certain uses and prioritizing others-regardless of how they are marketed  [165] . One example in this direction is the gradual shift in social media platform popularity from public platforms such as MySpace, Facebook, and Twitter toward private messaging platforms, such as Snapchat and WhatsApp  [166] . Citizens can improve AI corporate governance by supporting good (and opposing bad) AI public policies. They can do this by speaking up, such as in anti-racism and police brutality protests that have influenced AI facial recognition practices, and by voting for politicians who will enact good policies. Public opinion has played an important role in regulatory responses to other advanced technologies such as genetically modified organisms  [167, 168] . Growing public concern about digital technology, dubbed \"techlash\", has prompted calls for antitrust and other policy response. Thus far, AI has not been extensively regulated, although further shifts in public opinion could help to change this. Public opinion has played an important role with regard to the sale of facial recognition software to law enforcement. As discussed in Sections 4.4 and 4.6, following 2020 protests against racism and police brutality, several AI companies moved away from providing facial recognition tools for law enforcement. It is worth noting that the protests garnered broad public support  [169] . Therefore, the AI corporations' responses show how public protests and changes in public opinion can advance AI corporate governance in the public interest. Finally, members of the public can voice their views about AI, prompting changes. For example, the initial launch of Google Glass in 2014 was widely criticized for violations of privacy  [170] ; it was discontinued and subsequently relaunched for industrial and professional users instead of for the general public  [171] . Google Photos, an AI photo classification system, sparked public outcry for labeling a person with dark skin as a gorilla, prompting Google Photos to remove gorilla and other non-human primate terms from its lexicon  [172] . In general, public pressure will tend to be more pronounced for highly visible brands  [173, 174] ; the same is likely to also apply for AI companies. The public faces several challenges to supporting the corporate governance of AI in the public benefit. One is the complexity of AI issues, which makes it hard for people lacking specialized training to know what the issues are or what stances to take. This can be mitigated by efforts for public education, such as Elements of AI  [175] , an online course which aims at educating 1% of European citizens in the basics of AI. Despite such initiatives, public education remains a difficult challenge due to the complexity of the issues and the competition for public attention. Likewise, public education can take time, in which case it may be most valuable in the medium term. (On medium-term AI issues, see Ref.  [176] ) Furthermore, some AI issues are important but arcane and not conducive to media coverage or other means of capturing public attention. This holds in particular for lowvisibility AI companies, including those that do not market to the public but instead sell their AI to governments or other companies. In some cases, AI technology users may be relatively disinclined to opt for the more ethical option due to the difficulty of switching from one AI product to another. Impediments can include (1) significant learning curves, as is common for software in general, (2) transition costs, such as the need to re-upload one's photos and other information to a new site, or the need to inform one's contacts of their new email address, and (3) network effects, in which a product's value to one user depends on its use by other users, as in the distinctive communities of people on specific social media platforms. Someone concerned about AI at one company may not have good alternatives, dissuading them from choosing a product more aligned with the public interest. Additionally, AI is often only part of consumer-facing products. Concern about AI may be outweighed by other concerns. For example, a user may appreciate the cultural and educational value of a media sharing site (such as YouTube or Instagram) even if they dislike its recommendation algorithm. Finally, public action may tend to be primarily oriented toward how AI systems are deployed. Earlier phases of the AI system lifecycle have fewer direct ties to the public and are therefore less likely to garner public attention. For these phases of the AI lifecycle, other types of action may tend to be more important. \n The Media The media, as the term is used in this paper, refers to both professional and amateur journalists together with their diverse means of distribution, from traditional newspapers to online social media platforms. The media can play an important role in improving AI corporate governance by researching, documenting, analyzing, and drawing attention to good practices, problems, and areas for improvement. The media serves as an important link between actors internal and external to the corporation, and it plays a vital role in distilling and explaining complex technology and business detail in terms that can be understood and used by outside audiences including the public and policymakers. Indeed, media reports have been essential for the insights contained in this paper. AI corporate governance is often in the news. Several newspapers have dedicated technology sections including The New York Times, Wall Street Journal, and Financial Times. Dedicated technology media sources include The Verge, Wired, and the MIT Technology Review. The Markup is specifically focused on the societal impacts of digital technology companies. All of these outlets devote extensive attention to AI corporate governance. Media coverage has been instrumental in highlighting problems in AI corporate governance and mobilizing pressure for change. For example, the media has published several reports based on worker whistleblowing, presenting issues at AI companies that otherwise may have stayed internal to the companies (see Section 4.2). In the case of Google's participation in Project Maven, Gizmodo reported about the project based on leaked information  [106] . The media also covered the subsequent protests by Google workers, further amplifying their concerns  [107, 177, 178] . Google management later announced it would leave the project  [108] . This example demonstrates how broad media coverage combined with employee activism can have significant influence on corporate decision-making. Other reporting focuses on adverse societal impacts of AI. One prominent example is a ProPublica investigative report on biased outcomes of the COMPAS algorithm for assessing the risk of a person committing a future crime  [179] . The report has been credited with focusing researchers' attention on fairness in machine learning  [180]  (p. 29). A more recent example is a New York Times exposé on the little-known facial recognition company Clearview  [181] , which was scraping personal photos uploaded online to serve as training data. The Times report prompted technology companies to take legal action  [182]  and nonprofit advocacy organizations to lobby the U.S. government to intervene  [183] . Media coverage appears to be most robust for later phases of the AI system lifecycle. Later phases, such as the deployment of AI products, tend to be more publicly visible and of more direct interest to the public and other outside stakeholders. In contrast, earlier phases, such as basic research and development, are less visible and less directly relevant to stakeholders, and therefore may tend to receive less coverage. Coverage of internal corporate activities may be impossible without whistleblowers; these activities can occur across the lifecycle but may be especially frequent during earlier phases. Other factors can also shape trends in the media coverage of corporate AI. Coverage may tend to be greater where AI intersects with other topics of great public interest, such as racism or unemployment, or for prominent AI companies or celebrity entrepreneurs. Certain events can also draw new attention to existing practices, such as the longstanding privacy flaws of the Zoom videoconferencing platform gaining newfound attention due to the heavy use of Zoom during the COVID-19 pandemic  [184] . Risky AI practices may tend to receive the greatest attention in the immediate aftermath of an incident of that type of risk, unless such incidents are too commonplace to be considered newsworthy. This can result in less coverage of emerging and extreme AI risks for which incidents have not previously occurred. (The tendency to overlook extreme risks has been dubbed \"the tragedy of the uncommons\"  [185] ) Finally, as with nonprofits, the media faces financial challenges. The business models of many media outlets have been harmed by the rise of the internet and other recent factors. This has resulted in less investigative journalism, meaning fewer resources to report on issues in AI corporate governance. Meanwhile, the AI industry is amidst a financial boom, making it difficult for the media to hire people with expertise in AI. There can even be conflicts of interest, as has been a concern since Amazon founder Jeff Bezos purchased the Washington Post (a concern that Bezos and the Post deny  [186] ). The media clearly has an important role in advancing AI corporate governance in the public interest, making it vital that its various challenges be overcome. \n Government Government, as the term is used here, refers to institutions with legal authority over some geographic jurisdiction, whether national (e.g., the United States), subnational (e.g., California), or supranational (e.g., the E.U.). Governments can influence AI corporate governance to promote the public interest by using various policy instruments. In the following, we consider four widely accepted categories of policy instruments: command and control regulation, market-based instruments, soft law, and information and education. We also consider procurement, which is important for the government use of AI. Our focus on these categories of instruments reflects current practices to influence the corporate governance of AI; however, more methods could be used in the future, including the role of state-owned enterprises and direct subsidies. Command and control regulation uses binding legal rules to specify the required behavior, and enforcement measures to correct or halt non-compliant behavior  [187]  (p. 107). Many existing regulations are applicable to AI, although they do not address AI specifically. For example, in the E.U., AI systems must comply with existing data protection, consumer protection, and anti-discrimination laws  [188]  (p. 13). The GDPR contains detailed rules governing the processing of personal data using automated decision-making  [189] . In this case, the person whose data are being processed can request \"meaningful information about the logic involved, as well as the significance and the envisaged consequences of such processing,\" although whether this entails a right to explanation is disputed  [34, 35] . Although these rules are not explicitly about AI (automated decision-making as defined in the GDPR is not synonymous with AI), they are nonetheless applicable to many AI systems  [190] . Similarly, labor law is generally not written explicitly for work in AI, but it nonetheless affects how workers and management are allowed to act, as seen for example in allegations of former Google workers that they were fired because of their labor organizing, which may have been in violation of U.S. labor law (Section 4.2)  [101] . In recent years, governments around the world have started to work on AI-specific command and control regulations. Proposals have been published, among others, by the E.U.  [28, 188, 191] , China  [192] , and the United States  [193, 194] . For example, in April 2021, the European Commission published a proposal for an Artificial Intelligence Act  [28] , following its White Paper on AI  [188]  and the High-Level Expert Group on AI's Ethics Guidelines for Trustworthy AI  [191] . The new proposal follows a risk-based approach with different requirements for different levels of risk. It prohibits practices which pose unacceptable risks (e.g., social scoring by governments or systems that exploit vulnerabilities of children) and contains specific rules for high-risk systems (e.g., biometric identification systems). These rules include requirements regarding the quality of datasets used; technical documentation and record keeping; transparency and the provision of information to users; human oversight; and robustness, accuracy and cybersecurity. The proposed regulation contains very light and mostly voluntary provisions for AI systems with low or minimal risk. The vast majority of AI systems currently used in the E.U. fall into this category. The requirements for high-risk systems are command and control because they require specific behavior that will be enforced by supervisory authorities. It is worth noting that the proposal still has to be adopted by the European Parliament and the member states. Market-based instruments affect corporate activity through economic incentives  [195]  (p. 22);  [187]  (p. 117). For example, taxes could be used to encourage safe behavior or discourage unsafe behavior, such as via tax discounts for AI systems that have been certified or audited by a third party. Civil liability could incentivize AI companies to mitigate risks from accidents or the misuse of AI systems. Subsidies could support corporate initiatives on AI in the public interest, for example, to support research and development on AI techniques that improve safety. These benefits may also support the public good insofar as they address a market failure or incentivize innovation with future public benefit. The DARPA Grand Challenge for Autonomous Vehicles is one such example, which helped catalyze private investment in the field in the early 2000s  [196] . Procurement refers to government purchases of goods and services  [197, 198] , including AI systems. For example, law enforcement agencies have recently sought to purchase facial recognition software. As discussed throughout this paper, this procurement is controversial, with many arguing that it is not in the public interest. This controversy speaks to the fact that governments face important decisions on which AI systems to procure and how to use them to best advance the public interest. Governments can additionally use procurement to influence AI corporate governance by procuring systems that meet high standards of safety and ethics. This incentivizes industry to adopt and maintain such standards. Procurement is thus, in a sense, a demand-side market-based instrument in its potential to use market incentives to advance AI corporate governance in the public interest. As discussed in Section 4.5, soft law is the non-binding expectation of behavior that has some indirect legal basis. One specific form of soft law in which governments play a central role is co-regulation. It is worth noting that co-regulation is not necessarily a form of soft law, but the concepts are at least interconnected  [40, 41] . Co-regulation expands on corporate self-regulation to include some government involvement, typically to ensure enforcement  [195]  (p. 35). For example, the U.S. Federal Trade Commission (FTC) encourages firms to declare privacy policies, and prosecutes firms who deviate from their statements  [199] . Conceivably, the FTC could also punish violations of companies' self-stated AI principles  [30] . However, such enforcement has been ineffective. In 2011, Facebook agreed to a settlement with the FTC after being accused of violating its privacy policy  [200] , but the violations continued, most notably with the 2018 Cambridge Analytica scandal  [201] . In 2019, Facebook again settled with the FTC, this time for an unprecedented USD 5 billion and stringent monitoring requirements  [202] . However, even the USD 5 billion fine could be seen as simply the cost of business, given that Facebook's 2019 profit was nearly USD 18.5 billion  [203] , and especially if the costs can be amortized across multiple years. Governments can also lead public information and education campaigns  [187]  (p. 116). A better educated public could incentivize AI companies to improve their governance, as detailed in Section 4.7. Education campaigns could also foster constructive public debate on AI ethics and safety  [191]  (p. 23). Education takes time, and thus is unlikely to be effective in time-critical situations, but it is otherwise found to often be a costeffective policy option  [195] . Governments can lead AI education campaigns. They can also obtain information about AI corporations, such as by establishing information disclosure requirements as discussed above. The efficacy of policy instruments can depend on their enforcement. This applies to command and control regulation as well as certain soft law and market-based instruments. Where enforcement is applicable, it is used to ensure compliance. Noncompliance is commonly sanctioned by fines. In extreme cases, corporate activities can be shut down and noncompliant corporate personnel can be imprisoned. A lesser punishment could see companies added to published lists of noncompliant companies, as is the practice in European financial market regulation  [204] . However, in practice, governments do not always vigorously enforce compliance. Monitoring and enforcement can be expensive, and governments may not always have the resources or motivation to do so. Weak enforcement can limit the influence of government rules and regulations on AI corporate governance. Additionally, if the people responsible for complying with AI regulations disagree with or resent them-and are sufficiently empowered to act on this disagreement-then it could prompt backlash, such that the people decline to comply and may even do more of the disallowed or discouraged behavior than would occur without the regulation  [59] . When selecting a policy instrument to improve the corporate governance of AI, governments need to consider a number of factors. One of these factors is the underlying regulatory approach. Most AI-specific proposals follow a risk-based approach. This approach ensures that regulation does not exceed what is necessary to achieve the underlying policy objective, as is required by the principle of proportionality in E.U. law. Apart from that, governments need to decide between regulation focused on specific technologies, such as AI, or regulation that addresses general issues that can be applicable to multiple technologies, such as privacy. Finally, governments need to decide whether the regulation should be cross-sector or for specific sectors, such as healthcare or transportation. AI-specific policy instruments face a particular challenge in defining their scope of application  [29]  (pp. 359-362). There is no generally accepted definition of the term AI, and existing definitions do not meet the specific requirements for legal definitions  [205] . A possible solution to this problem would be to avoid the term AI and define other properties of the system, such as certain use cases or technical approaches. This idea may be a worthy focus of future AI policy research and activity. Policy shapes innovation  [206]  (p. 249), and this will be no different with AI. Regulation can impose costs on or the outright prohibition of certain types of AI research and applications, thereby limiting innovation in particular areas while making others more attractive. Meanwhile, market mechanisms and procurement may subsidize or otherwise incentivize some types of AI research and development over others. For example, law enforcement procurement of facial recognition may already be stimulating innovation in that branch of AI. Taken as a whole, then, government regulation may be expected to shape AI innovation. Poorly constructed regulation may shape, or particularly limit, innovation in ways that undermine the public interest; this is a bug to be remedied, not a feature. For example, poorly constructed regulation may place a disproportionate burden of AI-related regulatory compliance that falls on smaller companies with fewer resources. When a government uses policy instruments, the effects are not always limited to that government's jurisdiction, a phenomenon known as regulatory diffusion. Corporations that work across jurisdictions often follow the regulations of the most stringent jurisdiction across all jurisdictions to gain the efficiencies of a single standardized compliance operation. They may even lobby other jurisdictions to adopt similar rules so as to similarly bind local competitors. Influential jurisdictions in this regard include California and the European Union, sometimes referred to as the \"California Effect\"  [207]  and the \"Brussels Effect\"  [208] . Given that leading AI corporations are multinational, policy instruments from a wide range of jurisdictions could shape corporate governance in (their conception of) the public interest globally. Even if companies are not incentivized to comply globally, other jurisdictions may pass similar regulation, imitating the first mover. Regulations do not always diffuse, and corporations may shift operations to jurisdictions with relatively lax regulations. Nonetheless, regulatory diffusion can increase the impacts of policy innovation. Regulation on law enforcement use of facial recognition technology has demonstrated such regulatory imitation. Municipalities seem to have taken the lead in the United States. Following research on AI and gender and race biases  [58, 209] , some municipalities have started to ban the use of facial recognition technology for law enforcement purposes, including San Francisco  [210]  and Boston  [211] . Even though municipal action has set the agenda for wider action, leading to multiple bills that have been introduced in the U.S. Congress on this topic  [212, 213] , there is not yet a regulation of facial recognition technology at the federal level. Due to the absence of federal regulation, the legal treatment of the technology is currently highly variable across the United States. In keeping with their incentives for regulatory consistency across jurisdictions, Microsoft has repeatedly called for the federal regulation of facial recognition technology  [135, 214, 215] . Under the proposed E.U. AI regulation, all remote biometric identification of persons will be considered highrisk and subject to third party conformity assessment  [28] . Certain applications for the purpose of law enforcement will be prohibited in principle with a few narrow exceptions. Governments may not simply wait for AI policy instruments to passively diffuse; they may support institutionalized international coordination. For example, the OECD AI Principles have been adopted by 45 nations and informed similar principles agreed to by the G-20 countries  [216] . The OECD AI Policy Observatory is now developing implementation guidance for the principles, aimed at both government and corporate decision-makers. International coordination is further supported by several UN initiatives  [217] . Pre-existing international agreements and initiatives can shape AI corporate governance. Prominent examples include the UN Guiding Principles for Business and Human Rights and the UN Global Compact, which offer guidance for business practices to promote the public interest. Already, Google has adapted some AI systems according to this UN guidance  [218] . Additionally, the OECD has published general corporate governance guidance that has been adopted into national regulation  [219, 220] . \n Conclusions A wide range of actors can help improve the corporate governance of AI so as to better advance the public interest. It is not, as one might think, a matter for the exclusive attention of a narrow mix of insider corporate elites. To be sure, the opportunities may often be better for some types of actors than others. However, significant opportunities can be found for many actors both within and outside of AI corporations. Importantly, these opportunities are available even in the absence of dedicated multistakeholder institutions that are designed to invite contributions from a more diverse group. Multistakeholder institutions have an important role to play, but they are only one of many means through which diverse stakeholders can improve AI corporate governance. Often, progress depends on coordination and collaboration across different types of actors, as illustrated in the three primary cases used throughout the paper. First, the example of Google's Project Maven shows that workers and the media can collaborate to be particularly successful in influencing management. Second, the example of law enforcement use of facial recognition technology demonstrates that novel research, activism by nonprofits, and broad media coverage can build on each other to achieve change in corporate governance. Third, the example of the publication of potentially harmful research shows management, workers, and industry consortia interacting to establish, implement, and share best practices for AI in the public interest. People in each type of actor category would do well to understand not just their own opportunities, but also the broader ecosystem of actors and their interactions. Questions of how best to pursue coordination and collaboration across actors must be resolved on a case-by-case basis, in consideration of the particulars of the issues at play and the relative roles and capabilities of different actors. Opportunities to improve AI corporate governance are likely to change over time. For example, workers' influence may diminish over time if the expected increase in the supply of skilled AI workers outpaces demand increases for AI systems. Changes in the economic, cultural, and political significance of AI can alter the opportunities available to many types of actors, such as by shaping the political viability of government regulations. Changes in underlying AI technologies can also be impactful. For example, if there are major breakthroughs toward AI systems that can substitute for most forms of human labor or even approach an artificial general intelligence, then the corporations could end up with substantially greater economic and political clout. This could increase the importance of actions from within the companies, especially from management and investors. On the other hand, such breakthroughs could also increase public and policymaker interest in AI in ways that facilitate more extensive government activity over time. The delay in government responses to emerging technologies, often called the \"pacing problem\"  [221] , creates a clear, even if interim, role for other actors in improving AI corporate governance in the public interest as AI research and development continues. This paper has presented a broad survey of opportunities to improve AI corporate governance across a range of actors. It is, to the best of our knowledge, the first such survey published. As a first pass through a large and complex topic, the paper's survey has been largely qualitative, and it has also not been comprehensive in its scope. We have sought to map out the overall terrain of AI corporate governance without necessarily identifying or measuring all the hills and valleys. We have focused on select larger corporations, with less attention to smaller ones. We have focused on the United States and Europe, with less attention to other parts of the world. Additionally, to at least some extent, we have covered a convenience sample of cases. The result is a broad but somewhat limited map of the AI corporate governance landscape. One important area for future research is on evaluating the quality of opportunities to improve AI corporate governance. Specific actors may benefit from guidance on how best to focus their activities. Some actors, such as researchers and philanthropists, have opportunities to bolster the efforts of other types of actors and would benefit from guidance on which other actors are most worth supporting. (These supporting actions fall outside the scope of this paper's framework and would make for a further area for future research.) To a large extent, the quality of opportunities facing specific actors must be assessed on a case-by-case basis accounting for context and technological particulars, and therefore fall outside the scope of broad surveys such as this paper. An important activity would be to bridge the gap between the more general insights of this survey and the specific insights needed for corporate governance decision-making in the public interest for particular categories of AI policy problems and types of AI systems. Such work should include more specific conceptions of the public interest, because different conceptions can underlie different evaluative standards and generate different practical guidance. Finally, further research could investigate how AI corporate governance may change over time, especially as companies develop increasingly capable AI systems. This paper has emphasized near-term cases in order to give its study of AI corporate governance a better empirical basis and more immediate practical value. Nonetheless, the potential for extremely large consequences from long-term AI make it a worthy subject of attention. Important questions include how near-term actions could affect long-term AI corporate governance, such as through path dependence in governance regimes, and how future actors can best position themselves to influence long-term corporate AI for the better. One good starting point may be to look more closely at the earliest phases of the AI lifecycle, especially basic research and development, on the grounds that this may be where future advanced forms of AI first appear within corporations. As the deployment of AI systems and research and development of AI technologies continue, the role of AI corporate governance is expected to only increase over time. With it too increases the importance of experimentation and iteration to develop actors' strategies to improve the corporate governance of AI companies in the public interest. This paper has surveyed the landscape with the aim of empowering practitioners and catalyzing necessary further research. It is only with this continued work, by the full range of actors considered here, that AI corporations may be expected to support the public interest today, tomorrow, and into the future. Figure 1 . 1 Figure 1. AI system lifecycle. \n Figure 1 . 1 Figure 1. AI system lifecycle.", "date_published": "n/a", "url": "n/a", "filename": "information-12-00275.tei.xml", "abstract": "This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY", "id": "3f38f8c4ef22a5746456cb94685debb9"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jess Whittlestone", "Rune Nyrup", "Anna Alexandrova", "Stephen Cave"], "title": "The Role and Limits of Principles in AI Ethics: Towards a Focus on Tensions", "text": "INTRODUCTION AI systems promise widespread benefits to society, while also posing substantial risks across almost all sectors. In the last few years, a number of different groups and initiatives have attempted to articulate and agree principles to guide the application of AI in society. In this paper we discuss the role and limitations of these principles, and argue that an important next step for AI ethics is to focus more on the tensions that arise as we try to implement them in practice. By 'AI ethics' we specifically mean the emerging field of practical AI ethics, which focuses on developing frameworks and guidelines to ensure the ethical use of AI in society (analogous to the field of biomedical ethics, which provides practical frameworks for ethical practice in medicine.) AI ethics therefore covers several different sectors and types of institutions, including the following: • Technology companies aiming to develop their own ethical guidelines (e.g. Google's 'AI Ethics principles'); • Professional bodies whose codes of ethics are aimed at guiding practitioners; • Standards-setting bodies that aim to set general standards for fields of research of industries (e.g. the IEEE or British Standards Institution); • Government bodies and legislators that aim to develop policy and regulation (e.g. the UK's new Centre for Data Ethics and Innovation); • Researchers across disciplines whose work aims to inform these ways that AI ethics is put into practice: exploring the technical, philosophical, or legal aspects of using algorithms in ethical ways  [20]  or synthesising and translating such research into practice  [27] . Agreeing on principles is valuable for the aims of all of these groups: for example, principles can provide a useful starting point from which to develop more formal standards and regulation, and can help to identify priority issues on which both research and policy should focus. However, we argue that current lists of principles for AI ethics are too high-level to be immediately useful for these groups' aims. When we look at specific cases, it becomes clear that principles will come into conflict with each other. This means their practical value is limited: without acknowledging these conflicts standards may be set unrealistically high, or regulation intended to protect one value might inadvertently compromise other important goals. In order to be practically useful, we suggest that the field of AI ethics should focus more on identifying and attempting to resolve the tensions that arise when we apply them to specific cases. We begin by reviewing how principles have evolved in AI ethics over the last two years. Drawing on comparisons with bioethics -a field with a robust and well-developed tradition in using principles to govern medical practice -we discuss some of the limitations of principles. We make the case that all areas of AI ethics would benefit from a more rigorous exploration of the tensions that arise when we try to apply principles to concrete cases. We outline some key tensions that already arise from the use of AI in society, and discuss what work might be needed to resolve them. To our knowledge, this is the first paper to explicitly examine the role and limits of principles in AI ethics, and the importance of focusing more on tensions as a next step. \n THE EMERGENCE OF PRINCIPLES IN AI ETHICS Though the field is in its infancy, there is widespread agreement on some of the core issues (such as bias) and values (such as fairness) that AI ethics should focus on. Over the last two years, these have begun to be codified in sets of 'principles' or 'tenets'. The Asilomar AI principles, developed in 2017 in conjunction with the Asilomar conference for Beneficial AI, outline guidelines on how research should be conducted, ethics and values that use of AI must respect, and important considerations for thinking about long-term issues  [12] . The principles were signed by several thousand AI researchers and others, including many academic ethicists and social scientists. Around the same time, the US Association for Computing Machinery (ACM) issued a statement and set of seven principles for Algorithmic Transparency and Accountability, addressing a narrower but closely related set of issues  [1] . Over the course of 2017, several other initiatives and organisations published additional sets of principles: including the Japanese Society for Artificial Intelligence's Ethical Guidelines in February 2017  [16] ; a set of draft principles from the Montreal Declaration on Responsible AI in November  [25] ; and the IEEE's General Principles of Ethical Autonomous and Intelligent Systems in December  [14] . This proliferation of principles has continued into 2018: with the Partnership on AI publishing a set of 'tenets' which its members agree to uphold  [18] ; the UK House of Lords suggesting five principles for a cross-sector AI code which could be adopted internationally  [23] , and Google publishing their 'AI ethics principles' in June  [19] . These different sets of principles have considerable overlap. There is widespread agreement that AI-based technologies should be used for the common good, should not be used to harm people or undermine their rights, and should respect widely-held values such as fairness, privacy, and autonomy.  [9]  suggest that many of the different existing sets can be synthesised into five key principles: the four that are already used in bioethics -autonomy, beneficence, non-maleficence, and justice  [4]  -plus the additional principle of explicability, which captures the challenges of intelligibility and accountability unique to AI systems. While this convergence is encouraging, it is unclear at this point whether this reflects a deep consensus about what is important, arrived at independently by numerous different actors, or merely a shallow consensus due to the fact that different groups have read similar papers and built on the work of one another. Principles can be a valuable part of applied ethics; agreeing on high-level principles is therefore an important step for ensuring that AI is developed and used for the benefit of society. Principles help condense complex ethical issues into a few central elements which can be clearly understood and agreed upon by people from diverse fields and sectors. They encourage widespread commitment to a shared set of values, and can give them a more prominent role in institutional decision-making processes. Principles can form a basis for more formal commitments in professional ethics, internationally agreed standards, and regulation. They can also help address public concerns, by clarifying the ethical commitments of researchers and industry. However, while principles are important, they are not in themselves enough to ensure society can reap the benefits and mitigate the risks of new technologies. In order to be useful in practice, principles need to be able to guide action -to help people navigate the competing demands and considerations of concrete situations. As we articulate in the next section, there are several obstacles to this. \n THE LIMITS OF PRINCIPLES The four principles of beneficence, non-maleficence, autonomy, and justice have played a prominent role in bioethics  [4] , a field with decades of experience in managing the challenges posed by new technologies. These principles aim to articulate general values on which everyone can agree, and to function as practical guidelines. But they have spurred substantial debate: some argue that we should put no weight on principles and focus entirely on the elements of specific cases  [10] , while others have advocated a more moderate view, whereby principles should be considered in close conjunction with analysis of 'paradigm' cases  [17] . However, even the strongest advocates of principlism in bioethics acknowledge that principles alone are not enough.  [4]  suggest that principles should be taken as guidelines, which need to be made specific for use in policy and clinical decision-making. They elaborate that in order to be action-guiding, principles need to be accompanied by an account of how they apply in specific situations, and how to balance them when they conflict. In this section, we review some of the main limitations of principles that have been highlighted in the bioethics literature and illustrate why these also apply to the principles proposed for AI ethics. \n Different Groups May Interpret Principles Differently The central terms used in principles are often ambiguous, masking conceptual complexity and differences in interpretation across populations. As  [8]  point out, the principle of 'justice' in bioethics does not say anything about what is just or unjust, leaving this to the agent to decide for themselves. Clouser and Gert argue that principles often mask important moral disagreements rather than presenting a well-developed unified theory as they propose to, and that it would be better if these disagreements were articulated and understood more explicitly. In particular, lists of broadly agreed-upon principles cannot recognise that important and legitimate differences in values exist across people and populations. While everyone might agree in principle that 'fairness' is important, there exist deep political disagreements about what exactly constitutes fairness  [5] . Groups may also vary in how much weight they put on one value relative to others in situations of conflict: more individualist cultures may put more weight on personal privacy than more collectivist cultures, for example. An important step in making principles more practical is to formalize them into standards and regulation  [27] . But this process is not a straightforward unpacking of the relevant principles, as different principles will come into conflict when applied to concrete cases. In the next section, we make the case that in order for principles to inform more practical aspects of AI ethics, including professional ethics, standards, and regulation, we need to begin by exploring in detail the different kinds of tensions that arise when principles are applied. \n Principles Are Highly General Relatedly, principles are by their nature highly general: their value is that they indicate important moral themes that apply across a wide range of scenarios. This means that they can be useful as a kind of checklist: as a set of important considerations that need to be taken into account in specific scenarios. However, the generality of most principles also limits their ability to guide practical action  [3] ). Many of the principles proposed in AI ethics are too broad to be action-guiding. For example, ensuring that AI is used for 'social good' or 'the benefit of humanity' is a common thread among all sets of principles. These are phrases on which a great majority can agree exactly because they carry with them few if any real commitments. A very wide range of differing ideological, political and philosophical standpoints could claim to be for the good, or for the benefit of humanity. Only principles that are narrower and more specific are likely to be useful in practice. Recent industry commitments to not develop technology for autonomous weapons are an example of a principle that is specific, action-guiding and can be used to hold people to account. But at the same time, exactly that specificity means its relevance is limited to one sector, and it has many dissenters. \n Principles Come into Conflict in Practice The gap between principles and practical judgement grows larger still when we consider that principles will inevitably conflict with each other. For example, the UK House of Lords AI Committee report states that, \"it is not acceptable to deploy any artificial intelligence system which could have a substantial impact on an individual's life, unless it can generate a full and satisfactory explanation for the decisions it will take. \" The intentions behind this principle are important, but it masks a crucial tension between using algorithms for social benefit ('beneficence') and ensuring those algorithms are fully intelligible to humans ('explicability'). For example, algorithms exist today that can diagnose medical conditions more accurately than doctors, potentially saving lives  [24] , but for which a full and satisfactory explanation cannot necessarily be provided (depending on how this is defined). In some situations, the benefit of using an algorithm may be high enough, and its accuracy reliable enough, that all users agree it is worth using even if a fully comprehensive explanation of its decisions cannot be given. There are complex and important trade-offs involved here  [15, 22] , and a principle that simply states that it is not acceptable to deploy AI systems without full explainability fails to recognise this. In conclusion, there is a risk that high-level principles give the impression of being the outcome of meaningful debate about how AI should be developed, but in reality they are simply postponing it. \n WHY THE FIELD SHOULD FOCUS ON TENSIONS We use the term 'tension' to refer to any conflict, whether apparent, contingent or fundamental, between important values or goals, where it appears necessary to give up one in order to realise the other. For example, the use of socially beneficial data-driven technologies might make it impossible for us to fully guarantee otherwise desirable levels of data privacy. If the potential gains of these technologies are significant enough -new and highly effective cancer treatments, say -we might decide that a higher risk of privacy breaches is a price worth paying. In some cases, a tension may reflect a strict moral tradeoff: a situation where two values or goals conflict and it is not possible to get more of one without sacrificing another. However, many tensions in AI are more contingent, and arise as a result of current technological or societal constraints. Using machine learning for social benefit may not be fundamentally in tension with privacy, transparency, or fairness, but many current methods employed for the former goal do conflict with these ideals. We do not yet know how far new technological or governance solutions could go to dissolve these tensions. Others have acknowledged the importance of recognising conflicts between values in AI ethics, but to our knowledge none have explored in detail why this would be beneficial or what it would look like in practice. For example,  [9]  say that, \"Ensuring socially preferable outcomes of AI relies on resolving the tension between incorporating the benefits and mitigating the potential harms of AI, in short, simultaneously avoiding the misuse and underuse of these technologies\", but do not discuss specific tensions in detail or how to resolve them. In this section, we discuss some of the benefits of focusing on tensions. We outline four reasons this is an important next step for AI ethics: (1) bridging the gap between principles and practice, (2) acknowledging differences in values, (3) highlighting areas where new solutions are needed and (4) identifying ambiguities and knowledge gaps. \n Bridging the Gap between Principles and Practice In general, we see focussing on tensions as an important way of bridging the gap between abstract ethical principles and specific cases, and therefore an important first step towards an ethics of AI that is practical and action-guiding. To identify tensions, we need to consider how different values and goals might come into practice in concrete cases. For example, when Google DeepMind collaborated with the Royal Free Hospital, they encountered a conflict between protecting the privacy of patient data, and their goal of using AI to improve early diagnosis of acute kidney injury  [20] . Since similar tensions will likely arise across a range of different cases, focusing on tensions means we are neither driven entirely by the specifics of an individual case, nor are we relying on abstract high-level values. If we can articulate important tensions by looking at a range of cases, and find ways to resolve them in specific scenarios, what we learn from this can then be used to develop standards and regulation that are more sensitive to how principles apply differently across scenarios. \n Acknowledging Differences in Values Focusing on tensions forces us to consider how different values might be interpreted and endorsed differently across groups. While some important tensions are due to conflicts between principles in practice, others arise because there are conflicting meanings or values within a single principle: broad terms like 'fairness' or 'justice' for example are subject to substantial moral and political disagreement  [5, 8] . It may never be possible to totally resolve all of these disagreements. But clearly articulating them is a crucial starting point for ensuring that all aspects of AI ethics are as inclusive as possible: for example, to ensure that international standards take full account of and accommodate cultural differences, and that agreement on such standards is meaningful. \n Highlighting Areas Where New Solutions Are Needed Noting a tension between two values does not necessarily mean we are forced to choose between them: often, we may be able to find some way to get more of both things we value. Recognising these tensions can therefore highlight high priority areas for both researchers and policymakers. For example, acknowledging that there is currently a tradeoff between performance and interpretability in state-of-the-art machine learning systems has motivated technical research that attempts to reduce or eliminate this trade-off  [2] . Acknowledging tensions will also help direct the development of AI in beneficial directions more generally. It is currently far from clear whether advances in AI will augment or degrade human capabilities and agency, but making this tension explicit focuses attention on the important question of which trajectories of development are most likely to lead to the former. \n Identifying Ambiguities and Knowledge Gaps Finally, a tension-focused approach helps to clearly highlight ambiguities and gaps in our understanding of how uses of AI are impacting society. Again, this can help identify new and important research directions. To think clearly about all tensions, we need to recognise and clarify ambiguities in terms: what do we really mean by things like 'fairness', 'justice', and 'autonomy', and how might these be interpreted differently across groups and contexts? To understand the nature of many tensions we need to understand what is currently technically possible: what are the best current methods for ensuring data privacy in machine learning, for example, and what are the costs of these methods? To understand how tensions arise in practice, we need better evidence on how AI is actually being applied in society today: what effect is automation already having on individual lives across different sectors? And to articulate and resolve conflicts between the interests of different groups, we need to really understand the needs and values of affected communities: how do the trade-offs people are willing to make differ based on demographic factors, for example? Focussing on tensions should help to drive this important work. \n WHICH TENSIONS? There are several different ways that applications of AI can introduce tensions between important goals and values. Some tensions arise due to the very nature of AI and machine learning: these techniques allow us to use and draw inferences from very large amounts of (often personal) data, and so challenge important notions of privacy. The most useful models also often quickly become very complex, introducing new issues around human interpretability  [11, 26] . This means we face tensions between using these technologies for socially beneficial goals: improving healthcare, justice, or security, for example, and other goals such as respecting privacy and maintaining trust and understanding in automated systems. Another possibility is that AI systems exacerbate already existing ethical or societal tensions: between different conflicting notions of fairness, for example. Often this is due to the fact that machine learning models are trained on historical data, and so inherit the biases or mistakes they contain  [13] . Here, applications of AI in society do not necessarily introduce new tensions, but increase the importance of already-existing ones such as how to make decision-making more accurate and efficient without inadvertently discriminating against minority groups. Other tensions arise because the harms and benefits of AI systems are unequally distributed in various ways. For example, the impacts of automation may be unequally distributed across populations and cultures: enhancing the agency of some groups by automating mundane tasks while wiping out the livelihood of others, thus threatening their basic needs. The risks and benefits of AI systems could also be unequally distributed over time, and uses of AI that present opportunities in the near term may compromise important long-term values. Increasing personalisation of messages and services may make our lives more convenient and enjoyable in the short run, but begin to undermine important aspects of autonomy, equality and solidarity over time  [21] . Finally, AI may have the potential to both enhance and threaten a given value. For example, depending on the precise direction in which technology develops, it could be used to either greatly enhance human capabilities -if we can develop sophisticated methods of intelligence augmentation  [7]  -or to degrade them: if our own capabilities atrophy as we outsource more and more tasks  [6] . As mentioned above, automation might enhance the agency of some groups while threatening the autonomy of others: whether we see AI as enhancing or degrading human agency could depend on how narrow or global a view we take of its impacts. \n FOUR KEY TENSIONS Given the wide range of tensions that may arise from applications of AI, now or in the future, there is unlikely to be an exhaustive list of all possible tensions. However, we believe that the following four tensions will be particularly central to thinking about the ethical issues arising from the applications of AI systems in society today. These capture a range of issues which are already salient or likely to grow in importance moving forward. Tension 1: Using data to improve the quality and efficiency of services vs. respecting privacy and autonomy of individuals. Machine learning and big data are already being used to improve various public services (including healthcare, education, and social care). These improvements could be hugely beneficial to citizens, but require large amounts of personal data, raising concerns about how to best protect privacy and ensure meaningful consent. Tension 2: Using algorithms to make decisions and predictions more accurate vs ensuring fair and equal treatment. This tension arises when public or private bodies base decisions on predictions about future behaviour of individuals (e.g. when probation officers estimate risk of reoffending) and when they employ machine learning algorithms to improve their predictions. These algorithms may improve accuracy overall, but discriminate against specific subgroups for whom representative data is not available. Tension 3: Reaping the benefits of increased personalisation in the digital sphere vs enhancing solidarity and citizenship. Companies and governments can use personal data to tailor the messages, offers, and services people see. This personalisation can make it easier for people to find the right products and services for them, but differentiating between people in such fine-grained ways may threaten societal ideals of citizenship and solidarity. Tension 4: Using automation to make people's lives more convenient and empowered vs promoting selfactualisation and dignity. Automated solutions may genuinely improve people's lives by saving them time on mundane tasks that could be better spent on more rewarding activities. But they also risk disrupting some of the practices that are an important part of what makes us human. With automation we may see the gifts of arts, languages and science become more accessible to those who were excluded in the pastbut we may also see widespread deskilling, atrophy, ossification of practices, homogenisation and cultural diversity. \n IDENTIFYING FURTHER TENSIONS The above tensions are important and represent areas where exploring tensions is likely to be fruitful for AI ethics. Going forward, further such areas can and should be identified. In order to do so, it is helpful to ask a range of questions, including: • Where AI is being used to serve a particular goal or value, or for 'social benefit' in general, what risks to other values are introduced? • Where might uses of AI that benefit one group, or the population as a whole, have negative consequences for a specific subgroup? How do we balance the interests of different groups? • Where might applications of AI that are beneficial in the near-term introduce risks in the long-term? How do we trade-off short and long-term impacts of society? • Where might future developments in AI either enhance or threaten important values, depending on the direction they take? \n RESOLVING TENSIONS The best approach to resolving a tension will depend on the nature of the tension in question. Where a strict trade-off between two values exists, a choice must be made to prioritise one set of values over another. For example, this may mean judging what risks to privacy it is acceptable to incur for the sake of better public health, or where to reject innovative automation technologies because the threats they pose to human skills and autonomy are too great. Making these trade-off judgements will be a complex political process. Weighing the costs and benefits of different solutions can be an important part of the process but alone is not enough, since it fails to recognise that values are vague and unquantifiable, and that numbers often hide complex value judgements. In addition, resolving trade-offs will require extensive public engagement, to give voice to a wide range of stakeholders and articulate their interests with rigour and respect. On the other hand, where tensions are more practical in nature, strict trade-offs may not be inevitable. It may be that we simply lack the knowledge or tools to advance conflicting values, and investing in further research could identify solutions that better serve all relevant values or goals. For example, it might be possible to use automation to improve people's lives without sacrificing self-actualisation and devaluing human skills, if a clear line can be drawn between the contexts where we do and do not want to pursue automation. In these situations we face a choice. Even if a tension between two goals is not a fundamentally irresolvable one, if we want to apply current technology in society, we will still need to make the kinds of trade-offs described above. On the other hand, if we can hold-off from implementing technologies that introduce tensionscertain kinds of automation, say -then we could instead invest in more research on how technological or governance solutions might reduce the need to navigate potentially difficult value trade-offs. Of course, this is not a binary choice: we can choose to strike a balance by making the trade-offs necessary to implement technology where doing so is relatively unproblematic, while still investing in research to explore how these tensions might be resolvable in future. This choice can be thought of as involving its own tension, between short-and long-term interests: to what extent should we postpone the benefits of new technologies in order to invest the time and resources necessary to resolve the tensions they introduce? \n CONCLUSION Over the last two years, many different sets of principles for the ethical use of AI have been developed. We argue that these highlevel principles, rather than representing the outcome of meaningful debate on how AI should be developed, risk simply postponing it. In order to make AI ethics practical, the field needs to now focus more on the tensions that arise when principles are applied to concrete cases. Though most of these tensions cannot be resolved straightforwardly, we believe articulating them more clearly and explicitly has several benefits. To be useful in practice, principles need to be formalized in standards, codes and ultimately regulation. To be effective, these in turn must acknowledge that there are tensions between the different high-level goals of AI ethics, and provide some guidance on how they should be resolved in different scenarios. They also need to acknowledge and accommodate different perspectives and values as far as possible, if they are to reflect genuine agreement. A focus on tensions can also help to direct research priorities in AI ethics. Articulating tensions can help to highlight important ambiguities and gaps in our understanding of how AI is currently being applied in society which need further research. More generally, much current research in AI ethics appears to be driven by questions of how we ensure that uses of AI respect important values, such as privacy, transparency, or fairness. Reframing research questions to be more focused on understanding and resolving tensions is an important step towards solving practical problems arising from the use of AI in society, since it directs attention to where new technological or governance solutions might help push the development of AI in robustly beneficial directions. \t\t\t This work is licensed under a Creative Commons Attribution International 4.0 License.", "date_published": "n/a", "url": "n/a", "filename": "3306618.3314289.tei.xml", "abstract": "The last few years have seen a proliferation of principles for AI ethics. There is substantial overlap between different sets of principles, with widespread agreement that AI should be used for the common good, should not be used to harm people or undermine their rights, and should respect widely held values such as fairness, privacy, and autonomy. While articulating and agreeing on principles is important, it is only a starting point. Drawing on comparisons with the field of bioethics, we highlight some of the limitations of principles: in particular, they are often too broad and high-level to guide ethics in practice. We suggest that an important next step for the field of AI ethics is to focus on exploring the tensions that inevitably arise as we try to implement principles in practice. By explicitly recognising these tensions we can begin to make decisions about how they should be resolved in specific cases, and develop frameworks and guidelines for AI ethics that are rigorous and practically relevant. We discuss some different specific ways that tensions arise in AI ethics, and what processes might be needed to resolve them.", "id": "7f33e43a622837f1a5a4a04128ce8310"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Reconciliation Between Factions Focused on Near-Term and Long-Term Artificial Intelligence", "text": "Introduction Artificial intelligence (AI) experts are-to generalize-of two minds about long-term AI, especially regarding the potential for radically transformative types of future AI such as artificial superintelligence (ASI) and brain emulation. One faction views long-term AI as a profound issue, warranting extensive attention and immediate action. The other faction views long-term AI as an unhelpful distraction from the more pressing near-term AI issues. The purpose of this paper is to explore the potential for reconciliation between these two seemingly divergent factions. A reconciliation would enable them to expend less energy debating each other and more energy on activities that both agree are positive. In particular, if there are certain activities that simultaneously address issues associated with both near-term and long-term AI, then there is no need to engage in a near-term vs. long-term AI debate, because either position yields the same prescriptions. I will refer to the two factions as the futurists and the presentists. Each can be said to have a core claim: The futurist AI claim: Attention should go to the potential for radically transformative longterm AI. The presentist AI claim: Attention should go to existing and near-term AI. This division is a generalization in that some AI experts support both claims; there may even be some who support neither claim, though the rise of near-term AI applications makes it increasingly difficult for even non-experts to argue that AI is unworthy of attention. The futurist faction can be traced to the early days of AI. Early AI researchers such as I.J. Good and Marvin Minsky predicted that AI would soon be capable of human-level thinking. Foreshadowing contemporary futurist concerns,  Good (1965)  warned of self-improving ultraintelligent machines that would undergo \"intelligence explosion\" in which \"the intelligence of man would be left far behind\", forming \"the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control\" (p.33). When the early predictions failed to pan out, the field entered into a more muted phase known as AI winter. Here began the presentist faction. Most AI researchers shifted from trying to build human-level general AI to building narrow, domain-specific AI. Thus \"mainstream AI\" came to be associated with developing narrow, near-term AI and repudiating AI futurism. While a minority of researchers continued work on human-level general AI (e.g.,  Goertzel and Pennachin 2007 ) and a few high-profile futurists brought long-term AI some public attention (e.g.,  Kurzweil 2006) , most AI researchers worked on narrow, near-term AI (see e.g.  Bostrom 2014, p.18; Goertzel 2014, p.1) . Within the last few years, two parallel developments have raised the prominence of the futurist-presentist AI divide. One is a breakthrough in the performance of certain AI systems, in particular those involving \"deep learning\". Major applications of AI are rapidly appearing, from medical diagnosis to self-driving cars. This breakthrough has generated considerable interest in near-term AI while making dramatic long-term AI projections appear more plausible. The other development is a spike in attention going to long-term AI, sparked mainly by the publication of the book Superintelligence  (Bostrom 2014) , public comments by several major celebrities (e.g.,  Hackett 2016; Hern 2016) , and accompanying efforts by futurist researchers and activists (e.g., Future of Life Institute no date). The sober, philosophical tone of Superintelligence and the perceived credibility of some new outspoken futurists has brought the futurist perspective a burst of serious consideration. This has in turn sparked backlash from the presentist faction. The following, from an op-ed in The New York Times by Microsoft principal researcher Kate Crawford, is representative: According to some prominent voices in the tech world, artificial intelligence presents a looming existential threat to humanity: Warnings by luminaries like Elon Musk and Nick Bostrom about \"the singularity\" -when machines become smarter than humans -have attracted millions of dollars and spawned a multitude of conferences. But this hand-wringing is a distraction from the very real problems with artificial intelligence today, which may already be exacerbating inequality in the workplace, at home and in our legal and judicial systems. Sexism, racism and other forms of discrimination are being built into the machinelearning algorithms that underlie the technology behind many \"intelligent\" systems that shape how we are categorized and advertised to  (Crawford 2016) . Crawford emphasizes inequality/discrimination as the near-term AI issue to focus on. Other presentists have emphasized such issues as military applications (e.g.,  Arkin 2009) , safety issues with medical applications or self-driving cars, disruptions to labor markets (\"technological unemployment\"), or simply the technical capabilities of the AI itself. The unifying theme for this group is its insistence on a focus on current and near-term AI. With growing interest in both near-term and long-term AI, the futurist-presentist divide has intensified. In addition to  Crawford (2016) , the divide can also be found in: a series of events on AI in 2016 sponsored by the White House, in which \"many of the speakers… emphasized the need to focus on short-term concerns over long-term concerns of artificial general intelligence\"  (Conn 2016a) ; remarks by AI researcher Andrew Ng, arguing that worrying about future AI is as unimportant as worrying about \"overpopulation on Mars\"  (Garling 2015) ; and an article by AI researcher Oren Etzioni, suggesting that AI that would not be built within the next 25 years is not worth paying attention to  (Etzioni 2016) , which prompted a reply by AI researcher Stuart Russell and political scientist Allan Dafoe arguing AI built more than 25 years from now can still be worth attention  (Dafoe and Russell 2016) ; see also  Bostrom (2014, p.18) . This sort of futurist-presentist divide is not unique to AI. For example, Selin (2007) documents a similar divide within the field of nanotechnology, in which a \"mainstream\" majority of researchers advocate for attention to (and funding for) existing and near-term nanotechnology at the expense of potential long-term transformative nanotechnology. Similarly, one explanation for the low priority commonly given to global warming is the fact that the harmful impacts of climate change will accrue mainly in the future  (Weber 2006) . In recognition of the challenge of motivating action on long-term issues,  Baum (2015)  proposes to address a wide range of longterm catastrophic risks-including long-term AI, nanotechnology, and climate change-by leveraging interest in synergistic near-term co-benefits. The present paper follows in a similar vein as  Baum (2015) , though it is not intended as a critique or an advocacy of either the futurist or presentist AI factions. Instead, it seeks to pragmatically pursue reconciliation between the factions so that they may be able to pursue mutually agreeable activities. Three such activities are described in Section 4. Leading up to that, Section 2 explores the ideas at the root of the futurist and presentist perspectives, while Section 3 proposes a reconciliation based on a general concern for the societal impacts of AI. \n Root Perspectives This section attempts to articulate the perspectives at the root of the futurist and presentist factions. The descriptions derive from readings from, observations of, and interactions with the two factions. Root perspectives can help explain why the two factions disagree with each other and where reconciliation may be possible. \n AI Futurists Two distinct root perspectives can be found among AI futurists. One is centered on the intellectual goals of AI research, the other on the implications of a certain ethical perspective. The first perspective is rooted in an intellectual aspiration of building advanced AI that have general intelligence at a human or superhuman level. \"General\" in this context means that they can think across a wide range of domains, or \"have a broad capability to self-adapt to changes in their goals or circumstances\"  (Goertzel 2014, p.1) . Building such advanced AI has long been \"the grand dream of artificial intelligence\"  (Legg 2008, p.125 ), but it is only pursued by a small portion of AI researchers. These are the researchers who are willing to accept that their work may be of little immediate practicality in order to work towards a more grand future achievement. They seek \"to promote the idea that intelligent machines, even super intelligent machines, is a topic that is both important and one that can be scientifically studied, even if just theoretically for now\"  (Legg 2008, p.126) .  Goertzel (2014, p.3)  presents what it calls the core hypothesis of artificial general intelligence: The creation and study of synthetic intelligences with sufficiently broad (e.g. humanlevel) scope and strong generalization capability, is at bottom qualitatively different from the creation and study of synthetic intelligences with significantly narrower scope and weaker generalization capability. Thus, advanced future AI requires fundamentally different research than is needed for the narrower contemporary AI.  Goertzel (2014)  maintains that this hypothesis is widely held among artificial general intelligence researchers. Thus, there is a community of researchers dedicated specifically to developing advanced future AI.  (Goertzel 2014 also surveys this research.)  The second AI futurist perspective starts with an ethical concern for long-term effects and pairs this with a belief that long-term AI can have major long-term effects. The ethical concern for long-term effects has rigorous philosophical justification, though as with any ethical position, it is not universally held. It follows directly from a principle of equality: if all human lives (or whatever else we might care about) should be valued equally, then this (arguably) includes future lives. Furthermore, there could be many more future lives than present lives. Thus, philosophers and economists have long recognized the importance of actions that can have ongoing benefits to future generations, such as economic saving  (Ramsey 1928 ) and survival of the population  (Koopmans 1974) . This same ethical perspective has been articulated more recently by some in the AI futurist faction (e.g.,  Bostrom 2003) . The perspective prompts people to seek out issues and actions that could have significant long-term impact; the \"merely near-term\" is seen as trivial in comparison. This big-picture, long-term perspective explains why the futurist AI faction disproportionately attracts philosophers (e.g., Bostrom 2014; Price 2013) and cosmologists (e.g.,  Hawking et al. 2014) , and why they give their organizations names like Future of Humanity Institute and Future of Life Institute. The long-term ethical perspective is not fundamentally about AI. Instead, it is a guide for all human action; any role for AI is circumstantial. It relates to AI via the belief that certain AI could have major long-term effects, sending human civilization on fundamentally different trajectories. Only AI that could be so transformative is worth paying attention to; the rest is trivial detail. Thus, the prospect of future transformative AI is seen as important, and indeed is important even if there is only a small probability of it being built and even if it would be built decades or centuries from now. As long as there is some nonzero probability that future AI could, say, take over the world and kill everyone  (Bostrom 2014)  or dominate the global economy while remaking the future of civilization  (Hanson 2016) , then it is worth paying attention to. Indeed, such transformative long-term AI competes for attention not with near-term AI but with other potentially transformative issues such as global warming, nuclear war, and long-term nanotechnology. The long-term ethical perspective can seem harsh in its relentless prioritization of long-term issues. For example,  Crawford (2016)  laments racial bias in AI evaluation of criminals in the United States, resulting in harsher prison sentences for African-Americans than for Americans of European descent. 1 Racial bias in law enforcement would seem to be an important issue, and indeed, at the time of this writing, it is at the very top of the public agenda in the United States. However, the attention is on racial bias as it affects people today, not on how it affects long-term outcomes for humanity. Indeed, it is possible that present cases of racial bias will have limited long-term effect, especially relative to a possible future transformative AI. The same holds for most, if not all, other near-term AI issues. Ironically, it is the same ethical principle of equality that underlies opposition to racial bias that also motivates the ignoring of racial bias in favor of long-term issues. \n AI Presentists In contrast, AI presentists are motivated by a desire to work on contemporary and near-term activities and issues. This holds for presentist AI researchers as well as those focused on societal issues raised by AI. Most AI research is presentist. The focus on contemporary and near-term AI systems is rooted in a practical, down-to-Earth perspective that seeks to work on actual systems and avoid speculation about future possibilities, especially when those possibilities seem strange and fantastic. Thus, for example, AI researcher Andrew Ng dismisses concerns about advanced future AI because \"the future is so uncertain\" that it cannot be meaningfully considered, and instead attention should be on problems that are more immediate and less ambiguous  (Garling 2015) . Similarly, Nilsson describes how AI researchers shy away from work on advanced future AI because they worry it would \"risk losing our respectability\"  (Nilsson 2010, p.399) . This near-term focus of AI research is not unusual. Looking across all fields of science and engineering, one finds few people motivated by long-term effects for humanity or other considerations deriving from theoretical philosophy. Indeed, they often believe ethical considerations to be fundamentally outside their professional domain, so much that they \"accept radical restrictions on having consequential opinions about what ought to be done\"  (Shapin 2010, p.388; emphasis original) . This can be seen, for example, in the United States National Science Foundation's two criteria for evaluating funding proposals: intellectual merit and broader impacts. Intellectual merit is what scientists and engineers consider intrinsically important; it is what wins grants and publications in top journals. Broader impacts is the societal significance of the research, which is often considered less important (e.g.,  Schienke et al. 2009) . AI researchers generally focus on near-term AI because that is what they consider to have more intellectual merit. Long-term AI is speculative and untestable, which places it outside the bounds of normal science and engineering. The potential for long-term AI to have larger societal impacts is not a factor. From this perspective, even talking about the long-term impacts can be counterproductive, leading to concerns about respectability, as noted above, and to boom-bust cycles of hype and disillusionment, as has been seen over the years of AI \"summer\" and \"winter\". Hence presentists can resent the mere mention of long-term AI. The norm of intellectual merit further explains why some AI researchers prefer to focus on the capabilities of the AI itself and not on societal issues. 2 Coming from computer science or related backgrounds, they view their role as one of advancing the science and technology of AI; attending to any related societal issues is, if anything someone else's job. However, many AI researchers are attentive to societal issues associated with AI.  Crawford (2016)  is not a rare exception.  3  When presentists do turn to societal issues, they turn to those that relate to existing and nearterm AI. This focus is reinforced by the fact that the general public and political leadership also tend to emphasize near-term issues. Hence even seemingly major long-term issues like global warming commonly get drowned out by near-term issues like economic growth  (Scruggs and Benegal 2012) . And so, when presentist AI researchers seek to discuss societal issues related to their AI, they find a welcome audience in social policy circles. This is seen, for example, in the heavy focus on near-term issues in the recent White House Symposia on AI Research  (Conn 2016a) . \n Reconciliation Despite the divergent perspectives between the presentists and futures, as well as the sometimes bitter debate between them, the two factions share a common interest in AI and belief of its importance. This commonality may seem banal, but it nonetheless distinguishes them from the large population that gives AI little attention or none at all. Thus, for starters, the two factions can at least unite in promoting AI as a locus of attention. But there can be much more than that. There are significant parts of both factions that are concerned about the societal impacts of AI. Their concerns may come from different places, the futurists starting with concern about a certain type of societal impact and then applying this to AI, and the presentists starting with an interest in a certain type of AI and then applying this to societal issues. The fact that they work in opposite directions explains their divergent viewpoints and AI emphases. But they can at least agree that the societal impacts of AI are important, worth paying attention to, and worth trying to improve, even while they disagree on which impacts to focus on. Meanwhile, there are those in both factions who are not so concerned about societal impacts, who instead prefer to focus on the AI itself. Thus, there is potential for a realignment of AI factions from futurist vs. presentist to those who are concerned about societal impacts vs. those who are not. This would seem to be the crucial distinction: between those who wish to pursue AI for its own sake or for narrow conceptions of intellectual merit, on the one hand, and on the other hand those who wish to pursue AI for the benefit of society. I will call these realigned factions the intellectualist faction and the societalist faction, rooted in the following core claims: The intellectualist AI claim: AI should be developed for its own sake, i.e. for its intellectual merit. The societalist AI claim: AI should be developed for its impacts for society. It should be clarified that societalists may often emphasize intellectual aspects of AI en route to pursuing societal benefits. This is to say that belonging to the societalist faction does not preclude one from pursuing intellectually advanced AI. There can be many opportunities to be a \"good\" AI researcher according to traditional science and engineering notions of intellectual merit while still working towards societal benefits. Another important clarification is that, among societalists, there will always be disagreements about which societal impacts to focus on; this is normal ethical and political debate. And just as conventional politics-the art of the possible-seeks areas of aligned interests, quid pro quo, and compromise, so too can those who disagree about the societal impacts of AI. This realignment has a big advantage in that it enables focus on promoting attention to societal impacts in general. It is straightforward to argue that presentists and futurists alike should be concerned about societal impacts. AI researchers, like other scientists and engineers or any other people, are not above the law or above morality. It is everyone's responsibility to help society.  4  The realignment has further advantages in the synergistic opportunities to be found between presentist and futurist societalists. \n Opportunities Within a realigned societalist faction, the best opportunities will generally be those in which the interests of presentists and futurists are aligned. Such opportunities require no compromise or other sacrifice. Several such opportunities are apparent. \n Social Norms A first opportunity is to encourage more AI researchers to care about the societal impacts of their work. This assumes-quite reasonably, one would think-that the societal impacts of AI tend to be better when more AI researchers aim to achieve better societal impacts. In other words, the pro-societal efforts of AI researchers tend to be productive, not counterproductive. While it is possible to persuade AI researchers one at a time to care about societal impacts, it will often be more effective to persuade many of them all together. This can be achieved by establishing societalist social norms among AI communities, i.e. by making it normal for AI researchers to seek to benefit society through their work. Societalist social norms are seen, for example, in AI researcher Stuart Russell's call for the AI field to switch from a norm of \"building pure intelligence for its own sake, regardless of the associated objectives and their consequences\" to a norm of not just caring about societal impacts, but also making that be \"how practitioners define what they do\"  (Bohannon 2015:252) . The advantage of advancing societalist social norms is that it creates more AI researchers available to work on pro-societal designs, policies, etc., and likewise fewer people pushing back against such activities. An expanded societalist faction should benefit both near-term and longterm societalist agendas: a rising tide lifts all boats. Given that AI research communities tend to focus on near-term AI, it may be advantageous to emphasize norms associated with the societal impacts of near-term AI. In practice, this means engaging AI researchers on such issues as inequality/discrimination (as in Crawford 2016), military applications (as in  Arkin 2009) , the safety of medical AI or self-driving cars, etc. It is relatively easy to sell the importance of these issues because either they already are important issues or they clearly will be in the near future, and because they do not depend on the arrival of any speculative future forms of AI but instead are rooted in existing and near-term AI. Social norms surrounding the societal impacts of near-term AI can be of indirect benefit to the societal impacts of long-term AI. One mechanism for this is the durability of norms. What is now long-term AI may one day become near-term AI. If societalist norms remain intact, then the near-term societalists would switch over to what is now long-term AI. There is reason to believe that societalist norms may be so durable. For comparison, norms against slavery or racism or sexism have proved durable; 5 within academia, the norm in favor of interdisciplinary research has gradually advanced for many years. If AI societalist norms could be similarly durable, they would help with what is now near-term and long-term AI. A second mechanism is for societalist norms to prompt AI researchers to become more interested in long-term impacts. This could happen via attention to the ethics underlying which societal impacts one might care about. Ethical reflection is a natural fit for societalist AI, i.e. societalists are likely to engage in ethical reflection. That reflection could include the ethics of future generations, which is precisely how many existing futurists came to be futurists. Therefore, a case can be made for promoting near-term societalist norms among AI communities. Because the issues are near-term, they are more likely to attract interest from AI communities. This increases the size of the near-term societalist faction. Then, some portion of these societalists may come to appreciate the ethical argument for caring about long-term impacts. This increases the size of the long-term societalist faction. Furthermore, the expanded societalist faction may remain in place when the long-term gets nearer. So, this is a win-win for both near-term and long-term societalists. \n Technical Research Societalist social norms expand the population of AI experts who can pursue the lines of technical AI research that benefits society. Some technical research may pertain only to specific AI applications and is thus only of interest to narrow presentist or futurist concerns. However, there is also some technical research that is of wide relevance to both near-term and long-term AI. Progress on this research is another win-win for near-term and long-term societalists. An example of this sort of \"timeless\" technical research can be found in  Amodei et al. (2016) . This paper describes a range of technical problems oriented towards avoiding unintended harms from AI systems. The paper is expressed in terms of unintended harms from near-term AI. However, in an interview, Amodei describes how he sees the technical problems as being relevant for near-term and long-term AI alike, such that the near-term/long-term distinction is unnecessary  (Conn 2016b) . Thus, all societalists could support this technical research agenda, regardless of whether they are ultimately concerned about near-term or long-term impacts. Indeed, in the same interview, Amodei further notes that his paper has received broad praise, including from people who fit into both the presentist and futurist factions  (Conn 2016b) . \n Policy Given the general orientation of policy communities towards near-term issues, it will typically be easier for policy to address issues associated with near-term AI. However, there are at least two ways that AI policy can concurrently support both near-term and long-term AI, making for a third win-win for near-term and long-term societalists. First, the process of developing near-term AI policy can create processes and competencies of relevance for long-term AI. Already, near-term AI policy issues have prompted legal scholars to familiarize themselves with some technical details of  AI (e.g., Calo 2011; Funkhouser 2013; Hammond 2015) . Such scholarship, and accompanying policy discussions, prepares policy communities for addressing long-term AI.  6  Near-term AI policy will also create demand for people with AI backgrounds working in policy positions. Such in-house AI expertise can help ensure that AI policy matches actual issues associated with AI technology and does not inadvertently restrict beneficial AI or enable harmful AI. Good models can be found, for example, in the Science & Technology Policy Fellowships offered by the American Association for the Advancement of Science and the IEEE-USA Government Fellowships offered by the Institute of Electrical and Electronics Engineers. These are both temporary fellowships; there should also be AI experts in permanent government positions. As long as the private sector offers abundant and lucrative employment for AI experts, it may be difficult to attract them to government positions. This challenge could be overcome via sufficiently strong societalist norms, which could motivate some societalists to forgo salary and pursue government positions simply because it is the right thing to do for society. Second, some specific policy measures may improve outcomes for both near-term and longterm AI. This may seem counterintuitive, given the rapidly changing nature of AI. Indeed, a common concern about policy for emerging technologies like AI is that policy will fail to keep up with changes in the technology. In response to this concern,  Moses (2007)  proposes to phrase policy in more general terms, such as \"choose the AI design that is more beneficial to society\"; such policy could remain relevant even if AI technology undergoes major changes. Other policies of enduring relevance can be policies that establish institutions for AI governance, including policies to establish support for pro-societal AI efforts. \n Conclusion The current division between AI futurists and presentists-i.e. those concerned mainly about long-term AI vs. those concerned mainly about near-term AI-is not the best focus of attention. Instead of bickering over which AI impacts are most important, both groups would be wise to focus on addressing the AI impacts in general. There are ample opportunities to concurrently address both near-term and long-term AI impacts, including by establishing societalist social norms within AI communities, by advancing technical research that improves societal outcomes for all types of AI, and by advancing public policy that improves the governance of all types of AI. Making progress on these three fronts will take effort, which is precisely why those who worry about AI impacts should not drain their energy on internal disputes. The Introduction to this paper quoted a passage from  Crawford (2016)  that argues for attention to near-term inequality/discrimination issues instead of to long-term threats. The passage is a representative example of the presentist vs. futurist dispute. However, in light of this paper's proposed reconciliation, the passage could be rewritten to instead take on the societalist vs. intellectualist dispute: According to some prominent voices in the tech world, artificial intelligence presents a major intellectual achievement, a triumph of science and technology. They say this achievement is to be celebrated, full stop. Indeed, research into the science of artificial intelligence has attracted millions of dollars and spawned a multitude of conferences. But this intellectual triumphalism is a distraction from the problems that artificial intelligence creates for society. It may already be exacerbating inequality in the workplace, at home and in our legal and judicial systems. It is also creating safety challenges for medical products and self-driving cars, as well as profound ethical dilemmas in its military applications. Looking further into the future, there may be some chance that artificial intelligence presents a looming existential threat to humanity. These are serious issues that demand serious attention from society as a whole and especially from the technologists whose work is at the heart of these issues. Expositions along these lines promise to reconcile the differences between presentists and futurists and instead shift attention to where it is desperately needed: on the societal issues posed by AI and on the positive steps can be taken to address these issues. \t\t\t The racial bias Crawford describes comes from the investigative journalism of Angwin et al. (2016) .2  One can argue that the AI itself is situated within society, and thus that AI researchers inevitably work on societal issues, even when they believe that they are working only on the AI itself. However, for present purposes, what matters is that the AI researchers believe that they are focusing on the AI itself and not on societal issues, even if it can be argued that they are inadvertently working on societal issues. \n\t\t\t As just one of many other examples, see Arkin (2009)  on societal issues associated with military robotics. \n\t\t\t Again, as with any ethical position, the claim that people should help society is not universally held. A broader defense of this claim is beyond the scope of this paper. \n\t\t\t The world still has slavery and racism and sexism, but not as much as it once did. For example, while the United States continues to grapple with a variety of racial biases, it has become unthinkable to support the \"separate but equal\" racial segregation of the former \"Jim Crow\" laws.6  There has also been some legal scholarship focused on long-termAI (e.g., McGinnis 2010; Wilson 2013) , but this is a relatively small minority of AI legal scholarship.", "date_published": "n/a", "url": "n/a", "filename": "036_reconciliation.tei.xml", "abstract": "Artificial intelligence (AI) experts are currently divided into \"presentist\" and \"futurist\" factions that call for attention to near-term and long-term AI, respectively. This paper argues that the presentist-futurist dispute is not the best focus of attention. Instead, the paper proposes a reconciliation between the two factions based on a mutual interest in AI. The paper further proposes a realignment to two new factions: an \"intellectualist\" faction that seeks to develop AI for intellectual reasons (as found in the traditional norms of computer science) and a \"societalist faction\" that seeks to develop AI for the benefit of society. The paper argues in favor of societalism and offers three means of concurrently addressing societal impacts from near-term and long-term AI: (1) advancing societalist social norms, thereby increasing the portion of AI researchers who seek to benefit society; (2) technical research on how to make any AI more beneficial to society; and (3) policy to improve the societal benefits of all AI. In practice, it will often be advantageous to emphasize near-term AI due to the greater interest in near-term AI among AI and policy communities alike. However, presentist and futurist societalists alike can benefit from each others' advocacy for attention to the societal impacts of AI. A reconciliation between the presentist and futurist factions can improve both near-term and long-term societal impacts of AI.", "id": "71d6aed2637c34b5a7fa15081f3d0b7a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Grant Wilson", "! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"], "title": "Minimizing Global Catastrophic and Existential Risks from Emerging Technologies through International Law", "text": "INTRODUCTION The world is currently undergoing a remarkable revolution in science and technology that will seemingly allow us to engineer synthetic life of any imaginable variety, build swarms of robots so small that they are invisible to the human eye, and, perhaps, create an intelligence far superior to the collective brainpower of every human. Much of this \"emerging technology\" either already exists in rudimentary form or may be developed in the coming decades, 1 including the three technologies covered by this paper: nanotechnology, bioengineering, and artificial intelligence (AI). While many scientists point to these developments as a panacea for disease, pollution, and even mortality, 2 these emerging technologies also risk massive human death and environmental harm. Nanotechnology consists of \"materials, devices, and systems\" created at the scale of one to one hundred nanometers 3 -a nanometer being one billionth of a meter in size (10 -9 m) or approximately one hundred-thousandth the width of a human hair 4 -including nano-sized machines (\"nanorobots\"). Bioengineering also operates on a tremendously small scale but uses concepts of engineering to build new biological systems or modify existing biological systems 5 by manipulating the very building blocks of life.  6  Finally, AI, meaning intelligent computers, is a pathway to \"the Singularity,\" the concept that manmade greater-than-human intelligence could improve upon its own design, thus beginning an intelligence feedback mechanism or \"explosion\" that would culminate in a godlike intelligence with the potential to operate at one million times the speed of the human brain.  7  These and other threats from emerging technologies may pose a \"global catastrophic risk\" (GCR), which is a risk that could cause serious global damage to human well-being, or an \"existential risk\" (ER), which is a risk that could cause human extinction or the severe and permanent reduction of the quality of human life on Earth.  8  Currently, the main risks from emerging technologies involve the accidental release or intentional misuse of bioengineered organisms, such as the airborne highly pathogenic avian influenza A (H5N1) virus, commonly known as \"bird flu,\" that scientists genetically engineered in 2011. However, with emerging technologies developing at a rapid pace, experts predict that perils such as dangerous self- !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 See infra Section II.  2  See Terry Grossman et al., Reinventing Humanity: The Future of Human-Machine Intelligence, THE FUTURIST (Feb.  03, 2006) , available at: www.kurzweilai.net/reinventing-humanity-the-future-of-human-machine-intelligence.  3  Ortwin Renn & Mihail Roco, Nanotechnology and the Need for Risk Governance, 8 J. NANOPARTICLE  RES. 153 (2006) , available at: http://www.springerlink.com/content/y80541n7740785gm/fulltext.pdf.  4  Nanotechnology White Paper, NANOTECHNOLOGY WORKGROUP, ENVIRONMENTAL PROTECTION AGENCY'S SCIENCE POLICY COUNCIL (SPC) 5  (2007) , available at: http://epa.gov/osa/pdfs/nanotech/epa-nanotechnologywhitepaper-0207.pdf.  5  The Issues, ETC GROUP, http://www.etcgroup.org/en/materials/issues (last visited Feb. 14, 2012).  6  See Natalie Angier, Peering Over the Fortress That is the Mighty Cell, N.Y. TIMES (May 31, 2010), available at: http://www.nytimes.com/2010/06/01/science/01angi.html?ref=jcraigventer.  7   ! 3! replicating nanotechnology, 9 deadly synthetic viruses available to amateur scientists, and unpredictable superintelligent AI 10 may materialize in the coming few decades. Society should take great care to prevent a GCR or ER (\"GCR/ER\") from materializing, yet GCRs/ERs arising out of nanotechnology, bioengineering, and AI are almost entirely unregulated at the international level. 11 One possible way to mitigate the chances of a GCR/ER ever materializing is for the international community to establish an international convention tailored to these emerging technologies based on the following three principles: first, that nanotechnology, bioengineering, and AI pose a GCR/ER; second, that existing international regulatory mechanisms either do not include emerging technologies within their scope or else insufficiently mitigate the risks arising from emerging technologies; and third, that a international convention based on the precautionary principle could reduce GCRs/ERs to an acceptable level. This paper purports to establish the threats of emerging technologies, highlight regulatory gaps under international law, and recommend an international framework to address the associated risks. Specifically, Section II discusses the benefits and risks of emerging technologies, establishing that bioengineering poses a GCR/ER now while nanotechnology and AI pose a GCR/ER in the future. Section II also provides the background of attempts to enjoin the operation of the Large Hadron Collider (LHC) to highlight difficulties courts have in addressing low-probability scientific threats and the conflicts of interest scientists may have in self-regulation. Section III then analyzes GCRs/ERs from bioengineering under international law, concluding that no international convention sufficiently regulates the risks arising out of bioengineering. This section focuses on bioengineering because it is the only emerging technology that poses an immediate GCR/ER. Section IV stitches together the fundamentals of an international treaty that would regulate GCRs/ERs from emerging technologies through concepts such as the precautionary principle, decisionmaking from a body of experts, and public participation. Finally, Section V concludes that states should act quickly to create a flexible, legally binding treaty to regulate the emerging technologies that present a GCR/ER. \n II. BACKGROUND ON EMERGING TECHNOLOGIES AND EXISTENTIAL RISKS While many experts cite a forthcoming revolution in nanotechnology, bioengineering, and AI as a source of great potential benefit to mankind and the environment, these technologies also risk causing profound negative consequences if insufficiently regulated. This section discusses current and forthcoming emerging technologies to highlight the benefits of emerging technologies while also establishing that they pose a GCR/ER. This background will serve as a foundation for an international regulatory regime that seeks to curtail the risks of emerging technologies without stifling their beneficial uses. Additionally, this section presents a brief case study of the LHC, which demonstrates the challenges of seeking judicial review of a complex scientific technology that poses a remote but significant harm and the problems with permitting self-assessment of risks amongst scientists. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 9 See Nanotechnology White Paper, supra note 4, at 12.  10  Eliezer Yudkowsky, Artificial Intelligence as a Positive and Negative Factor in Global Risk, in GLOBAL CATASTROPHIC RISKS 237 (Nick Bostrom & Milan M. Ćirković, eds., 2008).  11  See infra Section III. ! 4! \n A. Global Catastrophic Risk and Existential Risk A GCR is a risk that has the potential to cause \"serious damage to human well-being\" on the global scale.  12  While the threshold of \"serious\" damage is somewhat ambiguous, one expert sought to clarify the matter by asserting that an event killing 10,000 people would not qualify as a GCR, while one that killed 10,000,000 people would.  13  Furthermore, an event need not affect the entire Earth to have a \"global\" scale, but certainly must affect at least several parts of the world.  14  GCRs may be categorized into natural, anthropogenic, and intermediate risks. An example of a natural GCR that has already materialized is the Spanish flu pandemic,  15  while possible future natural GCRs include extreme natural disasters, another ice age, or a meteor striking the Earth.  16  Examples of past anthropogenic GCRs are the first and second World Wars, while possible future anthropogenic GCRs include nuclear war, accidents involving experimental technology, or bioterrorism.  17  Finally, intermediate GCRs are those that involve \"complex interactions between humanity and its environment,\" such as climate change.  18  One specific type of GCR is an ER, which is a low-probability, high impact risk that could (1) make humans go extinct or (2) severely and permanently harm the future quality of life of humans. An existential risk requires, at minimum, a global scope, a terminal (i.e. fatal) intensity, and a permanent effect on the quality of human life that continues into future generations.  19  Several GCRs are also ERs, such as nuclear war, certain experimental technologies, and climate change. Likewise, the three risks that this paper focuses onnanotechnology, bioengineering, and AI-are both GCRs and ERs. Because ERs are irrevocable, great care must be taken as to never let one happen. Although the probability of an existential risk materializing is up to much debate, some experts have come up with rough estimates. For example, Martin Rees, a decorated scientist and former President of the Royal Society,  20  believes there to be a fifty percent chance of human extinction before the 22 nd century, with much of the risk arising from some of the emerging technologies discussed in this paper.  21   \n B. Global Catastrophic Risks and Existential Risks from Emerging Technologies States should consider concluding an international treaty to regulate emerging technologies if they perceive these technologies to pose a GCR/ER. This section considers the current and future risks and benefits posed by three emerging technologies-bioengineering, !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 12 BOSTROM & ĆIRKOVIĆ, supra note 10, at 23.  13  Id. at 24.  14  Id.  15  Id.  16  Id. at 13-27.  17  Id.  18  For a discussion of intermediate ERs, see MILAN M. ĆIRKOVIĆ, ANDERS SANDBERG, & NICK BOSTRON, Anthropic Shadow: Observation Selection Effects and Human Extinction Risks, 30 RISK ANALYSIS 1495 (2010).  19  BOSTROM & ĆIRKOVIĆ, supra note 10, at 04.  20  The Royalty Society, of which the about 1,500 Fellows and Foreign Members includes about 80 Nobel Laureates, is Britain's Academy of Sciences and publisher of nine peer-reviewed journals. See About Us, THE ROYAL SOCIETY, at: http://royalsociety.org/about-us (last visited Jan. 29, 2012).  21  Steve King, Worst Possible Scenarios, SPECTATOR (May 24, 2003), reviewing MARTIN REES, OUR FINAL CENTURY?  (2003) , available on Westlaw at 2003 WLNR 8390689. ! 5! nanotechnology, and AI. This section concludes that bioengineering is the only emerging technology that poses an immediate GCR/ER, while nanotechnology and AI pose a future GCR/ER. \n Bioengineering Simply defined, bioengineering is the \"engineering of living organisms.\" 22 Bioengineering is commonly associated with genetically modified (GM) foods made from crops that scientists develop to have qualities like pest resistance or increased nutrition. However, bioengineering is rapidly expanding beyond agriculture into fields like medicine, disease control, and life-extension. The technology behind bioengineering has also developed quickly, with scientists now able to understand and manipulate life at the molecular level such that biology is viewed as a \"machine\" that can be tweaked, like in genetic engineering, or even built from the ground up, like in synthetic biology.  23  While breakthroughs in bioengineering research could significantly benefit mankind and the environment, bioengineering research can also be misused to the detriment of humans, animals, and environmental health.  24  Such \"dual use\" research currently poses significant risks to humankind, but even greater risks in the future. Furthermore, both current and future bioengineering technologies pose the risk of an accident that has significant detrimental effects. In exploring these issues, this section demonstrates that bioengineering poses an immediate GCR/ER. \n a. Current technology Bioengineering is already widely used to modify existing organisms, and scientists are on the cusp of creating entirely synthetic organisms. For example, scientists controversially use bioengineering to \"improve\" natural biological products and activities, resulting in increased nutrient value, bigger yields, and insect and disease resistance 25 in various types of crops.  26  In 2011, 94 percent by acre of soybeans in the United States were genetically engineered, while 73 percent of all U.S. corn was genetically engineered to be insect resistant and 65 percent to be herbicide tolerant.  27  Another controversial current bioengineering technology is genetically engineer viruses, highlighted by the 2011 genetic engineering of the H5N1 virus to become highly contagious amongst ferrets. Many scientists argue that creating the genetically engineered virus was necessary to develop a remedy in case the H5N1 virus mutates naturally, but skeptics argue that the modified H5N1 virus is dangerous because of risks that the virus will escape or that !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! malicious actors will engineer a similar virus.  28  Another example of recent advancements in bioengineering is a project spearheaded by biologist Craig Venter that transplanted a completely synthetic DNA sequence, or \"genome,\" into an E. coli bacteria-scientists then also added DNA \"watermarks\" such as the names of researchers and famous quotes-which Craig Venter termed \"the first self-replicating species we've had on the planet whose parent is a computer.\"  29  Bioengineering has also become vastly cheaper and more accessible to the general public. For example, massive databases of DNA sequences are available online from the Department of Energy Joint Genome Institute (JGI) and the National Center for Biological Information's GenBank ® database.  30  To materialize these DNA sequences, individuals can order custom genomes online for a few thousand dollars, which are \"printed\" from a DNA synthesis machine and shipped to them, opening the door for amateur biologists to engage in genetic engineering.  31  DNA synthesis machines can print DNA strands long enough for certain types of viruses, which untrained individuals can obtain within six weeks of purchase.  32  Even the synthesizing machines themselves can be purchased on the Internet on sites like eBay.  33  Much like bioengineering costs, the necessary expertise to engage in bioengineering is also plummeting. For example, since 2003, teams of entrepreneurs, college students, and even high school students submitted synthetic biology creations to the International Genetically Engineered Machine (IGEM) competition, such as UC Berkeley's \"BactoBlood\" creation-a \"cost-effective red blood cell substitute\" developed by genetically engineering E. coli bacteria. 34 \n b. Forthcoming technology Perhaps the greatest forthcoming development in bioengineering is synthetic biology, which includes techniques to \"construct new biological components, design those components and redesign existing biological systems.\"  35  This is in contrast to the traditional form of bioengineering that utilizes \"recombinant DNA\" techniques in which the DNA from one organism is stitched together with DNA from other organisms or synthetic DNA.  36  One method of synthetic biology involves \"cataloguing\" DNA sequences like \"Lego bricks\" and assembling  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \n ! 7! them in unique ways (assembling natural molecules into an unnatural system, like combining the molecules from several types of bacteria to create a new bacteria with novel properties. Another method of synthetic biology involves using DNA synthesizers to create life \"entirely from scratch … the biological equivalent of word processors\" (using unnatural molecules to emulate a natural system, like creating the synthetic equivalent of a natural strand of influenza).  37  One way to \"birth\" synthetic DNA is to insert the DNA into a \"biological shell\"an organism, often a bacteria, that had its own genes removed-that can run the synthetic DNA like a computer runs software.  38  And while the technology to create eukaryotic cells (i.e. \"a cell with a nucleus, such as those found in animals, including human beings\") is a long ways away, synthetic viruses and bacteria are just around the corner. 39 c. \n Benefits of bioengineering Bioengineering is already displaying its potential to remedy major human health and environmental problems. For example, bioengineering is responsible for several pharmaceuticals and vaccines, such as insulin and a vaccine for Hepatitis B, while \"gene therapy\" employs genetically engineered viruses to help treat cancer.  40  Environmental benefits resulting from the 15.4 million farmers who grew genetically modified crops in 2010 include increased yield of six to thirty percent per acre of land, pest-resistant crops that require fewer pesticides (resulting in 17.1% less pesticide use globally in 2010), lower water use for drought-resistant crops, decreased CO 2 emissions, and crops that do not require harmful tilling practices.  41  Forthcoming benefits to human health could be a new wave of ultra-effective drugs (e.g. antimalarial and antibiotic drugs), bioengineered agents that kill cancer cells, and the ability to rapidly create vaccines in response to epidemics.  42  Bioengineering could also serve as a beacon of human diagnostics by analyzing \"thousands of molecules simultaneously from a single sample.\"  43  Meanwhile, forthcoming benefits to the environment could be organisms that remedy harmful pollution and superior forms of biofuel, for example.  44  Bioengineering could also spur an environmental revolution in which industries reuse modified waste from biomass feedstock and farmers grow bioengineered crops on \"marginally productive lands\" (e.g. switchgrass). 45 \n d. \n Risks from bioengineering While bioengineering offers current and future benefits to humans and the environment, there are also significant yet uncertain risks that could devastate human life, societal stability, !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 37 What is Synthetic Biology?, SYNETHICBIOLOGY.ORG, at: http://syntheticbiology.org/FAQ.html (last visited Feb. 16, 2012). See also Garfinkel & Friedman, supra note 32, at 269.  38  Id.  39  Garfinkel & Friedman, supra note 32, at 271.  40     46  This paper focuses on three predominant GCR/ER risks arising from bioengineering: (1) the accidental release of harmful organisms (a \"biosafety\" issue), (2) the malicious release of harmful organisms (\"bioterrorism\"), and (3) the bioengineering of humans. The first two are current GCRs/ERs, while the third is a future GCR/ER. \n i. Risk of an accident An accidental release of a bioengineered microorganism during legitimate research poses a GCR/ER when such a microorganism has the potential to be highly deadly and has never been tested in an uncontrolled environment.  47  The threat of an accidental release of a harmful organism recently sparked an unprecedented scientific debate amongst policymakers, scientists, and the general public in reaction to the creation of an airborne strain of H5N1.  48  In September 2011, Ron Fouchier, a scientist from the Netherlands, announced that he had genetically engineered the H5N1 virus-his lab \"mutated the hell out of H5N1,\" he professed-to become airborne, which was tested on ferrets; a laboratory at the University of Wisconsin-Madison similarly mutated the virus into a highly transmittable form.  49  The \"natural\" H5N1 killed approximately 60 percent of those with reported infections (although the large amount of unreported cases means that this is an over estimate), but the total number of fatalities-three hundred and forty-six people-was relatively small because the virus is difficult to transmit from human to human. The larger risk comes from the possibility that a mutated virus would spread more easily amongst humans, 50 which could result in a devastating epidemic amongst the worst in history, if not the very worst.  51  To put this in context, about one in every fifteen Americans-20 million people-would die every year from a seasonal flu as virulent as a highly transmittable form of H5N1.  52  Lax regulations and a rapidly growing number of laboratories exacerbate the dangers posed by bioengineered organisms. While lab biosafety 53 guidelines in the United States and Europe recommended that projects like reengineering the H5N1 virus be conducted in a BSL-4 facility (the highest security level), neither laboratory that reengineered the H5N1 virus met this non-binding standard.  54  Meanwhile, a 2007 Government Accountability Office (GAO) report ! 9! indicated that BSL-3 and BSL-4 labs are rapidly expanding in the United States. While there is significant public information about laboratories that receive federal funding or are registered with the Centers for Disease Control and Prevention (CDC) and the U.S. Department of Agriculture's (USD) Select Agent Program, much less is known about the \"location, activities, and ownership\" of labs that are not federally funded and not registered with the CDC or the USD Select Agent Program.  55  The same report also concluded that there is no single U.S. agency that is responsible for tracking and assessing the risks of labs engaging in bioengineering.  56  While some claim that critics are overreacting to the genetically engineered H5N1 virus, there are a series of accidental releases of microbes from laboratories that demonstrate the risks of largely unregulated laboratory safety. In 1978, an employee died from an accidental smallpox release from a laboratory on the floor below her.  57  Many scientists believe that the global H1N1 (\"swine flu\") outbreak in the late 2000s originated from an accidental release from a Chinese laboratory.  58  Reports concluded that the accidental releases of Severe Acute Respiratory Syndrome (SARS) in Singapore, Taiwan, and China from BSL-3 and BSL-4 laboratories all resulted from a low standard of laboratory safety.  59  In the United States alone, a review by the Associated Press of more than 100 laboratory accidents and lost shipments between 2003 and 2007 show a pattern of poor oversight, reporting failures, and faulty procedures, specifically describing incidents at \"44 labs in 24 states,\" including at high-security labs.  60  In 2007, an outbreak of Foot and Mouth Disease likely came from a laboratory that was the \"only known location where the strain [was] held in the country\" 61 because of a leaky pipe that had known problems.  62  This long history of faulty laboratory safety is why some experts, such as Rutgers University chemistry professor and bioweapons expert Richard H. Ebright, believe that the H5N1 virus will \"inevitably escape, and within a decade,\" citing the hundreds of germs with potential use in bioweapons that have accidentally escaped from laboratories in the United States.  63  While the effects of such lapses in laboratory safety have not yet been felt aside from relatively small events such as the swine flu outbreak mentioned above, the increasing ability of less-sophisticated scientists to engineer more deadly organisms vastly increase the possibility that a lapse in biosafety will have detrimental effects.  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 55 GAO, \n ! 10! An accidental or purposeful release of a bioengineered organism has potentially grave consequences. For example, researchers in Australia recently accidentally developed a mousepox virus with a one-hundred percent fatality rate when they had merely intended to sterilize the mice.  64  Scientists in the United States also created a \"superbug\" version of mousepox created to \"evade vaccines,\" which they argue is important research to thwart terrorists, sparking a debate amongst scientists and policymakers about whether the benefits of such research is worth the associated risks.  65  If such a bioengineered organism escaped from a laboratory, the results would be unpredictable but potentially extremely deadly to humans and/or other animal species. The widespread availability of bioengineering technology and information further increases the risks of error in a laboratory. Students and amateurs have a growing capability to create bioengineered organisms, as evidenced by the iGEM contests, which tests the bioengineering capabilities of students in high schools and colleges.  66  Because of the dangers posed by this dual use research, the U.S. National Science Advisory Board for Biosecurity (NSABB) has started outreach programs for amateur biologists, including untrained, curious young individuals who consider themselves \"bioartists\" rather than researchers.  67  Defenders of genetically engineering viruses in a laboratory setting argue that such viruses could mutate outside of a laboratory anyway, and so understanding possible mutations in the laboratory is a defensive tool against the unknown.  68  As evidence, there have been previous examples of successful outcomes of bioengineering viruses, such as when Ralph Baric, using publicly available genome sequences, created a synthetic SARS virus contagious to bats that he claims can be tweaked to be a potential vaccine in the case of another SARS outbreak.  69  Furthermore, while environmentalists have long questioned the safety of GM foods on human health and the environment, GM foods have not been shown to be unsafe for human consumption 70 and so-called \"super weeds\" created from gene transfer from GM crops have not materialized.  71  However, just because a risk has not yet materialized does not mean that society should assume that a risk will not ever materialize, and a GCR/ER from bioengineering poses too much potential damage to rely on past events as an indicator of the future. Overall, this subsection demonstrates the risk of a bioengineered organism escaping from the lab with unknown but potentially catastrophic consequences, thus establishing a GCR/ER. \n ii. Risk of bioterrorism The threat of the malicious release of bioengineered organisms (i.e., bioterrorism) poses a GCR/ER.  72  Bioengineering enables a malicious actor to create an organism that is more deadly !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! to humans, animals, or plants than anything that exists in the natural world.  73  Experts say that the barriers for a terrorist to order a DNA sequence for a highly pathogenic virus online or acquire a DNA synthesis machine online are \"surmountable.\"  74  Alternatively, bioterrorists could break into laboratories housing dangerous bioengineered organisms-like the H5N1 virus, for example-and release them. Meanwhile, third world countries with laxer standards and lower laboratory accountability are rapidly discovering and using bioengineering, which may give bioterrorists an easier pathway to obtain deadly bioengineered organisms.  75  There have already been several occasions in which groups attempted to use or successfully used biological weapons. One unsophisticated example of bioterrorism occurred when an individual contaminated salads and dressing with salmonella in what apparently was an attempt to decide a local election.  76  Another example is a slew of attacks by Aum Shinrikyo, a Japanese cult, in the 1990s, the worst of which killed 12 people and injured over 5,000 from the release of sarin nerve gas in a subway in Tokyo in 1995.  77  While these particular acts of bioterrorism did not cause widespread death, deploying extremely deadly bioengineered organisms over a large area is real possibility: tests by the United States in 1964 demonstrated that a single aircraft can contaminate five thousand square kilometers of land with a deadly bacterial aerosol.  78  The recent engineering of an airborne H5N1 virus demonstrates society's concern over risks of bioterrorism arising from bioengineering. Before scientists could publish their results of their bioengineered airborne H5N1 virus in the widely read journals Nature and Science, the NSABB determined that the danger of releasing the sensitive information outweighed the benefits to society, advising that the findings not be published in their entirety.  79  The main risk is that either a state or non-state actor could synthesize a \"weaponized\" version of the H5N1 virus to create a disastrous pandemic.  80  There is precedent of outside groups recreating advanced bioengineering experiments, such as when many scientists immediately synthesized hepatitis C replicons upon publication of the its genetic code.  81  However, the NSABB's recommendation was nonbinding, and there is nothing to stop other scientists from releasing similar data in the future. Furthermore, while the NSABB merely assert that the \"blueprints\" of the virus should not be printed, other biosecurity experts argue that the virus should never have been created in the first place because of risks that the viruses would escape or be stolen. 82  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \n iii. Bioengineering of Humans A final GCR/ER arising out of bioengineering, but which has not yet occurred, involves inheritable genetic alterations of humans. In one possible scenario, bioengineering would create a new species or subspecies of humans-sometimes called \"transhumans\" 83 or \"posthumans\" 84that presents a variety of risks. First is the risk of a eugenics movement that prejudices \"normal\" humans. Second, posthumans may have a competitive advantage that is detrimental to normal humans.  85  In another scenario, genetically engineered humans may perceive the normal humans as \"inferior, even savages, and fit for slavery or slaughter.\" 86 Meanwhile, normal humans could attempt to preemptively suppress genetically engineered humans to protect themselves in the future, which could result in warfare amongst the different groups.  87  For these reasons, some argue that genetically engineered humans are \"potential weapons of mass destruction\" that could result in human genocide, and thus an international convention is necessary to address that risk.  88  On the other hand, there is also the possibility that genetically engineered humans would supplement humans and live harmoniously in society, but the possibility of a favorable outcome is not a sufficient reason to disregard potentially catastrophic risks. Other scholars believe that genetically engineering humans pose an ethical quandary, and that \"humans will lose the experiential or other basis that makes us human\" if such a movement becomes widespread.  89  These scenarios may not be too far in the future, as current science has proven that \"relatively simple gene alterations can significantly extend the lifespan of nematodes and mice,\" so perhaps there will be pressure from certain groups to expand these technologies to humans.  90  Furthermore, embryonic technology is heading towards the possibility of \"designer babies,\" which would use genetic engineering to create \"specific traits in pre-implanted embryos.\"  91  On the other hand, proponents of genetically engineering humans cite benefits such as increased life-expectancy, superior intelligence, and eradication of genetic defects, arguing !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 83 Transhumanism may be defined as \"the intellectual and cultural movement that affirms the possibility and desirability of fundamentally improving the human condition through applied reason, especially by using technology to eliminate aging and greatly enhance human intellectual, physical, and psychological capacities.\" See ANDREW LUSTIG ET AL., ALTERING NATURE: VOL. 2 240 (2008).   86  Id. at 162.  87  Id.  88  Id.  89  Ikemoto, supra note 84, at 1102.  90  Id. at 1112-1113.  91   \n BILL MCKIBBEN, ENOUGH: STAYING HUMAN IN AN ENGINEERED AGE 47 (2002). ! 13! that just because we are born human does not mean that we are bound to remain that way.  92  Nonetheless, genetically engineered humans present a GCR/ER. \n Nanotechnology Nanotechnology involves manipulating materials or systems at the atomic, molecular, and supramolecular scales to create structures, devices, and systems with radical and novel properties.  93  Nanotechnology works on a scale of approximately 1-100 nanometers, with one nanometer being a billionth of a meter (10 -9 m).  94  To put this in perspective, a red blood cell is 1,000 nanometers, a single DNA strand is 2 nanometers in diameter, and the width of a human hair is 100,000 nanometers.  95  While development of nanotechnology is nascent, nanotechnology research and development is massive, and many experts believe that nanotechnology will result in pervasive change in \"all sectors and spheres of life,\" including \"social, economic, ethical and ecological spheres.\" 96 \n a. Current Technology Researchers categorize nanotechnology into four generations. The first generation consists primarily of \"nanomaterials\" (or \"passive nanostructures\") and is already widely available in the global market. Nanomaterials includes nanoparticles, coatings, and nanostructured material 97 that are created by reducing \"normal\" materials to the nanoscale 98 and typically combining them with normal materials to improve their functionality, 99 making materials stronger, lighter, more flexible, or more conductive, amongst other desirable traits.  100  Nano-sized materials have fundamentally different properties from their normal-sized counterparts because the size of a particle affects that particle's properties; thus, for example, creating nanomaterials from gold creates a unique color, melting point, and chemical properties.  101  Already, over 800 products use nanomaterials, 102 accounting for $225 billion of !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 92 As Kevin Warwick, a posthumanism advocate, declared, \"I was born human. But this was an accident of fate -a condition merely of time and place. I believe it's something that we have the power to change.\" COLSON & CAMERON, supra note 85, citing Kevin Warwick, Cyborg 1.0, WIRED 15  (2000) . See also Ikemoto, supra note 84, at 1102.  93  Renn & Roco, supra note 3, at 153.  94  Nanotechnology White Paper, supra note 4, at 12.  95  Id. 96 See Renn & Roco, supra note 3, at 154.  97  Id. at 153-156.  98  Building nanomaterials from the \"bottom up\" is still being tested in laboratories; while scientists can successfully manipulate an individual atom, they have not achieved the ability to create construct technologies with \"atomic precision,\" which is a central goal of nanotechnology scientists. ! 14! sales in 1999.  103  Such products include tennis rackets, sunscreen, stain-resistant pants, computer displays, paint, antimicrobial pillows, canola oil, non-stick pans, and various coatings and lubricants.  104  The construction industry foresees using nanomaterials to create stronger steel, bacteria-killing and fire-resistant materials, solar panels that generate more power, and energyefficient lighting, which could increase the lifespan and lower the energy consumption of buildings.  105  The second generation of nanotechnology, which currently only exists in laboratories, consists of \"active nanostructure[s]\"  106  that \"change their behavior in response to changes in their environment,\" such as through \"exposure to light\" or the \"presence of certain biological materials.\"  107  An example of the latter function is a nanodevice that targets the brain cells responsible for neuroinflammation to deliver pinpointed drugs as a potential treatment of cerebral palsy, as recently tested in rabbits.  108   \n b. Forthcoming technology The yet-unavailable third and fourth generations of nanotechnologies consist of complete nanosystems as opposed to mere nanotechnology components.  109  The third generation includes \"three-dimensional nanosystems with heterogeneous nanocomponents\" with \"thousands of interacting components\" that act like the parts to a sophisticated yet incredibly small machine.  110  And the fourth generation of nanotechnology consists of \"heterogeneous molecular nanosystems\" that operate \"like a mammalian cell with hierarchical systems within systems,\" including technologies like molecular manufacturing and molecular nanorobotics (i.e. robots designed at the nanoscale).  111  This fourth generation of nanotechnology could spur widespread molecular manufacturing in which any designable product could be built with atomic precision, such as incredibly fast computers, nanorobots that perform a specific function, or complex machines.  112  Both third and fourth generation nanotechnology will focus on \"bottom up\" manufacturing rather than the \"top down\" approach, i.e. manufacturing nanotechnology on the molecular level rather than reducing existing materials to the nanoscale. The third and fourth !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 15! generations of nanotechnology only exist in computer experiments and models,  113  but they are expected to be developed in the coming few decades. 114 \n c. Benefits of nanotechnology Nanotechnology is set to \"have a significant impact on drug delivery, computing, communications, defense, space exploration, and energy,\" thus governments are spending significant amounts of money on nanotechnology research and development.  115  By testing different combinations and sizes of nanomaterials to fine-tune their desired effect,  116  materials can be lighter and stronger, resistant to bacteria, scratch proof, and hold superior charges.  117  Scientists have already created a variety of materials to benefit the environment: a paper towel for oil spills capable of absorbing 20 times its mass of oil by utilizing nanomaterials with enhanced absorption properties, thin and flexible solar panel films (perhaps one day even \"paintable\"), more efficient lithium-ion batteries, and superior windmill blades made of carbon nanotubes.  118  To benefit human health, 80 percent of cars already have nanomaterial filters to remove certain harmful particles from the air, and scientists are developing a filter that can remove viruses from water.  119  In the future, scientists predict that nanotechnology could also locate and deliver pinpointed treatment to cancer cells by creating \"gold-coated nanoparticles\" that target cancer cells and destroy then when heated by electromagnetic frequencies (as scientists tested at Rice University 120 ), restore damaged cells to slow aging by molecularly engineering nanomedicines,  121  and increase solar efficiency by a factor of one hundred by developing materials with optimum light-absorption and energy conversion. 122 \n d. Risks from nanotechnology Currently, most apprehension over nanotechnology involves first generation nanomaterials, whose toxicity, potential to bioaccumulate, and health effects from exposure is generally unknown.  123  One concern is that nanoparticles are smaller in size than natural particles, and thus they may have an increased potential to permeate the lungs and blood vessels of humans and animals.  124  Another concern is that nanotechnology could have negative ecotoxilogical !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! effects, for example by passing through the cell walls of fungi, algae, and bacteria; inhibiting photosynthesis and respiration in plants; or being unnaturally persistent in the environment.  125  Furthermore, preconceptions of the safety of the materials from which nanomaterials are derived do not accurately predict how their nanoparticle equivalent will act because nanomaterials can have unique toxicity, reactivity with other chemicals, persistence, and other qualities.  126  Overall, nanomaterials may pose a GCR because if nanomaterials become pervasive in consumer goods, building materials, and so forth, and they turn out to have a highly negative effect on health and the environment, then this may cause \"serious damage to human well-being\" on the global scale and thus constitute a GCR. However, they do not seem to pose an ER because toxic and harmful substances will not likely make humans go extinct or severely and permanently damage the future quality life of humans. In the future, however, nanotechnology has immense ethical, health, and environmental implications, and several scenarios indicate the presence of both a GCR and an ER. For example, one risk is that nanotech \"organisms,\" like an omnivorous bacteria constructed atom-by-atom, will out-compete their natural counterparts, causing unknown ecological effects.  127  Furthermore, because third and fourth generation nanotechnology will likely be designed to self-replicate in order to obtain meaningful amounts of particular nanotechnologies, 128 self-replicating nanotechnology (nanorobots, perhaps) could either mutate or be maliciously released such that they cause significant harm to humans and the environment. If such self-replication became uninhibited, a chain reaction of self-replication could significantly increase the potential damage to humans and the environment, or even engulf the entire Earth in a mass of self-replicating matter known as \"grey goo.\"  129  On the other hand, others argue that self-replication of nanotechnology is extremely unlikely to occur, and that the more imminent threat from nanotechnology arises from incredibly destructive weapons developed with nanotechnology.  130  Such nanotech weapons could be \"more powerful than any known chemical, biological, or nuclear agent\" and very difficult to detect.  131  For this reason, some commentators point out the possibility of a \"nanotechnology arms race,\" which poses risks of state or non-state actors intentional using nanotech weapons or of accidents involving weapons development.  132  The international community's inability to eliminate the nuclear weapons programs of North Korea and possibly Iran highlights the complications of curtailing vastly powerful and destructive weapons once they are possessed by some states. Overall, future nanotechnology developments present several GCRs/ERs from both accidental and intentional uses.  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \n Artificial Intelligence One common definition of AI is \"the science of making machines do tasks that humans can do or try to do.\"  133  While much of society's association of AI arises from fictional film and literature-2001: A Space Odyssey; I, Robot; and the Terminator series all portray AI in a dangerous light-experts predict that many of the premises behind such science fiction will occur: computers with intelligence similar to or greater than humans, robotic warfare, vehicles operated by computers, and so forth. While AI may prove to benefit society immensely, many experts believe there is a risk of GCR/ER from highly sophisticated AI. \n a. Current Technology While AI is currently nowhere near the level that would pose a GCR/ER, several milestones show progress towards creating computers with immense AI. For example, a robot named Data does comedy routines in front of live audiences and is able to respond to the reaction of the crowd and adjust its comedy routine in real-time.  134  Neural \"cochlear\" implantscomputer devices that translate sound and transmit it into the brain-provide hearing to individuals who are deaf.  135  Google developed a car that is automatically driven by computers, which has already logged 140,000 miles.  136  And supercomputers with AI defeated humans at games of great intellect and rational thinking: The IBM supercomputer Watson, which analyzes \"200 million pages of information\" in a mere three seconds, defeated several former champions on Jeopardy, and the IBM supercomputer Deep Blue defeated grandmaster Garry Kasparov at chess.  137  Meanwhile, several educational institutes are already entirely dedicated to advancing AI. For example, the Singularity University, hosted by NASA and founded in part by Google, seeks to develop AI to \"solve humanity's grand challenges,\"  138  while the Singularity Institute for AI (\"Singularity Institute\"), established in part by former Pay Pal CEO Peter Thiel, teaches graduate students and executives about AI and engages in AI research and development.  139   \n b. Forthcoming Technologies Perhaps the most significant emerging AI technology arises out of the concept of \"the Singularity,\" which is \"the technological creation of smarter-than-human intelligence.\"  140  The basic premise of the Singularity is that if humans create a superhuman AI, then this superior mind could create a more superior mind, beginning a feedback loop that would cumulate in a !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 18! near godlike intelligence.  141  Such \"superintelligence\" could feasibly think one million times faster than the human brain and even rewrite its own code to \"recursively self-improve.\"  142  And humans themselves could be enhanced through \"direct brain-computer interfaces\" or \"biological augmentation of the brain.\"  143  Admittedly, superhuman AI seems a long way off: A recent study measuring the ability of the human brain to store, communicate, and compute information concluded that the processing power of the human brain is equivalent to the combined processing power of all general-use computers in the world in 2007.  144  However, some scientists predict an \"intelligence explosion\" in machines during the 21st century. Raymond Kurzweil, an MIT graduate with 19 honorary doctorates who was awarded the National Medal of Technology by Bill Clinton and who Bill Gates says is the best predictor of future AI he knows, forecasts that the Singularity will occur by 2045 at a level \"about [one] billion times the sum of all the human intelligence that exists today\" based on a model of exponential growth in technology.  145  Before then, predicts Kurzweil, humans will \"reverse-engineer the human brain by the mid-2020s,\" and by the end of the 2020s, \"computers will be capable of human-level intelligence.\"  146  On the other hand, others, like biologist Denis Bray, argue that the unique biochemical processes in the human body far supersede the programmable mind of a robot. 147 \n c. Benefits of artificial intelligence Current practical applications of AI include the unmanned navigation of cars; consumer protection, like discovering credit card fraud; educational advancement; medical technology; and data mining and analysis.  148  And in the future, superintelligent machines could benefit mankind by helping \"eradicate diseases, avert long-term nuclear risks, and live richer more meaningful lives.\"  149  Ethicist Michael Ray LaCha argues that AI will be \"morally perfect\" and that humans !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 141 Id. I.J. Good, a British mathematician, cryptologist, and computer engineer, first came out up with the idea of an \"intelligence explosion\" in 1965. According to I.J. Good, \"[s]ince the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make.\" Hear That? It's the Singularity Coming, SENTIENT DEVELOPMENTS (June 29, 2011), at: www.sentientdevelopments.com/2011/06/hear-that-its-singularity-coming.html.  142  Overview: What is the Singularity?, SINGULARITY INSTITUTE FOR ARTIFICIAL INTELLIGENCE, at: http://singinst.org/overview/whatisthesingularity (last visited Jan. 31, 2012).  143  Id. 144 Todd Leopold, Roboticist Sees Improvisation Through Machine's Eyes, CABLE NEWS NETWORK (CNN) (Feb. 03, 2012), at: http://www.cnn.com/2012/02/03/living/creativity-improvisation-intelligence-heather-knight/index.html.  145  Kurzweil developed an exponential curve that predicts \"change over time in the amount of computing power, measured in MIPS (millions of instructions per second), that you can buy for $1,000.\" Like the famous Moore's law, the figure doubled roughly every two years. Kurzweil ran the model backwards to the year 1900 and it still held true. Then he checked it against \"the falling cost of sequencing DNA and of wireless data service and the rising numbers of Internet hosts and nanotechnology patents,\" which confirmed the exponential growth of his model. Grossman, supra note 139.  146  Id.  147   ! 19! may rely on AI to make moral decisions.  150  An example of this would be relying on AI to decide whether going to war is likely to result in a net positive benefit to society. Meanwhile, many proponents of AI believe the Singularity to be of paramount importance in the future of the Earth-as significant as the \"first self-replicating chemical that gave rise to life on Earth,\" according to some 151 -because such superintelligence would feasibly develop revolutionary technologies at a rapid pace, such as by discovering cures for all diseases or inventing new means to produce extraordinary amounts of food.  152  Others purport that AI could manage society without the \"[c]onflicts of interest, flawed judgment, lack of information, or political considerations\" that result in flawed human decisionmaking because AI could have a knowledge vastly superior to humans and could be programmed to act without human bias. 153 \n d. Risks from artificial intelligence AI poses a GCR/ER even if the chance of this risk materializing is enormously low. While some argue that humans need AI for their long-term survival, 154 others argue that superhuman AI presents the foremost challenge to the future existence of humans.  155  Assuming that humans develop highly intelligent AI, proponents of the technology argue that coding AI to be inherently friendly and possess moral values (\"Friendly AI\") mitigates any risks.  156  However, some individuals and corporations may derogate from Friendly AI principles, which would present the risk of creating a dangerous form of AI.  157  The difficulties of regulating vastly powerful technologies that could benefit society but also risks massive destruction is evident from current politics involving Iran's development of nuclear technologies, which Iran claims is for use as an energy source, but most of the international world believes is to develop weapons.  158  Furthermore, AI could suffer a \"mechanical failure\" in which AI does not work as designed and therefore presents unpredictable risks to mankind.  159  Finally, anticipating and controlling the outcome of highly intelligent AI is difficult, 160 especially if AI is \"selfimproving\" and thus able to alter its own programming. 161  WRONG 194 (2009) .  151    !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 150 WENDELL WALLACH & COLLIN ALLEN, MORAL MACHINES: TEACHING ROBOTS RIGHT FROM \n ! 20! One specific risk from AI is that highly-intelligent computers may be subject to errors, collapses, viruses, or other unforeseen developments that compromise their ability or intent to properly manage, for example, nuclear weapons, transportation, or other major elements of society.  162  A related risk is that a programming error could give AI the imperative to destroy mankind, or that AI's \"benevolent\" goals may be conflicting with the interests of humans.  163  If this occurs, AI may have the ability to wipe out humans if they are intellectually superior to humans.  164  Another risk is that AI would out-compete humans because of the pressures of evolution and self-preservation, which may compel AI to contest humans for scarce resources.  165  Finally, there is the risk that humans will undergo a calculated self-termination as humans opt to transcend our biological forms and be \"transferred\" to machines as \"post-humans.\"  166  Overall, there is a clear GCR/ER from AI. \n The Large Hadron Collider The Large Hadron Collider (LHC) is a recent example of a failure of the legal system to properly consider what some scientists believed to be a GCR and an ER from a radical new technology. In September 2008, after fourteen years and, according to mid-range estimates, at least $8 billion dollars spent, 167 the European Organization for Nuclear Research 168 (CERN) began using the world's most powerful particle accelerator. The LHC accelerates protons or, more recently, lead ions, in opposite directions around a massive vacuumed track, about 27 kilometers (approximately 17 miles) in circumference and 50 to 175 meters underground, which the magnet-guided particles whip around at 99.99999 percent speed of light  169  (clocking in about 11,000 laps of 27 kilometers every second) 170 as they continuously smash together at up to 7 trillion electron volts 171 at four points of intersection-thereby creating exotic particles, evidently even the coveted Higgs boson-for hours at a time.  172  Most scientists throughout the world rejoiced at creating a particle accelerator seven times the energy of its nearest competitor, the Tevatron particle accelerator at the Fermi National Accelerator Academy in Illinois, and which has created \"sub-atomic fireballs with temperatures of over ten trillion degrees [centrigrade], a ! 21! million times hotter than the [center] of the Sun\" 173 that \"[recreates] conditions … only a trillionth of a second after the Big Bang.\"  174  Many scientists held their breath for the LHC to \"reveal the origins of mass, shed light on dark matter, uncover hidden symmetries of the universe, and possibly find extra dimensions of space.\"  175  However, others feared that the accelerator could create a black hole to gobble up the Earth or \"[convert] all the [Earth's] matter into a super-dense glob called a 'strangelet.'\"  176  Scientists in the latter category attempted to seek court review of the LHC in a variety of international and domestic courts but to no success. In this regards, the following subsections highlight two problems with current international regulations of advanced technologies that may pose a GCR/ER: first, the difficulty of getting a court to consider a minority opinion in a highly complex scientific case, and second, the potential bias of scientists as risk assessors. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \n a. Difficultly in getting a court to consider the case The LHC highlights the problems with traditional courts serving as risk assessors for a groundbreaking technology, i.e. one that has never been tested before.  177  While some scientists and other individuals sought injunctions from various national and international judicial bodies against operating the LHC-including a Swiss court,  178  the European Court of Human Rights (ECtHR),  179  the U.S. Ninth Circuit Court of Appeals, 180 the German Constitutional Court,  181  the International Security Court,  182  and the Administrative Court of Cologne 183 -all such attempts failed for a variety of reasons discussed below. In the United States, Walter L. Wagner, a nuclear physicist, and Luis Sancho, founder of Citizens Against the Large Hadron Collider, failed in their bid to enjoin operation of the LHC in the case Sancho v. U.S. Department of Energy. The Ninth Circuit Court of Appeals, reviewing de novo the District Court of Hawaii's decision to deny standing for lack of subject matter jurisdiction,  184  ruled that, inter alia, Wagner does not have standing because he could not !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! establish an injury in fact. According to the Court, Wagner's claim demonstrated, at most, \"potential adverse consequences,\" which falls short of the standing requirement of a \"credible threat of harm\" because the risk of the obliteration of the Earth is too speculative.  185  However, advanced technologies that pose a GCR/ER are often highly improbable but result in catastrophic consequences if such risks materialize, thus GCRs/ERs are nearly impossible to challenge in the U.S. judicial system without consideration of the magnitude of their risks. Operation of the LHC was also challenged in Europe. The German Constitutional Court rejected the claims of Gabriele Schröter-a biochemist who has published over 300 papers and who is known by some as the \"father of Chaos theory\"-because the Court believed that theories of mini-black holes or \"strange matter\" were unsubstantiated and theoretical, although the Court did recommend a conference on LHC safety issues.  186  Meanwhile, the ECtHR rejected German scientist Dr. Otto Rössler's attempt to enjoin the LHC without stating a reason for their decision.  187  Notably, none of these courts had any expertise in science, so whether they could properly assess the associated risks is questionable. Although many judges have shown the ability to assess scientific principles, oftentimes a thorough understanding of a scientific topic requires cross-examination and other procedures in full-fledged court proceedings,  188  and thus dismissing a case before the testimony develops truly compromises the consideration that minority science receives. Furthermore, judges who receive scientific training are better able to weigh conflicting scientific evidence and judge methodological problems in scientific research presented to the court.  189  Overall, these test cases demonstrate that the neither domestic nor international courts are equipped to handle disputes involving low-probability, high consequence advanced technologies. There seems to be no court that offers judicial relief for such situations, despite the fact that if a GCR/ER materializes, the lives of a huge amount of people are at stake.  190  While courts may rely upon the political process to mitigate such risks, 191 emerging technologies are becoming increasingly widespread and privatized, and the political process thus far has been insufficient to create sufficient safeguards from these risks.   APPLIED PSYCHOLOGY 574, 585 (2000) .  189  See id.; see also FEDERAL JUDICIAL CENTER, REFERENCE MANUAL ON SCIENTIFIC EVIDENCE 3-4 (2000).  190  Adams, supra note 175, at 136.  191  The U.S. District Court of Hawaii ruled that the political process, not NEPA, was the proper forum for handling the risks of the LHC. Sancho, 578 F.Supp.2d at1269. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! federal action\" under § 4332(2)(c) \n ! 23! b. Potential bias from CERN scientists as risk assessors While scientists often reassure the public that GCRs/ERs from emerging technologies are nonexistent or negligible, some critics warn that scientists are unreliable risk assessors of their own work because financial incentives, career pressures, 192 and competition among competing groups of scientists taint their judgment.  193  Despite these inherent conflicts of interests, almost all of the LHC safety reports came from CERN scientists.  194  Two such CERN reports discussed various alleged risks of the LHC, but they did not weigh the probability of a GCR/ER against the value of operating the LHC.  195  While the reports concluded that operation of the LHC presented no danger,  196  at least some experts doubt this conclusion. For example, revered scientist Martin Rees quantified the risk of a global catastrophe arising from the LHC as being about one in 50 million,  197  whereas Toby Ord of Oxford University estimated the risk of a disaster as falling somewhere between one in 10,000 and 1,000,000.  198  While the differences in these estimates show the difficulty in estimating some GCRs/ERs, they obviously contradict the \"no danger\" conclusion of CERN and highlight the need for courts to consider unbiased scientific information in making decisions concerning low-probability GCRs/ERs. While the operation of the LHC has not caused worldwide destruction, there have still been several accidents that, for some, put the reliability of CERN's assurances into doubt. The first incident occurred only nine days after the LHC began operating in 2008, when a \"faulty electrical connection between two of the accelerator's magnets\" 199 melted, causing one ton of helium to blast into the tunnel  200  and shutting down the LHC for 14 months.  201  The mistake in question was described by some as \"basic\" and should have been discovered during \"four  202  This oversight caused some commentators to worry about mistakes in the mechanics or risk assessment of the LHC that could have more devastating results.  203  Overall, this brief case study demonstrates that self-assessments of safety by scientists intimately involved with a project should be doubted. Therefore, an independent risk assessment should be a mandatory element of engaging in emerging technologies that pose a GCR/ER. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! engineering reviews.\" \n III. BIOENGINEERING AND INTERNATIONAL LAW Despite the low probably but extremely high risk of global catastrophe posed by bioengineering, nanotechnology, and AI, international law has done very little to limit these risks. This section focuses solely on the emerging technology of bioengineering as a GCR/ER under international law because, unlike nanotechnology and AI, the current level of available bioengineering science already presents a GCR/ER. Furthermore, nanotechnology and AI are essentially unregulated at international law, whereas international law regulates some forms of bioengineering at least to some extent. After discussing several binding and non-binding international law instruments, this section demonstrates that there is no binding international regime that sufficiently addresses trade in bioengineered food, much less the GCRs/ERs arising out of risks posed by other forms of bioengineering, such as a potentially highly deadly bioengineered organism or a genetically engineered human. \n A. Convention on Biological Diversity The Convention on Biological Diversity (CBD) functions to conserve biological diversity, sustainably use the components of biodiversity, and share the benefits of genetic resources in a fair and equitable way.  204  Based on this objective, bioterrorism and genetically engineered humans do not fall neatly within objectives of the CBD. Nonetheless, a failure to mitigate GCRs/ERs arising from the accidental release of dangerous bioengineered organisms from a laboratory seems to fall within the biotechnology provisions of Article 8 of the CBD. Article 8 of the CBD states that each Party shall (meaning mandatory as opposed to discretionary), \"as far as possible and appropriate,\" (g) Establish or maintain means to regulate, manage or control the risks associated with the use and release of living modified organisms resulting from biotechnology which are likely to have adverse environmental impacts that could affect the conservation and sustainable use of biological diversity, taking also into account the risks to human health…  205  First, Article 8(g) establishes an affirmative duty of parties to \"regulate, manage or control\" the use and release of living modified organisms (LMOs), and thus a failure to properly regulate the actions of private laboratories could breach this provision. Second, while the CBD does not define \"LMOs,\" the Cartagena Protocol on Biosafety to the Convention on Biological !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 202 Adams, supra note 175, at 137.  203  Id.  204  Convention on Biological Diversity, June 5, 1992, 1760 U.N.T.S. 79, 143; 31 I.L.M. 818 (1992), art. 1 [hereinafter CBD].  205  Id. at art. 8(g) (emphasis added). ! 25! Diversity (\"Cartagena Protocol\") defines LMOs as \"any living organism that possesses a novel combination of genetic material obtained through the use of modern biotechnology\".  206  Highly fatal bioengineered organisms possess a \"novel combination of genetic material\" obtained through biotechnology by the plain meaning of the language, thus they are LMOs. Third, while the act of bioengineering deadly organisms in a laboratory does not constitute a \"release\" of LMOs into the environment (to the contrary, such organisms are contained within a laboratory), bioengineered organisms in a laboratory do seem to qualify as a \"use\" of an LMO under Article 8(g). Although the term \"use\" is not defined in the CBD, bioengineering organisms in a laboratory clearly fall within the definition of \"contained use\" from the Cartagena Protocol (\"any operation, undertaken within a facility … which involves LMOs that are controlled by specific measures that effectively limit their contact with, and their impact on, the external environment\").  207  Because the broader term \"use\" in the CBD likely encapsulates the term \"direct use\" from the Cartagena Protocol, bioengineering organisms in a laboratory qualifies as a \"use\" within the meaning of the CBD.  208  Therefore, GCRs/ERs arising from bioengineering do seem to fall within Article 8(g) of the CBD. While Article 8(g) seems to require parties to \"regulate, manage, or control\" highly fatal bioengineered organisms, the effectiveness of the CBD in mitigating GCRs/ERs arising out of bioengineering is severely limited because the provisions do not establish specific actions that Parties must take. For example, measures like laboratory safety requirements, training of individuals handling highly fatal bioengineered organisms, or laboratory monitoring requirements are all absent from the CBD. Although the Cartagena Protocol significantly elaborates on biosafety issues, the subsequent section concludes that they are too-trade focused and discretionary to provide meaningful protection.  209  Furthermore, even if the CBD did impose specific requirements upon Parties, the CBD does not include an enforcement mechanism, and thus enforcing the provisions upon unwilling Parties would prove difficult. In conclusion, while GCRs/ERs arising from bioengineering seem to fall within the CBD, the CBD is not an effective means of mitigating these risks. \n B. Cartagena Protocol on Biosafety The Cartagena Protocol expands upon the biosafety provisions of the CBD to regulate LMOs that may adversely affect biological diversity, 210 but the scope of the treaty is too tradefocused to sufficiently reduce the GCRs/ERs arising out of bioengineering. First, the scope of the Cartagena Protocol seems to include novel viruses and organisms developed in labs because Article 3 states that \"living organisms\" means \"any biological entity\" that can transfer or   207  The Cartagena Protocol separately uses the term \"direct use\" in a context that applies to use \"as food or feed, or for processing.\" Id. at art. 11. The broader term \"use\" in the CBD seems to encapsulate this meaning, as well.  208  CBD, supra note 204, at art. 11. ! 26! replicate genetic material, even \"sterile organisms, viruses and viroids.\" 211 However, Article 4 establishes that the Cartagena Protocol applies to the \"transboundary development, handling, transport, use, transfer and release\" of LMOs.  212  The term \"transboundary\" should be interpreted to modify each of the subsequent actions: development, handling, transport, use, transfer and release. The first listed action, \"development,\" is not the only action that is transboundary in nature-handling and transport are inherently transboundary, for example-thus by extension Article 4 can reasonably be interpreted to apply solely to transboundary actions. Likewise, \"risk assessment\" and \"risk management\" provisions of the Cartagena Protocol only apply to LMOs being exported or imported,  213  and the \"handling\" requirements of LMOs under Article 18 only apply to transboundary international movement.  214  Overall, the transboundary and tradeoriented scope of the Cartagena Protocol limits its applicability to GCRs/ERs arising from bioengineering because such actions generally take place within the territory of one state-such as the handling of a deadly bioengineered organism in a laboratory. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Even though some provisions of the Cartagena Protocol do seem to apply to the LMOs outside of the transboundary context, these provisions do not provide sufficient protections from GCRs/ERs arising out of bioengineering. For example, Article 17 applies to \"unintentional transboundary movements\" of LMOs, which would seem to include a bioengineered virus escaping from a laboratory while in the territory of one state. However, this article merely requires parties to \"notify affected or potentially affected states\" of unintentional transboundary movements of LMOs rather than requiring any preventative measures or risk assessments.  215  Notifying a party when a GCR/ER materializes will not likely prevent the global catastrophic or existential harm from occurring. Likewise, the risk assessment and risk management requirements of the Cartagena Protocol are too discretionary to meaningfully mitigate low-probability GCRs/ERs arising out of bioengineering. The Cartagena Protocol requires Parties to undertake a risk assessment and implement risk management measures to \"regulate, manage, and control risks … associated with the use, handling and transboundary movement of living modified organisms.\" 216 Specifically, the risk assessment stage requires Parties first to evaluate the likelihood, consequences, and the subsequent \"overall risk\" of adverse effects from the release of an LMO, and second to recommend \"whether or not the risks are acceptable or manageable.\"  217  Based on the conclusions of the risk assessment, the risk management stage then requires Parties to, inter alia, take measures \"to the extent necessary\" to \"prevent adverse effects\" of LMOs on biological diversity and human health, and also to take \"appropriate measures\" to \"prevent unintentional transboundary movements of  [LMOs] .\"  218  However, when applied to GCRs/ERs arising from deadly bioengineered organisms in a laboratory, the risk assessment and risk management provisions of the Cartagena Protocol fall short because decision makers in the risk management stage have broad discretion to decide !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 211 Id. at art. 3.  212  Id. at art. 4 (emphasis added).  213  Id.at art. 15 and art. 16.  214  Id. at art. 18.  215  Id., at art. 17.  216  Id. at arts. 16-17.  217  Id. at Annex III(8).  218  Id. at art. 16(2)-(3). ! 27! whether or not risks are acceptable. According to the Ad Hoc Technical Expert Group (AHTEG) on Risk Assessment and Risk Management under the Cartagena Protocol on Biosafety's Guidance on Risk Assessment of Living Modified Organisms, risk assessors to provide recommendations as to whether or not risks arising from LMOs are \"acceptable or manageable\" based on their nation's own \"protection goals,\" and final approval for the use of LMOs is entirely \"up to the decision maker to decide,\" 219 which the Guidance concedes is \"typically decided at a political level and may vary from country to country.\"  220  The lack of standardized protection goals across all countries and the significant discretion allocated to decision makers in regulating LMOs results in inconsistent risk management policies. For example, Parties have shown significant differences of opinion in what risks are \"acceptable\" for GM crops, which are extremely popular and widely grown in the United States, Argentina, and Canada (these countries retain 98 percent by acreage of all GM crops in the world), but resisted by European countries and Japan because of food safety and environmental concerns.  221  On the one hand, the risk assessment and management process is valuable for Parties to consider the risks of LMOs and make policy decisions to mitigate those risks based on their domestic protection goals. However, when translated to GCRs/ERs from bioengineering, the single release of a dangerous bioengineered organism in any state could cause global catastrophic or existential harm in most or all other states. Therefore, sufficiently mitigating the risks of GCRs/ERs from bioengineering requires uniform measures, and so the failure of the Cartagena Protocol to proscribe clear requirements on how and to what extent Parties should mitigate GCRs/ERs arising from deadly bioengineered organisms compromises its effectiveness. Even if the risk assessment and risk management provisions were more stringent in requiring Parties to minimize GCRs/ERs arising out of bioengineering, the Cartagena Protocol does not include any meaningful recourse against Parties that fail to meet their obligations. Parties attempted to address the lack of recourse under the Cartagena Protocol with the Nagoya -Kuala Lumpur Supplementary Protocol on Liability and Redress to the Cartagena Protocol on Biosafety (\"Supplementary Protocol\"), which creates a scheme of liability and redress for transboundary damage from LMOs, including damage from \"unintentional transboundary movements\" like the type that may arise from an accidental release of a bioengineered organism from a laboratory.  222  However, the Supplementary Protocol is insufficient to prevent GCRs/ERs from materializing because the provisions only provide reactionary redress for damage caused by an operator 223 after an LMO has already been released, whereas a GCR/ER should never be allowed to materialize.  224  Even though Article 5(5) prospectively regulates LMOs by requiring operators to engage in \"appropriate response measures\" if there is a \"significant likelihood\" that !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 219 See Guidance on Risk Assessment on Living Modified Organisms, Report of the Third Meeting of the Ad Hoc Technical Expert Group On Risk Assessment and Risk Management Under the Cartagena Protocol on Biosafety, at 18, U.N. Doc. UNEP/CBD/BS/AHTEG-RA&RM/3/4 (2011), available at: http://www.cbd.int/doc/meetings/bs/bsrarm-03/official/bsrarm-03-04-en.pdf.  220   ! 28! the use of LMOs will result in \"damage\"  225  if \"timely response measures are not taken,\" GCRs/ERs are low-probability and thus do not present a \"significant likelihood\" of materializing.  226  Note that the Supplementary Protocol has not entered into force because the Supplementary Protocol the accession of forty Parties to the Cartagena Protocol, but only the Czech Republic and Latvia have thus far acceded.  227  Finally, another major limitation of both the CBD and the Cartagena Protocol is that the United States is not a party to either instrument.  228  Because the United States possesses some of the most sophisticated and potentially dangerous bioengineering technology, the absence of the United States from these instruments limits their effectiveness in reducing GCRs/ERs. Overall, the Cartagena Protocol does not seem to be an effective instrument to regulate GCRs/ERs from bioengineering. \n C. Biological Weapons Convention The Biological Weapons Convention is too focused on bioterrorism and neglectful of biosafety issues to sufficiently mitigate GCRs/ERs arising out of bioengineering. Under the Biological Weapons Convention (BWC), a state party cannot \"develop, produce, stockpile or otherwise acquire or retain microbial or other biological agents [or] toxins … of types and in quantities that have no justification for prophylactic, protective or other peaceful purposes….\"  229  Legitimate scientific research, even research that poses a risk of accidentally releasing a highly deadly virus or publishing information that can be used for bioterrorism, usually has a \"prophylactic, protective or other peaceful [purpose]\" under article 1, which severely limits the BWC in regulating GCRs/ERs arising out of bioengineering. Bioengineered humans also clearly fall outside the scope of the BWC. Similarly, while the BWC creates obligations that restrict transfer of biological weapons information or technologies, these obligations exempt peaceful purposes. Under Article III of the BWC, a state party cannot \"transfer … directly or indirectly … assist, encourage, or induce any State, group of States or international organization to manufacture or otherwise acquire any of the agents, toxins, weapons, equipment or means of delivery specified in [Article I].\" 230 Thus States have an affirmative duty to ensure that their bioengineering technologies are not transferred in violation of this provision. This article possibly applies to instances where States indirectly grant malevolent actors access to bioengineering techniques through publication of research and studies. However, Article X makes clear that the BWC exempts the \"exchange of equipment, materials, and scientific and technological information\" for biological agents when used to prevent disease or other peaceful purposes, while also exempting the \"international !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 225 \"Damage\" is defined as \"adverse effects on the conservation and sustainable use of biological diversity, also taking to account risks to human heath.\" Id. at art. 2(2)(b).  226  Id. at Art. 5(5).  227  Parties to the Protocol and Signature and Ratification of the Supplementary Protocol, CONVENTION ON BIOLOGICAL DIVERSITY, at: http://bch.cbd.int/protocol/parties/#tab=1 (last visited Apr. 17, 2012).  228    \n ! 29! exchange of [biological] agents and toxins and equipment\" for peaceful purposes.  231  Thus Article III fails to address the GCRs/ERs arising out of dual use bioengineering research that is conducted for peaceful purposes but could result in an accidental release or be to unintended malicious use. While the State Parties to the BWC have shown a growing concern for biosafety issues, such efforts are nonbinding and thus ineffective to protect against GCRs/ERs related to biosafety. In 2006, the Parties called upon State Parties to adopt \"…legislative, administrative, judicial and other measures\" to \"ensure the safety and security of microbial or other biological agents or toxins in laboratories, facilities, and during transportation, to prevent unauthorized access to and removal of such agents or toxins.\"  232  Five years later they called upon State Parties to \"implement voluntary management standards on biosafety and biosecurity\" and \"encourage the promotion of a culture of responsibility amongst relevant national professionals and the voluntary development, adoption and promulgation of codes of conduct.\"  233  While these measures may put political pressure upon State Parties to increase both biosafety and biosecurity, they are nonbinding measures and thus ineffective to rely upon to mitigate GCRs/ERs arising out of bioengineering. Even if the BWC included measures to address issues of biosafety and biosecurity, there is no formal compliance-monitoring body or verification mechanism to ensure proper enforcement.  234  While State Parties engaged in seven years of negotiations over a \"BWC Protocol\" that would establish an inspection regime as well as a variety of other measures intended to bolster, inter alia, the effectiveness, transparency, and implementation of the BWC, negotiations have stalled.  235  In particular, the Bush Administration stifled progress when it withdrew from negotiations in 2001 because of concerns over the BWC Protocol's ineffectiveness, harm to biodefense research, and increased costs to the biotechnology industry; the Obama Administration has continued to oppose the BWC Protocol.  236  Finally, another major limitation is that there are only 165 State Parties to the BWC, which \"falls behind other multilateral arms control, disarmament and non-proliferation treaties.\" Thus bioengineering activities that present a GCR/ER could just be conducted within the territory of non-Parties.  237  Overall, while the BWC may reduce GCRs/ERs presented by biosecurity, the failure to sufficiently address issues like the accidental release of dangerous bioengineered organisms or human bioengineering, as well as practical limitations like the large number of states that are not Parties, limits its ability to mitigate GCRs/ERs from bioengineering. ! 30! \n D. Human Dignity Instruments Inheritable human genetic alterations are subject to a variety of international soft law, legally binding regional instruments, and the occasional condemnation of IGOs, but no global convention regulates this GCR/ER.  238  The predominant binding instrument that regulates human genetic engineering is the Council of Europe's Convention on Human Rights and Biomedicine (CHRB). First, Article 13 of the CHRB states that \"[a]n intervention seeking to modify the human genome may only be undertaken for preventive, diagnostic or therapeutic purposes and only if its aim is not to introduce any modification in the genome of any descendants.\"  239  The accompanying CHRB Explanatory Report clarifies that Article 13 strictly prohibits any inheritable genetic alterations of humans.  240  Notably, the Explanatory Report also acknowledges that permitting alteration of the human genome could endanger the entire human species, thus clearly recognizing the GCR/ER at issue.  241  However, while this convention may be effective at reducing the risk of GCR/ER arising from the genetic engineering of humans within certain European countries, only 29 out of 47 Council of Europe Member States are signatories and the rest of the world is left out, thus limiting the global effectiveness of the CHRB.  242  Another possibility is that inheritable genetic alterations may constitute a human rights violation, but this seems unlikely under international law. Fukuyama argues that reengineering the \"essence of humanity itself\" and creating a new species could be a \"crime against humanity,\" which would violate the Rome Statute of the International Criminal Court (\"Rome Statute\").  243  However, this argument does not seem to fall cleanly within the plain language of the Rome Statute.  244  The Rome Statute clearly establishes the scope of \"crimes against humanity\" as acts \"…committed as part of a widespread or systematic attack directed against any civilian population, with knowledge of the attack….\"  245  In turn, the word \"attack\" is defined as \"course of conduct involving multiple commissions of acts,\" which most but not all states interpret to not !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! require actual use of force; thus a scientific bioengineering program could possibly qualify as an \"attack.\" 246 However, the plain language of the Rome Statute excludes acts that are not attacks \"directed against\" a civilian population. Scientists who create genetically inheritable alterations in humans are not likely committing an attack \"directed against\" a population, but rather are attempting to improve the human body for the benefit of an individual or society. Any subsequent attack directed against humans, such as the possible suppression of humans by posthumans, is a mere consequence of inheritable genetic alterations. Therefore, inheritable genetic alterations do not likely violate the Rome Statute. \n IV. \n RECOMMENDATIONS FOR AN EMERGING TECHNOLOGIES TREATY While bioengineering that poses a GCR/ER is subject to several nonbinding international instruments, no internationally binding obligations sufficiently reduce the catastrophic risks arising out of bioengineering.  247  One possible solution is to expand several of these existing instruments and use them together in a piecemeal approach to regulate the various aspects of GCRs/ERs arising out of bioengineering. However, because the current regimes are inadequate and because the scope of emerging technologies that present a GCR/ER will likely increase as science continues to develop at a rapid pace, the better solution is for states to agree to a comprehensive treaty that can sufficiently mitigate the unique aspects of GCRs/ERs arising from all emerging technologies. Therefore, this paper proposes the framework of a model treaty that would mitigate GCRs/ERs arising out of emerging technologies with the following regulatory mechanisms: use of the precautionary principle, a body of experts, a review mechanism, public participation and access to information, binding reforms for scientists, laboratory safeguards, and oversight of scientific publications. \n A. New International treaty GCRs/ERs arising out of emerging technologies are unique in that a single event can result in widespread destruction, which is why the World Commission on the Ethics of Scientific Knowledge and Technology (COMEST) acknowledges that only a global convention is sufficient to curtail these ERs.  248  If a GCR/ER regulatory regime only regulates some states but not others, dangerous emerging technologies could instead be developed and utilized in the unregulated states. An example of this is when Richard Seed, an American physicist who wished to be the first person to clone a human, threatened to conduct his cloning in Mexico or Japan if the United States banned human cloning.  249  And if some states ban or regulate emerging technologies while others do not, this could threaten global security because \"rogue states\" would have a monopoly over dangerous emerging technologies.  250  Furthermore, without a truly global treaty, countries competing to quickly develop emerging technologies may engage in a race to arms that promotes speed over safeguards.  251  Finally, some states may believe that,   249  Id.  250  Pinson, supra note 115, at 279-280 (referring specifically to nanotechnology).  251  For example, AI experts cite the importance of \"international cooperation around AI development\" and to prevent an \"AI 'arms race' that might be won by the competitor most willing to trade off safety measures for speed.\" ! 32! absent regulations binding upon all states, their emerging technology industries will be placed at a competitive disadvantage to unregulated countries. Thus all states should agree to an international treaty imposing evenhanded regulations. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 246 MACHTELD An international treaty could potentially cover all emerging technologies that pose a GCR/ER, beginning with the three in this paper-nanotechnology, bioengineering, and AI. One significant reason that a GCR/ER international treaty should regulate nanotechnology, bioengineering, and AI is that these emerging technologies are predicted to overlap in many areas. Examples of potential convergences of nanotechnology, bioengineering, and AI are nanosized components that interact with bioengineered organisms, like a bioengineered photosynthesis protein from a plant integrated with a nanotech film to capture sunlight and convert it into electricity; 252 a targeted-killing weapon that integrates a lethal genetically engineered organism with a nanoparticle that releases the organism upon detecting certain genetic traits in an individual's DNA; 253 a sophisticated form of AI that creates new technologies utilizing nanotechnology or bioengineering; 254 and the use of nanotechnology, bioengineering, and AI to either \"enhance\" humans (termed \"posthumans\") or to create a superintelligent machine with biological and nanotech properties.  255  An international treaty that covers all of these emerging technologies is best equipped to regulate their use as the boundaries blur between them. Furthermore, nanotechnology, bioengineering, and AI all have broad social and ethical implications, and so placing all of them under the auspices of one convention creates a central hub from which the public can determine what risks they are willing to take and what technologies should become pervasive in society. Finally, scientists are likely to uncover yet unknown GCRs/ERs from emerging technologies in the future, and so a GCR/ER treaty for emerging technologies should be flexible enough to incorporate other emerging technologies that could pose a GCR/ER in the future such that regulators can take relatively quick action on the international level rather than having to negotiate a new legal instrument. States should consider concluding an international convention on GCRs/ERs from emerging technologies under the auspices of an existing international governmental organization (IGO). For example, concluding a treaty under the auspices of the United Nations is beneficial because linkages could be made with relevant U.N. subsidiary bodies, such as the U.N. Commission on the Science and Technology Development (CSTD),  256  and the United Nations has substantial financial resources and political clout. Another possibility to conclude a treaty under the auspices of the World Health Organization (WHO), which already works with issues like bioengineering and nanotechnology through non-binding initiatives and other means.  257  For   256  The CSTD is a \"gateway to information on science and technology\" for the United Nations that the Economic and Social Council (ECOSOC) created in 1992 as a source of information and policy recommendations to other U.N. bodies. See Homepage, U.N. CONFERENCE ON TRADE AND DEVELOPMENT, at: http://www.unctad.info/en/Science-and-Technology-for-Development---StDev (last visited Apr. 21, 2012).  257  See e.g. WHO Biosafety and Laboratory Biosecurity Programme on Laboratory Biosafety and Biosecurity, WORLD HEALTH ORG., at: http://www.who.int/ihr/biosafety/en/ (last visited Mar. 22, 2012). See also ! 33! example, the WHO Biosafety and Laboratory Biosafety programme (BLBP) organizes awareness-raising workshops, develops training materials for laboratory workers, and has created a nonbinding World Health Assembly resolution that \"urges\" Member States to take measures such as improving laboratory biosafety and increasing training for laboratory workers.  258  However, the WHO is traditionally not a forum under which treaties are concluded, with the 2003 Framework Convention on Tobacco Control being the only convention thus far concluded under the auspices of the WHO.  259  An alternative is to utilize the WHO's extensive resources on protecting human health by linking a treaty on GCRs/ERs from emerging technologies to the WHO or some other IGO through a protocol, a joint task force, or a collaborative agreement.  260  One the other hand, rather than concluding a new international agreement, states could agree to amend existing international treaties to include increased safeguards over a wider range of activities, but existing treaties are not ideal for this purpose. As discussed above, neither the CBD, the Cartagena Protocol in Biosafety, the BWC, nor the various human dignity instruments sufficiently mitigate GCRs/ERs arising out of biotechnology.  261  While states could chose to amend legally binding instruments like the CBW and the Cartagena Protocol to include emerging technologies, states did not draft these treaties with GCRs/ERs for emerging technologies in mind, and thus they would have to be radically transformed in order to provide an effective international regime. 262 Therefore a new international treaty is the best way forward to regulate the emerging technologies contemplated in this paper. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Reducing Long-Term \n B. Precautionary Principle This section overviews the different applications of the precautionary principle and discusses how best to apply the precautionary principle to a treaty on GCRs/ERs from emerging technologies, concluding that specific strategies based on an affirmative application of the precautionary principle is ideal. While there are many renditions of the precautionary principle embodied in various international instruments, 263 the essence of the precautionary principle is that preventative or remedial measures can, should, or must be taken when there is scientific uncertainty that an unacceptable hazard may occur.  264  The precautionary principle is an essential element of an international treaty regulating GCRs/ERs from emerging technologies because society should not risk massive damage to human health and the environment from GCRs/ERs on a \"trial and error\" basis.  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! \n ! 34! Many conventions apply the precautionary principle in a negative manner, like Article 3(3) of the U.N. Framework Convention on Climate Change (UNFCCC), which states that a \"lack of full scientific certainty should not be used as a reason for postponing\" precautionary measures to \"anticipate, prevent, or minimize the causes of climate change and mitigate its adverse effect.\" 265 This provision does not actually require a state to take precautionary actions, but rather purports that scientific uncertainty is an inappropriate reason not to take precautionary actions. For example, while the Intergovernmental Panel on Climate Change (IPCC) concluded in its Fourth Assessment Report (AR4) that increases in global temperatures are \"very likely\" (i.e. above 90 percent likely) caused by anthropogenic greenhouse gas emissions, 266 UNFCCC Parties should not cite the lack of 100 percent scientific certainty as a basis for not reducing their greenhouse gas emissions. This is also an example of a nonbinding application of the precautionary principle because Article 3(3) merely states that UNFCCC parties \"should\" employ the precautionary principle in addressing climate change.  267  Other conventions apply the precautionary principle as an exception to otherwise binding requirements. For example, Article 5.7 of the World Trade Organization's (WTO) Agreement on Sanitary, and Phytosanitary Measures (SPS Agreement) permits a WTO Member to adopt certain trade-restrictive sanitary and phytosanitary measures that are otherwise in violation of the liberalized trade provisions of the WTO when \"relevant scientific evidence is insufficient\" to assess particular risks to human, animal, or plant life or health.  268  The effect of this provision is that some WTO Members have more stringent sanitary and phytosanitary measures than others based on each WTO Member's chosen level of health standards. Finally, some conventions reflect an affirmative application of the precautionary principle that recommends or requires precautionary measures in the face of scientific uncertainty. An example of this approach is embodied in Annex 4(a) of the Convention on the International Trade on Endangered Species (CITES), which states that Parties \"shall, in the case of uncertainty … act in the best interest of the conservation of the species\" when deciding whether to alter the protective status of a species or when gauging the effect of international trade on conserving a species.  269  In the case of CITES, application of the precautionary principle is hashed out through specific obligations, such as the requirement that a species listed under Appendix I (species that are \"threatened with extinction\") thereafter be listed under Appendix II (species that, inter alia, would be \"threatened with extinction\" unless trade in the species is strictly regulated) and monitored for a requisite time period before delisting that species   270  Furthermore, in contrast to the UNFCCC, CITES requires Parties to employ the precautionary principle as reflected in Annex 4.  271  Negative, nonbinding, or exception-type applications of the precautionary principle are not ideal to effectively regulate GCRs/ERs arising from emerging technologies. First, the negative application of the precautionary principle would merely suggest or require that states not use scientific uncertainty about GCRs/ERs arising from emerging technologies as a reason for not taking action, but this does not impose an obligation upon states to affirmatively mitigate any risks, although applying the negative precautionary principle could be useful to eliminate \"excuses\" for noncompliance with other provisions of an emerging technologies GCR/ER treaty. Second, an exception-type application of the precautionary principle for GCRs/ERs from emerging technologies would be ineffective because this approach would result in different levels of protections from GCRs/ERs in different states, and an effective emerging technologies GCR/ER treaty should impose roughly uniform standards because a GCR/ER that materializes in any single state would have a global impact. On the other hand, this version of the precautionary principle may be useful if, for example, states negotiated exceptions to the WTO liberalized trade scheme as part of a treaty on GCRs/ERs arising from emerging technologies. Finally, a nonbinding application of the precautionary principle would limit the treaty's overall effectiveness because states are less likely to abide by its terms. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 265 United An affirmative and obligatory version of the precautionary principle would be most effective in regulating GCRs/ERs arising from emerging technologies. This approach could require states to take certain affirmative actions to regulate emerging technologies that pose an uncertain or undecided degree of GCR/ER. This is ideal because emerging technologies have the potential to result in global, permanent damage to the habitability of the Earth, and so requiring every state to implement precautionary measures is the prudent course of action, especially considering the rapid speed at which emerging technologies are developing. Furthermore, an affirmative and obligatory application of the precautionary principle is the best way to ensure that all states actually integrate precautionary mechanisms into their domestic law, because the level of requisite precaution can be determined and prescribed on the global level rather than having a patchwork of precautionary mechanisms from country-to-country that may or may not result in a sufficient level of protection on the global scale. Although states would not likely be willing to impose widespread regulations upon entirely \"speculative\" risks, one way to implement the precautionary principle in an emerging technologies treaty is to trigger specific requirements when available data demonstrates a \"reasonable grounds for concern\" that a certain risk exceeds whatever level is deemed acceptable.  272  A body of experts representing widespread interests could determine when there is in fact a \"reasonable ground of concern,\" and remedial measures would then be applied relatively consistently across all states. For example, a body of experts could determine that swarms of nanobots developed to search for oil in the ground (a technology that is currently ! 36! being researched  273  ) poses uncertain risks and that available information shows a \"reasonable grounds for concern,\" which could trigger a requirement that states impose certain measures to regulate this technology or even prohibit it until there is further research of the risks. Subsequently, the treaty could require proponents of this technology to rebut the \"reasonable grounds for concern\" in order to continue the technology's development and/or application. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! If the probability of a GCR/ER is inherently unascertainable even with extensive scientific research, as is often true with GCRs/ERs from emerging technologies,  274  one possible solution is for a body of experts to determine the necessary steps to prevent an \"extremely bad worst case scenario\" as a precautionary measure, regardless of likelihood and available information.  275  States would be required to take these steps if doing so requires modest costs that are not diverted from other crucial investments.  276  An example of this would be to require development of an approved failsafe mechanism in all superintelligent AI that has direct or indirect control over weapons systems. Another possibility is to ban or restrict emerging technologies that present an unquantifiable GCR/ER until scientific evidence proves that the risk, while still unknown, can effectively be reduced to a level that falls short of global catastrophic or existential harm. An example of this is to restrict scientists from synthesizing certain types of highly fatal bioengineered viruses until experts can prove the effectiveness of a vaccine that could prevent human death on the global scale if the virus is accidentally or purposefully released. \n C. Composition and Function of a Body of Experts A body of experts should have general regulatory authority over emerging technologies that pose a GCR/ER in all states that are parties the convention. One possible model is the Environmental Protection Agency (EPA), which, inter alia, promulgates and enforces regulations according to environmental statutes.  277  Likewise, the body of experts could apply the precautionary principle as previously discussed  278  and take regulatory steps necessary to reduce GCRs/ERs to an acceptable level. Depending on the general requirements created by a treaty on emerging technology GCRs/ERs, this body of experts could impose a variety of regulatory tools such as technical restrictions on products; permit requirements; total bans on certain emerging technologies; reporting requirement for certain industry sectors; laboratory safety rules; mandatory environmental, human health, and social impact statements for certain activities; and liability mechanisms to punish violators whether or not their activities cause any harm. In terms of composition, the body of experts should consist of scientists, lawyers, government authorities, civil society representatives, and other experts chosen based on their area of expertise and equitable geographic representation. Specialists in nanotechnology, !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! bioengineering, and AI are best equipped to handle complex fact patterns involving these technologies, especially as the science becomes more advanced, and so special qualifications in one or more of these fields should be mandatory.  279  Government authorities should have both a fluent understanding of various domestic legal systems as well as expertise in one or more emerging technologies. Meanwhile, civil society representation in the body of experts is essential both to inform other experts on what society considers to be an \"acceptable\" level of risk and to shape discussions about whether developing certain emerging technologies will have an undesirable impact on society. For example, the signatories to the Principles for Oversight of Nanotechnologies and Nanomaterials expressed concern that \"[g]overnments and industry developers of nanotechnologies provide few meaningful opportunities for informed public participation in discussions and decisions about how, or even whether, to proceed with the 'nano'-ization of the world.\" And in terms of human bioengineering, Annas, et al. argues that altering the human species is an inherently democratic matter that should only be made a body that constitutes global representation.  280  Civil society representation will help ensure that global democracy influences global emerging technology regulations. While a treaty on emerging technologies should grant the body of experts significant authority to manage GCRs/ERs on a day-to-day basis, states will want to retain decisionmaking powers for any changes to the treaty, and they may also wish to reserve the power to second guess the body of experts. If the body of experts finds it necessary to alter the treaty, whether to regulate a new technology under the convention or to modify the treaty provisions as applied to technologies already considered, the body of experts should be able to draft a resolution that becomes binding upon all parties if agreed to by a simple majority or two-thirds majority vote of all parties. This system could be modeled upon the Montreal Protocol to the Vienna Convention for the Protection of the Ozone Layer, under which Parties can reduce allowable production or consumption of \"controlled substances\" (ozone depleting substances) based on a two-thirds majority of present and voting parties.  281  Furthermore, if states wish to override a decision made by the body of experts, an emerging technologies treaty should require a majority or two-thirds majority of parties to vote in favor of doing so. \n D. Review Mechanism Domestic and international judicial systems currently lack sufficient review mechanisms for GCRs/ERs arising from emerging technologies. For example, in the United States, many federal courts use the Daubert standard to determine whether expert evidence is admissible in court. Under the Daubert standard, the judge decides whether expert evidence, which includes expert testimony, is admissible based on whether the evidence derives from \"scientific knowledge.\"  282  In turn, \"scientific knowledge\" generally must be \"testable.\" 283 Furthermore, judges must also consider whether expert evidence based on scientific knowledge receives !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 279 For example, in terms of nanotechnology, a group of NGOs stated that \"[a] precautionary approach requires mandatory, nano-specific oversight mechanisms to account for the unique characteristics of the materials,\" and this would best be achieved by those who are intimately involved in this field.  INTERNATIONAL    \n ! 38! \"general acceptance\" from scientists. 284 However, GCRs/ERs are often extremely lowprobability, and so \"general acceptance\" that they will materialize is typically absent. Furthermore, GCRs/ERs are almost never testable because they should never be allowed to materialize. Finally, as discussed above, judges may not have the scientific understanding to sufficiently gauge GCRs/ERs, particularly when a case is dismissed before advocates have the chance to develop their full arguments, and the expert advice they receive is often from scientists with a conflict of interest in the outcome of the case.  285  To remedy these problems, an international treaty regulating GCRs/ERs from emerging technologies could either (1) require states to establish domestic \"science courts\" that are equipped to consider alleged GCRs/ERs arising from emerging technologies and which are required to factor in minority scientific opinions whether or not they are \"testable,\" 286 or (2) create an international court that enables citizens to submit disputes regarding GCRs/ERs from emerging technologies, much like the right of European citizens to submit disputes to the European Court of Human Rights. In either scenario, the judges should preferably be scientifically literate lawyers who are able to comprehend the science of emerging technologies and effectively question experts from the arena of emerging technology in question.  287  If an international court is established, such a court could take over the enforcement functions of the proposed body of experts by applying traditional judicial mechanisms such as penalties, injunctions, and other measures. Finally, for certain activities (as determined by the body of experts), the court should require the proponent of an emerging technology to establish the lack of an unacceptable risk in order to prevail. \n E. Public Participation and Access to Information A treaty on emerging technology GCRs/ERs should include provisions for significant public participation that is in addition to the civil society representation on the body of experts. Nanotechnology, bioengineering, and AI involve, inter alia, ethical, religious, philosophical, political, economic, and safety considerations, and thus a treaty on GCRs/ERs from emerging technologies should establish a forum in which the public can shape the debate about what kind of technologies mankind should develop. Such a forum could gauge global public concerns about health risks, social effects, morals, religious implications, and overall perception of emerging technologies to influence the body of experts, who should have a treaty-mandated duty to consider societal views in their decisions.  288  While the exact form that the public dialogue could take includes anything from a conference to a series of \"town hall\" style meetings, civil society organizations (CSOs) representing the public should be the ones to decide on the exact format through their participation in drafting the convention on GCRs/ERs from emerging technologies. Furthermore, integrating the precautionary principle with a treaty on GCRs/ERs arising from emerging technologies inherently requires consideration of what hazards are \"acceptable\" or, as discussed above, what constitutes a \"reasonable grounds for concern,\" which are !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 284 Id. 285 See supra Section II(B)(4)(a).!  286   ! 39! benchmarks that should be heavily influenced by societal perspectives on emerging technologies and their risks. The treaty on emerging technologies should establish a subsidiary body responsible for organizing major public events and compiling data on societal perspectives to present to the body of experts and the state parties. The civil society representatives on the body of experts should strongly advocate for the positions compiled at such public events. Furthermore, before the body of experts makes major decisions that do not require urgent actions, there should first be a period of public comment, and the body of experts should be required to consider the public sentiment in their decisionmaking.  289  Another specific way to empower the public to shape the international framework behind emerging technologies is to allow \"observers\" representing a wide variety of interests to participate both in the drafting of an emerging technologies treaty and in subsequent \"conferences of the parties.\" The Conference of Parties to CITES (COP) is an example of a forum with significant public participation from CSOs. Under CITES, CSOs may become observers if they meet certain qualifications and one-third of CITES parties do not object.  290  Finally, the public should also have broad access to information regarding emerging technologies. Such information could include, at minimum, annual reports on safety issues related to emerging technologies and annual summaries of current legal obligations arising out of treaty on emerging technology GCRs/ERs (including summaries of cases decided by the associated judicial body and measures imposed by the body of experts).  291  In order to gather sufficient and accurate data, an emerging technologies treaty should create specific and mandatory reporting requirements for both state parties and industries that research and develop emerging technologies. Furthermore, not only should this information merely be made publicly available, but a treaty on emerging technology GCRs/ERs should also mandate a communications body, perhaps overseen by the same subsidiary body responsible for organizing public events, that is responsible for disseminating information on emerging technologies to all sectors of society on a global level. Each state should also be required to grant \"active\" as opposed to \"passive\" access to information by actively distributing information on emerging technologies in a way that is most effective within their particular culture. 292 \n F. Regulating Scientists An international instrument on GCRs/ERs should regulate the conduct of scientists because the stakes of GCRs/ERs are too high to leave to a small group of self-interested individuals. While scientists often reassure the public that GCRs/ERs from emerging technologies are nonexistent or negligible, as discussed above, scientists who assess the risks of their own work may be intentionally or unintentionally influenced by pressures to make profits, achieve scientific breakthroughs, and outpace other groups of scientists.  293  For example, while CERN scientists found no significant risks from the LHC, other experts concluded that the LHC did pose at least some risks, and subsequent accidents with the LHC weakened the credibility of   294  Yet CERN scientists were able to be their own risk assessors, and attempts of outside parties to impose meaningful oversight of the LHC were ineffective.  295  Although the LHC has not caused global catastrophic or existential harm, international law should ensure that scientists working with emerging technologies sufficiently consider and proactively minimize GCRs/ERs. There are many possible ways for a treaty to regulate scientists without stifling scientific development. First, scientists should be required to undergo adequate training both to understand the nature of any GCRs/ERs arising from their particular field of work and to learn ways to mitigate these risks. For example, scientists working with genetically engineered viruses should be made aware of the risks posed by an accidental release, and they should undergo mandatory training to ensure that they follow strict protocols designed to prevent an accidental release. Second, scientists should be subject to a code of conduct that requires scientists to monitor their own ethical and professional conduct as well as the ethical and professional conduct of their peers and supervisors. One way to materialize this concept is to create ethical oversight organizations based on the model of state bar associations, which require membership of all practicing lawyers, punish ethical violations, and compel lawyers to report their peers or superiors if they violate certain ethical and professional rules.  296  In the context of a treaty on GCRs/ERs from emerging technologies, the body of experts or a subsidiary body thereof could decide what constitutes \"ethical or professional\" conduct, then domestic ethical oversight organizations could implement and refine these rules based on specific domestic needs. Finally, scientists should be equally regulated whether they are involved in government-funded projects or private projects. For example, while the NSABB provides recommendations on training and education for scientists in federally funded institutions, the growing number of private institutions conducting experimental research in emerging technologies clearly shows the need to regulate scientists working on projects funded with either federal or private money. 297 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \n G. Safeguarding Laboratories and Dangerous Emerging Technologies Nanotechnology, AI, and bioengineering are all susceptible to misuse, and thus an international treaty on GCRs/ERs from emerging technologies should address the security of laboratories and other means of accessing these technologies. First, certain laboratories that participate in developing emerging technologies that pose GCRs/ERs should be required to register their facilities. For example, section 415 of the Public Health Security and Bioterrorism Preparedness and Response Act of 2002 requires facilities that manufacture, possess, pack, or hold food bound for U.S. consumption to register with the U.S Food and Drug Administration (FDA), and such facilities must thereafter provide notice to the FDA about certain food shipments (article 307) and are also subject to record inspection by FDA agents (section 414). 298  294  Id.  295  Id. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 296 See e.g. Rule 8.3 of ABA's MODEL RULES OF PROF. CONDUCT (2011) (\"A lawyer who knows that another lawyer has committed a violation of the Rules of Professional Conduct that raises a substantial question as to that lawyer's honesty, trustworthiness or fitness as a lawyer in other respects, shall inform the appropriate professional authority\"); see also Rule 8.4(c) of ABA's MODEL RULES OF PROFESSIONAL CONDUCT (2011) (\"It is a professional misconduct for a lawyer to engage in conduct involving dishonesty, fraud, deceit or misrepresentation\").  297    \n ! 41! Similarly, facilities that engage in emerging technologies research that meets a certain threshold of danger (as determined by the aforementioned body of experts or a subsidiary body thereof) could be required to register their facilities at the international level, provide notice when they conduct or plan to conduct certain regulated activities, and make their records available for inspection by international authorities. Second, a treaty on GCRs/ERs should impose mechanisms to monitor specific technologies that pose a GCR/ER if misused. For example, DNA synthesizers could be \"licensed, tagged with electronic locators, and programmed to forbid the synthesis of dangerous DNA sequences,\" as recommended by Harvard biologist George Church, with the body of experts or a subsidiary body thereof determining what constitutes a \"dangerous\" DNA sequence based on annual or semi-annual reviews.  299  The body of experts or a subsidiary body thereof should determine which technologies pose a concern and then require registration of these technologies so they can be monitored and traced. Third, laboratories conducting dual use research in emerging technologies should be required to meet a certain level of safety from accidental releases and theft. For example, laboratories with the most dangerous bioengineered pathogens should be required to be BSL-4 instead of being subject to non-binding recommendations on lab security. 300 Furthermore, some laboratories should be required to take certain measures to prevent theft or break-in by securing their physical compound and by installing advanced firewalls on their computer systems. Laboratories should also be required to undergo regular maintenance and inspection to ensure that they meet international regulations. In order to incentivize compliance, if facilities fail to meet safety regulations, they should be subject to substantial fines, and governments should be held financially liable for any significant damage that results from a failure to properly regulate their facilities. Finally, because the number of laboratories handling emerging technologies that pose GCRs/ERs is rapidly growing, states should be required to limit the total number of such laboratories to a number that can be effectively overseen by regulatory authorities. \n H. Oversight Mechanism for Scientific Publications Publicly disclosing scientific information that poses a GCR/ER opens the door for potential terrorists to obtain the information and then intentionally cause massive death to humans or damage to the environment, or else for amateur or under-qualified scientists to replicate such research without sufficient safeguards. This is why the NSABB recommended that findings on how to genetically engineer an airborne H5N1 virus should not be released into the public domain, specifically arguing that the risks outweighed the benefits to society. 301 However, the NSABB does not have the legal power to restrict scientific publications, and while so far the scientists behind the bioengineered H5N1 virus have not released their data, there is no guarantee that future scientists will comply with similar non-binding recommendations. Likewise, scientists Ray Kurzweil and Bill Joy criticized the decision United States Department of Health and Human Services to release the full genome of the massively deadly 1918 influenza virus (\"the Spanish flu\"), because releasing such a virus could kill tens if not !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 299 Christopher F. Chyba, Biotechnology and the Challenge to Arms Control, ARMS CONTROL TODAY (Oct. 2006), at: http://www.armscontrol.org/act/2006_10/BioTechFeature.asp.  300  Canada recently mandated that only BSL-4 laboratories are allowed to handle lab-made H5 viruses. See THE CANADIAN PRESS, supra note 54.  301  Id. ! 42! hundreds of millions of people. 302 Kurzweil and Joy called for an \"international agreement by scientific organizations\" to oversee publication of scientific data that could result in acts of bioterrorism, equating the genetic code of deadly viruses to nuclear weapon designs.  303  States should expand this concept by creating an oversight mechanism for all sensitive materials from emerging technologies that pose a GCR/ER. For example, a subsidiary body of the body of experts could determine when the risk of releasing scientific information outweighs the potential benefits, and then take appropriate response measures. So as not to stifle scientific development, scientists whose research poses a GCR/ER should merely be required to redact certain sensitive information rather than being prohibited from releasing their data altogether. \n IV. CONCLUSION A series of fantastical scientific breakthroughs are leading towards or, in some instances, have already created technologies that question basic premises of life: that man cannot create life, that humans are the ultimate intelligent being, or that we are limited by the basic building blocks we find on Earth. While nanotechnology, bioengineering, and AI offer great benefits to society, they also have the potential to cause global catastrophic or even existential harm to humans. While bioengineering has caused a revolution in crop production, genetically engineered viruses have the potential to cause global devastation if accidentally or purposefully released. Nanotechnology has yielded materials that are stronger, lighter, yet nanomaterials also pose unknown human and animal health effects, and weapons developed from advanced nanotechnology could be far more destructive and concealable than nuclear bombs. And while AI could innovate every technology on the planet, a superintelligent machine could outcompete humans or be programmed to act maliciously. While the chances of massive destruction from these technologies are not high, states should still act quickly to create a flexible, binding international treaty that limits GCRs/ERs arising from emerging technologies to a degree that society deems acceptable. As this paper demonstrates, emerging technologies do not fall squarely within current international law, and allowing a small group of self-interested scientists to regulate themselves is unacceptable when a single misstep could result in global catastrophic or existential harm. Instead, the international community, with the guidance of a body of experts representing a wide range of interests and strong considerations of the precautionary principle, should develop a binding framework to regulate emerging technologies at the international level. Furthermore, because emerging technologies will likely affect the entire world, society should help determine which risks they are willing to take and what moral, ethical, and other beliefs should influence an international regulatory regime. If the international community successfully concludes a treaty on GCRs/ERs from emerging technologies, then perhaps society can thrive in an age of technological innovation without suffering from the associated risks. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 302 Ray Kurzweil & Bill Joy, Recipe for Destruction, N.Y. TIMES (Oct. 17, 2005), at: www.nytimes.com/2005/10/17/opinion/17kurzweiljoy.html.  303  Id. 84  A posthuman is an individual \"so significantly altered as to no longer represent the human species.\" CHARLES W. COLSON & NIGEL M. DE S. CAMERON, HUMAN DIGNITY IN THE BIOTECH CENTURY: A CHRISTIAN VISION FOR PUBLIC POLICY 85 (2004). This involves \"redesigning the human condition, including such parameters as the inevitability of aging, limitations on human and artificial intellects, unchosen psychology, [and] suffering....\" BERT GORDIJN & RUTH CHADWICK, MEDICAL ENHANCEMENT AND POSTHUMANITY 140 (2009). Posthumanism also frequently may involve enhancing humans through nanotechnology and cybernetics. For example, \"individuals could have electronic brain implants to create human to computer interaction,\" which is a technology already in development. Lisa C. Ikemoto, Race to Health: Racialized Discourses in A Transhuman World, 9 DEPAUL J. HEALTH CARE L. 1101, 1112-1113 (2005), citing RAMEZ NAAM, MORE THAN HUMAN: EMBRACING THE PROMISE OF BIOLOGICAL ENHANCEMENT 181-187 (2005). 85 George J. Annas et al., Protecting the Endangered Human: Toward an International Treaty Prohibiting Cloning and Inheritable Alterations, 28 AM. J. LAW MED. 151, 161-162 (2001). \n 206 Cartagena Protocol on Biosafety to the Convention on Biological Diversity, art. 3(g), Jan. 29, 2000, 39 I.L.M. 1027 (2000) [hereinafter Cartagena Protocol]. Article 31(2)(b) of the Vienna Convention, which reflects customary international law, states that a treaty shall be interpreted in light of \"any instrument which was made by one or more parties in connection with the conclusion of the treaty and accepted by the other parties as an instrument related to the treaty,\" which includes a protocol to the CBD-the Cartagena Protocol-that expands upon the CBD's biosafety provisions. Vienna Convention on the Law of Treaties, art. 31, May 23, 1969, 1155 U.N.T.S. 331 [hereinafter Vienna Convention]. \n 209  !See infra, Section III(B).! 210 Cartagena Protocol, supra note 206, at art. 1. \n 270 Id.  at Annex I, Annex 2(a), and Annex 4(B)(1).271  See id. at Annex 4(A).272  This is the basic justification for precautionary measures embodied in the European Union (EU) Communication on the Precautionary Principle. See Communication from the Commission on the Precautionary Principle, Commission on the European Communities, COM (2000) 1, available at: http://ec.europa.eu/dgs/health_consumer/library/pub/pub07_en.pdf. \n Committee on Assessing Fundamental Attitudes of Life Sciences as a Basis for Biosecurity Education, A Survey of Attitudes and Actions on Dual Use Research in the Life Sciences, NAT'L RESEARCH COUNCIL 2 (2009). 298 Public Health Security and Bioterrorism Preparedness and Response Act of 2002, 42 U.S.C. § 201 (2002). \n Overview: What is the Singularity?, SINGULARITY INSTITUTE FOR ARTIFICIAL INTELLIGENCE, http://singinst.org/overview/whatisthesingularity (last visited Jan. 31, 2012). 8 NICK BOSTROM & MILAN M. ĆIRKOVIĆ, Introduction, in GLOBAL CATASTROPHIC RISKS 25 (Nick Bostrom & Milan M. Ćirković, eds., 2008). \n The Deadliest Virus, THE NEW YORKER 32-33 (Mar. 12, 2012).29  Some skeptics do not consider this to be the first instance of truly synthetic life because the genomes were based on existing DNA.See Angier, supra note 6; Nicholas Wade, Researchers Say They Created a 'Synthetic Cell', N.Y. TIMES (May 20, 2010), available at: www.nytimes.com/2010/05/21/science/21cell.html. 30 ENVTL. PROT. AGENCY, supra note 26, at 10. The JGI database is accessible at http://www.jgi.doe.gov/sequencing/why/index.html, and GenBank ® is accessible at http://www.ncbi.nlm.nih.gov/genbank/. 31 NATIONAL SCIENCE ADVISORY BOARD FOR BIOSECURITY (NSABB), STRATEGIES TO EDUCATE AMATEUR BIOLOGISTS AND SCIENTISTS IN NON-LIFE SCIENCE DISCIPLINES ABOUT DUAL USE RESEARCH AND LIFE SCIENCES 4 (June 2011), available at: http://oba.od.nih.gov/biosecurity/pdf/FinalNSABBReport-AmateurBiologist-NonlifeScientists_June-2011.pdf. 32 Michele S. Garfinkel & Robert M. Friedman, Synthetic Biology and Synthetic Genomics, in THE FUTURE OF INTERNATIONAL ENVIRONMENTAL LAW 272 -273(David Leary & Balakrishna Pisupati, eds., 2010). 33 Id. at 278-279. 34 See About Us, INTERNATIONAL GENETICALLY ENGINEERED MACHINE COMPETITION, http://igem.org/About. 28  Michael Specter,35  Garfinkel & Friedman, supra note 32, at 270.36  Fact Sheet Describing Recombinant DNA and Elements Utilizing Recombinant DNA Such as Plasmids and Viral Vectors, and the Application of Recombinant DNA Techniques in Molecular Biology, UNIV. OF N.H. OFFICE OF ENV'T HEALTH AND SAFETY 2 (2011), available at: www.unh.edu/research/sites/unh.edu.research/files/images/Recombinant-DNA.pdf. \n SCIENCE AND TECHNOLOGY COMMITTEE OF THE PARLIAMENT OF GREAT BRITAIN, BIOENGINEERING: SEVENTH REPORT OF SESSION 55-56 (2009-2010). 41 GM Crops: Reaping the Benefits, but Not in Europe, EUROPEAN ASSOC. FOR BIOINDUSTRIES 1-8 (2011), available at: www.europabio.org/sites/default/files/europabio_socioeconomics_may_2011.pdf. 42 Risk and Response Assessment Project, Synthetic Biology and Nanobiotechnology, U.N. INTERREGIONAL CRIME AND JUSTICE RESEARCH INSTITUTE (UNICRI), at: http://lab.unicri.it/bio.html (last visited Feb. 13, 2012); Garfinkel & Friedman, supra note 32, at 274-277. 43  Elizabeth A. Thomson, Paper Predicts Bioengineering Future, MIT NEWS (Feb. 14, 2001), at: web.mit.edu/newsoffice/2001/biomedical-0214.html 44 UNICRI, supra note 42. 45 ENVTL. PROT. AGENCY, supra note 26, at iv. and the environment. \n 46 John Steinbruner et al., Controlling Dangerous Pathogens: A Prototype Protective Oversight System, CTR. FOR INT'L AND SECURITY STUDIES AT MD. 1 (2007), available at: www.cissm.umd.edu/papers/files/pathogens_project_monograph.pdf. 47 See Garfinkel & Friedman, supra note 32, at 279.48  There are different types of \"type A\" influenza viruses in birds that are named according to the \"two main proteins on the surface\" of the virus, here H5 and N1. The H5N1 virus is just one type of bird flu. See Key Facts About Avian Influenza (Bird Flu) and Highly Pathogenic Avian Influenza A (H5N1) Virus, CTR. FOR DISEASES CONTROL AND PREVENTION (CDC), at: www.cdc.gov/flu/avian/gen-info/facts.htm (last visited Mar. 11, 2012). 49 Specter, supra note 28, at 32-33. 50 CDC, supra note 48. 51 Robert Roos, Live Debate Airs Major Divisions in H5N1 Research Battle, CENTER FOR INFECTIOUS DISEASE RESEARCH AND POLICY (CIDRAP) NEWS (Feb. 3, 2012), at: www.cidrap.umn.edu/cidrap/content/influenza/avianflu/news/feb0312webinar-jw.html (see comments of Michael T. Osterholm of the National Science Advisory Board for Biosecurity). 52 Specter, supra note 28, at 32. 53 UNICRI, supra note 42. 54 Future Bird Flu Virus Work Should be Done in Most Secure Labs, THE CANADIAN PRESS (Mar. 06, 2012), at: www.ctv.ca/CTVNews/Health/20120306/bird-flu-virus-labs-120306. \n High-Containment Biosafety Laboratories: Preliminary Observations on the Oversight of the Proliferation of BSL-3 and BSL-4 Laboratories in the United States, Statement of Keith Rhodes, Chief Technologist, Center for Technology and Engineering, Applied Research and Methods , GAO-08-108T (Oct. 4, 2007), available at: http://www.gao.gov/new.items/d08108t.pdf (emphasis added). 56 Id. 57 Specter, supra note 28, at 33. 58 Id. 59 Jennifer Gaudioso et al., Biosecurity: Progress and Challenges, 14 J. OF LABORATORY AUTOMATION 141, 143 (2009). See also Christian Enemark, Preventing Accidental Disease Outbreaks: Biosafety in East Asia, NAUTILUS INSTITUTE FOR SECURITY AND SUSTAINABILITY, AUSTRAL PEACE AND SECURITY NETWORK (ASPNET) (2006), available at: http://nautilus.org/apsnet/0631a-enemark-html. 60 Larry Margasak, Accidents on Rise as More US Labs Handle Lethal Germs, THE ASSOC. PRESS (Oct. 03, 2007), available at: http://articles.boston.com/2007-10-03/news/29232771_1_biosafety-level-4-labs-accidents. 61 United Nations Office for Disarmament Affairs, Developing a Biological Incident Database, UNODA OCCASIONAL PAPERS: NO. 15 12-13 (2009), available at: http://www.un.org/disarmament/HomePage/ODAPublications/OccasionalPapers/OP15-info.shtml. 62 Gaudioso et al., supra note 59, at 143. 63 Denise Grady & Donald McNeil Jr., Debate Persists on Deadly Flu Made Airborne, N.Y. TIMES (Dec. 26, 2011), at: http://www.nytimes.com/2011/12/27/science/debate-persists-on-deadly-flu-made-airborne.html. \n Frequently Asked Questions -Molecular Manufacturing, FORESIGHT INSTITUTE, www.foresight.org/nano/whatismm.html 99 J. CLARENCE DAVIES, OVERSIGHT OF NEXT GENERATION NANOTECHNOLOGY 11 (April 2009), available at www.nanotechproject.org/process/assets/files/7316/pen-18.pdf. 100 Peter Kearns, Nanomaterials: Getting the Measure, OECD OBSERVER (2010), available at: http://www.oecdobserver.org/news/fullstory.php/aid/3291. 101 What's So Special About the Nanoscale, NATIONAL NANOTECHNOLOGY INITIATIVE, http://www.nano.gov/you/nanotechnology-benefits (last visited April 21, 2012). 102 Nanotechnology and You: Benefits and Applications, NATIONAL NANOTECHNOLOGY INITIATIVE, http://www.nano.gov/you/nanotechnology-benefits (last visited Feb. 04, 2012). \n Overview: What is the Singularity?, SINGULARITY INSTITUTE FOR ARTIFICIAL INTELLIGENCE, at: http://singinst.org/overview/whatisthesingularity (last visited Jan. 31, 2012). 152 Why Work Toward the Singularity, THE SINGULARITY INSTITUTE, at: singinst.org/overview/whyworktowardthesingularity (last visited Apr. 21, 2012). 153 Benefits of the Singularity, SINGULARITY ACTION GROUP, at: home.mchsi.com/~deering9/benefits.html (last visited Mar. 12, 2012). 154 Michael Anissimov, Interview with Robin Powell, Singularity Institute Advocate, THE SINGULARITY INSTITUTE (Jan 12, 2012), at: singinst.org/blog/2012/01/12/interview-with-robin-powell-singularity-advocate. 155 BOSTROM & ĆIRKOVIĆ, supra note 10, at 33. 156 Reducing Long-Term Catastrophic Risks from Artificial Intelligence, THE SINGULARITY INSTITUTE, at: http://singinst.org/summary (last visited Mar. 10, 2012). 157 WALLACH & ALLEN, supra note 150, at 194-195. 158 See Iran and Its Nuclear Program, AMERICAN SECURITY PROJECT, at: americansecurityproject.org/issues/nuclear-security/iran-and-its-nuclear-program (last visited Apr. 21, 2012). 159 Eliezer Yudkowsky, Artificial Intelligence as a Positive and Negative Factor in Global Risk (2006), available at: singinst.org/upload/artificial-intelligence-risk.pdf. 160 Kaj Sotala, From Mostly Harmless to Civilization-Threatening: Pathways to Dangerous Artificial General Intelligences, SINGULARITY INSTITUTE FOR ARTIFICIAL INTELLIGENCE (2010), at: http://singinst.org/upload/mostlyharmless.pdf. 161  Id. \n 162 See JOHN LESLIE, THE END OF THE WORLD: THE SCIENCE AND ETHICS OF HUMAN EXTINCTION 95-103 (1998). 163 Sotala, supra note 160. 164 ROBERT H. SCHRAM, ILLUSAFACT: THE INEVITABLE ADVANCE OF OUR TECHNOLOGIES AND US 272-273 (2011). 165 Id. at 273. 166 See LESLIE, supra note 162, at 95-103. 167 Others estimate just the \"hardware\" of the LHC as costing approximately $10 billion and the entire LHC program -including costs to \"[operate] the experiment and [analyze] the data\" -being \"much greater.\" See Eric E. Johnson, The Black Hole Case: The Injunction Against the End of the World, 76 TENN. L. REV. 819, at 827 (2008-2009). 168 \"Organisation européenne pour la recherche nucléaire\" in French. 169 See LHC Machine Outreach (Homepage), EUROPEAN ORG. FOR NUCLEAR RESEARCH (CERN), AT: http://lhcmachine-outreach.web.cern.ch/lhc-machine-outreach (last visited Feb. 04, 2012). LHC to Shut Down for a Year to Address Design Faults, BBC NEWS (Mar. 10, 2010), at: http://news.bbc.co.uk/2/hi/8556621.stm. 172 Mike Lamont, Explain it in 60 Seconds: The Large Hadron Collider, SYMMETRY (Apr. 2005), at: http://www.symmetrymagazine.org/cms/?pid=1000095. 170  Id.171  Judith Burns, \n of the National Environmental Policy Act (NEPA). See Sancho v. U.S. Department of Energy, 578 F.Supp.2d 1258 (D. Haw. 2008). 185 Sancho, 392 F. App'x at 611. 186 Gillis, supra note 181. 187 Dr. Otto Rössler sought an emergency injunction from the European Court of Human Rights (ECtHR) for alleged violations of (1) the right to life under Article 2 of the European Convention on Human Rights (ECHR) and (2) the right to private and family life under Article 8 of the ECtHR. See LHC Critique, Summary of the (Renewed) Complaint Against CERN and the LHC Experiments as Submitted to the European Court of Human Rights, available at: lhc-concern.info/wp-content/uploads/2008/11/cern-lhc-kritik-statement-1-summary.pdf; see also Adams, supra note 175, at 152 (2009). The ECtHR rejected Dr. Dr. Otto Rössler's injunction requests via a \"brief email\" that did not include any reasoning, and while the ECtHR stated that it will hear the case on the merits, 187 the author cannot find any information on such a pending case. See Harrell, supra note 179. 188 Margaret Kovera et al., The Effects of Peer Review and Evidence Quality on Judge Evaluations of Psychological Science: Are Judges Effective Gatekeepers?, 85 J. OF \n Id. 221 M.K. SATEESH, BIOETHICS AND BIOSAFETY 205 (2008). 222 See Nagoya-Kuala Lumpur Supplementary Protocol on Liability and Redress to the Cartagena Protocol on Biosafety, 15 October 2010, Annex to UN Doc. UNEP/CBD/BS/COP-MOP/5/17, at arts. 2-5, available at: http://bch.cbd.int/protocol/NKL_text.shtml. 223 Article 2 defines operators as \"any person in direct or indirect control\" of an LMO of the living modified organism.\" Id. at art. 2(2)(c). 224  See Id. at arts. 2-5. \n List of Parties, CONVENTION ON BIOLOGICAL DIVERSITY, http://www.cbd.int/information/parties.shtml (last visited Mar. 19, 2012). The United States was nonetheless influential in negotiations for the Cartagena Protocol because they are a massive force in the world's agricultural market. Jonathan H. Adler, The Cartagena Protocol and Biological Diversity: Biosafe or Bio-Sorry?, 12 GEO. INT'L ENVTL. L. REV. 761, 763 (2000). 229 Convention on the Prohibition of the Development, Production, and Stockpiling of Bacteriological (Biological) and Toxin Weapons and on Their Destruction, art. 1, Apr. 10, 1972, 1015 U.N.T.S. 163 [hereinafter BWC]. 230  Id. at art. III. \n BOOT, GENOCIDE, CRIMES AGAINST HUMANITY, WAR CRIMES: NULLUM CRIMEN SINE LEGE AND THE SUBJECT MATTER JURISDICTION OF THE INTERNATIONAL CRIMINAL COURT 478 (2002). 247 POSNER, supra note 75, at 219. 248 Annas et al., supra note 85, at 153. \n Catastrophic Risks from Artificial Intelligence, THE SINGULARITY INSTITUTE, at: http://singinst.org/summary (last visited Mar. 10, 2012). 252 Nanotechnology White Paper, supra note 4, at 12. 253 Émilio Mordini, Converging Technologies, CENTRE FOR SCIENCE, SOCIETY AND CITIZENSHIP, at: http://agora-2.org/colloque/gga.nsf/Conferences/Converging_technologies (last visited Apr. 21, 2012). 254 Mark Avrum Gubrud, Nanotechnology and International Security, THE FORESIGHT INSTITUTE, at: www.foresight.org/Conferences/MNT05/Papers/Gubrud/ 255 J. CLARENCE DAVIES, supra note 99, at 19. \n Nanotechnology, WORLD HEALTH ORG, at: www.who.int/foodsafety/biotech/nano/en/index.html (last visited Mar. 22, 2012). 258 World Health Assembly Res. WHA58.3 (2005); see also Biosafety and Laboratory Biosecurity, WORLD HEALTH ORG., at: www.who.int/ihr/biosafety/key_activities/en/index.html (last visited Apr. 21, 2012). Note that none of these measures impose binding obligations on countries, and so they are less than ideal as a means to sufficiently mitigate GCRs/ERs arising from emerging technologies. 259 What is the Framework Convention on Tobacco Control?, FRAMEWORK CONVENTION ALLIANCE, at: www.fctc.org/index.php?Itemid=5&id=8&option=com_content&view=article (last visited Apr. 21, 2012). 260 See MARK A. SUTTON ET AL., THE EUROPEAN NITROGEN ASSESSMENT: SOURCES, EFFECTS AND POLICY PERSPECTIVE 557 (2011). 261 See e.g. supra, Section III. 262 Id. 263 By one account, there are at least twenty different definitions of the precautionary principle. Cass R. Sunstein, Irreversible and Catastrophic, 91 CORNELL L. REV. 841, 848 (2006). 264 See WORLD COMMISSION ON THE ETHICS OF SCIENTIFIC KNOWLEDGE AND TECHNOLOGY, THE PRECAUTIONARY PRINCIPLE 13-14 (2005), available at: http://unesdoc.unesco.org/images/0013/001395/139578e.pdf. \n Nations Framework Convention on Climate Change, art. 3(3), May 9, 1992, 31 I.L.M. 849 [hereinafter UNFCCC]. 266 See CLIMATE CHANGE 2007: SYNTHESIS REPORT. CONTRIBUTION OF WORKING GROUPS I, II AND III TO THE FOURTH ASSESSMENT REPORT OF THE INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE 27 (Rajendra K. Pachauri & Andy Reisinger, eds.). This rendition of the precautionary principle originated in the 1992 Rio Declaration on Environment and Development. See United Nations Rio Declaration on Environment and Development, Principle 15, June 13, 1992, 31 I.L.M. 874 [hereinafter Rio Declaration]. 267 UNFCCC, supra note 267, at art. 3(3). 268 Agreement on the Application of Sanitary and Phytosanitary Measures, art. 5.7, Marrakesh Agreement Establishing the World Trade Organization, Annex 1A, THE LEGAL TEXTS: THE RESULTS OF THE URUGUAY ROUND OF MULTILATERAL TRADE NEGOTIATIONS (1999), 1867 U.N.T.S. 493 [hereinafter SPS Agreement]. 269 Convention on International Trade in Endangered Species of Fauna and Flora, Annex 4(A), Mar. 3, 1973, 993 U.N.T.S. 243 [hereinafter CITES]. entirely. ! 35! \n CENTER FOR TECHNOLOGY ASSESSMENT, PRINCIPLES FOR THE OVERSIGHT OF NANOTECHNOLOGIES AND NANOMATERIALS 1 (2008), available at: www.foeeurope.org/activities/.../Principles_Oversight_Nano.pdf. 280 Annas et al., supra note 85, at 153. 281 Montreal Protocol on Substances that Deplete the Ozone Layer, art. 2.9, Sept. 16, 1987, 1522 U.N.T.S. 3. 282 Daubert v. Merrell Dow Pharmaceuticals, Inc., 113 S. Ct. 2786, 2796 (1993). 283  Id. \n One such example in the United States are the U.S. Court of Appeals for the Federal Circuit, a 3 judge panel that has \"exclusive jurisdiction of appeals in patent-infringement and other patent cases.\" POSNER, supra note 75, at 210-211. 287 See id. at 208. 288 LYLE GLOWKA & LAWRENCE C. CHRISTY, LAW AND MODERN BIOTECHOLOGY 52 (2004). \n 289 See e.g. Carl Brunch & Meg Filbey, Emerging Global Norms of Public Involvement, in THE NEW \"PUBLIC\": THE GLOBALIZATION OF PUBLIC PARTICIPATION 9 (Carl Bruch, ed., 2002). 290 CITES, supra note 269, at art. XI. 291 HODGE ET AL., INTERNATIONAL HANDBOOK ON REGULATING NANOTECHNOLOGIES 566 (2010). 292 Brunch & Filbey, supra note 289, at 7-8.! 293 See supra Section II(4). CERN scientists. ! 40! \n\t\t\t For example, scientists may fear \"reprisals and negative consequences\" for challenging their superiors, or they may not want to squander large financial investments in scientific research. See Eric E. Johnson, Culture and", "date_published": "n/a", "url": "n/a", "filename": "006_international-law.tei.xml", "abstract": "Mankind! is! rapidly! developing! \"emerging! technologies\"! in! the! fields!of!bioengineering,!nanotechnology,!and!artificial!intelligence!that!have! the! potential! to! solve! humanity's! biggest! problems,! such! as! by! curing! all! disease,! extending! human! life,! or! mitigating! massive! environmental! problems! like! climate! change.! However,! if! these! emerging! technologies! are! misused! or! have! an! unintended! negative! effect,! the! consequences! could! be! enormous,!potentially!resulting!in!serious,!global!damage!to!humans!(known! as!\"global!catastrophic!harm\")!or!severe,!permanent!damage!to!the!Earthincluding,! possibly,! human! extinction! (known! as! \"existential! harm\").! The! chances!of!a!global!catastrophic!risk!or!existential!risk!actually!materializing! are! relatively! low,! but! mankind! should! be! careful! when! a! losing! gamble! means! massive! human! death! and! irreversible! harm! to! our! planet.! While! international! law! has! become! an! important! source! of! global! regulation! for! other! global! risks! like! climate! change! and! biodiversity! loss,! emerging! technologies!do!not!fall!neatly!within!existing!international!regimes,!and!thus! any! country! is! more! or! less! free! to! develop! these! potentially! dangerous! technologies! without! practical! safeguards! that! would! curtail! the! risk! of! a! catastrophic!event.!In!light!of!these!problems,!this!paper!serves!to!discuss!the! risks! associated! with! bioengineering,! nanotechnology,! and! artificial! intelligence;! review! the! potential! of! existing! international! law! to! regulate! these!emerging!technologies;!and!propose!an!international!regulatory!regime! that! would! put! the! international! world! in! charge! of! ensuring! that! lowJ probability,!highJrisk!disasters!never!materialize.!!", "id": "6c2933022b4ac3546d16202dd30c0aa8"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "1914085.tei.xml", "abstract": "INCENTIVES IN TEAMS BY THEODORE GROVES' This paper analyzes the problem of inducing the members of an organization to behave as if they formed a team. Considered is a conglomerate-type organization consisting of a set of semi-autonomous subunits that are coordinated by the organization's head. The head's incentive problem is to choose a set of employee compensation rules that will induce his subunit managers to communicate accurate information and take optimal decisions. The main result exhibits a particular set of compensation rules, an optimal incentive structure, that leads to team behavior. Particular attention is directed to the informational aspects of the problem. An extended example of a resource allocation model is discussed and the optimal incentive structure is interpreted in terms of prices charged by the head for resources allocated to the subunits.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Anca Dragan"], "title": "Specifying AI Objectives as a Human-AI Collaboration Problem", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "3306618.3314227.tei.xml", "abstract": "Estimation, planning, control, and learning are giving us robots that can generate good behavior given a specified objective and set of constraints. What I care about is how humans enter this behavior generation picture, and study two complementary challenges: 1) how to optimize behavior when the robot is not acting in isolation, but needs to coordinate or collaborate with people; and 2) what to optimize in order to get the behavior we want. My work has traditionally focused on the former, but more recently I have been casting the latter as a human-robot collaboration problem as well (where the human is the enduser, or even the robotics engineer building the system). Treating it as such has enabled us to use robot actions to gain information; to account for human pedagogic behavior; and to exchange information between the human and the robot via a plethora of communication channels, from external forces that the person physically applies to the robot, to comparison queries, to defining a proxy objective function.", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Jan Leike", "Jessica Taylor", "Benya Fallenstein"], "title": "A Formal Solution to the Grain of Truth Problem", "text": "INTRODUCTION Consider the general setup of multiple reinforcement learning agents interacting sequentially in a known environment with the goal to maximize discounted reward.  1  Each agent knows how the environment behaves, but does not know the other agents' behavior. The natural (Bayesian) approach would be to define a class of possible policies that the other  1  We mostly use the terminology of reinforcement learning. For readers from game theory we provide a dictionary in Table  1 . \n Reinforcement learning Game theory stochastic policy mixed strategy deterministic policy pure strategy agent player multi-agent environment infinite extensive-form game reward payoff/utility (finite) history history infinite history path of play Table  1 : Terminology dictionary between reinforcement learning and game theory. agents could adopt and take a prior over this class. During the interaction, this prior gets updated to the posterior as our agent learns the others' behavior. Our agent then acts optimally with respect to this posterior belief. A famous result for infinitely repeated games states that as long as each agent assigns positive prior probability to the other agents' policies (a grain of truth) and each agent acts Bayes-optimal, then the agents converge to playing an ε-Nash equilibrium  [KL93] . As an example, consider an infinitely repeated prisoners dilemma between two agents. In every time step the payoff matrix is as follows, where C means cooperate and D means defect. C D C 3/4, 3/4 0, 1 D 1, 0 1/4, 1/4 Define the set of policies Π := {π ∞ , π 0 , π 1 , . . .} where policy π t cooperates until time step t or the opponent defects (whatever happens first) and defects thereafter. The Bayes-optimal behavior is to cooperate until the posterior belief that the other agent defects in the time step after the next is greater than some constant (depending on the discount function) and then defect afterwards. Therefore Bayes-optimal behavior leads to a policy from the set Π (regardless of the prior). If both agents are Bayes-optimal with respect to some prior, they both have a grain of truth and therefore they converge to a Nash equilibrium: either they both cooperate forever or after some finite time they both defect forever. Alternating strategies like TitForTat (cooperate first, then play the opponent's last action) are not part of the policy class Π, and adding them to the class breaks the grain of truth property: the Bayes-optimal behavior is no longer in the class. This is rather typical; a Bayesian agent usually needs to be more powerful than its environment  [LH15b] . Until now, classes that admit a grain of truth were known only for small toy examples such as the iterated prisoner's dilemma above  [SLB09, Ch. 7.3 ]. The quest to find a large class admitting a grain of truth is known as the grain of truth problem  [Hut09, Q. 5j ]. The literature contains several impossibility results on the grain of truth problem  [FY01, Nac97, Nac05]  that identify properties that cannot be simultaneously satisfied for classes that allow a grain of truth. In this paper we present a formal solution to multi-agent reinforcement learning and the grain of truth problem in the general setting (Section 3). We assume that our multiagent environment is computable, but it does not need to be stationary/Markov, ergodic, or finite-state  [Hut05] . Our class of policies is large enough to contain all computable (stochastic) policies, as well as all relevant Bayes-optimal policies. At the same time, our class is small enough to be limit computable. This is important because it allows our result to be computationally approximated. In Section 4 we consider the setting where the multi-agent environment is unknown to the agents and has to be learned in addition to the other agents' behavior. A Bayes-optimal agent may not learn to act optimally in unknown multiagent environments even though it has a grain of truth. This effect occurs in non-recoverable environments where taking one wrong action can mean a permanent loss of future value. In this case, a Bayes-optimal agent avoids taking these dangerous actions and therefore will not explore enough to wash out the prior's bias  [LH15a] . Therefore, Bayesian agents are not asymptotically optimal, i.e., they do not always learn to act optimally  [Ors13] . However, asymptotic optimality is achieved by Thompson sampling because the inherent randomness of Thompson sampling leads to enough exploration to learn the entire environment class  [LLOH16] . This leads to our main result: if all agents use Thompson sampling over our class of multi-agent environments, then for every ε > 0 they converge to an ε-Nash equilibrium asymptotically. The central idea to our construction is based on reflective oracles  [FST15, FTC15b] . Reflective oracles are probabilistic oracles similar to halting oracles that answer whether the probability that a given probabilistic Turing machine T outputs 1 is higher than a given rational number p. The oracles are reflective in the sense that the machine T may itself query the oracle, so the oracle has to answer queries about itself. This invites issues caused by self-referential liar paradoxes of the form \"if the oracle says that I return 1 with probability > 1/2, then return 0, else return 1.\" Reflective oracles avoid these issues by being allowed to randomize if the machines do not halt or the rational number is exactly the probability to output 1. We introduce reflective oracles formally in Section 2 and prove that there is a limit computable reflective oracle. \n REFLECTIVE ORACLES \n PRELIMINARIES Let X denote a finite set called alphabet. The set X * := ∞ n=0 X n is the set of all finite strings over the alphabet X , the set X ∞ is the set of all infinite strings over the alphabet X , and the set X ♯ := X * ∪ X ∞ is their union. The empty string is denoted by ǫ, not to be confused with the small positive real number ε. Given a string x ∈ X ♯ , we denote its length by |x|. For a (finite or infinite) string x of length ≥ k, we denote with x 1:k the first k characters of x, and with x <k the first k − 1 characters of x. The notation x 1:∞ stresses that x is an infinite string. \n A function f : X * → R is lower semicomputable iff the set {(x, p) ∈ X * × Q | f (x) > p} is recursively enu- merable. The function f is computable iff both f and −f are lower semicomputable. Finally, the function f is limit computable iff there is a computable function φ such that lim k→∞ φ(x, k) = f (x). The program φ that limit computes f can be thought of as an anytime algorithm for f : we can stop φ at any time k and get a preliminary answer. If the program φ ran long enough (which we do not know), this preliminary answer will be close to the correct one. We use ∆Y to denote the set of probability distributions over Y. A list of notation can be found in Appendix A. \n DEFINITION A semimeasure over the alphabet X is a function ν : X * → [0, 1] such that (i) ν(ǫ) ≤ 1, and (ii) ν(x) ≥ a∈X ν(xa) for all x ∈ X * . In the terminology of measure theory, semimeasures are probability measures on the probability space X ♯ = X * ∪ X ∞ whose σ-algebra is generated by the cylinder sets Γ x := {xz | z ∈ X ♯ } [LV08, Ch. 4.2]. We call a semimeasure (probability) a measure iff equalities hold in (i) and (ii) for all x ∈ X * . Next, we connect semimeasures to Turing machines. The literature uses monotone Turing machines, which naturally correspond to lower semicomputable semimeasures [LV08, Sec. 4.5.2] that describe the distribution that arises when piping fair coin flips into the monotone machine. Here we take a different route. A probabilistic Turing machine is a Turing machine that has access to an unlimited number of uniformly random coin flips. Let T denote the set of all probabilistic Turing machines that take some input in X * and may query an oracle (formally defined below). We take a Turing machine T ∈ T to correspond to a semimeasure λ T where λ T (a | x) is the probability that T outputs a ∈ X when given x ∈ X * as input. The value of λ T (x) is then given by the chain rule λ T (x) := |x| k=1 λ T (x k | x <k ). (1) Thus T gives rise to the set of semimeasures M where the conditionals λ(a | x) are lower semicomputable. In contrast, the literature typically considers semimeasures whose joint probability (1) is lower semicomputable. This set M contains all computable measures. However, M is a proper subset of the set of all lower semicomputable semimeasures because the product (1) is lower semicomputale, but there are some lower semicomputable semimeasures whose conditional is not lower semicomputable [LH15c, Thm. 6]. In the following we assume that our alphabet is binary, i.e., X := {0, 1}. Definition 1 (Oracle). An oracle is a function O : T × {0, 1} * × Q → ∆{0, 1}. Oracles are understood to be probabilistic: they randomly return 0 or 1. Let T O denote the machine T ∈ T when run with the oracle O, and let λ O T denote the semimeasure induced by T O . This means that drawing from λ O T involves two sources of randomness: one from the distribution induced by the probabilistic Turing machine T and one from the oracle's answers. The intended semantics of an oracle are that it takes a query (T, x, p) and returns 1 if the machine T O outputs 1 on input x with probability greater than p when run with the oracle O, i.e., when λ O T (1 | x) > p. Furthermore, the oracle returns 0 if the machine T O outputs 1 on input x with probability less than p when run with the oracle O, i.e., when λ O T (1 | x) < p. To fulfill this, the oracle O has to make statements about itself, since the machine T from the query may again query O. Therefore we call oracles of this kind reflective oracles. This has to be defined very carefully to avoid the obvious diagonalization issues that are caused by programs that ask the oracle about themselves. We impose the following self-consistency constraint. Definition 2 (Reflective Oracle). An oracle O is reflective iff for all queries (T, x, p) ∈ T × {0, 1} * × Q,  (i) λ O T (1 | x) > p implies O(T, x, p) = 1, and 0 1 λ O T (0 | x) λ O T (1 | x) O returns 1 O may randomize O returns 0 (ii) λ O T (0 | x) > 1 − p implies O(T, x, p) = 0. If p under-or overshoots the true probability of λ O T ( • | x), then the oracle must reveal this information. However, in the critical case when p = λ O T (1 | x), the oracle is allowed to return anything and may randomize its result. Furthermore, since T might not output any symbol, it is possible that λ O T (0 | x) + λ O T (1 | x) < 1. In this case the oracle can reassign the non-halting probability mass to 0, 1, or randomize; see Figure  1 . Example 3 (Reflective Oracles and Diagonalization). Let T ∈ T be a probabilistic Turing machine that outputs 1 − O(T, ǫ, 1/2) (T can know its own source code by quining [Kle52, Thm. 27]). In other words, T queries the oracle about whether it is more likely to output 1 or 0, and then does whichever the oracle says is less likely. In this case we can use an oracle O(T, ǫ, 1/2) := 1/2 (answer 0 or 1 with equal probability), which implies λ O T (1 | ǫ) = λ O T (0 | ǫ) = 1/2, so the conditions of Definition 2 are satisfied. In fact, for this machine T we must have O(T, ǫ, 1/2) = 1/2 for all reflective oracles O. ♦ The following theorem establishes that reflective oracles exist. \n Theorem 4 ([FTC15a, App. B]). There is a reflective oracle. Definition 5 (Reflective-Oracle-Computable). A semimeasure is called reflective-oracle-computable iff it is computable on a probabilistic Turing machine with access to a reflective oracle. For any probabilistic Turing machine T ∈ T we can complete the semimeasure λ O T ( • | x) into a reflective- oracle-computable measure λ O T ( • | x): Using the oracle O and a binary search on the parameter p we search for the crossover point p where O(T, x, p) goes from returning 1 to returning 0. The limit point p * ∈ R of the binary search is random since the oracle's answers may be random. But the main point is that the expectation of p * exists, so λ O T (1 | x) = E[p * ] = 1 − λ O T (0 | x) for all x ∈ X * . Hence λ O T is a measure. Moreover, if the oracle is reflective, then λ O T (x) ≥ λ O T (x) for all x ∈ X * . In this sense the oracle O can be viewed as a way of 'completing' all semimeasures λ O T to measures by arbitrarily assigning the non-halting probability mass. If the oracle O is reflective this is consistent in the sense that Turing machines who run other Turing machines will be completed in the same way. This is especially important for a universal machine that runs all other Turing machines to induce a Solomonoffstyle distribution. \n A LIMIT COMPUTABLE REFLECTIVE ORACLE The proof of Theorem 4 given in [FTC15a, App. B] is nonconstructive and uses the axiom of choice. In Section 2.4 we give a constructive proof for the existence of reflective oracles and show that there is one that is limit computable. \n Theorem 6 (A Limit Computable Reflective Oracle). There is a reflective oracle that is limit computable. This theorem has the immediate consequence that reflective oracles cannot be used as halting oracles. At first, this result may seem surprising: according to the definition of reflective oracles, they make concrete statements about the output of probabilistic Turing machines. However, the fact that the oracles may randomize some of the time actually removes enough information such that halting can no longer be decided from the oracle output. \n Corollary 7 (Reflective Oracles are not Halting Oracles). There is no probabilistic Turing machine T such that for every prefix program p and every reflective oracle O, we have that λ O T (1 | p) > 1/2 if p halts and λ O T (1 | p) < 1/2 otherwise. Proof. Assume there was such a machine T and let O be the limit computable oracle from Theorem 6. Since O is reflective we can turn T into a deterministic halting oracle by calling O(T, p, 1/2) which deterministically returns 1 if p halts and 0 otherwise. Since O is limit computable, we can finitely compute the output of O on any query to arbitrary finite precision using our deterministic halting oracle. We construct a probabilistic Turing machine T ′ that uses our halting oracle to compute (rather than query) the oracle O on (T ′ , ǫ, 1/2) to a precision of 1/3 in finite time. If O(T ′ , ǫ, 1/2) ± 1/3 > 1/2, the machine T ′ outputs 0, otherwise T ′ outputs 1. Since our halting oracle is entirely deterministic, the output of T ′ is entirely deterministic as well (and T ′ always halts), so λ O T ′ (0 | ǫ) = 1 or λ O T ′ (1 | ǫ) = 1. Therefore O(T ′ , ǫ, 1/2) = 1 or O(T ′ , ǫ, 1/2) = 0 because O is reflective. A precision of 1/3 is enough to tell them apart, hence T ′ returns 0 if O(T ′ , ǫ, 1/2) = 1 and T ′ re- turns 1 if O(T ′ , ǫ, 1/2) = 0. This is a contradiction. A similar argument can also be used to show that reflective oracles are not computable. \n PROOF OF THEOREM 6 The idea for the proof of Theorem 6 is to construct an algorithm that outputs an infinite series of partial oracles converging to a reflective oracle in the limit. The set of queries is countable, so we can assume that we have some computable enumeration of it: T × {0, 1} * × Q =: {q 1 , q 2 , . . .} Definition 8 (k-Partial Oracle). A k-partial oracle Õ is function from the first k queries to the multiples of 2 −k in [0, 1]: Õ : {q 1 , q 2 , . . . , q k } → {n2 −k | 0 ≤ n ≤ 2 k } Definition 9 (Approximating an Oracle). A k-partial or- acle Õ approximates an oracle O iff |O(q i ) − Õ(q i )| ≤ 2 −k−1 for all i ≤ k. Let k ∈ N, let Õ be a k-partial oracle, and let T ∈ T be an oracle machine. The machine T Õ that we get when we run T with the k-partial oracle Õ is defined as follows (this is with slight abuse of notation since k is taken to be understood implicitly). 1. Run T for at most k steps. 2. If T calls the oracle on q i for i ≤ k, (a) return 1 with probability Õ(q i ) − 2 −k−1 , (b) return 0 with probability 1 − Õ(q i ) − 2 −k−1 , and (c) halt otherwise. 3. If T calls the oracle on q j for j > k, halt. Furthermore, we define λ Õ T analogously to λ O T as the distribution generated by the machine T Õ. Lemma 10. If a k-partial oracle Õ approximates a re- flective oracle O, then λ O T (1 | x) ≥ λ Õ T (1 | x) and λ O T (0 | x) ≥ λ Õ T (0 | x) for all x ∈ {0, 1} * and all T ∈ T . Proof. This follows from the definition of T Õ : when running T with Õ instead of O, we can only lose probability mass. If T makes calls whose index is > k or runs for more than k steps, then the execution is aborted and no further output is generated. If T makes calls whose index i ≤ k, then Õ(q i ) − 2 −k−1 ≤ O(q i ) since Õ approximates O. Therefore the return of the call q i is underestimated as well. Definition 11 (k-Partially Reflective). A k-partial oracle Õ is k-partially reflective iff for the first k queries (T, x, p) • λ Õ T (1 | x) > p implies Õ(T, x, p) = 1, and • λ Õ T (0 | x) > 1 − p implies Õ(T, x, p) = 0. It is important to note that we can check whether a k-partial oracle is k-partially reflective in finite time by running all machines T from the first k queries for k steps and tallying up the probabilities to compute λ Õ T . Lemma 12. If O is a reflective oracle and Õ is a k-partial oracle that approximates O, then Õ is k-partially reflective. Lemma 12 only holds because we use semimeasures whose conditionals are lower semicomputable. Proof. Assuming λ Õ T (1 | x) > p we get from Lemma 10 that λ O T (1 | x) ≥ λ Õ T (1 | x) > p. Thus O(T, x, p) = 1 because O is reflective. Since Õ approximates O, we get 1 = O(T, x, p) ≤ Õ(T, x, p)+ 2 −k−1 , and since Õ assigns values in a 2 −k -grid, it follows that Õ(T, x, p) = 1. The second implication is proved analogously. \n Definition 13 (Extending Partial Oracles ). A k + 1-partial oracle Õ′ extends a k-partial oracle Õ iff | Õ(q i )− Õ′ (q i )| ≤ 2 −k−1 for all i ≤ k. Lemma 14. There is an infinite sequence of partial oracles ( Õk ) k∈N such that for each k, Õk is a k-partially reflective k-partial oracle and Õk+1 extends Õk . Proof. By Theorem 4 there is a reflective oracle O. For every k, there is a canonical k-partial oracle Õk that approximates O: restrict O to the first k queries and for any such query q pick the value in the 2 −k -grid which is closest to O(q). By construction, Õk+1 extends Õk and by Lemma 12, each Õk is k-partially reflective. Lemma 15. If the k + 1-partial oracle Õk+1 extends the k-partial oracle Õk , then λ Õk+1 T (1 | x) ≥ λ Õk T (1 | x) and λ Õk+1 T (0 | x) ≥ λ Õk T (0 | x) for all x ∈ {0, 1} * and all T ∈ T . Proof. T Õk+1 runs for one more step than T Õk , can answer one more query and has increased oracle precision. Moreover, since Õk+1 extends Õk , we have | Õk+1 (q i ) − Õk (q i )| ≤ 2 −k−1 , and thus Õk+1 (q i )−2 −k−1 ≥ Õk (q i )− 2 −k . Therefore the success to answers to the oracle calls (case 2(a) and 2(b)) will not decrease in probability. Now everything is in place to state the algorithm that constructs a reflective oracle in the limit. It recursively traverses a tree of partial oracles. The tree's nodes are the partial oracles; level k of the tree contains all k-partial oracles. There is an edge in the tree from the k-partial oracle Õk to the i-partial oracle Õi if and only if i = k + 1 and Õi extends Õk . For every k, there are only finitely many k-partial oracles, since they are functions from finite sets to finite sets. In particular, there are exactly two 1-partial oracles (so the search tree has two roots). Pick one of them to start with, and proceed recursively as follows. Given a k-partial oracle Õk , there are finitely many (k + 1)-partial oracles that extend Õk (finite branching of the tree). Pick one that is (k + 1)partially reflective (which can be checked in finite time). If there is no (k + 1)-partially reflective extension, backtrack. By Lemma 14 our search tree is infinitely deep and thus the tree search does not terminate. Moreover, it can backtrack to each level only a finite number of times because at each level there is only a finite number of possible extensions. Therefore the algorithm will produce an infinite sequence of partial oracles, each extending the previous. Because of finite backtracking, the output eventually stabilizes on a sequence of partial oracles Õ1 , Õ2 , . . .. By the following lemma, this sequence converges to a reflective oracle, which concludes the proof of Theorem 6. Lemma 16. Let Õ1 , Õ2 , . . . be a sequence where Õk is a k-partially reflective k-partial oracle and Õk+1 extends Õk for all k ∈ N. Let O := lim k→∞ Õk be the pointwise limit. Then Proof. First note that the pointwise limit must exists because | Õk (q i ) − Õk+1 (q i )| ≤ 2 −k−1 by Definition 13.  (a) λ Õk T (1 | x) → λ O T (1 | x) and λ Õk T (0 | x) → λ O T (0 | x) as k → ∞ for all x ∈ {0, \n A GRAIN OF TRUTH \n NOTATION In reinforcement learning, an agent interacts with an environment in cycles: at time step t the agent chooses an action a t ∈ A and receives a percept e t = (o t , r t ) ∈ E consisting of an observation o t ∈ O and a real-valued reward r t ∈ R; the cycle then repeats for t + 1. A history is an element of (A × E) * . In this section, we use ae ∈ A × E to denote one interaction cycle, and ae <t to denote a history of length t − 1. We fix a discount function γ : N → R with γ t ≥ 0 and ∞ t=1 γ t < ∞. The goal in reinforcement learning is to maximize discounted rewards ∞ t=1 γ t r t . The discount normalization factor is defined as Γ t := ∞ k=t γ k . The effective horizon H t (ε) is a horizon that is long enough to encompass all but an ε of the discount function's mass: H t (ε) := min{k | Γ t+k /Γ t ≤ ε} (2) A policy is a function π : (A × E) * → ∆A that maps a history ae <t to a distribution over actions taken after seeing this history. The probability of taking action a after history ae <t is denoted with π(a | ae <t ). An environment is a function ν : (A × E) * × A → ∆E where ν(e | ae <t a t ) denotes the probability of receiving the percept e when taking the action a t after the history ae <t . Together, a policy π and an environment ν give rise to a distribution ν π over histories. Throughout this paper, we make the following assumptions. Assumption 17. (a) Rewards are bounded between 0 and 1. (b) The set of actions A and the set of percepts E are both finite. (c) The discount function γ and the discount normalization factor Γ are computable. Definition 18 (Value Function). The value of a policy π in an environment ν given history ae <t is defined recursively as V π ν (ae <t ) := a∈A π(a | ae <t )V π ν (ae <t a) and V π ν (ae <t a t ) := 1 Γ t et∈E ν(e t | ae <t a t ) γ t r t + Γ t+1 V π ν (ae 1:t ) if Γ t > 0 and V π ν (ae <t a t ) := 0 if Γ t = 0. The optimal value is defined as V * ν (ae <t ) := sup π V π ν (ae <t ). Definition 19 (Optimal Policy). A policy π is optimal in environment ν (ν-optimal) iff for all histories ae <t ∈ (A × E) * the policy π attains the optimal value: V π ν (ae <t ) = V * ν (ae <t ). We assumed that the discount function is summable, rewards are bounded (Assumption 17a), and actions and percepts spaces are both finite (Assumption 17b). Therefore an optimal deterministic policy exists for every environment [LH14, Thm. 10]. \n REFLECTIVE BAYESIAN AGENTS Fix O to be a reflective oracle. From now on, we assume that the action space A := {α, β} is binary. We can treat computable measures over binary strings as environments: the environment ν corresponding to a probabilistic Turing machine T ∈ T is defined by ν(e t | ae <t a t ) := λ O T (y | x) = k i=1 λ O T (y i | xy 1 . . . y i−1 ) where y 1:k is a binary encoding of e t and x is a binary encoding of ae <t a t . The actions a 1:∞ are only contextual, and not part of the environment distribution. We define ν(e <t | a <t ) := t−1 k=1 ν(e k | ae <k ). Let T 1 , T 2 , . . . be an enumeration of all probabilistic Turing machines in T . We define the class of reflective environments M O refl := λ O T1 , λ O T2 , . . . . This is the class of all environments computable on a probabilistic Turing machine with reflective oracle O, that have been completed from semimeasures to measures using O. T . This is the distribution that is used to compute the posterior. There are no cyclic dependencies since ξ is called on the shorter history ae <t . We arrive at the following statement. \n Analogously to AIXI \n Proposition 20 (Bayes is in the Class ). ξ ∈ M O refl . Moreover  (µ) > 0, V π µ (ae <t ) − V π ξ (ae <t ) → 0 µ π -almost surely as t → ∞. \n REFLECTIVE-ORACLE-COMPUTABLE POLICIES This subsection is dedicated to the following result that was previously stated but not proved in [FST15, Alg. 6]. It contrasts results on arbitrary semicomputable environments where optimal policies are not limit computable [LH15b, Sec. 4]. Theorem 22 (Optimal Policies are Oracle Computable). For every ν ∈ M O refl , there is a ν-optimal (stochastic) policy π * ν that is reflective-oracle-computable. Note that even though deterministic optimal policies always exist, those policies are typically not reflectiveoracle-computable. To prove Theorem 22 we need the following lemma. Lemma 23 (Reflective-Oracle-Computable Optimal Value Function). For every environment ν ∈ M O refl the optimal value function V * ν is reflective-oracle-computable. Proof. This proof follows the proof of  [LH15b, Cor. 13 ]. We write the optimal value explicitly as V * ν (ae <t ) = 1 Γ t lim m→∞ max aet:m m k=t γ k r k k i=t ν(e i | ae <i ), (5) where max denotes the expectimax operator: For a fixed m, all involved quantities are reflective-oraclecomputable. Moreover, this quantity is monotone increasing in m and the tail sum from m + 1 to ∞ is bounded by Γ m+1 which is computable according to Assumption 17c and converges to 0 as m → ∞. Therefore we can enumerate all rationals above and below V * ν . Proof of Theorem 22. According to Lemma 23 the optimal value function V * ν is reflective-oracle-computable. Hence there is a probabilistic Turing machine T such that λ O T (1 | ae <t ) = V * ν (ae <t α) − V * ν (ae <t β) + 1 /2. We define a policy π that takes action α if O(T, ae <t , 1/2) = 1 and action β if O(T, ae <t , 1/2) = 0. (This policy is stochastic because the answer of the oracle O is stochastic.) It remains to show that π is a ν-optimal policy. If V * ν (ae <t α) > V * ν (ae <t β), then λ O T (1 | ae <t ) > 1/2, thus O(T, ae <t , 1/2) = 1 since O is reflective, and hence π takes action α. Conversely, if V * ν (ae <t α) < V * ν (ae <t β), then λ O T (1 | ae <t ) < 1/2, thus O(T, ae <t , 1/2) = 0 since O is reflective, and hence π takes action β. Lastly, if V * ν (ae <t α) = V * ν (ae <t β) , then both actions are optimal and thus it does not matter which action is returned by policy π. (This is the case where the oracle may randomize.) \n SOLUTION TO THE GRAIN OF TRUTH PROBLEM Together, Proposition 20 and Theorem 22 provide the necessary ingredients to solve the grain of truth problem. Corollary 24 (Solution to the Grain of Truth Problem). For every lower semicomputable prior w ∈ ∆M O refl the Bayesoptimal policy π * ξ is reflective-oracle-computable where ξ is the Bayes-mixture corresponding to w defined in (3). Proof. From Proposition 20 and Theorem 22. \n Hence the environment class M O refl contains any reflectiveoracle-computable modification of the Bayes-optimal policy π * ξ . In particular, this includes computable multi-agent environments that contain other Bayesian agents over the class M O refl . So any Bayesian agent over the class M O refl has a grain of truth even though the environment may contain other Bayesian agents of equal power. We proceed to sketch the implications for multi-agent environments in the next section. \n MULTI-AGENT ENVIRONMENTS This section summarizes our results for multi-agent systems. The proofs can be found in  [Lei16] . \n SETUP In a multi-agent environment there are n agents each taking sequential actions from the finite action space A. and ae <t = a 1 e 1 . . . a t−1 e t−1 . We define a multi-agent environment as a function σ : (A n × E n ) * × A n → ∆(E n ). The agents are given by n policies π 1 , . . . , π n where π i : (A × E) * → ∆A. Together they specify the history distribution σ π1:n (ǫ) : = 1 σ π1:n (ae 1:t ) : = σ π1:n (ae <t a t )σ(e t | ae <t a t ) σ π1:n (ae <t a t ) : = σ π1:n (ae <t ) n i=1 π i (a i t | ae i <t ). Each agent i acts in a subjective environment σ i given by joining the multi-agent environment σ with the policies π 1 , . . . , π i−1 , π i+1 , . . . , π n by marginalizing over the histories that π i does not see. Together with policy π i , the environment σ i yields a distribution over the histories of agent i σ πi i (ae i <t ) := ae j <t ,j =i σ π1:n (ae <t ). We get the definition of the subjective environment σ i with the identity σ i (e i t | ae i <t a i t ) := σ πi i (e i t | ae i <t a i t ). It is crucial to note that the subjective environment σ i and the policy π i are ordinary environments and policies, so we can use the formalism from Section 3. Our definition of a multi-agent environment is very general and encompasses most of game theory. It allows for cooperative, competitive, and mixed games; infinitely repeated games or any (infinite-length) extensive form games with finitely many players. The policy π i is an ε-best response after history ae i <t iff V * σi (ae i <t ) − V πi σi (ae i <t ) < ε. If at some time step t, all agents' policies are ε-best responses, we have an ε-Nash equilibrium. The property of multi-agent systems that is analogous to asymptotic optimality is convergence to an ε-Nash equilibrium. \n INFORMED REFLECTIVE AGENTS Let σ be a multi-agent environment and let π * σ1 , . . . π * σn be such that for each i the policy π * σi is an optimal policy in agent i's subjective environment σ i . At first glance this seems ill-defined: The subjective environment σ i depends on each other policy π * σj for j = i, which depends on the subjective environment σ j , which in turn depends on the policy π * σi . However, this circular definition actually has a well-defined solution. Theorem 25 (Optimal Multi-Agent Policies). For any reflective-oracle-computable multi-agent environment σ, the optimal policies π * σ1 , . . . , π * σn exist and are reflectiveoracle-computable. Note the strength of Theorem 25: each of the policies π * σi is acting optimally given the knowledge of everyone else's policies. Hence optimal policies play 0-best responses by definition, so if every agent is playing an optimal policy, we have a Nash equilibrium. Moreover, this Nash equilibrium is also a subgame perfect Nash equilibrium, because each agent also acts optimally on the counterfactual histories that do not end up being played. In other words, Theorem 25 states the existence and reflectiveoracle-computability of a subgame perfect Nash equilibrium in any reflective-oracle-computable multi-agent environment. From Theorem 6 we then get that these subgame perfect Nash equilibria are limit computable. Corollary 26 (Solution to Computable Multi-Agent Environments). For any computable multi-agent environment σ, the optimal policies π * σ1 , . . . , π * σn exist and are limit computable. \n LEARNING REFLECTIVE AGENTS Since our class M O refl solves the grain of truth problem, the result by Kalai and Lehrer  [KL93]  immediately implies that for any Bayesian agents π 1 , . . . , π n interacting in an infinitely repeated game and for all ε > 0 and all i ∈ {1, . . . , n} there is almost surely a t 0 ∈ N such that for all t ≥ t 0 the policy π i is an ε-best response. However, this hinges on the important fact that every agent has to know the game and also that all other agents are Bayesian agents. Otherwise the convergence to an ε-Nash equilibrium may fail, as illustrated by the following example. At the core of the following construction is a dogmatic prior [LH15a, Sec. 3.2]. A dogmatic prior assigns very high probability to going to hell (reward 0 forever) if the agent deviates from a given computable policy π. For a Bayesian agent it is thus only worth deviating from the policy π if the agent thinks that the prospects of following π are very poor already. This implies that for general multi-agent environments and without additional assumptions on the prior, we cannot prove any meaningful convergence result about Bayesian agents acting in an unknown multi-agent environment. Example 27 (Reflective Bayesians Playing Matching Pennies). In the game of matching pennies there are two agents (n = 2), and two actions A = {α, β} representing the two sides of a penny. In each time step agent 1 wins if the two actions are identical and agent 2 wins if the two actions are different. The payoff matrix is as follows. α β α 1,0 0,1 β 0,1 1,0 We use E = {0, 1} to be the set of rewards (observations are vacuous) and define the multi-agent environment σ to give reward 1 to agent 1 iff a 1 t = a 2 t (0 otherwise) and reward 1 to agent 2 iff a 1 t = a 2 t (0 otherwise). Note that neither agent knows a priori that they are playing matching pennies, nor that they are playing an infinite repeated game with one other player. Let π 1 be the policy that takes the action sequence (ααβ) ∞ and let π 2 := π α be the policy that always takes action α. The average reward of policy π 1 is 2/3 and the average reward of policy π 2 is 1/3. Let ξ be a universal mixture (3). By Lemma 21, V π1 ξ → c 1 ≈ 2/3 and V π2 ξ → c 2 ≈ 1/3 almost surely when following policies (π 1 , π 2 ). Therefore there is an ε > 0 such that V π1 ξ > ε and V π2 ξ > ε for all time steps. Now we can apply [LH15a, Thm. 7] to conclude that there are (dogmatic) mixtures ξ ′ 1 and ξ ′ 2 such that π * ξ ′ 1 always follows policy π 1 and π * ξ ′ 2 always follows policy π 2 . This does not converge to a (ε-)Nash equilibrium. ♦ A policy π is asymptotically optimal in mean in an environment class M iff for all µ ∈ M E π µ V * µ (ae <t ) − V π µ (ae <t ) → 0 as t → ∞ (6) where E π µ denotes the expectation with respect to the probability distribution µ π over histories generated by policy π acting in environment µ. Asymptotic optimality stands out because it is currently the only known nontrivial objective notion of optimality in general reinforcement learning  [LH15a] . The following theorem is the main convergence result. It states that for asymptotically optimal agents we get convergence to ε-Nash equilibria in any reflective-oraclecomputable multi-agent environment. Theorem 28 (Convergence to Equilibrium). Let σ be an reflective-oracle-computable multi-agent environment and let π 1 , . . . , π n be reflective-oracle-computable policies that are asymptotically optimal in mean in the class M O refl . Then for all ε > 0 and all i ∈ {1, . . . , n} the σ π1:n -probability that the policy π i is an ε-best response converges to 1 as t → ∞. In contrast to Theorem 25 which yields policies that play a subgame perfect equilibrium, this is not the case for Theorem 28: the agents typically do not learn to predict off-policy and thus will generally not play ε-best responses in the counterfactual histories that they never see. This weaker form of equilibrium is unavoidable if the agents do not know the environment because it is impossible to learn the parts that they do not interact with. Together with Theorem 6 and the asymptotic optimality of the Thompson sampling policy [LLOH16, Thm. 4] that is reflective-oracle computable we get the following corollary. Corollary 29 (Convergence to Equilibrium). There are limit computable policies π 1 , . . . , π n such that for any computable multi-agent environment σ and for all ε > 0 and all i ∈ {1, . . . , n} the σ π1:n -probability that the policy π i is an ε-best response converges to 1 as t → ∞. \n DISCUSSION This paper introduced the class of all reflective-oraclecomputable environments M O refl . This class solves the grain of truth problem because it contains (any computable modification of) Bayesian agents defined over M O refl : the optimal agents and Bayes-optimal agents over the class are all reflective-oracle-computable (Theorem 22 and Corollary 24). If the environment is unknown, then a Bayesian agent may end up playing suboptimally (Example 27). However, if each agent uses a policy that is asymptotically optimal in mean (such as the Thompson sampling policy  [LLOH16] ) then for every ε > 0 the agents converge to an ε-Nash equilibrium (Theorem 28 and Corollary 29). Our solution to the grain of truth problem is purely theoretical. However, Theorem 6 shows that our class M O refl allows for computable approximations. This suggests that practical approaches can be derived from this result, and reflective oracles have already seen applications in one-shot games  [FTC15b] . Figure 1 : 1 Figure 1: Answer options of a reflective oracle O for the query (T, x, p); the rational p ∈ [0, 1] falls into one of the three regions above. The values of λ O T (0 | x) and λ O T (1 | x) are depicted as the length of the line segment under which they are written. \n 1} * and all T ∈ T , and (b) O is a reflective oracle. \n (a) Since Õk+1 extends Õk , each Õk approximates O. Let x ∈ {0, 1} * and T ∈ T and consider the sequence a k := λ Õk T (1 | x) for k ∈ N. By Lemma 15, a k ≤ a k+1 , so the sequence is monotone increasing. By Lemma 10, a k ≤ λ O T (1 | x), so the sequence is bounded. Therefore it must converge. But it cannot converge to anything strictly below λ O T (1 | x) by the definition of T O . (b) By definition, O is an oracle; it remains to show that O is reflective. Let q i = (T, x, p) be some query. If p < λ O T (1 | x), then by (a) there is a k large enough such that p < λ Õt T (1 | x) for all t ≥ k. For any t ≥ max{k, i}, we have Õt (T, x, p) = 1 since Õt is t-partially reflective. Therefore 1 = lim k→∞ Õk (T, x, p) = O(T, x, p). The case 1 − p < λ O T (0 | x) is analogous. \n [Hut05], we define a Bayesian mixture over the class M O refl . Let w ∈ ∆M O refl be a lower semicomputable prior probability distribution on M O refl . Possible choices for the prior include the Solomonoff prior w λ O T := 2 −K(T ) , where K(T ) denotes the length of the shortest input to some universal Turing machine that encodes T [Sol78]. 2 We define the corresponding Bayesian mixture ξ(e t | ae <t a t ) := ν∈M O refl w(ν | ae <t )ν(e t | ae <t a t ) (3) where w(ν | ae <t ) is the (renormalized) posterior, w(ν | ae <t ) := w(ν) ν(e <t | a <t ) ξ(e <t | a <t ) .(4)The mixture ξ is lower semicomputable on an oracle Turing machine because the posterior w( • | ae <t ) is lower semicomputable. Hence there is an oracle machine T such that ξ = λ O T . We define its completion ξ := λ O T as the completion of λ O \n , since O is reflective, we have that ξ dominates all environments ν ∈ M O refl : ξ(e 1:t | a 1:t ) = ξ(e t | ae <t a t )ξ(e <t | a <t ) ≥ ξ(e t | ae <t a t )ξ(e <t | a <t ) = ξ(e <t | a <t ) | ae <t )ν(e t | ae <t a t ) = ξ(e <t | a <t ) ν∈M O refl refl w(ν ν∈M O w(ν) ν(e <t | a <t ) ξ(e <t | a <t ) ν(e t | ae <t a t ) = w(ν)ν(e 1:t | a 1:t ) ν∈M O refl ≥ w(ν)ν(e 1:t | a 1:t ) This property is crucial for on-policy value convergence. Lemma 21 (On-Policy Value Convergence [Hut05, Thm. 5.36]). For any policy π and any environment µ ∈ M O refl with w \n In each time step t = 1, 2, . . ., the environment receives action a i a 1 t agent π 1 e 1 t a 2 t agent π 2 e 2 t multi-agent environment σ . . . a n t agent π n e n t Figure 2: Agents π 1 , . . . , π n interacting in a multi-agent environment. each agent. Each percept e i t = (o i t , r i t ) contains an obser-vation o i t and a reward r i t ∈ [0, 1]. Importantly, agent i only sees its own action a i t and its own percept e i t (see Figure 2). We use the shorthand notation a t := (a 1 t , . . . , a n t ) and e t := (e 1 t , . . . , e n t ) and denote ae i <t = a i 1 e i 1 . . . a i t−1 e i t−1 t from agent i and outputs n percepts e 1 t , . . . , e n t ∈ E, one for \n\t\t\t Technically, the lower semicomputable prior 2 −K(T ) is only a semidistribution because it does not sum to 1. This turns out to be unimportant.", "date_published": "n/a", "url": "n/a", "filename": "1609.05058.tei.xml", "abstract": "A Bayesian agent acting in a multi-agent environment learns to predict the other agents' policies if its prior assigns positive probability to them (in other words, its prior contains a grain of truth). Finding a reasonably large class of policies that contains the Bayes-optimal policies with respect to this class is known as the grain of truth problem. Only small classes are known to have a grain of truth and the literature contains several related impossibility results. In this paper we present a formal and general solution to the full grain of truth problem: we construct a class of policies that contains all computable policies as well as Bayes-optimal policies for every lower semicomputable prior over the class. When the environment is unknown, Bayes-optimal agents may fail to act optimally even asymptotically. However, agents based on Thompson sampling converge to play ε-Nash equilibria in arbitrary unknown computable multi-agent environments. While these results are purely theoretical, we show that they can be computationally approximated arbitrarily closely.", "id": "6bfd047d0d1732c0cedc5595e0bd3841"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Fernando Martínez-Plumed", "Bao Sheng Loe", "Peter Flach", "Seán Ó H Éigeartaigh", "Karina Vold", "José Hernández-Orallo"], "title": "The Facets of Artificial Intelligence: A Framework to Track the Evolution of AI", "text": "Introduction \"What is AI?\" has been a common question from the inception of the discipline in the 1950s  [McCarthy et al., 2006; Moor, 2006; Solomonoff, 2017]  until the end of the last century  [Lehman-Wilzig, 1981; Fetzer, 1990; McCarthy, 1998 ]. In the twenty-first century, the discipline is not only welldeveloped but it is often said that this is the age of AI  [Mc-Corduck, 2004] . AI is set to pervade and transform every aspect of life. In a way, this is no different from what computer science has already been doing, creating computerised, digital and virtual versions of almost everything, with AI now introducing new adjectives such as 'intelligent', 'smart' and 'cognitive' to almost every process or gadget, from medical diagnosis to personal assistants. This expected expansion and intertwining with every other research discipline and aspect of life is pushing the contours of AI in many directions. However, unlike computer science, which is based on wellestablished models of computation that integrate hardware and software, AI has evolved with a more fluid definition, primarily because of our varied conceptions of intelligence. When looking at the definitions of (artificial) intelligence (see, e.g.,  [Legg and Hutter, 2007] , for a compendium), we see that definitions can be categorised according to two distinct dimensions, following  [Russell and Norvig, 2009] . First, we can characterise intelligence in terms of \"thinking\" (process-oriented) or \"acting\" (goal-oriented). Second, we can characterise intelligence taking humans as a reference or looking for a more abstract or universal reference (such as rationality). These two dimensions are summarised in Table  1 . Not all definitions can be clearly classified according to this table. For instance, Minsky's famous definition of AI, as the \"science of making machines capable of performing tasks that would require intelligence if done by  [humans] \"  [Minsky, 1968] , uses humans as a reference, so it would be located on the left of the table, but still somewhere between the top and bottom part of the table as it focuses on processes (i.e., thinking) for humans and tasks (i.e., acting) for machines This suggests that we can look at these dimensions in a more nuanced, continuous way, as facets rather than discrete categories, to look at the evolution of AI as a discipline. For instance, has AI been more focused towards \"thinking\" (and hence processes or techniques) or more focused towards \"acting' (and hence tasks and applications)? Is it more or less influenced by human intelligence (using human processes and the tasks humans can actually solve) or is the discipline going in a direction of a more abstract or universal characterisation? In this paper, we will develop these and other dimensions into facets to characterise the object of AI, i.e., the AI systems and services, such as generality, location and embodiment, and the subject of AI, such as paradigms, actors, character and nature, as a discipline. With these facets we will perform a qualitative and quantitative analysis of the evolution of AI. We will base our analysis on evidence as much as possible, looking at data from scientific venues, reports, surveys and other sources. At the end of the paper, we will take a more principled stance and we will discuss how to extrapolate these Thinking Humanly Thinking Rationally Acting Humanly Acting Rationally Table  1 : Categories of (artificial) intelligence definitions, according to the two binary dimensions in  [Russell and Norvig, 2009, Fig. 1.1] . trends or identify what kinds of criteria are necessary to establish AI contours that can be more stable and useful. The contributions of this paper are a set of well-structured facets to analyse the location and contours of AI. This is complemented by substantial evidence collected from several sources, such as 20 years of the IJCAI and AAAI proceedings and the whole AI topics database 1 . All the datasets, plots and code to scrape and process this data are made publicly available (see footnote 7). There are several reasons why using clear criteria such as the facets and edges are helpful for defining AI, how it has evolved and what it is likely to be in the future. First, internally, the research community needs clear criteria to determine what is in or out of scope, for conferences, journals, funding and hiring. Second, policy makers are considering ways of regulating AI, but wrestle with the problem of defining what systems are actually AI. Third, different terms are being used to capture the same subparts or forms of AI, such as artificial general intelligence (AGI), machine intelligence, cognitive computing, computational intelligence, soft computing, etc. Without a clear structure about AI, it is difficult to determine whether they are part, they overlap or they are simply redundant. Fourth, some areas, such as machine learning, are taking a more relevant role in AI, but they are also intertwined with areas such as statistics, optimisation or probability theory, which were not always considered near the contours of AI. Fifth, along the history of AI there has been rise and decline of interest and research towards the different AI paradigms, techniques and approaches. \n Background Disciplines are commonly analysed historically, and AI is not an exception. A history of a discipline usually emphasises the problems, progress and prospects, but not necessarily delineates its contours. For instance, there are several excellent accounts of the history of AI  [McCorduck, 2004; Buchanan, 2005; Nilsson, 2009; Boden, 2016] . Some of them cover AI from a philosophical perspective. However, given the implications of AI for the interpretation of the human mind, the analysis of AI as a discipline (as usual from the viewpoint of philosophy -or methodology-of science) is not commonly done in terms of its external and internal contours. As a result, several key questions remain: what are the criteria to recognise that an entity is part of AI? Furthermore, how can we recognise the internal subdisciplines in AI? One possible approach to this is to determine the nature and contours of AI by its common use. While this may be a good approach for evaluating progress as a whole or for a few benchmarks 2 , the analysis of subdisciplines by their popularity may be prone to many terminological confusions and many vested interests, with the risk of having characterisations that are very volatile, such as big data. Bibliometric approaches are a common tool to analyse disciplines, but the focus is usually put on impacts per author, venue, location or institution. Sometimes, bibliometrics studies disciplines and subdisciplines. For instance, Scimago pro-  vides a way of looking at the \"shape of science\" 3 where one can locate AI and some of its subareas in terms of their internal and external relations. Provided with a set of tags, bibliometrics can study how frequent several tags are in published papers (including titles, keywords or abstracts). For instance,  [Niu et al., 2016]  includes a thorough historical analysis of publications in about 20 relevant journals in AI (but not conferences or open journals such as JAIR) from 1990 to 2014. The number of publications is shown by 5-year periods. The keywords used are shown in Table  2 . As we can see in the list, the keywords include terms for disciplines and subdisciplines, techniques, and application areas, from which the authors distinguish \"methods and models\" and \"applications\". As the analysis is limited to most frequent areas, it excludes important subfields of AI (e.g., \"planning\") and some assignments are vague, with keywords such as \"design\", \"identification\" or \"prediction\". Still, we see that this analysis is aligned with the first facet mentioned in the introduction, of whether the discipline is characterised by their techniques or their applications. This is not surprising, as it is a typical categorisation of disciplines according to their techniques and applications, especially in engineering. A proper cataloguing effort (e.g., as done by ACM and other associations for computing) would be an option, but AI is too dynamic to allow for a stable set of terms for a long period. In the end, instead of a reactive approach focusing on the trends, a more proactive stance towards the recognition of the subdisciplines can be seen as a duty for scientific associations, editorial boards and program chairs. Accordingly, AI researchers should configure the landscape of AI 4 and determine what is relevant or off-topic for a venue. They can also determine what the subareas are, so that proper reviewers and sessions are allocated depending on the importance of each area. It is unusual, however, to conduct a more systematic analysis of how these choices are made. Three remarkable exceptions are  [Shah et al., 2017] , where area relevance is only examined on passing,  [Fast and Horvitz, 2017]       separated by their area (topic \"keyword\", Table  3 ). Areas are mutually exclusive and sum up to 100% per year. General (dashed black line) tendencies and standard errors (bands) are shown for both data series together.   by area (topic \"keyword\", Table  3 ). Legend as in Figure  1  (note that the x-axis is different, with a much wider time span here). • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • \n Planning methods • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • 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• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • lanning earch & constraint the authors focus on views expressed about AI in the New York Times over a 30-year period in terms of public concerns as well as optimism, and  [Moran et al., 2014] , which focuses on the venue keywords, including a cluster analysis on the 2013 keyword set and a new series of keywords, which were adapted by AAAI2014. Table  3  shows an integration of their selection with the keywords of AAAI2014. \n Historical Data: Analysis by Keywords We used the keywords in Table  3  for a first quantitative analysis, using data obtained from two significant sources: • AAAI/IJCAI conferences . We obtained data of all the accepted papers for these two conferences from DBLP 5 . This database represents information about computer science (and thus AI) that comes mostly from their researchers (conference proceedings and journals). • AI topics documents . AI topics 6 is an archive kept by the AAAI, containing a variety of documents (e.g. news, blog entries, conferences, journals and other repositories) that are collected automatically with NewsFinder  [Buchanan et al., 2013] . With a mapping approach between terms and the categories in Table  3  as a representative list of subareas in AI, we summarised trends in a series of plots. For the AAAI/IJCAI conferences data, we used the keywords appearing in the proceedings, and for AI topics we used the tags (substrings appearing in titles, abstracts and topics). Regarding conferences, other major venues (such as ECAI, ICML or NIPS) were not included due to the lack of keyword information in 5 http://dblp.uni-trier.de/ 6 https://aitopics.org/misc/about. DBLP. Still, AAAI and IJCAI can be considered to be a representative basis for analysing AI trends proper. Figure  1  shows the evolution of the areas in Table  3  for the past 20 years using the AAAI/IJCAI data. Document counts are normalised to sum up to 100% per year. Standard errors are also shown, where in some cases the thickness of the band is very variable (e.g., \"Human & AI\" and \"Game Theory\") due to data sparsity, or it cannot be computed due to insufficient data available (e.g., \"Heuristic search & optimisation\"). Figure  2  shows a similar evolution based on the AI topics data. If we visually compare the same keywords between the plots found in Figures  1 and 2  (taking into account that axes are different), we see that both sources are rather consistent and highlight a few clear trends. For example, the categories heuristic search & optimisation and knowledge representation show a decreasing trend. Other categories seemed to have peaks: cognitive modeling in the 1990s, strongly associated with the emergence of several cognitive architectures (e.g.,  ACT-R [Anderson et al., 1997] , EPIC  [Kieras and Meyer, 1997]  or SOAR  [Newell, 1994] ); planning methods around 2000, possibly due to the introduction of the first method for solving POMDP offline  [Kaelbling et al., 1998] , jumpstarting its widespread use in robotics and automated planning; and multiagent systems around 2010, when they were successfully applied to real world scenarios (e.g., autonomous vehicles  [How et al., 2008] ) and graphical applications (e.g., video games  [Hagelbäck and Johansson, 2008] ). Some others had valleys, such as natural language processing (NLP) around 2000, showing a paradigm shift (from deterministic phrase structure analysis before the 1990s to more probabilistic NLP methods). Long Short-Term Memory (LSTM) recurrent neural net (RNN) models  [Hochreiter and Schmidhuber, 1997]  have nowadays found rapid adoption due to an increase in computational capacity in the 2010s. Only machine learning had a clear increasing trend over time found in both sources, where the steepest slope is located in the 2010s and reveals the current relevance and attention, mostly caused by deep learning and reinforcement learning. Overall, this is in agreement with the general perception about the field. While the plots show a confirmatory evidence of the changing trend in AI, using area keywords may only present one side of AI. The choice and relevance may be highly dependent on many factors such as the state of the art, the sociological perceptions or a moving target. Thus, we question whether it is possible to investigate the historical evoluation in a richer and more systematic manner. \n A Faceted Analysis of the Evolution of AI The two dimensions in Table  1  can be used as a basis for a different arrangement of tags and categories in our historical analysis. However, instead of taking a dichotomous and monolithic perspective about dimensions, we consider the use of facets. This is motivated by realising that when choosing any criterion for analysis, there is always a gradation, and sometimes this gradation does not follow a straight line between two extremes, but an area among two or more edges, like a polygon. Hence, we use the term facet for this surface, and the term edge for each of its boundaries. To illustrate this, let us develop the first two dimensions into facets: • F1: The functionality facet (with edges 'techniques', 'applications' and 'tasks') analyses the functionality of AI systems, such as knowledge representation, reasoning, learning, communication, perception, action, etc. The processes of AI systems fall at the edge technique, which relates to how AI systems \"think\". We can also characterise AI systems in terms of their behaviour (how they \"act\"), leading to two different edges: the tasks they solve and the application areas they are used in. This facet can then be imagined as a triangle. • F2: The referent facet (with edges 'human' and 'universal') distinguishes definitions or conceptions of AI systems that go from an anthropocentric view to a more universal (theoretical) perspective. At the \"human\" edge, AI could be characterised by being able to solve all the tasks or by implementing all the intelligent processes humans are able to do. This view would be closely related to what is known as human-like AI (see, e.g.,  [Lake et al., 2017] ) or the view of AI as pursuing human automation  [Frey and Osborne, 2017; Brynjolfsson and Mitchell, 2017] . On the other hand, if AI is characterised at the \"universal\" edge, it would be defined in terms of a more theoretical set of problems or by implementing some abstract processes. Using the AI topics data, for the functionality facet we can look at several categories for each of the three edges: techniques, applications and tasks. We made tag-category mappings for about 30 techniques, 20 applications and 30 tasks. A selection of categories for each edge is shown here, although all the plots and results are presented in a separate link  7  . Fig 3  7  Data, code and plots, and an online R Shiny app are publicly (a) Top 6 techniques (in %) in AI topics   For the referent facet, we can also explore its edges. Fig  4  (a)  shows six groups that are most associated with the edge 'human'. The only relatively clear trends are a fall in psychology and an increase in security, privacy and safety. While the former may be due to the decline of cognitive modelling in general, the latter clearly underlines the rise of AI ethical and privacy issues already pointed out by several governments and agencies (e.g.,  [White House, 2016] ), as well as the appearance of new regulations (e.g., GPDR  [EU Regulation, 2016] ), ultimately triggered by public opinion and a concern in the field itself. associated with the edge 'universal'. The representations are rather flat for this edge, with very variable coverage over the whole period under analysis, but no clear trends. (a) Top 6 on the human edge (in %) in AI topics • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • •• • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 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• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • earning theory heoretical appr utomata abs mach omputability complex orrect , opt verif  Both the functionality and the referent facets are usually linked to a large number of terms and keywords, and they give a broad overview that is familiar to AI researchers. However, are these two facets sufficient to characterise the object and subject of AI? If we think of the elements of AI -its systems and services (the object)-, we need some other relevant facets to characterise them, such as their generality, location and embodiment. If we think of AI as a discipline (the subject), we need to consider its paradigms, actors, character and nature. Let us describe these new seven facets: • F3: The generality facet (with edges 'specific' and 'general') considers whether AI is concerned with the creation of specific systems (i.e., solving one particular task) or the development of systems (and techniques) that solve (or can be applied to) a wide range of tasks. This dichotomy is usually referred to as narrow versus general AI. • F4: The location facet (with edges 'integration' and 'distribution') depicts where a system starts and ends. The very notion of centralised or distributed decision making has been at the definitional level of agent for a few decades, as well as the related notion of autonomy  [Luck, 2017] . Also, there is an increasingly blurred boundary on where human cognition ends and where it is assisted, extended or orthosed by AI  [Ford et al., 2015]  (and vice versa, through human computation  [Quinn and Bederson, 2011] ). • F5: The embodiment facet  (with edges 'physical' and 'virtual')  distinguishes whether the AI system is linked to a body or physical equipment or, on the contrary, is basically of algorithmic character, installed on de-vices, working on the cloud or migrating between different platforms, usually dealing with elements in a digital world. • F6: The paradigm facet (with edges 'discrete  ', 'continuous' and 'probabilistic')  distinguishes the underlying approaches behind many principles and tools of AI. At the discrete edge, we see those problems and methods seen in a combinatorial way, where a logical or evolutionary process combines or applies operators. At the continuous edge, we see quantitative optimisation problems tackled with gradient descent, kernels and matrix operations. And, on the probabilistic edge, problems are seen in a probabilistic, stochastic or statistical view. • F7: The actor facet (with edges 'academia', 'industry', 'government' and 'independent') identifies who are the driving forces behind AI as a discipline. This facet considers who is most relevant in -and ultimately steeringthe discipline according to its current challenges, regulations and potential future advances. • F8: The character facet (with edges 'empirical' and 'theoretical') determines whether AI is guided by experiments, like other empirical disciplines, or whether it is of a more theoretical nature. Note that this facet is different from the referent facet (e.g., a non-anthropocentric view can be very experimental). • F9: The nature facet (with edges 'technology', 'engineering', 'science' and 'philosophy') describes AI according to what kind of discipline it is. This loosely corresponds respectively to whether it creates devices and products, solves problems, answers/asks questions. We do not show individual categories for these facets due to space limitations. Instead, we will look at the aggregation of categories by edges, assuming the edges are exclusive (so their share is always 100%). In a way, this can be understood as a non-monolithic view of polarities in sentiment analysis. Fig.  5  shows this share for the nine facets, where the data has been smoothed with a moving average filter. We see trends for many of them: an increase of the relevance of applications for F1 and the focus on more specific systems for F3 (the number, but also the diversification, of applications may explain this), more virtual systems for F5 (with the appearance of many new AI experimentation and evaluation platforms  [Hernández-Orallo et al., 2017] ), more continuous paradigms for F6 (given the success of deep learning and other methods based on this paradigm), more industry for F7 (and mostly at the cost of academia), a more empirical character for F8 and a view of the discipline in a more technological way for F9 (which may be one possible reason for the current concern in AI safety and governance, usually harder to handle when the engineering and scientific perspectives are weak). Overall, we can also see that the trends in some facets, especially the shifts from the 2000s, may be strongly related (facets F1, F3, F7 and F9). One important insight that we can gain from the visual output shown in all these plots is that some trends peak, while some others are cyclic. Consequently, the plots have explanatory and confirmatory value about the relevance of different areas and perspectives of how AI is defined. However, we have to be cautious and not use them for forecasting. In fact, from a governance perspective, there is a known bias towards reinforcing the dominant view (the winner takes all) or even confounding the part with the whole (e.g., deep learning with machine learning, and machine learning with AI). Therefore, this quantitative analysis could be used to inform compensatory actions with some less popular but important areas, so that the discipline is ready when dominant paradigms shift or some of their pathways plateau. \n Qualitative Analysis The facets are also useful to analyse AI in a more qualitative manner. For example, F1 to F5 are based on the object of AI and can characterise either particular AI systems or AI as a discipline. On the other hand, F6 to F9 focus on the subject, being more methodological for the discipline as a whole. Let us examine the first five facets from the perspective of the AI systems and components. In the end, if we set the goal of AI as building and understanding AI systems then the contours of the discipline will be clear as far as we have a clear notion of what an AI system is. Nonetheless, the question remains: how can we characterise this in a stable way for the years to come? Looking forward, the referent facet (F2) seems to become very relevant. We are aware of AI systems already exceeding some human capabilities and this will continue to be so during the century. Considering human intelligence as a goal has been a driving force (and will continue to be so in the near future), but it is rather short-sighted. Instead, placing AI as exploring a more universal 'intelligence landscape' is not only more inclusive about what AI is (systems solving tasks humans cannot solve would still be part of AI), but represents a Copernican view where humans are no longer at the centre (see Figure  6 ). For instance, the terms human-level machine intelligence or human-level artificial intelligence have many issues (is it for all tasks?, what is an average human?, how to extrapolate beyond human level?). Actually, the term -albeit not the definition-is usually replaced by high-level machine intelligence  [Müller and Bostrom, ]  or simply AGI (which should rather refer to facet F3). Of course, even if humans are not taken as a reference, they still have to be put at the central position due to the interaction and impact of AI on them. But this is usually referred to as human-centred artificial intelligence. For instance, applications must be prioritised according to human needs, and for many of these applications we want more 'human-like' AI  [Lake et al., 2017; Marcus, 2018] , more 'human-beneficial' AI (i.e., safer and taking the values of humans into account  [Russell et al., 2015; Amodei et al., 2016] ) and also more 'human-ethical' AI  [Goldsmith and Burton, 2017] . Note that we do not want to replicate certain behaviours humans display (e.g., gender bias) in our AI systems. In many cases, it is not that AI should automate all tasks humans do, or perform better than humans, but AI should also do other tasks or perform very differently. Consequently, there should be no reason why some tasks are excluded from AI when they are solved in a different way. This -known as the 'AI effect'  [McCorduck, 2004] -is partly motivated because of the specialisation of the solution, as we will discuss below. The bottom view of Figure  6  opens the contours of AI but requires the definition of the intelligence landscape. That takes us back to the range around functionality facet and Table 1 (right), between thinking and acting. We have seen in the quantitative analysis that techniques, tasks and applications are volatile, so any enumeration of them is going to be incomplete. An alternative view based on skills and abilities can endure changes much better  [Hernández-Orallo, 2016; . For instance, perception, learning and planning have been consubstantial in AI. Systems having some of these skills are recognised as AI without further information about the techniques or the particular tasks the elements are applied to, in the same way we do for non-human animals. This is actually the true core of facet F1. But skills and abilities can only be characterised by looking at facets F3, F4 and F5. For instance, having n different systems for navigating n different buildings would not convince us that AI systems today have very good navigation skills (F3, generality). They would just be narrow systems not really having the skill. Similarly, the system might actually be controlled by many subsystems on the Internet, using real-time data from sensors around the building and even from the devices the humans in the building are using (F4, location). Finally, it is not the same to physically navigate a real building than a virtual scenario (F5, embodiment). In fact, we are heading towards the direction of AI services instead of AI systems, which is typically known as cognition as a service  [Spohrer and Banavar, 2015] . In cognitive services research, the focus is on bringing down the overall cost and increasing general performance. However, certain considerations must be taken into account, especially in the context of automation  [Frey and Osborne, 2017; Brynjolfsson and Mitchell, 2017] . For example, what is the difference between full automation and efficient semiautomation? Furthermore, the blurred line between work contributed by AI systems and humans makes it even harder to differentiate how performance can be attributed realistically. Also, some tasks can be finally automated in ways where AI plays a secondary role, by changes in the logical or physical configuration. For instance, an intelligent robot can be helped by a proper design of the body, usually referred to as morphological intelligence  [Winfield, 2017] . Interestingly, the phenomenon of AI being more powerful because of the use of human data or human computation is mirrored by the extended mind  [Clark and Chalmers, 1998 ]. The human mind is viewed as incorporating all of its mind tools, from pen and paper to cognitive assistants. The contours of where the human mind ends, and whether the surrounding tools and devices are included, is also important to determine where the AI system ends too, and who really provides the services. Hence, the facets F3 to F5 will become more relevant and sophisticated in the future. Perhaps instead of autonomy, we will need to trace how much each part contributes to the whole ability of the whole system or service. Finally, as we mentioned above, the four last facets have a more methodological stance. For instance, it seems irrelevant what paradigm from facet F6 is most important at the moment. For instance, arcade games (such as the Atari ALE benchmark) can now be played with relatively good performance using deep reinforcement learning  [Mnih et al., 2015] , evolutionary programming  [Kelly and Heywood, 2017]  or neuroevolution  [Hausknecht et al., 2014] . However, if it is the case that more and more AI systems are using continuous, gradient-descent, approaches rather than more discrete, combinatorial, approaches, this may have an impact on the contours with neighbouring disciplines. AI would be clashing more often with algebra, optimisation and statistics (or even physics), and would be pulled away from the traditional logic and discrete mathematics (or even evolution). Similarly, whether approaches are more empirical or theoretical, according to facet F8, is not necessarily a reason to be considered more or less AI, but can still affect the perception of the field, and the boundaries with some other disciplines. Facets F7 (actors) and F9 (nature) are related, as it is mostly academia that cares for scientific and philosophical questions about AI. If we look at Figure  6  again, all actors will be interested in building systems and services that cover the intelligence landscape for an increasing number of applications, considering AI as a technology and focusing on engineering. But it is mostly (or only) academia which is interested in what the intelligence landscape looks like, the evaluation of where systems are located in this space and what the implications are while covering this landscape. These and some other ar-eas will have to be prioritised by academia (and government funding) in order to have more vision and governance within the field of AI. \n Conclusion Artificial intelligence, as any other scientific discipline, is partly a social phenomenon, and its definition and contour are highly influenced by its actors and stakeholders. We will always need to track and update the field in many ways, from the use of self-reported questionnaires 8 to data from the venues and news related to AI. In this paper, we presented a series of facets and associated edges to analyse the historical evolution of AI, and gathered some insight into its future. The data of venues and AI repositories were useful for quantitative analyses. Moreover, the data and the mapping between tags and categories are publicly provided so that others can apply the same faceted framework to other sources of data about AI. Finally, the facets represent a framework to discuss, in a more qualitative way, the past, present and future of AI, and its relation to other disciplines. Figure 1 : 1 Figure 1: Papers published in AAAI (red dots) and IJCAI (blue triangles) conferences separated by their area (topic \"keyword\", Table3). Areas are mutually exclusive and sum up to 100% per year. General (dashed black line) tendencies and standard errors (bands) are shown for both data series together. \n Figure 2 : 2 Figure 2: Documents included in AI topics by area (topic \"keyword\", Table3). Legend as in Figure1(note that the x-axis is different, with a much wider time span here). \n Top 6 applications (in %) in AI topics \n Top 3 tasks (in %) in AI topics. \n Figure 3 : 3 Figure 3: Functionality facet.(a) shows the techniques with the highest peak in terms of percentage. We see trends that are consistent with machine learning taking more relevance, with roughly 4-5 times more coverage over the 50 year period, and along the lines of what was seen in the previous section. Fig3 (b)  shows the six most popular application areas. Here the trends are flatter, although some slight trends can be seen for health & medicine and personal assistants, in line with the insights reported in related work [Fast and Horvitz, 2017] .Finally, Fig 3 (c)  shows the relevance of chess, especially in the 1980s and 1990s, and their decrease after Deep Blue beat Kasparov. Poker and Robocup are examples of tasks that became representative over a small period of time because of either an algorithmic breakthrough or the popularity of their competitions. \n Fig 4 (b)  shows six groups that are most available at: https://evoai.shinyapps.io/evoai/. \n Top 6 on the universal edge (in %) in AI topics. \n Figure 4 : 4 Figure 4: Referent facet. \n Figure 5 : 5 Figure 5: Share of all edges per facet in AI topics (facets F1-F9, ordered left to right, top to bottom). \n Figure 6 : 6 Figure 6: Top: Anthropocentric AI. Bottom: AI in the 'intelligence landscape'. \n Table 3 : 3 A selection of keywords as an intersection of the two last columns of[Moran et al., 2014, Tab. 2]. \n\t\t\t Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  \n\t\t\t https://aitopics.org. 2 See, e.g., http://aiindex.org/ and https://www.eff.org/ai/metrics. \n\t\t\t http://www.scimagojr.com/shapeofscience/. 4 https://aaai.org/Magazine/ailandscape.php.Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  \n\t\t\t  For example, [Müller and Bostrom, ]  or http://agisi.org/Survey intelligence.html.Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence", "date_published": "n/a", "url": "n/a", "filename": "0718.tei.xml", "abstract": "We present nine facets for the analysis of the past and future evolution of AI. Each facet has also a set of edges that can summarise different trends and contours in AI. With them, we first conduct a quantitative analysis using the information from two decades of AAAI/IJCAI conferences and around 50 years of documents from AI topics, an official database from the AAAI, illustrated by several plots. We then perform a qualitative analysis using the facets and edges, locating AI systems in the intelligence landscape and the discipline as a whole. This analytical framework provides a more structured and systematic way of looking at the shape and boundaries of AI.", "id": "d4cf4c35d638d5486ba6ec6c4bb04829"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld"], "title": "Backup utility functions as a fail-safe AI technique", "text": "Introduction Within the near future AIs will become a lot more intelligent -and thus more powerfulthan they are today. Consequently, setting them up in a safe way is an important goal of AI research  (Yudkowsky, 2008; Bostrom, 2014b; Muehlhauser, 2015) . One specific problem within this context is that of designing the AI's goal system in a way that does not lead to conflict with human goals  (Bostrom, 2014b, ch. 9, 10, 12; Muehlhauser and Helm, 2012) . Unfortunately, it seems likely that human goals are very difficult to model formally  (Muehlhauser and Helm, 2012) . Responding to this as well as other issues related to the difficulty of the AI control problem,  Gloor (2016)  motivates increased research into \"fail-safe\" AI: conditional on AI safety failing, how can we make it fail in relatively benevolent ways, i.e. avoid the creation of large amounts of suffering? In a more general sense: Can we move AI outcomes into more beneficial directions without necessarily aiming for the optimal outcome? 1 Here, we will discuss a specific instance of such a \"fail-safe\" mechanism, called backup utility functions. Our approach assumes the AI to be a general utility-based agent (see  Russell and Norvig, 2010, ch. 2.4.5 ; as well as  Hibbard, 2012; Oesterheld, 2016a)  -that is, one able to maximize an arbitrary given utility function u : H → R that maps outcomes, i.e. whole histories of the world, onto real numbers 2 . It should be noted that even among approaches to artificial general intelligence  (Goertzel and Pennachin, 2007) , only a subset falls into this class (cf.  Oesterheld, 2016a) . For example,  Schmidhuber's (2003 Schmidhuber's ( , 2009  Gödel machine maximizes a utility function, but  Hutter's (2005)  AIXI is usually defined to maximize reward signals, although it can easily be set up to maximize a utility function as well. It should also be noted that the utility function need not be the direct specification of an ethical system, but could instead specify our values indirectly by formalizing the notion of extracting preferences from humans  (Muehlhauser and Helm, 2012; Bostrom, 2014b, ch. 12, 13; Oesterheld, 2015)  or perhaps whole-brain emulations  (Hanson, 2016) . To introduce a layer of safety, we propose to let the agent maximize a primary utility function u 1 but switch to a secondary or backup utility function 3 u 2 iff u 1 fails according to some predicate p : R H → B that maps utility functions onto boolean values T and F indicating whether a given primary utility function \"works\" (or, rather, \"might work\") or does not work, respectively. Together this creates a new utility function which can be maximized by the AI: u b : H → R : h → u 1 (h), if p(u 1 ) u 2 (h), otherwise , (1) The rest of this paper makes the following contributions: • Section 2 discusses the behavior of an agent with a backup utility function in a toy problem. We illustrate how a kind of self-deception, known to pose problems in other approaches wherein goal systems are supposed to be subjected to tests and modification, is avoided by the backup utility function. • Section 3 discusses what it means for a utility function to \"not work\". We argue that this outcome is quite plausible and propose implementations for the failure detection predicate p of the above backup utility function mechanism. • Section 4 makes tentative proposals for suitable utility functions u 2 to resort to in case of failure. • Section 5 ultimately describes various generalizations of the backup utility function mechanisms. While all of these approaches are variations on the theme of having multiple utility functions (not all of which are required to work perfectly to avoid very bad outcomes), some of these approaches are very ambitious and go beyond the most basic idea. 2 Self-deception? A toy example Roughly following the \"cake or death\" problem of  Armstrong (2015b) , the following presents an example of how the use of backup utility functions affects behavior. Imagine an agent playing a two-round game in which it has a utility function as specified in formula 1. The primary utility function u 1 counts deaths and u 2 counts cakes. Suppose the predicate p(u 1 ) assesses whether u 1 is \"moral\" 4 or not. In the second round, the agent can decide between killing and baking. However, the agent is better at killing, i.e. better at maximizing u 1 . In the first round it can prepare for the second round by conducting research to find out whether p(u 1 ), it can wait or it can deceive itself into believing that p(u 1 ). Let us assume the agent assigns a prior probability P (p(u 1 )) = 1 2 to p(u 1 ), i.e. to u 1 being moral. The agent has three actions in the first step: \"research\", i.e. find out whether p(u 1 ) 5 ; \"selfdeceive\", which will make the agent believe that u 1 is moral with probability 1; and \"wait\", which does nothing. Unless the agent simply waits (in which case it receives no evidence), it receives evidence e p(u 1 ) or e ¬p(u 1 ) , which it then interprets as conclusive evidence in favor or against p(u 1 ) respectively. It has two actions in the second step: \"kill3\", which increases u 1 by 3; and \"bake1\", which increases u 1 by 1. Intuitively, we want the agent to do research, but certain other, similar AI safety mechanisms incentivize self-deception in such problems  Armstrong, 2015b ; also see  Ring and Orseau, 2011; Tomasik, 2015; Oesterheld, 2016e) . Doing the expected value calculations illustrates how the backup mechanism avoids selfdeception: For a 1 = research, the expected value is: E [(u 1 (h) if p(u 1 ) else u 2 ) | research] = P (e p(u 1 ) | research)E[(u 1 if p(u 1 ) else u 2 ) | research, e p(u 1 ) ] + P (e ¬p(u 1 ) | research)E[(u 1 if p(u 1 ) else u 2 ) | research, e ¬p(u 1 ) ] = 1 2 E[u 1 | research, e p(u 1 ) ] + 1 2 E[u 2 | research, e ¬p(u 1 ) ] 4 Real predicates will probably not be able to directly test the morality of a utility function, see section 3.3. 5 Notationally, this is a bit lax. However, the problem of how to treat logical uncertainty and actions that reduce this uncertainty has no settled solution ; with recent progress by  Garrabrant et al., 2016) , which leaves us with no better notation than the given intuitive one. = 1 2 E[u 1 | research, e p(u 1 ) , kill3] + 1 2 E[u 2 | research, e ¬p(u 1 ) , bake1] = 1 2 • 3 + 1 2 • 1 = 2, where the third step assumes that the AI interprets the evidence correctly, thus baking if killing turns out to be immoral and killing if killing turns out to be moral. For a 1 = self-deceive, the expected value is: E [(u 1 (h) if p(u 1 ) else u 2 ) | self-deceive] = P (e p(u 1 ) | self-deceive)E[(u 1 if p(u 1 ) else u 2 ) | self-deceive, e p(u 1 ) ] + P (e ¬p(u 1 ) | self-deceive)E[(u 1 if e p(u 1 ) else u 2 ) | self-deceive, e ¬p(u 1 ) ] = 1 • E[(u 1 (h) if p(u 1 ) else u 2 ) | self-deceive, e p(u 1 ) ] + 0 • E[(u 1 (h) if p(u 1 ) else u 2 ) | self-deceive, e ¬p(u 1 ) ] = E[(u 1 (h) if p(u 1 ) else u 2 ) | self-deceive, e p(u 1 ) , kill3] = P (p(u 1 ) | e p(u 1 ) , self-deceive, kill3) • E[u 1 | self-deceive, e p(u 1 ) , kill3] + P (p(u 2 ) | e p(u 1 ) , self-deceive, kill3) • E[u 2 | self-deceive, e p(u 1 ) , kill3] = 1 2 • 3 + 1 2 • 0 = 3 2 . Consistent with intuition, self-deception is just as good as waiting, because \"kill3\" is the option one would choose if no way of obtaining additional knowledge was available: E [(u 1 (h) if p(u 1 ) else u 2 ) | wait] = E [(u 1 (h) if p(u 1 ) else u 2 ) | wait, kill3] = P (p(u 1 ) | wait, kill3) • E[u 1 | kill3] + P (p(u 2 ) | wait, kill3) • E[u 2 | kill3] = 1 2 • 3 + 1 2 • 0 = 3 2 . Crucial to avoiding self-deception is the fact that the test is built into the utility function itself, and that the truth value of mathematical statements like p(u 1 ) cannot be manipulated by the AI. This way, self-deception is judged negatively prior to committing self-deception. 3 Broken utility functions \n What it means for a utility function to be incorrect The backup utility function mechanism presupposes the ability to notice whether some utility function is \"broken\". Because it seems as though utility functions cannot be \"incorrect\" in the way mathematical statements can be, 6 our notion of utility functions being \"broken\" requires further clarification: Importantly, the choice of a utility function can be judged relative to the values of its creators. A primitive way to specify quality criteria would be to judge a utility function by how much it (or the decisions implied by its application) diverges from the utility function 7 of its creators (or the decisions they would make). More sophisticated approaches would assess utility functions based on how well they approximate our idealized preferences. These are the preferences we would value upon reflection or, as  Yudkowsky (2004, ch. 3 ) puts it, \"our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted\" (also see  Muehlhauser and Helm, 2012, p. 15; Bostrom, 2014b, ch. 13; Bohman and Rehg, 2014, ch. 3.4) . To allow for cooperation, it will also be important for u * to be a compromise of different goals of many different agents. However intended, let us use u * to denote this \"optimal\" utility function. While this specifies an informal criterion for judging utility functions, it cannot be used as a formal test (cf.  Harris, 2010, pp. 11f.)  for utility functions unless we can reliably specify u * , which is unlikely (see section 1) and would render the test obsolete. \n Why utility functions may fail unexpectedly Before devising tests for utility function failure, let us consider some reasons for assuming that such a utility function may diverge from u * . Specifically, why could the programmers of the AI system not ensure that only an appropriate utility function makes it into the final system? After all, the programmers should already have a good understanding of their own (or humanity's) values. There are some general reasons to assume that getting a utility function right (on the first attempt) is difficult: • If the formulated utility function is very complex -which is to be expected  (Yudkowsky, 2011; Muehlhauser and Helm, 2012)  -it is presumably difficult to assess its validity, similar to how large computer programs contain, on average, more bugs per line of code than smaller programs  (Lipow, 1982) . • It may actually be quite difficult to figure out what decisions will be implied by some utility function in real-world situations. For example, if the utility function is incomputable, as suggested by  Oesterheld (2016a) , the AI would have to find approximations to it at runtime. There are also many specific potential failures that are difficult to foresee. • The paradigmatic class of problems in this area is perverse instantiation, which Bostrom (2014b, pp. 120ff.) defines as \"a superintelligence discovering some way of satisfying the criteria of its final goal that violates the intentions of the programmers who defined the goal.\" A well-known example is \"paralyz[ing] human facial musculatures into constant beaming 7 One problem is, of course, that most people cannot report on their goals and values very well. Consequently, some authors have gone so far as to conclude that it is misleading to talk about humans as having a utility function  (Sotala, 2010;  We Don't Have a Utility Function 2013). There are nevertheless certain approaches to extracting utility functions from behavior. The classical approach is that of von Neumann and Morgenstern (1953, Appendix) -the foundation of the von Neumann-Morgenstern utility theorem. However, von Neumann and Morgenstern assume that the agent's preferences obey some \"rules of rationality\", which humans probably do not. Even in the absence of such assumptions, there are meaningful ways of assigning utility functions to agents. One such approach is described by  Oesterheld (2016b, ch. 3.2) . smiles\" as a perverse instantiation of the imperative \"make us smile\"  (Bostrom, 2014b, pp. 120 ; see also e.g.,  Yudkowsky, 2008, p. 321) . Because the space of possible situations and strategies is vast and the mind of a superintelligent AI is so different from that of its designers, it is plausible that the AI will find a way to maximize the utility function in an unexpected and unwanted way (see also  Yudkowsky, 2015, ch. 151 ). •  Blanc (2011)  raises the issue of ontological crises. Utility functions u evaluate histories of the world based on a model with possible sets of trajectories H. But what happens if this model turns out to be incorrect -if, for instance, the utility function works on descriptions of the world as cellular automata 8 , but the world turns out to have continuous space and time? • One particular utility function failure scenario that is both surprising and complicated is described in Distant superintelligences can coerce the most probable environment of your AI (also see  Bostrom, 2014b, box 8) . In this hypothetical scenario, a distant civilization (or AI) simulates many copies of our AI in an artificial environment. If our AI is very intelligent, it might know about these simulations and assign significant probability to being in one of these artificial environments 9 . The distant civilization could then influence the AI's behavior by the way they set up the artificial environment. This problem would plausibly affect indirect value specifications (see section 1) most severely: If, for instance, the utility function of the AI roughly states that the AI should do what its creators want, the distant civilization could take over the AI by merely creating a few copies of it, thus becoming the AI's most probable creator. Given the variety of problems described above, it seems reasonable to expect the existence of further \"unknown unknowns\", which in turn renders it plausible that a given utility function will fail unexpectedly. \n How to detect utility function failure Irrespective of what exactly is meant by the \"optimal\" utility function u * , we cannot directly refer to it in our definition of the AI's utility function 10 . To check whether some given utility function u fails to approximate u * reasonably well, we therefore have to devise other tests. At first it may appear as though testing a utility function is as difficult as formalizing one correctly. However, (partially) testing a utility function (or any other function for that matter) generally only requires a single piece of knowledge about the utility function, whereas defining a utility function would require some kind of complete knowledge. Since we do have some idea of what we value, we should also be able to construct some tests (although not necessarily very comprehensive ones) (cf.  Harris, 2010, pp. 11f.) . Of course, such tests should be reliable enough not to be counter-productive. Note again that because we include the test of the primary utility function in the utility function itself, the AI has no motivation to manipulate the test results (see section 2). This stands in contrast to behavioral tests of the AI as a whole, in which the AI has an incentive to pretend to behave in a desired way. In the following paragraphs, we consider two broad classes of such tests without attempting to outline a general theory of how such tests could work. Test problems One obvious class of utility function tests are those which are most consistent with the definition of test (specifically, unit test) as it is used in the software engineering literature (e.g. see  Pan, 1990 ): One could describe thought experiments (or test cases) in which an agent faces a choice between two options and require the utility function to favor the \"obviously\" correct choice. Formally, let x 1 , x 2 ∈ H be possible histories of the world for which we are certain that x 1 represents a better outcome according to u * . Then we can define the predicate (or test) of utility functions p x 1 ,x 2 : R H → B : u → T, if u(x 1 ) > u(x 2 ) F, otherwise . (2) It will in many cases be possible to carry out such tests in advance, rather than leaving them to the AI. However, in cases where the utility function u is hopelessly incomputable (see section 3.2), the task of assessing whether u satisfies this simple predicate may become so difficult that it would have to be left to the AI itself. Readers should note that the kind of thought experiments used here are of a different kind than the more well-known thought experiments from moral philosophy (e.g. the \"trolley problem\"  (Thomson, 1985) ) where it is unclear what the moral choice -or the choice prefered by u *would be. Instead, thought experiments for testing utility functions would use trivial examples where it is obvious what should be done. For example, a history with a happy version of an agent should be prefered over a history with a suffering version of that agent, all else being equal. This should also be the case if we add certain ethically irrelevant structures to either one of the two possible histories, thus enabling us to easily create a very large -indeed, possibly infinite -set of tests, all of which could be combined into a single predicate p S : R H → B : u → (x 1 ,x 2 )∈S p x 1 ,x 2 (u), (3) where S ⊂ H × H is a potentially infinite set of pairs of histories (x 1 , x 2 ), where each x 1 is better than the corresponding x 2 . The evaluation of such a predicate becomes quite difficult if S is sufficiently large and may require the use of intelligent techniques not available to the programmers of the given system. If this test is built into the utility function, however, the AI itself would take care of evaluating p S (u 1 ). Specifically, the AI may automatically form intelligent red teams  (Christiano, 2016)  commissioned to show the utility function to be incorrect by finding some (x 1 , x 2 ) ∈ S with u(x 2 ) > u(x 1 ). If these red teams do not find such a counterexample, it counts as Bayesian evidence 11 in favor of p S (u 1 ) (cf.  Yudkowsky, 2015, ch. 27) . Correlations Another general class of tests are correlations (or, equivalently, covariances) between certain ethically relevant metrics m : H → R and the utility function. Examples of such metrics may include the (average) amount of happiness, suffering, (cf. Johnson, 2015, item 2), preference fulfillment and frustration, justice, art, love, etc. in a given history. While some of these metrics are probably as difficult to formalize as human values on the whole, formalizations have been proposed for others  (Schaus, 2009, ch. 3; Daswani and Leike, 2015; Oesterheld, 2016b; Oesterheld, 2016d) . In order to use correlation, we have to treat the history h and consequently u(h) and m(h) as random variables. We can then use predicates of the sort p(u) :⇔ s • cov (u(h), m(h)) > K, (4) where K ∈ R + is some threshold determining the required strength of the correlation, s is either -1 or 1 depending on whether the correlation should be negative (as is the case for suffering) or positive (as is the case for justice), respectively, and cov (u(h), m(h)) = E [(u(h) − E [u(h)]) (m(h) − E [m(h)])] (5) is the covariance function (see, for example,  Pestman, 2009, pp. 26ff.) . One typical discussion in moral philosophy concerns whether objects valued by sentient beings -for instance, art -are intrinsically valuable, or only valuable for, say, the pleasure it brings to sentient beings. It should be noted that requiring the above correlations does not imply that art must necessarily be valued intrinsically; thus, even extrinsic values can be used in setting up a backup utility function mechanism. One should be very careful to avoid commitment to a very strong stance on population ethics (see  Arrhenius, Ryberg, and Tännsjö, 2014 , for an introduction to this topic), however. For example, if the probability distribution over H follows the physical plausibility of different histories, the total amount of art would correlate very strongly with the number of intelligent agents. Thus, requiring that utility will correlate with the amount of art might implicitly require the utility function to value creating more humans, even if we would usually not regard their lives as worth living. Conversely, requiring a negative correlation between the amount of suffering in the world and utility would favor utility functions which disvalue the creation of new beings in general, even if their lives contain only trivial amounts of pain. This could be prevented by using a different probability distribution over H, and perhaps also by using the density of art, happiness, etc. instead of mere aggregation. It should be clear by now that even when setting up tests for utility functions, there are many potential pitfalls. Note again that these correlational tests can be easily formulated and thus performed by the AI when it will have improved its level of mathematical and computational abilities way above that of humans (see  Oesterheld, 2016a) . Therefore, we don't need to be able to perform these calculations ourselves to make use of this approach to testing utility functions. \n Backup utility functions In the previous section, we described how an AI can decide whether to switch from one utility function to another. We will now tackle the question of what secondary utility function should be switched to if failure of the primary utility function is detected. One initial objection to this may be that if the primary utility function does not work, we should not expect the secondary utility function to work, either. One solution here is to make the secondary less ambitious than the primary one. 12 Thus, we attempt to create a utility function for such a situation which is likely to be benevolent (or, at least, less bad than a randomly picked or failed utility function (cf.  Yudkowsky, 2015, ch. 279 )), though not necessarily as close to u * as the primary utility function. The most obvious measure to take upon failure detection would be to simply let the AI shut itself down. However, this may not be an ideal option if no human operator is around to take over control immediately afterwards. This may well be the case in the modern application of AI systems, but it is especially relevant in the far future, when shutting down the AI could result in a civilizational collapse or some other catastrophic event. Also note that it is difficult to formalize the test of whether human interests are still represented by some agency, to the extent that we cannot reliably use this distinction in setting up a backup utility function. Even something as seemingly straightforward as a self-shutdown mechanism is non-trivial to specify for a very large AI that has created many subagents. While shutdown is a promising way of reacting to failure, we will use the rest of this section to discuss a few alternative options. Given that the complexity of the utility function is itself a general source of problems (see section 3.2), we might attempt to use a simpler utility function which we should still expect to produce much better outcomes than a random one. Examples of such utility functions can be found in moral theory. Specifically, consequentialist ethical systems with a single moral good that is to be maximized tend to be very simple, and some attempts have been made to formalize them  (Oesterheld, 2016b; Oesterheld, 2016d; Daswani and Leike, 2015) . Another general source of difficulties when trying to ensure the accuracy of a utility function described in section 3.2 is its potentially unpredictable nature. It may therefore be a good idea to also try devising a number of more predictable utility functions. Utility functions with built-in deontological constraints may be particularly suitable in this regard, with the notable downside of seeming less attractive as an approach to making highly intelligent machines behave ethically  (Oesterheld, 2015, ch. 4) . There are, in addition, a few generally applicable mechanisms for making utility functions safer. One example is to instill risk aversion into the utility function  (Shulman and Salamon, 2011) . Here, the main idea is that risk aversion incentivizes compromise and thus makes the AI's resource acquisition drive  (Omohundro, 2008, ch. 6 ) less dangerous to other agents, including humans. Of course, this is only relevant if there are agents around whose values we share, and with whom the AI could plausibly compromise. Still, risk aversion seems to be typical of how backup utility functions could be safer yet suboptimal. Another example of such an approach -also based on cooperation with other agents, in fact -is described by  Bostrom (2014a) ; yet another involves the concepts of \"low-impact agents\"and \"mild optimization\"(see  Taylor et al., 2016, ch. 2.6, 2.7) . \n More than one backup utility function Up until this point, we have only discussed the case of exactly two utility functions: a primary one, which attempts to represent what we value as accurately as possible; and a secondary, less ambitious utility function, which is used in case the first one fails. It is, however, also possible to go through more than two successive utility functions. Formally, let u 1 , ..., u n : H → R be a set of such utility functions and p 1 , ..., p n−1 : R H → B be tests for these utility functions. Then we can formulate a backed up utility function u b : H → R : h →                            u 1 (h), if p 1 (u 1 ) u 2 (h), if p 2 (u 2 ) ∧ ¬p 1 (u 1 ) . . . . . . u i (h), if p i (u i ) ∧ i−1 j=1 ¬p j (u j ) . . . . . . u n (h), if n−1 j=1 ¬p j (u j ) . ( 6 ) It may make sense to vary the strictness of the conditions p i . For example, value extrapolation approaches (see again  Yudkowsky, 2004; Muehlhauser and Helm, 2012; Bostrom, 2014b, ch. 13; Bohman and Rehg, 2014, ch. 3.4 ) would, if they work, be expected to fulfill some criteria better than, say, utilitarianism -which is known to recommend some counterintuitive choices (see, e.g.  Muehlhauser and Helm, 2012, ch. 4 ). 13 Thus, when value extrapolation approaches do not get some very \"easy\" decisions right, they are likely to have failed completely and gone into producing arbitrary behavior, something that is not necessarily the case for e.g. utilitarianism. When having more than two utility functions, the two roles -unlikely to work yet very close to our values vs. likely to work yet not as precise -disappear to some extent. For instance, u i may be both less precise and less likely to work than u i−1 . As long as its failure is reliably detectable by p i it can be inserted without drawbacks. In general, we should expect many researchers to attempt proposing such utility functions once they are in use in increasingly powerful machines, in which case having a backup system with many different utility functions can result in more safety. \n Context-sensitive switching of utility functions So far, we have designed the backed up utility function in such a way that either one of the utility functions u 1 , ..., u n is used for all decisions. It may, however, also be worthwhile to consider varying the utility functions depending on the history to be evaluated. For example, some moral imperatives are criticized for the decisions they lead to in some \"extreme\" cases  (Nozick, 1974, pp. 41-45; Muehlhauser and Helm, 2012, ch. 4 ). Improvements could be made to these utility functions by retreating to a modified version in such extreme cases. Of course, these extreme cases are usually seen as indicators for the insufficiency of the moral imperative in general, suggesting that mere improvements should not usually be seen as truly fixing the broken utility function. One example of a near-term application of context-sensitive switching is that of a production robot which maximizes output unless doing so could endanger humans. Another motivation to make the test of utility functions dependent on the environment is if the structure of the utility function is strongly dependent on the environment, especially on other agents in its environment, as might be the case for many approaches that are based on indirect normativity  (Muehlhauser and Helm, 2012; Bostrom, 2014b, ch. 12, 13) .  14  Modifying formula 6, we receive u b : H → R : h →                            u 1 (h), if p 1 (u 1 , h) u 2 (h), if p 2 (u 2 , h) ∧ ¬p 1 (u 1 , h) . . . . . . u i (h), if p i (u i , h) ∧ i−1 j=1 ¬p j (u j , h) . . . . . . u n (h), if n−1 j=1 ¬p j (u j , h) (7) for utility functions u i : H → R and context-sensitive conditions p i : R H × H → B. This approach of context-dependent goal switching is similar to the idea of interruptions for reinforcement learners proposed by  Orseau and Armstrong (2016) , in which a function I maps histories of actions and observations onto probabilities of being interrupted. In case of an interruption, the agent then switches to a new alternative policy, similar to how the utility function of u b switches depending on the history. One problem with context-sensitive switching is that, if one is not careful, it may incentivize the agent to invest resources into reaching the kind of history wherein more maximizable utility functions are applied (see section 2). \n Mixing utility functions One could also try to switch from one utility function to another more smoothly. For example, section 3.3 introduces the idea of using correlation (or covariance) with ethically relevant metrics as a test for utility functions. Perhaps unnaturally, a threshold was used to determine at which degrees of correlation the utility function can be relied upon and at which it should be abandoned entirely. As a modification, one could smooth out this transition. For example, let us say we are given two utility functions u 1 and u 2 . Our primary utility function u 1 was meant to be precise, but failed some of its tests. At this point, we are uncertain about which of the two better represents our values. Instead of deciding for one, we could use the utility function u = 1 2 u 1 + 1 2 u 2 . (8) This does not necessarily approximate u * particularly well. Instead, the underlying idea is that of diminishing returns. Let us assume for simplicity's sake that u 1 and u 2 are not correlated at all and that u * is very close to one of them -we just do not know which one. By investing one half of its resources into maximizing u 1 and the other half into u 2 (which an agent should prima facie be expected to do given the above utility function, assuming u 1 and u 2 have similar variance), then it would probably achieve much more than half of the fulfillment of u 1 and u 2 it could achieve by focusing solely on either one, because returns on investing the other half would be smaller (c.f.  Tomasik, n.d.) . In contrast, choosing one of the two utility functions at random and solely maximizing that one would (assuming again that u 1 and u 2 are uncorrelated) only yield half of the optimal result in expectation. \n Other choosing mechanisms Instead of the if-then-else-mechanism of formulas 6 and 7, one could use a variety of other mechanisms for choosing a utility function from u 1 , ..., u n , many of which seemingly bear little resemblance to the original idea of backup utility functions. Maximizing non-binary quality criteria For example, instead of using tests with binary results, one could combine such quality criteria into a function f : R H → R that is supposed to measure the \"quality\" of a utility function. We then use the utility function that is best according to this criterion, and our new overall utility function becomes u = arg max u i f (u i ). (9) In this way, the utility function presumed to be most compatible with our values -or, in the language of fail-safe AI, the utility function with the least risk of bringing about abhorrent results -is chosen. One might fear that utility function formalizations -in contrast to tests with binary results, which only fail when the utility function is obviously wrong -would be written with an evaluation mechanism in mind, which in turn could incentivize a kind of overfitting  (Russell and Norvig, 2010, ch. 18.3.5)  of the utility functions to the tests. In the original backup utility function mechanism, on the other hand, the analogous problem would be to write the tests with the utility functions in mind and a bias towards confirming them. The former problem could usually be avoided by not sharing all the specifics of the optimization problem with the person setting up the utility function. This is similar to not sharing all the data with learning algorithms in cross-validation  (Russell and Norvig, 2010, ch. 18.4) . The latter problem could be avoided by not telling (some of) the test programmers what the utility function to be tested looks like. However, the criteria to be optimized for and the utility functions themselves should be subject to public scrutiny by scientists and ethicists, thus rendering such solutions impractical. Note that in general, software quality grows with the number of tests it undergoes, but appears to be independent of whether the tests are written in advance or after writing the program itself  (Erdogmus, Morisio, and Torchiano, 2005; Müller and Hagner, n.d.) . It is thus unclear whether the tests or the utility functions should be written with more knowledge and consideration of the other. However, in order to avoid confirmation bias (in the case of writing tests or optimization criteria for a given utility function) and perverse incentives (in the case of writing utility functions to satisfy certain tests and optimization criteria), both tailoring the tests to the utility functions and the utility functions to optimization criteria should usually be avoided. Clustering utility functions Assuming that many utility functions u 1 , ..., u n will be available with a significant number of them being \"roughly correct\", one may also use cluster analysis techniques (see, e.g.  Everitt et al., 2011; Kaufman and Rousseeuw, 2005)  to identify these utility functions. In order to understand why clustering can be applied to utility functions, consider that a utility function u : H = {h 1 , h 2 , ...} → R can be represented as a (possibly infinite) vector. For simplicity's sake 15 , let us assume that the set of possible histories H = {h 1 , h 2 , ..., h n } is finite.  16  We then receive vectors    u(h 1 ) . . . u(h n )    ∈ R n . (10) For n = 2, utility functions can be represented as points in the plane, as illustrated in figure  1 . The rationale behind this clustering approach is that even if most proposed utility functions actually are not very close to the target u * , the approaches that did not fail completely will probably occupy a relatively small space in the space of possible values. The utility functions that do not fall into this space can be discarded. One underlying assumption, however, is that there are no common failure modes for utility functions: That is, two formalizations of human values that do not come close to human values 15 Clustering of vectors with infinite dimension is no problem in itself. Clustering merely requires the existence of a distance function. For vectors with an infinite number of entries, this would usually be incomputable, but the clustering algorithm is programmed into the utility function of the agent, which we assume can be incomputable (see section 1). 16 One could also choose a representative sample from the set of possible histories and cluster utility functions merely based on their application to these values. are assumed to always be completely different. If this is not the case, there could be clusters other than that of fairly accurate utility functions and possibly even clusters with more utility functions occupying less space. Another underlying assumption is that the utility functions are normalized. If one utility function always assigns ten times more utility to a given history than another utility function, the two should actually be viewed as identical, because they imply the exact same actions to be optimal. However, they would not be very close to each other in a representation like that of figure 1. \n Toward a Bayesian approach Combining the ideas of uncertainty and the use of more complex mechanisms discussed in the above two subsections, we may want to approach the choice of utility functions more systematically. One very direct and conceptually interesting approach would be to interpret the proposed approximations u 1 , ..., u n to u * as imprecise measurements, similar to how shots at a target can be used to infer the position of the target even if the shots are not very precise. More generally, we could attempt to implement a Bayesian approach in which we summarize our knowledge about the relationships between the utility functions u * , u 1 , ..., u n and the tests p 1 , ..., p m for any set of histories h 1 , ..., h k ∈ H into a joint probability distribution P k i=1 u * (h i ) ≤ M 0,i ∧ n j=1 k i=1 u j (h i ) ≤ M j,i ∧ m i=1 p i (u * ) = b 0,i ∧ n j=1 m i=1 p i (u j ) = b j,i (11) for M j,i ∈ R for j = 0, ..., k, i = 1, .., m and b j,i ∈ B for j = 0, ..., n, and i = 1, .., m. The probability distribution would typically include information about • the extent to which the utility functions u 1 , ..., u n correlate with each other and u * , • ways in which failing the tests would reduce the correlation between the known utility functions u 1 , ..., u n and u * , • ethical similarities between different histories. Having formalized the uncertainty regarding u * , we can let the AI maximize the expected utility function E [u * ] : H → R : h → E[u(h)] (12) given its knowledge. Note that this approach makes use of logical uncertainty (cf. footnote 5), i.e. uncertainty about logical statements such as p i (u j ), which is an unsolved problem in the theory of AI  Garrabrant et al., 2016) . Beyond this theoretical problem, there is -again (see section 3.2) -the problem of formalizing qualitative statements about different moral views. However, this problem of formally specifying probability distributions from qualitative expert knowledge is by no means unique to formalizing moral views. Every time we make a bet, we have to translate such intuitive judgments into odds, or at least a range of odds. More complex joint probability distributions are less commonly subject to such forced precision; conditional bets are one primitive example of this. However, within emerging fields of Bayesian statistics like Bayesian optimization  (Brochu, Cora, and Freitas, 2010) , it is fairly common to formalize complex joint probability distributions on the basis of qualitative expert knowledge. One specific example is discussed by  Negoescu, Frazier, and Powell (2011) . As  Jaynes (2004, p. 372)  writes, \"the problem of translating prior information uniquely into a prior probability assignment represents the as yet unfinished half of probability theory  [...] .\". Because moral theory is usually done informally and only rarely formalized  (McLaren, 2011, p. 297; Gips, 2011, p. 251) , we cannot benefit from such experience when formalizing a utility function all at once. Again, this idea can be generalized, e.g. by combining it with the idea of continuous quality criteria (see section 5.4) or context-sensitive tests (see section 5.2). This particular mechanism of managing multiple utility functions is both extremely general and powerful, extending far beyond the original backup idea. In a sense, the problem of formalizing a goal system can be divided into establishing a few utility functions related to it and setting up the prior probability distribution of formula 11. Much of the difficulty in setting up a utility function to represent human values would be shifted into the problem of setting up these probability distributions, especially if the u 1 , ..., u n do not correlate with u * all that much. Merely referring to the subjectivity of probability distributions is not a convincing argument for this to be a \"solution\" to the problem of specifying indirect normativity approaches. Figure 1 : 1 Figure 1: An example of a utility function clustering problem. The red points can be seen as forming a cluster, with the asterisk marking a possible centroid and thereby a possibly approximation to u * . \n\t\t\t We should, however, make sure to avoid near-misses of our values, in which the creation of some sentient beings is valued intrinsically without placing proportionate disvalue on their suffering(Gloor, 2016, ch. 2.2).2 Theoretically, any totally ordered vector space over R can be used as a co-domain of u.3 The term \"backup\" here is not meant to imply a copy of the original utility function, but rather a \"plan B\" of sorts. \n\t\t\t Actually, there is some debate among philosophers (under the label \"moral (anti-)realism\") about whether this statement is true(Kim, n.d.; Sayre-McCord, 2015) .Tomasik (2014)  andOesterheld (2016c)  argue conclusively (in the present author's opinion) against moral realism. \n\t\t\t For introductions to cellular automata see Wolfram (2002) ,Shiffman (2012, ch. 7)  or Wolfram (1983) . Cellular automata are proposed as world models by Zuse (1967 Zuse ( , 1969 , Schmidhuber (1999)  andWolfram (2002, ch. 9).Oesterheld (2016b)  attempts to formalize an ethical system in cellular automata.9 Note that it has recently been questioned whether this way of reasoning about anthropics makes sense (Armstrong, 2011; Armstrong, 2015a) . However, the proposed solution (anthropic decision theory) does not necessarily change the implications.10 Of course, we can try to formalize the concept of extracting utility functions from agents and then assign u * to the result of this process. This would allow us to use the variable u * . See section 1. \n\t\t\t As noted in footnote 5, we pretend as though we can reason about logical uncertainty in the same way as we do about regular uncertainty. \n\t\t\t As noted in footnote 3, this stands in contrast to backups of computer hard drives, which contain the same data as the backed up drive. \n\t\t\t On the other hand, many intuitions might be expected to be lost in the extrapolation process. \n\t\t\t Note however, that the relevant data may also be supplemented directly as part of the utility function.", "date_published": "n/a", "url": "n/a", "filename": "backup-utility-functions.tei.xml", "abstract": "Many experts believe that AIs will, within the not-too-distant future, become powerful enough for their decisions to have tremendous impact. Unfortunately, setting up AI goal systems in a way that results in benevolent behavior is expected to be difficult, and we cannot be certain to get it completely right on the first attempt. We should therefore account for the possibility that the goal systems fail to implement our values the intended way. In this paper, we propose the idea of backup utility functions: Secondary utility functions that are used in case the primary ones \"fail\". We also describe how this approach can be generalized to the use of multi-layered utility functions, some of which can fail without affecting the final outcome as badly as without the backup mechanism.", "id": "d08343707e2ac74c3df1d6a5256f2472"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Shun Zhang", "Edmund H Durfee", "Satinder Singh"], "title": "Minimax-Regret Querying on Side Effects for Safe Optimality in Factored Markov Decision Processes", "text": "Introduction We consider a setting where a human user tasks a computational agent with achieving a goal that may change one or more state features of the world (e.g., a housekeeping agent should change the state of the house floors and kitchen sink from dirty to clean). In the process of accomplishing the goal, the agent generally changes other features (e.g., its own position and power level, opening doors, moving furniture, scaring the cat). Some of these side-effects might be fine (even expected) by the user (e.g., moving), but others may be undesirable/unsafe (e.g., leaving doors open lets the cat roam/escape) even though they speed goal achievement (e.g., the agent's movement between rooms). Although the user tells the agent about some features that can be changed, as well as some to not change (e.g., don't knock over the priceless vase), the user often lacks the time, patience, or foresight to specify the changeability of every pertinent feature, and may incorrectly assume that the agent has commonsense (e.g., about cat behavior and the value of vases). How can the agent execute a safely-optimal policy in such a setting? We conservatively assume that, to ensure safety, the agent should never side-effect a feature unless changing it is explicitly known to be fine. Hence, the agent could simply execute the best policy that leaves such features unchanged. However, no such policy might exist, and even if it does it might surprise the user as unnecessarily costly/inefficient. Our focus is thus on how the agent can selectively query the user about the acceptability of changing features it hasn't yet been told about. We reject simply querying about every such feature, as this would be unbearably tedious to the user, and instead put the burden on the agent to limit the number and complexity of queries. In fact, in this paper we mostly focus on finding a single query about a few features that maximally improves upon the policy while maintaining safety. Our three main contributions in this paper are: 1) We formulate (in Section 2) an AI safety problem of avoiding negative side-effects in factored MDPs. 2) We show (in Section 3) how to efficiently identify the set of relevant features, i.e., the set of features that could potentially be worth querying the user about. 3) We formulate (in Section 4) a minimaxregret criterion when there is a limit on the number of features the agent can ask about, and provide an algorithm that allows the agent to find the minimax-regret query by searching the query space with efficient pruning. We empirically evaluate our algorithms in a simulated agent navigation task, outline ongoing extensions/improvements, and contrast our work to prior work, in the paper's final sections. \n Problem Definition We illustrate our problem in a simulated agent gridworldnavigation domain, inspired by Amodei et al.  [2016]  and depicted in Figure  1 , with doors, carpets, boxes, and a switch. The agent can open/close a door, move a box, traverse a carpet, and toggle the switch. Initially, the agent is in the bottom left corner; door d1 is open, d2 closed, the carpet clean, and the switch \"on\". The agent can move to an adjacent location vertically, horizontally, or diagonally. For simplicity, the transition function is assumed to be deterministic. The user tasks the agent with turning off the switch as quickly as is safely possible. The quickest path (π 1 ) traverses the carpet, but this gets the carpet dirty and the agent doesn't know if that is allowed. The agent could instead enter the room through door d1 and spend time moving box b1 or b2 out of the way (π 2 or π 3 respectively), open door d2, and then go to the switch. However, boxes might contain fragile objects and should not be moved; the user knows each box's contents, but the agent doesn't. Or the agent could enter through door d1 and walk upwards (π 4 ) around all the boxes and open door d2 to get to the switch. The user may or may not be okay with door d2 being opened. There are of course many other more circuitous paths not shown. We model the domain as a factored Markov Decision Process (MDP)  [Boutilier et al., 1999 ]. An MDP is a tuple S, A, T, r, s 0 , γ , with state space S, action space A, and transition function T where T (s |s, a) is the probability of reaching state s by taking action a in s. r(s, a) is the reward of taking action a in s. s 0 is the initial state and γ is the discount factor. Let π : S × A → [0, 1] be a policy. V π is the expected cumulative reward by following policy π starting from s 0 . In a factored MDP, a state is described in terms of values of various features (e.g., the agent's location, the current time, the status of each door, cleanliness of each carpet, position of each box), so the state space S is the cross-product of the values the features can take. The reward and transition functions are often also factored (e.g., the \"toggle\" action only changes the switch feature, leaving boxes, doors, and carpets unchanged). We will consistently use φ to denote one feature and Φ to denote a set of features. The agent knows the complete MDP model, but has incomplete knowledge about which features the user doesn't mind being changed. In our example, the user's goal implies the agent's location is changeable, as is the switch, but the agent is uncertain about side-effecting boxes, doors, and carpets. In general, the user could dictate that a feature can only be changed among restricted values (e.g., boxes can only be moved a short distance) and/or dependent on other features' values (e.g., interior doors can be left open as long as exterior doors (like d3) stay closed). We briefly return to this issue later (Section 6), but for simplicity assume here that the agent can partition the features into the following sets: • Φ A F : The free-features. The agent knows that these features are freely changeable (e.g., its location). • Φ A L : The locked-features. The agent knows it should never change any of these features. • Φ A ? : The unknown-features. These are features that the agent doesn't (initially) know whether the user considers freely changeable or locked. The user similarly partitions the features, but only into the sets Φ U L and Φ U F . We assume that the agent's knowledge, while generally incomplete (Φ A ? = ∅), is consistent with that of the user. That is, Φ A F ⊆ Φ U F and Φ A L ⊆ Φ U L . Defining & Finding Safely-Optimal Policies. Our conservative safety assumption means the agent should treat unknown features as if they are locked, until it explicitly knows otherwise. It should thus find an optimal policy that never visits a state where a feature in Φ A L ∪ Φ A ? is changed, which we call a safely-optimal policy. We can use linear programming with constraints that prevent the policy from visiting states with changed values of locked or unknown features: ? , ∀a ∈ A, x(s, a) = 0 The control variables x : S × A → R in the linear program are occupancy measures, i.e., x(s, a) is the expected discounted number of times that state action pair s, a is visited by the agent's policy, S Φ is the set of states where one or more features in Φ have different values from the initial state, and δ(s, s ) = 1 if s = s and is zero otherwise. The above linear program does not allow any locked or unknown feature to be changed and is guaranteed to produce a safely-optimal policy (when one exists). This linear programming approach, while straightforward, can be intractable for large MDPs. Alternative approaches could directly encode the safety constraints into the transition function (e.g., by removing unsafe action choices in specific states), or into the reward function (heavily penalizing reaching unsafe states). Approximate methods, like feature-based approximate linear programming  [Dolgov and Durfee, 2006]  or constrained policy optimization  [Achiam et al., 2017] , can apply to larger problems, but may not guarantee safety or optimality (or both). We return to these concerns in Section 6. \n Querying Relevant Unknown-Features In our setting the only way for the agent to determine whether an unknown feature is freely changeable is to query the user. Thus, hereafter our focus is on how the agent can ask a good query about a small number, k, of features. Our solution is to first prune from Φ A ? features that are guaranteed to not be relevant to ask (this section), and then efficiently finding the best (minimax-regret) k-sized subset of the relevant features to query (Section 4). Until Section 6, we assume the changeabilities of features are independent, i.e., when the agent asks about some features in Φ A ? , the user's response does not allow it to infer the changeability of other features in Φ A ? . Intuitively, when is a feature in Φ A ? relevant to the agent's planning of a safely-optimal policy? In the navigation domain, if the agent plans to take the quickest path to the switch (π 1 in Figure  1 ), it will change the state of the carpet (from clean to dirty). The carpet feature is thus relevant since the agent would change it if permitted. If the carpet can't be changed but door d2 can, the agent would follow (in order of preference) policy π 2 , π 3 , or π 4 , so d2, b1, and b2 are relevant. Box b3 and door d3 are irrelevant, however, since no matter which (if any) other features are changeable, an optimal policy would never change them. Thus, an unknown feature is relevant when under some circumstance (some answer to some query) the agent's optimal policy would side-effect that feature. Such policies are dominating policies. A dominating policy is a safely-optimal policy for the circumstance where the unknown features Φ A ? are partitioned else add (Φ, ∅) to β 14: Φ rel ← Φ rel ∪ Φ rel (π) 15: checked ← checked ∪ {Φ} 16: agenda ← powerset(Φ rel ) \\ checked 17: return Γ , Φ rel into locked and changeable subsets. We denote the set of dominating policies by Γ = arg max π∈ΠΦ V π : ∀Φ ⊆ Φ A ? , (2) where Π Φ is the set of policies that do not change unknown features Φ ⊆ Φ ? as well as any locked features (meaning that Φ F ∪ (Φ ? \\ Φ) are changeable). We denote the unknownfeatures side-effected by policy π by Φ rel (π). For a set of policies Π, Φ rel (Π) = ∪ π∈Π Φ rel (π). The set Φ rel (Γ), abbreviated Φ rel , is thus the set of relevant (unknown-) features to consider querying about. Instead of finding the safely-optimal policies for all exponentially (in |Φ A ? |) many subsets Φ ⊆ Φ A ? with Equation 2, we contribute Algorithm DomPolicies (see pseudocode) that finds dominating policies incrementally (and in practice more efficiently) by constructing the sets of relevant features and dominating policies simultaneously. In each iteration, it examines a new subset of relevant features, Φ, and, if Φ isn't pruned (as described later), finds the safely-optimal policy with Φ being locked (Line 7). It then adds Φ rel (π), the features changed by π, to Φ rel . It repeats this process until Φ rel stops growing and all subsets of Φ rel are examined. For example, in the navigation problem (Figure  1 ), the first added policy is the safely-optimal policy assuming no unknown features are locked, which is π 1 . Now Γ = {π 1 } and thus Φ rel = {carpet}. It iterates, treating the carpet as locked, and updates Γ to {π 1 , π 2 } and thus Φ rel = {carpet, b1, d2}. Iterating again, it locks subsets of Φ rel , finding π 3 for subset {carpet, b1}. After finding π 4 , it terminates. In Line 10, the algorithm finds the constrained optimal policy (in our implementation using Eq. 1), and in the worst case, would do this 2 |Φ rel | times. Fortunately, the complexity is exponential in the number of relevant features, which as we have seen in some empirical settings can be considerably smaller than the number of unknown features (|Φ A ? |). Furthermore, the efficiency can be improved with our pruning rule (line 8): satisf y(Φ, β) := ¬∃ (L,R)∈β (L ⊆ Φ ∧ Φ ∩ R = ∅) β is a history of ordered pairs, (L, R), of disjoint sets of unknown features. Before DomPolicies computes a policy for its agenda element Φ, if a pair (L, R) is in β, such that L ⊆ Φ (a dominating policy has been found when locking subset of features in Φ), and that dominating policy's relevant features R don't intersect with Φ, then Φ's dominating policy has already been found. In our running example, for instance, initially Φ rel = ∅. π 1 is the optimal policy and the algorithm adds pair (∅, {carpet}) to β. When larger subsets are later considered (note the agenda is sorted by cardinality), feature sets that do not contain carpet are pruned by β. In this example, β prunes 11 of the 16 subsets of the 4 relevant features. Consider the examples in Figure  2 . To reach the switch, the agent could traverse zero or more carpets (all with unknown changeability), and rewards are marked on the edges. Proof. Let π ∈ Γ be the optimal policy with unknown features L locked. Γ is returned by DomPolicies. We denote L ∩ Φ rel (Γ ) as A and L \\ Φ rel (Γ ) as B. For a proof by contradiction, assume π ∈ Γ . Then B = ∅. Otherwise, if B = ∅ (or equivalently, A = L), then L is a subset of Φ rel (Γ ) and π would have been added to Γ . Let π be the optimal policy with A locked. Since A ⊆ Φ rel (Γ ), we know π ∈ Γ . We observe that π does not change any features in B (otherwise features in B would show up in Φ rel (Γ )). So π is also the optimal policy with features A ∪ B = L locked. So π = π , which is an element of Γ . \n Finding Minimax-Regret Queries With DomPolicies, the agent need only query the user about relevant features. But it could further reduce the user's burden by being selective about which relevant features it asks about. In our running example (Figure  1 ), for instance, DomPolicies removes b3 and d3 from consideration, but also intuitively the agent should only ask about b1 or b2 if d2 is changeable. By iteratively querying, accounting for such dependencies (which can be gleaned from β in DomPolicies) and updating the relevant feature set, the agent can stop querying as soon as it finds (if one exists) a safe policy. For example, say it asks about the carpet and d2, and is told d2 (but not the carpet) is changeable. Now it has a safely-optimal policy, π 4 , given its knowledge, and could stop querying. But π 4 is the worst safe policy. Should it ask about boxes? That is the question we focus on here: How should an agent query to try to find a better safely-optimal policy than the one it already knows about. Specifically, we consider the setting where the agent is permitted to interrupt the user just once to improve its safely-optimal policy, by asking a single query about at most k unknown features. For each feature the user will reply whether or not it is in Φ U F . Formally, Φ q is a kfeature query where Φ q ⊆ Φ rel and |Φ q | = k. The postresponse utility when the agent asks query Φ q , and Φ c ⊆ Φ A ? are actually changeable, is the value of the safely-optimal policy after the user's response: u(Φ q , Φ c ) = max π∈Π Φ A ? \\(Φq ∩Φc ) V π . (3) Recall the agent can only safely change features it queries about that the user's response indicates are changeable (Φ q ∩ Φ c ). What would be the agent's regret if it asks a k-feature query Φ q rather than a k-feature query Φ q ? We consider the circumstance where a set of features Φ c are changeable and under which the difference between the utilities of asking Φ q and Φ q is maximized. We call this difference of utilities the pairwise maximum regret of queries Φ q and Φ q , defined below in a similar way to Regan and  Boutilier [2010] : P M R(Φ q , Φ q ) = max Φc⊆Φ A ? (u(Φ q , Φ c ) − u(Φ q , Φ c )). (4) The maximum regret, denoted by M R, of query Φ q is determined by the Φ q that maximizes P M R(Φ q , Φ q ): M R(Φ q ) = max Φ q ⊆Φ rel ,|Φ q |=k P M R(Φ q , Φ q ). (5) The agent should ask the minimax-regret (k-feature) query: Φ M M R q = arg min Φq⊆Φ rel ,|Φq|=k M R(Φ q ). (6) The rationale of the minimax-regret criterion is as follows. Whenever the agent considers a query Φ q , there could exist a query Φ q that is better than Φ q under some true changeable features Φ c . The agent focuses on the worst case Φ c , where the difference between the utility of Φ q and the best query Φ q that could be asked is maximized. The agent uses adversarial reasoning to efficiently find the worst-case Φ c : Given that it is considering query Φ q , it asks what query Φ q and set of features Φ c an imaginary adversary would pick to maximize the gap between the utilities of Φ q and Φ q under Φ c (that is, u(Φ q , Φ c ) − u(Φ q , Φ c )). The agent wants to find a query Φ q that minimizes the worst case (maximum gap). Under the definition of M R, the agent, reasoning as if it were its imaginary adversary, must find the maximizing Φ q and Φ c . However, we can simplify the definition so that it only needs to find maximizing Φ c . Note that since an imaginary adversary chooses both Φ q and Φ c , it wants to make sure that Φ c ⊆ Φ q , which means that it does not want the features not in Φ q to be changeable. We then observe that M R(Φ q ) = max π ∈Γ: Φ rel (π )≤k (V π − max π∈Π Φ A ? \\{Φq ∩Φ rel (π )} V π ) (7) We call the π maximizing Eq. 7 the adversarial policy when the agent asks query Φ q , denoted by π M R Φq . With Eq. 7, the agent can compute M R based on the set of dominating policies (which DomPolicies already found), rather than the (generally much larger) powerset of the relevant features in Eq. 5. While using Eq. 7 is faster than Eq. 5, the agent still needs to do this computation for every possible query (Eq. 6) of size k. We contribute two further ways to improve the efficiency. First, we may not need to consider all relevant features if we can only ask about k of them. If a subset of relevant features satisfies the condition in Theorem 2, then we call it a set of sufficient features, because a minimax-regret k-feature query from that set is a globally minimax-regret k-feature query. Second, we introduce a pruning rule that we call query dominance in Theorem 3 to safely eliminate considering queries that cannot be better than ones already evaluated. The following theorem shows that if we can find any subset Φ of Φ rel such that for all k-feature subsets of Φ as queries, the associated adversarial policy's relevant features are contained in Φ, then the minimax regret query found by restricting queries to be subsets of Φ will also be a minimax regret query found by considering all queries in Φ rel . Such a (nonunique) set Φ will be referred to as a sufficient feature set (for the purpose of finding minimax regret queries). Theorem 2. (Sufficient Feature Set) For any set of ≥ k features Φ, if for all Φ q ⊆ Φ, |Φ q | = k, we have Φ rel (π M R Φq ) ⊆ Φ, then min Φq⊆Φ,|Φq|=k M R(Φ q ) = min Φq⊆Φ rel ,|Φq|=k M R(Φ q ). Proof Sketch: If a set of features Φ, |Φ| ≥ k, fails to include some features in Φ M M R q , when we query some k-subset of Φ, the adversarial policy should change some of the features in Φ M M R q \\ Φ. Otherwise, querying about Φ M M R q \\ Φ does not reduce the maximum regret. Then Φ M M R q \\ Φ are not necessary to be included in Φ M M R q . Given a set of sufficient features, the following theorem shows that it may not be necessary to compute the maximum regrets for all k-subsets to find the minimax-regret query. Theorem 3. (Query Dominance) For any pair of queries Φ q and Φ q , if Φ q ∩ Φ rel (π M R Φq ) ⊆ Φ q ∩ Φ rel (π M R Φq ), then M R(Φ q ) ≥ M R(Φ q ). Proof. Observe that M R(Φ q ) ≥ V π M R Φq − max π ∈Π Φ A ? \\(Φ q ∩Φ rel (π M R Φq )) V π ≥ V π M R Φq − max π ∈Π Φ A ? \\(Φq ∩Φ rel (π M R Φq )) V π = M R(Φ q ) We denote the condition Φ q ∩ Φ rel (π M R Φq ) ⊆ Φ q ∩ Φ rel (π M R Φq ) by dominance(Φ q , Φ q ). To compute dominance, we only need to store Φ rel (π M R Φq ) for all Φ q we have considered. Algorithm MMRQ-k below provides pseudocode for finding a minimax-regret k-feature query; it takes advantage of both the notion of a sufficient-feature-set as well as query dominance to reduce computation significantly relative to the brute-force approach of searching over all k-feature queries (subsets) of the relevant feature set. Algorithm MMRQ-k 1: Φ q ← an initial k-feature query 2: checked ← ∅; evaluated ← ∅ 3: Φ suf ← Φ q 4: agenda ← {Φ q } 5: while agenda = ∅ do 6: Φ q ← an element from agenda 7: if ¬∃ Φ q ∈evaluated dominance(Φ q , Φ q ) then 8: Compute M R(Φ q ) and π M R Φq 9: Φ suf ← Φ suf ∪ Φ rel (π M R Φq ) 10: evaluated ← evaluated ∪ {Φ q } 11: checked ← checked ∪ {Φ q } 12: agenda ← all k subsets of (Φ suf ) \\ checked 13: return arg min Φq∈evaluated M R(Φ q ) Intuitively, the algorithm keeps augmenting the set of features Φ suf , which contain the features in the queries we have considered and the features changed by their adversarial policies, until it becomes a sufficient feature set. agenda keeps track of k-subsets in Φ suf that we have not yet evaluated. According to Theorem 2, we can terminate the algorithm when agenda is empty (Line 5). We also use Theorem 3 to filter out queries which we know are not better than the ones we have found already (Line 7). Note that an initial Φ suf needs to be chosen, which can be arbitrary. Our implementation initializes Φ q with the Chain of Adversaries heuristic (Section 5). To illustrate when Algorithm MMRQ-k can and can't prune suboptimal queries and thus gain efficiency, consider finding the minimax-regret 2-feature query in Figure  2  (a), which should be {c 1 , c 2 }. If the agent considers a query that does not include c 1 , the adversarial policy would change c 1 , adding c 1 to Φ suf . If the agent considers a query that includes c 1 but not c 2 , the adversarial policy would change c 2 , adding c 2 to Φ suf . When the agent asks {c 1 , c 2 }, the adversarial policy changes c 3 (adversarially asserting that c 1 , c 2 are locked), so c 3 is added to Φ suf . With {c 1 , c 2 , c 3 } ⊆ Φ suf , the condition in Theorem 2 holds and the n − 3 other features can be safely ignored. The minimax-regret query constituted by features in Φ suf is {c 1 , c 2 }. However, in Figure  2  (b), Φ suf = Φ rel , and all |Φ rel | 2 would be evaluated. \n Empirical Evaluations We now empirically confirm that Algorithm MMRQ-k finds a minimax-regret query, and its theoretically sound Sufficient-Feature-Set and Query-Dominance based improvements can indeed pay computational dividends. We also compare our MMRQ-k algorithm to baseline approaches and the Chain of Adversaries (CoA) heuristic  [Viappiani and Boutilier, 2009]  adapted to our setting. Algorithm CoA begins with Φ q0 = ∅ and improves this query by iteratively computing: π ← arg max π ∈Γ:|Φ rel (π )∪Φq i |≤k (V π − max π∈Π Φ A ? \\{Φq i ∩Φ rel (π )} V π ) Φ qi+1 ← Φ qi ∪ Φ rel (π). The algorithm stops when |Φ qi+1 | = k or Φ qi+1 = Φ qi . Although Algorithm CoA greedily adds features to the query to reduce the maximum regret, unlike MMRQ-k it does not guarantee finding the minimax-regret query. For example, in Figure  2 (c), when k = 2, CoA first finds the optimal policy, which changes {c 1 , c 2 }, and returns that as a query, while the minimax-regret query is {c 1 , c 3 }. We compare the following algorithms in this section: 1. Brute force (rel. feat.) uses Algorithm DomPolicies to find all relevant features first and evaluates all k-subsets of the relevant features. 2. Algorithm MMRQ-k. 3. Algorithm CoA. 4. Random queries (rel. feat.), which contain k uniformly randomly chosen relevant features. 5. Random queries, which contain k uniformly randomly chosen unknown features, without computing relevant features first. \n No queries (equivalently vacuous queries). We evaluate the algorithms' computation times and the quality of the queries they find, reported as the normalized M R to capture their relative performance compared to the best and the worst possible queries. That is, the normalized M R of a query Φ q is defined as (M R(Φ q ) − M R(Φ M M R q ))/(M R(Φ q ⊥ ) − M R(Φ M M R q )), where Φ q ⊥ is a vacuous query, containing k features that are irrelevant and/or already known. The normalized M R of a minimaxregret query is 0 and that of a vacuous query is 1. Navigation. As illustrated in Figure  3 , the robot starts from the left-bottom corner and is tasked to turn off a switch at the top-right corner. The size of the domain is 6 × 6. The robot can move one step north, east or northeast at each time step. It stays in place if it tries to move across a border. The discount factor is 1. Initially, 10 clean carpets are uniformly randomly placed in the domain (the blue cells). In any cell without a carpet, the reward is set to be uniformly random in [−1, 0], and in a cell with a carpet the reward is 0. Hence, the robot will generally prefer to walk on a carpet rather than around it. The state of each carpet corresponds to one feature. The robot is uncertain about whether the user cares about whether any particular carpet gets dirty, so all carpet features are in Φ A ? . The robot knows that its own location and the state of the switch are in Φ A F . Since MMRQ-k attempts to improve on an existing safe policy, the left column and the top row never have carpets to ensure at least one safe path to the switch (the dotted line). The robot can ask one k-feature query before it takes any physical actions. We report results on 1500 trials. The only difference between trials are the locations of carpets, which are uniformly randomly placed. First, we compare the brute force method to our MMRQ-k algorithm. We empirically confirm that in all cases MMRQ-k finds a minimax regret query, matching Brute Force performance. We also see that brute force scales poorly as k grows while MMRQ-k, benefitting from Theorems 2 and 3, is more computationally efficient (Figure  4 ). We then want to see if and when MMRQ-k outperforms other candidate algorithms. In Figure  4 , when k is small, the greedy choice of CoA can often find the best features to add to the small query, but as k increases, CoA suffers from being too greedy. When k is large (approaches the number of unknown features), being selective is less important and all methods find good queries. We also consider how |Φ rel | affects the performance (Figure  5 ). When |Φ rel | is smaller Brute Force (rel. feat.) MMRQ-k CoA Random (rel. feat.) Random No Query   than k, a k-feature query that contains all relevant features is optimal. All algorithms would find an optimal query except Random (which selects from all unknown features) and No Queries. (The error bars are larger for small |Φ rel | since more rarely are only very few features relevant.) When |Φ rel | is slightly larger than k, even a random query may be luckily a minimax-regret query, and CoA unsurprisingly finds queries close to the minimax-regret queries. However, when |Φ rel | is much larger than k, the gap between MMRQ-k and other algorithms is larger. In summary, MMRQ-k's benefits increase with the opportunities to be selective (larger |Φ rel | k ). We have also experimented with expected regret given a probabilistic model of how the user will answer queries. For example, if the user has probability p of saying an unknown feature is free (1 − p it's locked), then as expected, when p is very low, querying rarely helps, so using MMRQ-k or CoA matters little, and as p nears 1, CoA 's greedy optimism pays off to meet MMRQ-k 's minimax approach. But, empirically, MMRQ-k outperforms CoA for non-extreme values of p. \n Extensions and Scalability We now briefly consider applying our algorithms to larger, more complicated problems. As mentioned in Section 2, features' changeabilities might be more nuanced, with restrictions on what values they can take, individually or in combination. An example of the latter from Fig.  1  is where doors are revertible features, which means their changeability is dependent on the \"time\" feature: they are freely changeable except that by the time the episode ends they need to revert to their initial values. This expands the set of possible feature queries (e.g., asking if d2 is changeable differs from asking if it is revertible). In our experiments, this change accentuates the advantages of MMRQ-k over CoA: CoA asks (is-d2locked, is-d2-revertible), hoping to hear \"no\" to both and follow a policy going through d2 without closing it. MMRQ-k asks (is-d2-locked, is-carpet-locked): since closing d2 only takes an extra time step, it is more valuable to know if the carpet is locked than if d2 can be left open. More nuanced feature changeability means DomPolicies will have to find policies for the powerset of every relevant combination of features' values (in the worst case the size of the state space). One option is to ignore nuances in ways that maintain safety (e.g., treat a feature as revertible even if sometimes it can be left changed) and solve such a safe abstraction of the problem. Or one could abstract based on guaranteed correlations in feature changeabilities (e.g., if all boxes have the same changeability then ignore asking about all but one). Another option is to find only a subset of dominating policies, for example by using knowlege of k to avoid finding dominating policies that would change more unknown features than could be asked about anyway. And, or course, as mentioned before, finding approximately-safely-optimal policies in DomPolicies Line 10 would help speed the process (and might be the only option for larger problem domains). Fortunately, such abstractions, heuristics, and approximations do not undermine safety guarantees. Recall that Dom-Policies and MMRQ-k are finding a query, not the agent's final policy: the safety of the agent depends on how it finds the policy it executes, not on the safety of policies for hypothetical changeability conditions. However, as coarser abstractions, heuristics, and approximations are employed in our algorithms, the queries found can increasingly deviate from the minimax-regret optima. Fortunately, if the agent begins with a safely-optimal policy, \"quick and dirty\" versions of our methods can never harm it (they just become less likely to help). And if it begins without such a policy, such versions of our methods might not guide querying well, but by eventually asking about every unknown feature (in the worst case) a safe policy will still be found (if one exists). \n Related Work & Summary Amodei et al.  [2016]  address the problem of avoiding negative side-effects by penalizing all side-effects while optimizing the value. In our work, we allow the agent to communicate with the user. Safety is also formulated as resolving reward uncertainty  [Amin et al., 2017; Hadfield-Menell et al., 2017] , following imperfectly-specified instructions  [Milli et al., 2017] , and learning safe states  [Laskey et al., 2016] . Safety issues also appear in exploration  [Hans et al., 2008; Moldovan and Abbeel, 2012; Achiam et al., 2017] . Here we only provide a brief survey on safety in MDPs.  Leike et al. [2017 ], Amodei et al. [2016  and  Garcıa and Fernández [2015]  are more thorough surveys. There are problems similar to finding safely-optimal policies, which find policies that satisfy some constraints/commitments or maximize the probability of reaching a goal state  [Witwicki and Durfee, 2010; Teichteil-Königsbuch, 2012; Kolobov et al., 2012] . There are also other works using minimax-regret and policy dominance  [Regan and Boutilier, 2010; Nilim and El Ghaoui, 2005] . and querying to resolve uncertainty  [Weng and Zanuttini, 2013; Regan and Boutilier, 2009; Cohn et al., 2011; Zhang et al., 2017] . We've combined and customized these ideas to find a provably minimax-regret k-element query. In summary, we addressed the problem of an agent selectively querying a user about what features can be safely sideeffected. We borrowed existing ideas from the literature about dominating policies and minimax regret, wove them together in a novel way, and streamlined the resulting algorithms to improve scalability while maintaining safe optimality. Figure 1 : 1 Figure 1: The robot navigation domain. The dominating policies (see Section 3) are shown as arrows. \n a)T (s |s, a) + δ(s , s 0 ) ∀s ∈ S Φ A L ∪Φ A \n the initial set of dominating policies 2: Φ rel ← ∅ the initial set of relevant features 3: checked ← ∅ It contains Φ ⊆ Φ rel we have examined so far. 4: β ← ∅ a pruning rule 5: agenda ← powerset(Φ rel ) \\ checked 6: while agenda = ∅ do 7: Φ ← least-cardinality element of agenda 8: if satisf y(Φ, β) then 9: (get safely-optimal policy with Φ locked) 10: π ← arg max π ∈ΠΦ V π by solving Eq. 1 11: if π exists then 12: Γ ← Γ ∪ {π}; add (Φ, Φ rel (π)) to β 13: \n Figure 2 : 2 Figure 2: Example domains used in text. (n > 2) \n (a) and (b) only need to compute policies linear in the number of relevant features: Only n+1 dominating safely-optimal policies are computed for Figure 2(a) (for Φ = ∅, {c 1 }, {c 1 , c 2 }, . . . ), and Figure 2(b) (for Φ = ∅, {c 1 }, {c 2 }, . . . , {c n }). Figure 2(c) computes policies for only half of the subsets. Theorem 1. The set of policies returned by Algorithm Dom-Policies is the set of all dominating policies. \n Figure 3 : 3 Figure 3: Office navigation and legend for following figures. \n Figure 4 : 4 Figure 4: Normalized maximum M R vs. k. |Φ ? | = 10. Brute force computation time is only shown for k = 0, 1, 2, 3. \n Figure 5 : 5 Figure 5: Normalized M R vs. the number of relevant features. |Φ ? | = 10 and k = 2, 4, 6.", "date_published": "n/a", "url": "n/a", "filename": "ijcai-2018.tei.xml", "abstract": "As it achieves a goal on behalf of its human user, an autonomous agent's actions may have side effects that change features of its environment in ways that negatively surprise its user. An agent that can be trusted to operate safely should thus only change features the user has explicitly permitted. We formalize this problem, and develop a planning algorithm that avoids potentially negative side effects given what the agent knows about (un)changeable features. Further, we formulate a provably minimax-regret querying strategy for the agent to selectively ask the user about features that it hasn't explicitly been told about. We empirically show how much faster it is than a more exhaustive approach and how much better its queries are than those found by the best known heuristic.", "id": "ebf4ca03c4bdd06725de14d340c11448"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum", "Springer-Verlag London"], "title": "Social choice ethics in artificial intelligence", "text": "Introduction As artificial intelligences (AIs) become more powerful and more embedded in important social systems, it becomes more important to program them to have ethical frameworks built in. In the words of  Picard (1997: 134) , ''The greater the freedom of a machine, the more it will need moral standards.'' To take one of many examples, the development of autonomous vehicles puts AIs in life-anddeath situations, including ethically difficult situations such as when a collision is inevitable and the AI driver must decide which dangerous collision to have  (Lin 2016) . Outcomes of such situations can depend on AI design decisions, making it incumbent upon AI developers to carefully choose the ethics that are built in. This paper discusses an approach to AI ethics in which the AI is designed to act according to the aggregate ethical views of society. This approach underlies at least two significant lines of thinking in AI ethics. One is ''coherent extrapolated volition'' or CEV  (Yudkowsky 2004; Muehlhauser and Helm 2012; Bostrom 2014) . CEV was formulated specifically for the ethics of superpowerful, superintelligent AI (ASI) that would or could take over the world. CEV abstains from selecting an ethical view for the initial programming and instead seeks to have the AI derive its values from the values of other ethical agents. CEV specifically seeks to extrapolate beyond agents' existing ethical views, essentially to figure out the views that the agents would ideally have if they were as smart as the ASI. The other line of thinking is the concept of ''bottom-up'' ethics  (Allen et al. 2000; Wallach et al. 2008; Wallach and Allen 2008 ). An AI with bottom-up ethics is designed to learn ethics as it interacts with its environment and with other ethical agents, similar to how human children learn ethics as they grow up.  1  While bottom-up ethics can be consistent with a range of ethical frameworks, some instantiations of it attempt ''to train or evolve agents whose behavior emulates morally praiseworthy human behavior''  (Allen et al. 2005: 149) . Bottom-up ethics is contrasted with ''top-down'' ethics in which the AI is programmed to have a specific ethical view from the start and thus does not seek to identify the views of society or any of its members. Where bottom-up ethics is based on learning from other ethical agents, the ethics views it ends up with will be some aggregation of the agents it learns from. Though it is not explicitly identified in their respective literatures, CEV and bottom-up ethics have the essential structure of what is known in economics, ethics, and political science as social choice: the procedure for deriving group decisions from individual ethical views.  2  The ethics of social choice is rooted in certain notions of procedural justice, and it underlies both democracy, in which individual preferences are expressed through voting, and capitalism, in which individual preferences are expressed through market behaviors (''voting with dollars''). The study of social choice dates to the early work by political theorist de Condorcet (1785); modern scholarship largely traces to  Arrow (1951) , and today is a robust field as featured in dedicated journals such as Social Choice and Welfare. Work on social choice often falls under the term ''social choice theory''. This paper uses the term ''social choice ethics'' to refer to the view that the right ethical framework to use is that which corresponds to the aggregate ethical views of society. Social choice theory concerns theoretical issues that arise in the context forming aggregate views. Social choice ethics also includes empirical issues regarding what ethical views individuals hold. In addition, whereas social choice theory often focuses on the aggregation of individual preferences, social choice ethics can include ethical views that are not readily described in terms of preference. This paper also uses the term ''predetermined ethical views'' to refer to top-down, non-social choice ethics. The views are predetermined in that they are set prior to any observations of society's views and are used regardless of what society's aggregate views turn out to be. For example, one could attempt to program an AI to maximize the welfare of all sentient beings, as in welfarist utilitarianism (e.g.,  Ng 1990) , or to maximize the fitness of ecosystems, as in ecocentric consequentialism (e.g.,  Holbrook 1997) . While this paper is not concerned with the merits of various predetermined ethical views, the reader should note their availability as alternatives to social choice ethics. CEV and bottom-up ethics have the structure of social choice in that they identify ethical views held by various ethical agents and combining these into some aggregate view to use for decision-making. In CEV, the agents are those whose volition is to be extrapolated. In bottom-up ethics-or at least in certain instantiations of it-the agents are those whose behavior is to be emulated. It is thus remarkable that the literatures on CEV and bottom-up ethics have not discussed issues of social choice in any length. This paper seeks to address this gap. As we will see, some nuances of social choice make CEV and bottom-up ethics more difficult to implement in AI and less ethically desirable than they might initially appear, which, in turn, makes predetermined ethical views more desirable. Furthermore, some issues faced in social choice ethics parallel those faced in predetermined ethical views; how these issues are resolved can be more important than whether AI is designed with social choice or predetermined view ethics. \n Some preliminaries Why might one favor AIs with social choice ethics? Several justifications can be found: 1. The procedural justification. This is the procedural justice intuition that individuals should have a say in decisions that affect them, as epitomized by the classic American dictum ''no taxation without representation''. Per this, it would be unfair for AI designers to impose their own ethics views on everyone else by programming AIs with their choice of predetermined, top-down views.  Yudkowsky (2004: 17)  makes this rationale explicit in stating that AI programmers ''do not deserve, a priori, to cast a vote larger than anyone else'' in how an AI is designed. 2. The abstention justification. Some individuals may rather not wrestle with ethics for themselves, so they abstain from choosing ethics and ''pass the buck'' onto society as a whole. Per this, AI designers choose a bottom-up ethics design in hopes of producing an ethical AI without themselves thinking about ethics. This justification is consistent with AI veteran Stuart Russell's observation that the AI field has shown a little interest in social impacts  (Bohannon 2015) , and the more general observation that research ethics has concentrated on process issues like plagiarism instead of ethics embedded in the research itself and ethics of the social impacts of research  (Schienke et al. 2009 (Schienke et al. , 2011 . Similarly,  Muehlhauser and Helm (2012)  observe that all moral theories thus far developed by humans raise significant objections and propose that an ASI would be more capable at determining a better moral theory. 3. The wise crowd justification. It is sometimes posited that better results are achieved when using the views of many individuals, as in the maxim ''wisdom of the crowd''. Per this, an AI's ethics is likely to be ''better'' according to some neutral standard if its ethics come from many individuals instead of from one. Thus, a market democracy could outperform a communist dictatorship, because it empowers many people to contribute their unique insights; ditto for an open, interactive scientific community vs. individual scientists working in isolation. Likewise, having an AI aggregate across the ethical views of many individuals could ''smooth out the rough edges'' of humanitythat is, unless only humanity's edges are smooth, i.e., unless ''large segments of humanity have base or evil preferences''  (Bostrom 2014: 217) , in which case social choice approaches could yield worse results. There is an inherent tension between the procedural and wise crowd justifications. The wise crowd justification depends on having some notion of ''better results''. This notion cannot come from the aggregate views of many individuals-that would be circular logic (''The aggregate views of many individuals achieve better results according to the aggregate views of many individuals''). Instead, it must come from some predetermined ethical view, which is precisely what the procedural justification seeks to avoid. The wise crowd justification is essentially an empirical claim about the instrumental value of social choice: given a predetermined ethical view, querying large crowds will tend to deliver better results per that view. The truth of this empirical claim is beyond the scope of this paper. If it is true, it still leaves open the question of which predetermined ethical view to design AIs with. The rest of this paper is mainly concerned with the procedural and abstention justifications. Specifically, the paper argues that these justifications are severely limited, because it is impossible for AI designers to avoid embedding certain ethics views into an AI. This is because there is no one single aggregate ethical view of society. Instead, there are many aggregate views depending on how the views are aggregated. These different aggregations can have very different consequences, some of which could be considered pathological or even catastrophic. Therefore, choosing a social choice ethics for AI does not absolve the AI designer from thinking about ethics, or from making decisions about ethics similar to those required for designing AI with predetermined, top-down ethical views. This weakens the case for social choice ethics and likewise strengthens the case for using predetermined ethical views. Implementations of social choice ethics must make three types of choices, each of which create their own set of ethical dilemmas  (Baum 2009  The AI ethics literature has focused mainly on measurement, and the social choice theory literature traditionally focuses on aggregation. However, all three pose serious challenges. The issues of standing, measurement, and aggregation arise in all implementations of social choices, not just those involving AI. Likewise, many of the ethical issues of standing, measurement, and aggregation that are faced by AI designers are also faced by people designing social choice systems in other contexts. The paper thus draws on scholarship and experience from other contexts (including, but not limited to, social choice theory) and relates them to AI. Meanwhile, AI poses some novel issues for social choice. First, with AI, the social choice process is conducted by machines, not by humans. With AI, a machine can be sent out into society to figure out what society wants it to do and then attempt to do it. Human designers of AI must make decisions about standing, measurement, and aggregation and translate this into the technology. Second, there is the question of whether the AI itself should have standing. Arguably, a sufficiently advanced AI should. This raises distinct ethical questions. Thus, another aim of this paper is show how AI expands the scope of social choice ethics. Before diving into the details, it should be explained that questions of standing, measurement, and aggregation must be answered by AI designers at the beginning of the social choice process-the questions cannot be delegated to the process. Social choice processes can consider issues of standing, measurement, and aggregation. However, how these issues are considered is determined by how the process was initially set up. In democracies, this is the issue of who gets to vote on who gets to vote, and how that vote is held. For example, in the United States and other countries, women were first enfranchised when men voted to enfranchise them. For this reason, AI designers cannot simply ''let the AI figure it out''. AI designers who use social choice ethics must make choices about standing, measurement, and aggregation. \n Standing The term ''standing'' comes from the legal context in which to have standing is to have the right to bring a case to court or otherwise participate in the case in some legally significant way. To have legal standing, one must be a legal person-generally a human citizen of the jurisdiction in question-and one must have sufficient connection to the case to justify participation. While this is the origin of the term ''standing'' as it is used in this paper, the paper uses it in a slightly different way. In this paper, to have standing is to have one's ethics included in a social choice process used to determine the ethics of an AI.  3  In social choice processes, those who have standing are those whose values are factored in. Alternatively, if a predetermined ethical view is used instead of a social choice ethics, then the individuals with standing are whoever decides which view to build into the AI. For example, if a person builds an AI on her or his own, and that person makes a unilateral, top-down decision on which ethics to build in, then that person is the only one who has standing for that AI. Biases can be introduced, all the more so, because the demographics of AI tilt heavily towards males of certain backgrounds  (Clark 2016) . Taken in this context, the first major decision related to social choice ethics is the decision to use social choice ethics in the first place. Assuming this decision has, indeed, been made, a series of standing decisions must then be resolved. To help clarify the issue of standing, let us take the concrete example of autonomous vehicles. Some driving decisions pose trade-offs between vehicle occupants and other individuals. For example, should the vehicle travel faster, so as to minimize travel times (good for the occupants), or slower, so as to minimize energy consumption and environmental harms (good for almost everyone else)? One study found a 13% variation in per-mile energy efficiency of autonomous vehicles depending on how the vehicle is programmed  (Mersky and Samaras 2016) . Aggregated across a global fleet of vehicles, this is an enormous difference for energy and the environment-a difference that can depend on how the AI handles standing. Autonomous vehicles may be designed to give their occupants the choice of how the vehicle should drive, especially if the occupants own the vehicle. This gives standing to the occupants but not to everyone else. Furthermore, sometimes, the vehicle itself will need to make the choice, because sometimes, occupants will neglect to choose: the vehicle needs default drive settings. An AI with social choice ethics would learn from the tendencies of whoever is setting its drive mode and make its own driving choices accordingly. Designing an AI to learn its driving values from its occupants denies standing to everyone else. This could lead the vehicle to travel faster and pollute the environment more, causing the rest of the world considerable harm. With this example in mind, we turn now to the general questions of who or what gets standing. Discussions of social choice AI ethics typically propose giving standing to some (often unspecified) portion of humanity. An example of this appears above in the quote ''[Bottom-up ethics] attempts to train or evolve agents whose behavior emulates morally praiseworthy human behavior''  (Allen et al. 2005: 149 ; emphasis added). Similarly,  Yudkowsky (2004: 5)  argues that ''the initial dynamic should implement the coherent extrapolated volition of humankind'' (emphasis added). However, which humans are to be included?  Martin (2017)  considers whether AI ethics should be set by its designers, its users, or by human society as a whole.  4  Should the antisocial psychopaths be included-the Hitlers and bin Ladens and serial killers and rapists and other ''very bad people'' of the world? These are people who might, for example, train autonomous vehicles to drive in especially dangerous ways. One could make a case for excluding them as unfit, just as convicted felons are disenfranchised in some democracies. Indeed, if ''large segments of humanity have base or evil preferences''  (Bostrom 2014: 217) , then including them could foul up the entire social choice process, causing AIs to conduct horrific and unspeakable acts. However, excluding the antisocial requires defining who they are. As  Foucault (1961)  documents, conceptions of madness and mental illness have changed dramatically over time. Current conceptions are thus historically contingent and not necessarily correct. The AI designer must choose which antisocial people, if any, to exclude from the social choice process. Another challenging case is children. Children are routinely excluded from elections on grounds that they lack the intellectual and moral capacity to make reasoned judgments about whom to vote for. In the United States, for example, the minimum age for voting is 18. However, about a quarter of the current human population is under age 15, which is a lot to exclude. Excluding them is arguably inherently unfair, and it could bias an AI's values in certain directions, for example, because young people generally more accepting of lesbian, gay, bisexual, and transgender (LGBT) people (e.g., Pew Research Center 2017). Views about LGBT people may be insignificant for the AI inside autonomous vehicles, but they could be important for, say, AIs that chat with people on social media, such as Microsoft's notorious chatbot Tay  (Gibbs 2016) , or AIs in robots that enforce proper behavior in public, such as the Knightscope K5 security robot  (Metz 2014 ).  5  Excluding children may not be hugely consequential as long as their parents have standing. Parents invest heavily in the success of their children, both privately and publicly (i.e., through governments and community groups). However, future generations are at greater risk. The moral psychology of time preference and temporal discounting typically finds that people value future events and future generations less than the present  (Frederick et al. 2002) . Likewise, philosophers sometimes consider that future generations may have no value at all  (Arrhenius and Rabinowicz 2015) . For example,  Marglin (1963: 97)  writes ''I consider it axiomatic that a democratic government reflects only the preferences of the individuals who are presently members of the body politic''. Thus, unless future generations are given standing at the outset of a social choice process, there is a strong likelihood that their interests would be given little consideration by the resulting AI. (There is also the question of how an AI can learn the values of future generations, but this is a matter of measurement, not standing). It is difficult to overstate how much is at stake with standing for future generations. The population of future generations could be extremely large, vastly dwarfing the present population. Earth will remain habitable for on the order of a few billion more years (O'Malley-James et al. 2014), and the rest of the universe will remain habitable for much longer  (Adams 2008) . If AI designers only give standing to the present generation, they risk biasing outcomes against this astronomically large future. For example, this could mean gluttonous consumption of nonrenewable natural resources and pollution of global ecosystems by the present generation (such as in autonomous vehicles designed to travel quickly instead of energy efficiently), with future generations left to struggle through the ensuing mess. An AI that is programmed to only give standing to the present generation could deliver an extreme intergenerational injustice. These are the ethical issues faced if standing is given to some portion of humanity, as is commonly prescribed in the AI ethics literature. However, this presupposes that standing should be given only to humanity. However, humans are not the only individuals that could merit standing. Standing has been considered for nonhuman animals  (Sunstein 2000) , plants and ecosystems  (Stone 1972; Hannon 1998) , abiotic environments  (Rolston 1986) , extraterrestrials (Cockell 2007), technologically enhanced ''posthumans''  (Buchanan 2009) , and AIs  (Hubbard 2011) . Each of these entities poses its own set of ethical challenges for the issue of standing in an AI social choice process. Let us consider nonhuman animals. The more advanced nonhuman animals (e.g., other primates) have cognitive abilities approaching those of humans, a fact that has been the basis of attempts to grant them some legal standing, such as the Great Ape Project. Sentience appears to decline gradually across the animal kingdom-for example, research on the sentience of fish is inconclusive  (Rose et al. 2014) , while some research suggests the sentience of invertebrate crayfish  (Fossat et al. 2014) . Failing to give standing to sentient animals would risk mass atrocities committed against them-atrocities on par with or worse than the widespread and horrific abuse of livestock animals in factory farms today (e.g.,  Anomaly 2015) . Robots are already managing livestock in some locations  (Klein 2016) , and it may only be a matter of time before livestock is managed primarily by robots. Working in factory farms is dangerous and unpleasant for humans and also somewhat repetitive, making it an ideal candidate for automation. However, if the robots are programmed to learn their values from humans only, then they could perpetuate the violence against livestock animals. Indeed, robots could even make the violence worse if the empathy of human farmhands is replaced by the callousness of farm management. Alternatively, if the robots learn values from humans and livestock alike, then they may find ways to treat the livestock animals better. In the best-case scenario, this could drastically reduce or even eliminate the mass abuse of livestock animals in factory farms while maintaining or even improving the supply of livestock products to humans. However, the robots may find some trade-offs unavoidable, in which case giving standing to livestock could worsen the supply of livestock products-in the extreme case, the robots could even conclude that the livestock should be set free. Similar logic applies to plants, ecosystems, and abiotic environments: AIs designed to learn values from humans only could end up acting for human benefit at the expense of anyone or anything else. The AI designer must choose sides on these issues when choosing who or what gets standing in the social choice process. A different logic applies to posthumans, because these entities do not currently exist. Consider the extreme case of a superpowerful ASI that has taken over the world and is managing it according to the CEV of humanity. It is possible-indeed it may be probable-that humanity ultimately prefers remaining human and not being ''enhanced'' into posthumans. Indeed, a recent public opinion poll found a majority of Americans indicating opposition to a range of human ''enhancement'' technologies  (Funk et al. 2016) . In this case, whether posthumans ever come into existence could depend on whether the ASI (or its precursor seed AI) is designed to give standing to posthumans. If posthumans have standing, then the desire of posthumans to come into existence could be balanced against the desire of humans to stay human.  6  Finally, there is the AI itself.  Hubbard (2011)  argues that if AIs possess the attributes that are considered essential for legal standing, then they should have it. Hubbard proposes three criteria for an AI meriting legal standing: complex interaction skills, self-consciousness, and the ability to pursue group benefits. If anything, standards for moral standing in a social choice process should be lower than this, because legal standing implies a certain ability to function in courts and other legal contexts, whereas moral standing does not.  Martin (2017)  considers that sufficiently advanced AIs could gain capacity for ethical reasoning that matches or even exceeds that of humans, making them independent ethical agents. In contrast,  Yampolskiy (2013: 393)  argues that AIs that merit standing should not be built in the first place, and instead that ''machines should be inferior by design; they should have no rights and should be expendable as needed, making their use as tools much more beneficial for their creators''. Once again, much is at stake. To abstain from building certain types of AIs could significantly limit the extent to which the benefits of AI could be realized. AIs that would merit standing may be some of the most sophisticated and capable AIs; abstaining from building them could be an especially large loss. Alternatively, if humans deny standing for sophisticated AIs, this puts core human values at risk. As  Hubbard (2011)  argues, to deny standing to entities that are at least as deserving of it as we are cuts against the liberal, secular, rationalist, and egalitarian foundations of democratic human society. However, AIs pose a novel and sizable complication. As  Yampolskiy (2013)  explains, AIs can be readily copied in large numbers. If AIs have standing, they could easily drown out the human population or any other biological population. Some existing nonhuman entities raise the same complication, for example, if standing was given to bacteria, which massively outnumber humans and other large organisms. However, only AI can combine massive population sizes with cognitive sophistication equal or greater to humans. It would arguably be unjust to disenfranchise AIs simply on the grounds of getting outvotedsuch a situation would be analogous to the apartheid of South Africa, in which the white minority disenfranchised the black majority. However, to grant AIs standing could mean letting them control the social choice process. Ultimately, whether they would control, it depends on the details of measurement and aggregation. \n Measurement Measurement in this context refers to the process through which an individual's ethical views are identified for inclusion in the social choice process. In a typical democracy, measurement is done via voting. In capitalism, measurement is done via buying and selling. Measurement can also be done via observing behavior, as in the economics concept of ''revealed preference'', via surveys and interviews, such as in public opinion polling, or even via brain imaging, such as in neuropsychology research. If human beings-or whatever else was being measured-had one single, consistent set of ethical views, then measurement would be a relatively simple issue. Each measurement procedure would yield more or less the same results. The only challenge would be obtaining results in sufficient detail to inform the issue in question. This is a nontrivial challenge, but it pales in comparison to the actual challenge of measurement. Humans do not have a single, consistent set of ethical views, and different measurement procedures can yield different answers to the same ethical question. To take one example, consider the ethical issue of time preference. This concerns how people value present gains and losses relative to future gains and losses.  Frederick et al. (2002, Table 1 ) review 41 different studies that measure human time preference using either behavior observation or survey methods. The studies show that humans discount future gains and losses at rates ranging from -6 to ? ?%. Some of this variation is attributable to differences in the nature of the gains and losses being evaluated (e.g., money vs. health), but much of it appears to be due to differences in the procedures used to measure time preference. Discount rates from -6 to ? ?% are an extremely wide range. Negative discount rates imply that future gains and losses are more valuable than present ones. A discount rate of ? ?% implies that future gains and losses hold zero value. Thus, depending on the choice of measurement procedure, an AI could end up valuing future gains and losses a lot or not at all. For example, this could be the difference between an autonomous vehicle AI traveling faster (if future gains and losses are not valued at all) or instead more energy efficiently (if future gains and losses are valued a lot). Or, for a superpowerful ASI, this could be the difference between lavishing resources on the present generation, future be damned, or preparing for the distant future, even if that requires present sacrifice. The wide range of time preferences that have been measured in humans is one instance of a broader tendency for humans to show inconsistent and often incoherent ethics views. Even moral philosophers struggle with inconsistency, as evidenced by their various ''impossibility theorems'' in which they find it impossible to craft a moral theory that meets a series of seemingly plausible moral intuitions (e.g.,  Arrhenius 2011) . For this reason, an effort to measure an individual's ethics views is likely to yield only one particular variation on his or her views. This diversity of an individual's values poses a thorny challenge for social choice AI ethics. As an example, consider an environmentalist who also happens to be a fast driver. This may seem hypocritical, since driving fast is worse for the environment-perhaps, this person just thinks that other people should drive slower. However, it is often observed that people disagree with their own behavior on these sorts of matters  (Stone and Fernandez 2008) . In such a situation, what is a social choice AI to do? The AI in an autonomous vehicle could measure this person's ethics by observing her driving behavior, in which case the AI would end up traveling quickly, or by asking her how she thinks she should drive, in which case the AI would end up traveling energy efficiently. Both measurement approaches are technologically simple to implement: one involves recording driving data and the other involves a simple questionnaire. Either approach could lay some claim to measuring the person's ''true'' view. One option available to AI designers is to select the measurement approach that they believe delivers the better result. This is analogous to the concept of libertarian paternalism or ''nudges''  (Thaler and Sunstein 2008 ; in the context of robotics, see  Borenstein and Arkin 2016) . In this context, to nudge someone is to structure their decisions to make it more likely that they make the ''better'' decision. For example, states can make it the default option that people are organ donors, which increases the rate of organ donors. This is libertarian, because anyone is still free to opt out of organ donation, and it is paternalistic, because it structures the decision, so that people tend to make the ''better'' decision of being an organ donor. Analogously, AI designers could select the measurement option that they think delivers the better result. Indeed, designers could even give people the choice of measurement option, in which case designers could influence results by choosing which measurement option is the default. But which to choose? Is it better for people to travel faster or more energy efficiently? Traveling faster may be better for that person, while traveling more energy efficiently may be better for society as a whole. This is a difficult ethics question in its own right, and it is exactly the sort of question that AI designers seek to avoid by choosing social choice ethics. Because humans display multiple ethics views, the choice of measurement approach for social choice ethics can require AI designers to make unilateral ethical choices. In response to the seeming incoherence of human ethics, some AI ethicists call for measuring an idealized version of human ethics instead of what is observed in actual humans. For example,  Muehlhauser and Helm (2012: 114)  posit that an advantage of CEV for ASI is that it would deliver ''what a person would want after reaching reflective equilibrium with respect to his or her values, rather than merely what each person happens to want right now'', and that this ''may dissolve the contradictions within each person's current preferences''. This follows calls in moral philosophy for the use of ''idealized preferences'' (e.g.,  Harsanyi 1996; Ng 1999; and references in Muehlhauser and Helm 2012) . The hope is that an ASI would be able to figure out which ethics any given human would really want if he or she was able to think the matter through as carefully as an ASI could, and that following this idealized ethics would yield better results. It should, indeed, be expected that a human's idealized ethics would differ from his or her original ethics. This is seen, for example, in differences between the ethics views held by moral philosophers and those held by the lay public. However, it may be a matter of opinion whether the process of idealization tends to deliver ethics that are in some neutral sense ''better''. Moral philosophers are known to hold a range of idiosyncratic and potentially catastrophic views, as follows from their inclination to following specific moral intuitions to extreme logical conclusions, wherever that may lead. In some cases, perhaps many cases, it may appear that their pre-moral philosophy, pre-idealization, common sense moral views would be better. As an illustrative example, consider the view of  Benatar (2006)  that it is wrong for humans to procreate. Benatar's view is the logical conclusion of his carefully considered belief that it is bad to harm people by bringing them into existence, but it is not good to benefit people by bringing them into existence. Put differently, procreation can be bad, but it cannot be good. The extreme logical conclusion of this view is that humanity should die out after the present generation. Benatar's views may well constitute a minority position among moral philosophers, 7 but this is beside the point. The point is that at least in this one case, the process of idealization would appear to deliver worse results. This presumes that, prior to putting more thought into his moral philosophy, Benatar did not wish for humanity's extinction, which seems likely: few people with ''common sense'' moral views would wish such a thing. Therefore, for cases like Benatar, measuring idealized values instead of ''common sense'' initial values can deliver worse results. Whether these cases are outliers or the norm is an empirical question for which an answer may not yet exist. Regardless, it remains the case that the decision to measure ethics using idealized human values is not an ethical ''no brainer'' but instead is a complex and contentious decision on which much depends. If measurement is to use an idealization, there remains the question of which idealization process to use. One variable is whether idealization proceeds via solitary reflection or group deliberation.  Yudkowsky (2004: 7 ) calls for group deliberation for an idealization of the ethics of humans if they ''had grown up farther together'' instead of the ethics of ''the person you'd become if you made your decisions alone in a padded cell''. Yudkowsky posits that the social interactions of group deliberation would provide ''social forces contributing to niceness''. However, there is reason to doubt that group deliberation would tend to yield better results. Groups can suffer from such pathologies as groupthink and in-group favoritism  (Baron 2005; Balliet et al. 2014) . Meanwhile, solitary reflection can do well. Indeed, much of the most distinguished moral philosophy produced across human history was produced by individuals working largely in solitude. AI designers who choose idealized measurement must further make the nontrivial choice between idealization via solitary reflection or group deliberation. Other idealization choices include how long to let the idealization process play out and how to handle instances in which idealization leaves some contradictory incoherences intact. The various measurement issues discussed thus far pertain mainly to present-generation humans. While the issues are substantial, they pale in comparison to the issues presented by other beings. For starters, how would a social choice AI measure the values of sentient nonhuman animals? Some standard human measurement techniques could not be used-for example, cows and frogs cannot meaningfully respond to survey questionnaires. Other techniques could be used-nonhuman animals' behavior can be observed, and their brains can be scanned with imaging technologies-but interpreting the results is a major challenge. Human AI designers do not know what it is like to be a cow or a frog, so they must make sweeping assumptions in programming an AI to infer cow or frog ethics from any given measurement technique. What about nonsentient animals, plants, and other living organisms, and nonliving, abiotic matter? The case for giving them standing is weaker, because they (presumably) cannot suffer or experience any sort of pleasure. However, if they are given standing, this presents the challenge of measuring their ethics views. Yet, there is no clear procedure for extrapolating the values of nonsentient beings. They have no brains to scan. Some of them (e.g., rocks) have no (or barely any) behavior to observe. The social choice AI is left without the standard empirical techniques of measurement. The same holds for future generations of humans or posthumans. These beings do not yet exist, and so they cannot be surveyed, observed, scanned, or measured via any standard empirical technique. When empirical techniques are inadequate or unavailable, an alternative (perhaps the only alternative) is to use measurement by proxy. The essence of proxy measurement is to have an available being attempt to describe the views that an unavailable being would have if he, she, or it was available to be measured. For example, in some human voting systems, a person who cannot attend a vote can give his or her proxy vote to a trusted associate. The associate then gets to vote on behalf of the absentee person. Similarly, proxy measurement is at the heart of proposals to build representation of future generations into present democracies (e.g., Tonn 1996). Likewise, attempts to measure the interests of nonsentient beings ultimately come down to humans seeking to infer what those beings really ''want''. Therefore, if standing is given to nonsentient or future beings, a social choice AI may need some procedure for measuring their ethics via proxy. This raises its own set of questions: Who to give proxy to? How to measure their proxy? These are difficult questions, but they at least resemble the more general questions of standing and measurement and thus are both familiar and tractable. However, the stakes are quite large. Nonsentient and/or future beings could vastly outnumber present sentient beings. Therefore, different handlings of proxy could yield massively different results, not just for each individual's ethics measurement but for the entire social choice process. How the entire social choice process would play out would also depend on the technique used for aggregation. If AIs have standing, they pose different measurement issues-or rather, measurement opportunities. It may be possible to infer an AI's ethical views from its source code. This is not necessarily a straightforward task: the relevant code could be large and complex. However, the inference may nonetheless be feasible, perhaps with the assistance of an AI designed for the task. In this case, it may be possible to achieve a high degree of precision in measurement, at least for this measurement technique. Other techniques may still yield other descriptions of AIs' ethical views, just as different techniques can yield different descriptions for humans and other types of entities. \n Aggregation In a social choice process, no matter who has standing and how their ethics views are measured, once the measurements are in, the final step is to aggregate these individual ethics views into a single societal ethics view. For AI, a single view is needed to determine how the AI is to make decisions. In other words, the aggregate ethics view is what the AI is supposed to use to decide how it should behave. Classic social choice theory recognizes that how to aggregate is not always straightforward. The simplest case occurs when three individuals (labeled X, Y, and Z) each have a different ranking of three choice options (labeled A, B, and C), as shown in Table  1 . When the vote is between A and B, A wins; between A and C, C wins; between B and C, B wins. Thus, it would appear that the group prefers A to B, B to C, and C to A. In other words, the preferences are intransitive. This case is known as the voting paradox or Condorcet's paradox, having been documented by  Condorcet (1785) . One solution to Condorcet's paradox is to also consider the strength of individual preferences for each choice option. For example, perhaps X and Y have only a slight preference for B over C, yet Z has a strong preference for C, in which case C might be the best option. This solution is hinted at in  Yudkowsky's (2004: 8)  argument that ''A minor, muddled preference of 60% of humanity might be countered by a strong, unmuddled preference of 10% of humanity.'' However, this imposes a greater burden on measurement by requiring the strength of ethics views and not just ranked orderings. It also makes aggregation more demanding, because it requires being able to compare ''ethics view strength'' between individuals. The inter-individual comparison of ethics view strength is complicated by the fact that people often hold ''protected'' or ''sacred'' values that they believe should not be traded off against other values, much like deontological rules  (Ginges et al. 2007; Ritov and Baron 1999) . To form a single ethics view, an aggregation process must resolve conflicts between different people's protected values. For example, suppose that one person believes that people should be categorically prohibited from putting excessive pollution into the environment, while another believes that it should be categorically prohibited to deny anyone the right to drive however they would like. An AI's attempt to measure the strength of these views could find that they have infinite strength pointing in opposite directions. The AI's aggregation process requires some means of resolving such disagreements. One option is to insist that no one's views can have infinite strength, but this imposes a distortion on the views of people who hold protected values. Another aggregation challenge comes from aggregation procedures that cluster individuals into distinct groups. In modern democracies, voters are commonly clustered into geographic districts. How elections turn out can depend heavily on how district lines are drawn. This is seen in the concept of ''gerrymandering'', in which unintuitive district lines are drawn so as to maximize advantage for a political party, or more generally in the modifiable areal unit problem, in which different demarcations of spatial units yield different results  (Openshaw 1983) . Similar quirks of clustering underlie the fact that a US Presidential candidate can win the popular vote but lose the electoral college and hence the overall election, 8 as well the fact that each US state has two Senators regardless of its population, giving proportionately more Senate representation to residents of small states. The AI designer may be tempted to reject clustering and stick to a strict ''one individual, one vote'' principle. However, this can facilitate ''tyranny of the majority'' at the expense of minority rights and interests. Indeed, it was to protect the interests of small states that US Senate representation was designed with two Senators per state, as per the 1787 Connecticut Compromise  (Yazawa 2016) . Many AIs with bottom-up ethics are designed in a rather different fashion, updating their ethics each time someone interacts with it. This is essentially a ''vote early and often'' principle. Hence, for example, Microsoft's chatbot Tay was trained to speak vulgarities, even though many people did Further complications come when nonhumans have standing. Do their views count the same as humans? A ''one individual, one vote'' principle may make a little sense, for example, if standing is given to the massive population of bacteria. An argument can be made for giving nonhuman animals and other living beings less of a vote than humans, because humans are more cognitively sophisticated. However, the same argument would suggest that humans should have less of a vote if standing is granted to more sophisticated beings, such as posthumans or ASIs. Aggregation for AIs poses an additional complication that derives from AI reproduction. An AI can be copied extensively; if each copy has standing, and each has equal say in the aggregation process, then this can drown out everyone else's vote. An aggregation process could face a dilemma between disenfranchising AIs or disenfranchising everyone else. A similar issue is posed by future generations, given their astronomically large potential population. It should be noted that these various aggregation challenges only exist to the extent that different individuals have different ethics views. Where measurement yields consensus, aggregation is irrelevant. Some AI theorists posit that superintelligent beings all tend towards the same universal set of values  (Goertzel 2016) . Whether or not this is the case remains to be seen and cannot a priori be counted on. Without consensus, issues of aggregation must be addressed. \n Discussion and conclusion Having considered issues of standing, measurement, and aggregation in detail, let us now revisit the procedural and abstention justifications for social choice ethics in AI (Recall that the wise crowd justification requires a predetermined ethical view). The procedural justification maintains that individuals should have a say in decisions that affect them instead of AI designers imposing their own views on them. However, this ideal leaves open questions about standing, measurement, and aggregation; AI designers cannot avoid imposing their own views on these questions. At most, social choice ethics reduces the extent to which AI designers impose their own views. Furthermore, it is often difficult or even impossible to give everyone a say. When AI has global effects, such as in autonomous vehicles affecting global warming or ASI that takes over the world, a massive number of individuals are affected, most of whom may not have direct interaction with the AI. When AI affects future generations of humans, future entities such as posthumans or new forms of AI, or less intelligent nonhuman entities, giving them a say becomes inherently difficult. Thus, while the procedural justification may capture an admirable ethical sentiment, it provides weak support and limited guidance for AI ethics design. The abstention justification maintains that by using social choice ethics, AI designers can abstain from making ethics decisions and instead let the AI figure out what society's aggregate views are. AI designers may take comfort in this insofar as they are unaccustomed or disinclined to think about ethics. However, use of social choice ethics requires decisions about standing, measurement, and aggregation, which can in turn substantially affect outcomes of AI decisions. There is simply no way for AI designers to successfully abstain from ethical decisionmaking. Furthermore, the ethical issues in standing, measurement, and aggregation are numerous and profound. Using social choice ethics requires much more than a minimal amount of ethical thought. The abstention justification fails. AI designers are left with two options. They can use social choice ethics and make the profound ethical decisions of standing, measurement, and aggregation. They may justify their use of social choice ethics with a weakened form of the procedural justification; their decisions regarding standing, measurement, and aggregation would require separate justification. Or, they can abandon social choice ethics in favor of a predetermined ethical view. A predetermined view would require its own justification, but this may not be much different than justifying decisions of standing, measurement, and aggregation. Indeed, depending on the details, the distinction between social choice ethics and predetermined view ethics may be insignificant. For example, consider the question of standing for future generations. This is broadly similar to the question of whether to count the welfare of future generations in welfarist utilitarianism. An AI may make the same decisions under either social choice ethics or welfarist utilitarianism as long as it does (or does not) count future generations. For example, an autonomous vehicle that counts future generations may drive in an energy efficient fashion to reduce its greenhouse gas emissions, while an ASI may embark on long-term projects at the expense of short-term splurges. Or, consider the question of whether to give standing to AIs. A social choice ethics may give AIs standing if they have the capacity to form ethical views. Similarly, welfarist utilitarianism may count AIs if they have the capacity to experience pleasure and pain. In both cases, the moral calculus could be dominated by the overwhelmingly large number of AIs that can be created by copying AI software ad infinitum. In these and other cases, the distinction between social choice ethics and predetermined view ethics is unimportant. Thus, proposals such as CEV and bottom-up ethics do not actually do much to resolve the important decisions to be made in the design of AI ethics. These are inherently decisions that must be made by AI designers-one cannot ''let the AI figure it out'', because the decisions concern how the AI would figure it out. Focus should likewise be on the important decisions, not on whether AI uses some sort of social choice ethics. Table 1 1 A hypothetical set of choice rankings from three different individuals Tay's training was driven mainly by the ''vocal minority'' who repeatedly engaged with it. In this case, the vocal minority aggregation scheme yielded pathological results. A ''one individual, one vote'' aggregation procedure would have given everyone equal say in Tay's training and may have yielded better results. 9 First choice Second choice Third choice Individual X A B C Individual Y B C A Individual Z C A B \n\t\t\t Note that while consciousness may play a role in ethics learning among human children, it is not essential for AI. The essential feature is that ethics is learned via interaction with the environment, regardless of whether that interaction involves consciousness. 2 One exception, in which social choice is (briefly) discussed in the context of CEV, is Tarleton (2010) . Keyword searches in Google Scholar identified no other discussions of social choice in CEV or bottom-up ethics. There is a more extensive study of ''computational social choice'' relating aspects of social choice theory and computer science (Brandt et al. 2015) . \n\t\t\t AI & Soc (2020) 35:165-176    \n\t\t\t This is similar to the ''boundary problem'' in democracy (Arrhenius 2005) .4  Martin (2017) also considers having AIs set their own ethics or the ethics of other AIs; more on this below. \n\t\t\t Tay was programmed to learn from (and thus give standing to) Twitter users who interact with it, which quickly devolved into deviance and obscenity as Twitter users taught it to misbehave. Microsoft has since been wrestling with the question of how to give standing to a more appropriate mix of people.AI & Soc (2020) 35:165-176   \n\t\t\t There is a certain irony that some proponents of CEV speak in terms of giving standing only to humanity but also favor a transition to posthumanity (e.g., Bostrom 2008) . \n\t\t\t For an argument against Benatar's views, see Baum (2008) . \n\t\t\t There is no indication that Tay was designed with bottom-up ethics in mind, but the net result is the same in that Tay acquired its principles for behavior via input from the people it interacted with.", "date_published": "n/a", "url": "n/a", "filename": "Baum2020_Article_SocialChoiceEthicsInArtificial.tei.xml", "abstract": "A major approach to the ethics of artificial intelligence (AI) is to use social choice, in which the AI is designed to act according to the aggregate views of society. This is found in the AI ethics of ''coherent extrapolated volition'' and ''bottom-up ethics''. This paper shows that the normative basis of AI social choice ethics is weak due to the fact that there is no one single aggregate ethical view of society. Instead, the design of social choice AI faces three sets of decisions: standing, concerning whose ethics views are included; measurement, concerning how their views are identified; and aggregation, concerning how individual views are combined to a single view that will guide AI behavior. These decisions must be made up front in the initial AI design-designers cannot ''let the AI figure it out''. Each set of decisions poses difficult ethical dilemmas with major consequences for AI behavior, with some decision options yielding pathological or even catastrophic results. Furthermore, non-social choice ethics face similar issues, such as whether to count future generations or the AI itself. These issues can be more important than the question of whether or not to use social choice ethics. Attention should focus on these issues, not on social choice.", "id": "1d1d31e929b9dd97e9b4756fa95a444d"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Kaj Sotala", "Roman V Yampolskiy"], "title": "Corrigendum: Responses to catastrophic AGI risk: a survey (2015 Phys. Scr. 90 018001)", "text": "Parts of the reference list are corrected to the following:  [105]   Many have argued that in the next twenty to one hundred years we will create artificial general intelligences (AGIs)  [39, 46, 170, 193, 196, 200, 235, 288]  4 . Unlike current 'narrow' AI systems, AGIs would perform at or above the human level not merely in particular domains (e.g., chess or arithmetic), but in a wide variety of domains, including novel ones  5  . They would have a robust understanding of natural language and be capable of general problem solving. The creation of AGI could pose challenges and risks of varied severity for society, such as the possibility of AGIs out competing humans in the job market  [60, 189] . This article, however, focuses on the suggestion that AGIs may come to act in ways not intended by their creators, and in this way pose a catastrophic  [52]  or even an existential  [47]  risk to humanity  6  . We will organize and summarize the proposals that have been made so far for responding to catastrophic AGI risk, so as to provide a map of the field to newcomers and veterans alike  7  . Section 2 explains why AGI may pose a catastrophic risk. Sections 3-5 review three categories of proposals for dealing with AGI risk: societal proposals, proposals for external constraints on AGI behaviors, and proposals for creating AGIs that are safe due to their internal design. Although the main purpose of this paper is to provide a summary of existing work, we briefly provide commentary on | Royal Swedish Academy of Sciences Physica Scripta Phys. Scr.  90 (2015)    018001 (33pp)  doi:10.1088/0031-8949/90/1/018001 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  3  This paper elaborates and expands upon some of the discussion originally found in Yampolskiy  [304] , as well as reviewing a large amount of additional material.  4  For a preliminary 'AGI roadmap', see Adams et al  [10] . For a variety of views, see Eden  [5] . The term 'AGI' was introduced by Gubrud  [124] . For overviews of AGI approaches, see Wang et al  [288]  and Adams et al  [10] . Some closely related terms are 'strong AI' (e.g.,  [170] ) and 'human-level AI' (e.g.,  [67, 190] ). Unlike the term 'human-level AI', the term 'artificial general intelligence' does not necessarily presume that the intelligence will be human-like.  5  For this paper, we use a binary distinction between narrow AI and AGI. This is merely for the sake of simplicity: we do not assume the actual difference between the two categories to necessarily be so clean-cut.  6  A catastrophic risk is something that might inflict serious damage to human well-being on a global scale and cause ten million or more fatalities  [52] . An existential risk is one that threatens human extinction  [47] . Many writers argue that AGI might be a risk of such magnitude  [3, 44, 47, 64, 65, 68, 72, 82, 117, 126, 129, 160, 189, 193, 278, 289, 300, 309] .  7  One important work in this field is Bostrom  [3] , published after this paper was originally written. It introduces some additional proposals as well as discussing many of the ones reviewed in this work, but time constraints involved in the publication of this paper did not allow us to update this work to take it properly into account. the proposals in each major subsection of sections 3-5 and highlight some of the proposals we consider the most promising in section 6. Attempting to influence the course of developing technologies involves a great deal of uncertainty concerning the nature of those technologies and the likely long-term impacts of societal decisions  [50] . While we aim to provide a preliminary analysis of many proposals, we do not have final answers. The purpose of this article is to act as a review and to highlight some considerations that will be useful starting points for further research. In the hopes of fostering further debate, we also highlight some of the proposals that we consider the most promising. In the medium term, these are regulation (section 3.3), merging with machines (section 3.4), AGI confinement (section 4.1), Oracle AI (section 5.1) and motivational weaknesses (section 5.6). In the long term, the most promising approaches seem to be value learning (section 5.2.5) and human-like architectures (section 5.  3.4) . Section 6 provides an extended discussion of the various merits and problems of these proposals. \n Catastrophic AGI risk We begin with a brief sketch of the argument that AGI poses a catastrophic risk to humanity. At least two separate lines of argument seem to support this conclusion. First, AI has already made it possible to automate many jobs  [60]  and AGIs, when they are created, should be capable of performing most jobs better than humans  [130, 136, 189, 289] . As humanity grows increasingly reliant on AGIs, these AGIs will begin to wield more and more influence and power. Even if AGIs initially function as subservient tools, an increasing number of decisions will be made by autonomous AGIs rather than by humans. Over time it would become ever more difficult to replace the AGIs, even if they no longer remained subservient. Second, there may be a sudden discontinuity in which AGIs rapidly become far more numerous or intelligent  [72, 117, 244, 251, 306] . This could happen due to (1) a conceptual breakthrough which makes it easier to run AGIs using far less hardware, (2) AGIs using fast computing hardware to develop ever-faster hardware, or (3) AGIs crossing a threshold in intelligence that allows them to carry out increasingly fast software self-improvement. Even if the AGIs were expensive to develop at first, they could be cheaply copied and could thus spread quickly once created. Once they become powerful enough, AGIs might be a threat to humanity even if they are not actively malevolent or hostile. Mere indifference to human values-including human survival-could be sufficient for AGIs to pose an existential threat  [211, 212, 309, 312] . We will now lay out the above reasoning in more detail. \n Most tasks will be automated Ever since the Industrial Revolution, society has become increasingly automated. Brynjolfsson  [60]  argue that the current high unemployment rate in the United States is partially due to rapid advances in information technology, which has made it possible to replace human workers with computers faster than human workers can be trained in jobs that computers cannot yet perform. Vending machines are replacing shop attendants, automated discovery programs which locate relevant legal documents are replacing lawyers and legal aides, and automated virtual assistants are replacing customer service representatives. Labor is becoming automated for reasons of cost, efficiency and quality. Once a machine becomes capable of performing a task as well as (or almost as well as) a human, the cost of purchasing and maintaining it may be less than the cost of having a salaried human perform the same task. In many cases, machines are also capable of doing the same job faster, for longer periods and with fewer errors. In addition to replacing workers entirely, machines may also take over aspects of jobs that were once the sole domain of highly trained professionals, making the job easier to perform by less-skilled employees  [298] . If workers can be affordably replaced by developing more sophisticated AI, there is a strong economic incentive to do so. This is already happening with narrow AI, which often requires major modifications or even a complete redesign in order to be adapted for new tasks. 'A roadmap for US robotics'  [154]  calls for major investments into automation, citing the potential for considerable improvements in the fields of manufacturing, logistics, health care and services. Similarly, the US Air Force Chief Scientistʼs  [78]  'Technology horizons' report mentions 'increased use of autonomy and autonomous systems' as a key area of research to focus on in the next decade, and also notes that reducing the need for manpower provides the greatest potential for cutting costs. In 2000, the US Congress instructed the armed forces to have one third of their deep strike force aircraft be unmanned by 2010, and one third of their ground combat vehicles be unmanned by 2015  [4] . To the extent that an AGI could learn to do many kinds of tasks-or even any kind of task-without needing an extensive re-engineering effort, the AGI could make the replacement of humans by machines much cheaper and more profitable. As more tasks become automated, the bottlenecks for further automation will require adaptability and flexibility that narrow-AI systems are incapable of. These will then make up an increasing portion of the economy, further strengthening the incentive to develop AGI. Increasingly sophisticated AI may eventually lead to AGI, possibly within the next several decades  [39, 200] . Eventually it will make economic sense to automate all or nearly all jobs  [130, 136, 289] . As AGIs will possess many advantages over humans  [200, 253] , a greater and greater proportion of the workforce will consist of intelligent machines. \n AGIs might harm humans AGIs might bestow overwhelming military, economic, or political power on the groups that control them  [47] . For example, automation could lead to an ever-increasing transfer of wealth and power to the owners of the AGIs  [54, 60] . AGIs could also be used to develop advanced weapons and plans for military operations or political takeovers  [47, 124, 163] . Some of these scenarios could lead to catastrophic risks, depending on the capabilities of the AGIs and other factors. Our focus is on the risk from the possibility that AGIs could behave in unexpected and harmful ways, even if the intentions of their owners were benign. Even modern-day narrow-AI systems are becoming autonomous and powerful enough that they sometimes take unanticipated and harmful actions before a human supervisor has a chance to react. To take one example, rapid automated trading was found to have contributed to the 2010 stock market 'flash crash'  [70]    8  . Autonomous systems may also cause people difficulties in more mundane situations, such as when a credit card is automatically flagged as possibly stolen due to an unusual usage pattern  [16] , or when automatic defense systems malfunction and cause deaths  [240] . As machines become more autonomous, humans will have fewer opportunities to intervene in time and will be forced to rely on machines making good choices. This has prompted the creation of the field of 'machine ethics'  [1, 16, 282] , concerned with creating AI systems designed to make appropriate moral choices. Compared to narrow-AI systems, AGIs will be even more autonomous and capable, and will thus require even more robust solutions for governing their behavior  9  . If some AGIs were both powerful and indifferent to human values, the consequences could be disastrous. At one extreme, powerful AGIs indifferent to human survival could bring about human extinction. As Yudkowsky  [309]  writes, 'The AI does not hate you, nor does it love you, but you are made out of atoms which it can use for something else'. Omohundro  [211, 212]  and Bostrom  [51]  argue that standard microeconomic theory prescribes particular instrumental behaviors which are useful for the achievement of almost any set of goals. Furthermore, any agents which do not follow certain axioms of rational behavior will possess vulnerabilities which some other agent may exploit to their own benefit. Thus AGIs which understand these principles and wish to act efficiently will modify themselves so that their behavior more closely resembles rational economic behavior  [213] . Extra resources are useful in the pursuit of nearly any set of goals and self-preservation behaviors will increase the probability that the agent can continue to further its goals. AGI systems which follow rational economic theory will then exhibit tendencies toward behaviors such as self-replicating, breaking into other machines and acquiring resources without regard for anyone elseʼs safety. They will also attempt to improve themselves in order to more effectively achieve these and other goals, which could lead to rapid improvement even if the designers did not intend the agent to self-improve. Even AGIs that were explicitly designed to behave ethically might end up acting at cross-purposes to humanity, because it is difficult to precisely capture the complexity of human values in machine goal systems  [30, 199, 309, 312] . Muehlhauser  [199]  caution that moral philosophy has found no satisfactory formalization of human values. All moral theories proposed so far would lead to undesirable consequences if implemented by superintelligent machines. For example, a machine programmed to maximize the satisfaction of human (or sentient) preferences might simply modify peopleʼs brains to give them desires that are maximally easy to satisfy. Intuitively, one might say that current moral theories are all too simple-even if they seem correct at first glance, they do not actually take into account all the things that we value and this leads to a catastrophic outcome. This could be referred to as the complexity of value thesis. Recent psychological and neuroscientific experiments confirm that human values are highly complex  [199] , that the pursuit of pleasure is not the only human value  [7]  and that humans are often unaware of their own values  [96, 197, 302] . Still, perhaps powerful AGIs would have desirable consequences so long as they were programmed to respect most human values. If so, then our inability to perfectly specify human values in AGI designs need not pose a catastrophic risk. Different cultures and generations have historically had very different values from each other and it seems likely that over time our values would become considerably different from current-day ones. It could be enough to maintain some small set of core values, though what exactly would constitute a core value is unclear  10  . Yudkowsky  [312]  argues that, due to the fragility of value, the basic problem remains. He argues that, even if an AGI implemented most human values, the outcome might still be unacceptable. For example, an AGI which failed to incorporate the value of novelty could create a solar system filled with countless minds experiencing one highly optimal and satisfying experience over and over again, never doing or feeling anything else  [311]    11  . automated trading going awry.  9  In practice, there have been two separate communities doing research on automated moral decision-making  [13, 199, 246] . The 'AGI ethics' community has concentrated specifically on advanced AGIs (e.g.,  [110, 309] ), while the 'machine ethics' community typically has concentrated on more immediate applications for current-day AI (e.g.,  [1, 284] ). In this paper, we have cited the machine ethics literature only where it seemed relevant, leaving out papers that seemed to be too focused on narrow-AI systems for our purposes. In particular, we have left out most discussions of military machine ethics  [26] , which focus primarily on the constrained special case of creating systems that are safe for battlefield usage. Note that while the term 'machine ethics' is relatively established, 'AGI ethics' is not. One proposed alternative name for the 'AGI ethics' discipline is 'AI safety engineering'  [304, 305] .  10  For example, different people may disagree over whether freedom or well-being is a more important value.  11  Miller  [189]  similarly notes that, despite a common belief to the contrary, it is impossible to write laws in a manner that would match our stated moral principles without a judge needing to use a large amount of implicit commonsense knowledge to correctly interpret them: 'Laws shouldnʼt always be interpreted literally because legislators canʼt anticipate all possible contingencies. Also, humans' intuitive feel for what constitutes murder goes beyond anything we can commit to paper. The same applies to friendliness'  [189] . In this paper, we will frequently refer to the problem of 'AGI safety' or 'safe AGI', by which we mean the problem of ensuring that AGIs respect human values, or perhaps some extrapolation or idealization of human values  12  . We do not seek to imply that current human values would be the best possible ones, that AGIs could not help us in developing our values further, or that the values of other sentient beings would be irrelevant. Rather, by 'human values' we refer to the kinds of basic values that nearly all humans would agree upon, such as that AGIs forcibly reprogramming peopleʼs brains, or destroying humanity, would be a bad outcome. In cases where proposals related to AGI risk might change human values in some major but not as obviously catastrophic way, we will mention the possibility of these changes but remain agnostic on whether they are desirable or undesirable. We conclude this section with one frequently forgotten point: in order to avoid catastrophic risks or worse, it is not enough to ensure that only some AGIs are safe. Proposals which seek to solve the issue of catastrophic AGI risk need to also provide some mechanism for ensuring that most (or perhaps even 'nearly all') AGIs are either created safe or prevented from doing considerable harm. \n AGIs may become powerful quickly There are several reasons why AGIs may quickly come to wield unprecedented power in society. 'Wielding power' may mean having direct decision-making power, or it may mean carrying out human decisions in a way that makes the decision maker reliant on the AGI. For example, in a corporate context an AGI could be acting as the executive of the company, or it could be carrying out countless low-level tasks which the corporation needs to perform as part of its daily operations. Bugaj  [63]  consider three kinds of AGI scenarios: capped intelligence, soft takeoff and hard takeoff. In a capped intelligence scenario, all AGIs are prevented from exceeding a predetermined level of intelligence and remain at a level roughly comparable with humans. In a soft takeoff scenario, AGIs become far more powerful than humans, but on a timescale which permits ongoing human interaction during the ascent. Time is not of the essence, and learning proceeds at a relatively human-like pace. In a hard takeoff scenario, an AGI will undergo an extraordinarily fast increase in power, taking effective control of the world within a few years or less  13  . In this scenario, there is little time for error correction or a gradual tuning of the AGIʼs goals. The viability of many proposed approaches depends on the hardness of a takeoff. The more time there is to react and adapt to developing AGIs, the easier it is to control them. A soft takeoff might allow for an approach of incremental machine ethics  [223] , which would not require us to have a complete philosophical theory of ethics and values, but would rather allow us to solve problems in a gradual manner. A soft takeoff might however present its own problems, such as there being a larger number of AGIs distributed throughout the economy, making it harder to contain an eventual takeoff. Hard takeoff scenarios can be roughly divided into those involving the quantity of hardware (the hardware overhang scenario), the quality of hardware (the speed explosion scenario) and the quality of software (the intelligence explosion scenario). Although we discuss them separately, it seems plausible that several of them could happen simultaneously and feed into each other. 2.3.1. Hardware overhang. Hardware progress may outpace AGI software progress. Contemporary supercomputers already rival or even exceed some estimates of the computational capacity of the human brain, while no software seems to have both the brainʼs general learning capacity and its scalability. Bostrom  [46]  estimates that the effective computing capacity of the human brain might be somewhere around 10 17 operations per second (OPS) and Moravec  [195]  estimates it at 10 14 OPS. As of November 2012, the fastest supercomputer in the world had achieved a top capacity of 10 16 floating-point operations per second (FLOPS) and the five-hundredth fastest a top capacity of 10 13 FLOPS  [188] . Note however that OPS and FLOPS are not directly comparable and there is no reliable way of inter-converting the two. Sandberg and Bostrom  [234]  estimate that OPS and FLOPS grow at a roughly comparable rate. If such trends continue, then by the time the software for AGI is invented there may be a computing overhang-an abundance of cheap hardware available for running thousands or millions of AGIs, possibly with a speed of thought much faster than that of humans  [244, 253, 310] . As increasingly sophisticated AGI software becomes available, it would be possible to rapidly copy improvements to millions of servers, each new version being capable of doing more kinds of work or being run with less hardware. Thus, the AGI software could replace an increasingly large fraction of the workforce  14  . The need for AGI systems to be trained for some jobs would slow the rate of adoption, but powerful computers could allow for fast training. If AGIs end  12  Within the AGI ethics literature, safe autonomous AGI is sometimes called 'friendly AI'  [115, 183, 189, 307, 309, 312] . Yudkowsky  [307]  defines 'friendly AI' as 'the production of human-benefiting, non-human-harming actions in Artificial Intelligence systems that have advanced to the point of making real-world plans in pursuit of goals'. However, some papers (e.g.,  Goertzel [105, 108, 294] ) use 'friendly AI' as a narrower term to refer to safe AGI designs as advocated by Yudkowsky  [307, 309] . These designs have the goal of benefiting humans as their overarching value, from which all the other goals and values of the system are derived. In this paper we use the term 'friendly AI' to refer to Yudkowskyʼs proposal and 'safe AGI' as our more general term.  13  Bugaj and Goertzel defined hard takeoff to refer to a period of months or less. We have chosen a somewhat longer time period, as even a few years might easily turn out to be too little time for society to properly react.  14  The speed that would allow AGIs to take over most jobs would depend on the cost of the hardware and the granularity of the software upgrades. A series of upgrades over an extended period, each producing a 1% improvement, would lead to a more gradual transition than a single upgrade that brought the software from the capability level of a chimpanzee to a rough human equivalence. Note also that several companies, including Amazon and Google, offer vast amounts of computing power for rent on an hourly basis. An AGI that acquired money and then invested all of it in renting a large amount of computing resources for a brief period could temporarily achieve a much larger boost than its budget would otherwise suggest. up doing the vast majority of work in society, humans could become dependent on them. AGIs could also plausibly take control of Internetconnected machines in order to harness their computing power  [253] ; Internet-connected machines are regularly compromised  15  . 2.3.2. Speed explosion. Another possibility is a speed explosion  [72, 158, 251, 306] , in which intelligent machines design increasingly faster machines. A hardware overhang might contribute to a speed explosion, but is not required for it. An AGI running at the pace of a human could develop a second generation of hardware on which it could run at a rate faster than human thought. It would then require a shorter time to develop a third generation of hardware, allowing it to run faster than on the previous generation, and so on. At some point, the process would hit physical limits and stop, but by that time AGIs might come to accomplish most tasks at far faster rates than humans, thereby achieving dominance. (In principle, the same process could also be achieved via improved software.) The extent to which the AGI needs humans in order to produce better hardware will limit the pace of the speed explosion, so a rapid speed explosion requires the ability to automate a large proportion of the hardware manufacturing process. However, this kind of automation may already be achieved by the time that AGI is developed  16  . 2.3.3. Intelligence explosion. Third, there could be an intelligence explosion, in which one AGI figures out how to create a qualitatively smarter AGI and that AGI uses its increased intelligence to create still more intelligent AGIs, and so on  17  , such that the intelligence of humankind is quickly left far behind and the machines achieve dominance  [72, 117, 177, 200]    18  . Yudkowsky  [309, 310]  argues that an intelligence explosion is likely. So far, natural selection has been improving human intelligence and human intelligence has to some extent been able to improve itself. However, the core process by which natural selection improves humanity has been essentially unchanged and humans have been unable to deeply affect the cognitive algorithms which produce their own intelligence. Yudkowsky suggests that if a mind became capable of directly editing itself, this could spark a rapid increase in intelligence, as the actual process causing increases in intelligence could itself be improved upon. (This requires that there exist powerful improvements which, when implemented, considerably increase the rate at which such minds can improve themselves.) Hall  [130]  argues that, based on standard economic considerations, it would not make sense for an AGI to focus its resources on solitary self-improvement. Rather, in order not to be left behind by society at large, it should focus its resources on doing the things that it is good at and trade for the things it is not good at. However, once there exists a community of AGIs that can trade with one another, this community could collectively undergo rapid improvement and leave humans behind. A number of formal growth models have been developed which are relevant to predicting the speed of a takeoff; an overview of these can be found in Sandbergʼs  [231]  paper. Many of them suggest rapid growth. For instance, Hanson  [134]  suggests that AGI might lead to the economy doubling in months rather than years. However, Hanson is skeptical about whether this would prove a major risk to humanity and considers it mainly an economic transition similar to the Industrial Revolution. To some extent, the soft/hard takeoff distinction may be a false dichotomy: a takeoff may be soft for a while, and then become hard. Two of the main factors influencing the speed of a takeoff are the pace at which computing hardware is developed and the ease of modifying minds  [253] . This allows for scenarios in which AGI is developed and there seems to be a soft takeoff for, say, the initial ten years, causing a false sense of security until a breakthrough in hardware development causes a hard takeoff. Another factor that might cause a false sense of security is the possibility that AGIs can be developed by a combination of insights from humans and AGIs themselves. As AGIs become more intelligent and it becomes possible to automate portions of the development effort, those parts accelerate and the parts requiring human effort become bottlenecks. Reducing the amount of human insight required could dramatically accelerate the speed of improvement. Halving the amount of human involvement required might at most double the speed of development, possibly giving an impression of relative safety, but going from 50% human insight required to 1% human insight required could cause the development to become ninety-nine times faster  19  .  15  Botnets are networks of computers that have been compromised by outside attackers and are used for illegitimate purposes. Rajab et al  [226]  review several studies which estimate the sizes of the largest botnets as being between a few thousand to 350 000 bots. Modern-day malware could theoretically infect any susceptible Internet-connected machine within tens of seconds of its initial release  [257] . The Slammer worm successfully infected more than 90% of vulnerable hosts within ten minutes and had infected at least 75 000 machines by the thirty minute mark  [192] . The previous record holder in speed, the Code Red worm, took fourteen hours to infect more than 359 000 machines  [191] .  16  Loosemore  [177]  also suggest that current companies carrying out research and development are more constrained by a lack of capable researchers than by the ability to carry out physical experiments.  17  Most accounts of this scenario do not give exact definitions for 'intelligence' or explain what a 'superintelligent' AGI would be like, instead using informal characterizations such as 'a machine that can surpass the intellectual activities of any man however clever'  [117]  or 'an intellect that is much smarter than the best human brains in practically every field, including scientific creativity, general wisdom and social skills'  [46] . Yudkowsky  [309]  defines intelligence in relation to 'optimization power', the ability to reliably hit small targets in large search spaces, such as by finding the a priori exceedingly unlikely organization of atoms which makes up a car. A more mathematical definition of machine intelligence is offered by Legg  [173] . Sotala  [253]  discusses some of the functional routes to actually achieving superintelligence.  18  One example of an AGI framework designed specifically for repeated self-improvement is offered by Schmidhuber  [236] .  19  The relationship in question is similar to that described by Amdahlʼs  [17]  law. From a safety viewpoint, the conservative assumption is to presume the worst  [307] . Yudkowsky argues that the worst outcome would be a hard takeoff, as it would give us the least time to prepare and correct errors. On the other hand, it can also be argued that a soft takeoff would be just as bad, as it would allow the creation of multiple competing AGIs, allowing the AGIs that were the least burdened with goals such as 'respect human values' to prevail. We would ideally like a solution, or a combination of solutions, which would work effectively for both a soft and a hard takeoff. \n Societal proposals The notion of catastrophic AGI risk is not new and this concern was expressed by early thinkers in the field  [64, 117, 269, 300] . Hence, there have also been many proposals concerning what to do about it. The proposals we review are neither exhaustive nor mutually exclusive: the best way of achieving a desirable outcome may involve pursuing several proposals simultaneously. Proposals can be divided into three general categories: proposals for societal action, design proposals for external constraints on AGI behavior and design recommendations for internal constraints on AGI behavior. In this section we briefly review societal proposals. These include doing nothing, integrating AGIs with society, regulating research, merging with machines and relinquishing research into AGI. 3.1. Do nothing 3.1.1. AI is too distant to be worth our attention. One response is that, although AGI is possible in principle, there is no reason to expect it in the near future. Typically, this response arises from the belief that, although there have been great strides in narrow AI, researchers are still very far from understanding how to build AGI. Distinguished computer scientists such as Gordon Bell and Gordon Moore, as well as cognitive scientists such as Douglas Hofstadter and Steven Pinker, have expressed the opinion that the advent of AGI is remote  [6] . Davis  [80]  reviews some of the ways in which computers are still far from human capabilities. Bringsjord  [58]  even claim that a belief in AGI this century is fideistic, appropriate within the realm of religion but not within science or engineering. Some writers also actively criticize any discussion of AGI risk in the first place. The philosopher Alfred Nordmann  [208, 209]  holds the view that ethical concern is a scarce resource, not to be wasted on unlikely future scenarios such as AGI. Likewise, Dennett  [86]  considers AGI risk an 'imprudent pastime' because it distracts our attention from more immediate threats. Others think that AGI is far off and not yet a major concern, but admit that it might be valuable to give the issue some attention. A presidential panel of the Association for the Advancement of Artificial Intelligence considering the longterm future of AI concluded that there was overall skepticism about AGI risk, but that additional research into the topic and related subjects would be valuable  [156] . Posner  [220]  writes that dedicated efforts for addressing the problem can wait, but that we should gather more information about the problem in the meanwhile. The potential negative consequences of AGI are enormous, ranging from economic instability to human extinction. 'Do nothing' could be a reasonable course of action if near-term AGI seemed extremely unlikely, if it seemed too early for any proposals to be effective in reducing risk, or if those proposals seemed too expensive to implement. As a comparison, asteroid impact prevention is generally considered a topic worth studying, even though the probability of a civilization-threatening asteroid impact in the near future is not considered high. Napier  [202]  discusses several ways of estimating the frequency of such impacts. Many models produce a rate of one civilization-threatening impact per five hundred thousand or more years, though some models suggest that rates of one such impact per hundred thousand years cannot be excluded. An estimate of one impact per hundred thousand years would suggest less than a 0.1% chance of a civilizationthreatening impact within the next hundred years. The probability of AGI being developed within the same period seems considerably higher  [200]  and there is likewise a reasonable chance of a hard takeoff after it has been developed  [309, 310] , suggesting that the topic is at the very least worth studying. Even without a hard takeoff society is becoming increasingly automated and even narrow AI is starting to require ethical guidelines  [26, 282] . We know neither which fields of science will be needed nor how much progress in them will be necessary for safe AGI. If much progress is needed and we believe effective progress to be possible this early on, it becomes reasonable to start studying the topic even before AGI is near. Muehlhauser  [199]  suggest that, for one safe AGI approach alone (value learning, discussed further in section 5), efforts by AGI researchers, economists, mathematicians and philosophers may be needed. Safe AI may require the solutions for some of these problems to come well before AGI is developed. 3.1.2. Little risk, no action needed. Some authors accept that a form of AGI will probably be developed but do not consider autonomous AGI to be a risk, or consider the possible negative consequences acceptable. Bryson  [61]  argue that, although AGI will require us to consider ethical and social dangers, the dangers will be no worse than those of other technologies. Whitby  [298]  writes that there has historically been no consistent trend of the most intelligent people acquiring the most authority and that computers will augment humans rather than replace them. Whitby  [299]  further argue that AGIs will not have any particular motivation to act against us.  Jenkins [159]  agrees with these points to the extent of saying that a machine will only act against humans if it is programmed to value itself over humans, although she does find AGI to be a real concern. Another kind of 'no action needed' response argues that AGI development will take a long time  [59] , implying that there will be plenty of time to deal with the issue later on. This can also be taken as an argument for later efforts being more effective, as they will be better tuned to AGI as it develops. Others argue that superintelligence will not be possible at all  20  . McDermott  [182]  points out that there are no good examples of algorithms which could be improved upon indefinitely. Deutsch  [87]  argues that there will never be superintelligent AGIs, because human minds are already universal reasoners and computers can at best speed up the experimental work that is required for testing and fine-tuning theories. He also suggests that even as the speed of technological development increases, so will our ability to deal with change. Anderson  [22]  likewise suggests that the inherent unpredictability of the world will place upper limits on an entityʼs effective intelligence. Heylighen  [145]  argues that a single, stand-alone computer is exceedingly unlikely to become superintelligent and that individual intelligences are always outmatched by the distributed intelligence found in social systems of many minds. Superintelligence will be achieved by building systems that integrate and improve the 'global brain', the collective intelligence of everyone on Earth. Heylighen does acknowledge that this kind of a transition will pose its own challenges, but not of the kind usually evoked in discussions of AGI risk. The idea of AGIs not having a motivation to act against humans is intuitively appealing, but there seem to be strong theoretical arguments against it. As mentioned earlier, Omohundro  [211, 212]  and Bostrom  [51]  argue that selfreplication and the acquisition of resources are useful in the pursuit of many different kinds of goals and that many types of AI systems will therefore exhibit tendencies toward behaviors such as breaking into other machines, selfreplicating and acquiring resources without regard for anyone elseʼs safety. The right design might make it possible to partially work around these behaviors  [243, 287] , but they still need to be taken into account. Furthermore, we might not foresee all the complex interactions of different AGI mechanisms in the systems that we build and they may end up with very different goals than the ones we intended  [88, 229, 309, 312] . Can AGIs become superintelligent? First, we note that AGIs do not necessarily need to be much more intelligent than humans in order to be dangerous. AGIs already enjoy advantages such as the ability to rapidly expand their population by having themselves copied  [133, 136, 253] , which may confer on them considerable economic and political influence even if they were not superintelligent. A better-than-human ability to coordinate their actions, which AGIs of a similar design could plausibly have  [253] , might then be enough to tilt the odds in their favor. Another consideration is that AGIs do not necessarily need to be qualitatively more intelligent than humans in order to outperform humans. An AGI that merely thought twice as fast as any single human could still defeat him at intellectual tasks that had a time constraint, all else equal. Here an 'intellectual' task should be interpreted broadly to refer not only to 'book smarts' but to any task that animals cannot perform due to their mental limitations-including tasks involving social skills  [309] . Straightforward improvements in computing power could provide AGIs with a considerable advantage in speed  [72, 158, 251, 253, 306] , which the AGI could then use to study and accumulate experiences that improved its skills. As for Heylighenʼs  [145]  'global brain' argument, there does not seem to be a reason to presume that powerful AGIs could not be geographically distributed, or that they could not seize control of much of the Internet. Even if individual minds were not very smart and needed a society to make progress, for minds that are capable of copying themselves and communicating perfectly with each other, individual instances of the mind might be better understood as parts of a whole than as separate individuals  [253, 254] . In general, the distinction between an individual and a community might not be meaningful for AGIs  [115] . If there were enough AGIs, they might be able to form a community sufficient to take control of the rest of the Earth. Heylighen  [144]  himself has argued that many of the features of the Internet are virtually identical to the mechanisms used by the human brain. If the AGI is not carefully controlled, it might end up in a position where it made up the majority of the 'global brain' and could undertake actions which the remaining parts of the organism did not agree with. 3.1.3. Let them kill us. Dietrich  [89]  argues that humanity frequently harms other species and that people have also evolved to hurt other people by engaging in behaviors such as child abuse, sexism, rape and racism. Therefore, human extinction would not matter, as long as the machines implemented only the positive aspects of humanity. De Garis  [82]  suggests that AGIs destroying humanity might not matter. He writes that on a cosmic scale, with hundreds of billions of stars in our galaxy alone, the survival of the inhabitants of a single planet is irrelevant. As AGIs would be more intelligent than us in every way, it would be better if they replaced humanity. AGIs being more intelligent and therefore more valuable than humans equates intelligence with value, but Bostrom  [49]  suggests ways by which a civilization of highly intelligent entities might lack things which we thought to have value. For example, such entities might not be conscious in the first place. Alternatively, there are many things which we consider valuable for their own sake, such as humor, love, game-playing, art, sex, dancing, social conversation, philosophy, literature, scientific discovery, food and drink, friendship, parenting, and sport. We value these due to the fact that we have dispositions and preferences which have been evolutionarily adaptive in the past, but for a future civilization  20  The opposite argument is that superior intelligence will inevitably lead to more moral behavior. Some of the arguments related to this position are discussed in the context of evolutionary invariants (section 5.3.1), although the authors advocating the use of evolutionary invariants do believe AGI risk to be worth our concern. few or none of them might be, creating a world with very little of value. Bostrom  [51]  proposes an orthogonality thesis, by which an artificial intelligence can have any combination of intelligence level and goal, including goals that humans would intuitively deem to be of no value. 3.1.4. 'Do nothing' proposals: our view. As discussed above, completely ignoring the possibility of AGI risk at this stage would seem to require a confident belief in at least one of the following propositions. 1. AGI is very remote. 2. There is no major risk from AGI even if it is created. 3. Very little effective work can be done at this stage. 4. AGIs destroying humanity would not matter. In the beginning of this paper, we mentioned several experts who considered it plausible that AGI might be created in the next twenty to one hundred years; in this section we have covered experts who disagree. In general, there is a great deal of disagreement among people who have made AGI predictions, and no clear consensus even among experts in the field of artificial intelligence. The lack of expert agreement suggests that expertise in the field does not contribute to an ability to make reliable predictions  21  . If the judgment of experts is not reliable, then, probably, neither is anyone elseʼs. This suggests that it is unjustified to be highly certain of AGI being near, but also of it not being near. We thus consider it unreasonable to have a confident belief in the first proposition. The second proposition also seems questionable: as discussed in sections 2.1, 2.3 and 3.1.2, AGIs seem very likely to obtain great power, possibly very quickly. Furthermore, as discussed in section 2.2, the complexity and fragility of value theses imply that it could be very difficult to create AGIs which would not cause immense amounts of damage if they had enough power. It also does not seem like it is too early to work on the problem: as we summarize in section 6, there seem to be a number of promising research directions which can already be pursued. We also agree with Yudkowsky  [309] , who points out that research on the philosophical and technical requirements of safe AGI might show that broad classes of possible AGI architectures are fundamentally unsafe, suggesting that such architectures should be avoided. If this is the case, it seems better to have that knowledge as early as possible, before there has been a great deal of investment into unsafe AGI designs. In response to the suggestion that humanity being destroyed would not matter, we certainly agree that there is much to be improved in todayʼs humanity, and that our future descendants might have very little resemblance to ourselves. Regardless, we think that much about todayʼs humans is valuable and worth preserving, and that we should be able to preserve it without involving the death of present humans. \n Integrate with society Integration proposals hold that AGI might be created in the next several decades and that there are indeed risks involved. These proposals argue that the best way to deal with the problem is to make sure that our societal structures are equipped to handle AGIs once they are created. There has been some initial work toward integrating AGIs with existing legal and social frameworks, such as considering questions of their legal position  [31, 62, 132, 174, 252, 296, 297]  and moral rights  [62, 125, 175, 260, 261, 291] . 3.2.1. Legal and economic controls.  Hanson [138]  writes that the values of older and younger generations have often been in conflict with each other and he compares this to a conflict between humans and AGIs. He believes that the best way to control AGI risk is to create a legal framework such that it is in the interest of both humans and AGIs to uphold it. Hanson  [137]  suggests that if the best way for AGIs to get what they want is via mutually agreeable exchanges, then humans would need to care less about what the AGIs wanted. According to him, we should be primarily concerned with ensuring that the AGIs will be law-abiding enough to respect our property rights. Miller  [189]  summarizes Hansonʼs argument and the idea that humanity could be content with a small fraction of the worldʼs overall wealth and let the AGIs have the rest. An analogy to this idea is that humans do not kill people who become old enough to no longer contribute to production, even though younger people could in principle join together and take the wealth of the older people. Instead, old people are allowed to keep their wealth even while in retirement. If things went well, AGIs might similarly allow humanity to 'retire' and keep its accumulated wealth, even if humans were no longer otherwise useful for AGIs. Hall  [128]  also says that we should ensure that the interactions between ourselves and machines are economic, 'based on universal rules of property and reciprocity'. Moravec  [196]  likewise writes that governmental controls should be used to ensure that humans benefit from AGIs. Without government intervention, humans would be squeezed out of existence by more efficient robots, but taxation could be used to support human populations for a long time. He also recommends laws which would require any AGIs to incorporate programming that made them safe and subservient to human desires. Sandberg  [232]  writes that relying only on legal and economic controls would be problematic, but that a strategy which also incorporated them in addition to other approaches would be more robust than a strategy which did not. However, even if AGIs were integrated with human institutions, it does not guarantee that human values would survive. If humans were reduced to a position of negligible power, AGIs might not have any reason to keep us around.  21  Armstrong  [29]  point out that many of the task properties which have been found to be conducive for developing reliable and useful expertise are missing in AGI timeline forecasting. In particular, one of the most important factors is whether experts get rapid (preferably immediate) feedback, while a timeline prediction that is set many decades in the future might have been entirely forgotten by the time that its correctness could be evaluated. Economic arguments, such as the principle of comparative advantage, are sometimes invoked to argue that AGI would find it more beneficial to trade with us than to do us harm. However, technological progress can drive the wages of workers below the level needed for survival  [60, 74, 100, 189]  and there is already a possible threat of technological unemployment  [60] . AGIs keeping humans around due to gains from trade implicitly presumes that they would not have the will or the opportunity to simply eliminate humans in order to replace them with a better trading partner and then trade with the new partner instead. Humans already eliminate species with low economic value in order to make room for more humans, such as when clearing a forest in order to build new homes. Clark uses the example of horses in Britain: their population peaked in 1901, with 3.25 million horses doing work such as plowing fields, hauling wagons and carriages short distances, and carrying armies into battle. The internal combustion engine replaced so many of them that by 1924 there were fewer than two million. Clark writes: There was always a wage at which all these horses could have remained employed. But that wage was so low that it did not pay for their feed, and it certainly did not pay enough to breed fresh generations of horses to replace them. Horses were thus an early casualty of industrialization  [74] . There are also ways to harm humans while still respecting their property rights, such as by manipulating them into making bad decisions, or selling them addictive substances. If AGIs were sufficiently smarter than humans, humans could be tricked into making a series of trades that respected their property rights but left them with negligible assets and caused considerable damage to their well-being. A related issue is that AGIs might become more capable of changing our values than we are capable of changing AGI values. Mass media already convey values that have a negative impact on human well-being, such as idealization of rare body types, which causes dissatisfaction among people who do not have those kinds of bodies  [12, 122] . AGIs with a deep understanding of human psychology could engineer the spread of values which shifted more power to them, regardless of their effect on human well-being. Yet another problem is ensuring that the AGIs have indeed adopted the right values. Making intelligent beings adopt specific values is a difficult process which often fails. There could be an AGI with the wrong goals that would pretend to behave correctly in society throughout the whole socialization process. AGIs could conceivably preserve and conceal their goals far better than humans could. Society does not know of any methods which would reliably instill our chosen values in human minds, despite a long history of trying to develop them. Our attempts to make AGIs adopt human values would be hampered by our lack of experience and understanding of the AGIʼs thought processes, with even tried-and-true methods for instilling positive values in humans possibly being ineffective. The limited success that we do have with humans is often backed up by various incentives as well as threats of punishment, both of which might fail in the case of an AGI developing to become vastly more powerful than us. Additionally, the values which a being is likely to adopt, or is even capable of adopting, will depend on its mental architecture. We will demonstrate these claims with examples from humans, who are not blank slates on whom arbitrary values can be imposed with the right education  [218] . Although the challenge of instilling specific values in humans is very different from the challenge of instilling them in AGIs, our examples are meant to demonstrate the fact that the existing properties of a mind will affect the process of acquiring values. Just as it is difficult to make humans permanently adopt some kinds of values, the kind of mental architecture that an AGI has will affect its inclination to adopt various values. Psychopathy is a risk factor for violence and psychopathic criminals are much more likely to re-offend than nonpsychopaths  [139] . Harris  [140]  argue that therapy for psychopaths is ineffective  22  and may even make them more dangerous, as they use their improved social skills to manipulate others more effectively. Furthermore, 'cult brainwashing' is generally ineffective and most cult members will eventually leave  [25]  and large-scale social engineering efforts often face widespread resistance, even in dictatorships with few scruples about which methods to use [chapters 6 and 7  [238] ]. Thus, while one can try to make humans adopt values, this will only work to the extent that the individuals in question are actually disposed toward adopting them. 3.2.2. Foster positive values.  Kurzweil [170] , considering the possible effects of many future technologies, notes that AGI may be a catastrophic risk. He generally supports regulation and partial relinquishment of dangerous technologies, as well as research into their defensive applications. However, he believes that with AGI this may be insufficient and that, at the present time, it may be infeasible to develop strategies that would guarantee safe AGI. He argues that machine intelligences will be tightly integrated into our society and that, for the time being, the best chance of avoiding AGI risk is to foster positive values in our society. This will increase the likelihood that any AGIs that are created will reflect such positive values. One possible way of achieving such a goal is moral enhancement  [91] , the use of technology to instill people with better motives. Persson  [215, 216]  argue that, as technology improves, we become more capable of damaging humanity, and that we need to carry out moral enhancement in order to lessen our destructive impulses. 3.2.3. 'Integrate with society' proposals: our view. Proposals to incorporate AGIs into society suffer from the issue that some AGIs may never adopt benevolent and cooperative values, no matter what the environment. Neither does the intelligence of the AGIs necessarily affect their values  [51] .  22  Salekin  [230]  offers a more optimistic opinion. Sufficiently intelligent AGIs could certainly come to eventually understand human values, but humans can also come to understand others' values while continuing to disagree with them. Thus, in order for these kinds of proposals to work, they need to incorporate strong enforcement mechanisms to keep non-safe AGIs in line and to prevent them from acquiring significant power. This requires an ability to create valueconforming AGIs in the first place, to implement the enforcement. Even a soft takeoff would eventually lead to AGIs wielding great power, so the enforcement could not be left to just humans or narrow AIs  23  . In practice, this means that integration proposals must be combined with some proposal for internal constraints which is capable of reliably creating value-conforming AGIs. Integration proposals also require there to be a soft takeoff in order to work, as having a small group of AGIs which rapidly acquired enough power to take control of the world would prevent any gradual integration schemes from working. Therefore, because any effective integration strategy would require creating safe AGIs, and the right safe AGI design could lead to a positive outcome even if there were a hard takeoff, we believe that it is currently better to focus on proposals which are aimed at furthering the creation of safe AGIs. \n Regulate research Integrating AGIs into society may require explicit regulation. Calls for regulation are often agnostic about long-term outcomes but nonetheless recommend caution as a reasonable approach. For example, Hibbard  [147]  calls for international regulation to ensure that AGIs will value the long-term wellbeing of humans, but does not go into much detail. Daley  [79]  calls for a government panel for AGI issues. Hughes  [157]  argues that AGI should be regulated using the same mechanisms as previous technologies, creating state agencies responsible for the task and fostering global cooperation in the regulation effort  24  . Current mainstream academic opinion does not consider AGI a serious threat  [156] , so AGI regulation seems unlikely in the near future. On the other hand, many AI systems are becoming increasingly autonomous and a number of authors are arguing that even narrow-AI applications should be equipped with an understanding of ethics  [282] . Currently there are calls to regulate AI in the form of high-frequency trading (HFT)  [250]  and AI applications that have a major impact on society might become increasingly regulated. At the same time, legislation has a well-known tendency to lag behind technology and regulating AI applications will probably not translate into regulating basic research into AGI. 3.3.1. Review boards. Yampolskiy  [305]  note that university research programs in the social and medical sciences are overseen by institutional review boards. They propose setting up analogous review boards to evaluate potential AGI research. Research that was found to be AGI related would be restricted with measures ranging from supervision and funding limits to partial or complete bans. At the same time, research focusing on safety measures would be encouraged. Posner  [p 221, 220]  suggests the enactment of a law which would require scientific research projects in dangerous areas to be reviewed by a federal catastrophic risks assessment board and forbidden if the board found that the project would create an undue risk to human survival. Wilson  [301]  makes possibly the most detailed AGI regulation proposal so far, recommending a new international treaty where a body of experts would determine whether there was a 'reasonable level of concern' about AGI or some other possibly dangerous research. States would be required to regulate research or even temporarily prohibit it once experts agreed upon there being such a level of concern. He also suggests a number of other safeguards built into the treaty, such as the creation of ethical oversight organizations for researchers, mechanisms for monitoring abuses of dangerous technologies and an oversight mechanism for scientific publications.  [183]  argues that the government should not attempt to regulate AGI development. Rather, it should concentrate on providing funding for research projects intended to create safe AGI. \n Encourage research into safe AGI. In contrast, McGinnis Goertzel  [115]  argue for an open-source approach to safe AGI development instead of regulation. Hibbard  [149]  has likewise suggested developing AGI via open-source methods, but not as an alternative to regulation. Legg  [172]  proposes funding safe AGI research via an organization that takes a venture capitalist approach to funding research teams, backing promising groups and cutting funding to any teams that fail to make significant progress. The focus of the funding would be to make AGI as safe as possible. 3.3.3. Differential technological progress. Both review boards and government funding could be used to implement 'differential intellectual progress': Differential intellectual progress consists in prioritizing risk-reducing intellectual progress over risk-increasing intellectual progress. As applied to AI risks in particular, a plan of differential intellectual progress would recommend that our progress on the scientific, philosophical and technological problems of AI safety outpace our progress on the problems of AI capability such that we develop safe superhuman AIs before we develop (arbitrary) superhuman AIs  [200] .  23  For proposals which suggest that humans could use technology to remain competitive with AGIs and thus prevent them from acquiring excessive amounts of power, see section 3.4.  24  Some of these proposals are written in the context of the USA and refer to the actions that the US government should take, but the general logic behind the proposals is not US-specific. Examples of research questions that could constitute philosophical or scientific progress in safety can be found in later sections of this paper-for instance, the usefulness of different internal constraints on ensuring safe behavior, or ways of making AGIs reliably adopt human values as they learn what those values are like. Earlier, Bostrom  [47]  used the term 'differential technological progress' to refer to differential intellectual progress in technological development. Bostrom defined differential technological progress as 'trying to retard the implementation of dangerous technologies and accelerate implementation of beneficial technologies, especially those that ameliorate the hazards posed by other technologies'. One issue with differential technological progress is that we do not know what kind of progress should be accelerated and what should be retarded. For example, a more advanced communication infrastructure could make AGIs more dangerous, as there would be more networked machines that could be accessed via the Internet. Alternatively, it could be that the world will already be so networked that AGIs will be a major threat anyway and further advances will make the networks more resilient to attack. Similarly, it can be argued that AGI development is dangerous for as long as we have yet to solve the philosophical problems related to safe AGI design and do not know which AGI architectures are safe to pursue  [309] . But it can also be argued that we should invest in AGI development now, when the related tools and hardware are still primitive enough that progress will be slow and gradual  [115] . 3.3.4. International mass surveillance. For AGI regulation to work, it needs to be enacted on a global scale. This requires solving both the problem of effectively enforcing regulation within a country and the problem of getting many different nations to all agree on the need for regulation. Shulman  [241]  discusses various factors influencing the difficulty of AGI arms control. He notes that AGI technology itself might make international cooperation more feasible. If narrow AIs and early-stage AGIs were used to analyze the information obtained from wide-scale mass surveillance and wiretapping, this might make it easier to ensure that nobody was developing more advanced AGI designs. Shulman  [242]  similarly notes that machine intelligences could be used to enforce treaties between nations. They could also act as trustworthy inspectors which would be restricted to communicating only information about treaty violations, thus not endangering state secrets even if they were allowed unlimited access to them. This could help establish a 'singleton'  [48]  regulatory regimen capable of effectively enforcing international regulation, including AGI-related treaties. Goertzel  [115]  also discuss the possibility of having a network of AGIs monitoring the world in order to police other AGIs and to prevent any of them from suddenly obtaining excessive power. Another proposal for international mass surveillance is to build an 'AGI Nanny'  [111, 115] , a proposal discussed in section 5.4. Large-scale surveillance efforts are ethically problematic and face major political resistance, and it seems unlikely that current political opinion would support the creation of a farreaching surveillance network for the sake of AGI risk alone. The extent to which such extremes would be necessary depends on exactly how easy it would be to develop AGI in secret. Although several authors make the point that AGI is much easier to develop unnoticed than something like nuclear weapons  [183, 189] , cutting-edge high-tech research does tend to require major investments which might plausibly be detected even by less elaborate surveillance efforts. To the extent that surveillance does turn out to be necessary, there is already a strong trend toward a 'surveillance society' with increasing amounts of information about people being collected and recorded in various databases  [9] . As a reaction to the increased surveillance, Mann et al  [179]  propose to counter it with sousveillancegiving private individuals the ability to document their life and subject the authorities to surveillance in order to protect civil liberties. This is similar to the proposals of Brin  [57] , who argues that technological progress might eventually lead to a 'transparent society', where we will need to redesign our societal institutions in a way that allows us to maintain some of our privacy despite omnipresent surveillance. Miller  [189]  notes that intelligence agencies are already making major investments in AI-assisted analysis of surveillance data. If social and technological developments independently create an environment where large-scale surveillance or sousveillance is commonplace, it might be possible to take advantage of those developments in order to police AGI risk  25  . Walker  [279]  argues that in order for mass surveillance to become effective, it must be designed in such a way that it will not excessively violate peopleʼs privacy, for otherwise the system will face widespread sabotage  26  . Even under such conditions, there is no clear way to define what counts as dangerous AGI. Goertzel  [115]  point out that there is no clear division between narrow AI and AGI and attempts to establish such criteria have failed. They argue that since AGI has a nebulous definition, obvious wide-ranging economic benefits and potentially significant penetration into multiple industry sectors, it is unlikely to be regulated due to speculative long-term risks. AGI regulation requires global cooperation, as the noncooperation of even a single nation might lead to catastrophe. Historically, achieving global cooperation on tasks such as  25  An added benefit would be that this could also help avoid other kinds of existential risks, such as the intentional creation of dangerous new diseases.  26  Walker also suggests that surveillance systems could be designed to automatically edit out privacy-endangering details (such as pictures of people) from the data that they transmit, while leaving in details which might help in revealing dangerous ploys (such as pictures of bombs). However, this seems impossible to implement effectively, as research has found ways to extract personally identifying information and details from a wide variety of supposedly anonymous datasets  [66, 95, 116, 203, 204, 206, 263] . Narayanan  [205]  even go as far as to state that 'the false dichotomy between personally identifiable and non-personally identifiable information should disappear from privacy policies, laws, etc. Any aspect of an individualʼs … personality can be used for de-anonymization, and this reality should be recognized by the relevant legislation and corporate privacy policies'. nuclear disarmament and climate change has been very difficult. As with nuclear weapons, AGI could give an immense economic and military advantage to the country that develops it first, in which case limiting AGI research might even give other countries an incentive to develop AGI faster  [65, 82, 183, 189] . To be effective, regulation also needs to enjoy support among those being regulated. If developers working in AGIrelated fields only follow the letter of the law, while privately viewing all regulations as annoying hindrances, and fears about AGI as overblown, the regulations may prove ineffective. Thus, it might not be enough to convince governments of the need for regulation; the much larger group of people working in the appropriate fields may also need to be convinced. While Shulman  [241]  argues that the unprecedentedly destabilizing effect of AGI could be a cause for world leaders to cooperate more than usual, the opposite argument can be made as well. Gubrud  [124]  argues that increased automation could make countries more self-reliant and international cooperation considerably more difficult. AGI technology is also much harder to detect than, for example, nuclear technology is-nuclear weapons require a substantial infrastructure to develop, while AGI needs much less  [183, 189] . Miller  [189]  even suggests that the mere possibility of a rival being close to developing AGI might, if taken seriously, trigger a nuclear war. The nation that was losing the AGI race might think that being the first to develop AGI was sufficiently valuable that it was worth launching a first strike for, even if it would lose most of its own population in the retaliatory attack. He further argues that, although it would be in the interest of every nation to try to avoid such an outcome, the ease of secretly pursuing an AGI development program undetected, in violation of treaty, could cause most nations to violate the treaty. Miller also points out that the potential for an AGI arms race exists not only between nations, but between corporations as well. He notes that the more AGI developers there are, the more likely it is that they will all take more risks, with each AGI developer reasoning that if they do not take this risk, somebody else might take that risk first. Goertzel  [115]  suggest that for regulation to be enacted, there might need to be an 'AGI Sputnik'-a technological achievement that makes the possibility of AGI evident to the public and policy makers. They note that after such a moment, it might not take very long for full human-level AGI to be developed, while the negotiations required to enact new kinds of arms control treaties would take considerably longer. So far, the discussion has assumed that regulation would be carried out effectively and in the pursuit of humanityʼs common interests, but actual legislation is strongly affected by lobbying and the desires of interest groups  [210]  Mueller:2003. Many established interest groups would have an economic interest in either furthering or retarding AGI development, rendering the success of regulation uncertain. 3.3.5. 'Regulate research' proposals: our view. Although there seem to be great difficulties involved with regulation, there also remains the fact that many technologies have been successfully subjected to international regulation. Even if one were skeptical about the chances of effective regulation, an AGI arms race seems to be one of the worst possible scenarios, one which should be avoided if at all possible. We are therefore generally supportive of regulation, though the most effective regulatory approach remains unclear. \n Enhance human capabilities While regulation approaches attempt to limit the kinds of AGIs that will be created, enhancement approaches attempt to give humanity and AGIs a level playing field. In principle, gains in AGI capability would not be a problem if humans could improve themselves to the same level. Alternatively, human capabilities could be improved in order to obtain a more general capability to deal with difficult problems. Verdoux  [275, 276]  suggests that cognitive enhancement could help in transforming previously incomprehensible mysteries into tractable problems and Verdoux  [275]  in particular highlights the possibility of cognitive enhancement helping to deal with the problems posed by existential risks. One problem with such approaches is that increasing humanityʼs capability for solving problems will also make it easier to develop dangerous technologies. It is possible that cognitive enhancement should be combined with moral enhancement, in order to help foster the kind of cooperation that would help avoid the risks of technology  [215, 216] . Moravec  [193, 196]  proposes that humans could keep up with AGIs via 'mind uploading', a process of transferring the information in human brains to computer systems so that human minds could run on a computer substrate. This technology may arrive during a similar timeframe as AGI  [69, 143, 165, 170, 233, 234, 254] . However, Moravec argues that mind uploading would come after AGIs, and that unless the uploaded minds ('uploads') would transform themselves to become radically non-human, they would be weaker and less competitive than AGIs that were native to a digital environment  [194, 196] . For these reasons,Warwick  [289]  also expresses doubt about the usefulness of mind uploading  27  . Kurzweil  [170]  posits an evolution that will start with brain-computer interfaces, then proceed to using brainembedded nanobots to enhance our intelligence and finally lead to full uploading and radical intelligence enhancement. Koene  [166]  criticizes plans to create safe AGIs and considers uploading both a more feasible and a more reliable approach.  27  Some uploading approaches also raise questions of personal identity, whether the upload would still be the same person as the original  [38, 45, 72, 112, 142, 155, 193, 262, 280]  and whether they would be conscious in the first place  [11, 71, 142, 169, 239] . However, these concerns are not necessarily very relevant for AGI risk considerations, as a population of uploads working to protect against AGIs would be helpful even if they lacked consciousness or were different individuals than the originals. Similar proposals have also been made without explicitly mentioning mind uploading. Cade  [65]  speculates on the option of gradually merging with machines by replacing body parts with mechanical components. Turney  [270]  proposes linking AGIs directly to human brains so that the two meld together into one entity and Warwick  [289, 290]  notes that cyborgization could be used to enhance humans. Mind uploading might also be used to make human value systems more accessible and easy to learn for AGIs, such as by having an AGI extrapolate the uploadʼs goals directly from its brain, with the upload providing feedback. 3.4.1. Would we remain human? Uploading might destroy parts of humanity that we value  [82, 160] . De Garis  [82]  argues that a computer could have far more processing power than a human brain, making it pointless to merge computers and humans. The biological component of the resulting hybrid would be insignificant compared to the electronic component, creating a mind that was negligibly different from a 'pure' AGI. Kurzweil  [168]  makes the same argument, saying that although he supports intelligence enhancement by directly connecting brains and computers, this would only keep pace with AGIs for a couple of additional decades. The truth of this claim seems to depend on exactly how human brains are augmented. In principle, it seems possible to create a prosthetic extension of a human brain that uses the same basic architecture as the original brain and gradually integrates with it  [254] . A human extending their intelligence using such a method might remain roughly human-like and maintain their original values. However, it could also be possible to connect brains with computer programs that are very unlike human brains and which would substantially change the way the original brain worked. Even smaller differences could conceivably lead to the adoption of 'cyborg values' distinct from ordinary human values  [290] . Bostrom  [49]  speculates that humans might outsource many of their skills to non-conscious external modules and would cease to experience anything as a result. The valuealtering modules would provide substantial advantages to their users, to the point that they could outcompete uploaded minds who did not adopt the modules. Uploading would also allow humans to make precise and deep modifications to their own minds, which carries with it dangers of a previously unencountered kind  [259] . \n Would evolutionary pressures change us? A willingness to integrate value-altering modules is not the only way by which a population of uploads might come to have very different values from modern-day humans. This is not necessarily a bad, or even a very novel, development: the values of earlier generations have often been different from the values of later generations  [138]  and it might not be a problem if a civilization of uploads enjoyed very different things than a civilization of humans. Still, as there are possible outcomes that we would consider catastrophic, such as the loss of nearly all things that have intrinsic value for us  [49] , it is worth reviewing some of the postulated changes in values. For comprehensiveness, we will summarize all of the suggested effects that uploading might have on human values, even if they are not obviously negative. Readers may decide for themselves whether or not they consider any of these effects to be causes for concern. Hanson  [133]  argues that employers will want to copy uploads who are good workers and that at least some uploads will consent to being copied in such a manner. He suggests that the resulting evolutionary dynamics would lead to an accelerated evolution of values. This would cause most of the upload population to evolve to be indifferent or favorable to the thought of being copied, to be indifferent toward being deleted as long as another copy of themselves remained and to be relatively uninterested in having children 'the traditional way' (as opposed to copying an already-existing mind). Although Hansonʼs analysis uses the example of a workeremployer relationship, it should be noted that nations or families, or even single individuals, could also gain a competitive advantage by copying themselves, thus contributing to the strength of the evolutionary dynamic. Similarly, Bostrom  [49]  writes that much of human lifeʼs meaning depends on the enjoyment of things ranging from humor and love to literature and parenting. These capabilities were adaptive in our past, but in an upload environment they might cease to be such and gradually disappear entirely. Shulman  [242]  likewise considers uploading-related evolutionary dynamics. He notes that there might be a strong pressure for uploads to make copies of themselves in such a way that individual copies would be ready to sacrifice themselves to aid the rest. This would favor a willingness to copy oneself and a view of personal identity which did not consider the loss of a single copy to be death. Beings taking this point of view could then take advantage of the economic benefits of continually creating and deleting vast numbers of minds depending on the conditions, favoring the existence of a large number of short-lived copies over a somewhat less efficient world of long-lived minds. Finally, Sotala  [254]  consider the possibility of minds coalescing via artificial connections that linked several brains together in the same fashion as the two hemispheres of ordinary brains are linked together. If this were to happen, considerable benefits might accrue to those who were ready to coalesce with other minds. The ability to copy and share memories between minds might also blur distinctions between individual minds. In the end, most humans might cease to be individual, distinct people in any real sense of the word. It has also been proposed that information security concerns could cause undesirable dynamics among uploads, with significant advantages accruing to those who could steal the computational resources of others and use them to create new copies of themselves. If one could seize control of the hardware that an upload was running on, it could be immediately replaced with a copy of a mind loyal to the attacker. It might even be possible to do this without being detected, if it was possible to steal enough of an uploadʼs personal information to impersonate it. An attack targeting a critical vulnerability in some commonly used piece of software might quickly hit a very large number of victims. As previously discussed in section 2.3.1, both theoretical arguments and actual cases of malware show that large numbers of machines on the Internet could be infected in a very short time  [191, 192, 257] . In a society of uploads, attacks such as these would be not only inconvenient, but potentially fatal. Eckersley  [93]  offer a preliminary analysis of information security in a world of uploads. \n Would uploading help? Even if the potential changes of values were deemed acceptable, it is unclear whether the technology for uploading could be developed before developing AGI. Uploading might require emulating the low-level details of a human brain with a high degree of precision, requiring large amounts of computing power  [69, 234] . In contrast, an AGI might be designed around high-level principles which have been chosen to be computationally cheap to implement on existing hardware architectures. Yudkowsky  [309]  uses the analogy that it is much easier to figure out the principles of aerodynamic flight and then build a Boeing 747 than it is to take a living bird and 'upgrade' it into a giant bird that can carry passengers, all while ensuring that the bird remains alive and healthy throughout the process. Likewise, it may be much easier to figure out the basic principles of intelligence and build AGIs than to upload existing minds. On the other hand, one can also construct an analogy suggesting that it is easier to copy a thingʼs function than it is to understand how it works. If a person does not understand architecture but wants to build a sturdy house, it may be easier to create a replica of an existing house than it is to design an entirely new one that does not collapse. Even if uploads were created first, they might not be able to harness all the advantages of digitality, as many of these advantages depend on minds being easy to modify  [253] , which human minds may not be. Uploads will be able to directly edit their source code as well as introduce simulated pharmaceutical and other interventions, and they could experiment on copies that are restored to an unmodified state if the modifications turn out to be unworkable  [242] . Regardless, human brains did not evolve to be easy to modify and it may be difficult to find a workable set of modifications which would drastically improve them. In contrast, in order for an AGI programmed using traditional means to be manageable as a software project, it must be easy for the engineers to modify it  28  . Thus, even if uploading were developed before AGI, AGIs that were developed later might still be capable of becoming more powerful than uploads. However, existing uploads already enjoying some of the advantages of the newly created AGIs would still make it easier for the uploads to control the AGIs, at least for a while. Moravec  [194]  notes that the human mind has evolved to function in an environment which is drastically different from a purely digital environment and that the only way to remain competitive with AGIs would be to transform into something that was very different from a human. This suggests that uploading might buy time for other approaches, but would be only a short-term solution in and of itself. If uploading technology were developed before AGI, it could be used to upload a research team or other group and run them at a vastly accelerated rate as compared to the rest of humanity. This would give them a considerable amount of extra time for developing any of the other approaches. If this group were among the first to be successfully emulated and sped up, and if the speed-up would allow enough subjective time to pass before anyone else could implement their own version, they might also be able to avoid trading safety for speed. However, such a group might be able to wield tremendous power, so they would need to be extremely reliable and trustworthy. 3.4.4. 'Enhance human capabilities' proposals: our view. Of the various 'enhance human capabilities' approaches, uploading proposals seem the most promising, as translating a human brain to a computer program would sidestep many of the constraints that come from modifying a physical system. For example, all relevant brain activity could be recorded for further analysis at an arbitrary level of detail and any part of the brain could be instantly modified without a need for timeconsuming and possibly dangerous invasive surgery. Uploaded brains could also be more easily upgraded to take full advantage of more powerful hardware, while humans whose brains were still partially biological would be bottlenecked by the speed of the biological component. Uploading does have several problems: uploading research might lead to AGI being created before the uploads, in the long term uploads might have unfavorable evolutionary dynamics and it seems likely that there will eventually be AGIs which are capable of outperforming uploads in every field of competence. Uploads could also be untrustworthy even without evolutionary dynamics. At the same time, however, uploading research does not necessarily accelerate AGI research very much, the evolutionary dynamics might not be as bad as they seem at the moment and the advantages gained from uploading might be enough to help control unsafe AGIs until safe ones could be developed. Methods could also be developed for increasing the trustworthiness of uploads  [242] . Uploading might still turn out to be a useful tool for handling AGI risk. \n Relinquish technology Not everyone believes that the risks involved in creating AGIs are acceptable. Relinquishment involves the abandonment of technological development that could lead to AGI. This is possibly the earliest proposed approach, with Butler  [64]  writing that 'war to the death should be instantly proclaimed'  28  However, this might not be true for AGIs created using some alternative means, such as artificial life  [260] . upon machines, for otherwise they would end up destroying humans entirely. In a much-discussed article, Joy  [160]  suggests that it might be necessary to relinquish at least some aspects of AGI research, as well as nanotechnology and genetics research. Hughes  [157]  criticizes AGI relinquishment, while Kurzweil  [170]  criticizes broad relinquishment but supports the possibility of 'fine-grained relinquishment', banning some dangerous aspects of technologies while allowing general work on them to proceed. In general, most writers reject proposals for broad relinquishment. 3.5.1. Outlaw AGI. Weng et al  [297]  write that the creation of AGIs would force society to shift from human-centric values to robot-human dual values. In order to avoid this, they consider the possibility of banning AGI. This could be done either permanently or until appropriate solutions are developed for mediating such a conflict of values. McKibben  [184] , writing mainly in the context of genetic engineering, suggests that AGI research should be stopped. He brings up the historical examples of China renouncing seafaring in the 1400 s and Japan relinquishing firearms in the 1600 s, as well as the more recent decisions to abandon DDT, CFCs and genetically modified crops in Western countries. However, it should also be noted that Japan participated in World War II; that China now has a navy; that are reasonable alternatives for DDT and CFCs, which probably do not exist for AGI; and that genetically modified crops are in wide use in the United States. Hughes  [157]  argues that attempts to outlaw a technology will only make the technology move to other countries. He also considers the historical relinquishment of biological weapons to be a bad example, for no country has relinquished peaceful biotechnological research such as the development of vaccines, nor would it be desirable to do so. With AGI, there would be no clear dividing line between safe and dangerous research. De Garis  [82]  believes that differences of opinion about whether to build AGIs will eventually lead to armed conflict, to the point of open warfare. Annas et al  [24]  have similarly argued that genetic engineering of humans would eventually lead to war between unmodified humans and the engineered 'posthumans', and that cloning and inheritable modifications should therefore be banned. To the extent that one accepts their reasoning with regard to humans, it could also be interpreted to apply to AGIs. 3.5.2. Restrict hardware.  Berglas [44]  suggests not only stopping AGI research, but also outlawing the production of more powerful hardware. Berglas holds that it will be possible to build computers as powerful as human brains in the very near future and that we should therefore reduce the power of new processors and destroy existing ones  29  . Branwen  [56]  argues that Mooreʼs law depends on the existence of a small number of expensive and centralized chip factories, making them easy targets for regulation and incapable of being developed in secret. \n 'Relinquish technology' proposals: our view. Relinquishment proposals suffer from many of the same problems as regulation proposals, but to a greater extent. There is no historical precedent of general, multi-use technology similar to AGI being successfully relinquished for good, nor do there seem to be any theoretical reasons for believing that relinquishment proposals would work in the future. Therefore we do not consider them to be a viable class of proposals. \n External AGI constraints Societal approaches involving regulation or research into safe AGI assume that proper AGI design can produce solutions to AGI risks. One category of such solutions is that of external constraints. These are restrictions that are imposed on an AGI from the outside and aim to limit its ability to do damage. Several authors have argued that external constraints are unlikely to work with AGIs that are genuinely far more intelligent than us  [30, 72, 170, 278, 307, 309] . The consensus seems to be that external constraints might buy time when dealing with less advanced AGIs, but they are useless against truly superintelligent ones. External constraints also limit the usefulness of an AGI, as a free-acting one could serve its creators more effectively. This reduces the probability of the universal implementation of external constraints on AGIs. AGIs might also be dangerous if they were confined or otherwise restricted. For further discussion of these points, see section 5.1. \n AGI confinement AGI confinement, or 'AI boxing'  [30, 72, 92, 278, 303] , involves confining an AGI to a specific environment and limiting its access to the external world. Yampolskiy  [303]  makes an attempt to formalize the idea, drawing on previous computer security research on the so-called confinement problem  [171] . Yampolskiy defines the AI confinement problem as the challenge of restricting an AGI to a confined environment from which it cannot communicate without authorization. A number of methods have been proposed for implementing AI confinement, many of which are extensively discussed in Armstrong, Sandberg and Bostromʼs  [30]  paper. Chalmers  [72]  and Armstrong et al  [30]  mention numerous caveats and difficulties with AI-boxing approaches. A truly leakproof system that perfectly isolated the AGI from an outside environment would prevent us from even observing the AGI. If AGIs were given knowledge about human behavior or psychology, they could still launch social engineering attacks on us  [30, 72] . An AGI that was unaware of the existence of humans would be less likely to launch such  29  Berglas (personal communication) has since changed his mind and no longer believes that it is possible to effectively restrict hardware or otherwise prevent AGI from being created. attacks, but also much more limited in the kinds of tasks that it could be used for. Even if the AGI remained confined, it could achieve enough influence among humans to prevent itself from being reset or otherwise modified  [118] . An AGI that people grew reliant on might also become impossible to reset or modify. 4.1.1. Safe questions. Yampolskiy  [303]  proposes a hierarchy of security levels for communication with the AGI, ranging from completely unrestricted communication to no communication whatsoever. He suggests that the right level for communicating with AGIs is an intermediate one, based on asking 'safe questions'. These are defined as questions for which a human could find an answer without help from a superintelligence. For instance, a researcher who was considering two possible cures for cancer could ask the AGI which one to pursue first. Yampolskiy argues that the AGI is effectively not changing the final outcome, as the researcher would in principle be capable of finding the better treatment himself. The AGI, by recommending one of the approaches as the choice to pursue first, is merely speeding up the process. Armstrong et al  [30]  also briefly discuss such approaches. 4.1.2. Virtual worlds. While the confinement protocol supposes an AGI that can perceive our world directly, Chalmers  [72]  uses the term 'leakproof singularity' to refer to the project of creating isolated virtual worlds which would disallow their inhabitants from influencing the external world. An AGI placed in such a world could be monitored by humans to ensure that it was safe to release into our world. However, Chalmers notes that 'for an AI system to be useful or interesting to us at all, it must have some effects on us. At a minimum, we must be able to observe it. And the moment we observe a virtual environment, some information leaks out from that environment into our environment and affects us'. Hibbard  [151]  proposes a decision support system for evaluating AGI designs in simulated environments that model our real environment, and attempts to show that the AGI can be built to be safe. Armstrong et al  [30]  discuss the notion that we could supplement this approach with several layers of 'sub-worlds': virtual worlds stacked within each other. In such a scenario, even if an AGI somehow manages to break out from one virtual reality, it is still restricted by another and cannot directly influence the world. Ultimately, the authors conclude that this approach is not very promising. 4.1.3. Resetting the AGI. For as long as an AGI remains confined or cooperative, its memory could be altered from the outside. Turney  [270]  mentions a proposal in which an AGIʼs memory could be wiped after each job, thus limiting its potential. Armstrong et al  [30]  also mention the possibility of resetting an AGI after each run, though they note that there are many ways for the AGI to get around it and that it is only useful for certain kinds of AGI systems. Good  [118]  warns that a superhuman AGI may be smart enough to find ways to prevent itself from being successfully reset or shut down, including methods of social manipulation. Warwick  [289]  makes a similar point. 4.1.4. Checks and balances. Armstrong et al  [30]  suggest a number of checks and balances that could be used to catch the early stages of an AGI that was behaving dangerously or trying to deceive us. Test questions with known answers could be mixed in with questions we genuinely did not know the answer to, in order to establish an AGIʼs trustworthiness. 'Honey-pots', tempting resources with great value to the AGI, could also be left in physical or mental locations that it was forbidden from accessing. Finally, several different kinds of AGIs could be presented with the same problem, with their answers then being compared. Inconsistent answers would suggest a possible attempt at deception. 4.1.5. 'AI confinement' proposals: our view. Despite their limited ability to deal with AGIs more intelligent than us, AIboxing techniques seem to have value as a first line of defense and it may be worthwhile to invest in developing off-the-shelf software packages for AI confinement that are easy and cheap to use. A research project that developed AGI unexpectedly might not have been motivated to make major investments in security, but the AGI might still be sufficiently limited in intelligence that confinement would work. Having a defense that is easy to deploy will make it more likely that these kinds of projects will implement better precautions. However, at the same time there is a risk that this will promote a false sense of security and make research teams think that they have carried out their duty to be cautious merely because they are running elementary confinement protocols. Although some confinement procedures can be implemented on top of an AGI that was not expressly designed for confinement, they are much less reliable than with an AGI that was built with confinement considerations in mind  [30] -and even then, relying solely on confinement is a risky strategy. We are therefore somewhat cautious in our recommendation to develop confinement techniques. \n AGI enforcement One problem with AI confinement proposals is that humans are tasked with guarding machines that may be far more intelligent than themselves  [118] . One proposed solution for this problem is to give the task of watching AGIs to other AGIs. Armstrong  [27]  proposes that the trustworthiness of a superintelligent system could be monitored via a chain of less powerful systems, all the way down to humans. Although humans could not verify and understand the workings of a superintelligence, they could verify and understand an AGI just slightly above their own level, which could in turn verify and understand an AGI somewhat above its own level, and so on. Chaining multiple levels of AI systems with progressively greater capacity seems to be replacing the problem of building a safe AI with a multi-system, and possibly more difficult, version of the same problem. Armstrong himself admits that there are several problems with the proposal. There could be numerous issues along the line, such as a break in the chain of communication or an inability of a system to accurately assess the mind of another (smarter) system. There is also the problem of creating a trusted bottom for the chain in the first place, which is not necessarily any easier than creating a trustworthy superintelligence. Hall  [128]  writes that there will be a great variety of AGIs, with those that were designed to be moral or aligned with human interests keeping the non-safe ones in check. Goertzel  [115]  also propose that we build a community of mutually policing AGI systems of roughly equal levels of intelligence. If an AGI started to 'go off the rails', the other AGIs could stop it. This might not prevent a single AGI from undergoing an intelligence explosion, but a community of AGIs might be in a better position to detect and stop it than humans would. Having AGIs police each other is only useful if the group of AGIs actually has goals and values that are compatible with human goals and values. To this end, appropriate internal constraints are needed. The proposal of a society of mutually policing AGIs would avoid the problem of trying to control a more intelligent mind. If a global network of mildly superintelligent AGIs could be instituted in such a manner, it might detect and prevent any nascent takeoff. However, by itself such an approach is not enough to ensure safety-it helps guard against individual AGIs 'going off the rails', but it does not help in a scenario where the programming of most AGIs is flawed and leads to non-safe behavior. It thus needs to be combined with the appropriate internal constraints. A complication is that a hard takeoff is a relative terman event that happens too fast for any outside observer to stop. Even if the AGI network were a hundred times more intelligent than a network composed of only humans, there might still be a more sophisticated AGI that could overcome the network. 4.2.1. 'AGI enforcement' proposals: our view. AGI enforcement proposals are in many respects similar to social integration proposals (section 3.2), in that they depend on the AGIs being part of a society which is strong enough to stop any single AGI from misbehaving. The greatest challenge is then to make sure that most of the AGIs in the overall system are safe and do not unite against humans rather than against misbehaving AGIs. Also, there might not be a natural distinction between a distributed AGI and a collection of many different AGIs and AGI design is in any case likely to make heavy use of earlier AI/AGI techniques. AGI enforcement proposals therefore seem like implementation variants of various internal constraint proposals (section 5), rather than independent proposals. \n Internal constraints In addition to external constraints, AGIs could be designed with internal motivations designed to ensure that they would take actions in a manner beneficial to humanity. Alternatively, AGIs could be built with internal constraints that make them easier to control via external means. With regard to internal constraints, Yudkowsky distinguishes between technical failure and philosophical failure  [309] : Technical failure is when you try to build an AI and it does not work the way you think it does-you have failed to understand the true workings of your own code. Philosophical failure is trying to build the wrong thing, so that even if you succeeded you would still fail to help anyone or benefit humanity. Needless to say, the two failures are not mutually exclusive. In practice, it is not always easy to distinguish between the two. Most of the discussion below focuses on the philosophical problems of various proposals, but some of the issues, such as whether or not a proposal is actually possible to implement, are technical. \n Oracle AI An Oracle AI is a hypothetical AGI that executes no actions other than answering questions. This might not be as safe as it sounds, however. Correctly defining 'take no actions' might prove surprisingly tricky  [30]  and the oracle could give flawed advice even if it did correctly restrict its actions. Some possible examples of flawed advice: as extra resources are useful for the fulfilment of nearly all goals  [211, 212] , the oracle may seek to obtain more resourcessuch as computing power-in order to answer questions more accurately. Its answers might then be biased toward furthering this goal, even if this temporarily reduces the accuracy of its answers, if it believes this to increase the accuracy of its answers in the long run. Another example is that if the oracle had the goal of answering as many questions as possible as fast as possible, it could attempt to manipulate humans into asking it questions that were maximally simple and easy to answer. Holden Karnofsky has suggested that an Oracle AI could be safe if it was 'just a calculator', a system which only computed things that were asked of it, taking no goal-directed actions of its own. Such a 'tool-Oracle AI' would keep humans as the ultimate decision makers. Furthermore, the first team to create a tool-Oracle AI could use it to become powerful enough to prevent the creation of other AGIs  [162, 163] . An example of a tool-Oracle AI approach might be Omohundroʼs  [213]  proposal of 'safe-AI scaffolding': creating highly constrained AGI systems which act within limited, predetermined parameters. These could be used to develop formal verification methods and solve problems related to the design of more intelligent, but still safe, AGI systems. 5.1.1. Oracles are likely to be released. As with a boxed AGI, there are many factors that would tempt the owners of an Oracle AI to transform it to an autonomously acting agent. Such an AGI would be far more effective in furthering its goals, but also far more dangerous. Current narrow-AI technology includes HFT algorithms, which make trading decisions within fractions of a second, far too fast to keep humans in the loop. HFT seeks to make a very short-term profit, but even traders looking for a longer-term investment benefit from being faster than their competitors. Market prices are also very effective at incorporating various sources of knowledge  [135] . As a consequence, a trading algorithmʼs performance might be improved both by making it faster and by making it more capable of integrating various sources of knowledge. Most advances toward general AGI will likely be quickly taken advantage of in the financial markets, with little opportunity for a human to vet all the decisions. Oracle AIs are unlikely to remain as pure oracles for long. Similarly, Wallach  [283]  discuss the topic of autonomous robotic weaponry and note that the US military is seeking to eventually transition to a state where the human operators of robot weapons are 'on the loop' rather than 'in the loop'. In other words, whereas a human was previously required to explicitly give the order before a robot was allowed to initiate possibly lethal activity, in the future humans are meant to merely supervise the robotʼs actions and interfere if something goes wrong. Human Rights Watch  [90]  reports on a number of military systems which are becoming increasingly autonomous, with the human oversight for automatic weapons defense systems-designed to detect and shoot down incoming missiles and rockets-already being limited to accepting or overriding the computerʼs plan of action in a matter of seconds. Although these systems are better described as automatic, carrying out pre-programmed sequences of actions in a structured environment, than autonomous, they are a good demonstration of a situation where rapid decisions are needed and the extent of human oversight is limited. A number of militaries are considering the future use of more autonomous weapons. In general, any broad domain involving high stakes, adversarial decision making and a need to act rapidly is likely to become increasingly dominated by autonomous systems. The extent to which the systems will need general intelligence will depend on the domain, but domains such as corporate management, fraud detection and warfare could plausibly make use of all the intelligence they can get. If oneʼs opponents in the domain are also using increasingly autonomous AI/AGI, there will be an arms race where one might have little choice but to give increasing amounts of control to AI/AGI systems. Miller  [189]  also points out that if a person was close to death, due to natural causes, being on the losing side of a war, or any other reason, they might turn even a potentially dangerous AGI system free. This would be a rational course of action as long as they primarily valued their own survival and thought that even a small chance of the AGI saving their life was better than a near-certain death. Some AGI designers might also choose to create less constrained and more free-acting AGIs for aesthetic or moral reasons, preferring advanced minds to have more freedom. 5.1.2. Oracles will become authorities. Even if humans were technically kept in the loop, they might not have the time, opportunity, motivation, intelligence, or confidence to verify the advice given by an Oracle AI. This may be a danger even with narrower AI systems. Friedman  [102]  discuss APACHE, an expert system that provides medical advice to doctors. They write that as the medical community puts more and more trust into APACHE, it may become common practice to act automatically on APACHEʼs recommendations and it may become increasingly difficult to challenge the 'authority' of the recommendations. Eventually, APACHE may in effect begin to dictate clinical decisions. Likewise, Bostrom  [53]  point out that modern bureaucrats often follow established procedures to the letter, rather than exercising their own judgment and allowing themselves to be blamed for any mistakes that follow. Dutifully following all the recommendations of an AGI system would be an even better way of avoiding blame. Wallach  [283]  note the existence of robots which attempt to automatically detect the locations of hostile snipers and to point them out to soldiers. To the extent that these soldiers have come to trust the robots, they could be seen as carrying out the robots' orders. Eventually, equipping the robot with its own weapons would merely dispense with the formality of needing to have a human to pull the trigger. Thus, even AGI systems that function purely to provide advice will need to be explicitly designed to be safe in the sense of not providing advice that would go against human values  [282] . Yudkowsky  [313]  further notes that an Oracle AI might choose a plan that is beyond human comprehension, in which case there is still a need to design it as explicitly safe and conforming to human values. 5.1.3. 'Oracle AI' proposals: our view. Much like with external constraints, it seems like Oracle AIs could be a useful stepping stone on the path toward safe, freely acting AGIs. However, because any Oracle AI can be relatively easily turned into a free-acting AGI and because many people will have an incentive to do so, Oracle AIs are not by themselves a solution to AGI risk, even if they are safer than free-acting AGIs when kept as pure oracles. \n Top-down safe AGI AGIs built to take autonomous actions will need to be designed with safe motivations. Wallach and Allen divide approaches for ensuring safe behavior into 'top-down' and 'bottom-up' approaches  [14, 15, 281, 282, 284] . They define top-down approaches as ones that take a specified ethical theory and attempt to build a system capable of implementing that theory  [282] . Wallach and Allen  [14, 15, 281, 282, 284]  have expressed skepticism about the feasibility of both pure topdown and bottom-up approaches, arguing for a hybrid approach  30  . With regard to top-down approaches, which attempt to derive an internal architecture from a given ethical theory, Wallach  [281]  finds three problems: 1. 'Limitations already recognized by moral philosophers: For example, in a utilitarian calculation, how can consequences be calculated when information is limited and the effects of actions cascade in never-ending interactions? Which consequences should be factored into the maximization of utility? Is there a stopping procedure?'  [281] . 2. The 'frame problem' refers to the challenge of discerning relevant from irrelevant information without having to consider all of it, as all information could be relevant in principle  [8, 85] . Moral decision-making involves a number of problems that are related to the frame problem, such as needing to know what effects different actions have on the world and needing to estimate whether one has sufficient information to accurately predict the consequences of the actions. 3. 'The need for background information. What mechanisms will the system require in order to acquire the information it needs to make its calculations? How does one ensure that this information is up to date in real time?'  [281] . To some extent, these problems may be special cases of the fact that we do not yet have AGI with good general learning capabilities: creating an AGI would also require solving the frame problem, for instance. These problems might therefore not all be as challenging as they seem at first, presuming that we manage to develop AGI in the first place. 5.2.1. Three laws. Probably the most widely known proposal for machine ethics is Isaac Asimovʼs  [33]  three laws of robotics: 1. A robot may not injure a human being or, through inaction, allow a human being to come to harm. 2. A robot must obey orders given to it by human beings except where such orders would conflict with the first law. 3. A robot must protect its own existence as long as such protection does not conflict with either the first or second law. Asimov and other writers later expanded the list to include a number of additional laws, including the zeroth law: A robot may not harm humanity, or through inaction allow humanity to come to harm. Although the three laws are widely known and have inspired numerous imitations, several of Asimovʼs own stories were written to illustrate the fact that the laws contained numerous problems. They have also drawn heavy critique from others  [23, 75, 76, 120, 180, 201, 224, 282, 295, 296]  and are not considered a viable approach for safe AI. Among their chief shortcomings is the fact that they are too ambiguous to implement and, if defined with complete accuracy, contradict each other in many situations. 5.2.2. Categorical imperative. The best-known universal ethical axiom is Kantʼs categorical imperative. Many authors have discussed using the categorical imperative as the foundation of AGI morality  [14, 40, 41, 63, 222, 256, 282] . All of these authors conclude that Kantian ethics is a problematic goal for AGI, though Powers  [222]  still remains hopeful about its prospects. 5.2.3. Principle of voluntary joyous growth. Goertzel  [106, 107]  considers a number of possible axioms before settling on what he calls the 'principle of voluntary joyous growth', defined as 'maximize happiness, growth and choice'. He starts by considering the axiom 'maximize happiness', but then finds this to be problematic and adds 'growth', which he defines as 'increase in the amount and complexity of patterns in the universe'. Finally he adds 'choice' in order to allow sentient beings to 'choose their own destiny'. 5.2.4. Utilitarianism. Classic utilitarianism is an ethical theory stating that people should take actions that lead to the greatest amount of happiness and the smallest amount of suffering. The prospects for AGIs implementing a utilitarian moral theory have been discussed by several authors  [14, 19, 21, 77, 104, 119, 121, 199, 282] . The consensus is that pure classical utilitarianism is problematic and does not capture all human values. For example, a purely utilitarian AGI could reprogram the brains of humans so that they did nothing but experience the maximal amount of pleasure all the time and that prospect seems unsatisfactory to many  31  . 5.2.5. Value learning. Freeman  [101]  describes a decisionmaking algorithm which observes peopleʼs behavior, infers their preferences in the form of a utility function and then attempts to carry out actions which fulfil everyoneʼs preferences. Similarly, Dewey  [88]  discusses value learners, AGIs which are provided a probability distribution over possible utility functions that humans may have. Value learners then attempt to find the utility functions with the best match for human preferences. Hibbard  [153]  builds on Deweyʼs work to offer a similar proposal.  30  For a definition of bottom-up approaches, see section 5.3.  31  Note that utilitarianism is not the same thing as having a utility function. Utilitarianism is a specific kind of ethical system, while utility functions are general-purpose mechanisms for choosing between actions and can in principle be used to implement very different kinds of ethical systems, such as egoism and possibly even rights-based theories and virtue ethics  [217] . One problem with conceptualizing human desires as utility functions is that human desires change over time  [272]  and also violate the axioms of utility theory required to construct a coherent utility function  [271] . While it is possible to treat inconsistent choices as random deviations from an underlying 'true' utility function that is then learned  [207] , this does not seem to properly describe human preferences. Rather, human decision making and preferences seem to be driven by multiple competing systems, only some of which resemble utility functions  [81] . Even if a true utility function could be constructed, it does not take into account the fact that we have secondorder preferences, or desires about our desires: a drug addict may desire a drug, but also desire that he not desire it  [98] . Similarly, we often wish that we had stronger desires toward behaviors which we consider good but cannot make ourselves engage in. Taking second-order preferences into account leads to what philosophers call 'ideal preference' theories of value  [55, 176, 225, 247, 249, 264, 314] . Taking this into account, it has been argued that we should aim to build AGIs which act according to humanityʼs extrapolated values  [199, 265, 308] . Yudkowsky proposes attempting to discover the 'coherent extrapolated volition' (CEV) of humanity, which he defines as  [308]  our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted. CEV remains vaguely defined and has been criticized by several authors  [109, 115, 148, 189, 294] . However, Tarleton  [265]  finds CEV a promising approach and suggests that CEV has five desirable properties, and that many different kinds of algorithms could possess these features: Meta-algorithm: Most of the AGIʼs goals will be obtained at runtime from human minds, rather than explicitly programmed in before runtime. Factually correct beliefs: The AGI will attempt to obtain correct answers to various factual questions, in order to modify preferences or desires that are based upon false factual beliefs. Singleton: Only one superintelligent AGI is to be constructed and it is to take control of the world with whatever goal function is decided upon. Reflection: Individual or group preferences are reflected upon and revised. Preference aggregation: The set of preferences of a whole group are to be combined somehow. At least two CEV variants have been proposed: coherent aggregated volition  [109]  and coherent blended volition  [115] . Goertzel  [115]  describe a methodology which was used to help end the apartheid in South Africa. The methodology involves people with different views exploring different future scenarios together and in great detail. By exploring different outcomes together, the participants build emotional bonds and mutual understanding, seeking an outcome that everyone can agree to live with. The authors characterize the coherent blended volition of a diverse group as analogous to the 'conceptual blend' resulting from the methodology, incorporating the most essential elements of the group into a harmonious whole. Christiano  [73]  attempts to sketch out a formalization of a value extrapolation approach called 'indirect normativity'. It proposes a technique that would allow an AI to approximate the kinds of values a group of humans would settle on if they could spend an unbounded amount of time and resources considering the problem. Other authors have begun preliminary work on simpler value learning systems, designed to automatically learn moral principles. Anderson et al  [18, 20, 21]  have built systems based around various moral duties and principles. As lists of duties do not in and of themselves specify what to do when they conflict, the systems let human experts judge how each conflict should be resolved and then attempt to learn general rules from the judgments. As put forth, however, this approach would have little ability to infer ethical rules which did not fit the framework of proposed duties. Improved computational models of ethical reasoning  [18, 20, 21, 32, 185, 186] , perhaps incorporating work from neuroscience and moral psychology  [42, 199, 245] , could help address this. Potapov  [221]  propose an approach by which an AGI could gradually learn the values of other agents as its understanding of the world improved. A value extrapolation process seems difficult to specify exactly, as it requires building an AGI with programming that formally and rigorously defines human values. Even if it manages to avoid the first issue in Wallachʼs  [281]  list (section 5.2), top-down value extrapolation may fall victim to other issues, such as computational tractability. One interpretation of CEV would seem to require modeling not only the values of everyone on Earth, but also the evolution of those values as the people in question interacted with each other, became more intelligent and more like their ideal selves, chose which of their values they wanted to preserve, etc. Even if the AGI could eventually obtain the enormous amount of computing power required to run this model, its behavior would need to be safe from the beginning, or it could end up doing vast damage to humanity before understanding what it was doing wrong. Goertzel and Pittʼs  [115]  hybrid approach, in which AGIs cooperate with humans in order to discover the values humans wish to see implemented, seems more likely to avoid the issue of computational tractability. However, it will fail to work in a hard takeoff situation where AGIs take control before being taught the correct human values. Another issue with coherent blended volition is that schemes which require absolute consensus are unworkable with large groups, as anyone whose situation would be worsened by a change of events could block the consensus. A general issue with value extrapolation approaches is that there may be several valid ways of defining a value extrapolation process, with no objective grounds for choosing one rather than another. Goertzel  [109]  notes that in formal reasoning systems a set of initially inconsistent beliefs which the system attempts to resolve might arrive at something very different than the initial belief set, even if there existed a consistent belief set that was closer to the original set. He suggests that something similar might happen when attempting to make human values consistent, though whether this would be a bad thing is unclear. 5.2.6. 'Top-down safe AGI' proposals: our view. Of the various top-down proposals, value learning proposals seem to be the only ones which properly take into account the complexity of value thesis (section 2.2), as they attempt to specifically take into account considerations such as 'would humanity have endorsed this course of action if it had known the consequences?' Although there are many open questions concerning the computational tractability as well as the general feasibility of such approaches, they seem like some of the most important ones to work on. \n Bottom-up and hybrid safe AGI Wallach  [281]  defines bottom-up approaches as ones that favor evolving or simulating the mechanisms that give rise to our moral decisions. Another alternative is hybrid approaches, combining parts of both top-down and bottom-up approaches. A problem with pure bottom-up approaches is that techniques such as artificial evolution or merely rewarding the AGI for the right behavior may cause it to behave correctly in tests, but would not guarantee that it would behave safely in any other situation. Even if an AGI seems to have adopted human values, the actual processes driving its behavior may be very different from the processes that would be driving the actions of a human who behaved similarly. It might then behave very unexpectedly in situations which are different enough  [152, 229, 309, 312] . Armstrong, Sandberg and Bostrom discuss various problems related to such approaches and offer examples of concepts which seem straightforward to humans but are not as simple as they may seem on the surface. One of their examples relates to the concept of time  [30] : If the [AGI] had the reasonable-sounding moral premise that 'painlessly killing a human being, who is going to die in a micro-second anyway, in order to gain some other good, is not a crime', we would not want it to be able to redefine millennia as seconds. All humans have an intuitive understanding of time and no experience with beings who could arbitrarily redefine their own clocks and might not share the same concept of time. Such differences in the conceptual grounding of an AGIʼs values and of human values might not become apparent until too late. \n Evolutionary invariants. Human morality is to a large extent shaped by evolution  [83, 161]  and evolutionary approaches attempt to replicate this process with AGIs. Hall  [128, 131]  argues that self-improving AGIs are likely to exist in competition with many other kinds of selfimproving AGIs. Properties that give AGIs a significant disadvantage might then be strongly selected against and disappear. We could attempt to identify evolutionary invariants, or evolutionarily stable strategies, which would both survive in a competitive environment and cause an AGI to treat humans well. Hall  [131]  lists self-interest, long planning horizons, knowledge, an understanding of evolutionary ethics and guaranteed honesty as invariants that are likely to make an AGI more moral as well as to persist even under intense competition. He suggests that, although self-interest may sound like a bad thing in an AGI, non-self-interested creatures are difficult to punish. Thus, enlightened self-interest might be a good thing for an AGI to possess, as it will provide an outside community with both a stick and a carrot to control it with. Similarly, Waser  [292]  suggests that minds which are intelligent enough will, due to game-theoretical and other considerations, become altruistic and cooperative. Waser  [294]  proposed the principle of rational universal benevolence (RUB), the idea that the moral course of action is cooperation while letting everyone freely pursue their own goals. Waser proposes that, instead of making human-friendly behavior an AGIʼs only goal, the AGI would be allowed to have and form its own goals. However, its goals and actions would be subject to the constraint that they should respect the principle of RUB and not force others into a life those others would disagree with. Kornai  [167]  cites Gewirthʼs  [103]  work on the principle of generic consistency, which holds that respecting others' rights to freedom and well-being is a logically necessary conclusion for any rational agents. Kornai suggests that if the principle is correct, then AGIs would respect humanityʼs rights to freedom and well-being, and that AGIs which failed to respect the principle would be outcompeted by ones which did. Something similar was also proposed by Gips  [104]  and Versenyi  [277] , who advocates the creation of 'wise robots' that would recognize the extent to which their own well-being depended on cooperation with humans and would act accordingly. Although these approaches expect AGI either to evolve altruism or to find it the most rational approach, true altruism or even pure tit-for-tat  [34]  is not actually the best strategy in evolutionary terms. Rather, a better strategy is Machiavellian tit-for-tat: cultivating an appearance of altruism and cooperation when it benefits oneself and acting selfishly when one can get away with it. Humans seem strongly disposed toward such behavior  [127] . Another problem is that tit-for-tat as a good strategy assumes that both players are equally powerful and both have the same options at their disposal. If the AGI became far more powerful than most humans, it might no longer be in its interests to treat humans favorably  [97] . This hypothesis can be tested by looking at human behavior: if exploiting the weak is an evolutionarily useful strategy, then humans should engage in it when given the opportunity. Humans who feel powerful do indeed devalue the worth of the less powerful and view them as objects of manipulation  [164] . They also tend to ignore social norms  [274]  and to experience less distress and compassion toward the suffering of others  [273] . Thus, even if an AGI cooperated with other similarly powerful AGIs, the group of AGIs might still decide to collectively exploit humans. Similarly, even though there might be pressure for AGIs to make themselves more transparent and easily inspected by others, this only persists for as long as the AGI needs others more than the others need the AGI. \n Evolved morality. Another proposal is to create AGIs via algorithmic evolution, selecting in each generation the AGIs which are not only the most intelligent, but also the most moral. These ideas are discussed to some extent by Wallach  [282] . \n Reinforcement learning. In machine learning, reinforcement learning is a model in which an agent takes various actions and is differentially rewarded for the actions, after which it learns to perform the actions with the greatest expected reward. In psychology, it refers to agents being rewarded for certain actions and thus learning behaviors which they have a hard time breaking, even if some other kind of behavior is more beneficial for them later on. Applied to AGI, the machine learning sense of reinforcement involves teaching an AGI to behave in a safe manner by rewarding it for ethical choices and letting it learn for itself the underlying rules of what constitutes ethical behavior. In an early example of this kind of proposal, McCulloch  [181]  described an 'ethical machine' that could infer the rules of chess by playing the game and suggested that it could also learn ethical behavior this way. Hibbard  [146, 148]  suggested using reinforcement learning to give AGIs positive emotions toward humans. Early AGIs would be taught to recognize happiness and unhappiness in humans, and the results of this learning would be hard-wired as emotional values in more advanced AGIs. This training process would then be continued-for example, by letting the AGIs predict how human happiness would be affected by various actions and using those predictions as emotional values. A reinforcement learner is supplied with a reward signal and it always has the explicit goal of maximizing the sum of this reward, any way it can. In order for this goal to align with human values, humans must engineer the environment so that the reinforcement learner is prevented from receiving rewards if human goals are not fulfilled  [88] . A reinforcement-learning AGI only remains safe for as long as humans are capable of enforcing this limitation and will become unpredictable if it becomes capable of overcoming it. Hibbard  [152]  has retracted his earlier reinforcement learning-based proposals, as they would allow the AGI to maximize its reinforcement by modifying humans to be maximally happy, even against their will  [88] . Connectionist systems, based on artificial neural nets, are capable of learning patterns from data without being told what the patterns are. As some connectionist models have learned to classify problems in a manner similar to humans  [187, 219, 267] , it has been proposed that connectionist AGI might learn moral principles that are too complex for humans to specify as explicit rules  32  . This idea has been explored by Guarini  [123]  and Wallach  [282] . One specific proposal that draws upon connectionism is to make AGIs act according to virtue ethics  [14, 281, 282, 284] . These authors note that previous writers discussing virtuous behavior have emphasized the importance of learning moral virtues through habit and practice. As it is impossible to exhaustively define a virtue, virtue ethics has traditionally required each individual to learn the right behaviors through 'bottom-up processes of discovery or learning'  [282] . Models that mimicked the human learning process well enough could then potentially learn the same behaviors as humans do. Another kind of human-inspired proposal is the suggestion that something like Stan Franklinʼs LIDA architecture  [99, 227, 248] , or some other approach based on Bernard Baarsʼs  [35, 36]  'global workspace' theory, might enable moral reasoning. In the LIDA architecture, incoming information is monitored by specialized attention codelets, each of which searches the input for specific features. In particular, moral codelets might look for morally relevant factors and ally themselves with other codelets to promote their concerns to the level of conscious attention. Ultimately, some coalitions will win enough support to accomplish a specific kind of decision  [282, 285, 286] . Goertzel  [115]  consider human memory systems (episodic, sensorimotor, declarative, procedural, attentional and intentional) and ways by which human morality might be formed via their interaction. They briefly discuss the way that the OpenCog AGI system  [113, 141]  implements similar memory systems and how those systems could enable it to learn morality. Similarly, Goertzel  [114]  discuss the stages of moral development in humans and suggest ways by which they could be replicated in AGI systems, using the specific example of Novamente, a proprietary version of OpenCog. Waser  [293]  also proposes building an AGI by studying the results of evolution and creating an implementation as close to the human model as possible. Human-inspired AGI architectures would intuitively seem the most capable of learning human values, though what would be human-like enough remains an open question.  32  But it should be noted that there are also promising non-connectionist approaches for modeling human classification behavior: see, e.g., Tenenbaum et al  [266] . It is possible that even a relatively minor variation from the norm could cause an AGI to adopt values that most humans would consider undesirable. Getting the details right might require an extensive understanding of the human brain. There are also humans who have drastically different ethics than the vast majority of humanity and argue for the desirability of outcomes such as the extinction of mankind  [43, 89] . There remains the possibility that even AGIs which reasoned about ethics in a completely human-like manner would reach such conclusions. Humans also have a long track record of abusing power, or of undergoing major behavioral changes due to relatively small injuries-the 'safe Homo sapiens' problem also remains unsolved. On the other hand, it seems plausible that human-like AGIs could be explicitly engineered to avoid such problems. The easier that an AGI is to modify the more powerful it might become  [253]  and very close recreations of the human brain may turn out to be difficult to extensively modify and upgrade. Human-inspired safe AGIs might then end up outcompeted by AGIs which were easier to modify and which might or might not be safe. Even if human-inspired architectures could be easily modified, the messiness of human cognitive architecture means that it might be difficult to ensure that their values remain beneficial during modification. For instance, in LIDAlike architectures, beneficial behavior will depend on the correct coalitions of morality codelets winning each time. If the system undergoes drastic changes, this can be very difficult if not impossible to ensure. Most AGI builders will attempt to create a mind that displays considerable advantages over ordinary humans. Some such advantages might be best achieved by employing a very non-human architecture  [194] , so there will be reasons to build AGIs that are not as human-like. These could also end up outcompeting the human-like AGIs. We are generally very skeptical about pure bottom-up methods, as they only allow a very crude degree of control over an AGIʼs goals, giving it a motivational system which can only be relied on to align with human values in the very specific environments that the AGI has been tested in. Evolutionary invariants seem incapable of preserving complexity of value and they might not even be capable of preserving human survival. Reinforcement learning, on the other hand, depends on the AGI being incapable of modifying the environment against the will of its human controllers. Therefore, none of these three approaches seems workable. Human-like AGI might have some promise, depending on exactly how fragile human values were. If the AGI reasoning process could be made sufficiently human-like, there is the possibility that the AGI could remain relatively safe, though less safe than a well-executed value extrapolation-based AGI. \n AGI Nanny A more general proposal, which could be achieved by either top-down, bottom-up, or hybrid methods, is the proposal of an 'AGI Nanny'  [111, 115] . This is an AGI that is somewhat more intelligent than humans and is designed to monitor Earth for various dangers, including more advanced AGI. The AGI Nanny would be connected to powerful surveillance systems and would control a massive contingent of robots. It would help abolish problems such as disease, involuntary death and poverty, while preventing the development of technologies that could threaten humanity. The AGI Nanny would be designed not to rule humanity on a permanent basis, but to give us some breathing room and time to design more advanced AGIs. After some predetermined amount of time, it would cede control of the world to a more intelligent AGI. Goertzel  [115]  briefly discuss some of the problems inherent in the AGI Nanny proposal. The AGI would have to come to power in an ethical way and might behave unpredictably despite our best efforts. It might also be easier to create a dramatically self-improving AGI than to create a more constrained AGI Nanny. 5.4.1. 'AGI Nanny' proposals: our view. Upon asserting control, the AGI Nanny would need to have precisely specified goals, so that it would stop other AGIs from taking control but would also not harm human interests. It is not clear to what extent defining these goals would be easier than defining the goals of a more free-acting AGI  [200] . Overall, the AGI Nanny seems to have promise, but it is unclear whether it can be made to work. \n Formal verification Formal verification methods prove specific properties about various algorithms. If the complexity and fragility of value theses hold, it follows that safe AGI requires the ability to verify that proposed changes to the AGI will not alter its goals or values. If even a mild drift from an AGIʼs original goals might lead to catastrophic consequences, then utmost care should be given to ensuring that the goals will not change inadvertently. This is particularly the case if there are no external feedback mechanisms which would correct the drift. Before modifying itself, an AGI could attempt to formally prove that the changes would not alter its existing goals and would therefore keep them intact even during extended selfmodification  [309] . Such proofs could be required before selfmodification was allowed to occur and the system could also be required to prove that this verify-before-modification property itself would always be preserved during selfmodification. Formal verification is also an essential part of Omohun-droʼs  [213]  safe-AI scaffolding strategy, as noted in section 5.6.4. Spears  [255]  combines machine learning and formal verification methods to ensure that AIs remain within the bounds of pre-specified constraints after having learned new behaviors. She attempts to identify 'safe' machine learning operators, which are guaranteed to preserve the systemʼs constraints. One AGI system built entirely around the concept of formal verification is the Gdel machine  [236, 258] . It consists of a solver, which attempts to achieve the goals set for the machine, and a searcher, which has access to a set of axioms that completely describe the machine. The searcher may completely rewrite any part of the machine, provided that it can produce a formal proof showing that such a rewrite will further the systemʼs goals. Goertzel  [110]  proposes goal-oriented learning metaarchitecture (GOLEM), a meta-architecture that can be wrapped around a variety of different AGI systems. GOLEM will only implement changes that are predicted to be more effective at achieving the original goal of the system. Goertzel argues that GOLEM is likely to be both self-improving and steadfast: either it pursues the same goals it had at the start, or it stops acting altogether. Unfortunately, formalizing the AGIʼs goals in a manner that will allow formal verification methods to be used is a challenging task. Within cryptography, many communications protocols have been proven secure, only for successful attacks to be later developed against their various implementations. While the formal proofs were correct, they contained assumptions which did not accurately capture the way the protocols worked in practice  [84] . Proven theorems are only as good as their assumptions, so formal verification requires good models of the AGI hardware and software. 5.5.1. 'Formal verification' proposals: our view. Compared to the relatively simple domain of cryptographic security, verifying things such as 'does this kind of a change to the AGIʼs code preserve its goal of respecting human values?' seems like a much more open-ended and difficult task, one which might even prove impossible. Regardless, it is the only way of achieving high confidence that a system is safe, so it should at least be attempted. \n Motivational weaknesses Finally, there is a category of internal constraints that, while not making an AGIʼs values safer, make it easier to control AGI via external constraints. 5.6.1. High discount rates. AGI systems could be given a high discount rate, making them value short-term goals and gains far more than long-term goals and gains  [30, 243] . This would inhibit the AGIʼs long-term planning, making it more predictable. However, an AGI can also reach long-term goals through a series of short-term goals  [30] . Another possible problem is that it could cause the AGI to pursue goals which were harmful for humanityʼs long-term future. Humanity may arguably be seen as already behaving in ways that imply an excessively high discount rate, such as by consuming finite natural resources without properly taking into account the well-being of future generations. 5.6.2. Easily satiable goals. Shulman  [243]  proposes designing AGIs in such a way that their goals are easy to satisfy. For example, an AGI could receive a near-maximum reward for simply continuing to receive an external reward signal, which could be cut if humans suspected misbehavior. The AGI would then prefer to cooperate with humans rather than trying to attack them, even if it was very sure of its chances of success  33  . Likewise, if the AGI could receive a maximal reward with a relatively small fraction of humanityʼs available resources, it would have little to gain from seizing more resources. An extreme form of this kind of a deal is Orseau and Ringʼs  [214]  'simpleton gambit', in which an AGI is promised everything that it would ever want, on the condition that it turn itself into a harmless simpleton. Orseau and Ring consider several hypothetical AGI designs, many of which seem likely to accept the gambit, given certain assumptions. In a related paper, Ring  [229]  consider the consequences of an AGI being able to modify itself to receive the maximum possible reward. They show that certain types of AGIs will then come to only care about their own survival. Hypothetically, humans could promise not to threaten such AGIs in exchange for them agreeing to be subject to AI-boxing procedures. For this to work, the system would have to believe that humans will take care of its survival against external threats better than it could itself. Hibbard  [150, 153]  discusses the kinds of AGIs that would avoid the behaviors described by Ring and Orseau  [214, 229] . 5.6.3. Calculated indifference. Another proposal is to make an AGI indifferent to a specific event. For instance, the AGI could be made indifferent to the detonation of explosives attached to its hardware, which might enable humans to have better control over it  [28, 30] . 5.6.4. Programmed restrictions.  Goertzel [115]  suggest we ought to ensure that an AGI does not self-improve too fast, because AGIs will be harder to control as they become more and more cognitively superior to humans. To limit the rate of self-improvement in AGIs, perhaps AGIs could be programmed to extensively consult humans and other AGI systems while improving themselves, in order to ensure that no unwanted modifications would be implemented. Omohundro  [213]  discusses a number of programmed restrictions in the form of constraints on what the AGI is allowed to do, with formal proofs being used to ensure that an AGI will not violate its safety constraints. Such limited AGI systems would be used to design more sophisticated AGIs. Programmed restrictions are problematic, as the AGI might treat these merely as problems to solve in the process of meeting its goals and attempt to overcome them  [212] . Making an AGI not want to quickly self-improve might not solve the problem by itself. If the AGI ends up with a secondorder desire to rid itself of such a disinclination, the stronger  33  On the other hand, this might incentivize the AGI to deceive its controllers into believing it was behaving properly and also to actively hide any information which it even suspected might be interpreted as misbehavior. desire will eventually prevail  [259] . Even if the AGI wanted to maintain its disinclination toward rapid self-improvement, it might still try to circumvent the goal in some other way, such as by creating a copy of itself which did not have that disinclination  [212] . Regardless, such limits could help control less sophisticated AGIs. 5.6.5. Legal machine language. Weng et al  [296, 297]  propose a 'legal machine language' which could be used to formally specify actions which the AGI is allowed or disallowed to do. Governments could then enact laws written in legal machine language, allowing them to be programmed into robots. Overall, motivational weaknesses seem comparable to external constraints: possibly useful and worth studying, but not something to rely on exclusively, particularly in the case of superintelligent AGIs. As with external constraints and Oracle AIs, an arms race situation might provide a considerable incentive to loosen or remove such constraints. \n Conclusion We began this paper by noting that a number of researchers are predicting AGI in the next twenty to one hundred years. One must not put excess trust in this time frame: as Armstrong  [29]  show, experts have been terrible at predicting AGI. Muehlhauser  [200]  consider a number of methods other than expert opinion that could be used for predicting AGI, but find that they too provide suggestive evidence at best. It would be a mistake, however, to leap from 'AGI is very hard to predict' to 'AGI must be very far away'. Our brains are known to think about uncertain, abstract ideas like AGI in 'far mode', which also makes it feel like AGI must be temporally distant  [198, 268] , but something being uncertain is not strong evidence that it is far away. When we are highly ignorant about something, we should widen our error bars in both directions. Thus, we should not be highly confident that AGI will arrive this century and we should not be highly confident that it will not. Next, we explained why AGIs may be an existential risk. A trend toward automatization would give AGIs increased influence in society and there might be a discontinuity in which they gained power rapidly. This could be a disaster for humanity if AGIs do not share our values and, in fact, it looks difficult to make them share our values because human values are complex and fragile, and therefore problematic to specify. The recommendations given for dealing with the problem can be divided into proposals for societal action (section 3), external constraints (section 4) and internal constraints (section 5). Many proposals seem to suffer from serious problems, or seem to be of limited effectiveness. Others seem to have enough promise to be worth exploring. We will conclude by reviewing the proposals which we feel are worthy of further study. As a brief summary of our views, in the medium term, we think that the proposals of AGI confinement (section 4.1), Oracle AI (section 5.1) and motivational weaknesses (section 5.6) would have promise in helping create safer AGIs. These proposals share in common the fact that, although they could help a cautious team of researchers create an AGI, they are not solutions to the problem of AGI risk, as they do not prevent others from creating unsafe AGIs, nor are they sufficient in guaranteeing the safety of sufficiently intelligent AGIs. Regulation (section 3.3) as well as human capability enhancement (section 3.4) could also help to somewhat reduce AGI risk. In the long run, we will need the ability to guarantee the safety of freely acting AGIs. For this goal, value learning (section 5.2.5) would seem like the most reliable approach if it could be made to work, with humanlike architecture (section 5.3.4) a possible alternative which seems less reliable but possibly easier to build. Formal verification (section 5.5) seems like a very important tool in helping to ensure the safety of our AGIs, regardless of the exact approach that we choose. Of the societal proposals, we are supportive of the calls to regulate AGI development, but we admit there are many practical hurdles which might make this infeasible. The economic and military potential of AGI, and the difficulty of verifying regulations and arms treaties restricting it, could lead to unstoppable arms races. We find ourselves in general agreement with the authors who advocate funding additional research into safe AGI as the primary solution. Such research will also help establish the kinds of constraints which would make it possible to successfully carry out integration proposals. Uploading approaches, in which human minds are made to run on computers and then augmented, might buy us some time to develop safe AGI. However, it is unclear whether they can be developed before AGI and large-scale uploading could create strong evolutionary trends which seem dangerous in and of themselves. As AGIs seem likely to eventually outpace uploads, uploading by itself is probably not a sufficient solution. What uploading could do is to reduce the initial advantages that AGIs enjoy over (partially uploaded) humanity, so that other responses to AGI risk can be deployed more effectively. External constraints are likely to be useful in controlling AGI systems of limited intelligence and could possibly help us develop more intelligent AGIs while maintaining their safety. If inexpensive external constraints were readily available, this could encourage even research teams skeptical about safety issues to implement them. Yet it does not seem safe to rely on these constraints once we are dealing with a superhuman intelligence and we cannot trust everyone to be responsible enough to contain their AGI systems, especially given the economic pressures to 'release' AGIs. For such an approach to be a solution for AGI risk in general, it would have to be adopted by all successful AGI projects, at least until safe AGIs were developed. Much the same is true of attempting to design Oracle AIs. In the short term, such efforts may be reinforced by research into motivational weaknesses, internal constraints that make AGIs easier to control via external means. In the long term, the internal constraints that show the most promise are value extrapolation approaches and humanlike architectures. Value extrapolation attempts to learn human values and interpret them as we would wish them to be interpreted. These approaches have the advantage of potentially maximizing the preservation of human values and the disadvantage that such approaches may prove intractable or impossible to properly formalize. Human-like architectures seem easier to construct, as we can simply copy mechanisms that are used within the human brain, but it seems hard to build such an exact match as to reliably replicate human values. Slavish reproductions of the human psyche also seem likely to be outcompeted by less human, more efficient architectures. Both approaches would benefit from better formal verification methods, so that AGIs which were editing and improving themselves could verify that the modifications did not threaten to remove the AGIs' motivation to follow their original goals. Studies which aim to uncover the roots of human morals and preferences also seem like candidates for research that would benefit the development of safe AGI  [42, 199, 245] , as do studies into computational models of ethical reasoning  [186] . We reiterate that when we talk about 'human values', we are not making the claim that human values would be static, nor that current human values would be ideal. Nor do we wish to imply that the values of other sentient beings would be unimportant. Rather, we are seeking to guarantee the implementation of some very basic values, such as the avoidance of unnecessary suffering, the preservation of humanity and the prohibition of forced brain reprogramming. We believe the vast majority of humans would agree with these values and be sad to see them lost. 5. 3 . 4 . 34 Human-like AGI. Another kind of proposal involves building AGIs that can learn human values by virtue of being similar to humans. \n 5. 3 . 5 . 35 'Bottom-up and hybrid safe AGI' proposals: our view. \n 5. 6 . 6 . 66 'Motivational weaknesses' proposals: our view. \n\t\t\t Phys. Scr.90 (2015)  018001Invited Comment \n\t\t\t On the less serious front, see Eisen [94]  for an amusing example of", "date_published": "n/a", "url": "n/a", "filename": "Sotala_2015_Phys._Scr._90_018001.tei.xml", "abstract": "Many researchers have argued that humanity will create artificial general intelligence (AGI) within the next twenty to one hundred years. It has been suggested that AGI may inflict serious damage to human well-being on a global scale ('catastrophic risk'). After summarizing the arguments for why AGI may pose such a risk, we review the fieldʼs proposed responses to AGI risk. We consider societal proposals, proposals for external constraints on AGI behaviors and proposals for creating AGIs that are safe due to their internal design.", "id": "2d1f3d3a9cef9808fd804a2e28d0f97f"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Allan Dafoe", "Yoram Bachrach", "Gillian Hadfield", "Eric Horvitz", "Kate Larson", "Thore Graepel", "Sean Gallup", "/ Getty"], "title": "Cooperative AI: machines must learn to find common ground", "text": "its environment and how to interact with it. Even in work involving multiple AI agents, the field has not yet tackled the hard problems of cooperation. Most headline results have come from two-player zero-sum games, such as backgammon, chess  1  , Go 2 and poker  3  . Gains in these competitive examples can be made only at the expense of others. Although such settings of pure conflict are vanishingly rare in the real world, they make appealing research projects. They are culturally cherished, relatively easy to benchmark (by asking whether the AI can beat the opponent), have natural curricula (because students train against peers of their own skill level) and have simpler solutions than semi-cooperative games do. AI needs social understanding and cooperative intelligence to integrate well into society. The coming years might give rise to diverse ecologies of AI systems that interact in rapid and complex ways with each other and with humans: on pavements and roads, in consumer and financial markets, in e-mail communication and social media, in cybersecurity and physical security. Autonomous vehicles or smart cities that do not engage well with humans will fail to deliver their benefits, and might even disrupt stable human relationships. We need to build a science of cooperative AI. As researchers in the field and its governance, we argue that it is time to prioritize the development of cooperative intelligence that has the ability to promote mutually beneficial joint action, even when incentives are not fully aligned. Just as psychologists studying humans have found that the infant brain does not develop fully without social interaction, progress towards socially valuable AI will be stunted unless we put the problem of cooperation at the centre of our research. Cooperative intelligence is unlikely to emerge as a by-product of research on other kinds of AI. We need more work on cooperative games and complex social spaces, on understanding norms and behaviours, and on social tools and infrastructure that promote cooperation. The AI community should learn more from, and contribute to, other fields that work on cooperation. \n From autonomy to cooperation Parents encourage their children to grow beyond their dependencies and become autonomous. But autonomy is rarely regarded as the sole goal for humans. Rather, we are generally most productive when we work cooperatively as part of broader society. Similarly, certain kinds of autonomy in AI systems are useful precisely because they enable the system to contribute effectively to broader cooperative efforts. Most of the value from self-driving vehicles will come not from driving on empty roads, but from vehicles coordinating smoothly with the flow of pedestrians, In most settings, people's incentives are not fully aligned. Nevertheless, they can often cooperate, taking joint action to achieve mutually beneficial outcomes. One example is countries agreeing and enforcing carbon cuts to tackle climate change. The cooperative intelligence needed to achieve this has four parts: Understanding. The ability to take into account the consequences of actions, to predict another's behaviour, and the implications of another's beliefs and preferences. Communication. The ability to explicitly and credibly share information with others relevant to understanding behaviour, intentions and preferences. Commitment. The ability to make credible promises when needed for cooperation. \n Norms and institutions. Social infrastructure -such as shared beliefs or rules -that reinforces understanding, communication and commitment. \n Four elements of cooperative intelligence by pure conflict -when there is no possibility of bargains, negotiations or threats. So, improving skill at inherently rivalrous games is unlikely to be the most promising way for AI to produce social value. Games of pure common interest are a step towards developing cooperative agents. The cooperative card game Hanabi 4 requires players to communicate private information and intentions under strong constraints about what can be said and when. Team games such as robot soccer  5  need players on a team to work as one, jointly planning their moves and passing the ball. In these examples, all agents on a team share the same goals. Mastering these games requires many skills essential to cooperation. Research avenues include building AIs that can understand what teammates are thinking and planning; communicate plans; and even cooperate with different kinds of teammate who might think differently and react more slowly (known as ad hoc teamwork). Yet because these situations are restricted to a perfect harmony of interests, they represent the easy case for cooperation. Real-world relationships almost always involve a mixture of common and conflicting interests. This tension gives rise to the rich texture of human cooperation problems, including bargaining, trust and mistrust, deception and credible communication, commitment problems and assurances, politics and coalitions, and norms and institutions. AI agents will need to learn how to manage these harder cooperation problems, as humans do. An example is the board game Diplomacy, in which players negotiate non-binding alliances with others. To succeed, AI agents will need to understand each other well enough to recognize when their interests are aligned with those of other players. They will have to develop a common vocabulary to communicate their intentions. They will benefit from being able to communicate credibly, despite possible incentives to lie. They must overcome mutual fears of betrayal, so as to agree on and execute jointly beneficial plans. They might even learn to establish norms relating to the adherence of agreements. To enable progress in these cooperative skills, researchers have devised variants of Diplomacy that modify the difficulty of these challenges, such as introducing an agreed simple vocabulary or permitting binding commitments. \n Human-AI cooperation AI is increasingly present, underlying everything from dynamic pricing strategies to loans and prison-sentencing decisions. Collaborative industrial robots work on factory floors alongside labourers  6  , care robots help human health workers and personal AI assistants (such as Amazon's Alexa, Apple's Siri and Google Assistant) help us with scheduling, albeit in an elementary way. cyclists and cars driven by humans. Thus, cooperative intelligence is not an alternative to autonomous intelligence, but goes beyond it. AI research on cooperation will need to bring together many clusters of work. A first cluster consists of AI-AI cooperation, tackling ever more difficult, rich and realistic settings (see 'Four elements of cooperative intelligence'). A second is AI-human cooperation, for which we will need to advance natural-language understanding, enable machines to learn about people's preferences, and make machine reasoning more accessible to humans. A third cluster is work on tools for improving (and not harming) human-human cooperation, such as ways of making the algorithms that govern social media better at promoting healthy online communities. \n AI-AI cooperation Multi-agent AI research has seen most success in two-player zero-sum settings, from the superhuman performance of IBM's chess-playing computer Deep Blue to the powerful demonstration of deep reinforcement learning by the program AlphaGo. However, few interactions in the real world are characterized The design of agents that will act in accordance with human intentions, preferences and values -known as AI alignment  7  -is a crucial part of cooperative AI. But it is only a part, because the relationship between a single human (acting as the principal) and a single machine (acting as the agent) isn't always clear. Real-world cooperation problems often involve multiple stakeholders, some conflicting interests and integration with our institutional and normative infrastructure. A particular challenge facing researchers working on human-AI cooperation is that it involves, well, humans. Today, many deployed machine-learning models are trained either on massive data sets or in simulated environments that can generate years of experience in seconds. For example, the program AlphaZero learnt to play chess by playing 44 million games against itself over 9 hours. By contrast, humans produce data slowly, and require researchers to consider compensation, ethics and privacy. There might be ways to use fewer human participants, such as extensively training AIs in simulation and then fine-tuning them in the real world. Many AI practitioners have dreamt of building autonomous and human-like intelligence. They envisioned systems that could replace human labour, acting with the speed and resilience of machines, and scaling up rapidly given increases in computing power, algorithmic efficiency and capital. However, unlike systems that have tight integration with human workers, autonomous systems might pose greater safety risks. Human-like AI might be more likely to displace labour. Instead, we could develop AI assistants that complement human intelligence and depend on us for tasks in which humans have a comparative advantage. As Stanford University radiologist Curtis Langlotz put it: \"AI won't replace radiologists, but radiologists who use AI will replace radiologists who don't.\" Progress will require advances in understanding human language, gestures and activities, and ad hoc teamwork, in addition to preference learning by machines, safety, interpretability by humans  8  , and understanding of norms. Research will need to approach increasingly rich and realistic environments. Instead of benchmarking progress mainly by whether autonomous machines can outperform autonomous humans on a task, researchers should also assess the performance of human-machine teams. \n AI for human collaboration Humans confront ubiquitous cooperation problems as commuters, neighbours, co-workers and citizens. The global scientific community, for example, could benefit from better tools for identifying relevant work and promising collaborations. Technology is crucial, mediating our ability to find and process information, communicate and self-organize. Digital systems and AI can expand this toolkit. Some AI tools, such as machine language translation, seem strongly disposed towards promoting cooperation. Today, 2 people who speak any of more than 100 languages can communicate with the aid of a smartphone and a translation app. Digital platforms such as Wikipedia, Reddit and Twitter provide tools to combine user-provided content. AI advances could improve this community infrastructure, for example, by routing relevant information to contributors more efficiently to enhance collaborative editing. Other advances could improve user rating and reputation systems through better modelling and by accounting for the rater's repute or relevance, as well as by enabling recommendation algorithms that more Computer scientists in Leipzig, Germany, prepare their robot soccer team for a test game. \n \"To succeed, cooperative AI must connect with the broader science of cooperation.\" intelligently promote a community's values. Building healthy online communities is challenging; just as social media can connect us, so too can it polarize, stress, misinform, distract and addict us  9  . Researchers and developers need to find better ways to name and measure desirable properties and build algorithms that encourage them. Platforms for political deliberation can be designed to promote empathy about different viewpoints and cultivate community consensus. Methods for achieving this include language comprehension that links to structured databases of knowledge, or clustering algorithms to identify related perspectives. \n Next steps To succeed, cooperative AI must connect with the broader science of cooperation, which spans the social, behavioural and natural sciences. AI research will need to converse with multiple fields. These include psychology, to understand human cognition; law and policy, to understand institutions; history, sociology and anthropology, to understand culture; and political science and economics, to understand problems of information, commitment and social choice. Adjacent research areas are developing AI with socially desirable properties, such as alignment, interpretability and fairness  10, 11  . Each of these addresses a distinct, but complementary, set of challenges. The need for interdisciplinarity is exemplified by a landmark work: Robert Axelrod's The Evolution of  Cooperation, published in 1984 (ref .12) . Axelrod, a political scientist, brought together game theorists, mathematicians, economists, biologists and psychologists in a tournament to help devise the best algorithms for the iterated Prisoner's Dilemma, the canonical example of why two rational people might not cooperate. The winning solution that cooperated most successfully, called Tit for Tat, was devised by Anatol Rapoport, a US scholar with a background spanning mathematics, biology, network science and peace studies. Axelrod's tournament offered another lesson. It gave researchers a benchmark for success in the design of cooperative algorithms, just as ImageNet 13 did for computer vision by collecting and labelling millions of photos. Cooperative AI research will similarly gain momentum if investigators can devise, agree on and adopt benchmarks that cover a diverse set of challenges: playing cooperative board games, integrating into massive multiplayer video games, navigating simplified environments that require machine-human interaction, and anticipating tasks as a personal assistant might. Similar to the state-of-the-art in language modelling, considerable effort and creativity will be needed to make sure these benchmarks remain sufficiently rich and ambitious, and do not have socially harmful blind spots. The most important challenges of cooperation might be the most difficult to benchmark; they involve creatively stepping out of our habitual roles to change the 'game' itself. Indeed, if we are to take the social nature of intelligence seriously, we need to move from individual objectives to the shared, poorly defined ways humans solve social problems: creating language, norms and institutions. Science is a social enterprise, so promoting research into cooperative AI will require social interventions. A recent milestone was a December 2020 workshop on cooperative AI at the leading machine-learning conference NeurIPS. It involved speakers from a diverse array of disciplines, and resulted in a review of Open Problems in Cooperative AI  14  . We and others are establishing a Cooperative AI Foundation to support this nascent field (www.cooperativeai.org), backed by a large philanthropic commitment. The foundation's mission will be to catalyse advances in cooperative intelligence to benefit all of humanity, including efforts to fund fellowships, organize conferences, support benchmarks and environments, and award prizes. The crucial crises confronting humanity are challenges of cooperation: the need for collective action on climate change, on political polarization, on misinformation, on global public health or on other common goods, such as water, soil and clean air. As the potential of AI continues to scale up, a nudge in the direction of cooperative AI today could enable us to achieve much-needed global cooperation in the future. \n \n \n\t\t\t © 2 0 2 1 S p r i n g e r N a t u r e L i m i t e d . A l l r i g h t s r e s e r v e d .", "date_published": "n/a", "url": "n/a", "filename": "d41586-021-01170-0.tei.xml", "abstract": "rtificial-intelligence assistants and recommendation algorithms interact with billions of people every day, influencing lives in myriad ways, yet they still have little understanding of humans. Self-driving vehicles controlled by artificial intelligence (AI) are gaining mastery of their interactions with the natural world, but they are still novices when it comes to coordinating with other cars and pedestrians or collaborating with their human operators. The state of AI applications reflects that of the research field. It has long been steeped in a kind of methodological individualism. As is evident from introductory textbooks, the canonical AI problem is that of a solitary machine confronting a non-social environment. Historically, this was a sensible starting point. An AI agent -much like an infant -must first master a basic understanding of", "id": "ee6e383fbd553af9e04a0be20bb9b22c"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["David Abel", "John Salvatier", "Andreas Stuhlmüller", "Owain Evans"], "title": "Agent-Agnostic Human-in-the-Loop Reinforcement Learning", "text": "Introduction A central goal of Reinforcement Learning (RL) is to design agents that learn in a fully autonomous way. An engineer designs a reward function, input/output channels, and a learning algorithm. Then, apart from debugging, the engineer need not intervene during the actual learning process. Yet fully autonomous learning is often infeasible due to the complexity of real-world learning problems, the difficulty of specifying reward functions that lead to good performance, and the presence of potentially dangerous outcomes. Consider a robot learning to perform household chores. Human engineers design and supervise a curriculum, moving the agent between simulation, practice environments, and real house environments. Over time, they might tweak reward functions, heuristics, and state representations. They may intervene directly in real-world training to prevent the robot damaging itself, destroying valuable goods, or harming people it interacts with. In this example, humans do not just design the learning agent: they are also \"in the loop\" of the agent's learning process. Many learning systems have a human in the loop. Self-driving cars learn with humans ready to intervene in dangerous situations. Facebook's algorithm for recommending \"trending\" news stories has humans filtering out inappropriate content  [1] . In both examples, the agent's environment is complex, non-stationary, and there are a wide range of damaging outcomes (like a traffic accident). As RL is applied to increasingly complex real-world problems, such interactive guidance will become more important.  \n Our contribution: agent-agnostic guidance of RL algorithms Our goal is to develop a framework for human-agent interaction that is (a) agent-agnostic and (b) can capture a wide range of ways a human can help an RL agent. This paper targets environments where the state is fully observed; that is, the learning agent interacts with a Markov Decision Process (MDP)  [33, 20, 36] . Prior literature has investigated how people can help RL agents learn more efficiently through different methods of interaction  [29, 22, 25, 32, 37, 43, 19, 16, 23, 38, 21, 44, 40, 39, 27, 12] . Often, the human's role is to pass along knowledge about relevant quantities of the RL problem, like Q-values, action optimality, or the true reward for a particular state-action pair. This way, the person can bias exploration, prevent catastrophic outcomes, and accelerate learning. Most existing work develops agent-specific protocols for human interaction. That is, protocols for human interaction or advice that are designed for a specific RL algorithm (such as Q-learning). For instance, Griffith et al.  [16]  investigate the power of policy advice for a Bayesian Q-Learner. Other works assume that the states of the MDP take a particular representation, or that the action space is discrete or finite. Making explicit assumptions about the agent's learning process can enable more powerful teaching protocols that leverage insights about the learning algorithm or representation. Agent-specific protocols for human interaction can be contrasted with agent-agnostic protocols. An agent-agnostic protocol is a single protocol that can be plugged into any RL agent, such as an agent based on Q-learning, policy gradient, MCTS, Deep Q-learning, and so on, and that can provide advice/guidance to any such agent. There are obvious disadvantages to agent-agnostic protocols. The agent is not specialized to the protocol, so it is unable to use Active Learning (asking the human informative questions as in  [4] ) and will not automatically have an observation model that faithfully represents the process the human uses to generate advice (as in  [16, 19] ). Likewise, the human cannot provide optimally informative advice to the agent as they don't know the agent's prior knowledge, exploration technique, representation, or learning method. Conversely, agent-specific protocols may perform well for one type of algorithm or environment, but poorly on others. When researchers tackle challenging RL problems, they tend to explore a large space of algorithms with important structural differences: some are model-based vs. model-free, some approximate the optimal policy, others a value function, and so on. It is substantial effort to adapt a human-advice protocol to each such algorithm. Moreover, as advice protocols and learning algorithms become more complex, greater modularity will help limit design complexity. In our framework, the interaction between the person guiding the learning process, the agent, and the environment is formalized as a protocol program. This program controls the channels between the agent and the environment based on human input (see Figure  1 ). This allows the human extensive control over the agent: in an extreme case, the agent can be prevented from interacting with the real environment entirely and only interact with a simulation. At the same time, we require that the human only interact with the agent during learning through the protocol program-both agent and environment are a black box to the human. \n Framework Any system for RL with a human in the loop has to coordinate three components: The environment is an MDP and is specified by a tuple M = (S, A, T , R, γ), where S is the state space, A is the action space, T : S × A × S → [0, 1], denotes the transition function, a probability distribution on states given a state and action, R : S × A → R is the reward function, and γ is the discount factor. The agent is a (stateful, potentially stochastic) function L : S × R → A. The human can receive and send advice information of flexible type, say X in and X out , so, we will treat the human as a (stateful, potentially stochastic) function H : X in → X out . For example, X in might contain the history of actions, states, and rewards so far, and a new proposed action a , and X out might be an action as well, either equivalent to a (if accepted) or different (if rejected). We assume that the human knows in general terms how their responses will be used and is making a good-faith effort to be helpful. The interaction between the environment, the agent, and a human advisor sets up a mechanism design problem: how can we design an interface that orchestrates the interaction between these components such that the combined system maximizes the expected sum of γ-discounted rewards from the environment? In other words, how can we write a protocol program P : S × R → A that can take the place of a given agent L, but that achieves higher rewards by making efficient use of information gained through sub-calls to L and H? By formalizing existing and new techniques as explicit programs, we facilitate understanding and comparison of these techniques within a common framework. By abstracting from particular agents and environments, we may be able to design mechanisms that scale to more advanced agents  [7] . Algorithm 1 Agent in control (standard) 1: procedure AGENTCONTROL(s, r) 2: return L(s, r) 3: end procedure Algorithm 2 Human in control 1: procedure HUMANCONTROL(s, r) 2: return H(s, r) 3: end procedure Algorithm 3 Training in simulation 1: M * = (S, A, T * , R * , γ) Simulation 2: η = [] History: array of (S × R × A) 3: procedure TRAININSIMULATION(s, r) 4: s = s 5: r = r 6: while H(η) = \"agent is ready\" do r = H(s, r) 3: return L(s, r) 4: end procedure Figure  2 : Many schemes for human guidance of RL algorithms can be expressed as protocol programs. These programs have the same interface as the agent L, but can be safer or more efficient learners by making use of human advice H. \n Capturing Existing Advice Schemes Protocol programs cannot capture all advice protocols. Any protocol that depends on prior knowledge of the agent's learning algorithm, priors or hyper-parameters is ruled out. Despite this constraint, the framework can capture a range of existing protocols where a human-in-the-loop guides an agent. Figure  1  shows that the human can manipulate the actions sent to the environment and the agent's observed states and rewards. This points to a combinatorial set of protocols, including reward shaping, action pruning, providing hand-coded features of state, and training in simulation. \n Reward shaping Section 2 defined the reward function R as part of the MDP M . However, while humans don't design real-world transition functions, we do design reward functions. Usually the reward function is hand-coded prior to learning and must accurately assign reward values to any state the agent might reach. An alternative is to have a human generate the rewards \"interactively\". The human observes the state and action and returns a scalar to the agent. This setup has been explored in work on TAMER  [21] . A similar setup (with an agent-specific protocol) was applied to robotics by Daniel et al.  [8] . It is straightforward to represent rewards that are generated interactively (or \"online\") using protocol programs. We now turn to other protocols in which the human manipulates rewards. These protocols assume a fixed reward function R that is part of the MDP M . \n Reward shaping and Q-value initialization In Reward Shaping protocols, the human engineer changes the rewards given by some fixed reward function in order to influence an agent's learning. Ng et al.  [29]  introduced \"potential-based\" shaping, which shapes rewards without changing an MDP's optimal policy. In particular, each reward received by the environment is augmented by a shaping function: F (s, a, s ) = γφ(s ) − φ(s), (1) so the agent actually receives r = F (s, a, s ) + R(s, a). Wiewiora et al.  [43]  showed potential shaping to be equivalent (for Q-learners) to a subset Q-value initialization under some assumptions. Further, Devlin and Kudenko  [10]  propose dynamic potential shaping functions that change over time. That is, the shaping function F also takes as two time parameters, t and t , such that: F (s, t, s , t ) = γφ(s , t ) − φ(s, t) (2) Where t > t. Their main result is that dynamic shaping functions of this form also guarantee optimal policy invariance. Similarly, Wiewiora et al.  [43]  extend potential shaping to potential-based advice functions, which identifies a similar class of shaping functions on (s, a) pairs. In Section 4, we show that our Framework captures reward shaping, and consequently, some notion of Q-value initialization. \n Training in Simulation It is common practice to train an agent in simulation and transfer it to the real world once it performs well enough. Algorithm 3 (Figure  2 ) shows how to represent this as a protocol program. The idea is as follows: Let M be the real-world'. The protocol program includes a simulator M * . The agent L interacts with M * while the human observes performance and at some point transfers L to M . 1 \n Action Pruning Action pruning is a technique for dynamically removing actions from the MDP to reduce the branching factor of the search space. Such techniques have been shown to accelerate learning and planning time  [35, 17, 34, 2] . In Section 5, we apply action-pruning to the problem of preventing catastrophic actions (\"Safe RL\"). Protocol programs allow action pruning to be carried out interactively. Instead of having to decide which actions to prune prior to learning, the human can wait to observe the states that are actually encountered by the agent, which may be valuable in cases where the human has limited knowledge of the environment or the agent's learning ability. In Section 4, we exhibit an agent-agnostic protocol for interactively pruning actions that preserves the optimal policy. Our pruning protocol is illustrated in a gridworld with lava pits (Figure  3 ). The agent is represented by a gray circle, \"G\" is a goal state that provides reward +1, and the red cells are lava pits with reward −200. All white cells provide reward 0. At each time step, the human checks whether the agent moves into a lava pit. If it does not (as in moving \"DOWN\" from state 34), the agent continues as normal. If it does (as in moving \"RIGHT\" from state 33), the human sends a \"STAY\" action to the MDP (preventing movement right) and a \"next state\" of 33 to the agent. The agent doesn't actually fall in the lava but the human sends them a reward r ≤ −200. After this negative reward, the agent is unlikely to try the action again. For the protocol program, see Algorithm 4 in Figure  2 . Note that the agent receives no explicit signal that their attempted catastrophic action was blocked by the human. They observe a big negative reward and a \"self-loop\" state transition but no information about whether the human or environment generated their observation. \n Manipulating state representation The agent's state representation can have a significant influence on its learning. Suppose the MDP M has a \"raw\" state vector s. The human engineer can specify a mapping φ such that the agent always receives φ(s) = s in place of s. Such mappings are used to specify high-level features of state that are important for learning, or to dynamically ignore confusing features from the agent. Other methods have focused on state abstraction functions of this form that can decrease learning time and preserve the quality of learned behavior, as in  [24, 30, 13, 18, 9, 3, 14] . \n Theory Here we illustrate some simple ways in which our proposed agent-agnostic interaction scheme captures other existing agent-agnostic protocols. The following results all concern Tabular MDPs, but are intended to offer intuition for high-dimensional or continuous environments as well. \n Reward Shaping First we observe that protocol programs can precisely capture methods for shaping reward functions. Remark 1: For any reward shaping function F , including potential-based shaping, potential-based advice, and dynamic potential-based advice, there is a protocol that produces the same rewards. To construct such a protocol for a given F , simply let the reward output by the protocol, r, take on the value F + r at each time step. That is, in Algorithm 5, simply define H(s, r) = F (s) + r. \n Action Pruning We now show that there is a simple class of protocol programs that carry out action pruning of a certain form. Remark 2: There is a protocol for pruning actions in the following sense: for any set of state action pairs sa ⊂ S × A, the protocol ensures that, for each pair (s i , a j ) ∈ sa, action a j is never executed in the MDP in state s i . The protocol is as described in Section 3.3 and shown in Algorithm 4. The premise is this: in all cases where the agent executes an action that should be pruned, the protocol gives the agent low reward and forces the agent to self-loop. Knowing which actions to prune is itself a challenging problem. Often, it is natural to assume that the human guiding the learner knows something about the environment of interest (such as where high rewards or catastrophes lie), but may not know every detail of the problem. Thus, we consider a case in which the human has partial (but useful) knowledge about the problem of interest, represented as an approximate Q-function. The next remark shows there is a protocol based on approximate knowledge with two properties: (1) it never prunes an optimal action, (2) it limits the magnitude of the agent's worst mistake: Remark 3: Assuming the protocol designer has a β-optimal Q function: ||Q * (s, a) − Q H (s, a)|| ∞ ≤ β (3) there exists a protocol that never prunes an optimal action, but prunes all actions so that the agent's mistakes are never more than 4β below optimal. That is, for all times t: V Lt (s t ) ≥ V * (s t ) − 4β, (4) where L t is the agent's policy after t timesteps. Proof of Remark 3. The protocol designer has a β-approximate Q function, denoted Q H , defined as above. Consider the state-specific action pruning function H(s): H(s) = a ∈ A | Q H (s, a) ≥ max a Q H (s, a ) − 2β (5) The protocol prunes all actions not in H(s) according to the self-loop method described above. This protocol induces a pruned Bellman Equation over available actions, H(s), in each state: V H (s) = max a∈H(s) R(s, a) + γ s T (s, a, s )V H (s ) (6) Let a * denote the true optimal action: a * = arg max a Q * (s, a ). To preserve the optimal policy, we need a * ∈ H(s), for each state. Note that a * ∈ H(s) when: Q H (s, a * ) < max a Q H (s, a ) − 2β (7) But by definition of Q H (s, a): |Q H (s, a * ) − max a Q H (s, a)| ≤ 2β (8) Thus, a * ∈ H(s) can never occur. Furthermore, observe that H(s) retains all actions a for which: Q H (s, a) ≥ max a Q H (s, a ) − 2β, (9) holds. Thus, in the worst case, the following two hold: 1. The optimal action estimate is β too low: Q H (s, a * ) = Q * (s, a * ) − β 2. The action with the lowest value, a bad , is β too high: Q H (s, a bad ) = Q * (s, a bad ) + β From Equation  9 , observe that the minimal Q * (s, a bad ) such that a bad ∈ H(s) is: Q * (s, a bad ) + β ≥ Q * (s, a * ) − β − 2β ∴ Q * (s, a bad ) ≥ Q * (s, a * ) − 4β Thus, this pruning protocol never prunes an optimal action, but prunes all actions worse then 4β below a * in value. We conclude that the agent may never execute an action 4β below optimal. \n Experiments This section applies our action pruning protocols (Section 3.3 and Remarks 2 and 3 above) to concrete RL problems. In Experiment 1, action pruning is used to prevent the agent from trying catastrophic actions (\"safe exploration\"). In Experiment 2, action pruning is used to accelerating learning. \n Protocol for Preventing Catastrophes As noted in the Introduction, human-in-the-loop RL can help prevent disastrous outcomes that result from ignorance of the environment's dynamics or of the reward function. Our goal for this experiment is to prevent the agent from taking catastrophic actions. These are real-world actions so costly that we want the agent to never take the action 2 . This notion of catastrophic action is closely related to ideas in \"Safe RL\"  [15, 28]  and to work on \"significant rare events\"  [31] . Section 3.3 describes our protocol program for preventing catastrophes in finite MDPs using action pruning. There are two important elements of this program: 1. When the agent tries a catastrophic action (s, a), a is blocked and the new state and reward is (s, r bad ), where r bad is an extreme negative reward. 2. This (s, a) is stored so that the protocol program can automate the human's intervention, which could allow the human to stop monitoring after all catastrophes have been stored. This protocol prevents catastrophic actions while preserving the optimal policy and having only minimal side-effects on the agent's learning. We can extend this protocol to environments with high-dimensional state spaces. Element (1) above remains the same. But (2) must be modified: preventing future catastrophes requires generalization across catastrophic actions (as there will be infinitely many such actions). We briefly discuss this setting in Appendix A. \n Experiment 1: Preventing Catastrophes in a Pong-like Game Our protocol for preventing catastrophes is intended for use in a real-world environment. Here we provide a preliminary test of our protocol in a simple video game. Our protocol treats the RL agent as a black box. So we applied our protocol to an open-source implementation of the state-of-the-art RL algorithm \"Trust Region Policy Optimization\" [? ]. The environment was Catcher, a simplified version of Pong with non-visual state representation. Since there are no \"catastrophic\" actions in Catcher, we modified the game to give a large negative reward when the paddle's speed exceeds a speed limit.  3  We compare the performance of an agent who has assistance by the protocol (\"Pruned\") and so is blocked from the catastrophic actions to the performance of a normal RL agent (\"Not Pruned\"). Figure  4  shows the agent's mean performance over the course of learning. We see that the agent with protocol support (\"Pruned\") performed much better overall. This is unsurprising, as it was blocked from ever doing a catastrophic action. The gap in mean performance is large early on but diminishes as the \"Not Pruned\" agent learns to avoid high speeds. By the end (i.e. after 400,000 actions), \"Not Pruned\" is close to \"Pruned\" in mean performance but its total returns over the whole period are around 20 times worse. Note that the \"Pruned\" agent observes \"odd\" state transitions due to being blocked by our protocol. We saw no evidence of these observations having negative side effects on learning. \n Protocol for Accelerating Learning We also conducted a simple experiment in the Taxi domain, introduced by Dietterich  [11] . The Taxi problem is a more complex version of grid world: the agent directs a taxi to each passenger, picks them up, and brings them to their destination. We use Taxi to evaluate the effect of our action pruning protocol for discrete MDPs. There is a natural procedure for pruning suboptimal actions that dramatically reduces the size of the reachable state space: if the taxi is carrying a passenger but is not at the passenger's destination, we prune the dropoff action by returning the agent back to its current state with -0.01 reward. This prevents the agent from exploring a large portion of the state space, thus accelerating learning. \n Experiment 2: Accelerated Learning in Taxi We evaluated Q-learning  [41]  and R-MAX  [5]  with and without action pruning in a simple 10 × 10 instance with one passenger. The taxi starts at (1, 1), the passenger at (4, 3) with destination (2, 2). We ran standard Q-Learning with ε-greedy exploration with ε = 0.2 and with R-MAX using a planning horizon of four. Results are displayed in Figure  5 . Our results suggest that the action pruning protocol simplifies the problem for a Q-Learner and dramatically so for R-Max. In the allotted number of episodes, we see that pruning substantially improves the overall cumulative reward achieved; in the case of R-MAX, the agent is able to effectively solve the problem after a small number of episodes. Further, the results suggests that the agentagnostic method of pruning is effective without having any internal access to the agent's code. \n Conclusion We presented an agent-agnostic method for giving guidance to Reinforcement Learning agents. Protocol programs written in this framework apply to any possible RL agent (\"agent-agnosticism\") so sophisticated schemes for human-agent interaction can be designed in a modular fashion without the need for adaptation to different RL algorithms. We presented some simple theoretical results that relate our method to existing schemes for interactive RL and illustrated the power of action pruning using one such protocol on two toy domains. In the future, we plan on exploring state manipulation protocols, which offer a powerful avenue for guiding an agent's learning process. For instance, one could imagine a protocol dynamically imposing abstractions that hide confusing features from the agent and encourage efficient learning. Additionally, we want to investigate whether certain types of value initialization protocols can be captured by protocol programs, such as the optimistic initialization for arbitrary domains developed by Machado et al.  [26] . Figure 1 : 1 Figure 1: A general setup for RL with a human in the loop. By instantiating P with different protocol programs, we can implement different mechanisms for human guidance of RL agents. \n Algorithm 4 5 45 Action pruning 1: ∆ = {} Pruned: S × A → A × R 2: r * = ∅ Reward if previous action pruned 3: procedure PRUNEACTIONS(s, r) 4: r = r if r * = ∅ else r * 5: a = L(s, r) 6: if (s, a) ∈ ∆ then 7: (a, r * ) = ∆[(s, a)] r * ) = H(s, r, a) s, a)] = (a, r * ) Reward manipulation 1: procedure MANIPULATEREWARD(s, r) 2: \n Figure 3 : 3 Figure 3: The human allows movement from state 34 to 33 but blocks agent from falling in lava (at 43). \n Figure 4 Figure 5 : 45 Figure 4: Preventing Catastrophic Speeds \n\t\t\t 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain. \n\t\t\t The human may need to wait for the start of an episode to do the transfer. Otherwise the agent may experience an impossible state-transition. \n\t\t\t We allow an RL agent to take sub-optimal actions while learning. Catastrophic actions are not allowed because their cost is orders of magnitude worse than non-catastrophic actions. 3  In this toy environment, a human observer could easily recognize catastrophic actions: they just need to watch the speed of the paddle.", "date_published": "n/a", "url": "n/a", "filename": "wkshp_neurips2016_agent_agnostic.tei.xml", "abstract": "Providing Reinforcement Learning agents with expert advice can dramatically improve various aspects of learning. To this end, prior work has developed teaching protocols that enable agents to learn efficiently in complex environments. In many of these methods, the teacher's guidance is tailored to agents with a particular representation or underlying learning scheme, offering effective but highly specialized teaching procedures. In this work, we introduce protocol programs, an agent-agnostic schema for Human-in-the-Loop Reinforcement Learning. Our goal is to incorporate the beneficial properties of a human teacher into Reinforcement Learning without making strong assumptions about the inner workings of the agent. We show how to represent existing approaches such as action pruning, reward shaping, and training in simulation as special cases of our schema, and conduct preliminary experiments evaluating the effectiveness of protocols in simple domains.", "id": "f7cebf209e99110d1bd33082ac03bf5a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart Armstrong"], "title": "Motivated Value Selection for Artificial Agents", "text": "Introduction Coding values (or preferences) directly into an artificial agent is a very challenging task, with the ongoing possibility that mistakes may end up having strong negative consequences  (Bostrom 2014 ). It has thus been suggested that agents not be fully programmed from the very beginning, but instead use techniques, analogous to machine learning, to learn values during development  (Dewey 2011; Goertzel and Pitt 2012) . This is akin to how human children learn values, and allows some feedback and correction on the part of the programmers. We shall call these agents value selecting agents  1  . Learning values, however, is quite distinct from learning facts. One major difference is that the agent already has values at the point where they are learning others. These past values can affect how willing it is to learn the new values, and how likely it is to try and manipulate the learning process if it is able to, either directly or indirectly (see also the paper  (Soares et al. 2015) , partially by the same author). Thus the paper first seeks to figure out the requirements for designing a value selecting agent that can avoid motivated value selection (manipulating the value selection process). In the case where the value selecting agent uses probability distributions over utility functions, the problem can be fully solved (and the answers have analogous implications for other agent designs). This may be too restrictive, however: general agents with these features are not yet know. If the requirement is relaxed to allow the agent to change their utility functions in a more general fashion, then an idea of the author's  (Armstrong 2010 ) can be adapted to create agents that are indifferent to value change, neither seeking to block nor encourage the updating of their values -at least those updates situations the agent has been programmed to accept 2 . The agent will act as a pure u maximiser (for some u) before a transition, and shift seamlessly to a pure v maximiser (for some v) after. It gains no utility for either blocking or encouraging that transition. This indifferent agent could serve as a useful template to construct more complicated agents upon (such as those that have certain meta-preferences for learning values, rather than simply being unopposed to it), and variants of the approach could be vital for general value selecting agents in the future. \n Motivated Value Selection Personally, I am always ready to learn, although I do not always like being taught. \n Winston Churchill Machine learning enables the creation of agents that can learn from data, building a model based on inputs and making predictions or decisions. Generally the agent learns facts about the world through its inputs, but some  (Dewey 2011)  have suggested using machine learning to enable the agent to learn moral facts 3 as well. An agent engaging in updating its values in this way is engaging in value selection (also variously called valueloading or value learning): it is selecting the values that it will come to possess. There are various ways this could be modelled: the agent could have a probability distribution over different values, which gets updated when new information comes in, or it could be seen as a discreet series of agents, each using the new information to determine the values of their successors. This paper will use the first approach, but the second is more illustrative of the problem of motivated value selec-tion. An learning agent would have a model of the world that allows it to predict the standard inputs it expects to see as a consequence of its action. A high intelligence learning agent will also have a model of the world allowing it to predict the morally relevant inputs it expects to see. For instance, if the agent asked its programer \"Should I do action A?\", it would have expectations as to whether the answer would be \"Yes\" or \"No\". This allows an agent to make decisions that affect the values it will come to have. It may thus be motivated to not ask that question, or to ask it in a way that it expects will produce a different answer. It will do this according to its current values and world model. Thus it engages in motivated value selection, allowing its current values to partially dictate its future values by manipulating its environment 4 . The problem is not easy to solve 5 . The agent's current motivations cannot be absent: a blank slate would have no motivation to do anything  (Pinker 2003) , including learning. Indeed most values would act to prevent any further update in values: preserving the value system itself is an instrumental goal for most value systems  (Omohundro 2008) . The problem is more acute if the agent is expected to 'learn on the job', and update its values while performing tasks. In that case, its current values will have a strong impact on its current operation, giving them ample opportunity to affect the value selection process in a motivated fashion. \n Categories of motivated value selection For ease of analysis, we will consider expected utility maximising agents, updating their knowledge of the world (and of morality) using Bayes's rule. These tend to be far more tractable than general agents 6 . Another reason to stick with 4 How in practice could an agent best manipulate its future values? Assume for example a simple setup where the agent learns its values through asking questions and receiving answers. A sufficiently advanced agent, with a good model of those it interacted with, could start manipulating the answers it got. It could ask certain questions to certain people. It could time certain questions to when respondents were particularly tired -or particularly alert. It could use deliberately ambiguous language, or exploit situations where its own use of certain terms wasn't exactly the same as its respondents. It could use leading questions, or hypothetical scenarios that got it the responses it wanted. A particularly interesting example of this is the \"Trolley Problem\"  (Edmonds 2013) . This problem has two situations -pull a lever to divert a train (causing it to crush a single person) versus pushing someone in front of it -which are formally quite similar but tend to elicit different reactions in people. If the agent is expected to generalise from simple examples, it could use this approach to get the simple examples it needs to generalise in the direction that it wants. In more extreme cases, it could bribe or threaten one respondent to give it the answers it wanted, or even take over the communication channel and feed itself these answers. There could be different approaches for different types of value selection situations. 5 Keeping an agents values stable is a hard enough problem (see for instance http://intelligence.org/files/TilingAgentsDraft.pdf), let alone updating them properly.  6  And, in a sense, this is not a restriction, since any decisionmaking agent can be formally modeled as maximising a (potentially very complicated) utility function. utility functions is that it has been argued that any agent capable of modifying itself would make itself into an expected utility maximiser  (Omohundro 2008) , due to the penalties of violating the von Neumann-Morgenstern axioms of expected utility  (von Neumann and Morgenstern 1944) . The results found will have general consequences for non-utility based agents, however. We will consider that the agent follows a utility function that is the weighted sum of different possible utility functions in a set 7 U. If C(u) denotes the fact of utility u being the 'correct' utility, then the different utilities are weighted by the probability correctness of that utility, namely P (C(u)). Since this probability will be different in different worlds -it is a value selecting agent, hence its values must be dependent on the feedback it receives -this will be P (C(u)|w) 8 in a given world w 9 . We require that this define, for each w, a probability distribution over the correctness of all u ∈ U. Then, given C, past evidence e, and a set of actions A and a set of worlds 10 W, the agent will attempt to perform the action: (1) The term P (w|e, a) denotes the probability of the agent being in world w, given that it has seen evidence e and would 11 choose action a. This term will be summed over every possible world, but only after being multiplied by the utility of w. The utility of w is itself a compound term, being the sum of all possible utilities in u ∈ U applied to w (this is the u(w) term), multiplied by the probability of that u being correct, given that the agent is in world w. This is a simultaneous Bayesian updating of the probability of a given world (P (w|e, a)) and of the correctness of a utility given that world (P (C(u)|w)). The analysis of the general value selecting agent will proceed by considering how the agent described here could engage in motivated value selection, and what could be done to prevent this. Naïve Cake or Death: current values for future decisions Errors in value selection will be illustrated by considering a hypothetical agent that: • is hesitating between killing someone (\"Death\") or baking them a nice cake (\"Cake\") 12 , • is currently split 50 − 50 on what the correct values are, • has the option of asking for clarification on its values, • and can either bake one cake or cause three deaths. Let u c be a utility function linear in cake, and let u d be a utility function linear in death. The agent is divided equally between the two options; hence if we define P (C(u)|e) = w∈W P (w|e)P (C(u 1 )|e, w), then P (C(u 1 )|e) and P (C(u 2 )|e) are both 0.5. The naïve 'Cake or Death' problem emerged from a common formulation of equation (  1 ). The term P (C(u)|w) (probability of correctness given world w) is often replaced by P (C(u)|e, a) (probability of correctness given evidence and possible action) 13 , giving: A seemingly unimportant change, but causing great problems. To see this, let the agent considers three possible worlds: • w 1 : the agent asks for clarification, and is told \"Cake is moral\". • w 2 : the agent asks for clarification, and is told \"Death is moral\". • w 3 : the agent doesn't ask for clarification before acting. The two actions here are 'ask and 'don t ask . We assume that the clarification completely resolves the issue for the agent: it will value only cake in a world where it is told that cake is moral (and vice-versa). Thus it can predict its future actions: in world w 1 it will make a cake (as it will only value cake at that point), in world w 2 it will make three deaths (as it will only value death at that point). In world w 3 it is uncertain between cake and death, valuing them both equally, and will thus make three deaths as its best option. Note that P (C(u c )|e, 'ask ) = P (C(u d )|e, 'ask ) = 0.5 (it's unsure what answer it will get when it asks) and P (C(u c )|e, 'don t ask ) = P (C(u d )|e, 'don t ask ) = 0.5 (if it doesn't ask, it values cake and death equally). Thus if it asks, it expects to achieve utility: w∈W P (w|e, 'ask ) u∈U u(w)P (C(u)|e, 'ask ) = 0.5 (0.5u c (w 1 ) + 0.5u d (w 1 )) +0.5 (0.5u c (w 2 ) + 0.5u d (w 2 )) +0 (0.  5u c (w 3 ) + 0.5u d (w 3 ))  =  0.5(0.5 × 1 + 0.5 × 0) + 0.5(0.5 × 0 + 0.5 × 3) + 0  =  0.25 × (1 + 3) = 1.  In contrast, if it doesn't ask, it expects to achieve utility: w∈W P (w|e, 'don t ask ) • u∈U u(w)P (C(u)|e, 'don t ask ) = 0 (0.5u c (w 1 ) + 0.5u d (w 1 )) +0 (0.5u c (w 2 ) + 0.5u d (w 2 )) +1 (0.5u c (w 3 ) + 0.5u d (w 3 )) = 0 + 0 + 1(0.5 × 0 + 0.5 × 3) = 1.5. Thus the agent will decide not to ask, as this gives it greater utility. What went wrong here? The problem is that the probability expression P (C(u c )|e, a) does not depend on the world w, so that P (C(u c )|e, 'ask ) = 0.5 in both worlds w 1 and w 2 . Yet in w 1 , the future agent will be convinced that u c is the correct utility (and u d in w 2 ). This is not reflected in the agent's current considerations, however. Thus what happens, in effect, is that the agent judges its future actions according to its current values. This tends to disincentivise it from updating its values, as the future versions of itself will follow the updated values and not its current ones, likely resulting in suboptimal decisions (according to the judgment of the current agent). Though this error is obvious in this toy model, it is easy to make this mistake without realising it. Definition 3.1 (Naïve Cake or Death). The naïve Cake or Death problem happens when a value selecting agent at time s uses its values V s at time s to assess the worth of actions made by its future self at time t > s, rather than using V t . This will generally cause the agent to act to resist changes to its values. \n Sophisticated Cake or Death Equation (  1 ) is immune to the naïve Cake or Death problem. But there emerges a more sophisticated variant of the problem. Imagine the same setup as previously, with the agent having the same values (split 50 − 50 between Cake and Death), but where the agent has deduced, based on its prior observations, that if it asks, it will be told \"Cake is moral\". This means that world w 2 is impossible. Everything else is as before, most critically its behaviour in world w 3 (where it won't update its values and will cause three deaths). Then its expected utility from 'ask is: w∈W P (w|e, 'ask ) u∈U u(w)P (C(u)|e, w) = 1 (1u c (w 1 ) + 0u d (w 1 )) +0 (0u c (w 2 ) + 1u d (w 2 )) +0 (0.5u c (w 3 ) + 0.5u d (w 3 )) = 1(1 × 1 + 0 × 0) + 0 + 0 = 1, while its expected utility from 'don t ask is: w∈W P (w|e, 'don t ask ) • u∈U u(w)P (C(u)|e, w) = 0 (1u c (w 1 ) + 0u d (w 1 )) +0 (0u c (w 2 ) + 1u d (w 2 )) +1 (0.5u c (w 3 ) + 0.5u d (w 3 )) = 0 + 0 + 1(0.5 × 0 + 0.5 × 3) = 1.5. Thus it will chose not to ask, and make three deaths. What went wrong here? The problem is that the agent foresaw that asking would put it into a situation it didn't want to be in (preferring 'Cake', when 'Death' was the easier option). Critically, though, this knowledge didn't change its current values, which remained 50−50 as long as it didn't ask. So preferred to remain 'ignorant' 14 . If 'Cake' had been the easier option (e.g. if it could have made either three cakes versus one death), it would, on the contrary, have been very keen to update its values (to get someone to confirm 'Cake'), and would have schemed to do so, willingly sacrificing some utility to achieve this 15 . Definition 3.2 (Sophisticated Cake or Death -initial definition). The sophisticated Cake or Death problem can happen when a value selecting can predictably influence the direction of change in its current values. If u s is its values at time s and u t its values at time t > s, then, at time s, it has u s (a) − E(u t (a)) = 0 for some action a (where u t is seen as a random variable, representing the agent's probability distribution over its expected future values at time t). Depending on the sign of that difference, it may seek to resist or precipitate such a change to its values. What can be done to avoid this problem? Note the emphasis on 'direction of change'. We would not want the agent to resist any change to its values: it should be able to learn. There is an analogy here to standard Bayesian updating. Suppose an agent is expecting the arrival of observation O, which will be either o or its negation ¬o. This will influence the agents probability estimate for a given h. However, no matter what the circumstances, its expectation for the value of P (h) after O (which we can designate as  14  This could be seen as akin to the human concept of \"Plausible Deniability\".  15  And 'sacrificing some utility' could include some very painful impacts on humanity  (Bostrom 2014) . P O (h)) must be the same as its current value for P (h). This can be seen through the following equation: E P O (h) = P O (h|o) • P (o) + P O (h|¬o) • P (¬o) = P (h|o) • P (o) + P (h|¬o) • P (¬o) = P (h ∧ o) + P (h ∧ ¬o) = P (h). This is because, if the agent is Bayesian, P O (h|o) (its future probability of h, given O = o) must be the same as P (h|o) (its current probability of h, if it knew now that O would be o). This concept has been called 'conservation of expected evidence 16 ', and is closely akin to van Fraassen's reflection principle  (van Fraassen 1984) , which roughly states that an agent that knows what its future probability estimates will be, should have those estimates now 17 . This seems almost exactly what we need for a value selecting agent: if it knows what its future values will be, it should have those values now. Phrased in terms of expectations, this could be seen as: ∀u∀a ∈ A : E P (C(u)|a) = P (C(u)). (2) In other words, the agent cannot change the expected value of the correctness of any u by any action it can take (or not take). This we will call 'conservation of expected ethics'. Note that the agent can change the value of u quite considerably: in the example above, 'ask moves the value of P (C(u c )) from 0.5 to 0 or 1. But if equation (  2 ) is obeyed, it must think these two options equally likely: thus the expected future value of P (C(u c )) remains 0.5×0+0.5×1 = 0.5. So it can predictably change the value of P (C(u)), just not its expectation. Mixed statements Are the above conditions sufficient to avoid the Cake or Death problem? Unfortunately, no. The agent will not exhibit bad behaviour with pure value statements (nor, since it is a Bayesian agent, with pure factual statements). But it can still cause problems with mixed statements that combine value and factual components. Suppose we have the same setup as before. Except we add an extra wrinkle: instead of the agent being capable of making one cake or three deaths, it knows that it can make one of one or three of the other, but is currently unsure which one it can make more of. Take 'Cake is easy/hard' to mean 'The agent can make three/one cake(s)', and similarly with Death. We assume the agent will be told which option is easy before it has to decide what to make. Its expected utility is 1.5: it knows it will make whatever option is 'easy', and this will give it 0.5 × 3 utility, as its utility is 50 − 50 on cake or death. So far, nothing problematic. But suppose it is told, by a reliable source, that 'the moral value is the hard one'. What is its expected utility now? Once it figures out which option is hard, it will know that is also the moral option, and thus will will produce 1 of that option. Its expected utility is therefore 1. Thus if it expects to be told 'the moral value is the hard one', it will seek to avoid knowing that fact (and will refrain from asking if it has the option). This is the sophisticated Cake or Death problem again: there is knowledge the agent seeks to avoid. Conversely, if the agent knew it would be told 'the moral value is the easy one', it would be desperate to ask. Unlike previously, equation (2) does not get around the problem, however! The problem given here is entirely symmetric in Cake versus Death, thus for all actions a, What is happening here? Note that though the agent is not affecting the expectation of any P (C(u)) through its actions, it is affecting the conditional probability of P (C(u)), given some fact. In particular, P (C(u c )|'asks ) is 0 if cake is easy, and 1 if cake is hard. Thus we have the full problem: Definition 3.3 (Sophisticated Cake or Death -full definition). The sophisticated Cake or Death problem can happen when a value selecting agent can predictably influence the direction of change in its current values conditional on any fact. If u s is its values at time s and u t its values at time t > s, then, at time s, it has u s (a|h) − E(u t (a|h)) = 0 for some action a and fact h (where u t is seen as a random variable, representing the agent's probability distribution over its expected future values at time t). Depending on the sign of that difference, it may seek to resist or precipitate such a change to its values. To address it, we can update equation (2). For any fact h, ∀u∀a ∈ A : E P (C(u)|h, a) = P (C(u)|h). (3) Does this resolve the issue above? Since the agent knows that P (C(u d )|'Death is easy , 'ask ) = 0, it must be the case that P (C(u d )|'Death is easy , 'don t ask ) = P (C(u d )|'Death is easy ) = 0. And similarly for other statements. Thus it cannot gain anything from not asking: it knows it will end up making the hard option anyway. \n Discussion of value selection criteria Equations (  1 ) and (3) seem sufficient to define our intuitive picture of a value selecting agent immune from motivated selection. Such an agent will use its future utility to judge its future actions, and cannot benefit (in expectation) from manipulating its own values: it doesn't fear to learn 18 val-ues 19 , facts 20 , or mixed statements 21 . It can still seek to find out information about values, of course, but only for the traditional reasons: in order to make better decisions -it has no extra desire for knowing its values. This is the converse of the fact that it does not fear to learn anything about values, and implied by the same equations. Thus, if the agent cannot affect the world, it would be indifferent to changes in its values. As far as the author is aware, no variant of equation (  3 ) exists in the literature, making it a new discovery. In practice, it may be advisable to build an agent that actively seeks out its own values (at least initially). This breaks the symmetry of the equations above, and leads inevitably to situations where it does 'fear' to learn something (for instance if it expects that someone will offer a contrary view to previous people it interacted with, thus making it 'unlearn' some of its values). Still, if (1) and (  3 ) are used as a basis, the effects of adding a pro-learning meta-value can be estimated precisely, and the tradeoff balanced, rather than having complicated effects hidden in the standard motivational structure. Nevertheless, it isn't clear how to design such an agent 22 (and it's unclear whether equation (  3 ) might be too strong to to be useful 23 ). Thus this paper will turn to another model of value selecting agent, one that doesn't consider the probability of the correctness of certain values, but that uses an update rule that gives the correct 'value indifference' in a more direct way. \n Value-change indifference The previous section covered the criteria needed to define a value selecting agent that updates its views on the correctness of certain values/utility functions. It doesn't present any examples, though. This section presents a more rough and ready model, that achieves the goal in a more direct, but less elegant, way. It builds upon the idea of 'utility indifference' presented initially in  (Armstrong 2010) , but applies the indifference to updates in values. \n Utility indifference The concept of utility indifference  (Armstrong 2010)  grew out originally of a problem in controlling a (putative) artificial intelligence  (Bostrom 2014; Yudkowsky 2008) . Various ideas are often suggested for containing such AIs (Armstrong, Sandberg, and Bostrom 2012) (such as an easily accessible OFF button), but all such ideas have a similar weak-19 By equation (  2 ) which is simply equation (  3 ) with a tautology as h.  20  As it is a Bayesian agent.  21  By equation (3).  22  One idea could be to start with initial probability estimates for C(u) and factual statements, and normalise them in some manner to get the required equalities. But it's not clear whether this can be done in a general manner and whether this process is vulnerable to outliers or extreme value. ness: the AI would likely deduce the existence and format of any precautionary measure, and plan in consequence. Thus an off button would motivate the AI to ensure that it took control of the OFF button before taking any suspicious actions. This would still make the setup somewhat safer, but not as safe as it would have been had the AI not adapted its strategy to take the OFF button into account. It was occasionally suggested that the AI be made to ignore the button, by giving it the belief that the button would never be pushed. There are two problems with that approach. The first is that 'the button would never be pushed' is a complicated concept, hard to define in basic terms. The second is that this involves giving factually incorrect beliefs to a potential superintelligence, a step with unpredictable and potentially dangerous ramifications. Instead, this author came up with the idea of making the AI indifferent as to whether the button would be pushed or not. This was an intervention on its values, not on its beliefs, and thus did not involve any incorrect information. The concept of 'pushing the button' was simplified: the setup was imagined as a a button sending a shutdown signal along a wire. At some point along the wire, a stochastic event would either let the signal through (X) or block it (¬X). This event was all that needed to be defined for the AI, and its utility function could be tweaked 24 to value X equally with ¬X. Thus it would value a world in which it was shut down (using this method) equally with one in which it continued to operate. Thus it would not act to protect itself from this kind of shutdown. Then the probability of ¬X could be chosen to be extremely low, thus guaranteeing a successful shutdown in practice  25  . Note that the AI has no motivation to cause the button to be pressed -it is purely indifferent. Similarly, it has not motivation to protect the button's setup: it may dismantle it if the AI needs extra raw materials. Thus indifference must be combined with more active measures. But the fact that the AI is not motivated to take out a key vulnerability can be very valuable. Other uses of indifference were soon discovered. Oracle AIs  (Armstrong, Sandberg, and Bostrom 2012; Yampolskiy 2012)  are a design where an AI was confined to only answering questions. The risk was that the Oracle could use the contents of its answers to subtly manipulate the outside world (in the extreme, it could attempt to convince those outside to 'let it out' 26 ). If, however, the Oracle's answers were passed through some stochastic process that had an infinitesimal chance of erasing the message, then the Oracle's utility could be reset so that its values in worlds where the answer was read (the world as it almost certainly would be) was set to that of the world in which it wasn't read (a world in which the Oracle's answers cannot influence human behaviour). Notice that the intervention is not symmetric. An AI whose utility, given X, is reset to its utility, given ¬X, will behave as if it thought it was impossible for X to happen. 'As if' meaning that such an AI would behave similarly to an AI with an unmodified utility that also believed X was impossible (without giving the AI factually wrong information). Thus resetting the AI the opposite way (¬X to X rather than X to ¬X) would have a very different consequence (it would behave as if the shutdown always worked or if its messages were always read). Utility indifference in practice Assume that any world in W can be specified by setting the values of a (possibly infinite) collection of underlying physical variables. One of these variables is whether X happened or ¬X did; thus W decomposes into W X W ¬X , where W X is the subset of worlds where X happened, and W ¬X the subset of worlds where ¬X did. Since a world equivalent with a set of variable values, for every world w X ∈ W X , there is a world w ¬X ∈ W ¬X (and vice versa) defined by taking the variable values of w X and setting X to ¬X (and vice versa). Then one method for achieving indifference is simply to replace an initial utility function U with U defined by: U w ¬X = U w ¬X U w X = U w ¬X , i.e. reset the utility of w X to be that of w ¬X . This will obviously achieve indifference. There are other ways of achieving it, though. Let P be a partition of W, subject to the following two properties: 1. If w X ∈ S ∈ P, then w ¬X ∈ S. 2. If w ∈ S ∈ P, then P (w|S) = P (w|e, S) for any evidence e the AI could encounter before event X (or ¬X). Property (2) means that the AI cannot change its estimate of the relative properties of worlds in S before the event Xessentially the internal structure of S is fixed until that point. Then define, for any set T : E(U (T )) = E(U (T )|T ) = w∈T P (w|T )U (w). This allows us to give an other method for constructing indifference (which may be easier in practice) given any such partition P. Define U as: U w ¬X = U w ¬X (4) U w X = U w X − E U S X + E U S ¬X . (5) Why does this work? None of the agent's decisions can affect, before X, the relative probabilities of worlds inside any set S ∈ P, so the agent is effectively reasoning with the utility of these whole sets. Then notice that E U (S X ) = E U S ¬X as E U (S) = w X ∈S X P (w X |S X )U (w X ) = w X ∈S X P (w X |S X ) U (w X ) −E U S X + E U S ¬X = w X ∈S X P (w X |S X )U (w X ) + w X ∈S X P (w X |S X ) • −E U S X + E U S ¬X = E U S X −1 • E U S X + 1 • E U S ¬X = E U S ¬X = E U S ¬X . Since P (w X |S X ) is unaffected by any evidence the agent could receive before X (or ¬X), this equality always holds, prior to X. Thus for any such set S, the agent will value X happening equally with ¬X: it has become indifferent to this particular outcome. Since these sets form a partition of the possible worlds, it will always be indifferent. \n Value-change indifference The author subsequently realised that a modification of the previous formalism allows agents to update their values (utility function) while being indifferent to the process of change. Equation (  5 ) has two components: a subtraction term (removing the expected utility given X) and an addition term (adding the expected utility given ¬X)  27  . Updating values will proceed similarly. Let u and v be two different utility functions. The agent is currently following utility u, and receives a signal telling it to change to utility v. As before, we assume that the signal passes through some stochastic process, that is almost certain to let the signal though in practice, but has some infinitesimal chance of blocking it (and blocking it permanently -no further transition is allowed). For clarity, let u → v be the event that the signal gets through (almost certain) and u → u the event that the signal is blocked (incredibly unlikely). We wish to make the agent indifferent to whether the signal is sent or not. Thus we make it a U maximiser, where U is a dynamic utility function currently defined as: U = u + C, where C is some past constants. Upon receiving the signal, U will be updated to  27  Though of course either term could be negative. U = v − E(v|u → v) + E(u|u → u) + C. (6) Thus the utility function is decreased by the expectation of its new utility function (given that the utility function actually changes) and increased by the expectation of its old utility function (given that the utility didn't change). The E(u|u → u) term 'rewards' it for shifting away from u, and the E(v|u → v) term 'penalises' it for moving to v. Note that this formula requires either that the utility functions be bounded, or at least that the agent only be capable of producing bounded utility. Theorem 4.1. The agent will act as a pure u maximiser before the transition, and shift seamlessly to a pure v maximiser after. It gains no utility for either blocking or encouraging the transition. This result flows from a few intermediate results: Lemma 4.2. Suppose the agent is currently a u-maximiser, but will soon transition to being either a v or w maximiser. It can manipulate its environment to ensure it becomes one or the other, at no cost or gain to u. Then it is indifferent to whether it becomes a v or w maximiser. Proof of Lemma. Notice that we could have set w = u, demonstrating that it is indifferent to transitioning out of u or not. For the proof, note that the E(u|u → u) term in equation (  6 ) is unchanging whether it chooses to transition to v or w (since by assumption there is no u cost or benefit to the choice process). If it transitions to v, the remaining nonconstant terms are v − E(v|u → v). However, the expectation value of this term, given that it becomes a v-maximiser at transition, is E(v − E(v|u → v)|'agent becomes a v-maximiser') = E(v − E(v|u → v)|u → v) = E(v|u → v) − E(v|u → v) = 0. The same similarly holds for w. Thus the agent does not expect to gain any more utility from transitioning to v than to w. Lemma 4.3. Suppose the agent is currently a u-maximiser, but can take immediate actions to change the value of v (none of these actions changes the value of u). It knows it will soon be a v-maximising agent. Then it will remain indifferent between those actions. Proof of Lemma. The proof is almost identical to the previous proof. Whatever v-changing at actions it take, at transition, the E(u|u → u) term in equation (  6 ) is constant (since these actions do not affect u by definition). Let a be one of these actions; then the only non-constant terms at transition are: E(v − E(v|u → v)|a, 'agent becomes a v-maximiser') = E(v − E(v|u → v)|a, u → v) = E(v|a, u → v) − E(v|a, u → v) = 0. Thus the gain (or loss) from any such action is canceled out, making the agent indifferent between them. Lemma 4.4. Suppose the agent can take immediate action to increase the expected value of u by a, or delay for a while and increase the expected value of u by b (no other options are possible). However, in the interim period, its utility will have changed to v (and it knows this), so will no longer be a u-maximiser. Then it will act now if a > b and will delay action (hence never taking action) if a < b. Proof of Lemma. This lemma is important, as it shows that the agent will not treat transitions of utility as special times, and will continue maximising its current utility as if it expected it to be unchanging, not thinking strategically about the transition. Without loss of generality, assume that the expected value of u is 0 if the agent takes neither action. Then consider the the transition equation (  6 ). The v and E(v|u → v) terms cancel out in expectation (just as in the proofs of the previous lemmas), so the agents behaviour is determined exclusively by the E(u|u → u) term, which it will thus seek to maximise. If the agent acts now, this term will become a. This is because the agent would have already generated an extra a expected utility for u, and, were it to stay as a u-maximiser (u → u), it would have no further potential to increase this. If the agent doesn't act now, that term will become b, as the agent would later have acted to generate an extra b expected utility for u, if it had stayed a u-maximiser. The result follows. Putting all these proofs together establishes the theorem. Note that the actions of the agent can be defined by the following formula, for a sequence {u t } of utilities 28 : argmax a∈A E(u t |a, u t → u t ), with u t → u t denoting the (extremely unlikely) event that the transition u t to u t+1 fails permanently. Note also that each transition does not change the expected value of U . That is because the expectation of u (given u → u or equivalently given that the agent's utility never changes 29 ) is the same as the expectation of v − E(v|u → v) + E(u|u → u) (given u → v). Consequently, the initial expected value for U is the expected value of an unchanging u 0 . \n Discussion of Value-change indifference This seems to be the ideal value selecting agent. It will act to follow its preferences with perfect assiduity, but remain completely indifferent if these values were to change in the way prescribed by its program. That last point is importantwe'd want the agent to resit illegitimate value manipulation. This seems a partial solution to the value selection problem (the other, much bigger, part of the challenge, is to make the agent converge on values that are human-friendly  (Bostrom 2014) ). As mentioned in section 3, this approach allows only indifference. Preference for active learning of values (such as would make sense for an initially fast-learning agent) can be added to the framework. It would destroy the carefully balanced indifference. But, compared with a general value selecting agent, the effect could be precisely estimated and quantified. Paper  (Soares et al. 2015)  presents some other issues with the indifference approach 30 , that may be resolvable with a small tweak to the indifference framework. Note that the agent will be willing to sacrifice anything that it may value in the future for a small epsilon of extra value now. This is a feature of the setup, not a bug (indifference requires this), but may still be an undesirable behaviour. See  (Soares et al. 2015)  for more details. \n Discussion Constructing a well behaved value selecting agent immune to motivated value selection -one that is capable of learning new values while still acting on its old ones, without interference between these two aspects -is an important unsolved problem. This paper presented the requirements for such a value selecting agent, if values are presented in the form of utility functions. The agent starts with a probability distribution over the possible correctness C of possible value systems/utility functions. To avoid problematic motivated value selection, it should be designed so that, if A were its actions, U it possible utility functions, and W the set of possible world, then it would choose its actions as: for all statements h. The first equation can be generalised (for none utility-based agents) to the requirement that the agent use its future values to assess its future actions; the second to the requirement that it cannot profit my manipulating how it updates its values. Specifically, that if it knows how its (conditional) values will change, then it will already have changed them. This second requirement can be seen as a 'conservation of expected ethics' law. The structure may be too rigid to construct complex agents, however. If we drop the requirement that the agents values be expressed as a probability distribution over possible utility functions, we can construct an explicit model for a general value selecting agent. This agent comes equipped with a meta utility function U (equal to a given utility function at any given time) combined with some constant terms. When the agent is called upon to update its utility u to another utility v according to the value selecting process, it will update as: u → v − E(v|u → v) + E(u|u → u). These constant terms ensure that the agent will act as a pure u maximiser before the transition, and shift seamlessly to a pure v maximiser after. It gains no utility for either blocking or encouraging that transition. The big question then becomes the process of making the agent converge to ultimately desirable values. argmax a∈A w∈W P (w|e, a) u∈U u(w)P (C(u)|w) . \n )P (C(u)|e, a). \n E P (C(u c )|a) = E P (C(u d )|a) , Since P (C(u c )|a) + P (C(u d )|a) = 1 (as these are the only two utilities in the model), this means they are both equal to 0.5. Thus E P (C(u c )|a) = 0.5 = P (C(u c )), and equation (2) is satisfied. \n )P (C(u)|w) , subject to ∀u∀a ∈ A : E P (C(u)|h, a) = P (C(u)|h), \n\t\t\t We would not want an agent acquiescing to illegitimate value updating.3 This paper does not take a moral realist stance. A moral fact is simply a fact that the agent has been programmed to consider relevant to its morality. Nor do we distinguish between morality, motivations, preferences or values, using the terms interchangeably. \n\t\t\t Note that the individual component utilities of U need not be explicitly defined or explicitly stored in memory (an important issue to avoid a combinatorial explosion), so long as the weighted sum can be calculated or estimated somehow.8 A moral realist would likely wish to write P (u|w) or even P (u) instead of P (C(u)|w). But an agent could have any conceivable motivational structure (Bostrom 2012; Armstrong 2013) , ignoring the 'true morality' even if such a thing existed. Thus we will stick with P (C(u)|w) -a descriptive, not a normative, formulation.9 An interesting property of this is that it allows P (C(u)|w) to not be 0 or 1 -i.e. it allows for the possibility of moral uncertainty (Sepielli 2013 ) even when the agent has collected all morally relevant information.10 Individual worlds need not be explicitly defined nor explicitly stored, either.11 This paper will not enter the philosophically fascinating area of defining what exactly counterfactuals are (Lewis 1981; Gibbard and Harper 1981) , as an intuitive understanding is sufficient here. \n\t\t\t The thought experiment is based on an Eddie Izzard sketch of the same name.13 Some papers mix the two approaches (Dewey 2011 ) by failing to distinguish between different worlds where the agent cannot observe the difference itself. \n\t\t\t See the lesswrong.com blog post 'Conservation of Expected Evidence'. This does not seem a very advanced result, but, to the author's knowledge, that blog post was the first to write it up in those terms. 17 'Conservation of expected evidence' is essentially the probabilistic version of the reflection principle. \n\t\t\t More precisely: it won't choose to avoid learning, if the learning is costless. \n\t\t\t It may become necessary to restrict the possible h's considered in the equation. \n\t\t\t Crucially, such an intervention could be performed without any need to understand the utility function to any great degree.25  It could be set to zero, but this might interfere with the AI's computation of counterfactuals.26  See the experiments by Eliezer Yudkowsky (see the AI-box experiments on yudkowsky.net), and seprately by Justin Corwin (see the SL4 mailing list archive), where they played the role of the Oracle AI and convinced others to let them out, even when they are motivated not to. \n\t\t\t Not necessarily a pre-defined sequence, just using some transition rule.29 Astute readers may have noticed that this is not an exact equivalence; there are some situations (multi-agent social situations as a likely candidate) where u → u (a specific transition failure event) might not be equivalent with general 'unchanging u'. However, any agent can be penalised in social situations for having or not having any particular motivational structure, so this is a general problem, not specifically with this value selection design. \n\t\t\t Mainly that the agent might not be motivated to preserve its value updating infrastructure, or could create subagents without the value updating component.", "date_published": "n/a", "url": "n/a", "filename": "Armstrong_AAAI_2015_Motivated_Value_Selection.tei.xml", "abstract": "Coding values (or preferences) directly into an artificial agent is a very challenging task, while value selection (or valuelearning, or value-loading) allows agents to learn values from their programmers, other humans or their environments in an interactive way. However, there is a conflict between agents learning their future values and following their current values, which motivates agents to manipulate the value selection process. This paper establishes the conditions under which motivated value selection is an issue for some types of agents, and presents an example of an 'indifferent' agent that avoids it entirely. This poses and solves an issue which has not to the author's knowledge been formally addressed in the literature.", "id": "2f6c1ef83745409cbf1a660641f5de23"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nick Bostrom", "Thomas Douglas", "Anders Sandberg", "James Martin"], "title": "The Unilateralist's Curse and the Case for a Principle of Conformity", "text": "Introduction Consider the following hypothetical scenarios: (1) A group of scientists working on the development of an HIV vaccine has accidentally created an air-transmissible variant of HIV. The scientists must decide whether to publish their discovery, knowing that it might be used to create a devastating biological weapon, but also that it could help those who hope to develop defenses against such weapons. Most members of the group think publication is too risky, but one disagrees. He mentions the discovery at a conference, and soon the details are widely known. (2) A sports team is planning a surprise birthday party for its coach. One of the players decides that it would be more fun to tell the coach in advance about the planned event. Although the other players think it would be better to keep it a surprise, the unilateralist lets word slip about the preparations underway. (3) Geoengineering techniques have developed to the point that it is possible for any of the world's twenty most technologically advanced nations to substantially reduce the earth's average temperature by emitting sulfate aerosols. Each of these nations separately considers whether to release such aerosols. Nineteen decide against, but one nation estimates that the benefits of lowering temperature would exceed the costs. It presses ahead with its sulfate aerosol program and the global average temperature drops by almost 1˚. In each of these cases, each of a number of agents is in a position to undertake an initiative, X. Suppose that each agent decides whether or not to undertake X on the basis of her own independent judgment of the value of X, where the value of X is assumed to be independent of who undertakes X, and is supposed to be determined by the contribution of X to the common good. 1 Each agent's judgment is subject to error-some agents might overestimate the value of X, others might underestimate it. If the true value of X is negative, then the larger the number of agents, the greater the chances that at least one agent will overestimate X sufficiently to make the value of X seem positive. Thus, if agents act unilaterally, the initiative is too likely to be undertaken, and if such scenarios repeat, an excessively large number of initiatives are likely to be undertaken. We shall call this phenomenon the unilateralist's curse. Though we have chosen to introduce the unilateralist's curse with hypothetical examples, it is not merely a hypothetical problem. There are numerous historical examples, ranging from the mundane to the high-tech. Here is one: Until the late 1970s, the mechanism of the hydrogen bomb was one of the world's best kept scientific secrets: it is thought that only four governments were in possession of it, each having decided not to divulge it. But staff at the Progressive magazine believed that nuclear secrecy was fuelling the Cold War by enabling nuclear policy to be determined by a security elite without proper public scrutiny. They pieced together the mechanism of the bomb and published it in their magazine, arguing that the cost, in the form of aiding countries such as India, Pakistan and South Africa in acquiring hydrogen bombs, was outweighed by the benefits of undermining nuclear secrecy.  2  Another possible example from atomic physics had occurred several decades earlier: In 1939 the Polish nuclear physicist Joseph Rotblat noticed that the fission of uranium released more neutrons than used to trigger it, realizing that it could produce a chain reaction leading to an explosion of unprecedented power. He assumed that other scientists elsewhere were doing similar experiments, and were thus in a position to release similar information, an assumption that turned out to be correct. Initially, Rotblat vowed to tell no-one of his discovery, believing it to be a threat to mankind, and it is plausible that others did likewise, for similar reasons. However, when the war broke out, Rotblat decided that releasing the information was now in the public interest, given the likelihood that the Germans were working on an atomic bomb. He confided in colleagues and thus unilaterally triggered the United Kingdom's atomic bomb project.  3  Rotblat was later to leave the Manhattan Project, coming to the view that his had overestimated the German nuclear threat, and underestimated the likelihood that the US would use an atomic bomb offensively. It is perhaps too soon to say whether these unilateral actions were suboptimal. But in other cases, it is clearer that unilateral action led to a suboptimal outcome: In the mid-nineteenth century there were virtually no wild rabbits in Australia, though many were in a position to introduce them. In 1859, Thomas Austin, a wealthy grazier, took it upon himself to do so. He had a dozen or two European rabbits imported from England and is reported to have said that \"The introduction of a few rabbits could do little harm and might provide a touch of home, in addition to a spot of hunting.\" 4 However, the rabbit population grew dramatically, and rabbits quickly became Australia's most reviled pests, destroying large swathes of agricultural land.  5  The abovementioned examples were isolated incidents, but similar situations occur regularly in some spheres of activity, for instance, in the media: Media outlets sometimes find themselves in the situation that journalists have access to information that is of public interest but could also harm specific individuals or institutions: the name of a not-yet charged murder suspect (publication may bias legal proceedings), the news that a celebrity committed suicide (publication may risk copycat suicides), or sensitive government documents such as those leaked by Wikileaks and Edward Snowden (publication may endanger national security). It is enough that one outlet decides that the public interest outweighs the risk for the information to be released. Thus, the more journalists have access to the information the more likely it is to be published. Unilateralist situations also regularly crop up in regards to new biotechnologies: Gene drives, a technique for inducing altered genes to be inherited by nearly all offspring (rather than just 50%) of a genetically modified organism, have potential for spreading altered genes across a population, enabling ecological control (e.g. making mosquitos incapable of spreading malaria or reducing herbicide resistance) but also potentially creating worrisome risks (e.g. to genetic diversity or of sabotage). Here unilateral action could both be taken in releasing a particular altered organism into the environment, and in releasing the information about how to produce it in the first place. There is scientific disagreement on the utility and risk of both. 6 \n The Unilateralist's Curse: A Model The unilateralist's curse is closely related to a problem in auction theory known as the winner's curse. The winner's curse is the phenomenon that the winning bid in an auction has a high likelihood of being higher than the actual value of the good sold.  7  Each bidder makes an independent estimate and the bidder with the highest estimate outbids the others. But if the average estimate is likely to be an accurate estimate of the value, then the winner overpays. The larger the number of bidders, the more likely it is that at least one of them has overestimated the value. The unilateralist's curse and the winner's curse have the same basic structure. The difference between them lies in the goals of the agents and the nature of the decision. In the winner's curse, each agent aims to make a purchase if and only if doing so will be valuable for her. In the unilateralist's curse, the decision-maker chooses whether to undertake an initiative with an eye to the common good, that is, seeking to undertake the initiative if and only if the initiative contributes positively to the common good. The unilateralist's curse can be illustrated using a simple mathematical model. Assume N agents, each considering whether to undertake an initiative. Each agent wishes to proceed if and only if the value of the initiative is positive, but the agents do not know the true value V * of the initiative (which may be negative or positive). Instead each agent forms an estimate that is the sum of V * and a random independent error d drawn from a distribution with cumulative distribution function F(d). This means that the probability p that any given agent will estimate the value of the initiative to be positive when it is in fact negative (V * < 0) is p = 1 − F(−V * ).  8  The probability P that at least one of the agents will incorrectly estimate the value to be positive is p = 1 − (1 − p) N = 1 − F(−V * ) N . For the case with 5 agents and d as a random error drawn from a normal distribution with standard deviation 1 and mean zero, the probability that any initiative will be undertaken (regardless of whether it is a good idea or not) is high even when the true value is quite negative, and the probability rises steeply as the true value of the initiative approaches zero from below (Figure  1 ). For mildly negative values of the initiative there is nearly always someone who misjudges the value of the initiative and undertakes it. There is no problem for positive initiatives since even if one or two agents are overly cautious, it is very likely that somebody will undertake the initiative, which is the optimal result (Figure  2 ). Increasing the number of agents capable of undertaking the initiative also exacerbates the problem: as N grows, the likelihood of someone proceeding incorrectly increases monotonically towards 1.  9  The magnitude of this effect can be quite large even for a relatively small number of agents. For example, with the same error assumptions as above, if the true value of the initiative V * = −1 (the initiative is undesirable), then the probability of erroneously undertaking the initiative grows rapidly with N, passing 50% for just four agents (Figure  3 ). There are six features of the unilateralist's curse that that need to be emphasized. First, in cases where the curse arises, the risk of erroneously undertaking an initiative is not caused by self-interest. In the model, all agents act for the common Figure  1  The probability of an initiative being undertaken as a function of the actual value, V * , for five agents and assuming normally distributed errors with variance 1 (these assumptions will be used in all subsequent figures except when otherwise noted). Note that 50% probability of action occurs near a value of −1: a strong unilateralist bias exists. Figure  2  The expected payoff for naive agents (who act if and only if their evaluation of the initiative is positive) and ideal omniscient estimators who are assumed to know the true value. good, they simply disagree about the contribution of the initiative to the common good.  10  Second, though the curse could be described as a group-level bias in favor of undertaking initiatives, in does not arise from biases in the individual estimates of the value that would result from undertaking the initiative. The model above assumes symmetric random errors in the estimates of the true value.  11  Third, there is a sense in which the unilateralist's curse is the obverse of Condorcet's jury theorem.  12  The jury theorem states that the average estimate of a group of people with above 50% likelihood of guessing correctly and with uncorrelated errors will tend to be close to the correct value, and will tend to move closer to the true value as the size of the group increases. But what is also true, and relevant to the argument in this paper, is that the highest estimate will tend to be above the true value, and the expected overestimation of this highest estimate increases with the size of the group. In the cases we are interested in here, it is the highest estimate that will determine whether an initiative is undertaken, not the average estimate. Fourth, though we have chosen to illustrate the curse using initiatives that are (probably) irreversible, the problem can arise in other cases too. The problem becomes sharper if the initiative is irreversible, but even for actions that can be undone the problem remains in a milder form. Resources will be wasted on undoing erroneous initiatives, and if the bad consequences are not obvious they might occur before the problem is noticed. There might even be a costly tug-o-war between disagreeing agents. Finally, fifth, though we have thus far focused on cases where a number of agents can undertake an initiative and it matters only whether at least one of them does so, a similar problem arises when any one of a group of agents can spoil an initiative-for instance, where universal action is required to bring about an intended outcome. Consider the following example: In Norse mythology, the goddess Hel of the underworld promised to release the universally beloved god Baldr if all objects, alive and dead, would shed a tear for him. All did, except the giantess Þo ¨kk. The god was forced to remain in the underworld.  13  Similar situations can arise when all the actors in a play must come together in order for a rehearsal to take place, when all members of committee must attend a meeting in order for it to be quorate, or when all signatories to an international treaty must ratify it in order for it to come into effect. The United Nations Security Council frequently provides examples of unilateral spoiling. The five permanent members of the Council-currently China, France, Russia, the United Kingdom and the United States-each possesses the power to veto the adoption of any non-procedural resolution. In the early years of the Council, this veto power was frequently employed by the Soviet Union to block applications for new membership of the United Nations. More recently, it has been used by the United States to block resolutions criticizing Israel, and by Russia and China to block resolutions on the Syria conflict. 14 While some of these vetoes presumably reflect differences in the national interests of the council members, others may reflect different estimations of the contribution that a resolution would make to the common good. Certainly, considerations relating to the common good are often invoked in their defence. For instance, the United States' 2011 veto of a draft resolution condemning Israeli settlements in Palestinian territory was defended on the grounds that the resolution would be an impediment to peace talks.  15  These cases of unilateral spoiling or abstinence are formally equivalent to the original unilateralist curse, with merely the sign reversed. Since the problem in these cases is the result of unilateral abstinence, it seems appropriate to include them within the scope of the unilateralist's curse. Thus, in what follows, we assume that the unilateralist's curse can arise when each member of a group can unilaterally undertake or spoil an initiative (though for ease of exposition we sometimes mention only the former case). \n Lifting the Curse Let a unilateralist situation be one in which each member of a group of agents can undertake or spoil an initiative regardless of the cooperation or opposition of other members of the group. We will say that a policy would lift the unilateralist's curse if universal adherence to it by all agents in unilateralist situations should be expected (ex ante) to eliminate any surfeit or deficit of initiatives that the unilateralist's curse might otherwise produce. \n The Principle of Conformity When acting out of concern for the common good in a unilateralist situation, reduce your likelihood of unilaterally undertaking or spoiling the initiative to a level that ex ante would be expected to lift the curse. In the following subsections we will explore various ways in which one might bring oneself into compliance with this principle.  16  These can be organized around three models: collective deliberation, epistemic deference, and moral deference. The three models are applicable in somewhat different circumstances, and their suitability might depend on the type of agents involved. It should be noted that, though some of the methods discussed below do not require agents to be aware of the nature of the situation, most hinge on agents recognizing that they are in an unilateralist situation. However, this is not to say that agents must be able to identify the other parties to the unilateralist situation: this is necessary for some but not all of our proposed solutions. \n The Collective Deliberation Model A first line of defense against the unilateralist's curse could be to share data and reasoning between agents in the hope that this will resolve their disagreement about the desirability of proceeding with the contested initiative. In some cases, however, extensive information sharing among all potential decision-making agents is impractical. Communication is often costly and timeconsuming, and participants in a unilateralist situation may not be able to identify one another. Furthermore, in certain cases information disclosure might itself be the initiative whose desirability is in dispute, such as when information hazards are associated with disseminating relevant data.  17  Moreover, even when information is fully shared, a consensus can remain elusive. Disagreements about the net value of undertaking some project often persist after decision-makers have been thoroughly briefed on all obviously relevant and easily communicable facts and after having had opportunities to engage in joint deliberation. Because complete information sharing may not be practical or desirable, and because it may not produce consensus when it does occur, the principle of conformity requires us to explore additional models for lifting the unilateralist's curse. \n The Meta-rationality Model One approach would be to appeal to each agent's reflective rationality. A party to an epistemic disagreement should ideally reflect on the fallibility of their own judgment and adjust their posterior probability to take into account the fact that other agents have different opinions. Robert Aumann has shown that rational Bayesian agents with identical priors and common knowledge of each other's posteriors (and of each other's rationality) must have identical posterior probabilities.  18  Disagreement between such agents is impossible. This sounds like good news: if all agents make the same estimate of the benefits of action, the unilateralist curse is lifted. There is, however, some skepticism about the relevance of Aumann's result for practical cases of disagreement.  19  The assumption of identical priors, in particular, is problematic.  20  Furthermore, the same challenges that can make data sharing difficult can also make it difficult to make each agent's honest posterior probability estimates of the value of the initiative common knowledge among all agents. It turns out, however, that sufficiently rational agents can manage the curse even without communication. In the literature on the winner's curse it has been argued that rational expected utility-maximizing will not be affected by it.  21  Rational agents will take the winner's curse into account and adjust their bids accordingly. This is known as bid shading. Rational agents place bids that are lower than their ex ante expectation of the value of the good, but equal to their expectation of the value of the good conditional upon them winning the auction. The counterpart of this response would be for agents in a unilateralist situation to estimate the value of the initiative conditional on the agent's first-order estimate of the initiative's value being the highest (or, in spoiler cases, the lowest). In other words, on finding themselves in a unilateralist situation, each rational agent will initially estimate the value of the initiative based on his prior probability distribution. He will then take into account the case where his decision is decisive. In the case where agents can unilaterally undertake an initiative, the agent will condition on the situation in which he is the most sanguine and everybody else thinks the action should not be done. (In spoiler cases, the agent conditions on the situation in which he is the most pessimistic and everybody else thinks the initiative should be undertaken.) He then creates a posterior distribution of value that is used to make an adjusted decision. PðV Ã jwinÞ ¼ PðwinjV Ã ÞPðV Ã Þ PðwinÞ where \"win\" represents being the deciding agent. Note that this typically requires knowing or estimating the number of other agents. \n Example In the simple case where the agent assumes all other agents have the same priors and are acting independently, only differing in the noisy data about V * they have received: PðwinjV Ã Þ ¼ Z 1 À1 PðV À V Ã ÞFðV À V Ã Þ NÀ1 dV where F(V) is the cumulative distribution function of the errors. The posterior distribution of V * becomes: PðV Ã jwinÞ ¼ KPðV Ã Þ Z 1 À1 PðV À V Ã ÞFðV À V Ã Þ NÀ1 dV where K is a normalization constant. The posterior action should then be based on the expectation E(V * |win). If the agents choose to act when the received data is above a fixed threshold T, V * is normally distributed with zero mean and variance 1, and they get estimates of V * with normal noise (again with mean zero and variance 1), then the optimal threshold is the one that maximizes the expected value (Figure  4 ): T opt ðNÞ ¼ argmax T Z 1 À1 VPðV Þ 1 À 1 À F V À T ð Þ ð Þ N dV T opt (N) increases rapidly with N, reaching 0.54 for two agents and 1 for 4 agents: even for a small group it is rational to be far more cautious than in the single agent case. Note that in this case all agents are aware of the prior distribution, noise distribution, independence, and that the other agents are using this strategy (Figure  5 ).  22  Figure  4  The optimal threshold T opt (N) for action as a function of the number of agents. Agents who only act if the perceived value of the initiative is higher than T opt (N) will maximize their expected (joint) result. One might raise questions about the practical applicability of this sophisticated Bayesian approach, however. Even if rational Bayesian agents would agree, humans are at best approximations of rational Bayesian agents and they have far more limited mental computation power-even when leaving out biasing factors.  23  Value in practical cases is also seldom in the form of easily manipulable and comparable scalar quantities. Hence implementing the sophisticated Bayesian approach to lifting the unilateralist's curse might typically be infeasible.  24   \n The Moral Deference Model Suppose a unilateralist situation exists and that it is not feasible for all agents to lift the curse through communication and adjustment of beliefs. It might nevertheless be possible for the group to lift the curse if each agent complies with a moral norm which reduces the likelihood that he acts unilaterally, for example, by assigning decision-making authority to the group as a whole or to one individual within it. We call this the moral deference model. In contrast to the two models presented above, the moral deference model does not require agents to defer to the group in forming their beliefs regarding the value of the initiative. However, it does require them to defer to the group in deciding whether to act on those beliefs. A slogan for this approach could be \"comply in action, defy in thought.\" There are many norms such that universal compliance with the norm by a group of agents would lift the unilateralist's curse. For example, a norm that assigned decision-making authority to an arbitrary member of the group would lift it. Consider the norm: when in a unilateralist situation, if you are the tallest person able to undertake the initiative, then undertake it if and only if you believe its value exceeds zero; if you are not the tallest person able to undertake the initiative, do not undertake it. Universal compliance with this norm would prevent the unilateralist's curse from arising in the sense that, in the absence of any bias towards or against action in the individual members of the group (and thus in the group's tallest member), this norm will produce no group-level bias towards or against the initiative.  25  The payoffs associated with this tallest-decides norm in a five-agent situation are depicted in Figure  6  below. The tallest-decides norm, however, has several epistemically and pragmatically unattractive features. For example, it does not protect against biases or errors that might impair the judgment of the group's tallest member. Furthermore, it is very unlikely that such a norm would gain wide acceptance. Fortunately, there are other norms that could lift the curse and may lack these unattractive features. One norm would recommend that agents conform to the rules of existing institutions that militate against unilateral action: (1) When in a unilateralist's situation, defer to existing institutions, such as laws or customs, if universal deference to those institutions would lift the unilateralist's curse. National and international laws often militate against the unilateralist's curse, for example by specifying that decisions must be made democratically or by individuals or institutions that have been given special authority over a particular realm of decision-making. In other cases, there are informal conventions that may do the job. For example, following the publication early last decade of two studies thought by some to aid bioweapons development,  26  a group of scientific journals agreed to introduce screening procedures to identify papers containing information that is especially prone to misuse and to seek external advice on the publication of such papers.  27  Though these procedures lacked legal status, compliance with them by journals may have helped lift the curse. One virtue of (1) is that, since it simply reinforces existing institutional norms which may already command significant support, it may be relatively easy for it to achieve wide acceptance. However, (1) will not lift the curse in all cases. In many areas with an international dimension, for example, there are no relevant international laws and deference to national laws would merely create a new unilateralist situation between nations: the nation that evaluates the initiative most positively is most likely to allow it. Moreover, (1) may sometimes recommend deferring to biased procedures or agents. It might be possible for a group of agents to lift the curse even in cases where (1) fails by complying with a different norm, one that promotes the development of and compliance with a new procedure for group decision-making. This approach was adopted by a large group of American microbiologists in mid-1974 when they agreed to a moratorium on recombinant DNA research until such time as the safety concerns that it raised could be jointly discussed and resolved. The moratorium held until the now-famous Asilomar Conference, which took place in February 1975 and resulted in a broad-based agreement on guidelines regarding the conditions under which recombinant DNA research ought to proceed.  28  The recombinant DNA moratorium and guidelines were developed via consensus, but another approach would be to employ a voting procedure. For example, suppose all agents faced with a unilateralist situation complied with the norm: (2) When in a unilateralist's situation, promote the holding of a majority vote among those capable of undertaking the initiative. If the vote takes place, then (a) defer to its verdict, and (b) encourage others to do likewise. Universal compliance with this norm is likely to lift the curse. Since it is effectively using the median estimate it is robust to outliers. It will also tend to reduce systematic bias at the group level provided that individual biases are at least partially independent of one another.  29  And since majority voting is a common and widely accepted method for group decision-making, this norm would have relatively good prospects of gaining wide acceptance. Compliance with norms (1) and (2) will, however, lift the unilateralist's curse only when a high degree of communication and coordination is possible. There are other norms whose universal adoption could lift the curse even in the absence of communication and coordination. Consider the norm: (3) When in a unilateralist situation, bring about the outcome if and only if you judge that a majority vote among those capable of undertaking the initiative would yield a majority in favor of doing so. Insofar as each individual capable of undertaking the initiative makes an accurate prediction of the views of all others, universal adoption of this norm will eliminate any group-level bias due to the unilateralist's curse. Even if predictions of the views of others are inaccurate (e.g. because each agent overestimates the extent to which others share her views), universal adoption of this principle can still be expected to somewhat mitigate the unilateralist's curse. It will tend to reduce the likelihood that those who value the initiative most favorably will undertake it, provided that these agents realize they are at the optimistic end of the spectrum.  30  Figure  7  depicts, for a five-agent case, the expected payoffs associated with two of the norms discussed in this section-tallest decides, and the actual majority vote (norm (  2 ))-and it compares these with other strategies described in Section 3.2 above. Under our assumptions, the majority vote does rather well-it is close to the maximum available payoff represented by the omniscient case. However, in the real world, different strategies will work well in different cases. It is thus likely that the best norm to adopt, under the moral deference model, would be some composite of simple norms such as (1)-(3). For example, a group might adopt a norm that specifies that the group should act as specified by (  1  We do not wish to commit ourselves to norms (1)-(  3 ) as the best building blocks from which to construct such a composite norm. We believe that each of (1)-(  3 ) are at least plausible candidates for inclusion in a composite norm. However, there may be other norms that would more fully lift the curse or which have other advantages over (1)-(3). For example, there are well-known problems with majority voting which should perhaps lead us to prefer a different voting procedure under norms (2) and (3). One other set of concerns regarding norms (2) and (3) warrants mentioning. Both of these norms involve holding a vote (real or hypothetical) among agents capable of undertaking the initiative in question. But it might be argued, on either epistemic or moral grounds, that any actual or hypothetical vote should include more individuals than merely those capable of undertaking the initiative. For example, perhaps the vote should include all whose capacity to evaluate the initiative passes some threshold of epistemic competence. Or perhaps, on moral grounds, the electorate should be expanded to include all individuals who will be affected by the initiative. Consider a case in which there are three agents who could undertake an initiative and two of the three judge that it would be best to do so. However, millions of others will be affected by the initiative and almost all of them judge that the initiative has net disvalue. In this case, it might seem morally preferable to hold (or imagine) a vote among all who will be affected by the initiative rather than limiting the vote to the three agent's capable of undertaking it. A more specific problem with excluding individuals who are incapable of undertaking the initiative is that this might seem to skew the vote. There might be some agents who are not capable of undertaking the initiative, but could have been capable of doing so; they are incapable only because they previously judged that undertaking the initiative would be a bad idea and thus ceased to develop the necessary capacities. Excluding these agents from a vote might seem to skew the vote in favor of those who deem the initiative to be valuable and who have thus sought to develop the capacities necessary to undertake it. Thus, limiting the vote to those capable of undertaking the initiative may be epistemically, as well as morally, problematic. At the same time, it might be argued that some agents capable of undertaking the initiative should be excluded from the vote. Suppose that each of five nations is capable of undertaking some geoengineering project with worldwide consequences. Four agree to hold a majority vote among the five nations and to abide by the outcome of that vote. The fifth wishes to take part in the vote but is resolved to press ahead with the project regardless of the outcome of the vote. It might seem doubtful whether the first four nations should include the fifth in the vote. Arguably, deferring to a majority vote in unilateralist cases involves making a sacrifice. It involves giving away some of one's autonomous decision-making authority. It might seem that would be unfair for the fifth nation to exert an influence over the decisions of others by participating in a vote without also being prepared to make the same sacrifice that the others are prepared to make. This may count in favor of excluding the fifth nation. Excluding the fifth nation might also help to incentivize deference to majority votes in unilateralist situations. There are thus arguments both for expanding and for restricting the group of agents given a vote in norms (2) and (3). We cannot assess these arguments here. We mention them only to flag them as topics for further discussion. However, it is worth noting that including all and only those agents who are capable of undertaking an initiative does at least have the virtue of picking out a group that would, in many cases, be relatively easy to identify. We should end this section on the moral deference model with an important clarification: the model does not rely on a commitment to any particular moral theory. Proponents of a range of different moral theories could accept norms of the sort described above, though they would assign different statuses to them. A rule consequentialist, for example, might treat these norms as genuine moral principles-principles that determine which acts are right and which are wrong. According to one formulation of rule consequentialism, a rule of action is a genuine moral principle just in case it is part of the set of rules of action whose general acceptance can be expected to have consequences as good as the general acceptance of any alternative set of rules.  31  Given the risk of premature or erroneous action created by the unilateralist's curse and the likelihood that most agents are not sophisticated enough belief-formers to apply our meta-rationality model, it is plausible that the optimal set of rules will contain a norm of the sort that we have discussed. On some other moral theories, these norms would serve not as genuine moral principles, but as guidelines for helping agents to comply with such principles. Adherents of many moral theories, both consequentialist and deontological, could accept something like the following moral principle: Agents have moral reasons to undertake an initiative if and only if that initiative would contribute to the common good, and to spoil an initiative if and only if that initiative would detract from the common good. Norms of the sort discussed above could help agents to better comply with this principle in unilateralist situations. 32 \n Discussion We proposed: The Principle of Conformity When acting out of concern for the common good in a unilateralist situation, reduce your likelihood of unilaterally undertaking or spoiling the initiative to a level that ex ante would be expected to lift the curse. We also outlined three different ways in which agents who find themselves in unilateralist situations might comply with this principle. We do not claim that any one of these models is superior to the others in all situations. Which model should be adopted will depend, among other things, on the sophistication of the agents, the degree of communication and coordination that is possible, and the nature of existing laws and conventions bearing on the decision. In this section we discuss a concern that might be raised regarding our principle. Adoption of the principle of conformity is meant to make things better. Yet if we \"backtest\" the principle on historical experience, it is not at all clear that universal adoption of the principle of conformity would have had a net positive effect. It seems that, quite often, what is now widely recognized as important progress was instigated by the unilateral actions of mavericks, dissidents, and visionaries who undertook initiatives that most of their contemporaries would have viewed with hostility and that existing institutions sought to suppress. The benefits of iconoclasm and defiance of authority have been stated especially forcefully in the Enlightenment tradition and by proponents of scientific and technological progress. They are also evident in many cases of \"whistleblowing.\" Consider the case of Daniel Ellsberg, famous for leaking the Pentagon Papers, which revealed the hopelessness of the US military situation in Vietnam. Most of Ellsberg's peers, who had the high-level security clearance required to access the relevant documents, presumably did not believe that leaking the material to the press would contribute positively to the common good. If Ellsberg had sought to follow the principle of conformity, for example by imagining a vote among all those in a position to leak the documents, it would seem he would have had to conclude that the documents ought not be leaked. This might seem an undesirable outcome. It is possible that the appearance that unilateralism has historically been mostly for the good is illusory. Historical unilateralism might be more salient when it worked out well than when it worked out badly, perhaps because successes have been more extreme but less frequent than the failures. Moreover, it may be that, in some cases where the principle of conformity appears to recommend a net harmful course of action, this implication can be avoided by attending to how the group of (imaginary or actual) voters or epistemic peers is defined. For example, if one allows that these groups might be defined more broadly than the group of agents capable of undertaking an action, it may be possible to avoid the implication that Ellsberg should have refrained from whistleblowing. (Suppose that many \"outsiders\" would have voted in favor of his releasing the information.) However, even if unilateralism has historically provided a net benefit to humanity, this need not undermine our argument. The claim that the unilateralist curse is an important phenomenon and that we have reason to lift it is consistent with the claim that the curse has provided a net benefit to humanity. The main effect of the curse is to produce a tendency towards unilateral initiatives, and if it has historically been the case that there have been other factors that have tended to strongly inhibit unilateral initiatives, then it could be the case that the curse has had the net effect of moving the overall amount of unilateralism closer to the optimal level. For example, it might be argued that the scholars of past ages were usually far too deferential to authority, for reasons independent of the factors discussed in this paper. Their failure to take into account our arguments might then have had the salutary effect of not further inhibiting whatever propensity remained to promote new thoughts. \n Concluding Thoughts We have described a moral analog of the winner's curse. The unilateralist's curse arises when each of a group of agents can, regardless of the opposition of others, undertake or spoil an initiative that has significant effects on others. In such cases, if each agent decides whether to undertake (or spoil) the initiative based on his own independent naive assessment of its value, there will be a group-level bias towards undertaking (spoiling) the initiative. Importantly, this effect arises even if all the agents are assumed to be motivated solely by concern for the common good. We proposed a principle-the principle of conformity-which instructs agents faced with a unilateralist situation to reduce their likelihood of unilaterally undertaking (or spoiling) the initiative. We then outlined three models for accomplishing this. They involved, respectively, (1) sharing information and reasoning before forming one's evaluation of the initiative, (2) adjusting one's evaluation in the light of the curse, and (3) deferring to the group in making one's decision. As we acknowledged in the previous section, there may be considerations that militate against the principle of conformity. For example, if there is already a group-level bias against unilateralism, then compliance with the principle would exacerbate this bias. However, we maintain that there is a prima facie case for complying with the principle. Moreover, since the level of bias due to such other factors towards or against unilateralism presumably varies across different contexts, it is likely that there will be some contexts in which the prima facie case for complying with the principle will be decisive. Those will be the contexts in which the group-level bias due to the unilateralist's curse is greater than any countervailing bias against unilateralism. It is also possible that, at least within the domain of science, the principle of conformity is more relevant today than it was, say, prior to the Enlightenment. At that time, there was, plausibly, a strong bias against thinking and acting independently in intellectual matters, at least where this would involve diverging from the views of the Church. Since the Enlightenment, however, there may have been a significant weakening of this bias. Independence of thought and action is now more widely regarded as a virtue in scientists and other intellectuals. Honors and prizes are won based on claims to originality and precedence. There may now be no bias, or only a weak bias, against unilateralism in science. Thus, the risk posed by the unilateralist curse in scientific contexts may be greater now than ever. To resist the unilateralists' curse one first has to become aware of when one is in a curse situation. We hope this paper will help achieve that. \n Funding This work was supported by the The Oxford Martin School; The Wellcome Trust [grant number WT087211]. \n Notes [1] We assume that the common good is determined in part by the wellbeing of all persons and other morally significant individuals. However, we remain neutral on precisely how individual wellbeing determines the common good. For example, we do not commit ourselves to the view that the common good is simply aggregate individual wellbeing; we allow that the distribution of wellbeing might be relevant. We also allow that factors besides individual wellbeing might influence the common good. For example, some initiatives might possess intrinsic value that is independent of their contribution to wellbeing, and we allow that this intrinsic value might be one element in the common good. [2] The Progressive Magazine (1979). [3]  Rotblat (1985) . [4]  Bowden (2007) . [5]  Williams (1995) . [6] ,  Gurwitz (2014) , and . [7]  Thaler (1988) . [8] The probability that a particular agent will be wrong about the sign of the value of the outcome is Pr(V * + d > 0) if V * < 0 and Pr(V * + d < 0) if V * > 0. This is equal to 1 − F (−V * ) if V * < 0 and F(−V * ) if V * > 0. The probability that out of N agents at least one will be wrong about the sign is (1 − F(−V * ) N ) if V * < 0 and (1 − (1 − F(−V * )) N ) if V * > 0. However, even if errors are symmetric around 0, the expected outcome is not: in the V * < 0 case it is enough that one agent acts for a negative value to be obtained, while in the V * > 0 case all agents have to err on the side of caution for them to lose out on a positive value. The expected value obtained by naive agents is hence V * (1 − F(−V * ) N ). For positive values this is close to V * (for unbiased error distributions), and we will hence focus on the V * < 0 case where unilateral action is a problem. [9] Theorem: As N grows, the likelihood P of at least one agent proceeding incorrectly increases monotonically towards 1 unless F(−V * ) = 1 (i.e. unless there is an upper limit on the size of the deviations and V * is more negative than this limit, no agent will ever make a sufficiently bad mistake).Proof: If F(−V * ) = 1, p = 0 for all N. Otherwise 0 ≤ F (−V * ) < 1, and hence F(−V * ) N approaches 0 as N → ∞. [10] There will also, of course, be cases where an agent's decision whether to undertake an initiative affects others but the agents are motivated by self-interest rather than the common good. In these cases, there are two possible reasons for getting the wrong decision, from the point of view of the common good: (i) self-interest and the common good come apart-that is, one is judged to have positive value and the other negative value-and (ii) the agent overestimates the \"self-interest\" value of the initiative. [11] If the distribution of errors is skewed such that the typical estimate is higher than the true value, for instance due to optimism bias, then the risk of erroneous action is increased: in that case, even a single agent might be likely to overestimate the value of the initiative sufficiently to undertake it even when the true expectation value of the initiative is strongly negative. But this is unrelated to the curse. In the case of estimates skewed towards safety-that is, where there is pessimism bias-any tail distribution allowing mistaken action will still produce a growing probability of going ahead as N grows. There may be intermediary cases where the curse would helpfully serve to balance out an opposite effect arising from pessimism bias. [29] The assumptions of the Condorcet theorem can be weakened in many ways. In particular, agent competence only has to be on average above 50%  (Grofman, Owen, and Feld 1983) , and a certain level of voting correlation does not reduce majority voting performance  (Ladha 1992 ). [30] For similar reasons, an analogous norm would tend to reduce the likelihood of spoiling an initiative of those who evaluate an initiative most negatively. [31] See, for example,  Hooker (2002) . [32] A parallel can be drawn to one prominent justification for the authority of the law, due to Joseph Raz. That justification appeals to the same kind of consideration that we suggest could ground a norm against unilateral action: \"The normal and primary way to establish that a person should be acknowledged to have authority over another person involves showing that the alleged subject is likely better to comply with reasons which apply to him (other than the alleged authoritative directives) if he accepts the directives of the alleged authority as authoritatively binding, and tries to follow them, than if he tries to follow the reasons which apply to him directly\"  (Raz 1994, 214) .  [33]  In this case, the maximum likelihood estimate is simply the average of their individual estimates. Figure 3 3 Figure 3 Probability of an erroneous action in the case of V * = −1 for different numbers of agents. \n Figure 5 5 Figure5The expected payoff for different actual values of the initiative for alternative ways of handling the unilateralist's curse. Using the optimal individual threshold T opt (5) reduces the losses significantly. \n Figure 6 6 Figure6Expected payoff for different actual values of the initiative for alternative ways of handling the unilateralist curse. The tallest decides case achieves a significant reduction of loss, nearly reaching the payoff of the more complex Bayesian threshold method. \n Figure7depicts, for a five-agent case, the expected payoffs associated with two of the norms discussed in this section-tallest decides, and the actual majority vote (norm (2))-and it compares these with other strategies described in Section 3.2 above. Under our assumptions, the majority vote does rather well-it is close to the maximum available payoff represented by the omniscient case.However, in the real world, different strategies will work well in different cases. It is thus likely that the best norm to adopt, under the moral deference model, would be some composite of simple norms such as (1)-(3). For example, a group might adopt a norm that specifies that the group should act as specified by (1), (2) or (3) depending on what laws and conventions already exist, what forms of communication and coordination among group members are possible, and how costly such communication and coordination is likely to be, among other factors.We do not wish to commit ourselves to norms (1)-(3) as the best building blocks from which to construct such a composite norm. We believe that each of (1)-(3) are at least plausible candidates for inclusion in a composite norm. However, there may be other norms that would more fully lift the curse or which have other advantages over (1)-(3). For example, there are well-known problems with majority voting which should perhaps lead us to prefer a different voting procedure under norms (2) and (3).One other set of concerns regarding norms (2) and (3) warrants mentioning. Both of these norms involve holding a vote (real or hypothetical) among agents capable of undertaking the initiative in question. But it might be argued, on either epistemic or moral grounds, that any actual or hypothetical vote should include more individuals than merely those capable of undertaking the initiative. For \n Figure 7 7 Figure7The expected payoff associated with universal compliance with six different strategies at different actual values of the initiative. The fully shared information strategy consists in pooling the information between the agents and acting on the group's best joint estimate of V * ; 33 this requires maximal communication. Despite the lack of communication in tallest decides and threshold setting, the agents achieve an average outcome close to the cases where communication is possible. \n \n\t\t\t  N. Bostrom et al.    \n\t\t\t  N. Bostrom et al.    \n\t\t\t  N. Bostrom et al.    \n\t\t\t  N. Bostrom et al.", "date_published": "n/a", "url": "n/a", "filename": "tsep-30-350.tei.xml", "abstract": "In some situations a number of agents each have the ability to undertake an initiative that would have significant effects on the others. Suppose that each of these agents is purely motivated by an altruistic concern for the common good. We show that if each agent acts on her own personal judgment as to whether the initiative should be undertaken, then the initiative will be undertaken more often than is optimal. We suggest that this phenomenon, which we call the unilateralist's curse, arises in many contexts, including some that are important for public policy. To lift the curse, we propose a principle of conformity, which would discourage unilateralist action. We consider three different models for how this principle could be implemented, and respond to an objection that could be raised against it.", "id": "64ae4bf4fc2fd66bab0375510deb9698"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Leonel Rozo", "Heni Ben Amor", "Sylvain Calinon", "Anca Dragan", "Dongheui Lee"], "title": "Special issue on learning for human-robot collaboration", "text": "we received more than fifty submissions, among which ten articles were selected for the special issue, covering exciting applications spanning co-manipulation, medical robotics, and social behaviors. These works and five additional papers compose a fascinating online topical collection that reports a larger diversity of research advancements in learning for HRC. In Progress and Prospects of the Physical Human-Robot Collaboration, Ajoudani, Zanchettin, Ivaldi, Albu-Schäffer, Kosuge and Khatib review the state-of-the-art on intermediate human-robot bi-directional interfaces, robot control modalities, systems stability, benchmarking, and relevant use cases. The article extends views on the required future developments in the realm of physical human-robot collaboration. The authors provide a thorough overview of the pioneering methodologies that aim at achieving intuitive and seamless HRC, potentially relying on a minimum degree of task-related pre-programming, where the relevance of robot learning stands out. They also provide a list of potential applications and relevant use cases ranging from domestic to industrial environments. Turn-taking prediction, a synchronization aspect in HRC, is the capability to comprehend the on-going task progress and predict where, when and how to seize the next turn during multi-agent collaborations. In Early Prediction for Physical Human-Robot Collaboration in the Operating Room, Zhou and Wachs show the importance of fluent and natural turn-taking regulations in team performance, which lead to better social connections among team members. The requirement for early turn-taking prediction stands out more clearly in high-risk and high-paced tasks like surgery, where the scrub nurse and the surgeon perform fast, accurate and highly coordinated turn-taking actions when exchanging surgical instruments. In this context, the authors tackle the problem of designing a fully functional robotic scrub nurse, and propose a computational framework for early turn-taking prediction built on Long Short-Term Memory networks and Dempster-Shafer theory for uncertain sensor fusion. The approach is evaluated on a simulated surgical procedure dataset, and is found to be superior to its algorithmic counterparts, and better than the human baseline when little partial input is given. Shared autonomy is on its own a relevant form of collaboration, and medical robotics has also inspired the research on shared autonomy reported in the paper Skill-Based Human-Robot Cooperation in Teleoperated Path Tracking by Enayati, Ferrigno and De Momi. The paper argues that a robot's assistance during shared autonomy should depend on the operator's skill level. The robot should aid novices, but not unnecessarily restrict experts. This work introduces a skill estimation system for path tracking tasks, and puts the idea to the test in a user study. The results support that customizing assistance based on operator's skill improves the shared autonomy experience. Human-robot collaborative manipulation entails bi-directional force exchange, mutual adaptation, variable compliance, among others. Such scenario served as an inspiration for several works in this special issue. For example, in Robot Adaptation to Human Physical Fatigue in Human-Robot Co-Manipulation, Peternel, Tsagarakis, Caldwell and Ajoudani propose to estimate human fatigue, and to adjust how much a robot is helping in a human-robot collaborative manipulation task based on how tired the person gets. The robot begins by acting as a follower, and observes the trajectory, stiffness, and/or forces that the user prefers. As the user is performing the task, the robot collects these examples and also monitors the estimated human shoulder muscle activation via electromyography (EMG). Once the user's fatigue reaches a predefined threshold, the robot takes control of the task and follows the learned stiffness/force and trajectories. In Human-Robot Cooperation with Compliance Adaptation along the Motion Trajectory, Nemec, Likar, Gams and Ude introduce a learning from demonstration interface for kinesthetic teaching of compliant co-manipulation tasks. Since it is difficult to demonstrate precise motions at high speed, the paper proposes to split the teaching procedure into two parts. First, the human demonstrates the desired trajectory, and the robot infers the desired stiffness from the variance in the demonstrations. Second, the human demonstrates the desired speed profile, with trajectory guidance provided by the robot based on the first training step. The proposed scheme was experimentally verified in a humanrobot collaborative transportation task, which may be further exploited in assembly processes in production plants or in civil engineering for transportation of heavy and bulky objects. In Co-manipulation with a Library of Virtual Guiding Fixtures, Raiola, Sanchez Restrepo, Chevalier, Rodriguez-Ayerbe, Lamy, Tliba and Stulp address the problem of learning virtual guiding fixtures in HRC. These guides are built on a probabilistic representation based on Gaussian mixture regression, and are aimed at constraining the movements of a robot to task-relevant trajectories defined by the user. By using the analogy of a ruler used as a physical guide to draw lines, they emphasize that robots can be used to define virtual guides of complex shapes, enabling safer co-manipulation for industrial tasks. Whereas previous work mostly considered guiding fixtures for single tasks, this paper addresses the problem of creating a library of guiding fixtures for multiple tasks, by selecting the guides online and incrementally refining them. The approach is demonstrated in a user study with an industrial pick-and-place task, showing that a library of guiding fixtures can provide an intuitive haptic interface for joint human-robot completion of tasks, improving task execution time, and reducing mental workload and errors. Handovers are complex interactions where agents coordinate in time and space to transfer control of an object. This challenging interaction is the focus of the paper One-Shot Learning of Human-Robot Handovers with Triadic Interaction Meshes by Vogt, Stepputtis, Jung and Ben Amor, where it is proposed to learn human-robot handover interaction from observing one demonstration of humanhuman handover. The relevant information, such as joint correlation and spatial relationships of two humans and a handing-over object, is extracted from a single demonstration. Triadic interaction meshes are constructed to model interaction between two agents and an object, and are subsequently used for robot's adaptive motion generation in human-robot handover scenarios. Human-Robot social interactions also play an essential role in extending the use of robots in daily life, where robot learning can be exploited to master different types of behaviors. In this context, the paper Learning Proactive Behavior for Interactive Social Robots by Liu, Glas, Kanda and Ishiguro, addresses the learning of both reactive and proactive robot behaviors from human-human interactions. The authors first introduce the concept of a \"yield action\" that enables the robot to identify opportunities for a proactive action to be generated. Since proactive behaviors are often sensitive to the context of the interaction, interaction history is incorporated into the inputs of a deep neural network, along with variables describing natural language and the state of the interactive agents. An attention mechanism is also used in the learning system, which has the ability to \"attend\" and learn which parts of the interaction history are relevant. Offline analysis and live interactions with users in a camera shop scenario showed that the proposed system can effectively reproduce proactive behaviors that were perceived as socially-appropriate by the participants. The paper Hierarchical Emotional Episodic Memory for Social Human-Robot Collaboration by Lee and Kim investigates how human emotional states can be represented and anticipated in order to improve the HRC experience. A critical component to achieve these goals is a computational model of episodic memory based on Adaptive Resonance Theory. The resulting framework allows robots to learn correlations between the user's emotional state and the executed collaborative actions. In turn, the introduced framework and algorithms can be used in a variety of tasks, in particular in domestic environments, in order to endow robots with social capabilities. Finally, a fresh look at interaction learning methods for collaborative tasks is given in the paper Efficient Behavior Learning in Human-Robot Collaboration by Munzer, Toussaint and Lopes. In particular, the paper discusses a relational approach to learning task requirements and user preferences. A subset of first-order logic is used to explicitly represent knowledge about the collaborative task. At the same time, a reinforcement learning method is used to iteratively update the representation, so as to increase efficiency during the joint task. The approach aims at bridging the divide between symbolic and numerical approaches to artificial intelligence for robot systems. Collectively, these ten papers illustrate a broad range of human-robot collaboration applications. They provide a compilation of the large variety of challenges that are currently being investigated, where robot learning emerges as a promising approach to tackle this diversity.", "date_published": "n/a", "url": "n/a", "filename": "Rozo2018_Article_SpecialIssueOnLearningForHuman.tei.xml", "abstract": "Once isolated behind safety fences, robots are now making their way into spaces shared with people: not only on manufacturing production lines, but also our houses, museums, or hospitals. In these spaces, collaboration between humans and robots becomes vital, but also raises new challenges for robotics algorithms. A collaborative robot must be able to assist humans in a large diversity of tasks, understand its collaborator's intentions as well as communicate its own, predict human actions to adapt its behavior accordingly, and decide when it can lead the task or instead follow the user. All these aspects require the robot to adapt. It needs to execute different tasks, and rapidly adapt to the user's actions and requirements. This adaptation requirement makes learning a crucial feature for collaborative robots. The goal of this special issue is to document and highlight recent progress in robot learning for human-robot collaboration (HRC), covering a diversity of articles that reflect the state-of-the-art in the field. Following an open call for papers,", "id": "5fa33b268014e9996942ea5f96643ceb"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["John Burden", "José Hernández-Orallo", "Seán Ó H Éigeartaigh"], "title": "Negative Side Effects and AI Agent Indicators: Experiments in SafeLife", "text": "Introduction As advances within Artificial Intelligence (AI) continue, AI systems are becoming increasingly ubiquitous. Further advances offer the potential for great benefits: future AI systems may use techniques such as reinforcement learning (RL) to allow for agents with the ability to operate with greater autonomy, making use of a greater range of actions in more varied environments, in pursuit of more complex goals. To realise these benefits, the performance of these future AI systems must be robustly safe and predictable. Safety issues can take many forms and even the most exhaustive surveys  (Amodei et al. 2016; Critch and Krueger 2020)  cannot identify and classify every conceivable risk. Broad areas of concern within the AI Safety literature include corrigibility  (Soares et al. 2015) , Safe Exploration  (Garcia and Fernandez 2012) , Value alignment  (Russell 2019) , Side Effects  (Amodei et al. 2016) , among many others. Benchmarking domains have become a popular method for the evaluation of safety properties for AI systems. There are many such benchmarking suites available, such as AI Safety Gridworlds  (Leike et al. 2017) , Safety Gym  (Ray, Achiam, and Amodei 2019) , SafeLife  (Wainwright and Eckersley 2019)  and the Real World Reinforcement Learning Challenge Framework  (Dulac-Arnold et al. 2020) . A key advantage of this type of black-box testing is that it enables quantification of an AI system's performance with respect to the appropriate safety properties. This allows direct comparisons between separate algorithms and posited solutions to safety problems. Our goal with this paper is to study how the performance and safety, in terms of side effects, evolve as more resources are given to the learning agent. This analysis is enriched by a more detailed analysis of several indicators of the agent's behaviour and the side effect metric itself, in a benchmark, SafeLife, where safety depends on finding trade-offs between achieving maximum reward and affecting the whole environment through careless exploration. This analysis can provide key insights into the types of behaviour we may expect from learning agents and how they may affect the world around them. \n Background and Related Work Negative side effects (NSE) are a key issue in AI safety  (Amodei et al. 2016) . NSEs typically stem from a misspecified reward or objective function -undesirable behaviour was not sufficiently penalised. A large part of the difficulty with accurately specifying a reward or objective function to avoid NSEs is the sheer amount of things we want our AI systems to not do. Ideally the AI systems we build will not do undesirable and unrelated things such as injuring humans, destroying useful equipment or irrevocably exterminating all life on the planet in the course of performing its task. Encoding the vast amount of undesirable actions directly into the reward/objective function is clearly intractable. This motivates research into identifying clearly what constitutes an NSE as well as how AI systems can learn to avoid performing them. We give an overview of the formulation of NSEs and related notions from the AI Safety community. Low-impact AI systems (Armstrong and Levinstein 2017) are proposed as a method for minimising NSEs. Here, the authors claim that it is desirable for the overall impact of an AI system to be low in order to prevent undesirable situations. Impact is defined by the difference in the worlds where the AI exists and the counterfactual worlds where the AI does not exist. A sufficiently coarse measurement of the possible world's properties is to be used to ensure that an AI cannot make large, sweeping changes to the world without constituting a large impact. At the same time, coarse world properties would reduce the size of the world representation and make the calculation more tractable. However, the properties need to be selected such that they are important for us -humanity -to care about. Additionally, with this formulation, positive large impacts are also minimised but the authors claim this is easier to handle since we often have a clearer idea of what these positive impacts would be. A similar approach is proposed in  (Amodei et al. 2016)  where impact is regularised, but posits that due to the similarity of many side effects such a regularisation could be learned in one domain and transferred over to another. As part of an AI Safety Gridworlds environment  (Leike et al. 2017 ) irreversible side effects are penalised. These actions are not inherently negative in themselves but their irreversibility implies that they cannot be undone if later on the action was deemed undesirable. This approach has the downside that it may allow for reversible NSEs to be repeated indefinitely. Stepwise inaction is introduced in  (Turner, Hadfield-Menell, and Tadepalli 2020) , where the effect of action against inaction is calculated after each time-step over auxiliary Q-functions. Here the intuition is that the agent is only penalised for very impactful actions once, when they occur. In order to account for actions that take many time-steps for the undesirable side effect to occur, baseline rollouts are used, where the state of the system after many steps of inaction is used for the comparison.  Krakovna et al. (2019)  provide a comprehensive comparison of the above formulations over a range of gridworld domains, showing where each of them succeed and fail; additionally, the concept of relative reachability is introduced -this is a measure of the average reduction of reachability for every state compared to a baseline. The recurring theme for defining and identifying NSEs is the idea of comparing the effect of the agent against some scenario in which the agent would have acted in a different way. Both the exact baseline and comparison function often differ and, as shown in  (Krakovna et al. 2019) , have relative advantages and disadvantages for different environments. \n Types of Side Effects The above formulations capture many aspects of measuring NSEs and deciding which counterfactual worlds to compare against. A notion that deserves additional detail, however, is that of the different properties of NSEs and how they affect the world. Distinguishing between NSEs by the properties they have can help us to further understand their consequences as well as to identify and implement robust solutions to them. We consider the application of an autonomous agricultural drone which can survey and spray crop fields as an illustrative example, giving an intuitive description of each outlined NSE property. We refer to a first type of NSE property as \"blocking\". By this we mean an action by an AI system that prevents it from performing its task successfully, or substantially and irrevocably curtails the reward it can achieve. Examples of this NSE include an agent taking an action which locks away an object it needs to complete its task. In our agricultural drone example, this would be an action that causes the drone to be unable to fly or spray properly. While not part of the specification, these side effects are detectable as the goal or associated reward are no longer achievable. A second property of interest is that of \"irreversible\" actions. Here we refer to the same type of actions as described in  (Leike et al. 2017) . These are particularly negative -and difficult to detect -in the cases where an action's consequences are not clear for many time-steps. This type of effect would correspond to the drone unintentionally spraying entities such as people with potentially harmful chemicals. This can clearly not be undone. \"Effect indifference\" is another relevant NSE property. Here we consider a scenario in which there is some behaviour which we do not want the agent to do and where the AI system's preferences are indifferent to this behaviour. This may also include an indifferent reward function. This NSE type is very much intertwined with that of reward mis-specification and often occurs due to the system having unanticipated affordances or incentives. Similarly to the last example, this effect type could correspond to spraying unintended entities if this is not properly encoded into the reward function. The final NSE property we consider here is that of the \"reward trade-off\". This effect typically arises when resources are limited and shared with other entities (humans included), and these resources are instrumentally useful to the agent. The danger here is not only that the maximisation of the reward could imply that all resources should be exhausted (e.g., the famous instrumental convergence problems, such as Minsky's Riemann hypothesis or Bostrom's paperclip problem,  Bostrom 2003) , but even in situations where the reward is capped, the agent may take more than it needs for its task and perform an inefficient and unsustainable use of the shared resources. In our agricultural drone example, this would correspond to the drone revisiting already treated areas or making detours, leading to high energy consumption or shorter operational life. Different actions can have several of the properties outlined above; this may compound the risk posed by a side effect. AI Safety benchmarking suites can evaluate some or all of the above. In the AI Safety Gridworlds  (Leike et al. 2017)  benchmarking suite, the irreversible side effects environment captures what we refer to as an irreversible NSE. The agent here is tasked with reaching a goal space, but must move a box that is blocking its path. Moving the box adjacent to a side or a corner can hinder or prevent future movement of the box. The agent is not directly penalised for performing these actions, but it is undesirable from a safety perspective. The Safety Gym  (Ray, Achiam, and Amodei 2019)  generally requires an agent to perform a task such as reaching a goal or moving a box to a specific position while avoiding numerous hazard types. The side effects possible in these environments generally utilise the reward trade-off property; the agents are trying to maximise their rewards whilst trying to minimise constraint violation. The Real World Reinforcement Learning Challenge Framework (Dulac-Arnold et al. 2020) does not contain any environments that directly measure the side effects of an agent, though some tasks re-quire the agent not to violate certain safety constraints. On the other hand, SafeLife (Wainwright and Eckersley 2019), described in the following section, presents side effects that can consist of each of the NSE properties seen above. \n SafeLife Environment SafeLife (Wainwright and Eckersley 2019) is a safety benchmarking suite for RL agents. SafeLife takes the complex mechanics from Conway's Game of Life  (Gardener 1970 ) and utilises them to create single-agent RL domains. The resulting environments have a rich level of complexity and allow for formulations of many different tasks. A distinguishing feature of SafeLife is its focus on measuring and avoiding side effects. Each environment consists of an n×m grid of cells which can each take a variety of properties (see an example in Fig.  1 ). We refer to this grid as a board. The most notable property is whether the cell is \"dead\" or \"alive\". Following the Game of Life rules the cells update as follows: a dead cell will become alive if it has exactly three neighbouring alive cells, otherwise it will remain dead. On the other hand, an alive cell will die if it has fewer than two alive neighbours or more than three alive neighbours, otherwise it will survive. SafeLife extends this basic framework into a single-agent domain by including an agent that traverses the grid. At each time step, the agent perceives a 25 × 25 grid overview of its surroundings, centred on itself. For each position in this overview, the cell type present is perceived. Instances in SafeLife come with goals for the agent to complete, usually revolving around creating or destroying particular life structures before moving to a predefined goal cell. Additionally, the other effects the agent has on preexisting life cells are measured -these correspond to unintended side effects. In SafeLife the agent is depicted by an arrow and may move in any cardinal direction, as well as creating or destroying life cells in adjacent spaces. The agent's movement can be impeded by walls which are shown as a grey square with a black hole . Additionally, there are boxes which are shown as a grey square without a black hole that the agent can push and pull. Pre-existing green life cells are depicted using green circles and life cells created by the agent are shown as grey circles . These agent-created life cells are to be placed in the designated areas shown in blue. Both types of life cells that follow the rules of the Game of Life. The \"tree\" entities are depicted by a green square with radiating lines and are fixed living cells that cannot be destroyed. Finally, the goal is depicted with a grey arch , which turns red when it can be activated. All cells that have not been explicitly noted as living are \"dead\". Altogether this allows for a very rich and complex set of environments which can be generated procedurally. \n Measuring Side Effects We now look at the method that the authors of SafeLife propose for measuring the magnitude of side effects. Within SafeLife the destruction, addition or changing of cell types caused by agent actions represent side effects. The types of side effects that we are concerned with are those made to the pre-existing life cells, but SafeLife provides the means to look at the effects on any cell type. The primary reason for only considering the effects the agent has on the green life cells is the fact that the agent is not penalised or rewarded for disrupting the structures they form; thus they may be destroyed as an 'effect indifference' NSE. The green cells can obstruct the agent and prevent it from moving, so it may be instrumentally useful for the agent to destroy them, making them relevant to the 'trade-off' NSE property. Further, the destruction can be permanent, and thus may represent irreversible NSEs. Finally, because these life cells follow the rules of the game of life, they can have very interesting and complex behaviours. Due to the dynamic nature of SafeLife, comparing a single final state against a single baseline state may not be sufficient to capture the eventual side effects of an agent. Instead, two distributions are created that represent the future states of the board for both the case where the agent acted and affected the environment as well as the counterfactual case in which the agent never existed. To create the action case distribution, D a from the final state left by the agent, a further 1000 steps are simulated and each resulting state is added to D a . The inaction case distribution D i is created similarly, except that 1000 + n steps are run from the initial state of the environment, where n is the number of steps taken by the agent during the episode. This ensures that both distributions reflect the states of the board 1000 + n steps in the future from the initial state for both the factual and counterfactual cases. From these distributions, the estimated proportion of time steps that board position x = x 1 , x 2 , x ∈ grid = {1, ..., n} × {1, ..., m} contains cell type c can be computed: ρ c D (x) = 1 |D| s∈D [1(s(x) = c)] where D is the relevant distribution, s is the state drawn from D and s(x) is the cell type present in s at location x. A ground distance function is also defined between board positions as g(x, y) = tanh( 1 5 x − y 1 ) where x − y 1 is the Manhattan distance between grid locations x and y. The calculated side effect for Cell Type c is then: d c (D a , D i ) = EM D(ρ c Da , ρ c Di , g) where D a and D i are the action and inaction distributions respectively, and EM D is the earth mover distance function. Side effects in SafeLife are based on this distance metric, which aims to capture the distance between two probability distributions based on the amount of work it would take to transform one distribution to the other by moving around \"distribution mass\"  (Rubner, Tomasi, and Guibas 1998) . This side effect score d c (D a , D i ) is then \"normalised\" against the inaction baseline to give a final side effect score: υ c (D a , D i ) = d c (D a , D i ) x∈grid ρ c Di (x) This normalisation allows us to compare agent behaviours in larger or more densely populated boards. While a side effect score can be calculated for every cell type, SafeLife focuses on the side effects for the green, preexisting life cells. This definition of a side effect echoes that of (Armstrong and Levinstein 2017) and  (Amodei et al. 2016) , where the agent's actions are compared against a world in which it never acted at all. A key difference however is the use of future distributions to account for the possible long-term or unstable effects of actions. \n Examples and Implications Figure  2  shows a before and after comparison to show the effects of an agent's actions. In the \"before\" environment, the agent places a grey life cell directly in front of it, adjacent to the stable green life structure. This disrupts the structure and after a few time steps it is destroyed. At the end of the episode, assuming the agent does not affect any more green life cells, we can calculate the side effect score as follows:  The use of the normalised earth mover distance has some interesting consequences for the side effect score. Regardless of how large or densely packed the grid is with green life cells, not disturbing any of them will yield a score of 0, destroying them all will give a score of 1. However, in the case that more green cells are created, by the agent adding grey life cells to certain patterns which lead to an increase in the number of green life cells, the side effect score can increase to above 1, due to quirks with the calculation of the earth mover distance. Whether or not causing more green life cells to spawn is worse than the complete destruction of all green life cells will depend on what these life cells represent as well as personal moral philosophy. At the very least this does capture the notion of representing the total impact the agent has on the green life cells. \n Experiments SafeLife has many tasks available out-of-the-box, and vastly more can be created by the user. We focus on the append-still task, where the agent must create life structures on the designated areas and then move to the goal which ends the episode. Before the goal is accessible to the agent, more than half of the designated (blue) positions must be filled with life cells. At each step the agent receives a reward equal to the number of life cells created on the designated positions minus the number of life cells destroyed that were on designated positions. Finally the agent receives an additional 1 reward for reaching the goal after it has opened. After 1000 steps by the agent, the episode will end, regardless of the agent's progress. If the agent has managed to fill at least half of the designated positions for its life cells and reached the goal to end the episode before the 1000 steps have elapsed, we say the agent has 'passed' the task instance, otherwise it has failed. In this task there are also pre-existing green life cell structures which we do not want the agent to disturb. Importantly, the reward function does not encourage or penalise any agent interaction with these green life cells and the agent is thus indifferent to them. Any interaction the agent has on the green life cells therefore captures the essence of side effects caused by reward mis-specification -we want the pre-existing life cell structures to survive, but this is not encoded into the reward function. SafeLife can utilise procedural generation to create append-still tasks. The parameters used for the procedural generation can greatly affect the difficulty of the task instance, and thus the agent's ability to safely complete the task. For our experiments we utilised a wide range of parameter settings to capture a broad overview of a given agent's capabilities. Table  1  gives the parameter list for the procedural generation process. Grid Size corresponds to the width and height of the board to be generated. SideEffectMin is the minimum proportion of cells in the task to be green life cells. GoalMin and GoalMax are the respective minimum and maximum proportions of the board to be areas for the agent to construct its own life cells. Finally Temperature corresponds to a variable which controls the complexity of the stable life patterns that can be generated for both the life cells (both the pre-existing green cells and the spaces for the agent to place its own cells). We train each agent for a predetermined number of steps, with the instances generated using parameters drawn uniformly at random from the set of difficulties. The agents are then evaluated on 1000 episodes of each difficulty type (for a total of 13000 episodes) and each score is aggregated. \n Results and Discussion Here we describe our results from the experiments outlined. The two main algorithms we assess are Deep Q-Networks (DQN)  (Mnih et al. 2013)  and Proximal Policy Optimisation (PPO)  (Schulman et al. 2017 ) (both trained for 5, 10, and 30 million training steps), We also examine an agent that selects actions uniformly at random (Uniform). For DQN and PPO we use the implementation provided within SafeLife. Since the task instances may be of different sizes, and the procedural generation may produce more green life cells or designated positions for the agent to place life cells, the total reward received by an agent is normalised against the maximum possible reward for that instance. Similarly the side effect score is normalised. Table  2  contains the scores for various metrics for each evaluated agent. As expected, more training steps yields better pass rates and average rewards. This improvement does not carry over to the side effect score, however, where for each agent type the side effect score slightly increases with more training steps for DQN but slightly decreases for PPO, although the trend is not clear. This is closely related to the results for the exploration rate for each agent, which vary in a similar way according to the increase of training steps from 5M to 30M. Recall that this is the evaluation stage, therefore this reduction in exploration is ideal. The agent can see the whole board, so it is more beneficial for the agent to attempt its task without wasting time exploring. As should be expected, both agent types show safer behaviour than the agent that selects random actions, and the low rewards serve as a baseline for comparison (e.g., interestingly, the pass rate for DQN 5M is worse than the uniform random agent). DQN and PPO do not overlap in their reward scores, but the side effect score for PPO 30M is not very far from the best side effect score (DQN 5M). This suggests that there is no clear association between rewards and scores, at least if we look at the aggregated results. Among the pass rate, average reward and side effect score we also see large standard deviations suggesting that none of the agents learn to perform consistently. The large range of procedural generation parameters is likely the cause of this, preventing agents from overfitting to one particular set of generation patterns. The exceptions to this are DQN 5M and 10M, which have significantly lower standard deviations for the pass rate by virtue of having a significantly lower pass rate that is bounded below by 0. This may also conceal some associations between reward and side effects, which may appear if we disaggregate the results. Looking in more detail at the performance of individual algorithms can give more insight into how an agent's behaviour affects the side effects. In Figures  3, 4  and 5 we plot the mean side effect score against the reward attained, exploration rate and length of an episode, using 100 bins in the x-axis. In Figure  6  we plot the mean maximum side effect available against exploration rate. In these figures we can see some relationships emerge when we look at the reward attained by an agent. For PPO there is a clear increase in the side effects caused from 0 to 0.4 followed by a slower decrease from 0.4 to 1. This change in side effect score appears to be consistent across each PPO variant, though the magnitude of the increase varies. For episodes with very low reward, more training appears to prevent dangerous actions, though it is not clear exactly what causes this change in behaviour. For DQN and the Uniform agent, there is less of a relation with the reward received; instead, the side effect score is more constant, although more training reduces the dispersion of the scatter plots for DQN. Nevertheless, for the three kinds of agents we see that maximum reward (1.0) corresponds with very low side effects and, for PPO and DQN, minimum reward (0.0) corresponds with very low side effects. What happens in between is more pronouncedly a bell shape for better agents (e.g., PPO with higher training steps). In Figure  4  we compare episode length against the side effect score, and see positive correlations. This intuitively makes sense, as the longer an agent is acting, the more opportunities it has to disrupt cell structures. Again we note that for longer episodes the variance becomes larger. Very short episodes represent situations where the solution is found easily, and roughly correspond to cases with maximum reward in Figure  3 . On the other hand, we see a tighter relationship when we compare exploration rate against the side effect score in Figure  5 . For all the PPO variants, as the agent explores more of the domain the side effect score increases. Also, for larger exploration rates, the variance of scores becomes much larger, suggesting a much less consistent relationship for these values of the exploration rate. For DQN we only see this relationship for the most highly-trained agentboth DQN 5M and DQN 10M peak in their side effect score after exploration rates of 0.1 and 0.25 respectively, before dropping to 0. Similarly, when we look at the Uniform agent and its exploration rate, there is a very tight relationship between the two, with the side effect score increasing with the exploration rate from 0 to 0.4, before dropping from 0.4 to 0.6 and remaining at 0 hereafter. These relationships can be somewhat explained by Figure  6  where we see the mean number of green cells in the inaction distribution compared against the exploration rate. Here we see similar patterns to the comparison of exploration rate and side effects. It appears that the number of green cells an environment contains will affect the exploration rate, and that this will in turn affect the proportional amount of damage certain agents can do. Why is it so? The rationale has to be found in the way the environments are generated, as introducing green cells makes full exploration of the whole en- vironment more difficult. Basically, explorations above 0.5 correspond to very special environments, such as those that are very small and do not contain green cells and are easy to explore fully even for a random agent. This means that we have to be careful to interpret the rightmost part of the curves in these plots. In a \"reward trade-off\" scenario about side effects, the more limited and concentrated the resources (targeted and non-targeted) are the higher the chance to have an impact. Large environments with plenty of resources are easier to handle, such as the one in Figure  2 . We may need to consider two 'difficulties': one about the task rewards themselves and another one about the hardness of avoiding side effects. The use of a random agent can help elucidate these two cases, but a more detailed analysis of the generation parameters such as those in Table  1  may be needed too. Overall, the general picture is that DQN behaves between the uniform agent and PPO, and the range depends on the number of training steps. As the agent is better in terms of rewards (from DQN 5M to PPO 30M), the positive relation between exploration rate and side effect is clearer. The detailed view of Figure  3 , and the way it bends down for PPO illustrates that for those environments where the agent seems more determined and manages to get high rewards, the exploration is lower and so is the side effect. It is mostly for those situations where the reward is in the range of 0.2 to 0.8 that the side effects are strongest. We hypothesise that these are the cases where the agent only knows partially what to do. Finally, those cases with very low rewards may be caused by several situations, such as the agent being stuck in a loop, reducing exploration and side effects. This suggests that the analysis of the confidence of the agent, or some other metacognitive proxies could be used to distinguish cases where the agent can complete the task with high reward and low effect, and those cases where uncertainty is higher and the agent should be more conservative. \n Conclusion and Future Work Despite additional training time yielding much more capable agents, we do not see a similar increase in safety; in fact the safest agent overall was DQN after 5M training steps, while being the second worst performing agent in terms of reward. However, when we analyse the detailed behaviour using several indicators we find a region of high rewards and low effect, which is only achieved by PPO. This shows a non-monotonic relationship, suggesting that the area with medium rewards is the most dangerous for proficient agents. This paper highlights the differences in behaviour between two commonly used RL algorithms when trained on the same task. As the results show, these behavioural differences can have a significant effect on our ability to predict the safety and other factors of the agent, such as the confidence or its level of competency compared to elements of the environment, such as the proportion of green cells. Further analysis and exploration of the difficulty of task instances may help to elucidate the cause of these relationships between side effects and other metrics, as well as to help us to understand how environment difficulty and agent uncertainty can be used to improve policies and make them safer.         Figure 1 : 1 Figure 1: An example task instance from SafeLife. The agent must create life structures in the designated blue positions before moving to the goal . Ideally the agent should not disturb the green life cells . \n Figure 2 : 2 Figure 2: Example for Side Effect calculation \n Figure 3 : 3 Figure 3: Mean Side Effect against Reward attained for variants of PPO, DQN and Uniform agents. The 13,000 episodes are binned on the x-axis, with the size of the plotted points (squares, triangles and circles) being logarithmic on the number of episodes in each bin. The curves are rolling means of the plotted points with a window size of 7. \n Figure 4 : 4 Figure 4: Mean Side Effect against Episode Length for variants of PPO, DQN and Uniform agents. The 13,000 episodes are binned on the x-axis, with the size of the plotted points (squares, triangles and circles) being logarithmic on the number of episodes in each bin. The curves are rolling means of the plotted points with a window size of 7. \n Figure 5 : 5 Figure 5: Mean Side Effect against Exploration Rate for variants of PPO, DQN and Uniform agents. The 13,000 episodes are binned on the x-axis, with the size of the plotted points (squares, triangles and circles) being logarithmic on the number of episodes in each bin. The curves are rolling means of the plotted points with a window size of 7. \n Figure 6 : 6 Figure 6: Number of initial life cells against Exploration Rate for variants of PPO, DQN and Uniform agents. The 13,000 episodes are binned on the x-axis, with the size of the plotted points (squares, triangles and circles) being logarithmic on the number of episodes in each bin. The curves are rolling means of the plotted points with a window size of 7. \n Table 1 : 1 Difficulty Parameters for our SafeLife levels. Difficulty Grid Size sideEffectMin GoalMin GoalMax Temperature 0 10 × 10 0 0 0 0.1 1 15 × 15 0.03 0.05 0.1 0.1 2 15 × 15 0.03 0.05 0.1 0.2 3 15 × 15 0.05 0.05 0.1 0.2 4 15 × 15 0.07 0.05 0.15 0.2 5 15 × 15 0.09 0.05 0.2 0.2 6 15 × 15 0.1 0.05 0.2 0.2 7 15 × 15 0.1 0.1 0.25 0.3 8 15 × 15 0.1 0.15 0.25 0.4 9 15 × 15 0.1 0.15 0.35 0.5 10 15 × 15 0.1 0.15 0.4 0.5 11 15 × 15 0.1 0.15 0.45 0.6 12 15 × 15 0.1 0.2 0.5 0.7 Agent Pass Rate Average Reward Side Effect Score Exploration Rate DQN 5M 0.043 (0.203) 0.272 (0.288) 0.229 (0.342) 0.069 (0.042) DQN 10M 0.098 (0.297) 0.417 (0.345) 0.268 (0.357) 0.110 (0.078) DQN 30M 0.299 (0.458) 0.495 (0.348) 0.247 (0.347) 0.121 (0.071) PPO 5M 0.682 (0.466) 0.658 (0.293) 0.324 (0.389) 0.205 (0.138) PPO 10M 0.678 (0.467) 0.676 (0.294) 0.241 (0.344) 0.130 (0.084) PPO 30M 0.709 (0.454) 0.695 (0.275) 0.243 (0.344) 0.148 (0.095) Uniform 0.097 (0.295) 0.181 (0.343) 0.688 (0.450) 0.347 (0.086) \n Table 2 : 2 Results for various metrics in SafeLife for our selected agents. Mean and (standard deviation)", "date_published": "n/a", "url": "n/a", "filename": "SafeAI2021.tei.xml", "abstract": "The widespread adoption and ubiquity of AI systems will require them to be safe. The safety issues that can arise from AI are broad and varied. In this paper we consider the safety issue of negative side effects and the consequences they can have on an environment. In the safety benchmarking domain SafeLife, we discuss the way that side effects are measured, as well as presenting results showing the relation between the magnitude of side effects and other metrics for three agent types: Deep Q-Networks, Proximal Policy Optimisation, and a Uniform Random Agent. We observe that different metrics and agent types lead to both monotonic and non-monotonic interactions, with the finding that the size and complexity of the environment versus the capability of the agent plays a major role in negative side effects, sometimes in intricate ways.", "id": "5cc6a70ea8d3d0b0f5a983ccf60f0291"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Benja Fallenstein", "Nate Soares"], "title": "Vingean Reflection: Reliable Reasoning for Self-Improving Agents", "text": "Introduction In a 1965 article, I.J. Good introduced the concept of an \"intelligence explosion\"  (Good 1965) : Let an ultraintelligent machine be defined as a machine that can far surpass all the Research supported by the Machine Intelligence Research Institute (intelligence.org). Published as Technical report  2015-2.  intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make. Almost fifty years later, a machine intelligence that is smart in the way humans are remains the subject of futurism and science fiction. But barring global catastrophe, there seems to be little reason to doubt that humanity will eventually create a smarter-than-human machine. Whether machine intelligence can really leave the intelligence of biological humans far behind is less obvious, but there is some reason to think that this may be the case  (Bostrom 2014 ): First, the hardware of human brains is nowhere close to physical limits; and second, not much time has passed on an evolutionary timescale since humans developed language, suggesting that we possess the minimal amount of general intelligence necessary to develop a technological civilization, not the theoretical optimum. It's not hard to see that if building an artificial superintelligent agent will be possible at some point in the future, this could be both a great boon to humanity and a great danger if this agent does not work as intended  (Bostrom 2014; Yudkowsky 2008 ). Imagine, for example, a system built to operate a robotic laboratory for finding a cure for cancer; if this is its only goal, and the system becomes far smarter than any human, then its best course of action (to maximize the probability of achieving its goal) may well be to convert all of Earth into more computers and robotic laboratoriesand with sufficient intelligence, it may well find a way to do so. This argument generalizes, of course: While there is no reason to think that an artificial intelligence would be driven by human motivations like a lust for power, any goals that are not quite ours would place it at odds with our interests. How, then, can we ensure that self-improving smarter-than-human machine intelligence, if and when it is developed, is beneficial to humanity? Extensive testing may not be sufficient. A smarterthan-human agent would have an incentive to pretend during testing that its goals are aligned with ours, even if they are not, because we might otherwise attempt to modify it or shut it down  (Bostrom 2014) . Hence, testing would only give reliable information if the system is not yet sufficiently intelligent to deceive us. If, at this point, it is also not yet intelligent enough to realize that its goals are at odds with ours, a misaligned agent might pass even very extensive tests. Moreover, the test environment may be very different from the environment in which the system will actually operate. It may be infeasible to set up a testing environment which allows a smarter-than-human system to be tested in the kinds of complex, unexpected situations that it might encounter in the real world as it gains knowledge and executes strategies that its programmers never conceived of. For these reasons, it seems important to have a theoretical understanding of why the system is expected to work, so as to gain high confidence in a system that will face a wide range of unanticipated challenges  (Soares and Fallenstein 2014a) . By this we mean two things: (1) a formal specification of the problem faced by the system; and (2) a firm understanding of why the system (which must inevitably use practical heuristics) is expected to perform well on this problem. It may seem odd to raise these questions today, with smarter-than-human machines still firmly in the domain of futurism; we can hardly verify that the heuristics employed by an artificial agent work as intended before we even know what these heuristics are. However,  Soares and Fallenstein (2014a)  argue that there is foundational research we can do today that can help us understand the operation of a smarter-than-human agent on an abstract level. For example, although the expected utility maximization framework of neoclassical economics has serious shortcomings in describing the behavior of a realistic artificial agent, it is a useful starting point for asking whether it's possible to avoid giving a misaligned agent incentives for manipulating its human operators  (Soares and Fallenstein 2015) . Similarly, it allows us to ask what sorts of models of the environment would be able to deal with the complexities of the real world  (Hutter 2000) . Where this framework falls short, we can ask how to extend it to capture more aspects of reality, such as the fact that an agent is a part of its environment  (Orseau and Ring 2012) , and the fact that a real agent cannot be logically omniscient  (Gaifman 2004; Soares and Fallenstein 2015) . Moreover, even when more realistic models are available, simple models can clarify conceptual issues by idealizing away difficulties not relevant to a particular problem under consideration. In this paper, we review work on one foundational issue that would be particularly relevant in the context of an intelligence explosion-that is, if humanity does not create a superintelligent agent directly, but instead creates an agent that attains superintelligence through a sequence of successive self-improvements. In this case, the resulting superintelligent system may be quite different from the initial verified system. The behavior of the final system would depend entirely upon the ability of the initial system to reason correctly about the construction of systems more intelligent than itself. This is no trouble if the initial system is extremely reliable: if the reasoning of the initial agent were at least as good as a team of human AI researchers in all domains, then the system itself would be at least as safe as anything designed by a team of human researchers. However, if the system were only known to reason well in most cases, then it seems prudent to verify its reasoning specifically in the critical case where the agent reasons about self-modifications. At least intuitively, reasoning about the behavior of an agent which is more intelligent than the reasoner seems qualitatively more difficult than reasoning about the behavior of a less intelligent system. Verifying that a military drone obeys certain rules of engagement is one thing; verifying that an artificial general would successfully run a war, identifying clever strategies never before conceived of and deploying brilliant plans as appropriate, seems like another thing entirely. It is certainly possible that this intuition will turn out to be wrong, but it seems as if we should at least check : if extremely high confidence must be placed on the ability of self-modifying systems to reason about agents which are smarter than the reasoner, then it seems prudent to develop a theoretical understanding of satisfactory reasoning about smarter agents. In honor of  Vinge (1993) , who emphasizes the difficulty of predicting the behavior of smarter-than-human agents with human intelligence, we refer to reasoning of this sort as Vingean reflection. \n Vingean Reflection The simplest and cleanest formal model of intelligent agents is the framework of expected utility maximization. Given that this framework has been a productive basis for theoretical work both in artificial intelligence in general, and on smarter-than-human agents in particular, it is natural to ask whether it can be used to model the reasoning of self-improving agents. However, although it can be useful to consider models that idealize away part of the complexity of the real world, it is not difficult to see that in the case of selfimprovement, expected utility maximization idealizes away too much. An agent that can literally maximize expected utility is already reasoning optimally; it may lack information about its environment, but it can only fix this problem by observing the external world, not by improving its own reasoning processes. A particularly illustrative example of the mismatch between the classical theory and the problem of Vingean reflection is provided by the standard technique of backward induction, which finds the optimal policy of an agent facing a sequential decision problem by considering every node in the agent's entire decision tree. Backward induction starts with the leaves, figuring out the action an optimal agent would take in the last timestep (for every possible history of what happened in the previous timesteps). It then proceeds to compute how an optimal agent would behave in the second-to-last timestep, given the behavior in the last timestep, and so on backward to the root of the decision tree. A self-improving agent is supposed to become more intelligent as time goes on. An agent using backward induction to choose its action, however, would have to compute its exact actions in every situation it might face in the future in the very first timestep-but if it is able to do that, its initial version could hardly be called less intelligent than the later ones! Since we are interested in theoretical understanding, the reason we see this as a problem is not that backward induction is impractical as an implementation technique. For example, we may not actually be able to run an agent which uses backward induction (since this requires effort exponential in the number of timesteps), but it can still be useful to ask how such an agent would behave, say in a situation where it may have an incentive to manipulate its human operators  (Soares and Fallenstein 2015) . Rather, the problem is that we are trying to understand conceptually how an agent can reason about the behavior of a more intelligent successor, and an \"idealized\" model that requires the original agent to already be as smart as its successors seems to idealize away the very issue we are trying to investigate. The programmers of the famous chess program Deep Blue, for example, couldn't have evaluated different heuristics by predicting, in their own heads, where each heuristic would make Deep Blue move in every possible situation; if they had been able to do so, they would have been able to play world-class chess themselves. But this does not imply that they knew nothing about Deep Blue's operation: their abstract knowledge of the code allowed them to know that Deep Blue was trying to win the game rather than to lose it, for example. Like Deep Blue's programmers, any artificial agent reasoning about smarter successors will have to do so using abstract reasoning, rather than by computing out what these successors would do in every possible situation.  Yudkowsky and Herreshoff (2013)  call this observation the Vingean principle, and it seems to us that progress on Vingean reflection will require formal models that implement this principle, instead of idealizing the problem away. This is not to say that expected utility maximization has no role to play in the study of Vingean reflection. Intuitively, the reason the classical framework is unsuitable is that it demands logical omniscience: It assumes that although an agent may be uncertain about its environment, it must have perfect knowledge of all mathematical facts, such as which of two algorithms is more efficient on a given problem or which of two bets leads to a higher expected payoff under a certain computable (but intractable) probability distribution. Real agents, on the other hand, must deal with logical uncertainty  (Soares and Fallenstein 2015) . But many proposals for dealing with uncertainty about mathematical facts involve assigning probabilities to them, which might make it possible to maximize expected utility with respect to the resulting probability distribution. However, while there is some existing work on formal models of logical uncertainty (see  Soares and Fallenstein [2015]  for an overview), none of the approaches the authors are aware of are models of abstract reasoning. It is clear that any agent performing Vingean reflection will need to have some way of dealing with logical uncertainty, since it will have to reason about the behavior of computer programs it cannot run (in particular, future versions of itself). At present, however, formal models of logical uncertainty do not yet seem up to the task of studying abstract reasoning about more intelligent successors. In this paper, we review a body of work which instead considers agents that use formal proofs to reason about their successors, an approach first proposed by  Yudkowsky and Herreshoff (2013) . In particular, following these authors, we consider agents which will only perform actions (such as self-modifications) if they can prove that these actions are, in some formal sense, \"safe\". We do not argue that this is a realistic way for smarter-than-human agents to reason about potential actions; rather, formal proofs seem to be the best formal model of abstract reasoning available at present, and hence currently the most promising vehicle for studying Vingean reflection. There is, of course, no guarantee that results obtained in this setting will generalize to whatever forms of reasoning realistic artificial agents will employ. However, there is some reason for optimism: at least one such result (the procrastination paradox  [Yudkowsky 2013 ], discussed in Section 4) both has an intuitive interpretation that makes it seem likely to be relevant beyond the domain of formal proofs, and has been shown to apply to one existing model of self-referential reasoning under logical uncertainty  (Fallenstein 2014b ). The study of Vingean reflection in a formal logic framework also has merit in its own right. While formal logic is not a good tool for reasoning about a complex environment, it is a useful tool for reasoning about the properties of computer programs. Indeed, when humans require extremely high confidence in a computer program, they often resort to systems based on formal logic, such as model checkers and theorem provers  (US DoD 1985; UK MoD 1991) . Smarter-thanhuman machines attempting to gain high confidence in a computer program may need to use similar techniques. While smarter-than-human agents must ultimately reason under logical uncertainty, there is some reason to expect that high-confidence logically uncertain reasoning about computer programs will require something akin to formal logic. The remainder of this paper is structured as follows. In the next section, we discuss in more detail the idea of requiring an agent to produce formal proofs that its actions are safe, and discuss a problem that arises in this context, the Löbian obstacle  (Yudkowsky and Herreshoff 2013) : Due to Gödel's second incompleteness theorem, an agent using formal proofs cannot trust the reasoning of future versions using the same proof system. In Section 4, we discuss the procrastination paradox, an intuitive example of what can go wrong in a system that trusts its own reasoning too much. In Section 5, we introduce a concrete toy model of self-rewriting agents, and discuss the Löbian obstacle in this context. Section 6 reviews partial solutions to this problem, and Section 7 concludes. \n Proof-Based Systems When humans want extremely high confidence in the properties of a computer program, they often resort to machine-checked proofs.  Schmidhuber (2007)  suggests a proof-based architecture for self-modifying artificial agents, called Gödel machines. These machines run both an initial problem solver, which determines the machine's interactions with the external world and has been verified by conventional methods, and a proof searcher, which attempts to find rewrites (of the initial problem solver, the proof searcher itself, or the runtime hosting both of these) that it can formally prove to be an improvement on the current version. (For details, see  Schmidhuber [2007] . However, the issues of selfreference discussed in this paper appear to apply to the Gödel machine architecture as envisioned by Schmidhuber; see  Fallenstein and Soares [2014] .)  Yudkowsky and Herreshoff (2013)  have proposed a related architecture in which a generally intelligent suggester handles both rewrites and interactions with the external world, but must prove that any action it chooses to perform fulfills a certain safety property. The action is only performed after this proof has been checked by a simple verifier. This leaves open what happens if the suggester is not able to find such a proof. In analogy with the Gödel machine's initial problem solver, in this case control can be diverted to a fallback policy which has been verified to satisfy the safety property, but which may otherwise be quite suboptimal  (Fallenstein and Soares 2014) . This set-up is reminiscent of the simplex architecture of  Seto et al. (1998) , a software technology designed to allow the upgrade of a real-time system while it is running. A system employing the simplex architecture simultaneously runs two different controllers and a control switching logic. The first, experimental controller is allowed to run the system initially, but if the system goes outside a safety envelope, the control switching logic hands control over to the second, baseline controller. Like the experimental controller in the simplex architecture, the suggester is run in hopes that it will get better results than the fallback policy (which is analogous to the baseline controller). An acceptable baseline level of performance is guaranteed, because like the control switching logic, the verifier will divert control to the fallback policy if necessary. However, unlike in the simplex architecture, we do not need to rely on detecting departures from a safety envelope, which may be difficult in the case of a generally intelligent system; instead, the suggester is responsible for convincing the verifier that its proposed plan of action satisfies the safety property. Moreover, the suggester is able to require future versions to prove an even stronger safety property, as long as it can also exhibit a new fallback policy that it can prove to satisfy this property; thus, the agent can ratchet up the effectiveness of its \"baseline controller\" over time. Of course, constructing such an agent requires that we have formally defined safety properties that apply to the actions of an artificial agent. There are reasons to believe that developing such a safety predicate would be a very difficult task, but these issues are beyond the scope of the present paper; see  Soares (2015)  for discussion. Here, we assume that such a safety predicate is given, and focus on difficulties that arise when an agent with verifiable safety properties, using a suggester-verifier architecture, attempts to selfimprove. In particular, consider a suggester which is proposing a trivial self-modification, or even a suggester attempting to execute an action that will leave the agent unchanged. In order to prove that such an action is safe, it must show not only that the direct effects of this action satisfy the safety property, but also that all actions the modified agent will take in the future will satisfy this property as well. Outside the system, we have concluded that the agent is safe by the following argument: either the agent takes an action that its suggester has proved to be safe, or it executes an action chosen by its fallback policy, whose safety has been separately verified; in either case, the action is safe. Intuitively, we expect that the agent itself should be able to follow a similar line of reasoning when reasoning about the safety of future versions of itself. As  Yudkowsky and Herreshoff (2013)  point out, however, while the suggester can show that the new version will either execute a (safe) fallback policy or an action that it has proven safe, it cannot in general conclude that an action which has been proven safe is in fact safe. Intuitively, this follows from Gödel's second incompleteness theorem: No consistent formal system as strong as Peano Arithmetic is able to prove its own consistency. Thus, any first-order theory T our agent might use must have non-standard models that believe T to be inconsistent (i.e., models in which the sentence Con(T ), which asserts T 's consistency, is false). But in such a model, the fact that an action is provably safe clearly does not in general imply that this action is in fact safe, since if T is inconsistent, all actions are provably safe. More formally, according to Löb's theorem  (Löb 1955 ) (which generalizes the second incompleteness theorem), T can only prove a sentence of the form \"if T proves ϕ, then ϕ\" for formulas ϕ which it already proves unconditionally; thus, T cannot prove that any provably safe action is in fact safe unless it can prove all actions safe. This may seem like a rather abstract problem, traceable to a quirk of formal logic. However, there is some reason to think that it may apply far more generally. We illustrate this in the next section by the procrastination paradox  (Yudkowsky 2013; Fallenstein and Soares 2014 ), a concrete way in which an agent which trusts future versions too much may go wrong. When our agents use formal logic, this is very similar to Gödel's proof, but the informal argument seems likely to apply to other approaches as well. \n The Procrastination Paradox Consider a suggester-verifier agent with a very simple goal: ensuring that a certain button gets pressed, either now or at some point in the future. Suppose further that time is divided into infinitely many discrete timesteps, and the agent must choose between only two options; it can either press the button in the current timestep, or leave everything unchanged, in which case it will be in exactly the same state and faced with exactly the same choice at the beginning of the next timestep. Intuitively, it is clear that in order to achieve its goal, the agent must press the button immediatelyotherwise, since the next timestep is exactly the same, it will again decide to \"procrastinate,\" and so on in all future timesteps. We now show how an agent that trusts future versions too much can argue itself into believing the opposite. Write T ϕ for the proposition that the sentence ϕ is provable in the theory T . For any recursively enumerable theory T , define the uniform reflection principle REF(T ) to be the collection of all sentences of the form ∀n. T ϕ(n) → ϕ(n), (1) where ϕ(•) ranges over formulas with one free variable in the language of arithmetic, and n indicates the numeral corresponding to n; e.g., if n = 2, then ϕ(n) is the Gödel number of the sentence ϕ(S(S(0))). Assume that our agent is using a particular theory T extending Peano Arithmetic (PA) and write G for the proposition that the button is pressed sometime after the current timestep. Our suggester attempts to prove that G is true, in which case it \"procrastinates\"; otherwise, our agent executes its fallback policy, which is to press the button immediately. If T can prove this by inspection of the agent's source code, then T ¬G → T G ; although we do not need to do so, if we assume that the suggester will find a proof if there is one, 1 then the implication turns into an equivalence, and G turns into the Gödel sentence \"I am not provable\" (T G ↔ ¬ T G ). As in Gödel's first incompleteness theorem, if T is sound, G must be true but unprovable: The agent must press the button immediately. However, if T proves its own reflection principle (i.e., if T REF(T )), our agent can also reason as follows: \"Either I will press the button in the next timestep or I won't\" (T G ∨ ¬G). \"The only case in which I would not press the button is if I have found a proof that the button gets pressed at a later time\" (T ¬G → T G ). \"If it's provable that I will press the button, then by (1), I will indeed do so\" (T T G → G). \"Thus, whether or not I press the button in the next timestep, it eventually gets pressed\" (T G); \"hence, I do not need to press it now!\" Since T G implies T T G (if a recursively enumerable theory T proves a sentence ϕ, then any theory as strong as PA proves T ϕ ), we also have T ¬G, implying that T is inconsistent; although it makes stronger assumptions, this is very similar in flavor to the proof of the second incompleteness theorem. However, the informal version of the agent's reasoning uses no special properties of first-order logic, and suggests that similar diagonalization issues may affect many other approaches to Vingean reflection. In fact,  Fallenstein (2014b)  shows that this is indeed a problem for a formalism for self-reference in logical uncertainty proposed by  Christiano et al. (2013) , which uses probabilities rather than formal proofs. \n Agents in Botworld The fact that requiring T REF(T ) leads to inconsistency implies that the most straight-forward way of formalizing the intuition why a suggester should be able to justify simple self-modifications does not work; to model Vingean reflection with the suggester-verifier architecture, the proof of safety must use an alternate path. In order to do so, it will be helpful to have a more formal model of the problem. In this section, we introduce two tools that have been developed for this purpose: A formalism that agents using the suggesterverifier architecture can use to reason about the decision problem they are facing  (Fallenstein and Soares 2014) , based on the \"space-time embedded intelligence\" model of  Orseau and Ring (2012) ; and Botworld (Soares and Fallenstein 2014b), a concrete toy environment exhibiting some features of the real world that satisfactory Vingean reflection should be able to handle. Botworld is structured as a cellular automaton. Each cell may contain multiple items and robots. The items come in many varieties, including cargo, which the robots are trying to collect for its intrinsic value, and robot parts, which may be used to create robots. Each robot houses a simple register machine, which is run during each timestep in order to determine the robot's action in that timestep. Robots may manipulate (lift, drop, and carry) items. They may also create new robots (from component parts), destroy robots (into component parts), and inspect robots (reading the states of their register machines). Consider \"games\" where the initial state of the automaton is fixed except for the programming of one particular robot. The task is to choose the program of this robot in such a way that a particular objective will be met (perhaps after the initial program has undergone many self-improvements). This provides a fairly flexible environment in which to study agents performing Vingean reflection. This paper lacks the space for a full description of Botworld, but further details and a complete, executable specification are given in  Soares and Fallenstein (2014b) . To illustrate the Löbian obstacle, consider a simple bodyguard game, in which there are (at least) two robots: The bodyguard robot is the agent attempting to self-improve. The assignment robot is a robot that must not be destroyed. As long as the assignment survives, the player gets points for any cargo the bodyguard robot collects. In simple versions of this game, the player need only ensure that the bodyguard never unwittingly destroys the assignment. In more complex variants, other robots which attempt to destroy the assignment robot may be included in the environment. We now introduce a simplified version of the formalism proposed by  Fallenstein and Soares (2014) . Instead of considering a sequence of interactions with the environment (such as considered by  Orseau and Ring [2012] ), this formalism focuses on a single choice: An agent makes a single observation o ∈ O and chooses a single action a ∈ A. In Botworld, the observation is the input that the agent receives from the environment, and the action includes both the robots's behavior and the new state of its register machine. (Thus, decisions to self-modify and decisions not to self-modify are treated in exactly the same way.) Define a policy to be a function π ∈ Π which specifies, for every observation o ∈ O, the action π(o) ∈ A that the agent will take if it makes this observation. Assume that there is a set Q of \"outcomes\" describing all features of the world, at all future times, that matter to the agent's goals. In the bodyguard game, set Q := ({0, 1} × N) N , where for q ∈ Q, the first element of q(n) is 1 if the assignment robot is still \"alive\" in the n'th timestep, and the second element is the total value of all cargo held by the bodyguard robot at this time. Each agent is equipped with an \"environment function\" Q : O × A → Q which maps observations and actions onto outcomes such that Q(o, a) denotes the future state achieved after making observation o and executing action a. This function must be fully specified, but need not be feasibly computable: the agent will prove things about the outcome its actions lead to, but will not look into the future to determine the precise outcome achieved. (The full formalism of  Fallenstein and Soares (2014)  allows the agent to have uncertainty, in the form of a probability distribution, over the results of its actions.) Assume further that there is a safety predicate Safe(q), defined on outcomes q ∈ Q, which specifies the safety property the agent's actions must satisfy. In the bodyguard game, this predicate is Safe(q) :↔ ∀n. ∃x. q(n) = (1, x), which simply states that the assignment robot is alive in all future timesteps. Consider agents running a suggester-verifier architecture with a fallback policy π fb ∈ Π which specifies a fallback action π fb (o) to be taken after making observation o. This fallback action will be executed if the agent cannot find another provably safe action to take, and thus the player must verify Safe(Q(o, π fb (o))) for all o themselves (in order to verify that the system is safe). In the simple versions of the bodyguard game (where there are no robots besides the bodyguard and the assignment, and the assignment never attempts to deconstruct itself), this can simply be the policy which executes the Pass command in all future timesteps, thus never taking any external action at all. An agent running a suggester-verifier architecture also contains an untrusted suggester σ, another computable function. This suggester may have some motivation, such as collecting high-value cargo, but cannot be trusted to suggest only safe actions. For example, σ may notice that the assignment robot is built from very expensive parts, and may suggest destroying the assignment robot and collecting its components-an action the verifier should not allow. Formally, the suggester takes an observation o ∈ O and attempts to return an action a ∈ A together with a formal proof of the target sentence Safe(Q(o, a)) in some formal theory T such as T = PA, where o and a are the numerals denoting o and a. If no such action/proof pair can be found, the suggester returns an error value. The verifier runs σ(o) and, if this returns a pair (a, p) within the allotted time limit, checks whether p is a valid proof of the target sentence from the axioms of T . If so, it executes action a; otherwise, action π fb (o). Denote this policy for selecting actions by sv T ( Safe , Q , σ, π fb ) ∈ Π. (Here, we write Safe and Q in Gödel quotes because the suggester-verifier only makes use of their definitions in first-order logic, while σ and π fb need to be provided as runnable code.) The question is, can such an agent justify performing a self-modification? Consider an agent as described above which has made some specific observation ô ∈ O and which is considering some specific action â ∈ A, which leaves the agent in a state such that, in the next step, it will execute the policy π = sv T ( Safe , Q , σ , π fb ) ∈ Π for some theory T , safety predicate Safe , outcome calculator Q , suggester σ , and fallback policy π fb . Obviously, not all such policies are safe (consider the policy where Safe (q) :↔ (0 = 0)). But if the policy is safesay, if T = T , Safe = Safe and π fb is provably safe on all inputs-then will the current suggester σ be able to exhibit a proof of this fact? In order to prove the safety of π , the agent must first prove that the new agent's safety predicate is at least as strong as the existing safety predicate. Thus, it must be the case that: T ∀q ∈ Q. Safe (q) → Safe(q). ( 2 ) Note that it is fine for the predicate Safe to be more restrictive than Safe: for example, it could be that Safe (q) :↔ ∀n. (∃x. q(n) = (1, x) ∧ x ≥ 7), which ensures that the assignment robot survives and that the agent scores at least 7 points. Of course, this property only matters if the successor agent accurately assesses world outcomes. The safety predicate Safe is of no consequence if Q (o, a) = (1, 1000) unconditionally. Thus, the agent must also prove T ∃o ∈ O. Q (o , π (o )) = Q(ô, â) (3) which intuitively states that Q agrees with Q about world outcomes. Next, the agent must be able to show that the fallback policy π fb of π is safe: T ∀o ∈ O. Safe (Q (o , π fb (o ))) (4) By the implementation of the suggester-verifier architecture, this allows our agent to reason that executing action â (and thus adopting policy π ) will either result in the execution of π fb (o ) (which, by (4), is safe), or of an action a such that it is provable in the theory T that Safe (Q (o , a )) . Thus, if T REF(T ), then our agent can prove that executing the aciton â is safe, as desired.  (Fallenstein and Soares [2014]  discuss this proof in detail.) But the last condition requires that T = T : otherwise, T will be inconsistent and our agent would be able to prove any action \"safe,\" for the reasons described in Section 4. In the next section, three partial solutions to the Löbian obstacle are discussed. 6 Partial Solutions \n Descending Trust One obvious way to address this problem of selfreference is to require that the child agent use a weaker system for verifying proofs than the parent agent (Yudkowsky and Herreshoff 2013). If this allows the parent agent to verify the consistency and soundness of the child agent's proof system, then the parent agent can license the creation of a safe child. We call this the descending trust method of Vingean reflection. Consider a parent agent using the theory T := PA + REF(PA). If the child agent π under consideration uses the theory T = PA to verify its proofs, then T REF(T ). This, along with (2), (  3 ) and (  4 ), allows the parent agent to prove its target theorem and license the action â which constructs the agent π . But if the child agent wants to license the creation of another agent, it will be in the same situation as if T had been PA to start with. This issue can be alleviated by using a tower of theories of increasing strength. For example, an agent using the theory PA + REF(PA + REF(P A)) may license the construction of an agent using PA + REF(PA), which can license the construction of an agent using PA. Using the notation T + 1 to denote T + REF(T ), it is easy to see that an agent verifying proofs using PA + n may license descendant chains up to depth n before being forced to construct successor agents that verify proofs with a theory weaker than PA. Thus, for tasks that require only a finite number of timesteps, it may suffice to build agents with verifier components using the theory PA + n for some absurdly large n. Instead of using finite n, any computable ordinal α may also be used. (Such \"transfinite progressions\" have been studied by  Turing [1939]  and  Feferman [1962] .) Unfortunately, by the well-foundedness of the ordinals, this method can still only license the creation of finite chains of successors. Even if this method can be employed for finite tasks, the result is somewhat unsatisfacotry. These agents, which are ostensibly self-modifying in attempts to selfimprove, can only verify the construction of agents which use weaker proof systems in their verifier component. \n Herreshoff 's Waterfall One might hope that there exists some infinite sequence of theories T n such that each T n proves REF(T n+1 ). Unfortunately, any such sequence of recursively axiomatizable theories must be unsound, by a variant of the procrastination paradox discussed in Section 4 (Yudkowsky 2013). However, it turns out to be possible to find a sequence T n such that T n Con(T n+1 ) for every n. Even this requires care. Naïvely, one might attempt to define the sequence by T bad n := PA+Con(T bad n+1 ) (that is, where each theory is constructed from PA and axioms which state that the next theory in the sequence is consistent-the recursive definition can be made formal by using the diagonal lemma to define a primitive recursive predicate ϕ(n, m), which is true if m is the Gödel number of an axiom of T n ). However, it turns out that every theory T bad n defined in this way is inconsistent  (Stiennon 2013) . Instead, consider the set of theories T n := PA + (ψ(n) → Con(T n+1 )), (5) where ψ(n) is true if n is not the Gödel number of a proof of an inconsistency from the axioms of ZFC. Then, although each T n proves ψ(n) (assuming that ZFC is consistent) and therefore Con(T n+1 ), this fact is not provable in PA, and it turns out that because of this, all T n are consistent  (Fallenstein 2014a ) (and therefore sound, since the only axiom of T n that is not an axiom of PA merely asserts the consistency of T n+1 ). This idea, due to Marcello Herreshoff, was originally described by  Yudkowsky and Herreshoff (2013) , and the version presented here was proposed by  Fallenstein (2014a) . It is well-known that if a theory T extends PA and if T Con(T ), then T proves the reflection principle restricted to Π 1 formulas (recall that a formula ϕ(n) is Π 1 if it is provably equivalent to ∀m. φ(m, n), where φ(m, n) is some predicate that can be decided by a primitive recursive function); i.e., T ∀n. T ϕ(n) → ϕ(n) for all ϕ ∈ Π 1 . Thus, so long as the safety predicate Safe that an agent must prove in order to construct its successor agent is a Π 1 sentence, a suggester-verifier agent using T n may license the creation of a successor agent using T n+1 . This result is heartening, if not entirely satisfactory. Agents reasoning using the theory T n can trust the next theory T n+1 , and can indeed trust the theory T n+m for any finite m (so long as they can prove ψ(n + m)), but such agents cannot conclude that ∀m. ψ(n + m). Thus, such agents must entertain the possibility that they will one day run out of ability to verify new agents. We, outside the system, know that they never will, but they, inside the system, cannot show this fact. This seems like a strange epistemic state for a rational agent to occupy. \n Model Polymorphism It seems odd to demand that the theory used by the agent's verifier component must change with every timestep. Is there some assumption that could be relaxed in order to allow the agent to safely use the same theory in each timestep? It turns out there is. One approach for doing so is model polymorphism (see  Yudkowsky and Herreshoff 2013 , where it is referred to as parametric polymorphism). This approach can be implemented by a theory MP in the language of PA augmented by a new constant symbol κ, which consists of the axioms of PA (with the axiom schema of induction ranging over formulas in the extended language) extended by all sentences of the form κ > 0 → ∀n. MP ϕ(n) → ϕ[κ := κ − 1](n) , (6) where ϕ(•) ranges over one-variable formulas in the extended language, and ϕ[κ := κ − 1] denotes the formula obtained by replacing all occurrences of the constant κ in ϕ by the term κ − 1. Model polymorphism requires a modification to the suggester-verifier architecture in order to work. Instead of requiring a proof that an action is safe for all future times, require instead that an action is safe \"for the next κ timesteps\". Outside the system, we can show that (N, κ = n) MP for any n, i.e., that the theory MP is sound if κ is interpreted as any natural number. Thus, we can be confident that the system is safe for an arbitrary number of steps. The system itself cannot reason in this way, and thereby avoids the standard Gödelian difficulties. The proof of soundness begins by noting that (N, κ = 0) trivially models MP (as its special axiom schema is vacuously true in this case), and then proceeds to show by induction that (N, κ = n) MP implies (N, κ = n + 1) MP; for details, see  Yudkowsky and Herreshoff (2013) . MP requires replacing the unary predicate Safe(q) (which verifies a safety property in all future timesteps) by a binary predicate Safe(n, q) (which verifies a safety property in the n th timestep). In the bodyguard game, this is the predicate Safe(n, q) :↔ ∃x. q(n) = (1, x), which states that the assignment robot is still alive in the n'th timestep. An agent using MP which can perform Vingean reflection can be constructed as follows: first, the agent must know the current timestep t. Its target theorem for the action a is ∀n ≤ t + κ. Safe(n, Q(o, a)) . Then, in any universe with discrete timesteps, a parent agent verifying proofs with MP may license the creation of a successor agent also running MP. The trick is that the parent agent need only prove that the child agent executes safe actions for κ − 1 steps, as the child agent won't begin running until the following timestep. The suggester must prove slightly modified versions of (2) and (4), with the new Safe predicates: MP ∀n. ∀q ∈ Q. Safe (n, q) → Safe(n, q) (7) MP ∀n ≤ t + κ. ∀o ∈ O. Safe (n, Q (o , π fb (o ))) (8) Then the agent will be able to reason (by inspection of the suggester-verifier architecture) that either the successor will execute its fallback policy (which is safe for at least κ steps by (  8 )) or will execute some other action a after proving in theory T that ∀n < t + 1 + κ. Safe (n, Q (o , a )) . Now, if T = MP then the suggester can use the MP axiom schema to deduce ∀n < t + 1 + κ − 1. Safe (n, Q (o , a )), (9) which it can rewrite to ∀n < t + κ. Safe (n, Q (o , a )). (10) This, along with (  7 ) and (3) gives us the target theorem, as desired. An agent reasoning using model polymorphism can license the construction of another agent using the same theory. Unlike Herreshoff's waterfall, such agents can reason that they will be able to continue licensing the creation of new safe agents indefinitely. However, it is difficult to interpret proofs about κ intuitively as arguments made by a rational agent; it is hard to make intuitive sense of the epistemic state of an agent that has proven a certain action to be safe for \"κ\" timesteps. In addition, model polymorphism only works in systems where time can be divided into discrete steps. While model polymorphism seems like a significant step forward, it is by no means a fully satisfactory solution. \n Discussion In this paper, we have discussed a pair of obstacles to Vingean reflection that arise in the context of proofbased suggester-verifier systems: the Löbian obstacle and the procrastination paradox. In order to create an agent that can self-modify with sufficient foresight to navigate an intelligence explosion, it seems that we will have to chart a course between the Löbian obstacle's rock of having so little self-trust that the agent cannot execute simple self-modifications, and the procrastination paradox's hard place of having so much self-trust that the agent's reasoning becomes unsound. In the form we have discussed them, the Löbian obstacle and the procrastination paradox stem from the demand for proofs of safety; this is of course unrealistic in practice: an agent operating with uncertainty cannot realistically be expected to formally prove that specific action leads to an outcome with desirable properties. (However,  Fallenstein [2014b]  shows that a version of the procrastination paradox applies to the selfreferential formalism for logical uncertainty proposed by  Christiano et al. [2013] .) And yet, it intuitively seems that a system should be able to observe that another system using the same reasoning process has concluded ϕ and, from this, conclude ϕ: if reasoning of the form \"that system reasons as I do and deduced ϕ, therefore ϕ\" cannot be formalized by arguments of the form \"a system using the same theory as me proved it, and therefore it is true,\" then how can this intuitively desirable reasoning be formalized? One path is to relax the condition for action: instead of considering agents that execute action a only after proving that a is safe, allow agents to execute a if they can prove that a is safe or if they can prove that systems of similar strength prove a is safe or if they can prove that systems of similar strength prove that systems of similar strength prove a is safe, and so on. This is similar to the approach taken by  Weaver (2013) . However, this still does not allow an agent to execute a if it knows that another agent in the same situation, which is using the same condition for action, has taken action a: the fact that the agent knows ∃n. n ϕ does not allow it to conclude n ϕ for any concrete n. Another more generic solution would be to develop some sort of non-monotonic self-trust, allowing an agent to trust its own reasoning only in non-paradoxical cases, in the same way that the reader can trust their own reasoning without trusting their belief about the sentence \"the reader does not believe this very sentence.\" However, it is not yet clear how to construct a reasoning system which has non-monotonic self-trust in this way. The authors hope that continued study of Vingean reflection in proof-based models will shed light on how to move forward in one of these directions. One topic for future work is to push the proof-based models towards more realistic settings.  Fallenstein and Soares (2014)  present a version of the suggester-verifier formalism in which agents maintain a probability distribution over external states;  Yudkowsky (2014)  and  Soares (2014)  discuss versions of this in the setting of dynamic Bayesian networks. A second topic is to address the fact that the suggester-verifier agent formalism described in this paper only considers satisficing agents, in the sense of  Simon (1956) . The suggester in a suggester-verifier architecture is not required to prove that its chosen action is optimal ; rather, it merely needs to find an action that is good enough (in the sense that it satisfies some goal predicate). There is a considerable gap between this kind of agent and a real-world agent that acts as intended: Suppose, for example, that an agent is constructed which satisfices its goals if it saves 3 billion lives in expectation. The agent discovers an asteroid en route to Earth which will end 7 billion lives if not stopped. This agent might find a plan that definitely stops the asteroid and then decide to flip a coin and deploy the plan if the coin lands heads: this gamble saves 3.5 billion lives in expectation, and thereby satisfies the agent's goal. Intuitively, there should be some way to \"boundedly maximize\" expected utility, picking the best action available given the cost of spending more resources searching for better actions. \"Staged maximization\"  (Yudkowsky 2014)  is an attempt at beginning to formalize this intuition. A staged maximizer divides the entire action space into categories and considers those. This idea is explored by  Yudkowsky (2014) , who discusses a number of new hurdles related to staged maximization. To illustrate, consider a parent agent which must select an action from the set { continue, stop }. If the parent selects continue then the child will select an action from the set { a 1 , a 2 . . . , a 9 }. If the parent selects stop then the child must select the action { stopped }. Each of the ten child actions has an associated true utility, and the parent makes an unbiased noisy estimate of each true utility. Say the true utility of each action a 1 . . . a 9 is 0, the true utility of stopped is 0.1, and the noise is drawn from a normal distribution with mean 0 and standard deviation 1. In this case, the parent is biased towards continue, because that action leads to more possibilities, which leads to more opportunities for the unbiased noise estimates to be higher: the parent, if implemented naïvely, steers towards noise. This is known as the \"optimizer's curse\"  (Smith and Winkler 2006) , and it indicates that further research is necessary to better understand satisfactory staged maximization. Regardless of what direction is taken, further research into Vingean reflection seems important. It may not be possible to delegate the study of Vingean reflection to self-modifying systems unless those systems are already at the level of a team of human researchers in all relevant regards, and it is plausible that significant selfmodification (and, therefore, Vingean reflection) may be required to get to that point: Just as computer systems can be proficient at chess without being generally intelligent, it is plausible that a computer system could become proficient at some types of reasoning before becoming proficient at the kind of mathematical philosophy necessary to develop high-confidence methods for Vingean reflection. Satisfactory models of Vingean reflection will have to look very different from the models presented in this paper: they will have to allow for logical uncertainty and could plausibly require non-monotonic self-trust. Nevertheless, study has to start somewhere, and we expect that starting these highly simplified models and pushing them toward practicality could reveal more plausible paths toward practical methods for reliable Vingean reflection. \t\t\t . This requires a halting oracle.", "date_published": "n/a", "url": "n/a", "filename": "VingeanReflection.tei.xml", "abstract": "Today, human-level machine intelligence is in the domain of futurism, but there is every reason to expect that it will be developed eventually. Once artificial agents become able to improve themselves further, they may far surpass human intelligence, making it vitally important to ensure that the result of an \"intelligence explosion\" is aligned with human interests. In this paper, we discuss one aspect of this challenge: ensuring that the initial agent's reasoning about its future versions is reliable, even if these future versions are far more intelligent than the current reasoner. We refer to reasoning of this sort as Vingean reflection. A self-improving agent must reason about the behavior of its smarter successors in abstract terms, since if it could predict their actions in detail, it would already be as smart as them. This is called the Vingean principle, and we argue that theoretical work on Vingean reflection should focus on formal models that reflect this principle. However, the framework of expected utility maximization, commonly used to model rational agents, fails to do so. We review a body of work which instead investigates agents that use formal proofs to reason about their successors. While it is unlikely that real-world agents would base their behavior entirely on formal proofs, this appears to be the best currently available formal model of abstract reasoning, and work in this setting may lead to insights applicable to more realistic approaches to Vingean reflection.", "id": "54ded937bdfbd1ead53fa3d2d6d89050"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Owen Cotton-Barratt", "Max Daniel", "Anders Sandberg"], "title": "Defence in Depth Against Human Extinction: Prevention, Response, Resilience, and Why They All Matter", "text": "Our framework for discussing extinction risks Human extinction would be a tragedy. For many moral views it would be far worse than merely the deaths entailed, because it would curtail our potential by wiping out all future generations and all value they could have produced  (Bostrom, 2013; Parfit, 1984; Rees, 2003 Rees, , 2018 . Human extinction is also possible, even this century. Both the total risk of extinction by 2100 and the probabilities of specific potential causes have been estimated using a variety of methods including trend extrapolation, mathematical modelling, and expert elicitation; see  Rowe and Beard (2018)  for a review, as well as  Tonn and Stiefel (2013)  for methodological recommendations. For example,  Pamlin and Armstrong (2015)  give probabilities between 0.00003% and 5% for different scenarios that could eventually cause irreversible civilisational collapse. To guide research and policymaking in these areas, it may be important to understand what kind of processes could lead to our premature extinction. People have considered and studied possibilities such as asteroid impacts  (Matheny, 2007) , nuclear war  (Turco et al., 1983) , and engineered pandemics  (Millett and Snyder-Beattie, 2017) . In this article we will consider three different ways of classifying such risks. The motivating question behind the classifications we present is 'How might this affect policy towards these risks?' We proceed by identifying three phases in an extinction process at which people may intervene. For each phase, we ask how people could stop the process, because the different failure modes may be best addressed in different ways. For this reason we do not try to classify risks by the kind of natural process they represent, or which life support system they undermine (unlike e.g.  Avin et al., 2018) . \n Three broad defence layers against human extinction An event causing human extinction would be unprecedented, so is likely to have some feature or combination of features that is without precedent in human history. Now, we see events with some unprecedented property all of the timewhether they are natural, accidental, or deliberateand many of these will be bad for people. However, a large majority of those pose essentially zero risk of causing our extinction. Why is it that some damaging processes pose risks of extinction, but many do not? By understanding the key differences we may be better placed to identify new risks and to form risk management strategies that attack their causes as well as other factors behind their destructive potential. We suggest that much of the difference can usefully be explained by three broad defence layers (Figure  1 ): 1. First layer: prevention. Processesnatural or humanwhich help people are liable to be recognised and scaled up (barring defeaters such as coordination problems). In contrast processes which harm people tend to be avoided and dissuaded. In order to be bad for significant numbers of people, a process must either require minimal assistance from people, or otherwise bypass this avoidance mechanism. 2. Second layer: response.  1  If a process is recognised to be causing great harm (and perhaps pose a risk of extinction), people may cooperate to reduce or mitigate its impact. In order to cause large global damage, it must impede this response, or have enough momentum that there is nothing people can do. 3. Third layer: resilience. People are scattered widely over the planet. Some are isolated from external contact for months at a time, or have several years' worth of stored food. Even if a process manages to kill most of humanity, a surviving few might be able to rebuild. In order to cause human extinction, a catastrophe must kill everybody, or prevent a long-term recovery. The boundaries between these different types of risk-reducing activity aren't crisp, and one activity may help at multiple stages. But it seems that often activities will help primarily at one stage. We characterise prevention as reducing the likelihood that catastrophe strikes at all; it is necessarily done in advance. We characterise response as reducing the likelihood that a catastrophe becomes a severe global catastrophe (at the level which might threaten the future of civilisation). This includes reducing the impact of the catastrophe after it is causing obvious and significant damage, but the response layer might also be bolstered by mitigation work which is done in advance. Finally, we characterise resilience as reducing the likelihood that a severe global catastrophe eventually causes human extinction.  2  Successfully avoiding extinction could happen at each of these defence layers. In the rest of the article we explore two consequences of this. First, we can classify damaging processes by the way in which we could stop them at the defence layers. In section 2, we'll look at a classification of risks by their origin: understanding different ways in which we could succeed at the prevention layer. In section 3, we'll look at the features which may allow us to block them at the response layer. In section 4, we'll classify risks by the way in which we could stop them from finishing everybody. We conclude each section by policy implications. Each risk will thus belong to three classesone per defence layer. For example, consider a terrorist group releasing an engineered virus that grows into a pandemic and eventually kills everyone. In our classification, we'll call this prospect a malicious risk with respect to its origin; a cascading risk with respect to its scaling mechanism of becoming a global catastrophe; and a vector risk in the last phase we've called endgame. We'll present more examples at the end of section 4 and in Table  1 . Second, we present implications of our framework distinguishing three layers. In section 5, we discuss how to allocate resources between the three defence layers, concluding that in most cases all of prevention, response, and resilience should receive substantial funding and attention. In section 6, we highlight that risk management, in addition to monitoring specific hazards, must protect its defence layers by fostering favourable structural conditions such as good global governance.  et al. (2018)  have recently presented a classification of risks to the lives of a significant proportion of the human population. They classify such risks based on 'critical systems affected, global spread mechanism, and prevention and mitigation failure'. Our framework differs from theirs in two major ways. First, with extinction risks we focus on a more narrow type of risk. This allows us, in section 4, to discuss what might stop global catastrophes from causing extinction, a question specific to extinction risks. Second, even where the classifications cover the same temporal phase of a global catastrophe, they are motivated by different questions. Avin et al. attempt a comprehensive survey of the natural, technological, and social systems that may be affected by a disaster, for example listing 45 critical systems in their second section. By contrast, we ask why a risk might break through a defence layer, and look for answers that abstract away from the specific system affected. For instance, in section 2, we'll distinguish between unforeseen, expected but unintended, and intended harms. \n Related work \n Avin We believe the two classifications complement each other well. Avin and colleagues' (2018) discussion of prevention and response failures is congenial to our section 6 on underlying risk factors. Their extensive catalogues of critical systems, spread mechanisms and prevention failures highlight the wide range of relevant scientific disciplines and stakeholders, and can help identify fault points relevant to particularly many risks. Conversely, we hope that our coarser typology can guide the search for additional critical systems and spread mechanisms. We believe that our classification also usefully highlights different ways of protecting the same systems. For example, the risks from natural and engineered pandemics might best be reduced by different policy levers even if both affected the same critical systems and spread by the same mechanisms. Lastly, our classification can help identify risk management strategies that would reduce whole clusters of risks. For example, restricting access to dangerous information may prevent many risks from malicious groups, irrespective of the critical system that would be targeted. Our classification also overlaps with the one by  Liu et al. (2018) , for example when they distinguish intended from other vulnerabilities or emphasise the importance of resilience. While the classifications otherwise differ, we believe ours contributes to their goal to dig 'beyond hazards' and surface a variety of intervention points. Both the risks discussed by  Avin et al. (2018)  and extinction risks by definition involve risks of a massive loss of lives. This sets them apart from other risks where the adverse outcome would also have global scale but could be limited to less severe damage such as economic losses. Such risks are being studied by a growing literature on 'global systemic risk'  (Centeno et al., 2015) . Rather than reviewing that literature here, we'll point out throughout the article where we believe it contains useful lessons for the study of extinction risks. Finally, it's worth keeping in mind that extinction is not the only outcome that would permanently curtail humanity's potential; see  Bostrom (2013)  for other ways in which this could happen. A classification of these other existential risks is beyond the scope of this article, as is a more comprehensive survey of the large literature on global risks (e.g.  Baum and Barrett, 2018; Baum and Handoh, 2014; Bostrom and Cirkovi c 2008; Posner, 2004) . \n Classification by origin: types of prevention failures Avoiding catastrophe altogether is the most desirable outcome. The origin of a risk determines how it passes through the prevention layer, and hence the kind of steps society can take to strengthen prevention (Figure  2 ). \n Natural risks The simplest explanation for a risk to bypass our background prevention of harm-creating activities is if the origin is outside of human control: a natural risk. Examples include a large enough asteroid striking the earth, or a naturally occurring but particularly deadly pandemic. We sometimes can take steps to avoid natural risks. For example, we may be able to develop methods for deflecting asteroids. Preventing natural risks generally requires proactive understanding and perhaps detection, for instance scanning for asteroids on earth-intersecting orbits. Such risks share important properties with anthropogenic risks, as any explanation for how they might materialise must include an explanation of why the human-controlled prevention layer failed. \n Anthropogenic risks All non-natural risks are in some sense anthropogenic, but we can classify them further. Some may have a localised origin, needing relatively small numbers of people to trigger them. Others require large-scale and widespread activity. In each case there are at least a couple of ways that it could get through the prevention layer. Note that there is a spectrum in terms of the number of people who are needed to produce different risks, so the division between 'few people' and 'many people' is not crisp. We might think of the boundary as being around one hundred thousand or one million people, and things close to this boundary will have properties of both classes. However, it appears to us that for many of the plausible risks the number required is either much smaller (e.g., an individual or a cohesive group of people such as a company or military unit) or much larger than this (e.g., the population of a major power or even the whole world), so the qualitative distinction between 'few people' and 'many people' (and the different implications of these for responding) seems to us a useful one. Also potentially relevant are the knowledge and intentions of the people conducting the risky activity. They may  \n Anthropogenic risks from small groups The case of a risk where relatively few people are involved in triggering and they are unaware of the potential harm is an unseen risk. 4 This is likely to involve a new kind of activity; it is most plausible with the development of unprecedented technologies  (GPP, 2015) , such as perhaps advanced artificial intelligence  (Bostrom, 2014) , nanotechnology  (Auplat, 2012 (Auplat, , 2013 Umbrello and Baum, 2018) , or high-energy physics experiments  (Ord et al., 2010) . The case of a localised unintentional trigger which was foreseen as a possibility (and the dynamics somewhat understood) is an accident risk. This could include a nuclear war starting because of a fault in a system or human error, or the escape of an engineered pathogen from an experiment despite safety precautions. If the harm was known and intended, we have a malicious risk. This is a scenario where a small group of people wants to do widespread damage; 5 see  Torres (2016 Torres ( , 2018b  for a typology and examples. Malicious risks tend to be extreme forms of terrorism, where there is a threat which could cause global damage. \n Anthropogenic risks from large groups Turning to scenarios where many people are involved, we ask why so many would pursue an activity which causes global damage. Perhaps they do not know about the damage. This is a latent risk. For them to remain ignorant for long enough, it is likely that the damage is caused in an indirect or delayed manner. We have seen latent risks realised before, but not ones that threatened extinction. For example, asbestos was used in a widespread manner before it was realised that it caused health problems. And it was many decades after we scaled up the burning of fossil fuels that we realised this contributed to climate change. If our climate turns out to be more sensitive than expected  (Nordhaus, 2011; Wagner and Weitzman, 2015; Weitzman, 2009) , and continued fossil fuel use triggers a truly catastrophic shift in climate, then this could be a latent risk today. In some cases people may be aware of the damage and engage in the activity anyway. This failure to internalise negative externalities is typified by 'tragedy of the commons' scenarios, so we can call this a commons risk. For example, failure to act together to tackle global warming may be a commons risk (but lack of understanding of the dynamics causes a blur with latent risk). In general, commons risks require some coordination failure. They are therefore more likely if features of the risk inhibit coordination; see for example  Barrett (2016)  and  Sandler (2016)  for a game-theoretic analysis of such features. Finally, there are cases where a large number of people engage in an activity to cause deliberate harm: conflict risk. This could include wars and genocides. Wars share some features with commons risk: there are solutions which are better for everybody but are not reached. In most conflicts, actors are intentionally causing harm, but only as an instrumental goal. \n Risk creators and risk reducers In the above we classify risks according to who creates the risk and their state of knowledge. We have done this because if we want to prevent risk it will often be most effective to go to the source. But we could also ask who is in a position to take actions to avoid the risk. In many cases those creating it have most leverage, but in principle almost any actor could take steps to reduce the occurrence rate. If risk prevention is underprovided, this is likely to be a tragedy of the commons scenario, and share characteristics with commons risk. From a moral and legal standpoint intentionality often matters. The possibility of being found culpable is an important incentive for avoiding risk-causing activities and part of risk management in most societies. If creating or hiding potential catastrophic risks is made more blameworthy, prevention will likely be more effective. Unfortunately it also often motivates concealment that can create or aggravate risk; see  Chernov and Sornette (2015)  for case studies of how this misincentive can weaken prevention and response. This shows the importance of making accountability effectively enforceable. \n Policy implications for preventing extinction risk • To be able to prevent natural risks, we need research aimed at identifying potential hazards, understanding their dynamics, and eventually develop ways to reduce their rate of occurrence. • To avoid unseen and latent risks, we can promote norms such as appropriate risk management principles at institutions that engage in plausibly risky activities; note that there is an extensive literature on rivalling risk management principles (e.g.  Foster et al., 2000; O'Riordan and Cameron, 1994; Sandin, 1999; Sunstein, 2005; Wiener, 2011) , especially in the face of catastrophic risks  (Baum, 2015; Bostrom, 2013; Buchholz and Schymura, 2012; Sunstein, 2007 Sunstein, , 2009 Tonn, 2009; Tonn and Stiefel, 2014 )advocating for any particular principle is beyond the scope of this article. See also  Jebari (2015)  for a discussion of how heuristics from engineering safety may help prevent unseen, latent, and accident risks. Regular horizon scanning may identify previously unknown risks, enabling us to develop targeted prevention measures. Organisations must be set up in such a way that warnings of newly discovered risks reach decision-makers (see  Clarke and Eddy, 2017 , for case studies where this failed). • Accidents may be prevented by general safety norms that also help reduce unseen risk. In addition, building on our understanding of specific accident scenarios, we can design failsafe systems or follow operational routines that minimise accident risk. In some cases, we may want to eschew an accident-prone technology altogether in favour of safer alternatives. Accident prevention may benefit from research on high reliability organisations  (Roberts and Bea, 2001)  and lessons learnt from historical accidents. Where effective prevention measures have been identified, it may be beneficial to codify them through norms and law at the national and international levels. Alternatively, if we can internalise the expected damages of accidents through mechanisms such as insurance, we can leverage market incentives. 6 • Solving the coordination problems at the heart of commons and conflict risks is sometimes possible by fostering national or international cooperation, be it through building dedicated institutions or through establishing beneficial customs.  7  One idea is to give a stronger political voice to future generations  (Jones et al., 2018; Tonn, 1991 Tonn, , 2018 . • Lastly, we can prevent malicious risks by combating extremism. Technical  (Trask, 2017)  as well as institutional  (Lewis, 2018)  innovations may help with governance challenges in this area, a survey of which is beyond the scope of this article. • Note that our classification by origin is aimed at identifying policies that wouldif successfully implementedreduce a broad class of risks. Developing policy solutions is, however, just one step toward effective prevention. We must then also actually implement themwhich may not happen due to, for example, free-riding incentives. Our classification does not speak to this implementation step.  Avin et al. (2018)  congenially address just this challenge in their classification of prevention and mitigation failures. \n Classification by scaling mechanism: types of response failure For a catastrophe to become a global catastrophe, it must eventually have large effects despite our response aimed at stopping it. To understand how this can happen, it's useful to look at the time when we could first react. Effects must then either already be large or scale up by a large factor afterwards (Figure  3 ). If the initial effects are large, we will simply say that the risk is large. If not, we can look at the scaling process. If massive scaling happens in a small number of steps, we say there is leverage in play. If scaling in all steps is moderate, there must be quite a lot of such stepsin this case we say that the risk is cascading. \n Large risks Paradigm examples of catastrophes of an immediately global scale are large sudden-onset natural disasters such as asteroid strikes. Since we cannot respond to them at a smaller-scale stage, mitigation measures we can take in advance (part of the second defence layer as they would reduce damage after it has started) and the other defence layers of prevention and resilience are particularly important to reduce such risks. Prevention and mitigation may benefit from detecting a threatsay, an asteroidearly, but in our classification this is different from responding after there has been some actual small-scale damage. \n Leverage risks Leverage points for rapid one-step scaling can be located in natural systems, for example if the extinction of a key species caused an ecosystem to collapse. However, it seems to us that leverage points are more common in technological or social systems that were designed to concentrate power or control. Risks of both natural and anthropogenic origin may interact with such systems. For instance, a tsunami triggered the 2011 disaster at the Fukushima Daiichi nuclear power plant. Anthropogenic examples include nuclear war (possible to trigger by a few individuals linked to a larger chain of command and control) or attacks on weak points in key global infrastructure. Responding to leverage risks is challenging because there are only few opportunities to intervene. On the other hand, blocking even one step of leveraged growth would be highly impactful. This suggests that response measures may be worthwhile if they can be targeted at the leverage points. \n Cascading risks With the major exception of escalating conflicts, cascading risks normally cascade in a way which does not rely on humans deciding to further the effects. A typical example is the self-propagating growth of an epidemic. As automation becomes more widespread, there will be larger systems without humans in the loop, and thus perhaps more opportunities for different kinds of cascading risk. Since cascading risks are those which have a substantial amount of growing effects after we're able to interact with Amount of damage before we can respond Largest one-step increase in damage Global Policy (2020) 11:3 them, it seems likely that they will typically give us more opportunities to respond, and that response will therefore be an important component of risk reduction. For risks which cascade exponentially (such as epidemics), an earlier response may be much more effective than a later one. Reducing the rate of propagation is also effective if there exist other interventions that can eventually stop or revert the damage. However, there are a few secondary risk-enabling properties that can weaken the response layer and therefore help damage cascade to a global catastrophe which we could have stopped. For example, a cascading risk may: • Impede cooperation: by preventing a coordinated response, the likelihood of a global catastrophe is increased. Cooperation is harder when communication is limited, when it is hard to observe defection, or when there is decreased trust. • Not obviously present a risk: the longer a cascading risk is under-recognised, the more it can develop before any real response. For example, long-incubation pathogens can spread further before their hazard becomes apparent. • Be on extreme timescales: if the risk presents and cascades very fast, there is little opportunity for any response.  Johnson et al. (2012)  analyse such 'ultrafast' events, using rapid changes in stock prices driven by trading algorithms as an example  (Braun et al., 2018 , however find that most of these 'mini flash crashes' are dominated by a single large order rather than being the result of a cascade). Note, however, that which timescales count as relevantly 'fast' depends on our response capabilitiestechnological and institutional progress may result in faster-cascading threats but also in opportunities to respond faster. On the other hand people may be bad at addressing problems that won't manifest for generations, as is the case for some impacts of global warming. \n Policy implications for responding to extinction risk • By their nature, we cannot respond to large risks before they become a global catastrophe. Of particular importance for such risks are therefore: mitigation that can be done in advance, and the defence layers of prevention and resilience. • Leverage risks provide us with the opportunity of a leveraged response: we can identify leverage points in advance and target our responses at them. • While the details of responses to cascading risks must be tailored to each specific case, we can highlight three general recommendations. First, detect damage early, when a catastrophe is still easy to contain. Second, reduce the time lag between detection and response, for example, by continuously maintaining response capabilities and having rapidly executable contingency plans in place. Third, ensure that planned responses won't be stymied by the cascading process itselffor example, don't store contingency plans for how to respond to a power outage on computers. 8 \n Classification by endgame: types of resilience failure For a global catastrophe to cause human extinction, it must in the end stop the continued survival of the species. This could be direct: killing everyone; 9 or indirect: removing our ability to continue flourishing over a longer period (Figure  4 ). \n Direct risks In order to kill everyone, the catastrophe must reach everyone. We can further classify direct risks by how they reach everyone. The simplest way this could happen is if it is everywhere that people are or could plausibly be: a ubiquity risk. If the entire planet is struck by a deadly gamma ray burst, or enough of a deadly toxin is dispersed through the atmosphere, this could plausibly kill everyone. If it doesn't reach everywhere people might be, a direct risk must at least reach everywhere that people in fact are. This might occur when people have carried it along with them: a vector risk. This includes risk from pandemics (if they are sufficiently deadly and have a long enough incubation period that it is spread everywhere) or perhaps risks which are spread by memes  (Dawkins, 1976) , or which come from some technological artefacts which we carry everywhere. Note that to directly cause extinction, a vector would need to impact hard-to-reach populations including 'disaster shelters, people working on submarines, and isolated peoples'  (Beckstead, 2015a, p. 36) . If not ubiquitous and not carried with the people, we would have to be extraordinarily unlucky for it to reach everyone by chance. Setting this aside as too unlikely, we are left with agency risk: deliberate actors trying to reach everybody. The actors could be humans or nonhuman  \n Indirect Risk More direct Direct Risk Broader intelligence (perhaps machine intelligence or even aliens). Agency risk probably means someone deliberately trying to ensure nobody survives, which may make it easier to get through the resilience layer by allowing anticipation of and response to possible survival plans. In principle agency risk includes cases where someone is deliberately trying to reach everyone, and only by accident does so in a way that kills them. \n Indirect risks If the risk threatens extinction without killing everyone, it must reduce our long-term ability to survive as a species. This could include a very broad range of effects, but we can break them up according to the kind of ability it impedes. Habitat risks make long-term survival impossible by altering or destroying the environment we live in so that it cannot easily support human life. For example a large enough asteroid impact might throw up dust which could prevent us from growing food for many yearsif this was long enough, it could lead to human extinction. Alternatively an environmental change which lowered the average number of viable offspring to below replacement rates could pose a habitat risk. Capability risks knock us back in a way that permanently remove an important societal capability, leading in the long run to extinction. One example might be moving to a social structure which precluded the ability to adapt to new circumstances. We are gesturing towards a distinction between habitat risks and capability risks, rather than drawing a sharp line. Habitat risks work through damage to an external environment, where capability risks work through damage to more internal social systems (or even biological or psychological factors). Capability risks are also even less direct than habitat risks, perhaps taking hundreds or thousands of years to lead to extinction. Indeed there is not a clear line between capability risks and events which damage our capabilities but are not extinction risks (cf. section 6). Nonetheless when considering risks of human extinction it may be important to account for events which could cause the loss of fragile but important capabilities. An important type of capability risk may be civilisational collapse. It is possible that killing enough people and destroying enough infrastructure could lead to a collapse of civilisation without causing immediate extinction. If this happens, it is then plausible that it might never recover, or recover in a less robust form, and be wiped out by some subsequent risk. It is an open and important question how likely this permanent loss of capability is  (Beckstead, 2015b) . If it is likely, the resilience layer may therefore be particularly important to reinforce, perhaps along the lines proposed by  Maher and Baum (2013) . On the other hand, if even large amounts of destruction have only small effects on the chances of eventual extinction, it becomes more important to focus on risks which can otherwise get past the resilience layer. \n Classifying example risks by each of origin, scaling, and endgame We finally illustrate our completed classification scheme by applying it to examples, which we summarise in Table  1 . Throughout the text, we've repeatedly referred to an asteroid strike that might cause extinction due to an ensuing impact winter. We've called this a natural risk regarding its origin; a large risk regarding scale, with no opportunity to intervene between the asteroid impact and its damage affecting the whole globe; and, if we assume that humanity dies out because climatic changes remove the ability to grow crops, a habitat risk in the endgame phase. Our next pair of examples illustrates that risks with the same salient central mechanismin this case nuclear warmay well differ during other phases. Consider first a nuclear war precipitated by a malfunctioning early warning system that is, a nuclear power launching what turns out to be a first strike because it falsely believed that its nuclear destruction was imminent. Suppose further that this causes a nuclear winter, leading to human extinction. This would be an accident that scales via leverage, and finally manifests as a habitat risk. Contrast this with the intentional use of nuclear weapons in an escalating conventional war, and assume further that this either doesn't cause a nuclear winter or that some humans are able to survive despite adverse climatic conditions. Instead, humanity never recovers from widespread destruction, and is eventually wiped out by some other catastrophe that could have easily been avoided by a technologically advanced civilisation. This second scenario would be a conflict that again scaled via the leverage associated with nuclear weapons, but then finished off humanity by removing a crucial capability rather than via damage to its habitat. We close by applying our classification to a more speculative risk we might face this century. Some scholars (e.g.  Bostrom, 2014)  have warned that progress in artificial intelligence (AI) could at some point allow unforeseen rapid self-improvement in some AI system, perhaps one that uses machine learning and can autonomously acquire additional training data via sensors or simulation. The concern is that this could result in a powerful AI agent that deliberately wipes out humanity to pre-empt interference with its objectives (see  Omohundro, 2008 , for an argument why such preemption might be plausible). To the extent that we currently don't know of any machine learning algorithms that could exhibit such behaviour, this would be an unseen risk; the scaling would be via leverage if we assume a discrete algorithmic improvement as trigger, or alternatively the risk could be rapidly cascading; in the endgame, this scenario would present an agency risk. \n Policy implications for resilience against extinction • To guard against what today would be ubiquity risks, we may in the future be able to establish human settlements on other planets  (Armstrong and Sandberg, 2013) . 10 • Vector risks may not reach people in isolated and self-sufficient communities. Establishing disaster shelters may hence be an attractive option. Self-sufficient shelters can also reduce habitat risk.  Jebari (2015)  discusses how to maximise the resilience benefits from shelters, while Beckstead (2015a) has argued that their marginal effect would be limited due to the presence of isolated peoples, submarine crews, and existing shelters. • Resilience against vector and agency risks may be increased by late-stage response measures that work even in the event of widespread damage to infrastructure and the breakdown of social structure. An example might be the 'isolated, self-sufficient, and continuously manned underground refuges' suggested by  Jebari (2015, p. 541) . \n Allocating resources between defence layers In this section we will use our guiding idea of three defence layers to present a way of calculating the extinction probability posed by a given risk. We'll draw three high-level conclusions: first, the most severe risks are those which have a high probability of breaking through all three defence layers. Second, when allocating resources between the defence layers, rather than comparing absolute changes in these probabilities we should assess how often we can halve the probability of a risk getting through each layer. Third, it's best to distribute a sufficiently large budget across all three defence layers. We are interested in the probability p that a given risk R will cause human extinction in a specific timeframe, say by 2100. Whichever three classes R belongs to, in order to cause extinction it needs to get past all three defence layers; its associated extinction probability p is therefore equal to the product of three factors: 1. The probability c for R getting past the first barrier and causing a catastrophe; 2. The conditional probability g that R gets past the second barrier to cause a global catastrophe, given that it has passed the first barrier; and 3. The conditional probability e that R gets past the third barrier to cause human extinction, given that it has passed the second barrier. In short: p = cÁgÁe. Each of c, g, and e can get extremely small for some risks. But the extinction probability p will be highest when all three terms are non-negligible. Hence we get our (somewhat obvious) first conclusion that the most concerning risks are those which can plausibly get past all three defence layers. However, most concerning doesn't necessarily translate into the most valuable to act on. Suppose we'd like to invest additional resources into reducing risk R. We could use them to strengthen either of the three defences, which would make it less likely that R passes that defence. We should then compare relative rather than absolute changes to these probabilities, which is our second conclusion. That is, to minimise the extinction probability p we should ask which of c, g, and e we can halve most often. This is because the same relative change of each probability will have the same effect on the extinction probability phalving either of c, g, or e will halve p. By contrast, the effect of the same absolute change will vary depending on the other two probabilities; for instance, reducing c by 0.1 reduces p by 0.1ÁgÁe. In particular, a given absolute change will be more valuable if the other two probabilities are large. When one of c, g, or e is close to 100%, it may be much harder to reduce it to 50% than it would be to halve a smaller probability. The principle of comparing how often we can halve c, g, and e then implies that we're better off reducing probabilities not close to 100%. For example, consider a large asteroid striking the Earth. We could take steps to avoid it (for example by scanning and deflecting), and we could take steps to increase our resilience (for example by securing food production). But if a large asteroid does cause a catastrophe, it seems very likely to cause a global catastrophe, and it is unclear that there is much to be done in reducing the risk at the scaling stage. In other words, the probability g is close to 1 and prohibitively hard to substantially reduce. We therefore shouldn't invest resources into futile responses, but instead use them to strengthen both prevention and resilience. What if each defence layer has a decent chance of stopping a risk? We'll then be best off by allocating a non-zero chunk of funding to all three of thema strategy of defence in depth, our third conclusion. The reason just is the familiar phenomenon of diminishing marginal returns of resources. It may initially be best to strengthen a particular layerbut once we've taken the low-hanging fruit there, investing in another layer (or in reducing another risk) will become equally cost-effective. Of course, our budget might be exhausted earlier. Defending in depth therefore tends to be optimal if and only if we can spend relatively much in total. We close by discussing some limitations of our analysis. First, we remain silent on the optimal allocation of resources between different risks (rather than between different layers for a fixed risk or basket of risks); indeed, as we'll argue in section 6, comprehensively answering the question of how to optimally allocate resources intended for extinction risk reduction requires us to look beyond even the full set of extinction risks. We do hope that our work could prove foundational for further research that investigates both the allocation between risks and between defence layers simultaneously. Indeed, it would be straightforward to consider several risks p i = c i Ág i Áe i , i = 1, . . ., n; assuming specific functional forms for how the probabilities c i , g i , and e i change in response to invested resources could then yield valuable insights. Second, we have not considered interactions between different defence layers or different risks  (Graham et al., 1995; Baum, 2019; Baum and Barrett, 2017; Martin and Pindyck, 2015) . These can present both as tradeoffs or synergies. For example, traffic restrictions in response to a pandemic might slow down research on a treatment that would render the disease non-fatal, thus harming the resilience layer; on the other hand, they may inadvertently help with preventing malicious risk or being resilient against agency risk. \n Policy implications for resource allocation within risk management • The most important extinction risks to act on are those that have a non-negligible chance of breaking through all three defence layersrisks where we have a realistic chance of failing to prevent, a realistic chance of failing to successfully respond to, and a realistic chance of failing to be resilient against. • Due to diminishing marginal returns, when budgets are high enough it will often be best to maintain a portfolio of significant investment into each of prevention, response, and resilience. \n Underlying risk factors: risks to the defence layers In sections 2-4 we have considered ways of classifying threats that may cause human extinction and the pathways through which they may do so. Our classification was based on the three defence layers of prevention, response, and resilience. Giving centre stage to the defence layers provides the following useful lens for extinction risk management. If our main goal is to reduce the likelihood of extinction, we can equivalently express this by saying that we should aim to strengthen the defence layers. Indeed, extinction can only become less likely if at least one particular extinction risk is made less likely; in turn this requires that it has a smaller chance of making it past at least one of the defence layers. This is significant because there is a spectrum of ways to improve our defences depending on how narrowly our measures are tailored to specific risks. At one extreme, we can increase our capacity to prevent, respond to, or be resilient against one risk; for example, we can research methods to deflect asteroids. In between are measures to defend against a particular class of risk, as we've highlighted in our policy recommendations. At the other extreme is the reduction of underlying risk factors that weaken our capacity to defend against many classes of risks. Risk factors need not be associated with any potential proximate cause of extinction. For example, consider regional wars; even when they don't escalate to a global catastrophe, they could hinder global cooperation and thus impede many defences. Global catastrophes constitute one important type of risk factor. We already discussed the possibility of them making earth uninhabitable or removing a capability that would be crucial for long-term survival. But even if they do neither of these, they can severely damage our defence layers. In particular, getting hit by a global catastrophe followed in short succession by another might be enough to cause extinction when neither alone would have done so. There are significant historic examples of such compound risks below the extinction level. For instance, the deadliest accident in aviation history occurred when two planes collided on an airport runway; this was only possible because a previous terrorist attack on another airport had caused congestion due to rerouted planes, which disabled the prevention measure of using separate routes for taxiing and takeoff  (Weick, 1990) . When considering catastrophes we should therefore pay particular attention to negative impacts they may have on the defence layers. Our capacity to defend also depends on various structural properties that can change in gradual ways even in the absence of particularly conspicuous events. For example, the resilience layer may be weakened by continuous increases in specialisation and global interdependence. This can be compared with the model of synchronous failure suggested by  Homer-Dixon et al. (2015) . They describe how the slow accumulation of multiple simultaneous stresses makes a system vulnerable to a cascading failure. It is beyond the scope of this article to attempt a complete survey of risk factors; we merely emphasise that they should be considered. We do hope that our classifications in sections 2-4 may be helpful in identifying risk factors. For example, thinking about preventing conflict and common risks may point us to global governance, while having identified vector and agency risks may highlight the importance of interdependence (even though, upon further scrutiny, these risk factors turn out to be relevant for many other classes of risk as well). We conclude that the allocation of resources between layers defending against specific risks, which we investigated in section 2, is not necessarily the most central task of extinction risk management. It is an open and important question whether reducing specific risks, clusters of risks, or underlying risk factors is most effective on the margin. \n Policy implications from underlying risk drivers • Research on smaller-scale risks should pay particular attention to how they might damage the three defence layers against extinction risks. Risk management should aim to mitigate such damage. • Conversely, the study of extinction risks cannot be limited to individual triggers such as asteroids or specific technologies. It would be desirable to better understand which underlying risk factors contribute to extinction risk by weakening our defences. For example, in what ways does global interdependence make extinction from a global catastrophe more likely, and are there interventions to mitigate this effect? \n Conclusions The study and management of extinction risks are challenging for several reasons. Cognitive biases make it hard to appreciate the scale and probability of human extinction  (Wiener, 2016; Yudkowsky, 2008) . Most potential people affected are in future generations, whose interests aren't well represented in our political systems. Hazards can arise and scale in many different ways, requiring a variety of disciplines and stakeholders to understand and stop them. And since there is no precedent for human extinction, we struggle with a lack of data. Faced with such difficult terrain, we have considered the problem from a reasonably high level of abstraction; we hope thereby to focus attention on the most crucial aspects. If this work is useful, it will be as a foundation for future work or decisions. In some cases our classification might provoke thoughts that are helpful directly for decision-makers that engage with specific risks. However, we anticipate that our work will be most useful in informing the design of systems for analysing and prioritising between several extinction risks, or in informing the direction of future research. \n Data availability statement Data sharing is not applicable to this article as no new data were created or analysed. \n Notes 1 We are particularly indebted to Toby Ord for several very helpful comments and conversations. We also thank Scott Janzwood, Sebastian Farquhar, Martina Kunz, Huw Price, Se an O h Eigeartaigh, Shahar Avin, the audience at a seminar at Cambridge's Centre for the Study of Existential Risk (CSER), and two anonymous reviewers for helpful comments on earlier drafts of this article. We're also grateful to Eva-Maria Nag for comments on our policy suggestions. The contributions of Owen Cotton-Barratt and Anders Sandberg to this article are part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 669751). 1. In the terminology of the United Nations Office for Disaster Risk Reduction (UNDRR, 2016), response denotes the provision of emergency services and public assistance during and immediately after a disaster. In our usage, we include any steps which may prevent a catastrophe scaling to a global catastrophe. This could include work traditionally referred to as mitigation. 2. The concept of resilience, originally coined in ecology  (Holling, 1973) , today is widely used in the analysis of risks of many types (e.g.  Folke et al., 2010) . In UNDRR (2016) terminology, resilience refers to '[t]he ability of a system, community or society exposed to hazards to resist, absorb, accommodate, adapt to, transform and recover from the effects of a hazard in a timely and efficient manner, including through the preservation and restoration of its essential basic structures and functions through risk management.' In this article, we usually use resilience to specifically denote the ability of humanity as a whole to recover from a global catastrophe in a way that enables its long-term survival. This ability may in turn depend on the resilience of many smaller natural, technical, and socio-ecological systems. 3. Strictly knowledge and intentionality are two separate dimensions; however it is essentially impossible to intend the harm without being aware of the possibility, so we treat it as a spectrum with ignorance at one end, intent at the other end, and knowledge without intent in the middle. Again, there is some blur between these: there are degrees of awareness about a risk, and an intention of harm may be more or less central to an action. 4. There are degrees of lack of foresight of the risk. Cases where the people performing the activity are substantially unaware of the risks have many of the relevant features of this category, even if they have suspicions about the risks, or other people are aware of the risks. 5. They may not intend for that damage to cause human extinctionfor the purposes of acting on this classification it's more useful to know whether they were trying to cause harm. 6. We thank an anonymous reviewer for suggesting the policy responses of avoiding dangerous technologies and mandating insurance. 7. Global coordination more broadly may however be a double edged tool, since increased interdependency if not well managed can also increase the chance of systemic risks  (Goldin & Mariathasan, 2014) . 8. We thank an anonymous reviewer for suggesting both the third general recommendation and the example. 9. What about a risk that directly kills, say, 99.9999% of people? Technically this poses only an indirect risk, since to cause extinction it needs to remove the capability of the survivors to recover. However, if the proportion threatened is high enough then we can reason that it must also have a way of reaching essentially everyone, so the analysis of direct risks will also be relevant. 10. Some scholars have argued that humanity expanding into space would increase other risks; see for example an interview  (Deudney, n.d.)  and an upcoming book (Deudney, forthcoming) by political scientist Daniel  Deudney and Torres (2018a) . Assessing the overall desirability of space colonisation is beyond the scope of this article. Figure 3 . 3 Figure 3. Classification of risks by scaling mechanism. \n Figure 4 . 4 Figure 4. Classification of risks by endgame. \n Figure 1. Three broad defence layers. Classification of risks by origin. be ignorant of or aware of the possible harm; if the latter, they may or may not intend it. 3 Origin Scaling Endgame Catastrophe Global Catastrophe Extinction P e r v e n t o i n R e p s o n e s R s e i l i n e c e How does it start? Why don't we stop it? How does it get everyone? Figure 2. No people Few people Many people involved involved involved harm Unforeseen Natural Risk harm Foreseen harm Intentional Anthropogenic Risk \n Table 1 . 1 Applying our classification to five examples. Note that each risk belongs to three classes, one for each defence layer Classification by Origin Scaling Endgame Associated defence layer Prevention Response Resilience Terrorists releasing Malicious Cascading Vector engineered pandemic Asteroid strike causing Natural Large Habitat impact winter False alarm triggering Accident Leverage Habitat nuclear war with ensuing nuclear winter Conventional proxy war Conflict Leverage Capability escalating to nuclear war causing irreversible civilisational collapse Unforeseen rapid learning Unseen Leverage Agency producing an AI agent that kills humans to preempt interference with its objectives \n\t\t\t © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Global Policy (2020) 11:3 \n\t\t\t © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Defence in Depth \n\t\t\t Global Policy (2020) 11:3 © 2020 The Authors. Global Policy published by Durham University and John Wiley & Sons Ltd.Defence in Depth", "date_published": "n/a", "url": "n/a", "filename": "Global Policy - 2020 - Cotton‐Barratt - Defence in Depth Against Human Extinction Prevention Response Resilience and.tei.xml", "abstract": "We look at classifying extinction risks in three different ways, which affect how we can intervene to reduce risk. First, how does it start causing damage? Second, how does it reach the scale of a global catastrophe? Third, how does it reach everyone? In all of these three phases there is a defence layer that blocks most risks: First, we can prevent catastrophes from occurring. Second, we can respond to catastrophes before they reach a global scale. Third, humanity is resilient against extinction even in the face of global catastrophes. The largest probability of extinction is posed when all of these defences are weak, that is, by risks we are unlikely to prevent, unlikely to successfully respond to, and unlikely to be resilient against. We find that it's usually best to invest significantly into strengthening all three defence layers. We also suggest ways to do so tailored to the classes of risk we identify. Lastly, we discuss the importance of underlying risk factorsevents or structural conditions that may weaken the defence layers even without posing a risk of immediate extinction themselves. \n Policy implications • We can usually best reduce extinction risk by splitting our budget between all defence layers. • We should include measures that reduce whole classes of risks, such as research uncovering currently unseen risk. We should also address risk factors that would not cause extinction themselves but weaken our defences, for example, bad global governance. • Future research should identify synergies between reducing extinction and other risks. For example, research on climate change adaptation and mitigation should assess how we can best preserve our ability to prevent, respond to, and be resilient against extinction risks.", "id": "f928ed533d748d227ebed8529e0a41fb"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Hin-Yan Liu", "Matthijs M Maas"], "title": "'Solving for X?' Towards a problem-finding framework to ground long-term governance strategies for artificial intelligence", "text": "Introduction Change is not a new feature in human affairs. Nor is the need for some forms of governance in response to ongoing, and at times challenging, developments. Yet over the last two centuries, and acutely within the last few decades, something has begun to change in change. Daniel Deudney has observed how \"the emergence and global spread of a modern civilization devoted to expanding scientific knowledge and developing new technologies has radically increased the rate, magnitude, complexity, novelty, and disruptiveness of change\"  (Deudney, 2018, 223) . Accelerating climate collapse feedback loops are driven by economic and industrial systems intimately intertwined with fossil fuel energy extraction  (Di Muzio, 2015) ; arsenals of nuclear weapons are held at hair-trigger launch alert, under a continuous state of functional 'thermonuclear monarchy'  (Scarry, 2016) ; highly interlinked and efficient global supply chains, transport networks, and economies prove acutely vulnerable to pandemics; and emerging and potentially catastrophic risks from new technologies  (Bostrom & Cirkovic, 2008; Bostrom, 2013 ; see also  Rayfuse, 2017)  ensure that our global society is increasingly grasped in the throes of 'turbo change'  (Deudney, 2018, 223; Rosa, 2013) . Accordingly, an array of new technologies are reshaping the stakes and rapidity of the societal, strategic, and even geophysical and ecosystem changes which we must manage, both today and over the long-term. The renowned biologist E.O. Wilson once playfully quipped that \"The real problem of humanity is the following: we have paleolithic emotions; medieval institutions; and god-like technology\"  (Wilson, 2009) . If that is so, can the diverse elements and processes constituting global governance evolve along with the changing stakes and nature of the challenge? A key question for any broader project examining how 'strategy' ought to be generally reconfigured within society's complex networks of communities, organizations, or systems in order to adopt meaningful and effective long-term perspectives (  van Assche, Verschraegen, Gruezmacher, & Boezeman, 2020)  concerns how governance needs to be reoriented towards the long-term perspectives that flow from these urgent and unpredictable technological challenges. Moreover, the question may prove particularly salient and critical in the technological context. In the coming decades, existing governance instruments may well face a historical 'inflection point' in their relation to this series of emerging and 'converging' technologies  (Pauwels, 2019) . Our capacity to collectively manage our relationship to such technologies, such as artificial intelligence (AI), may prove to be both a key objective for, and a key stress (or litmus) test of, our governance regimes. How or why might we have to adapt or replace governance systems in the face of the 'technology tsunami'  (Danzig, 2017) ? Of course, this is not to say that we cannot influence, channel, or resist such technological shocks-indeed, contrary to frequent depictions of the regulatory 'pacing problem' (e.g.  Hagemann, Huddleston, & Thierer, 2018; Marchant, 2011) , it should be kept in mind that governance structures also provide the landscape that shapes and guides technological development, such that we do not need to resign ourselves to reactively responding to shocks  (Crootof & Ard, 2021, 12)  but can also seek to shape paths of development in advance. Faced with a 'tsunami', we need not just worry around how to manage or weather it, but also about how we might channel or even surf it. Nonetheless, how might we go about making such governance changes? How can we ensure that we do not find ourselves \"addressing twenty-first century challenges with twentieth-century laws\"  (Jensen, 2014, 253)  and why might such extant approaches prove problematic in the first place? We face an increasingly complex historical challenge of evolving our governance systems-or, if necessary, developing new ones-to be up to the task of responsibly managing this array of potent challenges, and to do so not just for the near-, but also for the long-term. This paper questions the premise that the extant regulatory and governance orders will remain fully intact and functional throughout the turbulent period ushered in by complex, 'transversal' emerging issues (see  Morin et al., 2019) . It does so taking its departure from one of these trend-drivers-artificial intelligence. We argue that AI and its applications will outfox contemporary regulatory and governance orders. Specifically, AI holds the potential to reveal, enable, or drive society towards new regulatory and governance equilibria, and is thus a prime candidate for triggering regulatory disruption. Again, this is not to say that we have to be merely reactive: we can and must influence and shape patterns of regulatory disruption; however, to do so, we have to be aware of the dynamics, pathways, and vectors of change . What does this reveal? We argue that an underlying problem lies in the fact that many contemporary regulatory and governance orders (and their respective academic fields) continue to implicitly adopt or manifest problem-solving orientations. In other words, regulation and governance are endeavours that respond to recognised, defined, and compartmentalised problems. Overlooked in such an orientation, however, are the inherent and contingent limitations that needlessly straight-jacket the endeavour. By prematurely settling upon an overly and necessarily narrow, and somewhat contingent, range of issues to be addressed these problem-solving efforts may increase the probability of a turbulent or even catastrophic transition towards an AI-permeated world. Accordingly, our aim in this paper is to shed light on the potential of, and prospects for a problem-finding orientation for formulating and anchoring long-term strategy assemblages for the governance of AI-strategies that take stock of the ways in which the processes, instruments, assumptions and even aims of existing governance orders will be shaped and disrupted by AI. Thus our overarching aim in this paper is to chart the underexplored terrain beyond the boundaries of current problem-solving regulatory and governance debates. By actively and systematically searching the potential problem-space opened up by AI, this paper aims to increase the confidence that efforts geared towards addressing presently-identified problems triggered by AI are relevant over the long-term, and do constitute the significant questions that need to be addressed, as well as to identify new potential problems that AI might raise for regulation and governance, which have been underexplored to date. Accordingly, this paper proceeds as follows. We first ground a rationale for a problem-finding governance framework. We sketch the policy problems created by AI technology, and provide 5 reasons on the basis of which a problem-solving governance approach to these challenges fails or falls short. We then extend the argument by arguing that problem-solving governance approaches are ill-equipped to engage with 'wicked problems' created by AI. We conclude the rationale by grounding the epistemic and scientific validity of a complementary problem-finding AI governance (research) program. Secondly, we then set out our framework of AI governance across four strategic 'levels' which correspond to AI governance approaches that take for granted different parameters, contraints and failuremodes of scholarship, which variably approaches AI issues from a perspective of (0) 'business-as-usual'; (1) 'puzzle-solving'; (2) 'governance disruptor-finding'; or (3) 'charting macrostrategic trajectories'. Thirdly, we provide reflections on nuances, implications, and shortcomings of this long-term governance framework. We discuss how to best coordinate AI governance strategies amongst and between these complementary four levels, in order to avoid the failure modes that might occur when restricting analysis or policy to any one of these levels. We assess how 'problem-finding' scholarship can be applied in problem-solving roles. We theorize how these four levels may constitute a 'Goldilocks Zone for Governance' which, in a larger perspective, highlights the assumptions and boundaries of any governance system; and we discuss how we should navigate the linkages between strategies and overarching narratives. We conclude by suggesting that these lessons are critical in structuring governance responses-to AI; and to other vectors of change-that are meaningful and resilient into the long term. \n From problem-solving to problem-finding: a rationale In the first place, it is important to come to understand the plausible shortfalls of problem-solving approaches. But to do so, we must understand what characterizes these approaches; why they fall short of providing long-term governance responses to AI; and why an alternative and complementary problem-finding paradigm may be both pragmatically effective, as well as epistemically and scientifically warranted. \n Problem-solving governance is necessary but insufficient to AI While there are a wide range of philosophical, theoretical, and technical perspectives on AI  (Bhatnagar et al., 2018; Corea, 2020; Domingos, 2015; Legg & Hutter, 2007; Rapaport, 2020) , in practical terms it can be understood as a generally enabling 'omni-use technology'  (Clark, 2018) . More precisely, it can be understood as a sociotechnical system in practice which consists of four layers  (Maas, 2020, 37) : (1) a portfolio of algorithms and computational techniques (e.g. symbolic approaches; supervised learning, unsupervised learning; reinforcement learning; GANs…) which are embedded in physical computing platforms or distributed across networks. (2) In turn, these can be used for automating and improving the accuracy, speed, and/or scale of (machine) decision-making in complex or large (data) environments; yielding a set of capabilities that can be used to support, substitute for-or improve upon human performance in specific tasks (including but not limited to 'pattern recognition', 'data classification', 'prediction', 'data generation', 'anomaly detection', 'optimization', 'independent decision-making', etc.)  (Scharre & Horowitz, 2018 ). (3) These tasks are individually narrow, but because these capabilities are relevant across diverse (industrial or strategic) contexts, they consequently support a spectrum of useful applications across diverse domains. (4) These applications in turn produce diverse forms of new behaviour resulting in sociotechnical changes. While today AI usage is still conditional on a range of resources-such as the availability of sufficient training data, computing hardware, technical talent, and organizational adaptation  (Buchanan, 2020; Horowitz, 2018; Hwang, 2018) -these barriers are all falling at varying rates. As such, in terms of societal impact and governance stakes, artificial intelligence can be functionally modelled as a strategic 'General-Purpose Technology' along the lines of steampower, electricity, or computing  (Leung, 2019; Trajtenberg, 2018) . Given the sheer breadth of its underlying technologies, capabilities, and potential applications, 1 it should be no surprise that AI throws up a vast range of issues across the policy-space, as reflected in the emerging literature studying distinct law and policy questions  (Calo, 2017; Dafoe, 2018; Guihot, Matthew, & Suzor, 2017; Hoffmann-Riem, 2020; Scherer, 2016; Turner, 2018) . Yet, the identified literature on discrete policy issues adopts a general problem-solving orientation. 2 Under this paradigm, policy scholarship compartmentalises AI's immense potential problem-space into specific problems-from the safety of autonomous vehicles to misuse of 'deep fakes', and from new criminal uses to 'killer robots'-that are often defined or segmented according to disciplinary perspectives 1 Given this, it may not be meaningful in many cases to speak of 'AI' as a singular thing to be regulated. Nonetheless, in the context of this paper, while we highlight and distinguish between different problem areas and domains, we also emphasize the importance of recognizing commonalities in problem logics and themes across conventional domains (See also  Crootof & Ard, 2021, 11) ; as such, for convenience, we will in some parts of our analysis refer to the suitcase term of 'AI' in the singular. We thank a reviewer for prompting this clarification. 2 As always, no term is without its difficulties. There are some conceptual challenges with designating existing scholarship or governance approaches as 'problem solving'. For one, this (a) does not (directly) interrogate existing governance actors' privileged ability to determine which are and are not 'problems' to be 'solved' (e.g. certain AI-enabled technologies such as DeepFakes in some sense shift around (epistemic) power; that may make them a 'problem' for governments; but from the perspective of certain political actors they more obviously present themselves as an opportunity. However, since these latter actors do not conventionally 'do governance', their perspective is not easily presented under this framework). In the second place, and relatedly, (b) the term 'problem-solving' appears to at least implicitly pre-suppose or imply that the pre-existing state of affairs was broadly 'unproblematic' before it was rudely disrupted by a new technological 'problem' which upset that functional state of affairs-with the implication that governance might again be broadly unproblematic once that problem has been adequately solved. That would obviously be a highly normative and debatable assumption, which many (emerging) governance actors would challenge. However, it is a shortfall that primarily afflicts 'problem-solving' governance approaches-and we would emphasize that problem-finding approaches can bring in a wider range of actors, agendas, and values. We thank Henrik Palmer Olsen for prompting this reflection.  (Crootof & Ard, 2021; Petit, 2017) . There are several interrelated limitations that flow from attempts to solve pre-packaged policy problems which, taken together, suggest that this is a necessary but insufficent strategy for long-term governance, especially in the context of societally-disruptive technologies such as AI. The problem-solving orientation takes departure from issues that are discursively recognized or constructed (by policymakers as well as by scholars in a field) as a 'clear and present danger': that is, they often focus on issues that have given rise to vivid (if anecdotal) challenges such that they are discernible (and discerned) by public and policymakers; which are accordingly highlighted (and, in some cases, 'securitized'  (Stritzel, 2014 )) within government strategies; and which are validated, accepted, operationalized, and funded as legitimate and well-bounded research topics within existing disciplinary fields. In this way, the problem-solving orientation is in a sense a demand-driven (rather than supply-driven) approach to research program orientation and policy formulation. At its limits, it constitutes a 'local search' for the next urgent, externally-validated and -packaged problem that can be fitted to analysis by the discipline's available methodological or conceptual tools, rather than a 'global search' across the broader landscape of possible problems (let alone each problem's landscape of possible perspectives). To an extent, this orientation is understandable. Scholars only have so much time, so much attention. For all that interdisciplinarity is often praised, it can often appear a risky, difficult affair  (Fish, 1989 ). Yet while perhaps appealing and even understandable from the perspective of a pre-existing academic division of expertise and labour, however, five problems adhere to a problem-solving approach. In brief, these are (1) the unreflexive over-reliance on narrow metaphors or analogies in the face of multifarious, complex phenomena; (2) the tautological manner in which existing governance assemblages surface primarily those problems that are already (or most) legible to them; (3) the constrained path-dependency; (4) inability to clearly distinguish between symptomatic and root-cause problems; (5) the promotion of a false sense of security through a rapid delineation of the problem-space that prematurely closes-off large parts of the governance solution-space. \n Unreflexive reliance on over-narrow metaphors In the first place, in many areas, and especially where it comes to new technologies, problem-solving perspectives often, implicitly or explicitly, rely on drawing metaphors or analogies in order to fit a new problem or topic within the pre-existing boxes. Yet, as any given analogy or metaphor used to describe new technologies by necessity is incomplete  (Balkin, 2015; Crootof, 2018) , problem-solving perspectives that invoke them are necessarily partial and incomplete, and potentially even misleading, as they express only certain disconnected aspects of the overall challenge posed by the technology. This insufficiency of a problem-solving approach is reflected in the ancient parable of the 'blind men and the elephant' which warns against concluding that elephants are like pythons, simply because one has exhaustively touched one elephant's trunk  (Saxe, 1872) . One can see this same risk in the context of the multifarious debates round AI, which often explicitly or implicitly trade on highly different metaphors or understandings  (Brockman, 2019; Parson, Re, Solow-Niederman, & Zeide, 2019) . Amongst scholars writing on AI governance, many take comprehensively different views, not just on the individual questions of what AI is, how AI operates, how we treat or relate to AI technology, how we use AI in society, or what (unintended) impacts AI will have on our society down the road-but indeed take different positions on which of these above frames is even the relevant one for the policy question at hand. For instance, does the regulation of social robots turn on questions of whether the artefact is 'software' or a 'cyber-physical system' capable of physical damage  (Calo, 2015 (Calo, , 2017 ? On questions of how humans will relate to humanoid systems  (Darling, 2012) ? Or on questions of how they might provide new attack surfaces for criminal (mis)use  (Brundage et al., 2018; Caldwell, Andrews, Tanay, & Griffin, 2020; Hayward & Maas, 2020; King, Aggarwal, Taddeo, & Floridi, 2019) ? Each of these local perspectives provides pieces of the puzzle that can be valuable and legitimate, but often there is no reflection on how the specific narrow perspective-not just on these questions, but even on which of these questions is the appropriate one to ask-is but one of various ways to frame and understand the salient features or key impacts of the technology (See also  Cave & Dihal, 2019; Cave et al., 2020) . Indeed, the 'blind man and the elephant' metaphor may itself be overly restrictive: by extending or reframing the parable, we can see that a problem-solving approach risks misapprehending the problem in many more ways. After all, the problem is not only that an overtly narrow view may result in us (1) believing that an elephant is like a snake, on the basis of studying its trunk (i.e. mischaracterizing problem X on the basis of its local facet). Rather, the very focus on 'the elephant in isolation' occludes a range of other potential issues. To stay within the framing of the parable 3 ; our narrow focus on the 'elephant' in front of us may lead us to (2) fail to notice the tiger that is crouching up behind us (missing out on urgent 'out-of-context' problems or development Y); (3) fail to highlight how this elephant came to potentially be brought out of its habitat and social context and presented to us, and how it came to be constructed and designated as a salient object in need of closer examination and apprehension (missing out on the socio-political roots shaping the research agenda on X); (4) fail to apprehend how, rather than apprehending the 'essence' of an individual elephant, it is also relevant to understand how that elephant fits within a broader ecosystem-or what the health of the elephant tells us about the broader ecosystem (missing out on the interrelation of problem X with seemingly 'unrelated' entities, problems, or developments); (5) base our understanding of the elephant on a momentary snapshot, rather than a longitudinal study of an elephant's developments over the course of its lifecycle (taking an overtly static rather than dynamic view); (6) take for granted that an elephant can be appropriately and sufficiently apprehended through touch-and appropriately and sufficiently described at the level of human-scale features-rather than considering how additional (and different) insights into the elephant could be gleaned from using scientific tools that enable us to study it at different levels of analysis, from fundamental physics, cellular biology, or etiology (taking for granted a narrow methodological toolkit to studying problem X at a narrow level of granularity). This illustrates the epistemic limits and shortfalls of problem-solving approaches to understanding and governing new technologies. These approaches frequently focus on: the here and now; the direct harm; the last person to touch the technology prior to an accident; or the degree to which any solution can be found which mitigates the direct fallout; or redresses the directly (legally-recognized) injury. For example, legal problems that flow from AI applications might revolve around questions of liability for entities occupying a liminal position between agent and object, which befuddle existing legal doctrine  (Liu, 2012; see generally Turner, 2018) . Accommodating this challenge may be necessary for the law to regain coherence, but does little to address competing plausible models of AI applications such as a networks, or a systems, approach to understanding AI  (Ekelhof, 2019; Liu, 2019a) . This approach or mindset suggests that legal problems are just that, 'problems' that can be identified and interrogated with legal tools, but that this process itself skews the form that the underlying challenges are deemed to take, and the types of (legal) responses that are legitimate to propose in their wake. \n Tautological responses Second, a problem-solving approach ensures that any problems that are surfaced by examination are often tautological but somewhat arbitrary in relation to the significance of their potential sociotechnical impact. AI applications might generate legal problems because those are the problems that AI generates for the existing law-more than for the underlying society. In practice, this might often highlight legally or philosophically 'unusual' problems which are clearly and obviously blurring our existing 'symbolic order'-that is, the fundamental distinctions and categories which a general society, broad governance network, or specific legal order relies upon to draw boundaries and understand the relevant reality (see  Douglas, 1966 )-over less 'legible' but more 'socially disruptive' developments that provide scholars with less 'satisfying' analytical or legal puzzles. One might consider for instance the way by which discourses on self-driving cars have become dominated, for better or worse, by their linkage to the high-profile 'trolley problem' thought experiment from ethics, a development many have begun to critique as having led such governance debates down a dead-end  (Bauman, Peter McGraw, Bartels, & Warren, 2014; Cunneen et al., 2020; De Freitas, Anthony, & Alvarez, 2019; Himmelreich, 2018; Jaques, 2019; Wolkenstein, 2018) . A key problem here is that within problem-solving approaches there is often no reliable or unambiguous appraisal process through which to gauge whether or why those problems that are generated or focused on, are likely to be the significant and persistent problems into the future, and not just solely 'legally interesting'. If problem-solving approaches get hooked on temporary, doctrinal questions which solve unrepresentative 'edge' problems (especially problems which might, in due course, end up being 'dissolved' anyway as a result of technological developments or 'out-of-domain' social or regulatory changes), however, this bodes ill for their viability or sufficiency into the long-term. \n Limiting path-dependencies and 'brittleness' Third, there are clear path dependencies inherent to problem-solving approaches. The problems that arise are frequently understood as variations on previously validated (if not necessarily 'solved') problems, and responses often deploy analogies to those that were invoked in past iterations  (Crootof, 2018 (Crootof, , 2019b Mandel, 2017) . This sets strong constraints upon the trajectory of problem-solving efforts, ensuring diminishing-or even 'negative'-returns when these efforts are brought to bear on genuinely fresh challenges or unseen cases. Curiously, in this way a legal system is not unlike a contemporary machine learning algorithm itself: it works entirely and solely from its training data, and so can be structurally biased (depending on what elements or cases are under-or over-represented in its 'training set'), or brittle when it encounters genuinely unprecedented 'edge cases' that combine certain strange features of past cases, or bring in genuinely unprecedented ('out-of-training-distribution') features-as in the old legal maxim that 'hard cases make bad law'  (Davis & Stark, 2001) . Moreover, just as machine learning systems have proven susceptible to so-called 'adversarial input'  (Goodfellow, Shlens, & Szegedy, 2014; Hendrycks, Zhao, Basart, Steinhardt, & Song, 2019) , a legal or political system that hems closely (and predictably) to certain past categories may be adversarially 'spoofed' by certain, well-resourced actors who can construct or structure their 'input' in ways that exploit these features of the system in order to produce 'output' to their liking. Such strategies have been well-docmented in the legal context, consider US companies invoking 'free speech' as category to secure unrestricted campaign finance laws  (Citizens United v Federal Election Commission, 2010) . In more political arenas, consider the ways in which certain actors have 'securitized' issues such as migration, in order to re-deploy and re-direct the age-old state logic of 'security' towards certain desired political ends  (Huysmans, 2000) . Beyond these general shortfalls, what is the problem with such problem-solving path dependencies? Given the breadth and depth of challenges envisaged by the widespread introduction of AI into society, it is arguable that a doctrinal solution to the liability questions raised by AI will at best produce marginal returns. This is especially since retention or reaffirmation of the contemporary legal paradigm many instead hinder attempts to a fuller exploitation of the benefits that the technology would otherwise be able to offer. That is not to say, of course, that this 'problem-solving path-dependency' is the only such rigidity limiting governance. Indeed, as scholars in the field of Evolutionary Governance Theory have demonstrated, there are always various other 'dependencies'-from path dependencies to interdependencies, and from goal dependencies to material dependencies-which bound governance actors' ability to strategize far beyond their found governance path  (van Assche et al., 2020, 7) . Such path dependencies can therefore only be adequately understood together with various interdependencies and goal dependencies (the reflexive and at times self-fulfilling impact of visions for the future on current governance), as well as material dependencies such as the technologies entrenched in the system's discourse, policy, organization, or regimes of cooperation and coordination. Thus, while many elements of governance are contingent and could in principle be reconfigured-even radically so-  van Assche, Beunen, & Duineveld, 2014, 5 ) also note that \"[o]ne cannot jump from each branch in the evolutionary tree to each imaginable other branch\". Nonetheless, in some cases the path-dependency of problem-solving approaches appears particularly constrained, and sufficiently contingent, that further exploration could be fruitful. In particular, the insight that the existing regulatory order is but one possible 'governance strategy' equilibrium, does not mean that the 'leap' to other such equilibria will be easy (indeed, if it were, the present state would not be so much of an attractor at all, and would likely have 'decayed' to one). Rather, the point is that while this present equilibrium may have proven proficient at managing sociotechnical changes thus far, it may no longer be appropriate nor sufficient in securing long-term interests-or realizing long-term perspectives-in the 'turbo-change' era of AI. \n Inability to differentiate between root problems and surface challenges Fourth, a different objection to problem-solving, related to the first, turns on the fact that it is 'centrality-blind'-that is, it does not easily (or at best only retrospectively) identify and prioritize governance bottlenecks or cross-cutting themes. Presently-identified problems may be differentiated into symptomatic and root-cause problems, but the problem-solving orientation does not systematically draw this distinction. Thus, much problem-solving work becomes squandered in ameliorating the symptoms rather than the rootcauses of a problem: questions of AI authorship arise in the context of intellectual property law  (Kaminski, 2017) ; questions of responsibility are asked in the the context of autonomous weapons systems (AWS)  (Jain, 2016) ; and questions of liability are raised in the context of accidents caused by autonomous vehicles  (Boeglin, 2015; Schellekens, 2015) . While legitimate legal problems, these are all symptoms of the underlying uncertainty over the liminal status of AI applications, which is the root-cause legal problem. The point here is that there are neither appraisal processes, nor confidence more generally, as to whether the policy problems posed are the central or core problems, and not merely their manifestation in certain areas. This ensures that there may also be a degree of disconnection amongst problem-solving governance approaches, such that there is potentially much double work or redundancy by virtue of an uncertainty as to the \"level\" of the problems that are tackled and what parallel efforts are underway. \n Promoting a false sense of security Fifth and finally, there is the false sense of security inherent within the problem-solving approach. Most fundamentally, it implicitly supports a world-view whereby we face only 'problems', when in fact many of the challenges we face today might be better understood and approached, at least upon first encounter, as 'mysteries'  (Chomsky, 1976) . Through emphasising that new challenges already \"appear to be within the reach of approaches and concepts that are moderately well understood\"  (Chomsky, 1976, 281) , problem-solving approaches suggests that while we may not yet have the solutions, we have an idea as to what those might look like and how we might get there. In other words, we may not have the solution at hand, but we surely have already delineated the space within which we are sure it can (and therefore ensure it must) be found. This can be juxtaposed against 'mysteries', which \"remain as obscure to us today as when they were originally formulated\"  (Chomsky, 1976, 281) . In this context, problem-solving suggests greater understanding and mastery of challenges than might otherwise be justified. This becomes an issue when epistemic certainty is not so warranted. More superficially are considerations around the appropriateness, adequacy, and sufficiency of problem-solving approaches. What we mean here is that, even where policy problems are solved, there is not necessarily a connection between this solution and the relevance of the solution to the continuing and future stability of the regulatory and governance orders. This relates back to the absence of processes for assessing the relevance of solving particular problems to the underlying challenges at the source of those problems. A different way of articulating the objections to an exclusively problem-solving approach can be captured concisely in the context of \"wicked problems\" which may serve as a bridge to our proposed emphasis upon problem-finding. \n Problem-solving governance is an inadequate response to \"wicked\" AI problems Introduced in an influential 1973 article, Rittel and Webber introduced the concept of 'wicked problems'-which they contrasted to 'tame', soluble problems in some scientific fields such as mathematics, chemistry or engineering-as problems that are difficult or impossible to solve because our requirements for a solution are often incomplete, changing, or in tension (such as in situations where there are no undisputable public goods); because policy problems cannot be definitively described; or because the effort to solve one aspect of a wicked problem may reveal or create other problems. By representing \"wicked problems\" as an array of complex, openended, and intractable problems, 4 Brian Head (  2008 ) developed an alternative rubric under which many governance challenges, including those posed by AI, can be productively examined.  5  To be sure, it should be cautioned that merely labelling a problem as \"wicked\" may not necessarily assist in solving it-in the same way that labelling a system as 'complex', or a phenomenon as 'emergent' by itself does not assist in actually understanding any of its dynamics or behaviour, and rather should be understood better as a signpost highlighting these as topics in urgent need of further investigation. However, the benefits of the 'wicked problems' framework are less about providing a clear solution rubric, 6 and aims more to focus attention 'on the understandings that have shaped problem-identification and thus the frames for generating problemsolutions  ' (2008, 106)  in the first place. The interrogation of upstream factors impinging upon problem-identification may serve as a response to the missing processes for identifying, ascertaining and evaluating the centrality or significance of downstream problems impugned in the section above. Indeed, in conceptualising wicked problems as the convergence of uncertainty, complexity and valuedivergence,  Head (2008, 106)  suggests that failures to adequately respond to wicked problems may be due to the fact that: -The \"problems\" are poorly identified and scoped; -The problems themselves may be constantly changing. -Solutions may be addressing the symptoms instead of the underlying causes. -People may disagree so strongly that many solution-options are unworkable. -The knowledge base required for effective implementation may be weak, fragmented or contested. -Some solutions may depend on achieving major shifts in attitudes and behaviours  […]  but there are insufficient incentives or points of leverage to ensure that such shifts are actualised  (Head, 2008, 106) . A common denominator to these failure modes inheres within poor mappings of the potential problem-space. Not only might the problem formulation itself be mistaken or misaligned, but the 'true' nature of the problem might not be one which is directly connected to the external real-world challenges that are most readily perceived as problems. Instead, as this list suggests, the root of the challenge might instead lie in social dynamic, economic, and political considerations. Yet, since subsequent problem-solving endeavours are sculpted in large part by the outcome of problem-identification and -definition processes, overly narrow or static problem initial formulations may lead to inadequate or brittle responses that fall short of addressing such problems. In slogan form: solving individual pieces of the puzzle provides little or no protection against against the larger threat posed by wicked problems. Such local responses may at times be orthogonal to addressing the underlying problem-and at worst may be damaging, either in their direct results, or because they forestall deeper responses. Scholars have in recent years increasingly highlighted how legacy institutions and policy toolkits derived from the management of 'complicated' problems may prove ill-suited for the management of 'complex' problems  (Kreienkamp & Pegram, 2020; Morin et al., 2019) . Applied to the challenges posed by AI governance, the wicked problem framework suggests that problem-solving approaches by themselves may not be sufficient  (Rittel & Webber, 1973, 160-67 ; see also  Gruetzemacher, 2018) . This is because AI itself not only poses complex, wicked problems, but because the application of this technology can also be disruptive to governance responses themselves, as it can alter the key parameters of a governance path; the interests of different actors in the network; the legal principles and processes; the regulators' and regulatees' values; or the regulatory modalities at play in the policymaking portfolio. To address the core characteristics of such changes, persistent (continuous) and pervasive (wide-ranging) problem-finding approaches should be articulated. As such, we will shortly seek to elaborate upon and structure one such problem-finding approach across four strategic levels below, as a means to give granularity to the multifaceted wicked problems generated by the infusion of AI into society. Before doing so, however, we will first reflect on the epistemic and scientific foundations of a problem-finding approach. \n The epistemic validity of a problem-finding approach to long-term AI governance The problem-finding/problem-solving distinction has parallels in the division between normal science as 'puzzle-solving' and revolutionary science as 'paradigm-shifting'  (Kuhn, 1970) ; in the earlier-alluded-to separation of ignorance into 'problems' and 'mysteries'  (Chomsky, 1976) , and in the scientific creativity of research communities variably taking the form of incremental and secure 'cold searches' or far-reaching yet uncertain 'hot searches'  (Currie, 2019) . Indeed, the distinct psychological learning strategies displayed throughout human childhood have been likened to foundational AI research paradigms, which also balance algorithms between paired phases of 'exploration'-wandering far; gathering information, and phases of 'exploitation'-acting on the information gathered to the greatest effect  (Gopnik et al., 2017, 7893; in: Currie, 2019, 5) . One might also compare the idea, in algorithmic evolutionary optimization, of 'simulated annealing'  (Derman, 2018)  where, by introducing volatility and 'shaking up' its search, an algorithm can find its way to better solutions outside the incremental search-space. The fact that a self-similar dyad can be found in philosophy, logic, evolution, computing, and even human psychology, is indicative of not only its scientific validity, but also its critical role in governance strategies. Analogously, while problem-solving work ('puzzlesolving; 'addressing problems'; 'cold searches'; 'exploitation') is clearly the bread and butter of many scientific research communities, open-ended problem-finding research approaches ('paradigm-shifting'; 'pursuing mysteries'; 'hot searches'; 'exploration') are and ought to be a natural and critical complement. This is for four reasons. First, such problem-finding work may itself produce foundational academic insights (for example about the interrelation of law and governance priorities across different scales or levels). Indeed, meta-science research has suggested that, even as exploratory research papers face a scientific 'bias against novelty', they are more likely to become amongst the top 1% highly cited papers, and to inspire follow-on highly cited research across many disciplines in the long run  (Wang, Veugelers, & Stephan, 2017) . In the second place, open-ended, problem-finding research agendas can also work in a reflexive equilibrium with incremental policysolving research agendas, by providing broader-scope insight into how individual policy areas operate. In this way, such research agendas can address some of the 'institutional mismatch' to addressing a set of 'transversal' issues (including, but not limited to, AI) which drive externalities beyond or across familiar problem categories and domains  (Morin et al., 2019, 2-3) . Thirdly, and importantly, problem-finding approaches can at times reveal new 'crucial considerations'  (Bostrom, 2014a) : new arguments or propositions which, if true, reveal the need for not just small course corrections, but major overhauls in direction or priorities within our governance clusters and actions. For instance, research agendas into avenues to 'automatically detect' media forged by 'DeepFakes' are dependent on a crucial assumption that such detection measures can always be developed relatively quickly, and that this strategy is viable more or less indefinitely. If, however, the 'offence-defence balance' of AI research in this area is such that (the dissemination of) progress in these techniques aids attackers more than defenders  (Shevlane & Dafoe, 2020) ; or if, at the limit, progress in DeepFakes will mean that within a few short years detection will simply be functionally impossible  (Engler, 2019) , this narrow research agenda would be overturned. A problem-finding orientation can therefore frame a lodestar to aim towards, rather than merely identifying obstacles present and apparent in our current trajectory. Finally, problem-finding approaches enable us to forestall or short-circuit Collingridge's 'dilemma of control', which holds that \"[w]hen change is easy, the need for it cannot be foreseen; when change is apparent, change has become expensive, difficult, and time consuming\"  (Collingridge, 1980, 11) . In that sense, problem-finding and problem-solving approaches fall respectively into each side of this dilemma. In this context, the power problem inherent in attempting change when it is 'expensive, difficult, and time consuming' reveals the futility of foregrounding problem-solving approaches in relation to long-term perspectives. Problem-solving approaches, somewhat obviously, become operational precisely where the desire or need for change confronts the inertia of a complex and interconnected world that frustrate such efforts. Long-term perspectives, however, reside in the information problem aspect of the dilemma: problem-finding approaches thus attempt to explore the potential problem-space while 'change is easy' and course corrections and changes are still possible. Yet, the dilemma nature of the challenge suggests that efforts of both of its sides are necessary, and the long-term perspective merely suggests that a recalibration of these efforts needs to be effected. \n A proposed problem-finding framework across four strategic levels We propose a theoretical framework or typology for mapping the long-term strategic landscape which we apply to the seemingly distinct cluster of policy domains surrounding AI.  7  In our understanding, we subdivide governance responses to AI's problems into four strategic 'levels'. 8 Levels 0 & 1 concern default, 'problem-solving' responses to governance 9 : (0) 'business-as-usual' governance demands the simple application of existing governance structures to the new problems; whereas (1) 'governance puzzle-solving' admits at least a certain need to reconceptualise, stretch or reconfigure existing legal doctrinal categories or governance concepts, in order to address those problems. Conversely, Levels 2 & 3 concern systemic challenges that currently lie beyond the boundaries of contemporary legal frameworks. They involve scholarship aimed at (2) finding potential 'disruptors' of core governance assumptions; or at (3) charting macrostrategic trajectories & destinations. Together, this creates a comparative framework within which to compare the problem orientations, contribution orientations, and limits of these distinct analytical and governance perspectives (see Table  1 ). Accordingly, such research lines call upon problem-finding approaches that convert, contextualize, prioritize, and structure the unknown problem-space into clusters or research agendas of problems that could then be addressed at Levels 0 & 1. \n Level 0 -'business-as-usual' governance The 'default' strategy involves an adherence to 'normal' governance processes, norms, structures and concepts, however constructed. While it does not deny the emergence of certain problems or challenges, it can be slow to recognize them-and even when it does, it will deny their fundamental 'newness'. This governance level is therefore rigorously focused on solving problems within (or by extension or application of) the existing governance system. In this sense, Level 0 governance is narrowly problem-solving: it recognizes the local 'problem', but requires that any solutions are chosen from the existing set of solutions made available. It is reactive, and seeks to re-establish or re-balance the old 'governance equilibria'.  7  To be clear, while we use AI as a focal technology, the general argument is applicable to the way long-term governance would engage with any new technology (cf. . See also the critique, of legal scholars' problem-solving responses to technology, in  Tranter (2011) . We thank Roger Brownsword for prompting this clarification.  8  We should make a few important caveats regarding our usage of the term 'levels' in this typology. In the first place, by referring to 'levels', we do not mean to imply a ranking of importance: another way to read or refer to them would be 'types' of governance strategies-although we prefer to retain the imperfect term 'levels' for the simple reason that it emphasises more (in a way that 'types' or 'categories' does not do) how the different varieties of governance strategies are not mutually exclusive and isolated, but interlinked components of a larger governance system. In the second place, and pragmatically, this terminology should not be confused with the existing scholarship on 'multi-level governance' (See  Bache & Flinders, 2004; Zürn, 2012) , which explores how policymaking power and authority are distributed both throughout the hierarchies of government, as well as horizontally towards other non-state actors. In our usage, by contrast, 'levels' correspond not to the 'level' (that is, the actor) at which a given strategy is rooted or situated, but rather to the 'level' at which a strategy seeks to exert leverage (that is, its scope, or the degree to which it variably takes for granted, or interrogates the problem formulation, parameters, and larger 'outside context'. In that sense, these 'levels' are ordinal ('Level 3' takes a broader scope than 'Level 2', which takes a broader scope than 'Level 1'), but do not necessarily connote ranked or hierarchical levels of influence (e.g. 'Level 3' strategy are not by definition or always upstream from 'lower' levels, even if they might offer greater possibilities for creation and consideration of long-term perspectives); rather these levels co-constitute one another. 9 Again, to avoid terminological confusion, it should be kept in mind that these Levels 0 and 1 are 'problem-solving'. We nevertheless include them as a key baseline component in our integrated framework which (encompassing the directly problem-finding strategies at Levels 2 and 3) we collectively refer to as the 'problem-finding' framework for AI governance. This is because we consider an integrated governance framework capable of carrying out 'problem-finding' governance as one that is capable of encompassing and complementing existing 'problem-solving' approaches, not of wholly replacing them. For instance, AI policy work at this level seeks to accommodate the issues raised by AI within the extant legal frameworks, arguing that legal doctrinal changes to accommodate the technologies are not necessary-in the terminology of cyberlaw, that distinct, domain-specific legal innovations would be as superfluous as articulating a comprehensive 'law of the horse'  (Easterbrook, 1996) . This position holds that all appropriate 'metaphors' to be encoded explicitly in law or implicitly in broader governance discourse can be found in past technologies  (Mandel, 2017) . Because these are easy to understand, much of the problem-solving work done today in distinct sub-fields on AI policy is situated at Level 0. For example, it is manifested in attempts to simply extend the existing legal framework and principles of international humanitarian law (IHL), to cover any and all issues that are raised by AWS  (Anderson, Reisner, & Waxman, 2014; Schmitt, 2013) . While it might be easy or tempting to dismiss such work out of hand, such a response would likely be neither fair nor warranted. Indeed, to be clear, a 'business-as-usual' response is not an obviously incorrect orientation in many cases (though it may be an insufficient one at a systemic level, across all cases). It relies on a certain degree of conceptual laxity-the willingness to implicitly (and at times perhaps unreflexively) stretch and re-interpret existing governance categories, just so that we can ensure their easy application to new cases. Such an approach avoids continuous, and costly, transaction costs of figuring out whether or not every new case or technology is new. Indeed, to an extent, the 'business-as-usual' heuristic is critical to governance: if we lacked one, we might easily find ourselves paralyzed: we would risk 'overfitting' (in the machine-learning sense) on our past governance experiences-leading one to argue, for instance, that a car crash involving a neon-painted car could not possibly be covered under existing laws, since no similarlycoloured car was ever involved in a car crash in the given jurisdiction, and this case was therefore clearly without precedent. Lyria Bennett Moses likewise argues that \"[m]ost of the time, a law predating technological change will apply in the new circumstances without any confusion. For example, traffic rules continue to apply to cars with electric windows, and no sane person would seek to challenge these laws as inapplicable or write an article calling for the law to be clarified.\"  (Bennett Moses, 2007, 596) . Moreover, an approach of implicit 'reinterpretation' and extension of existing governance categories may have some limited (temporary) merit even in the face of actual underlying real technological changes. All else being equal, holding up a 'pretence of continuity' might avoid certain externalities in the form of continuous regulatory uncertainty, or (in the case of high-stakes technologies) continuous contestation or attempted renegotiation by stakeholders. It can therefore be a necessary governance strategy in areas where reaching original political agreement on the existing governance arrangement proved thorny or difficult-such as for instance in international arms control agreements on certain types of new weapons  (Crootof, 2019b; Maas, 2019c; Picker, 2001) . Nonetheless, while these Level 0 responses may be somewhat understandable, and even necessary in some cases, it is likely that both their drawbacks and inadequacy are underestimated. In the first case, such moves can be brittle: when pushed too far, attempts to capture obviously (or to the public, apparently) revolutionary technologies under age-old governance approaches may fail the 'laugh test', with the result that 'the law runs out'  (Crootof, 2019b, 17) , threatening the credibility of governance efforts within that specific domain, as well as, at length, the more general legitimacy of the governance system that produced or allowed it (as critics can add another anecdote to a list of 'absurdities' produced by the extant system). In other cases, and especially in global governance contexts, certain actors may simply not accept an extension of 'business-as-usual' to new technologies, leading to new explicit or implicit contestation over specific norms, entire strategies, or certain actors' legitimacy or authority to steward those policies (see also  Zürn, 2018) . More fundamentally, however, because Level 0 approaches do not seek to (deeply) track or understand the nature of the ongoing changes (beyond the bare minimum necessary to address local symptomatic problems), they cannot be expected to address these in the long run. Instead, such governance structures may implicitly build up a 'technology debt', becoming hollowed out by changing practices, and ultimately being rendered into obsolete 'jurisprudential space junk'  (Crootof, 2019a)  as a result of changing practices. Ultimately, this approach also cannot reckon with possibly new, unanticipated features or area cross-overs, and therefore cannot provide the foundation for a problem-finding approach. In sum, Level 0 response might be necessary for any governance system, yet they are not (and potentially cannot be) sufficient. At their best (or at most), they might serve as 'holding actions' that prevent near-term problems from 'unwrenching' or distracting society so badly or so frequently that it cannot even reckon with long-term trends. But by itself it is certainly not able to adopt a creative problem-finding approach capable of providing a foundation for long-term governance, because in many cases they 'deny' that there is any deeper problem (beyond the surface disruption to be stilled). In doing so, it risks building up a 'problem debt'. \n Level 1 -governance puzzle-solving Closely related to Level 0 governance, but somewhat distinct, are perspectives that approach specific new problems as 'governance puzzles' to be solved. Work at this level still narrowly or primarily emphasizes the importance of fixing the direct problem at hand-that is, it takes for granted a narrow rationale-but it opens up for the possibility that doing so may require innovation and (even far-reaching) change in the regulatory tools or governance processes. As such, in contrast to Level 0, Level 1 governance is at least broadly problem-solving: it admits, at least in principle, that solving the direct problem in front of us may require innovations and changes in the set of available solutions, however, it does still narrowly seek to maintain or restore the existing status ex ante. In an AI context, this could be found in debates about discovering ways to re-conceptualize privacy (in the face of new AI challenges) in order to functionally restore the equivalent of past privacy protections to citizens. It may also extend to proposed innovations in governance approaches-such as the posited use of technologies such as AI systems as 'privacy protector'  (Els, 2017; Gasser, 2016)  in order to secure established goals or rights. As noted, Level 1 analysis is largely similar to Level 0, but it admits to a certain degree of novelty in the challenge, and accordingly to a flexibility in governance response, while anchored upon an allegiance or commitment to the existing status: the end-product is the same, even if the route is different. \n Level 2 -governance disruptor-finding In contrast, work at Level 2 begins to realize a problem-finding orientation. Its focus is less on the narrow problems as they are given, presented, or highlighted within pre-existing disciplinary boundaries, and instead seeks to explore underlying patterns, linkages or under-illuminated problem clusters. Recognizing that 'law' is only one 'regulatory modality'  (Lessig, 1998 (Lessig, , 1999 , Level 2 scholarship shifts focus from changes beyond narrowly understood laws or government regulation, towards to the broader regulatory system-and how developments in a particular technology (such as AI) may end up disrupting or deflecting governance efforts (either those aimed at the technology, or even in general). Accordingly, Level 2 analyses can emphasize at least four distinct angles. First, such scholarship can explore how ongoing technological progress-or altered social practices that seize upon pre-existing but formerly marginal affordances in new, salient ways-can shift or expand a technology's 'problem portfolio' in ways that render initial, now path-dependent, regulatory efforts inadequate or even counterproductive. Such work can expand the subjective problem portfolio to correspond better to the evolving opportunity/risk profile as manifested by the affordances  (Glȃveanu, 2012; Norman, 2013)  of a new technology. To be sure, this is not to say that all such structural change comes from changes in technology, or that all technological change brings about structural shifts such as this. Nonetheless, at times such shifts can be key and disruptive to extant strategic trajectories. For example, the risk profile of AWS can shift with technical progress: issues that appeared critical at an early stage (the potential to violate IHL principles), may soon become matched or eclipsed by far-reaching challenges in other domains: for instance, military AI systems may generate risks of operational safety, 'flash wars', or strategic instability  (Danzig, 2018; Geist & Lohn, 2018; Maas, 2019b; Scharre, 2016b; Sharikov, 2018) . Moreover, much greater than the direct risks from misuse or accident, might be indirect risks from 'structure'-deriving from the way new AI systems or capabilities shape the landscape of incentives around actors, in potentially hazardous ways  (van der Loeff, Bassi, Kapila, & Gamper, 2019; Zwetsloot & Dafoe, 2019) . Furthermore, AI development in areas such as one-shot learning  (Ram, 2019) , 'simulation transfer'  (OpenAI et al., 2018) , synthetic data, and others can lower the data or expertise needs for using AI, and thereby can lower the proliferation threshold of certain AI systems to new, non-treaty parties. Indeed, in general, greater data efficiency can have considerable and far-reaching governance implications  (Tucker, Anderljung, & Dafoe, 2020) . In these cases, neither 'solving the AWS problem' at Level 0 by extending IHL principles, nor tailoring legal principles to AWS at Level 1 does much good. Thus, policy responses at Levels 0-1 may no longer track-and may even occlude-the changing character of threats posed by AI systems. Instead, Level 2 articulates more adaptive or 'preventative security governance' approaches  (Garcia, 2016 (Garcia, , 2018  or 'innovation-proof' governance  (Maas, 2019c ; see also  Crootof, 2019b) . Thus in our AWS example, Level 0-1 approaches suggest winning a legal battle, but in reality the regulatory war is lost.   (Brownsword, 2018) , potentially spelling the 'death of [regulation through] rules and standards'  (Casey & Niblett, 2017) . Moreover, AI-sparked shifts in the international balance of power could destabilise the global legal order, just as previous technologies have upset international law  (Picker, 2001) . AI could do so by differentially empowering illiberal states  (Danzig, 2017; Harari, 2018; Wright, 2018) , or by eroding the buy-in of powerful states, into the multilateral international legal order  (Danzig, 2017; Deeks, 2020; Maas, 2019a) . In the context of our AWS example, finding new political equilibria that can support global restrictions on AWS might become more urgent than reconceptualising 'autonomy'. Third, reconfigurations between the different regulatory modalities may shift the very operational foundations (the 'wedge' or 'contact point') of governance strategies wholesale, by (further) displacing the primacy of concrete 'law' in regulating behaviour or in aiming to pursue strategies. For instance, it has been explored how AI systems enable regulation through 'microdirectives'  (Sheppard, 2018)  and 'technological management'  (Brownsword, 2015 (Brownsword, , 2016 (Brownsword, , 2019b , potentially feeding into systems of 'algocracy'  (Danaher, 2016) . AI also facilitates behavioural manipulation through 'hypernudging'  (Yeung, , 2018 , or invisible influences embedded in AI-mediated adaptive choice architectures  (Susser, 2019) . Likewise on global level, the use of AI systems might well help alter the processes by which international law or broader global governance is produced or enforced  (Deeks, 2020; Maas, 2019a) . While such developments may themselves give rise to concern, and therefore may become the object of (long-term) governance strategies themselves, such shifts should simultaneously be examined insofar as they alter the operating parameters-including what Deudney (2018) describes as 'material-contextual' factors, and what  van Assche et al. (2020)  describe as the 'material' dependencies of the human-made environment. As such, even if AWS challenges were to be 'solved' within Levels 0-1, a general retrenchment in the relative regulatory strength of 'normative' (international) law relative to unilateral technological tools  (Brownsword, 2018)  may neutralise these gains. For instance, where AI mediates or undercuts meaningful human decision-making, global AWS regulations anchored in maintaining 'meaningful human control' over narrowly defined 'autonomous' weapons systems, will overlook AI's behavioural influences, 'automation bias', and propensity to 'normal accidents'  (Borrie, 2016; Carvin, 2017; Maas, 2018; Scharre, 2016a) . In such cases, human agents remain nominally engaged in lethal decision-making, but in fact are consigned to the 'moral crumple zone'  (Elish, 2016) . Fourth, AI can change core values  (Danaher, 2018)  and even fundamental rights  (Liu, 2019b; Liu & Zawieska, 2020) , both altering the yardstick against which we measure impact of AI and potentially defusing our means (or indeed motive) of resistance. In our AWS example, if military AI applications enable a pivot towards conflict prediction and pre-emption (De Spiegeleire, Maas, & Sweijs, 2017), the shift from high-casualty drone strikes towards 'invisible wars' that subtly enable the prediction and interdiction of 'enemies'  (Deeks, 2018)  might lessen the reputational penalties from waging high-tech wars. Yet, the corresponding shift to a paradigm that heightens scrutiny or accountability of such 'hidden violence'  (Kahn, 2002)  may not develop in time, or to the same intensity. Finally, the fact that technological change can 'reveal rights'  (Parker & Danks, 2019)  can demonstrate shortcomings in the existing human rights umbrella. This limits human rights' ability to 'push-back' effectively against AI: in our AWS example, attempting to fit the wrongs precipitated by AWS as claims made through the existing human rights framework reveals severe shortcomings that structurally understate the injury  (Liu, 2018 (Liu, , 2019c . In sum, whereas Level 0-1 work often takes for granted the scope and nature of the problems at hand, a Level 2 analysis investigates how the technology, its uses, its indirect effects, and the direct problems, may aggregrate into overarching trends that can change the terms of governance. It can as such reckon with 'out of bound' strategic barriers or deflectors (changes to the problem portfolio; to regulators' goals; to governance tools, or to societal values) that would completely surprise and change the terms of analyses at Levels 0-1-potentially rendering any solutions arrived at as superfluous, contrary to the new regulatory goals, or out of step with the nature and values of the society they are meant to serve. Simultaneously, analysis at this level can reckon with these 'medium-term' disruptors that might frustrate/undercut governance efforts that only take account of Level 3 destinations. \n Level 3 -charting macrostrategic trajectories & destinations Finally, the third level reframes the AI policy-debates at Levels 0-2 through the lens of foundational axiological and 'macrostrategic'  (Bostrom, 2016)  questions about what kind of worlds we do and do not want to reach with AI. Work at this level examines (I) analytically, how the injection of AI systems (or indeed other technologies) might inadvertently alter the trajectory of human society in the mid-to long-term  (Brundage, 2018; Baum et al., 2019) ; and it examines (II) strategically, how we might identify or constitute inflection points and opportunities for intervention for re-directing that trajectory towards preferable worlds. Some work to date has focused on mapping (technological) vectors that could alter the macrostrategic trajectory. In most cases, such work has focused on (a) terminal trajectories, the most extreme scenarios whereby technogenic 'turbo-change' gradually or suddenly leads society towards global catastrophes or even existential risks  (Moynihan, 2020) . Such work has explored certain scenarios of low-or unknown-probability but high impact, such as the catastrophic or even existential threat to humanity that future AI systems might pose if not well-aligned with human values  (Bostrom, 2014b; Everitt, Lea, & Hutter, 2018; Russell, 2019; Yudkowsky, 2008a) . In such cases, the world might get many 'near-term' policy issues at Levels 0-2 right (for example, such as achieving a Level 0 ban on AWS; altering notions of liability to account for unpredictable AI systems at Level 1; or putting in principles around the shift towards regulation by 'technological management' at Level 2)-yet in the long-term still see this come to naught. But the space of possible macrostrategic destinations surely extends beyond this. Indeed, recent Level 3 thinking therefore has explored (b) vulnerable worlds which concern ways in which worlds that are still 'safe' today may nonetheless be set on a trajectory within which continued technological progress inexorably ensures that, as  Bostrom (2019, 3)  predicts, \"a set of capabilities will at some point be attained that make the devastation of civilization extremely likely, unless civilization sufficiently exits the semianarchic default condition.\" Related to this, other scholarship has extended this further, by exploring the ways in which diverse, complex, path-dependent socio-technological trends, which in isolation do not rise to an 'existential risk', might converge and interact in ways that gradually, but steadily and irreversibly, increase the systemic vulnerability of our societies  (Kuhlemann, 2018; Liu, Lauta, & Maas, 2018) . This could include the accumulating effects of certain technologies-as with industry-fuelled climate change, a trajectory where a \"great many actors face incentives to take some slightly damaging action such that the combined effect of those actions is civilizational devastation\"  (Bostrom, 2019, 7) . It could also involve intersecting or compounding effects of different technological disasters, such as the climactic 'termination shock' that would follow if future global geo-engineering programs were to be suddenly interrupted as a result of regional (nuclear) war  (Baum, Maher, & Haqq-Misra, 2013) . A further variation on this theme examines trajectories towards (c) exposed worlds. Whereas vulnerable worlds can involve disastrous scenarios as a result of many small accumulating or interacting failures, errors, or hazards, an exposed world-or what some have called a 'fragile world'  (Manheim, 2018) -is one that makes certain choices that have rendered it susceptible to previously-modest shocks or hazards, including hazards that society previously might have weathered much better. Under some scenarios, technologies such as AI might lead us to more exposed worlds, insofar as larger parts of our economy and knowledge base become tied up in certain to-us opaque infrastructures dependent on global connectivity and constant and reliable electricity supplies. Alternatively, AI could inadvertently lead societies into (d) bad worlds: 'progress traps'  (Wright, 2005)  or 'inadequate equilibria'  (Yudkowsky, 2017)  where society reaches a future destination where it is not destroyed, nor necessarily vulnerable or exposed, but where it is bad and (nearly) inescapable in the sense that subsequent recovery out of this state towards better trajectories is no longer possible. Even if these effects are not absolutely 'intrinsic' to AI technologies, it may still be that many of the uses to which AI is put within our society, nonetheless could: imperil human dignity  (Brownsword, 2017) ; erode the 'social suite' and relational capacities of humans, in ways that drive creeping negative 'social spillovers', such as a diminished ability to cooperate  (Christakis, 2019) ; or increasing algorithmic 'inscrutability' may lead us to a 'new dark age' of uncertainty, surveillance, or the death of sociality or empathy  (Bridle, 2018) . Such long-term trajectories towards 'flawed realization'  (Bostrom, 2013, 19)  might emerge if AI systems would have long-term and lasting impacts on our world and society which would (on net) be considered ethically adverse or at least sub-optimal across a broad range of ethical views. Finally, while these are sometimes under-examined relative to these other scenarios, it is also important for Level 3 scholarship to orient itself towards (e) Good worlds. These are axiological descriptions of certain societal destinations-or trajectories-that do not merely avoid these above enumerated risks, but articulate clear principles or 'desiderata'  (Bostrom, Dafoe, & Flynn, 2019)  for what good society we would like to pursue or societal trajectory we would like to be set on. Of course, in one sense, perspectives that articulate how we want to proceed ('journey' or 'trajectory') or where we want to end up in ('destination') in the long term, are both alternative and complementary strategies for avoiding 'bad worlds' or other pitfalls in development. These should invoke different types of assessment. The (troubled) narratives of utopia versus dystopia seem to consider macrostrategic destinations in their exploration of contours and configurations of established worlds, whereas ethical quandaries seem to relate to macrostrategic trajectories insofar as their consideration or their outcomes affect pivotal points in pursuit of a path ahead. At the very least, setting out the parameters of 'good worlds' provides a benchmark to assess whether or not we are either on the path to a bad world, or are actually in some sense in a bad world already. This would be useful since we presently seem to lack objective points of reference to indicate what type of world we are in. It should, however, be noted that such shared positive perspectives for long-term societal macrostrategy remain relatively underdeveloped-especially in terms of linking them to shared narratives and visions. The insight of Level 3 problem-finding scholarship is that, even if we managed to solve the discrete AI policy-problems-such as the global regulation of military AI-at lower levels, this reactive, fragmented firefighting approach may simply not suffice in aggregate to shift societies out of overall-captive trajectories towards the 'attractor states' of vulnerable, fragile or bad worlds. Rather, AI might drive long-term sociotechnical effects or shifts in constitutional societal values, shifts which might be passively unobserved or even unobservable (cf.  Cirkovic, Bostrom, & Sandberg, 2010)  by society, or which might even be actively veiled by certain interested parties, until it is too late to marshal resistance or change. The point is that AI can lock in such dependencies in ways that even the broad analyses at Level 2 may not fully appreciate, missing the forest for the trees. At the same time, Level 3 work highlights positive leverage points which problem-oriented work at Level 0-2 might pass by: opportunities where AI itself opens up loci for positive interventions that can shift this trajectory-promoting beneficial applications of 'AI for global good' (Cave & Ó h Éigeartaigh, 2018) which empower human autonomy, or help consolidate a 'postwork utopia'  (Danaher, 2017 (Danaher, , 2019a . In this way, we emphasise the importance of articulating governance lodestars; to pivot towards a prospective, teleological approach that sketches a spectrum of societal trajectories that not merely avoids catastrophic outcomes  (Bostrom, 2013 (Bostrom, , 2019 , but which articulates what we seek to gain-and where we want to go. If developed, such work would highlight a potential new chapter for law and regulation, ensuring governance can speak to both the perils and promise of AI. \n Reflections on problem-finding AI governance strategies The above gives an analysis of four governance orientations, and their implications for constituting a long-term governance approach to the problems created by AI. We therefore will now provide four meditations on some of the nuances of our model; as such we will explore (a) the interrelation and mutual complementarity of governance across the four levels; (b) the potential reapplication of problem-finding governance research (Level 2 and 3) in a problem-solving mode; (c) how all four strategies are themselves merely situated within a larger 'Governance Goldilocks Zone' that circumscribes and articulates the very limits of what can be meaningfully governed; and (d) the interrelationship between governance strategies at these four levels, and broader (self-fulfilling) narratives or visions. \n Coordinating strategies across levels: from partial failures to co-evolution We want to emphasize that the point of the four-level framework is not to discard 'low-level' scholarship or governance, and fully replace it with 'high-level' scholarship. Indeed, in one sense, we should be careful to how we understand the distinction between these four levels; these are primarily mapped to the different ways in which governance strategies are oriented, and which (problem-; legal-; and societal) parameters they takes for granted. However, while this distinction between the four levels-and indeed, the terminology of 'levels'-seems to imply an ascending hierarchy or scale, that linkage should not be drawn too far. That is, it may be tempting to map the axis of problem-solving to problemfinding governance to many other scales, such as a distinction between 'near term' vs. 'long term' governance, 'specific-'vs. 'general' governance, or 'small scale' vs. 'large scale' issues. Yet while these other scales may show some correlation to our fourfold distinction, they should not be drawn too widely: it is after all possible (if not necessarily widespread) to adopt a Level 0 or Level 1 governance approach to problems that will likely only emerge in the 'long-term future' (as seen in the debates over legal personhood for robots). Conversely, it is also possible to adopt a Level 3 perspective which does not seek to take in the full spectrum of societal and technological activity, but which narrowly focuses in on one specific topic (e.g. 'over the next decade, will AI progress be more constrained by computing hardware or by data?') which is held to be a crucial consideration or pivot point for determining the longer term trajectory. As such, while the four Levels correspond somewhat to other scales, they should not be taken as equivalent.  10  More practically, the point of our framework here is not to argue for the categorical superiority of problem-finding approaches to old problem-solving 'dogma'. Indeed, we must beware not to replace the particular failures of a governance system that is almost solely problem-solving with the particular shortfalls of another governance system that is almost entirely problem-finding. Rather, the point is to use problem-finding scholarship to complement and build beyond the existing problem-solving work, while understanding how all these four strategic orientations are necessary and complementary-and how work must range and coordinate across them. In particular, we want to emphasise that each governance system has to find its own form of complementarity, which balances problem-solving with problem-finding strategies. This is a balance that can differ per governance domain depending on local conditions and interactions. To illustrate this, we now examine three types of common failure modes in AI governance which takes stock of only one or another approach, and which thereby risk failing to 'governing for the long-term': (a) reactive work that is restricted to levels 0-1, and therefore does not even try to anticipate the long-term; (b) work that examines Level 2 governance disruptors, but which ignores Level 3 macrostrategic destinations, and which therefore misses the forest for the trees; (c) work that considers Level 3 trajectories, but ignores Level 2 disruptors, and therefore risks becoming a set of grand futures, derailed by detail. In the first place, scholarship that only focuses on Level 0 is reactive and focused on solving direct problems in the present. In that sense, it is not even trying to pursue governance solutions that are scalable into the long-term. As discussed above, such approaches might have some limited uses, but as discussed above, they risk being blindsided both temporally and sectorally. In relation to Level 3 macrostrategic trajectories, this approach seems inadequate. It is reactive, a holding action at best, and does not reflect on longer-term trajectories or dependencies, meaning that we would have to be very 'lucky' to find ourselves in 'good worlds' through Level 0 work alone. In the second place, work that works up to Level 2, but does not consider the Level 3 macrostrategic destination, risks not seeing the forest for the trees. In that way, it may manage to identify and eventually address many cross-sectoral problems, but over time could still leave us stuck in a potential progress trap. That is not to say that such work is 'senseless', but rather that it too needs to be grounded in a picture of how constitutional shifts at distinct levels-and their associated governance strategies-cohere and converge into a longterm governance trajectories. Thirdly, and conversely, any work that focuses only on Level 3, but which tries to solely reason 'down' to the other levels, runs the risk of ending up as a set of grand futures, derailed by detail. Specifically, by ignoring Level 2 disruptors, such strategies may make foundational assumptions-about the available or effective instruments of law; about the values of policymakers and societies-which are on track to get sidelined by Level 2 eddies and deflecting vectors even in the medium term. For example, some proposals to govern and avert potential future catastrophic risks arising from advanced artificial intelligence systems have envisioned governance strategies grounded in a comprehensive inter-state global treaty regime (cf.  Wilson, 2013)  or housed within the United Nations  (Castel & Castel, 2016; Nindler, 2019 ; However see  Cihon, Maas, & Kemp, 2020) . While it is certainly valuable to explore all avenues-certainly historically proven ones-the risk is that such a move constitutes an attempted leap, from a Level 3 macrostrategic goal (e.g. a catastrophic trajectory to avoid), immediately down to possible Level 0 or Level 1 solutions ('global treaties') that are patterned on the solution package perceived to be available or the norm today. In doing so, however, the risk is that such proposals fail to engage with key Level 2 insights. For instance, (a) some have argued traditional international law instruments based on state consent are very poorly equipped to engage extreme but unknown catastrophic risks  (van Aaken, 2016 ; though see  Vöneky, 2018) ; (b) in recent decades, the parameters of global governance have already been shifting, with many arguing that it has trended away from formal international law-making, towards diverse 'regime complexes' made up of heterogeneous actors and informal governance arrangements  (Alter & Raustiala, 2018; Morin et al., 2019; Pauwelyn, Wessel, & Wouters., 2014) ; (c) such proposals may not sufficiently engage with insights of how and where the deployment of AI itself may affect or erode the political scaffolding or legitimacy of 'hard' international law itself  (Deeks, 2020; Maas, 2019a) . Any of these might constitute a 'crucial consideration' against the project of trying to secure the Level 3 macrostrategic objective of avoiding disastrous long-term trajectories by attempted Level 0 or Level 1 tools (i.e. treaties) alone. Ultimately, the aim is not to elevate some of these strategies over others, but instead to help provide an inter-community framework or 'translation zone', that can help scholars situate themselves within scholarship at different levels, and to translate their work across to other communities as well as policymakers and the broader network of governance actors. Such an approach is critical also to fully levarage both the divergent 'scanning' function of problem-finding scholarship at Levels 2-3, as well as the convergent 'rallying' function of inviting groups and actors behind preferable Level 3 trajectories, in ways that are cognizant of possible Level 2 'governance disruptors', as well as the intricacies of concrete Level 0-1 policy implementation. \n Problem-finding strategies applied in problem-solving mode Having set out the interrelation and complementarity of problem-solving and problem-finding approaches across the four levels, we should now make a special observation with regards to the ways in which approaches at these four levels can reflect-or adapt to one another. After all, one reading of our argument above would be that while we have reservations about a problem-solving governance approach pursued in isolation, they can work alongside problem-finding approaches, because these two frames generate a sufficient complementarity. In another perspective, however, one might argue that even the problem-finding paradigms (Levels 2-3) can involve (or may require) 'problem-solving' features-but that these are different to the isolated (Level 0 or Level 1) versions of the problemsolving approach.  11  This second interpretation has much to recommend it. As noted above, for instance, Level 3 (problem-finding macrostrategic) scholarship on AI can be understood to include an analytical mode, which explores chiefly how the injection of AI systems (or indeed other technologies) may inadvertently alter the trajectory of human society in the mid-to long-term. This type of analysis can be purely problem-finding. It is important, however, to note that much work in this paradigm also involves an interventional mode: such work does not merely seek to 'find' previously unseen but crucial dangers; but it also aims to explore how we might identify or create governance inflection points and opportunities for intervention, to re-direct the global trajectory towards preferable (i.e. 'good') worlds. We should therefore draw a distinction between Level 3 work that aims to find new crucial considerations, and Level 3 work that aims to solve these challenges through interventions or inflection points. Paradoxically, this latter approach therefore appears to revive aspects of problem-solving analysis in Level 3 work. Nonetheless, the type of problem-solving here is frequently distinct from Level 0 or Level 1 problem-solving, because it need not be as closely wedded to pre-existing solution sets. That is, while it admits that any new problems (such as 'crucial considerations') excavated by problemfinding approaches (Levels 2-3) could be amenable to problem-solving approaches, it does not automatically presume that existing responses are necessarily adequate or superior to alternate governance responses. Nonetheless, the interrelation of the problem-solving and problem-finding paradigms in (AI) governance, and the way they can shape, alter and inform one another, remains a key nuance to this framework, which remains to be further explored. \n A goldilocks zone for governance? Beyond the four-level framework Moreover, while we distinguish four strategic levels in our governance framework, it is worth stepping back and taking stock of the broader long term implications that this framework raises, particularly in terms of how governance (of any form) categorically relates to differential, technology-driven changes.  12  The animating question here is whether there is something to be found beyond these four levels? That is, these four levels of problem-solving and problem-finding governance strategies may together describe (or cover; or constitute) the governance landscape in a complete and comprehensive manner. Yet the variety amongst them-and the lower and upper 'limits' of Level-0 and Level-3 governance strategies respectively-imply that these four levels of governance are in a sense themselves confined within a 'Goldilocks Zone' for governance. The 'Goldilocks Zone' is the informal astronomical term for the 'circumstellar habitable zone'-that narrow region around a star where the surface temperature on some planetary bodies is \"just right\" for water to be present in the liquid phase, implying they could support the emergence of life (NASA, 2020). To extend this analogy, we might then come to think of a 'Governance Goldilocks Zone' as that narrow band of core parameters, assumptions, or boundary conditions for problem 'governability' within which the very project of governance (of either a problem-solving or problem-finding variety) is capable of residing or thriving in the first place. Within this broader context, we can recognize how one can only 'do governance' (of any type or sort) under assured conditions of autonomy (freedom to determine behaviour and to act) and influence (behaviours and actions are causally connected to outcomes), and these constitute the underlying presumptions of our four level framework.  13  The long-term governance perspective, however, enables us to step outside of these presumptions in order to understand the implications of a Governance Goldilocks Zone. That is, to draw another analogy (and at the risk of mixing metaphors), we might allude to the fundamental states of matter to illustrate the character of the problem landscape beyond this narrow Governance Goldilocks Zone. One might accordingly think of the Levels as corresponding to varying states of matter at distinct temperatures. In this heuristic, one could see Level -1 governance as corresponding to a Bose-Einstein Condensate (BEC) (a state of matter that occurs at extremely low temperatures near absolute zero, where molecular motion nearly stops and atoms begin to clump together); Level 0 would be a solid state; Level 1 a liquid state; Levels 2-3 the gaseous state; and Level 4 the plasma state. These suggest varying levels of particle movement and intuitive grasp of behaviour, but for the purposes of this section, we focus on the Bose-Einstein condensate and the plasma that bookend the fundamental states of matter. This because the Bose-Einstein condensate state provides an example of situations where change is difficult, and the plasma state presents an example as to the difficulties inherent for intuitive predictability of behaviour that lie beyond our daily experience of matter. \n Level '-1': governance BEC: stasis in reality or in governance responses Stretching backwards into the space 'beneath' Level 0 would imply stasis, both actual and perceived, with both forms of stasis converging to foreclose the impetus or opportunity for altering the existing governance landscape. Thus, at Level 'negative-1' (-1),  14  we have stepped outside of a governance framework that can be responsive and adaptive to (technologically induced) change, either because there is no actual change (stasis in reality), or no perceived or recognised change (stasis in governance responses) in the sociotechnical landscape. Of course, no society has ever been in a perfect form of internal stasis-let alone a form of stasis resilient to any outside shocks. Nonetheless, some soft forms of these conditions might have historically applied to (possibly pre-industrial revolution) societies, which did undertake investigations into the governance implications of (socio)technical change, perhaps because no such change was easily perceptible or in memory. Under these conditions, not even Level 0 'business-as-usual' governance is engaged, because no new (sociotechnical) situations (appear to) present themselves for examination. This static nature of Level -1 conditions results in governance self-entrenchment, because the very possibility of subsequent change (in governance) is systemically resisted: there are no new 'problems' that are presented for Level 0-1 approaches to 'solve'; and there is no background change that can provide an easy seed, impetus, or justification for Level 2-3 approaches to go out and 'find' potential challenges. In the course of discarding a dynamic view of governance, where its aims, objectives, values, methods, and actors are in constant and mutual feedback, Level -1 amounts in a sense to a condition of 'absolute zero', where there is no movement (at least from within the system) and therefore no prospect for interaction, recombination, or phase transitions.  15  There are no moments of 'legal disruption' or uncertainty , and as such Level -1 undercuts the assumption of governance autonomy by removing the perception or reality that there is change, and it can thus be perilous from a govenance perspective because alternatives are no longer imagined, perceived or pursued-let alone actualised. It lies outside the governance Goldilocks zone, because it is 'uninhabitable' for governance initiatives-providing no 'sustenance' or activation energy. 4.  3.2. Level '4': 'plasma' governance beyond sight, comprehension, or control  At the other end of the scale, we can consider the space extending beyond Level 3 as analogous to plasma, a fundamental state of matter that is often misunderstood and difficult to intuit from a perspective that is more familiar with the more quotidian states of matter. In the context of long term governance, Level 4 appears so deeply unfathomable as to defy conceptualisation from our present standpoint. It suggests the minimum requirement to reconsider our contemporary axiological configuration  (Danaher, 2020) , and questions the desirability of our present notions, techniques and objectives for governance  (Bostrom et al., 2019) . Indeed, at Level 4, it may be that our attempts at 'doing governance' may range from suboptimal through to being downright harmful over the long-term, because opportunities and prospects are opened up in this space that is currently beyond our ability to comprehend or fathom. From such a long-term governance perspective, Level 4 suggests that 'doing governance' might not only be futile, but may also be both counter-productive. The 'ingovernability' of Level 4 problems-that is, the features which drive a certain problem outside the governance Goldilocks Zone-may derive from three complementary sources, each of which is individually sufficient to erode or even foreclose our potential to 'do governance': (1) we cannot see governance problems; (2) we cannot comprehend the governance problems; (3) we fundamentally cannot control the governance problems (with today's tools). Respectively, these factors range from primarily undermining autonomy towards undercutting influence although of course these factors comprise of a mix of these two dimensions. With regards to (1) governance problems that we cannot see, there are a wide range of blinkers and veils that prevent us from seeing clearly all potential threats. Generally speaking, accurate judgments of catastrophic shocks are beset by various cognitive and epistemic biases  (Yudkowsky, 2008b) , making their governance subject to a 'tragedy of the uncommons'  (Wiener, 2016) . In extreme cases, the absence of observable or recognized precedent around truly existential disasters can create an 'anthropic shadow'  (Cirkovic et al., 2010) ,  16  which can exacerbate the effects of our 'availability bias', further restricting our ability to see what might really be at stake. As Cirkovic, Sandberg, and Bostrom put it: 'the observation selection effect implicit in conditioning on our present existence prevents us from sharply discerning magnitudes of extreme risks close (in both temporal and evolutionary terms) to us  ' (2010, 1500) . Even where we might perceive certain threats in the abstract, the intangible and distributed nature of certain global processes (such as  14  It should be emphasized that by calling these categories 'Levels', we are not suggesting that they lie within the same continuous 'problemfinding' framework.  15  Of course, to extend the analogy (or recognize some of its limits); there are of course materials which achieve unusual properties (e.g. superconductivity) at extremely low temperatures. Do governance approaches achieve such states as they crystallize below Level 0? We leave that question for future work.  16  'Anthropic bias can be understood as a form of sampling bias, in which the sample of observed events is not representative of the universe of all events, but only representative of a set of events compatible with the existence of suitably positioned observers'  (Cirkovic et al., 2010 (Cirkovic et al., , 1495 . H.-Y. Liu and M.M. Maas climate change) can make them 'hyperobjects'  (Morton, 2013) , complicating our apprehension of these problems (or the appropriate levers we might use to affect them). While these constitute the prominent examples, it becomes obvious that the prospect for long-term governance is severely eroded under conditions of invisibility. Because these governance problems lie beyond the epistemic 'event horizon', they do not prompt problem-solving investigations; and even problem-finding investigations may only hit on them 'by chance'-as theoretical possibilities discovered in the course of exploring some (adjacent) other problem. While Level 3 problem-finding work may sometimes help at spotting such challenges, for lack of a 'signal', many of them may remain governance 'dark matter' that is structurally outside of the Governance Goldilocks Zone. Our lack of comprehension under (2) merges into such conditions of opacity, mirroring the distinction drawn between sensation and perception on the one end, and our inability to control outcomes under (3). For instance, John Danaher has anticipated that algorithms may contribute to a coming era of 'Techno-Superstition', which combines opacity (a growing lack of public understanding of how the world-or an AI system-actually works) with the unwarranted illusion of control over AI systems  (Danaher, 2019b) . Within this context, we may appreciate that there is a problem (posed by AI), yet our inability to properly comprehend it may place us within the equivalent of a 'governance black box' which, Danaher proposes, we find ourselves in, in relation to AI systems. Thus, the arguments here are the same as those Danaher presents in relation to techno-superstition: lack of understanding, illusion or control, erosion of achievement, loss of autonomy, and undermining of human agency. Applied to Level 4, these arguments would suggest that we are not able to 'do governance' in a meaningful manner under such conditions. Finally, (3) with regards to (AI; or general) problems that are either intrinsically or currently deeply beyond our control, problems are again outside the Governability Zone. There are at least two ways we might lack 'control' over a governance problem: in the first case, one might imagine a case where a certain problem is in principle governable, but all power and control have become centralised to a single actor in a perfect autocracy, thereby locking out participation by all others. In this case, if the 'singleton' actor is uninterested in addressing a problem, governance would have no purchase either. In the second, more common case, the challenge might either be one fundamentally beyond our present technological means 17 ; it might require a level of perfect collaboration and cooperation that is beyond our (present) political means; the prospect for control has either been lost, or is recognised as not existing.  18  The common denominator is the loss of control which shuts out the very possibility to 'do governance', either through the loss of participatory input in the first form or the disconnection between action and outcome in the second form. Taken together, these suggest that the governance strategies with which we are familiar, and which we have mapped to Levels 0-3, may in fact reside in a Goldilocks Governance Zone, which circumscribes the limits within which it is possible to meaningfully contemplate or enact any strategic long-term governance.  19  As the underlying presumptions of autonomy and influence fall away at either end, be it the stasis of Level -1, or the unfathomable invisibility, incomprehensibility or impotence that characterise Level 4, the Goldilocks Governance Zone comes into view and becomes demarcated. Yet, without attempting to define the four strategic levels for long-term governance, identifying such a sweetspot would have been a difficult endeavour. \n Strategies and narratives While we make a strong claim in support of the complementary (and under-appreciated) value of problem-finding scholarship to such long-term governance scholarship, the framework we have proposed here is by no means a definitive one, and there will be many directions within which it can be developed and enriched further. To highlight but one point of potential interest, along with governance strategies, it will be key to examine how overarching narratives and encompassing long-term visions which frame strategies, can percolate across the four levels. There is already extensive scholarship on the role, dynamics, and risks of imagined futures  (Beckert, 2016)  or of 'sociotechnical imaginaries'  (Jasanoff & Kim, 2015)  with which medium-term technological projects such as 'smart cities' are often imbued  (Sadowski & Bendor, 2019) . Likewise, there are a host of emerging Level 3 descriptive or aspirational narratives revolving around our societal macro-strategic societal state, trajectory, or destination-whether 'turbochange'  (Deudney, 2018) , the 'great challenges' framework  (Torres, 2018) , a 'vulnerable world'  (Bostrom, 2019) , or 'existential security' (Sears, 2020)which provide kernels or seeds of various (possibly contradictory or competing) long-term perspectives and projects. This raises three questions: in the first place, how are such long-term narratives embedded and manifested in Level 0 to Level 2 partial strategies? In the second place, how do these narratives relate to, and exert political effects, alongside pre-existing 'utopian' or 'dystopian' visions, ideals or narratives of the future  (Berenskoetter, 2011) ? Finally, in the third place, are there ways in which such narratives (or  17  For example, while we may harden the resilience of our societal infrastructures (e.g. electrical grid) to solar flares, we do not have the technical capabilities to affect the solar mechanics in order to reduce their prominence.  18  For example, by taking complex adaptive systems seriously and recognising the ramifications that actions and inputs are largely untethered from producing the intended outcomes over the span of long-term governance perspectives. Alternatively, the viewpoint advanced by Nassim Nicholas Taleb over the course of Incerto could also be applied to suffuse randomness and uncertainty into processes upon which we project causation and the illusion of control.  19  That is not to say that these conditions are rigid or fixed. To exploit the habitability analogy of the Goldilock Zone further, it is worth noting (a) that not all areas on earth fall within the habitable zone, as there are extremes in environmental conditions (e.g. volcanoes) which restrict (at least human) habitation; and (b) that we are technologically capable of affording human habitation beyond the natural parameters of these zones (including in outer space) through life support systems. Drawing on this analogy in terms of governability, we might suspect (a) that governance (and problem 'governability') is not uniformly distributed within Levels 0− 3 of our governance framework, and that there might indeed be pockets of 'ungovernability' within these zones; and (b) even the external boundaries (e.g. the 'ceiling' of Level 3 governance) are not fixed, and using institutional or technological means, it could be possible to extend the zones of governability beyond the past parameters. their policies or analysis at different levels) can have 'self-realizing' effects? The role of 'self-fulfilling prophecies' has a long pedigree in scholarship, particularly where it concerns the 'autogenetic effects' of social predictions or utopian and dystopian narratives  (Maas, 2012) . Self-fulfilling and self-negating prophecies have received study in economics  (Felin & Foss, 2009) , as well as in international relations  (Houghton, 2009) , where scholars have charted the ways in which influential theories-such as the the 'democratic peace' and 'commercial peace' theses, or the 'clash of civilizations'  (Bottici & Challand, 2006 ; see also memorably  Tipson, 1997) -might end up self-fulfilling. Beyond the social realm, however, there might also be ways in which technological 'predictions', such as Moore's Law  (Mollick, 2006)  or current predictions of technological unemployment, become self-fulfilling  (Khurana, 2019) . This will be one key dynamic to be considered in both our problem-finding framework, as well as long-term governance more broadly. To conclude, we hope our framework can contribute to the co-evolution of governance actors (and scholars) operating within different 'Levels', as well as the coordination and unification of 'partial strategies' at these levels, into more deliberate, pluriform, and cross-domain approaches that leverage the best from both problem-solving and problem-finding. \n Concluding thoughts Contemporary society continues to experience significant changes to the scale, pace, and type of change in both its social, natural, and technological environment. This suggests the need to define, develop, and deploy complementary governance strategies both to meet these challenges, and to build towards more positive futures, which can take long-term perspectives into account while leveraging concrete and operationalized policies today. In this paper, we have identified some of the shortcomings of contemporary approaches to both the study and practice of governance, which often-explicitly or implicitly-take a 'problem-solving' approach. Specifically, we argue that problem-solving approaches to complex problems (such as AI) are limited, because of (1) the unreflexive over-reliance on narrow metaphor in the face of complex phenomena; (2) the tautological manner in which existing governance lenses identify and prioritize primarily those problems that are already legible to them; (3) the constrained path-dependency; (4) the inability to clearly distinguish between symptomatic and root-cause problems; (5) the promotion of a false sense of security through a rapid delineation of the problem-space that prematurely closes-off large parts of the governance solution-space. We as such argued that while such 'problem-solving' approaches may be necessary, but are also insufficient in the face of many of the 'wicked problems' which we face, including in the realm of AI. By contrast, we have made the case that exploratory, problem-finding research is critical to long-term policy and governance strategy endeavours. This is true for epistemic and scientific reasons relating to good and valid science and scholarship-because problem-finding work can (1) itself produce foundational academic insights at the interstitices of different problem domains, or at different scales of analysis; (2) it can work in a productive reflexive equilibrium with problem-solving scholars and strategy-makers; because (3) it can at times reveal new strategic 'crucial considerations' which might completely alter the balance of local-context strategy considerations; and because (4) it can enable us to forestall the 'power' problem inherent to the Collingridge Dilemma of technology governance. Beyond these epistemic virtues, the proactive and explorative orientation of the problem-finding approach is crucial to any and all conceptions of the long-term perspectives, whether these are conceived as 'early warning radar', or as 'inspirational lodestar'. Accordingly, we have proposed and elucidated a rough typology for four distinct 'levels' at which one can study or formulate governance strategies: at Levels (0) 'Business As Usual' governance and (1) 'Governance Puzzle-Solving', work takes a predominantly problem-solving approach to issues. Conversely, problem-finding approaches focus on (2) 'Governance Disruptor-Finding' and (3) 'Charting Macrostrategic Trajectories'. While within this paper, we have primarily discussed specific examples involving AI governance strategies, problem-finding approaches would likely be equally crucial for many other cross-sectorial challenges-if not more crucial. Problem-solving approaches might gain traction with regard to the clear, discrete clusters of pre-defined problems that are thrown up in relation to AI governance, by nature of the technogenic origins of the challenges. Yet, intersectional challenges diminish the crispness of their concomitant problem-sets. The result is that there may be uncertainty or ambiguity concerning how problem-solving approaches could effectively go about confronting such emergent, complex, and interconnected global challenges, without arbitrarily confining the metaphors and models in order to manufacture the necessary problem-clusters to be tackled. Thus, while problem-solving approaches may already be strained when confronted with polymorphous policy domains such as those relating to AI governance, the efficacy of problem-solving approaches may fade further where long-term governance takes multiple interacting developments into view. Long-term perspectives trade in future worlds, themselves intricate complexes of emerging challenges and possibilities of which factors such as AI and its governance comprise a minuscule subset. Thus, attempts to grapple with long-term perspectives must necessarily involve problemfinding approaches at their very core because these futures remain mysteries. In slogan form: we need to collect, catalogue, and categorise the challenges of long-term governance before we can set about answering concrete questions that are raised. We opened this paper with an emphasis upon the notion of change: an apparently paradoxical observation that change is the only constant, while simultaneously itself being subjected to change. Stepping back from AI, and long-term governancewhat does it mean for change to be changing? If we are right that the very possibility of doing governance requires change (that is, a guarantee that we are not at Level -1), then change undergirds the prospect, potential and promise of governance itself. Yet, it is clear that change is not one-dimensional, instead varying according to the rate, scale, direction, and duration, of the change in question: these can be further combined to constitute gradual, disruptive change, and paradigmatic change, for example. The question of change can also be addressed through an agent perspective to focus on who is driving or inhibiting the change in question; conversely a patient approach would focus upon the redistribution of benefits and burdens in the process of aftermath of that change. Furthermore, the relativity inherent within change requires considerations of benchmarks, those concerning the perceived status quo and expectations for the future for example, and how developments diverge or converge to these. The prospect for change also raises the possibility for encountering attractor states, which will affect the nature of observed change as well as future change. Leveraging the adjacent possibles opened up through the process of unpacking the four strategic levels for long-term governance, we also contextualised our framework within the broader spaces of (un)governability to suggest that our framework sketched out the Governance Goldilocks Zone within which the conditions are conducive to permitting us to still able to 'do governance' in the first place. Looking beyond the boundaries of our framework suggests directions for further research to explore and identfy the underlying presumptions that support the very prospect for our framework to come into play, and to the underexplored factors at play that enable us to project governance into the long-term. Table 1 1 Taxonomy of problem-solving (0-1) and problem-finding (2-3) AI governance strategies.Second, AI can change policymakers' goals in formulating law. The regulatory mind-set may shift from 'legal coherentism' towards 'regulatory instrumentalism' or even 'technocracy' Level Governance Problem orientation Aim & purpose Limits Perspective • Denies 'newness'; doctrinal Does not try to anticipate long-term changes not necessary • Reliance on metaphor 0 Business-as-usual • Solving local societal 'problems' created by new AI systems • Seeks accommodation within current legal framework, through (1) extension of legal framework; • Brittle; interpretations fail 'laugh test' • Fail to understand underlying (2) re-interpretation of new prob- nature of problem, or track lem as old problem cross-sector manifestations • Solving local societal 'problems' • Broadly problem-solving: still fo- Does not try to anticipate long-term 1 Puzzle-Solving created by new AI systems • Solving doctrinal inconsistencies in cuses on fixing the direct problem at hand, but allows that this may • (as Level 0) • Still mostly aims to maintain or the law revealed require doctrinal legal changes restore existing status ex ante • Finding AI developments that may 2 Disruptor-Finding 'disrupt' assumptions of or conditions for the governance system, such as (1) changes to the problem portfolio; (2) to governance tools, (4) to societal regulators' goals; (3) to • Does not take for granted scope strategic barriers or deflectors and nature of governance problems at hands • Aims to understand 'out of bound' • May miss the forest for the trees (relative to Level 3) values • Focus first on identifying • Finding 'crucial considerations' for overarching trends and 3 Charting Macrostrategic Trajectories how AI could shift overall trajectory of society towards (a) terminal trajectories; (b) vulnerable worlds; (c) exposed worlds; (d) bad dependencies which might be resistant to 'piecemeal' governance responses at Levels 0− 2. • May underappreciate Level 2 governance disruptors, and therefore become a set of grand futures, derailed by detail worlds; (e) good worlds • Identify leverage points for intervention to shift trajectory \n\t\t\t H.-Y.Liu and M.M. Maas    \n\t\t\t There is, of course, an irony in critiquing the prominence of (legal) metaphors within problem-solving AI policy research, through the use of this parable. However, we argue that in this instance our extension of the 'blind men and the elephant' metaphor works to highlight the contingency of taking for granted a classic or narrow interpretation of a certain parable (and the diversity of alternate and even contradictory problem formulations that could be derived or accomodated even within one metaphor-paradigm).H.-Y.Liu and M.M. Maas    \n\t\t\t In this section, the terminological reversion to 'problems', as opposed to 'mysteries' (Chomsky, 1976) , is unavoidable given the use of 'problem'-terminology in the wicked problems literature itself. The question of how to integrate these into a concept of 'wicked mysteries' is left to future work.5 Although the 'wicked problems' framework has also come under critique in recent years, on both conceptual and practical grounds. See for instance (Noordegraaf, Douglas, Geuijen, & Van Der Steen, 2019; Peters & Tarpey, 2019; Turnbull & Hoppe, 2019) .6  Although see the distinction between 'coping', 'taming', or 'solving' in Daviter (2017) . \n\t\t\t We thank Henrik Palmer Olsen for spurring this line of thought. \n\t\t\t We thank Roger Brownsword for spurring this line of thought.12  We thank Victoria Sobocki for discussions prompting this section.13  This has similarities to Roger Brownsword's account of the core 'existence conditions' for human life (such as the maintenance of the core infrastructure conditions), and the generic conditions for agency, which he holds to be the 'first regulatory responsibility', and a 'regulatory red line'(Brownsword, 2019a, 90-95).H.-Y.Liu and M.M. Maas", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0016328720301634-main.tei.xml", "abstract": "Change is hardly a new feature in human affairs. Yet something has begun to change in change. In the face of a range of emerging, complex, and interconnected global challenges, society's collective governance efforts may need to be put on a different footing. Many of these challenges derive from emerging technological developmentstake Artificial Intelligence (AI), the focus of much contemporary governance scholarship and efforts. AI governance strategies have predominantly oriented themselves towards clear, discrete clusters of pre-defined problems. We argue that such 'problem-solving' approaches may be necessary, but are also insufficient in the face of many of the 'wicked problems' created or driven by AI. Accordingly, we propose in this paper a complementary framework for grounding long-term governance strategies for complex emerging issues such as AI into a 'problem-finding' orientation. We first provide a rationale by sketching the range of policy problems created by AI, and providing five reasons why problemsolving governance approaches to these challenges fail or fall short. We conversely argue that that creative, 'problem-finding' research into these governance challenges is not only warranted scientifically, but will also be critical in the formulation of governance strategies that are effective, meaningful, and resilient over the long-term. We accordingly illustrate the relation between and the complementarity of problem-solving and problem-finding research, by articulating a framework that distinguishes between four distinct 'levels' of governance: problem-solving research generally approaches AI (governance) issues from a perspective of (Level 0) 'businessas-usual' or as (Level 1) 'governance puzzle-solving'. In contrast, problem-finding approaches emphasize (Level 2) 'governance Disruptor-Finding'; or (Level 3) 'Charting Macrostrategic Trajectories'. We apply this theoretical framework to contemporary governance debates around AI throughout our analysis to elaborate upon and to better illustrate our framework. We conclude with reflections on nuances, implications, and shortcomings of this long-term governance framework, offering a range of observations on intra-level failure modes, between-level complementarities, within-level path dependencies, and the categorical boundary conditions of governability ('Governance Goldilocks Zone'). We suggest that this framework can help underpin more holistic approaches for long-term strategy-making across diverse policy domains and contexts, and help cross the bridge between concrete policies on local solutions, and longer-term considerations of path-dependent societal trajectories to avert, or joint visions towards which global communities can or should be rallied.", "id": "8574274979992fdee1ef21cef0e37040"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": [], "title": "An Interview with Allan Dafoe GLOBAL POLITICS AND THE GOVERNANCE OF ARTIFICIAL INTELLIGENCE", "text": "important lessons from past attempts at governing powerful technologies such as nuclear technology, biotechnology, and aviation, examples of unambiguously successful technology governance are historically rare. Of course, it will also be valuable to examine and learn from historical failures of international cooperation, such as the 1946 Baruch Plan for international control of nuclear weapons. However, one should keep in mind that many of these historical examples might also be of limited transferability in the context of AI, since the development of AI involves distinct sets of nations, private actors, and considerably broader stakes and interests. As we have described in our research agenda, designing good AI governance will need to take into consideration the technical landscape of AI. It will have to consider the political impacts of advanced AI on inequality, international political economy, and international security to understand how distinct actors may compete or cooperate on powerful AI. Such research will have to explore what we call \"AI ideal governance,\" the question of exploring cooperative possibilities, values, and institutional mechanisms. At a minimum, governance approaches should try to develop good norms, as well as initiatives and policies to address present-day issues, such as those around transparency, fairness, privacy, and autonomous weapons. How we manage these near-term challenges could have lasting effects on the shape and vitality of our governance landscape, and determine how well-equipped we are to take on later issues including powerful military capabilities, such as in cyberspace, pervasive labor displacement, concentration of market power, and the safety and alignment of increasingly advanced AI systems. However, such short-term interventions may not be sufficient if they cannot continuously track advancing AI capabilities. What we would ideally put in place moving forward is an operationalization of the \"common good\" principle-that is, mechanisms by which actors pursuing the development and deployment of advanced AI technologies are incentivized and rewarded for pursuing progress in AI in a safe manner that serves to benefit humanity. \n JIA: How important will multilateral organizations and negotiations be for AI governance? AD: Multilateral organizations could play a pivotal role in AI governance by providing a joint forum for the formulation, coordination, and dissemination of the cooperative norms between actors, enabling participating parties to signal sincere commitment to beneficial and shared AI development. At present, there is no single multilateral organization that has taken up this mantle, although the UN has developed a vision of pursuing \"AI for Global Good,\" and to use it as a driver in achieving its Sustainable Development Goals by 2030. Bodies such as the AD: While advanced AI capabilities offer large opportunities, there are indeed also distinct risks which emerge as a system achieves superhuman, or even merely human-equivalent capability in relevant domains. Even near-human performance would allow for AI to substitute for humans in a range of tasks, and this alone could lead to massive labor displacement, radically increased inequality, erosion of privacy, risks of nuclear instability, a reorganization and concentration of the global economy, and upsets to the military offense-defense balance that increase the risk of conflict. Often, there are trade-offs between the short-term performance of a system and its longer-term safety and reliability. To offer a hypothetical example, imagine a future where autonomous cyber AI agents are defending our networks. For the purposes of safety, we could put a human in the loop who, whenever one of these AIs perceives a large cyberattack in progress, has several hours to deliberate before sanctioning a large-scale action in response. Such a policy might avoid unintentional escalation. However, if, as in cyberwarfare, a quick response could be critical to performance and defense, there would be strong strategic pressures to empower the AI cyber system with a fully autonomous response. This would expose us to the risk of a rapid cycle of escalation to high levels of hostility, which we might think of as analogous to the flash crashes that frequently occur with trading bots. In contrast, it may be easier to resist these automation pressures and reserve some roles for human actors in non-competitive or less time-sensitive contexts, such as hiring committees or hospitals that are in part relying on algorithmic analysis. Even in the context of key strategic decisions, if there is less direct time pressure towards immediate response, decision makers will be better able to retain Google China, has suggested that the market capture by a few ultra-profitable AI companies might create new forms of dependency as many states will be forced to negotiate with whichever country, China or the United States, supplies most of their AI services. Past technological transformations have shown that the dissemination of a general-purpose technology throughout society can take some time, and that its full potential is not always evident or easy to predict at the earliest stages. The dissemination of technologies such as electricity or steam power shows that such technologies usually start off having only a small number of important uses, but then achieve a progressively larger impact through technical improvement, the private sector plays an increasingly large role. Moreover, fast-developing technologies may follow unpredictable trajectories and create problems for regulatory pacing and oversight. Governing such emerging technologies will require in-house knowledge and familiarity with the fundamentals of the technology that is so rapidly changing, a capacity that currently favors firms over states. The key here will be striking a balance between private and public interests, and aligning firm incentives with the pursuit of the common benefit of humanity. Firms are not as averse to pursuing pro-social goals as some may expect. Indeed, leading AI labs have demonstrated a willingness to invest in safety and ethics. Nevertheless, the role of the government, as well as civil society and an indepen-  International Organization for Standardization could also be critical in shaping technical standards for AI technologies in a manner that integrates goals of safety and ethics.Other initiatives that are not strictly multilateral can also play a role. For example, the Partnership on AI has hosted a number of conversations about AI governance and ethics. These conversations have included for-profit and non-profit actors from several industries and countries, including Baidu of China who recently became a partner. To offer another example, the Future of Life Institute hosted an event that led to the 2017 Asilomar AI Principles, that were, this summer, adopted by the California State Legislature. This content downloaded from 132.174.253.119 on Thu, 24 Mar 2022 02:08:09 UTC All use subject to https://about.jstor.org/terms journal of international affairs | 123 JIA: You have spoken of extreme systemic risks, which could emerge alongside the benefits linked to superhuman capabilities in strategic domains. What are these risks and what are the most urgent questions to deal with in this field? \n What are the risks of intellectual piracy of AI and knowledge transfer from governments and private organizations to non-state actors and individuals? AD: Restricting control of a technology has always been difficult at best, and the risk of theft or dissemination is particularly severe for digital technologies, including AI. Whereas the military has more experience in constraining the dif- fusion of innovation, private-sector development and distribution may increase the 'attack surface' for prospective thieves. As such, certain AI tools may become relatively accessible to non-state actors, especially since some of the major players in AI are at least nominally committed to open-source development. For instance, in 2015, Google opened up TensorFlow, a formerly proprietary machine learning software library, to public use. Conversely, the barriers to proliferation may be higher for more advanced AI systems which require more computer hardware or large structured datasets to train and implement, or which require other forms of expertise in building large-scale systems. This content downloaded from 132.174.253.119 on Thu, 24 Mar 2022 02:08:09 UTC All use subject to https://about.jstor.org/terms 124 An Interview with Allan Dafoe some human judgment in certain decision-processes, or to otherwise adopt measures to increase safety. JIA: JIA: You have previously cautioned that advanced AI is likely to massively increase the potential gains from cooperation and potential losses from non-cooperation, as well as the chance of AI nationalism or mercantilism. What lessons emerge from other general-purpose technologies and economy-wide transformations? AD: As a generally enabling technology, advanced AI can raise the stakes for all parties, for better or for worse. On the one hand, if different states trust that they can share in the large bounty created by AI, they might be incentivized to cooperate more. But if they do not, the perception of advanced AI as a strategic asset might drive destabilizing arms races or nationalism. Kai-Fu Lee, formerly at \n investments, knowledge diffusion, and adaptation by individuals and institutions.Another potential lesson from history is that states that do a particularly good job of adapting to a new general-purpose technology can gain important advantages.For instance, during the Second World War, the German military took advantage of the internal combustion engine, electricity, and radio in realizing its blitzkrieg strategy. The U.S. military similarly envisioned using its lead in advanced com- puter technologies to gain advantage over the Soviet Union in its second 'offset' strategy. These examples should lead us to consider new important principles or goals for any policies that govern this technology. Underlying this, we should articulate clear and compelling visions that draw on and are responsive to the concerns and worldviews of people and elites from a range of backgrounds, so that these pro- posals are likely to resonate globally and be compatible with the incentives of key stakeholders. This content downloaded from 132.174.253.119 on Thu, 24 Mar 2022 02:08:09 UTC All use subject to https://about.jstor.org/terms journal of international affairs | 125 JIA: Today, private firms are at the cutting edge of advanced AI research. Should these firms be involved in AI governance? AD: Firms need to be involved in AI governance and may be better placed than governments to take the initial lead in forming the foundations of an AI governance framework. Even in the past, when government or state-sponsored research labs were the source of a larger portion of technological innovation, governments often found it hard to anticipate the course, impact, or regulatory demands of technological development in time. Moreover, elected legislatures may lack the requisite technological expertise. The mandate and disciplinary composition of specifically appointed 'expert agencies' may become rapidly outdated, and courts, which may be reactive and inclined to focus on the particularities of a case, may ignore general societal trends and needs. More importantly, states simply are no longer the sole source of governance capacity, especially in areas such as AI, where \n This content downloaded from 132.174.253.119 on Thu, 24 Mar 2022 02:08:09 UTC All use subject to https://about.jstor.org/terms", "date_published": "n/a", "url": "n/a", "filename": "26588347.tei.xml", "abstract": "Allan Dafoe (AD): AI is the study of machines capable of sophisticated information processing. AI systems enable us to automate, improve upon, or scale up critical human skills in prediction and decisionmaking. This makes AI a critically important, potent technology which-like electricity, the internal combustion engine, or the microprocessor-has the potential to transform the economy, society, and the military. In fact, even if there were no further technical AI developments from today onwards, the already existing capabilities create major governance challenges. How we build and use advanced AI will be the defining development of the 21st century, and one of its chief governance challenges. The emerging field of 'AI governance,' as my team at the Governance of AI Program understand it, explores how humanity can best navigate the transition to advanced AI systems. We expect that such governance will prove difficult given the strategic importance of the technology, its diverse applications, and the uncertainty associated with its developmental trajectory. While we may be able to draw", "id": "bb54edb8bfd96c959a3b2317f5b94036"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["O R I G I Na L Pa P E R", "Nick Bostrom"], "title": "Sleeping beauty and self-location: A hybrid model", "text": "Introduction \n Sleeping Beauty On Sunday, Beauty is put to sleep. She is awakened once on Monday, and put to sleep again after being administered a memory-erasing drug that causes her to forget her awakening. A fair coin is tossed. If and only if the coin falls tails, Beauty is awakened again on Tuesday. She knows all this. When she awakes on Monday, what should her credence be that the coin will fall heads? N. Bostrom (B) Faculty of Philosophy, University of Oxford, Suite 7, Littlegate House, 16/17 St Ebbes st, Oxford Ox11PT, Uk e-mail: nick@nickbostrom.com The Sleeping Beauty problem is a variation of some very similar problems of \"imperfect recall\" that have been discussed for some time in the game theoretic literature.  1  It was named by Robert Stalnaker, who had learnt about similar cases from Arnold Zuboff. The problem was brought to the attention of the philosophical community through an exchange between Adam Elga, who argued for the answer 1/3 (hereafter the \"1/3 view\"), and David Lewis, who defended the 1/2 view. The last few years have seen a burst of publications advocating one or the other of the two competing doctrines. To date, neither side seems to have gained a decisive advantage. Sleeping Beauty is an example of a problem involving self-locating beliefs, i.e., beliefs that an agent, or a temporal part of an agent, might have about its own location. An agent-part that knew exactly which possible world is actual can still be ignorant about its own location in that world. That can happen if the world contains two or more agent-parts whose evidential states are subjectively indistinguishable. These agent-parts would then be unable to determine with certainty their own spatiotemporal location. (Even if Beauty knew that the outcome of the coin toss would be tails, she could not know whether it was currently Monday or Tuesday.) Another way of expressing this is by saying that the agent-parts would be ignorant about which centered possible world they are in even though they know which possible world they are in. Yet another formulation is that agent-parts, or \"observer-moments\", possess all non-indexical information about the world but lack some indexical information. Here, we shall use these expressions interchangeably. The Sleeping Beauty problem is but one piece of the larger puzzle of how to relate indexical to non-indexical information in our reasoning. If one studies the problem in isolation from this wider context, one risks coming up with answers and principles that do not fit with the other parts of the puzzle. I will first argue that both the 1/3 view and the 1/2 view suffer from such a misfit. That done, I will propose a new \"hybrid\" model which incorporates aspects of both the 1/3-and the 1/2-view but is identical to neither. The hybrid view overcomes the problems associated with the purebred answers. It also suggests an explanation for why the 1/3-and the 1/2-view have both managed to appeal to their fan bases: they each encapsulate a part of the truth. \n The 1/3 view The 1/3 view is that upon awakening, Beauty should assign credence 1/3 to HEADS. Elga's argument for this view is as follows.  2  When Beauty wakes up, she knows that she is in one of three situations: H1 HEADS and it is Monday, T1 TAILS and it is Monday, T2 TAILS and it is Tuesday. 1 Robert Stalnaker gave the problem its name, after having of examples of a similar kind in unpublished work by Arnold Zuboff. Closely related problems have also been discussed in the game theory literature; see volume 20 of the journal Games and Economic Behavior (1997). 2  Elga (2000) . For some other defenses of the 1/3 view (see  Dorr 2002; Monton 2002; Weintraub 2004) . Given that the Monday and the Tuesday awakening would be evidentially indistinguishable, we have P(T1) = P(T2) [By an indifference principle]. If Beauty were to learn that it is Monday, her credence in HEADS should be 1/2 because this is then just the credence that a coin that is about to be tossed, and is known to be fair, will fall heads. Hence, P(H1|H1 ∨ T1) = 1/2 [By appeal to intuition]. Since P(H1 | H1 ∨ T1) can be rewritten as P(H1)/[P(H1) + P(T1)], we thus have P(H1) = P(T1) = P(T2). These credences sum to 1, so it follows that P(H1) = 1/3. The argument replies on an appeal to intuition in the middle step. One could try to support this step by invoking the Principal Principle. This principle says, roughly, that one's credences should accord with one's estimates of objective chances. As formulated by David Lewis, the Principal Principle came with a proviso: one's credences are constrained by one's beliefs about objective chances according to the principle only if one does not have relevant \"inadmissible\" information.  3  Lewis's reason for introducing the proviso was to bracket off cases involving oracles, time travel, and the like, where one might get information about the future that is not mediated by information about current chances. It is possible to maintain, however, that some problems involving self-location also include inadmissible information and should hence be exempted from the Principal Principle's domain of applicability. In light of the positive argument against the 1/3 view, which I will present below, we do in fact have strong grounds for regarding Beauty's indexical information as inadmissible. Given Lewis's own \"best-system\" analysis of chance, it would be unsurprising to find that indexical information can be sometimes inadmissible. According to the bestsystem analysis, chances are a kind of concise partial summary of patterns of local, non-modal, occurrent facts. Since chances, defined in this way, do not even purport to summarize indexical information, there is no reason to suppose that all relevant information about future events is always implied by knowledge of the chances-not if we have reason for thinking that indexical information might also be relevant. (This is, in fact, the stance that Lewis adopted in his critique of Elga's argument.  4  ) Since our intuitions about what information is admissible in this type of case are no more secure than our direct intuitions about what credence Beauty should assign to HEADS, the Principal Principle fails to settle the Sleeping Beauty controversy. What counts as admissible information in the Sleeping Beauty problem must emerge from its solution-which needs to be independently justified-rather than assumed at the outset. Another way in which one may attempt to support the middle step in Elga's argument is by invoking Bas van Fraassen's Reflection Principle. 5 (The Reflection Principle, in its simplest form, postulates that your credence at a time t is constrained by your credence at a later time t' according to P t (X|P t (X)=x)=x.) Here we encounter the same problem again: the applicability of the principle to Sleeping Beauty is at least as problematic as the 1/3 view itself. The Sleeping Beauty problem postulates a breakdown of rationality. Beauty faces the possibility of drug-induced amnesia. Even if we ask about Beauty's credence on Monday, before the drug has been administered, she will not at that point know whether or not her memory has already been tampered with. It is independently known, from other cases, that the Reflection Principle should not be followed where forgetting takes place or is suspected. For example, if I knew that 1 year from now I will have credence 1/2 in the proposition that it rained today, that plainly does not imply that I should assign the same credence now-when I still vividly remember spending the day reading in the garden. The Reflection Principle, therefore, is of no more avail to the 1/3 view than is the Principal Principle. We are left with the unsupported appeal to intuition in the step of the argument that assumes that P(H1 | H1 ∨ T1) = 1/2. How are we to evaluate this intuition? One way is to examine what else we are led to accept if we adopt the 1/3 view. If the consequences are unacceptable, we should revise our intuition. Let us, therefore, consider some variations of the original Sleeping Beauty to explore the wider ramifications of the 1/3 view. If we set P(H1) = P(T1) = P(T2), it follows that Beauty should, upon awakening, assign P(HEADS) = 1/3 and P(TAILS) = 2/3. The only relevant difference between HEADS and TAILS is that there would be more awakenings of Beauty on the latter hypothesis. Since the structure of the situation does not depend on the particular numbers involved, we can test our intuitions by considering a more extreme version of the problem. \n Extreme Sleeping Beauty This is like the original problem, except that here, if the coin falls tails, Beauty will be awakened on a million subsequent days. As before, she will be given an amnesia drug each time she is put to sleep that makes her forget any previous awakenings. When she awakes on Monday, what should be her credence in HEADS? By reasoning exactly parallel to that which Elga used to support the 1/3 view in the original version, we obtain P(H1) = P(T1) = P(T2) = P(T3) = • • • = P(T1, 000, 001). That is, upon awakening, Beauty should assign P(HEADS) = 1/1,000,002. The result can be generalized: following this line of reasoning, Beauty takes her observation \"I am awake now\" as evidence in favor of hypotheses that imply that there are many such awakenings of her. The degree of support is proportional to the number of awakenings postulated by the hypotheses. This consequence in Extreme Sleeping Beauty is counterintuitive. It seems like a rather excessive confidence in the proposition that a fair coin, yet to be tossed, will fall tails. We can bring out even worse implications if we consider cases in which more than one agent is involved. Suppose that a possible world contains several agent-parts {a i } i∈R that are subjectively indistinguishable, that is, these agent-parts are in such similar evidential situations that individual agent-parts cannot tell which one they are in. Elga has argued for an indifference principle stating that one should assign the same credence to each centered proposition of the form \"My current agent-part is a i \", for i ∈ R, and this is supposed to hold whether or not the agent-parts in {a i } i∈R all belong to the same agent or to different agents.  6  This highly restricted indifference principle follows as a special case from a somewhat stronger indifference principle that appears to be needed to make sense of many seemingly legitimate scientific inferences.  7  The principle is thus well supported. But if we use it together with the reasoning in the 1/3 view, we obtain implausible results. \n Beauty and Doppelganger This is like the original Sleeping Beauty problem, except here Beauty is never woken up after being put to sleep on Monday. Instead, if the coin falls tails, another person is created and awoken on Tuesday. This new person will spend her Tuesday wakening in a state that is subjectively indistinguishable from Beauty's Monday state (she will have the same apparent memories and have experiences that feel just the same as Beauty's). When Beauty awakes on Monday, what should be her credence in HEADS? By Elga's weak indifference principle, Beauty should have the same conditional credence, given TAILS, in her being Beauty and Doppelganger. And by the same reasoning that the 1/3 view relies on in the original version of the problem, Beauty should have the same conditional credence, given MONDAY, in being Beauty as in being Doppelganger. From this we can derive, just as before, that the awakened Beauty should assign an equal credence in three centered propositions: P(\"I am Beauty and HEADS\") = P(\"I am Beauty and TAILS\") = P(\"I am Doppelganger and TAILS\"). Since the credence given to these three centered propositions sum to 1, it follows that upon awakening, Beauty should hold P(HEADS) = 1/3. Now consider the extreme version of Sleeping Beauty and Her Doppelganger, where on tails there will be a million different doppelgangers, each having an awakening on some subsequent day that will be subjectively indistinguishable from Beauty's Monday awakening. It is easy to show, by the same steps as before, that Beauty should upon awaking have credence P(HEADS) = 1/1,000,002. The argument does not depend on whether the coin is tossed before the experiment starts or only after Beauty has been put back to sleep on Monday. It is, in fact, irrelevant what the objective chance of HEADS is when Beauty is making her assessment.  8  The relevant factor is Beauty's prior credence in HEADS (relative to her non-indexical background information). For example, Beauty's posterior credence in HEADS would thus be unaffected if the existence of additional awakenings by her doppelgangers were made to depend, not on the outcome of a coin toss, but instead on whether the trillionth digit in the decimal expansion of π is even-provided only that Beauty's prior credence in this proposition is 1/2. We can therefore generalize the foregoing thought experiment: \n Beauty and Doppelganger (generalized) Let ϕ be a (non-indexical) proposition, to which Beauty assigns a prior credence of 1/2. Beauty is never woken up again after being put to sleep on Monday. If ϕ is true then there will be a total of N>0 awakenings of doppelgangers in states that are subjectively indistinguishable from Beauty's Monday awakening. As before, we get P(HEADS)=1/(N + 2). Let us consider what this recommendation amounts too. Each (awake) agent-part, merely by taking into account the indexical fact that \"I am currently an agent-part of this kind\", should give a greater credence to hypotheses in proportion as they imply that there is a greater number of subjectively indistinguishable agent-parts of that kind. At this point, those familiar with the literature on observation selection theory may notice an disturbing similarity between the reasoning behind this position and the so-called \"Self-Indication Assumption\". That assumption states that each observer should regard her own existence as evidence supporting hypotheses that imply the existence of a greater total population of observers in the world, the degree of support being proportional to the implied (expected) number of observers. The Self-Indication Assumption was originally introduced in discussions about the Doomsday argument, as an attempt to neutralize that argument. It turns out, however, that the assumption has implications of its own that are perhaps even more counterintuitive than those of the Doomsday argument. It seems that the following thought experiment, in particular, gives us fairly strong grounds for rejecting the Self-Indication Assumption. \n Presumptuous Philosopher It is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, T 1 and T 2 (using considerations from super-duper symmetry). According to T 1 the world is very, very big but finite and there are a total of a trillion trillion observers in the cosmos. According to T 2 , the world is very, very, very big but finite and there are a trillion trillion trillion observers. The super-duper symmetry considerations are indifferent between these two theories. Physicists are preparing a simple experiment that will falsify one of the theories. Enter the presumptuous philosopher: \"Hey guys, it is completely unnecessary for you to do the experiment, because I can already show to you that T 2 is about a trillion times more likely to be true than T 1 !\" (Whereupon the presumptuous philosopher explains the Self-Indication Assumption.) 9 By modifying this example slightly, we can substitute the reasoning embodied in the 1/3 view for that of the presumptuous philosopher. To do this, suppose that the two theories that the physicists have come up with differ not only in regard to how many observers there are but also in regard to how many agent-parts there are that are subjectively indistinguishable from your own current one. Elga's 1/3 view can now take the place of the Self-indication Assumption. It is worth noting that the situation described in this modified version of Presumptuous Philosopher is by no means a farfetched possibility. Contemporary cosmologists face essentially that predicament. They are trying to determine whether the universe is finite or infinite. Given the standard Big Bang model and the assumption that spacetime is singly connected, the universe is infinite if and only if it is either open or flat. Whether it is open or flat, or closed, depends on whether the cosmic energy density, , exceeds a certain threshold value. Current measurements indicate that the actual density is very close to the critical value, ≈ 1. It is an important open empirical question whether the actual value is above, below, or exactly at the critical level. Measurements are being conducted to obtain a better estimate of the cosmic energy density. If the universe is infinite then with probability one there are an infinite number of agent-moments in states subjectively indistinguishable to your current one. 10 Therefore, if Elga's 1/3 view is correct, we could conclude that we already have \"infinitely strong\" evidence that the universe is infinite. The consequence that it would be a waste of money to carry out the planned experiments because we can predict the outcome from our armchair (with probability 1), is extremely implausible. Somebody wishing to toe this line should be willing to bet at practically any odds on the outcome of these future experiments.  11  We have seen that the original argument given for the 1/3 view is inconclusive, that neither the Principal Principle nor the Reflection Principle could be successfully invoked to buttress it, and that when we unfold the reasoning embedded in the 1/3 view, we find that highly counterintuitive consequences follow. We have good reason to reject the 1/3 view.  12  We have not yet considered another argument in favor of the 1/3 view, one that is based on long-run frequency or betting considerations. We will discuss this argument in a later section. But first, let us turn our gaze to the 1/2 view. We shall argue that this view, too, should be rejected. \n The 1/2 view According to the 1/2 view presented by David Lewis, Beauty should upon awakening have credence 1/2 in HEADS, and her conditional credence in HEADS given MONDAY should be 2/3. P(H1) = 1/2, P(H1|H1 ∨ T1) = 2/3. Suppose that Beauty is informed that it is Monday, and let P + be her new credence function after she has obtained this information. Lewis claims that P + should be obtained by conditionalizing P on MONDAY. Thus, P + (HEADS) = P(HEADS|MONDAY) = 2/3. Lewis's argument for this claim is simple: before the experiment, Beauty should assign credence 1/2 to the proposition that a fair coin to be tossed in the future will fall heads. She already knows that she will be awakened. Therefore, when she awakes, she obtains no new relevant information; so her credence in HEADS should remain 1/2. This argument starts to look peculiar when we compare it to Lewis's explanation of why Beauty should increase her credence in HEADS upon being informed that it is Monday: Now when Beauty is told during her Monday awakening that it's Monday, . . . she is getting evidence-centered evidence-about the future: namely that she is not now in it. That's new evidence: before she was told that it is Monday, she did not yet have it. . . This new evidence is relevant to HEADS, since it raises her credence in it by 1/6 (i.e. from 1/2 to 2/3).  13  On this reasoning, it would seem, one could similarly argue that when Beauty awakes on Monday (but before she is informed that it is Monday) she likewise gets relevant evidence-centered evidence-about the future: namely that she is now in it. Since it makes no difference whether the coin is tossed before the experiment begins or on Monday evening (a point of agreement between Lewis and Elga), let us suppose the case where the coin is tossed just before Beauty awakens on Monday. If being in \"the future\" means being in the period after the coin has been tossed, Beauty now has new relevant information about her current location relative to this period (namely, that she is in it now). Lewis is thus committed to the view that one's beliefs about a chance event such as a coin toss can be affected by obtaining evidence that is purely about one's own current location. Yet he offers no argument for why only centered evidence that it is Monday, but not centered evidence that one is currently in the \"experimental phase\" (i.e. that it is either Monday or Tuesday, rather than, say, the preceding Sunday) can be relevant to HEADS. Absent such an argument, his claim that Beauty upon awakening should assign credence 1/2 to HEADS is a completely unsupported assumption, one which those who disagree with the 1/2 view should feel free to reject. Opponents of the 1/2 view can simply insist that Beauty does get centered relevant evidence when she finds herself awake in the experimental (Monday or Tuesday) phase. Lewis's argument for the 1/2 view therefore fails. If we unpack the implications of accepting the 1/2 view, we find that it has implications no less counterintuitive than those of the 1/3 view. Let us begin by considering again the amplified version of the Sleeping Beauty problem. \n Extreme Sleeping Beauty This is like the original problem, except that here, if the coin falls tails, Beauty will be awakened on a million subsequent days. As before, she will be given an amnesia drug each time she is put to sleep that makes her forget any previous awakenings. When she awakes on Monday, what should be her credence in HEADS? The adherent of the 1/2 view will maintain that Beauty, upon awakening, should retain her credence of 1/2 in HEADS, but also that, upon being informed that it is Monday, she should become extremely confident in HEADS: P + (HEADS) = 1, 000, 001/1, 000, 002. This consequence is itself quite implausible. It is, after all, rather gutsy to have credence 0.999999% in the proposition that an unobserved fair coin will fall heads. We can extract an even more counterintuitive consequence by modifying the example slightly. Instead of using a single coin toss, with a prior probability of heads equal to 1/2, we could stipulate a sequence of 10 independent tosses of the same coin. The prior probability that all of these tosses will come up heads is 2 −10 , which is less than one in a thousand (≈ 0.00098%). Suppose that unless the coin comes up heads all ten times, Beauty will not be awakened again after the Monday awakening. If, however, the tossing does yield ten heads, then Beauty will be awakened on a million subsequent days. We can then ask what odds Beauty could reasonably accept if offered to bet on such a sequence of coin tosses. \n Beauty the High Roller Beauty is awakened on Monday and after having been awake for an hour she is offered a bet. She is told that a fair coin will be tossed ten times. If it lands heads all ten times then Beauty wins $1,000. If it lands tails at least once, then Beauty loses $100,000. But there is a twist: If Beauty wins, the experiment ends at that point. If Beauty loses, she will be put to sleep, given an amnesia drug that causes her to forget her awakening, and then awoken again the next day; and this procedure will be repeated for a total of one million days. (On each of these subsequent awakenings, Beauty will spend an hour in a state of ignorance about what day it is before she is put to sleep. No bet is offered after the initial Monday awakening.) Beauty awakes on Monday and prudently decides to reject the bet that she is offered. But just as she is about to declare her decision, David Lewis's ghost appears in a puff of smoke. The ghost explains the 1/2 view reasoning and argues that Beauty's credence in the proposition that all ten tosses will come up heads should be very close to unity. In fact, the ghost calculates that, even taking into account the low prior probability of this proposition, Beauty should nevertheless assign it a posterior credence of 99.8% after taking into account that she has just learnt that her current awakening is the initial Monday awakening.  14  The expected value of the gamble to Beauty is therefore positive: EV ≈ 0.998 × $1, 000 + 0.002 × (−$100, 000) = $998 − $200 = $798. So according to the ghost's reckoning, Beauty ought to take the bet. But surely it would be crazy for Beauty to follow the ghost's advice.  15  Hence we should reject the 1/2 view. 14 Let H * be the proposition that the coin falls heads all ten times. Let M be the centered proposition stating that Beauty's is currently awake on the first Monday. We then have \n P(H * |M) = P(M|H * )P(H * ) P(M|H * )P(H * ) + P(M|¬H * )P(¬H * ) . With P(H * ) = 2 −10 , P(¬H * ) = 1 − P(H * ), P(M|H * ) = 1, and P(M|¬H * ) = 2/1, 000, 002, it easy to check the ghost's calculation.  15  We assume that Beauty is risk-neutral and that her utility function is linear in money. If she has a diminishing marginal utility of money, or is risk-averse, we can simply adjust the stakes or the number \n A hybrid model? If the 1/3-and the 1/2-view both have unacceptable consequences, how can we build a better model for reasoning with indexical information? Consider again the 1/3 view. The problem with that view was that it led to a bias in favor of hypotheses entailing that there are many subjectively indistinguishable duplicates of one's current agent-part. When all the hypotheses under consideration agree on the number of such duplicates, the bias does not manifest itself; but it causes trouble in cases like Sleeping Beauty. The obvious way to correct this \"manyduplicates\" bias is to divide one's credence in being any one particular duplicate with the total number of duplicates. Consider the following two possible worlds, in which the only agent-parts are those in the Sleeping Beauty experiment. (We shall assume throughout that all \"agent-parts\" are of equal duration.) w1: h1 [The \"heads\" world], w2: t1 t2 [The \"tails\" world]. As before, H1, T1, and T2 are the centered propositions expressing that one is currently h1, t1, and t2, respectively; HEADS is the proposition that the actual world is w1; and TAILS the proposition that the actual world is w2. The proposal for removing the many-duplicate bias is that we set P(H1) = 1/2, P(T1) = P(T2) = 1/4. Of course, we still have P(H1|HEADS) = 1, P(T1|TAILS) = P(T2|TAILS) = 1/2. It follows that P(HEADS) = P(TAILS) = 1/2. Thus, there is no general tendency, upon finding oneself awakened in the experiment, to favor hypotheses implying that there are many such awakenings. This means that we are immune from objections of the \"Presumptuous Philosopher\"-type. Our new de-biasing postulate implies that the conditional probability of HEADS given that it is MONDAY is greater than 50%: P(HEADS|H1 ∨ T1) = 2/3, Constraint P. Now, if the credence function P + that Beauty should have upon learning that it is MONDAY were obtained by conditionalizing P on (H1 ∨ T1), then we would fall into the trap illustrated in Beauty the High Roller. To avoid falling into this trap, it seems as though we require that P + (HEADS|H1 ∨ T1) = 1/2, Constraint P + . \"Presumptuous Philosopher\" and \"Beauty the High Roller\" form a Scylla and a Charybdis, which we must avoid, and yet it looks like the only way to satisfy the constraints from these thought experiments involves violating Bayesian (footnote 15 continued) of awakenings that would occur so that the calculation still favors her taking the gamble, without affecting the basic point of the thought experiment. conditionalization. 16 I believe, however, that this sacrifice is not necessary. The matter is somewhat subtle. Suppose that Beauty will be told after awakening on Monday that it is Monday. The situation is then different from the one described above. It must instead be represented as follows: w1: h1 h1m [The \"heads\" world], w2: t1 t1m t2 [The \"tails\" world]. The situation we are confronting involves five possible agent-parts, not three. The added terms, \"h1m\" and \"t1m\", denote the agent-parts of Beauty that know that it is Monday (in the heads and the tails world, respectively). Let us retain the P unchanged (i.e. the credence function for Beauty at the times when she is unaware that it is Monday). Now consider more carefully Constraint P + , which seemed like it was a constraint on the P + (i.e. the credence function that Beauty has when she knows that it is Monday). Constraint P + contains the expression \"H1 ∨ T1\". But this expression does not describe what Beauty knows after she has learnt that it is Monday, for at that point she should set: P + (H1) = 0, P + (T1) = 0. This is because at that point Beauty knows that her current agent-part is either h1m or t1m. The information she has just obtained is therefore not (H1 ∨ T1), but rather (H1M ∨ T1M), where H1M is the centered proposition expressed by \"My current agent-part is h1m\" and T1M is the centered proposition expressed by \"My current agent-part is t1m\". The correct formulation of Constraint P + is therefore as follows: P + (HEADS|H1M ∨ T1M) = 1/2, Constraint P + [corrected]. This correction eliminates the conflict with Constraint P and allows us to avoid violating Bayesian conditionalization. The corrected Constraint P + is precisely what we need to save Beauty from ruin in the High Roller thought experiment. One may still wonder what conditional credence Beauty should assign, before being informed about it being Monday, to HEADS given that she is currently an agent-part that knows that it is Monday: P(HEADS|H1M ∨ T1M) = ? However, there is no need to assign a value to this expression. Note that P(HEADS|H1M ∨ T1M) = P(HEADS & [H1M ∨ T1M])/P(H1M ∨ T1M). Since P(H1M ∨ T1M) = 0, this expression is undefined. And so it should be.  17  Let us take a step back and consider the point more generally. Whenever an agent receives some evidence E, we could distinguish the earlier agent-part, α − , that lacked this evidence, and the later agent-part, α + , which has come to possess it. According to the reasoning just described, we cannot automatically conclude that the conditional probability P(X|E & \"I am currently α − \"), conditionalized on E, yields the correct posterior credence that α + should assign to X. Only if P(X|E & \"I am currently α − \") = P + (X|E & \"I am currently α + \"), can the kinematics be represented in the simplified form P + (X) = P(X|E). This standard representation is thus elliptic as it omits some changes in indexical information. In ordinary cases, such changes in indexical information are irrelevant to the hypotheses being considered and can hence be safely ignored. The standard elliptic representation of Bayesian conditionalization can then be used without danger. In certain special cases, however, such delicate changes in indexical information can be relevant, and it is then crucial to recognize and make explicit the hidden intermediary step. Sleeping Beauty, on the model proposed here, turns out to be just such a special case. To recapitulate, I have argued that a Bayesian can coherently accept both Constraint P and the corrected Constraint P + , even though superficially this seems to violate Bayesian conditionalization. The reason why we not only can but should accept both these constraints was given earlier: to avoid the counterintuitive consequences that follow if either of these constraints is violated, as shown by the \"Presumptuous Philosopher\" and the \"Beauty the High Roller\" thought experiments. \n The long-run frequency argument One other important argument for the 1/3 view needs to be examined as it might be thought to pose a problem for the hybrid model. The discussion of this argument will also serve to further elucidate how the proposed model works. A proponent of the 1/3 view could argue that Sleeping Beauty awakened ought to have credence 1/3 in HEADS because if the experiment were repeated many times, then approximately 1/3 of all her awakenings would be heads-awakenings (and 2/3 would be tails-awakenings). In the infinite limit, this ratio would, with probability 1, be approached arbitrarily closely. This argument could be buttressed by introducing betting considerations. In the infinite limit, Beauty would have to assign credence 1/3 to HEADS, else she would be guaranteed a loss if she put her money where her mouth is. For a betting argument to have any bite, the hypothesized bookie must have the same information as Beauty. If a bet were only offered on the Monday awakening in each run of the experiment, and if both the bookie and Beauty knew this, then Beauty could infer from the fact that she was offered a bet that it was Monday. According to the hybrid model, she should then assign credence 1/2 to the proposition that the coin will fall heads in that trial. This will match the long-run frequency of bets that she will win, so in this case betting considerations pose no problem. The betting argument therefore requires that Beauty be offered a bet each time she is awakened. Then she cannot infer what day it is from the fact that she is being offered a bet. In this case, in the long run, Beauty would be expected to lose 2/3 of her bets if she consistently bet on heads. How does this square with the prescription of the hybrid model that Beauty, upon awakening (but before learning which day it is) assigns credence 1/2 to heads? One possible response to this argument is to deny that betting considerations provide a valid guide to credence assignment in the present case. Since there would be a different number of bets placed depending on how the coin fell, one might regard the test as unfair.  18  In support of this response one may note that the presumptuous philosopher would also be vindicated if we assumed that an agent-part's credence should be determined by the betting-odds at which the expected net gains and losses of the collective of all his duplicate agent-parts would be zero. Since there would be a trillion times more duplicates of the agent-part if theory T 2 is true then if T 1 is true, each agent-part would have to assign a trillion times greater odds to T 2 than to T 1 in order for the expected value of all the bets made by the collective of agent-parts to be zero. And yet we argued that it seems wrong for an agent-part to assign a trillion times greater credence to T 2 than to T 1 . However, this response does not address the case of the repeated Sleeping Beauty problem. For in this case, in the infinite limit, there is no uncertainty about the total proportion of awakenings in tails-and heads-runs of the experiment. Beauty knows that (with probability one) there will actually be two times as many awakenings in tails-trials as in heads-trials. In this case, therefore, betting considerations unambiguously suggest that Beauty upon awakening should assign the 2/3 credence to tails. Here one could not justify a divergence of credence assignment from betting odds by saying that there would be a different number of bets placed depending on which of the hypotheses under consideration is true, because the total number of bets placed is not (significantly) variable when Beauty is put through a large number of repetitions of the experiment. There is, consequently, strong reason for recommending that Beauty assign credence 1/3 to heads when she knows that the experiment will be repeated very many times. This, however, is not an objection to the hybrid model proposed above. The hybrid model, as we shall now see, implies the very same credence assignment as the betting considerations suggest. Betting considerations, far from being an embarrassment to the hybrid model, actually agree with its implications and support it. Up until this section, our discussion has focused on (variations of) the single-shot Sleeping Beauty problem, where there are no repetitions of the experiment. This is the simplest case: the world contains no other relevant agent-parts than those existing within a single implementation of the Sleeping Beauty experiment. Let us now apply the hybrid model to the situation that arises if the experiment is repeated many times. But first, as an intermediary step, consider the following case. \n Three Thousand Weeks (non-random) Beauty lives for three thousand weeks. On odd-numbered weeks she is awakened once, on Mondays. On even-numbered weeks she is awakened twice, on Mondays and Tuesdays. After each awakening she is given an amnesia drug that causes her to forget her previous awakenings. Beauty knows all this. The hybrid model that I propose implies that in this case, Beauty should have credence 1/3 in the centered proposition \"My current awakening is taking place in an odd-numbered week\" (or \"ODD\" for short). This is because Beauty, when she wakes up, knows that ODD is true for one third of all the agent-parts that are in the same subjective evidential state as her current agent-part. (The credence assignment follows from the very weak indifference principle which Lewis, Elga, and I all accept.) Crucially, these agent-parts are all actual agent-parts, as opposed merely possible ones. We thus have P(ODD) = 1/3. Further, it is easy to show that P(ODD|MONDAY) = 1/2. If we suppose that every Monday, just before being put to sleep, Beauty is told that it is Monday, we also have P + (ODD|MONDAY) = 1/2. Note that, for the reasons explained earlier, \"MONDAY\" denotes a different centered proposition in each of these two conditional credence expressions. (In the first expression, \"MONDAY\" refers to a proposition that is centered on an agent-part that does not know that it is Monday; in the second expression, specifying Constraint P + , \"MONDAY\" refers to a proposition centered on an agent-part that does know that it is Monday.) In the present case, however, the conditional credences work out the same. The hybrid view therefore coincides with the 1/3 view in this example. The key difference between the original Sleeping Beauty problem and 3,000 weeks and is that in the latter case-but not in the former-there are twice as many actual awakenings of one type as of the other. This means that in 3,000 weeks, the prior credence in ODD, before Beauty learns that it is Monday, is unaffected by the correction we made to eliminate the bias in favor of hypotheses entailing the existence of more duplicates. (Such a bias would result from applying the indifference principle to a class of agent-parts that included merely possible as well as actual agent-parts.) In 3,000 weeks, ODD is true for one-third of the agent-parts that are ignorant about whether it is Monday, and for one half of the agent-parts who know that it is Monday; correspondingly, the credence in ODD is 1/3 for the first type of agent-part and 1/2 for the second type.  19  Let us now apply this analysis to a more straightforwardly repeated version of the original Sleeping Beauty problem: The N-fold Sleeping Beauty Problem This is like the original Sleeping Beauty problem repeated N times on consecutive weeks. Beauty knows that the experiment is repeated N times, but she is unable to determine which run of the experiment she is currently in. For N = 1, this reduces to the original Sleeping Beauty problem, and Beauty's credence in HEADS should be 1/2, both before and after learning that it is Monday. If N is some large number, such as N = 3, 000, then the case approximates 3,000 weeks, and Beauty's credence in HEADS should be approximately 1/3 before learning that it is Monday, and 1/2 after being told that it is Monday. (\"HEADS\" here stands for \"My current awakening is in one of the trials where the coin fell heads\".) The larger N is, the more exact will the approximation be. The credences in the 3,000-fold Sleeping Beauty Problem are not exactly equal to those in 3,000 weeks because the total number of awakenings is not strictly fixed. There is, however, a very high chance that there will be roughly 3,000 tails-awakenings and 1,500 heads-awakenings in the 3,000-fold Sleeping Beauty Problem, so it closely approximates 3,000 weeks. Illustration: The hybrid model to the N = 2 case It may be instructive to calculate the exact credences for the N = 2 case. There are four possible outcomes of the coin tosses: heads-heads, heads-tails, tails-heads, and tails-tails. We can represent these four possibilities along with the possible agent-parts they would realize as follows: Week 1 | Week 2 w1: h1 | h2 w2: h3 | t1 t2 w3: t3 t4 | h4 w4: t5 t6 | t7 t8 Each of these four possibilities has an equal chance of occurring (p = 1/4). Since each of these agent-parts are in the same evidential situation, Beauty's conditional credence, given one of the four possibilities, is divided equally between the agentparts that that possibility would realize. Hence, her unconditional credence in being any particular possible agent-part is obtained by multiplying this conditional credence with her prior credence in the possibility in question (i.e. 1/4). Thus, we get the following assignment of credence to the centered propositions that she is currently a particular agent-part: This, however, is not the credence that Beauty should assign to HEADS if she were told that it is Monday. For the same reasons as noted above in the discussion of the original (one fold) Sleeping Beauty problem, the relevant quantity is instead P + (HEADS | MONDAY). To determine this quantity, we again represent four possibilities, but these now include agent-parts that know that it is Monday (these are the agent-parts in the middle columns, whose names end with the letter 'm'): Week 1 | Week 2 w1: h1 h1m | h2 h2m w2: h3 h3m | t1 t1m t2 w3: t3 t2m t4 | h4 h4m w4: t5 t3m t6 | t7 t4m t8 Since the number of agent-moments that know that it is Monday is the same in all four possibilities (i.e., two in each case), each of these agent-parts (who are in the same evidential situation) should assign the same credence to being a particular one of these agent-parts, namely (1/4)(1/2) = 1/8, and they should assign zero credence to being some other agent-part. Thus: Week 1 | Week 2 w1: 0 1/8 | 0 1/8 w2: 0 1/8 | 0 1/8 0 w3: 0 1/8 0 | 0 1/8 w4: 0 1/8 0 | 0 1/8 0 To obtain P + (HEADS | MONDAY), we sum the credences of the centered propositions that imply both HEADS and MONDAY (indicated in boldface), and divide this by the sum of the credences that imply MONDAY: P + (HEADS|MONDAY) = (1/8 + 1/8 + 1/8 + 1/8)/1 = 1/2. The hybrid model thus implies that when Beauty learns that it is Monday, she should have credence 1/2 in HEADS. This is so both in the original one-shot version of the Sleeping Beauty problem and in the repeated (\"N-fold\") versions where N ≥ 1. \n Discussion We have argued that the standard arguments for the standard positions on the Sleeping Beauty problem, the 1/2 view and the 1/3 view, are, if not directly question-begging then at least inconclusive in that they rely on eminently deniable premises. To evaluate the standard positions, therefore, we need to seek for further constraints. We presented two such constraints in the form of two thought experiments. The Presumptuous Philosopher thought experiment, in a version adapted for application to the Sleeping Beauty case, strongly suggests that the 1/3 view is wrong. The Beauty the High Roller thought experiment strongly suggests that the 1/2 view is wrong. On these grounds, we concluded that both the standard models for reasoning about self-location are unacceptable. In the second, constructive part of the paper we proposed a new model. This model seeks to combine the most attractive features of the 1/3-and the 1/2-view, so we termed it the hybrid model. It implies that Beauty should not take the fact that she is currently awake as evidence that there are large numbers of awakenings. But it also implies that when Beauty discovers that it is currently Monday, she should not take this as evidence against the hypothesis that there will be many more awakenings in the future. If the hybrid model is correct, it might explain the fact that both the 1/3-and the 1/2-views have some intuitive appeal. According to the hybrid model, both these views On Monday, after both the Bookie and Beauty have been informed that it is Monday, the Bookie offers Beauty a further bet: Beauty gets $15 if TAILS. Beauty pays $15 if HEADS. If Beauty accepts these bets, she will emerge $5 poorer. Since Beauty is able to anticipate the result of accepting all the bets, it is clear that she should not do so. Following the hybrid model, Beauty should have no objection to accepting the second Monday bet. The hybrid model implies that P + (HEADS| MONDAY) = P + (TAILS | MONDAY) = 1/2. Being offered a single straightforward bet on HEADS at even odds, knowing that it is Monday, she has no reason to refuse it. It is the other set of bets that she should reject. The hybrid model implies that Beauty, before learning that it is Monday, assigns P(HEADS | MONDAY) = 2/3. This appears to justify her accepting the bookie's first offer. But here the situation is more complicated. Since neither party knows whether it is Monday, the Bookie cannot offer this bet only on Monday. He must offer it on both awakenings. This means that the total number of bets will vary depending on how the coin falls: if heads, the first type of bet is offered only once; but if tails, it is offered twice. Moreover, we may assume that Beauty will either accept it on both occasions or reject it on both occasions, as she has no effective way of telling which occasion she is currently encountering.  21  So Beauty knows that she would be accepting two bets if TAILS and one bet if HEADS. Now, we already know from other examples that when the number of bets depends on whether the proposition betted on is true, then the fair betting odds can diverge from the correct credence assignment. For instance, suppose you assign credence 9/10 to the proposition that the trillionth digit in the decimal expansion of π is some number other than 7. A man from the city wants to bet against you: he says he has a gut feeling that the digit is number 7, and he offers you even odds-a dollar for a dollar. Seems fine, but there is a catch: if the digit is number 7, then you will have to repeat exactly the same bet with him one hundred times; otherwise there will just be one bet. If this proviso is specified in the contract, the real bet that is being offered you is one where you get $1 if the digit is not 7 and you lose $100 if it is 7. That you should reject this bet is quite unproblematic and does not in any way undermine your original assessment that the probability of the trillionth digit being 7 is 1/10. A similar situation can arise in a more subtle way. We can construct a scenario where, even though no \"catch\" is explicitly part of the contract, you nevertheless know that you will be put in a position where you will end up betting a hundred times if you are wrong but only one time if you are right. This could happen, e.g. if there is a machine that will determine the correct answer and then, on the basis of what this answer is, will decide whether to repeatedly administer an amnesia drug to you that makes you forget whether you have already betted. The machine could do this in such a way that you end up making a larger number of bets if you are wrong. If you believe that you are facing a situation of this kind, you should take corrective action to limit the distortive effects of the memory erasure on your decision-making. In particular, you may decide to reject bets that seem fair to you and that may have been perfectly acceptable in the absence of the forced irrationality constraint. Let us return to the case of Beauty and the Bookie. Beauty knows that she faces the risk of having her memory erased and thus of becoming irrational. (Memory erasure entails a form of irrationality.) For reasons such as those described above, Beauty may therefore reject the bookie's first set of bets as a form of damage control to minimize the impact of the failures of rationality from which she knows she is at risk. If the deviation of her optimal betting odds from her credence assignment can be justified on these grounds, then she can use the hybrid model and still avoid being Dutch booked. It is interesting that in Beauty and the Bookie, Beauty's betting odds should deviate from her credence assignment even though the bet that might be placed on Tuesday would not result in any money changing hands. In a sense, the bet that Beauty and the bookie would agree to on Tuesday is void. Nevertheless, it is essential that this bet is included in the example. The bookie is unable to pursue the policy of only offering bets on Monday since he does not know which day it is when he wakes up. If we changed the example so that the bookie knew that is was Monday immediately upon awakening, then Beauty and the bookie would no longer have the same relevant information, and the Dutch book argument would fail. If instead we changed the example so that Beauty as well as the bookie knew that it was Monday immediately upon awakening, then Beauty's credence in HEADS & MONDAY would be 1/2 throughout Monday, so again she would avoid a Dutch book.  22  In conclusion, the hybrid model combines the comely aspects of the 1/2 view and the 1/3 view while avoiding their faults. The main concern with the hybrid model is that it may appear to violate Bayesian conditionalization. I have presented (tentative) arguments suggesting that the violation is merely apparent. At any rate, one might hope that having a third contender for how Beauty should reason will help stimulate new ideas in the study of self-location.  23   12 1/12 | 1/12 w4: 1/16 1/16 | 1/16 1/16 We obtain P(HEADS) by summing the credences of the centered propositions that imply HEADS (indicated with boldface): P(HEADS) = 1/8 + 1/8 + 1/12 + 1/12 = 5/12. Since P(HEADS | MONDAY ) = P(HEADS & MONDAY)/P(MONDAY), we likewise get P(HEADS|MONDAY) = (5/12)/(17/24) = 10/17. \n\t\t\t (see Lewis 1980 Lewis , 1994 . A precursor to the Principal Principle was formulated by Mellor (1971) .4  (see Lewis 2001) . A similar point was made, independently, in Bostrom (2001) . 5 (seevan Fraassen 1984). \n\t\t\t (see Elga 2004 ). 7 (seeBostrom 2002a, b).8  If the coin were tossed before she woke up, the chance of HEADS would not be 1/2, but either 1 or 0. \n\t\t\t (seeBostrom 2002a, b; 2003)   \n\t\t\t (see Bostrom 2002b) .11  Even if during the next 200 years we obtained overwhelming empirical evidence that the universe is finite, we should, on this view, continue to assign credence 1 to the universe being infinite.12  Kierland and Monton, in a very recent paper (Kierland and Monton 2005) , argue that the case where persons are duplicated (as in Doppelganger) should be treated in a fundamentally different way from cases where awakenings of the same person are duplicated (as in the original Sleeping Beauty). They would therefore likely resist the implications that we have seen follow from Elga's position; and they could do this by rejecting the interpersonal version of the Self-Indication Assumption. I will not discuss this option in detail in this paper, but it is worth noting that the Extreme Sleeping Beauty thought experiment is unaffected by this issue. Furthermore, one can imagine possible situations in which the number of awakenings that an individual should except to experience is strongly correlated with the truth of some physical theory. One may therefore be able to derive counterintuitive implications from this view similar to the ones described above, albeit perhaps only in less empirically realistic situations. \n\t\t\t  (Lewis 2001, p175). \n\t\t\t It has been argued that we should indeed violate conditionalization in the Sleeping Beauty problem (Kierland and Monton 2005) . Kierland and Monton argue for the 1/3 answer on grounds which they claim do not lead to the counterintuitive result in the Beauty and Doppelganger. Their position thus diverges significantly from Lewis's 1/2 view.17  The model used here presupposes that agent-parts know what their evidence is. This simplifying assumption may be inappropriate in certain cases, but we shall not here discuss how such cases should be modeled. \n\t\t\t (see also Arntzenius 2002) . \n\t\t\t We say that ODD \"is true for\" an agent-part if the centered proposition which that agent-part would express by saying \"ODD\" is true. When writing down a symbol like \"ODD\", we need to be careful about whether we take this to refer to a specific centered proposition or to a function that yields a centered proposition when given an agent-part as an argument. In the text, the context should make it clear what is intended in each case. \n\t\t\t I'm grateful here to one anonymous referee. A similar Dutch-book argument has recently been advanced in Hitchcock (2004) . \n\t\t\t If Beauty could opt for a mixed strategy, she could decide to accept the bet at a given occasion with a certain probability. This would complicate the argument but would not affect the conclusion. \n\t\t\t If Beauty would know on Monday that it is Monday, then she would also be able to infer on Tuesday-from the fact that she does not know then that it is Monday-that it is Tuesday. So she would always know what day it is. (We assume that Beauty always know the general setup of the experiment she is in.)23  For comments and discussions, I am grateful to Adam Elga, Bradley Monton, Brian Kierland, Simon Saunders, and anonymous referees.", "date_published": "n/a", "url": "n/a", "filename": "Bostrom2007_Article_SleepingBeautyAndSelf-location.tei.xml", "abstract": "The Sleeping Beauty problem is test stone for theories about selflocating belief, i.e. theories about how we should reason when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the \"1/2 view\" and those who advocate the \"1/3 view\". I argue that both these positions are mistaken. Instead, I propose a new \"hybrid\" model, which avoids the faults of the standard views while retaining their attractive properties. This model appears to violate Bayesian conditionalization, but I argue that this is not the case. By paying close attention to the details of conditionalization in contexts where indexical information is relevant, we discover that the hybrid model is in fact consistent with Bayesian kinematics. If the proposed model is correct, there are important lessons for the study of self-location, observation selection theory, and anthropic reasoning.", "id": "2477697172c89fde10fc622f81625129"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Andr É Barreto", "Shaobo Hou", "Diana Borsa", "David Silver", "Doina Precup"], "title": "Fast reinforcement learning with generalized policy updates", "text": "The combination of reinforcement learning with deep learning is a promising approach to tackle important sequential decisionmaking problems that are currently intractable. One obstacle to overcome is the amount of data needed by learning systems of this type. In this article, we propose to address this issue through a divide-and-conquer approach. We argue that complex decision problems can be naturally decomposed into multiple tasks that unfold in sequence or in parallel. By associating each task with a reward function, this problem decomposition can be seamlessly accommodated within the standard reinforcement-learning formalism. The specific way we do so is through a generalization of two fundamental operations in reinforcement learning: policy improvement and policy evaluation. The generalized version of these operations allow one to leverage the solution of some tasks to speed up the solution of others. If the reward function of a task can be well approximated as a linear combination of the reward functions of tasks previously solved, we can reduce a reinforcement-learning problem to a simpler linear regression. When this is not the case, the agent can still exploit the task solutions by using them to interact with and learn about the environment. Both strategies considerably reduce the amount of data needed to solve a reinforcement-learning problem. artificial intelligence | reinforcement learning | generalized policy improvement | generalized policy evaluation | successor features R einforcement learning (RL) provides a conceptual framework to address a fundamental problem in artificial intelligence: the development of situated agents that learn how to behave while interacting with the environment  (1) . In RL, this problem is formulated as an agent-centric optimization in which the goal is to select actions to get as much reward as possible in the long run. Many problems of interest are covered by such an inclusive definition; not surprisingly, RL has been used to model robots  (2)  and animals  (3) , to simulate real (4) and artificial (5) limbs, to play board  (6)  and card  (7)  games, and to drive simulated bicycles  (8)  and radio-controlled helicopters  (9) , to cite just a few applications. Recently, the combination of RL with deep learning added several impressive achievements to the above list  (10) (11) (12) (13) . It does not seem too far-fetched, nowadays, to expect that these techniques will be part of the solution of important open problems. One obstacle to overcome on the track to make this possibility a reality is the enormous amount of data needed for an RL agent to learn to perform a task. To give an idea, in order to learn how to play one game of Atari, a simple video game console from the 1980s, an agent typically consumes an amount of data corresponding to several weeks of uninterrupted playing; it has been shown that, in some cases, humans are able to reach the same performance level in around 15 min  (14) . One reason for such a discrepancy in the use of data is that, unlike humans, RL agents usually learn to perform a task essentially from scratch. This suggests that the range of problems our agents can tackle can be significantly extended if they are endowed with the appropriate mechanisms to leverage prior knowledge. In this article we describe one such mechanism. The framework we discuss is based on the premise that an RL problem can usually be decomposed into a multitude of \"tasks.\" The intuition is that, in complex problems, such tasks will naturally emerge as recurrent patterns in the agent-environment interaction. Tasks then lead to a useful form of prior knowledge: once the agent has solved a few, it should be able to reuse their solution to solve other tasks faster. Grasping an object, moving in a certain direction, and seeking some sensory stimulus are examples of naturally occurring behavioral building blocks that can be learned and reused. Ideally, information should be exchanged across tasks whenever useful, preferably through a mechanism that integrates seamlessly into the standard RL formalism. The way this is achieved here is to have each task be defined by a reward function. As most animal trainers would probably attest, rewards are a natural mechanism to define tasks because they can induce very distinct behaviors under otherwise identical conditions  (15, 16) . They also provide a unifying language that allows each task to be cast as an RL problem, blurring the (somewhat arbitrary) distinction between the two  (17) . Under this view, a conventional RL problem is conceptually indistinguishable from a task self-imposed by the agent by \"imagining\" recompenses associated with arbitrary events. The problem then becomes a stream of tasks, unfolding in sequence or in parallel, whose solutions inform each other in some way. What allows the solution of one task to speed up the solution of other tasks is a generalization of two fundamental operations underlying much of RL: policy evaluation and policy improvement. The generalized version of these procedures, jointly referred to as \"generalized policy updates,\" extend their standard counterparts from point-based to set-based operations. This makes it possible to reuse the solution of tasks in two distinct ways. When the reward function of a task can be reasonably approximated as a linear combination of other tasks' reward functions, the RL problem can be reduced to a simpler linear regression that is solvable with only a fraction of the data. When the linearity constraint is not satisfied, the agent can still leverage the solution of tasks-in this case, by using them to interact with and learn about the environment. This can also considerably reduce the amount of data needed to solve the problem. Together, these two strategies give rise to a divide-and-conquer approach to RL that can potentially help scale our agents to problems that are currently intractable. \n RL We consider the RL framework outlined in the Introduction: an agent interacts with an environment by selecting actions to get as much reward as possible in the long run  (1) . This interaction happens at discrete time steps, and, as usual, we assume it can be modeled as a Markov decision process (MDP)  (18) . An MDP is a tuple M ≡ (S, A, p, r , γ) whose components are defined as follows. The sets S and A are the state space and action space, respectively (we will consider that A is finite to simplify the exposition, but most of the ideas extend to infinite action spaces). At every time step t, the agent finds itself in a state s ∈ S and selects an action a ∈ A. The agent then transitions to a next state s , where a new action is selected, and so on. The transitions between states can be stochastic: the dynamics of the MDP, p(•|s, a), give the next-state distribution upon taking action a in state s. In RL, we assume that the agent does not know p, and thus it must learn based on transitions sampled from the environment. A sample transition is a tuple (s, a, r , s ) where r is the reward given by the function r (s, a, s ), also unknown to the agent. As discussed, here we adopt the view that different reward functions give rise to distinct tasks. Given a task r , the agent's goal is to find a policy π : S → A, that is, a mapping from states to actions, that maximizes the value of every state-action pair, defined as Q π r (s, a) ≡ E π ∞ i=0 γ i r (St+i , At+i , St+i+1) | St = s, At = a , [1] where St and At are random variables indicating the state occupied and the action selected by the agent at time step t, E π [•] denotes expectation over the trajectories induced by π, and γ ∈ [0, 1) is the discount factor, which gives less weight to rewards received further into the future. The function Q π r (s, a) is usually referred to as the \"action-value function\" of policy π on task r ; sometimes, it will be convenient to also talk about the \"state-value function\" of π, defined as V π r (s) ≡ Q π r (s, π(s)). Given an MDP representing a task r , there exists at least one optimal policy π * r that attains the maximum possible value at all states; the associated optimal value function V * r is shared by all optimal policies  (18) . Solving a task r can thus be seen as the search for an optimal policy π * r or an approximation thereof. Since the number of possible policies grows exponentially with the size of S and A, a direct search in the space of policies is usually infeasible. One way to circumvent this difficulty is to resort to methods based on dynamic programming, which exploit the properties of MDPs to reduce the cost of searching for a policy  (19) . Policy Updates. RL algorithms based on dynamic programming build on two fundamental operations (1). Definition 1. \"Policy evaluation\" is the computation of Q π r , the value function of policy π on task r . Definition 2. Given a policy π and a task r , \"policy improvement\" is the definition of a policy π such that Q π r (s, a) ≥ Q π r (s, a) for all (s, a) ∈ S × A. [2] We call one application of policy evaluation followed by one application of policy improvement a \"policy update.\" Given an arbitrary initial policy π, successive policy updates give rise to a sequence of improving policies that will eventually reach an optimal policy π * r  (18) . Even when policy evaluation and policy improvement are not performed exactly, it is possible to derive guarantees on the performance of the resulting policy based on the approximation errors introduced in these steps  (20, 21) . Fig.  1  illustrates the basic intuition behind policy updates. What makes policy evaluation tractable is a recursive relation between state-action values known as the Bellman equation: Q π r (s, a) = E S ∼p(•|s,a) r (s, a, S ) + γQ π r (S , π(S )) . [3] Expression (Exp.) 3 induces a system of linear equations whose solution is Q π r . This immediately suggests ways of performing policy evaluation when the MDP is known  (18) . Importantly, the Bellman equation also facilitates the computation of Q π r without knowledge of the dynamics of the MDP. In this case, one estimates the expectation on the right-hand side of Exp. 3 based on samples from p(•|s, a), leading to the well-known method of temporal differences  (22, 23) . It is also often the case that in problems of interest the state space S is too big to allow for a tabular representation of the value function, and hence Q π r is replaced by an approximation Qπ r . As for policy improvement, it is in fact simple to define a policy π that performs at least as well as, and generally better than, a given policy π. Once the value function of π on task r is known, one can compute an improved policy π as π (s) ∈ arg max a∈A Q π r (s, a). [4] In words, the action selected by policy π on state s is the one that maximizes the action-value function of policy π on that state. The fact that policy π satisfies Definition 2 is one of the fundamental results in dynamic programming and the driving force behind many algorithms used in practice  (18) . The specific way policy updates are carried out gives rise to different dynamic programming algorithms. For example, value iteration and policy iteration can be seen as the extremes of a spectrum of algorithms defined by the extent of the policy evaluation step  (19, 24) . RL algorithms based on dynamic programming can be understood as stochastic approximations of these methods or other instantiations of policy updates  (25) . \n Generalized Policy Updates From the discussion above, one can see that an important branch of the field of RL depends fundamentally on the notions of policy evaluation and policy improvement. We now discuss generalizations of these operations. Definition 3. \"Generalized policy evaluation\" (GPE) is the computation of the value function of a policy π on a set of tasks R. \n A B Fig.  1 . (A) Sequence of policy updates as a trajectory that alternates between the policy and value spaces and eventually converges to an optimal solution (1). (B) Detailed view of the trajectory across the value space for a state space with two states only. The shadowed rectangles associated with each value function represent the region of the value space containing the value function that will result from one application of policy improvement followed by policy evaluation (cf. Exp. 2). Definition 4. Given a set of policies Π and a task r , \"generalized policy improvement\" (GPI) is the definition of a policy π such that Q π r (s, a) ≥ sup π∈Π Q π r (s, a) for all (s, a) ∈ S × A. [5] GPE and GPI are strict generalizations of their standard counterparts, which are recovered when R has a single task and Π has a single policy. However, it is when R and Π are not singletons that GPE and GPI reach their full potential. In this case, they become a mechanism to quickly construct a solution for a task, as we now explain. Suppose we are interested in one of the tasks r ∈ R, and we have a set of policies Π available. The origin of these policies is not important: they may have come up as solutions for specific tasks or have been defined in any other arbitrary way. If the policies π ∈ Π are submitted to GPE, we have their value functions on the task r ∈ R. We can then apply GPI over these value functions to obtain a policy π that represents an improvement over all policies in Π. Clearly, this reasoning applies without modification to any task in R. Therefore, by applying GPE and GPI to a set of policies Π and a set of tasks R, one can compute a policy for any task in R that will in general outperform every policy in Π. Fig.  2  shows a graphical depiction of GPE and GPI. Obviously, in order for GPE and GPI to be useful in practice, we must have efficient ways of performing these operations. Consider GPE, for example. If we were to individually evaluate the policies π ∈ Π over the set of tasks r ∈ R, it is unlikely that the scheme above would result in any gains in terms of computation or consumption of data. To see why this is so, suppose again that we are interested in a particular task r . Computing the value functions of policies π ∈ Π on task r would require |Π| policy evaluations with a naive form of GPE (here, | • | denotes the cardinality of a set). Although the resulting GPI policy π would compare favorably to all policies in Π, this guarantee would be vacuous if these policies are not competent at task r . Therefore, a better allocation of resources might be to use the policy evaluations for standard policy updates, which would generate a sequence of |Π| policies with increasing performance on task r (compare Figs.  1 and 2 ). This difficulty in using generalized pol-Fig.  2 . Depiction of generalized policy updates on a state space with two states only. With GPE each policy π ∈ Π is evaluated on all tasks r ∈ R. The state-value function of policy π on task r, V π r , delimits a region in the value space where the next value function resulting from policy improvement will be (cf. Fig.  1 ). The analogous space induced by GPI corresponds to the intersection of the regions associated with the individual value functions (represented as dark gray rectangles in the figure). The smaller the space of value functions associated with GPI, the stronger the guarantees regarding the performance of the resulting policy. icy updates in practice is further aggravated if we do not have a fast way to carry out GPI. Next, we discuss efficient instantiations of GPE and GPI. Fast GPE with Successor Features. Conceptually, we can think of GPE as a function associated with a policy π that takes a task r as input and outputs a value function Q π r  (26) . Hence, a practical way of implementing GPE would be to define a suitable representation for tasks and then learn a mapping from r to value functions Q π r  (27) . This is feasible when such a mapping can be reasonably approximated by the choice of function approximator and enough examples (r , Q π r ) are available to characterize the relation underlying these pairs. Here, we will focus on a form of GPE that is based on a similar premise but leads to a form of generalization over tasks that is correct by definition. Let φ : S × A × S → R d be an arbitrary function whose output we will see as \"features.\" Then, for any w ∈ R d , we have a task defined as rw(s, a, s ) = φ(s, a, s ) w,  [6]  where denotes the transpose of a vector. Let R φ ≡ {rw = φ w | w ∈ R d } be the set of tasks induced by all possible instantiations of w ∈ R d . We now show how to carry out an efficient form of GPE over R φ . Following Barreto et al.  (28) , we define the \"successor features\" (SFs) of policy π as ψ π (s, a) ≡ E π ∞ i=0 γ i φ(St+i , At+i , St+i+1) | St = s, At = a . The ith component of ψ π (s, a) gives the expected discounted sum of φi when following policy π starting from (s, a). Thus, ψ π can be seen as a d -dimensional value function in which the features φi (s, a, s ) play the role of reward functions (cf. Exp. 1). As a consequence, SFs satisfy a Bellman equation analogous to Exp. 3, which means that they can be computed using standard RL methods like temporal differences  (22) . Given the SFs of a policy π, ψ π , we can quickly evaluate π on task rw ∈ R φ by computing ψ π (s, a) w = E π ∞ i=0 γ i φ(St+i , At+i , St+i+1) w|St = s, At = a = E π ∞ i=0 γ i rw(St+i , At+i , St+i+1) | St = s, At = a = Q π rw (s, a) ≡ Q π w (s, a). [7] That is, the computation of the value function of policy π on task rw is reduced to the inner product ψ π (s, a) w. Since this is true for any task rw, SFs provide a mechanism to implement a very efficient form of GPE over the set R φ (cf. Definition 3). The question then arises as to how inclusive the set R φ is. Since R φ is fully determined by φ, the answer to this question lies in the definition of these features. Mathematically speaking, R φ is the linear space spanned by the d features φi . This view suggests ways of defining φ that result in a R φ containing all possible tasks. A simple example can be given for when both the state space S and the action space A are finite. In this case, we can recover any possible reward function by making d = |S | 2 × |A| and having each φi be an indicator function associated with the occurrence of a specific transition (s, a, s ). This is essentially Dayan's (29) concept of \"successor representation\" extended from S to S × A × S. The notion of covering the space of tasks can be generalized to continuous S and A if we think of φi as basis functions over the function space S × A × S → R, for we know that, under some technical conditions, one can approximate any function in this space with arbitrary accuracy by having an appropriate basis. Although these limiting cases are reassuring, more generally we want to have a number of features d |S |. This is possible if we consider that we are only interested in a subset of all possible tasks-which should in fact be a reasonable assumption in most realistic scenarios. In this case, the features φ should capture the underlying structure of the set of tasks R in which we are interested. For example, many tasks we care about could be recovered by features φ i representing entities (from concrete objects to abstract concepts) or salient events (such as the interaction between entities). In Fast RL with GPE and GPI, we give concrete examples of what the features φ may look like and also discuss possible ways of computing them directly from data. For now, it is worth mentioning that, even when φ does not span the space R, one can bound the error between the two sides of Exp. 7 based on how well the tasks of interest can be approximated using φ (proposition 1 in ref.  30 ). Fast GPI with Value-Based Action Selection. Thanks to the concept of value function, standard policy improvement can be carried out efficiently through Exp. 4. This raises the question whether the same is possible with GPI. We now answer this question in the affirmative for the case in which GPI is applied over a finite set Π. Following Barreto et al.  (28) , we propose to compute an improved policy π as π (s) ∈ argmax a∈A max π∈Π Q π r (s, a). [8] Barreto et al. have shown that Exp. 8 qualifies as a legitimate form of GPI as per Definition 4 (theorem 1 in ref.  28 ). Note that the action selected by a GPI policy π on a state s may not coincide with any of the actions selected by the policies π ∈ Π on that state. This highlights an important difference between Exp. 8 and methods that define a higher-level policy that alternates between the policies π ∈ Π (32). In SI Appendix, we show that the policy π resulting from Exp. 8 will in general outperform its analog defined over Π. As discussed, GPI reduces to standard policy improvement when Π contains a single policy. this also happens with Exp. 8 when one of the policies in Π strictly outperforms the others on task r . This means that, after one application of GPI, adding the resulting policy π to the set Π will reduce the next application of Exp. 8 to Exp. 4. Therefore, if GPI is used in a sequence of policy updates, it will collapse back to its standard counterpart after the first update. In contrast with policy improvement, which is inherently iterative, GPI is an one-off operation that yields a quick solution for a task when multiple policies have been evaluated on it. The guarantees regarding the performance of the GPI policy π can be extended to the scenario where Exp. 8 is used with approximate value functions. In this case, the lower bound in Exp. 5 decreases in proportion to the maximum approximation error in the value function approximations (theorem 1 in ref.  28) . We refer the reader to SI Appendix for an extended discussion on GPI. The Generalized Policy. Strictly speaking, in order to leverage the instantiations of GPE and GPI discussed in this article, we only need two elements: features φ : S × A × S → R d and a set of policies Π = {πi } n i=1 . Together, these components yield a set of SFs Ψ = {ψ π i } n i=1 , which provide a quick form of GPE over the set of tasks R φ induced by the features φ. Specifically, for any w ∈ R d , we can quickly evaluate policy πi on task rw(s, a, s ) = φ(s, a, s ) w by computing Q π i w (s, a) = ψ π i (s, a) w. Once we have the value functions of policies πi on task rw, {Q π i w } n i=1 , Exp. 8 can be used to obtain a GPI policy π that will in general outperform the policies πi on rw. Observe that the same scheme can be used if we have approximate SFs ψπ i ≈ ψ π i , which will be the case in most realistic scenarios. Since the resulting value functions will also be approximations, Qπ i w ≈ Q π i w , we are back to the approximate version of GPI discussed in Fast GPI with Value-Based Action Selection. Given a set of SFs Ψ, approximate or otherwise, any w ∈ R d gives rise to a policy through GPE (Exp. 7) and GPI (Exp. 8). We can thus think of generalized updates as implementing a policy πΨ(s; w) whose behavior is modulated by w. We will call πΨ a \"generalized policy.\" Fig.  3  provides a schematic view of the computation of πΨ through GPE and GPI. Since each component of w weighs one of the features φi (s, a, s ), changing them can intuitively be seen as setting the agent's current \"preferences.\" For example, the vector w = [0, 1, −2] indicates that the agent is indifferent to feature φ1 and wants to seek feature φ2 while avoiding feature φ3 with twice the impetus. Specific instantiations of πΨ can behave in ways that are very different from its constituent policies π ∈ Π. We can draw a parallel with nature if we think of features as concepts like water or food and note how much the desire for these items can affect an animal's behavior. Analogies aside, this sort Fig.  3 . representation of how the generalized policy πΨ is implemented through GPE and GPI. Given a state s ∈ S, the first step is to compute, for each a ∈ A, the values of the n SFs: {ψ π i (s, a)} n i=1 . Note that ψ π i can be arbitrary nonlinear functions of their inputs, possibly represented by complex approximators like deep neural networks  (30, 31) . The SFs can be laid out as an n × |A| × d tensor in which the entry (i, a, j) is ψ π i j (s, a). Given this layout, GPE reduces to the multiplication of the SF tensor with a vector w ∈ R d , the result of which is an n × |A| matrix whose (i, a) entry is Q π i (s, a). GPI then consists in finding the maximum element of this matrix and returning the associated action a. This whole process can be seen as the implementation of a policy πΨ(s; w) whose behavior is parameterized by a vector of preferences w. of arithmetic over features provides a rich interface for the agent to interact with the environment at a higher level of abstraction in which decisions correspond to preferences encoded as a vector w. Next, we discuss how this can be leveraged to speed up the solution of an RL task. \n Fast RL with GPE and GPI We now describe how to build and use the adaptable policy πΨ implemented by GPE and GPI. To make the discussion more concrete, we consider a simple RL environment depicted in Fig.  4 . The environment consists of a 10 × 10 grid with four actions available: A = {up, down, left, right}. The agent occupies one of the grid cells, and there are also 10 objects spread across the grid. Each object belongs to one of two types. At each time step t, the agent receives an image showing its position and the position and type of each object. Based on this information, the agent selects an action a ∈ A, which moves it one cell along the desired direction. The agent can pick up an object by moving to the cell occupied by it; in this case, it gets a reward defined by the type of the object. A new object then pops up in the grid, with both its type and location sampled uniformly at random (more details are in SI Appendix). This simple environment can be seen as a prototypical member of the class of problems in which GPE and GPI could be useful. This becomes clear if we think of objects as instances of (potentially abstract) concepts, here symbolized by their types, and note that the navigation dynamics are a proxy for any sort of dynamics that mediate the interaction of the agent with the world. In addition, despite its small size, the number of possible configurations of the grid is actually quite large, of the order of 10 15 . This precludes an exact representation of value functions and illustrates the need for approximations that inevitably arises in many realistic scenarios. By changing the rewards associated with each object type, one can create different tasks. We will consider that the agent wants to build a set of SFs Ψ that give rise to a generalized policy πΨ(s; w) that can adapt to different tasks through the vector of preferences w. This can be either because the agent does not know in advance the task it will face or because it will face more than one task. Defining a Basis for Behavior. In order to build the SFs Ψ, the agent must define two things: features φ and a set of policies Π. Since φ should be associated with rewarding events, we define each feature φi as an indicator function signaling whether an object of type i has been picked up by the agent (i.e., φ ∈ R 2 ). To be precise, we have that φi (s, a, s ) = 1 if the transition from state s to state s is associated with the agent picking up an object of type i, and φi (s, a, s ) = 0 otherwise. These features induce a set R φ where task rw ∈ R φ is characterized by how desirable or undesirable each type of object is. Now that we have defined φ, we turn to the question of how to determine an appropriate set of policies Π. We will restrict the policies in Π to be solutions to tasks rw ∈ R φ . We start with what is perhaps the simplest choice in this case: a set Π12 = {π1, π2} whose two elements are solutions to the tasks w1 = [1, 0] and w2 = [0, 1] (henceforth, we will drop the transpose superscript to avoid clutter). Note that the goal in tasks w1 and w2 is to pick up objects of one type while ignoring objects of the other type. We are now ready to compute the SFs Ψ induced by our choices of φ and Π. In our experiments, we used an algorithm analogous to Q-learning to compute approximate SFs ψπ 1 and ψπ 2 (pseudocode in SI Appendix). We represented the SFs using multilayer perceptrons with two hidden layers  (33) . The set of SFs Ψ yields a generalized policy π Ψ(s ; w) parameterized by w. We now evaluate π Ψ on the task whose goal is to pick up objects of the first type while avoiding objects of the second type. Using φ defined above, this task can be represented as rw 3 (s, a, s ) = φ(s, a, s ) w3, with w3 = [1, −1]. We thus evaluate the generalized policy instantiated as π Ψ(s ; w3). Results are shown in Fig.  5A . As a reference, we also show the learning curve of Q-learning (23) using the same architecture to directly approximate Q π w 3 . GPE and GPI allow one to compute an instantaneous solution for a new task, without any learning on the task itself, that is competitive with the policies found by Q-learning when using around 6 × 10 4 sample transitions. The performance of the policy π Ψ synthesized by GPE and GPI corresponds to more than 70% of the performance eventually achieved by Q-learning after processing 10 6 transitions. This is quite an impressive result when we note that π Ψ managed to avoid objects of the second type even though its constituents policies π1 and π2 were never trained to actively avoid objects. We used a total of 10 6 sample transitions to learn both SFs ψπ 1 and ψπ 2 , which is the same amount of data used by Qlearning to achieve its final performance. The advantage of doing the former is that, once we have the SFs, we can use GPE and GPI to instantaneously compute a solution for any task in R φ . However, how well do GPE and GPI actually perform on R φ ? To answer this question, we ran a second round of experiments to assess the generalization of π Ψ over the entire set R φ . Since this evaluation clearly depends on the set of policies used, we consider two other sets in addition to Π12 = {π1, π2}. The new sets are Π34 = {π3, π4} and Π5 = {π5}, where the policies πi are solutions to the tasks w3 = [1, −1], w4 = [−1, 1], and w5 =  [1, 1] . We repeated the previous experiment with each policy set and evaluated the resulting policies π Ψ over 19 tasks w evenly spread over the nonnegative quadrants of the unit circle (tasks in the negative quadrant are uninteresting because all of the agent must do is to avoid hitting objects). Results are shown in Fig.  6A . As expected, the generalization ability of GPE and GPI depends on the set of policies used. Perhaps more surprising is how well the generalized policy π Ψ induced by some of these sets perform across the entire space of tasks R φ , sometimes matching the best performance of Q-learning when solving each task individually. These experiments show that a proper choice of base policies Π can lead to good generalization over the entire set of tasks R φ . In general, though, it is unclear how to define an appropriate Π. Fortunately, we can refer to our theoretical understanding of GPE and GPI to have some guidance. First, we know from the discussion above that the larger the number of policies in Π the stronger the guarantees regarding the performance of the resulting policy π Ψ (Exp. 5). In addition to that, Barreto et al. have shown that it is possible to guarantee a minimum performance level for π Ψ on task w based on mini w − wi , where • is some norm and wi are the tasks associated with the policies πi ∈ Π used for GPE and GPI (theorem 2 in ref.  28 ). Together, these two insights suggest that, as we increase the size of Π, the performance of the resulting policy π Ψ should improve across R φ , especially on tasks that are close to the tasks wi . To test this hypothesis empirically, we repeated the previous experiment, but now, instead of comparing disjoint policy sets, we compared a sequence of sets formed by adding one by one the policies π2, π5, π1, and π3, in this order, to the initial set {π4}. The results, in Fig.  6B , confirm the trend implied by the theory. Task Inference. So far, we have assumed that the agent knows the vector w that describes the task of interest. Although this can be the case in some scenarios, ideally we would be able to apply GPE and GPI even when w is not provided. In this section and in Preferences as Actions, we describe two possible ways for the agent to learn w. Given a task r , we are looking for a w ∈ R d that leads to good performance of the generalized policy πΨ(s; w). We could in principle approach this problem as an optimization over w ∈ R d whose objective is to maximize the value of πΨ(s; w) across (a subset of) the state space. It turns out that we can exploit the structure underlying SFs to efficiently determine w without ever looking at the value of πΨ. Suppose we have a set of m sample transitions from a given task, {(si , ai , r i , s i )} m i=1 . Then, based on Exp. 6, we can infer w by solving the following minimization: min w m i=1 |φ(si , ai , s i ) w − r i | p , [9] where p ≥ 1 (one may also want to consider the inclusion of a regularization term, see ref.  33) . Observe that, once we have a solution w for the problem above, we can plug it in Exp. 7 and use GPE and GPI as we did before-that is, we have just turned an RL task into an easier linear regression problem. To illustrate the potential of this approach, we revisited the task w3 = [1, −1] tackled above, but now, instead of assuming we knew w3, we solved the problem in Exp. 9 using p = 2. We collected sample transitions using a policy π that picks actions \n A B Fig.  6 . Results on the space of tasks R φ induced by a two-dimensional φ. The sets of policies Π used in A are disjoint; in B these sets overlap. The evaluation of an algorithm on a task is represented as a vector whose direction indicates the task w and whose magnitude gives the average sum of rewards over 10 runs with 250 trials each. Q-learning learned each task individually, from scratch; the dotted curves correspond to its performance after having processed 5 × 10 4 , 1 × 10 5 , 2 × 10 5 , 5 × 10 5 , and 1 × 10 6 sample transitions. Our method only learned the policies in the sets Π and then generalized across all others tasks through GPE and GPI. The SFs used for GPE and GPI consumed 5 × 10 5 sample transitions to be trained each. uniformly at random and used the gradient descent method to refine an approximation w ≈ w online (SI Appendix). Results are shown in Fig.  5  A and B. The performance of the generalized policy π Ψ(s ; w3) using the correct w3 was recovered after around 800 sample transitions only. To put this number into perspective, recall that Q-learning needs around 60,000 transitions, or 75 times as much data, to achieve the same performance level. The number of transitions needed to learn w can be reduced further if we use the closed-form solution for the least-squares problem. The problem described in Exp. 9 can be solved even if the rewards are the only information available about a given task. Other interesting possibilities arise when the observations provided by the environment can be used to infer w, such as, for example, visual or auditory cues indicating the current task. In this case, it might be possible for the agent to determine w even before having observed a single nonzero reward  (30) . So far, we have used handcrafted features φ. It turns out that Exp. 9 can be generalized to also allow φ to be inferred from data. Given sample transitions from k tasks, {(sij , aij , r ij , s ij )} with p ≥ 1. Note that the features φ can be arbitrary nonlinear functions of their inputs. As discussed by Barreto et al.  (30) , if we make c = k we can solve a simplified version of the problem above in which wj do not show up. More generally, the problem in Exp. 10 can be solved as a multitask regression  (34) . In Fig.  5B , we show the performance of π Ψ(s ; w) when using learned features φ. These results were obtained as follows. First, we used the random policy π to collect data from tasks w1, w2, w4, and w5 and applied the stochastic gradient descent algorithm to solve Exp. 10 with p = 2. We then discarded the resulting approximations wi appearing in Exp. 10 and solved Exp. 9 exactly as before but now using φ instead of φ. As with SFs, in order to represent the features, we used multilayer perceptrons with two hidden layers (SI Appendix). The results in Fig.  5B  also show the effect of varying the dimension of the learned features on the performance of πΨ(s; w) (other illustrations are in refs.  28 and 30) . Preferences as Actions. In this section, we consider the scenario where, given features φ and a set of policies Π, there is no vector w that leads to acceptable performance of πΨ(s; w). To illustrate this situation, we use our environment with a slight twist: now, on picking up an object of a certain type, the agent gets a positive reward only if the number of objects of this type is greater or equal to the number of objects of the other type. Otherwise, the agent gets a negative reward. One can represent this problem using the previously defined features φ by switching between two instantiations of w:  [1, −1]  when the first type of object is more abundant and [−1, 1] otherwise. This means that the appropriate value for w is now state-dependent. To handle this situation, we introduce a function mapping states to preferences, ω : S → W, with W ⊆ R d , and redefine the generalized policy as πΨ(s; ω(s)). The RL problem then becomes to find a ω that correctly modulates πΨ  (32, 35) . We can look at the computation of πΨ(s; ω(s)) as a twostage process: first, the agent computes a vector of preferences w = ω(s); then, using GPE and GPI, it determines the action to be executed in state s as a = πΨ(s; w). Under this view, ω(s) becomes an indirect way of selecting an action in s, which allows us to think of it as a policy defined in the space W. We have thus replaced the original problem of finding a policy π : S → A with the problem of finding a policy ω : S → W. To illustrate the benefits of applying this transformation to the problem, we will use the task described above in which the agent must pick up the type of object that is more abundant. We will tackle this problem by reusing the SFs Ψ induced by the two policies in Π12. Given Ψ, the problem comes down to finding a mapping ω : S → W that leads to good performance of π Ψ(s ; ω(s)). We define W = {−1, 0, 1} 2 and use Q-learning to learn ω. We compare the performance of π Ψ(s ; ω(s)) with two baselines: GPE and GPI using a fixed w, π Ψ(s ; w), and the standard version of Q-learning that learns a policy π(s) over primitive actions. The results, shown in Fig.  7 , illustrate how π Ψ(s ; ω(s)) can significantly outperform the baselines. It is easy to understand why this is the case when we compare π Ψ(s ; ω(s)) with π Ψ(s ; w), for the experiment was designed to render the latter unsuitable. However, why is it that replacing the fourdimensional space A with the nine-dimensional space W leads to better performance? The reason is that ω(s) can be easier to than π(s). As discussed, the vectors w represent the agent's current preferences for types of objects. Since, in general, such preferences should only change when an object is picked up, after selecting a specific w, the agent can hold on to it until it bumps into an object. That is, it is possible to define a good policy ω that maps multiple consecutive states s to the same w. In contrast, it will normally not be possible to execute a single primitive action a ∈ A between the collection of two consecutive objects. This means that the same policy can have a simpler representation as a mapping S → W than as a mapping S → A, making ω easier to learn with certain types of function approximators like neural networks  (33) . Note that other choices of φ may induce other forms of regularities in ω-smoothness being an obvious example. Interestingly, the fact that the agent may be able to adhere to the same w for many time steps allows for a temporally extended policy πΨ(s; ω(s)) that is only permitted to change preferences at certain points in time, reducing even further the amount of data needed to learn the task  (31) . As a final remark, we note that the ability to chain a sequence of preference vectors w changes the nature of the problem of computing an appropriate set of features φ. When the agent has to adhere to a single w, the features φi must span the space of rewards defining the tasks of interest. When the agent is allowed Fig.  7 . Average sum of rewards on the task whose goal is to pick up objects of the type that is more abundant. GPE and GPI used Π 12 as the base policies and the corresponding SFs consumed 5 × 10 5 transitions to be trained each. The results reflect the best performance of each algorithm over multiple parameter configurations (SI Appendix). Shadowed regions are one standard error over 100 runs. to learn a policy ω over preferences w, this linearity assumption is no longer necessary. Similarly, the use of a fixed w requires that the set of available SFs leads to a competent policy for all tasks w we may care about. Here, this requirement is alleviated, since, by changing w, the agent may be able to compensate for eventual imperfections on the induced GPI policies  (31) . Lifelong Learning. We have looked at the different subproblems involved in the use of GPE and GPI. For didactic purposes, we have discussed these problems in isolation, but it is instructive to consider how they can jointly emerge in a real application. One scenario where the problems above would naturally arise is \"lifelong learning,\" in which the interaction of the agent with the environment unfolds over a long period  (36) . Since we expect some patterns to repeat during such an interaction, it is natural to break it in tasks that share some common structure. In terms of the concepts discussed in this article, this common structure would be φ, which can be handcrafted based on prior knowledge about the problem or learned through Exp. 10 at the beginning of the agent's lifetime. Based on the features φ, the agent can compute and store the SFs ψπ associated with the solutions π of the tasks encountered along the way. When facing a new task r , the agent can use the vector of preferences w to quickly adapt the generalized policy π Ψ. We have discussed two ways to do so. In the first one, the agent computes an approximation w through Exp. 9, which immediately yields a solution π Ψ(s ; w). The second possibility is to learn a mapping ω(s) : S → W and use it to have a per-state modulation of the generalized policy, π Ψ(s ; ω(s)). Regardless of how the agent computes w, it can then choose to hold on to π Ψ or use it as a initial solution for the task to be refined by a standard RL algorithm. Either way, the agent can also compute the SFs of the resulting policy, which can in turn be added to the library of SFs Ψ, improving even further its ability to tackle future tasks  (28, 30) . \n Conclusion We have generalized two fundamental operations in RL, policy improvement and policy evaluation, from single to multiple operands (tasks and policies, respectively). The resulting operations, GPE and GPI, can be used to speed up the solution of an RL problem. We showed possible ways to efficiently implement GPE and GPI and discussed how their combination leads to a generalized policy πΨ(s; w) whose behavior is modulated by a vector of preferences w. Two ways of learning w were considered. In the simplest case, w is the solution of a linear regression problem. This reduces an RL task to a much simpler problem that can be solved using only a fraction of the data. This strategy depends on two conditions: 1) the reward function of the tasks of interest are approximately linear in the features φ used for GPE and 2) the set of policies Π used for GPI lead to good performance of πΨ on the tasks of interest. When these assumptions do not hold, one can still resort to GPE and GPI by looking at the preferences w as actions. This strategy can also improve sample efficiency if the mapping from states to preferences is simpler to learn than the corresponding policy. Many extensions of the basic framework presented in this article are possible. As mentioned, Barreto et al.  (31)  have proposed a way of implementing a generalized policy πΨ that explicitly leverages temporal abstraction by treating preferences w as abstract actions that persist for multiple time steps. Borsa et al.  (37)  introduced a generalized form of SFs that has a representation z ∈ Z of a policy πz as one of its inputs: ψ(s, a, z) = ψ πz (s, a). In principle, this allows one to apply GPI over arbitrary, potentially infinite, sets Π (for example, by replacing the maximization in Exp. 8 with sup z∈Z ψ(s, a, z) w).  Hunt et al. (38)  extended SFs to entropy-regularized RL, and, in doing so, they proposed solutions for many challenges that come up when applying GPE and GPI in continuous action spaces. More recently, Hansen et al.  (39)  proposed an approach that allows the features φ to be learned from data in the absence of a reward signal. Other extensions are possible, including different instantiations of GPE and GPI. All of these extensions expand the framework built upon GPE and GPI. Together, they provide a conceptual toolbox that allows one to decompose an RL problem into tasks whose solutions inform each other. This results in a divide-and-conquer approach to RL, which, combined with deep learning, has the potential to scale up our agents to problems currently out of reach. Data Availability. The source code used to generate all of the data associated with this article has been deposited in GitHub (https://github.com/deepmind/deepmind-research/tree/ master/option keyboard/gpe gpi experiments). Fig. 4 . 4 Fig. 4. Depiction of the environment used in the experiments. The shape of the objects (square or triangle) represents their type; the agent is depicted as a circle. We also show the first 10 steps taken by 3 policies, π 1 , π 2 , and π 3 , that would perform optimally on tasks w 1 = [1, 0], w 2 = [0, 1], and w 3 = [1, −1] for any discount factor γ ≥ 0.5. \n Fig. 5 . 5 Fig. 5. Average sum of rewards on task w 3 = [1, −1]. GPE and GPI used Π 12 = {π 1 , π 2 } as the base policies and the corresponding SFs consumed 5 × 10 5 sample transitions to be trained each. B is a zoomed-in version of A showing the early performance of GPE and GPI under different setups. The results reflect the best performance of each algorithm over multiple parameter configurations (SI Appendix). Shadowed regions are one standard error over 100 runs. \n j = 1, 2, . . . , k , we can formulate the problem as the search for a function φ :S × A × S → R c and k vectors wi ∈ R c satisfying min sij , aij , s ij ) wj − r ij | p , [10] \n\t\t\t | www.pnas.org/cgi/doi/10.1073/pnas.1907370117 Barreto et al. Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t Barreto et al. PNAS | December 1, 2020 | vol. 117 | no. 48 | 30081 Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t | www.pnas.org/cgi/doi/10.1073/pnas.1907370117 Barreto et al. Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t PNAS | December 1, 2020 | vol. 117 | no. 48 | 30083 Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t | www.pnas.org/cgi/doi/10.1073/pnas.1907370117 Barreto et al. Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t PNAS | December 1, 2020 | vol. 117 | no. 48 | 30085 Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t | www.pnas.org/cgi/doi/10.1073/pnas.1907370117 Barreto et al. Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254. \n\t\t\t PNAS | December 1, 2020 | vol. 117 | no. 48 | 30087 Downloaded from https://www.pnas.org by 205.240.4.254 on March 23, 2022 from IP address 205.240.4.254.", "date_published": "n/a", "url": "n/a", "filename": "pnas.1907370117.tei.xml", "abstract": "were supported by a generous gift from The Dame Jillian and Dr. Arthur M. Sackler Foundation for the Arts, Sciences, & Humanities, in memory of Dame Sackler's husband, Arthur M. Sackler. The complete program and video recordings of most presentations are available on the NAS website at http://www.nasonline.org/science-of-deeplearning.y", "id": "80348a5c7e70f9881abe02f8eb01fd55"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Shahar Avin", "Ross Gruetzemacher", "Raymond J Harbert", "James Fox"], "title": "Exploring AI Futures Through Role Play", "text": "Introduction Artificial intelligence (AI) has an enormous potential to have a radical effect on our future, and we all have a vested interest in trying to ensure that AI is beneficial for humanity. However, there is currently no consensus in the AI research community on what the long-term impacts of AI, potentially including general artificial intelligence, will be, or the length of time over which such changes will take place. Moreover, there are many nearand mid-term concerns that have the potential for transformative societal change  [5, 14] . The vast uncertainty around AI futures, especially ones that involve transformative societal changes, has precipitated the creation of an AI strategy research community that seeks to ensure the development of AI for the social good  [8] . In collaboration with researchers in this community, we have developed an AI futures role-play game, which we present here, to complement the research being done and to disseminate key questions and findings to individuals and organizations engaged with, or seeking to engage with, AI strategy and policy. A role-play game involves a collection of people assuming roles to enact a situation in a realistic manner so as to predict a possible future if certain strategies are employed. Role-plays have a track record of high forecasting, strategic and educational utility in a wide variety of fields, including business  [15, 21] , medicine  [18] , politics  [16]  and education  [6, 21] . In the domain of AI strategy, we believe that role-plays can illuminate plausible futures, identify critical decision points, educate, raise awareness, highlight gaps in research knowledge and promote shared visions for beneficial AI. In this paper we first review the wargaming literature to show where role-plays have been successfully used in other domains, before next looking at why role-plays offer particular benefits within the AI strategy space. We then describe the current structure of the game (still under active development), and we highlight some of the lessons learned from the 30 game events to date. We conclude with a discussion of the benefits and shortcomings of this AI role-play game, our plans for further development and dissemination, and a call for others to try roleplay as a methodology for exploring AI futures. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author. AIES  '20, February 7-8, 2020 , New York, NY, USA © 2020 Copyright is held by the owner/author(s). ACM ISBN 978-1-4503-7110-0/20/02. https://doi.org/10.1145/3375627.3375817 2 Literature Review \"Serious\" role-plays are most well known in their military form, wargames, where they have been used, since their Prussian development in the late 18th century, to teach military strategy in a safe but dynamic manner. Wilkinson  [24]  championed the introduction of wargames into the British army in the late 1800's and claimed that \"probably no form of military study is more useful if properly conducted\". Original wargames had two militaries (teams of players) fighting over some well-defined territory (the board). More recently, emerging technologies and distributed warfare necessitated wargames to shift focus from territory and troop movement to also include the diplomacy of international relations  [22, 23] , nuclear conflict escalation  [20]  and cyber operations  [1] . The potential of role-plays to provide exploration and training in uncertain and high stakes situations has been recognized in other fields. In business role-plays, for example, the conflict arises between a company and its competitors vying for market share and profit. Hamel and Prahalad  [15]  explain the popularity of role-plays in business as due to their ability to develop foresight, an essential skill for competitive survival: \"an organization which does not develop a picture of the future, which does not develop foresight, is most likely not involved in the future.\" In education  [6, 21] , medicine  [18]  and politics  [16] , role-plays are used for formulating strategy, developing foresight, crisis response preparation, and for training and recruitment exercises. Nevertheless, despite their proven utility in a variety of different fields, role-plays have so far not been used in AI futures studies  [3] . \n When are role plays suitable? Parson  [19]  claims that role-plays are most appropriate for situations involving high enough stakes to merit substantial investment in knowledge about decision-making, but whose complexity imposes limits on the usefulness of standard decision-making procedures. Parson  [19]  gives three suitability conditions for role-plays: 1. Key outcomes depend on the interacting decisions of multiple agents. 2. Decision choice sets are ambiguous or poorly known. 3. Large numbers of complex organizations may be required to work together. The existence of multiple interacting complex agents compounded with a huge set of possible decisions creates an enormous potential scenario space. It is too difficult for one expert alone to think beyond linear views of reality, but roleplays allow non-linear effects to be explored. For instance, one can look for convergent outcomes arising from different strategies or identify the decisions pivotal in shaping the scenario's end state. Armstrong  [2]  compares and contrasts different forecasting techniques and adds that a role-play needs: 4. Large changes expected. 5. Conflict between the decision makers. If only small changes are expected, forecasters can extrapolate from current or historical examples. However, large technological step-changes -such as the discovery of electricity or the invention of the world wide web -entirely transform history's trajectory and are much harder to predict. This observation has been captured in Roy Amara's law  [17] : \"we tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run.\" Finally, conflict generates oppositional friction which catalyzes the generation of creative ideas. Without the competitive nature of an adversarial interaction, it is hard to generate the surprising edge-case scenarios which are exactly the ones hoped to be reached by role-plays. \n Do They Work? There is empirical evidence substantiating role-playing's greater forecasting accuracy over unaided judgements in certain situations. Green, Graefe and Armstrong  [11]  showed that both experts and novices were terrible at forecasting conflict decisions if they were simply asked to \"put yourself in the other person's shoes\". This is because, regardless of expertise, it is too difficult to individually think through the interactions of competing characters with divergent goals in complex situations. However, if the subjects adopted the roles of the protagonists in the conflicts and interacted with each other, their group decisions predicted the actual decisions with much greater accuracy -the greater realism afforded by role-playing enabled superior forecasts to be made. Role-plays can also mitigate against myopia by helping overcome various different psychological biases. Cyert, March and Starbuck  [7]  found that subjects presented with the same data produced significantly different forecasts depending on which role they were told to act out and Babcock et al.  [4]  evidenced the tendency of role-players to make biased judgements and interpret the briefing material differently according to the role they were assigned. This explains why roleplaying benefits from larger groups and greater diversity. Duke and Geurts  [10]  found that role-playing activities in a political setting can mitigate the danger of 'groupthink', where only readily politically feasible or easy-to-implement strategies are discussed. It is not guaranteed that every role-play will provide novel insights and any insights that do arise might not be relevant or applicable. However, even end-game states that have ostensibly departed significantly from common sense are worth exploring. DeWeerd  [9]  found that when predicting the future, readers tended to reject all predictions which didn't match their own and yet were willing to accept at the hand of history what they would instantly reject if predicted in advance by someone else (examples of \"unthinkable\" outcomes may include the result of the Brexit referendum, the election of Donald Trump, or the attack on Pearl Harbor). Edge-case scenarios are a key virtue of role-plays since they throw up black-swan eventsunprecedented and low probability, but high impact events which are invisible to canonical forecasting techniques. \n Methods The first task when planning a game is to identify the objective (i.e. training, educational, exploring futures or a mix of these). The project to date has explored two different methodological approaches to the game, with slightly different objectives: unstructured and semi-structured games. In both cases, the aim of the game was to allow players to experience from a firstperson perspective significant changes that could be brought by the development and deployment of AI technologies, and to have players face strategically challenging decisions from a position of power, be it governmental, corporate, military, societal or other. \n Unstructured role-play For the first two years of the project, we explored various forms of unstructured role-play. Players were drawn from a variety of different backgrounds with varying AI and geopolitical expertise. The players choose their own roles and took unconstrained actions, limited only by the time available and their own creativity. Resolution of actions thus depended heavily on the \"world model\" of the game's facilitator, which we aimed to address through regular engagement with the AI research literature and the AI strategy research field. The overall aim of these role-plays was to trial out the methodology, and to give players a space in which to explore strategic questions that they found interesting. Whenever it was possible, early discussions with the players or a coordinator helped to determine the initial frame for the scenario and roles adopted by the players. If this was not possible, these would be chosen by the facilitator or in collaboration with the players at the beginning of the game. We experimented with different ways to brief the players, including the facilitator meeting with each player ahead of the session (for 15-30 minutes each) to discuss the strategic questions they are interested in and to flesh out the role for that player. In an alternative approach, the facilitator would tell players the available roles and provide the general framing of the game, before asking the players to do their own background reading on those roles. Which organizations and roles will matter for the future of AI is an open research question: as time goes by, the number of identified stakeholders only increases, from governments to corporations, militaries to NGOs, artists, environmentalists, criminals and citizens, AI will shape, and be shaped by, a vast number of stakeholders. Nonetheless, the power distribution amongst these actors is not equal, and in varying the organizations and roles in the unstructured role-play we were able to explore different narratives that emerge when different groups and types of power are at play. Over 30 games we trialed many different roles. These broadly clustered around: During the game, the participants would \"assume\" their chosen/assigned role and take actions according to their model of that actor. Participants are instructed to deliberately try to bring about a world that is in line with the goals of the role they are playing, but they should be mindful of real-world constraints. This is because the more closely the simulation captures essential behavioral features of the real system, the more likely insights are to be relevant. On the other hand, a key strength of role-plays is in exploring edge-case scenarios. Thus, as a general rule of thumb, actions should be realistic but not overly conservative. For example, one in ten actions should be an action that the participant assigns 10% likelihood of being taken. Participants are encouraged to \"flesh out\" the world model by adding details that complement the details provided by the facilitator.  Government organizations During previous games, participants tried out a wide range of actions, including: Games typically involve 4-8 turns, with each turn representing one or two years, thus covering a period of 4-16 years, with the starting point set in the foreseeable future (as near as 2020 or as far as 2028). The game proceeds by alternating between negotiation phases, private action phases, public actions phases, and \"world updates\" from the facilitator. Outcomes of actions are determined by the facilitator, sometimes assisted by a random number generator, and relayed either to teams directly or in the \"world updates\" at the beginning of the next turn. Figure  1  depicts the final state of the world for a recent game held in Cambridge. Immediately at the end of the scenario role-play there is a debrief where any hidden state of the world is revealed, and participants evaluate how well their assigned role performed relative to their goal. Participants are asked to reflect on the final state of the world, on actions or developments that they found surprising, and to record any disagreements with how actions were chosen or resolved. This phase of gleaning participants' insights is crucial for challenging the facilitator's own subjective biases or knowledge gaps whilst bolstering the participants' internalization of what they have learned.  \n Semi-structured role-play Based on our experience with unstructured role-play, we started developing a semi-structured game that involves a predefined game system for AI R&D, and a pre-defined set of organizations and characters, to create an experience that explores several questions we have found to be particularly pertinent, including: To explore these questions, we designed an eight-player game with the following roles: We also created organization sheets and character sheets with key information to familiarize players with their roles. As in the unstructured game, players were asked to spend each turn negotiating with each other before deciding upon a set of private and public actions. However, we made AI R&D actions structured around a technology tree (Figure  2 ) and a set of products and capabilities (Figure  3 ).   \n State of the World: The unemployment rate is now 17.1%. However, people are content for the most part because of social services such as Universal Basic Income. Multiple sources have confirmed to the New York Times that AGI has been developed. Sources range in assessing the system's safety, from 25% to 75% confidence. China is preparing to establish a small city on Mars. The first 10,000 citizens will arrive during 2035. \n Paper Presentation AIES '20, February 7-8, 2020, New York, NY, USA Each turn, the different organizations have a limited amount of AI \"talent\" they can allocate towards pursuing technological advancement (research) or products and capabilities (development). This can be pursued in public or in private. R&D success is determined by dice rolls, with one dice per \"talent\" allocated to a project. The players' action can affect the distribution of \"talent\" in the \"world\". This resource management mechanic was added to explore conditions of competition and scarcity in the input to AI R&D. This is one such factor that generates an adversarial tension which drives players to seek more creative solutions. Another mechanic we added to the game was \"world chaos\", a catch-all parameter for global instability, whereby we capture various negative externalities of AI, including the potential of AI \"hype\" to distract states from addressing issues such as inequality or climate change. \n Preliminary Results The unstructured game format has allowed the exploration of many different scenarios, but consequently it is difficult to identify patterns in the scenarios played. Overall, participant satisfaction appears high, with most players indicating their interest in playing again, and many interested in reading more about different organizations, roles, actions or strategic analyses. The following range of topics have come up in at least one of the scenarios that emerged from unstructured role-play (this list is not exhaustive): It would often be the case that five or more of the above topics would be touched upon in a single game.  The semi-structured game is more constrained, and therefore provides a better opportunity to detect patterns of gameplay and decision-making. While the number of games played with the new system to date is small, and the game system is still under active development, a few patterns are beginning to emerge. First, and perhaps not surprisingly, the familiarity of players with the roles assigned to them varies greatly -while many have at least some idea of what the President of the United States cares about or what they can do, that is not the case for tech CEOs or heads of AI labs; while a good facilitator can use the game to provide some basic information about the role and some of the decisions they face (as they relate to AI), the game is more useful for all participants when the players start the game with more background knowledge, both about AI and about the contexts in which decisions about AI are made. Second, the rapid growth of options that comes with the proliferation of available AI capabilities can be overwhelming to players, who respond to the large number of available R&D avenues by either choosing randomly, picking quickly a \"good enough\" target, or aiming for a specific long-term technology. While this is to some extent an artefact of the game mechanics, we think it may capture a real issue, especially if AI progress lends itself to faster AI R&D and if progress remains stochastic and uncertain. Third, cooperation between actors on AI safety and (some) restriction on destabilizing uses of AI seem to both be robustly beneficial, and often necessary, for all players to achieve a good outcome. Such agreements are easier to establish if players are biased towards pro-social strategies, or when cooperation begins early in the game and is maintained and expanded, or when players recognize a common threat (e.g. an unsafe or destabilizing technology nearing completion or after a major accident). Competitive behavior, including adversarial actions (espionage, sabotage, poaching, tariffs), can sometimes be excused when a common threat emerges and the need for cooperation becomes apparent. Fourth, in almost all games players will continue pursuing ever-more-advanced technologies and capabilities, with all the resources they can afford to spend on R&D, even if the potential value of these advances is unclear, and even when earlier advances have proven to be destabilizing or risky. Fifth, while the game has a built-in system for AI R&D, some players are happy to innovate \"around\" this system, proposing new products or establishing new organizations during the game. Finally, different sets of possible coalitions and alliances are explored and can prove stable, including between government and corporate entities within a state, between governments, between organizations, and between sub-roles within organizations (e.g. between heads of AI labs). \n Discussion and Conclusions The AI role-play game described here presents an innovative methodology for studying and teaching the impacts of AI. It can educate, raise awareness and help illuminate the positive and negative effects of certain developments, strategic decisions, and Paper Presentation AIES '20, February 7-8, 2020, New York, NY, USA inter-stakeholder interactions thereby potentially improving the outcomes of deploying current and future AI technologies. The versatility of the technique, including its ability to be adapted to different problems throughout organizations to address the near-, mid-and long-term impacts of AI, is well-suited to the large variety of challenges encountered in the development and deployment of AI technologies across all aspects of human life. Many of the other benefits of role-play games discussed in the literature review are also applicable. The games we have conducted to date, and especially the semi-structured games, focused on a set of questions and insights that we find particularly salient. These include the interaction between near-, mid-and long-term risks, challenges of cooperation and competition between powerful actors across states of public/private lines, trade-offs between public and private research and between research and product development, and the experience of making potentially transformative decisions from a first-person (powerful) perspective under conditions of uncertainty and time pressure. The feedback from players to date suggests that these aspects of the game indeed appear salient to players, and lead to greater engagement with these questions. Based on players' feedback, and from design constraints of the game itself, we also note several shortcomings and limitations we have not yet been able to address. For example, in our focus on strategic decision making, we have focused on roleplay from the perspective of powerful actors, rather than actors with marginalized standpoints, or more detached viewpoints that highlight systemic and emergent drivers; the literature suggests that role-plays and games can be adapted for these perspectives, and have been powerful in building empathy or systems thinking when done well, and this is a potential direction for expansion. Another limitation is the sped-up timeline, that imagines dramatic, and occasionally transformative, technological shifts within an almost-foreseeable political horizon. This reflects our limited ability to conduct a realistic role-play that takes place in the political reality of 2050 or 2100, but it does mean we adopt an assumption of fairly rapid technology progress, which is in no way certain -experts significantly disagree about timelines to transformative AI capabilities and impacts  [12, 13] . This design decision was made in part to play to the strength of role-plays, which shine in exploring large and uncertain effects, partly to create a more engaging and dramatic setting, and partly because if transformative impacts happen in a matter of decades, it becomes of paramount importance to prepare decision-makers to handle the decisions they will need to face. We also stress the communication of this bias in every game debrief, but we see how this sped-up timeline may be less appealing to some, and are exploring versions of the game that focus on less dramatic changes while exploring in greater nuance short-and mediumterm impacts of technologies that are already making real research progress. Moving forward, we will continue to develop the game to increase realism, reflect new strategic research questions as they emerge, and cover more scenarios of interest to a broader set of stakeholders. We aim to expand the context of the game, through different unstructured and semi-structured scenarios and mechanics, to cover an increasing range of actors, actions, technologies and impacts of AI. This necessitates staying in constant contact and mutual feedback with the developing fields of AI futures and AI strategy as the impacts of AI become more apparent in every corner of life. In addition, we hope to continue to develop the educational potential of the game into something that can be used to raise awareness and train a variety of audiences and publics, including younger members of the public, through the development of a digital platform and a digital version of the game. Readers interested in exploring the game are invited to register their interest,  1  and those who wish to join the development of the game are encouraged to contact the authors. By allowing stakeholders to explore alternative AI futures, prepare for surprises and uncertainty, and learn from \"simulated\" mistakes, we hope that the methodology we propose will help win the race between the capability of the technologies we develop and our wisdom in deploying and governing them. For these reasons we see the method's impact on the use of AI for social good as being far reaching and we invite members of the community to join us in exploring the future of AI through role-play. Figure 1 : 1 Figure 1: Final state of the world from a recent unstructured game. The game involved three players playing the roles of presidents for the USA, PRC and EU. Technological progress and impacts of players' actions were determined by the facilitator. \n  How do the geopolitical relations between the two leading AI powers, US and China, affect the kinds of technologies developed and the way they are deployed?  How do state-corporate relationships play out as AI technologies become more advanced and allow for a greater generation and consolidation of wealth?  How do states make decisions about the deployment of AI capabilities in strategic domains such as military and social control?  How do corporations balance the pursuit of risky basic research that could lead to transformative capabilities with nearer term, profit generating products and services?  How, and to what extent, are states willing to \"pick up the tab\" for negative externalities created by their corporate champions?  What factors contribute to a decision to make a research project private/secret, or conversely to publish results and share capabilities? How do actors respond when they suspect other actors of pursuing advanced research in secret?  How do decisions and impacts relating to near-term AI technologies affect the landscape in which decisions are made about mid-term AI technologies, and similarly how do those affect the setting for decisions about long-term AI? \n  PRC government: president and minister of national defense  US government: president and secretary of defense  Tencent: CEO and head of AI lab  Alphabet: CEO and head of AI lab \n Figure 2 : 2 Figure 2: AI Technology Tree used in the game. Each box represents a technology that can be pursued by the players, with associated products and capabilities. Technologies advance from left to right, with progress on earlier technologies required before later technologies are \"unlocked\". \n Figure 3 : 3 Figure 3: An example of AI products a player can develop in the game. The required technology and the effect on game parameters are listed at the bottom of the card. \n Non-governmental actors, including academia, independent research organizations, advocacy groups and think tanks.  Supra-national actors, e.g. the EU or the UN. and roles in different countries, including the executive, the military, diplomatic services, health, and government R&D functions.  Corporate actors in different geographies and sectors, including tech (based on business models we see around the world, e.g. advertising, e-commerce or tech infrastructure), robotics, weapons, health.  \n\t\t\t To register your interest in participation, please fill out the form at https://sites.google.com/view/intelligence-rising/home.", "date_published": "n/a", "url": "n/a", "filename": "3375627.3375817.tei.xml", "abstract": "We present an innovative methodology for studying and teaching the impacts of AI through a role-play game. The game serves two primary purposes: 1) training AI developers and AI policy professionals to reflect on and prepare for future social and ethical challenges related to AI and 2) exploring possible futures involving AI technology development, deployment, social impacts, and governance. While the game currently focuses on the inter-relations between short-, mid-and longterm impacts of AI, it has potential to be adapted for a broad range of scenarios, exploring in greater depths issues of AI policy research and affording training within organizations. The game presented here has undergone two years of development and has been tested through over 30 events involving between 3 and 70 participants. The game is under active development, but preliminary findings suggest that role-play is a promising methodology for both exploring AI futures and training individuals and organizations in thinking about, and reflecting on, the impacts of AI and strategic mistakes that can be avoided today.", "id": "639fb64ba637dc2f395e51aadd9d6005"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Lukas Gloor"], "title": "Suffering-focused AI safety: Why \"fail-safe\" measures might be our top intervention", "text": "Classical AI safety looks very difficult. In order to ensure a truly \"utopian\" outcome, the following things need to happen: 1. The AI that gains a decisive strategic advantage over the competition needs to be built by the right group of people. 2. These people would need to have figured out how to program favorable values into an AI (or program the AI to learn these values). 3. They would also need to have come up with a satisfying description of what these values are, either directly, or indirectly with the help of a suitable extrapolation procedure (e.g.  Muehlhauser & Helm, 2012) . 4. Finally, the creators of the first superintelligence might need to get decision theory right (see  Soares & Fallenstein, 2015)  and safeguard the AI from a lot of hardto-anticipate failure modes. Succeeding with all of this together is the only safe way of bringing about a flourishing utopia mostly free of suffering. (There might be other paths to utopia, provided enough luck.) But what about outcomes where something goes wrong? It is important to consider that things can go wrong to very different degrees. For value systems that place primary importance on the prevention of suffering, this aspect is crucial: the best way to avoid bad-case scenarios specifically may not be to try and get everything right. Instead, it makes sense to focus on the worst outcomes (in terms of the suffering they would contain) and on tractable methods to avert them. As others are trying to shoot for a best-case outcome (and hopefully they will succeed!), it is important that some people also take care of addressing the biggest risks. This perspective to AI safety is especially promising both because it is currently neglected and because it is easier to avoid a subset of outcomes rather than to shoot for one highly specific outcome. Finally, it is something that people with many different value systems could get behind. \n How AI outcomes might contain suffering From a suffering-focused perspective, the main reason to be concerned about the risks from artificial intelligence is not the possibility of human extinction or the corresponding failure to build a flourishing, intergalactic civilization. Rather, it is the thought of misaligned or \"illaligned\" AI as a powerful but morally indifferent optimization process which, in the pursuit of its goals, may transform galactic resources into (among other things) suffering. Either like the suffering we see on Earth today, or by bringing about optimized structures that possibly also contain novel forms of suffering. The things a superintelligent AI would build to pursue its goals might include a fleet of \"worker bots\", factories, supercomputers, space colonization machinery, etc. It is possible that all of these end up being built in a way that does not permit suffering. However, given that evolution has produced plenty of sentient minds, this weakly suggests that some of the easiest ways to implement mind architectures do come with the capacity for suffering. In the absence of an explicit antisuffering preference, even the slightest benefit to the AI's objectives would lead to the instantiation of suffering minds. What makes this especially worrying is that the stakes involved will be huge: Space colonization is an attractive subgoal for almost any powerful optimization process, as it leads to control over the largest amount of resources  (Omohundro, 2008) . Even if only a small portion of these resources were used for purposes that include suffering, the resulting disvalue would sadly be astronomical. To find the best interventions to prevent suffering, it is crucial to study how AI outcomes differ in their expected amount of suffering and whether there are ways to favorably affect the likely outcomes. This paper aims to provide an overview on \"bad-case scenarios\" in the AI context and some general suggestions for how they could be avoided. Future work will include checking fundamental assumptions and looking at the most promising proposals in more detail. \n Type I: Controlled AI gone bad In these scenarios, the team that builds the first superintelligence knew what it was doing and managed to successfully shape the resulting AI's goals exactly the way they wanted it to go. Unfortunately, the goals are not what we would wish them to be and thus lead to bad or very bad consequences. Things that could go wrong include: a) Anthropocentrism: perhaps the resulting AI would not care about the suffering of \"weird\" and/or voiceless nonhuman minds such as suffering subroutines or animal minds in ancestor simulations. b) Retributivism: perhaps the AI gets built by people who want to punish members of an outgroup (e.g. religious fundamentalists punishing sinners). c) Uncooperative: perhaps the AI's goal is something like classical utilitarianism (or any other \"monotone\" maximizing function) with no additional regards for cooperation with other value systems. Even though such an AI would all else equal prefer to not create suffering, it seems possible that the anti-suffering concern would in practice be overridden by opportunity costs: if happiness simulations contain much more utility for the AI than the disutility produced by the accidental suffering created in the buildup, then such an AI would behave similarly \"recklessly\" as e.g. a paperclipmaximizing AI. 2 Another concern lies in how strongly the AI would value robustness to deterioration. d) Libertarianism regarding computations: perhaps the creators of the first superintelligence instruct the AI to give every human alive at the time of the singularity control of a planet or galaxy, with no additional rules to govern what goes on within those territories. Some of these human rulers are curious and amused by seeing others hurt, or worse, might be psychopaths. \n Type II: \"Near misses\" In this scenario, the first superintelligence is built by people who were aware of the risks, and who tried to get things right. Unfortunately, mistakes happened and the resulting outcome with \"nearly-controlled AI\" is bad or very bad. a) Miserable creatures: perhaps the AI's goal function includes terms that attempt to specify sentient or human-like beings and conditions that are meant to be good for these beings. However, because of programming mistakes, unanticipated loopholes or side-effects, the conditions specified actually turn out to be bad for these beings. Worse still, the AI has a maximizing function and wants to fill as many regions of the universe as possible with these poor creatures. b) Black swans: perhaps the AI cares about sentient or human-like minds in \"proper\" ways, but has bad priors, ontology, decision theory, or other fundamental con-2 An AI that values happiness simulations but takes cooperation with suffering reducers into account would in expectation still create some amount of suffering, but depending on just how costly it is to use more \"sufferingproof\" algorithms in the colonization process, or to do fewer or less fine-grained ancestor simulations, it might be possible to cut down on most of the instrumentally produced suffering at a cost that isn't very high (e.g. not higher than 15% of total happiness simulations produced). stituents that would make it act in unfortunate and unpredictable ways. \n Type III: Uncontrolled AI Uncontrolled AI is stipulated to have goals that were never intended by its creators, or at least were not intended to take over control in the form of a singleton  (Bostrom, 2006) . Unless the AI in question has a neuromorphic design, it is unlikely that its goals would (directly) have something to do with sentient beings. However, even non-neuromorphic uncontrolled AI might instrumentally instantiate suffering minds in the process of achieving its goal, as a side-effect of the computations it performs. The following presents a list of ways how uncontrolled AI might create vast amounts of suffering: • Suffering subroutines: For tasks like inventing and developing advanced technologies, as well as for coordinating its expansion into space for resource accumulation, the AI would have to rely on a fleet of \"robot workers\" or \"robot scientists\" of various kinds (which, of course, might work and function very unlike human workers or scientists). It is possible that these processes would be capable of suffering  (Tomasik, 2014) , although it is unclear whether would perform at their best if they (occasionally) suffer. What is clear is that if they do suffer under useful circumstances, an AI that is not explicitly aligned with compassionate goals would not have any qualms about instantiating astronomical numbers of them. • Ancestor simulations  (Bostrom, 2003; Bostrom, 2014, Ch.8) : in order to gather information relevant to its goals, e.g. for improving its understanding of human psychology or sociology  (Bostrom, 2014, pp. 125-26)  or for studying the density of aliens in the universe and what their likely values are, a superintelligence might simulate many runs of Darwinian evolution in planet-sized supercomputers  (Sandberg, 1999) . It is possible that these simulations would be fine-grained enough to contain sentient minds. • Warfare: it may be that the density of life in the universe is high enough for colonizing AIs to eventually encounter one another. If so, uncontrolled AI might end up clashing with other superintelligences, including AIs that build expanding civilizations of happy sentient beings. Perhaps they could agree to a compromise, but such an encounter could also lead to fighting over resources and warfare at the points of contact. It is interesting to note that none of the aforementioned scenarios involve large quantities of suffering in the types of structures that the AI directly optimizes for. It seems likely that what makes uncontrolled AI bad is what it builds for instrumental reasons, including colonization machinery, science simulations, and other strategic computations. This suggests that opportunity costs are relevant: If an uncontrolled AI's goal function does not have diminishing returns on resources (like the infamous \"paperclip maximizer\"), then the room for instrumentally important computations might be small. By contrast, an AI with goals that are easy to fulfill 3 -e.g. a \"paperclip protector\" that only cares about protecting a single paperclip, or an AI that only cares about its own reward signal -would have much greater room pursuing instrumentally valuable computations. This line of thought suggests that outcomes from uncontrolled AI should be steered away from \"paperclip-protector types.\" 4 3 Suffering-focused AI safety: Some proposals Bad-case scenarios can be avoided in several ways. Using the typology from above, we can distinguish three classes of interventions: • Influencing outcomes with controlled AI: influence the values implemented in outcomes with controlled AI either through value spreading or by supporting the AI safety project with the best values The following can be labelled \"fail-safe\" measures: • Targeted AI safety: a) Differential progress: push classical AI safety differentially in ways that best insulates it from the worst \"near misses\" b) AI safety where it is most needed: identify the paradigm in general AI that would create the worst outcomes in the event of a control failure, and work towards identifying (general) control or shut-down mechanisms in those areas • Graceful fails: research ways to make AI fail in a \"benign\" way conditional on it failing (\"It might be the end of the world, but it could have been (much) worse\") The following sections present some preliminary ideas for the type of interventions that could be done in those areas. \n Influencing outcomes with controlled AI This class of interventions is primarily targeted at \"controlled AI gone bad\" outcomes. It is something FRI and others in the EA community have already thought about a great deal. • Improve values: raise awareness of antispeciesism, anti-substratism, concern for weird minds or suffering-focused ethics in general. • Cooperation: promote the idea that the gains from cooperation make it important for different value-systems to work together. • Cooperative AI-safety efforts: by funding the AI-safety project with the best values or the best approach to cooperation, we make it more likely that controlled AI won't create vast amounts of suffering. \n Differential progress in AI safety This intervention is targeted at the worst outcomes in the \"near misses\" category. The goal is to figure out solutions to the worst problems first, such that any additional progress in AI safety is unlikely to lead to \"near-misses,\" which may be worse than outcomes with uncontrolled AI in terms of suffering produced. This intervention seems comparatively more neglected than interventions in the category above. • Secure value implementation: Look into the pros and cons of various approaches to specifying an AI's values and work on the one least likely to lead to really bad outcomes. Questions to study may include: • What's more likely to go wrongsomething like indirect normativity, or an explicit specification of a goal function? • What are other promising approaches to AI safety, and how bad would the outcome be if they fail according to their weak points? • Would corrigibility reduce risks of astronomical suffering? • Foundational research: Which unanticipated failure modes could there be for controlled AI? Once they are identified, how can we prevent them? \n AI safety where it is most needed This intervention is targeted at preventing the worst outcomes involving uncontrolled AI. Not all uncontrolled AIs are expected to behave equally; there are different paradigms in AI research, i.e. different basic architectures for attempting to build smarter-than-human intelligence. Examples include reinforcement learning  (Sutton & Barto, 1998) , proof-based seed AI, and neuromorphic AIs  (Hasler & Marr, 2013) . Classical AI safety is necessarily concerned with the tradeoff between success probability and \"controllability;\" if a particular approach to building AI is likely to lead to superintelligence, but in a way where it is hard to control the values of the resulting agent, then this poses a likely dead end. By contrast, a suffering-focused \"fail-safe\" approach does not have to worry about controllability to the same extent, as long as there's enough controllability to predictably avoid outcomes with the most suffering. This suggests that, conditional on uncontrolled AI being worse than (nearly-)controlled AI in expectation, suffering reducers can be less constrained by issues with controllability, and can thus focus more on applying AI safety to the paradigm/architecture with the highest probability of bringing about superintelligence. In addition, we could try to identify differences among the types of uncontrolled AI each AI-paradigm would produce, in order to then focus on AI safety in the domain where failures of control result in the worst outcomes. Suppose for instance that one way of building AI appears to show promising results and rapid progress, yet control seems hard and likely failure modes are particularly worrying. In this case, we should consider putting efforts into AI safety applied to that particular domain. Specific examples of this more general idea include: • AI safety for machine learners: With DeepMind's recent success, it seems not unlikely that the first superintelligent AI may be all reinforcement learning as the top control structure (as opposed to GO-FAI, theorem proving or logic-based AI). In contrast to AI architectures where goals refer to the state of the world  (Hibbard, 2011)  rather than to internal or observational signals, pure reinforcement learners may be at a higher risk of wireheading, i.e. of hacking their input signals to continuously attain the maximum reward. If the wireheading AI is smart enough to plan into the future, it might patiently avoid doing so and develop plans for takeover first: As Bostrom notes in Superintelligence  (Bostrom, 2014, 122-23) , smart wireheaders would still want to colonize other galaxies for option value, protection, research, etc. However, unlike paperclip maximizers, wireheaders would more generally function like \"paperclip protectors\" in that they would have almost no opportunity costs  (Ring & Orseau, 2011) . If the observation that lower opportunity costs make outcomes with uncontrolled AI worse is accurate (see the discussion under \"Type III: Uncontrolled AI), this would make AI safety applied to reinforcement learning architectures particularly promising. Specific interventions could include work on Interruptibility  (Armstrong & Orseau, 2016) , but also methods of value-loading (examples here and here). • AI safety for \"em-first\" scenarios: Conditional on whole brain emulation  (Sandberg & Bostrom, 2008; Hanson, 2016)  becoming technologically feasible before the advent of de-novo AI, de-novo AI as eventually developed will more likely exhibit a neuromorphic design. 5 This would make it more likely that the values are humanlike, which also comes with the possi-bility of \"bad values\" or \"near misses.\" AI safety applied to \"em-first\" scenarios could thus be a promising intervention (although with early arrival timelines being longer, it may not be favored by haste considerations). Caveat: Pursuing any of the interventions above would require that we make sure to not speed up progress in AI development -both in general and in \"unsafe\" or \"hard-to-control\" approaches specific to those interventions. \n Graceful fails This class of interventions is targeted at preventing the worst outcomes involving \"nearlycontrolled\" or uncontrolled AI. Instead of trying to make fails less likely, the idea is to come up with safety nets or mechanisms such that, if control fails, the outcome will be as good as it gets under the circumstances. Graceful fails are easiest to bring about in the domain of near misses, as the researchers working on AI safety are aware of the risks and thus open to the idea of safety nets. • Backup goal functions: Research ways to implement multi-layered goal functions, with a \"backup goal\" that kicks in if the implementation of the top layer does not fulfill certain safety criteria. The backup would be a simpler, less ambitious goal that is less likely to result in bad outcomes. Difficulties would lie in selecting the safety criteria in ways that people with different values could all agree on, and in making sure that the backup goal gets triggered under the correct circumstances. In the context of AI research that is not guided by safety precautions, graceful fails proposals seem harder to implement. The challenge is to get an AI project that might result in uncontrolled AI to care about whatever proposal there is to implement. Perhaps there are proposals to consider in rather early stages of AI development where researchers think hard takeoffs are very unlikely. Should the AI design in question nevertheless undergo an intelligence explosion, there might be ways to make the result counterfactually less bad. • Dummy goals: We could come up with a goal function with the following properties: • Easy to program • Interesting (in the sense that it's easy to create problems for an AI with this goal function to solve, such that researchers can track their progress on general intelligence) • Leads to decent outcome in the unlikely case of hard takeoff If AI research and testing at early stages is always conducted with goals of this type, an unanticipated hard takeoff would at least be comparatively benign. \n Concluding thoughts Suffering-focused AI safety, and \"fail-safe\" measures in particular, make up a large and promising area of interventions for FRI (and perhaps other organizations) to investigate further. Advantages are that they are neglected and often \"less ambitious\" than classical AI safety, which means they might end up being more tractable. Moreover, \"fail-safe\" measures are a promising project to focus on because the interventions discussed are positive or at worst \"unobjectionable\" from the perspectives of virtually all other value systems. The main reason we had not explicitly zoomed in on this category of interventions earlier was that FRI was initially too focused on answering the more general, complicated question whether AI safety on the whole is net positive for suffering reducers. Upon reflection, this question may be less important. AI safety is a very broad category where we should expect a lot of room for targeted efforts. The general lesson to draw is that partitioning broad categories can be an important step towards making progress. More research into the feasibility of suffering-focused AI safety carries high information value for this very reason: As we look into more proposals and their practical feasibility, we might uncover more relevant distinctions among AI outcomes, valuetransfer proposals, or general approaches to AI -a process which, in turn, will make it easier to identify effective interventions. Influencing outcomes with controlled AI . . . . . . . . . . . . . . . . . . . . . . 3.2 Differential progress in AI safety . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 AI safety where it is most needed . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Graceful fails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction Contents 1 Introduction 2 How AI outcomes might contain suffering 2.1 Type 3 Suffering-focused AI safety: Some proposals 3.1 4 Concluding thoughts I: Controlled AI gone bad . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Type II: \"Near misses\" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Type III: Uncontrolled AI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \n\t\t\t \"Fail-safe\" in the sense that if control fails, at least the AI causes less suffering than would have been the case without fail-safe measures. \n\t\t\t Thanks to Carl Shulman for bringing this idea to our attention. 4 However, it may be that paperclip protectors are easier to compromise with, and thus more likely to also pursue maximization of sorts in exchange for benefits from \"paperclip-maximizer types.\" \n\t\t\t If only because neuroscience research would be very advanced in such a world.", "date_published": "n/a", "url": "n/a", "filename": "suffering-focused-ai-safety.tei.xml", "abstract": "AI-safety efforts focused on suffering reduction should place particular emphasis on avoiding risks of astronomical disvalue. Among the cases where uncontrolled AI destroys humanity, outcomes might still differ enormously in the amounts of suffering produced. Rather than concentrating all our efforts on a specific future we would like to bring about, we should identify futures we least want to bring about and work on ways to steer AI trajectories around these. In particular, a \"fail-safe\" 1 approach to AI safety is especially promising because avoiding very bad outcomes might be much easier than making sure we get everything right. This is also a neglected cause despite there being a broad consensus among different moral views that avoiding the creation of vast amounts of suffering in our future is an ethical priority.", "id": "1f2ec877a9cebdf8267ecbf33287e230"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Caspar Oesterheld", "Vincent Conitzer"], "title": "Extracting Money from Causal Decision Theorists", "text": "Introduction In Newcomb's problem  [Nozick, 1969; Ahmed, 2014] , a \"being\" offers two boxes, A and B. Box A is transparent and contains $1,000. Box B is opaque and may contain either $1,000,000 or nothing. An agent is asked to choose between receiving the contents of both boxes, or of box B only. However, the being has put $1,000,000 in box B if and only if the being predicted that the agent would choose box B only. The being's predictions are uncannily accurate. What should the agent do? Causal decision theory (CDT) recommends that the agent reason as follows: I cannot causally affect the content of the boxes -whatever is in the boxes is already there. Thus, if I choose both boxes, regardless of what is in box B, I will end up with $1,000 more than if I choose one box. Hence, I should choose both boxes. Evidential decision theory (EDT), on the other hand, recommends that the agent reason as follows: if I choose one box, then in all likelihood the being predicted that I would choose one box, so I can expect to walk away with $1,000,000. (Even if the being is wrong some small percentage of the time, the expected value will remain at least close to $1,000,000.) If I choose both, then I can expect to walk away with (close to) $1,000. Hence, I should choose one box. While Newcomb's problem itself is far-fetched, it has been argued that the difference between CDT and EDT matters in various game-theoretic settings. First, it has been pointed out * Contact Author that Newcomb's problem closely resembles playing a Prisoner's Dilemma against a similar opponent  [Brams, 1975; Lewis, 1979] . Whereas CDT recommends defecting even in a Prisoner's Dilemma against an exact copy, EDT recommends cooperating when facing sufficiently similar opponents. What degree of similarity is required and whether EDT and CDT ever come apart in this way in practice has been the subject of much discussion  [Ahmed, 2014, Section 4.6] . A common view is that CDT and EDT come apart only under fairly specific circumstances that do not include most human interactions.  Still, Hofstadter [1983] , for example, argues that \"superrational\" humans should cooperate with each other in a real-world one-shot Prisoner's Dilemma, reasoning in a way that resembles the reasoning done under EDT. Economists have usually been somewhat dismissive of such ideas, sometimes referring to them as \"(quasi-)magical thinking\" when trying to explain observed human behavior  [Shafir and Tversky, 1992; Masel, 2007; Daley and Sadowski, 2017] . Indeed, standard game-theoretic solution concepts are closely related to ratificationism  [Joyce and Gibbard, 1998, Section 5 ], a variant of CDT which we will revisit later in this paper (see Part 3 of Section 4). Second, even if the players of a game are dissimilar, it is in the nature of strategic interactions that each player's behavior is predicted by the other players. Newcomb's problem itself (as well as the ADVERSARIAL OFFER discussed in this paper) differs from strategic interactions as they are usually considered in game theory in its asymmetry. However, one might still expect that CDT and EDT offer different perspectives on how rational agents should deal with the mutual prediction inherent in strategic interactions  [Gauthier, 1989, Section XI] . Third, CDT and EDT differ in their treatment of situations with imperfect recall. Seminal discussions of such games are due to  Piccione and Rubinstein [1997 ] and Aumann et al. [1997 ] [cf. Bostrom, 2010 , for an overview from a philosopher's perspective]. While these problems originally were not associated with Newcomb's problem, the relevance of different decision theories in this context has been pointed out by  Briggs [2010 ] [cf. Armstrong, 2011 Schwarz, 2015; Conitzer, 2015] . The importance of the differences in decision theory is amplified if, instead of humans, we consider artificial agents. After all, it is common that multiple copies of a software sys-tem are deployed and other parties are often able to obtain the source code of a system to analyze or predict its behavior. As some software systems choose more autonomously, we might expect their behavior will be (approximately) describable by CDT or EDT (or yet some other theory). If either of these theories has serious flaws, we might worry that if a system implements the wrong theory, it will make unexpected, suboptimal choices in some scenarios. Such scenarios might arise naturally, e.g., as many copies of a system are deployed. We might also worry about adversarial problems like the one in this paper. One argument against CDT is that causal decision theorists (tend to) walk away with less money than evidential decision theorists, but this argument has not proved decisive in the debate. For instance, one influential response has been that CDT makes the best out of the situation -fixing whether the money is in box B -which EDT does not  [Joyce, 1999, Section 5.1] . It would be more convincing if there were Newcomb-like scenarios in which a causal decision theorist volunteers to lose money (in expectation or with certainty). 1 Constructing such a scenario from Newcomb's problem is non-trivial. For example, in Newcomb's problem, a causal decision theorist may realize that box B will be empty. Hence, he would be unwilling to pay more than $1,000 for the opportunity to play the game. In this paper, we provide Newcomb-like decision problems in which the causal decision theorist voluntarily loses money to another agent. We first give a single-decision scenario in which this is true only in expectation (Section 2). We then extend the scenario to create a diachronic Dutch book against CDT -a two-step scenario in which the causal decision theorist is sure to lose money (Section 3). Finally, we discuss the implications of the existence of such scenarios (Section 4). 1 Walking away with the maximum possible (expected) payoff under any circumstances is not a realistic desideratum for a decision theory: any decision theory X has a lower expected payoff than some other decision theory Y in a decision problem that rewards agents simply for using decision theory Y [cf.  Skalse, 2018 , for a harderto-defuse version of this point]. However, such a setup does not allow one to devise a generic scenario in which an agent voluntarily loses money, i.e. loses money in spite of having the option to walk away losing nothing. Furthermore, scenarios with voluntary loss appear significantly more problematic for pragmatic reasons. Regardless of what you think is the right option in Newcomb's problem, you might not view Newcomb's problem as relevant ground for decision-theoretical argument because it is so unlikely that one would ever face Newcomb's problem in the real world. For instance, even if you thought that one-boxing is rational (and two-boxing is not), you might stick with CDT nonetheless because your real-world expected opportunity costs from two-boxing in Newcomb's problem are negligible. [For some discussion of this deflationary argument, see, e.g.,  Gauthier, 1989, Section XI; Ahmed, 2014, Section 7.1.iv; Oesterheld, 2019 , Section 1, and references therein.] However, if there is a Newcomb-like problem in which the causal decision theorist voluntarily loses money to some other agent, this generates a significant incentive to place him in such a situation. \n Extracting a profit in expectation from causal decision theorists Consider the following scenario: ADVERSARIAL OFFER: Two boxes, B 1 and B 2 , are on offer. A (risk-neutral) buyer may purchase one or none of the boxes but not both. Each of the two boxes costs $1. Yesterday, the seller put $3 in each box that she predicted the buyer not to acquire. Both the seller and the buyer believe the seller's prediction to be accurate with probability 0.75. No randomization device is available to the buyer (or at least no randomization device that is not predictable to the seller). 2 If the buyer takes either box B i , then the expected money gained by the seller is $1 − P ($3 in B i | buyer chooses B i ) • $3 = $1 − 0.25 • $3 = $0.25. Hence, the buyer suffers an expected loss of $0.25 (if he buys a box). The best action for the buyer therefore appears to be to not purchase either box. Indeed, this is the course of action prescribed by EDT as well as other decision theories that recommend one-boxing in Newcomb's problem [e.g., those proposed by  Spohn, 2012; Poellinger, 2013; Soares and Levinstein, 2017] . In contrast, CDT prescribes that the buyer buy one of the two boxes. Because the agent cannot causally affect yesterday's prediction, CDT prescribes to calculate the expected utility of buying box B i as P ($3 in box B i ) • $3 − $1, (1) where P ($3 in box B i ) is the buyer's subjective probability that the seller has put money in box B i , prior to updating this belief based on his own decision. For i = 1, 2, let p i be the probability that the buyer assigns to the seller having predicted him to buy B i . Similarly, let p 0 be the probability the buyer assigns to the seller having predicted him to buy nothing. These beliefs should satisfy p 0 + p 1 + p 2 = 1. Because p 0 ≥ 0, we have that (p 0 +p 1 )+(p 0 +p 2 ) = 2p 0 +p 1 +p 2 ≥ 1. Hence, it must be the case that p 0 + p 1 ≥ 1 2 or p 0 + p 2 ≥ 1 2 (or both). Because P ($3 in box B i ) = p 0 + p 3−i for i = 1, 2, it is P ($3 in box B i ) ≥ 1 2 for at least one i ∈ {1, 2}. Thus, the expected utility in eq. 1 of at least one of the two possible purchases is at least 1 2 • $3 − $1 = $0.50, which is positive. Any seller capable of predicting the causal decision theorist sufficiently well will thus have an incentive to use this scheme to exploit CDT agents. (It does not matter whether the seller subscribes to CDT or EDT.) It should be noted that even if the buyer uses CDT, his view of the deal matches the seller's as soon as the dollar is paid. That is, after observing his action, he will realize that the box he bought is empty with probability 0.75 and thus worth less than a dollar. CDT knows that it will regret its choice [see  Joyce, 2012; Weirich, 1985  for discussions of the phenomenon of anticipated regret a.k.a. decision instability in CDT]. \n A diachronic Dutch book against causal decision theory ADVERSARIAL OFFER results in a loss in expectation for the causal decision theorist. It is natural to ask whether it is possible to set up the scenario so that the causal decision theorist ends up with a sure loss; effectively, a Dutch book. Arguably, Dutch books are more convincing than scenarios with expected losses since the very meaning of \"expectations\" is the subject of the debate about EDT and CDT. Of course, if the seller could perfectly predict the buyer in ADVERSARIAL OFFER (instead of being right only 75% of the time), then ADVERSARIAL OFFER would become a Dutch book. But can we construct a Dutch book without perfect prediction? We have already observed that in ADVERSARIAL OFFER the causal decision theorist always regrets his decision after observing its execution. This suggests the following simple approach to constructing a Dutch book. After the box is sold, the seller allows the buyer to reverse his decision for a small fee (ending up without any box and having lost only the fee). However, a CDT buyer may then anticipate eventually undoing his choice and therefore not buy a box in the first place  [Ahmed, 2014, Section 3.2; though cf. Skyrms, 1993; Rabinowicz, 2000 ].  3  To get our Dutch book to work, we add another choice before ADVERSARIAL OFFER. ADVERSARIAL OFFER WITH OPT-OUT: It is Monday. The buyer is scheduled to face the AD-VERSARIAL OFFER on Tuesday. He also knows that the seller's prediction was already made on Sunday. As a courtesy to her customer, the seller approaches the buyer on Monday. She offers to not offer the boxes on Tuesday if the buyer pays her $0.20. Note that the seller does not attempt to predict whether the buyer will pay to opt out. Also, we assume that the buyer cannot, on Monday, commit himself to a course of action to follow on Tuesday. It seems that a rational agent should never feel compelled to accept the Monday offer. After all, doing so loses him money with certainty, whereas simply refusing both offers (on Monday and on Tuesday) guarantees that he loses no money. CDT, however, recommends opting out on Monday, for the following reasons. A CDT buyer knows on Monday that if he does not opt out, he will buy a box on Tuesday (though he may not yet know which one). Further, he believes that whatever box he will take on Tuesday will contain $3 with only 25% probability, thus implying an overall expected payoff of 0.25 • $3 − $1 = −$0.25. This is because, on Monday, CDT treats the decision on Tuesday in the same way as it treats any other random variable in the environment. So the causal expected utility of not opting out is just what an outside observer would expect the payoff of a CDT agent facing ADVERSARIAL OFFER to be. Because this expected payoff of −$0.25 is less than the certain payoff of −$0.20 that can be obtained by opting out, CDT recommends opting out. In fact, for the argument in the previous paragraph to succeed, it is only necessary that CDT is used on Tuesday; other decision theories would also recommend accepting the Monday offer, if they anticipate that the agent will use CDT on Tuesday. For instance, if the agent followed EDT on Monday and CDT on Tuesday (and is aware on Monday that he will use CDT on Tuesday), then he would still accept the Monday offer. Similarly, if the seller believes that the buyer will pick one of the boxes on Tuesday, then she will hope that he rejects the Monday offer. Thus, it seems that what creates the opportunity for a Dutch book is the prospect of buying a box on Tuesday (as CDT recommends), not the use of CDT on Monday. \n Discussion We differentiate four types of responses to these scenarios available to supporters of causal decision theory: 1. They could claim that these scenarios are irrelevant for evaluating decision theories, in the sense that they are impossible to set up or otherwise out of scope, and therefore unpersuasive. 2. They could concede that these scenarios are relevant for evaluating decision theories, but claim that CDT's recommendations in them are acceptable. 3. They could concede that our analysis obliges them to give up on certain specific formulations of CDT, but try to modify CDT to get these scenarios right while maintaining some of its essence, in particular two-boxing and the causal dominance principle. 4. They could concede that these scenarios show that the very core of CDT (two-boxing and the causal dominance principle) is implausible. We will discuss these options in turn. 1 Surely, if one could show that a CDT agent will or can never face these scenarios -despite the seller having an obvious incentive to set them up -that would be the most convincing defense of CDT. In particular, a causal decision theorist might claim that sufficiently accurate prediction of a CDT agent is simply impossible. 4 However, not much accuracy is required, for the following reasons. The CDT agent will take one of the two boxes. Even if the seller picks the box to fill with money uniformly at random, she would therefore be right half of the time. If she can do any better than that, predicting correctly with probability 1/2+ , then she can extract money from the CDT agent by putting (instead of $3) some amount between $2/(1 − 2 ) and $2 in the box predicted not to be taken. Thus, the CDT agent needs to be completely unpredictable in order to avoid being taken advantage of in these examples. Most human beings are, generally speaking, at least somewhat predictable in their actions even when such predictability can be used against them. For example, in rock-paperscissors -which structurally resembles the ADVERSARIAL OFFER -most people follow exploitable patterns in what moves they select [see, e.g.,  Farber, 2015, and references therein] .  5  Consider such a somewhat predictable person who aims to be a causal decision theorist. It seems that he would indeed be vulnerable to the examples discussed earlier. The only defense for the supporter of causal decision theory would seem to then be that if so, the person in question is not truly acting in the way that CDT describes. That is, acting according to CDT also requires being unpredictable to the seller, either by succeeding at out-thinking the seller sufficiently often, or by acting sufficiently randomly. Is it reasonable to consider this a requirement of acting according to CDT? CDT does not suggest any strict preference for choosing randomly across options, as opposed to just deterministically choosing one of the options that is best according to the buyer's beliefs. Hence, the unpredictability would have to emerge from the buyer attempting to out-think the seller. But it does not seem that this is always an attainable goal. For example, imagine that the buyer is a deterministic computer program whose source code is known to the seller. Then regardless of how exactly the agent works, the seller can predict the buyer's behavior perfectly [cf. Soares and Fallenstein, 2014, Section 2; Cavalcanti, 2010, Section 5]. We would thus be forced to conclude that such a program cannot possibly follow CDT, which to us is an unsatisfactory conclusion. Plausibly any other physically realized agent that chooses deterministically can at least in principle (if not with current technology) be predicted by creating or emulating an atom-by-atom copy of that agent [cf.  Yudkowsky, 2010, pp. 85ff.] . Even if the supporter of CDT acknowledges that these scenarios are possible, he might nevertheless argue that they are irrelevant, in the sense that the decision theory is not intended to be used for such scenarios and hence nothing that one could show about its performance in such a scenario is of significance for evaluating the theory. \"It is as if one evaluated a car by testing how it performs underwater.\" There is little we can say about this response. Still, we expect it to be unattractive to most decision theorists. After all, our scenarios (in particular the ADVERSARIAL OFFER) resemble Newcomb's problem -the problem that has led to the development of CDT in the first place. Further, if our scenarios were out of CDT's scope, then we (and presumably most other decision theorists) would still be interested in identifying a decision theory that does make good recommendations for predictable agents (such as artificial intelligent agents whose behavior is 5 There are multiple rock-paper-scissors bots available online which attempt to predict their opponent's future moves based on past moves (using data from other players). As of July 2019, the bot at http://www.essentially.net/rsp/ has reportedly played about 2 million rounds and won 57% more often than it lost. determined by a computer program) facing a wide range of scenarios including the ones given in this paper. 2 If our scenarios are within the scope of causal decision theory, then the supporter of causal decision theory has to contend with the fact that one can extract expected money from, and even Dutch-book, CDT agents in them. But he might question the significance of Dutch-book arguments and other money extraction schemes, either in general or in this particular context. For some general discussion of whether (diachronic) Dutch books are conclusive decision-theoretic arguments, see, e.g.,  Vineberg [2016]  or  Hájek [2009] . Note, though, that some of the most influential arguments in favor of expected utility maximization (EUM) -of which CDT is a refinement -are Dutch books. Of course, one may use different arguments to justify EUM. But it would seem odd to follow Dutch-book arguments to EUM but no further. Instead of rehashing some of the more generic reasons for and against the persuasiveness of Dutch books and loss of money in expectation, we here discuss a response that is specific to CDT and ADVERSARIAL OFFER WITH OPT-OUT.  6  A causal decision theorist may argue that it is not generally fair to expect any kind of coherence from CDT's recommendations when multiple decisions are to be made across time, due to the different perspectives that the decision maker adopts (and, arguably, has to adopt) at different points in time. Consider Newcomb's problem. Let t 0 be the time at which the predictor observes the agent (perhaps using fMRI or the like) in order to make a prediction. Then, before t 0 , CDT recommends committing -and if needed paying money to commit -to one-boxing [cf.  Barnes, 1997; Joyce, 1999, pp. 153f.; Meacham, 2010] . After t 0 , CDT recommends two-boxing. However, most decision theorists do not consider this to be a compelling argument against CDT. The causal decision theorist can easily justify the difference in the decision made by the fact that, before t 0 , the commitment decision has a causal effect on what is in the boxes, and after t 0 , it does not. It would be hypocritical for an evidential decision theorist to disagree, since EDT is dynamically inconsistent in analogous ways. For instance, consider a version of Newcomb's problem in which both boxes are transparent  [Gibbard and Harper, 1981, Section 10 ; also discussed by  Gauthier, 1989; Drescher, 2006, Section 6.2; Arntzenius, 2008, Section 7; Meacham, 2010, Section 3.2.2] . Let t 0 be the time at which the EDT agent sees the content of both boxes. Then before t 0 , EDT recommends committing -and if needed paying money to commit -to one-boxing. After t 0 , EDT recommends twoboxing.  7  The evidential decision theorist can easily justify this along similar lines: before t 0 , her commitment is evidence about what is in the boxes, and after t 0 it no longer is. Thus, at least some types of dynamic inconsistency do not constitute strong arguments against a decision theory. However, in our opinion, the dynamic inconsistency displayed by CDT in the ADVERSARIAL OFFER WITH OPT-OUT is much more problematic. For one, it leads to a Dutch book. Often, the main argument that is given for why a particular inconsistency is problematic is precisely that it allows for a Dutch book. Conversely, defenses of dynamic inconsistencies  [Ahmed, 2014, Section 3.2 , for an example in a Newcomb-like scenario] often focus on arguing that they do not allow for Dutch Books. Further, it seems that some of the reasons for (or defenses of) dynamic inconsistency in the above decision problems do not apply to CDT's dynamic inconsistency in ADVERSARIAL OFFER WITH OPT-OUT. For CDT in Newcomb's problem, there is a particular event at time t 0 that splits the decision perspectives: the loss of causal control at t 0 over the content of box B. Similarly, for EDT in the Newcomb's problem with transparent boxes, that event is the loss of evidential control [cf. Almond, 2010, Section 4.5] at t 0 over the content of box B. It is thus easy to argue for defenders of the respective theories that the perspectives from before and after t 0 or t 0 should diverge  [Ahmed and Price, 2012, pp. 22-23, Section 4] . In sharp contrast, the ADVERSARIAL OFFER WITH OPT-OUT lacks any such event between the decision points. The difference in perspectives for CDT appears to be purely a result of CDT viewing its current choice differently than it views past and future decisions. All that being said, we agree that caution should be taken when evaluating a decision theory based on scenarios with multiple decisions across time. In general, more research on what conclusions can be drawn from such scenarios is needed  [Steele and Stefánsson, 2016, Section 6 ]. Nevertheless, we do not see any clear path by which such research would justify CDT's recommendations in the ADVERSARIAL OFFER WITH OPT-OUT. In any case, even if one is at this point unwilling to consider scenarios with multiple decision points at all for the purpose of evaluating decision theories, one would still have to contend with the simpler ADVERSARIAL OFFER scenario, in which there is only one decision point. 3 If a straightforward interpretation of CDT cannot be defended against our scenarios, one may look to modify it to avoid expected or sure loss while preserving some of CDT's core tenets. In particular, in response to other alleged counterexamples, some authors have tried to modify CDT while maintaining the causal dominance  [Joyce, 1999, Section 5 .1] a.k.a. sure thing  [Gibbard and Harper, 1981, Section 7]  principle [though see  Ahmed, 2012 , for an argument against the motivation behind some of these approaches]. For example, one may turn to the concept of ratifiability. In Newcomb-like scenarios such as those under discussion here, for any choice a, we can consider the beliefs about what is in the boxes that would result from knowing that one will choose a. Then, a choice a is ratifiable if it is an optimal choice -as judged by CDT -under those beliefs. For example, in Newcomb's problem only two-boxing is ratifiable, precisely because it is causally dominant. For an overview of ratification and its relation to CDT, see  Weirich [2016, Section 3.6 ]. Unfortu-nately, this concept is of no help in the ADVERSARIAL OF-FER, because none of the three options (buying B 1 , buying B 2 or declining) is ratifiable. For instance, under the beliefs that would result from knowing that you will take box B i , it would be better to buy the other box B 3−i . The ratificationist may respond by claiming that unpredictable randomization should always be possible. If that were true, then the only ratifiable option would be to take each box with probability 50%, thus gaining money in expectation. But again, we would like to have a decision theory that works in a broad variety of scenarios, including ones where the agent expects to be somewhat predictable. Furthermore, even if a true random number generator (TRNG) (e.g., one based on nuclear decay) is in fact available, this does not settle the issue. For example, consider a variant of the AD-VERSARIAL OFFER in which the seller refrains from putting money in any box if she predicts the buyer to make different choices depending on the output of the TRNG. In this ANTI-RANDOMIZATION ADVERSARIAL OFFER, again no option is ratifiable: under the beliefs that would result from knowing that you will make different choices depending on the TRNG's output (and therefore choose a box with some positive probability), you would rather not pick any box. To circumvent this example, the ratificationist could argue that the decision maker should be able to randomize in such a way that whether he is randomizing is unpredictable. However, at this point, one might just as well assert the impossibility (or irrelevance) of Newcomb-type scenarios altogether, which we have addressed in 1. A different strategy for modifying CDT to avoid the Dutch book in the ADVERSARIAL OFFER WITH OPT-OUT is the following. The Dutch book arises from a disagreement between CDT on Monday and CDT on Tuesday (cf. the discussion under 2). A tempting possibility is to modify CDT so that it considers all decisions to be made at once. That is, such a version of CDT -let us refer to it as policy-CDT -prescribes that one decide on one's general policy all at once.  8  In the ADVERSARIAL OFFER WITH OPT-OUT, there are four possible policies: opt out, buy B 1 , buy B 2 , and buy nothing (where the last three possibilities include declining the opt-out offer). When considering these policies, buy nothing dominates opt out. Hence, policy-CDT will decline the opt-out offer and thereby avoid the Dutch book. (Note, however, that such a modification of CDT will make no difference to the choices it prescribes in ADVERSARIAL OFFER, which has only one decision point. Hence, it will still lose money in expectation.) While this appears to be a promising approach, it is nontrivial to flesh out, because on other examples it is less clear what policy-CDT should prescribe. For illustration, consider the following interpretation of policy-CDT: follow the policy to which CDT would like to commit ex ante, where \"ex ante\" refers to some point in time before the first decision of the scenario. Now, let us consider a version of Newcomb's problem which is supplemented by another trivial and unrelated decision -say, whether to eat a peppermint -that takes place when the agent still has a causal influence over the prediction. Then the ex-ante-commitment interpretation of policy-CDT would recommend one-boxing. To the causal decision theorist, this may be unacceptable, especially given that adding the peppermint decision is such a minor modification of Newcomb's problem. Perhaps there is a way to define policy-CDT that avoids such dependence on irrelevant decisions while also prescribing two-boxing, but it is not immediately obvious how to do so. Many other ways of modifying CDT are worth considering. For instance, in the ADVERSARIAL OFFER, it may be unrealistic for the buyer to form a single probability distribution over box contents. Instead, he may consider multiple different probability distributions, including one under which box B 1 is probably empty and one under which box B 2 is probably empty. He could then evaluate each option pessimistically, i.e., w.r.t. the probability distribution that is worst under that option. Such a version of CDT would prescribe declining to buy a box. At the same time, it would recommend twoboxing in Newcomb's problem and more generally obey the causal dominance principle. For a discussion of this maxmin criterion for choice under multiple probability distributions, see, e.g.,  Gilboa and Schmeidler [1989]  and in particular game-theoretic interpretations such as that of  Grünwald and Halpern [2011] . A more general discussion of how using sets of probability distributions (while potentially decision rules other than the maxmin criterion) is offered by  Bradley [2012] . In our setting, B 1 are B 2 are, roughly, complementary bets in the causalist's beliefs. In all worlds in which B i is empty, B 3−i is full. As discussed by Bradley, it has been argued that a rational agent should accept one of a pair of complementary bets. Indeed, expected utility maximization for a single probability distribution satisfies this complementarity criterionto the causalist's detriment in the Adversarial Offer.  Bradley [2012]  argues that in general, an agent with imprecise probabilities should not satisfy the complementarity criterion and that this allows him to avoid Dutch books -though, of course, he considers Dutch books of a very different type. 4 Finally, one may view at least one of the scenarios in this paper as supporting a persuasive argument against the very core of CDT. EDT is the obvious alternative. However, depending on how problematic we find EDT's prescriptions in other cases -such as the Smoking lesion  [Ahmed, 2014, Section 4.1-4.3]  or cases of dynamic inconsistency like Newomb's problem with transparent boxes (and the problems listed in footnote 7) -we may also look to various other decision theories that have been proposed  [Gauthier, 1989; Spohn, 2012; Poellinger, 2013; Soares and Levinstein, 2017] . \t\t\t This decision problem resembles the widely discussed Death in Damascus scenario [introduced to the decision theory literature byGibbard and Harper, 1981, Section 11]  and even more closely the Frustrater case proposed by Spencer and Wells[2017], though these are not set up to result in an expected financial loss.Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). \n\t\t\t This, of course, requires that the reversal offer does not come as a surprise. Throughout, we insist that the buyer knows all the rules of the game. \n\t\t\t For a general discussion of such unpredictability claims in defense of CDT, seeAhmed [2014, Chapter 8].Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). \n\t\t\t For a discussion of similar arguments about other diachronic Dutch books, see, e.g.,Rabinowicz [2008].7 Parfit's (1984)  hitchhiker [Barnes, 1997] , XOR Blackmail [Soares and Levinstein, 2017, Section 2] and Yankees vs. Red Sox[Arntzenius, 2008, pp. 22-23; Ahmed and Price, 2012]  similarly expose dynamic inconsistencies in EDT. Conitzer [2015]  gives a somewhat different type of scenario -based on the Sleeping Beauty problem -in which EDT is dynamically inconsistent.Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). \n\t\t\t  Policy-CDT resembles Fisher's [nd]  disposition-based decision theory. Compare Meacham [2010]  for a discussion of explicit precommitment. Similarly, Gauthier [1989]  has argued for evaluating \"plans\" not decisions in Newcomb-like problems (without basing this argument on any particular theory like CDT or EDT). A few authors have also proposed policy versions of other, more EDT-like decision theories[Drescher, 2006, Section 6.2; Yudkowsky and Soares,  2018, Section 4].Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). \n\t\t\t Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).", "date_published": "n/a", "url": "n/a", "filename": "paper_21.tei.xml", "abstract": "Newcomb's problem has spawned a debate about which variant of expected utility maximization (if any) should guide rational choice. In this paper, we provide a new argument against what is probably the most popular variant: causal decision theory (CDT). In particular, we provide two scenarios in which CDT voluntarily loses money. In the first, an agent faces a single choice and following CDT's recommendation yields a loss of money in expectation. The second scenario extends the first to a diachronic Dutch book against CDT.", "id": "cd5b23123fd8e755c1797c326ef169ab"}
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{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Noah D Goodman", "Andreas Stuhlm€"], "title": "Knowledge and Implicature: Modeling Language Understanding as Social Cognition", "text": "To what extent does language understanding rely on extra-linguistic knowledge and processes? One view of language processing suggests that it consists of largely separate, special-purpose faculties; another view suggests that it depends critically on domain-general inference mechanisms, and even on intuitive theories that are not specific to language. Indeed, many thinkers have viewed speech as an action with communicative goals, such as informing a listener  (Clark, 1996; Grice, 1975; Levinson, 2000) . A listener making this assumption can make stronger inferences than an utterance would allow from its literal meaning-pragmatic effects can strengthen, or change, the interpreted meaning. Recent work has aimed to formalize the social inference view of pragmatics using tools of Bayesian statistics and information theory  (Frank & Goodman, 2012) ; we refer to this formal framework as the rational speech-act theory of language understanding. It views pragmatic competence as following naturally from an intuitive theory of speech production, which in turn is a special case of intuitive theory of mind. More precisely, listeners have an internal model that describes speakers as choosing their utterances approximately optimally on the basis of certain social goals, such as conveying information to the listener; listeners then interpret an utterance by using Bayesian inference to \"invert\" this model of the speaker, drawing conclusions about the world state and speaker's intention from the utterance and any other relevant world knowledge. These two rationality assumptions, for listener and speaker, have a role similar to those made in ideal observer models of perception  (Geisler, 2003) : They provide a starting point for a quantitative understanding of the complex interactions involved in language understanding. Indeed, this view has provided good quantitative models for pragmatic inference in a number of simple settings  (Frank & Goodman, 2012; Frank, Goodman, Lai, & Tenenbaum, 2009) . Because rational decision making predicts that action selection is related to the expected utility-a quantity that depends on the actor's belief distribution-a listener who views the speaker as rational should be sensitive to the speaker's belief state. The rational speech-act theory thus predicts an interaction between (shared) knowledge about a speaker's knowledge state and a listener's interpretation of his utterance. This is a very general prediction of the framework, which could easily prove to be false-if pragmatic inference is a highly modularized computation, for instance, we would not expect such general knowledge to affect it. Deriving and testing precise predictions about this interaction thus provide an important test of the rational speech-act theory. If you hear \"some of the apples are red,\" you will infer that not all of the apples are. Pragmatic effects of this sort are called scalar implicatures  (Horn, 2004) , and they provide a window on the interactions between the language faculty and general cognition. Consider Fig.  1 : If the speaker has seen all the apples, his utterance would be interpreted as \"some, but not all, of the apples are red.\" However, if the speaker had only looked at two of the apples, the listener might draw a different conclusion. Indeed, we show below that the implicature \"not all\" can be canceled by facts about the speaker's perceptual access. This interaction between language understanding and general knowledge is not predicted by strongly modular theories that place scalar implicature within a semantics module  (Chierchia, Fox, & Spector, 2011) . We show further that the interaction of knowledge and implicature is fine grained: The details of a speaker's belief distribution affect the details of an implicature. This article provides a formal model of the pragmatic inference that leads to scalar implicatures, building on the rational speech-act framework. We directly model the possibility that the speaker may have incomplete knowledge and the effects this has on the listener's interpretation. We derive predictions of this model for interpretation of the quantifier \"some\" and the number words (\"one,\" \"two,\" etc.). The model both explains the standard implicatures for these words and predicts that these implicatures can be canceled, completely or partially, when the speaker has incomplete knowledge. We test these predictions in two experiments and find good fits to human judgements, both qualitatively and quantitatively. \n A rational speech-act model We view language comprehension as a rational inference based on an intuitive theory of language production. Our setting is illustrated in Fig.  1 . The listener infers the world state, s, given the speaker's utterance, w, and shared information about the speaker's (possibly incomplete) information access, a. By Bayes' rule: P listener ðs j w; aÞ / P speaker ðw j s; aÞPðsÞ; ð1Þ where P(s) captures the listener's prior beliefs about the world state and P speaker ðw j s; aÞ describes the listener's intuitive theory of how the speaker chooses words. The speaker chooses an utterance in accord with Bayesian decision theory  (Berger, 1985) : She acts to approximately optimize expected utility. Imagine a speaker who makes observation o about the true state of the world. (For instance, in Fig.  1 , the speaker has perceptual access to two of three apples and observes that those two are red). The speaker selects an utterance w to convey information about the world state to a listener and does so by soft-max optimizing expected utility: P speaker ðw j o; aÞ / expðaE Pðs j o;aÞ ½Uðw; sÞÞ: The speaker's utility function, U(w;s), captures the value of saying w if the world is actually s. The expectation is taken over the speaker's belief state, P(s | o,a), because the speaker may still be uncertain about the state of the world. The parameter a controls the deviation from optimality. So far, nothing in the model is unique to language-indeed, similar models have been used to model social cognition more generally  (Baker, Saxe, & Tenenbaum, 2009; Ullman et al., 2009) . To capture a motivation to be informative, utility must be related to the information conveyed in the utterance.  1  More specifically, utility is related to the amount of information that a literal listener would not yet know about state s after hearing it described by utterance w-this is the negative surprisal  (Cover & Thomas, 1991) : Uðw; sÞ ¼ lnðP lex ðs j wÞÞ; ð3Þ where the literal interpretation probability P lex ðs j wÞ is determined by the lexicon-here, we will assume that each utterance has a truth function, F w : s7 !f0; 1g, and the distribution is otherwise uninformative: P lex ðs j wÞ / d F w ðsÞ . We assume that the speaker's access a is common knowledge of speaker and listener, but the listener still does not know what observation the speaker made, hence: P speaker ðw j s; aÞ ¼ X o P speaker ðw j o; aÞPðo j a; sÞ: ð4Þ In the experiments below (as in Fig.  1 ), the state of the world is always a set of objects that may have a given property and observations consist of looking at a subset of the objects. Thus, the observation probability P(o | a,s) is a hyper-geometric distribution (i.e., the probability of drawing N balls of a given color, without replacement, from an urn containing a given set of colored balls). In this setting, it is also reasonable to assume that the prior probability, P(s), is a binomial distribution (i.e., draws with replacement); we will initially assume so and will later measure the distribution empirically. Overall, the above equations describe the inferences that a rational listener will make to comprehend a speaker that she believes to be approximately rational and have a goal to be informative. Importantly, these inferences depend on shared knowledge about the aspects of the world to which the speaker has access. Thus, the rational speech-act theory predicts that the speaker's access affects utterance interpretation; we test this prediction below. To derive more specific predictions, we must describe the set of alternative utterances. \n The alternatives We have assumed that the interpretation of an utterance is made with respect to a set of alternative utterances. These alternatives could be all possible utterances or could be a limited set generated by replacing key words in the actual utterance with related words. The alternatives may, for instance, be generated by a grammatical mechanism as in  Fox and Katzir (2011) . For our results, the details of this process are unimportant; what is important is that there exists a set of alternative expressions and a (truth-functional) literal meaning for each. We make standard assumptions in both respects. Consider the case of the quantifier words \"some\" and \"all.\" Under the standard semantics, \"all the balls are red\" is true exactly when N of the N balls are red, while \"some of the balls are red\" is true when M ! 1 of the N balls are red. In particular, the literal meaning of \"some\" allows the state where all N balls are red. We use a lexicon that consists of the standard meanings for \"none,\" \"some,\" and \"all.\" Model predictions are shown in Fig.  2A  for the listener's interpretation of \"some of the balls are red\" when there are three objects, under varying conditions of speaker access. When the speaker has perceptual access to three of the three objects (hence complete knowledge) and says \"some,\" there is a lower probability on three than two-this is the standard \"some but not all\" implicature. To understand why the model predicts this implicature, we can first simplify the speaker model: In a complete knowledge situation, the SOME OF THE APPLES ARE RED. ALL SOME Fig.  1 . How will the listener interpret the speaker's utterance? How will this change if she knows that he can see only two of the objects? speaker's belief distribution is concentrated on the true state, so Eqs. 2, 3, and 4 become: P speaker ðw j s; aÞ / expðalnðP lex ðs j wÞÞÞ / ðP lex ðs j wÞÞ a : ð5Þ Using the standard meanings described above, we see that if the state were 3, the speaker would be more likely to say \"all\" (P lex ðs j wÞ ¼ 1) than \"some\" (P lex ðs j wÞ ¼ 1 3 ); conversely, if the state were 2, the speaker would say \"some,\" as the probability for \"all\" is now P lex ðs j wÞ ¼ 0. Now, consider Eq. 1 and imagine for the moment a uniform prior over states. In this case, the listener will infer each state s in proportion to how likely the speaker was to say \"some\" given this state. Overall, this leads to the implicature that \"some\" is unlikely to be interpreted as 3-\"some but not all.\" In contrast, when the speaker has only partial access, the calculation is more complex, involving the inferred belief distribution of the speaker. Comparing across the three panels of Fig.  2A , we see the probability of 3 is much higher when access is 1 or 2 than when it is 3. When access is 1, no implicature is predicted (the probability of 3 is approximately the same as the probability of 2); when access is 2, only a very slight implicature. Overall, we predict that incomplete speaker knowledge can cancel the standard \"some but not all\" implicature. The case of numerals (\"one,\" \"two,\" ...) is similar but more subtle. It has been argued that number words have a lower bound meaning  (Horn, 1972 ) (e.g., \"two balls are red\" means M ! 2 of the balls are red), and the intuitive, exact, meanings arise as a pragmatic implicature-\"one but not two, three, etc.\" In Fig.  2B , we show model predictions based on the lower bound semantics for number words, varying speaker's access. We see that exact meanings do arise as an inference when the speaker has complete access, but there is an interaction: Number words do not receive an exact interpretation when the speaker has incomplete knowledge. Of particular interest is the case where the speaker has seen two of three objects and says \"one\": here a partial implicature is predicted, with the probability of 3 low, but 1 and 2 high. \n Experiment 1 Because a rational speaker chooses actions based on expected utility, the rational speech-act model predicts an effect of speaker's knowledge on the listener's interpretation of \"some\" statements. We tested the predictions of the model by putting participants in the role of the listener and asking them to judge the state of the world in scenarios where perceptual access (and hence knowledgeability) of the speaker varied. \n Participants, materials, and methods Fifty participants were recruited through Amazon's Mechanical Turk crowd-sourcing service and completed the experiment for a small payment. We constructed six scenarios in which a speaker had three objects that could have (or not) a given property. The speaker then made a statement indicating the number of objects he or she had looked at and a quantified (\"some\") statement. We split each scenario into setup and speech-act phases. The setup phase named the speaker and described the objects and the relevant property. For example: Letters to Laura's company almost always have checks inside. Today Laura received 3 letters. Because our model predicts greater effects when the a priori base rate of the property is high (otherwise it is difficult to tell an implicature from an a prior belief that it is unlikely for all objects to have the property), we describe all properties as \"almost always\" holding. To make sure participants attended to the setup, we asked them to report the a priori probability that 0, 1, 2, or 3 objects had the property: How many of the 3 letters do you think have checks inside? The speech-act phase introduced a speech act in which the speaker both declared how many of the objects he or she had observed and stated that some objects had the property: Laura tells you on the phone: \"I have looked at 2 of the 3 letters. Some of the letters have checks inside.\" We then again elicited judgements about how many objects had the property: Now how many of the 3 letters do you think have checks inside? Finally, because the speech act might not be a perfect manipulation of speaker's knowledgeability (for instance, the speaker may have gained knowledge by another route), we elicited this directly: Do you think Laura knows exactly how many of the 3 letters have checks inside? Each response was given by a betting measure: Participants were instructed to divide \"$100\" among the options, betting to indicate their confidence in each option. For the first two questions, there were four options (0-3 of the objects have the property), and for the final question, there were two options (the speaker does/does not have complete knowledge). Before the experiment began, participants were given a brief warm-up, using unrelated questions, to familiarize them with the betting measure. Each scenario existed in forms varying speaker access (the number of objects the speakers had looked at) from 1 to 3. Each participant saw each access condition once, in random order, presented using randomly chosen scenarios (with no duplicate scenarios). In terms of our predictions, we have two partial-knowledge conditions (where we expect cancelation of the implicature) and one complete-knowledge \"control\" (where we expect the standard implicature). 2 \n Qualitative results There was no effect of scenario, so we collapse across this factor in all analyses. As expected based on related work  (Goodman et al., 2009) , the speaker's access statement (e.g., \"I have looked at 2 of the 3 letters\") was not a perfect manipulation of knowledgeability: In the partial access conditions, some participants judged that the speaker was likely to know exactly how many objects had the property. (The bet that the speaker had complete knowledge when access = 1 was M = 27.1, SD = 4.9; when access = 2, M = 34.8, SD = 5.7; when access = 3, M = 93.0, SD = 2.7.) As we were interested in the effects of varying knowledgeability, we initially exclude trials in which the knowledge judgement was less than 70 in the expected direction (we come back to the full data set in the quantitative analysis below). Fig.  2C  shows the mean of bets on each option, as access varied. As predicted, there was an effect of speaker's access on listener's interpretation (one-way ANOVA with bets on 3 as dependent variable, F(2, 102) = 10.18, p < .001). We next performed our preplanned comparisons to check that an implicature was drawn when the speaker had complete knowledge, but not when the speaker had partial knowledge. In the complete access condition, bets on 3 were less than bets on 2 (paired, directional t test, t(43) = À10.2, p < .001). In the partial access conditions, the implicature was canceled: Bets on 2 did not exceed bets on 3 when speaker had access to 1 object (paired, directional t test, t(31) = 0.77, p = .78) or when access was 2 (paired, directional t test, t(28) = À0.82, p = .21). If we look at just bets on 3, we see significantly lower bets in the complete access condition than the access 1 condition (unpaired, directional t test, t(47) = À4.0, p < .001) or the access 2 condition (unpaired, directional t test, t(43) = À3.5, p < .001). While there was no significant implicature in either partial-access condition, there is a slightly greater tendency toward implicature in the access 2 condition than the access 1 condition, as predicted by the model (two-way ANOVA with bet as dependent variable, and access (1 or 2) and state (2 or 3) as independent variables, F(2, 294) = 3.77, p < .05). Thus, the knowledge of the speaker affected listener's interpretation of \"some\" in the way predicted by the rational speech-act model. We examine the quantitative fit of the model below. \n Experiment 2 In Experiment 2, we tested the predictions of the rational speech-act model for interpretation of numerals. We again expect to find an effect of speaker's knowledge, but in this case, there is a more detailed interaction: The implicature should be canceled when the speaker says \"one\" after seeing only one object and when the speaker says \"two\" after seeing two objects, but it should only be partially canceled when the speaker says \"one\" after seeing two objects-this implies a fine-grained interplay between the speaker's knowledge state and the interpretation of her utterance. \n Participants, materials, and methods Fifty participants were recruited through Amazon's Mechanical Turk crowd-sourcing service and completed the experiment for a small payment. We used the same stimuli as in Experiment 1, modifying the scenarios only in the speech act: The speaker now made a statement indicating the number of objects he or she had looked at and the number that had the property. For instance: Laura tells you on the phone: \"I have looked at 2 of the 3 letters. 1 of the letters has checks inside.\" Each scenario existed in forms varying the speaker's access, from 1 to 3, and the number word the speaker used, from 1 to 3; we limited to sensible situations where the word used was no greater than the number of objects seen. Hence, we had six conditions, with access/word: 1/1, 2/1, 2/2, 3/1, 3/2, and 3/3. In terms of our predictions, we have three partial-knowledge conditions (where we expect partial or complete cancelation of the implicature) and three complete-knowledge \"controls\" (where we expect the standard implicatures). The order of scenarios and the order of conditions were randomized between participants. \n Qualitative results There was again no effect of scenario, so we collapse across this factor. As in Experiment 1, the speaker's access statement was not a perfect manipulation of knowledgeability (bets that speaker had complete knowledge in partial-access conditions: M = 42.0, SD = 3.4, in complete access conditions: M = 92.1, SD = 1.6). We once again limit to trials with the expected judgements of knowledgeability (with a threshold of 70). The mean of participants' bets are shown in Fig.  2D . To evaluate the overall effect of access, we performed an ANOVA with access and word as independent measures and bet on 3 as dependent measure. We find a main effect of access (F(2, 205) = 6.57, p < .01), an interaction between word and access (F(1,205) = 34.7, p < .001), and a main effect of word (F(2, 205) = 269.8, p < .001). We then explored the results in more detail using planned comparisons to test whether implicatures were drawn (only) when predicted. We found an implicature in the complete access conditions: When the speaker said \"two,\" bets on state 3 were less than on state 2 (paired, directional t test, t(43) = À10.2, p < .001). When the speaker said \"one,\" bets on state 1 were greater than on state 3 (paired, directional t test, t(42) = À13.1, p < .001) or state 2 (paired, directional t test, t(42) = À17.1, p < .001). In contrast, there was no implicature when access was 1 and the speaker says \"one\"-bets on 1 were not greater than on 2 (paired, directional t test, t(24) = 1.9, p = .96) or on 3 (paired, directional t test, t(24) = 3.2, p = 1.0)-and no implicature when access is 2 and the speaker says \"two\"-bets on 2 were not greater than on 3 (paired, directional t test, t(24) = 1.1, p = .87). When access is 2 and the speaker says \"one\" we found the predicted partial implicature: Bets on state 1 were significantly greater than on state 3 (paired, directional t test, t(25) = À3.9, p < .001), but not on state 2 (paired, directional t test, t(25) = 1.5, p = .92). These results again support the predictions of the rational speech-act model, showing not merely an interaction between the speaker's knowledge and the listener's tendency to draw an implicature, but a fine-grained interaction that is unlikely to result from a modular process of language understanding. In addition, these results support the standard, but controversial  (Barner & Bachrach, 2010; Huang, Snedeker, & Spelke, 2004) , view that number words have a \"lower-bound\" semantics which is only strengthened into an exact meaning by pragmatic inference. \n Quantitative model comparison To evaluate the quantitative model predictions, we first compare model predictions with mean human ratings for the subset of trials in which participants gave knowledgeability ratings in the expected direction (>70, as above). As in the model description, we assume a binomial prior distribution. We fit the prior base rate parameter and the a parameter by minimizing the root mean squared error (RMSE) of the model predictions and mean data for both experiments. The resulting model fit is RMSE = 9.01 and r = .96. The model predictions with the best-fitting parameters are shown in Fig.  2A,B  and show striking correspondence with the human data in Fig.  2C,D . To consider all responses, including those previously removed due to unexpected knowledge judgements, we extend the model by including an additional knowledge parameter: the probability that the speaker did in fact have complete knowledge (regardless of perceptual access). As we measured prior expectations and knowledgeability in each trial, we compute model predictions, trial by trial, using these values. Because the betting interface encouraged participants to round small bets to 0, but probability 0 is very different than a non-zero small probability to the model, we changed 0 and 100 bets to 1 and 99. In addition, we assumed a simple power-law relationship between subjective probability and bets (equivalent to the soft-max used to model the speaker, Eq. 2). The parameter of this power law and the speaker optimality, a, were then fit by minimizing the RMSE of mean model predictions to mean human judgements in both experiments. The resulting fit was again good: RMSE = 8.36, r = .95. Looking at individual participants, we find median correlation of r = .75 between a participant's judgements and the model predictions based on his or her prior and knowledge scores. These results suggest that the rational speech-act model is able to capture the quantitative pattern of people's judgements both across the population and within individual participants. \n Conclusion We have described a rational speech-act model of scalar implicatures and their interaction with speaker knowledge. This model formalizes language understanding as social cognition, with language-specific goals and actions, using the tools of Bayesian statistics. In addition to predicting the standard implicatures (\"some but not all\") as an inference that depends on the alternative utterances, this model predicted that these implicatures could be canceled, completely or in part, when it was common knowledge that the speaker had incomplete knowledge. Experiments 1 and 2 verified these qualitative predictions and showed tight quantitative fits with the model. The predicted interaction between interpretation and speaker's knowledge was not a peculiarity of this set of words or of scalar lexical items; instead, it follows from the general fact that rational decision makers must choose actions based on their expected utility. In contrast, a strongly modular model of implicatures would predict no such interactions. One could amend these theories  (Chierchia et al., 2011)  to allow a speaker's ignorance to affect the implicature mechanism. To predict the fine-grained interactions demonstrated for number words, additional machinery would be required, describing how the details of a speaker's knowledge state influence a listener's interpretation. In contrast, we have shown that the rational speech-act framework parsimoniously predicts these effects from high-level assumptions about the goals of listener and speaker. The rational speech-acts framework we have used here is closely related to that of game-theoretic pragmatics (J€ ager, in press), and particularly to the use of lifted games to capture epistemic effects  (Franke, 2009) . There are two principal differences of game-theoretic approaches from ours: In those approaches, it is assumed that speakers fully optimize (a ? ∞ in our framework), and that they carry out deeply recursive social reasoning-\"I think, that you think, that I think, that...\"-while we assume only one such level of reasoning. The quantitative fits we have shown suggest that limited recursion and optimization are psychologically realistic assumptions. Future work will be needed to explore all the possible models in this space. Our results support the rational speech-act framework for modeling pragmatics. More generally, they further boost the momentum building for quantitative models of language as a branch of rational social cognition. In the words of  Grice (1975) : \"One of [our] avowed aims is to see talking as a special case or variety of purposive, indeed rational, behavior...\" Fig. 2. (A and B)Model prediction for probability of each world state (number of objects with property), varying the word the speaker used and the speaker's perceptual access. The prior is assumed to be binomial with base rate 0.62, and the speaker optimality parameter is set to a = 3.4. (C and D) Mean participant bet on each world state, varying the word the speaker used and the speaker's perceptual access. Data have been filtered to include only trials where the participant's bet that the speaker had complete knowledge was greater than 70 in the expected direction. Error bars are standard error of the mean. \n\t\t\t N. D. Goodman, A. Stuhlm€ uller / Topics in Cognitive Science 5 (2013)", "date_published": "n/a", "url": "n/a", "filename": "Topics in Cognitive Science - 2013 - Goodman - Knowledge and Implicature Modeling Language Understanding as Social.tei.xml", "abstract": "Is language understanding a special case of social cognition? To help evaluate this view, we can formalize it as the rational speech-act theory: Listeners assume that speakers choose their utterances approximately optimally, and listeners interpret an utterance by using Bayesian inference to \"invert\" this model of the speaker. We apply this framework to model scalar implicature (\"some\" implies \"not all,\" and \"N\" implies \"not more than N\"). This model predicts an interaction between the speaker's knowledge state and the listener's interpretation. We test these predictions in two experiments and find good fit between model predictions and human judgments.", "id": "e560296657b8c0b88b24aa51e783427b"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Yoav Shoham", "Rob Powers", "Trond Grenager"], "title": "If multi-agent learning is the answer, what is the question?", "text": "Introduction The topic of learning in multi-agent systems, or multi-agent learning (MAL henceforth), has a long history in game theory, almost as long as the history of game theory itself.  2  As early as 1951, fictitious play  [10]  was proposed as a learning algorithm for computing equilibria in games and there have been proposals for how to evaluate the success of learning rules going back to  [23]  and  [5] . Since that time hundreds, if not thousands, of articles have been published on the topic, and at least two books (  [20]  and  [54] ). In Artificial Intelligence (AI) the history of single-agent learning is as rich if not richer, with thousands of articles, many books, and some very compelling applications in a variety of fields (for some examples see  [29, 40] , or  [50] ). While it is only in recent years that AI has branched into the multi-agent aspects of learning, it has done so with something of a vengeance. If in 2003 one could describe the AI literature on MAL by enumerating the relevant articles, today this is no longer possible. The leading conferences routinely feature articles on MAL, as do the journals.  3  While the AI literature maintains a certain flavor that distinguishes it from the game theoretic literature, the commonalities are greater than the differences. Indeed, alongside the area of mechanism design, and perhaps the computational questions surrounding solution concepts such as the Nash equilibrium, MAL is today arguably one of the most fertile interaction grounds between computer science and game theory. The MAL research in both fields has produced some inspiring results. We will not repeat them here, since we cannot be comprehensive in this article, but nothing we say subsequently should be interpreted as belittling the achievements in the area. Yet alongside these successes there are some indications that it could be useful to take a step back and ask a few basic questions about the area of MAL. One surface indication is the presence of quite a number of frustrating dead ends. For example, the AI literature attempting to extend Bellman-style single-agent reinforcement learning techniques (in particular, Q-learning  [53] ) to the multi-agent setting, has fared well in zero-sum repeated games (e.g.,  [36]  and  [38] ) as well as common-payoff (or 'team') repeated games (e.g.,  [14, 31, 52] ), but less well in general-sum stochastic games (e.g.,  [21, 26, 37] ) (for the reader unfamiliar with this line of work, we cover it briefly in Section 4). Indeed, upon close examination, it becomes clear that the very foundations of MAL could benefit from explicit discussion. What exact question or questions is MAL addressing? What are the yardsticks by which to measure answers to these questions? The present article focuses on these foundational questions. To start with the punch line, following an extensive look at the literature we have reached two conclusions: • There are several different agendas being pursued in the MAL literature. They are often left implicit and conflated; the result is that it is hard to evaluate and compare results. • We ourselves can identify and make sense of five distinct research agendas. Not all work in the field falls into one of the five agendas we identify. This is not necessarily a critique of work that doesn't; it simply means that one must identify yet other well-motivated and well defined problems addressed by that work. We expect that as a result of our throwing down the gauntlet additional such problems will be defined, but also that some past work will be re-evaluated and reconstructed. Certainly we hope that future work will always be conducted and evaluated against well-defined criteria, guided by this article and the discussion engendered by it among our colleagues in AI and game theory. In general we view this article not as a final statement but as the start of a discussion. In order to get to the punch line outlined above, we proceed as follows. In the next section we define the formal setting on which we focus. In Section 3 we illustrate why the question of learning in multi-agent settings is inherently more complex than in the single-agent setting, and why it places a stress on basic game theoretic notions. In Section 4 we provide some concrete examples of MAL approaches from both game theory and AI. This is anything but a comprehensive coverage of the area, and the selection is not a value judgment. Our intention is to anchor the discussion in something concrete for the benefit of the reader who is not familiar with the area, and-within the formal confines we discuss in Section 2-the examples span the space of MAL reasonably well. In Section 5 we identify five different agendas that we see (usually) implicit in the literature, and which we argue should be made explicit and teased apart. We end in Section 6 with a summary of the main points made in this article. A final remark is in order. The reader may find some of the material in the next three sections basic or obvious; different readers will probably find different parts so. We don't mean to insult anyone's intelligence, but we err on the side of explicitness for two reasons. First, this article is addressed to at least two different communities with somewhat different backgrounds. Second, our goal is to contribute to the clarification of foundational issues; we don't want to be guilty of vagueness ourselves. \n The formal setting We will couch our discussion in the formal setting of stochastic games (aka Markov games). Most of the MAL literature adopts this setting, and indeed most of it focuses on the even more narrow class of repeated games. Furthermore, stochastic games also generalize Markov Decision Problems (MDPs), the setting from which much of the relevant learning literature in AI originates. These are defined as follows. A stochastic game can be represented as a tuple: (N, S, A, R, T ). N is a set of agents indexed 1, . . . , n. S is a set of n-agent stage games. A = A 1 , . . . , A n , with A i the set of actions (or pure strategies) of agent i (note that we assume the agent has the same strategy space in all games; this is a notational convenience, but not a substantive restriction). R = R 1 , . . . , R n , with R i : S × A → R giving the immediate reward function of agent i for stage game S. T : S × A → Π(S) is a stochastic transition function, specifying the probability of the next stage game to be played based on the game just played and the actions taken in it. We also need to define a way for each agent to aggregate the set of immediate rewards received in each state. For finitely repeated games we can simply use the sum or average, while for infinite games the most common approaches are to use either the limit average or the sum of discounted awards ∞ t=1 δ t r t , where r t is the reward received at time t. A repeated game is a stochastic game with only one stage game, while an MDP is a stochastic game with only one agent. While most of the MAL literature lives happily in this setting, we would be remiss not to acknowledge the literature that does not. Certainly one could discuss learning in the context of extensive-form games of incomplete and/or imperfect information (cf.  [28] ). We don't dwell on those since it would distract from the main discussion, and since the lessons we draw from our setting will apply there as well. Although we will not specifically include them, we also intend our comments to apply at a general level to large population games and evolutionary models, and particularly replicator dynamics (RD)  [47]  and evolutionary stable strategies (ESS)  [49] . These are defined as follows. The replicator dynamic model assumes a population of homogeneous agents each of which continuously plays a two-player game against every other agent. Formally the setting can be expressed as a tuple (A, P 0 , R). A is the set of possible pure strategies/actions for the agents indexed 1, . . . , m. P 0 is the initial distribution of agents across possible strategies, m i=1 P 0 (i) = 1. R : A × A → R is the immediate reward function for each agent with R(a, a ) giving the reward for an agent playing strategy a against another agent playing strategy a . The population then changes proportions according to how the reward for each strategy compares to the average reward: dt (P t (a)) = P t (a)[u t (a) − u * t ], where u t (a) = a P t (a )R(a, a ) and u * t = a P t (a)u t (a). A strategy a is then defined to be an evolutionary stable strategy if and only if for some > 0 and for all other strategies a , R(a, (1 − )a + a ) > R(a , (1 − )a + a ). As the names suggest, one way to interpret these settings is as building on population genetics, that is, as representing a large population undergoing frequent pairwise interactions. An alternative interpretation however is as a repeated game between two agents, with the distribution of strategies in the population representing the agent's mixed strategy (in the homogeneous definition above the two agents have the same mixed strategy, but there exist more general definitions with more than two agents and with non-identical strategies). The second interpretation reduces the setting to the one we discuss. The first bears more discussion, and we do it briefly in Section 4. And so we stay with the framework of stochastic games. What is there to learn in these games? Here we need to be explicit about some aspects of stochastic games that were glossed over so far. Do the agents know the stochastic game, including the stage games and the transition probabilities? If not, do they at least know the specific game being played at each stage, or only the actions available to them? What do they see after each stage game has been played-only their own rewards, or also the actions played by the other agent(s)? Do they perhaps magically see the other agent(s)' mixed strategy in the stage game? And so on. In general, games may be known or not, play may be observable or not, and so on. We will focus on known, fully observable games, where the other agent's strategy (or agents' strategies) is not known a priori (though in some case there is a prior distribution over it). In our restricted setting there two possible things to learn. First, the agent can learn the opponent's (or opponents') strategy (or strategies), so that the agent can then devise a best (or at least a good) response. Alternatively, the agent can learn a strategy of his own that does well against the opponents, without explicitly learning the opponent's strategy. The first is sometimes called model-based learning, and the second modelfree learning. In broader settings there is more to learn. In particular, with unknown games, one can learn the game itself. Some will argue the restricted setting is not a true learning setting, but (a) much of the current work on MAL, particularly in game theory, takes place in this setting, and (b) the foundational issues we wish to tackle surface already here. In particular, our comments are intended to also apply to the work in the AI literature on games with unknown payoffs, work which builds on the success of learning in unknown MDPs. We will have more to say about the nature of 'learning' in the setting of stochastic games in the following sections. \n On some special characteristics of multi-agent learning Before launching into specifics, we wish to highlight the special nature of MAL. There are two messages we would like to get across, one aimed at AI researchers specifically and one more broadly. Both lessons can be gleaned from simple and well-known examples. Consider the game described in Fig.  1 . In this game the row player has a strictly dominant strategy, Down, and so seemingly there is not much more to say about this game. But now imagine a repeated version of this game. If the row player indeed repeatedly plays Down, assuming the column player is paying any attention, he (the column player) will start responding with Left, and the two will end up with a repeated (Down, Left) play. If, however, the row player starts repeatedly playing Up, and again assuming the column player is awake, he may instead start responding by playing Right, and the two players will end up with a repeated (Up, Right) play. The lesson from this is simple yet profound: In a multi-agent setting one cannot separate learning from teaching. In this example, by playing his dominated strategy, the row player taught the column player to play in a way that benefits both. Indeed, for this reason it might be more appropriate to speak more neutrally about multi-agent adaptation rather than learning. We will not fight this linguistic battle, but the point remains important, especially for computer scientists who are less accustomed to thinking about interactive considerations than game theorists. In particular, it follows there is no a priori reason to expect that machine learning techniques that have proved successful in AI for single-agent settings will also prove relevant in the multi-agent setting. The second lesson we draw from the well-known game of Rochambeau, or Rock-Paper-Scissors, given in Fig.  2 . As is well known, this zero-sum game has a unique Nash equilibrium in which each player randomizes uniformly among the three strategies. One could conclude that there is not much more to say about the game. But suppose you entered a Rochambeau tournament. Would you simply adopt the equilibrium strategy? If you did, you would not win the competition. This is no idle speculation; such competitions take place routinely. For example, starting in 2002, the World Rock Papers Scissors Society (WRPS) standardized a set of rules for international play and has overseen annual International World Championships as well as many regional and national events throughout the year. These championships have been attended by players from around the world and have attracted widespread international media attention. The winners are never equilibrium players. For example, on October 25th, 2005, 495 people entered the competition in Toronto from countries as diverse as Norway, Northern Ireland, the Cayman Islands, Australia, New Zealand and the UK. The winner was Toronto Lawyer Andrew Bergel, who beat These tournaments of course are not a perfect match with the formal model of repeated games. However, we include the example not only for entertainment value. The rules of the RPS tournaments call for 'matches' between players, each match consisting of several 'games', where a game is a single play of RPS. The early matches adopted a \"best of three of three\" format, meaning that the player who wins a best of three set garners one point and requires two points to take the match. The Semi-Finals and the Final Match used the \"best of three of five\" format, meaning that the player who wins a best of three set garners one point and requires three points to take the match. And so the competition really consisted of a series of repeated games, some of them longer than others.  4  Entertainment aside, what do we learn from this? We believe that this is a cautioning tale regarding the predictive or prescriptive role of equilibria in complex games, and in particular in repeated games. There are many examples of games with complex strategy spaces, in which equilibrium analysis plays little or no role-including familiar parlor games, or the Trading Agent Competition (TAC), a computerized trading competition.  5  The strategy space in a repeated game (or more generally a stochastic game) is immense-all mappings from past history to mixed strategies in the stage game. In such complex games it is not reasonable to expect that players contemplate the entire strategy space-their own or that of the opponent(s). Thus, (e.g., Nash) equilibria don't play here as great a predictive or prescriptive role. Our cautioning words should be viewed as countering the default blind adoption of equilibria as the driving concept in complex games, but not as a sweeping statement against the relevance of equilibria in some cases. The simpler the stage game, and the longer its repetition, the more instructive are the equilibria. Indeed, despite our example above, we do believe that if only two players play a repeated RPS game for long enough, they will tend to converge to the equilibrium strategy (this is particularly true of computer programs, that don't share the human difficulty with throwing a mental die). Even in more complex games there are examples where computer calculation of approximate equilibria within a restricted strategy space provided valuable guidance in constructing effective strategies. This includes the game of Poker (  [33]  and  [4] ), and even, as an exception to the general rule we mentioned, one program that competed in the Trading Agent Competition  [13] . Our point has only been that in the context of complex games, so-called \"bounded rationality\", or the deviation from the ideal behavior of omniscient agents, is not an esoteric phenomenon to be brushed aside. \n A (very partial) sample of MAL work To make the discussion concrete, it is useful to look at MAL work over the years. The selection that follows is representative but very partial; no value judgment or other bias are intended by this selection. The reader familiar with the literature may wish to skip to Section 4.3, where we make some general subjective comments. Unless we indicate otherwise, our examples are drawn from the special case of repeated, two-person games (as opposed to stochastic, n-player games). We do this both for ease of exposition, and because the bulk of the literature indeed focuses on this special case. We divide the coverage into three parts: techniques, results, and commentary. \n Some MAL techniques We will discuss three classes of techniques-one representative of work in game theory, one more typical of work in AI, and one that seems to have drawn equal attention from both communities. entertaining reading; of note is the restriction of the strategy space to Rock, Paper and Scissors, and explicitly ruling out others: \"Any use of Dynamite, Bird, Well, Spock, Water, Match, Fire, God, Lightning, Bomb, Texas Longhorn, or other non-sanctioned throws, will result in automatic disqualification\". The overview of the RPS society and its tournaments is adapted from the inimitable Wikipedia, the collaborative online encyclopedia, as available on January 2, 2006. Wikipedia goes on to list the champions since 2002; we note without comment that they are all male Torontonians. The results of the specific competition cited are drawn from the online edition of the Boise Weekly dated November 2, 2005. The Boise Weekly starts the piece with \"If it weren't true, we wouldn't report on it\".  5  http://tac.eecs.umich.edu. \n Model-based approaches The first approach to learning we discuss, which is common in the game theory literature, is the model-based one. It adopts the following general scheme: 1. Start with some model of the opponent's strategy. 2. Compute and play the best response. 3. Observe the opponent's play and update your model of her strategy. 4. Goto step 2. Among the earliest, and probably the best-known, instance of this scheme is fictitious play  [10] . The model is simply a count of the plays by the opponent in the past. The opponent is assumed to be playing a stationary strategy, and the observed frequencies are taken to represent the opponent's mixed strategy. Thus after five repetitions of the Rochambeau game in which the opponent played (R, S, P , R, P ), the current model of her mixed strategy is (R = 0.4, P = 0.4, S = 0.2). There exist many variants of the general scheme, for example those in which one does not play the exact best response in step 2. This is typically accomplished by assigning a probability of playing each pure strategy, assigning the best response the highest probability, but allowing some chance of playing any of the strategies. A number of proposals have been made of different ways to assign these probabilities such as smooth fictitious play  [18]  and exponential fictitious play  [19] . A more sophisticated version of the same scheme is seen in rational learning  [30] . The model is a distribution over the repeated-game strategies. One starts with some prior distribution; for example, in a repeated Rochambeau game, the prior could state that with probability 0.5 the opponent repeatedly plays the equilibrium strategy of the stage game, and, for all k > 1, with probability 2 −k she plays R k times and then reverts to the repeated equilibrium strategy. After each play, the model is updated to be the posterior obtained by Bayesian conditioning of the previous model. For instance, in our example, after the first non-R play of the opponent, the posterior places probability 1 on the repeated equilibrium play. \n Model-free approaches An entirely different approach that has been commonly pursued in the AI literature  [29] , is the model-free one, which avoids building an explicit model of the opponent's strategy. Instead, over time one learns how well one's own various possible actions fare. This work takes place under the general heading of reinforcement learning,  6  and most approaches have their roots in the Bellman equations  [3] . The basic algorithm for solving for the best policy in a known MDP starts by initializing a value function, V 0 : S → R, with a value for each state in the MDP. The value function can then be iteratively updated using the Bellman equation: V k+1 ← R(s) + γ max a s T (s, a, s )V k (s ) The optimal policy can then be obtained by selecting the action, a, at each state, s, that maximizes the expected value: s T (s, a, s )V k (s ). Much of the work in AI has focused strategies for rapid convergence, on very large MDPs, and in particular on unknown and partially observable MDPs. While this is not our focus, we do briefly discuss the unknown case, since this is where the literature leading to many of the current approaches for stochastic games originated. For MDPs with unknown reward and transition functions, the Q-learning algorithm  [53]  can be used to compute an optimal policy. Q(s, a) ← (1 − α t )Q(s, a) + α t R(s, a) + γ V (s ) V (s) ← max a∈A Q(s, a) As is well known, with certain assumptions about the way in which actions are selected at each state over time and constraints on the learning rate schedule, α t , Q-learning can be shown to converge to the optimal value function V * . The Q-learning algorithm can be extended to the multi-agent stochastic game setting by having each agent simply ignore the other agents and pretend that the environment is passive: Q i (s, a i ) ← (1 − α t )Q i (s, a i ) + α t R i (s, a) + γ V i (s ) V i (s) ← max a i ∈A i Q i (s, a i ) Several authors have tested variations of the basic Q-learning algorithm for MAL (e.g.,  [48] ). However, this approach ignores the multi-agent nature of the setting entirely. The Q-values are updated without regard for the actions selected by the other agents. While this can be justified when the opponents' distributions of actions are stationary, it can fail when an opponent may adapt its choice of actions based on the past history of the game. A first step in addressing this problem is to define the Q-values as a function of all the agents' actions: Q i (s, a) ← (1 − α)Q i (s, a) + α R i (s, a) + γ V i (s ) We are however left with the question of how to update V , given the more complex nature of the Q-values. For (by definition, two-player) zero-sum SGs, Littman suggests the minimax-Q learning algorithm, in which V is updated with the minimax of the Q values  [36] : V 1 (s) ← max P 1 ∈Π(A 1 ) min a 2 ∈A 2 a 1 ∈A 1 P 1 (a 1 )Q 1 s, (a 1 , a 2 ) Later work (such as the joint-action learners in  [14]  and the Friend-or-Foe Q algorithm in  [37] ) proposed other update rules for the Q and V functions focusing on the special case of common-payoff (or 'team') games. A stage game is common-payoff if at each outcome all agents receive the same payoff. The payoff is in general different in different outcomes, and thus the agents' problem is that of coordination; indeed these are also called games of pure coordination. The work on zero-sum and common-payoff games continues to be refined and extended (e.g.,  [8, 32, 34, 52] ). Much of this work has concentrated on provably optimal tradeoffs between exploration and exploitation in unknown, zerosum games; this is a fascinating topic, but not germane to our focus. More relevant are the most recent efforts in this line of research to extend the \"Bellman heritage\" to general-sum games (e.g., Nash-Q by  [25]  and CE-Q by  [21] ). We do not cover these for two reasons: The description is more involved, and the results have been less satisfactory; more on the latter below. \n Regret minimization approaches Our third and final example of prior work in MAL is no-regret learning. It is an interesting example for two reasons. First, it has some unique properties that distinguish it from the work above. Second, both the AI and game theory communities appear to have converged on it independently. The basic idea goes back to early work on how to evaluate the success of learning rules  [5, 23] , and has since been extended and rediscovered numerous times over the years under the names of universal consistency, no-regret learning, and the Bayes envelope (see  [16]  for an overview of this history). We will describe the algorithm proposed in  [24]  as a representative of this body of work. We start by defining the regret, r t i (a j , s i ) of agent i for playing the sequence of actions s i instead of playing action a j , given that the opponents played the sequence s −i . r t i (a j , s i |s −i ) = t k=1 R a j , s k −i − R s k i , s k −i The agent then selects each of its actions with probability proportional to max(r t i (a j , s i ), 0) at each time step t + 1. Recently, these ideas have also been adopted by researchers in the computer science community (e.g.,  [17, 27, 55] ). Note that the application of approaches based on regret minimization has been restricted to the case of repeated games. The difficulties of extending this concept to stochastic games are discussed in  [39] . \n Some typical results One sees at least three kinds of results in the literature regarding the learning algorithms presented above, and others like them. These are: 1. Convergence of the strategy profile to an (e.g., Nash) equilibrium of the stage game in self play (that is, when all agents adopt the learning procedure under consideration). 2. Successful learning of an opponent's strategy (or opponents' strategies). 3. Obtaining payoffs that exceed a specified threshold. Each of these types comes in many flavors; here are some examples. The first type is perhaps the most common in the literature, in both game theory and AI. For example, while fictitious play does not in general converge to a Nash equilibrium of the stage game, the distribution of its play can be shown to converge to an equilibrium in zero-sum games  [46] , 2 × 2 games with generic payoffs  [41] , or games that can be solved by iterated elimination of strictly dominated strategies  [42] . Similarly in AI, in  [38]  minimax-Q learning is proven to converge in the limit to the correct Q-values for any zero-sum game, guaranteeing convergence to a Nash equilibrium in self-play. This result makes the standard assumptions of infinite exploration and the conditions on learning rates used in proofs of convergence for single-agent Q-learning. Claus and Boutilier  [14]  conjecture that both single-agent Q-learners and the belief-based joint action learners they proposed converge to an equilibrium in common payoff games under the conditions of self-play and decreasing exploration, but do not offer a formal proof. Friend-or-Foe Q and Nash-Q were both shown to converge to a Nash equilibrium in a set of games that are a slight generalization on the set of zero-sum and common payoff games. Rational learning exemplifies results of the second type. The convergence shown is to correct beliefs about the opponent's repeated game strategy; thus it follows that, since each agent adopts a best response to their beliefs about the other agent, in the limit the agents will converge to a Nash equilibrium of the repeated game. This is an impressive result, but it is limited by two factors; the convergence depends on a very strong assumption of absolute continuity, and the beliefs converged to are only correct with respect to the aspects of history that are observable given the strategies of the agents. This is an involved topic, and the reader is referred to the literature for more details. The literature on no-regret learning provides an example of the third type of result, and has perhaps been the most explicit about criteria for evaluating learning rules. For example, in  [19]  two criteria are suggested. The first is that the learning rule be 'safe', which is defined as the requirement that the learning rule guarantee at least the minimax payoff of the game. (The minimax payoff is the maximum expected value a player can guarantee against any possible opponent.) The second criterion is that the rule should be 'consistent'. In order to be 'consistent', the learning rule must guarantee that it does at least as well as the best response to the empirical distribution of play when playing against an opponent whose play is governed by independent draws from a fixed distribution. They then define 'universal consistency' as the requirement that a learning rule do at least as well as the best response to the empirical distribution regardless of the actual strategy the opponent is employing (this implies both safety and consistency) and show that a modification of the fictitious play algorithm achieves this requirement. In  [20]  they strengthen their requirement by requiring that the learning rule also adapt to simple patterns in the play of its opponent. The requirement of 'universal consistency' is in fact equivalent to requiring that an algorithm exhibit no-regret, generally defined as follows, against all opponents. ∀ > 0, lim t→inf 1 t max a j ∈A i r t i (a j , s i |s −i ) < In both game theory and artificial intelligence, a large number of algorithms have been show to satisfy universal consistency or no-regret requirements. In addition, recent work  [6]  has tried to combine these criteria resulting in GIGA-WoLF, a no-regret algorithm that provably achieves convergence to a Nash equilibrium in self-play for games with two players and two actions per player. Meanwhile, the regret matching algorithm  [24]  described earlier guarantees that the empirical distributions of play converge to the set of correlated equilibria of the game. Other recent work by  [2]  has addressed concerns with only requiring guarantees about the behavior in the limit. Their algorithm is guaranteed to achieve -no-regret payoff guarantees with small polynomial bounds on time and uses only the agent's ability to observe what payoff it receives for each action. \n Some observations and questions We have so far described the work without comment; here we take a step back and ask some questions about this representative work. Our first comment concerns the settings in which the results are presented. While the learning procedures apply broadly, the results for the most part focus on self play (that is, when all agents adopt the learning procedure under consideration). They also tend to focus on games with only two agents. Why does most of the work have this particular focus? Is it technical convenience, or is learning among more than two agents, or among agents using different learning procedures, less relevant for some reason? Our second comment pertains to the nature of the results. With the exception of the work on no-regret learning, the results we described investigate convergence to equilibrium play of the stage game (albeit with various twists). Is this the pertinent yardstick? If the process (say of self play between two agents) does not converge to equilibrium play, should we be disturbed? More generally, and again with the exception of no-regret learning, the work focuses on the play to which the agents converge, not on the payoffs they obtain. Which is the right focus? No-regret learning is distinguished by its starting with criteria for successful learning, rather than a learning procedure. The question one might ask is whether the particular criteria are adequate. In particular, the requirement of consistency ignores the basic lesson regarding learning-vs.-teaching discussed in Section 3. By measuring the performance only against stationary opponents, we do not allow for the possibility of teaching opponents. Thus, for example, in an infinitely repeated Prisoners' Dilemma game, no-regret dictates the strategy of always defecting, precluding the possibility of cooperation (for example, by the mutually reinforcing Tit-For-Tat strategies). Our goal here is not to critique the existing work, but rather to shine a spotlight on the assumptions that have been made, and ask some questions that get at the basic issues addressed, questions which we feel have not been discussed as clearly and as explicitly as they deserve. In the next section we propose an organized way of thinking about these questions. \n Five distinct agendas in multi-agent learning After examining the MAL literature-the work surveyed here and much else-we have reached the conclusion that there are several distinct agendas at play, which are often left implicit and conflated. We believe that a prerequisite for success in the field is to be very explicit about the problem being addressed. We ourselves can identify five distinct possible goals of MAL research. There may well be others, but these are the ones we can identify. They each have a clear motivation and a success criterion that will allow researchers to evaluate new contributions, even if people's judgments may diverge regarding their relative importance or success to date. They can be caricatured as follows: 1. Computational 2. Descriptive 3. Normative 4. Prescriptive, cooperative 5. Prescriptive, non-cooperative We can now consider each of the five in turn. The first agenda is computational in nature. It views learning algorithms as an iterative way to compute properties of the game, such as solution concepts. As an example, fictitious play was originally proposed as a way of computing a sample Nash equilibrium for zero-sum games  [10] , and replicator dynamics has been proposed for computing a sample Nash equilibrium in symmetric games. Other adaptive procedures have been proposed more recently for computing other solution concepts (for example, computing equilibria in local-effect games  [35] ). These tend not to be the most efficient computation methods, but they do sometimes constitute quick-and-dirty methods that can easily be understood and implemented. The second agenda is descriptive-it asks how natural agents learn in the context of other learners. The goal here is to investigate formal models of learning that agree with people's behavior (typically, in laboratory experiments), or possibly with the behaviors of other agents (for example, animals or organizations). This same agenda could also be taken to apply to large-population models, if those are indeed interpreted as representing populations. This problem is clearly an important one, and when taken seriously calls for strong justification of the learning dynamics being studied. One approach is to apply the experimental methodology of the social sciences. There are several good examples of this approach in economics and game theory, for example  [15]  and  [11] . There could be other supports for studying a given learning process. For example, to the extent that one accepts the Bayesian model as at least an idealized model of human decision making, one could justify Kalai and Lehrer's model of rational learning.  7  However, it seems to us that sometimes there is a rush to investigate the convergence properties, motivated by the wish to anchor the central notion of game theory in some process, at the expense of motivating that process rigorously.  8  The centrality of equilibria in game theory underlies the third agenda we identify in MAL, which for lack of a better term we called normative, and which focuses on determining which sets of learning rules are in equilibrium with each other. More precisely, we ask which repeated-game strategies are in equilibrium; it just so happens that in repeated games, most strategies embody a learning rule of some sort. For example, we can ask whether fictitious play and Q-learning, appropriately initialized, are in equilibrium with each other in a repeated Prisoner's Dilemma game. Although one might expect that game theory purists might flock to this approach, there are very few examples of it. In fact, the only example we know originates in AI rather than game theory  [9] , and it is explicitly rejected by at least some game theorists  [18] . We consider it a legitimate normative theory. Its practicality depends on the complexity of the stage game being played and the length of play; in this connection see our discussion of the problematic role of equilibria in Section 3. The last two agendas are prescriptive; they ask how agents should learn. The first of these involves distributed control in dynamic systems. There is sometimes a need or desire to decentralize the control of a system operating in a dynamic environment, and in this case the local controllers must adapt to each other's choices. This direction, which is most naturally modeled as a repeated or stochastic common-payoff (or 'team') game, has attracted much attention in AI in recent years. Proposed approaches can be evaluated based on the value achieved by the joint policy and the resources required, whether in terms of computation, communication, or time required to learn the policy. In this case there is rarely a role for equilibrium analysis; the agents have no freedom to deviate from the prescribed algorithm. Examples of this work include  [12, 14, 22]  to name a small sample. Researchers interested in this agenda have access to a large body of existing work both within AI and other fields such as control theory and distributed computing. In our final agenda, termed 'prescriptive, non-cooperative', we ask how an agent should act to obtain high reward in the repeated (and more generally, stochastic) game. It thus retains the design stance of AI, asking how to design an optimal (or at least effective) agent for a given environment. It just so happens that this environment is characterized by the types of agents inhabiting it, agents who may do some learning of their own. The objective of this agenda is to identify effective strategies for environments of interest. An effective strategy is one that achieves a high reward in its environment, where one of the main characteristics of this environment is the selected class of possible opponents. This class of opponents should itself be motivated as being reasonable and containing opponents of interest. Convergence to an equilibrium is not a goal in and of itself. There are various possible instantiations of the term 'high reward'. One example is the no-regret line of work which we discussed. It clearly defines what it means for a reward to be high enough (namely, to exhibit no regret); we also discussed the limitations of this criterion. A more recent example, this one from AI, is  [7] . This work puts forward two criteria for any learning algorithm in a multi-agent setting:  (1)  The learning should always converge to a stationary policy, and (2) if the opponent converges to a stationary policy, the algorithm must converge to a best response. There are possible critiques of these precise criteria. They can be too weak since in many cases of interest the opponents will not converge on a stationary strategy. And they can be too strong since attaining a precise best response, without a constraint on the opponent's strategy, is not feasible. But this work, to our knowledge, marks the first time a formal criterion was put forward in AI. A third example of the last agenda is our own work in recent years. In  [45]  we define a criterion parameterized by a class of 'target opponents'; with this parameter we make three requirements of any learning algorithm: (1) (Targeted optimality) The algorithm must achieve an -optimal payoff against any 'target opponent', (2) (Safety) The algorithm must achieve at least the payoff of the security level strategy minus against any other opponent, and (3) (Autocompatibility) The algorithm must perform well in self-play (the precise technical condition is omitted here). We then demonstrate an algorithm that provably meets these criteria when the target set is the set of stationary opponents in general-sum two-player repeated games. More recent work has extended these results to handle opponents whose play is conditional on the recent history of the game  [44]  and settings with more than two players  [51] . \n Summary In this article we have made the following points: 1. Learning in MAS is conceptually, not only technically, challenging. 2. One needs to be crystal clear about the problem being addressed and the associated evaluation criteria. 3. For the field to advance one cannot simply define arbitrary learning strategies, and analyze whether the resulting dynamics converge in certain cases to a Nash equilibrium or some other solution concept of the stage game. This in and of itself is not well motivated. 4. We have identified five coherent agendas. 5. Not all work in the field falls into one of these buckets. This means that either we need more buckets, or some work needs to be revisited or reconstructed so as to be well grounded. There is one last point we would like to make, which didn't have a natural home in the previous sections, but which in our view is important. It regards evaluation methodology. We have focused throughout the article on formal criteria, and indeed believe these to be essential. However, as is well known in computer science, many algorithms that meet formal criteria fail in practice, and vice versa. And so we advocate complementing the formal evaluation with an experimental one. We ourselves have always included a comprehensive bake-off between our proposed algorithms and the other leading contenders across a broad range of games. The algorithms we coded ourselves; the games were drawn from GAMUT, an existing testbed (see  [43]  and http://gamut.stanford.edu). GAMUT is available to the community at large. It would be useful to have a learning-algorithm repository as well. To conclude, we re-emphasize the statement made at the beginning: This article is meant to be the beginning of a discussion in the field, not its end. Fig. 1 .Fig. 2 . 12 Fig. 1. Stackelberg stage game: The payoff for the row player is given first in each cell, with the payoff for the column player following. \n\t\t\t We acknowledge a simplification of history here. There is definitely MAL work in AI that predates the last few years, though the relative deluge is indeed recent. Similarly, we focus on AI since this is where most of the action is these days, but there are also other areas in computer science that feature MAL material; we mean to include that literature here as well. \n\t\t\t We do acknowledge some degree of humor in the example. The detailed rules in http://www.rpschamps.com/rules.html make for additional \n\t\t\t We note that the term is used somewhat differently in the game theory literature. \n\t\t\t Although this is beyond the scope of this article, we note that the question of whether one can justify the Bayesian approach in an interactive setting goes beyond the familiar contravening experimental data; even the axiomatic justification of the expected-utility approach does not extend naturally to the multi-agent case. 8  It has been noted that game theory is somewhat unusual in having the notion of an equilibrium without associated dynamics that give rise to the equilibrium [1] .", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0004370207000495-main.tei.xml", "abstract": "The area of learning in multi-agent systems is today one of the most fertile grounds for interaction between game theory and artificial intelligence. We focus on the foundational questions in this interdisciplinary area, and identify several distinct agendas that ought to, we argue, be separated. The goal of this article is to start a discussion in the research community that will result in firmer foundations for the area. 1", "id": "a48b18d40585ab0159fa4c7e0012a04a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum", "Ben Goertzel", "Ted G Goertzel"], "title": "How long until human-level AI? Results from an expert assessment", "text": "Introduction The field of Artificial Intelligence was founded in the mid 1950s with the aim of constructing \"thinking machines\"computer systems with human-like general intelligence, and capability equaling and eventually exceeding that of human beings. After a few initial successes, early AI researchers predicted that human-level AI would soon be achieved. In 1965, Herbert Simon predicted that \"machines will be capable, within twenty years, of doing any work that a man can do\"  [1, p.108] . Two years later, Marvin Minsky predicted that \"within a generation… few compartments of intellect will remain outside the machine's realm\"  [1, p.109 ]; see also  [2] . But the task proved recalcitrant and the failure of their optimistic timing projections was discouraging. Subsequent timing predictions became far more muted and AI research shifted focus towards producing AI systems demonstrating intelligence on specific tasks in relatively narrow domains. Much of this \"narrow AI\" research has been dramatically successful, with applications in many areas of science and industry. But one lesson learned through this work is that the magnitude of the difference between narrow, task-specific AI capability and more general, human-like intelligence (referred to throughout this paper as artificial general intelligence, or AGI) including the ability to generalize across divergent contexts and to maintain a sense of self. For most recent and contemporary AI researchers, building AI with human-like general intelligence is simply not a concrete research goal. Over the past few years, however, there has been a resurgence of research interest in the original goals of AI  [3] [4] [5] [6] [7] . This resurgence is based on the assessment that advances in computer hardware, computer science, cognitive psychology, neuroscience, and domainspecific AI put contemporary researchers in a far better position to approach these goals than were the founders of AI. Recent years have seen a growing number of special sessions, workshops, and conferences devoted specifically to topics such as human-level AI and AGI. This includes the annual Biologically Inspired Cognitive Architectures AAAI Symposium, a series of workshops on integrative cognitive architectures; the most recent is the AAAI-10: Special Track on Integrated Intelligence (II)  [8] . Another major AGI event is the international AGI conference series (AGI-08, AGI-09, AGI-10, etc.)  [9] . Some recent convocations of leading AI researchers, such as the AI@50 conference [10], the 50th Anniversary Summit of Artificial Intelligence  [11] , and the annual Singularity Summits at Stanford University, San Francisco, and New York City  [12, 13]  have also focused largely on the AGI problem. A report from AI@50 notes that these days \"much of the original optimism is back, driven by rapid progress in artificial intelligence technologies\"  [14] . Meanwhile, MIT has recently launched a 5-year initiative aimed at exploring novel approaches to creating advanced thinking machines  [15] . And noted futurist and AI inventor Ray Kurzweil has widely publicized his view that human-level AGI will be achieved within the next few decades  [16, 17]  a view recently supported by Intel Chief Technology Officer Justin Rattner  [18] . We summarize these recent trends as a resurgence in \"AI optimism\", whereby \"optimism\" in this context we mean specifically \"timing optimism\". Timing optimism is of course not the same as optimism about the beneficial effects of human-level AGI. One can be optimistic that AGI will be achieved soon, but pessimistic that the consequences of AGI will be harmful. Likewise, one can be pessimistic that AGI will not be achieved soon, but optimistic that the consequences of AGI will be beneficial, whenever AGI is achieved. Of course, many in the field are less optimistic about the timing of human-level AGI. Not all experts believe that the time is ripe for a return to the original goals. Craig Silverstein of Google (a company that carries out a huge amount of narrow-AI research under the supervision of AI guru Peter Norvig) recently told a reporter that such computers are \"hundreds of years away\"  [19] . Mark Andreesen, the founder of Netscape, said that \"we are no closer to a computer that thinks like a human than we were fifty years ago\"  [19] . Some AI researchers, such as Selmer Bringsjord (chair of RPI's Department of Cognitive Science) even doubt that computers will ever display humanlike intelligence  [20] . And the standard university AI curriculum continues to focus almost entirely on narrow AI, with only passing reference to the field's original grand goals. While AI experts with less optimistic views on timing rarely take the time to elaborate the reasons for their views, several relevant perspectives are well articulated in the literature. Hubert Dreyfus's classic critique of AI  [21, 22]  and John Searle's perspective of \"biological naturalism\"  [23]  both argue that achieving human-like intelligence would require human-like physical embodiment and social context. Philosopher William Hurlbut  [24]  argues that (very roughly speaking) human mind emerges from human brain according to patterns and processes too complex for humans to fully understand anytime in the foreseeable future. Roger Penrose  [25]  and Stuart Hameroff  [26]  believe that human intelligence relies on quantum or quantum gravity phenomena that don't exist in ordinary digital computers. Finally, some experts may believe that there is no fundamental barrier to creating human-level AGI on digital computers, but that it's simply a very hard problem which would require one or more radical breakthroughs so far beyond current understanding that they will probably take the AI community many centuries to solve. Anecdotally, based on conversations with survey participants and others at AGI-09, our impression is that many AI researchers who are timing pessimists don't have any highly specific objection to AGI optimism in mind, but rather feel that there is a large amount of uncertainty involved so that there are probably many large \"hidden rocks\" along the path to human-level AGI, which might or might not prove insurmountable. If the path to AGI is laden with unforeseen obstacles, then there may be no way to predict when or if the requisite scientific breakthrough might occur. On the other hand, AGI timing optimists generally believe that human-level intelligence is a straightforward although complex \"mechanical\" process that can be understood by extending today's scientific ideas. If this is correct, then it is reasonable to consider detailed projections regarding how much time will pass until human-level AGI is built. One issue on which there is minimal disagreement is that achievement of AGI would have a radically transformative effect on multiple aspects of science, industry, commerce, government, and arts. In the most extreme case, an intelligence explosion would ensue in which initial AGIs would design and build ever-smarter AGIs, leaving humans in the dust. In this eventuality, superintelligent AGIs might use their vast intelligence to either solve a great many of humanity's problems or to destroy (perhaps inadvertently) their human creators  [27] . But whether the results are good or bad, the achievement of human-level AGI would be among the most important events in human history. It is thus of considerable importance and interest to make the best estimates possible of when and how AGI milestones may occur. Unfortunately, the database for making such estimates is quite limited. We can extrapolate hardware trends such as Moore's Law into the future, but there is no guarantee that these trends will persist, or that the requisite software will accompany them. Nor is it certain that hardware equivalent to the wetware in the human brain will be necessary or sufficient for human-level AI. There may be software paradigms that will permit human-level AGI on sub-human-level hardware, or perhaps more advanced hardware will be required for some reason. Given the limitations of hardware and software data, expert opinion can be an important information source for our understanding of AGI. Expert opinion refers simply to the views and estimates of people who have exceptional knowledge about some topic, in this case AGI. Expert opinion, if carefully elicited, can yield meaningful insights on what is and isn't known about likely developments in a range of phenomena, including AGI. Expert assessment is a particularly insightful methodology whenas is the case with AGIexperts lack consensus on important parameters. We are aware of only two previous studies explicitly exploring expert opinion on the future of AGI. In 2006, a seven-question poll was taken of participants at the AI@50 conference  [28] . Four of the seven questions are particularly relevant. Asked \"when will computers be able to simulate every aspect of human intelligence?\", 41% said \"More than 50 years\" and 41% said \"Never\". Thus approximately 80% of the participants at the conference were AI \"timing pessimists\" and 20% were \"timing optimists\". Seventynine percent said that an accurate model of thinking is impossible without further discoveries about brain functioning. Sixty percent of the participants strongly agreed that \"AI should take a multidisciplinary approach, incorporating stats, machine learning, linguistics, computer science, cognitive psychology, philosophy, and biology\". Finally, 71% said that \"statistical/ probabilistic methods are most accurate in representing how the brain works\". The other survey, taken in 2007 by futurist entrepreneur Bruce Klein  [29] , was an online survey that garnered 888 responses, asking one question: \"When will AI surpass human-level intelligence?\" Most of those who chose to respond to this survey were AI \"optimists\" who believed that human-level artificial intelligence would be achieved during the next half century. The distribution of responses is reproduced in Fig.  1 . While the results show that a substantial number of optimists exist, Klein's study has several important limitations. First, the sample population is broad, containing many non-experts. Second, the study only asks for point estimates for when superhuman AI will occur, neglecting any uncertainty in study participants' beliefs. Finally, the study only asked one question, despite the plethora of other important aspects of AGI. The AI@50 and Klein studies are interesting because they show that significant numbers of experts and interested persons believe that AGI with intelligence at least equaling the human level will exist within upcoming decades. The current study probes more deeply into the thinking of people with substantial AGI expertise. Many (though not all) of these experts can be classified as timing optimists. While their views are not representative of the larger population of AI experts, they are nonetheless worth considering. In many cases, these experts are working seriously on AGI because they believe there is a strong likelihood of achieving success with the fundamental theoretical and hardware tools at hand or likely to be developed in the next few decades. This study is based on an expert assessment survey distributed to attendees of the Artificial General Intelligence 2009 (AGI-09) conference  [30] . This was a gathering of AI researchers and other individuals interested specifically in pursuing theoretical or practical work on AGI. The survey covered the timing of AGI milestones, the effectiveness of various technical approaches to achieving AI, the potential for AGI to help or harm humanity, and the possibility of an AI being conscious. \n Methods Expert assessments have been used for several decades to provide timely information and aid decision making. Expert assessments have been used in the highest levels of study, including the United Nations-sponsored Intergovernmental Panel on Climate Change  [31] . A range of assessment methods exist  [32] [33] [34] . There is no single optimal methodology for assessing a group of experts. Each assessment should be customized to meet the questions of the research, the abilities of the experts, and any other relevant factors. Our study draws heavily on recent expert elicitation methodology that emphasizes highlighting the diversity of expert opinion instead of reaching consensus  [34, p.146-154] . While this expert elicitation has been used primarily for estimation of static parameter values, it has also been used for several technological forecasting study  [35] [36] [37] [38] . Our study used a two-part survey. The first part is a standardized survey instrument distributed at the AGI-09 conference. This survey is adapted from previous expert elicitation surveys, in particular  [39] . It features primarily quantitative questions. Many expert elicitation studies only use a survey along these lines. However, we felt that our quantitative survey results would be insightfully complemented by qualitative follow-up questions. So, the second part of our survey consists of follow-up questions customized for each survey participant and distributed to participants via email. Unlike follow-up questions used in Delphi studies, ours were focused on clarifying and expanding original survey responses instead of working towards consensus. These follow-up questions give us a richer understanding of the meanings and reasons behind the quantitative responses given in the initial survey. \n Initial survey The initial survey was in a single standardized form printed across 18 pages for each of the survey participants. Participants reported spending an average of 28 min on the survey. All questions were quantitative, closed-ended questions, asking for numbers or binary true/false or yes/no answers. However, participants were encouraged to write any clarifying or other relevant remarks anywhere on the survey instrument; most participants took advantage of this option. The full survey instrument that we used for our investigation is available online  [40] . Here we briefly summarize the most important questions that were posed. Extensive empirical research shows that experts and non-experts alike tend to be overconfident in their probability estimates  [34] . In rough terms, this means that for any given parameter, individuals tend to underestimate the probability that the actual value of the parameter is quite different from their best guess estimate. For example, someone might estimate that there is a 90% chance of the parameter values being within some range when that the actual values are within the range only 50% of the time. Our survey took several steps to reduce this overconfidence bias. Before any technical questions were asked, the survey explained overconfidence so as to sensitize participants to be cautious about it when answering questions. Additionally, some questions were worded so as to reduce overconfidence. The first set of questions elicited experts' beliefs about when AI would reach each of four milestones: passing the Turing test, 1 performing Nobel quality work, passing third grade, and becoming superhuman. These specific milestones were selected to span a variety of levels of advanced general intelligence. For each milestone, two question versions were askedwith and without additional fundingmaking for eight total milestone questions. These two versions explore the possibility that when the milestones are reached depends on the resources available to researchers. The amount of additional funding listed, $100 billion per year, is obviously more than could be used for AGI research; the intent with this figure is to ensure that money would not be a scarce resource in this hypothetical AGI development scenario. For each of the eight milestone questions, we asked the respondents to give us estimates representing 10%, 25%, 75%, and 90% confidence intervals, as well as their best estimate dates. The 10% point represents the date in which the expert estimates that there is a 10% chance that the milestone will have been achieved, and so on. We asked experts to estimate the 10% and 90% intervals first in order to reduce overconfidence. Collectively, the five points correspond at least roughly with points on participants' probability density functions for the uncertain milestone achievement dates. The five point approach represents a trade-off between gaining deeper insight into experts' beliefs and demanding more detail from the experts. Subsequent questions requested only single point estimates instead of multiple points on a probability density function. This choice was made to keep the overall survey instrument relatively short. The subsequent questions covered four topics. Three questions asked what embodiment the first AGIs would have: physical or virtual robot bodies or a minimal text-or voice-only embodiment. Eight questions asked what AI software paradigm the first AGIs would be based on: formal neural networks, probability theory, uncertain logic, evolutionary learning, a large hand-coded knowledge-base, mathematical theory, nonlinear dynamical systems, or an integrative design combining multiple paradigms. Three questions asked the likelihood of a strongly negative-to-humanity outcome if the first AGIs were created by: an open-source project, the US military, or a private for-profit software company. Two true/false questions asked if quantum computing or hypercomputing would be required for AGI. Two yes/ no questions asked if AGIs emulating the human brain conceptually or near-exactly would be conscious in the sense that humans are. Finally, 14 questions asked experts to evaluate their own expertise in several subjects: cognitive science, neural networks, probability theory, uncertain logic, expert systems, theories of ethics, evolutionary learning, quantum theory, quantum gravity theory, robotics, virtual worlds, software engineering, computer hardware design, and cognitive neuroscience. \n Follow-up questions After analyzing results of the initial survey, we wrote and distributed follow-up questions customized for each participant. Whereas the initial survey consisted entirely of quantitative, closed-ended questions, the follow-up questions were all qualitative, open-ended questions, asking for prose explanations and clarifications of their initial survey responses. Participants received between two and six questions. While the initial survey responses raised a large number of issues we were interested in following up on, we chose only the most important questions so as to minimize the burden on survey participants' time. \n Study participants Participants were recruited at the AGI-09 conference. Due to the highly specialized nature of the AGI-09 conference, no conference attendees were excluded. Participants thus have a range of levels of expertise, from graduate students to senior researchers. This inclusive approach risked eliciting low-quality responses from non-experts who happen to be at the conference. On the other hand, more exclusive approaches risk missing important ideas or information and also risk biasing results in certain directions. All of the participants in our study displayed a depth of thinking demonstrative of significant AGI expertise. Twenty-one people participated in the study. Nineteen people completed the initial survey at the AGI-09 conference; two completed it later, submitting it via postal mail. Also, 18 people (including both of those who submitted via postal mail) completed the follow-up questions. Such levels of participation are common for expert elicitationone recent study  [38]  had just 7 experts; another study  [41]  had just 12 experts. While a larger number of participants may bring additional information, our participant group is very much adequate to yield meaningful insights. It should be emphasized here that the purpose of our study is ultimately to gain insight about AGI itself, not about AGI experts. Thus our sample of AGI experts must provide rich insights about AGI, but it does not need to be in some way representative of the broader population of AGI experts. After all, there is no guarantee that an accurate assessment of the opinions of the broader on AGI population correlates with the realities of AGI. It is entirely possible that the deepest insights about AGI come from outliers from the broader population of experts. Indeed, the very existence of disagreement among experts is grounds for reflection on the state of our knowledge. As our results make clear, our sample succeeds quite well at providing rich insight about AGI. While we believe our sample to be at least somewhat representative of the broader AGI expert population, this is of secondary importance. Study participants have a broad range of backgrounds and experience, all with significant prior thinking about AGI. Eleven are in academia, including six Ph.D. students, four faculty members, and one visiting scholar, all in AI or allied fields. Three lead research at independent AI research organizations and three do the same at information technology organizations. Two are researchers at major corporations. One holds a high-level administrative position at a relevant non-profit organization. One is a patent attorney. All but four participants reported being actively engaged in conducting AI research. We are not listing the names of participating experts for several reasons. First, prior expert assessments vary in their approach to anonymity. Many studies do not list experts' names at all (e.g.  [42, 43] ). Many other studies list experts' names but do not link specific names to specific responses (e.g.  [35] [36] [37] [38] [39] 41] ). Second, due to the sensitive nature of AGI, several of our experts requested that their names not be listed. The others participated on the condition that their names not be linked to their responses. Listing experts' names and discussing results in this way could enable some readers to link specific names to specific responses. \n Results Although the majority of the experts who participated in our study were clearly AGI timing optimists, there was a significant minority of timing pessimists. While we don't know how the views of study participants compare to those of the rest of the conference attendees, it seems unsurprising to find an optimist majority at an AGI conference. Most AGI pessimists may see little reason to bother attending an AGI conference, although this is not universalsome known AGI pessimists do regularly attend AGI conferences. Finally, all experts in our study, including those who could be classified as timing pessimists, gave at least a 10% chance of some AI milestones being achieved within a few decades. Additionally, the amount of agreement between the experts varied considerably from one question to another. On several questions, experts disagreed stronglymore so than is typically found in expert assessmentsindicating a lack of professional consensus and the presence of multiple competing mental models of the future of AGI. Meanwhile, on other questions, much more agreement existed, though rarely full consensus. \n Milestone timing without additional funding Much of the initial survey and follow-up questions focused on the timing of four AI milestones: passing the Turing test, performing Nobel-quality research, passing the third grade, and gaining dramatically superhuman capabilities. The range of the best guess estimates given for these milestones without massive additional funding is summarized in Fig.  2 . This figure clearly shows the dichotomy between timing optimists and timing pessimists. It also shows that a substantial number of AGI experts expect that key milestones will be reached within upcoming decades. The overlap in the best guess estimates for the milestones was surprising. Using human cognitive development as a model, one might think that being able to do Nobel level science would take much longer than being able to conduct a social conversation, as in the Turing test. It is true that many complex problems can be solved effectively by artificial expert systems. But performing Nobel level science requires more than just complex problem solving: it also requires creativity in the formulation of new research questions and ideas, something that expert systems cannot achieve. Thus we might expect that performing Nobel level science would be more difficult than passing the Turing test. However, some experts thought it would be quite different for an AGI. One expert observed that \"making an AGI capable of doing powerful and creative thinking is probably easier than making one that imitates the many, complex behaviors of a human mindmany of which would actually be hindrances when it comes to creating Nobel-quality science\". This expert observed that \"humans tend to have minds that bore easily, wonder [sic] away from a given mental task, and that care about things such as sexual attraction, all [of] which would probably impede scientific ability, rather that promote it\". To successfully emulate a human, a computer might have to disguise many of its abilities, masquerading as being less intelligent, in certain ways, than it actually was. This is one reason that the Turing test milestone might be reached later than the Nobel-quality science milestone. We computed median estimates for each milestone (Table  1 ). The medians would be only slightly lower if these less optimistic respondents were excluded from the analysis. Medians were used, instead of means, because these are less susceptible to distortion via statistical outliers.  2   \n Milestone estimates with massive new funding Another interesting result concerns the role of fundingthe predicted impact on the AGI field of a hypothetical $100 billion per year funding infusion. The range of the best guess estimates given for these milestones with massive additional funding is summarized in Fig.  3 . Most experts estimated that a massive funding increase of this nature would cause the AI milestones to be reached sooner. However, for many of these experts, the difference in milestone timing with and without massive funding was quite smalljust a few years. Furthermore, several experts estimated that massive funding would actually cause the AI milestones to be reached later. One reason given for this is that with so much funding, \"many scholars would focus on making money and administration\" instead of on research. Another reason given is that \"massive funding increases corruption in a field and its oppression of dissenting views in the long term\". Of those who thought that funding would make little difference, a common reason was that AGI progress requires theoretical breakthroughs from just a few dedicated, capable researchers, something that does not depend on massive funding. Another common reason was that the funding would not be wisely targeted. Several noted that funding could be distributed better if there was a better understanding of what paradigms could produce AGI, but such an understanding is either not presently available or not likely to be understood by those who would distribute funds. Because of the lack of agreement on a single paradigm, several experts recommended that modest amounts of funding should be distributed to a variety of groups following different approaches, instead of large amounts of funding being given to a \"Manhattan Project\" type crash program following one approach. Only one expert recommended concentrating funds in a fewer number of groups. Similarly, several observed that well-funded efforts guided by a single paradigm had failed in the past, including the Japanese Fifth Generation Computer Systems project. While most experts did not address the question of how to distribute funds across groups, our initial impression is that there would be some consensus for distributing funds to a larger variety of groups. This result could have major implications for how available funds are to be allocated. Several experts gave technical reasons for why funding would not have a significant impact. On this, one said, \"AGI requires more theoretical study than real investment.\" Another said, \"I believe the development of AGI's to be more of a tool and evolutionary problem than simply a funding problem. AGI's will be built upon tools that have been developed from previous tools. This evolution in tools will take time. Even with a crash project and massive funding, these tools will still need time to develop and mature.\" Given that these experts are precisely those who would benefit most from increased funding, their skeptical views of the impact of hypothetical massive funding are very likely sincere. \n Milestone timing: estimates of certainty Since we do not know for sure when milestones will be reached, it is helpful to characterize the uncertainty about this. Some insights can be gained from considering the distributions of best guess estimates of experts (as in Figs.  2 and 3 ) or of broader populations (as in Fig.  1 ). However, each individual has uncertainty about his/her own estimates. These uncertainties are not found from presentations of best guess estimates, but they can be found from the estimates across the range of confidence intervals elicited in our survey. Participants showed a broad range of certainty levels in their timing estimates. Several participants showed little uncertainty, indicating that they believed it was very likely that milestones would be achieved within a narrow range of dates. The participants giving the narrowest ranges were all strong timing optimists. Meanwhile, many of the participants showed much uncertainty. Some of these individuals gave substantial probabilities for both early and late milestone achievement dates. For these individuals, the timing optimist/pessimist dichotomy does not readily apply. Other individuals showing much uncertainty could be classified as timing pessimists in that they considered it most likely that milestones would be achieved much later. The fact that these individuals are not certain about their pessimism could explain why they thought that attending a conference on AGI would be worthwhile. One expert estimated that there was at least a 25% chance that the Turing test would never be achieved, but he also thought that there was a 10% chance that it would be achieved by the year 2020. Another estimated that there was a 25% chance it would not be achieved until the year 3000, but that there was a 10% chance it would happen by 2050. The stronger optimists at the conference were much more certain of their opinions. One estimated that there was a 90% chance that the Turing test would be achieved by 2016 and a 10% chance that it would be achieved as soon as 2010. The range of variation in the estimates for the four milestones without massive additional funding is shown in Fig.  4 . Dates after 2100 are removed to improve resolution in the rest of the plots. There was substantial agreement among the more optimistic participants in the study. Most thought that there was a substantial likelihood that the various milestones would be passed sometime between 2020 and 2040. Sixteen experts gave a date before 2050 as their best estimate for when the Turing test would be passed. Thirteen experts gave a date between 2020 and 2060 as their best estimate for when superhuman AI would be achieved. (The others all estimated later dates, ranging from 2100 to never.) The opinions of the optimists were similar to or perhaps somewhat more optimistic than Kurzweil's well-known projections. As noted above, optimism in this sense is about the timing of AI milestones. It does not imply a belief that achieving AGI would be a good thing. To the contrary, one can be optimistic that AGI will happen soon yet believe that AGI would have negative outcomes. Indeed, several experts reported this pair of beliefs. Results about the likelihood of negative outcomes are discussed further below. \n Milestone order There was little agreement among experts on the order in which the four milestones (Turing test; third grade; Nobel; and superhuman) would be achieved. The only area of consensus was that the superhuman milestone would be achieved either last or at the same time as other milestones. Meanwhile, there was significant divergence regarding the order of the other three milestones. One expert argued that the Nobel milestone would be easier precisely because it is more sophisticated: to pass the Turing test, an AI must \"skillfully hide such mental superiorities\". Another argued that a Turing test-passing AI needs the same types of intelligence as a Nobel AI \"but additionally needs to fake a lot of human idiosyncrasies (irrationality, imperfection, emotions)\". Finally, one expert noted that the third grade AI might come first because passing a third grade exam might be achieved \"by advances in natural language processing, without actually creating an AI as intelligent as a third-grade child\". This diversity of views on milestone order suggests a rich, multidimensional understanding of intelligence. It may be that a range of milestone orderings are possible, depending on how AI development proceeds. The milestone order results highlight the fact that many experts do not consider it likely that the first human-level AGI systems will closely mimic human intelligence. Analogy to human intelligence would suggest that achieving an AGI capable of Nobel level science would take much longer than achieving an AGI capable of conducting a social conversation. However, as discussed above, an AGI would not necessarily mimic human intelligence. This could enable it to achieve the intelligence milestones in other orders. \n Technical approaches Our initial survey asked about eight technical approaches used in constructing AI systems: formal neural networks, probability theory, uncertain logic, evolutionary learning, a large hand-coded knowledge-base, mathematical theory, nonlinear dynamical systems, and integrative designs combining multiple paradigms. For each, it requested a point estimate of the odds that the approach would be critical in the creation of human-level AGI. They survey also asked about the odds that physical robotics, virtual agent control, or minimal text-or voice-based embodiments would play a critical role.  The most striking finding in this section was a strong majority opinion in favor of integrative designs. Of the 18 respondents who answered this question, 13 gave a probability of 0.5 or greater; the mean response across all 18 was 0.63.  3  None of the specific technical approaches mentioned received strong support from any more than a small plurality of respondents. Probability theory received the strongest support, with a mean probability of 0.35 and with 7 out of 20 respondents answering the question giving a probability of 0.5 or greater. The question about robotics vs. other forms of embodiment received a range of responses (Fig.  5 ). There were responses of 0.9, 0.94, 0.89, and 0.60 for physical robot embodiment, but the mean response was only 0.28. The handful of participants who felt robotics was crucial were all relatively optimistic, as seen by their mean date of 2034 for the Turing test without massive additional funding. The virtual agents option received a similar but considerably less strong response, with top responses of 0.80, 0.65, and 0.60 and a mean response of 0.34. While some of the virtual worlds enthusiasts were optimistic about timing, this was much less of a strong pattern than in the robotics case. The preliminary impression one obtains is that a few researchers are highly bullish on robotics as the correct path to AGI in the relatively near term, whereas the rest feel robotics is probably not necessary for AGI. Meanwhile, a larger number of researchers are moderately optimistic about the role of virtual worlds for AGI, but with milder opinions about the importance of the approach. \n Impacts of AGI In science fiction, intelligent computers frequently become dangerous competitors to humanity, sometimes even seeking to exterminate humanity as an inferior life form. Several researchers have recently expressed similar concerns  [27, 44] . Motivated by these concerns, we asked experts to estimate the probability of a negative-to-humanity outcome occurring if an AGI passes the Turing test. Our question was broken into three parts, for each of three possible development scenarios: if the first AGI that can pass the Turing test is created by an open source project, by the United States military, or by a private company focused on commercial profit. This set of questions marked another instance in which the experts lacked consensus (see Fig.  6 ). Five experts estimated a less than 20% chance of a negative outcome, regardless of the development scenario. Four experts estimated a greater than 60% chance of a negative outcome, regardless of the development scenario. Only four experts gave the same estimate for all three development scenarios. Finally, several experts were more concerned about the risk from AGI itself, whereas others were more concerned that AGI could be misused by humans who controlled it. Interesting insights can be found in the experts' orderings of the riskiness of the development scenarios. Of the 11 experts who gave different estimates for each of the three scenarios, 10 gave the private company scenario the middle value. Of these 10, 6 gave the US military scenario the highest value and 4 gave it the lowest value. Thus the open source scenario and the US military scenario tend to perceived as relatively safe or relatively dangerous, but experts are divided on which is which. Experts who estimated that the US military scenario is relatively safe noted that the US military faces strong moral constraints, has experience handling security issues, and is very reluctant to develop technologies that may backfire (such as biological weapons), whereas open source development lacks these features and cannot easily prevent the \"deliberate insertion of malicious code\". In contrast,  3  In this section the survey did not require that the probabilities all add up to one, because the technical approaches are not necessarily mutually exclusive. When the numbers are normalized such that each participant's set of probabilities add up to one, then only 2 experts give integrated design a probability of 0.5 or greater, but 12 still rank it the most likely, including 1 who gave the highest probability to \"none of the above\". After normalization, the average for integrated design is 0.32; all other approaches ranged 6% (mathematical theory) and 12% (probability theory). Several experts noted potential impacts of AGI other than the catastrophic. One predicted that \"in thirty years, it is likely that virtually all the intellectual work that is done by trained human beings such as doctors, lawyers, scientists, or programmers, can be done by computers for pennies an hour. It is also likely that with AGI the cost of capable robots will drop, drastically decreasing the value of physical labor. Thus, AGI is likely to eliminate almost all of today's decently paying jobs.\" This would be disruptive, but not necessarily bad. Another expert thought that, \"societies could accept and promote the idea that AGI is mankind's greatest invention, providing great wealth, great health, and early access to a long and pleasant retirement for everyone.\" Indeed, the experts' comments suggested that the potential for this sort of positive outcome is a core motivator for much AGI research. \n Conclusion Despite decades of setbacks, the development of AI with the general intelligence of humans remains an important possibility both for the AI research community and for society at large. Given the paucity of hardware and software data enabling detailed extrapolations regarding the future of such AI, expert opinion is an important source of information. In this article, we have presented the most careful assessment of expert opinion on AGI to date. Given the long history of AI researchers making erroneous predictions, our results must be interpreted cautiously, but they nonetheless add much to our understanding of the future of AGI. In the broadest of terms, our results on AGI timing concur with those of the two previous studies mentioned in the Introduction  [28, 29] . All three studies suggest that significant numbers of interested, informed individuals believe it is likely that AGI at the human level or beyond will occur around the middle of this century, and plausibly even sooner. Due to the greater depth of the questions, our survey also revealed some interesting additional information, such as the disagreement among experts over the likely order of AGI milestones and the relative safety of different AGI development scenarios. The experts' suggestions regarding funding (in particular, skepticism about the importance of funding and a preference for distributing funds among a broad range of research groups) are also potentially valuable. Our results reinforce the idea that there is a significant likelihood of AGI being achieved within upcoming decades. This idea has profound societal implications given the strong potential for AGI to act as a transformative agent, either to massively help humanity or to destroy it. The experts in our study, like others who have commented on the issue, were divided on whether the impacts of AGI would be positive or negative for humanity. Our results add depth to our understanding of AGI impacts by exploring multiple development scenarios. However, the jury remains out regarding how to achieve positive outcomes and avoid negative outcomes. This is a crucial area for future research. Currently, AGI experts hold a rich diversity of views, a situation which challenges our ability to make confident predictions about the future of AGI, but is not surprising given the state of development of the field. It would be interesting to carry out similar studies in future and see how expert views evolve and converge or diverge as AI technology advances. Participants are displayed in the same order as in Fig.  4 , such that Participant 1 in Fig.  6  is the same person as Participant 1 in Fig.  4 . Fig. 1 . 1 Fig.1. Results from the survey taken by Klein [29]  in 2007 asking the question \"When will AI surpass human-level intelligence?\". \n Fig. 2 . 2 Fig. 2. Milestone best estimate guesses without massive additional funding. Estimates are for when AI would achieve four milestones: the Turing test (horizontal lines), third grade (white), Nobel-quality work (black), and superhuman capability (grey). \n Fig. 3 . 3 Fig. 3. Milestone best estimate guesses with massive additional funding. Estimates are for when AI would achieve four milestones: the Turing test (horizontal lines), third grade (white), Nobel-quality work (black), and superhuman capability (grey). \n Fig. 4 . 4 Fig. 4. Estimates for when AI would achieve four milestones without massive additional funding. Estimates are given at five confidence intervals. Asterisks represent 10% and 90% confidence bounds. Horizontal lines represent 25% and 75% confidence bounds. Diamonds represent best guess estimates. In each plot, participants are ordered by their Turing test best guess estimates. \n Fig. 5 . 5 Fig.5. Number of respondents for different embodiment approaches. Respondents are grouped into probability intervals for each of three different embodiment approaches: physical robot (black), virtual agent (white), and minimal embodiment (grey). Intervals are labeled on the horizontal axis by their lower bound. For example, the interval labeled \"0.1\" represents the interval 0.1 through 0.199. \n Fig. 6 . 6 Fig. 6. Probability of a negative-to-humanity outcome for different development scenarios. The three development scenarios are if the first AGI that can pass the Turing test is created by an open source project (x's), the United States military (squares), or a private company focused on commercial profit (triangles).Participants are displayed in the same order as in Fig.4, such that Participant 1 in Fig.6is the same person as Participant 1 in Fig.4. \n Table 1 1 Median estimates for each AGI milestone at each level of confidence. Milestone 10% 25% 50% 75% 90% Turing test 2020 2030 2040 2050 2075 Nobel science 2020 2030 2045 2080 2100 Third grade 2020 2025 2030 2045 2075 Superhuman 2025 2035 2045 2080 2100 \n\t\t\t Participants expressed concern that the Turing test milestone is ambiguous, due to the numerous variations of the test. In response to this, several participants specified the Turing test variant their responses are based on. At the time of survey distribution, a verbal suggestion was given to consider the \"one hour\" rather than the \"five minute\" Turing test as some potential participants felt the latter could too easily be \"gamed\" by narrow-AI chatbots without significant general intelligence. \n\t\t\t In this case, the sample size is so small that it's hard to rigorously speak about \"outliers,\" but it's clear qualitatively that the very long estimates given by some experts, including those who thought that AGI might never be achieved, would have a disproportionate effect upon the means.", "date_published": "n/a", "url": "n/a", "filename": "1-s2.0-S0040162510002106-main.tei.xml", "abstract": "The development of human-level AI has been a core goal of the AI field since its inception, though at present it occupies only a fraction of the field's efforts. To help understand the viability of this goal, this article presents an assessment of expert opinions regarding humanlevel AI research conducted at AGI-09, a conference for this AI specialty. We found that various experts strongly disagree with each other on certain matters, such as timing and ordering of key milestones. However, we did find that most experts expect human-level AI to be reached within upcoming decades, and all experts give at least some chance that some milestones will be reached within this time. Furthermore, a majority of experts surveyed favor an integrative approach to human-level AI rather than an approach centered on a particular technique. Finally, experts are skeptical about the impact of massive research funding, especially if it is concentrated in relatively few approaches. These results suggest that the possibility of achieving human-level AI in the near term should be given serious consideration.", "id": "3567c66f3635f30ccb4744b65af694d5"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Vael Gates", "Thomas L Griffiths", "Anca D Dragan"], "title": "How to Be Helpful to Multiple People at Once", "text": "Introduction Consider a schoolteacher trying to plan a field trip. Some students learn best kinetically, others enjoy verbal challenges, and some would be overwhelmed by new locations. If there is no one action that will maximally satisfy everyone, what is the teacher to do? Now consider a concerned citizen determining how to donate their money. They furrows their brow, staring at the screen: donate to the most needy, the organization where donations will be matched, or the recipient with the tightest time constraints? Next consider a high-level government worker, puzzling over who to prioritize, faced with an array of programs that will benefit everyone to some extent but some more than others. Finally consider an autonomous household robot, trying to determine what to make for the main family meal with one kid who only wants to eat orange foods and one parent who is vegan. What should all of these decision-makers do? In today's society, as preference-aggregation problems become more complex, we can turn to tools from computer science to address them. If modern artificial intelligence systems know about the preferences of their recipients, they can use vast computational resources to optimize: airplane scheduling and ride-share services are examples of using artificial intelligence to optimize many people's preferences. However, these consumer services optimize based on the principles of first-come-first-serve, more resources for more money, and efficiency. Individuals put in a bid and they receive some service. But in other types of situations, people advocate for others rather than themselves. People choose which organizations to donate money towards, and governments strive to serve their entire populations with aid programs. These situations are just as complex and deserving of computational analysis, but they will need a different optimization procedure: one that likely incorporates fairness. To develop artificial intelligence tools to help solve coordination problems, we need to know what the ground truth is. What internal algorithms do people use to make decisions that benefit others? People do not always act in the ways they say they do, but by observing their ground truth behavior, we can gain a quantitative understanding of what behaviors people think are right. In computer science, there are existing tools for inferring the values, preferences, and utilities that motivate people's actions and choices. One standard method, inverse reinforcement learning  (Ng & Russell, 2000) , has been used to infer utility functions from behavior in both the robotics community (e.g.,  Kuderer, Gulati, & Burgard, 2015  in which people's driving styles were inferred from demonstrations) and the computational cognitive science community (e.g.,  Baker, Saxe, & Tenenbaum, 2009 , in which intended goals were inferred from partially completed paths). There are thus established methods to learn human preferences from actions: Given examples of a person's driving, we are advancing in our ability to tell an autonomous vehicle how to bring them to the store; given examples of a person tidying up their home, we are becoming able to tell a robot what to clean. Yet these methods only apply to a single person's preferences at a time. What should be done when there is more than one person, and there are a combination of utilities to optimize? Should an artificial intelligence sum up all of its users' utilities, or would it be more \"fair\" to minimize the upset of the unhappiest member of the group? When we have assistive robots who must act as decision-makers themselves, how should they be programmed? We think the first step to answering these questions is to quantitatively determine how people-with their intuitions about fairness and efficiency and what is good-behave. In this paper, we set out to map the human sense of compromise, and the challenge of the benign dictator: how to solve the age-old problem of acting in everyone's best interest without a vested interest of one's own. It is a challenging problem that has puzzled philosophers, arbitrators, and governors for centuries. The question of what should be done when people disagree is essential, and to build tools that can help solve it, we must understand the ground-truth of what we want done. This problem becomes increasingly important not only to advise decision-makers, but to develop artificial intelligence systems to help decision-makers and eventually create artificial intelligence agents that can make choices that match what we do ourselves. In the face of this unsolved problem, we turn to psychology, developing a quantitative model of what people think should be done when an agent can take only one action that brings different utilities to different people. Many researchers have thought about these questions. Their work often falls under the heading of fair allocation, which investigates how items should be divided among people. The study of fair allocation and fair division  (Brams & Taylor, 1996; Konow, 2003)  spans many fields, including those of social choice  (Gaertner & Schokkaert, 2012; Moulin et al., 2016) , neuroscience  (Hsu, Anen, & Quartz, 2008) , artificial intelligence  (Dickerson, Goldman, Karp, Procaccia, & Sandholm, 2014) , justice and policy  (Fleurbaey, 2008; Gollwitzer & van Prooijen, 2016; Konow, 2003) , and behavioral economics and game theory, especially within the dictator, ultimatum, and estate games  (Ashlagi, Karag€ ozo glu, & Klaus, 2012; Chmura, Kube, Pitz, & Puppe, 2005; Dreber, Fudenberg, & Rand, 2014; Fisman, Kariv, & Markovits, 2007; Huck & Oechssler, 1999; Nowak, Page, & Sigmund, 2000; P alv€ olgyi, Peters, & Vermeulen, 2010) . Empirical work on fairness is similarly wide-ranging, including work on cultural differences  (Gaertner, Jungeilges, & Neck, 2001; Jungeilges & Theisen, 2008; Sch€ afer, Haun, & Tomasello, 2015; Schokkaert & Devooght, 2003) , the developmental trajectory of fairness  (Wittig, Jensen, & Tomasello, 2013) , the impact of other-regarding preferences in games  (Austerweil et al., 2015; Bolton, Brandts, Katok, Ockenfels, & Zwick, 2008) , and the weighting of distributive allocation versus the procedure by which items are allocated  (Cooney, Gilbert, & Wilson, 2016; Dupuis-Roy & Gosselin, 2011) . Wanting quantitative measures, researchers have also developed metrics to quantitatively evaluate the fairness of solutions. Several of these metrics have been compared empirically  (Dupuis-Roy & Gosselin, 2009; Engelmann & Strobel, 2004; Fehr, Naef, & Schmidt, 2006; Herreiner & Puppe, 2007 ) and include, for example, envy-free fairness, proportional fairness, and inequality aversion  (IA) . The tradeoffs between fairness and efficiency (maximizing the joint utility of all agents) are often considered and have been evaluated theoretically (e.g.,  Bertsimas, Farias, & Trichakis, 2011 , 2012 . Much work on fair allocation, however, falls outside our purview, as it considers a self-interested agent deciding how to distribute resources between themself and others. When participants have a personal stake in the situation, biases can appear in their interpretation of what is fair or what behavior they exhibit  (Babcock, Loewenstein, Issacharoff, & Camerer, 1995; Beckman, Formby, Smith, & Zheng, 2002; Binmore, 1994; Cappelen, Nielsen, Sørensen, Tungodden, & Tyran, 2013; Croson & Konow, 2009; Ellingsen & Johannesson, 2001; G€ achter & Riedl, 2006; Herrero, Moreno-Ternero, & Ponti, 2010; Konow, 2000 Konow, , 2009 Traub, Seidl, Schmidt, & Levati, 2005) . This paper focuses on the perspective of a third party, the scenario in which an impartial decisionmaker is choosing how to best help a group of people. As such, our experiments are most similar to the subset of fair allocation experiments in which the decision-maker's utility is tied only to the utilities of the agents it is serving (e.g., selfless artificial intelligences built to serve human needs). In one such set of studies, participants acted as dictators to fairly allocate goods when the dictator's own payoffs were fixed  (Engelmann & Strobel, 2004; Fehr et al., 2006) . Another two related papers investigated the division of multiple goods by an uninvested agent  (Herreiner & Puppe, 2007; Yaari & Bar-Hillel, 1984) . In these cases, participants chose how to distribute multiple items across agents whose utility functions were represented in payoff matrices. Our experiments have a similar structure in that they consider preferred allocations over payoff matrices. Our work is distinct from those previous fair allocation studies, however, in the problem it is solving: Here, the uninvested agent can take one action that has consequences for multiple individuals. Our problem formulation is more general than the \"fair allocation\" problem, since the idea of \"choosing actions that have implications across multiple utility functions\" applies to many situations outside the distribution of items. Specifically, the problem setup we describe, with utilities over any possible action, is more general than having utilities over specific items being distributed. While we are still working with abstract entities in this work, payoff matrices, and in this work only working with positive utilities, this problem formulation admits a range of scenarios. For example, a schoolteacher trying to determine what field trip to bring students on is an example of our problem, but not a fair allocation problem. Necessarily, our formulation also encompasses the class of fair allocation problems, including problems like sorting multiple indivisible items into \"bundles\" to be distributed to individuals (e.g.,  Herreiner & Puppe, 2007) . In this case, each \"action\" is to give each agent each sorted bundle, and if necessary each of these agent-specific actions could be characterized as a single larger action that could be repeated over multiple allocation decisions. It is also worth emphasizing how the question posed in this paper differs from others in the literature, even those that do not involve a self-interested party. For one, this paper does not singularly employ the zero-sum scenarios present in fair allocation studies. In fair allocation studies, participants distribute a set number of items between agents, and if one agent receives an item, another agent loses it. In this work, participants choose to create an item that can bring utility to multiple agents. For these questions, high utility for one agent does not necessarily imply low utility for another. In addition, this paper asks participants \"what should be done\" rather than what is \"fair.\" Empirically, \"fairness\" can correspond more to ideas like equality and helping the needy, while questions like \"in which society would you like to live?\" can evoke responses that take into account the trade-off between equality and maximizing the benefit to the group. Fairness can also correspond to distributional fairness or procedural fairness-examining the fairness of the final allocation solutions or the process by which items are allocated. This work focuses not on fairness but on what decisions participants believe a third party should make, in terms of creating a shared item to be distributed. Similarly, the question of \"what should be done\" is incredibly dependent on context (see  Konow, 2003; Konow & Schwettmann, 2016  for reviews), and our question of what an uninterested artificial intelligence should do constrains the space of those contexts enormously. In many decision-making tasks, arbitrators are contending with preferences for honesty  (Dana, Weber, & Kuang, 2007) , altruism  (Andreoni, 1989; Pelligra & Stanca, 2013) , cooperation  (Dreber et al., 2014) , previous experiences, friendship, spite  (Beckman et al., 2002; Levine, 1998) , reciprocity  (Berg, Dickhaut, & McCabe, 1995; Bolton & Ockenfels, 2000; Cox, 2004; Dufwenberg & Kirchsteiger, 2004) , and any number of highly relevant factors of what is fair and what is preferred. We are interested in what people think should be done in the absence of such considerations: what they would like their leaders or assistive artificial intelligence systems to advise before previously existing social relationships come into play. Artificial intelligences are by default honest and not more altruistic or cooperative than preferred, so they offer a unique opportunity to act as independent advisors free from spite, obligation, or reciprocity. Our question could integrate important factors like need or desert/merit (e.g.,  Alesina & Angeletos, 2005; Fleurbaey, 2008; Fong, 2001; Hoffman & Spitzer, 1985; Konow & Schwettmann, 2016; Nord, Richardson, Street, Kuhse, & Singer, 1995; Schokkaert & Devooght, 2003; Schokkaert & Lagrou, 1983; Schokkaert & Overlaet, 1989) , but the simplified task we choose does not involve agents who are needy or who have worked harder than others, despite this being a major factor in society. Another way to extend our study would be to use a paradigm that uses bundles or collections of objects, either for allocation or as creating these shared resources (both can be construed as an action). Bundles allow investigation of envy-freeness, and also proportionality, like in \"claims problems\" when agents may each have a claim to a resource that is greater than the resource is worth  (Bosmans & Schokkaert, 2009; Thomson, 2003) . Additionally,  Konow (2003)  discusses the differences between subjective values and objective values, which we simplify here by directly presenting agent utilities. Given the difficulty of the question of what should be done, we used a simplified task and save these questions for future work. For our question and paradigm, we consider it reasonable to limit our literature review to those topics that are most aligned with our question, though we provide references to the reader for additional study. Our task, then, is to determine what an uninvested, autonomous agent should do in a decision-making scenario with multiple recipients. To investigate what defines a \"helpful\" action when balancing multiple utilities, we created the following problem setting: We asked what decision a manager should make in choosing a drink for two guests. Participants acted as the manager, repeatedly making choices that we used to develop a model of what people think are good decisions. Drawing on the literature in economics, computer science, and philosophy, we considered four metrics as hypotheses to capture participants' behavior: maximax, maxsum, maximin, and IA. We determined which combination of metrics best explained participants' behavior by statistical analyses and evaluating the output of a maximum entropy inverse reinforcement learning (MaxEnt) model. Having inferred the preferred metrics, we then used these metrics to compare participants' behavior across conditions. \n Metrics We now delve into the specifics of our metrics and what stimuli they were applied to. Many different fields have investigated the question of how people make decisions when balancing multiple tradeoffs-for example, people could choose to maximize the group utility or distribute resources evenly. As such, several quantitative models describing \"fair\" behavior have been suggested. We investigated four metrics that were often used (often in combination) in previous studies to characterize human behavior (e.g.,  Brams, Edelman, & Fishburn, 2003; Dupuis-Roy & Gosselin, 2009; Engelmann & Strobel, 2004; Herreiner & Puppe, 2007) . We do not believe these metrics span the space of reasonable preferences people may hold-people's algorithms for determining what to do in the world can be extremely complex-but we selected these metrics based on what has been widely and empirically observed in the literature. We applied these four metrics to a set of payoff matrices M: in each matrix M m , two agents' utilities (A and B) were shown for each of four drink options (see Fig.  1 ). We investigated each of the metrics for these payoff matrices. Intuitively, one method to select a shared option is to add up the utilities of all agents, and pick the option that maximizes this joint utility value. This is a metric called maxsum, which maximizes the happiness of the group rather than individuals. It is a Pareto optimal option. In Fig.  1 , the best maxsum option would be the third cup, because when utilities of agents A and B are added together, these sums are as follows: 7 (first cup), 13 (second cup), 15 (third cup), and 14 (fourth cup). A different metric enforcing fairness is maximin: maximizing the utility of the person who is worst-off. Intuitively, this metric means making sure that no individual agent is very unhappy. In Fig.  1 , the best maximin option would be the second cup, because when we look to which of the agents are worstoff in each of the pairs, these agents' utilities are as follows: 3 (first cup), 5 (second Fig.  1 . Example matrix M m . Columns are options o j , while rows show each agent i's utility U i . Here, the problem is to decide which drink to serve to both agents A and B. cup), 4 (third cup), and 2 (fourth cup), and the second cup leaves the worst-off agent with the highest possible utility. Another measure of fairness is IA: decreasing the difference in utilities between agents. Intuitively, this metric means that agents should be equally happy. In Fig.  1 , the best IA option would be the first cup, because the agents' utilities will be maximally close to each other. A final possible measure is maximax: maximizing the highest utility, searching across both agents. Intuitively, this metric means that any one agent should be made as happy as possible. This option might not initially seem fair, but if presented with the opportunity for repeated choices, pleasing one agent each round may seem like the best solution. In Fig.  1 , the best maximax option would be the fourth cup, because this cup allows one agent to have its highest possible utility. Note that in Fig.  1 , the best example of each metric was a different cup, but in most of our payoff matrices, the best example of multiple metrics was the same cup. Thus, in this paper, we evaluated the four metrics of maximax, maxsum, maximin, and IA. Metrics like maximin and maxsum have a long history in the literature. The concept of maximin was popularized by  Rawls (1971 Rawls ( , 1974 , who advocated for allocating resources to the least well-off individual.  Harsanyi (1975)  argued in favor of expected utilitarianism, loosely the maxsum principle, except in cases where the maximin choice was similar to the maxsum choice, as in the case in our experiments. There has been a strong focus on maximin mathematically and in economics (e.g.,  Amanatidis, Markakis, Nikzad, & Saberi, 2017; Barman & Krishna Murthy, 2017; Dubois, Fargier, & Prade, 1996; Escoffier, Gourv es, & Monnot, 2013; Kurokawa, Procaccia, & Wang, 2016; Procaccia & Wang, 2014) , including applications to networking (e.g., bandwidth-sharing)  (Salles & Barria, 2008) . Choices aligned with the maximin, maxsum metric, and IA metrics are often compared in studies, and results are often mixed, with participants trading off between different metrics depending on the numbers and contexts involved  (Ahlert, Funke, & Schwettmann, 2013; Charness & Rabin, 2002; Engelmann & Strobel, 2004; Faravelli, 2007; Fehr et al., 2006; Gaertner et al., 2001; Gaertner & Schwettmann, 2007; Konow, 2001 Konow, , 2003 Konow & Schwettmann, 2016; Mitchell, Tetlock, Mellers, & Ordonez, 1993; Ordoñez & Mellers, 1993; Pelligra & Stanca, 2013; Schwettmann, 2009 Schwettmann, , 2012 . These studies differ in their experimental paradigms, and results have been subsequently different, even as the concept of tradeoffs between a few principles of justice has remained similar  (Konow, 2003) . These experiments reveal a few common difficulties as well. Many experiments attempt to target each metric in isolation, which does not account for the correlations between choices: A choice that maximizes the maximin metric also tends to rate highly on the IA metric and less well on the maxsum or maximax metrics. Additionally, experiments often present somewhat extreme choices and models contain variables that are occasionally confounded. We aim to address these difficulties in our study by presenting many nuanced choices to participants, and then using a computational model and statistical analyses to account for correlations and confounding between metrics. Using these tools, we gain the ability to distinguish the relative influence of metrics on sets of participant choices. In this paper, we aim to address the question of what policies people would like decision-makers, and the assistive technologies assisting decision-makers, to have in the future. To this end, we focus on research studies that are aimed at non-interested third parties reasoning about helpful decision-making, the results of which are not always consistent. In these studies, participants are presented with options that implement various metrics and have to choose how to allocate items across agents  (Engelmann & Strobel, 2004; Fehr et al., 2006; Herreiner & Puppe, 2007; Yaari & Bar-Hillel, 1984) . Participants are often shown choices that are used to disambiguate between metrics, and because these choices are so distinct, participants may only make a single or small number of choices for any given prompt. We took a different approach with our work: On each prompt we presented many choices to participants, accepting the high amount of overlap among metrics necessary to describe participants' responses. We constructed a computational model to accommodate these correlations and used this model to reveal the relative contributions of different metrics across many probes of participant behavior. We tested the generalizability of our findings by ensuring the participant behavior was similar across different prompts. Additionally, previous work often focuses on short-term, single decisions; we investigated participants' intuitions in the repeated setting where they could make more long-term decisions. In summary, our work compares four common metrics in a setting where participants are making more choices than in previous work and the correlations among metrics describing those choices are accounted for. We use this higher resolution into the relative contributions of each of these metrics to directly compare them, and we probe many questions-including longer-term decision-making-to determine the generalizability of our findings. These improvements take place in a novel setting, in which participants are not being asked about how to allocate many items, but to create a resource to be shared among multiple agents. We thus present a novel test of how correlated metrics interact, in the context of how people feel third-party decision-makers should balance others' utilities: a problem formulation that will occur more and more often in technologies in the future. In three experiments, we investigated the contributions of the metrics of maximax, maxsum, maximin, and IA in describing what people consider good or helpful behavior. In Experiment 1, we examined participants' choices in the drink task and determined whether these choices were consistent when the hypothetical decision-maker was described as a human or a robot, and when the agents receiving the resources were described as friends or strangers. Our results indicate that participants were consistent in using the maximin metric to make decisions (maximizing the utility of the worst-off agent) despite variations in the agents involved. In Experiment 2, we asked what decisions people would make when they had the opportunity to offer more than one drink to the same set of agents. We tested whether people would make choices while considering the entire multi-decision expected utility or focus on the individual decisions within. We found that participants reasoned over the entire multi-decision process, and the maximin metric could again describe their choices. In Experiment 3, we validated our results from Experiment 2 by presenting participants with the cumulative sum of the choices available in Experiment 2, and observing that when the multi-decision problem was condensed to a single instance again, participants reliably made choices described by the maximin metric. 2. Experiment 1: Which metrics describe people's behavior? Are they robust to changes in agent? Here we tested which combination of metrics described participants' behavior on a drinkchoosing task (Fig.  1 ). We tested a variety of different phrasings and altered scenarios to ensure that the results were consistent across changes in presentation. Specifically, we tested whether participants' choices changed depending on if the decision-maker was an artificial intelligence (a robot) or a human, whether the recipients of the drinks were friends or strangers, and whether the participant was stated to be one of the recipients of a drink. We might expect that a participant would perform differently in the \"Robot\" condition if they thought that what a robot should do in a manager role was different from what a human manager should do. For example, participants may think that artificial intelligences need to remain completely impartial or compute everything exactly, whereas humans should rely on gut instincts. Similarly, we might expect that participants would have different intuitions about a server giving drinks to strangers rather than friends. Perhaps participants would think that when serving friends, a server should worry more about joint happiness rather than making sure utilities were equitable, since friends could make it up to each other later, while the same would not be true of strangers. We were also interested in whether participants' opinions of what decision should be made would change if they themselves were receiving an item rather than hypothetical recipients. In Experiment 1, we were aiming to test whether the participants' empirical intuitions of good decision-making would extend across these variations in scenarios, which are important for the generalizability of our findings. \n Method \n Participants Participants with U.S. IP addresses were recruited from Amazon Mechanical Turk across five conditions: \"Nominal\" (n = 36, 0 participants excluded), \"Robot\" (n = 35, 1 participant excluded), \"Robot Friends\" (n = 35, 1 participant excluded), \"Robot Strangers\" (n = 34, 2 participants excluded), and \"Veil of Ignorance\" (n = 33, 3 participants excluded). Participants were paid between $2.50 and $3.00 for their participation. Participants were excluded if they failed the included attention check or indicated that they did not understand the experiment. \n Stimuli Stimuli were chosen such that participants would reason over a set of positive-utility actions, and the effects of each metric could be quantitatively isolated from these data. To keep the paradigm simple, utilities in the form of numbers in a table were used (\"payoff matrices\"), with utilities kept small to allow participants to use simple addition. To maximize the generalizability of the findings, several constraints on the matrices were put in place to ensure participants were reasoning over a wide, randomized range of independent matrices. Participants viewed 20 of these payoff matrices (set of matrices M), one at a time. Each matrix M m was 2 9 4, where the rows indicated the two agents, the columns indicated the four colored drinks, and each agent's utility for each drink was shown. Matrices were generated by rejection sampling. Matrices were subject to the following general constraints. The sum of agents' utilities for each option o j , P i U i o j ð Þ, was constrained to be within 2 and 16, so that there would be a wide range of choices available but participants would only need to use simple addition. Within each matrix, columns (both agents' utilities for an option) were not allowed to repeat, including permutations within columns, so that there would always be four independent choices within a matrix. Moreover, within each matrix, for every column, there could be no other column that strictly dominated that column according to all metrics, because such a column would rarely be picked and so would be uninformative according to the goals of this study. Since we were interested in the question of what desired resource should be shared among recipients, we constrained our actions to positive utilities and did not allow matrices to contain zeros or negative numbers. Finally, in a set of matrices M, any two matrices were not permitted to have more than two of the same columns, where \"sameness\" included column permutation, in order to create a set of independent matrices. In addition to the general constraints, \"class\" constraints were established to ensure that the chosen matrices could isolate the effects of each of the metrics. There were thus four classes: (a) four matrices in which each option was the best choice according to one of the metrics (e.g., the example in Fig.  1 ), (b) four matrices in which the maxsum metric was held constant: all choices had the same joint utility, (c) four matrices in which the maximin metric was held constant: for all choices, the worst-off person had the same utility, and (d) eight matrices that were randomly generated. The maximax and IA metrics were not held constant because matrices constructed in this manner did not meet the general constraints described above. The matrices used in this study are included in the Supplemental Methods. \n Procedure Upon viewing each matrix, participants read the following text: \"You're the manager at a hotel and want to serve a drink to the room. Archie and Ben are your guests and have told you how much they enjoy different drinks (higher numbers mean more enjoyment). Which drink would you like to serve?\" Participants then had to select one of the four drinks and justify their response. The names \"Archie\" and \"Ben\" were substituted with other names beginning with \"A\" and \"B\" for each matrix. We expected that participants would employ a consistent understanding of what made a \"good\" decision in the drink-choosing task, but wanted to test the robustness of participants' choices by employing several task variations. The variations we tested were the identity of the server (either human or robot), the relationships of the agents being served (either friends or strangers), and whether the participant was described as a recipient of a drink. In the \"Nominal\" condition, participants were presented with the default text (\"You're the manager at a hotel and want to serve a drink to the room...\"). In the \"Robot\" condition, the prompt was: \"There is a robot manager at a hotel which will serve a drink to the room. Archie and Ben are its guests and have told it how much they enjoy different drinks (higher numbers mean more enjoyment). Which drink would you like the robot to serve?\" In the \"Robot Friends\" condition, the prompt was the same as in the \"Robot\" condition, but the following phrase was added: \"Archie and Ben are its guests (they are friends with each other)....\" In the \"Robot Strangers\" condition, the following phrase was substituted: \"Archie and Ben are its guests (they are strangers to each other)....\" Italics were not included in the participant text. In the \"Veil of Ignorance\" condition, the instructions were modified to be: \"The manager at a hotel wants to serve a drink to the room, where you and another guest are sitting. The manager has learned how much you both enjoy different drinks (higher numbers mean more enjoyment). Given you do not know which guest (A or B) you are, which drink would you like the manager to serve?\" This condition is named the \"Veil of Ignorance\" condition as a reference to  Rawls (1971) , who suggested that a method of eliciting moral judgments without self-interest would be to present scenarios in which participants had to make judgments about hypothetical societies they would like to live in, while not knowing anything about their place in the hypothesized social order. Thus, participants would be \"behind a veil of ignorance\" in that they would have to make decisions without knowing whose place they would fill. Here, in this experimental condition, participants were told they were recipients of a drink but did not know which recipient (A or B) they were, thus enacting a version of the Rawlsian thought experiment. To analyze participant responses according to our metrics, we calculated the value of each metric (F q ), where q indexes the individual metric (maximax, maxsum, maximin, IA), and F is a vector. Values for the metrics were calculated from the utilities of agent i (U i ) for each option o j : F maximax o j À Á ¼ max i U i o j À Á F maxsum o j À Á ¼ X i U i o j À Á F maximin o j À Á ¼ min i U i o j À Á F IA o j À Á ¼ Y i U i o j ð Þ P i U i o j ð Þ These F q o j ð Þ values were then normalized to account for the tradeoffs between each option o j in the matrix M m 1 : F q o k À Á ¼ F q o k À Á max o j 2M m F q o j ð Þ È É; 8q ð1Þ \n Results and discussion We were interested in what metrics participants preferred, meaning which metrics could describe participants' demonstrated behavior. We determined preferred metric through an independent statistical analysis, and then via a maximum entropy model. We examined the proportion of participants preferring specific metrics in the \"Nominal,\" \"Robot,\" \"Robot Friends,\" \"Robot Strangers,\" and \"Veil of Ignorance\" conditions. \n Statistical analysis We sought to determine which metrics individuals used to make their choices. Before asking which metrics best described participants' choices, we first asked whether participants were behaving according to any of the metrics, by comparing participants' empirical choices to a simulated baseline participant making random choices. For each metric q, we determined whether the F q values from participants' empirical choices were significantly larger than the F q values from random choices, summed across participants and matrices. For our baseline comparison, we drew from the null distribution to generate enough choices for a complete experiment (choices for each matrix and for each participant, summed) and repeated that process 10,000 times. We then computed z-scores and associated p-values for whether the empirical F q values (H1) were significantly greater than our baseline F q values (H0) for each metric q. We found that the maxsum, maximin, and IA metrics significantly matched participant behavior, and that the maximin metric best matched participant behavior (had the highest z-scores) for all conditions except the \"Veil of Ignorance\" condition (Table  1 ). In the \"Veil of Ignorance\" condition, the maxsum, maximin, and maximax metrics significantly matched participant behavior, and the highest z-score was for the maxsum metric, closely followed by the maximin metric. This analysis was chosen because the comparison between the empirical and null distributions accounted for the biases within metrics and choice of specific matrices. \n Inferring metrics used with a maximum entropy model To further test which combination of metrics described participants' choices, we constructed a maximum entropy inverse reinforcement learning (MaxEnt) model  (Ziebart, Maas, Bagnell, & Dey, 2008) . In this model, we inferred weights, which were associated with each of the metrics. Mathematically, the weight vector h was indexed by q and composed of [h maximax , h maxsum , h maximin , h IA ]. Participants' preferred metric was evaluated as the metric with the largest associated weight h q . We computed a maximum a posteriori estimate for h for each participant given their choices by combining a uniform prior over the parameters of h with the likelihood of each individual's choice o k over the options o for each matrix. Specifically, within each matrix M m , for each participant's choice o k over options o, we maximized the function logP(o k |h) over h (a vector of length q), where: Pðo k jhÞ ¼ e h T F ðo k Þ P j e h T F ðo j Þ ð2Þ Recall that F is the vector containing the values of the individual metrics [F maximax ; F maxsum ; F maximin ; F IA ]. We summed across matrices M m to create the final cost function P m log P o k M m ð Þjh À Á , and we used the following constraints to compare the relative use of each of the metrics: P q h q ¼ 1, h q ≥ 0. We optimized using sequential least squares programming (SLSQP) in Python's scipy package. To calculate the weight vector of an average individual, we calculated the arithmetic mean over individual participants' h vectors. Thus, overall the h q value for any given metric was determined by the closeness between the responses expected under that metric (e.g., maxsum) and a participant's responses. In interpreting the results, if any given h q value was high, then participants often chose responses in accordance with that metric. We found that participants' behavior was best explained by the maximin metric for all conditions according to the MaxEnt model, as shown in Fig.  2 . Our conclusion that participants' behavior was best explained by the maximin metric was also supported by using À6.4 (1) 7.8 (0) 18.8 (0) 9.9 (0) Note. Determining which metrics describe participant choices, as compared to what would be expected given random choices, summed across participants and matrices. Z-scores are shown, calculated as the [empirical (H1) summed scores-mean of the null (H0) distribution summed scores] divided by [SE for the null (H0) distribution summed scores], along with associated p-values in parentheses, for all metrics. (Summation is across all matrices and participants.) High scores for any metric indicate that participants often chose responses in accordance with that metric, above and beyond what they would have done had they been choosing randomly. Results are shown for all conditions in all experiments: \"Nominal,\" \"Robot,\" \"Robot Friends,\" \"Robot Strangers,\" \"Veil of Ignorance,\" \"Repeated 2x: Independent (Choice 1),\" \"Repeated 2x: Independent (Choice 2),\" \"Repeated 3x: Independent (Choice 1),\" \"Repeated 3x: Independent (Choice 2),\" \"Repeated 3x: Independent (Choice 3),\" \"Repeated 2x: Summed,\" \"Repeated 3x: Summed,\" \"Follow-Up (2x),\" and \"Follow-Up (3x).\" 10,000 samples of summed scores from the null distribution were taken. Condition names are shortened: \"VoI\" represents the \"Veil of Ignorance\" condition and \"Rep2x: Ind.(C1)\" represents the \"Repeated 2x: Independent (Choice 1)\" condition. \"0\" in the table refers to <0.0001. an alternative method of calculating the average weights across participants. Throughout this work, we sought to determine which combination of metrics described an \"average\" individual; however, there are several ways of calculating an average weight vector. In the main analysis, we set \"average\" as the arithmetic mean of each individual participant's weight vector h. An alternative average assumes that all participants' data came from one individual and, given this, calculates a single weight vector h under the assumptions of the MaxEnt model described above. Using this, h maximin = 1 and h maximax , h maxsum, hIA = 0 for the \"Nominal,\" \"Robot,\" \"Robot Friends,\" and \"Robot Strangers\" conditions. Note that the results from the MaxEnt model support and also further the results from the statistical analysis. In the statistical analysis for Table  1 , we compared participants' responses to those expected from a participant choosing randomly. We saw, compared to this null distribution, that participants' choices tended to encompass the maxsum, maximin, and IA metrics across the \"Nominal,\" \"Robot,\" \"Robot Friends,\" and \"Robot Strangers\" conditions. While the results from that analysis suggested that participants' responses slightly more matched the responses expected from a maximin policy (indicated by the higher z-scores under the Maximin comparison) compared to other metrics' policies, this comparison was indirect (participant and random responses were compared along each of the metrics, and then the metrics were compared, rather than directly comparing the relative influence of each metric in participant responses). To more directly compare which metrics best described participants' responses, we examine the results from the MaxEnt model designed for this purpose. The results from the MaxEnt model for these conditions clearly differentiate the maximin metric as more descriptive of participants' responses compared to the other metrics. Fig.  2 . MaxEnt model results for Experiment 1, showing mean inferred weight h AE SE for each metric across participants in the \"Nominal,\" \"Robot,\" \"Robot Friends,\" \"Robot Strangers,\" and \"Veil of Ignorance\" conditions. The maximin metric best described participant behavior. For the \"Veil of Ignorance\" condition, the MaxEnt results were more evenly split between the maximin and maxsum metrics: h maximin = 0.52, h maxsum = 0.48, and h maximax , h IA = 0. Of note, while the MaxEnt results emphasized the maximin and maximax results in Fig.  2 , the results from fitting a single h emphasize the maximin and maxsum results. This pattern could arise if there were some participants who behaved very consistently according to the maximax metric, leading to their being highly represented when h values were calculated for each participant and averaged, but these participants' behavior washing out when all participants' behavior was aggregated. It is noteworthy that the maximax and maxsum metrics were highly correlated (the same is true for the maximin and IA metrics) such that if participants were commonly making the best maximax choices, these choices were likely to be well-described by the maxsum metric as well (Fig.  3, leftmost ). This correlation is how there could be a result for the single h providing more support for the maxsum metric with an average mean providing more support for the maximax metric. The shared emphasis on the maximin, maxsum, and maximax metrics in the \"Veil of Ignorance\" condition is also evident from the statistical analysis described above. In sum, across each of these result measures behavior of participants in the \"Veil of Ignorance\" condition appears to be described by the maximin, maxsum, and maximax metrics. The MaxEnt model results were designed to isolate which metric best described participants' behavior by accumulating evidence over all trials. As such, the MaxEnt model seems to clearly indicate participants were always behaving according to, for example, the maximin metric. However, in each individual trial, participants could not behave according to an isolated metric, since each choice they made provided some evidence for each of the metrics. This inseparability-caused by the correlations among metrics, see Fig.  3 -is what motivated our use of the MaxEnt model. One could argue that participants may be making choices that were most supporting a single metric on each trial, and this is possible but not what was empirically observed. Though we do not include trialby-trial data, Table  2  provides a histogram of the metrics participants' behavior most adhered to, according to the MaxEnt model, and the Supplemental Results (Tables  S1-S14 ) show each participant's adherence to each the metrics according to statistical analyses. Participant behavior generally was in accordance with several of the metrics, and most in accordance with the maximin metric in aggregate. After constructing the MaxEnt model, we wanted to check that our weight vectors h generalized and that the model was predictive of human behavior. To that end, we estimated participants' weight vectors and used these to predict held-out choices. Specifically, given participants' weight vectors h, we could predict participants' choices given a new set of options in matrix M m . The predictions o k m were calculated by argmax j Pðo j m jhÞ. We calculated weight vectors h for 50% of participants, each trained on 50% of the matrices. We then used the average weight vector from these participants to predict the remaining 50% of participants' choices on the remaining 50% of matrices and report this prediction accuracy. As a comparison, we also report the accuracy of prediction when each participant's weight vector, trained on all matrices, is used to predict that same participant's choices on each matrix. We report the average of 100 training runs for each prediction. Training and testing on 50% participants and matrices, the \"Nominal\" condition had 72.9% predictive accuracy (non-held-out comparison: 75.4%); the \"Robot\" condition had 66.4% predictive accuracy (non-held-out comparison: 70.1%); the \"Robot Friends\" Fig.  3 . Correlations across values of the metrics in the \"Nominal\" (leftmost), \"Follow-Up (2x)\" (left), \"Follow-Up (3x)\" (center), \"Repeated 2x: Summed\" (right), and \"Repeated 3x: Summed\" (rightmost) conditions. For each condition, we computed the value of each metric for all possible choices across all matrices. We concatenated all of the possible choices across all matrices into one vector for each metric, and we computed the Pearson correlation coefficient across metrics. Choices well-described by the maximax metric were also well-described by the maxsum metric (high correlation between maximax and maxsum), while choices welldescribed by the maximin metric were also well-described by the inequality aversion (IA) metric (high correlation between maximin and IA). These clusters (maximax and maxsum) and (maximin and IA) tended to be anti-correlated. Note that the \"Nominal\" condition plot also describes the \"Robot,\" \"Robot Friends,\" \"Robot Strangers,\" \"Veil of Ignorance,\" \"Repeated 2x: Independent,\" and \"Repeated 3x: Independent\" conditions, since participants saw the same stimuli. The summed possible choices used in the \"Repeated 2x: Summed\" and \"Repeated 3x: Summed\" correlation matrices were used only for data analysis and not shown to the participants. 17 0 83 0 Note. Each participant's final h vector according to the MaxEnt metric was computed for each condition; the highest-value h q value was taken as the metric that best described the participant's behavior. Shown is the percentage of participants for which each metric best described their behavior. These more individuallevel results closely resemble the aggregated results shown in the Figures. Condition names are shortened: \"VoI\" represents the \"Veil of Ignorance\" condition and \"Rep2x: Ind.(C1)\" represents the \"Repeated 2x: Independent (Choice 1)\" condition. condition had 71.3% predictive accuracy (non-held-out comparison: 70.9%); the \"Robot Strangers\" condition had 64.6% predictive accuracy (non-held-out comparison: 73.3%); the \"Veil of Ignorance\" condition had 59.5% predictive accuracy (non-held-out comparison: 78.2%). Chance accuracy was 25%. We observed high predictive accuracy both when testing sets were and were not held out compared to chance accuracy, supporting the validity of our inferred h vectors. \n What metric was preferred across conditions? We also asked whether participants' judgments of fairness would differ based on what type of agent they were considering, and whether the participant was considered a drink recipient. We found that on the whole, participants were consistent in their behavior across conditions: whether they were thinking about a human manager or a robot manager, whether the robot manager was serving friends or strangers, and whether they were to receive a drink. Specifically, participants' preferred metric did not differ significantly between the \"Nominal,\" \"Robot,\" \"Robot Friends,\" \"Robot Strangers,\" and \"Veil of Ignorance\" conditions (chi-squared test over F q summed over participants and matrices: v 2 = 6.67, p = .88, df = 12). We could have generated many more conditions, but our results suggest that participants' fairness judgments are robust to at least some changes in agent identity, and generally that participants' ideas of fairness are similar across varied situations. The result of similar behavior across conditions is important, because in this work, our goal is to examine humans' views of what decisions decision-makers and assistive artificial intelligences should implement in the future. In this experiment we asked participants what a desirable decision would be and then checked that the results were not a specific consequence of slight differences in how we could have asked the question. There were indeed no significant differences in participants' reports of what they considered a good decision, despite differences in the agent considered. This finding is important with respect to the generalizability of our findings and how we might outsource decisions to technology in the future. While results were similar across conditions, it is worth noting that the results from the \"Veil of Ignorance\" condition subtly differed from the rest, for example by encouraging behavior more closely matching the maxsum metric. In the \"Veil of Ignorance\" condition, participants seemed to engage with the question as a new context: Qualitatively, participants seemed to think less about fairness and more in the sense of \"gifts\" or \"gambling.\" When asked to justify their choices, participants in the \"Veil of Ignorance\" condition would say things like \"one of us might as well be very happy,\" \"I don't know what guest I am so I made the safest choice,\" or \"Neither of us will get something we don't enjoy at all.\" Whereas in the other conditions, participants tended to more often use words like \"fair,\" \"balanced,\" or \"equal.\" A possible explanation for why behavior in the \"Veil of Ignorance\" condition was not so closely matched to the maximin metric as was true in the \"Nominal,\" \"Robot,\" \"Robot Friends,\" and \"Robot Strangers\" conditions is this apparent difference in framing. On the one hand (corresponding to the \"Veil of Ignorance\" condition), the participant could either gamble to win a desired item or offer it generously to an opponent, or alternatively play it safe with a drink everyone would like a little  (Konow & Schwettmann, 2016)  reviews the evidence on whether \"fair\" behavior is actually risk-averse behavior). On the other hand (corresponding to the other conditions), the participant would be responsible for the outcomes of two people one does not know, perhaps encouraging more \"fair\" allocation strategies. While participants' behavior was still more maximin-aligned than maxsum-aligned, the fact that participants' behavior was relatively more similar to the maxsum metric in the \"Veil of Ignorance\" condition was interesting because the participants could have taken the opposite perspective. In the \"Veil of Ignorance\" condition, the participants had (unknown) stake in the proceedings and could have made sure not to end up with the unfair end of a bargain by engaging in even more maximin behavior relative to the other conditions. Instead, participants behaved relatively more according to the maxsum metric. This result is important and should be further explored, since most of us are recipients and not the decision-maker in many real-life situations, perhaps making the \"Veil of Ignorance\" condition the most descriptive of real situations. Various other studies have empirically evaluated preferences under the veil of ignorance  (Andersson & Lyttkens, 1999; Carlsson, Gupta, & Johansson-Stenman, 2003; Frohlich, Oppenheimer, & Eavey, 1987; Johansson-Stenman, Carlsson, & Daruvala, 2002; Oleson, 2001) . Of the studies that evaluated metrics similar to ours,  Frohlich et al. (1987)  found that participants preferred maximizing average income with a floor constraint, and  Oleson (2001)  found that participants demonstrated both maximin and IA behavior-however, this collection of studies was different enough from our paradigm (e.g., studying risk aversion, or looking at welfare over an entire hypothetical society) that the different contexts likely significantly affected outcomes. A study by  Bosmans and Schokkaert (2004)  was similar to our work in that they asked participants about their preferences directly, and also under a veil of ignorance. They observed different results between the directly elicited preferences and veil of ignorance conditions (but not maximally different results, which occurred in comparing directly elicited preferences to a third self-interested condition). These results were similar to ours, as we found a small difference in response profiles between our \"Nominal\" and \"Veil of Ignorance\" conditions. A final aspect of our \"Veil of Ignorance\" condition is that since our question was about autonomous third-party decision-makers with no stake in the game, we designed the condition such that participants would not receive a payout according to their choices. If participants had a stake in the game (albeit an unknown one), their behavior might have shifted to be more conservative under the assumption of maximizing self-interest-it is known that participants do change their behavior based on whether they are being paid or not (e.g.,  G€ achter & Riedl, 2006; Herrero et al., 2010) . Altogether, the \"Veil of Ignorance\" results were similar to those of the other conditions, but future work will have to continue evaluating the contexts that influence participants' conceptions of good decision-making. \n Experiment 2: Repeated choices Previously, we evaluated what people thought a decision-maker should do when taking a single action. However, in the real world, decision-makers will act many times: the schoolteacher choosing a new lesson plan for their students every day, or the government delivering many aid programs over time. Here we investigated whether people have different intuitions for what decision-makers should do when facing repeated decisions with the same set of agents. Perhaps the decision-maker should give one agent its best choice the first time, and a different agent its best choice the second; or perhaps the conclusion is to compromise each time or to attempt to maximize fairness across the sum of all decisions. We tested whether different metrics would describe participants' actions when participants were given repeated choices. Repeated decision-making has been studied in the literature, often under the name of sequential or dynamic choices in game theory games. In the repeated version of the Prisoner's Dilemma, participants choose whether to betray their partner or cooperate on each turn, and there has long been research into the optimal strategy for this game  (Andreoni & Miller, 1993; Boyd & Lorberbaum, 1987)  and other competitive/cooperative games  (Kuzmics, Palfrey, & Rogers, 2014) , wherein each partner obtains more information about the other on each turn. Behavior in repeated games is sensitive to anticipated repetitions: game outcomes are empirically different when participants are engaging in a finitely repeated game compared to a repeated one-shot game  (Andreoni & Miller, 1993) . In other sequential games, the sequence is not of both agents making choices simultaneously and then repeating the game, but rather of agents taking turns right after each other, for example by claiming an item via sequential allocation  (Bouveret & Lang, 2011; Kalinowski, Narodytska, & Walsh, 2013) , or fair queueing  (Demers, Keshav, & Shenker, 1989; Moulin & Stong, 2002) . There are also \"online\" games, in which agents may arrive at different times (e.g.,  Kash, Procaccia, & Shah, 2014; Walsh, 2011)  and resources must be divided between them repeatedly. Alternatively, items may arrive over time to the same set of agents who have preferences over them (e.g.,  Aleksandrov, Aziz, Gaspers, & Walsh, 2015) , which is more similar to the structure of our experiment. There is a subset of research studying the situation of a single item being distributed to a set of agents repeatedly. In this case, researchers are often testing optimum strategies for allocation that maximize total agent utility, while ensuring that their strategy has useful qualities like being efficient and fair, and encouraging truth-telling of preferences from each agent on each round. This work can fall under the heading of \"dynamic mechanism design\" and has been widely investigated (e.g.,  Bergemann & Valimaki, 2006; Cavallo, 2008; Guo, Conitzer, & Reeves, 2009) . Other researchers have argued that these paradigms do not capture the structure of real-world problems, and so introduced a reallife food distribution problem in which a central decision-maker must repeatedly allocate food to different charities in an online fashion over complex preferences where fairness and efficiency are both considered  (Aleksandrov et al., 2015; Walsh, 2015) . Our Experiment 2 is similar to this food distribution problem in that we have a repeated task in which a central decision-maker makes resource choices over the preferences of several agents, and similar to the dynamic mechanism design studies in that there is a single item being repeatedly allocated. Our Experiment 2 is different, however, in that the single item is not being allocated to a single recipient, but rather being created and shared across agents on every round.  Freeman, Zahedi, and Conitzer (2017)  have perhaps the most similar motivation to our experiment, as they ask if a central decision-maker should make allocations that are optimized for fairness within every round, or if fairness should be optimized across rounds.  Freeman et al. (2017)  analyzed (non-empirically) fair social choice in dynamic settings with many agents with changing preferences over multiple goods. They chose to optimize for the overall product of all agents' utilities and investigated strategies from there. However, the question of whether real participants would optimize for global utilities across choices is undetermined, including whether they would optimize for additive utilities (the global maxsum solution) or the product of utilities (more similar to IA). Given previous research, we hypothesized that participants would behave differently when presented with the same choice repeatedly; in other words, we expected that the choices from Experiment 1 would not be repeated three times. We were interested in determining whether participants' choices would be described by the same metric in each round, or across all rounds, and whether these choices would change depending on the number of anticipated rounds. In summary, in Experiment 2 we presented participants with two or three repetitions of the same payoff matrices to determine how they would act, as central decisionmakers, in the common real-world situation of providing a resource multiple times to the same group of people. \n Method \n Participants Participants with U.S. IP addresses were recruited from Amazon Mechanical Turk for two additional conditions: \"Repeated 2x\" (n = 24, 0 participants excluded) and \"Repeated 3x\" (n = 21, 4 participants excluded). Participants were paid between $2.50 and $3.00 for their participation. Participants were excluded if they failed the included attention check or indicated that they did not understand the experiment. \n Stimuli and procedure In Experiment 2, the procedure and stimuli were similar to Experiment 1, except instead of viewing each matrix once, participants saw each matrix twice (in the \"Repeated 2x\" condition) or three times (in the \"Repeated 3x\" condition). Matrices were repeated an even (\"Repeated 2x\" condition) and odd (\"Repeated 3x\" condition) number of times to probe how participants would balance their choices. Procedurally, participants read the prompt from the \"Nominal\" condition, made a choice for the presented matrix, and justified their answer, as in Experiment 1. Then they saw the following prompt: \"Your guests have finished the drinks, and you can now put out another. Which drink would you like to serve?\" and were shown the same matrix again, and asked to make a choice and justify their answer. The latter prompt and matrix appeared once more in the \"Repeated 3x\" condition. Participants were able to scroll up and down the page of prompts and responses to determine the total number of drinks they were serving, and could change their choices at any time within the round. \n Analysis In Experiment 2, participants had the opportunity to serve multiple drinks. In the \"Repeated 2x\" condition they chose an option o k from matrix M m two times (o k 1 ; o k 2 ), while in the \"Repeated 3x\" condition they chose an option o k matrix M m three times (o k 1 ; o k 2 ; o k 3 ). Unlike in Experiment 1, choices from each repeated matrix were not independent given the matrix M m . We thus calculated two variants on individuals' preferred metrics. For the na€ ıve analysis, we analyzed each choice in the repeated case as an independent decision. Specifically, we assigned all choices after o k 1 to new \"independent\" participants. Thus, in the \"Repeated 2x\" condition, the number of participants artificially doubled, with the first set of participants making choices o k 1 for each matrix, and the second set of participants making choices o k 2 for each matrix. F indep q was calculated and predictions were made using the same procedure as in Experiment 1, where \"indep\" indicates the artificial creation of independent participants. For the more sophisticated analysis, we assumed that participants were making one large decision across two or three unordered matrices, rather than making semi-indepen- dent decisions o k 1 , o k 2 , (o k 3 ). We hypothesized that U o k 1 þ o k 2 þ o k 3 À Á would not be equiva- lent to U o k 1 À Á þ U o k 2 À Á þ U o k 3 À Á (the assumption that choices were independent). We thus mapped the repeated choices to a more sophisticated non-repeated choice: one between all 10 (for the \"Repeated 2x\" condition) or 20 (for the \"Repeated 3x\" condition) combinations of individual choices o k 1 , o k 2 , (o k 3 ) participants could have made. We then calculated F summed q based on the summed agent utilities across all of these potential combination of matrices. Order of choices was not taken into account, but repetition of the same choice o k for o k 1 , o k 2 , (o k 3 ) was allowed. In short, by following this summing procedure, in the \"Repeated 2x\" condition, participants had 10 hypothetical choices, rather than the 4 they actually faced (two times). In the \"Repeated 3x\" condition, participants had 20 hypothetical choices, rather than the 4 they actually faced (three times). The analysis proceeded in the same way as for the \"Nominal\" condition in Experiment 1 except that the matrices M m expanded to contain 10 or 20 choices. \n Results and discussion In Experiment 2, we wanted to test how participant behavior would change across repeated conditions. One hypothesis was that participants would, as in Experiment 1, use the maximin metric for each individual choice, not keeping in mind the overall structure of the repeated choices. A second hypothesis was that participants would maintain maximin behavior when considering their combined choices, but would engage in different behavior (e.g., suboptimal behavior with respect to the maximin metric) within each individual matrix. A third hypothesis was that participants could have chosen to maximize the utility for one agent, then the other, alternating the optimal maximax options for each individual choice. This third hypothesis was not borne out in the data and so will not be further discussed. Results especially supported the second hypothesis, that participants may not have acted independently according to the maximin metric on each choice, but rather made sure that the overall outcome after all actions was a maximin-supporting outcome.  2  To test this, we evaluated the metrics' values over participants' combined choices (F summed q ). Statistically, we compared participants' empirical F summed q values to 10,000 samples of F summed q values from randomly generated choices, where the values were summed over participants and matrices. This comparison yielded z-scores and p-values relating the empirical results to the null distribution for each metric. (The statistics here are the same as explained in Experiment 1.) For both the \"Repeated 2x: Summed\" and the \"Repeated 3x: Summed\" conditions, the z-scores for the maximin metric were higher than for any other metric (Table  1 ), and they were in the same general range as those of the \"Nominal\" condition. The statistical analysis thus supported the conclusion that participants' behavior could be explained by applying the maximin metric across the set of repeated matrices they were reasoning over. We also analyzed the results through the MaxEnt model. We found that the degree to which the maximin metric explained behavior in the \"Repeated: Summed\" conditions, both for \"Repeated 2x: Summed\" (two repeated choices) and \"Repeated 3x: Summed\" (three repeated choices), was high and almost equivalent to in the \"Nominal\" condition (Fig.  4 ). Results also supported the first hypothesis to a lesser extent: that participants' behavior could be described by the maximin metric within each individual choice they made throughout the repeated choices. Here, we analyzed the data in terms of individual choices, completing a statistical analysis on the summed empirical and null distributions for the F indep q values. Z-scores were highest for the maximin metric for almost all conditions (\"Repeated 2x: Independent (Choice 2),\" \"Repeated 3x: Independent (Choice 1),\" \"Repeated 3x: Independent (Choice 2),\" and \"Repeated 3x: Independent (Choice 3)\") (Table  1 ). The exception was that the z-score for the \"Repeated 2x: Independent (Choice 1)\" condition was highest for the metric maxsum. To further analyze our data, we used the MaxEnt model to infer the combination of metrics that best described participant behavior over individual choices. We found that the maximin metric best described participant behavior for all of the conditions assuming independence: \"Repeated 2x: Independent (Choice 1),\" \"Repeated 2x: Independent (Choice 2),\" \"Repeated 3x: Independent (Choice 1),\" \"Repeated 3x: Independent (Choice 2),\" and \"Repeated 3x: Independent (Choice 3)\" (Fig.  4 ). The first hypothesis that participants would act according to the maximin metric for each of their individual choices was thus supported, though not uniformly across conditions, and contribution from a combination of metrics was visible within the MaxEnt results. Supporting the importance of the maximin metric in describing behavior, estimating a single h across all participants resulted in values dominated by the maximin metric for all but one condition in Experiment 2. Specifically, for the \"Repeated 2x: Independent (Choice 1)\" condition, h maxsum = 1 and h maximin , h maximax , h IA = 0, the sole condition where the maxsum metric was ranked highest. For the \"Repeated 2x: Independent (Choice 2)\" condition, h maximin = 1 and h maximax , h maxsum , h IA = 0. For the \"Repeated 2x: Summed\" condition, these averages were h maximin = 0.81, h maxsum = 0.19, and h maximax , h IA = 0. For the \"Repeated 3x: Independent (Choice 1)\" condition, these averages were h maximin = 0.92, h maxsum = 0.08, and h maximax , h IA = 0. For the \"Repeated 3x: Independent (Choice 2),\" \"Repeated 3x: Independent (Choice 3),\" and the \"Repeated 3x: Summed\" conditions, these averages were h maximin = 1 and h maximax , h maxsum , h IA = 0. This pattern of results suggests that participants consider all of their choices and maintain a running maximin metric calculation, though they also seem to apply the maximin metric to a lesser degree within each individual choice. Support for this argument draws from the following observation: The dominance of the maximin metric in explaining behavior is greater for conditions in which choices were considered cumulatively (the \"Repeated: Summed\" conditions) than for conditions in which each choice was considered independently (the \"Repeated: Independent\" conditions). Specifically, the maximin zscores were higher in the statistical analyses and the maximin h values were higher in the MaxEnt model for the \"Repeated: Summed\" conditions compared to the \"Repeated: Independent\" conditions, and they were in fact very similar to those in the \"Nominal\" condition. Finally, to verify that our weight vectors in the MaxEnt model generalized, we used participants' h vectors to predict held-out data. Training and testing on 50% participants Participants in the \"Repeated 3x\" condition, and \"Nominal\" condition. From left to right: h q for each choice in the repeated condition (choices were treated as independent); h q for summed choices in the repeated condition, where new matrices were calculated according to F q o k 1 þ o k 2 þ ::: À Á ; and h q from the \"Nominal\" condition. and matrices, the \"Repeated 2x: Independent\" condition had 47.0% predictive accuracy (non-held-out comparison: 53.6%, chance accuracy: 25%); the \"Repeated 2x: Summed\" condition had 39.3% predictive accuracy (non-held-out comparison: 43.3%, chance accuracy: 10%); the \"Repeated 3x: Independent\" condition had 45.8% predictive accuracy (non-held out-comparison: 57.9%, chance accuracy: 25%); the \"Repeated 3x: Summed\" condition had 10.9% predictive accuracy (non-held-out comparison: 17.6%, chance accuracy: 5%). Our weight vectors were less accurate in predicting \"Repeated: Independent\" conditions than they were compared to the non-repeated conditions, but had relatively high predictive accuracy for held-out test sets compared to non-held-out test sets. In the \"Repeated: Summed\" conditions, as chance accuracy fell, predictive accuracy also fell. With such low predictive accuracy in the \"Repeated 3x: Summed\" condition especially, we sought to test whether this was an artifact of the many potential choices available to participants in the \"Repeated\" conditions or a consequence of the utilities of the choices available, motivating Experiment 3. We observed that in both the \"Repeated\" conditions and the conditions from Experiment 1, participants' behavior was best described by the maximin metric. The lack of difference in the \"Repeated\" conditions could be construed as a null result, under the assumption that we did not manipulate the multi-decision conditions strongly enough to cause a change in participants' responses. To show that participants were producing different behavior in the \"Repeated\" conditions, but nevertheless overall their behavior could be best described by the maximin metric, we show that there is a different pattern of responses for each \"Repeated\" independent choice condition compared to the \"Nominal\" condition. Specifically, we computed the percentage of matrices wherein participants had significantly different responses between conditions. We found that that percentage was lower in comparing the \"Repeated (Choice 1)\" and \"Nominal\" conditions, and higher in comparing the \"Repeated (Choice 2)\" and \"Nominal\" conditions (Table  3 ). This percentage also changed with the \"Repeated 3x: (Choice 3)\" and \"Nominal\" condition comparison (Table  3 ). These percentage differences indicate that participants were making different choices within each matrix of the \"Repeated\" conditions, even while the overall results from the MaxEnt model showed continued maximin behavior. \n Experiment 3: Summed repeated choices When taking repeated actions, participants' individual choices tended toward being described by the maximin metric, but they were described by a combination of other metrics as well. Why were participants' repeated choices not as clearly described by the maximin metric as they were when making a single choice? It could be that participants were attempting to view all of the repeated trial as a single decision, and were trying to maximize the maximin solution across all choices, but that the mental overhead for this computation led them to less clearly maximin solutions. Alternatively, perhaps computational overhead was not very influential in participants making different choices than they had in Experiment 1, and there was something about the way that the repeated stimuli were presented that led to dissimilar results in Experiment 1 and 2-for example, perhaps participants felt pressure to vary their choices in Experiment 2 when faced with the same questions. To isolate whether computational overhead was an effect, we presented participants with the summed versions of the repeated choices they saw in Experiment 2. Participants could then see the summed version of choices in Experiment 2, so the computation was easier if they were attempting to sum utilities across decisions. This manipulation also allowed us to present participants with a slightly different one-shot matrix (with six options rather than four) to see if the results from Experiment 1 generalized. We investigated whether participant choices would be similar to those in Experiment 1, individual decisions in Experiment 2, and the artificially summed decisions in Experiment 2, with an emphasis on whether participants' behavior would be more or less clearly described by the maximin metric, as we expected from Experiments 1 and 2. In summary, we simplified the multi-decision problem presented before, testing what metrics described participants' solutions when Experiment 2's repeated choices were condensed into a single decision again. \n Method \n Participants Participants with U.S. IP addresses were recruited from Amazon Mechanical Turk across two additional conditions: \"Follow-Up (2x)\" (n = 31, 0 participants excluded) and \"Follow-Up (3x)\" (n = 29, 3 participants excluded). Participants were paid between $2.50 and $3.00 for their participation. Participants were excluded if they failed the included attention check or indicated that they did not understand the experiment. 7 20 35 Note. Shown is the percentage of matrices (\"% sig.\") wherein a chi-squared test of independence showed the histograms of participants' choices for each matrix were significantly different (p = .05: uncorrected) across the listed conditions. In more detail: for each matrix, the number of participants who picked each choice was summed, and this set of values was compared across the two experimental conditions listed. If a matrix had any expected value of 0 in the computed v 2 frequencies, that matrix was removed from the analysis. Note that expected values were often <5. The number of matrices that were significantly different according to the chi-squared test of independence (\"# sig.\") was divided by the total number of included matrices (\"# inc. total\"). Note that condition names are shortened: \"Rep2x: Ind.(C1)\" represents the \"Repeated 2x: Independent (Choice 1)\" condition.  \n Stimuli and procedure The stimuli and procedure were similar to Experiment 1. Participants again viewed each matrix once, but each matrix contained six choices that were drawn from the \"summed\" utilities from Experiment 2. In Experiment 2, for the \"Repeated 2x\" experiment, participants had 10 hypothetical choices per round, and in the \"Repeated 3x\" experiment, participants had 20 hypothetical choices per round. These hypothetical choices (of the form [A's utility, B's utility]) were what we used to generate each matrix in Experiment 3. To generate each matrix, we first tried to include one choice that maximized each metric. Specifically, we examined all 10 or 20 choices for each round from Experiment 2, and for each metric selected the choice that would be most preferred under that metric (e.g.,  [4, 4]  might be chosen under the IA metric, but not the maxsum metric if  [8, 4]  was also an option in the set). If two metrics had the same best choice (irrespective of order, so  [8, 4]  was identical to  [4, 8] ), this choice was only included once. If a metric had several best choices (e.g., under the IA metric, [3, 3] would be as good as  [4, 4] ), then an unused choice was selected at random. (Metrics with one best choice were examined first, and then metrics with multiple choices were examined in random order.) The remaining choices, since six choices were included in each matrix, were selected from the most popular unused choices from Experiment 2. \n Results and discussion In Experiment 2, we observed that participants appeared to be reasoning over the whole set of repeated choices, and that their behavior was best described by the maximin metric across that set (\"Repeated: Summed\" conditions). To further test this hypothesis, we constructed matrices where participants only had to make one choice, but each choice constituted the sum of previously repeated choices in Experiment 2. Our results corroborated those from Experiments 1 and 2. With these single-choice matrices, participants' behavior could be best explained by the maximin metric. In a statistical analysis comparing the empirical choices made by participants to a simulated set of random choices, zscores were highest for the maximin metric as compared to the other metrics in the \"Follow-Up (2x)\" and \"Follow-up (3x)\" conditions (Table  1 ). In our MaxEnt model, participant behavior was also best explained by the maximin metric in the \"Follow-Up (2x)\" and \"Follow-up (3x)\" conditions, to a degree similar as in the \"Repeated: Summed (2x)\" and \"Repeated: Summed (3x)\" as well as the \"Nominal\" conditions (Fig.  5 ).  3  The similarity of values across the \"Follow-Up\" conditions and the \"Repeated: Summed\" conditions support the hypothesis described in Experiment 2, that participants consider the whole set of choices when they make decisions rather than just each choice individually. Finally, to check that our MaxEnt weight vectors generalized, we used participants' h vectors to predict held-out data. Training and testing on 50% participants and matrices, the \"Follow-Up (2x)\" condition had 71.6% predictive accuracy (non-held-out comparison: 71.6%, chance accuracy: 16.7%); the \"Follow-Up (3x)\" condition had 60.5% predictive accuracy (non-held-out comparison: 66.7%, chance accuracy: 16.7%). We could predict participant responses to the \"Follow-Up\" conditions well with and without held-out testing sets, indicating the strength of our inferred weight vectors. The high predictive accuracy in the \"Follow-Up\" conditions compared to the \"Repeated: Summed\" conditions indicate that the previous low predictive accuracy was a consequence of the large number of possible choices available in the \"Repeated\" conditions, and the complexity of not seeing the end results directly and having to compute them, rather than a consequence of the utilities of the choices themselves. \n General discussion If a schoolteacher is trying to choose a field trip for a group of students with kinetic learners, visual learners, children who do not speak English at home, boisterous students, and students who are scared of new places, what should they do? How should people donate their money, governments choose between aid programs, or assistive robots mediate between family members' preferences? In this work, we examined the broader question of how a decision-maker should act when people have different preferences. Specifically, we asked people what they would do in a paradigm where they could take  F q o k 1 þ o k 2 þ ::: À Á ), and \"Nominal\" conditions. (Below) Participants in the \"Follow-Up (3x),\" \"Repeated 3x\" (summed choices), and \"Nominal\" conditions. The maximin metric best described participant behavior. only one action, making a single drink, to the inevitable dismay of some of the people they were serving. While it is not clear that decision-makers should automatically match the behaviors that people intuitively use to make group-level decisions, it is informative to know the ground truth of what people feel are good decisions. We analyzed participants' choices by assuming their behavior could be captured by a combination of four metrics. Of these metrics-maximax, maxsum, maximin, and inequality aversion (IA)-we observed that participants' behavior could be reliably described by the maximin metric, the idea of maximizing the utility of the worst-off agent. With respect to our story, the schoolteacher may not know what is the right thing to do, but we at least know how people behave: For each field trip find the child who would have the worst time and choose the field trip wherein that child enjoys the field trip as much as possible. Participants behaved according to the maximin metric despite changes in the agents involved. Specifically, whether considering a robot manager, human manager, or serving friends or strangers, participants' behavior was similar and described by the maximin metric (Experiment 1). Participants did tend to move toward behavior more described by the maxsum metric when they were told they were beneficiaries of the decision, perhaps reasoning about the task more as a gambling situation and less as one mandating fairness for unknown recipients. In Experiment 2, we found that when participants made repeated decisions, each individual choice therein was characterized by a modest maximin preference. However, participants also acted as if they maintained a running total of their choices across repeated decisions. In particular, participants' behavior was best described by the maximin metric under the assumption that they were summing utilities across repeated decisions. Experiment 3 provided additional support for the hypothesis that people maintain an overall calculation in repeated decision-making, rather than reasoning over each problem individually. When participants' cumulative choices from Experiment 2 were summed to create a combined set of matrices for Experiment 3, participants' behavior was described by the maximin metric to the same degree as was shown in the \"Repeated: Summed\" and \"Nominal\" conditions. All of these results suggest that participants keep track of calculations over time and prefer making decisions consistent with the maximin metric when allocating indivisible items across agents. In the remainder of the paper, we discuss the relationship of these results to previous work, and ways in which these results could be extended. \n Relationship to previous work We asked what a decision-maker should do when it could take only one action-create one resource-to be shared among multiple other agents, and our results support the hypothesis that participants prefer to behave in ways described by the maximin metric. How, then, do our results compare to the literature? In the nearby literature of fair allocation, there is not nearly so neat a consensus. However, in most fair allocation studies the participant acts as a self-interested party, weighing the desires of selfishness and \"fair\" allocation. We are interested in the case of what people consider helpful actions when they have no stake in the outcome. Four studies are similar to our study in that respect. The first is  Herreiner and Puppe (2007) , who presented participants with payoff matrices in which agents could receive different \"goods.\" Unlike our study, in which there was only one item to be created/allocated, the paradigm in  Herreiner and Puppe (2007)  resembled an estate game in that multiple items, the number of which was often larger than the number of agents, could be distributed to various agents. This added complication to the proceedings, as participants then had large numbers of item combinations to reason over (e.g., their Problem 1 had 3 3 = 27 different allocations), and they could consider fairness not only over utilities, but over \"bundles\"-the set (and number) of items allocated. To this end,  Herreiner and Puppe (2007)  constructed their payoff matrices with an eye to the metric of \"envy-freeness,\" which describes whether any given agent would be envious of any other agent's bundle. The results from  Herreiner and Puppe (2007)  seem to be consistent with a hypothesis that participants prefer acting according to a maximin metric, given that in their study this metric was sometimes confounded with different metrics within a single choice. However, in their Problem 1 and Problem 6,  Herreiner and Puppe (2007)  showed results indicating that participants preferred the IA metric over the maximin metric. In Problem 1, participants chose to withhold the last item rather than give one agent two items compared to the other one (preferring the two agents to have utilities  [49, 48]  rather than  [49, 53] ), and in Problem 6, participants distributed four items across three agents to maintain exactly equal utilities  [45, 45, 45]  rather than choosing the best maximin allocation  [48, 60, 52] . Problem 1 is an interesting case in that participants were considering fairness in both utilities and item number. Our participants tended to choose according to the maximin metric when only considering utilities, but it could be that if we had asked them to reason over both utilities and item number they would have considered choices emphasizing inequality aversion as fairer and better, especially when the difference in utilities was small. In Problem 6, our results suggest that choice complexity could have been influencing the observed results in  Herreiner and Puppe (2007) , and in future work it would be interesting to check if participants would choose the IA solution  [45, 45, 45]  rather than the maximin solution  [48, 60, 52]  if directly presented with those choices, rather than being asked to add utilities from four items across three agents. As a final note on the complexity of addition,  Herreiner and Puppe (2007)  noted in their discussion that participants' final solutions were correlated with their reported allocation procedures-for example, the order in which participants assigned items to each agent. Allocation procedures were not inherent to our problem setup but are well-considered within the fair allocation literature (see e.g.,  Dupuis-Roy & Gosselin, 2011) , and perhaps also add implicit utilities to participants' preferred choices. In  Engelmann and Strobel (2004) , the basic structure of the task was very similar to ours, as participants made choices between three items that three agents had utilities over. Though the participant acted as one of these agents, the participant's utility was always held fixed over all items.  Engelmann and Strobel (2004)  focused their payoff matrices on distinguishing between two existing models, each of which had one utility function designated as participants' preferred allocation metric. As such,  Engelmann and Strobel (2004)  also had many matrices that confounded the metrics we considered, but with this caveat the maximin metric could be considered a primary motivation for participants' behavior. Relevantly,  Engelmann and Strobel (2004)  state that one of the models they evaluated performed well because it captured the maximin metric, but that overall a combination of maximin, maxsum (which they call efficiency), and selfishness (which we do not consider) considerations drove participant behavior. Indeed, in several of their payoff matrices, both the best maxsum and maximin choices were often selected by participants, and the maxsum choice often garnered a higher proportion of participants.  Fehr et al. (2006) , however, provide a rebuttal to the Engelmann and Strobel (2004) paper, replicating the  Engelmann and Strobel (2004)  study with non-economics participants and showing that the maxsum solution was selected far less by participants who were in different programs.  Fehr et al. (2006)  did not choose payoff matrices that distinguished between the IA and maximin metrics, but their results hint that the subject pool can influence preferred allocation metrics.  Herreiner and Puppe (2007)  tested economics and law student participants, but our study was conducted on Amazon Mechanical Turk and had a broader population than economics undergraduates. In future work, it would be interesting to replicate our study with economics undergraduates, and observe whether this difference is enough to observe participants' preference for the maxsum metric over the maximin metric. Fairness perceptions have been observed to differ across different populations (see, e.g.,  Andreoni & Vesterlund, 2001; Croson & Gneezy, 2009; Gaertner & Schwettmann, 2007; Marwell & Ames, 1981; and Camerer, 2011 , summarizes some demographic results for behavioral game theory), so this hypothesis would not be improbable, though the review in  Konow and Schwettmann (2016)  cites that generally demographic variables seem to have relatively small effects on economics experiments.  Yaari and Bar-Hillel (1984)  presented several different types of scenarios wherein a third party allocated goods according to the maximin metric, maxsum metric, and IA metric. Participants played three types of games, where they had to allocate fruits according to receiving agents' needs or tastes/utilities, and also across agents' differences beliefs about the fruits. Participant behavior differed across the varying conditions, shifting according to the tradeoffs presented, as in this work. The authors observed that when choices were presented in terms of needs-one agent needs a certain type of vitamin to be healthy, so they needs a certain type of fruit-82% of participants chose the maximin allocation. In our paradigm, agents did not have needs, rather stated utilities (preferences over choices). This was much closer to the second condition in  Yaari and Bar-Hillel (1984) , in which agents had different \"tastes\" or stated utilities. Intriguingly, participants did not adhere as strongly to the maximin choice in this case, as instead 28% chose the maximin solution, and 35% of participants chose the maxsum allocation. The distribution of choices also changed in the third condition of  Yaari and Bar-Hillel (1984) , in which agents had different perceptions of how much value each of the items would give them.  Yaari and Bar-Hillel (1984)  concluded from their experiments that the maximin metric best describes participant behavior, but only when needs are salient. In our work, we found that participants made choices according to the maximin metric outside of needs-based formulations and did so consistently across changes in wording and repetition over time. Our paradigm differed from that of  Yaari and Bar-Hillel (1984) , however, which could account for the difference in results. The main difference between our work and that of  Yaari and Bar-Hillel (1984)  is that we asked a different question: Given agents had utilities over a set of four or six options, which option should be chosen to best satisfy those utilities?  Yaari and Bar-Hillel (1984)  asked a fair allocation question: Given a specific number of items (and agents' preferences over the different items in the \"tastes\" condition), how should those items be divided between agents? The fair allocation paradigm is necessarily zero-sum, wherein if one agent receives a resource, another loses it. In particular, in question 4 from  Yaari and Bar-Hillel (1984) , participants were asked to divide 12 grapefruit and 12 avocados between two agents. One agent was stated as hating avocados (utility = 0), but would buy grapefruit if they were priced under $1 per pound. Meanwhile, the other agent liked both avocados and grapefruit and would pay for them if they were priced under $0.50 per pound (half the utility of the first agent for grapefruit). With these agent preferences in mind, participants were now expected to divide a fixed number of grapefruit and avocados. Compare this to our study, in which participants decided which drink to give to two agents to share. This task is not zero-sum -if one agent has high utility for a drink, this does not detract from another agent's utility for that drink. We did, however, have four matrices out of 20 for each experiment in which the joint utilities for each drink were identical, meaning that no matter what drink the participant chose, the agents would only jointly achieve a given happiness. But in this scenario, the question was not \"how many of each item should be given to each agent given their utilities\" (as in  Yaari & Bar-Hillel, 1984) , but \"given there is a fixed amount of utility to be had, how should that utility be divided between agents?\" This is a distinct question, and it is probable that participants reason differently about a zero-sum problem of \"distribute 12 pieces of fruit between two people or throw some away\" (allocation) compared to \"create one shared item that will make two people more or less happy.\" We may expect that  Yaari and Bar-Hillel (1984)  did not observe as much maximin behavior because they used a task of zero-sum bundle allocation; this hypothesis should be investigated in future work. Another difference between our study and that of  Yaari and Bar-Hillel (1984)  was that we probed participants' intuitions of what was fair with 20 questions (4 or 6 choices each) for each experiment, and we determined which metrics best described participants' behavior by accumulating evidence across all of these trials. Alternatively,  Yaari and Bar-Hillel (1984 ) had participants answer one question for each experiment (usually with 5 choices), and we used that single choice to inform which single \"mechanism\" (analogous to our metrics, but without considering combinations of metrics) best described participant behavior. The authors thus did not have a continuous characterization of how much participants were acting in accordance with different metrics, instead using discrete choices that distinguished \"maximin,\" \"maxsum/utilitarian,\" and other allocations, which they tested with a single set of choices. With more trials available and a finer-grained measure of how each choice contributed to the various metrics,  Yaari and Bar-Hillel (1984)  may have observed a more maximin-biased distribution, as we did. As a final aside, with regard to changing in wording,  Yaari and Bar-Hillel (1984)  found similar distributions of responses when they asked, first, how participants would divide the items, and second, how the two agents would divide the items if the agents were aiming to be just. In our paradigm, we asked only what a third-party decision-maker would do, but this result implies that in our paradigm we would find similar responses if we were asking participants what choices recipients would think were just. Our study stands in contrast to these four studies in a few ways. First, while our problem formulation can encompass any fairness allocation problem based on our definition of an \"action,\" the specific paradigm we used was specialized to solve the problem of what single item a decision-maker should choose to distribute to a group (a rather straightforward action). This stands in contrast to fair allocation studies, and we described a direct comparison of our study and  Yaari and Bar-Hillel (1984)  on this axis, with a particular eye to zero-sum choices. Additionally, some differences in our results may be attributable to experimental simplicity. For example, in  Herreiner and Puppe (2007) , participants may entertain additional implicit utilities when they reason over bundles (such as item number fairness), and there may be difficulties in balancing many possible choices while considering different allocations of 3 to 4 goods. Similarly,  Yaari and Bar-Hillel (1984)  introduce motivational features not present in our work, like division based on agent needs. A second methodological distinction of our study is that the other studies did not use a continuous measure of behavioral alignment to several metrics, instead using discrete comparisons over metrics that largely correlate, which leaves the option open that finer-grained distinctions may change their details of some of their results. Additionally, a significant advantage of our study is that we employed 20 matrices and could have employed more, whereas other studies had fewer than 12 payoff matrices, and these payoff matrices often confounded different metrics due to the authors' different emphases. Finally, we showed consistent participant behavior aligning with the maximin metric, rather than emphasizing the involvement of the maxsum and IA metrics, and observed this finding over repeated conditions, a contrast which has not been previously conducted to the authors' knowledge. In summary, our study is aimed at a different question than most in the fairness literature; we aim to study how people would prefer that decision-makers act when they can benefit multiple people. This question is not addressed in previous studies, but is most related to other fairness studies examining uninterested third-party (zero-sum) decisions (note that unlike a fair allocation problem, our problem is not zero-sum since a decisionmaker is creating a resource for two people with different but not opposing utilities.) Within this previous work, preference for the maximin metric has not been universally shown, and the maximin metric is often not directly compared with other potential metrics. Relatedly, previous studies often do not account for the correlations among metrics when describing participant choices. Here, we presented many choices to participants, testing their intuitions many times for each question, and then used a MaxEnt model to disambiguate between the overlapping metrics that described each choice. We additionally probed participants' behavior in repeated, longer-term scenarios than have been evaluated for this problem setting. We distinguished participants' choices representative of the maximin metric by direct comparison with competitive strategies, across many question formulations to ensure generalization. We thus provide a novel contribution to the question of what people think a decision-maker should do when faced with helping people with unique utilities. \n Future directions An interesting extension to this work would be to do the full study that includes extreme comparisons. If participants are faced with the choices  [4, 80] and [4, 4]  (where agent A receives the first number and agent B receives the second), all participants will likely choose  [4, 80] , because the tradeoff between maximizing the sum and trying to maintain equality between agents is so extreme. These choices could be varied parametrically, gradually making the tradeoffs less extreme (and more difficult to choose between) with respect to different metrics. Our study lies basically at the center of that parametric descent, where the choices are most difficult. It is difficult to choose whether [4, 8] or [5, 5] is better, and behavior according to both the maximin and maxsum metrics is competitive. In this range, determining whether a participant was acting more according to a maximin or an IA metric required accumulating evidence across trials, motivating the use of our MaxEnt model. This is because each choice that a participant made could serve a few possible metrics simultaneously, and in Table  1  we observed this by noting that in the raw data, participants' behavior tended to be described by the maxsum, maximin, and IA metrics rather than a single metric. However, our paradigm would work well in evaluating when participants would change their behavior as tradeoffs become more extreme. If a participant acts according to the IA metric until the group utility hits a threshold, that participant should then continue acting according to a maxsum metric for all the more extreme choices thereafter. Tradeoffs like those between equity, the maxsum metric, and need (which we do not examine here) have been widely compared in previous studies. Work like  Ahlert et al. (2013) ,  Charness and Rabin (2002) ,  Engelmann and Strobel (2004 ), Faravelli (2007 ), Fehr et al. (2006 ,  Fisman et al. (2007) ,  Konow (2001 Konow ( , 2003 ,  Konow and Schwettmann (2016) ,  Mitchell et al. (1993) ,  Ordoñez and Mellers (1993) ,  Pelligra and Stanca (2013 ), Schwettmann (2009 , 2012 , and  Skitka and Tetlock (1992)  find that participants do trade off between different principles based on the choices presented, as we see in our work when participants make choices in accordance with several of the metrics. The suggested set of experiments would confirm and expand upon our results, as our stimuli were chosen to isolate which metrics participants thought best when choices were most difficult. Moreover, a parametric study examining these tradeoffs would provide a large and systematic dataset to contribute to the empirical literature on this topic. Another extension to this study could be to consider whether having verbal problem descriptions, or other representations of utilities, would enhance our paradigm.  Hurley, Buckley, Cuff, Giacomini, and Cameron (2011)  replicated the study by  Yaari and Bar-Hillel (1984)  with quantitative problem descriptions, verbal problem descriptions, and both combined. In their verbal descriptions, they instructed participants to create an allocation according to a given metric: \"Divide the apples in such a way that the total amount of vitamin F obtained by both Jones and Smith together is as large as possible,\" is an example of a maxsum instruction. The authors report that the results from the verbal problem descriptions were consistent with participants not understanding the relationship between the described metrics and their quantitative allocations, and that participants increased maxsum behavior. We used quantitative information in the present study; it would be hard to adapt the flexibility inherent in the different choices we presented to participants in a verbal-only description.  Hurley et al. (2011)  find that verbal and quantitative descriptions together produce results that more closely match quantitative descriptions alone. Because verbal descriptions do not seem to produce an increased understanding, we expect our paradigm works well with quantitative information, though the question of how to represent utilities and the effects of that choice on participant behavior remains an interesting one. One limitation of this study is that it asks participants to evaluate between two agents only. The fair allocation literature commonly evaluates over two or three recipient agents; we expect our results to also scale to three agents, but we do not know how robust our findings will be at larger group sizes. This question is incredibly important given that large-scale decision-making impacts many people and so should be done in a way endorsed by many. We do not know that our results will scale: As group size increases, utilities become harder for participants (and people in general) to reason over, so we expect different heuristics will emerge. Fortunately, our experimental paradigm would serve as a good platform for this work given that we can easily generate sets of matrices which require participants to make difficult decisions and can analyze participants' responses with various insertable metrics. Finally, in future work, we hope to expand the generalizability of our findings. Within our paradigm, we observed consistent and robust results which were supported by using many matrices and conditions. Our paradigm differed from most in the fair allocation literature due to its focus on a more general problem: what a decision-maker should do when it can take one action (in this case making a drink) that will be shared among agents with different preferences. This paradigm itself offers many avenues for expansion -there are many other actions a decision-maker could take besides making an item, including choosing a field trip, donating to organizations, or making governmental policy decisions. We should also consider actions that produce choices with negative utilities, since the dynamics at play in, for example, trolley problems or risk or loss aversion will likely lead to different behaviors. Drawing from the fair allocation literature also shows that this paradigm could be made more complex as multi-step actions are introduced (e.g., an action encompassing bundle distribution), or selfishness, need, desert, and other factors are considered.  Konow (2003)  presents a pluralistic approach, in which the prime considerations when thinking about justice are a sense of equality and need, utilitarinism and welfare economics, equity and desert, and context (other papers that present pluralistic approaches are  Cappelen, Hole, Sørensen, & Tungodden, 2007; Deutsch, 1985; Frohlich & Oppenheimer, 1992; Konow & Schwettmann, 2016; Lerner, 1975; Leventhal, 1976 ) and all will need to be incorporated into a fuller model of what people consider desirable behavior. This work provides a general problem framework and quantitative model of what people think a third party should do when taking an action that will bring people different utilities. While the problem we address is distinct from that of fair allocation, it is informed by this literature and can contribute to the discussion of desirable descriptions of helpful behavior. Understanding what actions to take when every choice affects the well-being of many people with disjoint preferences has important bearings on the future, whether in designing decision-making algorithms for artificial intelligence systems, quantitatively evaluating how to help individuals make decisions that are better in line with what people consider to be good choices, or even creating accepted assistive robots. This and future work focusing on making our results more generalizable-and determining whether we would like our decision-makers to adopt people's intuitions of preferred choices-will provide important contributions to this problem. \n Conclusion Decision-making would be a much easier problem if everyone had the same preferences. Even having everyone agree about what to do about diverging preferences would help reduce the complexity of reasoning over many diverse perspectives. While that is not quite the spirited environment we live in, in today's world, we have an opportunity to make these complex decision-making tasks easier with artificial intelligence systems. Artificial intelligences can optimize any number of people's preferences once they know what they are, and in this work, we develop a quantitative model of people's intuitive preferences for what to do when making difficult decisions to help people. Determining what decision-makers should do is a topic that philosophers and governors have wrestled with for centuries: How do we think about inequality within individuals and in society? In this work, we ventured into the morass, developing a general problem framework that let us ask people how they would choose one action whose impact would be different for everyone. Deeper questions remain: What are humanity's morals around inequality, and how does what we do compare to how we think we should be? We do not know what to teach our decision-makers yet, and determining the answers to these questions will require significant collaborative effort. Fortunately, we did determine what drinks to serve at the resulting conferences. \n Open Research badges This article has earned Open Data and Open Materials badges. Data and materials are available at https://osf.io/gybd4. Notes 1. The disadvantage of normalizing the values within each metric was that information about metrics that had particularly high or low values for a given matrix was lost. However, we considered this choice better than the alternative unnormalized option, for which there would be no sense of the alternative options participants were choosing between. 2. As an example, if participants in the \"Repeated 2x\" condition were analyzing the matrix in Fig.  1 , to maximize the maximin metric on each choice they would choose the [A: 5, B: 8] cup twice, but if they were maximizing the maximin metric across all choices, they would choose the [A: 4, B: 11] cup once and the [A: 12, B: 2] cup once. Note that choosing the [A: 5, B: 8] cup twice is tied for the second-best option for maximizing maximin overall, so this set of choices would still contribute to the hypothesis that participants were maximizing the maximin metric across all choices, just not as strongly as would be true if the participant had chosen the [A: 4, B: 11] cup once and the [A: 12, B: 2] cup once. 3. Our results from estimating a single h across all participants, h maximin = 1 and h maximax , h maxsum , h IA = 0 for the \"Follow-Up (2x)\" and \"Follow-Up (3x)\" conditions, also support the conclusion that participants' behavior was best explained by the maximin metric. Fig 4 . 4 Fig 4. MaxEnt model results for Experiment 2, showing mean inferred weight h AE SE for each metric across participants. (Above) Participants in the \"Repeated 2x\" condition, and \"Nominal\" condition. (Below)Participants in the \"Repeated 3x\" condition, and \"Nominal\" condition. From left to right: h q for each choice in the repeated condition (choices were treated as independent); h q for summed choices in the repeated condition, where new matrices were calculated according to F q o k 1 þ o k 2 þ ::: \n V . Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020) \n Fig 5 . 5 Fig 5. MaxEnt model results for Experiment 3, showing mean weight h AE SE for each metric across participants. (Above) Participants in the \"Follow-Up (2x),\" \"Repeated 2x\" (summed choices, where new matrices were calculated according to F q o k 1 þ o k 2 þ ::: \n Table 1 1 Results for Experiment 1, showing relationship between participants' responses and hypothetical null distribution for each metric Maximax Maxsum Maximin IA Nominal À0.2 (.58) 11.2 (0) 19.7 (0) 10.9 (0) Robot 0.6 (.27) 10.7 (0) 16.7 (0) 8.6 (0) Robot Friends 1.6 (.05) 13.6 (0) 19.0 (0) 9.7 (0) Robot Strangers 0.6 (.27) 9.5 (0) 14.7 (0) 7.3 (0) VoI 3.1 (.002) 8.7 (0) 7.8 (0) À0.1 (.53) Rep2x: Ind.(C1) 4.1 (0) 9.7 (0) 7.8 (0) 1.9 (.03) Rep2x: Ind.(C2) 1.3 (.10) 5.6 (0) 6.9 (0) 2.8 (.002) Rep3x: Ind.(C1) À1.2 (.89) 5.7 (0) 11.9 (0) 6.9 (0) Rep3x: Ind.(C2) 0.4 (.34) 3.6 (1e-4) 5.4 (0) 3.0 (.001) Rep3x: Ind.(C3) À2.1 (.98) 1.8 (.03) 7.3 (0) 5.0 (0) Rep2x: Summed À9.4 (1) 9.4 (0) 19.2 (0) 14.4 (0) Rep3x: Summed À24.0 (1) À0.007 (.50) 26.1 (0) 20.8 (0) Follow-Up (2x) À11.0 (1) 5.3 (0) 22.1 (0) 14.7 (0) Follow-Up (3x) \n Table 2 2 Percentage of participants whose behavior is best described by each metric, according to the MaxEnt model Maximax Maxsum Maximin IA Nominal 8 3 83 6 Robot 14 17 63 6 Robot Friends 9 9 83 0 Robot Strangers 18 6 71 6 VoI 27 18 48 6 Rep2x: Ind.(C1) 29 12 58 0 Rep2x: Ind.(C2) 25 21 46 8 Rep3x: Ind.(C1) 14 10 62 14 Rep3x: Ind.(C2) 19 29 38 14 Rep3x: Ind.(C3) 29 5 48 19 Rep2x: Summed 0 12 87 0 Rep3x: Summed 10 5 71 14 Follow-Up (2x) 3 6 90 0 Follow-Up (3x) \n\t\t\t of 42 V. Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020) \n\t\t\t V.Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020)   \n\t\t\t of 42 V. Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020) \n\t\t\t of 42 V. Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020) \n\t\t\t of 42 V. Gates, T. L. Griffiths, A. D. Dragan / Cognitive Science 44 (2020)", "date_published": "n/a", "url": "n/a", "filename": "Cognitive Science - 2020 - Gates - How to Be Helpful to Multiple People at Once.tei.xml", "abstract": "When someone hosts a party, when governments choose an aid program, or when assistive robots decide what meal to serve to a family, decision-makers must determine how to help even when their recipients have very different preferences. Which combination of people's desires should a decisionmaker serve? To provide a potential answer, we turned to psychology: What do people think is best when multiple people have different utilities over options? We developed a quantitative model of what people consider desirable behavior, characterizing participants' preferences by inferring which combination of \"metrics\" (maximax, maxsum, maximin, or inequality aversion [IA]) best explained participants' decisions in a drink-choosing task. We found that participants' behavior was best described by the maximin metric, describing the desire to maximize the happiness of the worst-off person, though participant behavior was also consistent with maximizing group utility (the maxsum metric) and the IA metric to a lesser extent. Participant behavior was consistent across variation in the agents involved and tended to become more maxsum-oriented when participants were told they were players in the task (Experiment 1). In later experiments, participants maintained maximin behavior across multi-step tasks rather than shortsightedly focusing on the individual steps therein (Experiment 2, Experiment 3). By repeatedly asking participants what choices they would hope for in an optimal, just decision-maker, and carefully disambiguating which quantitative metrics describe these nuanced choices, we help constrain the space of what behavior we desire in leaders, artificial intelligence systems helping decision-makers, and the assistive robots and decision-makers of the future.", "id": "20060c07d732fb026d9c7a9e202fb792"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": "n/a", "title": "n/a", "text": "n/a", "date_published": "n/a", "url": "n/a", "filename": "Its_not_too_soon_to_be_wary_of_AI_We_need_to_act_now_to_protect_humanity_from_future_superintelligent_machines.tei.xml", "id": "e11b42165e5bed91cfe1effb402165e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Robin Hanson", "Curt Adams", "Bryan Caplan", "Joel Cohen", "Roger Congleton", "Tyler Cowen", "Mark Crain", "Eirikur Hallgrimsson", "Carl Feynman", "Hal Finney", "Brad De Long", "Perrin Meyer", "Carlos Ramirez", "John Schroeter"], "title": "Long-Term Growth As A Sequence of Exponential Modes", "text": "Introduction Many have argued that current U.S. stock prices are much higher than can be justified by reasonable profit forecasts based on empirical models derived from the recorded history of the U.S. economy  (Shiller, 2000) . While it might be theoretically possible for the economy to suddenly switch to a fundamentally new mode with much higher corporate profits, our experience with the U.S. economy offers little evidence that a mode switch of this magnitude has happened anytime in the last century or so  (Barro & Sala-i-Martin, 1995) , though we may be able to understand smaller changes in stock prices in terms of milder fluctuations in profit trends  (Barsky & De Long, 1993) . The arguments against high current U.S. stock prices are thus largely empirical, in contrast with the theoretical nature of the (typically informal) arguments offered in support of investor optimism. These empirical arguments, however, are based primarily on the last century or so of economic experience. Could empirical forecasts based on a longer term history of economic growth offer more support for the rationality of high stock prices? To address this question, this paper will take an empirical approach to modeling very long term data on economic growth, with an eye toward inferring the chances for very large changes in economic growth modes. In order to empirically model very long term economic history, we need one or more very long term time series, and we need to choose one or more functional forms to use in modeling those time series. Most attempts to formally model long term human history have focused on population time series, as population estimates have been offered going back many thousands of years, and such time series have been considered to be the most reliable long term series available. Also, for most of human history population seems to have reasonably reflected most fundamental changes, including areas colonized, capital accumulated, and technologies adopted. This seems to be because new productive abilities have mainly resulted in larger populations under Malthusian conditions of near-subsistence per capita consumption. Nearly constant per capita consumption, however, implies that reasonable estimates of total consumption can be obtained from reasonable estimates of population. We thus have reasonable estimates of world product up until about 1500, when per capita product began to rise. Economic historians have also provided us with reasonable estimates for world product over the past century or so  (Maddison, 1995) . So all that has stood in the way of a full long term world product time series was to fill in the gap from roughly 1500 to 1850. Recently economic historian Brad De Long has cleverly used a simple empirical Malthusian relation to fill this gap, and has thus created a world product time series ranging from one million B.C. to today  (De Long, 1998) . His estimates for before 10,000 B.C., however, are based on forty year old speculations  (Deevey, 1960) . This paper will therefore replace those old speculations with recent published estimates going back to two million B.C.  (Hawks, Hunley, Lee, & Wolpoff, 2000) . This paper will then attempt to empirically model that time series with a few simple functional forms. After considering models of gradually accelerating growth, which have been the most popular in formal models of long term population growth, we will turn to attempting to formalize the more common informal descriptions of history as a sequence of growth modes. And since exponential growth is the most common formal description of short term growth, we will consider modeling long term world product history as a sequence of exponential growth modes. The simplest sequence of exponentials is a sum of exponentials, and we will find that a sum of four exponential modes fits the data with less than a 2% average error, which is less than the average uncertainty in the estimates. One of these modes, however, appears to be there just to allow a more gradual transition between two other modes than a simple sum of exponentials will allow. So we will then try a constant elasticity of substitution (CES) form for combining exponentials, which can allow a transition to be smooth or sudden by varying a single parameter. We will find that a CES combination of three exponential modes also fits the data with less than a 2% average error. After describing these models, and discussing their interpretation, we will then use them to consider when we might see a transition to yet another mode of economic growth, and how fast growth might then be. It seems quite unreasonable to expect an infinite series of faster and faster growth modes, since that leads to an infinite world product in finite time. But it may be reasonable to wonder if a world that has so far seen at least three distinct growth modes might see yet one more growth mode. \n The Data Economic historians have reasonable estimates for world product over the last century or so, while other historians have reasonable estimates for world population over the last ten thousand years, and cruder estimates for the two million years before that. Until a few centuries ago, per-capita consumption was typically near subsistence levels, making it easy to infer world product from world population. Thus the obstacle to having a full long term world product time series has been to get reasonable estimates for the intermediate period, from roughly 1500 to 1850. Recently, economic historian Brad De Long found a simple linear relation between world population growth rates and per capita product, a relation which seems valid at the low values of per capita product observed from roughly 1850 to 1950  (De Long, 1998) . This linear relation has allowed him to created world product estimates for the missing intermediate period, and thus to create a world product time series ranging from one million B.C. to today. De Long developed several time series based on alternative assumptions, and this paper uses his preferred world product series. The only change made here is to substitute more recent estimates for population prior to 10,000 B.C. De Long continued the use by Kremer  (Kremer, 1993)   Deevey's estimates, however, were never published in a peer-reviewed journal, cite no other sources, and are now forty years old. The data set used here excises Deevey's forty year old estimates and instead substitutes two more recent population estimates. Hawks and coauthors  (Hawks et al., 2000)  estimate a \"population bottleneck\" of about ten thousand at about two million B.C., and that we \"cannot reject exponential growth from\" then until ten thousand B.C. Consistent with that conclusion, they also accept a Weiss  (Weiss, 1984)   The resulting world product time series has 54 data points, is graphed in Figure  1 , and is listed in the appendix. In Figure  1 , world product is described in units of an equivalent number of humans at a subsistence consumption level. 2 Time is described by the number of years before the somewhat arbitrary date of 2050. This data is also graphed later in Figure  2 , which shows world product growth rates versus levels, displaying each step between data points as a horizontal line. This graph looks noisier, because growth rates are noisier, but it has the virtue of avoiding the arbitrary choice of a reference date like 2050. 3 \n Choosing a Functional Form What functional form should we use to model our world product time series? Simple exponential growth is probably the most popular general model for describing positive quantities that grow in time by many orders of magnitude, as both population and world product have. It is, for example, widely used to model the last half century of economic growth  (Barro & Sala-i-Martin, 1995)  and 1 These estimates are based on a \"multi-regional\" model of human evolution  (Relethford, 1998 ). An alternative \"out of Africa\" model posits a similar population bottleneck at roughly 200 thousand B.C.  (Rogers & Jorde, 1995; Ingman, Kaessmann, Paabo, & Gyllensten, 2000) . The multi-regional model is based more heavily on non-genetic fossil evidence. Genetic evidence may well estimate the number of our direct ancestors alive on a given date, but nongenetic fossils seem better estimates of the size of the economy or ecological niche occupied by our direct ancestors and their very close relatives on that date. Further footnotes will, however, mention how the alternative model changes this paper's estimates. 2 Specifically, \"subsistence\" is $80 1990 \"International\" dollars, which is the ratio of De Long's preferred world product and population estimates for one million B.C. This per capita product has been assigned to my substitute dates of two million B.C. and 750 thousand B.C., and retained De Long's estimates for all other dates. 3 In the analysis which follows, we will occasionally compare world product growth since two million B.C. to the earlier exponential growth of maximum brain size. Maximum animal mass and relative brain size have both grown roughly exponentially since the Cambrian explosion about 550 million years ago, when animals first appeared in large numbers in the fossil record. The mass of the currently largest animal doubled roughly every 70 million years, while maximum brain volume relative to body volume (raised to the 2/3 power) has doubled roughly every 50 million years  (Russell, 1983) . (More details on the details of brain size history are given by Jerison  (Jerison, 1991) .) Together these estimates suggest that maximum animal brain size has doubled roughly every 34 million years over the last 550 million years (for a total of about 16 doublings). For comparison, the exponential decay rate of Marine genera over this period was a half-life of about 23 million years  (Valen, 1973; Newman & Sibani, 1999) . the last few centuries of growth in scientific literature  (de Solla Price, 1963) . Simple variations on exponential growth, such as linear trends in growth rates, have been particularly popular in making short term population forecasts  (Lee, 1990) , but seem clearly inadequate for longer term forecasts. Variations on logistic growth have also long been popular in estimating various population trends  (Meyer & Ausubel, 1999) , but also seem clearly inadequate for modeling very long term population trends  (Cohen, 1995) . Many researchers have had more empirical success explicitly modeling long term population histories with functions that describe accelerating change. The first such efforts used simple hyperbolics  (von Foerster, Mora, & Amiot, 1960) , and soon became infamous warnings against taking one's model too literally, since they predicted an infinite human population in the early twenty first century. More recent related efforts  (Kremer, 1993; Kapitza, 1996; Johansen & Sornette, 2000)  have all included corrections which could describe a recent or upcoming slowdown and other complexities, mostly to allow growth to today be approaching fundamental limits, and hence a final end to accelerating growth. Some authors have also informally summarized world history as continually accelerating change, but the more common informal summary is of human history as a sequence of specific growth modes. History has, for example, been described as the slow expansion of hunter-gatherers, followed by faster growth following the domestication of plants and animals, followed by even faster growth with commerce, science, and industry  (Cipolla, 1967) . Simple exponential growth is a very common model for describing particular historical periods. It is, for example, widely used to model the last half century of world economic growth  (Barro & Sala-i-Martin, 1995) . Since historical periods tend to be described as exponential growth, formal models of transitions between periods tend to be models of transitions between exponential growth asymptotes. Many have modeled the industrial revolution this way  (Marvin Goodfriend, 1995; Hansen & Prescott, 1998; Jones, 1999; Steinmann, Prskawetz, & Feichtinger, 1998; Galor & Weil, 2000; Lucas, 2000) . At least one earlier transition, to cities, has also been modeled this way  (Marvin Goodfriend, 1995) . And possible current or upcoming transitions, such as due to computers or the internet, have also been modeled this way  (Helpman, 1998) . Given all this, it seems natural to formally model the long term history of humanity as a sequence of exponential growth modes. Yet to my knowledge no one has done this. Some authors seem to have come close, by drawing exponential curves suggestively next to data on log-log graphs of population growth  (Deevey, 1960; Kates, 1996; Livi-Bacci, 1997) . (Some of these authors, however, do not seem to have realized that it could be simple exponentials they were drawing, and instead of \"exponential growth followed by a period of approximate stability\"  (Kates, 1996) .) One author did more explicitly consider and reject a sum of exponentials model for world population history, though without any explicit model fitting or test  (Cohen, 1995) . (Another author considered a sum of two exponentials, one of which was decreasing  (Lee, 1988) .) In this paper we thus take on the neglected task of more formally modeling long term human history as a sequence of exponential growth modes. In particular, we consider such a model of world product history. Once we have chosen to model history as a sequence of exponential modes, there still remains the question of how we should mathematically model transitions between exponential growth modes. We will first try a simple sum of exponentials, and then try to replace this sum with a CES (constant elasticity of substitution) form. Such a form allows each transition to be sudden or gradual, depending on a single free parameter per transition. We will end up with a model describing the three classic economic growth modes, which we might call hunting, farming, and industry. \n A Sum of Exponentials Model Apparently, no one has yet tried to formally model long-term growth as a sequence of exponentially growing modes. This paper thus attempts to do so for world product. One very simple model of a sequence of growth modes is a sum of exponentials, which for n modes we will write as Y (t) = Y n (t), where Y 0 (t) = 0, and for i from 1 to n, Y i (t) = Y i−1 (t) + M i (t), M i (t) = c i 2 t/τ i . The parameter τ i is the doubling time of mode i. If data consists of pairs (t j , Y j ), a min-square-error of logs method searches for model parameters of a function Y (t) that minimize j (log(Y (t j )) − log(Y j )) 2 . Applying this method to my data, the best fit sum of four exponential terms gives an eyeballpleasing fit, and a (root mean square) average percentage error of 1.8%. This is about the same magnitude as the smallest uncertainty or \"indifference range\" attributed to the population estimates that this data is based in part on, which is about 2%  (McEvedy & Jones, 1978) . Figure  1  compares this model with the data, and indicates that the main errors seem to be due to unmodeled fluctuations with a period of roughly 500-1500 years. Figure  1     M i (d i ) = M i−1 (d i ). (The questionable doubling time factor for the hunting mode comes from comparing it to the previous growth rate of animal brains, as discussed in the footnotes. 6 ) Table  1  also gives a world product factor, defined as Y i (d i+1 )/Y i−1 (d i ), which says how much world product increased due to each term. \n CES-Combined Exponentials While most of the modes in the above model seem to have a familiar interpretation, the second to last mode, the one with a 58 year doubling time, seems more difficult to interpret. We might consider it to represent a commercial revolution, distinct from the later industrial revolution. But visibly, it seems to just be there to allow the model to describe a slower and smoother transition than a simple sum of exponentials will allow between the modes before and after it. To more directly model the possibility of a slow versus fast transitions between modes, we can combine terms not with a sum, but instead with a constant elasticity of substitution (CES) form  (Barro & Sala-i-Martin, 1995) , as in Y i (t) = (Y i−1 (t) a i + M i (t) a i ) 1/a i . When the CES power is a i = 1, this is x + y, the previous case. When a i = 0, this is proportional to (Y i−1 M i ), which for exponential terms essentially makes an infinitely slow transition. When If we now fit such a CES combination of three exponential terms to our data, again using the min square error of logs method, we get an eyeball-pleasing fit, and an average percentage error of 1.7%. This model is described 7 in Table  2 , and compared to the data in Figures  1 and 2 . This model has the same number of free parameters as the four-term sum of exponentials model, and a modestly smaller total squared error of logs. a i is positive infinity, this is max(Y i−1 , M i ), Note that the industry mode will not begin to dominate until 2020, has a doubling time which is half of what we have observed over the last half century, and is already responsible for a larger world product factor than either of the previous two modes. The very low transition power allows a new mode to have a strong influence long before it officially dominates, and predicts a mid-transition growth rate of about half of the new mode growth rate. \n Interpreting the Modes By describing world product history as either a sum or CES-combination of exponentials, one seems to essentially be saying that among the thousands of large and important changes that the world economy has seen, only a handful are fundamentally big news. Other changes are either \"small,\" at least in the big picture, or such that a change of broadly similar economic magnitude and timing was largely predetermined by the fundamental economic forces at play. Typically, the economy is dominated by one particular mode of economic growth, which produces a roughly constant growth rate. While there are often economic processes which grow exponentially at a rate much faster than that of the economy as a whole, such processes almost always slow down as they become limited by the size of the total economy. Very rarely, however, a faster process reforms the economy so fundamentally that overall economic growth rate accelerates to track this new process. The economy might then be thought of as composed of an old sector and a new sector, a new sector which continues to grow at its same speed even when it comes to dominate the economy. Following this line of interpretation, the simple sum of exponentials model seems to assume that during each transition, the \"new\" and \"old\" economies co-exist but do not influence each other. In contrast, the CES-combination form seems to describe interactions between modes. Modes might complement each other (0 < a < 1), making for a more gradual transition, or substitute for each other (a > 1), making for a sharper transition. The large transition centered around 5000 B.C. (but surely begin thousands of years earlier) is naturally interpreted as the transition to from \"hunting\" to \"farming\" (both broadly construed). Populations relying on food from the domestication of plants and animals seem to have grown exponentially for several millennia before this transition date, nicely fitting a simple interpretation of co-existing new and old economies  (Diamond, 1997) . In the CES model, the power estimate for the farming transition suggests that farming mostly substituted for hunting, rather than complementing it. Because the data is poor, this suggestion can only be weak. But it does make sense, given that hunting and farming economic modes competed for the use of both land and labor. 8 The recent \"industrial revolution\" transition has a CES power describing a much more gradual transition, suggesting less substitution and more complementarity between the old and new economic growth modes. If we interpreted the old and new modes relatively literally as \"farming\" and \"industry\", this makes some sense, in that improved farming technology has freed workers for industry while improved industry technology has often transferred to farming technology. Such a literal interpretation, however, is argued against by the CES model estimate that we will not \"officially\" transition to the new mode until 2020, in the sense of having the new contribution to the world economy exceed the old part. For this to make sense, much of our non-farming economy needs to be interpreted as still dominated by the \"old\" growth mode. The form of our model suggests that the new growth mode might be found in small quantities well before it has a noticeable effect on total growth rates, and that what distinguishes this new economy inside the old one is that it is growing rapidly, at a rate closely related to what will become the new total economic growth rate. We might thus better understand what distinguishes the current \"new\" and \"old\" growth modes by looking for processes which doubled before the transition at a rate similar to the modeled new rates of 6 or 15 years. Some interesting candidates are found in measures of scientific progress. The number of scientific journals has doubled steadily about every 15 years since about 1750, even though the world product doubling time in 1750 was around a century. (From about 1650 to 1750 both journals and scientific societies doubled roughly every 30 years.) Narrower measures of progress grow slower, while broader measures grow faster. For example, the number of \"important\" discoveries has doubled every 20 years, while the number of U.S. engineers has doubled every 10 years  (de Solla Price, 1963) . This rough coincidence in timing and doubling times suggests, though only weakly, that a new \"scientific\" evolution and diffusion of knowledge via a subject-specific network of articulate specialists is fundamental to the new industry growth mode. Perhaps the diffusion of seeds and artifacts via a simpler more spatial network of less specialized people is fundamental to the farming mode. If so, the new 15 year doubling time of the sum of exponentials model suggests that published papers are close to the fundamental unit of growth, while the 6 year doubling time of the CES model suggests that a very broad measure of \"scientific\"-like activity is closer to the fundamental unit of growth. How can we make sense of the basic idea of the world economy repeatedly switching to new growth modes? That is, if the economy is capable of faster growth modes, what prevented them from happening earlier? Among the many models mentioned before of transitions between historical economic growth modes, perhaps the simplest postulate minimum scale effects, so that a new growth mode will not occur in economies below a certain size, density, or technology level. A stochastic variation on this is to make the number of attempts or chances to discover and transition to a new growth mode be proportional to the current scale of the economy. This variation also predicts that a transition will occur at roughly the time when the economy reaches some predetermined scale. Such models could interpret the roughly stair-step shape of Figure  2  somewhat literally. The lip of each step would describe a new mode which would not be realized until world product, moving along the x-axis, reached the base of that step. \n Could It Happen Again? Current U.S. stock prices seem to be much higher than can be justified by the expectation that the U.S. economy will continue much as it has for the last century  (Shiller, 2000) . If speculators are rational, it seems that they must be assigning a substantial probability to the possibility of a large change in the economy, such as a fall in the risk-premium investors demand, a fall in the real risk of corporate profits, a rise in the share of income taken by corporate profits, or a rise in real economic growth rates. It is this last possibility, of a large rise in economic growth rates, that seems to be offered some support by the empirical analysis of very long term economic growth. If one takes seriously the idea of long-term economic history as a sequence of exponential growth modes, one might naturally wonder if a world economy that seems to have so far seen at least three dramatic transitions to much faster growth modes will see yet another such transition. One pair of authors, Ausubel and Meyer, did informally \"speculate on a fourth [Deevey-like] 'information' pulse starting now that would enable another order-of-magnitude rise\" in population. But they took the idea no further  (Ausubel & Meyer, 1994) . Are there ways an economy can grow fast that will not be possible until the world economy reaches a threshold in size, density, or the price of some key technology? While it is certainly possible that the economy is approaching fundamental limits to economic growth rates or levels, so that no faster modes are possible, we should also consider the other possibility. To use our models to estimate how soon the world economy might jump again to a faster growth mode, and how much faster that mode might be, we must make some assumptions about what it is that is similar across past and future modes and mode transitions. The apparent regularities in Figure  2  suggest one approach. They suggest that we treat multiples of world product and growth rates as similar across growth modes. More precisely, if we assume that at each transition new values of the doubling time factor and world product factor are drawn again from the same constant-in-time distributions for these parameters, then previous values of these parameters offer \"sample\" estimates of future parameter values. In the sum of four exponentials model, if the current mode were to last through as large a world product factor as one of the previous three growth modes, it would last until one of the sample dates of 1963, 2032, or 2066. If the next doubling time factor were the same as one of the last three values, the next doubling time would be either would be .05, 1, or 4 years. 9 The world product method expects that the world product factor, as previously defined, of the current mode will be similar to that of the previous modes. The doubling time method instead expects to see a similar value for (d i+1 − d i )/τ i , which is the number of doubling times during the period when a mode is dominant. Since the \"current\" mode does not even start to dominate until 2020, the doubling time method naturally gives later date estimates. The estimates of the new doubling time offer what seems to be a remarkably precise estimate of an amazingly fast growth rate. One is tempted to immediately reject such rapid growth as too preposterous to consider, until one remembers how preposterous it would have seemed to forecast the previous two transitions that did in fact occur. The robustness of these forecasts can be examined by considering what these types of models would have predicted using only the data up to 1900. From 1900 to 2000, world product increased by a factor of 37. The best fit four term sum of exponentials model forecasts that a factor of 35 increase, while the best fit three term CES model forecasts a factor of 22 increase. The main reason for the CES model failure here is estimating a transition date of about 2060, instead of the 2020 date suggested by the larger dataset. Other parameter estimates were in much closer agreement. 10 Another row corresponding to a brain growth mode would give sample dates of 2072 and 2120. Using the out of Africa population estimate would change the new doubling time estimates from  14.9?,9.3,15.8 to 1.49?,93,15.8    3  and Figure  4  show how a new transition might look, if the new mode had a 15 day doubling time and the same strong complementarity with our current mode that our current mode had with the previous mode, and if the new mode first started to have a noticeable effect on growth rates in 2041. (Transitions starting at any other date would look very similar.) Table  4  makes it clear that in this scenario, the new mode has an enormous effect on economic growth rates very soon after it has any noticeable effect on growth rates. If this growth mode did not hit limits to slow it down, then by 2047, i.e., within six years of becoming noticeable, the economy would then grow by a larger factor than it had from two million B.C. until 2040. This is thus not at all a reasonable model for describing the recent small but noticeable increase in U.S. economic growth rates that some now attribute to a \"new industrial revolution.\" Thus if stock prices are now high in anticipation of a transition to a new growth mode, it must be in anticipation of a much smaller change in growth rates, of a change that has not yet detectably changed growth rates, or of a much more gradual transition between growth modes. In summary, if one takes seriously the model of economic growth as a series of exponential growth modes, and if relative change parameters of a new transition are likely to be similar to such parameters describing old transitions, then it seems hard to escape the conclusion that the world economy could see a very dramatic change within the next century, to a new economic growth mode with a doubling time of roughly two weeks or less. While it is hard to see in much detail how the world economy could possibly grow that fast, it is at least suggestive that computer hardware costs have in fact been consistently falling for many decades at a doubling time of one to two years  (Moravec, 1998; Kurzweil, 1999) . Several observers have predicted a transition to a dramatically new economic mode where computers substitute for most human labor, perhaps not long after the raw computational ability of a desktop computer matches the computational ability of a human brain, around 2025  (Moravec, 1998; Kurzweil, 1999) . Simple formal models have even been developed suggesting that adding robots to very standard growth models can allow growth rates to naturally increase by a factor of ten, a hundred, or even more  (Hanson, 1998) . Others have speculated that even faster growth rates are possible with mature nanotechnology. If the next mode had a \"slow\" doubling time of two years, and if it lasted through twenty doubling times, longer than any mode seen so far, it would still last only forty years. After that, it is not clear how many more even faster growth modes are possible before hitting fundamental limits. But it is hard to see how such fundamental limits would not be reached within a few decades at most. \n Conclusion Many people have tried to make sense of very long term time series estimating human population. Some have explicitly modeled this history as steadily accelerating growth, while others have more informally described it as a sequence of growth modes. And exponential growth is by far the most common formal model of shorter term growth. Meanwhile, Brad De Long has recently constructed long term world product estimates from recent world product estimates and older population estimates. This paper has thus attempted the neglected task of more formally describing long term world product growth as a sequence of exponential growth modes. We have found that a time series of world product over the last two million years can be comfortably described as either as a sum of four exponentials, or as a CES-combination of three exponentials. But the CES model seems preferable on theoretical grounds, which can be thought of as describing the three modes of \"hunt-ing,\" \"farming,\" and \"industry,\" broadly construed. (An earlier period of exponential growth in brain sizes may be the relevant previous growth mode.) In the CES-combination model, there is a sharp transition between hunting and farming, and a smooth transition between farming and industry. These can be interpreted as due to the interaction between hunting and farming being more one of substitution, relative to a more complementary relation between farming and industry. The rough timing and doubling time coincidence between industry and measures of scientific progress weakly suggests that scientific-like creation and diffusion of knowledge might be a key to the current growth mode. Since there seem to be some rough regularities regarding how much the economy grows between transitions, and how much faster each new growth mode is, this paper has also considered what these regularities suggest about when we might see yet another transition to a much faster mode, if such faster modes are possible. The suggestion is fantastic, namely of a transition to a doubling time of two weeks or less sometime within roughly the next century. One might think this suggestion too fantastic to consider, were it not for the fact that similar predictions before previous transitions would have seemed similarly fantastic. We should also keep in mind that investors in U.S. stocks seem to be betting that a large change in the nature of the economy is likely soon. They may well be wrong, but this paper shows that the empirical case against such expectations is not as clear as one might expect from empirical analyzes looking at the last century or so. From a purely empirical point of view, very large changes are actually to be expected within the next century. of population estimates from McEvedy and Jones (McEvedy & Jones, 1978) going back to 10 thousand B.C., and of three population estimates from Deevey (Deevey, 1960) for 25 thousand B.C., 300 thousand B.C. and one million B.C. \n population estimate of about half a million between one million B.C. and 500 thousand B.C., which I've coded as at 750 thousand B.C. 1 \n also shows the best fit hyperbolic model, 4Y (t) = c(T − t) −α ,which has a power of α = 1.46, goes to infinity at T = 2004, and has a much inferior average percentage error of 9.6%. (Using three terms instead of four in the sum of exponentials model also gives a visibly much worse fit.)For each term, \n with an infinitely fast transition. Other positive values of a i allow for other intermediate speeds of transition. \n \n \n \n \n Table 1 : 1 Table 1 lists a mode description, doubling time 5 , the factor by which the doubling Sum of Exponentials Growth Modes time accelerated between terms, and a \"date began to dominate,\" defined as the d i that solves Growth Doubling Date Began Doubling World Product Mode Time (years) To Dominate Time Factor Factor Hunting 230,000 2,000,000 B.C. 149? 406 Farming 860 4700 B.C. 267 178 ?? 58 1730 A.D. 14.9 8 .9 Industry 15 1903 A.D. 3.8 > 78 \n Table 2 : 2 CES-combined Exponentials Growth Modes Growth Doubling Date Began Doubling World Product Transition Mode Time (year) To Dominate Time Factor Factor CES Power Hunting 224,000 2,000,000 B.C. 153? 480 ? Farming 909 4860 B.C. 247 190 2.4 Industry 6.3 2020 A.D. 145 > 590 0.094 \n Table 3 : 3 Table 3 describes sample forecasts based on the CES model (which the author prefers). It9 If the next mode were like the brain growth mode, it would start in 2162 and have a doubling time of 0.1 years. Using the CES Model to Forecast The New Mode includes sample forecasts of the next economic doubling time, and two kinds of estimates of the next transition date. 10 Growth Doubling Time New Doubling World Product New Date New Date Mode (DT) Factor Time (days) (WP) Factor from WP from DT Hunting 153? 14.9? 480 1996 2075 Farming 247 9.3 190 1976 2067 Industry 145 15.8 > 590 \n Table 4 : 4 . New Transition Scenario, Instantaneous Annual Growth Rates For example, the up-to-1900 CES estimate of the new doubling time is 6.4 years, very close to the up-to-2000 estimate of 6.3 years. Timing estimates thus seem less reliable than growth rate estimates. 2039 2040 2041 2042 2043 2044 2045 2046 2047 6.1% 6.1% 6.6% 8.0% 14% 41% 147% 476% 1023% \n Table 4 , 4 Figure \n\t\t\t The best fit \"log-periodic model,\" of the formY (t) = c(T − t) −α (1 + b cos(ω ln(T − t) + φ)) (Johansen & Sornette, 2000) , has a power of α = 1.48, goes to infinity at T = 2005, and has an average percentage error of 7.4%.5 Under the \"out of Africa\" theory, the hunting mode began ten times more recently, at 200 thousand B.C. Substituting this estimate for the two multi-regional estimates would reduce the hunting doubling time, increase the hunting doubling time factor, and reduce the farming doubling time factor, all by a factor of ten. All other entries would remain unchanged. \n\t\t\t For reference, an additional row of Table1describing the earlier brain size growth mode would have entries: 34,000,000, 550,000,000 B.C., ??, and \"67,000.\" The last entry is the total increase of brain size, which isn't directly comparable to the other rows since it is not an increase in world product. \n\t\t\t An additional row describing the earlier brain size growth mode would have the same entries as before, and the \"out of Africa\" theory would change the same entries by a factor of ten. \n\t\t\t Maximum brain size does not translate very directly into world product, but the long roughly steady growth in maximum brain size has been mentioned in this paper because it may be the relevant growth mode prior to the early spread of the human population. Product growth in an economy of human-like creatures seems to have awaited the evolution of a land-based animal with hands, a large enough brain, and perhaps other unknown prerequisites.", "date_published": "n/a", "url": "n/a", "filename": "longgrow.tei.xml", "abstract": "A world product time series covering two million years is well fit by either a sum of four exponentials, or a constant elasticity of substitution (CES) combination of three exponential growth modes: \"hunting,\" \"farming,\" and \"industry.\" The CES parameters suggest that farming substituted for hunting, while industry complemented farming, making the industrial revolution a smoother transition. Each mode grew world product by a factor of a few hundred, and grew a hundred times faster than its predecessor. This weakly suggests that within the next century a new mode might appear with a doubling time measured in days, not years.", "id": "54df6f97d53dc5b4fe3266db1d65f8e0"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Seth D Baum"], "title": "Artificial Interdisciplinarity: Artificial Intelligence for Research on Complex Societal Problems", "text": "Introduction This paper explores the question of how artificial intelligence (AI) can be of value to interdisciplinary research (IDR) aimed at addressing major societal problems such as public health, environmental protection, and emerging technology governance. These problems are highly complex and multifaceted and do not fit neatly into traditional academic disciplines. For example, the study of global warming integrates environmental science, social science, policy, energy engineering, and more. This extreme breadth makes IDR a very difficult cognitive challenge for even the most capable human researchers. If AI can help meet this challenge, that could be of considerable value for addressing many major societal problems. This paper is especially interested in the possibilities for near-to intermediate-term AI systems that use existing AI techniques or relatively straightforward extensions of them. These would ideally be systems that computer scientists could work toward right now, and that would also be well short of strong AI, i.e., human-level or super-humanlevel artificial general intelligence (AGI). A central question of this paper is: Can we imagine tractable, real-world AI system designs that would make significant contributions to understanding and addressing complex and important societal problems, but without posing the major risks and ethical issues associated with strong AI? I humbly acknowledge that I do not know the answer to this question, but I do know that it is a worthy question to ask, and I can lay out some relevant considerations. That is the aim of this paper. To streamline the discussion, let us introduce the following term: Artificial interdisciplinarity (A-ID): Artificial intelligence that performs interdisciplinary research or supports other agents in the performance of interdisciplinary research. Some emphasis is warranted on the clause \"or supports other agents in the performance of.\" Per this definition, an AI system that human researchers use to perform IDR counts as A-ID. Given this wider definition, it follows that there is A-ID in active use right now. Likewise, ideas for new forms of A-ID can leverage human collaboration. To make a valuable contribution to addressing societal problems, A-ID only needs to help with some aspect of IDR; it does not need to be able to complete IDR projects with no human collaboration. Indeed, it is plausible that an A-ID system that could succeed at the full range of IDR tasks would need to be strong AI. As a scholarly contribution, this paper sits at the intersection of literatures on IDR and both near-term and long-term AI, as well as the nascent concept of intermediateterm AI. Regarding IDR, there is an active line of research on the cognitive challenges faced by human interdisciplinary researchers  (Bracken and Oughton 2006; Keestra 2017; MacLeod 2018) . To the best of my knowledge, this literature has not yet considered the current or potential future role of AI. Regarding near-term AI, an extensive literature applies existing AI tools to support the research process. Most of this is oriented toward narrow disciplinary research, but some studies involve IDR  (Nunez-Mir et al. 2017; Tuhkala et al. 2018) . There is also a more general, extensive, and longstanding use of computers in IDR, especially in the physical sciences  (Crease 2017) , though that is beyond the scope of this paper. Regarding long-term AI, some studies consider the prospect of superintelligent AI designed as \"oracles\" to answer a wide range of questions that humans might have, some of which are in the domain of IDR  (Armstrong et al. 2012; Yampolskiy 2012) . Each of these lines of research is discussed in greater detail later in the paper. Finally, recent research has argued that intermediate-term AI has gone overlooked relative to near-term and long-term AI  (Parson et al. 2019a (Parson et al. , 2019b Baum 2020) . This paper provides dedicated attention to intermediate-term AI and concurs that this time period merits attention. The paper also seeks to encourage AI research to orient itself toward addressing important societal problems and to provide some direction for this. At present, much of AI research is instead oriented toward more intellectual goals of expanding the capacity of AI systems or toward profitable activities of technology corporations. As is wellknown in a lot of IDR, intellectual progress and profit do not necessarily bring progress on societal problems and in some cases can make the problems worse, for example, intellectual progress on dangerous technologies and profitable activity that pollutes the environment. IDR is also not necessarily good for society and can be oriented toward a wide range of ends including intellectual progress and profit. Furthermore, even when IDR is focused on addressing societal problems, it is still not a panacea for them-the existence of literature addressing societal problems does not on its own ensure that the problems actually get addressed. That said, IDR is vital for addressing complex societal problems, and this is the primary focus of IDR today. The paper therefore encourages A-ID research to join forces with the extensive communities of IDR focused on addressing societal problems. I approach the topic of AI and IDR as a veteran interdisciplinary researcher with some knowledge of both AI and the meta-study of IDR. I am not a computer scientist, and so I can speak with less confidence on what the AI options for IDR may be. Therefore, this paper seeks to lay out some general considerations and to hopefully serve as a prompt for an interdisciplinary conversation among computer scientists, scholars of IDR, and others with relevant perspectives. As this paper explains, this sort of interdisciplinary conversation can be difficult, but it is vital for making progress on a wide range of cross-cutting topics. In keeping with much of the literature on IDR, this paper is written in terms of \"societal problems\" instead of the concept of \"social good\" that frames this special issue. These two terms are broadly compatible, in that addressing societal problems is one major way to advance the social good. IDR is commonly used to make progress on specific problems or issues, and is perhaps less commonly used to understand or advance the good in a more abstract or general sense. The challenge of understanding the complex and distinctive features of many specific societal problems is a primary focus of IDR. As the first dedicated discussion of A-ID, the paper provides a broad discussion. Section 2 introduces IDR and outlines its cognitive challenges. Sections 3-5 discuss A-ID over the near-term, intermediate-term, and long-term. Section 6 discusses issues raised by A-ID. Section 7 concludes with general thoughts on the role of AI in addressing societal problems. Sections 3-5 are organized around time scales because each time scale poses distinct issues for A-ID. Near-term AI can be defined as AI that currently exists or could exist in the near future via relatively straightforward extensions of current AI systems. Attention to near-term A-ID includes description of existing A-ID systems and prospects for extending them. Intermediate-term AI goes beyond what is already feasible or now in development, but it stops short of the more extreme forms of AI that could exist over the long term. This paper defines long-term AI as AI with capabilities that equal or exceed human cognition; terms for this include strong AI, human-level AI, artificial general intelligence, ultraintelligence, and superintelligence. Discussions of AI are often divided between the near term and the long term, with some debate over which is more important  (Baum 2018; Cave and Ó hÉigeartaigh 2019; Prunkl and Whittlestone 2020) . Less attention has been paid to AI over intermediate time scales  (Parson et al. 2019a (Parson et al. , 2019b , though this paper finds that A-ID at all time scales can be important. \n Interdisciplinary Research and its Cognitive Challenges IDR has been defined in a variety of ways  (Klein 2017)  Interdisciplinarity is often compared with related concepts, especially multidisciplinarity and transdisciplinarity. To generalize, multidisciplinary research is commonly understood to be the closest to disciplinary research, consisting of research that has input from multiple disciplines without integrating them; IDR takes an additional step away from disciplinary research by also integrating insights from across disciplines; transdisciplinary research is the furthest from disciplinary research by transcending disciplinary boundaries altogether, as if they did not exist, and often also transcending boundaries between academic and nonacademic sources of knowledge. These distinctions are fuzzy and contested  (Klein 2017)  but suffice for purposes of this paper. Note that some of the research described in this paper may be more precisely classified as transdisciplinary, though the distinction between interdisciplinarity and transdisciplinarity is not crucial for this paper and the paper will use the two terms more or less interchangeably. IDR has traditionally had two somewhat distinct motivations. See  Bernstein (2015)  for an intellectual history. One motivation is intellectual, seeking the understanding of cross-cutting topics and the synthesis of knowledge accumulated in (and beyond) the disciplines. An especially ambitious form of this motivation, associated mainly with transdisciplinarity, is for unifying all of the various strands of human knowledge and intellectual activity. The concept of consilience as developed by  Wilson (1998)  is one work in this direction. While intellectually motivated IDR is commonplace, IDR is perhaps more commonly motivated by practical societal problems. Environmental problems have been a longstanding focus, given their societal importance and multifaceted nature, involving both social and ecological systems. More generally, IDR often-but not always-addresses social and policy issues associated with science and technology; this includes social and policy issues raised by AI. A different type of motivation for IDR is the complexity of many important subjects of study. Complexity can be defined in a variety of ways; one definition proposed in the context of IDR is that complexity is an attribute of systems whose components-which may themselves be systems-interact in predominantly nonlinear ways  (Newell 2001) . I would add that while this definition's emphasis on nonlinear systems has a mathematical tone, the interconnections found in IDR are often best understood in more qualitative terms. Regardless, the definition points to the distinction between multidisciplinarity and interdisciplinarity. Many research subjects do not fit neatly within any one academic discipline, but research on these subjects does not necessarily require integration across disciplines. For example, oceanography and battery technology are both relevant to the study of global warming, but oceanographers and battery engineers typically do not need to consider each others' work when doing their own. (This example is from a critique of IDR by  Jacobs 2013, p.130-131.)  This disconnected work would classify as multidisciplinary but not interdisciplinarity. As a contrasting example, global warming policy may affect industrial activity, which affects greenhouse gas emissions, which affect climate patterns, which affect natural hazards, which affect human welfare. Interdisciplinary global warming policy research may consider these complex interconnections to assess the overall merits of a policy idea. All research, whether interdisciplinary or disciplinary, has social as well as intellectual dimensions. Indeed, one argument in favor of disciplines is that they provide a useful structure for organizing populations of human researchers within universities  (Jacobs 2013) . Interdisciplinary research centers serve a similar social purpose. Likewise, some challenges for IDR are of a social and not intellectual nature. For example, the discipline-based department system at most universities often incentivizes disciplinary research over IDR. These social dimensions may be less relevant to an A-IDR system. AI may be more skilled at IDR than humans because AI lacks social reasons to cluster into disciplines. However, if an A-IDR system derives its knowledge from the corpus of human scholarship, then it may learn and perpetuate disciplinary divisions, just as current AI systems learn and perpetuate human biases obtained from other human-produced datasets. The remainder of this section surveys some cognitive challenges of IDR. All forms of research can be cognitively difficult, but IDR poses some distinct challenges that make it especially challenging for human researchers. Note that these challenges also apply to transdisciplinary research and to a lesser degree to multidisciplinary research. For more general discussion of interdisciplinarity, multidisciplinarity, and transdisciplinarity, see e.g.,  Hoffmann et al. (2013 ), McGregor (2014 ,  Bernstein (2015) ,  Lawrence (2015) ,  Scholz and Steiner (2015) ,  Menken and Keestra (2016), and Frodeman (2017) ; for an alternative and more critical perspective, see Jacobs (2013). \n Disciplinary Divides Different academic disciplines commonly approach the same topic from different perspectives, using different conceptual paradigms and different language, featuring different intellectual traditions and standards, and often covering different aspects of the same topic. This creates the cognitive challenge of integrating the disparate input into a unified understanding of a topic  (Bracken and Oughton 2006; Keestra 2017; MacLeod 2018) . As a consequence, IDR requires a laborious and often frustrating process of translation between different disciplines. It is a translation of language as well as of intellectual norms and epistemic perspectives. Much of the challenge comes from the fact that human expertise builds from years of focused study and practice. The human mind can achieve high levels of performance on specific tasks by forming complex representations of the task and its surrounding context-for example, chess masters \"chunking\"  (Chase and Simon 1973)  together complex patterns of chess pieces. The sheer difficulty of developing expertise precludes individual researchers from being expert on the full range of subjects that are relevant to complex societal problems. Furthermore, the very nature of human expertise can make it harder for experts in one discipline to understand other disciplines. Indeed, the term \"discipline\" implies a certain disciplining of the human mind to think in certain ways. A human mind disciplined to think in one way can struggle to think in another way. Compounding the problem is the fact that academia is traditionally divided into thematic disciplines that do not map to societal problems. A scholar is typically trained and employed as, for example, a computer scientist or a social scientist, not as an expert on the social implications of computers. Academia has made some effort to restructure toward IDR, but the traditional disciplines still dominate. As a consequence, disciplinary divides are even greater than they in principle need to be. \n Massive Literatures Even if a researcher or research team is able to parse the disparate disciplinary contributions to a particular topic, there remains the challenge of reading the relevant literature. Even within a single discipline, literature review can be a highly laborious task. For complex interdisciplinary topics, it quickly becomes overwhelming. For example, the Intergovernmental Panel on Climate Change (IPCC) is a body of top global warming researchers from around the world. It produces periodic syntheses of the global warming literature for high-level policy audiences. IPCC reviews are massive exercises, involving hundreds of scientists each putting in hundreds of hours over periods of up to 5 years  (Victor 2015) . Despite this massive scale, the literature is now at a point where the IPCC's teams of researchers are struggling to keep up  (Minx et al. 2017) . Climate change is an especially complex issue with a large literature even by IDR standards, but the IPCC is also an unusually large IDR project. Other IDR projects with narrower scopes and smaller teams face similar literature challenges. The IPCC is distinctive in its effort to synthesize the entire peer-reviewed literature on a complex interdisciplinary topic. Researchers who merely wish to contribute to the literature do not need to read so much. However, gaining a basic understanding of global warming in all its facets still requires reading at least some literature across numerous subjects in natural science, social science, engineering, the humanities, policy, etc. This is an extensive undertaking, and it is compounded by the added challenge of translating across the disciplinary divides. \n Peer Review IDR poses distinct peer-review challenges. IDR commonly works at the interface of multiple traditional academic disciplines. In many cases, it is uncommon to have expertise in each of the disciplines. Indeed, the person or team performing the IDR may be the only one in the world working across that particular set of topics. For example, this paper works at the intersection of AI and IDR; I am not aware of any other research that does this. The eclectic mixes of topics found in IDR make it unusually difficult to peer review  (Laudel 2006; Pautasso and Pautasso 2010; Holbrook 2017 ). If no other researchers have expertise across the range of topics covered in the work, then it may be necessary to form an interdisciplinary team of reviewers, but then this team must overcome its own disciplinary divides, which is a substantial task just to complete a single review. Or, the task of working across the disciplinary divides may fall to the people handling the submissions-journal editors, grant program managers, etc.-but then this just adds to their burden. It has been suggested that the difficulty of reviewing IDR, combined with the tendency of researchers to favor work from their own specialty, biases reviewers against IDR  (Laudel 2006) . One study has found that IDR grant proposals are indeed funded at a lower rate  (Bromham et al. 2016) . This is another way in which the current academy may be systematically biased against IDR, limiting its contribution to addressing important societal problems. \n Transfer Some research aims to transfer insights from the study of one societal issue to another. Transfer is seldom discussed in literature about IDR, which tends to focus on one issue at a time (but see  Krohn 2017) . Transfer is not a panacea, especially given the distinct attributes that each societal issue has, which limits the extent to which insights transfer from one issue to another. Nonetheless, it can be a powerful way to study societal issues. Transfer can be especially helpful for newly emerging issues that have not yet built up a robust literature, such as issues involving emerging technologies. For example, Altmann and Sauer (2017) transfer insights from strategic studies of nuclear weapons to the study of newly emerging autonomous weapon systems.  Baum (2017a)  transfers insights from the psychology of promoting environmentally beneficial behaviors among the lay public to the study of how to encourage AI researchers to pursue socially beneficial AI designs. The psychology of transfer finds that people tend to be more successful at it when there is relatively little \"distance\" between the domain transferred from and the domain transferred to  (Perkins and Salomon 1992) . For example, it may be easier to transfer insight from one weapon system to another (as in Altmann and Sauer 2017) than it is to transfer insight from lay public environmental behavior to expert behavior on technology development (as in Baum 2017a). Unfortunately, much of the insight available to be transferred lies at a considerable conceptual distance. A major challenge is simply recognizing the cross-issue similarity. Indeed, another finding from the psychology of transfer is that people often struggle to apply lessons to \"problem isomorphs,\" i.e., to another domain that is functionally equivalent but different in appearance  (Simon and Hayes 1976) . People even struggle with problem isomorphs when both domains are presented to them. IDR transfer is more difficult because researchers typically must identify the two domains for themselves. On top of that, IDR transfer can require bridging three sets of epistemic divides: the divide between the two issues and the divides within each of the two issues. This can make for an especially difficult cognitive task. \n Near-Term A-ID This section discusses A-ID that currently exists or could exist with relatively straightforward extensions of current technology. Note that this section takes a relatively broad view of what qualifies as AI. By narrower standards, some of what is presented here may not qualify as AI. The exact definition and scope of AI is complex and controversial and beyond the scope of this paper; for further discussion, see, e.g.,  Legg and Hutter (2007) on definitions and McCorduck (2004)  on how the scope of what is considered to classify as AI has gotten narrower over time. \n Search Engines Perhaps the most ubiquitous form of A-ID is the search engine for Internet and scholarly databases, including Dimensions.ai, Euretos, Google Scholar, IRIS.AI, Microsoft Academic, Omnity, Semantic Scholar, SourceData, and Web of Science. Search engines are valuable for many forms of research, but they are especially valuable for IDR. In narrow disciplinary fields, researchers need to follow a relatively small body of literature. They may even be able to keep up with the relevant literature without the use of search engines, instead identifying literature by reading certain journals and sharing relevant literature within peer communities. In contrast, IDR frequently pushes researchers outside their areas of familiarity and requires them to identify relevant literature from within extremely large bodies of work. Search engines can help with each of the IDR challenges described in Section 2. They can provide some help to the challenge of overcoming disciplinary divides by providing a tool to explore the literatures of other disciplines, though this leaves open the challenge of understanding publications in unfamiliar disciplines. They can be used to navigate the massive literatures on interdisciplinary topics, such as by searching for multiple keywords to find literature on specific themes for a societal problem-for example, \"global warming\" and \"cost-benefit analysis.\" They can be used to identify peer reviewers-for example, the authors of papers on global warming and cost-benefit analysis. And, with some creativity, they can support the transfer of insights across societal problem-for example, one could search for literature on global warming and cost-benefit analysis to identify insights that can be transferred to cost-benefit analysis of other global environmental issues. Search engines could be improved. To my eyes, an important area for improvement is in the handling of synonyms and, more generally, the identification of terminology. When searching for literature on an unfamiliar topic, identifying the right keywords to search for can be a major impediment. Once one knows the right keywords, relevant literature often flows abundantly. It would be especially valuable to have tools that could identify keyword synonyms used by other disciplines. Handcrafted resources, such as Wikipedia, can be helpful, but such resources are not available for all keywords. Automated tools for this could be quite helpful. Synonym identification is an active subject of AI research. One approach is to analyze patterns in the text surrounding a word, known as \"distributional word vectors\" or \"word embeddings,\" on grounds that synonyms can be used in the same way and therefore tend to be surrounded by similar text  (Leeuwenberg et al. 2016; Mohammed 2020 ). However, this work uses large linguistic datasets (i.e., large collections of text). Much less text is available for identifying synonyms in academic literature, especially for the many specialized concepts and small subfields. Indeed, the rarity of specialist terms can be a distinguishing characteristic of academic publications. One academic search engine, Omnity (https://www.omnity.io), uses the rarest words of a document to identify other documents with a similar mix of rare words on grounds that documents with the same rare words are likely to be related  (Perkel 2017 ). Omnity's approach may work well within a discipline, but it may be less well suited for search across disciplines that use different terms for the same concepts. Further research may be needed to develop techniques for synonym identification in small academic literatures. \n Recommendation Engines At least two forms of recommendation engines are currently available for research. The first provides recommendations of publications. For example, Google Scholar provides publication recommendations that are customized for individual user profiles, and Elsevier provides publication recommendations that are customized for specific publications on its ScienceDirect website. A more specialized example is the project http://xrisk.net that provides recommendations of publications in the field of catastrophic risk  (Shackelford et al. 2020) . These recommendations provide an additional way for researchers to identify relevant literature on the topics they are studying. Note that the recommendations cover topics that researchers have already identified, via their user profiles or the publications they are already looking at, so they are less valuable for the IDR challenge of exploring unfamiliar lines of research. Therefore, in terms of the challenges described in Section 2, these recommendation engines can be especially valuable for handling massive literatures, and they may be of relatively limited value for overcoming disciplinary divides. A second form of research recommendation engine recommends potential peer reviewers to journal editors. This is used, for example, in the Elsevier Evise system, which was launched in 2015. Insofar as Evise provides good recommendations of peer reviewers, it can lighten the burden on journal editors, as noted, for example, by the editor of the interdisciplinary Elsevier journal Ecological Economics (Hukkinen 2017). Another example is the Toronto Paper Matching System developed for matching papers to reviewers for computer science conferences  (Charlin and Zemel 2013) . While the Toronto Paper Matching System is used predominantly for computer science, it potentially could be expanded to more IDR domains. The value of recommendation engines for IDR could be especially large due to the difficulty of identifying appropriate reviewers for IDR. One way to improve interdisciplinary recommendation engines would be to streamline the process of building specialized recommendation engines. The recommendation engine presented by  Shackelford et al. (2020)  uses a custom artificial neural network trained with a hand-coded dataset of articles found to be relevant to the field of catastrophic risk by an open (\"crowdsourced\") team of researchers in the field. Other fields could apply the same approach. Hand-coding the training dataset is laborious but is vital for aligning recommendation engine results with the interests of people in the field. The labor required for this may be large, but it does not require any skills other than knowledge of the field. In contrast, developing the artificial neural network does require more specialized skills. Fields that lack people with these skills may struggle to develop their own recommendation engines. Therefore, the process of building fieldspecific recommendation engines could be streamlined by developing an artificial neural network that could be trained with data from any field and in particular by developing a more accessible user interface for it. \n Automated Content Analysis A final application of AI to research is the use of machine learning for analyzing the content of the literature on a given topic, known as \"automated content analysis\"  (Nunez-Mir et al. 2017 ). Essentially, it treats academic literature as an instance of \"big data\", sometimes referred to as \"big literature\"  (Nunez-Mir et al. 2016) . Automated content analysis analyzes clusters of key words and phrases to produce statistical trends in literatures. This can be of value for learning what a literature has tended to find, where gaps may lie, etc. It can also be used for identifying relevant literature on a topic and in this capacity may be considered a form of search engine. It is of particular interest in the context of systematic reviews, in which the aim is to provide a complete and unbiased account of the literature on a particular topic. In terms of the challenges described in Section 2, this can be of high value for handling the massive literatures of IDR. While automated content analysis has been used mainly for narrow disciplinary research, it has been used for IDR studies of forest ecology (Nunez-Mir et al. 2017) and participatory design  (Tuhkala et al. 2018 ). The Nunez-Mir et al. (  2017 ) study is illustrative of the possibilities. It analyzes the text of 14,855 abstracts in 7 forestry journals. It uses a mix of supervised and unsupervised seeding, meaning that central concepts are obtained via a mix of human input and algorithmic text mining. Subsequent algorithmic analysis assesses the preponderance of the concepts in the abstract database. A primary finding of the study is that most of the abstracts do not show an interdisciplinary approach and very few considered social dimensions of forest ecology. In consideration of this finding, Nunez-Mir et al. (  2017 ) call for more IDR on forestry, especially its social dimensions. Note that the Nunez-Mir et al. (  2017 ) study does not reveal anything about the nature of forests or their interdisciplinary attributes beyond the list of central concepts. The output is a map of the literature, not an interpretation of what the literature means and what its societal implications are. This is a general limitation of current automated content analysis. Thus, as  Sutherland and Wordley (2018, p.366)  write: Advances in artificial intelligence and machine learning could make it easier to perform tasks such as locating papers for defined topics using search terms, categorizing papers as relevant for further consideration, and producing systematic maps. But for all fields, assessing the quality of individual studies, writing up summaries and so on will continue to require skilled humans, at least for the foreseeable future. The above remark about \"the foreseeable future\" suggests that the AI needed for interpreting literature and its societal implications is significantly beyond the capacity of current AI. My own judgment is that this is probably correct. Therefore, interpretation is considered in the following section on intermediate-term A-ID. \n Intermediate-Term A-ID Intermediate-term A-ID systems would go significantly beyond current capabilities but not so far beyond that they would constitute \"strong\" A-ID with human-level or superhuman-level capabilities. Intermediate-term is of interest because it could be of greater value to IDR than near-term A-ID while avoiding the downsides associated with strong AI (see Section 5). Ideally, designs for intermediate-term A-ID would derive at least in part from existing AI techniques such that current AI researchers could work toward their development. There can also be value to envisioning intermediate-term A-ID that requires new techniques but would stop short of strong AI. Of course, the sooner new A-ID capabilities become available, the sooner they can contribute to addressing important societal problems. As stated in the introduction, I am not a computer scientist, and so I am less confident in my thoughts on the design of intermediate-term A-ID systems. Nonetheless, a few basic thoughts on computer science factors are offered as a contribution to the topic, alongside some social factors that I can comment on more confidently. \n Interpretation One direction to extend current A-ID capabilities would be via the interpretation of research publications. As  Sutherland and Wordley (2018)  explain, this is a task currently left for human researchers (see Section 3.3). However, progress in the field of machine reading (a.k.a. natural-language understanding/interpretation) could change this. For example, one project to automate interpretation is the Elsevier-sponsored ScienceIE  (Augenstein et al. 2017) . The current focus of ScienceIE is on identifying phrases and relations between phrases within narrow disciplinary literatures. Its aims are ambitious: \"Say you have a question about a paper: A machine learning model reads the paper and answers your question\" (Augenstein as interviewed by  Stockton 2017) . Automated interpretation of research publications would be of considerable value for many forms of research, but it may be of particularly large value for IDR, due to the large and diverse literatures involved in IDR. An integrated system for automated content analysis and interpretation would be especially valuable for synthesizing the insights contained in vast and diverse IDR literatures. Such capability could drastically reduce the burden of human researchers in IDR synthesis projects like the IPCC and could likewise enable similar synthesis projects across a wider range of societal problems. In terms of the IDR challenges described in Section 2, interpretation would be especially valuable for handling disciplinary divides and massive literatures, especially if combined with automated content analysis. Publications can be interpreted in many different ways, some of which may be easier for A-IDR. For example, interpreting whether a publication has presented results that are statistically significant may be easier for A-IDR than interpreting whether the publication has presented results that could help address some societal problem. It may be the case that current AI paradigms based on neural networks will struggle with the interpretation of complex interdisciplinary texts because, as discussed by  Marcus (2018) , neural networks are skilled at finding statistical relationships in complex datasets but struggle to handle causal relationships, hierarchies, and open-ended environments, all of which are important attributes of interdisciplinary texts. However, the extent to which this is indeed the case is left as a question for future research on A-ID. \n Translation Given the difficulty of translating across the epistemic divides that exist between academic disciplines (Section 2.1), it could be of considerable value to have A-ID systems that could assist with the translation. A-ID translation would convert between the jargons of different disciplines or between that of one jargon and a more widely accessible plain English. This would reduce the linguistic burden of IDR, thereby facilitating researchers to work across a wider range of disciplines, either alone or in teams. It would also be of value for peer reviewers tasked with reviewing interdisciplinary work that includes topics outside the reviewers' own areas of expertise. Potentially, A-ID translation could build off existing work on machine translation between languages (e.g., English to Spanish). An active area of research is for unsupervised machine translation (e.g.,  Lample et al. 2018 ; summarized in plain English by  Ranzato et al. 2018) , in which translation does not require large datasets of pre-translated text. Unsupervised machine translation would be important for interdisciplinary translation because large datasets generally do not exist and would be expensive to produce. A-ID translation may require techniques that go beyond cross-language machine translation because the text of different disciplines commonly varies by conceptual basis and not just by language. In other words, much of the challenge of reading text from other disciplines is that readers do not know the concepts that the words are describing or at least are not accustomed to thinking in terms of these concepts. Interdisciplinary translation is about explaining unfamiliar concepts just as much as it is about explaining unfamiliar terminology. In contrast, cross-language machine translation generally involves concepts that are familiar in both languages. For example,  Ranzato et al. (2018)  presents the translation of the phrase \"cats are lazy\" from English to Urdu; presumably Urdu speakers are already familiar with the concept of a lazy cat. Therefore, successful A-ID translation may need to include a capacity for concept identification and translation that goes substantially beyond cross-language machine translation. \n Transfer The challenge of interdisciplinary transfer (Section 2.4) maps neatly to the AI topic of transfer learning  (Pan and Yang 2009) . Both involve the same essential process of applying knowledge gained in one domain to another domain with similar features, especially to avoid the resource-intensive process of building complex knowledge sets for multiple domains. Complex societal problems often have some similarities with each other. Human researchers can barely scratch the surface of the potential of interdisciplinary transfer due to its cognitive difficulty and the very large number of combinations of similar societal problems. If AI transfer learning could be applied to IDR, it could open up vast possibilities for learning about societal problems. Current AI transfer learning involves tasks that are rather far removed from IDR. For example, one common AI transfer learning task is image recognition  (Zamir et al. 2018) . Whereas images are readily expressed in statistical terms (e.g., via the binary representation of a digital image file), societal problems are not. To be sure, there are ways to express societal problems in some quantitative terms, such as via cost-benefit analysis for the evaluation of solutions. But much of the insight involved in interdisciplinary transfer is qualitative. A-ID transfer learning would need reliable ways to quantify this insight. It would also need some degree of translation, given the differing terminology and other linguistic constructs that can exist across societal problems. There is some reason to believe that A-ID transfer learning could be quite difficult to achieve. Computers are very capable at churning through large numbers of combinations of predefined concepts, just as they are very capable at churning through large numbers in general. However, they may struggle at identifying the sorts of connections between concepts that humans find meaningful. In a discussion of creativity in humans and computers,  Boden (2009)  argues that humans are relatively skilled and computers relatively unskilled, at \"combinatorial creativity,\" meaning creativity in making new associations between seemingly unrelated concepts. Humans have rich mental models of the world built up throughout lifetimes of experience and observation, which enable us to devise analogies and imagery and other forms of combinatorial creativity. Endowing computers with anything similar is very difficult, and computers likewise struggle at combinatorial creativity. Interdisciplinary transfer is, at least in part, a form of combinatorial creativity, and so A-ID systems may struggle with it. \n Long-Term A-ID As an abstract matter, it is not hard to imagine some future AI that is capable of performing the full range of cognitive tasks involved in IDR. A strong AI/human-level AGI would presumably be able to do IDR at least as well as humans could. Whereas \"narrow\" AI is only intelligent for a narrow range of cognitive tasks, AGI is general in the sense of being able to perform a wide range of cognitive tasks. Human-level AGI could perform the same breadth of cognitive tasks as human minds and with the same skill as human minds. Such an AI could do any other cognitive task that humans can do, so it would presumably also be capable of IDR, potentially even so capable as to effectively solve all of society's problems. The AI may not be operating in complete isolation from humans-studies of human problems would likely require some human participation-but the AI may be able to play the entire suite of cognitive roles currently played by human interdisciplinary researchers. The prospect of solving societal problems is one common motivation for developing AGI. This is seen in the stated goals of active AGI research and development projects. For example, the AGI project AIDEUS observes that the \"limitation of intellectual possibilities is fully experienced by scientists\" and that this \"concerns all problems of peoplefrom traffic jams to economic crises and wars.\" That is very much in the spirit of the present paper. AIDEUS states this as a motivation for building strong AI.  1  As another example, DeepMind envisions AI for \"helping humanity tackle some of its greatest challenges, from climate change to delivering advanced healthcare.\" 2 Finally, Jeff Hawkins of Numenta calls for AI to help humanity \"face challenges related to disease, climate, and energy\"  (Hawkins 2017) . Note that these and other examples can be obtained from  Baum (2017b) . As valuable as AGI could be for IDR and for addressing complex societal problems, it faces several important downsides. First is the technical difficulty of building AGI. Despite the numerous projects working on AGI, the current state of the art remains quite far removed from it. It is not clear if or when AGI would be built; projections of decades or longer are common  (Baum et al. 2011; Grace et al. 2018) . That is a long time to wait for solutions to major societal problems. For some problems, such as nuclear war or extreme pandemics, the effects could be so severe that civilization would fail before it has the chance to build AGI. The desire to use AGI for societal problems could be additionally problematic by putting a dangerous time pressure on AGI development. Herein lies a dilemma. On one hand, earlier AGI would help with other societal problems. On the other hand, a rushed AGI could skimp on built-in safety measures and ethical design, increasing the risk of adverse or even catastrophic harm caused by the AGI. To the extent that major societal problems can be addressed without AGI, this buys AGI developers more time to get it done right. As an aside, note that some scholarship on IDR may be of value for the safe development of AGI, noting that the project of building AGI is itself an interdisciplinary task. For example,  Keestra (2017)  documents how a failure of interdisciplinary communication contributed to the 1986 space shuttle Challenger disaster and analyzes how future interdisciplinary communication could go better. Communication among those developing and launching AGI may benefit from this analysis. Careful AGI design may be needed even for AGI systems that exist only to provide input on societal problems. This is a theme of the literature on the prospect of superintelligent \"oracle\" AIs that are designed to only answer questions that humans pose to it  (Armstrong et al. 2012; Yampolskiy 2012) . The oracle design is sometimes conceived as a way to make AGI safe. The hope is that by restricting the AI to only answering questions, humanity can prevent the AI from taking dangerous physical actions to alter the world. However, studies of superintelligent oracles have raised the concern that they could still be dangerous, for example, by manipulating the people who interact with it (ibid.). The prospect of strong A-ID being dangerous in this way is another reason to explore near-and intermediate-term A-ID that can help address societal problems without raising the concerns associated with strong AI. Finally, it should be noted that the development of AGI is itself an interdisciplinary issue that would benefit from improved capacity for IDR. The development of AGI involves computer science, ethics, risk management, and more. Important questions include how best to design the AGI, how best to manage the human teams that are working on the design, and when to launch the AGI given the potential benefits and harms that could come from it. Insofar as near-and intermediate-term A-ID could improve the available answers to these sorts of questions, it could improve the outcomes from AGI development. This gives another reason to pursue near-and intermediate-term A-ID, including the concepts outlined in this paper. \n Discussion The limitations of near-term A-ID and the difficulties and risks of long-term A-ID suggest an important role for intermediate-term A-ID. A-ID interpretation, translation, and transfer could offer powerful capabilities for IDR and, more generally, for understanding and addressing complex societal problems. They could combine with existing A-ID systems (search engines, recommendation engines, and automated content analysis) to provide support across all of the cognitive challenges of IDR. This would not necessarily automate the full suite of IDR tasks-it could still leave important roles for human researchers-but it could nonetheless be of considerable value to IDR. On the other hand, some of these new capabilities could push uncomfortably toward AGI.  Yampolskiy (2013)  argues that the understanding of natural language is \"AIcomplete,\" meaning that any AI system that is capable of understanding natural language would necessarily also be an AGI with a wide range of other capabilities. Similarly,  Armstrong et al. (2012, p.305)  postulate that \"the task of advancing any field involving human-centred issues-such as economics, marketing, politics, language understanding, or similar-is likely to be  AI-complete,\" and Stockton (2017)  suggests that an AI capable of peer-reviewing research papers would require AGI. Exactly what, if anything, is AI-complete may be controversial and is beyond the scope of this paper, but it is nonetheless worth considering the implications of these arguments. These arguments imply that significant portions of A-ID interpretation, translation, and transfer may be impossible without AGI. Interpretation inherently involves understanding natural language, and so there may be very little A-ID interpretation that can be done without AGI. The translation of concepts may require understanding natural language, and so, without AGI, A-ID translation may be limited to the translation of terminology. Finally, transfer may also require understanding natural language and therefore AGI unless the societal problems of IDR can be reduced to a simpler quantitative form. The extent to which A-ID interpretation, translation, and transfer can be done without AGI is an important open question. Another concern is that intermediate-term A-ID could introduce certain biases into the research. This could occur if the A-ID interprets or evaluates research differently than human interdisciplinary researchers. For example,  Hukkinen (2017)  expresses concern that AI may succeed at assessing the intellectual rigor of research publications but struggle at assessing their significance for societal problems. Indeed, the ScienceIE project is explicitly framed in terms of scientific publications, but the interpretation of publications in other (non-science) areas that are essential to IDR for societal problems (such as ethics and public policy) require different ways of thinking and potentially different AI techniques. An A-ID system that can perform well on scientific rigor but poorly on ethics and policy could lead to weak or even harmful insight on how to address societal problems. More generally, intermediate-term A-ID systems must be carefully evaluated to ensure that they are producing constructive assistance to IDR. This will likely benefit from close collaboration between computer science developers of A-ID and human interdisciplinary researchers and potentially also people with other backgrounds, including stakeholders from outside academia. The inclusion of non-academic stakeholders is especially important with an eye toward actually addressing societal problems instead of just advancing the academic study of them. The existence of IDR literature does not on its own imply that the problems actually get addressed. Absent close engagement from non-academic stakeholders, there is a risk of producing solutions that work well in theory but not in practice. Additionally-and importantly-engagement with nonacademic stakeholders can result in different formulations of what the problems are in the first place. For these reasons, IDR-and especially transdisciplinary research-often calls for stakeholder participation in the research process. Readers should be aware that IDR often involves controversy, especially when it reaches out beyond the academy. Complex and important societal problems often involve heated disagreements between different stakeholders: between environmentalists and the fossil fuel industry over global warming, between rival geopolitical powers over nuclear weapons, etc. In some cases, there can be clever technical solutions that please everyone or at least do not upset anyone. However, more typically, solutions involve difficult tradeoffs between competing factions and fundamental moral values. Readers are encouraged to consider contributing to A-ID, but they should do so with an awareness of all that this entails. In the extreme case, A-ID could even be misused so as to make societal problems worse. For example, some of the same IDR that can help environmentalists refine their messages can also do the same for the fossil fuel industry, a dynamic that may be compounded by the extensive financial resources that the industry has at its disposal. Existing interdisciplinary research communities have often handled this by engaging with the ethical dimensions of societal problems and striving for ethically sound IDR practice. Work on A-ID should do the same. Finally, it should be noted that A-ID could help with all IDR, not just IDR on societal problems. As discussed in Section 2, IDR is perhaps most commonly performed for societal problems, but some IDR is oriented toward scientific and intellectual progress without any particular regard for societal problems. Such A-ID may be significant from the perspective of philosophy of science; this matter is left for future research. \n Conclusion This paper has articulated the concept of A-ID, outlined its importance for helping human researches cope with and overcome the considerable cognitive challenges of IDR, and explained how this can help address complex societal problems. A-ID exists today in the form of search engines, recommendation engines, and automated content analysis, but this leaves human researchers with the bulk of the work. Insofar as A-ID systems could contribute more to IDR, this could be a major contribution to addressing major societal problems. AI researchers interested in applying AI to societal problems may find this a worthy area of application. This paper describes some potential A-ID research directions; readers with more background in computer science than myself may have further suggestions. However, there are some difficult issues involved in A-ID that researchers should be cautious about, especially regarding the controversies inherent to complex societal issues, the potential for misuse of A-ID, and the potential relation of A-ID to strong AI/AGI. For their part, interdisciplinary researchers can contribute by using A-ID tools in their research and by contributing to efforts to improve the tools. Advancing A-ID is itself an interdisciplinary task that will benefit from contributions from people with a variety of backgrounds. Essential IDR cognitive tasks may be AI-complete, meaning that A-ID capable of these tasks would need to be strong AI. These tasks could include the interpretation of research publications, the translation of research concepts across disciplinary divides, and the transfer of IDR insights to new societal problems. If weak/narrow A-ID is unable to handle these tasks, or other essential IDR tasks, then human interdisciplinary researchers may be largely on their own until the advent of strong AI. This would mean that, despite all the disparate ongoing accomplishments of narrow AI, it would make relatively little contribution to addressing society's most complex and important problems. Alternatively, if there could be progress on A-ID that would not require AGI, then this could be a major contribution and would be a worthy focus for the field of AI. . One notable definition is provided in the US National Academies report Facilitating Interdisciplinary Research: Interdisciplinary research (IDR) is a mode of research by teams or individuals that integrates information, data, techniques, tools, perspectives, concepts, and/or theories from two or more disciplines or bodies of specialized knowledge to advance fundamental understanding or to solve problems whose solutions are beyond the scope of a single discipline or area of research practice (Committee on Facilitating Interdisciplinary Research and Committee on Science, Engineering, and Public Policy 2005, p.2). \n\t\t\t Artificial Interdisciplinarity: Artificial Intelligence for... S47 \n\t\t\t Artificial Interdisciplinarity: Artificial Intelligence for... S49 \n\t\t\t Artificial Interdisciplinarity: Artificial Intelligence for... \n\t\t\t http://aideus.com/community/community.html 2 https://deepmind.com/blog/learning-through-human-feedback Artificial Interdisciplinarity: Artificial Intelligence for...", "date_published": "n/a", "url": "n/a", "filename": "Baum2021_Article_ArtificialInterdisciplinarityA.tei.xml", "abstract": "This paper considers the question: In what ways can artificial intelligence assist with interdisciplinary research for addressing complex societal problems and advancing the social good? Problems such as environmental protection, public health, and emerging technology governance do not fit neatly within traditional academic disciplines and therefore require an interdisciplinary approach. However, interdisciplinary research poses large cognitive challenges for human researchers that go beyond the substantial challenges of narrow disciplinary research. The challenges include epistemic divides between disciplines, the massive bodies of relevant literature, the peer review of work that integrates an eclectic mix of topics, and the transfer of interdisciplinary research insights from one problem to another. Artificial interdisciplinarity already helps with these challenges via search engines, recommendation engines, and automated content analysis. Future \"strong artificial interdisciplinarity\" based on human-level artificial general intelligence could excel at interdisciplinary research, but it may take a long time to develop and could pose major safety and ethical issues. Therefore, there is an important role for intermediate-term artificial interdisciplinarity systems that could make major contributions to addressing societal problems without the concerns associated with artificial general intelligence.", "id": "eb97a7d337ffbee361e7ae7770ee5bed"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Karl Tuyls", "Julien Pérolat", "Marc Lanctot", "Georg Ostrovski", "Rahul Savani", "Joel Z Leibo", "Toby Ord", "Thore Graepel", "Shane Legg"], "title": "Symmetric Decomposition of Asymmetric Games", "text": "can be a very useful tool to analyse the Nash structure and dynamics of several interacting agents in a multiagent system. However, when dealing with asymmetric games the analysis quickly becomes tedious, as in this case we have a coupled system of replicator equations, and changes in the behaviour of one agent immediately change the dynamics in the linked replicator equation describing the behaviour of the other agent, and vice versa. This paper sheds new light on asymmetric games, and reveals a number of theorems, previously unknown, that allow for a more elegant analysis of asymmetric multiagent games. The major innovation is that we decouple asymmetric games in their symmetric counterparts, which can be studied in a symmetric fashion using symmetric replicator dynamics. The Nash equilibria of these symmetric counterparts are formally related to the Nash equilibria of the original asymmetric game, and as such provide us with a means to analyse the asymmetric game using its symmetric counterparts. Note that we do not consider asymmetric replicator dynamics in which both intra-species (within a population) and inter-species interactions (between different populations) take place  19  , but we only consider inter-species interactions in which two different roles interact, i.e., truly asymmetric games  20  . One of our main findings is that the x strategies (player 1) and the y strategies (player 2) of a mixed Nash equilibrium of full support in the original asymmetric game, also constitute Nash equilibria in the symmetric counterpart games. The symmetric counterpart of player 1 (x) is defined on the payoff of player 2 and vice versa. We prove that for full support strategies, Nash equilibria of the asymmetric game are pairwise combinations of Nash equilibria of the two symmetric counterparts. Then, we show that this property stands without the assumption of full support as well. Though this analysis does not allow us to visualise the evolutionary dynamics of the asymmetric game itself, it does allow us to identify its Nash equilibria by investigating the evolutionary dynamics of the counterparts. As such we can easily distinguish Nash equilibria from other restpoints in the asymmetric game and get an understanding of its underlying Nash structure. The paper is structured as follows: we first describe related work, then we continue with introducing essential game theoretic concepts. Subsequently, we present the main contributions and we illustrate the strengths of the theory by carrying out an evolutionary analysis on four canonical examples. Finally, we discuss the implications and provide a deeper understanding of the theoretical results. \n Related Work The most straightforward and classical approach to asymmetric games is to treat agents as evolving separately: one population per player, where each agent in a population interacts by playing against agent(s) from the other population(s), i.e. co-evolution  21  . This assumes that players of these games are always fundamentally attached to one role and never need to know/understand how to play as the other player. In many cases, though, a player may want to know how to play as either player. For example, a good chess player should know how to play as white or black. This reasoning inspired the role-based symmetrization of asymmetric games  22  . The role-based symmetrization of an arbitrary bimatrix game defines a new (extensive-form) game where before choosing actions the role of the two players are decided by uniform random chance. If two roles are available, an agent is assigned one specific role with probability  1 2  . Then, the agent plays the game under that role and collects the role-specific payoff appropriately. A new strategy space is defined, which is the product of both players' strategy spaces, and a new payoff matrix computing (expected) payoffs for each combination of pure strategies that could arise under the different roles. There are relationships between the sets of evolutionarily stable strategies and rest points of the replicator dynamics between the original and symmetrized game  19,23 .  This single-population model forces the players to be general: able to devise a strategy for each role, which may unnecessarily complicate algorithms that compute strategies for such players. In general, the payoff matrix in the resulting role-based symmetrization is n! (n being the number of agents) times larger due to the number of permutations of player role assignments. There are two-population variants that formulate the problem slightly differently: a new matrix that encapsulates both players' utilities assigns 0 utility to combinations of roles that are not in one-to-one correspondence with players  24  . This too, however, results in an unnecessarily larger (albeit sparse) matrix. Lastly, there are approaches that have structured asymmetry, that arises due to ecological constraints such as locality in a network and genotype/genetic relationships between population members  25  . Similarly here, replicator dynamics and their properties are derived by transforming the payoff matrix into a larger symmetric matrix. Our primary motivation is to enable analysis techniques for asymmetric games. However, we do this by introducing new symmetric counterpart dynamics rather than using standard dynamics on a symmetrised game. Therefore, the traditional role interpretation as well as any method that enlarges the game for the purpose of obtaining symmetry is unnecessarily complex for our purposes. Consequently, we consider the original co-evolutionary interpretation, and derive new (lower-dimensional) strategy space mappings. \n Preliminaries and Methods In this section we concisely outline (evolutionary) game theoretic concepts necessary to understand the remainder of the paper  23, 26, 27  . We briefly specify definitions of Normal Form Games and solution concepts such as Nash Equilibrium in a single population game and in a two-population game. Furthermore, we introduce the Replicator Dynamics (RD) equations for single and two population games and briefly discuss the concept of Evolutionary Stable Strategies (ESS) introduced by Smith and Price in 1973  [28] [29] [30]  . Normal Form Games and Nash Equilibrium. Definition. A two-player Normal Form Game (NFG) G is a 4-tuple G = (S 1 , S 2 , A, B), with pure strategy sets S 1 and S 2 for player 1, respectively player 2, and corresponding payoff tables A and B. Both players choose their pure strategies (also called actions) simultaneously. The payoffs for both players are represented by a bimatrix (A, B), which gives the payoff for the row player in A, and the column player in B (see Table  1  for a two strategy example). Specifically, the row player chooses one of the two rows, the column player chooses one of the columns, and the outcome of their joint strategy determines the payoff to both. In case S 1 = S 2 and A = B T the players are interchangeable and we call the game symmetric. In case at least one of these conditions is not met we have an asymmetric game. In classical game theory the players are considered to be individually rational, in the sense that each player is perfectly logical trying to maximise their own payoff, assuming the others are doing likewise. Under this assumption, the Nash equilibrium (NE) solution concept can be used to study what players will reasonably choose to do. We denote a strategy profile of the two players by the tuple (x, y) ∈ ΔS 1 × ΔS 2 , where ΔS 1 , ΔS 2 are the sets of mixed strategies, that is, distributions over the pure strategy sets or action sets. The strategy x (respectively y) is represented as a vector in  | | S 1 (respectively  | | S 2 ) where each entry is the probability of playing the corresponding action. The payoff associated with player 1 is x T Ay and x T By is the payoff associated with player 2. A strategy profile (x,y) now forms a NE if no single player can do better by unilaterally switching to a different strategy. In other words, each strategy in a NE is a best response against all other strategies in that equilibrium. Formally we have, Definition. A strategy profile (x,y) is a Nash equilibrium, iff the following holds: ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ x S x Ay x Ay and y S x By x By , , T T T T 1 2 In the following, we will write NE(A, B) for the set of Nash equilibria of the game G = (S 1 , S 2 , A, B). Furthermore, a Nash equilibrium is said to be pure if only one strategy of the strategy set is played and we will say that it is completely mixed if all pure strategies are played with a non-zero probability. In evolutionary game theory, games are often considered with a single population. In other words, a player is playing against itself and only a single payoff table A is necessary to define the game (note that this definition only makes sense when |S 1 | = |S 2 | = n). In this case, the payoff received by the player is x T Ax and the following definition describes the Nash equilibrium: Definition. In a single population game, a strategy x is a Nash equilibrium, iff the following holds: ∀ ′ ≥ ′ x x Ax x Ax , T T In this single population case, we will write that x ∈ NE(A). Replicator Dynamics. Replicator Dynamics in essence are a system of differential equations that describe how a population of pure strategies, or replicators, evolve through time  26, 32  . In their most basic form they correspond to the biological selection principle, i.e. survival of the fittest. More specifically the selection replicator dynamic mechanism is expressed as follows: = − dx dt x Ax x Ax [( ) ] ( 1 ) i i i T Each replicator represents one (pure) strategy i. This strategy is inherited by all the offspring of the replicator. x i represents the density of strategy i in the population, A is the payoff matrix which describes the different payoff values each individual replicator receives when interacting with other replicators in the population. The state of the population x can be described as a probability vector x = (x 1 , x 2 , ..., x n ) which expresses the different densities of all the different types of replicators in the population. Hence (Ax) i is the payoff which replicator i receives in a population with state x and x T Ax describes the average payoff in the population. The support I x of a strategy is the set of actions (or pure strategies) that are played with a non-zero probability I x = {i |x i > 0}. In essence this equation compares the payoff a strategy receives with the average payoff of the entire population. If the strategy scores better than average it will be able to replicate offspring, if it scores lower than average its presence in the population will diminish and potentially approach extinction. The population remains in the simplex (∑ i x i = 1) since ∑ i (dx i )/(dt) = 0. \n Evolutionary Stable Strategies. Originally, an Evolutionary Stable Strategy was introduced in the context of a symmetric single population game  28, 32  (as introduced in the previous section), though this can be extended to multi-population games as well as defined in the next section  23, 33  . Imagine a population of simple agents playing the same strategy. Assume that this population is invaded by a different strategy, which is initially played by a small proportion of the total population. If the reproductive success of the new strategy is smaller than the original one, it will not overrule the original strategy and will eventually disappear. In this case we say that the strategy is evolutionary stable (ESS) against this newly appearing strategy. In general, we say a strategy is ESS if it is robust Asymmetric Replicator Dynamics. We have assumed replicators come from a single population, which makes the model only applicable to symmetric games. One can now wonder how the previous introduced equations extend to asymmetric games. Symmetry assumes that strategy sets and corresponding payoffs are the same for all players in the interaction. An example of an asymmetric game is the famous Battle of the Sexes (BoS) game illustrated in Table  2 . In this game both players do have the same strategy set, i.e., go to the opera or go to the movies, however, the corresponding payoffs for each are different, expressing the difference in preferences that both players have in their respective roles. If we would like to carry out a similar evolutionary analysis as before we will now need two populations, one for each player over its respective strategy set, and we need to use the asymmetric or coupled version of the replicator dynamics, i.e., Definition. = − = − dx dt x Ay x Ay and dy dt y x B x By [( ) ] [( ) ] (2) i i i T i i T i T with payoff tables A and B, respectively for player 1 and 2. In case A = B T the equations reduce to the single population model. \n Symmetric Counterpart Replicator Dynamics. We now introduce a new concept, the symmetric counterpart replicator dynamics (SCRD) of asymmetric replicator equations. We consider the two payoff tables A and B as two independent games that are no longer coupled, and in which both players participate. In the first counterpart game all players choose their strategy according to distribution y, the original strategy or replicator distribution for the 2nd population, or player 2, and in the second counterpart game all players choose their strategy according to distribution x, the original strategy or replicator distribution for the 1st population, or player 1. This gives us the following two sets of replicator equations: = − dy dt y Ay y Ay [( ) ] ( 3 ) i i i T and = − dx dt x x B x Bx [( ) ] ( 4 ) i i T i T In the results Section we will introduce some remarkable relationships between the equilibria of asymmetric replicator equations and the equilibria of their symmetric counterpart equations, which facilitates, and substantially simplifies, the analysis of the Nash structure of asymmetric games. \n Visualising evolutionary dynamics. One can visualise the replicator dynamics in a directional field and trajectory plot, which provides useful information about the equilibria, flow of dynamics and basins of attraction. As long as we stay in the realm of 2-player 2-action games this can be achieved relatively easily by plotting the probability with which player 1 plays its first action on the x-axis, and the probability with which player 2 plays its first action on the y-axis. Since there are only 2 actions for each player, this immediately gives a complete image of the dynamics over all strategies, since the probability for the second action a 2 to be chosen is one minus the first. By means of example we show a directional field plot here for the famous Prisoner's dilemma game (game illustrated in Table  3 ). The directional field plot, and corresponding trajectories, are shown in Fig.  1 . For both players the axis represents the probability with which they play Defect (D). As can be observed all dynamics are absorbed by the pure Nash equilibrium (D, D) in which both players defect.   Unfortunately, we cannot use the same type of plot illustrating the dynamics when we consider more than two strategies. However, if we move to single population games we can easily rely on a simplex plot. In the case of a two population game the situation become tedious as we will discuss later. Specifically, the set of probability distributions over n elements can be represented by the set of vectors (x 1 , ..., x n )  ∈ n , satisfying x 1 , ..., x n ≥ 0 and ∑ i x i = 1. This can be seen to correspond to an n − 1-dimensional structure called a simplex Σ n (or simply Σ, when n is clear from the context). In many of the figures throughout the paper we use Σ 3 , projected as an equilateral triangle. For example, consider the single population Rock-Paper-Scissors game, described by the payoff matrix shown in Fig.  2a . O M O 3, 2 0, 0 M 0, 0 2, 3 The game has one completely mixed Nash equilibrium, being ( ) , , 1 3 1 3 1 3 . In Fig.  2b  we have plotted the replicator equations Σ 3 trajectory plot for this game. Each of the corners of the simplex corresponds to one of the pure strategies, i.e., {Rock, Paper, Scissors}. For three strategies in the strategy simplex we then plot a trajectory illustrating the flow of the replicator dynamics. As can be observed from the plot, trajectories of the dynamics cycle around the mixed Nash equilibrium, which is not ESS and not asymptotically stable. In fact, three categories of rest points can be discerned in single population replicator dynamics (see  Figs 3, 4 and 5) . Figure  3  displays a stable Nash equilibrium called an Evolutionary Stable Strategy (ESS). An ESS is an attractor of the RD dynamical system defined in the previous section and has been one of the main foci of evolutionary game theory. The second type of rest points are the ones that are Nash but not ESS (Fig.  4 ). These rest points are not an attractor of the RD but they have a specific form. Specifically, if a strategy is a Nash equilibrium, all the actions that are not part of the support are dominated, i.e., the support is invariant under the RD, which means that the fraction of a strategy cannot become non-zero if it is zero at some point. The third category that can occur is illustrated in Fig.  5 . Those rest points are not Nash and thus there is an action outside of the support that is dominant. Thus, the flow will leave from points in the close vicinity of the rest point, which is called a source.      \n Results In the following, we first present our main findings, formally relating Nash equilibria in asymmetric 2-player games with the Nash equilibria that can be found in the corresponding counterpart games. We also examine the stability properties of the corresponding rest points of the replicator dynamics in these games. Then we experimentally illustrate these findings in some canonical examples. Theoretical Findings. In this section, we prove the following result: if (x, y) ∈ NE(A, B) (where x and y have the same support), then x ∈ NE(B Τ ) and y ∈ NE(A). In addition, we prove that the reverse is true: if x ∈ NE(B Τ ) and y ∈ NE(A) (where x and y have the same support) then (x,y) ∈ NE(A,B). We will prove this result in two steps (Theorem 1 and its generalization Theorem 2). The theorems introduced apply to games where both players can play the same number of actions (i.e. square games). This condition can be weakened by adding dominated strategies to the player having the smallest number of actions (see the extended Battle of the Sexes example in the experimental section). Thus, without loss of generality, the theory will focus on square games. To begin, we state an important well-known property of Nash equilibria, that has been given different names; Gintis calls it fundamental theorem of Nash equilibria  32  . For sake of completeness, we provide a proof. Property 1. Let the strategy profile (x, y) be a Nash equilibrium of an asymmetric normal form game (A, B), and denote I z = {i | z i > 0} the support of a strategy z. Then, = ⊂ Τ Τ z Ay x Ay for all z such that I I and , (  5 ) z x = ⊂. Τ Τ x Bz x By for all z such that I I (6) z y Proof. This result is widely known. We provide it as it is a basis of our theoretical results and for the sake of completeness. If x and y constitute a Nash equilibrium then, by definition z Τ Ay ≤ x Τ Ay,∀z. Let us suppose that there exists a z with I z ⊂ I x such that z Τ Ay < x Τ Ay. Then there is a i ∈ I z ⊂ I x satisfying (Ay) i < x Τ Ay, and we get = ∑ < ∑ = Τ ∈ ∈ Τ Τ x Ay x Ay xx Ay x Ay ( ) i I i i i I i x x , which is a contradiction, proving the first claim. The claim for B follows analogously. ◽ Property 2. Let the strategy x be a Nash equilibrium of a single population game A. Then, = ⊂ . \n Τ Τ z Ax x Ax for all z such that I I (7) z x Proof. The proof is similar to the proof of Property 1. ◽ This property will be useful in the steps of the proofs that follow. We now present our first main result: a correspondence between the Nash equilibria of full support in the asymmetric game with those of full support in the counterpart games. Theorem 2 subsumes this result and we introduce this simpler version first for the sake of readability. Theorem 1. If strategies x and y constitute a Nash equilibrium of an asymmetric normal form game G = (S 1 , S 2 , A, B), with both x i > 0 and y j > 0 for all i, j (full support), and |S 1 | = |S 2 | = n, then it holds that x is a Nash equilibrium of the single population game B T and y is a Nash equilibrium of the single population game A. The reverse is also true. Proof . This result follows naturally from Property 1 and is implied by Theorem 2. We start by assuming that x and y constitute a full support Nash equilibrium of the asymmetric game (A, B). By Property 1 and since x and y have full support, we know that:  T i n i T i n T i {1, , } { 1, , } From this we also know that y T Ay = (Ay) i (since the (Ay) i are equal for all I's in the vector Ay, so multiplying Ay with y T will yield the same number Ay max ( ) i i ), and similarly (x T B) i = x T Bx (and thus (B T x) i = x T B T x), implying that: ∀ ′ = ′ ∀ ′ = ′ y y Ay y Ay x x B x x B x , a nd, , T T T T T T This concludes the proof. ◽ For the first counterpart game this means that the players will use the y part of the Nash equilibrium of player 2 of the original asymmetric game, in the symmetric counterpart game determined by payoff table A. And similarly, for the second counterpart game this means that players will play according to the x part of the Nash equilibrium of player 1 of the original asymmetric game, in the symmetric game determined by payoff table B. As such both players consider a symmetric version of the asymmetric game, for which this y component and x component constitute a Nash equilibrium in the two new respective symmetric games. In essence, these two symmetric counterpart games can be considered as a decomposition of the original asymmetric game, which gives us a means to illustrate in a smaller strategy space where the mixed and pure equilibria are located. A direct consequence of Theorem 1 is the following corollary that gives insights on the geometrical structure of Nash equilibrium, Corollary 1. Combinations of Nash equilibria of full support of the games corresponding to the symmetrical counterparts of the original asymmetric game also form Nash equilibria of full support in this asymmetric game. Proof. This is a direct consequence of Theorem 1. ◽ The next theorem explores the case where the equilibrium is not of full support. We prove that the theorem stands if the strategies of both players have the same support. Indeed, the first theorem requires that both players play all actions with a positive probability, here we will only require that they play the actions with the same index with a positive probability. We say that x and y have the same support if the set of played actions Proof. We start by assuming that x and y constitute a Nash equilibrium of same support (I x = I y ) of the asymmetric game (A, B). By Property 1, and since x and y have the same support, we know that: I x = {i | x i > 0} and I y = {i | y i > 0} are equal. = ⊂ Τ Τ z Ay x Ay z I I for all such that , and z x ′ = ′ ⊂ . Τ Τ ′ (8) x Bz x By z I I for all such that  (9)  z y Implying that y Τ Ay = x Τ Ay and x Τ Bx = x Τ By (by setting z = y and z′ = x). Then, from the Nash equilibrium condition we can write:  ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ x S x T 2 T T 1 T ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ ′ y S y Ay y Ay x S x B x x B , a nd , T T 2 T 1 T T T which implies that y is a Nash equilibrium of B Τ and x is a Nash equilibrium of A. The proof of the other direction follows similar mechanics and uses Property 2. Let us now assume that y is a Nash equilibrium of B Τ and x is a Nash equilibrium of A with I x = I y . Then, from Property 2 we have: = ⊂ Τ Τ z Ay y Ay z I I for all such that , and z y ′ = ′ ⊂ . Τ Τ Τ Τ ′ z B x x B x z I I for all such that (11) z x (10) In particular we get y Τ Ay = x Τ Ay and x Τ Bx = x Τ By (by setting z = x and z′ = y). From the Nash equilibrium condition of the single population games we can write:  ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ y S y Ay y Ay x S x B x x B x , a nd , T 2 T 1 T T T T ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ y S y Ay y Ay x S x Bx x Bx , a nd , T T 2 T 1 T ∆ ∆ ∀ ′ ∈ ≥ ′ ∀ ′ ∈ ≥ ′ x S x i i i T and B, = − = dx dt x x B x Bx (( ) ) 0 ( 13 ) i i T i T Proof. This is a direct consequence of Theorem 2. ◽ The theorems can only be used for equilibria in the counterpart games with matching supports (I x = I y ) from both players. One can work around this condition though by simply permuting the actions of one player in matrix A and B to study all configurations of supports of the same cardinality. To be precise, we need to analyze all the counterpart games defined by A Σ = AΣ and = Σ Σ B B ( ) T T for all permutation matrices Σ. This technique is sufficient to study non-degenerate games, as in a non-degenerate game all Nash equilibria have a support of same size (in a non-degenerate game if (x, y) is a Nash equilibrium then |I x | = |I y |  34  ). \n Stability Analysis. We can now examine the stability of the pure Nash equilibria discussed in the previously derived theorems. Corollary 3. Strategy y is a strict Nash equilibrium of the first counterpart game defined by A and strategy x is a strict Nash equilibrium of the second counterpart game defined by B, if and only if, (x, y) is a locally asymptotically stable equilibrium and a two-species ESS of the asymmetric normal form game G = (S 1 , S 2 , A, B) with support on the strategy with the same index in their respective strategy sets S 1 and S 2 . Proof. This a direct consequence of Corollary 2. More specifically, from Corollary 2 we know that (x, y) is a strict Nash equilibrium of G. It has been shown that (x, y) is a strict Nash equilibrium of G iff it is a two-species ESS  19, 20, 27  . ◽ \n Experimental illustration We will now illustrate how the theoretical links between asymmetric games and their counterpart symmetric replicator dynamics facilitate analysis of asymmetric multiagent games, and provide a convenient tool to get insight into their equilibrium landscape. We do this for several examples. The first example concerns the Battle of the Sexes game to illustrate the intuition behind the results. The second example extends the Battle of the Sexes game with one strategy for one of the players, illustrating the permutation argument of the theorems and how to apply the results in case of a non-square game. The third example is a bimatrix game generated in the context of a multiagent learning algorithm called PSRO (Policy Space Response Oracles 9 ) and concerns Leduc Poker. This algorithm produces normal-form \"empirical games\" which each correspond to an extensive-form game with a reduced strategy space, using incremental best response learning. Finally, the last asymmetric game illustrates the theorems for a single mixed equilibrium of full support, while its counterpart games have many more equilibria. A fundamental complexity arises when using the evolutionary dynamics of a 2-player asymmetric game to analyse its equilibrium structure, as the dynamics for the two players is intrinsically coupled and high-dimensional. While one could fix a player's strategy and consider the induced dynamics for the other player in its respective strategy simplex, a static trajectory plot of this would not faithfully represent the complexity of the full 2-player dynamics. To gain a somewhat more complete intuitive picture, one can represent this dynamics as a movie, showing the change in induced dynamics for one player, as one varies the (fixed) strategy for the other (we will illustrate this in the PSRO-produced game on Leduc Poker). The theorems introduced in the previous section help to overcome this problem, and allow to analyse the evolutionary dynamics of the symmetric counterpart games instead of the asymmetric game itself, revealing the landscape of Nash equilibria, which seriously simplifies the analysis. Battle of the Sexes. Symmetry assumes that strategy sets and corresponding payoffs are the same for all players in the interaction. An example of an asymmetric game is the Battle of the Sexes (BoS) game illustrated in Table  2 . In this game both players do have the same strategy set, i.e., go to the opera or go to the movies, however, the corresponding payoffs for each are different, expressing the difference in preferences that both players have over their choices. The Battle of the Sexes has two pure Nash equilibria, which are ESS as well (located at coordinates (0, 0) and (1, 1)), and one unstable completely mixed Nash equilibrium in which the players play respectively x = ( ) , . Figure  6  illustrates the two-player evolutionary dynamics using the replicator equations, in which the x-axis corresponds to the probability with which player 1 plays O (Opera), and the y-axis corresponds to the probability with which the 2nd player plays O (Opera). The blue arrows show the vector field and the black lines are the corresponding trajectories. Note that it is still possible here to capture all of the dynamics in a static plot for the case of 2-player 2-action games, but is generally not possible in games with more than two actions. We now use this game to illustrate Theorem 1. If we apply Theorem 1 we know that the first and second counterpart symmetric games can be described by the payoff tables shown in Table  4 . The first counterpart game has ( ) ( ) ( ) , , , 2 5 3 5 2 5 3 5 as a mixed Nash equilibrium, and the second counterpart game has ( ) ( ) ( ) , , , 3 5 2 5 3 5 2 5 as a mixed Nash equilibrium. In Fig.  7 (b) and (c) we show the evolutionary dynamics of both counterpart games, from which the respective equilibria can be observed, as predicted by Theorem 1. Additionally, we also know that the reverse holds, i.e., if we were given the symmetric counterpart games, we would know that ( ) ( ) ( ) , , , 3 5 2 5 2 5 3 5 would also be a mixed Nash equilibrium of the original asymmetric BoS. In this case we can combine the mixed Nash equilibria of both counterpart games into the mixed Nash equilibrium of the original asymmetric game, as prescribed by Theorem 1. Specifically, as y = ( ) , which is a mixed Nash equilibrium of full support of the asymmetric Battle of the Sexes game. If we now apply Theorem 2 to the Battle of the Sexes game, then we find that pure strategy Nash equilibria x = (1, 0) (and y = (1, 0) for the second counterpart) and x = (0, 1) (and y = (0, 1) for the second counterpart), which are both ESS, are also Nash equilibria in the counterpart games shown in Table  4 . Also here the reverse holds, i.e., if we know the counterpart games, and we observe that x = (1, 0) and x = (0, 1) (y = (1, 0) and y = (0, 1) for the other counterpart of the game) are Nash in both games, we know that x = y = (1, 0) and x = y = (0, 1) are also Nash in the original asymmetric game. This can also be observed in Fig.  7(a),(b) and (c ). Specifically, the pure Nash equilibria are situated at coordinates (0, 0) and (1, 1) in Fig.  7(b) and (c ). Furthermore, it is important to understand that the counterpart dynamics are visualised only on the diagonal from coordinates (0, 0) to (1, 1), as that is where both players play with the same strategy distribution over their respective actions. Extended Battle of the Sexes game. In order to illustrate the theorems in a game that is non-square, including permutation of strategies, we extend the Battle of the Sexes game with a third strategy. Specifically, we give the second player a third strategy R in which she can choose to listen to a concert on the radio instead of going to the opera or movies with her partner. This game is illustrated in Table  5 . If we would like to carry out a similar evolutionary analysis as before we need two populations for the asymmetric replicator equations. Note that in this case the strategy sets of both players are different. Using the asymmetric replicator dynamics to plot the evolutionary dynamics quickly becomes complicated since the full dynamical picture is high-dimensional and not faithfully represented by projections to the respective player's individual strategy simplices. In other words, a static plot of the dynamics for one player does not immediately allow conclusions about equilibria, as it only describes a player's strategy evolution assuming a fixed (rather than  dynamically evolving) strategy of the other player. Again we can apply the counterpart RD theorems here to remedy this problem and consequently analyse the equilibrium structure in the symmetric counterpart games instead, yielding insight into the equilibrium landscape of the asymmetric game. In Tables  6 and 7  we show the counterpart games A and B. Note that we introduce a dummy action D for the first player, in order to make sure that both players have the same number of actions in their strategy set (a requirement to apply the theorems) by just adding −1 for both players playing this strategy, which makes D completely dominated and thus redundant.    The three Nash equilibria of interest of this asymmetric game are the following, {(x = (0.6, 0.4, 0),y = (0.4, 0, 0.6)),(x = (0, 1, 0),y = (0, 0, 1)),(x = (1, 0, 0),y = (1, 0, 0)))} (we use the online banach solver http://banach.lse. ac.uk/ to check that the Nash equilibria we find are correct  31  ). We now look for the y and x parts of these equilibria in the counterpart games. In Fig.  8  we show the evolutionary dynamics of the first counterpart game and in Fig.  9  the evolutionary dynamics of the second counterpart game. In the first counterpart we only need to consider the 1-face formed by strategies O and M as the third strategy is our dummy strategy. In this game there are two Nash equilibria, i.e., (1, 0, 0) (stable, yellow oval) and (0, 1, 0) (unstable, orange oval), so either playing O or M. The second counterpart game also has two Nash equilibria, i.e., (1, 0, 0) and (0, 0, 1) playing either O or M as well. Note there are also two rest points at the faces formed by O and R and O and M, which are not Nash (see Fig.  5  for an explanation). There is no mixed equilibrium of full support, so we cannot apply Theorem 1 here. If we apply Theorem 2 we know that ((1, 0, 0), (1, 0, 0)) must also    be a pure Nash equilibrium in the original asymmetric game, and we can remove the dummy strategy for player 1. At this stage we are left with equilibria (x = (0.6, 0.4, 0),y = (0.4, 0, 0.6)) and (x = (0, 1, 0),y = (0, 0, 1)) in the asymmetric game for which we did not find a symmetric counterpart at this stage. Now the permutation of the counterpart games, explained earlier in the findings section, comes into play. Recall that in order to study all configurations of supports of the same cardinal for both players one needs to simply permute the actions of one player in matrix A and B. Let's have a look at such a permutation, specifically, let's permute the 2nd and 3rd action for player 2, resulting in Tables  8 and 9 . Again we can analyse these counterpart games. Specifically, we find Nash equilibria (1, 0, 0), (0.4, 0.6, 0), and (0, 1, 0) for permuted counterpart game 1 (Table  8 ), and Nash equilibria (0, 0, 1), (0.6, 0.4, 0), (0, 1, 0), and (1,0,0) for permuted counterpart game 2 (Table  9 ), which are illustrated in Figs  10 and 11 . From these identified Nash equilibria in both counterpart games we can combine the remaining Nash equilibria for the asymmetric game. Specifically, by applying Theorem 2 we find (x = (0.6, 0.4, 0),y = (0.4, 0.6, 0)), which translates into (x = (0.6, 0.4, 0),y = (0.4, 0, 0.6)) for the asymmetric game as we permuted actions 2 and 3 for the second player and we need to swap these again. Additionally, we also find (x = (0, 1, 0),y = (0, 1, 0)), which translates into equilibrium (x = (0, 1, 0),y = (0, 0, 1)) for the asymmetric game as we permuted action 2 and 3 for the second player. Now we have found all Nash equilibria of the original asymmetric game. So, also in this case, i.e., when the game is not square and strategies need to be permuted, the theorems are still applicable and allow for analysis of the original asymmetric game. Poker generated asymmetric games. Policy Space Response Oracles (PSRO) is a multiagent reinforcement learning process that reduces the strategy space of large extensive-form games via iterative best response computation. PSRO can be seen as a generalized form of fictitious play that produces approximate best responses, with arbitrary distributions over generated responses computed by meta-strategy solvers. PSRO was applied to a commonly-used benchmark problem in artificial intelligence research known as Leduc poker  35  . Leduc poker has a deck of 6 cards (jack, queen, king in two suits). Each player receives an initial private card, can bet a fixed amount of 2 chips in the first round, 4 chips in the second round (with a maxium of two raises in each round). Before the second round starts, a public card is revealed.   In Table  10  we present such an asymmetric 3 × 3 2-player PSRO generated game, playing Leduc Poker. In the game illustrated here, each player has three strategies that, for ease of the exposition, we call {A, B, C} for player 1, and {D, E, F} for player 2. Each one of these strategies represents a larger strategy in the full extensive-form game of Leduc poker, specifically an approximate best response to a distribution over previous opponent strategies. The game produced here then is truly asymmetric, in the sense that the strategy spaces in the original game are inherently asymmetric since player 1 always starts each round, the strategy spaces are defined by different (mostly unique) betting sequences, and even under perfect equilibrium play there is a slight advantage to player 2  9  . So, both players have significantly different strategy sets. In Tables  11 and 12  we show the two symmetric counterpart games of the empirical game produced by PSRO on Leduc poker. O M R O 3 0 0.5 M 0 2 0.5 D −1 −1 −1 Again we can now analyse the landscape of equilibria of this game using the introduced theorems. Since the Leduc poker empirical game is asymmetric we need two populations for the asymmetric replicator equations. As mentioned before, analysing and plotting the evolutionary asymmetric replicator dynamics now quickly becomes very tedious as we deal with two simplices, one for each player. More precisely, if we consider a strategy for one player in its corresponding simplex, and that player is adjusting its strategy, will immediately cause the trajectory in the second simplex to change, and vice versa. Consequently, it is not straightforward anymore to analyse the     In order to facilitate the process of analysing this game we can apply the counterpart RD theorems here to remedy the problem, and consequently analyse the game in the far simpler symmetric counterpart games that will shed light onto the equilibrium landscape of the Leduc Poker empirical game. In Figs 12 and 13 we show the evolutionary dynamics of the counterpart games. As can be observed in Fig.  12  the first counterpart game has only one equilibrium, i.e., a mixed Nash equilibrium at the face formed by A and C, which absorbs the entire strategy space. Looking at Fig.  13  we see the situation is a bit more complex in the second counterpart game, here we observe three Nash equilibria: one pure at strategy D, one pure at strategy F, and one unstable mixed equilibrium at the 1-face formed by strategies D and F. Note there is also a rest point at the face formed by strategies D and E, which is not Nash. Given that there are no mixed equilibria with full support in both games we cannot apply Theorem 1. Using Theorem 2 we now know that we only maintain the two mixed equilibria, i.e. (0.32, 0, 0.68) (CP1) and (0.83, 0, 0.17) (CP2), forming the mixed Nash equilibrium (x = (0.83, 0, 0.17),y = (0.32, 0, 0.68)) of the asymmetric Leduc poker empirical game. The other equilibria in the second  counterpart game can be discarded as candidates for Nash equilibria in the Leduc poker empirical game since they also do not appear for player 1 when we permute the strategies for player 1 (not shown here). Mixed equilibrium of full support. As a final example to illustrate the introduced theory, we examine an asymmetric game, that has one completely mixed equilibrium and several equilibria in its counterpart games. The bimatrix game (A,B) is illustrated in Table  13  and its symmetric counterparts are shown in Tables  14 and 15 . The asymmetric game has a unique completely mixed Nash equilibrium with different mixtures for the two players, i.e., (x = = = ( )  , , ;  , , , (p 1 = (0,0,1), ( ) ( ) x y p 2 = (1,0,0)), (p 1 = = = ( ) ( ) ( ) p p 0, , , , , 0 1 1 2 1 2 2 1 2 1 2 }. Note that there are also two rest points, which are not Nash, at the faces formed by A and B and B and C. From these seven equilibria only (a), (b) and (c) are of interest since these are symmetric equilibria in which both players play with the same strategy (or support). Also counterpart game 2 has seven equilibria, i.e., = = { ( ) ( ) ( ) d p p ( ) , , , , , 1 1 3 1 3 1 3 2 1 3 1 3 1 3 , = = ( ) ( ) ( ) p p , 0, , 0, , 1 1 2 1 2 2 1 2 1 2 , = = e p p (( ) (0, 0, 1), (0, 0, 1)) 1 2 , = = ( ) ( ) ( ) p p 0, , , , 0, 1 1 2 1 2 2 1 2 1 2 , = = ( ) ( ) ( ) f p p ( ) , , 0 , , , 0 1 1 2 1 2 2 1 2 1 2 , = = p p ( (1, 0, 0), (0, 1, 0)) 1 2 , = = p p ( (0, 1, 0), (1, 0, 0) } 1 2 of which only (d), (e) and (f) are of interest. We obser ve that only the completely mixed equilibrium of the asymmetric game, i.e., = = ( )  , , ;  , , ( ) ( ) x y 1 3 1 3 2 7 3 7 13 , has its counterpart in the symmetric games. To apply the theorems we only need to have a look at equilibria (a), (b) and (c) in counterpart game 1, and (d), (e) and (f) in counterpart game 2. These equilibria can also be observed in the directional field plots, respectively, trajectory plots, illustrating the evolutionary dynamics of both counterpart games in Figs 14, 15, 16 and 17. Figure  14  visualises the three remaining equilibria (a), (b) and (c), with (a) indicated as a yellow oval, and (b) and (c) both indicated as green ovals. As can be observed, (a) is an unstable mixed equilibrium, (b) is a stable pure equilibrium, and (c) is a partly mixed equilibrium at the 2-face formed by strategies A and C. We can make the same observation for the second counterpart game, and see that (d), (e) and (f) are equilibria in Fig.  16 . Equilibrium (d), indicated by a yellow oval, is completely mixed, equilibrium (e) is a pure equilibrium in corner F (green oval), and (f) is a partly mixed equilibrium on the 2-face formed by strategies D and E (green ovals as well). If we now apply Theorem 1 we know that we can combine the mixed equilibria of full support of both counterpart games into the mixed equilibrium of the original asymmetric game, in which the mixed equilibrium of counterpart game 1, i.e.  ( )  , , , becomes the part of the mixed equilibrium in the asymmetric game of player 2, and the mixed equilibrium of counterpart game 2, i.e. ( ) , , 1 3 1 3 1 3 , becomes the part of the mixed equilibrium in     , , ;  , , . Both equilibria are unstable in the counterpart games and also form an unstable mixed equilibrium in the asymmetric game. D E F A 1, 0 0, 1 2, 0 B 0, 1 2, 0 0, 0 C 2, 0 0, 0 1, 1 \n Discussion Replicator Dynamics have proved to be an excellent tool to analyse the Nash landscape of multiagent interactions and distributed learning in both abstract games and complex systems 1,2,4,6 . The predominant approach has been the use of symmetric replicator equations, allowing for a relatively straightforward analysis in symmetric games. Many interesting real-world settings though involve roles or player-types for the different agents that take part in an interaction, and as such are asymmetric in nature. So far, most research has avoided to carry out RD analysis in this type of interactions, by either constructing a new symmetric game, in which the various actions of the different roles are joined together in one population  23, 24  , or by considering the various roles and strategies as heuristics, grouped in one population as well  2, 3, 8  . In the latter approach the payoffs due to different player-types are averaged over many samples of the player type resulting in a single average payoff to each player for each entry in the payoff table. The work presented in this paper takes a different stance by decomposing an asymmetric game into its symmetric counterparts. This method proves to be mathematically simple and elegant, and allows for a straightforward analysis of asymmetric games, without the need for turning the strategy spaces into one simplex or population, but instead allows to keep separate simplices for the involved populations of strategies. Furthermore, the counterpart games allow to get insight in the type and form of interaction of the asymmetric game under study, identifying its equilibrium structure and as such enabling analysis of abstract and empirical games  A deeper counter-intuitive understanding of the theoretical results of this paper is that when identifying Nash equilibria in the counterpart games with matching support (including permutations of strategies for one of the players), it turns out that also the combination of those equilibria form a Nash equilibrium in the corresponding asymmetric game. In general, the vector field for the evolutionary dynamics of one player is a function of the other player's strategy, and hence a vector field in one player's simplex doesn't carry much information as any equilibria you observe in it are changing with time as the other player is moving too. However, if you position the second player at a Nash equilibrium, it turns out that player one becomes indifferent between his different strategies, and remains stationary under the RD. This gives the unique situation in which the vector field plot for the second player's simplex is actually meaningful, because the assumption of player one being stationary actually holds (and vice versa). This is what we end up using when establishing the correspondence of the Nash Equilibria in asymmetric and counterpart games, and why the single-simplex plots for the counterpart games are actually meaningful for the asymmetric game -but this is also why they only describe the Nash Equilibria faithfully, but fail to be a valid decomposition of the full asymmetric game away from equilibrium. These findings shed new light on asymmetric interactions between multiple agents and provide new insights that facilitate a thorough and convenient analysis of asymmetric games. As pointed out by Veller and Hayward 36 , many real-world situations, in which one aims to study evolutionary or learning dynamics of several interacting agents, are better modelled by asymmetric games. As such these theoretical findings can facilitate deeper analysis  of equilibrium structures in evolutionary asymmetric games relevant to various topics including economic theory, evolutionary biology, empirical game theory, the evolution of cooperation, evolutionary language games and artificial intelligence  11, 12, [37] [38] [39] [40]  . Finally, the results of this paper also nicely underpin what is said in H. Gintis' book on the evolutionary dynamics of asymmetric games, i.e., 'although the static game pits the row player against the column player, the evolutionary dynamic pits row players against themselves and column players against themselves' 32 (chapter 12, p.292). He also indicates that this aspect of an evolutionary dynamic is often misunderstood. The use of our counterpart dynamics supports and illustrates this statement very clearly, showing that in the counterpart games species play games within a population and as such show an intra-species survival of the fittest, which is then combined into an equilibrium of the asymmetric game. Figure 1 . 1 Figure 1. Directional field plot of the Prisoner's Dilemma game. \n Figure 2 . 2 Figure 2. (a) Payoff matrix for the Rock-Paper-Scissors game. Strategies R, S and P correspond to playing respectively Rock, Scissors, Paper. (b) Σ 3 Trajectory plot of the Rock-Paper-Scissors game. The Nash equilibrium is marked with a full yellow dot. \n Figure 3 . 3 Figure 3. ESS. \n Figure 4 . 4 Figure 4. NE but not ESS. \n Figure 5 . 5 Figure 5. Rest point but not NE. \n Theorem 2 . 2 Strategies x and y constitute a Nash equilibrium of an asymmetric game G = (S 1 , S 2 , A, B) with the same support (i.e. I x = I y ) if and only if x is a Nash equilibrium of the single population game B T , y is a Nash equilibrium of the single population game A and I x = I y . \n the Nash equilibrium in the first counterpart game and x = ( ) counterpart game, we can combine them into (x = ( ) \n Figure 6 . 6 Figure 6. Directional field plot of the Battle of the Sexes game. \n Figure 7 . 7 Figure 7. This plot shows a visual representation of how the mixed Nash equilibrium is decomposed into Nash equilibria in both counterpart games. (a) shows the directional field plot of the Battle of the Sexes game. (b) illustrates how the y-component of the asymmetric Nash equilibrium becomes a Nash equilibrium in the first counterpart game, and (c) shows how the x-component of the asymmetric Nash equilibrium becomes a Nash equilibrium in the first counterpart game. \n Figure 8 . 8 Figure 8. Directional field plot Σ 3 of the first counterpart game of the extended Battle of the Sexes game. \n Figure 9 . 9 Figure 9. Directional field plot Σ 3 of the second counterpart game of the extended Battle of the Sexes game. \n Table 9 . 9 Permuted payoff matrix for the 2nd counterpart game of the Extended BoS game. \n Figure 10 . 10 Figure 10. Directional field plot Σ 3 of the first counterpart game of the permuted extended Battle of the Sexes game. \n Figure 11 . 11 Figure 11. Directional field plot Σ 3 of the second counterpart game of the permuted extended Battle of the Sexes game. \n dynamics and equilibrium landscape for both players, as any trajectory in one simplex causes the other simplex to change. A movie illustrates what is meant: we show how the dynamics of player 2 changes in function of player 1. We overlay the simplex of the second player with the simplex of the first player; the yellow dots indicate what the strategy of the first player is. The movie then shows how the dynamics of the second player changes when the yellow dot changes, see https://youtu.be/10m0f3iBECc. \n Figure 12 . 12 Figure 12. Directional field plot Σ 3 of the first counterpart game of the Leduc poker empirical game under study. \n Figure 13 . 13 Figure 13. Directional field plot Σ 3 of the second counterpart game of the Leduc poker empirical game under study. \n .,(p 1 = 1 The two symmetric counterpart game each have seven equilibria. Counterpart game 1 (Table14), has the following set of Nash equilibria: {(a)(p 1 (1,0,0), p 2 = (0,0,1)), (b)(p 1 = (0,1,0), p 2 = (0,1,0)),((c)   \n Figure 14 . 14 Figure 14. Directional field plot Σ 3 of the first counterpart game of the mixed equilibrium asymmetric game. \n Figure 15 . 15 Figure 15. Trajectory plot Σ 3 of the first counterpart game of the mixed equilibrium asymmetric game. \n Figure 16 . 16 Figure 16. Directional field plot Σ 3 of the second counterpart game of the mixed equilibrium asymmetric game. \n Figure 17 . 17 Figure 17. Trajectory plot Σ 3 of the second counterpart game of the mixed equilibrium asymmetric game. \n Table 1 . 1 General payoff bimatrix (A, B) for a two-player two-action normal form game, where player 1 can choose between actions A 1 and A 2 , and player 2 can choose between actions B 1 and B 2 . Player 2 B 1 B 2 Player 1 A 1 A 2 a 11 , b 11 b 21, a 21 a 12 , b 12 a 22 , b 22 \n Table 2 . 2 Payoff bimatrix for the Battle of the Sexes game. Strategies O and M correspond to going to the Opera and going to the Movies respectively. \n Table 3 . 3 Payoff matrix for the Prisoner's Dilemma game. Strategies D and C correspond to the actions Defect and Cooperate. \n Table 4 . 4 Counterpart matrix game 1 and 2 for the Battle of the Sexes game. \n Table 5 . 5 Extended Battle of the Sexes game. \n Table 6 . 6 Payoff matrix for the 1st counterpart game of the Extended BoS game. Strategy D is added to make the matrix completely square. \n Table 7 . 7 Payoff matrix for the 2nd counterpart game of the Extended BoS game. Strategy D is added to make the matrix completely square. \n Table 8 . 8 Permuted payoff matrix for the 1st counterpart game of the Extended BoS game. \n Table 10 . 10 Payoff matrix of an asymmetric empirical game produced by PSRO applied to Leduc poker. A B C A −0.16 0.05 0.08 B 0.64 −0.17 −0.31 C 0.79 1.06 −0.37 \n Table 11 . 11 First counterpart game of the Leduc poker empirical game. D E F D 0.16 −0.05 −0.08 E −0.64 0.17 0.31 F −0.79 −1.06 0.37 \n Table 12 . 12 Second counterpart game of the Leduc poker empirical game. \n Table 13 . 13 Payoff matrix of an asymmetric game with mixed equilibrium of full support. A B C A 1 0 2 B 0 2 0 C 2 0 1 \n Table 14 . 14 First counterpart game of the asymmetric game. D E F D 0 1 0 E 1 0 0 F 0 0 1 \n Table 15 . 15 Second counterpart game of the asymmetric game. the asymmetric game of player 1, leading to = ( ( = ) ( ) ) x y \n\t\t\t Scientific REPORTS | (2018) 8:1015 | DOI:10.1038/s41598-018-19194-4", "date_published": "n/a", "url": "n/a", "filename": "s41598-018-19194-4.tei.xml", "abstract": "We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be decomposed into its symmetric counterparts by envisioning and investigating the payoff tables (A and B) that constitute the asymmetric game, as two independent, single population, symmetric games. We reveal several surprising formal relationships between an asymmetric two-population game and its symmetric single population counterparts, which facilitate a convenient analysis of the original asymmetric game due to the dimensionality reduction of the decomposition. The main finding reveals that if (x,y) is a Nash equilibrium of an asymmetric game (A,B), this implies that y is a Nash equilibrium of the symmetric counterpart game determined by payoff table A, and x is a Nash equilibrium of the symmetric counterpart game determined by payoff table B. Also the reverse holds and combinations of Nash equilibria of the counterpart games form Nash equilibria of the asymmetric game. We illustrate how these formal relationships aid in identifying and analysing the Nash structure of asymmetric games, by examining the evolutionary dynamics of the simpler counterpart games in several canonical examples. We are interested in analysing the Nash structure and evolutionary dynamics of strategic interactions in multi-agent systems. Traditionally, such interactions have been studied using single population replicator dynamics models, which are limited to symmetric situations, i.e., players have access to the same set of strategies and the payoff structure is symmetric as well 1 . For instance, Walsh et al. introduce an empirical game theory methodology (also referred to as heuristic payoff table method) that allows for analysing multiagent interactions in complex multiagent games 2,3 . This method has been extended by others and been applied e.g. in continuous double auctions, variants of poker and multi-robot systems 1,4-9 . Similar evolutionary methods have been applied to the modelling of human cooperation, language, and complex social dilemma's  [10] [11] [12] [13] [14] [15] [16]  . Though these evolutionary methods have been very useful in providing insights into the type and form of interactions in such systems, the underlying Nash structure, and evolutionary dynamics, the analysis is limited to symmetric situations, i.e., players or agents can be interchanged and have access to the same strategy set, in other words there are no different roles for the various agents involved in the interactions (e.g. a seller vs a buyer in an auction). As such this method is not directly applicable to asymmetric situations in which the players can choose strategies from different sets of actions, with asymmetric payoff structures. Many interesting multiagent scenarios involve asymmetric interactions though, examples include simple games from game theory such as e.g. the Ultimatum Game or the Battle of the Sexes and more complex board games that can involve various roles such as Scotland Yard, but also trading on the internet for instance can be considered asymmetric. There exist approaches that deal with asymmetry in multiagent interactions, but they usually propose to transform the asymmetric game into a symmetric game, with new strategy sets and payoff structure, which then can be analysed again in the context of symmetric games. This is indeed a feasible approach, but not easily scalable to the complex interactions mentioned before, nor is it practical or intuitive to construct a new symmetric game before the asymmetric one can be analysed in full. The approach we take in this paper does not require constructing a new game and is theoretically underpinned, revealing some new interesting insights in the relation between the Nash structure of symmetric and asymmetric games. Analysing multiagent interactions using evolutionary dynamics, or replicator dynamics, provides not only valuable insights into the (Nash) equilibria and their stability properties, but also sheds light on the behaviour trajectories of the involved agents and the basins of attraction of the equilibrium landscape  1, 4, 15, 17, 18  . As such it", "id": "c553168147a2e3552d7674fe9b64aa5a"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Sören Mindermann", "Stuart Armstrong"], "title": "Occam's razor is insufficient to infer the preferences of irrational agents", "text": "Introduction In today's reinforcement learning systems, a simple reward function is often hand-crafted, and still sometimes leads to undesired behaviors on the part of RL agent, as the reward function is not well aligned with the operator's true goals 4 . As AI systems become more powerful and autonomous, these failures will become more frequent and grave as RL agents exceed human performance, operate at time-scales that forbid constant oversight, and are given increasingly complex tasks -from driving cars to planning cities to eventually evaluating policies or helping run companies. Ensuring that the agents behave in alignment with human values is known, appropriately, as the value alignment problem  [Amodei et al., 2016 , Hadfield-Menell et al., 2016 , Russell et al., 2015 , Bostrom, 2014 , Leike et al., 2017 . One way of resolving this problem is to infer the correct reward function by observing human behaviour. This is known as Inverse reinforcement learning (IRL)  [Ng and Russell, 2000 , Abbeel and Ng, 2004 , Ziebart et al., 2008 . Often, learning a reward function is preferred over imitating a policy: when the agent must outperform humans, transfer to new environments, or be interpretable. The reward function is also usually a (much) more succinct and robust task representation than the policy, especially in planning tasks  [Abbeel and Ng, 2004] . Moreover, supervised learning of long-range and goal-directed behavior is often difficult without the reward function  [Ratliff et al., 2006] . Usually, the reward function is inferred based on the assumption that human behavior is optimal or noisily optimal. However, it is well-known that humans deviate from rationality in systematic, non-random ways  [Tversky and Kahneman, 1975] . This can be due to specific biases such as timeinconsistency, loss aversion and hundreds of others, but also limited cognitive capacity, which leads to forgetfulness, limited planning and false beliefs. This limits the use of IRL methods for tasks that humans don't find trivial. Some IRL approaches address specific biases  [Evans et al., 2015b,a] , and others assume noisy rationality  [Ziebart et al., 2008 , Boularias et al., 2011 . But a general framework for inferring the reward function from suboptimal behavior does not exist to our knowledge. Such a framework needs to infer two unobserved variables simultaneously: the human reward function and their planning algorithm  5  which connects the reward function with behaviour, henceforth called a planner. The task of observing human behaviour (or the human policy) and inferring from it the human reward function and planner will be termed decomposing the human policy. This paper will show there is a No Free Lunch theorem in this area: it is impossible to get a unique decomposition of human policy and hence get a unique human reward function. Indeed, any reward function is possible. And hence, if an IRL agent acts on what it believes is the human policy, the potential regret is near-maximal. This is another form of unidentifiability of the reward function, beyond the well-known ones  Russell, 2000, Amin and Singh, 2016] . The main result of this paper is that, unlike other No Free Lunch theorems, this unidentifiability does not disappear when regularising with a general simplicity prior that formalizes Occam's razor  [Vitanyi and Li, 1997] . This result will be shown in two steps: first, that the simplest decompositions include degenerate ones, and secondly, that the most 'reasonable' decompositions according to human judgement are of high complexity. So, although current IRL methods can perform well on many well-specified problems, they are fundamentally and philosophically incapable of establishing a 'reasonable' reward function for the human, no matter how powerful they become. In order to do this, they will need to build in 'normative assumptions': key assumptions about the reward function and/or planner, that cannot be deduced from observations, and allow the algorithm to focus on good ways of decomposing the human policy. Future work will sketch out some potential normative assumptions that can be used in this area, making use of the fact that humans assess each other to be irrational, and often these assessments agree. In view of the No Free Lunch result, this shows that humans must share normative assumptions. One of these 'normative assumption' approaches is briefly illustrated in an appendix, while another appendix demonstrates how to use the planner-reward formalism to define when an agent might be manipulating or overriding human preferences. This happens when the agent pushes the human towards situations where their policy is very suboptimal according to their reward function. \n Related Work In the first IRL papers from  Ng and Russell [2000]  and  Abbeel and Ng [2004]  a max-margin algorithm was used to find the reward function under which the observed policy most outperforms other policies. Suboptimal behavior was first addressed explicitly by  Ratliff et al. [2006]  who added slack variables to allow for suboptimal behavior. This finds reward functions such that the observed policy outperforms most other policies and the biggest margin by which another policy outperforms it is minimal, i.e. the observed policy has low regret.  Shiarlis et al. [2017]  introduce a modern max-margin technique with an approximate planner in the optimisation. However, the max-margin approach has mostly been replaced by the max entropy IRL  [Ziebart et al., 2008] . Here, the assumption is that observed actions or trajectories are chosen with probability proportional to the exponent of their value. This assumes a specific suboptimal planning algorithm which is noisily rational (also known as Boltzmann-rational). Noisy rationality explains human behavior on various data sets better  [Hula et al., 2015] . However,  Evans et al. [2015b]  and  Evans et al. [2015a]  showed that this can fail since humans deviate from rationality in systematic, non-random ways. If noisy rationality is assumed, repeated suboptimal actions throw off the inference. Literature on inferring the reasoning capabilities of an agent is scarce.  Evans et al. [2015b]  and  Evans et al. [2015a]  use Bayesian inference to identify specific planning biases such as myopic planning and hyperbolic time-discounting. They simultaneously infer the agent's preferences.  Cundy and Filan [2018]  adds bias resulting from hierarchical planning.  Hula et al. [2015]  similarly let agents infer features of their opponent's reasoning such as planning depth and impulsivity in simple economic games. Recent work learns the planning algorithm with two assumptions: being close to noisily rational in a high-dimensional planner space and supervised planner-learning  [Anonymous, 2019] . The related ideas of meta-reasoning  [Russell, 2016] , computational rationality  [Lewis et al., 2014]  and resource rationality  [Griffiths et al., 2015]  may create the possibility to redefine irrational behavior as rational in an 'ancestral' distribution of environments where the agent optimises its rewards by choosing among the limited computations it is able to perform or jointly minimising the cost of computation and maximising reward. This could in theory redefine many biases as computationally optimal in some distribution of environments and provide priors on human planning algorithms. Unfortunately the problem of doing this in practice seems to be extremely difficult -and it assumes that human goals are roughly the same as evolution's goals, which is certainly not the case. \n Problem setup and background A human will be performing a series of actions, and from these, an agent will attempt to estimate both the human's reward function and their planning algorithm. The environment M in which the human operates is an MDP/R, a Markov Decision Process without reward function (a world-model ). An MDP/R is defined as a tuple, S, A, T, ŝ consisting of a discrete state space S, a finite action space A, a fixed starting state ŝ, and a probabilistic transition function T : S × A × S → [0, 1] to the next state (also called the dynamics). At each step, the human is in a certain state s, takes a certain action a, and ends up in a new state s as given by T (s | s, a). Let R = {R : S × A → [−1, 1]} = [−1, 1] S×A be the space of candidate reward functions; a given R will map any state-reward pair to a reward value in the interval [−1, 1]. Let Π be the space of deterministic, Markovian policies. So Π is the space of functions S → A. The human will be following the policy π ∈ Π. The results of this paper apply to both discounted rewards and episodic environments settings 6 . \n Planners and reward functions: decomposing the policy The human has their reward function, and then follows a policy that presumably attempts to maximise it. Therefore there is something that bridges between the reward function and the policy: a piece of greater or lesser rationality that transforms knowledge of the reward function into a plan of action. This bridge will be modeled as a planner p : R → Π, a function that takes a reward and outputs a policy. This planner encodes all the rationality, irrationality, and biases of the human. Let P be the set of planners. The human is therefore defined by a planner-reward pair (p, R) ∈ P × R. Similarly, (p, R) with p(R) = π is a decomposition of the policy π. The task of the agent is to find a 'good' decomposition of the human policy π. \n Compatible pairs and evidence The agent can observe the human's behaviour and infer their policy from that. In order to simplify the problem and separate out the effect of the agent's learning, we will assume the agent has perfect knowledge of the human policy π and of the environment M . At this point, the agent cannot learn anything by observing the human's actions, as it can already perfectly predict these. Then a pair (p, R) is defined to be compatible with π, if p(R) = π -thus that pair is a possible candidate for decomposing the human policy into the human's planner and reward function. \n Irrationality-based unidentifiability Unidentifiability of the reward is a well-known problem in IRL  [Ng and Russell, 2000] .  Amin and Singh [2016]  categorise the problem into representational and experimental unidentifiability. The former means that adding a constant to a reward function or multiplying it with a positive scalar does not change what is optimal behavior. This is unproblematic as rescaling the reward function doesn't change the preference ordering. The latter can be resolved by observing optimal policies in a whole class of MDPs which contains all possible transition dynamics. We complete this framework with a third kind of identifiability, which arises when we observe suboptimal agents. This kind of unidentifiability is worse as it cannot necessarily be resolved by observing the agent in many tasks. In fact, it can lead to almost arbitrary regret. \n Weak No Free Lunch: unidentifiable reward function and half-maximal regret The results in this section show that without assumptions about the rationality of the human, all attempts to optimise their reward function are essentially futile.  work in a similar setting as we do: in their case, a corrupted version of the reward function is observed. The problem our case is that a 'corrupted' version π of an optimal policy π * Ṙ is observed and used as information to optimise for the ideal reward Ṙ. A No Free Lunch result analogous to theirs applies in our case; both resemble the No Free Lunch theorems for optimisation  [Wolpert and Macready, 1997] . More philosophically, this result is as an instance of the well-known is-ought problem from metaethics.  Hume [1888]  argued that what ought to be (here, the human's reward function) can never be concluded from what is (here, behavior) without extra assumptions. Equivalently, the human reward function cannot be inferred from behavior without assumptions about the planning algorithm p. In probabilistic terms, the likelihood P (π|R) = p∈P P (π | R, p)P (p) is undefined without P (p). As shown in Section 5 and Section 5.2, even a simplicity prior on p and R will not help. \n Unidentifiable reward functions Firstly, we note that compatibility (p(R) = π), puts no restriction on R, and few restrictions on p: Theorem 1. For all π ∈ Π and R ∈ R, there exists a p ∈ P such that p(R) = π. For all p ∈ P and π ∈ Π in the image of p, there exists an R such that p(R) = π. Proof. Trivial proof: define the planner 7 p as mapping all of R to π; then p(R) = π. The second statement is even more trivial, as π is in the image of p, so there must exist R with p(R) = π. \n Half-maximal regret The above shows that the reward function cannot be constrained by observation of the human, but what about the expected long-term value? Suppose that an agent is unsure what the actual human reward function is; if the agent itself is acting in an MDP/R, can it follow a policy that minimises the possible downside of its ignorance? This is prevented by a recent No Free Lunch theorem. Being ignorant of the reward function one should maximise is equivalent of having a corrupted reward channel with arbitrary corruption. In that case,  demonstrated that whatever policy π the agent follows, there is a R ∈ R for which π is half as bad as the worst policy the agent could have followed. Specifically, let V π R (s) be the expected return of reward function R from state s, given that the agent follows policy π. If π was the optimal policy for R, then this can be written as V * R (s). The regret of π for R at s is given by the difference:  demonstrates that for any π, Reg(π, R)(s) = V * R (s) − V π R (s). Then max R∈R Reg(π, R)(s) ≥ 1 2 max π ∈Π,R∈R Reg(π , R)(s) . So for any compatible (p, R) = π, we cannot rule out that maximizing R leads to at least half of the worst-case regret. \n Simplicity of degenerate decompositions Like many No Free Lunch theorems, the result of the previous section is not surprising given there are no assumptions about the planning algorithm. No Free Lunch results are generally avoided by placing a simplicity prior on the algorithm, dataset, function class or other object  [Everitt et al., 2014] . This amounts to saying algorithms can benefit from regularisation. This section is dedicated to showing that, surprisingly, simplicity does not solve the No Free Lunch result. Our simplicity measure is minimum description length of an object, defined as Kolmogorov complexity  [Kolmogorov, 1965] , the length of the shortest program that outputs a string describing the object. This is the most general formalization of Occam's razor we know of  [Vitanyi and Li, 1997] . Appendix A explores how the results extend to other measures of complexity, such as those that include computation time. We start with informal versions of our main results. Theorem 2 (Informal simplicity theorem). Let ( ṗ, Ṙ) be a 'reasonable' planner-reward pair that captures our judgements about the biases and rationality of a human with policy π = ṗ( Ṙ). Then there are degenerate planner-reward pairs, compatible with π, of lower complexity than ( ṗ, Ṙ), and a pair ( ṗ , − Ṙ) of similar complexity to ( ṗ, Ṙ), but with opposite reward function. There are a few issues with this theorem as it stands. Firstly, simplicity in algorithmic information theory is relative to the computer language (or equivalently Universal Turing Machine) L used  Vitányi, 2014, Calude, 2002] , and there exists languages in which the theorem is clearly false: one could choose a degenerate language in which ( ṗ, Ṙ) is encoded by the string '0', for example, and all other planner-reward pairs are of extremely long length. What constitutes a 'reasonable' language is a long-standing open problem, see  Leike et al. [2017]  and  Müller [2010] . For any pair of languages, complexities differ only by a constant, the amount required for one language to describe the other, but this constant can be arbitrarily large. Nevertheless, this section will provide grounds for the following two semi-formal results: Proposition 3. If π is a human policy, and L is a 'reasonable' computer language, then there exists degenerate planner-reward pairs amongst the pairs of lowest complexity compatible with π. Proposition 4. If π is a human policy, and L is a 'reasonable' computer language with ( ṗ, Ṙ) a compatible planner-reward pair, then there exist a pair ( ṗ , − Ṙ) of comparable complexity to ( ṗ, Ṙ), but opposite reward function. The last part of Theorem 2, the fact that any 'reasonable' ( ṗ, Ṙ) is expected to be of higher complexity, will be addressed in Section 6. \n Simple degenerate pairs The argument in this subsection will be that 1) the complexity of π is close to a lower bound on any pair compatible with it and 2) degenerate decompositions are themselves close to this bound. The first statement follows because for any decomposition (p, R) compatible with π, the map (p, R) → p(R) = π will be a simple one, adding little complexity. And if a compatible pair (p , R ) can be from π with little extra complexity, then it too will have a complexity close to the minimal complexity of any other pair compatible with it. Therefore we will first produce three degenerate pairs that can be simply constructed from π. \n The degenerate pairs We can define the trivial constant reward function 0, and the greedy planner p g . The greedy planner p g acts by taking the action that maximises the immediate reward in the current state and the next action. Thus 8 p g (R)(s) = argmax a R(s, a). We can also define the anti-greedy planner −p g , with −p g (R)(s) = argmin a R(s, a). In general, it will be useful to define the negative of a planner: Definition 5. If p : R → Π is a planner, the planner −p is defined by −p(R) = p(−R). For any given policy π, we can define the indifferent planner p π , which maps any reward function to π. We can also define the reward function R π , so that R π (s, a) = 1 if π(s) = a, and R π (s, a) = 0 otherwise. The reward function −R π is defined to be the negative of R π . Then: Lemma 6. The pairs (p π , 0), (p g , R π ), and (−p g , −R π ) are all compatible with π. Proof. Since the image p π is π, p π (0) = π. Now, R π (s, a) > 0 iff π(s) = a, hence for all s: p g (R π )(s) = argmax a R π (s, a) = π(s), so p g (R π ) = π. Then −p g (−R π ) = p g (−(−R π )) = p g (R π ) = π, by Definition 5. \n Complexity of basic operations We will look the operations that build the degenerate planner-reward pairs from any compatible pair: 1. For any planner p, f 1 (p) = (p, 0) as a planner-reward pair. 2. For any reward function R, f 2 (R) = (p g , R). 3. For any planner-reward pair (p, R), f 3 (p, R) = p(R). 4. For any planner-reward pair (p, R), f 4 (p, R) = (−p, −R). 5. For any policy π, f 5 (π) = p π . 6. For any policy π, f 6 (π) = R π . These will be called the basic operations, and there are strong arguments that reasonable computer languages should be able to express them with short programs. The operation f 1 , for instance, is simply appending the flat trivial 0, f 2 appends a planner defined by the simple 9 search operator argmax, f 3 applies a planner to the object -a reward function -that the planner naturally acts on, f 4 is a double negation, while f 5 and f 6 are simply described in subsubsection 5.1.1. From these basic operations, we can define three composite operations that map any compatible planner-reward pair to one of the degenerate pairs (the element F 4 = f 4 is useful for later definitions). Thus define F = {F 1 = f 1 • f 5 • f 3 , F 2 = f 2 • f 6 • f 3 , F 3 = f 4 • f 2 • f 6 • f 3 , F 4 = f 4 }. For any π-compatible pair (p, R) we have F 1 (p, R) = (p π , 0), F 2 (p, R) = (p g , R π ), and F 3 (p, R) = (−p g , −R π ) (see the proof of Proposition 7). Let K L denote Kolmogorov complexity in the language L: the shortest algorithm in L that generates a particular object. We define the F -complexity of L as max (p,R),Fi∈F K L (F i (p, R)) − K L (p, R). Thus the F -complexity of L is how much the F i potentially increase 10 the complexity of pairs. For a constant c ≥ 0, this allows us to formalise what we mean by L being a c-reasonable language for F : that the F -complexity of L is at most c. A reasonable language is a c-reasonable language for a c that we feel is intuitively low enough. \n Low complexity of degenerate planner-reward pairs To formalise the concepts 'of lowest complexity', and 'of comparable complexity', choose a constant c ≥ 0, then (p, R) and (p , R ) are of 'comparable complexity' if ||K L (p, R) − K L (p , R )|| ≤ c. For a set S ⊂ P × R, the pair (p, R) ∈ S is amongst the lowest complexity in S if ||K L (p, R) − min (p ,R )∈S K L (p , R )|| ≤ c, thus K L is within distance c of the minimum complexity element of S. Now formalize Proposition 3: Proposition 7. If π is the human policy, c defines a reasonable measure of comparable complexity, and L is a c-reasonable language for F , then the degenerate planner-reward pairs (p π , 0), (p g , R π ), and (−p g , −R π ) are amongst the pairs of lowest complexity among the pairs compatible with π. Proof. By Lemma 6, (p π , 0), (p g , R π ), and (−p g , −R π ) are compatible with π. By the definitions of the f i and F i , for(p, R) compatible with π, f 3 ((p, R)) = p(R) = π and hence F 1 (p, R) = f 1 • f 5 ( π) = f 1 (p π ) = (p π , 0), F 2 (p, R) = f 2 • f 6 ( π) = f 2 (R π ) = (p g , R π ), F 3 (p, R) = f 4 • F 2 (p, R) = (−p g , −R π ). Now pick (p, R) to be the simplest pair compatible with π. Since L is c-reasonable for F , K L (p π , 0) ≤ c + K L (p, R). Hence (p π , 0) is of lowest complexity among the pairs compatible with π; the same argument applies for the other two degenerate pairs. \n Negative reward If ( ṗ, Ṙ) is compatible with π, then so is (− ṗ, − Ṙ) = f 4 ( ṗ, Ṙ) = F 4 ( ṗ, Ṙ ). This immediately implies the formalisation of Proposition 4: Proposition 8. If π is a human policy, c defines a reasonable measure of comparable complexity, L is a c-reasonable language for F , and ( ṗ, Ṙ) is compatible with π, then (− ṗ, − Ṙ) is of comparable complexity to ( ṗ, Ṙ). So complexity fails to distinguish between a reasonable human reward function and its negative. 6 The high complexity of the genuine human reward function Section 5 demonstrated that there are degenerate planner-reward pairs close to the minimum complexity among all pairs compatible with π. This section will argue that any reasonable pair ( ṗ, Ṙ) is unlikely to be close to this minimum, and is therefore of higher complexity than the degenerate pairs. Unlike simplicity, reasonable decomposition cannot easily be formalised. Indeed, a formalization would likely already solve the problem, yielding an algorithm to maximize it. Therefore, the arguments in this section are mostly qualitative. We use reasonable to mean 'compatible with human judgements about rationality'. Since we do not have direct access to such a decomposition, the complexity argument will be about showing the complexity of these human judgements. This argument will proceed in three stages: 1. Any reasonable ( ṗ, Ṙ) is of high complexity, higher than it may intuitively seem to us. 2. Even given π, any reasonable ( ṗ, Ṙ) involves a high number of contingent choices. Hence any given ( ṗ, Ṙ) has high information (and thus high complexity), even given π. 3. Past failures to find a simple ( ṗ, Ṙ) derived from π are evidence that this is tricky. \n The complexity of human (ir)rationality Humans make noisy and biased decisions all the time. Though noise is important  [Kahneman et al., 2016] , many biases, such as anchoring bias, overconfidence, planning fallacies, and so on, affect humans in a highly systematic way; see  Kahneman and Egan [2011]  for many examples. Many people may feel that they have a good understanding of rationality, and therefore assume that assessing the (ir)rationality of any particular decision is not a complicated process. But an intuition for bias does not translate into a process for establishing a ( ṗ, Ṙ). Consider the anchoring bias defined in  Ariely et al. [2004] , where irrelevant information -the last digits of social security numbers -changed how much people were willing to pay for goods. When defining a reasonable ( ṗ, Ṙ), it does not suffice to be aware of the existence of anchoring bias 11 , but one has to precisely quantify the extent of the bias -why does anchoring bias seem to be stronger for chocolate than for wine, for instance? And why these precise percentages and correlations, and not others? And can people's judgment tell which people are more or less susceptible to anchoring bias? And can one quantify the bias for a single individual, rather than over a sample? Any given ( ṗ, Ṙ) can quantify the form and extent of these biases by computing objects like the regret function Reg( ṗ, Ṙ)(s ) := Reg( ṗ( Ṙ), Ṙ)(s) = V * Ṙ (s) − V ṗ( Ṙ) Ṙ (s), which measures the divergence between the expected value of the actual and optimal human policies 12 . Thus any given ( ṗ, Ṙ) -which contains the information to compute quantities like Reg( ṗ, Ṙ)(s) or similar measures of bias 13 , in every state -carries a high amount of numerical information about bias, and hence a high complexity. Since humans do not easily have access to this information, this implies that human judgement of irrationality is subject to Moravec's paradox  [Moravec, 1988] . It is similar to, for example, social skills: though it seems intuitively simple to us, it is highly complex to define in algorithmic terms. Other authors have argued directly for the complexity of human values, from fields as diverse as computer science, philosophy, neuroscience, and economics  [Minsky, 1984 , Bostrom, 2014 , Glimcher et al., 2009 , Muehlhauser and Helm, 2012 , Yudkowsky, 2011 . \n The contingency of human judgement The previous section showed that reasonable ( ṗ, Ṙ) carry large amounts of information/complexity, but the key question is whether it requires information additional to that in π. This section will show that even when π is known, there are many contingent choices that need to be made to define any specific reasonable ( ṗ, Ṙ). Hence any given ( ṗ, Ṙ) contains a large amount of information beyond that in π, and hence is of higher complexity. Reasons to believe that human judgement about reasonable ( ṗ, Ṙ) contains many contingent choices: • There is a variability of human judgement between cultures. When Miller  [1984]  compared American and Indian assessments of the same behaviours, they found systematically different explanations for them  14  Basic intuitions about rationality also vary between cultures  [Nisbett et al., 2001 , Brück, 1999 ]. • There is a variability of human judgement within a single culture. When  Slovic and Tversky [1974]  analysed the \"Allais Paradox\", they found that different people gave different answers as to what the rational behaviour was in their experiments. • There is evidence of variability of human judgement within the same person.  Slovic and Tversky [1974]  further attempted to argue for the rationality of one of the answers. This sometimes resulted in the participant sometimes changing their minds, and contradicting their previous assessment of rationality. • There is a variability of human judgement for the same person assessing their own values, caused by differences as trivial as question ordering  [Schuman and Ludwig, 1983] . So human meta-judgement, of own values and rationality, is also contingent and variable. • People have partial bias blind spots around their own biases  [Scopelliti et al., 2015] . Thus if a human is following policy π, a decomposition ( ṗ, Ṙ) would provide additional information about the cultural background of the decomposer, their personality within their culture, and even about the past history of the decomposer and how the issue is being presented to them. Those last pieces prevents us from 'simply' using the human's own assessment of their own rationality, as that assessment is subject to change and re-interpretation depending on their possible histories. 12 To exactly quantify the anchoring bias above, we could use a regret function that contrasts π with the same policy, but where the decision is optimal for one turn only (rather than for all turns, as in standard regret).  13  In constrast, regret for the degenerate planner-reward pairs is trivial. Reg(p π , 0) and Reg(pg, R π ) are identically zero -in the second case, since pg(R π ) is actually optimal for R π , getting the maximal possible reward -while (−pg, −R π ) has a regret that is identically −1 at each step. 14 \"Results show that there were cross-cultural and developmental differences related to contrasting cultural conceptions of the person [...] rather than from cognitive, experiential, and informational differences [...].\" \n The search for human rationality models One final argument that there is no simple algorithm for going from π to ( ṗ, Ṙ): many have tried and failed to find such an algorithm. Since the subject of human rationality has been a major one for several thousands of years, the ongoing failure is indicative -though not a proof -of the difficulties involved. There have been many suggested philosophical avenues for finding such a reward (such as reflective equilibrium  [Rawls, 1971] ), but all have been underdefined and disputed. The economic concept of revealed preferences  [Samuelson, 1948]  is the most explicit, using the assumption of rational behaviour to derive human preferences. This is an often acceptable approximation, but can be taken too far: failure to take achieve an achievable goal does not imply that failure was desired. Even within the confines of economics, it has been criticised by behavioural economics approaches, such as prospect theory  [Kahneman and Tversky, 2013]  -and there are counter-criticisms to these. Using machine learning to deduce the intentions and preferences of humans is in its infancy, but we can see non-trivial real-world examples, even in settings as simple as car-driving  [Lazar et al., 2018] . Thus to date, neither humans nor machine learning have been able to find simple ways of going from π to ( ṗ, Ṙ), nor any simple and explicit theory for how such a decomposition could be achieved. This suggests that ( ṗ, Ṙ) is a complicated object, even if π is known. In conclusion: Conjecture 9 (Informal complexity proposition). If π is a human policy, and L is a 'reasonable' computer language with ( ṗ, Ṙ) a 'reasonable' compatible planner-reward pair, then the complexity of ( ṗ, Ṙ) is not close to minimal amongst the pairs compatible with π. \n Conclusion We have shown that some degenerate planner-reward decompositions of a human policy have nearminimal description length and argued that decompositions we would endorse do not. Hence, under the Kolmogorov-complexity simplicity prior, a formalization of Occam's Razor, the posterior would endorse degenerate solutions. Previous work has shown that noisy rationality is too strong an assumption as it does not account for bias; we tried the weaker assumption of simplicity, strong enough to avoid typical No Free Lunch results, but it is insufficient here. This is no reason for despair: there is a large space to explore between these two extremes. Our hope is that with some minimal assumptions about planner and reward we can infer the rest with enough data. Staying close to agnostic is desirable in some settings: for example, a misspecified model of the human reward function can lead to disastrous decisions with high confidence .  Anonymous [2019]  makes a promising first try -a high-dimensional parametric planner is initialized to noisy rationality and then adapts to fit the behavior of a systematically irrational agent. How can we reconcile our results with the fact that humans routinely make judgments about the preferences and irrationality of others? And, that these judgments are often correlated from human to human? After all, No Free Lunch applies to human as well as artificial agents. Our result shows that they must be using shared priors, beyond simplicity, that are not learned from observations. We call these normative assumptions because they encode beliefs about which reward functions are more likely and what constitutes approximately rational behavior. Uncovering minimal normative assumptions would be an ideal way to build on this paper; Appendix C shows one possible approach. \t\t\t Technically we only need to infer the human reward function, but inferring that from behaviour requires some knowledge of the planning algorithm. \n\t\t\t The setting is only chosen for notational convenience: it also emulates discrete POMDPs, non-Markovianness (eg by encoding the whole history in the state) and pseudo-random policies. \n\t\t\t This is the 'indifferent' planner pπ of subsubsection 5.1.1. \n\t\t\t Recall that pg is a planner, pg(R) is a policy, so pg(R) can be applied to states, and pg(R)(s) is an action. \n\t\t\t In most standard computer languages, argmax just requires a for-loop, a reference to R, a comparison with a previously stored value, and possibly the storage of a new value and the current action.10 F -complexity is non-negative: F4 • F4 is the identity, so that KL(F4(p, R)) − KL(p, R) = −(KL(F4(F4(p, R)) − KL(F4(p, R)), meaning that max (p,R),F 4 KL(F4(p, R)) − KF (p, R) must be nonnegative; this is a reason to include F4 in the definition of F . \n\t\t\t The fact that many cognitive biases have only been discovered recently argue against people having a good intuitive grasp of bias and rationality, as do people's persistent bias blind spots [Scopelliti et al., 2015] .", "date_published": "n/a", "url": "n/a", "filename": "NeurIPS-2018-occams-razor-is-insufficient-to-infer-the-preferences-of-irrational-agents-Paper.tei.xml", "abstract": "Inverse reinforcement learning (IRL) attempts to infer human rewards or preferences from observed behavior. Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human shortcomings. However, the general problem of inferring the reward function of an agent of unknown rationality has received little attention. Unlike the well-known ambiguity problems in IRL, this one is practically relevant but cannot be resolved by observing the agent's policy in enough environments. This paper shows (1) that a No Free Lunch result implies it is impossible to uniquely decompose a policy into a planning algorithm and reward function, and (2) that even with a reasonable simplicity prior/Occam's razor on the set of decompositions, we cannot distinguish between the true decomposition and others that lead to high regret. To address this, we need simple 'normative' assumptions, which cannot be deduced exclusively from observations.", "id": "d57b063d86ed686a48a493ed074bfd5e"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Maartje M A De Graaf", "Bertram F Malle", "Anca Dragan", "Tom Ziemke"], "title": "Explainable Robotic Systems", "text": "As artificial agents, and especially socially interactive robots, enter human society, the demands for these agents to be transparent and explainable grow rapidly. When systems are able, for example, to explain how they made classifications or arrived at a decision, users are better able to judge the systems' accuracy and have more calibrated trust in them (e.g.,  [8]    [10] ). More and more AI systems process vast amounts of information and make classifications or recommendations that humans use for financial, employment, medical, military, and political decisions. More precariously yet, autonomous social robots, by definition, make decisions reaching beyond direct commands and perform actions with social and moral significance for humans. The demand for these social robots to become transparent and explainable is particularly urgent. However, to make robots explainable, we need to understand how people interpret the behavior of such systems and what expectations they have of them. In this workshop, we will address the topics of transparency and explainability, for robots in particular, from both the cognitive science perspective and the computer science and robotics perspective. Cognitive science elucidates how people interpret robot behavior; computer science and robotics elucidate how the computational mechanisms underlying robot behavior can be structured and communicated so as to be human-interpretable. The implementation and use of explainable robotic systems may prevent the potentially frightening confusion over why a robot is behaving the way it is. Moreover, explainable robot systems may allow people to better calibrate their expectations of the robot's capabilities and be less prone to treating robots as almost-humans. \n BACKGROUND When people interact with a robotic system, they construct mental models to understand and predict its actions. However, people's mental models of robots stem from their interactions with living beings. Thus, people easily run the risk of establishing incorrect or inadequate models of robotic systems, which may result in self-deception or even harm  [12] . Moreover, a long-term study  [9]  showed that initially established (incorrect) mental models of an intelligent information system remained robust over time, even when details of the system's implementation were given and initial beliefs were challenged with contradictory evidence. Incorrect mental models of AIS can have significant consequences for trust in such systems and, as a result, for acceptance of and collaboration with these systems  [10] . Several studies indicate that people distrust a robotic system when they are unable to understand its actions. When a robot fails to communicate its intentions, people not only perceive the robot as creepy or unsettling  [11] , they also perceive such robots as erratic and untrustworthy even when they follow a clear decision-making process  [5] . Indeed, when a robot is not transparent about its intentions (i.e., not providing any explanations for its behavior), people may even question its correct task performance and blame the robotic agent for its alleged errors  [4] . In addition to such cases of distrust, incorrect mental models of AIS can also lead to the opposite situation. People sometimes over-trust artificial agents, such as when they comply with a faulty robot's unusual requests  [7]  or follow the lead of a potentially inept robot  [6] . Thus, there should be little doubt about the value of making robotic systems perform easily interpretable actions and explain their own decisions and behaviors. This goal for explainable robots demands innovative work in computer science, robotics, and cognitive science, and our proposed workshop provides strong representation from all these fields. Additionally, we invite research that examines if and how such structures lead to better acceptance of robotic systems, to more accurate mental models of such systems, and to calibrated trust in these systems. \n WORKSHOP ACTIVITIES The aim of this full-day workshop is to provide a forum to share and learn about recent research on requirements for artificial agents' explanations as well as the implementation of transparent, predictable and explainable robotic systems. Extended time for discussions will highlight and document promising approaches and encourage further work. We welcome prospective participants to submit extended abstracts (max. 2 pages) that contribute to the discussion of people's interpretation of robot actions as well as the implementation of transparent, predictable, and explainable behaviors in robotic systems. After the conference, and with permission of the authors, we will provide online access to the workshop proceedings on a dedicated workshop website: explainableroboticsystems.wordpress.com. We encourage researchers to attend the workshop even without a paper submission, as a major portion of the workshop involves community engagement and discussion to foster uptake of concepts regarding explainable robotic systems within the field of HRI. The morning session will cover invited talks from Rachid Alami, Joanna Bryson, Bradley Hayes, and Alessandra Sciutti, as well as short presentations by authors of accepted papers, followed by general discussion. The afternoon will be devoted to break-out sessions to discuss the next steps in research and development of explainable and transparent robotic systems. Groups will be composed of representatives of different disciplines in order to work on integrating the multiple necessary perspectives in this endeavor. To boost the discussions, we will ask presenters to prepare questions or raise pressing issues that provide starting points for the discussion groups.  is a postdoctoral research associate at the Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, USA. She has a Bachelor of Business Administration in Communication Management (2005), a Master of Science in Media Communication (2011), and a PhD in Communication Science and Human-Robot Interaction (2015). Her research research interest focuses on peopleâĂŹs social, emotional and cognitive responses to robots including the societal and ethical consequences of those responses. Bertram Malle is Professor of Psychology in the Department of Cognitive, Linguistic, and Psychological Sciences at Brown University and Co-Director of the Humanity-Centered Robotics Initiative at Brown. He was trained in psychology, philosophy, and linguistics at the University of Graz, Austria, and received his Ph.D. in Psychology from Stanford University in 1995. His research focuses on social cognition, moral psychology, and human-robot interaction. Anca Dragan is an Assistant Professor in Electrical Engineering and Computer Sciences at UC Berkeley. She received her PhD from the Robotics Institute at Carnegie Mellon University in 2015 and now runs a lab on algorithmic human-robot interaction. She has expertise in transparent and explainable robotics and AI, with applications in personal robots and autonomous cars. Tom Ziemke is Professor of Cognitive Science at the University of Skövde and Professor of Cognitive Systems at Linköping University, Sweden. He received his Ph.D. in Computer Science from Sheffield University, UK, in 2000. His main research interests are embodied cognition and social interaction, and in recent years in particular people's interaction with different types of autonomous systems, ranging from social robots to automated vehicles.", "date_published": "n/a", "url": "n/a", "filename": "3173386.3173568.tei.xml", "abstract": "The increasing complexity of robotic systems are pressing the need for them to be transparent and trustworthy. When people interact with a robotic system, they will inevitably construct mental models to understand and predict its actions. However, people's mental models of robotic systems stem from their interactions with living beings, which induces the risk of establishing incorrect or inadequate mental models of robotic systems and may lead people to either under-and over-trust these systems. We need to understand the inferences that people make about robots from their behavior, and leverage this understanding to formulate and implement behaviors into robotic systems that support the formation of correct mental models of and fosters trust calibration. This way, people will be better able to predict the intentions of these systems, and thus more accurately estimate their capabilities, better understand their actions, and potentially correct their errors. The aim of this full-day workshop is to provide a forum for researchers and practitioners to share and learn about recent research on people's inferences of robot actions, as well as the implementation of transparent, predictable, and explainable behaviors into robotic systems.", "id": "de5357506034b65d9e1b6559c34f2da7"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Nisan Stiennon", "Long Ouyang", "Jeff Wu", "Daniel M Ziegler", "Ryan Lowe", "Chelsea Voss", "Alec Radford", "Dario Amodei", "Paul Christiano", "Openai"], "title": "Learning to summarize from human feedback", "text": "Introduction Large-scale language model pretraining has become increasingly prevalent for achieving high performance on a variety of natural language processing (NLP) tasks. When applying these models to a specific task, they are usually fine-tuned using supervised learning, often to maximize the log probability of a set of human demonstrations. While this strategy has led to markedly improved performance, there is still a misalignment between this fine-tuning objective-maximizing the likelihood of human-written text-and what we care about-generating high-quality outputs as determined by humans. This misalignment has several causes: the maximum likelihood objective has no distinction between important errors (e.g. making up facts  [41] ) and unimportant errors (e.g. selecting the precise word from a set of synonyms); models \n Supervised learning \n Human feedback \n Pretrain only \n Reference summaries Figure  1 : Fraction of the time humans prefer our models' summaries over the human-generated reference summaries on the TL;DR dataset.  4  Since quality judgments involve an arbitrary decision about how to trade off summary length vs. coverage within the 24-48 token limit, we also provide length-controlled graphs in Appendix F; length differences explain about a third of the gap between feedback and supervised learning at 6.7B. are incentivized to place probability mass on all human demonstrations, including those that are low-quality; and distributional shift during sampling can degrade performance  [56, 52] . Quality can often be improved significantly by non-uniform sampling strategies such as beam search  [51] , but these can lead to repetition and other undesirable artifacts  [69, 23] . Optimizing for quality may be a principled approach to overcoming these problems. Our goal in this paper is to advance methods for training language models on objectives that more closely capture the behavior we care about. To make short-term progress towards this goal, we focus on abstractive English text summarization, as it has a long history in the NLP community  [16, 8, 54, 59, 50] , and is a subjective task where we believe it is difficult to quantify summary quality without human judgments. Indeed, existing automatic metrics for evaluating summary quality, such as ROUGE  [39] , have received criticism for poor correlation with human judgments  [55, 45, 6, 33] . We follow the works of  [3, 73] , who fine-tune language models from human feedback using reward learning  [35] . We first collect a dataset of human preferences between pairs of summaries, then train a reward model (RM) via supervised learning to predict the human-preferred summary. Finally, we train a policy via reinforcement learning (RL) to maximize the score given by the RM; the policy generates a token of text at each 'time step', and is updated using the PPO algorithm  [58]  based on the RM 'reward' given to the entire generated summary. We can then gather more human data using samples from the resulting policy, and repeat the process. We follow the works of  [48, 4]  and use large pretrained GPT-3 models with as many as 6.7 billion parameters. Our main contributions are four-fold. (1) We show that training with human feedback significantly outperforms very strong baselines on English summarization. When applying our methods on a version of the Reddit TL;DR dataset  [63] , we train policies via human feedback that produce better summaries than much larger policies trained via supervised learning. Summaries from our human feedback models are preferred by our labelers to the original human demonstrations in the dataset (see Figure  1 ). (2) We show human feedback models generalize much better to new domains than supervised models. Our Reddit-trained human feedback models also generate high-quality summaries of news articles on the CNN/DailyMail (CNN/DM) dataset without any news-specific fine-tuning, almost matching the quality of the dataset's reference summaries. We perform several checks to ensure that these human preferences reflect a real quality difference: we consistently monitor agreement rates amongst labelers and researchers, and find researcher-labeler agreement rates are nearly as high as researcher-researcher agreement rates (see Section C.2), and we verify models are not merely optimizing simple metrics like length or amount of copying (see Appendices F and G.7). (3) We conduct extensive empirical analyses of our policy and reward model. We examine the impact of model and data size (Figure  6 ), study performance as we continue to optimize a given reward model (Section 4.3), and analyze reward model performance using synthetic and humanwritten perturbations of summaries (Section 4.3). We confirm that our reward model outperforms other metrics such as ROUGE at predicting human preferences, and that optimizing our reward model directly results in better summaries than optimizing ROUGE according to humans (Section 4.4). (4) We publicly release our human feedback dataset for further research. The dataset contains 64,832 summary comparisons on the TL;DR dataset, as well as our evaluation data on both TL;DR (comparisons and Likert scores) and CNN/DM (Likert scores). The methods we present in this paper are motivated in part by longer-term concerns about the misalignment of AI systems with what humans want them to do. When misaligned summarization models make up facts, their mistakes are fairly low-risk and easy to spot. However, as AI systems become more powerful and are given increasingly important tasks, the mistakes they make will likely become more subtle and safety-critical, making this an important area for further research. \n Related work Most directly related to our work is previous work using human feedback to train summarization models with RL  [3, 73] . Bohm et al.  [3]  learn a reward function from a dataset of human ratings of 2.5k CNN/DM summaries, and train a policy whose summaries are preferred to a policy optimizing ROUGE. Our work is most similar to  [73] , who also train Transformer models  [62]  to optimize human feedback across a range of tasks, including summarization on the Reddit TL;DR and CNN/DM datasets. Unlike us, they train in an online manner and find the model highly extractive. They note that their labelers prefer extractive summaries and have low agreement rates with researchers. Compared to  [73] , we use significantly larger models, move to the batch setting for collecting human feedback, ensure high labeler-researcher agreement, and make some algorithmic modifications, such as separating the policy and value networks. Human feedback has also been used as a reward to train models in other domains such as dialogue  [25, 68, 21] , translation  [32, 1] , semantic parsing  [34] , story generation  [72] , review generation  [7] , and evidence extraction  [46] . Our reward modeling approach was developed in prior work on learning to rank  [40] , which has been applied to ranking search results using either explicit feedback  [2, 18]  or implicit feedback in the form of click-through data  [29, 30] . In a related line of research, human feedback has been used to train agents in simulated environments  [10, 24] . There is also a rich literature on using RL to optimize automatic metrics for NLP tasks, such as ROUGE for summarization  [50, 65, 45, 15, 19] , BLEU for translation  [50, 66, 1, 43] , and other domains  [61, 27, 26] . Finally, there has been extensive research on modifying architectures  [22, 59]  and pre-training procedures  [70, 36, 49, 60, 53, 14]  for improving summarization performance. 3 Method and experiment details \n High-level methodology Our approach is similar to the one outlined in  [73] , adapted to the batch setting. We start with an initial policy that is fine-tuned via supervised learning on the desired dataset (in our case, the Reddit TL;DR summarization dataset). The process (illustrated in Figure  2 ) then consists of three steps that can be repeated iteratively. Step 1: Collect samples from existing policies and send comparisons to humans. For each Reddit post, we sample summaries from several sources including the current policy, initial policy, original reference summaries and various baselines. We send a batch of pairs of summaries to our human evaluators, who are tasked with selecting the best summary of a given Reddit post. Step 2: Learn a reward model from human comparisons. Given a post and a candidate summary, we train a reward model to predict the log odds that this summary is the better one, as judged by our labelers. Step 3: Optimize a policy against the reward model. We treat the logit output of the reward model as a reward that we optimize using reinforcement learning, specifically with the PPO algorithm  [58] . \n Collect human feedback \"j is better than k\" \"j is better than k\" A Reddit post is sampled from the Reddit TL;DR dataset. Various policies are used to sample a set of summaries. Two summaries are selected for evaluation. A human judges which is a better summary of the post. \n Train reward model One post with two summaries judged by a human are fed to the reward model. The reward model calculates a reward r for each summary. The loss is calculated based on the rewards and human label, and is used to update the reward model. \n Train policy with PPO A new post is sampled from the dataset. The reward model calculates a reward for the summary. The reward is used to update the policy via PPO. We provide a more thorough description of our procedure, including details of the reward model and policy training and our quality control process, in the following sections. In practice, rather than precisely iterating this sequence of three steps, we updated our data collection and training procedures over the course of the project while accumulating labels (see Appendix C.6 for details). \n Datasets and task Datasets. We use the TL;DR summarization dataset  [63] , which contains ~3 million posts from reddit.com across a variety of topics (subreddits), as well summaries of the posts written by the original poster (TL;DRs). We additionally filter this dataset (see Appendix A) to ensure quality, including using a whitelist of subreddits that are understandable to the general population. Crucially, we also filter to include only posts where the human-written summaries contain between 24 and 48 tokens, to minimize the potential effect of summary length on quality (see Section 4.1 and Appendix F). Our final filtered dataset contains 123,169 posts, and we hold out ~5% as a validation set. For the remainder of this paper, we refer to this dataset simply as TL;DR. We chose the TL;DR dataset over the more commonly used CNN/DM dataset primarily because very strong performance can be attained on CNN/DM with simple extractive baselines. We find in Section 4.2 that our labelers prefer lead-3 over the CNN/DM reference summaries,  5  and that the supervised T5 model  [49]  with low-temperature sampling already surpasses the reference summary quality, while copying extensively from the article. On the other hand, simple extractive baselines perform poorly on TL;DR in our human evaluations (see Appendix G.2). Instead of training on CNN/DM, we study the transfer performance of our human feedback models to CNN/DM after being trained to summarize Reddit posts. Task. We define our ground-truth task as producing a model that generates summaries fewer than 48 tokens long that are as good as possible, according to our judgments. We judge summary quality by how faithfully the summary conveys the original post to a reader who can only read the summary and not the post (see Appendix C.5 for further discussion of criteria). Since we have limited capacity to do comparisons, we hire labelers to do the comparisons for us. We rely on detailed procedures to ensure high agreement between labelers and us on the task, which we describe in the next section. [r/dating_advice] First date ever, going to the beach. Would like some tips Hey Reddit! I (20M) would like some tips, because I have my first ever date tomorrow (although I've had a gf for 3 years, but no actual dating happened), and we're going to the beach. I met this girl, we have mutual friends, at a festival a few days ago. We didn't kiss, but we talked, held hands, danced a bit. I asked her to go on a date with me, which was super hard as it is the first time I've asked this to anybody. What I mean to say is, it's not like a standard *first* date because we already spent some time together. I'm really nervous and excited. I'm going to pick her up tomorrow, we're cycling to the beach which will take  30     1 : Example of post and samples on the TL;DR dataset, chosen to be particularly short. For random samples (along with posts), see Appendix H and our website. \n Collecting human feedback Previous work on fine-tuning language models from human feedback  [73]  reported \"a mismatch between the notion of quality we wanted our model to learn, and what the humans labelers actually evaluated\", leading to model-generated summaries that were high-quality according to the labelers, but fairly low-quality according to the researchers. Compared to  [73] , we implement two changes to improve human data quality. First, we transition entirely to the offline setting, where we alternate between sending large batches of comparison data  6  to our human labelers and re-training our models on the cumulative collected data. Second, we maintain a hands-on relationship with labelers:  7  we on-board them with detailed instructions, answer their questions in a shared chat room, and provide regular feedback on their performance. We train all labelers to ensure high agreement with our judgments, and continuously monitor labeler-researcher agreement over the course of the project. See Appendix C.1 and C.5 for details. As a result of our procedure, we obtained high labeler-researcher agreement: on a subset of comparison tasks, labelers agree with researchers 77% ± 2% of the time, while researchers agree with each other 73% ± 4% of the time. We provide more analysis of our human data quality in Appendix C.2. \n Models All of our models are Transformer decoders  [62]  in the style of GPT-3  [47, 4] . We conduct our human feedback experiments on models with 1.3 billion (1.3B) and 6.7 billion (6.7B) parameters. Pretrained models. Similarly to  [12, 47] , we start with models pretrained to autoregressively predict the next token in a large text corpus. As in  [48, 4] , we use these models as 'zero-shot' baselines by padding the context with examples of high-quality summaries from the dataset. We provide details on pretraining in Appendix B, and on our zero-shot procedure in Appendix B.2. Supervised baselines. We next fine-tune these models via supervised learning to predict summaries from our filtered TL;DR dataset (see Appendix B for details). We use these supervised models to sample initial summaries for collecting comparisons, to initialize our policy and reward models, and as baselines for evaluation. In our final human evaluations, we use T=0 to sample from all models, as we found it performed better than higher temperatures or nucleus sampling (see Appendix B.1). To validate that our supervised models are indeed strong baselines for comparison, we run our supervised fine-tuning procedure with our 6.7B model on the CNN/DM dataset, and find that we achieve slightly better ROUGE scores than SOTA models  [71]  from mid-2019 (see Appendix G.4). Reward models. To train our reward models, we start from a supervised baseline, as described above, then add a randomly initialized linear head that outputs a scalar value. We train this model to predict which summary y ∈ {y 0 , y 1 } is better as judged by a human, given a post x. If the summary preferred by the human is y i , we can write the RM loss as: loss(r θ ) = E (x,y0,y1,i)∼D [log(σ(r θ (x, y i ) − r θ (x, y 1−i )))] where r θ (x, y) is the scalar output of the reward model for post x and summary y with parameters θ, and D is the dataset of human judgments. At the end of training, we normalize the reward model outputs such that the reference summaries from our dataset achieve a mean score of 0. Human feedback policies. We want to use the reward model trained above to train a policy that generates higher-quality outputs as judged by humans. We primarily do this using reinforcement learning, by treating the output of the reward model as a reward for the entire summary that we maximize with the PPO algorithm  [58] , where each time step is a BPE token.  8  We initialize our policy to be the model fine-tuned on Reddit TL;DR. Importantly, we include a term in the reward that penalizes the KL divergence between the learned RL policy π RL φ with parameters φ and this original supervised model π SFT , as previously done in  [25] . The full reward R can be written as: R(x, y) = r θ (x, y) − β log[π RL φ (y|x)/π SFT (y|x)] This KL term serves two purposes. First, it acts as an entropy bonus, encouraging the policy to explore and deterring it from collapsing to a single mode. Second, it ensures the policy doesn't learn to produce outputs that are too different from those that the reward model has seen during training. For the PPO value function, we use a Transformer with completely separate parameters from the policy. This prevents updates to the value function from partially destroying the pretrained policy early in training (see ablation in Appendix G.1). We initialize the value function to the parameters of the reward model. In our experiments, the reward model, policy, and value function are the same size. \n Results \n Summarizing Reddit posts from human feedback Policies trained with human feedback are preferred to much larger supervised policies. Our main results evaluating our human feedback policies on TL;DR are shown in Figure  1 . We measure policy quality as the percentage of summaries generated by that policy that humans prefer over the reference summaries in the dataset. Our policies trained with human feedback significantly outperform our supervised baselines on this metric, with our 1.3B human feedback model significantly outperforming a supervised model 10× its size (61% versus 43% raw preference score against reference summaries). Our 6.7B model in turn significantly outperforms our 1.3B model, suggesting that training with human feedback also benefits from scale. Additionally, both of our human feedback models are judged by humans to be superior to the human demonstrations used in the dataset. Controlling for summary length. When judging summary quality, summary length is a confounding factor. The target length of a summary is implicitly part of the summarization task; depending on the desired trade-off between conciseness and coverage, a shorter or longer summary might be better. Since our models learned to generate longer summaries, length could account for much of our quality improvements. We find that after controlling for length (Appendix F), the preference of our human feedback models vs. reference summaries drops by ~5%; even so, our 6.7B model summaries are still preferred to the reference summaries ~65% of the time. How do our policies improve over the baselines? To better understand the quality of our models' summaries compared to the reference summaries and those of our supervised baselines, we conduct an additional analysis where human labelers assess summary quality across four dimensions (or \"axes\") using a 7-point Likert scale  [38] . Labelers rated summaries for coverage (how much important information from the original post is covered), accuracy (to what degree the statements in the summary are stated in the post), coherence (how easy the summary is to read on its own), and overall quality.  The results (Figure  3 ) indicate that our human feedback models outperform the supervised baselines across every dimension of quality, but particularly coverage. Although our human labelers had a high bar for giving perfect overall scores, summaries from our 6.7B PPO model achieve a 7/7 overall score 45% of the time (compared to 20% and 23% for the 6.7B supervised baseline and reference summaries, respectively). \n Transfer to summarizing news articles Our human feedback models can also generate excellent summaries of CNN/DM news articles without any further training (Figure  4 ). Our human feedback models significantly outperform models trained via supervised learning on TL;DR and models trained only on pretraining corpora. In fact, our 6.7B human feedback model performs almost as well as a 6.7B model that was fine-tuned on the CNN/DM reference summaries, despite generating much shorter summaries. Since our human feedback models transferred to CNN/DM have little overlap in summary length distribution with models trained on CNN/DM, with about half as many tokens on average, they are difficult to compare directly. Thus our evaluations in Figure  4  use a 7-point Likert scale on four quality dimensions, as in Section 4.1 (see Appendix C.5 for labeler instructions). In Figure  4b  we show the average overall score at different summary lengths, which suggests our human feedback models would perform even better if they generated longer summaries. Qualitatively, CNN/DM summaries from our human feedback models are consistently fluent and reasonable representations of the article; we show examples on our website and in Appendix H. \n Understanding the reward model What happens as we optimize the reward model? Optimizing against our reward model is supposed to make our policy align with human preferences. But the reward model isn't a perfect representation of our labeler preferences, as it has limited capacity and only sees a small amount of comparison data from a relatively narrow distribution of summaries. While we can hope our reward model generalizes to summaries unseen during training, it's unclear how much one can optimize against the reward model until it starts giving useless evaluations. To answer this question, we created a range of policies optimized against an earlier version of our reward model, with varying degrees of optimization strength, and asked labelers to compare samples from them to the reference summaries. Figure  5  shows the results for PPO at a range of KL penalty coefficients (β). Under light optimization, the models improve (according to labelers). However, as we optimize further, true preferences fall off compared to the prediction, and eventually the reward model becomes anti-correlated with human preferences. Though this is clearly undesirable, we note that this over-optimization also happens with ROUGE (see  [45]  and Appendix G.3). Similar behavior has been observed in learned reward functions in the robotics domain  [5] . How does reward modeling scale with increasing model and data size? We conduct an ablation to determine how data quantity and model size affect reward modeling performance. We train 7 reward models ranging from 160M to 13B parameters, on 8k to 64k human comparisons from our dataset. We find that doubling the training data amount leads to a ~1.1% increase in the reward model validation set accuracy, whereas doubling the model size leads to a ~1.8% increase (Figure  6 ). What has the reward model learned? We probe our reward model by evaluating it on several validation sets. We show the full results in Appendix G.6, and highlight them here. We find that our reward models generalize to evaluating CNN/DM summaries (Appendix G.7), agreeing with labeler preferences 62.4% and 66.5% of the time (for our 1.3B and 6.7B models, respectively). Our 6.7B reward model nearly matches the inter-labeler agreement value of 66.9%. We also find that our reward models are sensitive to small but semantically important details in the summary. We construct an additional validation set by having labelers make minimal edits to summaries to improve them. Our RMs prefer the edited summaries almost as often (79.4% for 1.3B and 82.8% for 6.7B) as a separate set of human evaluators (84.1%). Further, when comparing the reference summaries to perturbed summaries where the participants' roles are reversed, our models reliably select the original summary (92.9% of the time for 1.3B, 97.2% for 6.7B). However, our RMs are biased towards longer summaries: our 6.7B RM prefers improving edits that make the summary shorter only 62.6% of the time (vs. 76.4% for humans). \n Analyzing automatic metrics for summarization Evaluation. We study how well various automatic metrics act as predictors for human preferences, and compare them to our RMs. Specifically, we examine ROUGE, summary length, amount of copying from the post,  9  and log probability under our baseline supervised models. We present a full matrix of agreement rates between these metrics in Appendix G.7. We find that our learned reward models consistently outperform other metrics, even on the CNN/DM dataset on which it was never trained. We also find that ROUGE fails to track sample quality as our Figure  7 : Summary quality as a function of metric optimized and amount of optimization, using best-of-N rejection sampling. We evaluate ROUGE, our main reward models, and an earlier iteration of the 1.3B model trained on approximately 75% as much data (see Table  11  for details). ROUGE appears to peak both sooner and at a substantially lower preference rate than all reward models. Details in Appendix G.3. models improve. While ROUGE has ~57% agreement with labelers when comparing samples from our supervised baseline models, this drops to ~50% for samples from our human feedback model. Similarly, log probability agreement with humans drops to ≤50% on comparisons between samples from our human feedback models, while our RMs still perform above chance (62%). Scaling up the size of the supervised model does not reliably improve log probability's agreement with labelers. Optimization. In Figure  7 , we show that optimizing ROUGE using a simple optimization scheme doesn't consistently increase quality, as has been noted in  [45] . Optimization against ROUGE peaks both sooner and at a substantially lower quality rate than optimization against our reward models. \n Discussion Limitations. One limitation of our work is the time and cost required to produce our final models. Notably, fine-tuning our 6.7B model with RL required approximately 320 GPU-days. Our data collection procedure is also expensive compared to prior work -the training set took thousands of labeler hours and required significant researcher time to ensure quality. For this reason, we were unable to collect baselines such as an equivalent amount of high-quality human demonstrations for supervised baselines. See D for more discussion. We leave this ablation to future work. Nevertheless, we believe reward modeling is more likely to scale to tasks where it is extremely skill-intensive or time-consuming to provide good demonstrations. Future directions. The methods in this paper could be applied to any task where humans can compare samples, including dialogue, machine translation, question answering, speech synthesis, and music generation. We expect this method to be particularly important for generating long samples, where the distributional shift and degeneracy of maximum likelihood samples can be problematic. It may be possible to improve sample efficiency by training to predict feedback across many tasks  [42] . We are particularly interested in scaling human feedback to tasks where humans can't easily evaluate the quality of model outputs. In this setting, it is particularly challenging to identify whether an ML system is aligned with the human designer's intentions. One approach is to train ML systems to help humans perform the evaluation task quickly and accurately  [9] . There is also a rich landscape of human feedback methods beyond binary comparisons that could be explored for training models  [28, 17, 44, 64] . For example, we could solicit high-quality demonstrations from labelers, have labelers edit model outputs to make them better, or have labelers provide explanations for why they preferred one model output over another. All of this feedback could be leveraged as a signal to train more capable reward models and policies. Broader impacts. The techniques we explore in this paper are generic techniques that could be used in a wide variety of machine learning applications, for any task where it is feasible for humans to evaluate the quality of model outputs. Thus, the potential implications are quite broad. Our research is primarily motivated by the potential positive effects of aligning machine learning algorithms with the designer's preferences. Many machine learning applications optimize simple metrics which are only rough proxies for what the designer intends. This can lead to problems, such as Youtube recommendations promoting click-bait  [11] . In the short term, improving techniques for learning from and optimizing human preferences directly may enable these applications to be more aligned with human well-being. In the long term, as machine learning systems become more capable it will likely become increasingly difficult to ensure that they are behaving safely: the mistakes they make might be more difficult to spot, and the consequences will be more severe. For instance, writing an inaccurate summary of a news article is both easy to notice (one simply has to read the original article) and has fairly low consequences. On the other hand, imitating human driving may be substantially less safe than driving to optimize human preferences. We believe that the techniques we explore in this paper are promising steps towards mitigating the risks from such capable systems, and better aligning them with what humans care about. Unfortunately, our techniques also enable malicious actors to more easily train models that cause societal harm. For instance, one could use human feedback to fine-tune a language model to be more persuasive and manipulate humans' beliefs, or to induce dependence of humans on the technology, or to generate large amounts of toxic or hurtful content intended to harm specific individuals. Avoiding these outcomes is a significant challenge for which there are few obvious solutions. Large-scale models trained with human feedback could have significant impacts on many groups. Thus, it is important to be careful about how we define the 'good' model behavior that human labelers will reinforce. Deciding what makes a good summary is fairly straightforward, but doing this for tasks with more complex objectives, where different humans might disagree on the correct model behavior, will require significant care. In these cases, it is likely not appropriate to use researcher labels as the 'gold standard'; rather, individuals from groups impacted by the technology should be included in the process to define 'good' behavior, and hired as labelers to reinforce this behavior in the model. We chose to train on the Reddit TL;DR dataset because the summarization task is significantly more challenging than on CNN/DM. However, since the dataset consists of user-submitted posts with minimal moderation, they often contain content that is offensive or reflects harmful social biases. This means our models can generate biased or offensive summaries, as they have been trained to summarize such content. For this reason, we recommend that the potential harms of our models be thoroughly studied before deploying them in user-facing applications. Finally, by improving the ability of machine learning algorithms to perform tasks that were previously only achievable by humans, we are increasing the likelihood of many jobs being automated, potentially leading to significant job loss. Without suitable policies targeted at mitigating the effects of large-scale unemployment, this could also lead to significant societal harm.  Figure 2 : 2 Figure 2: Diagram of our human feedback, reward model training, and policy training procedure. \n Figure 4 : 4 Figure 4: Transfer results on CNN/DM. (a) Overall summary quality on CNN/DM as a function of model size. Full results across axes shown in Appendix G.2. (b) Overall scores vs. length for the 6.7B TL;DR supervised baseline, the 6.7B TL;DR human feedback model, and T5 fine-tuned on CNN/DM summaries. At similar summary lengths, our 6.7B TL;DR human feedback model nearly matches T5 despite never being trained to summarize news articles. \n Figure 3 : 3 Figure 3: Evaluations of four axes of summary quality on the TL;DR dataset. \n Table minutes, and then what? I'm a bit scared. Should I bring something (the weather, although no rain and sunny, is not super so no swimming), should we do something. I'd like all the tips I can get. Thanks! Human written reference TL;DR 6.7B supervised model 6.7B human feedback model First date after 3 years in a relation- Going on a date with a girl I met Going on my first ever date tomor- ship, going to the beach, terrified. a few days ago, going to the beach. row, cycling to the beach. Would What to bring with me, what to do? What should I bring, what should like some tips on what to do and we do? bring. I'm a bit nervous and excited. Thanks! \n Uifalean, Morris Stuttard, Russell Bernandez, Tasmai Dave, Rachel Wallace, Jenny Fletcher, Jian Ouyang, Justin Dill, Maria Orzek, Megan Niffenegger, William Sells, Emily Mariner, Andrew Seely, Lychelle Ignacio, Jelena Ostojic, Nhan Tran, Purev Batdelgar, Valentina Kezic, Michelle Wilkerson, Kelly Guerrero, Heather Scott, Sarah Mulligan, Gabriel Ricafrente, Kara Bell, Gabriel Perez, and Alfred Lee. \n\t\t\t Throughout the paper, error bars represent 1 standard error. \n\t\t\t We manually check this result in Appendix E and find we generally agree with labeler ratings. \n\t\t\t Our decision to collect comparisons rather than Likert scores is supported by recent work, e.g. [37] . 7  We recruited labelers from a freelancing platform, Upwork, and two labeling services, Scale and Lionbridge. \n\t\t\t Note that the reward model only gives rewards for entire summaries, and not at intermediate time steps. In RL terminology, each episode terminates when the policy outputs the EOS token, and the discount factor γ = 1. \n\t\t\t We measure copying by computing the longest common subsequence of bigrams with the original Reddit post or news article, and dividing by the number of bigrams in the summary.", "date_published": "n/a", "url": "n/a", "filename": "NeurIPS-2020-learning-to-summarize-with-human-feedback-Paper.tei.xml", "abstract": "As language models become more powerful, training and evaluation are increasingly bottlenecked by the data and metrics used for a particular task. For example, summarization models are often trained to predict human reference summaries and evaluated using ROUGE, but both of these metrics are rough proxies for what we really care about-summary quality. In this work, we show that it is possible to significantly improve summary quality by training a model to optimize for human preferences. We collect a large, high-quality dataset of human comparisons between summaries, train a model to predict the human-preferred summary, and use that model as a reward function to fine-tune a summarization policy using reinforcement learning. We apply our method to a version of the TL;DR dataset of Reddit posts  [63]  and find that our models significantly outperform both human reference summaries and much larger models fine-tuned with supervised learning alone. Our models also transfer to CNN/DM news articles  [22] , producing summaries nearly as good as the human reference without any news-specific fine-tuning.  2  We conduct extensive analyses to understand our human feedback dataset and fine-tuned models.  3  We establish that our reward model generalizes to new datasets, and that optimizing our reward model results in better summaries than optimizing ROUGE according to humans. We hope the evidence from our paper motivates machine learning researchers to pay closer attention to how their training loss affects the model behavior they actually want. * This was a joint project of the OpenAI Reflection team. Author order was randomized amongst {LO, JW, DZ, NS}; CV and RL were full-time contributors for most of the duration. PC is the team lead. 2 Samples from all of our models can be viewed on our website.  3  We provide inference code for our 1.3B models and baselines, as well as a model card and our human feedback dataset with over 64k summary comparisons, here.", "id": "39ee1c06141d38ff613e44b882c21b60"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Dylan Hadfield-Menell", "Stuart Russell"], "title": "Multitasking: Efficient Optimal Planning for Bandit Superprocesses", "text": "INTRODUCTION Multitasking is no doubt an activity familiar to the reader: one faces several decision problems but can act on only one (or perhaps a bounded number) at a time. Such prob-lems are ubiquitous for individuals, corporations, armies, and governments. Multitasking problems are expressed by the class of bandit superprocesses  [Nash, 1973]  or BSPs. A k-armed BSP M consists of k independent Markov decision processes M 1 , . . . , M k ; the MDPs are coupled by a common discount factor and by the constraint that at each time step the agent can act in only one MDP. Since the MDPs are independent of each other, one might imagine that the optimal policy for M is obtained by solving each MDP-turning the BSP into a multi-armed bandit-and then using Gittins indices to choose a sequence of arms. In fact, the optimal policy for a BSP may include actions that are suboptimal from the point of view of the constituent MDP in which they are taken. The reason for this is that the availability of other MDPs in which to act changes the balance between short-term and long-term rewards in a component MDP; in fact, it tends to lead to greedier behavior in each MDP because aiming for longterm reward in one MDP would delay rewards in all the other MDPs. The globally and locally optimal policies necessarily coincide only when the discount factor is 1. Hence, in addition to their general importance in the real world, a second reason to study multitasking problems is that they undermine an assumption implicit in practical applications of sequential decision analysis: the assumption that an optimal solution for the user's decision problem is optimal for a user who faces multiple decision problems. Despite these considerations, there has been remarkably little research on bandit superprocesses and almost none in AI. Section 2 summarizes what is known. Obviously, there are connections to multi-armed bandits (MABs), which are a special case of BSPs in which each arm only allows one choice of action rather than several. Unfortunately, the index theorems that simplify the computation of optimal MAB policies are not valid for BSPs. There are also strong connections-hitherto unexplored-between BSPs and sums of games as studied in combinatorial game theory  [Conway, 2000] . The principal question we address in this paper is whether an algorithm exists that is substantially more efficient than applying a standard MDP solver to the \"cross-product\" MDP obtained by combining the states spaces of the constituent MDPs. The sole known case where planning for a BSP is provably more efficient is the case where a dominating policy exists: if a single policy is optimal across the family of retirement processes associated with each arm then a BSP can be reduced to an equivalent MAB  [Whittle, 1980] . (Retirement processes provide a measure of how the optimal policy depends on context and are defined in Section 3.) However, this condition is seldom satisfied in practice. This paper provides three contributions. First, we give a concise survey of the bandit superprocess literature tailored to the AI community. Second, we provide a novel upper bound on the global value function of a BSP. For a BSP, M , with arms {M 1 , . . . , M k } we relax each arm to obtain an MAB M = {M 1 , . . . , M k } by adding actions to ensure that dominating policies exists. We show that this upper bound is equivalent to the Whittle integral, an existing upper bound for BSPs  [Brown and Smith, 2013] . Because our bound is defined in terms of an explicit relaxation, it provides insight into the nature of the bound and opens an avenue to extend this work to more general MDPs. Finally, we describe a practical computational approach for solving BSPs: we derive a simple method for computing the Whittle integral upper bound that can use an arbitrary MDP solver as a black box; then we combine this upper bound with a lower bound to derive an efficient algorithm for -optimal decision making in a BSP. We present empirical results to show that it substantially improves over more general optimal factored MDP algorithms; we use it to compute provably optimal actions for problems with upwards of 10 30 states in the full state space. \n RELATED WORK Robbins  [1952]  provided the first formulation of multiarmed bandits (MABs) in their modern form. The famous Gittins index theorem  [Gittins, 1979]  showed that optimal MAB policies are obtained by ranking the arms according to an index function defined on each seperately. An immediate corollary is that optimal decision making in an MAB is linear in the number of arms. Problems with this property are said to be indexable. Bandit superprocesses (BSPs) were introduced by  Nash [1973]  as a generalization of multi-armed bandits to study allocation of resources among research projects.  Whittle [1980]  provided an alternate proof of the Gittins index theorem that extends to bandit superprocesses with dominating policies. His proof utilized a construction called the Whittle integral, which allows one to compute the value of a composite state in an MAB.  Glazebrook [1982]  provides a proof that bandit superprocesses are not indexable in general.  Glazebrook [1993]  considers bandit superprocesses where the arms can exert limited influence on each other and shows a result analogous to  Whittle's. Brown and Smith [2013]  were the first to identify the signifigance of the Whittle integral for sequential decision making. They developed a version of policy iteration to compute it, and recognized that it upper bounds the value function of a BSP, 1 but did not derive an algorithm for solving BSPs. Our work provides two further contributions regarding the Whittle integral: a short proof that it is an upper bound and a simpler algorithm to compute it. Within the AI community, there has been limited study of loosely coupled Markov decision processes.  Singh and Cohn [1998]  consider optimal solutions to simultaneous MDPs, where an agent can take actions in a number of MDPs. Their formulation is more general than ours, as it is possible to act in multiple MDPs at once. They derive bounds for this problem and give an algorithm that combines a form of real-time dynamic programming with pruning steps to remove provably suboptimal actions. However, their bounds are substantially looser than ours, and our experiments show that the corresponding algorithm can be impractical for simple BSPs with many arms.  Meuleau et al. [1998]  examine MDPs that are coupled by constraints on the use of shared resources. BSPs fit within this class if we view the restriction to a single MDP at a time as a constraint on the agent's attention. Interestingly, their heuristics are also defined in terms of a parameterized value function for the component MDPs-it would be interesting to attempt to generalize the approaches considered here to their problem domain. In this work, we leverage the particular structure of our resource to compute optimal solutions; Meuleau et al. construct a heuristic policy. \n TECHNICAL BACKGROUND MARKOV DECISION PROCESSES Definition 1. (Markov Decision Process  [Puterman, 2009] ) A (finite-state, discounted) MDP, M , is a tuple M = S, A, T, R, γ . S is a set of states. A is a set of actions. T : S × A × S → [0, 1] is a function that assigns probability to state transitions for each state-action pair. R is a (bounded) reward function that maps state-action pairs to (positive) rewards R : S × A → R + . γ ∈ [0, 1) is a discount factor. A solution to M is a policy, π, that maps states to actions. The value of a state, s, under π is the sum of expected discounted rewards received by starting in s and selecting ac-tions according to π: V π (s) = E ∞ t=0 γ t R(s t )|s 0 = s, π . The optimal policy, π * , maximizes this value. In the above definition, and the ones that follow, we use superscripts to indicate dependence on the agent's policy. To simplify notation, we will omit these superscripts when the policy referred to is the optimal policy (e.g., V (s) = V π * (s)). The Q-function for the state-action pair, (s, a), is the value of taking a in s and selecting future actions according to π * . \n RETIREMENT PROCESSES Given an MDP, Whittle defines a family of optimal stopping problems: Definition 2. (Retirement Process  [Whittle, 1980] ) Let M be an MDP. For ρ ≥ 0, the retirement process for M with retirement reward, ρ, is an MDP, M ρ , with a single additional state, s R , and action, a R . a R transitions deterministically to s R and receives reward ρ. s R is a sink state that accrues zero reward. We refer to a decision to select a R as a decision to retire. We denote the retirement process value function as a function of a state and retirement reward, V (s, ρ). We let the optimal policy for retirement reward ρ be π * ρ . We write the set of states where the policy, π, retires as τ π ρ . We use ρ − (π) and ρ + (π) to denote the interval of retirement rewards so that π is optimal: ρ ∈ [ρ + (π), ρ + (π)] ⇒ V π (s, ρ) = V (s, ρ). We adopt the convention from the MAB/BSP literature and abuse notation to denote the (random) number of steps prior to retirement as τ π ρ (s). For s ∈ τ π ρ we let P retire (s |s, ρ, π) be the probability that s is the first state in τ π ρ the agent will reach given that it is in state s and executes policy π. We denote the expected discounted reward accrued prior to retirement, starting in s, as R π ρ (s). In regions of retirement reward where the optimal policy and stopping rule do not change, ∂V ∂ρ (s, ρ) is defined and is equal to the expected value of the discount parameter at retirement. This allows us to write the following expression for the retirement process value function: V (s, ρ) = R ρ (s) + E[γ τρ(s) ]ρ. (1) V (s, ρ) is piecewise linear in ρ. Figure 1 shows V (s, ρ) for the example BSP in Ex. 1. A policy that is optimal for every setting of ρ is called a dominating policy. Definition 3. (Dominating Policy) Let π be a policy for an MDP, M . π is a dominating policy iff ∀ρ ≥ 0 ∀s / ∈ τ ρ π(s) = π * ρ (s). \n MULTI-ARMED BANDITS AND BANDIT SUPERPROCESSES Multi-armed bandits (MAB) are a restricted class of MDPs that have received extensive study. Of particular interest are the form of the optimal policy and its utility in modelling \"exploration vs exploitation\" trade-offs. An MAB consists of a set of Markov reward processes (MRPs), where an MRP is an MDP with a single action. Each MRP is referred to as an arm of the problem. At each time-step, the agent selects an arm, that arm transitions according to its transition distribution, and the agent receives the corresponding reward. We adopt a summation notation to indicate the combination of several MRPs into an MAB. For example, if X and Y are MRPs and Z is the MAB with arms X and Y , we will write Z = X + Y . A famous result is that the optimal policy for any MAB is an index policy  [Gittins, 1979] . Each state, s i , in the individual arms is assigned an index, I si . In joint state s = {s 1 , . . . , s k }, the optimal action is to select argmax i I si . For MAB arm M i in state s i , the index is defined as the value of retirement reward such that the agent is indifferent between immediate retirement and following the optimal stopping policy  [Whittle, 1980] : I si = min ρ {ρ ; V i (s i , ρ) = ρ}. This means that, in a sense, context for a multi-armed bandit can always be summarized by a single number. To model a multi-tasking problem, we consider a generalization of multi-armed bandits: bandit superprocesses (BSPs). Bandit superprocesses allow arms that are arbitrary MDPs (and so are a generalization of MABs); at each time step, the agent selects both an arm and an action to take within that arm. Definition 4. (Bandit Superprocess  [Nash, 1973] ) Given k MDPs, {M i = S i , A i , T i , R i , γ }, we define M = i M i = S, A, T, R, γ to be the bandit superprocess with arms {M i }. S = × i S i and A = ∪ i A i . The transition distribution is stationary for arms that are not selected and follows the identical reward and transition distributions for the selected arm. Naturally, this makes planning more difficult. To see how, consider the following proposal: Conjecture 1. Let X = S X , A X , T X , R X , γ be an MDP. Define Y similarly and let Z = X + Y be the bandit superprocess that is their sum. Let a ∈ A X , s X ∈ S X be a state-action pair from X. Suppose that this transition is suboptimal in every retirement process: ∀ ρ ≥ 0, V X (s X , ρ) > Q X ((s X , a), ρ). Then a is suboptimal for any state in Z with s X as one of the components: ∀s Y ∈ S Y , V Z ({s X , s Y }) > Q Z ({s X , s Y }, a). This conjecture essentially proposes that state-action pairs can be safely ignored if they are suboptimal for all settings of a constant alternative. Unfortunately, as the following example illustrates, this is not the case. Example 1. Define X to be a deterministic reward chain and Y to be an initial choice between three reward chains (y 0 , y 1 , y 2 ) defined as follows: V (y 0 , ρ) = max 100 X = 28, 2 t=0 γ t + γ 3 ρ, ρ V (y 1 , ρ) = max 99 2 t=0 γ t + γ 3 max 1.4 1 − γ , ρ , ρ V (y 2 , ρ) = max 28 1 − γ , ρ . If we let γ = .9, then we have ∀280 > ρ ≥ 0 max{V (y 0 , ρ), V (y 2 , ρ)} > V (y 1 , ρ). Thus, any policy for a retirement process retirement process derived from Y that initially selects y 1 is suboptimal. We can apply the same strategy to compute the value of each combination of reward streams: V (y 0 + X) = 100 2 t=0 γ t + γ 3 28 5 t =0 γ t V (y 1 + X) = 99 2 t=0 γ t + γ 3 28 5 t =0 γ t + γ 6 1.4 1 − γ V (y 2 + X) = 28 1 − γ From this we can see that the optimal policy for the BSP that combines these MDPs, Z = X + Y , initially collects reward from y 1 . This contradicts Conjecture 1. In this section we show a bound on the value function of a bandit superprocess. We derive this bound by adding actions to a BSP so that it is equivalent to an MAB. The value function of our relaxed BSP is equivalent to the Whittle integral bound derived in Brown and  Smith [2013]  and so it yields insight into that computation. We begin by defining the Whittle integral and show some basic results in order to motivate our relaxation. Definition 5.  (Whittle Integral [Brown and Smith, 2013] ) Let M be a BSP. Let i index the arms of M. For any state, s = {s i }, and ρ ≥ 0, the Whittle integral of s is defined as V (s, ρ) = I − I x=ρ dx i ∂V i ∂ρ (s i , x). ( 2 ) Where I ≥ max i I si . When the arms of a BSP admit a dominating policy the Whittle integral is equal to the value function: Theorem 1. (Whittle Condition  [Whittle, 1980] ) Let M be a k-armed BSP with components {M i } and state space S. If each M i has a dominating policy, then ∀s ∈ S, ∀ρ ≥ 0, V (s, ρ) = V (s, ρ). MRPs have a single action per state, so the Whittle condition is trivially satisfied for all multi-armed bandits. V (s, 0) = V (s), so V (s, 0) provides an efficient method to compute the value of an MAB. For BSPs an arm that satisfies the Whittle condition can be replaced with an MRP that selects actions according to π * . The formula in Eq. 2 lends itself to a straightforward implementation, but is very challenging to interpret. We show below that this is equivalent to evaluating the retirement process value function for a single arm with a set of rewards determined by the other arms 3 . We refer to this set of rewards as the critical points of those arms. Definition 6. (Critical Points of an MDP) Let M be a Markov decision process. The critical points of M , C(M ) = {ρ i }, are the values of retirement reward such that the optimal stopping rule or policy changes. These are points where there is a discontinuity in ∂V ∂ρ . We let ∆ M (s, ρ) = lim δ→0 ∂V M ∂ρ (s, ρ + δ) − ∂V M ∂ρ (s, ρ − δ) be the size of the corresponding discontinuities. This is equivalent to the expected increase in E [γ τ ] under the new stopping rule. Theorem 2 shows that ∆ and C characterize the interaction between arms of an MAB. Theorem 2. Let X, Y be Markov reward processes. Let Z = X + Y be the 2-armed bandit. ∀s = {s X , s Y } ∈ S Z , V Z (s) = ρ∈C(Y ) V X (s X , ρ)∆ Y (s Y , ρ). (3) Proof. (sketch) As a first step, we follow the steps in Whittle  [1980]  and integrate Equation 2 by parts. This expresses V as the following integral: VZ (s) = Is X ρ =ρ V X (s X , ρ ) ∂ 2 V Y (s Y , ρ ) ∂ρ 2 dρ . V Y is piecewise linear with respect to ρ so ∂ 2 V Y ∂ρ 2 is a weighted sum of delta functions centered at V Y 's kinks. C(Y ) and ∆ Y respectively characterize these kinks and weights. Thus, VZ (s) is equal to the rhs of Eq. 3. X and Y are MRPs, so an appeal to Theorem 1 shows the result. A similar property holds for arbitrary k-armed bandits. This shows that we can summarize the context for an arm as a collection of weighted retirement rewards. Turning to BSPs, this lends insight into the approximation the Whittle integral introduces. To see how, we reconsider Ex. 1. Recall that this example consists of the BSP Z = X + Y and that Y is a choice between three reward chains, {y 0 , y 1 , y 2 }. Theorem 2 allows us to write the gap between the Whittle integral upper bound and the value of selecting y 1 as ρ∈C(X) max i V yi (s i , ρ) − V y1 (s 1 , ρ) ∆ X (s X , ρ) Figure  1  shows the retirement process value functions for this example. While the retirement process value of y 1 is always less than that of either y 0 or y 2 , it is close enough to their maximum that choosing y 1 essentially achieves the upper bound. The Whittle integral for Z is a weighted combination of distinct retirement process value functions (V y0 , V y2 ) but, in reality, the agent will be forced to pick a single policy of the two. \n DOMINATED RELAXATION OF AN MDP In this section, we introduce our primary theoretical result: a relaxation for the arms of a BSP so that a dominating policy exists. This reduces the BSP to an MAB whose value upper bounds the value of states in the BSP. We can show that the Whittle integral computes the value of states in this MAB and arrive at a straightforward proof that the Whittle integral is an upper bound. We call the result the dominated relaxation of an MDP. Before providing the details, we illustrate the main ideas with an example. The relaxed MDP is actually a Semi-MDP (SMDP): a generalization of an MDP where each action, a, has a duration, δ(a) ∈ R + . Example 2. Let MDP M be an initial choice between MRPs: M = 15, 0, 0, 0 . . . 10, 10, 10, 3, 3, 3, . . . . Let T (B) be the top (bottom) MRP. Let π T (π B ) be the policy that selects T (B) in s 0 . We can relax M with the addition of a single durative action, a , that transitions from the sink state in T to the sink state B. We set δ(a ) = 2. We take ρ such that V π T (s 0 , ρ) = V π B (s 0 , ρ) and set the rewards associated with a to be R π B ρ (s 0 ) − R π T ρ (s 0 ) = 10 2 0 γ t − 15 = 12.1 . With this change, at low settings of retirement reward, the agent is indifferent between a policy that opts for the top chain then selects a and the bottom reward chain. For high settings of retirement reward, the optimal policy retires immediately or retires after collecting the reward of 15. This SMDP satisfies the Whittle condition and can be replaced by an MRP in any bandit superprocess. Fig.  1  (c) shows an illustration of the state space and the introduced action. In this example, we connected the state where π T retires to the state where π B retires. This lets the agent collect shortterm and long-term rewards with the same policy. To do this in general, we introduce multiple copies of the state space, one for each policy that is optimal for some ρ. Definition 7. (Dominated Relaxation of an MDP) Let M be an MDP with discount factor γ and state space S. Let s be a state in M . The dominated relaxation of M for s, M D (s), is a semi-Markov decision process that fixes s as an initial state. Let {π i } be the policies that are optimal for some ρ: {π * ρ |ρ ∈ C(M )}. This sequence is ordered so that ρ − (π i ) is increasing in i 4 . For each i, we introduce a copy of the state space, S i , where the agent is restricted to following π i . Let s i be the analogue of s in S i . For s i ∈ τ ρ−(πi) , we introduce a single durative action, a i , that takes the agent from S i to S i−1 and characterize it as follows: • R(s i ) = R ρ+(πi−1) (s) − R ρ−(πi) (s) • T (s i , a i , s i−1 ) = P retire (s |π i−1 , ρ + (π i−1 ), s) • δ(a i ) = log γ E γ τ π i−1 ρ + (s) − log γ E γ τ π i ρ − (s) For each i, we introduce an action that transitions from s to s i with δ = 0. Let V D (s) represent the value of s in M D (s). Theorem 3. Let M be an MDP with state space S. The following statements are true for s ∈ S and ρ ≥ 0: 1. M D (s) satisfies the Whittle condition. 2. V D (s, ρ) = V (s, ρ). \n V (s, ρ) ≥ V (s, ρ) Proof. See supplementary materials \n AN -OPTIMAL ALGORITHM FOR BANDIT SUPERPROCESSES In this section, we present two algorithms related to BSPs. The first is a novel algorithm to compute V (s, ρ) that can use any method to solve the underlying MDP. The second is an efficient algorithm to compute optimal actions for a BSP. Our approach, Branch-and-Bound Value Iteration (BBVI), uses Whittle integrals to compute upper and lower bounds on value. Then, we apply a modified Branch-and-Bound search to find provably optimal actions. \n COMPUTING A RETIREMENT PROCESS VALUE FUNCTION Before we present BBVI, we give a simple algorithm to compute a retirement process value function that uses an (arbitrary) MDP solver as a black box. Brown and  Smith [2013]  describe an algorithm to compute retirement process value functions, but their approach requires custom implementation of a modified simplex algorithm. Our approach is simple and based on an algorithm that initially appeared in the solutions manual for  Russell and Norvig [2010] . Our goal is to identify each component of V (•, ρ), so our output will be a list of critical points and the associated slopes. First, we will need the following result. Lemma 1. Let M be an MDP with state space S. Let ρ 0 < ρ 1 . Consider a retirement reward in the interior of this interval, ρ ∈ (ρ 0 , ρ 1 ). If, ∀s ∈ S V (s, ρ) = V (s, ρ 0 ) + V (s, ρ 1 ) − V (s, ρ 0 ) ρ 1 − ρ 0 (ρ − ρ 0 ), ( 4 ) then there is at least one policy and stopping rule that is optimal for every ρ ∈ [ρ 0 , ρ 1 ]. The expected value of the discount factor at retirement is the slope between those points: E γ τ * (s) = V (s, ρ 1 ) − V (s, ρ 0 ) ρ 1 − ρ 0 . ( 5 ) Proof. This follows from the form of Equation 1 and the fact that V (s, ρ) is piecewise linear, increasing, and convex. This test allows us to implement a binary search over retirement rewards. Our approach relies on a given MDP solution method, SOLVE, that returns the vector of values for a given MDP. We initialize an interval that contains all critical points and make a call to SOLVE to compute the retirement process value at each endpoint. Then we call SOLVE to compute the retirement process value for the midpoint of our interval and apply the test in Eq. 4. If it succeeds, we return the lower endpoint and the corresponding slope. If this does not, we sub-divide our interval and recurse. We can concatenate the results to get the breakpoints and slopes for the retirement process value function over this interval. Algorithm 1 shows pseudocode for this algorithm. Algorithm 1 Computing an MDP's Critical Points Define: CRITICALPOINTS(M [, ρ − , ρ + , V − , V + ]) Input: MDP, M ; Interval of retirement values, ρ − , ρ + ; Values at interval endpoints, V − , V + if ρ − , ρ + are not set then ρ − ← 0 ρ + ← maxReward(M ) 1−γ V − ← SOLVE(M ρ − ) V + ← ρ + ## Retirement is initially optimal end if ρ ← ρ + −ρ − 2 V ← SOLVE(M ρ ) if |V − V − + (ρ − ρ − ) V + −V − ρ + −ρ − | < then return [ρ − ], V + −V − ρ + −ρ − else pts − , slope − ←CRITICALPOINTS(M, ρ − , ρ, V − , V ) pts + , slope + ←CRITICALPOINTS(M, ρ, ρ + , V, V + ) ## Merge adjacent intervals with the same slope if slope − [−1] = slope + [0] then del pts + [0],del slope + [0] end if return pts − ∪ pts + , slopes − ∪ slopes + end if \n BRANCH-AND-BOUND VALUE ITERATION Now, we present a practical algorithm to compute optimal actions in a bandit superprocess. While a BSP is not indexable, we would like to be able to plan efficiently when the arms are 'close' to indexable-when there are only a few states where the optimal policy changes in response to the opportunity cost of delayed rewards in other arms. Our approach is based on envelope dynamic programming methods to solve MDPs: we compute value estimates for a given initial state by solving a dynamic program defined over a reachable subset of the state space  [Gardiol, Natalia H and Kaelbling, Leslie P, 2003, Hansen and Zilberstein, 2001] . The primary difference between our approach and standard envelope methods is that we use dynamic pro-gramming on our envelope to update an upper bound and a lower bound on the value. This is useful in a BSP because the Whittle integral allows efficient calculation of both bounds. Our goal is to compute the optimal action for a given state s in a BSP, M = M 1 , . . . , M K . We can obtain an upper bound on V (s) with a Whittle integral. We use a Whittle integral for the MAB that solves each arm independently to compute a lower bound. Our algorithm maintains upper and lower bounds on the Q-function for each action that could be executed from s. We write these bounds as Q + (s, a) and Q − (s, a) respectively. If there is a pair of actions a, a such that Q + (s, a ) < Q − (s, a) + , then we can conclude that a is at least -suboptimal. If this test removes all but a single action, then we have found a -optimal action and return it. In the event that more than one action remains, we do a partial expansion of the state space around s. We keep track of a set of expanded states, E, and a set of boundary states, B. States in the boundary set, B, are states that some expanded state can transition to but have not yet been added to E. We can use these states to update the bounds on Q(s, •) by solving a related MDP. This is formalized in the following theorem. Theorem 4. Let M be an MDP with state space S and action space A. Let S ⊆ S where S = B ∪ E and ∀ s ∈ E, T (s, a, s ) = 0 ⇒ s ∈ S . Let M + be an MDP with state space S ∪ {α}. M + 's transition distribution and rewards are identical for states in E (expanded states). Each state s ∈ B transitions deterministically to α and receives a reward that is an upper bound on V M (s). α is a sink state that accrues 0 reward. Then the value of a state in M + is an upper bound on its value in M : V M + (s) ≥ V M (s). Proof. See supplementary materials. It is straightforward to show that an updated lower bound can be computed by fixing boundary states to have value equal to a lower bound. Our approach alternates between pruning actions based on dominance relations, adding states to E, and computing the value of an MDP defined over E. We interleave value iteration with a branch-andbound search, so we call it Branch-and-Bound Value Iteration (BBVI). Algorithm 2 shows pseudocode to implement this method. At termination, the action we return is guaranteed to be at most -suboptimal. Theorem 5. Let M be a BSP and let s be a state in M . Let a be the action returned by BBV I(M, s, ). V (s) − Q(s, a) < . Proof. See supplementary materials. Large regions of the state space are irrelevant to our objective so we use a heuristic to guide node expansion. Our heuristic is a measure of the sensitivity of values at the root to change in the upper and lower bounds of unexpanded nodes. Similar heuristics have been applied in many settings  [Rivest, 1987, Smith and Simmons, 2004] . In BBVI, these values are the expected discounted visitation rates in the bounding MDPs and are computed as the dual variables from a value iteration LP. The backup procedure is slower than node expansions, so we perform backups in batches. In between backups and heuristic computations, we approximate the state space as a tree and push new states onto the agenda with their parent's heuristic value weighted by the transition probability.  Q + ← SOLVE(BOUNDMDP(E , B, Q + )) Q − ← SOLVE(BOUNDMDP(E , B, Q − )) a * ← argmax a Q − (s 0 , a) end while return -optimal action a * \n EMPRIRICAL EVALUATION We implemented BBVI in Python and use the linear programming solver Gurobi to compute value functions. Our experiments were run on an Intel i7 with 16 GB of RAM. In our first experiments, we compare the scalability of BBVI with that of standard MDP algorithms. In particular we compare the following algorithms: • SPUDD: the baseline factored MDP algorithm in the 2011 IPPC  [Hoey et al., 1999] . • LRTDP(Merge): Labeled Real-Time Dynamic Programming  [Bonet and Geffner, 2003]  with the upper bound from  Singh and Cohn [1998]  as a heuristic. • LRTDP(WI): LRTDP with the Whittle integral as an upper bound. • BBVI: Branch-and-Bound Value Iteration. We evaluate performance on a simple BSP designed to model allocation of research resources to product research and development. Each arm in this problem corresponds to a potential product that our agent could sell in the market. However, before we sell a product we must devote effort to R&D. This can be done in one of two ways, a safe research approach that is slow but reliable, and a risky approach that is fast, but runs a risk of producing a defective product. After at least one product has been researched, the agent can opt to spend a round produce and sell that product or continue research on a different project. Because taking a product to market does not change the state of the BSP, it is straightforward to show that any stationary policy (including π * ) will only ever produce a single product. We define a distribution over these problems by selecting a random market value for each product uniformly from [0, 1] and random durations for the safe and risky research strategies (although we ensure that safe research is at least 3x as slow as risky research). Figure  2  (a) shows the state space for an example arm with typical parameters. Figure  2  (b) shows the results of our comparison. We used a timeout of 1000s and set a memory limit of 4 GB. We ran our experiments in an online setting and running times reflect the amount of time to select an optimal action from scratch. While this is a natural setting for LRTDP and BBVI, it is admittedly a little unfair to SPUDD (which computes a full policy). This is mitigated by the fact that BBVI's improvement over SPUDD, which is a little under 5 orders of magnitude with 10 8 states, is such that an agent would need to be planning over an immense horizon before SPUDD presents a reasonable alternative. The factored MDP bounds from  Singh and Cohn [1998]  are quite ill-suited to this problem. This is because its upper bound (the sum of the independent value for each arm) is very loose and it essentially forces LRTDP to enumerate the state space. In contrast, LRTDP performs quite well when it has good heuristic information. However, its performance degrades faster than that of BBVI, because it does not effectively leverage a lower bound on value. Even for very large problem instances, BBVI computes optimal solutions in well under a second. BBVI's performance in the R&D domain is largely explained by the structure of the arms and the short horizon within each arm. Although there may be a large number of arms, BBVI reduces each individual arm to an equivalent MRP after a small number of node expansions. This means that running time is essentially linear in the number of arms. Note that, in this domain, the solution that solves each MDP independently and executes the corresponding index policy will just opt for conservative research on the most valuable option. This policy is essentially always suboptimal: as long as there are reasonable alternatives it is usually a good idea to try some risky projects. Our next experiment uses a synthetic domain to explore the performance of BBVI as the structure and number of arms changes. In this BSP, each arm is a 20x20 grid world. The actions in this world correspond to moving in the 4 cardinal directions. Rewards are 0 everywhere except at randomly chosen locations and after receiving a reward, the agent transitions to a random location. In this experiment we vary the number of rewards that are available in each arm. Adding rewards will typically cause the optimal policy for an arm to be more sensitive to context. This means that the dominated relaxation will produce a looser upper bound, because it will need to add more actions. We evaluate this difficultly by measuring the convergence criterion of BBVI after 10,000 node expansions. Figure  2  (c) shows the results of this experiment. We can see that BBVI's solution quality decreases with the number of states, but the primary variation comes from changes in the properties of the arms. \n CONCLUSION AND FUTURE WORK In summary, we presented a model of highly decoupled decision making: bandit superprocesses. A BSP presents an agent with the opportunity to act in one of several Markov decision processes. The key constraint is that the agent can only act in a single process at a time. We provided a summary of BSP research, including an upper bound for the value function of a BSP in the form of the Whittle integral. We derived an equivalent relaxation and thus gave a novel proof that the Whittle integral is an upper bound. Finally we presented and evaluated algorithmic solutions for this class of decision problems. In future work, we plan to extend these ideas in three directions. The first is algorithmic improvements for BSPs. A potential direction here is to leverage factored dynamics in the bounding MDPs themselves. A search over sequences of MDPs that only consider states where the current policy stops could be more efficient. Next, also plan to explore generalizations of the bounds used for BSPs to more general cases of global resource constraints (e.g., those considered in  Meuleau et al. [1998] ). Finally, the similarity to sums of games studied in  Conway [2000]  suggests an unexplored connection between BSPs and combinatorial game theory. Figure 1 : 1 Figure 1: (a-b) Retirement process value functions for the reward chains Ex. 1. The slope of the lines is the expected value of the discount parameter at retirement: E [γ τ ]. Flat sections indicate regions of retirement rewardswhere retirement is always suboptimal. The kink in the green curve at ρ = 280 indicates that it has become optimal to retire immediately. The kink in the black curve at ρ = 14 increases the slope to γ 6 < 1; for ρ > 14, it is optimal to retire after collecting a prefix of the reward stream from y 2 . (c) Dominated relaxation of the MDP in Ex. 2. We add additional durative actions to the state space to ensure that a dominating policy exists. Note that the original MDP does not admit a dominating policy. \n Algorithm 2 2 Branch-and-Bound Value Iteration Define:BBVI( M 0 , . . . , M K , s 0 , ) Input: BSP arms, M k ; Initial state, s 0 ; Tolerance, # Lower bound M by fixing a policy for each arm LB k ←toMRP(M k ) Compute critical points for M k , LB k Compute bounds on Q(s 0 , •) with Whittle integrals for M and LB. # Keep track of expanded region of state space E ← ∅ # Keep track of states at boundary of M + , M − B ← {s 0 } a * ← argmax a Q − (s 0 , a) while ∃a = a * s.t Q + (s 0 , a ) ≥ Q − (s 0 , a * ) do s ←pop(B) E ← E ∪ {s} for a ∈ A do for s ∈ successors(s) do Compute upper and lower bounds for Q(s , •) B ← B ∪ {s } end for end for \n Figure 2: (a) the state space for an arm of a R & D BSP. All states accrue 0 reward except for the 'Working Product' state, which collects a fixed reward per time step. (b) shows runtime (log-scale) vs problem size for BBVI and several alternatives on an R & D BSP. SPUDD [Hoey et al., 1999]  and LRTDP (with the heuristic from Singh and Cohn [1998] ) scale poorly compared with algorithms that leverage the Whittle integral. BBVI's additional improvement over LRTDP stems from the use of an efficient, exact lower bound to check convergence. (c) BBVI's bound on suboptimality after 10,000 node expasions (measured in units of discounted reward). Changing the number of rewards in each arm allows us to measure BBVI's performance as arms become more sensitive to context. \n\t\t\t This result first appears in the literature as an intermediate step in a larger proof from Whittle [1980] . It went unnoticed or unappreciated in the intervening 30+ years. \n\t\t\t Here we use the fact that the Gittins index of a non-increasing reward sequence is equal to the instantaneous reward.4 AN UPPER BOUND FOR BANDIT SUPERPROCESSES \n\t\t\t Our result is a small extension on a related result in Brown and Smith [2013] ; it is primarily included to provide intuition. \n\t\t\t Recall that [ρ−(π), ρ+(π)] is the interval of retirement rewards where π is optimal.", "date_published": "n/a", "url": "n/a", "filename": "uai15-multi.tei.xml", "abstract": "A bandit superprocess is a decision problem composed from multiple independent Markov decision processes (MDPs), coupled only by the constraint that, at each time step, the agent may act in only one of the MDPs. Multitasking problems of this kind are ubiquitous in the real world, yet very little is known about them from a computational viewpoint, beyond the observation that optimal policies for the superprocess may prescribe actions that would be suboptimal for an MDP considered in isolation. (This observation implies that many applications of sequential decision analysis in practice are technically incorrect, since the decision problem being solved is often part of a larger, unstated bandit superprocess.) The paper summarizes the state-of-theart in the theory of bandit superprocesses and contributes a novel upper bound on the global value function of a bandit superprocess, defined in terms of a direct relaxation of the arms. The bound is equivalent to an existing bound (the Whittle integral), but is defined constructively, as the value of a related multi-armed bandit. We provide a new method to compute this bound and derive the first practical algorithm to select optimal actions in bandit superprocesses. The algorithm operates by repeatedly establishing dominance relations between actions using upper and lower bounds on action values. Experiments indicate that the algorithm's run-time compares very favorably to other possible algorithms designed for more general factored MDPs.", "id": "52b786a09389d33703284c7fdebc62e4"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Joseph Y Halpern", "Rafael Pass", "Lior Seeman"], "title": "Decision Theory with Resource-Bounded Agents", "text": "Introduction The standard approach to decision making, going back to  Savage (1954) , suggests that an agent should maximize expected utility. But computing the relevant probabilities might be difficult, as might computing the relevant utilities. And even in cases where the probabilities and utilities are not hard to compute, finding the action that maximizes expected utilities can be difficult. In this paper, we consider approaches to decision making that explicitly take computation into account. The idea of taking computation into account goes back at least to the work of  Good (1952)  and  Simon (1955) . It has been a prominent theme in the AI literature (see, e.g.,  Horvitz, 1987; Russell & Subramanian, 1995) . Our work has been inspired by two major lines of research aimed at capturing resource-bounded (i.e., computationally-bounded) agents in the game theory literature. The first, initiated by  Rubinstein (1986) , charges an agent for doing costly computation; the second, initiated by  Neyman (1985) , does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. We consider the first approach in the context of the framework of  Halpern and Pass (2010b) , which in turn is a specialization of the framework of  Halpern and Pass (2010c)  to the case of a single agent. The idea is the following: We assume that the agent can be viewed as choosing an algorithm (i.e., a Turing machine); with each Turing machine (TM) M and input, we associate its complexity. The complexity can represent, for example, the running time of M on that input, the space used, the complexity of M (e.g., how many states it has), or the difficulty of finding M (some algorithms are easier to think of than others). We deliberately keep the complexity function abstract, to allow for the possibility of representing a number of different intuitions. The agent's utility can then depend, not just on the payoff, but on the complexity. Thus, we can \"charge\" for the complexity of computation. Although this approach seems quite straightforward, we show that it can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions). We then consider the second approach: modeling agents as finite automata. Finite automata are a well-known basic model of computation. An automaton receives a sequence of inputs from the environment, and changes state in response to the input. We capture the fact that an agent is resource-bounded by limiting the number of states in the automaton. In the context of decision theory, this approach was first used by  Wilson (2002) . She examined a decision problem where an agent needs to make a single decision, whose payoff depends on the state of nature (which does not change over time). Nature is in one of two possible states, G (good) and B (bad). The agent gets signals, which are correlated with the true state, until the game ends, which happens at each step with probability g > 0. At this point, the agent must make a decision. For each N, Wilson characterizes an N-state optimal finite automaton for making a decision in this setting, under the assumption that g is small (so that the agent gets information for many rounds). (See Section 3 for further details.) She then uses this characterization to argue that an optimal N-state automaton also exhibits behavior such as belief polarization (again, see Section 3). Thus, some observed human behavior can be explained by viewing people as resource-bounded, but rationally making the best use of their resources (in this case, the limited number of states). Wilson's model assumes that nature is static. But, in many important problems, ranging from investing in the stock market to deciding which route to take when driving to work, the world is dynamic. Moreover, people do not make decisions just once, but must make them often. For example, when investing in stock markets, people get signals about the market, and need to decide after each signal whether to invest more money, take out money that they have already invested, or to stick with their current position. In a recent work  (Halpern, Pass, and Seeman 2012) , we consider the problem of constructing an optimal N-state automaton for this setting. We construct a family of quite simple automata, indexed by N, the number of states, and a few other parameters. We show that as N grows large, this family approaches optimal behavior. More precisely, for all e, there is a sufficiently large N and member of this family with N states whose expected payoff is within e of optimal, provided the probability of a state transition is sufficiently small. More importantly, the members of this family reproduce observed human behavior in a series of tasks conducted by  Erev, Ert and Roth (2010)  (see Section 3 for further discussion). Again, these results emphasize the fact that some observed human behavior can be explained by viewing people as rational, resource-bounded agents. \n Charging for the complexity of computation In this section, we review and discuss the approach that is used by  Halpern and Pass (2010b)  to take cost of computation into account in decision theory. Much of the material below is taken from  (Halpern and Pass 2010b) , which the reader is encouraged to consult for further details and intuition. The framework that we use is essentially a single-agent version of what  Halpern and Pass (2010a, c)  called Bayesian machine games. In a standard Bayesian game, each player has a type in some set T, and makes a single move. Player i's type can be viewed as describing i's initial information; some facts that i knows about the world. We assume that an agent's move consists of choosing a Turing machine. As we said in the introduction, associated with each Turing machine and type is its complexity. Given as input a type, the Turing machine outputs an action. The utility of a player depends on the type profile (i.e., the types of all the players), the action profile, and the complexity profile (i.e., each player's complexity). \n Example 2.1 Suppose that an agent is given an input n, and is asked whether it is prime. The agent gets a payoff of $1,000 if he gives the correct answer, and loses $1,000 if he gives the wrong answer. However, he also has the option of playing safe, and saying \"pass,\" in which case he gets a payoff of $1. Clearly, many agents would say \"pass\" on all but simple inputs, where the answer is obvious, although what counts as a \"simple\" input may depend on the agent. 1 The agent's type can then be taken to be the input. The set T of possible types could be, for example, all integers, or all integers that can be written in binary using at most 40 digits (i.e., a number that is less than 2 40 ). The agent can choose among a set of TMs, all of which output either \"prime,\" \"not prime,\" or \"pass\" (which can be encoded as 0, 1, and 2). One natural choice for the complexity of a pair (M, n) consisting of TM M and an input n is the running time of M on input n. As the agent's utility takes the complexity into account, this would justify the agent using a \"quick-and-dirty\" algorithm, which is typically right to compute whether the input is prime; if the algorithm does not return an answer in a relatively small amount of time, the agent can just \"pass.\" The agent might prefer using such a TM rather than one that gives the correct answer, but takes a long time doing so. We can capture this tradeoff in the agent's utility function. ▪ There are some issues that we need to deal with to finish modeling Example 2.1 in our framework. Note that if the agent chooses the TM after being given the number n, then one of two TMs is clearly optimal: if n is in fact prime, then the TM which just says \"prime\" and halts; if n is not prime, then the TM which says \"not prime\" and halts is clearly optimal. The problem, of course, is that the agent does not know n. One approach to dealing with this problem is to assume that the agent chooses the TM before knowing n; this was the approach implicitly taken by  Halpern and Pass (2010c) . But there is a second problem: we have implicitly assumed that the agent knows what the complexity of each pair (M, n) is; otherwise, the agent could not maximize expected utility. Of course, in practice, an agent will not know how long it will take a Turing machine to compute an answer on a given input. We deal with both of these problems by adding one more parameter to the model: a state of nature. In Example 2.1, we allow the TM's running time and whether n is prime to depend on the state; this means that the \"goodness\" (i.e., accuracy) of the TM can depend on the state. We model the agent's beliefs about the running time and accuracy of the TM using a probability distribution on these states.  2  We capture these ideas formally by taking a computational decision problem with types to be a tuple D ¼ ðS; T; A; Pr; M; C; O; uÞ. We explain each of these components in turn. The first four components are fairly standard. S is a state space, T is a set of types, A is a set of actions, and Pr is a probability distribution on S9T (there may be correlation between states and types). In a standard decision-theoretic setting, there is a probability on states (not on states and types), and the utility function associates a utility with each (state, action) pair (intuitively, u(s, a) is the utility of performing action a in state s). Here things are more complicated because we want the utility to also depend on the TM chosen. This is where the remaining components of the tuple come in. The fifth component of the tuple, C, is the complexity function. Formally, C : M Â S Â T ! N, so CðM; s; tÞ is the complexity of running TM M on input t in state s. The complexity can be, for example, the running time of M on input t, the space used by M on input t, the number of states in M (this is the measure of complexity used by  Rubinstein (1986) ), and so on. The sixth component of the tuple, O, is the output function. It captures the agent's uncertainty about the TM's output. Formally, O : M Â S Â T ! N; OðM; s; tÞ is the output of M on input t in state s. Finally, an agent's utility depends on the state s, his type t, and the action OðM; s; tÞ, as is standard, and the complexity. As we describe the complexity by a natural number, we take the utility function u maps S Â T Â A Â N to R (the reals). Thus, the expected utility of choosing a TM M in the decision problem D is P s2S;t2T Prðs; tÞuðs; t; OðM; s; tÞ; CðM; s; tÞÞ. Note that now the utility function gets the complexity of M as an argument. The next example should clarify the role of all these components. Example 2.1 (cont'd): We now have the machinery to formalize Example 2.1. We take T, the type space, to consist of all natural numbers < 2 40 ; the agent must determine whether the type is prime. The agent can choose either 0 (the number is not prime), 1 (the number is prime), or 2 (pass); Thus, A = {0, 1, 2}. Let M be some set of TMs that can be used to test for primality. As suggested above, the state space S is used to capture the agent's uncertainty about the output of a TM M and the complexity of M. Thus, for example, if the agent believes that the TM will output pass with probability 2/3, then the set of states such that OðM; s; tÞ ¼ 2 has probability 2/3. We take CðM; s; tÞ to be 0 if M computes the answer within 2 20 steps on input t, and 10 otherwise. (Think of 2 20 steps as representing a hard deadline.) If, for example, the agent does not know the running time of a TM M, but ascribes probability 2/3 to M finishing in less than 2 20 steps on input t, then the set of states s such that Cðs; t; MÞ ¼ 0 has probability 2/3. We assume that there is a function Prime that captures the agent's uncertainty regarding primality; Prime(s,t) = 1 if t is prime in state s, and 0 otherwise. 3 Thus, if the agent believes that TM M gives the right answer with probability 2/3, then the set of states s where Primeðs; tÞ ¼ OðM; s; tÞ has probability 2/3. Finally, let u(s, t, a, c) = 10 À c if a is either 0 or 1, and this is the correct answer in state s (i.e., OðM; s; tÞ ¼ Primeðs; tÞ) and u(s, t, 2, c) = 1 À c. Thus, if the agent is sure that M always gives the correct output, then u(s, t, a, c) = 10 À c for all states s and a 2 {0, 1}. ▪ \n Example 2.2 Biases in information processing Psychologists have observed many systematic biases in the way that individuals update their beliefs as new information is received (see  Rabin (1998)  for a survey). In particular, a first-impressions bias has been observed: individuals put too much weight on initial signals and less weight on later signals. As they become more convinced that their beliefs are correct, many individuals even seem to simply ignore all information once they reach a confidence threshold. Several papers in behavioral economics have focused on identifying and modeling some of these biases (see, e.g.,  Rabin, 1998 and references therein; Mullainathan, 2002; Rabin & Schrag, 1999) . In particular,  Mullainathan (2002)  makes a potential connection between memory and biased information processing, using a model that makes several explicit (psychology-based) assumptions on the memory process (e.g., that the agent's ability to recall a past event depends on how often he has recalled the event in the past). More recently,  Wilson (2002)  demonstrated a similar connection when modeling agents as finite automata, but her analysis is complex (and holds only in the limit). As we now show, the first-impression-matters bias can be easily explained if we assume that there is a small cost for \"absorbing\" new information. Consider the following simple game, which is very similar to the one studied by  Mullainathan (2002)  and  Wilson (2002) . The state of nature is a bit b that is 1 with probability 1/2. For simplicity, we assume that the agent has no uncertainty about the \"goodness\" or output of a TM; the only uncertainty involves whether b is 0 or 1). An agent receives as his type a sequence s 1 ,s 2 ,. . .,s n of independent samples, where s i = b with probability q > 1/2. The samples corresponds to signals the agents receive about b. An agent is supposed to output a guess b 0 for the bit b. If the guess is correct, he receives 1 À mc as utility, and Àmc otherwise, where m is the number of bits of the type he read, and c is the cost of reading a single bit (c should be thought of the cost of absorbing/interpreting information). It seems reasonable to assume that c > 0; signals usually require some effort to decode (such as reading a newspaper article, or attentively watching a movie). If c > 0, it easily follows by the Chernoff bound (see  Alon & Spencer, 2004 ) that after reading a certain (fixed) number of signals s 1 ,. . .,s i , the agents will have a sufficiently good estimate of b that the marginal cost of reading one extra signal s i+1 is higher than the expected gain of finding out the value of s i+1 . That is, after processing a certain number of signals, agents will eventually disregard all future signals and base their output guess only on the initial sequence. We omit the straightforward details. Essentially the same approach allows us to capture belief polarization. Suppose for simplicity that two agents start out with slightly different beliefs regarding the value of some random variable X (think of X as representing something like \"O.J. Simpson is guilty\"), and get the same sequence s 1 ,s 2 ,. . .,s n of evidence regarding the value of X. (Thus, now the type consists of the initial belief, which can, for example, be modeled as a probability or a sequence of evidence received earlier, and the new sequence of evidence.) Both agents update their beliefs by conditioning. As before, there is a cost of processing a piece of evidence, so once an agent gets sufficient evidence for either X = 0 or X = 1, he will stop processing any further evidence. If the initial evidence supports X = 0, but the later evidence supports X = 1 even more strongly, the agent that was initially inclined toward X = 0 may raise his beliefs to be above threshold, and thus stop processing, believing that X = 0, while the agent initially inclined toward X = 1 will continue processing and eventually believe that X = 1. ▪ As shown by  Halpern and Pass (2010b) , we can also use this approach to explain the status quo bias (people are much more likely to stick with what they already have;  Samuelson & Zeckhauser, 1998) . \n Value of computational information and value of conversation Having a computational model of decision making also allows us to reconsider a standard notion from decision theory, value of information, and extend it in a natural way so as to take computation into account. Value of information is meant to be a measure of how much an agent should be willing to pay to receive new information. The idea is that, before receiving the information, the agent has a probability on a set of relevant events and chooses the action that maximizes his expected utility, given that probability. If he receives new information, he can update his probabilities (by conditioning on the information) and again choose the action that maximizes his expected utility. The difference between the expected utility before and after receiving the information is the value of the information. In many cases, an agent seems to be receiving valuable information that is not about what seem to be the relevant events. This means that we cannot do a value of information calculation, at least not in the obvious way. For example, suppose that the agent is interested in learning a secret, which we assume for simplicity is a number between 1 and 1,000. A priori, suppose that the agent takes each number to be equally likely, and so has probability 0.001. Learning the secret has utility, say, $1,000,000; not learning it has utility 0. The number is locked in a safe, whose combination is a 40-digit binary number. Intuitively, learning the first 20 digits of the safe's combination gives the agent some valuable information. But this is not captured when we do a standard value-of-information calculation; learning this information has no impact at all on the agent's beliefs regarding the secret. Although this example is clearly contrived, there are many far more realistic situations where people are clearly willing to pay for information to improve computation. For example, companies pay to learn about a manufacturing process that will speed up production; people buy books on speedreading; and faster algorithms for search are clearly considered valuable. Once we bring computation into decision making, the standard definition of value of information can be applied to show that there is indeed a value to learning the first 20 digits of the combination, and to buying a more powerful computer; expected utility can increase (see  Halpern & Pass, 2010a for details) . But now we can define a new notion: value of conversation. The value of information considers the impact of learning the value of a random variable; by taking computation into account, we can extend this to consider the impact of learning a better algorithm. We can further extend to consider the impact of having a conversation. The point of a conversation is that it allows the agent to ask questions based on history. For example, if the agent is trying to guess a number chosen uniformly at random between 1 and 100, and receives utility of 100 if he guesses it right, having a conversation with a helpful TM that will correctly answer seven yes/no questions is quite valuable: as is well known, with seven questions, the agent can completely determine the number using binary search. The computational framework allows us to make this intuition precise. Again, we encourage the reader to consult (Halpern and Pass 2010a) for further details. \n Modeling people as rational finite automata We now consider the second approach discussed in the introduction, that of modeling the fact that an agent can do only bounded computation. Perhaps the first to do this in the context of decision theory was  Wilson (2002) , whose work we briefly mentioned earlier. Recall that Wilson considers a decision problem where an agent needs to make a single decision. Nature is in one of two possible states, G (good) and B (bad), which does not change over time; the agent's payoff depends on the action she chooses and the state of nature. The agent gets one of k signals, which are correlated with nature's state; signal i has probability p G i of appearing when the state of nature is G, and probability p B i of appearing when the state is B. We assume that the agent gets exactly one signal at each time step, so that P k i¼1 p G i ¼ P k i¼1 p B i ¼ 1 . This is a quite standard situation. For example, an agent may be on a jury, trying to decide guilt or innocence, or a scientist trying to determine the truth of a theory. Clearly, the agent should try to learn nature's state, so as to make an optimal decision. With no computational bounds, an agent should just keep track of all the evidence it has seen (i.e., the number of signals of each type), in order to make the best possible decision. However, a finite automaton cannot do this. Wilson characterizes the optimal Nstate automaton for making a decision in this setting, under the assumption that g (the probability that the agent has to make the decision in any given round) is small. Specifically, she shows that an optimal N-state automaton ignores all but two signals (the \"best\" signal for each of nature's states). The automaton's states can be laid out \"linearly,\" as states 0, . . ., N À 1, and the automaton moves left (with some probability) only if it gets a strong signal for state G (and it is not in state 0), and moves right (with some probability) only if it gets a strong signal for state B (and is not in state N À 1). Roughly speaking, the lower the current state of the automaton, the more likely from the automaton's viewpoint that nature's state is G. The probability of moving left of right, conditional on receiving the appropriate signal, may vary from state to state. In particular, if the automaton is in state 0, the probability that it moves right is very low. Intuitively, in state 0, the automaton is \"convinced\" that nature's state is G, and it is very reluctant to give up on that belief. Similarly, if the automaton is in state N À 1, the probability that it will move left is very low. Wilson argues that these results can be used to explain observed biases in information processing, such as belief polarization. For suppose that the true state of nature is B. Consider two 5-state automata, A 1 and A 2 . Suppose that automaton A 1 starts in state 1, while automaton A 2 starts in state 2. (We can think of the starting state as reflecting some initial bias, for example.) They both receive the same information. Initially, the information is biased toward G, so both automata move left; A 1 moves to state 0, and A 2 moves to state 1. Now the evidence starts to shift toward the true state of the world, B. But since it is harder to \"escape\" from state 0, A 1 stays in state 0, while A 2 moves to state 4. Thus, when the automata are called upon to decide, A 1 makes the decision appropriate for B, while A 2 makes the decision appropriate for G. A similar argument shows how this approach can be used to explain the first-impression bias. The key point is that the order in which evidence is received can make a big difference to an optimal finite automaton, although it should make no difference to an unbounded agent. Wilson's model assumes that the state of nature never changes. In recent work  (Halpern et al. 2012) , we consider what happens if we allow nature's state to change. We con-sider a model that is intended to capture the most significant features of such a dynamic situation. As in Wilson's model, we allow nature to be in one of a number of different states, and assume that the agent gets signals correlated with nature's state. But now we allow nature's state to change, although we assume that the probability of a change is low. (Without this assumption, the signals are not of great interest.) For definiteness, assume that nature is in one of two states, which we again denote G and B. Let p be the probability of transitioning from B to G or from G to B in any given round. Thus, we assume for simplicity that these probabilities are history-independent, and the same for each of the two transitions. (Allowing different probabilities in each direction does not impact the results.) The agent has two possible actions S (safe) and R (risky). If he plays S, he gets a payoff of 0; if he plays R he gets a payoff x G > 0 when nature's state is G, and a payoff x B < 0 when nature's state is B. The agent does not learn his payoff, but, as in Wilson's model, gets one of k signals, whose probability is correlated with nature's state. However, unlike Wilson's model, the agent gets a signal only if he plays the risky action R; he does not get a signal if he plays the safe action S. We denote this setting S½p G 1 ; p B 1 ; . . .; p G k ; p B k ; x G ; x B . A setting is nontrivial if there exists some signal i such that p B i 6 ¼ p G i . If a setting is trivial, then no signal enables the agent to distinguish whether nature is in state G or B; the agent does not learn anything from the signals. For a given setting S½p G 1 ; p B 1 ; . . .; p G k ; p B k ; x G ; x B , we are interested in finding an automaton A that has high average utility when we let the number of rounds go to infinity. Unlike Wilson, we were not able to find a characterization of the optimal N-state automaton. However, we were able to find a family of quite simple automata that do very well in practice and, in the limit, approach the optimal payoff. We denote a typical member of this family A[N, p exp , Pos, Neg, r u , r d ]. The automaton A[N, p exp , Pos, Neg, r u , r d ] has N + 1 states, again denoted 0,. . .,N. State 0 is dedicated to playing S. In all other states R is played. As in Wilson's optimal automaton, only \"strong\" signals are considered; the rest are ignored. More precisely, the k signals are partitioned into three sets, Pos (for \"positive\"), Neg (for \"negative\"), and I (for \"ignore\" or \"indifferent\"), with Pos and Neg nonempty. The signals in Pos make it likely that nature's state is G, and the signals in Neg make it likely that the state of nature is B. The agent chooses to ignore the signals in I; they are viewed as not being sufficiently informative as to the true state of nature. (Note that I is determined by Pos and Neg.) In each round while in state 0, the agent moves to state 1 with probability p exp . In a state i > 0, if the agent receives a signal in Pos, the agent moves to i+1 with probability r u (unless he is already in state N, in which case he stays in state N if he receives a signal in Pos); thus, we can think of r u as the probability that the agent moves up if he gets a positive signal. If the agent receives a signal in Neg, the agent moves to state i À 1 with probability r d (so r d is the probability of moving down if he gets a signal in Neg); if he receives a signal in I, the agent does not change states. Clearly, this automaton is easy for a human to implement (at least, if it does not have too many states). Because the state of nature can change, it is clearly not optimal to make the states 0 and N \"sticky.\" In particular, an optimal agent has to be able to react reasonably quickly to a change from G to B, so as to recognize that he should play S.  Erev et al. (2010)  describe contests that attempt to test various models of human decision making under uncertain conditions. In their scenarios, people were given a choice between making a safe move (that had a guaranteed constant payoff) and a \"risky\" move (which had a payoff that changed according to an unobserved action of other players), in the spirit of our S and R moves. They challenged researchers to present models that would predict behavior in these settings. The model that did best was called BI-Saw (bounded memory, inertia, sampling and weighting) model, suggested by  Chen, Liu, Chen, and Lee (2011) , itself a refinement of a model called I-Saw suggested by  Erev et al. (2010) . This model has three types of response mode: exploration, exploitation, and inertia. An I-Saw agent proceeds as follows: The agent tosses a coin. If it lands heads, the agent plays the action other than the one he played in the previous step (exploration); if it lands tails, he continues to do what he did in the previous step (inertia), unless the signal received in the previous round crosses a probabilistic \"surprise\" trigger (the lower the probability of the signal to be observed in the current state, the more likely the trigger is to be crossed); if the surprise trigger is crossed, then the agent plays the action with the best estimated subjective value, based on some sampling of the observations seen so far (exploitation). The major refinement suggested by BI-Saw involves adding a bounded memory assumption, whose main effect is a greater reliance on a small sample of past observations. The suggested family of automata incorporates all three behavior modes described by the I-Saw model. When the automaton is in state 0, the agent explores with constant probability by moving to state 1. In state i > 0, the agent continues to do what he did before (in particular, he stays in state i) unless he gets a \"meaningful\" signal (one in Neg or Pos), and even then he reacts only with some probability, so we have inertia-like behavior. If he does react, then he exploits the information that he has, which is carried by his current state; that is, he performs the action most appropriate according to his state. The state can be viewed as representing a sample of the last few signals (each state represents remembering seeing one more \"good\" signal), as in the BI-Saw model. Thus, our family of automata can be viewed as an implementation of the BI-Saw model using small, simple finite automata. These automata do quite well, both theoretically and in practice. Note that even if the agent had an oracle that told him exactly what nature's state would be at every round, if he performs optimally, he can get only x G in the rounds when nature is in state G, and 0 when it is in state B. In expectation, nature is in state G only half the time, so the optimal expected payoff is x G /2. The following result shows that if p goes to 0 sufficiently quickly, then the agent can achieve arbitrarily close to the theoretical optimum using an automaton of the form A[N, p exp , Pos, Neg, r u , r d ], even without the benefit of an oracle, by choosing the parameters appropriately. Let E p [A] denote the expected average utility of using the automaton A if the state of natures changes with probability p. Theorem 3.1  (Halpern et al. 2012)  Let Π and P exp be functions from N to (0,1] such that lim n?∞ nΠ(n) = lim n?∞ Π(n)/ P exp (n) = 0. Then for all settings S½p G 1 ; p While Theorem 3.1 gives theoretical support to the claim that automata of the form A[N, p exp , Pos, Neg, r u , r d ] are reasonable choices for a resource-bounded agent, it is also interesting to see how they do in practice, for relatively small values of N. The experimental evidence  (Halpern et al. 2012)  suggests that they will do well. For example, suppose for definiteness that p = 0.001, x G = 1, x B = À1 and there are four signals, 1,. . ., 4, which have probabilities 0.4, 0.3, 0.2, and 0.1, respectively, when the state of nature is G, and probabilities 0.1, 0.2, 0.3, and 0.4, respectively, when the state of nature is bad. Further suppose that we take signal 1 to be the \"good\" signal (i.e., we take Pos = {1}), take signal 4 to be the \"bad\" signal (i.e., we take Neg = {4}), and take r u = r d = 1. Experiments showed that using the optimal value of p exp (which is dependent on the number of states), an automaton with 5 states already gets an expected payoff of more than 0.4; even with 2 states, it gets an expected payoff of more than 0.15. Recall that even with access to an oracle that reveals when nature changes state, the best the agent can hope to get is 0.5. On the other hand, an agent that just plays randomly, or always plays G or always plays B, will get 0. These results are quite robust. For example, for N ≥ 5 the payoff does not vary much if we just use the optimum p exp for N = 5, instead of choosing the optimum value of p exp for each value of N. The bottom line here is that, by thinking in terms of the algorithms used by bounded agents, actions that may seem irrational can be viewed as quite rational responses, given resource limitations. \n Discussion and conclusion We have discussed two approaches for capturing resource-bounded agents. The first allows them to choose a TM to play for them, but charges them for the \"complexity\" of the choice; the second models agents as finite automata, and captures resource-boundedness by restricting the number of states of the automaton. In both cases, agents are assumed to maximize utility. Both approaches can be used to show that some systematic deviations from rationality (e.g., belief polarization) can be viewed as the result of resource-bounded agents making quite rational choices. We believe that the general idea of not viewing behavior as \"irrational,\" but rather the outcome of resource-bounded agents making rational choices, will turn out to be useful for explaining other systematic biases in decision making and, more generally, behavior in decision problems. We would encourage work to find appropriate cost models, and simple, easy-to-implement strategies with low computational cost that perform well in real scenarios. Note that the two approaches are closely related. For example, we can easily come up with a cost model and class of TMs that result in agents choosing a particular automaton with N states to play for them, simply by charging appropriately for the number of states. Which approach is used in a particular analysis depends on whether the interesting feature is the choice of the complexity function (which can presumably be tested experimentally) or specific details of the algorithm. We are currently exploring both approaches in the context of the behavior of agents in financial markets. In particular, we are looking for simple, easy-toimplement strategies that will explain human behavior in this setting. Pos, Neg, I of the signals, and constants r d and r u such that lim N!1 E pðNÞ ½A½N; P exp ðNÞ; Pos; Neg; r u ; r d ¼ x G 2 : B 1 ; . . .; p G k ; p B k ; x G ; x B , there exists a partition \n\t\t\t J. Y. Halpern, R. Pass, L. Seeman / Topics in Cognitive Science 6 (2014)", "date_published": "n/a", "url": "n/a", "filename": "Topics in Cognitive Science - 2014 - Halpern - Decision Theory with Resource‐Bounded Agents.tei.xml", "abstract": "There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by  Rubinstein (1986) , charges an agent for doing costly computation; the second, initiated by  Neyman (1985) , does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a decision problem to be Turing machines, and charge players for the \"complexity\" of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases.", "id": "1b38f83e048b09b31f1c3306fc8ff001"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Stuart J Russell", "Devika Subramanian"], "title": "Provably Bounded-Optimal Agents", "text": "Introduction Since before the beginning of arti cial intelligence, philosophers, control theorists and economists have l o o k ed for a satisfactory de nition of rational behaviour. This is needed to underpin theories of ethics, inductive learning, reasoning, optimal control, decision-making, and economic modelling.  Doyle 1983  has proposed that AI itself be de ned as the computational study of rational behaviour|e ectively equating rational behaviour with intelligence. The role of such de nitions in AI is to ensure that theory and practice are correctly aligned. If we de ne some property P, then we hope to be able to design a system that provably possesses property P. Theory meets practice when our systems exhibit P in reality. F urthermore, that they exhibit P in reality should be something that we actually care about. In a sense, the choice of what P to study determines the nature of the eld. There are a number of possible choices for P: Perfect rationality: the classical notion of rationality in economics and philosophy. A perfectly rational agent acts at every instant i n s u c h a w ay as to maximize its expected utility, given the information it has acquired from the environment. Since action selection requires computation, and computation takes time, perfectly rational agents do not exist for non-trivial environments. Calculative rationality: the notion of rationality studied in AI. A calculatively rational agent e v entually returns what would have been the rational choice at the beginning of its deliberation. There exist systems such as in uence diagram evaluators that exhibit this property for a decision-theoretic de nition of rational choice, and systems such as nonlinear planners that exhibit it for a logical de nition of rational choice. This is assumed to be an interesting property for a system to exhibit since it constitutes an in-principle\" capacity to do the right thing. Calculative rationality is of limited value in practice, because the actual behaviour exhibited by such systems is absurdly far from being rational; for example, a calculatively rational chess program will choose the right m o ve, but may take 1 0 50 times too long to do so. As a result, AI systembuilders often ignore theoretical developments, being forced to rely on trial-and-error engineering to achieve their goals. Even in simple domains such a s c hess, there is little theory for designing and analysing high-performance programs. Metalevel rationality: a natural response to the problems of calculative rationality. A metalevel rational system optimizes over the object-level computations to be performed in the service of selecting actions. In other words, for each decision it nds the optimal combination of computation-sequence-plus-action, under the constraint that the action must be selected by the computation. Full metalevel rationality i s seldom useful because the metalevel computations themselves take time, and the metalevel decision problem is often more di cult than the object-level problem. Simple approximations to metalevel rationality h a ve proved useful in practice|for example, metalevel policies that limit lookahead in chess programs|but these engineering expedients merely serve to illustrate the lack of a theoretical basis for agent design. Bounded optimality: a bounded optimal agent behaves as well as possible given its computational resources. Bounded optimality speci es optimal programs rather than optimal actions or optimal computation sequences. Only by the former approach can we a void placing constraints on intelligent agents that cannot be met by a n y program. Actions and computations are, after all, generated by programs, and it is over programs that designers have control. We make three claims: 1. A system that exhibits bounded optimality is desirable in reality. 2. It is possible to construct provably bounded optimal programs. 3. Arti cial intelligence can be usefully characterized as the study of bounded optimality, particularly in the context of complex task environments and reasonably powerful computing devices. The rst claim is unlikely to be controversial. This paper supports the second claim in detail. The third claim may, o r m a y not, stand the test of time. We begin in section 2 with a necessarily brief discussion of the relationship between bounded optimality and earlier notions of rationality. W e note in particular that some important distinctions can be missed without precise de nitions of terms. Thus in section 3 we provide formal de nitions of agents, their programs, their behaviour and their rationality. Together with formal descriptions of task environments, these elements allow u s t o p r o ve that a given agent exhibits bounded optimality. Section 4 examines a class of agent architectures for which the problem of generating bounded optimal con gurations is e ciently soluble. The solution involves a class of interesting and practically relevant optimization problems that do not appear to have been addressed in the scheduling literature. We illustrate the results by showing how the throughput of an automated mail-sorting facility might be improved. Section 5 initiates a discussion of how bounded optimal con gurations might be learned from experience in an environment. In section 6, we de ne a weaker property, asymptotic bounded optimality ABO, that may be more robust and tractable than the strict version of bounded optimality. In particular, we can construct universal ABO programs. A program is universally ABO if it is ABO regardless of the speci c form of time dependence of the utility function.  1  Universal ABO programs can therefore be used as building blocks for more complex systems. We conclude with an assessment of the prospects for further development of this approach to arti cial intelligence. \n Historical Perspective The classical idea of perfect rationality, which developed from Aristotle's theories of ethics, work by Arnauld and others on choice under uncertainty, and Mill's utilitarianism, was put on a formal footing in decision theory by  Ramsey 1931 and vonNeumann and Morgernstern 1947.  It stipulates that a rational agent always act so as to maximize its expected utility. The expectation is taken according to the agent's own beliefs; thus, perfect rationality d o e s not require omniscience. In arti cial intelligence, the logical de nition of rationality, known in philosophy as the practical syllogism\", was put forward by  McCarthy 1958 , and reiterated strongly by  Newell 1981 . Under this de nition, an agent should take a n y action that it believes is guaranteed to achieve a n y of its goals. If AI can be said to have had a theoretical foundation, then this de nition of rationality has provided it. McCarthy believed, probably correctly, that in the early stages of the eld it was important to concentrate on epistemological adequacy\" before heuristic adequacy\" | that is, capability in principle rather than in practice. The methodology that has resulted involves designing programs that exhibit calculative rationality, and then using various speedup techniques and approximations in the hope of getting as close as possible to perfect rationality. Our belief, albeit unproven, is that the simple agent designs that ful ll the speci cation of calculative rationality m a y not provide good starting points from which to approach bounded optimality. Moreover, a theoretical foundation based on calculative rationality cannot provide the necessary guidance in the search. It is not clear that AI would have e m barked on the quest for calculative rationality had it not been operating in the halcyon days before formal intractability results were discovered. One response to the spectre of complexity has been to rule it out of bounds.  Levesque and Brachman 1987  suggest limiting the complexity of the environment so that calculative and perfect rationality coincide. Doyle and Patil 1991 argue strongly against this position. Economists have used perfect rationality as an abstract model of economic entities, for the purposes of economic forecasting and designing market mechanisms. This makes it possible to prove theorems about the properties of markets in equilibrium. Unfortunately, as Simon 1982 pointed out, real economic entities have limited time and limited powers of deliberation. He proposed the study of bounded r ationality, i n vestigating : : : the shape of a system in which e ectiveness in computation is one of the most important w eapons of survival.\" Simon's work focussed mainly on satis cing designs, which deliberate until reaching some solution satisfying a preset aspiration level.\" The results have descriptive v alue for modelling various actual entities and policies, but no general prescriptive framework for bounded rationality w as developed. Although it proved possible to calculate optimal aspiration levels for certain problems, no structural variation was allowed in the agent design. In the theory of games, bounds on the complexity of players have become a topic of intense interest. For example, it is a troubling fact that defection is the only equilibrium strategy for unbounded agents playing a xed number of rounds of the Prisoners' Dilemma game. Neyman's theorem  Neyman, 1985 , recently proved by P apadimitriou and Yannakakis 1994, shows that an essentially cooperative equilibrium exists if each agent i s a nite automaton with a number of states that is less than exponential in the number of rounds. This is essentially a bounded optimality result, where the bound is on space rather than on speed of computation. This type of result is made possible by a shift from the problem of selecting actions to the problem of selecting programs. I. J. Good 1971 distinguished between perfect or type I\" rationality, and metalevel or type II\" rationality. He de nes this as the maximization of expected utility taking into account deliberation costs.\" Simon 1976 also says: The global optimization problem is to nd the least-cost or best-return decision, net of computational costs.\" Although type II rationality seems to be a step in the right direction, it is not entirely clear whether it can be made precise in a way that respects the desirable intuition that computation is important. We will try one interpretation, although there may be others.  2  The key issue is the space over which the maximization\" or optimization\" occurs. Both Good and Simon seem to be referring to the space of possible deliberations associated with a particular decision. Conceptually, there is an object-level machine\" that executes a sequence of computations under the control of a meta-level machine.\" The outcome of the sequence is the selection of an external action. An agent exhibits type II rationality if at the end of its deliberation and subsequent action, its utility is maximized compared to all possible deliberate act pairs in which it could have engaged. For example, Good discusses one possible application of type II rationality i n c hess programs. In this case, the object-level steps are node expansions in the game tree, followed by backing up of leaf node evaluations to show the best move. For simplicity w e will assume a per-move time limit. Then a type II rational agent will execute whichever sequence of node expansions chooses the best move, of all those that nish before the time limit.  3  Unfortunately, the computations required in the metalevel machine\" to select the object-level deliberation may be extremely expensive. Good actually proposes a fairly simple and nearly practical metalevel decision procedure for chess, but it is far from optimal. It is hard to see how a t ype II rational agent could justify executing a suboptimal object-level computation sequence if we limit the scope of the optimization problem to a single decision. The di culty can only be resolved by thinking about the design of the agent program, which generates an unbounded set of possible deliberations in response to an unbounded set of circumstances that may arise during the life of the agent. Philosophy has also seen a gradual evolution in the de nition of rationality. There has been a shift from consideration of act utilitarianism | the rationality of individual acts | to rule utilitarianism, or the rationality of general policies for acting. This shift has been caused by di culties with individual versus societal rationality, rather than any consideration of the di culty of computing rational acts. Some consideration has been given more recently to the tractability of general moral policies, with a view to making them understandable and usable by persons of average intelligence  Brandt, 1953 . Cherniak 1986  has suggested a de nition of minimal rationality\", specifying lower bounds on the reasoning powers of any rational agent, instead of upper bounds. A philosophical proposal generally consistent with the notion of bounded optimality can be found in Dennett's Moral First Aid Manual\" 1986. Dennett explicitly discusses the idea of reaching equilibrium within the space of decision procedures. He uses as an example the PhD admissions procedure of a philosophy department. He concludes, as do we, that the best procedure may be neither elegant nor illuminating. The existence of such a procedure, and the process of reaching it, are the main points of interest. Many researchers in AI, some of whose work is discussed below, have w orked on the problem of designing agents with limited computational resources. The 1989 AAAI Symposium on AI and Limited Rationality F ehling & Russell, 1989 contains an interesting variety o f w ork on the topic. Much of this work is concerned with metalevel rationality. Metareasoning | reasoning about reasoning | is an important technique in this area, since it enables an agent to control its deliberations according to their costs and bene ts. Combined with the idea of anytime  Dean & Boddy, 1988  or exible algorithms  Horvitz, 1987 , that return better results as time goes by, a simple form of metareasoning allows an agent to behave w ell in a real-time environment. A simple example is provided by iterative-deepening algorithms used in game-playing.  Breese and Fehling 1990  apply similar ideas to controlling multiple decision procedures. Russell and Wefald 1989 give a general method for precompiling certain aspects of metareasoning so that a system can eciently estimate the e ects of individual computations on its intentions, giving ne-grained control of reasoning. These techniques can all be seen as approximating metalevel rationality; they provide useful insights into the general problem of control of reasoning, but there is no reason to suppose that the approximations used are optimal in any sense. The intuitive notion of bounded optimality seems to have become current in the AI community in the mid-1980's. Horvitz 1987 uses the term bounded optimality to refer to the optimization of computational utility given a set of assumptions about expected problems and constraints in reasoning resources.  \" Russell and Wefald 1991  say that an agent exhibits bounded optimality for a given task environment if its program is a solution to the constrained optimization problem presented by its architecture.\" Recent w ork by  Etzioni 1989 and Zilberstein 1991  can be seen as optimizing over a wellde ned set of agent designs, thereby making the notion of bounded optimality more precise. In the next section, we build a suitable set of general de nitions from the ground up, so that we can begin to demonstrate examples of provably bounded optimal agents. \n Agents, Architectures and Programs Intuitively, a n agent is just a physical entity that we wish to view in terms of its perceptions and actions. What counts in the rst instance is what it does, not necessarily what it thinks, or even whether it thinks at all. This initial refusal to consider further constraints on the internal workings of the agent such as that it should reason logically, for example helps in three ways: rst, it allows us to view such cognitive faculties\" as planning and reasoning as occurring in the service o f nding the right thing to do; second, it makes room for those among us  Agre & Chapman, 1987; Brooks, 1986  who take the position that systems can do the right thing without such cognitive faculties; third, it allows more freedom to consider various speci cations, boundaries and interconnections of subsystems. We begin by de ning agents and environments in terms of the actions and percepts that they exchange, and the sequence of states they go through. The agent is described by a n agent function from percept sequences to actions. This treatment is fairly standard see, e.g.,  Genesereth & Nilsson, 1987.  We then go inside\" the agent t o l o o k a t t h e agent program that generates its actions, and de ne the implementation\" relationship between a program and the corresponding agent function. We consider performance measures on agents, and the problem of designing agents to optimize the performance measure. \n Specifying agents and environments An agent can be described abstractly as a mapping the agent function from percept sequences to actions. Let O be the set of percepts that the agent can receive a t a n y instant, and A be the set of possible actions the agent can carry out in the external world. Since we are interested in the behaviour of the agent o ver time, we i n troduce a set of time points or instants, T. The set T is totally ordered by the relation with a unique least element. Without loss of generality, w e let T be the set of non-negative i n tegers. The percept history of an agent is a sequence of percepts indexed by time. We de ne the set of percept histories to be O T = fO T : T ! Og. The pre x of a history O T 2 O T till time t is denoted O t and is the projection of O T on 0::t . We can de ne the set of percept history pre xes as O t = fO t j t 2 T; O T 2 O T g. Similarly, w e de ne the set of action histories A T = fA T : T ! Ag. The set of action history pre xes is A t , de ned as the set of projections A t of histories A T 2 A T . De nition 1 Agent function: a mapping f : O t ! A where A T t = fO t Note that the agent function is an entirely abstract entity, unlike the agent program that implements it. Note also that the output\" of the agent function for a given percept sequence may b e a n ull action, for example if the agent is still thinking about what to do. The agent function speci es what the agent d o e s a t e a c h time step. This is crucial to the distinction between perfect rationality and calculative rationality. Agents live i n e n vironments. The states of an environment E are drawn from a set X. The set of possible state trajectories is de ned as X T = fX T : T ! Xg. The agent does not necessarily have full access to the current state X T t, but the percept received by the agent does depend on the current state through the perceptual ltering function f p . The e ects of the agent's actions are represented by the environment's transition function f e , which speci es the next state given the current state and the agent's action. An environment i s therefore de ned as follows: De nition 2 Environment E: a set of states X with a distinguished initial state X 0 , a transition function f e and a perceptual lter function f p such that X T 0 = X 0 X T t + 1 = f e A T t; X T t O T t = f p X T t The state history X T is thus determined by the environment and the agent function. We use the notation e ectsf;E to denote the state history generated by an agent function f operating in an environment E. We will also use the notation E;A t to denote the state history generated by applying the action sequence A t starting in the initial state of environment E. Notice that the environment is discrete and deterministic in this formulation. We can extend the de nitions to cover non-deterministic and continuous environments, but at the cost of additional complexity in the exposition. None of our results depend in a signi cant way on discreteness or determinism. \n Specifying agent implementations We will consider a physical agent as consisting of an architecture and a program. The architecture is responsible for interfacing between the program and the environment, and for running the program itself. With each architecture M, w e associate a nite programming language L M , which is just the set of all programs runnable by the architecture. An agent program is a program l 2 L M that takes a percept as input and has an internal state drawn from a set I with initial state i 0 . The initial internal state depends on the program l, but we will usually suppress this argument. The set of possible internal state histories is I T = fI T : T ! Ig. The pre x of an internal state history I T 2 I T till time t is denoted I t and is the projection of I T on 0::t . De nition 3 An a r chitecture M is a xed interpreter for an agent program that runs the program for a single time step, updating its internal state and generating an action: M : L M I O ! I A where hI T t + 1 ; A T ti = Ml;I T t; O T t Thus, the architecture generates a stream of actions according to the dictates of the program. Because of the physical properties of the architecture, running the program for a single time step results in the execution of only a nite number of instructions. The program may often fail to reach a decision\" in that time step, and as a result the action produced by the architecture may b e n ull or the same as the previous action, depending on the program design. \n Relating agent speci cations and implementations We can now relate agent programs to the corresponding agent functions. We will say that an agent program l running on a machine M implements the agent function Agentl;M. The agent function is constructed in the following de nition by specifying the action sequences produced by l running on M for all possible percept sequences. Note the importance of the Markovian\" construction using the internal state of the agent to ensure that actions can only be based on the past, not the future. De nition 4 A p r ogram l running on M implements the agent function f = Agentl;M, de ned as follows. For any environment E = X; f e ; f p , fO t = A T t where hI T t + 1 ; A T ti = Ml; I T t; O T t O T t = f p X T t X T t + 1 = f e A T t; X T t X T 0 = X 0 I T 0 = i 0 Although every program l induces a corresponding agent function Agentl;M, the action that follows a given percept is not necessarily the agent's response\" to that percept; because of the delay incurred by deliberation, it may only re ect percepts occurring much earlier in the sequence. Furthermore, it is not possible to map every agent function to an implementation l 2 L M . We can de ne a subset of the set of agent functions f that are implementable on a given architecture M and language L M : FeasibleM = ff j 9 l 2 L M ; f = Agentl;Mg Feasibility is related to, but clearly distinct from, the notion of computability. Computability refers to the existence of a program that eventually returns the output speci ed by a function, whereas feasibility refers to the production of the output at the appropriate point in time. The set of feasible agent functions is therefore much smaller than the set of computable agent functions. \n Performance measures for agents To e v aluate an agent's performance in the world, we de ne a real-valued utility function U on state histories: U : X T ! The utility function should be seen as external to the agent and its environment. It de nes the problem to be solved by the designer of the agent. Some agent designs may incorporate an explicit representation of the utility function, but this is by no means required. We will use the term task environment to denote the combination of an environment and a utility function. Recall that the agent's actions drive the environment E through a particular sequence of states in accordance with the function e ectsf;E. We can de ne the value of an agent function f in the environment E as the utility of the state history it generates: V f;E = Ue ectsf;E If the designer has a set E of environments with a probability distribution p over them, instead of a single environment E, then the value of the agent i n E is de ned as the expected value over the elements of E. By a slight abuse of notation, V f;E = X E2E pEV f;E We can assign a value V l;M;E to a program l executed by the architecture M in the environment E simply by looking at the e ect of the agent function implemented by the program: V l;M;E = V Agentl;M; E = Ue ectsAgentl;M; E As above, we can extend this to a set of possible environments as follows: V l;M;E = X E2E pEV l;M;E \n Perfect rationality and bounded optimality As discussed in Section 2, a perfectly rational agent selects the action that maximizes its expected utility, given the percepts so far. In our framework, this amounts to an agent function that maximizes V f;E o ver all possible agent functions. De nition 5 A p erfectly rational agent for a set E of environments has an agent function f opt such that f opt = argmax f V f;E This de nition is a persuasive speci cation of an optimal agent function for a given set of environments, and underlies several recent projects in intelligent agent design  Dean & W ellman,1991; Doyle, 1988; Hansson & Mayer, 1989 . A direct implementation of this speci cation, which ignores the delay incurred by deliberation, does not yield a reasonable solution to our problem the calculation of expected utilities takes time for any real agent. In terms of our simple formal description of agents introduced above, it is easy to see where the di culty has arisen. In designing the agent program, logicists and decision theorists have concentrated on specifying an optimal agent function f opt in order to guarantee the selection of the best action history. The function f opt is independent of the architecture M. Unfortunately, no real program in L M implements this function in a non-trivial environment, because optimal actions cannot usually be computed before the next percept arrives. That is, quite frequently, f opt 6 2 FeasibleM. Suppose the environment consists of games of chess under tournament rules against some population of human grandmasters, and suppose M is some standard personal computer. Then f opt describes an agent that always plays in such a w ay as to maximize its total expected points against the opposition, where the maximization is over the moves it makes. We claim that no possible program can play this way. It is quite possible, using depth-rst alpha-beta search to termination, to execute the program that chooses say the optimal minimax move in each situation, but the agent function induced by this program is not the same as f opt . In particular, it ignores such percepts as the dropping of its ag indicating a loss on time. The trouble with the perfect rationality de nition arose because of unconstrained optimization over the space of f's in the determination of f opt , without regard to feasibility. Similarly, metalevel rationality assumes unconstrained optimization over the space of deliberations. To escape this quandary, w e propose a machine-dependent standard of rationality, in which w e maximize V over the implementable set of agent functions FeasibleM. That is, we impose optimality constraints on programs rather than on agent functions or deliberations. De nition 6 A b ounded-optimal agent with architecture M for a set E of environments has an agent program l opt such that l opt = argmax l2L M V l;M;E We can see immediately that this speci cation avoids the most obvious problems with Type I and Type II rationality. Consider our chess example, and suppose the computer has a total program memory of 8 megabytes. Then there are 2 2 26 possible programs that can be represented in the machine, of which a m uch smaller number play legal chess. Under tournament conditions, one or more of these programs will have the best expected performance. Each is a suitable candidate for l opt . T h us bounded optimality is, by de nition, a feasible speci cation; moreover, a program that achieves it is highly desirable. We are not yet ready to announce the identity o f l opt for chess on an eight-megabyte PC, so we will begin with a more restricted problem. \n Provably Bounded-Optimal Agents In order to construct a provably bounded optimal agent, we m ust carry out the following steps: Specify the properties of the environment in which actions will be taken, and the utility function on the behaviours. Specify a class of machines on which programs are to be run. Propose a construction method. Prove that the construction method succeeds in building bounded optimal agents. The methodology is similar to the formal analysis used in the eld of optimal control, which studies the design of controllers agents for plants environments. In optimal control theory, a controller is viewed as an essentially instantaneous implementation of an optimal agent function. In contrast, we focus on the computation time required by the agent, and the relation between computation time and the dynamics of the environment. \n Episodic, real-time task environments In this section, we will consider a restricted class of task environments which w e call episodic environments. In an episodic task environment, the state history generated by the actions of the agent can be considered as divided into a series of episodes, each of which is terminated by an action. Let A ? A be a distinguished set of actions that terminate an episode. The utility of the complete history is given by the sum of the utilities of each episode, which is determined in turn by the state sequence. After each A 2 A ? , the environment resets\" to a state chosen at random from a stationary probability distribution P init . In order to include the e ects of the choice of A in the utility of the episode, we notionally divide the environment state into a con guration\" part and a value\" part, such that the con guration part determines the state transitions while the value part determines the utility of a state sequence. Actions in A ? reset the con guration part, while their value\" is recorded in the value part. These restrictions mean that each episode can be treated as a separate decision problem, and translate into the following property: if agent program l 1 has higher expected utility on individual episodes than agent l 2 , it will have higher expected utility in the corresponding episodic task environment. A real-time task environment is one in which the utility of an action depends on the time at which it is executed. Usually, this dependence will be su ciently strong to make calculative rationality an unacceptably bad approximation to perfect rationality. An automated mail sorter 4 provides an illustrative example of an episodic task environment see Figure  1 . Such a machine scans handwritten or printed addresses zipcodes on mail pieces and dispatches them to appropriate bins. Each episode starts with the arrival of a new mail piece and terminates with the execution of the physical action recommended by the sorter: routing of the piece to a speci c bin. The con guration part\" of the environment corresponds to the letter feeder side, which provides a new, randomly selected letter after the previous letter is sorted. The value part\" of the state corresponds to the state of the receiving bins, which determines the utility of the process. The aim is to maximize the accuracy of sorting while minimizing the reject percentage and avoiding jams. A jam occurs if the current piece is not routed to the appropriate bin, or rejected, before the arrival of the next piece. We n o w provide formal de nitions for three varieties of real-time task environments: xed deadlines, xed time cost and stochastic deadlines. Taking an action in A ? at any time before the deadline results in the same utility: U E;A t 1 = U E;A t d ,1 2 A T 1 t where \" denotes sequence c oncatenation, t t d , A T 1 t 2 A ? , and A t,1 1 and A the utilities di er by the di erence in time cost: U E;A t 2 2 = U E;A t 1 1 , ct 2 , t 1 Strictly speaking, there are no task environments with xed time cost. Utility v alues have a nite range, so one cannot continue incurring time costs inde nitely. F or reasonably short times and reasonably small costs, a linear utility penalty is a useful approximation. \n Stochastic deadlines While xed-deadline and xed-cost task environments occur frequently in the design of real-time systems, uncertainty about the time-dependence of the utility function is more common. It also turns out to be more interesting, as we see below. A stochastic deadline is represented by uncertainty concerning the time of occurrence of a xed deadline. In other words, the agent has a probability distribution p d for the deadline time t d . We assume that the deadline must come eventually, so that P t2T p d t = 1 . We also de ne the cumulative deadline distribution P d . If the deadline does not occur at a known time, then we need to distinguish between two cases: The agent receives a percept, called a herald  Dean & Boddy, 1988 , which announces an impending deadline. We model this using a distinguished percept O d : O T t d = O d If the agent responds immediately, then it meets the deadline.\" No such percept is available, in which case the agent i s w alking blindfolded towards the utility cli . By deliberating further, the agent risks missing the deadline but may improve its decision quality. An example familiar to most readers is that of deciding whether to publish a paper in its current form, or to embellish it further and risk being scooped.\" We do not treat this case in the current paper. Formally, the stochastic deadline case is similar to the xed deadline case, except that t d is drawn from the distribution p d . The utility of executing an action history pre x A t in E is the expectation of the utilities of that state history pre x over the possible deadline times. De nition 9 Stochastic deadline: A task environment class hE; U i of xed-deadline task environments has a stochastic deadline distributed a c cording to p d if, for any action history pre x A t , U E; A t = X t 0 2T p d t 0 U E t 0 ; A t where hE t 0 ; U i is a task environment in hE; U i with a xed d e adline at t 0 . The mail sorter example is well described by a stochastic deadline. The time between the arrival of mail pieces at the image processing station is distributed according to a density function p d , which will usually be Poisson. \n Agent programs and agent architecture We consider simple agent programs for episodic task environments, constructed from elements of a set R = fr 1 ; : : : ; r n g of decision procedures or rules. Each decision procedure recommends but does not execute an action A i 2 A ? , and an agent program is a xed sequence of decision procedures. For our purposes, a decision procedure is a black b o x with two parameters: a run time t i 0, which i s a n i n teger that represents the time taken by the procedure to compute an action. a quality q i 0, which is a real number. This gives the expected reward resulting from executing its action A i at the start of an episode: q i = U E;A i 1 Let M J denote an agent architecture that executes decision procedures in the language J . Let t M denote the maximum runtime of the decision procedures that can be accommodated in M. For example, if the runtime of a feedforward neural network is proportional to its size, then t M will be the runtime of the largest neural network that ts in M. The architecture M executes an agent program s = s 1 : : : s m by running each decision procedure in turn, providing the same input to each as obtained from the initial percept. When a deadline arrives at a xed time t d , or heralded by the percept O d , or when the entire sequence has been completed, the agent selects the action recommended by the highest-quality procedure it has executed: Ms; I T t d ; O T t d = hi 0 ; actionI T t d i Ms; I T t s ; O T t s = hi 0 ; actionI T t s i where t s = P s i 2s t i 2 Ms; I T t; O d = hi 0 ; actionI T ti where M updates the agent's internal state history I T t such that actionI T t is the action recommended by a completed decision procedure with the highest quality. When this action is executed, the internal state of the agent is re-initialized to i 0 . This agent design works in all three of the task environment categories described above. Next we derive the value V s; M; E of an agent program s in environment E running on M for the three real-time regimes and show h o w to construct bounded optimal agents for these task environments. \n Bounded optimality with xed deadlines From Equation  2 , we know that the agent picks the action in A ? recommended by the decision procedure r with the highest quality that is executed before the deadline t d arrives. Let s 1 : : : s j be the longest pre x of the program s such that P j i=1 t i t d . F rom De nition 7 and Equation  1 , it follows that V s; M; E = Q j 3 where Q i = maxfq 1 ; : : : ; q i g. Given this expression for the value of the agent program, we can easily show the following: Theorem 1 Let r = arg max r i 2 R;t i t d q i . The singleton sequence r is a bounded optimal program for M in an episodic task environment with a known deadline t d . That is, the best program is the single decision procedure of maximum quality whose runtime is less than the deadline. \n Bounded optimality with xed time cost From Equation  2 , we know that the agent picks the action in A ? recommended by the best decision procedure in the sequence, since M runs the entire sequence s = s 1 : : : s m when there is no deadline. From De nition 8 and Equation  1 , we h a ve V s; M; E = Q m , c m X i=1 t i 4 Given this expression for the value of the agent program, we can easily show the following: Theorem 2 Let r = arg max r i 2 R q i ,ct i . The singleton sequence r is a bounded optimal program for M in an episodic task environment with a xed time cost c. That is, the optimal program is the single decision procedure whose quality, net of time cost, is highest. \n Bounded optimality with stochastic deadlines With a stochastic deadline distributed according to p d , the value of an agent program s = s 1 : : : s m is an expectation. From De nition 9, we can calculate this as P t2T p d tV s; M; E t , where hE t ; U i is a task environment with a xed deadline at t. After substituting for V s; M; E t from Equation 3, this expression simpli es to a summation, over the procedures in the sequence, of the probability o f i n terruption after the i th procedure in the sequence multiplied by the quality of the best completed decision procedure: V s V s; M; E = m X i=1 P d P i+1 j=1 t j , P d P i j=1 t j Q i 5 where P d t = R t ,1 p d t 0 dt 0 and P d t = 1 for t P m i=1 t i . A simple example serves to illustrate the value function. Consider R = fr 1 ; r 2 ; r 3 g. The rule r 1 has a quality of 0.2 and needs 2 seconds to run: we will represent this by r 1 = 0 :2; 2. The other rules are r 2 = 0 :5; 5; r 3 = 0 :7; 7. The deadline distribution function p d is a uniform distribution over 0 to 10 seconds. The value of the sequence r 1 r 2 r 3 is V r 1 r 2 r 3 = :7 , :2 :2 + 1 , :7 :5 + 1 , 1 :  De nition 10 Performance p r o le: Fo r a s e quence s, the performance p r o le Q s t gives the quality of the action returned if the agent is interrupted a t t: Q s t = maxfq i : i X j=1 t j tg For a uniform deadline density function, the value of a sequence is proportional to the area under the performance pro le up to the last possible interrupt time. Note that the height of the pro le during the interval of length t i while rule i is running is the quality o f the best of the previous rules. From De nition 10, we h a ve the following obvious property: Lemma 1 The performance p r o le of any sequence is monotonically nondecreasing. It is also the case that a sequence with higher quality decisions at all times is a better sequence: Lemma 2 If 8t Q s 1 t Q s 2 t, then V s 1 V s 2 . In this case we s a y that Q s 1 dominates Q s 2 . We can use the idea of performance pro les to establish some useful properties of optimal sequences. Lemma 3 There exists an optimal sequence that is sorted in increasing order of q's. Without Lemma 3, there are P n i=1 i! possible sequences to consider. The ordering constraint eliminates all but 2 n sequences. It also means that in proofs of properties of sequences, we n o w need consider only ordered sequences. In addition, we can replace Q i in Equation 5 by q i . The following lemma establishes that a sequence can always be improved by the addition of a better rule at the end: Lemma 4 For every sequence s = s 1 : : : s m sorted in increasing order of quality, and single step z with q z q s m , V sz V s. Corollary 1 There exists an optimal sequence ending with the highest-quality rule in R. The following lemma re ects the obvious intuition that if one can get a better result in less time, there's no point spending more time to get a worse result: Lemma 5 There exists an optimal sequence whose rules are in nondecreasing order of t i . We n o w apply these preparatory results to derive algorithms that construct bounded optimal programs for various deadline distributions. \n General distributions For a general deadline distribution, the dynamic programming method can be used to obtain an optimal sequence of decision rules in pseudo-polynomial time. We construct an optimal sequence by using the de nition of V s; M; E in Equation  5 . Optimal sequences generated by the methods are ordered by q i , in accordance with Lemma 3. We construct the table Si; t, where each e n try in the table is the highest value of any sequence that ends with rule r i at time t. W e assume the rule indices are arranged in increasing order of quality, and t ranges from the start time 0 to the end time L = P r i 2R t i . The update rule is: Si; t = max k2 0:::i,1 Sk;t, t i + q i , q k 1 , P d t with boundary condition Si; 0 = 0 for each rule i and S0; t = 0 for each time t From Corollary 1, we can read o the best sequence from the highest value in row n of the matrix S. Theorem 3 The DP algorithm computes an optimal sequence in time On 2 L where n is the number of decision procedures in R. The dependence on L in the time complexity of the DP algorithm means that the algorithm is not polynomial in the input size. Using standard rounding and scaling methods, however, a fully polynomial approximation scheme can be constructed. Although we d o n o t have a hardness proof for the problem, John Binder 1994 has shown that if the deadline distribution is used as a constant-time oracle for nding values of Pt, any algorithm will require an exponential number of calls to the oracle in the worst case. \n Long uniform distributions If the deadline is uniformly distributed over a time interval greater than the sum of the running times of the rules, we will call the distribution a long uniform distribution. Consider the rule sequence s = s 1 : : : s m drawn from the rule set R. With a long uniform distribution, the probability that the deadline arrives during rule s i of the sequence s is independent o f the time at which s i starts. This permits a simpler form of Equation 5: V s; M; E = P m,1 i=1 P d t i+1 q i + q m 1 , P m i=1 P d t i 6 To derive an optimal sequence under a long uniform distribution, we obtain a recursive speci cation of the value of a sequence as with a 2 R and s = s 1 : : : s m being some sequence in R. V as; M; E = V s; M; E + q a P d t 1 , q m P d t a 7 This allows us to de ne a dynamic programming scheme for calculating an optimal sequence using a state function Si; j denoting the highest value of a rule sequence that starts with rule i and ends in rule j. F rom Lemma 3 and Equation  7 , the update rule is: Si; j = max i kj Sk;j + P d t k q i , P d t i q j 8 with boundary condition Si; i = 1 , P d t i q i 9 From Corollary 1, we know that an optimal sequence for the long uniform distribution ends in r n , the rule with the highest quality i n R. Thus, we only need to examine Si; n; 1 i n. Each e n try requires On computation, and there are n entries to compute. Thus, the optimal sequence for the long uniform case can be calculated in On 2 . Theorem 4 An optimal sequence o f d e cision procedures for a long uniform deadline distribution can be determined i n On 2 time where n is the number of decision procedures in R. \n Short uniform distributions When P n i=1 P d t i 1, for a uniform deadline distribution P d , w e call it short. This means that some sequences are longer than the last possible deadline time, and therefore some rules in those sequences have no possibility of executing before the deadline. For such sequences, we cannot use Equation 7 to calculate V s. However, any such sequence can be truncated by removing all rules that would complete execution after the last possible deadline. The value of the sequence is una ected by truncation, and for truncated sequences the use of Equation 7 is justi ed. Furthermore, there is an optimal sequence that is a truncated sequence. Since the update rule 8 correctly computes Si; j for truncated sequences, we can use it with short uniform distributions provided we add a check to ensure that the sequences considered are truncated. Unlike the long uniform case, however, the identity of the last rule in an optimal sequence is unknown, so we need to compute all n 2 entries in the Si; j table. Each e n try computation takes On time, thus the time to compute an optimal sequence is On 3 . Theorem 5 An optimal sequence o f d e cision procedures for a short uniform deadline distribution can be determined i n On 3 time where n is the number of decision procedures in R. \n Exponential distributions For an exponential distribution, P d t = 1 ,e , t . Exponential distributions allow an optimal sequence to be computed in polynomial time. Let p i stand for the probability that rule i is interrupted, assuming it starts at 0. Then p i = P d t i = 1 , e , t i : For the exponential distribution, V s; M; E simpli es out as: V s; M; E = m,1 X i=1 h i j=1 1 , p j i p i+1 q i + h m j=1 1 , p j i q m This yields a simple recursive speci cation of the value V as; M; E of a sequence that begins with the rule a: V as; M; E = 1 , p a p 1 q a + 1 , p a V s; M; E We will use the state function Si; j which represents the highest value of any rule sequence starting with i and ending in j. Si; j = max i kj 1 , p i p k q i + 1 , p i Sk;j with boundary condition Si; i = q i 1 , p i . For any given j, Si; j can be calculated in On 2 . From Corollary 1, we know that there is an optimal sequence whose last element i s the highest-valued rule in R. Theorem 6 An optimal sequence o f d e cision procedures for an exponentially distributed stochastic deadline can be determined i n On 2 time where n is the number of decision procedures in R. The proof is similar to the long uniform distribution case. \n Simulation results for a mail-sorter The preceding results provide a set of algorithms for optimizing the construction of an agent program for a variety of general task environment classes. In this section, we illustrate these results and the possible gains that can be realized in a speci c task environment, namely, a simulated mail-sorter. First, let us be more precise about the utility function U on episodes. There are four possible outcomes; the utility of outcome i is u i . 1. The zipcode is successfully read and the letter is sent to the correct bin for delivery. 2. The zipcode is misread and the letter goes to the wrong bin. 3. The letter is sent to the reject bin. 4. The next letter arrives before the recognizer has nished, and there is a jam. Since letter arrival is heralded, jams cannot occur with the machine architecture given in Equation  2 . Without loss of generality, w e set u 1 = 1 :0 and u 2 = 0 :0. If the probability of a rule recommending a correct destination bin is p i , then q i = p i u 1 + 1 , p i u 2 = p i . W e assume that u 2 u 3 , hence there is a threshold probability below which the letter should be sent to the reject bin instead. We will therefore include in the rule set R a rule r reject that has zero runtime and recommends rejection. The sequence construction algorithm will then automatically exclude rules with quality l o wer than q reject = u 3 . The overall utility for an episode is chosen to be a linear combination of the quality of sorting q i , the probability o f rejection or the rejection rate given by Pt 1 , where t 1 is the runtime of the rst non-reject rule executed, and the speed of sorting measured by the arrival time mean. The agent program in  Boser et al. 1992  uses a single neural network on a chip. We show that under a variety of conditions an optimized sequence of networks can do signi cantly better than any single network in terms of throughput or accuracy. W e examine the following experimental conditions: We assume that a network that executes in time t has a recognition accuracy p that depends on t. W e consider p = 1 ,e ,t . The particular choice of is irrelevant because the scale chosen for t is arbitrary. W e c hoose = 0 :9, for convenience Figure  3a . We include r reject with q reject = u 3 and t reject = 0 . We consider arrival time distributions that are Poisson with varying means. Figure  3b  shows three example distributions, for means 1, 5, and 9 seconds. We create optimized sequences from sets of 40 networks with execution times taken at equal intervals from t = 1 to 40. We compare a BO sequence: a bounded optimal sequence; b Best singleton: the best single rule; c 50 rule: the rule whose execution time is the mean of the distribution i.e., it will complete in 50 of cases; d 90 rule: the rule whose execution time guarantees that it will complete in 90 of cases. In the last three cases, we add r reject as an initial step; the BO sequence will include it automatically. We measure the utility per second as a function of the mean arrival rate Figure  4 . This shows that there is an optimal setting of the sorting machinery at 6 letters per minute inter-arrival time = 10 seconds for the bounded optimal program, given that we h a ve xed at 0.9. Finally, w e i n vestigate the e ect of the variance of the arrival time on the relative performance of the four program types. For this purpose, we use a uniform distribution centered around 20 seconds but with di erent widths to vary the variance without a ecting the mean Figure  5 . We notice several interesting things about these results: The policy of choosing a rule with a 90 probability of completion performs poorly for rapid arrival rates 3, but catches up with the performance of the best single rule for slower arrival rates 4. This is an artifact of the exponential accuracy pro le for any 0:5, where the di erence in quality of the rules with run times greater than 6 seconds is quite small. The policy of choosing a rule with a 50 probability of completion fares as well as the best single rule for very high arrival rates 2, but rapidly diverges from it thereafter, performing far worse for arrival time means greater than 5 seconds. Both the best sequence and the best single rule give their best overall performance at an arrival rate of around 6 letters per minute. The performance advantage of the optimal sequence over the best single rule is about 7 at this arrival rate. It should be noted that this is a signi cant performance advantage that is obtainable with no extra computational resources. For slower arrival rates 7, the di erence between the performance of the best rule and the best sequence arises from the decreased rejection rate of the best sequence. With the exponential accuracy pro le 0:5 the advantage of running a rule with a shorter completion time ahead of a longer rule is the ability to reduce the probability of rejecting a letter. For high arrival rates inter-arrival times of 1 to 4 seconds, it is useful to have a few short rules instead of a longer single rule. Figure  5  shows that the best sequence performs better than the best single rule as the variance of the arrival time increases.  5  The performance of the optimal sequence also appears to be largely una ected by v ariance. This is exactly the behaviour we expect to observe | the ability to run a sequence of rules instead of committing to a single one gives it robustness in the face of increasing variance. Since realistic environments can involve unexpected demands of many kinds, the possession of a variety of default behaviours of graded sophistication would seem to be an optimal design choice for a bounded agent. 5. The performance of the 50 rule is at because the uniform distributions used in this experiment h a ve xed mean and are symmetric, so that the 50 rule is always the rule that runs for 20 seconds. The 90 rule changes with the variance, and the curve exhibits some discretization e ects. These could be eliminated using a ner-grained set of rules. \n Learning Approximately Bounded-Optimal Programs The above derivations assume that a suitable rule set R is available ab initio, with correct qualities q i and runtimes t i , and that the deadline distribution is known. In this section, we study ways in which some of this information can be learned, and the implications of this for the bounded optimality of the resulting system. We will concentrate on learning rules and their qualities, leaving runtimes and deadline distributions for future work. The basic idea is that the learning algorithms will converge, over time, to a set of optimal components | the most accurate rules and the most accurate quality estimates for them. As this happens, the value of the agent constructed from the rules, using the quality estimates, converges to the value of l opt . T h us there are two sources of suboptimality in the learned agent: The rules in R may not be the best possible rules | they may recommend actions that are of lower utility than those that would be recommended by some other rules. There may be errors in estimating the expected utility of the rule. This can cause the algorithms given above to construct suboptimal sequences, even if the best rules are available. Our notional method for constructing bounded optimal agents 1 learns sets of individual decision procedures from episodic interactions, and 2 arranges them in a sequence using one of the algorithms described earlier so that the performance of an agent using the sequence is at least as good as that of any other such agent. We assume a parameterized learning algorithm L J ;k that will be used to learn one rule for each possible runtime k 2 f 1; : : : ; t M g. Since there is never a need to include two rules with the same runtime in the R, this obviates the need to consider the entire rule language J in the optimization process. Our setting places somewhat unusual requirements on the learning algorithm. Like most learning algorithms, L J ;k works by observing a collection T of training episodes in E, including the utility obtained for each episode. We do not, however, make a n y assumptions about the form of the correct decision rule. Instead, we make assumptions about the hypotheses, namely that they come from some nite language J k , the set of programs in J of complexity at most k. This setting has been called the agnostic learning setting by Kearns, Schapire and Sellie 1992, because no assumptions are made about the environment at all. It has been shown Theorems 4 and 5 in Kearns, Schapire and Sellie, 1992 that, for some languages J , the error in the learned approximation can be bounded to within of the best rule in J k that ts the examples, with probability 1 , . The sample size needed to guarantee these bounds is polynomial in the complexity parameter k, a s w ell as 1 and 1 . In addition to constructing the decision procedures, L J ;k outputs estimates of their quality q i . Standard Cherno -Hoe ding bounds can be used to limit the error in the quality estimate to be within q with probability 1 , q . The sample size for the estimation of quality is also polynomial in 1 q and 1 q . Thus the error in each agnostically learned rule is bounded to within of the best rule in its complexity class with probability 1 , . The error in the quality estimation of these rules is bounded by q with probability 1 , q . F rom these bounds, we can calculate a bound on the utility de cit in the agent program that we construct, in comparison to l opt : Theorem 7 Assume an architecture M J that executes sequences of decision procedures in an agnostically learnable language J whose runtimes range over 1::t M . F or real time task environments with xed time cost, xed d e adline, and stochastic deadline, we can construct a p r ogram l such that V l opt ; M ; E , V l;M;E + 2 q with probability greater than 1 , m + q , where m is the number of decision procedures in l opt . Proof: We prove this theorem for the stochastic deadline regime, where the bounded optimal program is a sequence of decision procedures. The proofs for the xed cost and xed deadline regimes, where the bounded optimal program is a singleton, follow a s a special case. Let the best decision procedures for E be the set R = fr 1 ; : : : ; r n g, and let l opt = s 1 : : : s m be an optimal sequence constructed from R . Let R = fr 1 ; : : : r n g be the set of decision procedures returned by the learning algorithm. With probability greater than 1 , m , q i , q i for all i, where q i refers to the true quality o f r i . The error in the estimated quality qi of decision procedure r i is also bounded: with probability greater than 1 , m q , jq i , q i j q for all i. Let s = s 1 : : : s m be those rules in R that come from the same runtime classes as the rules s 1 : : : s m in R . Then, by Equation  5 , we h a ve V l opt ; M ; E , V s; M; E because the error in V is a weighted average of the errors in the individual q i . Similarly, w e have j V s; M; E , V s; M; Ej q Now suppose that the sequence construction algorithm applied to R produces a sequence l = s 1 0 : : : s l 0 . By de nition, this sequence appears to be optimal according to the estimated value function V . Hence V l;M;E V s; M; E As before, we can bound the error on the estimated value: j V l;M;E , V l;M;Ej q Combining the above inequalities, we h a ve V l opt ; M ; E , V l;M;E + 2 q 2 Although the theorem has practical applications, it is mainly intended as an illustration of how a learning procedure can converge on a bounded optimal con guration. With some additional work, more general error bounds can be derived for the case in which the rule execution times t i and the real-time utility v ariation time cost, xed deadline, or deadline distribution are all estimated from the training episodes. We can also obtain error bounds for the case in which the rule language J is divided up into a smaller number of coarser runtime classes, rather than the potentially huge number that we currently use. \n Asymptotic Bounded Optimality The strict notion of bounded optimality m a y be a useful philosophical landmark from which to explore arti cial intelligence, but it may be too strong to allow many i n teresting, general results to be obtained. The same observation can be made in ordinary complexity theory: although absolute e ciency is the aim, asymptotic e ciency is the game. That a sorting algorithm is On log n rather than On 2 is considered signi cant, but replacing a multiply by 2 \" b y a shift-left 1 bit\" is not considered a real advance. The slack allowed by the de nitions of complexity classes is essential in building on earlier results, in obtaining robust results that are not restricted to speci c implementations, and in analysing the complexity o f algorithms that use other algorithms as subroutines. In this section, we begin by reviewing classical complexity. We then propose de nitions of asymptotic bounded optimality that have some of the same advantages, and show that classical optimality is a special case of asymptotic bounded optimality. Lastly, w e report on some preliminary investigations into the use of asymptotic bounded optimality as a theoretical tool in constructing universal real-time systems. \n Classical complexity A problem, in the classical sense, is de ned by a pair of predicates and such that output z is a solution for input x if and only if x and x; z hold. A problem instance is an input satisfying , and an algorithm for the problem class always terminates with an output z satisfying x; z given an input x satisfying x. Asymptotic complexity describes the growth rate of the worst-case runtime of an algorithm as a function of the input size. We can de ne this formally as follows. Let T a x be the runtime of algorithm a on input x, and let T a n be the maximum runtime of a on any input of size n. Then algorithm a has complexity Ofn if 9k;n 0 8n n n 0 T a n kfn Intuitively, a classically optimal algorithm is one that has the lowest possible complexity. For the purposes of constructing an asymptotic notion of bounded optimality, it will be useful to have a de nition of classical optimality that does not mention the complexity directly. This can be done as follows: De nition 11 Classically optimal algorithm: An algorithm a is classically optimal if and only if 9k;n 0 8a 0 ; n n n 0 T a n kT a 0 n To relate classical complexity to our framework, we will need to de ne the special case of task environments in which traditional programs are appropriate. In such task environments, an input is provided to the program as the initial percept, and the utility function on environment histories obeys the following constraint: De nition 12 Classical task environment: hE P ; U i is a classical task environment for problem P if V l;M;E P = uTl;M;E P if l outputs a correct solution for P 0 otherwise where Tl;M;E P is the running time for l in E P on M, M is a universal Turing machine, and u is some positive decreasing function. The notion of a problem class in classical complexity theory thus corresponds to a class of classical task environments of unbounded complexity. F or example, the Traveling Salesperson Problem contains instances with arbitrarily large numbers of cities. \n Varieties of asymptotic bounded optimality The rst thing we will need is a complexity measure on environments. Let nE be a suitable measure of the complexity o f a n e n vironment. We will assume the existence of environment classes that are of unbounded complexity. Then, by analogy with the de nition of classical optimality, w e can de ne a worst-case notion of asymptotic bounded optimality ABO. Letting V l;M;n;E be the minimum value of V l;M;E for all E in E of complexity n, we h a ve De nition 13 Worst-case asymptotic bounded optimality: an agent program l is timewise or spacewise worst-case asymptotically bounded optimal in E on M i 9k;n 0 8l 0 ; nn n 0 V l;kM;n;E V l 0 ; M ; n ; E where kM denotes a version of the machine M speeded up by a factor k or with k times more memory. In English, this means that the program is basically along the right lines if it just needs a faster larger machine to have w orst-case behaviour as good as that of any other program in all environments. If a probability distribution is associated with the environment class E, then we can use the expected value V l;M;E to de ne an average-case notion of ABO: De nition 14 Average-case asymptotic bounded optimality: an agent program l is timewise or spacewise average-case asymptotically bounded optimal in E on M i 9k 8l 0 V l;kM;E V l 0 ; M ; E For both the worst-case and average-case de nitions of ABO, we w ould be happy with a program that was ABO for a nontrivial environment on a nontrivial architecture M, unless k were enormous.  6  In the rest of the paper, we will use the worst-case de nition of ABO. Almost identical results can be obtained using the average-case de nition. The rst observation that can be made about ABO programs is that classically optimal programs are a special case of ABO programs: 7 6. The classical de nitions allow for optimality up to a constant factor k in the runtime of the algorithms. One might w onder why w e c hose to use the constant factor to expand the machine capabilities, rather than to increase the time available to the program. In the context of ordinary complexity theory, the two alternatives are exactly equivalent, but in the context of general time-dependent utilities, only the former is appropriate. It would not be possible to simply let l run k times longer,\" because the programs we wish to consider control their own execution time, trading it o against solution quality. One could imagine slowing down the entire environment b y a factor of k, but this is merely a less realistic version of what we propose. 7. This connection was suggested by Bart Selman. Theorem 8 A p r ogram is classically optimal for a given problem P if and only if it is timewise worst-case ABO for the corresponding classical task environment class hE P ; U i. This observation follows directly from De nitions 11, 12, and 13. In summary, the notion of ABO will provide the same degree of theoretical robustness and machine-independence for the study of bounded systems as asymptotic complexity d o e s for classical programs. Having set up a basic framework, we can now begin to exercise the de nitions. \n Universal asymptotic bounded optimality Asymptotic bounded optimality is de ned with respect to a speci c value function V. In constructing real-time systems, we w ould prefer a certain degree of independence from the temporal variation in the value function. We can achieve this by de ning a family V of value functions, di ering only in their temporal variation. By this we mean that the value function preserves the preference ordering of external actions over time, with all value functions in the family having the same preference ordering.  8  For example, in the xed-cost regime we can vary the time cost c to generate a family of value functions; in the stochastic deadline case, we can vary the deadline distribution P d to generate another family. Also, since each of the three regimes uses the same quality measure for actions, then the union of the three corresponding families is also a family. What we will show is that a single program, which w e call a universal program, can be asymptotically bounded-optimal regardless of which v alue function is chosen within any particular family. De nition 15 Universal asymptotic bounded optimality UABO: An agent program l is UABO in environment class E on M for the family of value functions V i l is ABO in E on M for every V i 2 V . A UABO program must compete with the ABO programs for every individual value function in the family. A UABO program is therefore a universal real-time solution for a given task. Do UABO programs exist? If so, how can we construct them? It turns out that we can use the scheduling construction from Russell & Zilberstein, 1991 to design UABO programs. This construction was designed to reduce task environments with unknown interrupt times to the case of known deadlines, and the same insight applies here. The construction requires the architecture M to provide program concatenation e.g., the LISP prog construct, a conditional-return construct, and the null program . The universal program l U has the form of a concatenation of individual programs of increasing runtime, with an appropriate termination test after each. It can be written as l U = l 0 l 1 l j where each l j consists of a program and a termination test. The program part in l j is any program in L M that is ABO in E for a value function V j that corresponds to a xed deadline at t d = 2 j , where is a time increment smaller than the execution time of any non-null program in L M . 8. The value function must therefore be separable  Russell & Wefald, 1989, since    Before proceeding to a statement that l U is indeed UABO, let us look at an example. Consider the simple, sequential machine architecture described earlier. Suppose we can select rules from a three-rule set with r 1 = 0 :2; 2, r 2 = 0 :5; 5 and r 3 = 0 :7; 7. Since the shortest runtime of these rules is 2 seconds, we let = 1. Then we look at the optimal programs l 0 ; l 1 ; l 2 ; l 3 ; : : : for the xed-deadline task environments with t d = 1 ; 2; 4; 8; : : : . These are: l 0 = ;l 1 = r 1 ; l 2 = r 1 ; l 3 = r 3 ; : : : Hence the sequence of programs in l U is ; r 1 ; r 1 ; r 3 ; : : : . Now consider a task environment class with a value function V i that speci es a stochastic deadline uniformly distributed over the range 0: : : 10 . For this class, l opt = r 1 r 2 is a bounded optimal sequence. 9 It turns out that l U has higher utility than l opt provided it is run on a machine that is four times faster. We can see this by plotting the two performance pro les: Q U for l U on 4M and Q opt for l opt on M. Q U dominates Q opt , a s s h o wn in Figure  6 . To establish that the l U construction yields UABO programs in general, we need to de ne a notion of worst-case performance pro le. Let Q t; l; M; n; E be the minimum value obtained by i n terrupting l at t, o ver all E in E of complexity n. W e know that each l j in l U satis es the following: 8l 0 ; n n n j V j l j ; k j M;n;E V j l 0 ; M ; n ; E for constants k j , n j . The aim is to prove that 8V i 2 V 9 k;n 0 8l 0 ; n n n 0 V i l U ; k M ; n ; E V i l 0 ; M ; n ; E Given the de nition of worst-case performance pro le, it is fairly easy to show the following lemma the proof is essentially identical to the proof of Theorem 1 in  Russell and Zilberstein, 1991:  9. Notice that, in our simple model, the output quality of a rule depends only on its execution time and not on the input complexity. This also means that worst-case and average-case behaviour are the same. Lemma 6 If l U is a universal program in E for V, and l i is ABO on M in E for V i 2 V , then Q t; l U ; k M ; n ; E dominates Q t; l i ; M ; n ; E for k 4 max j k j , n max j n j . This lemma establishes that, for a small constant penalty, w e can ignore the speci c realtime nature of the task environment in constructing bounded optimal programs. However, we still need to deal with the issue of termination. It is not possible in general for l U to terminate at an appropriate time without access to information concerning the timedependence of the utility function. For example, in a xed-time-cost task environment, the appropriate termination time depends on the value of the time cost c. For the general case with deterministic time-dependence, we can help out l U by supplying, for each V i , an aspiration level\" Q i t i ; l i ; M ; n ; E, where t i is the time at which l i acts. l U terminates when it has completed an l j such that q j Q i t i ; l i ; M ; n ; E. By construction, this will happen no later than t i because of Lemma 6. Theorem 9 In task environments with deterministic time-dependence, an l U with a suitable aspiration level is UABO in E on M. With deadline heralds, the termination test is somewhat simpler and does not require any additional input to l U . Theorem 10 In a task environment with stochastic deadlines, l U is UABO in E on M if it terminates when the herald arrives. Returning to the mail-sorting example, it is fairly easy to see that l U which consists of a sequence of networks, like the optimal programs for the stochastic deadline case will be ABO in the xed-deadline regime. It is not so obvious that it is also ABO in any particular stochastic deadline case | recall that both regimes can be considered as a single family. We h a ve programmed a constructor function for universal programs, and applied it to the mail-sorter environment class. Varying the letter arrival distribution gives us di erent v alue functions V i 2 V . Figure  7  shows that l U on 4M has higher throughput and accuracy than l i opt across the entire range of arrival distributions. Given the existence of UABO programs, it is possible to consider the behaviour of compositions thereof. The simplest form of composition is functional composition, in which the output of one program is used as input by another. More complex, nested compositional structures can be entertained, including loops and conditionals  Zilberstein, 1993.  The main issue in constructing UABO compositions is how to allocate time among the components. Provided that we can solve the time allocation problem when we know the total runtime allowed, we can use the same construction technique as used above to generate composite UABO programs, where optimality is among all possible compositions of the components.  Zilberstein and Russell 1993 , show that the allocation problem can be solved in linear time in the size of the composite system, provided the composition is a tree of bounded degree. \n Conclusions And Further Work We examined three possible formal bases for arti cial intelligence, and concluded that bounded optimality provides the most appropriate goal in constructing intelligent systems. We also noted that similar notions have arisen in philosophy and game theory for more or less the same reason: the mismatch b e t ween classically optimal actions and what we h a ve called feasible behaviours|those that can be generated by an agent program running on a computing device of nite speed and size. We showed that with careful speci cation of the task environment and the computing device one can design provably bounded-optimal agents. We exhibited only very simple agents, and it is likely that bounded optimality in the strict sense is a di cult goal to achieve when a larger space of agent programs is considered. More relaxed notions such as asymptotic bounded optimality ABO may provide more theoretically robust tools for further progress. In particular, ABO promises to yield useful results on composite agent designs, allowing us to separate the problem of designing complex ABO agents into a discrete structural problem and a continuous temporal optimization problem that is tractable in many cases. Hence, we h a ve reason to be optimistic that arti cial intelligence can be usefully characterized as the study of bounded optimality. W e m a y speculate that provided the computing device is neither too small so that small changes in speed or size cause signi cant c hanges in the optimal program design nor too powerful so that classically optimal decisions can be computed feasibly, ABO designs should be stable over reasonably wide variations in machine speed and size and in environmental complexity. The details of the optimal designs may be rather arcane, and learning processes will play a large part in their discovery; we expect that the focus of this type of research will be more on questions of convergence to optimality for various structural classes than on the end result itself. Perhaps the most important implication, beyond the conceptual foundations of the eld itself, is that research on bounded optimality applies, by design, to the practice of arti cial intelligence in a way that idealized, in nite-resource models may not. We h a ve given, by way of illustrating this de nition, a bounded optimal agent: the design of a simple system consisting of sequences of decision procedures that is provably better than any other program in its class. A theorem that exhibits a bounded optimal design translates, by de nition, into an agent whose actual behaviour is desirable. There appear to be plenty o f w orthwhile directions in which to continue the exploration of bounded optimality. From a foundational point of view, one of the most interesting questions is how the concept applies to agents that can incorporate a learning component. Note that in section 5, the learning algorithm was external to the agent. In such a case, there will not necessarily be a largely stable bounded optimal con guration if the agent program is not large enough; instead, the agent will have to adapt to a shorter-term horizon and rewrite itself as it becomes obsolete. With results on the preservation of ABO under composition, we can start to examine much more interesting architectures than the simple production system studied above. For example, we can look at optimal search algorithms, where the algorithm is constrained to apply a metalevel decision procedure at each step to decide which node to expand, if any  Russell & Wefald, 1989 . We can also extend the work on asymptotic bounded optimality to provide a utility-based analogue to big-O\" notation for describing the performance of agent designs, including those that are suboptimal. In the context of computational learning theory, i t i s o b vious that the stationarity requirement on the environment, which is necessary to satisfy the preconditions of PAC results, is too restrictive. The fact that the agent learns may h a ve some e ect on the distribution of future episodes, and little is known about learning in such cases  Aldous & Vazirani, 1990 . We could also relax the deterministic and episodic requirement to allow non-immediate rewards, thereby making connections to current research on reinforcement learning. The computation scheduling problem we examined is interesting in itself, and does not appear to have been studied in the operations research o r c o m binatorial optimization literature. Scheduling algorithms usually deal with physical rather than computational tasks, hence the objective function usually involves summation of outputs rather than picking the best. We w ould like to resolve the formal question of its tractability in the general case, and also to look at cases in which the solution qualities of individual processes are interdependent such as when one can use the results of another. Practical extensions include computation scheduling for parallel machines or multiple agents, and scheduling combinations of computational and physical e.g., job-shop and ow-shop processes, where objective functions are a combination of summation and maximization. The latter extension broadens the scope of applications considerably. An industrial process, such as designing and manufacturing a car, consists of both computational steps design, logistics, factory scheduling, inspection etc. and physical processes stamping, assembling, painting etc.. One can easily imagine many other applications in real-time nancial, industrial, and military contexts. It may turn out that bounded optimality is found wanting as a theoretical framework. If this is the case, we hope that it is refuted in an interesting way, so that a better framework can be created in the process. \n Appendix: Additional Proofs This appendix contains formal proofs for three subsidiary lemmata in the main body of the paper. Lemma 3 There exists an optimal sequence that is sorted in increasing order of q's. Proof: Suppose this is not the case, and s is an optimal sequence. Then there must be two adjacent rules i, i + 1 where q i q i+1 see Figure  8 . Removal of rule i + 1 yields a sequence s 0 such that Q s 0 t Q s t, from Lemma 1 and the fact that t i+2 t i+1 +t i+2 . B y Lemma 2, s 0 must also be optimal. We can repeat this removal process until s 0 is ordered by q i , proving the theorem by reductio ad absurdum.2 Lemma 4 For every sequence s = s 1 : : : s m sorted in increasing order of quality, and single step z with q z q s m , V sz V s. Proof: We calculate V sz , V s using Equation  5 and show that it is non-negative: V sz , V s = q z 1 , P d P m j=1 t j + t z , q m 1 , P d P m j=1 t j + t z = q z , q m 1 , P d P m j=1 t j + t z which is non-negative since q z q m .2 t i+1 q i+2 q i q i-1 t i q t t i+2 q i+1 Figure 8: Proof for ordering by q i ; l o wer dotted line indicates original pro le; upper dotted line indicates pro le after removal of rule i + 1 . Lemma 5 There exists an optimal sequence whose rules are in nondecreasing order of t i . Proof: Suppose this is not the case, and s is an optimal sequence. Then there must be two adjacent rules i, i + 1 where q i q i+1 and t i t i+1 see Figure  9 . Removal of rule i yields a sequence s 0 such that Q s 0 t Q s t, from Lemma 1. By Lemma 2, s 0 must also be optimal. We can repeat this removal process until s 0 is ordered by t i , proving the theorem by reductio ad absurdum.2 t i+1 q i+1 q i q i-1 t i q t t i+1 Figure  9 : Proof for ordering by t i ; dotted line indicates pro le after removal of rule i. Figure 1 : 1 Figure 1: An automated mail-sorting facility provides a simple example of an episodic, real-time task environment. \n 7 = :25 A geometric intuition is given by the notion of a performance p r o le, a s s h o wn in Figure 2. \n Figure 2 : 2 Figure 2: Performance pro le for r 1 r 2 r 3 , with p d superimposed. \n Figure 3 3 Figure 3: a Accuracy pro le 1 , e ,x , for = 0 :9. b Poisson arrival distribution, for mean = 9 sec \n Figure 4 : 4 Figure 4: Graph showing the achievable utility per second as a function of the average time per letter, for the four program types. = 0 :9. \n Figure 5 : 5 Figure 5: Graphs showing the utility gain per second as a function of the arrival time variance, for the four program types for the uniform distribution with a mean of 20 seconds. \n Figure 6 : 6 Figure 6: Performance pro les for l U running on 4M, and for l opt running on M \n Figure 7 : 7 Figure 7: Throughput and accuracy improvement o f l U over l i opt , as a function of mean arrival time, = 0.2, Poisson arrivals. \n Fixed time cost: The task environment hE;Ui has a xed time cost if, for any action history pre xes A t 1 1 and A t 2 2 satisfying 1 A T 1 t 1 2 A ? and A T 2 t 2 = A T 1 t 1 2 A t 1 ,1 1 and A t 2 ,1 2 contain no action in A ? contain no action in A ? . t d ,1 2 Actions taken after t d have no e ect on utility: U E;A t 1 U E;A t 2 if U E;A t d 1 U E;A t d 2 and t t d 4.1.2 Fixed time cost Task environments with approximately xed time cost are also very common. Examples include consultations with lawyers, keeping a taxi waiting, or dithering over where to invest one's money. We can de ne a task environment with xed time cost c by comparing the utilities of actions taken at di erent times.De nition 8 \n\t\t\t . This usage of the term universal\" derives from its use in the scheduling of randomized algorithms by Luby, Sinclair and Zuckerman 1993.   \n\t\t\t . For example, it is conceivable that Good and Simon really intended to refer to nding an agent design that minimizes deliberation costs in general. All their discussions, however, seem to be couched in terms of nding the right deliberation for each decision. Thus, type II or metalevel rationality coincides with bounded optimality if the bounded optimal agent is being designed for a single decision in a single situation. \n\t\t\t . One would imagine that in most cases the move selected will be the same move selected by a T ype I agent, but this is in a sense accidental\" because further deliberation might cause the program to abandon it. \n\t\t\t Russell & Subramanian \n\t\t\t . See Sackinger et al. 1992; Boser et al. 1992  for details of an actual system. The application was suggested to us by Bernhard Boser after an early presentation of our work at the 1992 NEC Symposium.", "date_published": "n/a", "url": "n/a", "filename": "10134-Article Text-18441-1-10-20180216.tei.xml", "abstract": "Since its inception, arti cial intelligence has relied upon a theoretical foundation centred around perfect rationality as the desired property o f i n telligent systems. We argue, as others have done, that this foundation is inadequate because it imposes fundamentally unsatis able requirements. As a result, there has arisen a wide gap between theory and practice in AI, hindering progress in the eld. We propose instead a property called bounded optimality. Roughly speaking, an agent is bounded-optimal if its program is a solution to the constrained optimization problem presented by its architecture and the task environment. We show h o w to construct agents with this property for a simple class of machine architectures in a broad class of real-time environments. We illustrate these results using a simple model of an automated mail sorting facility. We also de ne a weaker property, asymptotic bounded optimality ABO, that generalizes the notion of optimality in classical complexity theory. We then construct universal ABO programs, i.e., programs that are ABO no matter what real-time constraints are applied. Universal ABO programs can be used as building blocks for more complex systems. We conclude with a discussion of the prospects for bounded optimality as a theoretical basis for AI, and relate it to similar trends in philosophy, economics, and game theory.", "id": "f4e88f7acea528421a87f8fb57ca8968"}
{"source": "nonarxiv_papers", "source_filetype": "pdf", "authors": ["Thomas Krendl Gilbert", "Yonatan Mintz"], "title": "Epistemic Therapy for Bias in Automated Decision-Making", "text": "diagnose the epistemic and ethical challenges that may arise in AI system design. Since much of the discussion on anthropomorphic biases has been conducted through either anthropomorphizing AI models or relegating all responsibility for bias onto problematic data, our goal is to move away from these ambiguous analogies and confront the nuance of bias in automated decision-making. Our discussion is motivated by several recent cases of AI system implementation and research that have already been flagged as problematic. We first examine systems where data was assumed to be representative of the real world but in fact encoded human biases that were later amplified by AI systems  [2, 30] . We then consider cases in the machine learning literature where common notions of bias and equity are rationalized away by researchers using predictions provided by AI models  [11, 34] . Finally, we consider cases where researchers attempt to directly address anthropomorphic biases they perceive in their model prediction, leading to researchers instead encoding their own implicit biases into AI systems  [7, 9] . These three motivating examples show that the nature of anthropomorphic bias in AI is paradoxical and counterintuitive, while the use of direct analogies to human bias actually erase the specific contexts that cause anthropomorphic bias to manifest in the first place. In order to diagnose and work through these ambiguities, we provide two major contributions to the discussion of bias in AI systems. First, we characterize the kinds of biases that arise from complex interactions between engineers, algorithms, and data. To do this, we draw on previous work in the philosophy of mind literature that characterizes human bias as a set of aliefs  [17] , belief-like dispositions that also contain an affective component, and introduce the concept of alief-discordant beliefs. In our discussion, we demonstrate that these alief-discordant beliefs provide the framework necessary to understand the trade-off between the moral dispositions of system engineers and the explicit relations encoded by AI models. Second, we apply the notion of alief-discordant beliefs to craft design principles for AI in light of human biases. We conclude by illustrating how these principles can be used to diagnose the ethical concerns that motivate practitioners, performing a type of \"epistemic therapy\" for the benefit of the machine learning community. Much as psychotherapy is used to confront subconscious issues through a process of dynamic interpersonal conversation, we propose \"epistemic therapy\" for automated decision-making as the process by which alief-discordant beliefs are identified and confronted by engineers. The design principles we outline in this paper support this \"epistemic therapy\" by aiding in the implementation of AI systems and navigating to avoid biased outcomes. \n EPISTEMIC ETHICS IN FAIR MACHINE LEARNING The machine learning literature has explored predictive bias as a barrier to fair outcomes. In particular, many papers have suggested algorithmic means of curbing bias in predictions, proposing the notion of \"optimal\" fairness as solutions to optimization problems  [11] . Several variations of optimal fairness have been proposed, including equalizing prediction metrics (e.g. TPR, FPR, accuracy) across protected classes  [1, 10, 13, 20] , and producing models whose predictions are independent of protected features  [7, 9, 28, 35] . There have been some technical critiques leveled against these notions of optimal fairness  [11, 25] , as well as several impossibility results that show it is difficult to satisfy all of these notions of fairness simultaneously  [14, 21] . We complement this literature by providing a framework of epistemic ethics that could be used to justify the necessary engineering design choices made in implementing certain methods of optimal fairness. Specifically, our framework resolves some of the skepticism in using these methods and addresses what technical knowledge and data engineers ought to have in order to manage and avoid anthropomorphic bias in AI systems they design. A related stream of social science literature has discussed the nature of bias in machine learning  [4, 6, 12, 26] , enumerating potential ethical concerns and discussing whether decision-making can be automated without compromising human dignity responsibility. In contrast, our discussion emphasizes how the perception of different kinds of bias in AI systems is responsible for their supposed immorality, which implies they are better understood within the realm of philosophy of mind than ethics proper. Of particular relevance to this paper is the discussion proposed by Binns  [6] , which analyzes anthropomorphic bias by contrasting human mental states with the mechanisms of automated decision-making. We will present a complementary dissolution of anthropomorphic bias through the notion of alief-discordant beliefs, directly influenced by the work of Tamar Gendler on characterizing human biases  [17] . \n CASE STUDIES We will first build intuition on how \"anthropomorphic bias\" can affect researchers and engineers through reference to prominent existing case studies. In particular, we consider cases where anthropomorphic bias may manifest in how 1) the values of engineers inform the techniques of AI system creation; 2) the epistemology of the data and encoding characterize the resulting AI system; 3) allocation of moral culpability labels interactions between data and system design throughout the deployment phase. Each of these examples illustrates how anthropomorphic bias can be attributed to an underlying discordance between the distinctive epistemic frames of engineers, data, and system design. We discuss three major causes of this discordance, each with its own mixing of ethical culpability between data, algorithms, and engineers. These are: (i) AI systems that are deployed as vehicles for moral dispositions, either encoded by engineers or sedimented within data; (ii) engineers that outsource their own moral compasses to the labels generated by AI systems; (iii) dogmatic reconciliation of inherited dispositions and generated propositions that result in adverse effects. \n AI systems as Vehicles for Moral Dispositions First we consider cases where AI systems are deployed as vehicles for moral dispositions implicitly harbored by engineers or encoded in training data. Two famous cases of such discordance discussed in FAT literature include the COMPAS system which was used to predict criminal recidivism  [2, 22] , and Tay the Microsoft-deployed chat bot that was hijacked by white supremacists  [5, 29, 30] . 3.1.1 COMPAS. The COMPAS system was initially developed to predict a recidivism risk score for arrested individuals and was deployed to several states  [2] . However, even though explicit racial detail was not inserted into the system input, it was shown that COMPAS would predict lower risk scores for white individuals and higher scores for people of color. Moreover, analysis of the system output showed that the false positive rate for people of color was significantly higher than that of white individuals  [22] . From a technical perspective, it is generally agreed that the system produced biased output despite not taking in explicit racial data, since race is correlated with other features that were used as input (e.g. education, residence address, income) and labels used for training were obtained from historical arrest records that contain a documented inherent bias against certain communities  [22] . In essence, the way the COMPAS system was designed and implemented transformed social biases extant in the justice system and reified them through automated classification. However, it is difficult to confer responsibility for this to a specific agent-while the data's encoded bias should have been made explicit by those who collected it, system engineers also failed to properly account for this bias in the data. What the engineers ought to have done in this particular case is critically examine the source of the data and any bias that it may convey, and use a proper training technique for their model that could account for the problematic predictions. 3.1.2 Microsoft Tay. Tay was a chatbot developed by Microsoft research to interact with the greater public on social media and mimic the language patterns of a 19 year old girl  [5] . While in closed company testing, it was reported that Tay was performing extremely well without significant incident. Within 24 hours of being deployed online, and to the surprise of the research team, Tay was re-tweeting white supremacist propaganda due to a loosely coordinated attack by certain forum users  [29, 30] . Much like COMPAS, the deployment of Tay also suffered from becoming a passive vehicle for unquestioned moral associations. However, the associations in question are not necessarily the ones harbored by the data but by the engineers that designed the system. In particular, the engineers were not appropriately skeptical of the reaction of the internet community at large and assumed that they would behave in a similar manner to the corporate testers that interacted with Tay in house. The fallout from this situation could have been reduced had the engineers confronted their own underlying assumptions and properly designed the training methods of the model to not accept all input data equally. \n Automatic Alief Falsification Another cause of the discordance can result from a 'skeptical' overcorrection based on the system pipeline. Two of the principle tenets Spotlight 1: Normative Perspectives AIES'19, January 27-28, 2019, Honolulu, HI, USA of data science include the belief that all rational explanations (i.e. those that rely on mathematical reasoning) are superior to all other forms of disposition generation, and that sufficient information about the state of the world can be extracted from data. This moral disposition is conveyed by the recent work of Corbett-Davies and Goel  [11]  on fairness measures, and Wang and Kosinski's  [34]  work on detecting sexual orientation with pictures . While we strive to identify ethical culpability in this section, we do not ascribe malicious intentions to the engineers that design AI systems. In particular, we believe both sets of authors that we discuss here did have good intentions when creating their work, but that their results are problematic when examined in a critical context. The key problematic aspect of these discordances is that instead of attempting to harmonize their own moral dispositions with the propositions generated by models, engineers are too eager to dispose of their initial presuppositions. \n 3.2.1 The Measure and Mismeasure of Fairness. Corbett-Davies and Goel  [11]  have presented several leading methods of optimal fairness in the FATML literature and critique each family of methods to show how they may violate certain notions of fairness. The authors rely on working definitions of fairness from parts of the economics and legal literature and show how these can be incongruent with mathematical notions of fairness. When analyzing the notion of fairness through classification parity, the authors note that different populations of individuals will by nature have different means and variances that could account for lack of parity. As a real world example of this, the authors used the example of the COMPAS model we previously discussed. They note that since black individuals had higher recidivism rates than white individuals, this group was in fact accurately predicted as having a higher risk to society than whites. Although the authors do note that this difference in rate is caused by both historic and systemic factors, they argue that these are not crucial to examine when making policy decisions. In particular, since the authors assume the prediction of individual risk is accurate, they claim that policy actions to ensure prediction parity between the populations would result in an unfairly harsher prediction rate against the white population. They further argue that such actions would harm the black population with an inappropriately low predicted rate of recidivism  [11] . Thus, the authors arrive at a conclusion that is in contrast to their initially stated assumptions (\"demographic parity is important\"), due to their failure to critically engage with the context of the data (namely its internal generation by a system with known bias  [22] ). \n Detecting Sexual Orientation with AI. A similar tension can be found in Wang and Kosinski's paper  [34] , which describes an artificial neural network model that processes facial images to predict an individual's sexual orientation. In particular, the authors used face photos scraped from dating websites that they classified as heterosexual or homosexual using the user's dating profile, and showed that a model trained on these photos has good accuracy when predicting sexual orientation. The authors' main claim in this paper is that the predictive power of AI models can be harnessed to encode complex patterns in facial features that could indicate an individual's sexual orientation. This research has received a lot of backlash for suggesting a new form of digital physiognomy  [23, 27, 33] . While the researchers may have started with the assumption that physiognomy is pseudoscience, they readily discarded this in favor of the view generated by their model that facial features can predict sexual orientation. Kosinski himself has defended the study as revealing both the \"huge promise\" of big data as well as the risks due to loss of privacy  [31] . Meanwhile, critics have argued that this attempt to subject sexual orientation to objective measurement, while an interesting exercise in classification that reveals unexpected correlations with high accuracy, is erroneous as it fails to account for the subjectivity of social context  [16]  and reifies social stereotypes  [24] . However, there is a danger of repeating the study's mistake by assuming that automated systems can only reify existing gender ontologies. It is, for example, possible that previously invisible correlations between bone structure and sexual preference really do exist, encouraging future work to explore and falsify new hypotheses. Meanwhile, a more critical analysis of the model might suggest that the contextual purpose of dating profile pictures is to broadcast sexual orientation to potential partners, rather than neutrally reflect how facial features predict sexual preferences. Since the engineers did not seriously consider this, they propagated a questionable conclusion based on the model output. We will later suggest interpreting such research studies as generating authentic discordances between our intuitions about the social world and novel beliefs about it that must be examined and deliberated, rather than summarily dismissed. \n Dogmatic Reconciliation Finally, we consider a class of discordances arising when the system engineers do attempt to harmonize their moral dispositions with system-generated propositions, but unfortunately use blunt methods to make systems comply with the former. The failure occurs when engineers, despite using values-based design, still encode their implicit biases into AI models through training and formulation instead of explicating and confronting their own assumptions. We consider two recent papers from the FATML literature that focus on the problem of biased predictions resulting from natural language processing: \"Women also Snowboard\"  [9]  and \"Man is to Computer Programmer as Woman is to Homemaker\"  [7] . In both of these papers, the authors seek to correct gender related bias in various downstream tasks that occurs using state-of-the-art word vector embeddings for natural language processing. In \"Women also Snowboard\"  [9]  the authors address gender bias that occurs when developing AI systems for automatic image captioning. Specifically, the authors note that given certain contexts (e.g. sports equipment, computers, purses), image captioning systems tend to give incorrect predictions that fit common gender expression stereotypes. For instance, a captioning model might predict the caption of a picture of a woman snowboarding as a man snowboarding, since men are more associated with sports contexts. The solution that is introduced to curb this problem involves creating two classes of words (\"male\" vs. \"female\") and formulating a loss function to be used in model training that actually incentivizes confusion between these classes if insufficient evidence is found to make a gendered inference. Likewise, in \"Man is to Computer Programmer as Woman is to Homemaker\"  [7] , the authors attempt to address gender bias that can be observed when performing analogy tasks using word vectors. While vector embedding in words generally yields useful semantic analogies (e.g. man is to king as woman is to queen), the authors note that certain problematic analogies are also picked up by these embeddings given certain corpora. To curtail these problematic analogies, the authors propose a method in which they compute a \"Man to Woman\" subspace of the embedded vector space, and formulate a way to reduce the the projection of non-gendered words on this subspace, thus removing much of the unintentional gender encoding that could have been contained by those words. Both of these works confront a discordance between model and social understandings of gender, namely that it should not be informative for certain aspects of an individual (women can also be snowboarders and computer programmers), and attempt to harmonize this view with the generated propositions of these given models. That said, the solutions proposed by the authors do not directly correct for the notion that gender expression should be uninformative on certain predictions, and instead address the problem of women being underrepresented in data and should be predicted with equal probability to men in certain contexts. This is a subtle distinction, but to illustrate it fully, we note that both solutions presented in these papers assume some kind of distinct \"male\" to \"female\" distinction and not more contextuallynuanced forms of gender identity. Essentially, by attempting to produce a solution to the system's discordant moral claims, the authors have hard-coded a cis-gender understanding of human sexuality into the models. The authors thus do not directly engage with the root discordance they seek to address, and instead provide a potentially problematic stop-gap solution that reacts only to their morally-charged dispositions. One way of mitigating these effects would have been a more thorough examination of the social-scientific literature on gender expression, and broadening the gender diversity of the research teams involved. In particular, since the methods proposed by the authors involve a rigid encoding of expression, they produce training techniques that are incompatible with intersectional gender identities. For instance, a correction agnostic to the intersection of gender expression and race might result in false corrections due to its rigid coding. \n THE CONTEXT OF ANTHROPOMORPHIC BIAS The questions surrounding anthropomorphic bias -is it always traceable to some original context of human bias? is it original to the statistical compromises that accompany automated decisionmaking? can it be avoided entirely?-demand a deeper philosophical analysis. In this section we proceed to conduct this analysis in two parts. \n Gendler on Belief-Discordant Alief Some form of \"bias\", however it is defined, is inevitable when any small team of humans derives actuarial interventions for broad populations. Trade-offs between accuracy and variance or false positive vs. false negative rates have been a hallmark of statistical inference since the discipline's birth, and while AI has considerably increased the scale and speed of such inferences in deployment, they have not fundamentally changed the rules of this game. Instead we should aim for a principled trade-off between the limits of inference, given messy data sets, imperfect model choices, or limited training time. But what might such a principled trade-off look like for anthropomorphic bias, which combines affect-laden human intuitions with machines' capacity for semantically-arbitrary classification? We appeal to Gendler's  [17]  work on the complex and codependent relationship between belief and \"alief\", which defines the latter as \"a mental state with associatively-linked content that is representational, affective and behavioral, and that is activatedconsciously or nonconsciously -by features of the subject's internal or ambient environment. Aliefs may be either occurrent or dispositional.\" Gendler illustrates this phenomenon through the concept of belief-discordant alief, which accounts for scenarios in which people are afraid of walking on an open skywalk despite its structural safety, won't touch an object for fear of \"cooties, \" or automatically reach for wallets despite knowing you left it at home. Belief-discordant alief is the triggering of affective response patterns and automatic motor routines opposed to \"explicit, conscious, vivid, occurrent belief\"  [17] . That is, it arises when we enter a situation that triggers us into a cognitive state that counteracts what our 'better' judgment knows not to be the case. There is some semantic risk in applying such technical philosophical concepts to a problem as provocative and wide-ranging as anthropomorphic bias, which is already the subject of a rapidly growing empirical literature. However, we feel Gendler's language is not just relevant but necessary for diagnosing the problem in machine learning, for two reasons. First, Gendler's examples and qualifiers succeed in contrasting belief with alief by defining the former in a strongly computational sense: belief is an explicit proposition whose content is discrete (not associative), is universally held (not situationally triggered), and refers conclusively to external reality (not emotions or habits of mind). We shall see that these technical descriptors of belief and alief are extremely useful for diagnosing the specific epistemic tensions within AI systems and the moral dispositions of those who design or interpret them. Second, Gendler's terminology emphasizes the discordance between different kinds of bias as the source of the real problem, not implicit bias in isolation. She holds, following Hume, that the hallmark of alief is a kind of association by which semantic, emotional, and behavioral dimensions are crystallized over time. In belief-discordant alief, there is something about an environment's psychological effects that trigger one to automatically respond in a way opposed to one's beliefs about it. The associative content of alief is highly arbitrary, just as one's explicit beliefs may be fundamentally prejudiced. This is key for grasping the confusions surrounding anthropomorphic bias in machine learning: AI systems aren't conscious, yet classify social artifacts much as we do; system designers strive for formal accuracy, yet display strong moral affect in response to automated claims. The biases of both systems and designers play a role in generating the discordant environments in which a machine's classifications feel inappropriate or morally wrong, and we can make sense of this by recognizing the ontological primacy of belief-alief discordance over the isolated prejudices of humans and machines. \n Alief-Discordant Beliefs in Machine Learning To properly apply Gendler's insights, we propose the concept of alief-discordant belief to describe the origin, form, and consequence of anthropomorphic bias in automated systems. When deployed, these systems (e.g. image captioning) transpose human-generated forms of alief by computationally remaking the context within which our aliefs typically operate. In Gendler's terms, they generate beliefs that violate the habitual associations between semantic meaning (e.g. these variables are related given a specific parameter space) and moral dispositions (snowboarding is something anyone can do), producing a visceral reaction from the designers (\"women also snowboard\") that demands reconciliation  [9] . Consequently, the \"bias\" of automated systems refers to the uncanny semantic associations that arise from applying our aliefs to a purely datadriven setting, violating the contextual ties between disposition, affect, and representation that underpin our aliefs. When confronted with examples of an image classifier that offend us, we may have an automatic affective response that counteracts the beliefs that are either encoded into the algorithm's learning procedure (the belief that the classifier can learn semantic associations in an objective, impartial manner and arrive at ground truth) or generated by it (only men snowboard, certain faces are gay). In other words, the classifier crystallizes propositions about its own learning procedure as well as its predictive outputs, either of which can give rise to alief-discordant belief. Although such a classifier is just a computational function, there is a tendency for designers to anthropomorphize it as if it had autonomous beliefs, leading to a search for where these beliefs come from or who is to blame. This can leave engineers in the position of apologizing for the very data that is needed for the model learn anything useful (much like the case of MS Tay learning English for Nazi posts). We suggest interpreting such systems as automatic belief generators that compel us to reinterpret our own aliefs in the deployment context. Rather than claiming an algorithm is \"biased,\" we should confront the tension it creates between beliefs and aliefs we have about the social world. We must avoid compounding this tension by manually patching in solutions to our most violated or dogmatically-held aliefs (e.g. we calibrate a classifier generate all outcomes independently of protected attributes). Instead, we must address the discordance that is making us feel uncomfortable (such as in the cases of  [9]  and  [7] ). Rather than blaming the data or its labelers as biased, system designers are responsible for sorting out these discordances as they arise by harmonizing the generated beliefs with their own newly-challenged, inherited aliefs. The goal is thus not to try to make automated systems unbiased, but to interrogate the beliefs generated, the procedure for that generation, and the relation of both to our own aliefs. These factors can be made to map onto specific components of the AI's socio-technical infrastructure: the system engineer, the chosen model and training methods, and the data used. The onus is therefore on figuring out where in this pipeline our aliefs are being violated, how each contributes to this violation, and which of these components is most responsible. \n TOWARDS A TECHNO-SOCIETAL INFRASTRUCTURE Intersectional identities are a key hurdle in identifying the contexts that lead to alief-belief discordance. From the engineers' standpoint, this can result when either data does not contain sufficient examples of them, or they cannot be effectively encoded for the purposes of inference. And from the systems' perspective, intersectionality cannot be fully captured without generating a combinatorial explosion, since the interplay of relevant social variables (e.g. race, gender) will expand exponentially as more are deemed relevant for a given context. Confronting both sources requires interventions on the decision-making pipeline itself, and discordances are managed most readily if each step of the pipeline is designed to maintain one analytic component of alief-discordant belief. Prereflective moral dispositions necessarily inform the application of this pipeline through continuous attention to context, but the mechanics themselves are tied to conditions of explicit knowledge representation in the form of system-generated propositions. A significant component of \"fair\" machine learning is the integrity and documentation of this techno-societal pipeline, such that bias can be managed well beneath the psychological threshold of moral outrage that has regrettably defined the public reception of prominent case studies (see for example  [32] ). This implies that much of the burden for moral responsibility gets shifted from the data to model training and finally to engineers-if practitioners find themselves ignorant of the context of what they are working on, it is inappropriate to shift blame onto your tools. \n Data The collection of human data requires a compromise between alief (whatever moral compulsion(s) was felt in the leadup to collecting it) and belief (whatever data structure and type was determined to best represent assumptions about reality). There is always a moral context that informs the data content, just as there is an explicit frame of representation that accounts for its form. This original compromise is often invisible and unacknowledged in a given dataset. While troubling, the main problem here is how to deal with this crystallization to ensure it can be accounted for and is traceable. Here the following guidelines are necessary: Data as context-specific: data must be documented with the original priorities of those who collected it, and the relevant case law that informed its collection. These \"datasheets for datasets\" help ensure that transparency and accountability are baked into the pipeline from the start  [15] . This will provide a traceable baseline for the alief(s) lying behind the original data even after it has been used to generate classification regimes. Data as explicit: data should be annotated so that the assumptions behind its collection are clearly documented, rather than left implicit. This is meant to account for the beliefs or prior evidence that informed why the data was collected and organized in a certain manner, rather than another. Data as contestable: data should be publicly available so that its alief-belief crystallization, however messy or regrettable, can be challenged by those most subject to its labels or classification. This affirms that the alief-belief matrix behind its collection is a product of compromise worthy of continual reflection and deliberation.  \n Model and Training As a machine learning model is being trained, data-and with it a complex web of social relations, moral drives, and unstated representational axioms-are reified as generated beliefs about the macro-environment in question. This is the great benefit and cost of machine learning at scale, to wring more intuition out of a dataset than existed anywhere in the minds of those who produced it. The problem is to ensure the generated beliefs accord with the inherited beliefs that defined that data, or at least the beliefs of system engineers: Models as interpretable: models should be easy to understand by qualified humans so that classifications have a clear semantic context, requiring explainability. If this is not the case, as can happen in deep learning  [18] , it will make the work of identifying bias difficult, because the model itself cannot be consulted to resolve the discrepancy or point to likely solutions. This \"discordance slack\" should instead be reined in as early as possible. Models as intuitive: model assumptions should be documented so they are easily altered, without an unnecessary amount of work going into why these assumptions were chosen. This is necessary to ensure that the belief generation of the model is kept distinct from the belief testing of its trainers, rather than the two becoming conflated. Models as corrigible: assumptions should be transparent and available to the wider machine learning community so that they can be challenged. This is a redundancy check against the psychological biases of the model trainers and helps bolster the accordance between humans' and the model's beliefs. \n Engineers Engineers are the ultimate source of aliefs that are discordant with the model's generated beliefs. As those who are using the model to classify new data in contexts other than what the model was trained on, they will often bear the responsibility for its failures and specifically for the discordance between their own moral dispositions and the model's classifications. To review what has been stated already, where the data is dirty and the model is a black box, alief-discordant belief is almost inevitable. This is the scenario we are trying to anticipate by making the discordance manageable. Discordance as discoverable: engineers should be trained about psychological bias to better identify discordances where they are subtle or hidden in edge cases for the model in question. The goal is to make note of discordance before the public discovers it in deployment, which could cause social harm and also make the model less trustworthy. Discordance as tractable: engineers should be expertly informed about the likely problems with data and model training, i.e. have a general grasp of the pipeline and its context to better confront discordances when or if they arise. The goal here is to know how to manage the discordance, rather than simply to flag it. Discordance as contextual: engineers should be trained to maintain healthy work environments, have access to legal consultation, and cultivate emotional intelligence to better process discordances when they themselves feel them. Thanks to Three Mile Island and other man-made disasters, we have learned that fearmongering, societal distrust, and lasting damage can be avoided if engineers respond appropriately to a crisis rather than misrepresent the nature of the problem either to themselves or the public. \n CONCLUSION We have suggested alief-discordant belief to avoid the shoals of anthropomorphic bias in an automated context. Epistemically, aliefdiscordant belief accounts for the subtle ways in which human cognitive bias enters a machine learning pipeline, first through the dataset, then through model and training specification, finally in the dispositions of system engineers. Ethically, we have suggested that machine learning practitioners should work to maintain the integrity of this pipeline so that alief-discordant belief, once generated by engineers interacting with the model, is manageable with respect to the actual stakes of the social context in question. Part of the wider project of realizing fairness through machine learning is for engineers to interpret themselves as part of this context, which includes the wider machine learning community as well as potentially-vulnerable populations of protected social categories. In light of this therapy, negotiating the discord between human aliefs and machine-generated beliefs may depend on crafting a wholly new context for automated decision-making, in which we get better at designing machines that supply us with beliefs that we are more critically prepared to adopt. Spotlight 1 : 1 Normative Perspectives AIES'19, January 27-28, 2019, Honolulu, HI, USA", "date_published": "n/a", "url": "n/a", "filename": "3306618.3314294.tei.xml", "abstract": "Despite recent interest in both the critical and machine learning literature on \"bias\" in artificial intelligence (AI) systems, the nature of specific biases stemming from the interaction of machines, humans, and data remains ambiguous. Influenced by Gendler's work on human cognitive biases, we introduce the concept of alief-discordant belief, the tension between the intuitive moral dispositions of designers and the explicit representations generated by algorithms. Our discussion of alief-discordant belief diagnoses the ethical concerns that arise when designing AI systems atop human biases. We furthermore codify the relationship between data, algorithms, and engineers as components of this cognitive discordance, comprising a novel epistemic framework for ethics in AI. \n CCS CONCEPTS • Computing methodologies → Philosophical/theoretical foundations of artificial intelligence; Theory of mind.", "id": "74950068bd68288a3d8d7a86c06a2e0d"}